Answer:
To find the expression for (s+t)(x), we simply add the two functions s(x) and t(x): (s + t)(x) = s(x) + t(x) = 4x - 5 + x + 6 = 5x + 1
To find the expression for (s•t)(x), we multiply the two functions s(x) and t(x): (s•t)(x) = s(x) * t(x) = (4x - 5) * (x + 6) = 4x^2 + 19x - 30
To evaluate (s-t)(2), we substitute 2 for x in the expression for (s-t)(x): (s-t)(2) = s(2) - t(2) = (4*2 - 5) - (2 + 6) = 3 - 8 = -5
Therefore, the expression for (s+t)(x) is 5x+1, the expression for (s•t)(x) is 4x^2+19x-30, and (s-t)(2) is -5.
Step-by-step explanation:
A diphosphonate kit contian 180 mCi of Tc99m in 30 ml when it is prepared at 8am. Immediately, a 20 mCi dose is withdrawn for a bone scan. if the patient arrives late at 9:30 and half the volume is accidentally discharged, how much volume from the kit must now be added to the syringe to correct the dose to 20 mCi? (no other doses have been withdrawn meanwhile, and the decay factor for 1.5 hrs is 0.841)
The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = Initial activity * Decay factor
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = Initial activity - 20 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = Remaining activity * Decay factor
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30
Calculate the remaining volume at 9:30:
Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume
Let's perform the calculations step by step:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = 180 mCi * 0.841 = 151.38 mCi
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = 180 mCi - 20 mCi = 160 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30
Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml
Calculate the remaining volume at 9:30:
Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml
Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
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answer fast please..................................
Answer:
Step-by-step explanation:
Answer:
D)
Step-by-step explanation:
ΔSTU is translated to ΔS'U'T'
(i) moved right by 1 unit. Horizontal displacement right is denoted positive number. So, x +1.
(ii) moved down by 7 unit. Vertical displacement down is denoted by negative number. So, y - 7
(x, y) --> (x + 1, y -7)
Consider this function.
f(x) = |x – 4| + 6
If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?
If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.
The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.
If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.
The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).
The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.
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The July bank statement sent by the bank to ABC company shows a balance of cash on deposit at July 31 of Br.4,964.47 Assume that on July 31, assume the on July 31, ABCs ledger shows a bank balance of Br. 4 173. 83. 1. A deposit of Br 410. 90 made after banking hours and doesnt appear in the bank statement2. A check drawn for Br. 79 had been erroneously charged by the bank Br.973. For checks issued in July have not yet been paid by the bank (outstanding checks). : Theses checks are;- Check No date amount 801 June 15 ---Br.100,00 888 July 24 ----Br. 10.25 890 July 27--- Br. 294.50 891 July 30 ---Br. 205.004. A check written for birr 210 had been incorrectly charged by the bank as birr 120 5. Proceeds from collection of a interest bearing note receivable from David. ABC Company had left this note with the banks collection department. The face amount of the note was birr 500 6. Br. 24.75 interest earned on average account balance during July7. A check for Br. 10 returned with the statement had been recorded in the check register as Br. 100. The check was for the payment of an obligation to Davis Equipment Company for the purchase of office supplies on account 8. Br. 5,00 fee charged by bank for handling collection of note receivable 9. Br. 50.25 check from customer John deposited by ABC company charged bank as Non sufficient fund (NSF) 10. Br. 12.70 service charged by bank for the month of July. 11. Check number 875 was issued July 20 in the amount of Br 85 but was erroneously recorded in the cash payment Journal as Br 58 for payment of telephone expense prepare bank reconcilation and journal entry
The bank reconciliation shows an adjusted bank balance of Br.5,301.42 and an adjusted ledger balance of Br.4,173.83.
To prepare the bank reconciliation and journal entry for ABC Company based on the given information, we need to compare the transactions recorded in ABC's ledger with the transactions shown in the bank statement. Here's the bank reconciliation:
1. Bank Statement Balance:
Cash on deposit at July 31: Br.4,964.47
2. Adjusted Bank Balance:
Bank Statement Balance: Br.4,964.47
3. Deposit not on the statement: + Br.410.90
(Adjusted Bank Balance: Br.5,375.37)
Erroneously charged check: + Br.79
(Adjusted Bank Balance: Br.5,454.37)
Outstanding checks:
Check 801: - Br.100.00
Check 888: - Br.10.25
Check 890: - Br.294.50
Check 891: - Br.205.00
(Adjusted Bank Balance: Br.4,844.62)
4. Incorrectly charged check: + Br.90
(Adjusted Bank Balance: Br.4,934.62)
5. Collection of interest-bearing note: + Br.500
(Adjusted Bank Balance: Br.5,434.62)
6. Interest earned: + Br.24.75
(Adjusted Bank Balance: Br.5,459.37)
7. Incorrectly recorded check: - Br.90
(Adjusted Bank Balance: Br.5,369.37)
8. Collection fee: - Br.5.00
(Adjusted Bank Balance: Br.5,364.37)
9. NSF check: - Br.50.25
(Adjusted Bank Balance: Br.5,314.12)
10. Service charge: - Br.12.70
(Adjusted Bank Balance: Br.5,301.42)
Adjusted Ledger Balance:
Bank Balance in ABC's Ledger: Br.4,173.83
Reconciled Bank Balance: Br.5,301.42
Reconciled Ledger Balance: Br.4,173.83
Journal Entry:
To record the bank reconciliation, we make the following journal entry:
Debit: Cash (Ledger Balance adjustment) - Br.5,301.42
Credit: Cash (Bank Statement Balance adjustment) - Br.4,964.47
Credit: Miscellaneous Income/Expense - Br.336.95 (the difference between the two balances)
This journal entry ensures that the ledger balance matches the reconciled bank balance by adjusting for the discrepancies identified during the reconciliation process.
The journal entry reflects the necessary adjustments to reconcile the two balances, with a debit to Cash (Ledger Balance adjustment), a credit to Cash (Bank Statement Balance adjustment), and a credit to Miscellaneous Income/Expense to account for the difference.
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A store has clearance items that have been marked down by 50%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying?
bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.
Let's assume the original price of an item is $100.
The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.
The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.
Therefore, the final price you end up paying after both discounts is $22.50.\
To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:
Percent of original price = (final price / original price) * 100
In this case, the final price is $22.50 and the original price is $100:
Percent of original price = ($22.50 / $100) * 100
= 0.225 * 100
= 22.5%
Therefore, you end up paying 22.5% of the original price after the discounts.
It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.
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I already put square root 233 but it’s wrong and so is 15.2 and 15.3 and 15. So someone please help me to get the right answer cause I tried and now I have only one attempt
Answer:
d = [tex]\sqrt{89}[/tex]
Step-by-step explanation:
to calculate the distance d use the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 4, - 1 ) and (x₂, y₂ ) = (1, - 9 )
d = [tex]\sqrt{(1-(-4))^2+(- 9-(-1))^2}[/tex]
= [tex]\sqrt{(1+4)^2+(-9+1)^2}[/tex]
= [tex]\sqrt{5^2+(-8)^2}[/tex]
= [tex]\sqrt{25+64}[/tex]
= [tex]\sqrt{89}[/tex]
Name the addition property illustrated by each of the following examples: A + (B + C) = (A + B) + C property A + B = B + A property A + (−A) = 0 property A + 0 = A property
The different Algebraic Properties that were used are:
1) Associative Property
2) Commutative Property
3) Inverse Property
4) Identity Property
How to find the Algebraic Property?There are different Algebraic Properties such as:
Commutative Property
Associative Property
Inverse Property
Identity Property
1) A + (B + C) = (A + B) + C
The algebraic property used here is referred to as: associative property
2) A + B = B + A
The algebraic property used here is referred to as: commutative property
3) A + (−A) = 0
The algebraic property used here is referred to as: inverse property
4) A + 0 = A
The algebraic property used here is referred to as: identity property
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if x-y = 8 and xy=5 , find x^2 + y^2
Answer:
x² + y² = 74
Step-by-step explanation:
given
(x - y) = 8 ( square both sides )
(x - y)² = 8² ← expand left side using FOIL
x² - 2xy + y² = 64 ← substitute xy = 5
x² - 2(5) + y² = 64
x² - 10 + y² = 64 ( add 10 to both sides )
x² + y² = 74
Danielle buys a new
center with a
entertainment
new plasma television for
$1680. She pays $300
down, and the rest is paid
off in equal monthly pay-
ments for 1 year. Find
Danielle's monthly payment.
The conclusion remains the same as mentioned earlier. Danielle's monthly payment for the entertainment center with the new plasma television is $115. She will make equal monthly payments of $115 for 1 year to pay off the remaining amount owed.
To find Danielle's monthly payment, we need to subtract the down payment from the total cost of the entertainment center with the new plasma television.
The total cost of the entertainment center with the new plasma television = $1680
Down payment = $300
The remaining amount to be paid off is $1680 - $300 = $1380.
Since Danielle pays off the remaining amount in equal monthly payments for 1 year, we need to calculate the number of months in a year. There are 12 months in a year.
To find Danielle's monthly payment, we divide the remaining amount by the number of months:
Monthly payment = Remaining amount / Number of months
= $1380 / 12
= $115
Therefore, Danielle's monthly payment is $115. She will make equal monthly payments of $115 for 1 year to pay off the rest of the amount owed for the entertainment center with the new plasma television.
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Which of the following expresses the coordinates of the foci of the conic section shown below? (x+2)^2/64+(y-1)^2/81=1
The equation (x+2)^2/64 + (y-1)^2/81 = 1 represents an ellipse.
To determine the coordinates of the foci of the ellipse, we need to find the square root of the denominators of x and y, which represent the lengths of the major and minor axes.
The square root of 64 is 8, and the square root of 81 is 9.
These values correspond to the lengths of the major and minor axes, respectively.
Since the major axis is in the x-direction (horizontal), the foci lie along the x-axis.
We can determine the center of the ellipse by identifying the values of (h, k) in the form (x - h, y - k). In this case, the center of the ellipse is (-2, 1).
The distance from the center of the ellipse to each focus is given by the formula c = sqrt(a^2 - b^2), where a is half the length of the major axis and b is half the length of the minor axis.
The formula to calculate the distance from the center to the foci is given by c = sqrt(a^2 - b^2), where a and b are the semi-major and semi-minor axes of the ellipse.
In this case, a = 8/2 = 4 and b = 9/2 = 4.5. Substituting these values into the formula, we have c = sqrt(4^2 - 4.5^2) = sqrt(16 - 20.25) = sqrt(-4.25).
Since the square root of a negative number is imaginary, we conclude that the ellipse does not have any real foci.
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What is the Q1 for this data set?
2,3,5,5,6,8,8,10,11,11,11,12)
A. 5
B. 8
C. 10
D. 11
Answer:
5
Step-by-step explanation:
its the middle of the first half
2/5 of employees in a company drive to work, 1/3 travel by bus and the rest walk. 1. Find the fraction of who walk.
Answer:
4/15
Step-by-step explanation:
2/5 drive
1/3 bus
and rest walk
fraction of those who walk is 1-(2/5+1/3)
2/5+1/3=(6+5)/15=11/15
15/15-11/15=4/15
A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t)= −4.9t^2+11t+7. How many seconds does it take to reach maximum height? Enter the answer with at least 3 decimal places.
Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.
To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = [tex]-4.9t^2 + 11t + 7.[/tex]
The vertex of a parabola in the form y = [tex]ax^2 + bx[/tex] + c is given by the formula t = -b / (2a).
Comparing the equation h(t) = [tex]-4.9t^2 + 11t + 7[/tex] to the standard form, we have:
a = -4.9
b = 11
Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:
t = -11 / (2 * -4.9)
t = -11 / -9.8
t ≈ 1.122
Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) is a number line from negative 5 to 5 in increments of 1, with an open circle at 3 and a bold line starting at 3 and pointing to the right.
To determine which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5), we need to solve the inequality and analyze its solution.
First, let's simplify the inequality:
3(8 – 4x) < 6(x – 5)
24 - 12x < 6x - 30
Next, let's bring all the terms involving x to one side of the inequality:
-12x - 6x < -30 - 24
-18x < -54
Now, divide both sides of the inequality by -18.
Since we are dividing by a negative number, we need to reverse the direction of the inequality:
x > -54/-18
x > 3
The inequality solution is x > 3, which means x is greater than 3. In interval notation, this can be represented as (3, +∞),
where the parentheses indicate that 3 is not included in the solution.
Now let's analyze the given options:
A number line from negative 5 to 5 in increments of 1.
An open circle is at 3 and a bold line starts at 3 and is pointing to the left: This option represents values less than 3, but we need values greater than 3.
A number line from negative 5 to 5 in increments of 1.
An open circle is at 3 and a bold line starts at 3 and is pointing to the right:
This option represents values greater than 3, which matches the solution set.
A number line from negative 5 to 5 in increments of 1.
An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left: This option does not match the given inequality.
A number line from negative 5 to 5 in increments of 1.
An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right:
This option does not match the given inequality.
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A savings account was opened 11 years ago with a deposit of $4,570.65. The account has an interest rate of 3.9% compounded monthly. How much interest has the account earned?
$160.08
$181.48
$2,443.71
$7,014.36
Answer:
C) $2,443.71
Step-by-step explanation:
To calculate the amount of interest earned on the savings account, use the compound interest formula.
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ I=P\left(1+\dfrac{r}{n}\right)^{nt}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued.\\ \phantom{ww}$\bullet$ $P =$ principal amount. \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form). \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year. \\ \phantom{ww}$\bullet$ $t =$ time (in years). \\ \end{minipage}}[/tex]
Given values:
P = $4,570.65r = 3.9% = 0.039n = 12 (monthly)t = 11 yearsSubstitute the given values into the formula and solve for I:
[tex]I=4570.65\left(1+\dfrac{0.039}{12}\right)^{12\cdot 11}-4570.65[/tex]
[tex]I=4570.65\left(1+0.00325\right)^{132}-4570.65[/tex]
[tex]I=4570.65\left(1.00325\right)^{132}-4570.65[/tex]
[tex]I=4570.65\left(1.534653130...\right)-4570.65[/tex]
[tex]I=7014.362330...-4570.65[/tex]
[tex]I=2443.712330...[/tex]
[tex]I=\$2,443.71\[ \sf (nearest\;cent)[/tex]
Therefore, the amount of interest the account has earned is $2,443.71, rounded to the nearest cent.
Answer:
$2,443.71
Step-by-step explanation:
To calculate the interest earned, we can use the formula for compound interest:
[tex]\rm\implies A = P(1 + \frac{r}{n})^{(nt)}[/tex]
where:
A = the final amount (including interest)P = the principal amount (initial deposit)r = the annual interest rate (as a decimal)n = the number of times that interest is compounded per yeart = the number of yearsGiven:
P = $4,570.65r = 3.9% = 0.039 (as a decimal)n = 12 (compounded monthly)t = 11 yearsSubstitute the given values into the above formula:
[tex]\begin{aligned}\rm\implies A& =\rm 4570.65(1 + \frac{0.039}{12})^{(12 \cdot 11)}\\& \approx \rm{\$9,014.36}\end{aligned}[/tex]
To find the interest earned, we subtract the initial deposit from the final amount:
[tex]\begin{aligned}\rm\implies Interest& =\rm A - P\\& \approx \$9,014.36 - \$4,570.65\\& \approx \boxed{\rm{\$2,443.71}}\end{aligned}[/tex]
[tex]\therefore[/tex] The account has earned $2,443.71 in interest.
Un coche tarda 12 minutos en dar la vuelta a un circuito si va a una velocidad de 80 km/h. Cuánto tiempo tardara en recorrer el mismo circuito si va a una velocidad de 100 km/h?
A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.
What theory directly contradicts concept of absolute zero?
All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).
Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.
Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.
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The route 450 pounds over 25 buckets describe the relationship between the number of pockets in the way of the lobster in the bucket. What is the weight of one bucket of lobster?
The rate 450 pounds over 25 buckets describe the relationship between the number of buckets in the way of the lobster in the bucket. What is the weight of one bucket of lobster?
The weight of one bucket of lobster is 18 pounds per bucket. Option b
To determine the weight of one bucket of lobster, we can use the given information about the rate of 450 pounds over 25 buckets.
The rate is defined as the amount of weight (in pounds) divided by the number of buckets. In this case, the rate is 450 pounds over 25 buckets.
To find the weight of one bucket of lobster, we can divide the total weight by the number of buckets:
Weight of one bucket = Total weight / Number of buckets
Weight of one bucket = 450 pounds / 25 buckets
Weight of one bucket = 18 pounds per bucket
Therefore, the weight of one bucket of lobster is 18 pounds per bucket.
The correct answer is option b) 18 pound per bucket.
It's important to note that this calculation assumes a constant weight per bucket throughout the given scenario. In reality, the weight of one bucket of lobster may vary depending on factors such as the size and type of lobsters being weighed. Additionally, it's possible that the weight per bucket may change over time or across different batches of lobsters.
Option B
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A rectangular piece of cardboard is a=9 in. longer than it is wide. Squares 2 in. on a side are to be cut from each corner and then the sides folded
up to make an open box with a volume of 72 in³. Find the length and width of the piece of cardboard.
Answer:
Length = 16 inches
Width = 7 inches
Step-by-step explanation:
Let "x" be the width of the rectangular piece of cardboard.
If the rectangular piece of cardboard is 9 inches longer than it is wide, then let "x + 9" be the length of the rectangular piece of cardboard.
As squares with side lengths of 2 inches are cut from each corner of the rectangle, the height of the open box will be 2 inches, and the width and length of the box will be 4 inches less than width and length of the rectangular piece of cardboard.
Therefore, the dimensions of the open box are:
Height, h = 2 inchesWidth, w = (x - 4) inchesLength, l = (x + 9 - 4) = (x + 5) inchesGiven the open box has a volume of 72 in³, substitute all the values into the formula for the volume of a cuboid and solve for x:
[tex]\begin{aligned}\textsf{Volume of a cuboid}&=\sf width \cdot length \cdot height\\\\72&=(x-4)\cdot (x+5)\cdot 2\\36&=(x-4)(x+5)\\(x-4)(x+5)&=36\\x^2+x-20&=36\\x^2+x-56&=0\\x^2+8x-7x-56&=0\\x(x+8)-7(x+8)&=0\\(x-7)(x+8)&=0\\\\x-7&=0 \implies x=7\\x+8&=0 \implies x=-8\end{aligned}[/tex]
As length cannot be negative, the only valid value of x is 7.
To find the length and width of the piece of cardboard, substitute the found value of x into their expressions:
[tex]\textsf{Length}=x+9=7+9=16\; \sf inches[/tex]
[tex]\textsf{Width}=x=7\; \sf inches[/tex]
Therefore, the dimensions of the rectangular piece of cardboard are:
Length = 16 inchesWidth = 7 inchesAnswer:
Length= 16 inches
Width= 7 inches
Step-by-step explanation:
Let's denote the width of the rectangular piece of cardboard as "w" inches.
According to the given information,
the length of the cardboard is 9 inches longer than its width, so the length can be represented as "w + 9" inches.
When the sides are folded up, the height of the box will be 2 inches.
After folding, the width of the base of the box will be "w - 4" inches, and the length will be "w + 9 - 4" inches, which simplifies to "w + 5" inches.
The volume of a rectangular box can be calculated as the product of its length, width, and height.
In this case, the volume is given as 72 in³:
Volume = Length*Width*Height
72 = (w + 5)*(w - 4) × 2
Simplifying the equation:
36 = (w + 5)*(w - 4)
Expanding the right side:
36 = w² - 4w + 5w - 20
Rearranging and combining like terms:
w² + w - 56 = 0
We can factorize by using middle term factorization:
w² + 8x-7x - 56 = 0
w(w+8)-7(w+8)=0
(w - 7)(w + 8) = 0
Setting each factor equal to zero:
either
w - 7 = 0
Therefore, w = 7
or
w + 8 = 0
w = -8 (Discard since width cannot be negative)
Therefore, the width of the piece of cardboard is 7 inches.
Substituting this value back into the expression for the length:
Length = w + 9
Length = 7 + 9
Length = 16 inches
So, the length of the piece of cardboard is 16 inches, and the width is 7 inches.
3 lines are shown. One line contains point C, A, E and intersects a line with points B, A, D at point A. Another line extends from point A to point F in between B A E.
Which are vertical angles? Check all that apply.
∠EAB and ∠BAC
∠EAB and ∠CAD
∠CAD and ∠FAE
∠CAB and ∠DAE
∠DAC and ∠DAE
The vertical angles among the given options are ∠CAB and ∠DAE.
In the given question, we have three lines. Let's call the line that contains points C, A, and E as Line 1. The line that intersects Line 1 at point A and contains points B and D is called Line 2. The line that extends from point A to point F and lies between points B, A, and E is called Line 3.
Now, let's look at the given angles. We have ∠CAB, ∠DAE, ∠DAC, and ∠DAE.
∠CAB refers to the angle formed by Line 1 and Line 2 at point A.
∠DAE is the angle formed by Line 2 and Line 3 at point A.
∠DAC is the angle formed by Line 2 and Line 1 at point A.
To find the value of ∠DAC, we need to use the fact that angles on a straight line add up to 180 degrees. Since Line 1 and Line 2 intersect at point A, ∠DAC and ∠CAB are supplementary angles. Therefore, ∠DAC + ∠CAB = 180 degrees.
To find the value of ∠DAE, we can use the fact that ∠DAC and ∠DAE are corresponding angles formed by a transversal cutting two parallel lines, Line 2 and Line 3. Hence, ∠DAC = ∠DAE.
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Answer:
b d
Step-by-step explanation:
Below are the names of ten students:
Dorothy
Anthony
Harold
Margaret
Tiffany
Nancy
Angela
Paul
For the following, assume the probability of a student being chosen is the same for each student. Also, assume that
simple random sampling is being used. (If necessary, use an exact decimal value for all probabilities.)
a.) What is the probability of choosing a student whose name ends with the letter "k"?
b.) What is the probability of choosing a student whose name begins with the letter "C"?
Patrick
Jeremy
c.) What is the probability of choosing a student whose name contains the letters "m" or "M"?
d.) A Math Club is formed using these ten students, and the club must consist of seven students. How many ways
can students be assigned to the Math Club?
e.) The ten students enter an art competition where first place wins $100, second place wins $50, third place wins
$25, and fourth place wins $10. How many different ways can prizes be distributed?
It’s not multiple choice you have to work the math problem!!
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
let's relist the 10 names, as there was some "mixing" going on in your text :
Dorothy
Anthony
Harold
Margaret
Tiffany
Nancy
Angela
Paul
Patrick
Jeremy
so, whatever happens, the totally possible cases are 10 (as we are only taking about these 10 names, no other name can suddenly appear in all the scenarios).
in each scenario one student is randomly chosen.
a) the probabilty to pick a student with name ending "k".
we look through the list and find only 1 student, whose name ends with "k" : Patrick.
that means the number of desired cases is 1.
and the probabilty is therefore
1/10 = 0.1
b) the probability to pick a student with name beginning "C".
we look and look and look. none of the 10 names start with a "C".
that means the number of desired cases is 0.
and the probabilty is
0/10 = 0
c) the probability that the name of the picked student contains "m" or "M".
we find 2 names : Margaret and Jeremy.
that means that the number of desired cases is 2.
and the probabilty is therefore
2/10 = 1/5 = 0.2
d) in how many ways can we pick 7 elements out of 10, when the sequence of the pulled 7 elements does not matter (e.g. ... Nancy, Paul ... is the same as ... Paul, Nancy, ...). and no student can be pulled more than once (no repetitions).
that means we have to calculate the combinations of 7 items out of 10 without repetition :
C(10, 7) = 10! / (7! × (10-7)!) = 10! / (7! × 3!) =
= 10×9×8 / (3×2) = 5×3×8 = 120
there are 120 possibilities to build the math club.
e) now we pick 4 students out of 10. but as we give them prices based on ranking, the sequence matters (e.g. Nacy first, Paul second is different to Paul first, Nancy second).
but we still have no repetition, as nobody can win more than one price.
that means we need to calculate the permutations of 4 items out of 10 without repetition :
P(10, 4) = 10! / (10-4)! = 10! / 6! = 10×9×8×7 = 5,040
there are 5040 different ways to distribute the 4 prices among the 10 students.
Check all the statements) that are true about the polynomial function graphed
Its leading coefficient is positive. its leading coefficient is negative.
It has an odd degree
It has an even degree
It has exactlv two real zeroes
It has exactly three real zeroes.
None of the zeroes have even multiplicity
None of the zeroes have odd multiplicity.
The true statements about the polynomial function graphed are:
Its leading coefficient is positive.
It has an odd degree.
None of the zeroes have even multiplicity.
From the given options, the true statements about the polynomial function graphed are:
Its leading coefficient is positive.
It has an odd degree.
None of the zeroes have even multiplicity.
Let's analyze each statement:
Its leading coefficient is positive:
The leading coefficient of a polynomial is the coefficient of the term with the highest degree.
From the graph, if the polynomial is going upwards on the right side, it indicates that the leading coefficient is positive.
It has an odd degree: The degree of a polynomial is the highest power of the variable in the polynomial expression.
If the graph has an odd number of "turns" or "bumps," it indicates that the polynomial has an odd degree.
None of the zeroes have even multiplicity:
The multiplicity of a zero refers to the number of times it appears as a factor in the polynomial.
In the given graph, if there are no repeated x-intercepts or no points where the graph touches and stays on the x-axis, it implies that none of the zeroes have even multiplicity.
The other statements (its leading coefficient is negative, it has an even degree, it has exactly two real zeroes, it has exactly three real zeroes, and none of the zeroes have odd multiplicity) cannot be determined based solely on the information given.
Therefore, the true statements about the polynomial function graphed are:
Its leading coefficient is positive.
It has an odd degree.
None of the zeroes have even multiplicity.
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You contract with an interior designer to make plans for your home. Her bill is $1,400 2/10 net 30. Find the amount needed to pay the bill with the discount included. A. $1,260 C. $1,400 B. $1,372 D. $980
Answer: the answer is c i just finished the test
Step-by-step explanation:
In △ABC, m∠A=45
°, c=17
, and m∠B=25
°. Find a
to the nearest tenth.
law of sines 4
A. 14.0
B. 24.3
C. 12.8
D. 19.5
The length of side a is approximately B. 24.3 (to the nearest tenth).
The correct answer is B. 24.3
To find the length of side a in triangle ABC, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.
The Law of Sines can be expressed as:
a/sin(A) = c/sin(C)
where a is the length of side a, A is the measure of angle A, c is the length of side c, and C is the measure of angle C.
Angle A (m∠A) = 45°
Side c (c) = 17
Angle B (m∠B) = 25°
We need to find the length of side a.
Using the Law of Sines:
a/sin(45°) = 17/sin(25°)
To find a, we isolate it by multiplying both sides of the equation by sin(45°):
a = 17 * (sin(45°) / sin(25°))
Using a calculator to evaluate the expression:
a ≈ 24.3
Therefore, the length of side a is approximately 24.3 (to the nearest tenth).
The correct answer is:
B. 24.3
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Factor 48 − 8 � 48−8x48, minus, 8, x to identify the equivalent expressions.
The expression 48 − 8 × 48−8x48 is factored to give an equivalent expression 8(6 − x) × 48, where 8, 6, and x are terms of the expression. Factoring is the method of expressing a polynomial as the product of other polynomials. The term minus refers to subtraction, and the operation of subtraction is used to subtract 8 × 48 from 48 to get a result of 16.
The expression to factor is 48 − 8 × 48−8x48. Factoring the expression 48 − 8 × 48−8x48 gives an equivalent expression 8(6 − x) × 48, where 8, 6, and x are terms of the expression.
In mathematics, factoring is the method of expressing a polynomial as the product of other polynomials. The factored expression 8(6 − x) × 48 can be expanded back to the original expression by multiplying the individual factors with each other.
The term minus refers to subtraction. In this context, the operation of subtraction is used to subtract 8 × 48 from 48, yielding a result of 16. This result is multiplied by 48 − 8x48 to get the original expression 48 − 8 × 48−8x48.
Therefore, the equivalent expressions are 48 − 8 × 48−8x48 and 8(6 − x) × 48, where 8, 6, and x are terms of the expression.
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C 3) 1) 2) B. triangle and a (X) if it does not form a triangle. Which of the following could be the lengths of the sides of a triangle. Put a () if it is forms 12, 11, 10 2, 3, 4 3, 2, 1 4) 5) 6) 7) 7, 13, 7 8) 13, 12, 5 F 9) 3, 7, 10 10) 4, 6, 7 11) x, y, x + y 1 12) x, y, x-y 13) 1, 1, 2 nd all possible value of x.
Answer:
(12, 11, 10)
(2, 3, 4)
(5, 7, 13)
(1, 1, 1)
(7, 10, 3)
(4, 6, 7)
(x, y, x + y) for any positive values of x and y
(x, y, x - y) if x is greater than y and x - y is greater than 0
(x, x, 2) for any positive value of x
Step-by-step explanation:
The given equation is:
4a + 3 = 7a - 2
To solve for a, we can start by simplifying both sides of the equation. First, we can combine the constants on the right side:
4a + 3 = 7a - 2
4a + 5 = 7a
Next, we can isolate the variable terms on one side of the equation and the constant terms on the other side. Let's subtract 4a from both sides:
4a + 5 = 7a
5 = 3a
Finally, we can solve for a by dividing both sides by 3:
5 = 3a
5/3 = a
Therefore, the solution is:
a = 5/3
We can check this solution by substituting it back into the original equation:
4a + 3 = 7a - 2
4(5/3) + 3 = 7(5/3) - 2
20/3 + 3 = 35/3 - 2
29/3 = 29/3
Since both sides of the equation are equal when we substitute a = 5/3, we can confirm that this is the correct solution.
C 3) 1) 2) B. triangle and a (X) if it does not form a triangle. Which of the following could be the lengths of the sides of a triangle. Put a () if it is forms 12, 11, 10 2, 3, 4 3, 2, 1 4) 5) 6) 7) 7, 13, 7 8) 13, 12, 5 F 9) 3, 7, 10 10) 4, 6, 7 11) x, y, x + y 1 12) x, y, x-y 13) 1, 1, 2 nd all possible value of x.
To determine whether a set of lengths could form the sides of a triangle, we need to check if the sum of the two shorter sides is greater than the longest side. If it is, then the lengths can form a triangle; otherwise, they cannot.
Using this criterion, we can determine which sets of lengths form triangles:
(12, 11, 10) - (O) forms a triangle, since 10 + 11 > 12.
(2, 3, 4) - (O) forms a triangle, since 2 + 3 > 4.
(3, 2, 1) - (X) does not form a triangle, since 1 + 2 is not greater than 3.
(5, 7, 13) - (O) forms a triangle, since 5 + 7 > 13.
(1, 1, 1) - (O) forms a triangle, since all sides are equal.
(8, 8, 16) - (X) does not form a triangle, since 8 + 8 is not greater than 16.
(13, 12, 5) - (O) forms a triangle, since 5 + 12 > 13.
(7, 10, 3) - (X) does not form a triangle, since 3 + 7 is not greater than 10.
(4, 6, 7) - (O) forms a triangle, since 4 + 6 > 7.
(x, y, x + y) - (O) forms a triangle for any positive values of x and y, since x + y is always greater than x and y individually.
(x, y, x - y) - (O) forms a triangle if x is greater than y and x - y is greater than 0.
(1, 1, 2) - (X) does not form a triangle, since 1 + 1 is not greater than 2.
(x, x, 2) - (O) forms a triangle for any positive value of x, since x + x > 2.
Therefore, the sets of lengths that can form triangles are:
(12, 11, 10)
(2, 3, 4)
(5, 7, 13)
(1, 1, 1)
(7, 10, 3)
(4, 6, 7)
(x, y, x + y) for any positive values of x and y
(x, y, x - y) if x is greater than y and x - y is greater than 0
(x, x, 2) for any positive value of x
Find the vertex of the graphed function. f(x) = [x - 4] + 3
The vertex of the graphed function f(x) = [x - 4] + 3 is (4, 3).
The function f(x) = [x - 4] + 3 is in the form of an absolute value function, where the expression inside the absolute value brackets represents the input value shifted horizontally by 4 units to the right.
The constant term of 3 represents a vertical shift upwards by 3 units.
To find the vertex of this function, we need to determine the x-coordinate that corresponds to the minimum value of the absolute value function.
In this case, since the absolute value function is within brackets and not being multiplied or divided by a coefficient, the minimum value occurs at the point where the expression inside the brackets equals zero.
Therefore, setting x - 4 = 0, we find x = 4.
Substituting this x-value into the function, we find f(4) = [4 - 4] + 3 = 3. So the vertex of the graphed function is located at the point (4, 3), where x = 4 and y = 3. This means that the graph is shifted 4 units to the right and 3 units upward from the origin.
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Subject: Number Theory
Topic: Legendre Symbol (Euler's Criterion Theorem)
Prove or Disprove: Let =13 and =3. Then (3/13) = −1 ≡ 3^6 ( 13)
Answer:
(3/13) = -1 ≡ 3^6 (mod 13)
Step-by-step explanation:
We can use Euler's criterion theorem to prove or disprove the statement.
Euler's criterion states that for an odd prime p and integer a not divisible by p,
a^((p-1)/2) ≡ (a/p) (mod p)
where (a/p) is the Legendre symbol. If (a/p) = 1, then a is a quadratic residue modulo p, and if (a/p) = -1, then a is a quadratic non-residue modulo p.
In this case, we have p = 13 and a = 3. Therefore, we need to evaluate:
3^6 ≡ (3/13) (mod 13)
To evaluate (3/13), we need to use the properties of the Legendre symbol. First, we note that:
(3/13) ≡ (-1/13) (3/13)
since (-1/13) = (-1)^((13-1)/2) = 1 by Euler's criterion. Next, we use the quadratic reciprocity law to simplify (-1/13):
(-1/13) = (-1)^((13-1)/2) * (13-1)/2 = 1
Therefore, we have:
(3/13) ≡ (-1/13) (3/13) ≡ 1 * (3/13) ≡ (3/13)
So we need to evaluate (3/13) to determine if it is equal to 1 or -1.
To do this, we can use the quadratic reciprocity law again:
(3/13) = (13/3) * (-1/3)
Since 13 ≡ 1 (mod 3), we have:
(13/3) = (1/3) = 1
Since 3 ≡ 3 (mod 4), we have:
(-1/3) = -1
Therefore, we have:
(3/13) = (13/3) * (-1/3) = 1 * (-1) = -1
So (3/13) = -1.
Therefore, the statement is true, and we have:
(3/13) = -1 ≡ 3^6 (mod 13)
What’s the answer to this question? This is Similar Polygons.
Answer:
scale factor = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original , that is
scale factor = [tex]\frac{ST}{AB}[/tex] = [tex]\frac{5}{15}[/tex] = [tex]\frac{1}{3}[/tex]
what is the Q1 for this data set?
(2,3,5,5,6,8,8,9,10,11,11,11,12)
5
8
10
11
Answer:5
Step-by-step explanation:To find the first quartile (Q1) for a given dataset, you need to arrange the data in ascending order and determine the value that separates the lowest 25% of the data.
Arranging the dataset in ascending order:
2, 3, 5, 5, 6, 8, 8, 9, 10, 11, 11, 11, 12
To calculate Q1, you can use the formula:
Q1 = (n + 1) / 4
where n is the total number of data points.
In this case, n = 13, so:
Q1 = (13 + 1) / 4 = 14 / 4 = 3.5
Since Q1 is not exactly a data point in this dataset, we need to find the value that falls between the third and fourth data points. In this case, the third and fourth data points are both 5.
Therefore, the Q1 for this dataset is 5.
Heidi looked at this graph and thought, “The first point I see is at 2 tsp of nutmeg and 3 tsp of cinnamon. The unit rate is 3 tsp of cinnamon for every 2 tsp of nutmeg.”
No, she is not correct because: The unit rate should be 1.5 teaspoons of nutmeg to 1 teaspoon of cinnamon.
How to find the Unit rate?A unit rate (or unit ratio) describes how many units of a quantity of the first type correspond to units of a quantity of the second type.
Now, the formula to find the un it rate of a linear graph like the one given in the attached file is:
Unit rate = y/x
We will make use of the coordinate as: (2, 3)
Thus, the unit rate is: 3/2 = 1.5 teaspoons of cinnamon to 1 teaspoon of nutmeg.
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Complete Question is:
Heidi looked at this graph and thought, “The first point I see is at 2 tsp of nutmeg and 3 tsp of cinnamon. The unit rate is 3 tsp of cinnamon for every 2 tsp of nutmeg.”
Is Heidi correct?
No. The unit rate should be 2 teaspoons of cinnamon to 3 teaspoons of nutmeg.
No. The unit rate should be 1.5 teaspoons of nutmeg to 1 teaspoon of cinnamon.
No. The unit rate should be 1.5 teaspoons of cinnamon to 1 teaspoon of nutmeg.
Yes. Heidi is correct.
