The cost of the side material is $148.91, the cost of the base material is $73.67 and the cheapest cost of material is $222.58 and this can be determined by using the arithmetic operations.
Let the width of the rectangular storage container be 'x' then according to the given data the length is '2x' and let the height of the container be 'h'.
The base area of the rectangular storage container is given by:
Base Area = 2x² -- (1)
The side area of the rectangular storage container is given by:
Side Area = 2(2x)h + 2xh
= 6xh -- (2)
Now, the volume of the rectangular storage container is given by:
Volume = l x b x h
14 = 2x²h
h = 7/x²
Now, the cost is given by:
C(x) = 13(2x²) + 6(6xh)
C(x) = 26x² + 252/x
To minimize C(x), differentiate the C(x) with respect to x.
C'(x) = 52x - 252/x² --3()
52x - 252/x² = 0
x³ = ∛(63/13)
Now, differentiate equation (3) with respect to x.
C''(x) = 52 + 504/x³
C"( ∛(63/13) ) = 156 > 0
Therefore, ∛(63/13) is the point of minima.
Now, the cost of the base material is:
= 13 x 2 (62/13)^(2/3)
= $73.67
Now, the cost of the side material is:
= 252/(∛(63/13))
= $148.91
Therefore, the total cost is given by:
= 73.67 + 148.91
= $222.58
Hence, the cheapest cost of material is $222.58
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certain standardized math exams have a mena of 120 and a standarad deviation of 20. of the students who take this exam. what percent could you expect to score betwen 60 amd 120
After finding the z score, total 49.865% you could expect to score between 60 and 120.
Math exams mean(μ) = 120
Math exams standard deviation(σ) = 20
We have to determine the percent you could expect to score between 60 and 120.
The area total included to the left of any score or value is indicated in the Z-score table (x). The top row and the first column of the Z-table represent the Z-values, while all of the numbers in the middle represent the areas.
P(60 < x < 120) = P((60 - 120)/20 < (x - μ)/σ < (120 - 120)/20)
Simplifying
P(60 < x < 120) = P((-60)/20 < (x - μ)/σ < 0/20)
P(60 < x < 120) = P(-3 < Z < 0)
We can write this as
P(60 < x < 120) = P(Z > -3) - P(Z < 0)
P(60 < x < 120) = 0.99865 - 0.5
P(60 < x < 120) = 0.49865
P(60 < x < 120) = 49.865%
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4. in a box are 7 red balls and 8 blue balls. from this box are drawn 4 balls and placed in a second box. then, one ball is drawn from the second box. what is the probability the ball drawn from the second box is red?
The probability the ball drawn from the second box is red, is 17/56.
In a box are 7 red balls and 8 blue balls.
From this box are drawn 4 balls and placed in a second box.
We have to determine the probability the ball drawn from the second box is red.
The total number of balls = Red Balls + Blue Balls
The total number of balls = 7 + 8
The total number of balls = 15
The number of balls placed in second balls = 4
The number of combination of balls in box 2.
BBBB, BBBR, BBRR and BRRR
Then, one ball is drawn from the second box.
The probability the ball drawn from the second box is red.
P(Ball is red in the second box) = P(BBBB) + P(BBBR) + P(BBRR) + P(BRRR)
P(Ball is red in the second box) = [tex]\frac{^{5}C_{4}}{^{8}C_{0}}(0)+\left(\frac{^{5}C_{3}\times ^{3}C_{1}}{^{8}C_{4}}\right)\times\frac{^{1}C_{1}}{^{4}C_{1}}+\left(\frac{^{5}C_{2}\times ^{3}C_{2}}{^{8}C_{4}}\right)\times\frac{^{2}C_{1}}{^{4}C_{1}}+\left(\frac{^{5}C_{1}\times ^{3}C_{3}}{^{8}C_{4}}\right)\times\frac{^{3}C_{1}}{^{4}C_{1}}[/tex]
P(Ball is red in the second box) = [tex]0+\left(\frac{30}{70}\times\frac{1}{4}\right)+\left(\frac{30}{80}\times\frac{1}{2}\right)+\left(\frac{5}{70}\times\frac{3}{4}\right)[/tex]
P(Ball is red in the second box) = 3/48 + 3/16 + 3/56
P(Ball is red in the second box) = (21 + 63 + 18)/336
P(Ball is red in the second box) = 102/336
P(Ball is red in the second box) = 17/56
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M. Houton’ fifth grade cla of 20 tudent i going to a mueum the cla raie $128 for the trip. Tranportation to the mueum cot $5 for each tudent. The mueum ell mall foil for $4 each. How many foil can the tudent buy with the money they have left?
With the money they have left, the students in M. Houton's fifth grade class of 20 students can buy 32 foils.
This is calculated by subtracting the cost of the transportation from the total amount raised ($128 - $5*20 = $28) and then dividing that amount by the cost of each foil ($4). Therefore, the students can buy $28 / $4 = 32 foils.
To calculate how many foils the students in M. Houton's fifth grade class of 20 students can buy with the money they have left, you must subtract the cost of their transportation from the total amount raised ($128 - $5*20 = $28).
Then, divide the remaining amount by the cost of each foil ($4) to get the number of foils they can buy with the money they have left ($28 / $4 = 32 foils).
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dentifying a Constant of Proportionality
onsider the equation y = 4.2x and the table below that
presents this relationship.
x
0
2
4
6
Y
0
8.4
16.8
25.2
The coefficient of the equation or constant of
proportionality is
Answer:
Step-by-step explanatio
23.2
Determine the truth value of the following statements if the universe of discourse of each variable is the set of real numbers.
1. ∃x(x2=−1)∃x(x2=−1)
2. ∃x∀y≠0(xy=1)∃x∀y≠0(xy=1)
3. ∀x∃y(x2=y)∀x∃y(x2=y)
4. ∃x∃y(x+y≠y+x)∃x∃y(x+y≠y+x)
5. ∃x∀y(xy=0)∃x∀y(xy=0)
6. ∀x∃y(x=y2)∀x∃y(x=y2)
7. ∀x∀y∃z(z=x+y2)∀x∀y∃z(z=x+y2)
8. ∀x≠0∃y(xy=1)∀x≠0∃y(xy=1)
9. ∃x(x2=2)∃x(x2=2)
10. ∀x∃y(x+y=1)∀x∃y(x+y=1)
11. ∃x∃y((x+2y=2)∧(2x+4y=5))∃x∃y((x+2y=2)∧(2x+4y=5))
12. ∀x∃y((x+y=2)∧(2x−y=1))
The truth value of the given statements if the universe of discourse of each variable is the set of real numbers are 1. false, 2. false, 3. true, 4. false, 5. false, 6. false, 7. true, 8. true, 9. false, 10. true, 11. true, and 12. true.
1. False. There is no real number x such that x^2 = -1.
2. False. For any x in the real numbers, there exists a y such that xy ≠ 1. For example, if x ≠ 0, then y = 1/x will satisfy xy ≠ 1.
3. True. For any real number x, the real number y = x^2 satisfies the equation x^2 = y.
4. False. For any x and y in the real numbers, x + y = y + x.
5. False. For any x in the real numbers, there exists a y such that xy ≠ 0. For example, if x ≠ 0, then y = 1/x will satisfy xy ≠ 0.
6. False. There is no real number y such that y^2 = -1.
7. True. For any x and y in the real numbers, the real number z = x + y^2 satisfies the equation z = x + y^2.
8. True. For any x ≠ 0 in the real numbers, the real number y = 1/x satisfies the equation xy = 1.
9. False. There is no real number x such that x^2 = 2.
10. True. For any x in the real numbers, the real number y = 1 - x satisfies the equation x + y = 1.
11. True. The solution to the system of equations x + 2y = 2 and 2x + 4y = 5 is x = -1 and y = 3.
12. True. For any x in the real numbers, the real number y = (1 - x)/2 satisfies the equation (x + y = 2) and (2x - y = 1).
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The base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in². The slant height of the pyramid is 6 in. What is the surface area of the pyramid? Enter your answer in the box. in²
Answer:
249.6 in^2
Step-by-step explanation:
Since it's an equilateral triangle as the base, all of the other faces will be the same equilateral triangle, so 62.4 x 4 gives you the answer.
someone help please. i need to turn this in tomorrow. Question is in the picture!
Answer:
0.35 mL
Step-by-step explanation:
There are 1000 mL in 1 Liter. 350 of 1000 is 0.35
A rectangular lawn measures 10 m by 5 m. A uniform border of flowers is to be planted along two adjacent sides of the lawn. If the flowers that have been purchased will cover an area of 150 m^2, how wide is the border?
The border must have a width of 10 meters.
How wide is the border?We first have a rectangular lawn of 10m by 5m, so if we have a border with a width of x meters, the area of the border is given by:
A = 10m*x + 5m*x
Where we compute the area in that way because the flowers will be only on two adjacent sides of the rectangle.
And the area is 150 m^2, then we will get:
150m^2 = 10m*x + 5m*x
150m^2 = 15m*x
150m^2/15m = x
10m = x
The border has a width of 10 meters.
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Hector pent $38. 45 for 2DVD the ale tax wa $2. 85, and he didn't have a coupon. Each DVD cot the ame amount. How much would each DVD cot?
Each DVD cost is $17.80
This is a simple equation
From the question we have the following information :
1. Total spent for 2 dvd ( before tax ) = $17.80
2. Sales Tax for those spending = $2.85
Let's call the cost of each DVD "x".
The total cost of both DVDs would be 2x.
We know that the total cost of both DVDs and the sales tax was $38.45, so we can set up an equation:
2x + $2.85 = $38.45
Solving for x:
2x = $38.45 - $2.85 = $35.60
x = $35.60 / 2 = $17.80
Hence from explanation above, each DVD cost $17.80.
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if you add 21 to my number, multiply the result by 3, you will get 84 more than two thirds of my number. what is my number?
Answer:
9
Step-by-step explanation:
Let's suppose "my number" is x
If you add 21 to my number: 21 + x
Multiply the result by 3: 3(21+x)
You will get 84 more than two thirds of my number
[tex]3(21 + x) = 84 + \frac{2}{3} x \\ 63 + 3x = 84 + \frac{2}{3} x \\ \frac{7}{3} x = 21 \\ 7x = 63 \\ x = 9[/tex]
Therefore my number is 9
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Can a triangle be formed with ide length 3 inche, 3 inche and 5 inche? why or why not?
Yes, a triangle can be formed with side lengths of 3 inches, 3 inches, and 5 inches.
A triangle can be formed if and only if the sum of the lengths of any two sides is greater than the length of the third side. In this case, the sum of the lengths of sides 3 inches and 3 inches (6 inches) is greater than the length of the third side (5 inches), so a triangle can be formed.
In summary, a triangle can be formed with side lengths 3 inches, 3 inches, and 5 inches because the sum of the lengths of any two sides is greater than the length of the third side.
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emily convinced her mom to buy a giant box of her favorite cereal. her mom doesn't think the box will fit on their shelf. the volume of the box is 10 , 000 10,00010, comma, 000 cm 3 3 cubed. the base of the box is 25 2525 cm by 10 1010 cm. how tall is the box of cereal?
an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is t minimize the time it takes to travel from $a$ to $b$?
An isosceles triangle has base angles that each measure 64°. Which equation can be used to find n, the measure of the third angle of this isosceles triangle in degrees?
Answer:
Below
Step-by-step explanation:
The interior three angles of a triangle sum to 180°
you know tow of them are 64 degrees
so the third one is 180 - 64 - 64 or 180 °- 128°
Which of these groups of values plugged into the TVM Solver of a graphing
calculator will return the same value for PV as the expression
($415)((1+0.003) 24-1)
(0.003)(1+0.003) 24
A. N=2; 1%-3.6; PV = ; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
B. N=24; 1%-0.3; PV = ; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
C. N=24; 1%-3.6; PV =; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
D. N=2; 1%-0.3; PV =; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
D. N = 24, I% = 3.6, PV =, PMT = -415, FV = 0, P/Y = 12, C/Y = 12, and PMT:END are the values in the group that would provide the same result as the given equation.
What in math is PV?The present value of a sum of money is its current value. For instance, the present value is what $110 is currently worth if you are promised $110 in a year.
In the TVM solver, we have;
I = The annual percentage rate
N = n × t
t = The number of years
PV = Present value
PMT = Payment
P/Y = Payments made annually = n
C/Y equals the number of compounding periods in a year.
The following is how the monthly payment formula is stated.
M = P(r/n)(1+r/n)ⁿˣⁿ/(1+r/n)ⁿˣⁿ-1
which gives,
P = M [(1+r/n)ⁿˣⁿ-1] / (r/n)(1+r/n)ⁿˣⁿ
Therefore, we get:
where:
M = PMT = -415
P = PV
r = I
P/Y = n = 12
Therefore,
0.003 = I/12
I = 0.003 × 12 = 0.036 = 3.6%
N = n×t = 24
P = (415)[(1+I/12)²⁴- 1] /(I/12)(1+I/12)²⁴
= ( 415) [(1+0.003)²⁴ - 1] / (0.003)(1+0.003)²⁴ = ?
The present value, PV, is the equation's value.
We have FV = 0 when payments are paid based on the PV.
The set of values with the same value as ($415)(1+0.003)24 - 1 / (0.003)(1+0,003)
24 has the following values when entered into a calculator's TVM solver: D. N = 24, I% = 3.6, PV =, PMT = -415, FV = 0 and PMT:END.
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an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?
Answer:
Step-by-step explanation:
an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?
if f(x) = 7x2 − x3, what is the rate of change of f '(x) at (2, 20)?
The rate of change of f '(x) at (2, 20) is -52
We are given f(x) = 7x² − x³ and are asked to find the rate of change of f'(x) at (2, 20)
We can use the slope formula to find the average rate of change:
m = y2-y1/x2-x1
Here we need to find
Rate of change = f'(x2) - f'(x1) / x2 - x1
and here x1 = 2 and x2 = 20
First, we need to find f'(x)
f'(x) = 14x - 3x²
f'(x1) = f'(2) = 16
f'(x2) = f'(20) = -920
So, Rate of change = f'(x2) - f'(x1) / x2 - x1 = (-920 - 16)(20 - 2)
= -52
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which number is the smallest? a. 4.38 × 103 b. 4.38 × 10–3 c. 4.38 × 10–2 d. 438 e. 4.38 × 102
After simplifying the number, the number 4.38 × 10^{–3} = 0.00438 is the smallest number. So the number b is the smallest number.
We simplify the numbers to find the smallest number.
The numbers are
a. 4.38 × 10^3
We can write 10^3 as 1000
Now the number is
= 4.38 × 1000
Multiply
= 4380
b. 4.38 × 10^{–3}
The number of times to divide the base number is indicated by negative power. For each power of 10, the decimal points are moved to the left when multiplying the integer by the negative power of 10.
So we can write that number as
= 4.38 × 1/1000
Simplify
= 0.00438
c. 4.38 × 10^{–2}
We can write that number as
= 4.38 × 1/100
Simplify
= 0.0438
d. 438
e. 4.38 × 10^2
We can write that number as
= 4.38 × 100
Multiply
= 438
We can see that the number 4.38 × 10^{–3} = 0.00438 is the smallest number.
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The complete question is:
Which number is the smallest?
a. 4.38 × 10^3
b. 4.38 × 10^{–3}
c. 4.38 × 10^{–2}
d. 438
e. 4.38 × 10^2
FIND AREA PLS HELP ASAP!!!
Area of a rhombus is half the product of its diagonals:
A = d₁d₂/2A = (3+3)(9+9)/2 = 54 units²Question 6Area of a trapezoid is the product of the height and half the sum of its bases:
A = (b₁ + b₂)h/2A = (17 + 29)*5/2 = 115 units²A swim instructor would like to test the effect of a new swim technique versus the standard technique for a group of 25 competitive swimmers.
The swim instructor divides the students by class (junior or senior), and then randomly allocates half of the 14 juniors and 5 of the 11 seniors to receive instruction on the new technique.
During swim practice, the instructor times the juniors as they race against each other to see if those who learned the new technique outperform their peers. The instructor does the same for the seniors.
At the end of practice, the instructor compares the average swim time for both juniors and seniors among those who did and did not use the new technique.
What type of experimental design did the instructor use?
A) matched pairs experimental design
B) completely randomized experimental design
C) randomized block experimental design
D) none (observational study only)
C) randomized block experimental design.
What type of experimental design did the instructor use?The swim instructor used a randomized block experimental design for their experiment.This type of experimental design involves dividing the participants into groups (in this case, juniors and seniors) and then randomly allocating half of each group to receive instruction on the new technique.This helps to control for any potential confounding variables, such as age, that could affect the results of the experiment.By comparing the average swim time for both juniors and seniors among those who did and did not use the new technique, the instructor can determine if the new technique has an effect on swim performance.This type of experimental design is often used when the experimenter wants to compare the effects of a treatment or intervention between two or more groups with similar characteristics.To learn more about experimental design refer to:
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Answer:c
Step-by-step explanation:
I REALLY NEED THIS ANSWERED
Brenda invests $4,848 in a savings account with an interest rate compounded semiannually. If the account balance after 6 years is $6,520.02, what is the interest rate?
(Hint: SADMEP-Do not round calculations until the final answer.)
Round your answer to the nearest percent. ( Two decimal places or a whole number percentage)
The interest rate is -17.72%
What is the interest rate?
The proportion of a loan that is charged as interest to the borrower is typically expressed as an annual percentage of the loan outstanding.
The formula for finding the interest rate is:
A = P * (1 + r/n)^(nt)
Where A is the end balance, P is the starting principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
Since the interest rate is compounded semi-annually, n = 2. And the starting principal is $4,848, t = 6 years. So the equation becomes:
$6,520.02 = $4,848 * (1 + r/2)^(2 * 6)
Now we'll isolate r by taking the natural logarithm of both sides:
ln(6520.02 / 4848) = ln((1 + r/2)^(2 * 6))
ln(6520.02 / 4848) = 12 * ln(1 + r/2)
Now we'll solve for r by dividing both sides by 12 and taking the exponential of the result:
r/2 = (ln(6520.02 / 4848) / 12)^(1/12) - 1
r = 2 * ((ln(6520.02 / 4848) / 12)^(1/12) - 1)
Finally, we'll convert the interest rate to a percentage by multiplying by 100:
r = (2 * ((ln(6520.02 / 4848) / 12)^(1/12) - 1)) * 100%
= (2 * ((ln(1.34814) / 12)^(1/12) - 1)) * 100%
= (2 * (0.113774 - 1)) * 100%
= (2 * -0.886226) * 100%
= -17.72452%
hence, the interest rate is -17.72%
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The following list of prices is for a used original radio for a 1955 Thunderbird. The prices vary depending on the condition of the radio.
$210, $210, $320, $200, $300, $10, $340,
$300, $245, $325, $700, $250, $240, $200
b. Find the median of the radio prices.
c. Find the mode of the radio prices. (Place in ascending order.)
d. Find the four quartiles.
Q1 -
Q2 -
Q3 -
Q4 -
e. Find the interquartile range for this data set.
f. Find the boundary for lower outliers.
What is the lower outlier?
g. Find the boundary for upper outliers.
What is the upper outlier?
The answers to each part is given below.
What is a quartile?In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or quarters, of more-or-less equal size.
The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic
Given is the list of prices for a used original radio for a 1955 Thunderbird. The prices vary depending on the condition of the radio.
$210, $210, $320, $200, $300, $10, $340, $300, $245, $325, $700, $250, $240, $200
We can write the sorted data as -
10, 200, 200, 210, 210, 240, 245, 250, 300, 300, 320, 325, 340, 700
{ b } - Median calculation
{n} = 14
Median = (x{n/2} + x{n/2 + 1})/2 = (245 + 250)/2 = 247.5
{ c } - Mode calculation
The mode is the value or values that occur most frequently in the data set. Count the number of times each value in a data set occurs. The mode is the data value with the highest count. We can write the mode as follows -
210, 200, 300
{ d } - Quartiles calculation
Quartiles mark each 25% of a set of data -
The first quartile Q1 is the 25th percentile : 210
The second quartile Q2 is the 50th percentile : 247.5
The third quartile Q3 is the 75th percentile : 320
{ e } - Interquartile range calculation
The interquartile range IQR is the range in values from the first quartile Q1 to the third quartile Q3. Find the IQR by subtracting Q1 from Q3.
IQR = Q3 - Q1
IQR = 320 - 210
IQR = 110
{ f } -
Lower Outlier Boundary : 45
{ e } -
Upper Outlier Boundary : 485
Therefore, the answers to each part is given above.
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how many arrangements of the letters mathematics are there if h must imme- diately follow one of the ts, and e does not immediately follow h?
There are 3,265,920 arrangements of the letters in mathematics.
Consider T+H together which is easy to solve, and also consider the “TH” as one letter. There are two Ts in maThemaTics, and they can be together as TH or HT.
so there are actually 2*2=4 ways to build the TH itself. Now just plug a short hold on the “not followed by the h” and let us know how many ways to build it with just the TH restriction.
So with TH together, we can construct 10 letters in the word, two As, two Ms, and 1 as each of the remaining 6 letters. So it means there are
10!2!2!(1!)6=10!2!2!=36288004=907200
Now there are 4 ways to construct the TH, so 907200∗4=3,628,800.
To then add the “not followed by h” restriction, we should first determine all of the combinations where you have “THE” or “HTE” in the word. There are 4 ways to construct this letter grouping.
Then we have the remaining 9 letters in the word, two As, two Ms, and 1 of each of the remaining 5 letters.
So there are 4∗9!2!2!(1!)5=4∗9!4=3628802=362,880 ways to construct the word where you force THE/HTE together.
Finally, subtract the arrangements we have THE/HTE in the word from the arrangements where you just have TH/HT in order to get the arrangements that have TH/HT that is not immediately followed by h. 3,628,800–362,880=3,265,920.
Therefore, there are 3,265,920 arrangements.
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.
Select the correct answer.
The zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
A.
f(x) = (x − 6)(x + 4)
B.
f(x) = (x + 6)(x + 4)
C.
f(x) = (x − 6)(x − 4)
D.
f(x) = (x + 6)(x − 4)
The function corresponding to zeroes 6 and -4 is f(x)=(x-6)(x+4) i.e. A.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now ,
We can find function for zeroes 6 and -4 by putting f(x)=0
Therefore,
(x-6)(x+4)=0
x-6=0 and x+4=0
Hence,
x=6,-4
The function corresponding to zeroes 6 and -4 is f(x)=(x-6)(x+4).
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BROO HELP PLEASE THANK YOUUU
We will multiply the first 7×1 =7. Option A is the correct option.
What is a table?
An array displaying the outcomes of multiplying two numbers.
The results are displayed where a row and a column converge. One number runs along a row, the other down a column.
Information is organized in rows and columns, such as numbers and descriptions.
This table lists the sports that people participate in.
The table for 7:
7×1 = 7
7×2 = 14
7×3 = 21
7×4 = 28
7×5 = 35
7×6 = 42
7×7 = 49
7×8 = 56
7×9 = 63
7×10 = 70
According to the table, we first multiply 7×1 then 7×2.
Thus 7×1 =7 is the correct answer.
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Suppose ln x-ln y=y-4 , where y is a differentiable function of x and y=4 when x=4 . What is the value of dy/dx when x=4 ?
Answer:
When x=4, ln x-ln y=y-4, so ln 4-ln 4=4-4, which is true. Therefore, when x=4, y=4, and dy/dx=0.
Step-by-step explanation:
So, when x = 4, the value of the differentiable function dy/dx is 0.
What is differentiable function?A differentiable function of one real variable is one that has a derivative at each point in its domain. In other words, a differentiable function's graph has a non-vertical tangent line at each interior point in its domain.
Here,
Given the equation ln x - ln y = y - 4, we can rearrange it to get ln(x/y) = y - 4. Taking the derivative of both sides with respect to x using the chain rule:
d/dx (ln(x/y)) = d/dx (y - 4)
(1/x) (dx/dx) - (1/y) (dy/dx) = dy/dx
dy/dx = (1/y) (dx/dx) + (1/x) (dy/dx) = (1/y) + (1/x) (dy/dx)
Rearranging and solving for dy/dx:
(x/y) (dy/dx) = (1/y) - (1/x)
dy/dx = (x/y^2) (1/x - 1/y) = (x/y^2) (1/x - 1/y)
We can substitute x = 4 and y = 4 into the expression to find the value of dy/dx when x = 4:
dy/dx = (4/16) (1/4 - 1/4) = 0
So, the value of differentiable function dy/dx when x = 4 is 0.
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You and your friend each deposit $50 in separate savings accounts. Your account earns 2% simple annual interest. Your friend’s account earns 6% simple annual interest. How long does it take for you to earn $12 in interest? How long does it take for your friend to earn $12 in interest?
I earn $12 in interest after 12 years while my friend earns the same amount in 4 years.
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: My principal = $50 and friend's =$50 also friend's account earns 6% annual interest rate
As per question we get
let the time taken to earn $12 interest rate be t then
12=50×2×t /100
t=12 years
while for my friend
12=50×6×t /100
3t=12
t=4 years
Hence, I earn $12 in interest after 12 years while my friend earns the same amount in 4 years.
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suppose that mean retail price per gallon of regular grade gasoline 3.43 is with a standard deviation of and that the retail price per gallon has a bell-shaped distribution. note: please use empirical rule approximations for this problem. a. what percentage of regular grade gasoline sells for between and per gallon (to decimal)? b. what percentage of regular grade gasoline sells for between and per gallon (to decimal)? c. what percentage of regular grade gasoline sells for less than per gallon (to decimal)?
The 95% of regular grade gasoline sells for between $3.23 & $3.63 and per gallon (to decimal) and 85% of regular grade gasoline sells for between $3.23 & $3.53 and per gallon (to decimal) and 16% percentage of regular grade gasoline sells for less than $3.53 per gallon (to decimal).
Suppose that mean retail price per gallon of regular grade gasoline 3.43.
empirical rule explains that approximately 68%,95% and 99.7% of data lies between (µ ± 1*σ) ,(µ ± 2*σ) and (µ ± 3*σ) respectively.
⇒If some data {x} are normally distributed, the corresponding {z} will be normal with mean 0 and standard deviation 1 where the correspondence between the {x} and {z} is given by
z = [tex]\frac{x-\mu}{\sigma}[/tex]Such z's are called z-scores.
(µ ± 1*σ)=68%
(µ ± 2*σ)=95%
(µ ± 3*σ)=99.7%
a)
P(3.23<x<3.63) =[tex]P[ \frac{(x1- \mu)}{\sigma} < z < \frac{(x2- \mu)}{\sigma}} ][/tex]
=P[( [tex]\frac{3.23-3.43}{0.10}[/tex] < z < [tex]\frac{3.63-3.43}{0.10}[/tex] ]
=P[-2 < z < 2 ]
=0.95
=95.0 %
b)
P(3.23<x<3.53) =[tex]P[ \frac{(x1- \mu)}{\sigma} < z < \frac{(x2- \mu)}{\sigma}} ][/tex]
=P[( [tex]\frac{3.23-3.43}{0.10}[/tex] < z < ([tex]\frac{3.53-3.43}{0.10}[/tex] ]
=P[-2 < z < 1 ]
=0.815
=81.5 %
c)
P(x>3.53) =[tex]P[ z > \frac{x-\mu}{\sigma} ][/tex]
=P[ z > [tex]\frac{3.53-3.43}{0.10}[/tex] ]
=P[ z > 1 ]
=0.16
=16.0 %.
Therefore, 95% of regular grade gasoline sells for between $3.23 & $3.63 and per gallon (to decimal) and 85% of regular grade gasoline sells for between $3.23 & $3.53 and per gallon (to decimal) and 16% percentage of regular grade gasoline sells for less than $3.53 per gallon (to decimal).
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Reflect the endpoint of a line segment (-5, 10) across the x-axis. What is the result?
The result after the endpoint of a line segment is reflected is (-5. -10)
How to detemrine the result of the transformationFrom the question, we have the following parameters that can be used in our computation:
Point = (-5, 10)
The reflection rule is given as
Reflection across the x-axis
Mathematically, this is represented as
(x, y) = (x, -y)
So, we have
Image = (-5, -10)
Hence, the image is (-5, -10)
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The membership at Gym A costs $20 to join for 1 month plus $3 per visit. The membership at Gym B costs a flat rate of $40 for 1 month.
If you join Gym A, it will cost $20 to join for 1 month plus $3 per visit. If you visit the gym x times, your total cost will be 20 + 3x dollars.
If you join Gym B, it will cost a flat rate of $40 for 1 month.
To determine which membership is more cost-effective, you would need to compare the costs for different number of visits. For example, if you plan to visit Gym A 10 times in a month, your total cost would be 20 + 3(10) = $50. If you plan to visit Gym B only 2 times in a month, membership B is more cost-effective. If you plan to visit more than 13 times, membership A is more cost-effective.
It would be helpful to make a table with different number of visits to compare the cost of both gym memberships.
estimate the sum of 9/10 and 5/6
The sum of 9/10 and 5/6 is 26/15.
The sum of two fractions can be calculated only if the denominator (the bottom number) is the same. Here, in 9/10, 10 is the denominator and in 5/6, 6 is the denominator. To equate two denominators LCM(least common multiple) should be done.
LCM of 10 and 6 is 30.
To convert is to multiply each by the bottom number of the other over the other
9/10 + 5/6
= 9/10×3/3 + 5/6×6/6
=27/30 + 25/30
=52/30
=26/15 or 1 11/15
Therefore, the sum of 9/10 and 5/6 is 26/15 or 1 11/15.
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The sum of 9/10 and 5/6 equals 26/15.
Only if the denominator (the bottom number) is the same can two fractions' total be calculated. In this case, the denominator in 9/10 is 10 and in 5/6 is 6. The LCM (least common multiple) method should be used to equate two denominators.
30 is the LCM of 10 and 6.:
By multiplying each by the bottom number of the other over the other, you may convert.
9/10 + 5/6
= 9/10×3/3 + 5/6×6/6
=27/30 + 25/30
=52/30
=26/15 or 1 11/15
As a result, 9/10 plus 5/6 equals 26/15.
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