Let's call x to the pre-tax subtotal
Then, the amount of money he pays in taxes is: 0.076x
Therefore, the total cost is: x + 0.076x, which is equal to $236.72. That is:
x + 0.076x = 236.72
1.076x = 236.72
x = 236.72/1.076
x = 220
The pre-tax subtotal was $220
Find the average of the numbers 4 2/3, 6 4/15, 8 4/5, and 9 2/3. Write the solution as a mixed number or a fraction in lowest terms
Answer:
Step-by-step explanation:
Add all the terms together and divide by however many terms you have.
4 2/3 + 6 4/15 + 8 4/5 + 9 2/3 = 147/5
Since there's 4 terms (I'm assuming the fractions are separate and not being multiplied).
We divide 147/5 by 4.
147/20 or 7 and 35/100
8) Type your answers in the boxes.
A sequence is given by the equation an= 1/4n where a1 = 512 and n > 1 and is a
whole number.
What are the first 4 terms of the series?
Series:
The first 4 terms of the sequence are 512 , 128 , 32 and 8 .
In mathematics, a sequence is a named collection of elements where repeats are allowed and order matters.
It has pieces, much like a set (also called elements, or terms). The number of items determines how long the series is (potentially infinite). The same elements could appear in a sequence more than once at different places in contrast to a set, where the order is crucial. Formally, a sequence can be defined as a relationship between the items at each of the positions in the sequence and natural numbers (the positions of the sequence's constituents). It is possible to think of an indexed family, which is a function from any index set, as a generalization of the concept of a sequence.The formula for the sequence is given by aₙ = 1/4 aₙ₋₁
It is given that a₁ = 512
Hence a₂ = 1/4 a₁ = 1/4 × 512 = 128
a₃ = 1/4 a₂ = 32
a₄ = 1/4 a₃ = 8
Therefore the first 4 terms of the sequence are 512 , 128 , 32 and 8 .
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what is the equation of the line that contains point (-2, -2) and a slope of 4
Given the a point and a slope
point coordinate ( -2 , -2 )
Slope (m) = 4
Step 1: Write the formula for the point-slope equation
[tex]y-y_1=m(x-x_1)[/tex]Step 2: Identify the x and y values
[tex]\begin{gathered} x_1=-2 \\ y_1=-2 \\ m=4 \end{gathered}[/tex]Step 3: substitute the values in the point-slope equation formula
[tex]\begin{gathered} y-(-2)=4(x-(-2)) \\ y+2=4(x+2) \\ y+2=4x+8 \\ y=4x+8-2 \\ y=4x+6 \end{gathered}[/tex]Hence, the equation of the line is y = 4x+6
Select the correct answer.
What is the solution to the equation 41xl - 8 = -8?
O A.
O B.
O C.
O D. No solutions exist.
X=0
X = -16
x = -4 or x = 4
Answer:
A
Step-by-step explanation:
Adding 8 to both sides,
[tex]4|x|=0 \\ \\ |x|=0 \\ \\ x=0[/tex]
Select the correct answer.Consider these three numbers expressed in scientific notation: 2.4 x 104,6.3 105, and 9.6 x 10”. Which number is the greatest, and by howmany times Is It greater than the smallest number?OA. The greatest number is 9.6 % 10%. It is 400 times greater than the smallest number.ОВ.The greatest number is 6.3 x 105. It is 40 times greater than the smallest number.OCThe greatest number is 6.3 x 109. It is 400 times greater than the smallest numberODThe greatest number is 9.6 x 10'. It is 4,000 times greater than the smallest number.
We have the next numbers
[tex]\begin{gathered} 2.4\cdot10^4 \\ 6.3^{}\cdot10^5 \\ 9.6\cdot10^7 \end{gathered}[/tex]In this case, the greatest number will be the number that is multiplied by 10 a greater number of times.
So, the greatest number is 9.6 x 10^7,
Then, the smallest number will be the number that us multiplied by 10 a smaller number of times.
So, the smallest number is 2.4 x 10^4,
Now, to know the number of times that the greatest number is greater than the smallest number we must divide it
[tex]\frac{9.6\cdot10^7}{2.4\cdot10^4}=4\cdot10^3=4000[/tex]Finally, The greatest number is 9.6 × 10^7. It is 4,000 times greater than the smallest number. (Letter D).
using the information given, select the statement that can deduce the line segments to be parallel. if there are none, then select none. when m<2 = m<3
The answer is the third option, None
Because the fact that angle 2 is equal to angle 3 does not imply that AB is parallel to DC ot that AD is parallel to BC
Name the constant variation for this equation y = 5x
Answer:
The constant is 5 and the variation is known as the slope of the equation which is the rate of change of y with respect to x. In other words how much does y change when x changes by 1 unit
Step-by-step explanation:
I will send u a picture of the topic it is hard to explain in words. it job is to find the measure of each labeled angle so 5x and 4x
According to the given image, we have a parallelogram whose two consecutive angles are 5x and 4x.
Remember that two consecutive interior angles in a parallelogram sum 180°, so we can express the following equation.
[tex]5x+4x=180[/tex]Now, we solve for x.
[tex]\begin{gathered} 9x=180 \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]We use this value to find each angle.
[tex]\begin{gathered} 5x=5(20)=100 \\ 4x=4(20)=80 \end{gathered}[/tex]Therefore, the angles are 100° and 80°.Aisha earned some money doing odd jobs last summer and put it in a savings account that earns 14% interest compounded monthly. After 7 years, there is $300.00 in the account. How much did Aisha ea doing odd jobs? Round your answer to the nearest cent.
Aisha earned some money doing odd jobs
Let P be the amount earned doing odd jobs
she saved the money for 7 years
The interest is 14%
Using the formula
A = p(1 + r/n)^nt
Let P = principal
t= time
r = rate
n = compounded period
Since, the money is compounded monthly, then n = 12
A = $300.00
r = 14%
r = 14/100 = 0.14
t = 7
n = 12
substituting the above figures in to the formula
$300 = P( 1 + 0.14/12)^12 x 7
300 = P( 1 + 0.0116)^84
300 = P (1.0116)^84
300 = P(2.635)
300 = 2.635P
Divide both sides by 2.635
300/2.635 = 2.635P/2.635
P = $113.85
Approximately $114
The money she earned doing odd jobs is $114
Select all the correct answers.Which two transformations preserve the side lengths and angles of the preimage? a reflection across line a stretch by a factor of 4 a dilation by a factor of 4 a translation to the right
Which two transformations preserve the side lengths and angles of the preimage:
Rotations and reflections both preserve a polygon's side lengths. Dilations and translations both preserve a polygon's angle measures.
A reflection across line will preserve the angles
A dilation by a factor of 4 will preserve the both
Hence the correct answer is Option A and D
Answer:
1: a translation to the right
2: a reflection across line m
Step-by-step explanation:
I'm not sure how to find the degrees for angle d
Answer
a° = 58°
b° = 48°
c° = 74°
d° = 122°
Explanation
To answer this, we need to first know
- what alternate angles are.
- that the sum of angles in a triangle is 180°.
- The sum of angles on a straight line is 180°.
Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines. If the two lines are parallel to each other, then alternate angles are equal.
We can see that
a° = 58°
b° = 48°
Then, for c°,
48° + 58° + c° = 180° (Sim of angles in a triangle is 180°)
106° + c° = 180°
c° = 180° - 106°
c° = 74°
Then, for d°,
58° + d° = 180° (Sum of angles on a stright line is 180°)
d° = 180° - 58°
d° = 122°
Hope this Helps!!!
What is the range of this function? 8 5 O A f-8,-3,5,7) B. {6, 8, 10, 12) O C. (-8, -3, 5, 6, 7, 8, 10, 12} O D. 4-3,7,8, 12)
Remember that the range is formed by all the numbers inside the output set, the right one.
Therefore, the range is[tex]\mleft\lbrace-8,-3,5,7\mright\rbrace[/tex]The answer is A.a sample of 49 customers was taken at a computer store. each customers was asked the price of the computer she brought. find the mean price sampleround to the nearest dollar
The mean is computed as follows:
[tex]\operatorname{mean}=\frac{\text{ sum of the terms}}{\text{ number of terms}}[/tex]In this case, the number of terms is the number of computers.
To find the sum of the terms, we need to multiply the number of computers by each price and add them, that is,
[tex]\begin{gathered} \operatorname{mean}=\frac{17\cdot2050+18\cdot1050+14\cdot1000}{17+18+14} \\ \operatorname{mean}=\frac{34850+18900+14000}{49} \\ \operatorname{mean}=\frac{67750}{49} \\ \operatorname{mean}=1383\text{ \$} \end{gathered}[/tex]what is the order of operations for the following expression: 5x("*3)-5?
The order of operations for the given expression are open exponent, multiplication, and subtraction as per the PEMDAS rule.
What is the PEMDAS rule?PEMDAS rule states that the order of operation starts with the calculation enclosed in brackets or the parentheses first. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and then addition and subtraction.
The expression is given in the question as:
⇒ 5×(3)² - 5
To determine the evaluation of the given expression
⇒ 5×(3)² - 5
We have to apply the PEMDAS rule to the expression
As per the PEMDAS rule, the solution would be:
⇒ 5×(9) - 5
Apply the multiplication operation,
⇒ 45 - 5
Apply the subtraction operation,
⇒ 40
Thus, the order of operations for the given expression are open exponent, multiplication, and subtraction as per the PEMDAS rule.
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If you buy a car for $24,686 and it depreciates linearly at a rate of 8% per year, what will be its value after 6 months?
The value of a car after 6 months will be $23,698.56.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Cost of a car = $24,686
And, The cost of a car is depreciates linearly at a rate of 8% per year.
Now,
The depreciated cost of a car in 1 year = 8% of $24,686
= 8/100 x $24,686
= $1,974.88
So, The depreciated cost of a car in 1 year will be $1,974.88
Since, In 1 year there is 12 month.
Hence, The depreciated cost of a car in 6 month = $1,974.88 ÷ 2
= $987.44
Therefore, The value of a car after 6 month = $24,686 - $987.44
= $23,698.56
Hence, The value of a car after 6 months will be $23,698.56.
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Find the y-intercepts of the graph of the following quadratic function. If there is more than one intercept, separate them with commas. If there are no x-intercepts type DNE.
f(y) = 5y^2 - 240
y-intercept(s): __________
The y-intercepts are the values of y such that f(y) = 0, solving that we will get:
y-intercepts: -6.93, 6.93.
How to find the y-intercepts of the function?
Here we have a function that depends of y, and we want to find the y-intercepts.
The function is:
f(y) = 5*y^2 - 240
The y-intercepts are the values of y such that the function becomes zero, so we need to solve:
0 = 5*y^2 - 240
240 = 5*y^2
240/5 = y^2
48 = y^2
Now we apply the square root in both sides to get:
±√48 = y
±6.93 = y
So the two y-intercepts are:
y = 6.93
y = -6.93
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. Erin deposited $1,300 into a savings account that earns6% simple interest for 3 years.
The simple interest formula is:
A = P(1 + rt)
where A is the final amount, P is the principal, r is the annual interest rate (as a decimal) and t is time in years.
Substituting with P = 1,300, r = 0.06 and t = 3, we get:
A = 1,300(1 + 0.06*3)
A = 1,300*1.18
A = 1,534
The final amount will be $1,534
A consumer group buys identical radios at 14 different stores. if the mean(average)price per radio is $23.50, how much did the consumer group spend for all the radios?
If the consumer group bougth 14 different radios it means they bought 14 units and to calculate how much did they spend.
[tex]14\cdot(23.50)=329[/tex]they spend about $329 in the 14 radios.
Which equation is equivalent to the equation 6z +9= 12?
A: x+9=6
B=2x+3=4
C=3x+9=6
D=6x+12=9
If two systems of equations have the same solution, they are equivalent (s).
To solve analogous equations, use these five steps: Use the distributive property in Step 1 if necessary. Step 2: If necessary, group similar terms on the same side of the equal sign.
What other formula is the same as 6z + 9= 12?
A: x+9=6
B=2x+3=4
C=3x+9=6
D=6x+12=9
Answer: B;
Step-by-step explanation:
We get 6x + 9 = 12 if we divide both sides by 3. 6x + 9x/3 = 12/3;
2x + 3 = 4;
this corresponds to choice B. In general, something is considered equal if two of them are the same.
Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are entered into the formula.
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On the driving range, Tiger Woods practices his swing with a particular club by hitting many, many balls.
When Tiger hits his driver, the distance the ball travels follows a Normal distribution with mean 304 yards and standard deviation 8 yards.
a) What percent of Tiger's drives travel at least 290 yards?
b) What percent of Tiger's drives travel between 305 and 325 yards?
Q) What if our z does not show on table A?
Using the normal distribution, it is found that:
a) 95.99% of Tiger's drives travel at least 290 yards.
b) 44.40% of Tiger's drives travel between 305 and 325 yards.
c) If the z-scores do not show on table A, they represent too low or too high values, with probabilities very close to either 0 or 1.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.If the z-score does not show on the z-table, they represent too low or too high values, with probabilities very close to either 0 or 1.The mean and the standard deviation for the length of Tiger Woods's swings are given as follows:
[tex]\mu = 304, \sigma = 8[/tex]
The proportion of golf swings that are at least 290 years is one subtracted by the p-value of Z when X = 290, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (290 - 304)/8
Z = -1.75
Z = -1.75 has a p-value of 0.0401.
1 - 0.0401 = 0.9599.
Hence the percentage is of 95.99%.
The proportion of golf swings that are between 325 yards and 305 yards is the p-value of Z when X = 325 subtracted by the p-value of Z when X = 305, hence:
X = 325:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (325 - 304)/8
Z = 2.63
Z = 2.63 has a p-value of 0.9957.
X = 305:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (305 - 304)/8
Z = 0.13
Z = 0.13 has a p-value of 0.5517.
0.9957 - 0.5517 = 0.4440.
Hence the percentage is of 44.40%.
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19. Jaylen makes the statement shown below. "When multiplying two whole numbers that end in zeros, the
product always has the exact same number of zeros at the end as the number of zeros from the end of the two
numbers combined. For example, the product of 70 x 300 has exactly three zeros at the end since 70 ends in
one zero and 300 ends in two zeros."
Which expression proves Jaylen's statement is not correct?
A. 20 x 100
B. 20 x 700
C. 50 x 600
D. 90 x 500
50 x 600= 30,000 which has more zeros than 50 and 600 combined
Translate each sentence into a formula. The area of a parallelogram is the product of the base of the parallelogram and the height of the parallelogram. a. A=h-bb. b=h/A c. A=b/hd. A=bh
Question: Translate each sentence into a formula. The area of a parallelogram is the product of the base of the parallelogram and the height of the parallelogram.
Solution: The product between two objects means the multiplication between these two objects, then the correct solution would be:
d. A=bh
write the rule for the quadratic function in the form you would use to graph it. then graph the function
The quadratic function is already written in a recognizable way:
[tex]f(x)=x^2-6x+11[/tex]Evaluate the function at some values to find points on the graph of f:
[tex]\begin{gathered} \\ f(-1)=(-1)^2-6(-1)+11=18 \\ f(0)=(0)^2-6(0)+11=11 \\ f(1)=(1)^2-6(1)+11=6 \\ f(2)=(2)^2-6(2)+11=3 \\ f(3)=(3)^2-6(3)+11=2 \\ f(4)=(4)^2-6(4)+11=3 \\ f(5)=(5)^2-6(5)+11=6 \\ f(6)=(6)^2-6(6)+11=11 \\ f(7)=(7)^2-6(7)+11=18 \end{gathered}[/tex]Plot the points (x,f(x)) on a coordinate plane:
Draw a smooth line through those points:
What is the present value of an investment that will be worth $7000 at the end of five years? Assume an APR of 6% compounded monthly. (Round your answer to the nearest cent.)
The Solution:
Let the present value of the investment be represented with P.
We shall use the formula below:
[tex]\begin{gathered} A=P(1+\frac{r}{100\alpha})^{n\alpha} \\ \text{Where} \\ A=\text{amount (after 5years)}=\text{ \$7000} \\ r=rate\text{ (in \%)=6 \%} \\ n=\text{ number of years =5 years} \\ \alpha=\text{ number of periods per annum =12} \\ P=\text{ Principal = initial investment=?} \end{gathered}[/tex]Substituting these values in the formula above, we get
[tex]\begin{gathered} 7000=P(1+\frac{6}{100\times12})^{(5\times12)} \\ \\ 7000=P(1+\frac{6}{1200})^{60} \end{gathered}[/tex]So,
[tex]\begin{gathered} 7000=P(1+0.005)^{60} \\ \\ 7000=P(1.005)^{60} \\ \text{Dividing both sides by 1.005}^{60},\text{ we get} \\ P=\frac{7000}{1.005^{60}}=\frac{7000}{1.348850153}=5189.605\approx\text{ \$5189.61 (518961cent)} \end{gathered}[/tex]Thus, the present value of the investment that will yield $7000 at the end of 5 years is $5189.61 (or 518961 cents )
Therefore, the correct answer is $5189.61 (or 518961 cents )
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The length of a bacterial cell is about 3 x 10^−6 m, and the length of an amoeba cell is about 4.5 x 10^−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
2 x 10^2
2 x 10^3
0.7 x 10^1
6.67 x 10^2
Answer:6.67x10^2
Step-by-step explanation:
hey guys im confused
The values of the function are-
Part a: Value of (f/g)(x) = x - 9Part b: Domain of (f/g)(x) = Real numbers.What is termed as the domain and range of the function?The domain of the a function is the collection of values that can be plugged into it. This set contains the x values inside a function like f(x). A function's range is the set of values which the function can take. This is the set of values which the function returns after we enter an x value.For the given function;
f(x) = x - 3
g(x) =(x - 3)/(x - 9)
Part a: Value of (f/g)(x)
For the finding the value of (f/g)(x) simply divide the function g(x) by f(x).
(f/g)(x) = (x - 3)/ [(x - 3)/(x - 9)]
As, (x -3) will get cancelled.
(f/g)(x) = x - 9
Part b: Domain of (f/g)(x)
(f/g)(x) = x - 9
As, the resultant function is a polynomial function, thus the domain of the function is all real numbers.
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What is the fundamental difference in the algebraic representation of a polynomial function and a rational function? How do their graphs differ? To earn full credit be sure to address both parts to this question.
Polynomial function is a generic function in the form (linear, quadratic, cubic, and so on.)
Rational function is a function of two polynomial functions written as a fraction or quotient of two polynomial function in the form :
[tex]f(x)=\frac{P(x)}{Q(x)}[/tex]So the difference is rational function shows a quotient of two polynomial functions.
The graph of a polynomial function is continuous while the graph of a rational function is discontinuous as the denominator will become zero at some point. When the denominator is 0, the function will be undefined, thus resulting to a discontinuous graph.
Suppose we want to choose 5 objects, without replacement, from 9 distinct objects. If the order of the choices is relevant, how many ways can this be done? If the order of the choices is not relevant, how many ways can this be done?
If the order of choice is relevant, use permutation. We have to choose 5 objects in a total of 9:
[tex]9\times8\times7\times6\times5=15120\text{ ways}[/tex]Obs: Initially we have 9 objects, you choose one, then we have 8, you choose another, then you have 7..... (this is the reasoning)
If the order of choice is not relevant, use a combination. This can be done by the equation above:
[tex]C_{9,5}=\frac{9!}{(9-5)!\times5!}[/tex][tex]C_{9,5}=\frac{9!}{4!\times5!}[/tex][tex]C_{9,5}=\frac{9\times8\times7\times6\times5!}{4!\times5!}[/tex][tex]C_{9,5}=\frac{9\times8\times7\times6}{4\times3\times2\times1}[/tex][tex]C_{9,5}=126\text{ ways}[/tex]Obs: It is a combination of 9 elements chosen 5 by 5.
the data to the right represent the top seed in kilometers per hour of all the players a certain soccer of a construct a frequency distribution is a frequency histrogram in a realative frequency histogram.what percentage of players had top speed between 18 and 21.9 km H what percentage of players had a top speed less than 13.9 kmh
The relative frequency is the percentage of a count over the total count.
To get the relative frequency, here are the steps:
1. Get the total count.
[tex]\begin{gathered} N=4+8+20+74+336+212 \\ N=654 \end{gathered}[/tex]2. Divide each frequency or count by 654.
For example, the frequency between 10 - 13.9 km/h is 4 players.
[tex]\begin{gathered} P=\frac{x}{N} \\ P=\frac{4}{654} \\ P=0.0061 \end{gathered}[/tex]Hence, the relative frequency for the first class interval is 0.0061.
Moving on to the next interval 14 - 17.9 km/h. x = 8 players
[tex]P=\frac{x}{N}=\frac{8}{654}=0.0122[/tex]Moving on to the next interval 18-21.9 km/h. x = 20 players
[tex]P=\frac{x}{N}=\frac{20}{654}=0.0306[/tex]Moving on to the 4th interval 22 - 25.9 km/h . x = 74 players
[tex]P=\frac{x}{N}=\frac{74}{654}=0.1131[/tex]At 5th interval 26 - 29.9 km/h, x = 336 players.
[tex]P=\frac{x}{N}=\frac{336}{654}=0.5138[/tex]Finally, at the last interval 30 - 33.9 km/h, x = 212 players.
[tex]P=\frac{x}{N}=\frac{212}{654}=0.3242[/tex]Completing the table, we have:
Solve the following equation. Show your work.
7y = −84
Answer:
-11
Step-by-step explanation:
7y=-84
7y=-84/7 you have to divide the whole equation by 7 to get rid of the 7 in fron of the y
y=-11
Answer:
7y = -84
y = -84/7
y = -12
Final answer after checking will be the following:-
7(-12) = -84
