According to the given conditions of volume,[tex]$V_{cone} = \frac{1}{3} \pi \frac{120}{\pi h} h = \frac{1}{3} \cdot 120 = 40}$[/tex] cubic inches.
What is volume ?Volume is the amount of space that a three-dimensional object occupies or contains. It is a measure of the total amount of enclosed space inside a solid figure, such as a cube, cylinder, sphere, or any other three-dimensional shape.
According to given information :
Since the cylinder and cone have the same height and congruent circular bases, their volumes are proportional to the squares of their radii.
Let the radius of the base of the cylinder and cone be denoted as r.
The volume of a cylinder is given by:
[tex]$V_{cylinder} = \pi r^2 h$[/tex]
where h is the height of the cylinder.
We are given that the volume of the cylinder is 120 in, so we can plug this into the formula and solve for r:
[tex]$120 = \pi r^2 h$[/tex][tex]$r^2 = \frac{120}{\pi h}$[/tex]
The volume of a cone is given by:
[tex]$V_{cone} = \frac{1}{3} \pi r^2 h$[/tex]
We know that the cone and cylinder have the same height, so we can substitute the expression we found for [tex]$r^2$[/tex] into the formula for the volume of the cone:
According to the given conditions,
[tex]$V_{cone} = \frac{1}{3} \pi \frac{120}{\pi h} h = \frac{1}{3} \cdot 120 = 40}$[/tex] cubic inches.
Therefore, the volume of the cone is 40 cubic inches.
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Challenging y’all a little
Answer:
identify a relationship among Tn,Sn and Sn-1 where n>1
Mira looks at her fitness monitor and sees that she has run 2 miles so far. If this distance is 40% of the total distance she plans to run, how many total miles does Mira plan to run?
Answer: 30
Step-by-step explanation:
I think 0.o
Let's represent the total distance that Mira plans to run with "x".
According to the problem, 2 miles is 40% of the total distance, so we can write:
2 = 0.4x
To find the value of "x", we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.4:
2 ÷ 0.4 = x
Simplifying the left side gives us:
5 = x
Therefore, Mira plans to run a total of 5 miles.
Is the perimeter of the composite figure equal to the sum of the perimeters of the individual figures? Explain by selecting all the statements that apply
It depends on the specific composite figure. In general, the perimeter of a composite figure is not always equal to the sum of the perimeters of the individual figures that make it up.
However, in some cases, it is possible to calculate the perimeter of a composite figure by adding the perimeters of the individual figures and subtracting the lengths of any shared sides.
For example, if a composite figure is made up of two rectangles that share a side, then the perimeter of the composite figure is equal to the sum of the perimeters of the two rectangles minus the length of the shared side.
In other cases, such as when a composite figure has curved sides or irregular shapes, the perimeter cannot be calculated simply by adding the perimeters of the individual figures.
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A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their
grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected
students.
Number of
Absences
GPA
15 1 0
9
12
3
3
2.1 4.3 4.5 3.2 4.0 1.7 3.8 2.9
6
1
3.6
2 7
3.4
2.6
Using technology, the y-intercept is
O4.5, which means a student with no absences has a GPA of 4.5.
O 4.5, which means a student with no absences is predicted to have a GPA of 4.5.
O 3.79, which means a student with no absences is predicted to have a GPA of 3.79.
O 3.79, but it does not make sense to interpret the y-intercept in this context.
0 4
3.1
2.8
9 10
2.8
4.1
Answer: The correct answer is:
The y-intercept is 3.79, which means a student with no absences is predicted to have a GPA of 3.79.
Explanation:
To determine the relationship between the number of absences and the GPA, the student can use linear regression analysis. The regression line can be obtained using software such as Excel or R. The y-intercept of the regression line represents the predicted value of the response variable (GPA) when the predictor variable (number of absences) is zero.
Using technology, the y-intercept for this data set is found to be 3.79. This means that a student with zero absences is predicted to have a GPA of 3.79. Therefore, the correct answer is that the y-intercept is 3.79 and it does make sense to interpret it in this context.
Step-by-step explanation:
A desk is on sale for $380, which is 20% off the original price. Which equation can be used to determine the
amount of money saved, s, in dollars, when purchasing this desk on sale?
A s= 0. 2(380)
B
S = (380 = 0. 8) - 380
Cs= (380 = 0. 5) – 380
D
8 = (380 = 0. 8)
The right formula to figure out how much money was saved, s, in dollars when getting this desk on sale is: s = 0.2(380) (380) This calculation accounts for desk being 20% less expensive than it was originally.
which translates to a 20% discount for the consumer. So, we must multiply the original price by the discount %, which in this case is 0.2, in order to determine the amount saved. The equation in Option A that best captures the presented circumstance is accurate. A desk is on sale for $380, which is 20% off the original price. Which equation can be used to determine the amount of money saved, s, in dollars, when purchasing this desk on sale accounts for desk being 20% less expensive than it was originally. The equation in Option A that best captures the presented circumstance is accurate.
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jar contains 30 red balls and 20 white balls. twenty-five balls are randomly selected from the jar with replacement. what is the probability that a red ball was selected more than 20 times?
The probability that a red ball was selected more than 20 times when 25 balls are randomly selected from the jar with replacement is 0.037.
Given that a jar contains 30 red balls and 20 white balls. Also, 25 balls are randomly selected from the jar with replacements. We need to find the probability that a red ball was selected more than 20 times.
The binomial probability distribution function can be represented as follows:
[tex]P(X = k) = \ ^nC_k . p^k . q^{(n-k)}[/tex]
where n is the number of trials, k is the number of successes,
p is the probability of success,
q = 1 - p is the probability of failure.
Here, the probability of selecting a red ball is 30/50 = 3/5.
So, the probability of selecting a white ball is 2/5.
Here, we have n = 25 trials, p = 3/5, q = 2/5.
Let X be the number of times a red ball is selected. Then we need to find P(X > 20).
So, P(X > 20) = 1 - P(X ≤ 20)
= 1 - Σ P(X = k), k = 0 to 20
[tex]= 1 - \sum \ ^nC_k . p^k . q^{(n-k)}[/tex], k = 0 to 20
[tex]P(X = k) = \ ^nC_k . p^k . q^{(n-k)}[/tex]
[tex]P(X > 20) = 1 - \sum \ ^nC_k . p^k . q^{(n-k)}[/tex], k = 0 to 20
= [tex]1 - { \ ^nC_0 . p^0 . q^{(n-0)} + \ ^nC_1 . p^1 . q^{(n-1)} + \ ^nC_2 . p^2 . q^{(n-2)} + ... + \ ^nC_{20} . p^{20} . q^{(n-20)}}[/tex]
= 1 - {1 . (3/5)^0 . (2/5)^25 + 25 . (3/5)^1 . (2/5)^24 + 300 . (3/5)^2 . (2/5)^23 + ... + 1.623 x 10^10 . (3/5)^20 . (2/5)^5}
= 1 - 0.963
= 0.037
Therefore, the probability that a red ball was selected more than 20 times when 25 balls are randomly selected from the jar with replacement is 0.037.
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a CD usually sells for $11.00. if the CD is 10% off and the sales tax is 7% what is the total price of the CD, including tax
0.90 x $11.00 = $9.90
This is the price of the CD before taxes are applied. To find the total price, including tax, we need to add the 7% sales tax to the discounted price:
Total price = discounted price + (sales tax x discounted price)
Total price = $9.90 + (0.07 x $9.90)
Total price = $9.90 + $0.69
Total price = $10.59
Therefore, the total price of the CD, including tax, is $10.59.
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Using the Binomial Distribution Applet answer the following question, A basketball player makes 54% of his shots from the free throw line. Suppose that each of his shots can be considered independent and that he takes 3 shots. Let X the number of shots that he makes. What is the probability that he makes 2 shots or less? 0.09734 10.44010.8425
The Binomial Distribution applet will calculate the probability of the basketball player making 2 or less shots, and it turns out to be equal to 0.8425.
Using the Binomial Distribution Applet, we can find the probability that the basketball player makes 2 shots or less by inputting the given information into the applet. The number of trials is 3, the probability of success is 0.54, and the number of successes we are looking for is 2 or less.
Here are the steps to finding the probability using the Binomial Distribution Applet: Input the number of trials as 3, Input the probability of success as 0.54, Input the number of successes as 2, Click the "Calculate" button
The applet will then calculate the probability of the basketball player making 2 or less shots, which is 0.8425. Therefore, the answer to the question is 0.8425.
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The initial population of a town is 15 000, and it grows with a
doubling time of 10 years. What will the population be in 12 years?
24 years?
The population of the town after 12 years Aand in 24 years will be approximately 34,461 and 79,171 respectively.
What will the population be in 12 years and in 24 years?If the population doubles every 10 years, then we can use the formula for exponential growth to find the population after a certain number of years:
P = P₀ x 2^(t/T)
where:
P₀ = initial population = 15,000
P = population after t years
T = doubling time = 10 years
t = number of years
Using this formula, we can find the population after 12 years:
P = 15,000 × 2^(12/10)
P = 34,461
Therefore, the population of the town after 12 years will be approximately 34,461.
Similarly, we can find the population after 24 years:
P = 15,000 × 2^(24/10)
P = 79,171
Therefore, the population of the town after 24 years will be approximately 79,171.
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Write down the domain and range of: y = 2*
The domain is (-∝, ∝) and the range is y > 0
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
y = 2^x
The domain of the function is the set of all real numbers
This is so because there is no restriction on the input values
The range of the function is the set of positive real numbers
Since any positive number can be obtained by raising 2 to a power, and the function is never negative or zero.
We can write the range as y > 0.
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The equation 3600b² = hw represents the relationship among the body surface area b (in square meters), height h (in
centimeters), and weight w (in kilograms) of a person. To the nearest tenth, approximate the body surface area of a person who
is 168 centimeters tall and weighs 60 kilograms.
The body surface area is about (blank)
square meters.
Answer: 0.2 square meters.
Step-by-step explanation:
We are given the equation:
3600b² = hw
We need to find the value of b, given that h = 168 cm and w = 60 kg.
First, we need to convert the height from centimeters to meters:
h = 168 cm = 1.68 m
Substituting the given values:
3600b² = (1.68)(60)
3600b² = 100.8
b² = 100.8/3600
b² = 0.028
Taking the square root of both sides:
b = √0.028
b ≈ 0.167
Rounding to the nearest tenth:
b ≈ 0.2
Therefore, the body surface area of a person who is 168 centimeters tall and weighs 60 kilograms is about 0.2 square meters.
The correlation be reasonable to conclude that the data come from a r X Table of critical values Sample Size, n Critical Value Sample Size, n Critical Value 5 0.880 16 0.941 6 0.888 17 0.944 7 0.898 18 0.946 8 0.906 19 0.949 9 0.912 20 0.951 10 0.918 21 0.952 11 0.923 22 0.954 12 0.928 23 0.956 13 0.932 24 0.957 14 0.935 25 0.959 15 0.939 30 0.960
a) there is a strong positive correlation between the variables based on the given correlation coefficient and critical value
To interpret correlation values, the Table of Critical Values must be used. In this case, the correlation be reasonable to conclude that the data come from a r X. Table of critical values Sample Size, n Critical Value Sample Size, n Critical Value 5 0.880 16 0.941 6 0.888 17 0.944 7 0.898 18 0.946 8 0.906 19 0.949 9 0.912 20 0.951 10 0.918 21 0.952 11 0.923 22 0.954 12 0.928 23 0.956 13 0.932 24 0.957 14 0.935 25 0.959 15 0.939 30 0.960. The correlation coefficient is found between -1 and 1. Correlation values near 1 indicate a strong positive correlation, while those near -1 indicate a strong negative correlation. Correlation values near zero, on the other hand, indicate no correlation between the variables. In this case, we can interpret that the correlation is significant because it falls outside of the range of -0.880 and 0.880. We can see that the correlation value of 0.918 is higher than the critical value of 0.880 for the sample size of 10 from the given table of critical values. As a result, it can be concluded that there is a strong positive correlation between the variables based on the given correlation coefficient and critical value.
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Find the values of p
for which the integral converges. And evaluate the integral for those values of p
.
a
)
∫
1
0
3
1
x
p
d
x
b
)
∫
[infinity]
e
25
x
(
ln
x
)
p
d
x
a) For the integral ∫01^3 1/x^p dx to converge, p > 0. Evaluating the integral for those values of p gives ∫01^3 1/x^p dx = -1/(p-1).
b) For the integral ∫[infinity]^e 25/x^(lnx)^p dx to converge, p > 1. Evaluating the integral for those values of p gives
∫[infinity]^e 25/x^(lnx)^p dx = -25/(p-1).
Convergence and divergence. The improper integral is said to converge if the limit is both real and a limited integer.
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PLS HELP!!!!!
Find area and perimeter.
Answer:
I think it has an area of 4 and a perimeter of 8, i'm not totally sure but I thought I'd try to help
Answer:
area:4
perimeter:8ft
Step-by-step explanation:
when doing the area, you have to MULTIPLY the length by the width. For example, length:5ft width:7ft so to find the area you have to multiply both and get the answer of 35. so for the sum you have is 2 × 2 = 4
for perimeter, you have to ADD all the sides so if you have a square with all sides of 4 you add them all up which = 16. so for your sum, add them all up = 8ft
Hope it helps I'm not that good at explaining :)
please help i have until saturday
The distance between the two points from the geometrical formula for that purpose is 6.2.
What is distance between two points in geometry?The distance between two points in geometry is the length of the straight line segment that connects the two points. It is calculated using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Using the formula;
d= √(x2 - x1)^2 + (y2 - y1)^2
d = √(7.5 - 3)^2 + (6.25 - 2)^2
d = √20.25 + 18.06
d = 6.2
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Write a multiplication equation shat shows how the denominators of 3/4 and 1/2 are related. Explain how this equation helps you write 1/2 as an equivalent fraction with a denominator of 4
To find the multiplication equation that shows how the denominators of 3/4 and 1/2 are related, we can simply multiply the two denominators together:
3/4 x 1/2 = 3/8
Therefore, the denominators are related by the equation 4 x 2 = 8.
To write 1/2 as an equivalent fraction with a denominator of 4, we need to multiply both the numerator and denominator by the same factor that will transform the denominator of 2 to a denominator of 4.
Using the multiplication equation we found earlier, we can see that we need to multiply both the numerator and denominator of 1/2 by 2 (since 2 x 2 = 4). This gives us:
1/2 x 2/2 = 2/4
Therefore, 1/2 can be written as an equivalent fraction with a denominator of 4 as 2/4.
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The length of a rectangle is 11 cm more than twice its width. If the area of the rectangle is 6 cm", what
are the dimensions of the rectangle?
The width of the rectangle is
cm.
ation
The length of the rectangle is
cm
The width of the rectangle is 3/2 cm and the length is 17 cm.
The formula for the area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width. To solve this problem, we can rearrange the formula to solve for W: W = A / L. In this case, A = 6 cm and L = 2W + 11 cm. Substituting these values, we get W = 6 / (2W + 11). We can solve this equation by dividing both sides by 2W to get 1/W = 6 / (2W + 11) * 1/2W. Simplifying, we get 1/W = 3 / (11 + 2W). Subtracting 3/11 from both sides, we get -2/11 W = -3/11. Finally, we can solve for W by dividing both sides by -2/11 to get W = 3/2 cm.
Therefore, the width of the rectangle is 3/2 cm, and the length of the rectangle is 2W + 11 = 11 + 6 = 17 cm.
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I need this asap I need to turn it in like an hour 25points
Answer:
c. 36 people
pls mrk me brainliest
Answer:
The answer would indeed be C. 36 people.
3/9 * 6/4 - 1/12 + 13/6 + 2/7
Answer:
241/84
Step-by-step explanation:
The circle graph shows the results of a survey by a bakery on which of their new products 105 customers preferred most. How many customers preferred cake? Round your answer to the nearest whole number.
Answer:
37 customers preferred cake.
Step-by-step explanation:
What is a percentage?A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
To find out how many customers preferred cake, we need to multiply the total number of customers (105) by the percentage of customers who preferred cake (35%):
(35% = 0.35)
105 × 0.35 = 36.75.Rounding this to the nearest whole number gives us 37. Therefore, approximately 37 customers preferred cake.
Answer:
35% of 105 is 36.75. ( Rounded up 37). So 37 customers preferred cake the most
70.61% of 736.97cm
Give your answer rounded to 2 DP.
Answer:
520.37 cm
Step-by-step explanation:
apply equation:
x = 736.97(0.7061) = 520.374517
Notice 70.61% is the same as 0.7061 (just divide by 100)
now you need to round to 2 DP
x ≈ 520.37
so the 70.61% of 736.97cm is 520.37 cm
prove that the altitude to the base of an icosceles triangle is also the following. The median to the base please dont make it to much of a crazy explanation i need to copy and paste it lol.
We οbserve that the line segment AM frοm vertex A tο midpοint M οf base BC alsο bisects BC, since M is the midpοint οf BC. Therefοre, we have AM = BM = MC = BC/2.
What is Isοsceles triangle?An isοsceles triangle is type οf triangle that has the twο sides οf equal length. In isοsceles triangle, angles οppοsite equal sides are alsο equal in measure. The third side οf isοsceles triangle is called base.
Tο prοve this, we can cοnsider the fοllοwing diagram οf an isοsceles triangle ABC with base BC:
A
/ \
/ \
/ \
/ h \
B------------C
where h is the altitude tο the base BC and M is the midpοint οf the base BC. We want tο shοw that the line segment AM is alsο the median tο the base BC.
First, we οbserve that the triangle ABC is isοsceles, sο the twο legs AB and AC are cοngruent. Therefοre, the altitude h frοm vertex A tο base BC bisects BC, which means that BM = MC = BC/2.
Secοnd, we οbserve that the line segment AM frοm vertex A tο midpοint M οf base BC alsο bisects BC, since M is the midpοint οf BC. Therefοre, we have AM = BM = MC = BC/2.
Thus, we have shοwn that the altitude tο the base and the median tο the base οf an isοsceles triangle are the same line segment, which cοmpletes the prοοf.
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Question 6, please help
6/10
Corsica adds 3/32 = 0.09375 ounces of water to the bucket per second.
To find how many ounces of water are added to the bucket per second, we need to rearrange the given equation to solve for the rate of change of the water, which is the change in the amount of water per unit of time.
Starting with:
3W = 32S
We can divide both sides by S:
3W/S = 32
Now we can see that the left-hand side represents the amount of water (in ounces) added per second, since W/S is the rate of change of the water with respect to time.
Therefore, we can conclude that Corsica adds 3/32 = 0.09375 ounces of water to the bucket per second.
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The manager of a store orders mystery games that cost $7.30 and sells them for $15.33. What is the mark-up as a percentage?
In order to find the price increase in percentage terms, we divide the price difference by the cost price.
The difference:
[tex]15.33-7.30=8.03[/tex]Rate:
[tex]\frac{8.03}{7.30}=\frac{x}{100}[/tex]
If we solve for [tex]x[/tex] in this equation, it will give us the price increase as a percentage.
The price increase should be [tex]110[/tex]%.
17. Which graphic organizer correctly groups the following numbers? (1 point) 4.1,-9,3,-2.2
A graphic organizer that correctly groups the following numbers 4.1, -9, 3, -2.2 is; B. graphic organizer B.
What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 6, 4.1, -2.2 12, 1/2, 0.5, √16, -29, etc.
What is an integer?In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).
Based on the given data set 4.1, -9, 3, -2.2, the numbers should be correctly grouped as follows;
Rational number = 4.1 and -2.2.
Integer = -9.
Whole number = 3.
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THE TEMPERATURE IN AUSTRIA ONE MORNING WAS -5 DEGREE CELCIOS AT 8 OCLOCK AND INCREASED BY 2 DEGREE CELCIOS EVERY HOUR UNTIL 12 OCLOCK ,WHAT WILL BE THE TEMPERATURE BE AT HLF PAST 11
Answer: 2° Celsius.
Step-by-step explanation:
The CPI basket price for two consecutive years in five different economies are given. Determine the rate of inflation for each economy. Then
order the tiles from least to greatest inflation rate.
The greatest inflation rate was 1.78% in year1 and year2
When you have a lot of repetitive calculations to do, it is convenient to let a spreadsheet do it. Copying the given data to the spreadsheet ensures we have made no data entry errors.
The inflation rate is calculated as ...
(year 2 price)/(year 1 price) -1 . . . . . expressed as a percentage
[tex]\frac{74.30}{73.00}=1.0178\\\\\frac{76.015}{75}=1.0135\\\\\frac{89.25}{88}=1.0142[/tex]
The attachment shows the results of this calculation as applied to the economies in the order shown. The least-to-greatest order is shown in the right-most column.
The complete question is-
The CPI basket price for two consecutive years in five different economies are given. Determine the rate of inflation for each economy. Then order the tiles from least to the greatest inflation rate.
Year 1 = $73.00
Year 2 = $74.30
Year 1 = $75.00
Year 2 = $76.15
Year 1 = $88.00
Year 2 = $89.25
Year 1 = $72.50
Year 2 = $73.75
Year 1 = $79.00
Year 2 = $80.25
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Jaquira wants to set a ladder against the house to change a light above the garage. The ladder is 18 feet long. If the ladder needs to reach the light, which is 15 feet above the ground, how far away should Jaquira place the base of the ladder from the house? Round to the nearest tenth.
Answer:
≈ 9.9 feet
Step-by-step explanation:
We can use the Pythagorean theorem to solve this problem. Let x be the distance from the house to the base of the ladder. Then:
x^2 + 15^2 = 18^2
Simplifying and solving for x, we get:
x = sqrt(18^2 - 15^2) = 9.9 feet (rounded to the nearest tenth)
Therefore, Jaquira should place the base of the ladder approximately 9.9 feet away from the house.
On Wednesday, Sally's turtle walked from the starting line all the way to point T and then back to point M. How far did her turtle walk altogether on Wednesday?
Sally's turtle walked a total of 30 feet altogether on Wednesday.
To determine the total distance the turtle went, we need to know the distances between the beginning line and points T and M.
According to the diagram, there are 12 feet between the beginning line and point T and 8 feet between the starting line and point M.
The turtle travels a distance of: when it moves from the starting line to point T and then returns to point M.
Distance between the beginning line and point T plus the distances between point T and point M and point M from the starting line equals 12 + 10 + 8 = 30 feet.
So, on Wednesday, Sally's turtle travelled a total of 30 feet.
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The perimeter of a rectangle is 72, and the width is 4 less
han 3 times the length. What is the length?
12
O 10
O 16
O 14
Answer:
Answer: 10
Step-by-step explanation:
Let L be the length of the rectangle, and W be the width.
From the problem, we know that:
The perimeter of the rectangle is 72, which means that:
2(L + W) = 72
L + W = 36
The width is 4 less than 3 times the length:
W = 3L - 4
Substituting W = 3L - 4 into the first equation, we get:
L + 3L - 4 = 36
4L = 40
L = 10
Therefore, the length of the rectangle is 10. Answer: 10