area of triangle is = 1/2 * base * altitude
1- each side is made 8 times
so the net change in area is 64 times
The area of A'B'C' is 64 times the area of ABC
2- each side is made 4 times
so the net change in area is 16 times
The area of D'E'F' is 16 times the area of DEF
3- each side is made 3 times
so the net change in area is 9 times
The area of A'B'C' is 9 times the area of ABC
Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.
A cube-shaped bin has an edge length of 34 yard.
What is the volume of the container?
Answer:
[tex]V=\frac{27}{64}yd^3[/tex]
Step-by-step explanation:
The edge length of the cube shaped bin is [tex]\frac{3}{4}\text{ yards}[/tex]
Hence, [tex]s=\frac{3}{4}\text{ yards}[/tex]
The volume of the cube is given by
[tex]V=s^3[/tex]
Plugging the value of s, we get
[tex]V=(\frac{3}{4})^3[/tex]
This can be further simplified as
[tex]V=\frac{3\times3\times3}{4\times4\times4}\\\\V=\frac{27}{64}[/tex]
Hence, the volume of the container is 27/64 cubic yards.
A campground consists of 5 square campsites arranged in a line along a beach. The distance from the edge of a campsite to the water at the end of the beach is 4 yd. The area of the campground, including the beach, is 950 sq yd. What is the width of one campsite?
A. 14.35 yd
B. 13.93 yd
C. 11.93 yd
To find the width of one campsite, we subtract the area of the beach from the total area and divide by 5 (the number of campsites). We set up a quadratic equation and solve for the width, finding that it is approximately 13.93 yd.
Explanation:The student's question is about finding the width of one campsite in a linear arrangement of five campsites along a beach. Given that the area of the campground, including the beach, is 950 sq yd and the distance from the edge of a campsite to the water is 4 yd, we can set up an equation to find the total width of the five campsites. The total width of the campsites will be the total area minus the area of the beach, divided by the length of the campsites (which is 5 times the width of one campsite).
Let's call the width of one campsite 'w'. The area of the beach is 5w * 4 yd, since it extends the entire length of the campsites and is 4 yd wide. Therefore, the area of just the campsites is 950 sq yd - 5w * 4 yd. Since we have five campsites, all of equal width, the total width of the campsites is 5w. So we can set up the following equation:
950 - 5w * 4 = 5w2
Now solve for w:
950 - 20w = 5w25w2 + 20w - 950 = 0Using the quadratic formula, we find that w is approximately 13.93 yd, so the correct answer is B. 13.93 ydB. 13.93 yd. The approximate width of one campsite is 13.81 yards.
Explanation:To find the width of one campsite, we need to divide the area of the campground by the number of campsites. The given area of the campground is 950 sq yd, and there are 5 campsites. So, the area of one campsite is 950 sq yd / 5 = 190 sq yd. Since the campsite is square, the width and length are equal. Let's assume the width of one campsite is 'x' yards. Then the equation becomes x^2 = 190. By taking the square root of both sides, we get x = √190 ≈ 13.81 yards. Therefore, the approximate width of one campsite is 13.81 yards.
The westside bakery uses 440 pounds of flour to make 1,000 loaves of bread.Each loaf contains the same amount of flour.How many pounds of flour are used in each loaf of bread
Final answer:
Each loaf of bread from the Westside bakery contains 0.44 pounds of flour.
Explanation:
To determine the amount of flour used in each loaf of bread, we need to divide the total amount of flour used by the number of loaves produced. In this case, the bakery uses 440 pounds of flour to make 1,000 loaves of bread. So, to find out the amount of flour used in each loaf, we divide 440 by 1,000.
440 ÷ 1,000 = 0.44 pounds of flour
Therefore, each loaf of bread contains 0.44 pounds of flour.
30 for 48.30 or 32 for 49.60
Alexander found the means-to-MAD ratio of two data sets to be 3.4
What can he conclude about the distributions?
A.
They are similar.
B.
They are somewhat similar.
C.
They are different.
D.
They are identical.
Answer: the answer is c
Step-by-step explanation:
How to solve a linear equation
Step-by-step explanation:
Let's use this equation as an example - [tex]102=-7r+4[/tex]
The whole point of a linear equation is to find what the variable (which in our case is r ) equals to.
Our equation: [tex]102=-7r+4[/tex]
First step is to try to get r alone on one side.
First step: [tex]102-4=-7r[/tex] we wouldn't do [tex]102+4=-7r[/tex] (notice it's negative and not positive) since we're switching the positive 4 to the other side we'd switch the positive to a negative, making it [tex]102-4[/tex].
Know that everytime we switch a number or variable to the other side we must always switch the sign to the opposite of what it is. If it's dividing, we multiply, if we subtract, we add, etc. Same with the other way around.
Second step is to solve both sides of the equation.
Second step: [tex]98=-7r[/tex]
Third step is to divide the both sides by the number with the variable, making it 98 divided by -7r and -7r divided by -7
Third Step: [tex]\frac{98}{-7} =\frac{-7r}{-7}[/tex] = [tex]-14=r[/tex]
Now we've found our variable.
Answer: [tex]-14=r[/tex]
Conplete the square to solve the quadratic equation. x
[tex]1 {x}^{2} - 6x + 12 = 2x + 20[/tex]
Answer:
[tex]\large\boxed{x=4\pm2\sqrt6}[/tex]
Step-by-step explanation:
[tex]x^2-6x+12=2x+20\qquad\text{subtract}\ 2x\ \text{and}\ 12\ \text{from both sides}\\\\x^2-8x=8\\\\x^2-2(x)(4)=8\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\x^2-2(x)(4)+4^2=8+4^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-4)^2=24\iff x-4=\pm\sqrt{24}\\\\x-4=\pm\sqrt{4\cdot6}\\\\x-4=\pm\sqrt4\cdot\sqrt6\\\\x-4=\pm2\sqrt6\qquad\text{add 4 to both sides}\\\\x=4\pm2\sqrt6[/tex]
Final answer:
The quadratic equation x² - 6x + 12 = 2x + 20 is solved by completing the square, resulting in the solution x = 4 ± √24.
Explanation:
To solve the quadratic equation x² - 6x + 12 = 2x + 20 by completing the square, we first need to rearrange the equation to get 0 on one side. We do this by subtracting 2x and 20 from both sides, which gives us:
x² - 8x - 8 = 0
Next, we find the value to complete the square for the x terms. We take half of the coefficient of x, which is 8/2 = 4, and then square it, getting 4² = 16. We add 16 to both sides of the equation to form a perfect square on the left:
x² - 8x + 16 = 8 + 16
This simplifies to:
(x - 4)² = 24
To find the value of x, we take the square root of both sides:
x - 4 = ±√24
Finally, we solve for x:
x = 4 ± √24
Which property justifies the fact that 5(x-2) is equivalent to 5x-10
What fraction of a batch of trail mix consists of peanuts
The fraction of a batch of trail mix consisting of peanuts is 43/6.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Number of cups for peanuts = 2(2/3)
Total number of cups in the trial mix.
= 2(2/3) + 3/4 + 2(1/2) + 1(1/4)
= 8/3 + 3/4 + 5/2 + 5/4
= (32 + 9 + 30 + 15)/12
= 86/12
= 43/6
= 7(1/6)
Thus,
The fraction of peanuts is 43/6.
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The volume of the crate is 72 cubic feet but the length is 3ft the base is 6ft and the height is unknown
Demostrar que si las magnitudes de la suma y la diferencia de dos vectores son iguales, entonces los vectores son perpendiculares.
A baseball team played 147 regular season games. The ratio of the number of games they won to the number of games they lost was four thirds 4/3. How many games did they win? How many games did they lose?
Final answer:
To find the number of games won and lost by the baseball team, use the given win to loss ratio of 4/3 and the total number of games played (147) to establish a system of equations and solve for the number of wins and losses. The team won 84 games and lost 63 games.
Explanation:
The student has asked how many games a baseball team won and lost given that they played 147 regular season games with a win to loss ratio of 4/3. To solve this, let w represent the number of games won and l represent the number of games lost. According to the ratio, we have w/l = 4/3. Because the total number of games is 147, we can express this as w + l = 147.
First, express the number of losses in terms of wins using the ratio: l = 3w/4.
Next, substitute l in the total games equation: w + 3w/4 = 147.
Solving for w gives w = 84 (number of games won).
To find l, substitute w back into l = 3w/4 to get l = 63 (number of games lost).
The baseball team won 84 games and lost 63 games.
Help with 8!!!!! Plz
What is the most specific name for the quadrilateral on number #28?
At a school, 40% of sixth grade students said that hip-hop is their favorite kind of music. If 100 sixth grade students prefer hip-hop music, how many sixth grade students are at school
Determine the better buy. 12 oz for $2.69 or 16 oz for $2.49?
A merchant buys a television for $125 and sells it for a retail price of $200. What is the markup
The markup is 60%.
Given that,
A merchant buys a television for $125 and sells it for a retail price of $200.
Based on the above information, the calculation is as follows:
[tex]= (\$200 - \$125)\div \$125[/tex]
= 60%
Therefore we can conclude that The markup is 60%.
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A city has a population of 260,000 people. Suppose that each year the population grows by 5.5% . What will the population be after 8 years?
Write the missing numbers to complete the pattern: 3, 6, 12 and so on
Which statements about the opposite of −12 are true?
Select each correct answer.
A. −12 and its opposite are on located on the same side of zero on a number line
B. The opposite of −12 is -1/12
C.−12and its opposite are located the same distance from zero on a number line.
D.The opposite of the opposite of −12 is −12
The regular price of a Space Invader game is $52, but it’s on sale. The discount is $13. What percent discount is the Space Invader game?
Which of the following are factors of 6x^2+30x-36?
A) x-1
B)x+2
C)2
D)3
E)x+6
F)x-6
G)x-2
Ray has $36 to buy masonry nails and finishing nails for his project. Masonry nails sell for $5.50 per box, and finishing nails cost $3.50 per box. Only full boxes are available for purchase. If Ray buys 3 boxes of masonry nails, what is the maximum number of boxes of finishing boxes he can buy?
Answer:
5 boxes
Step-by-step explanation:
Given that;
The total amount Ray has with him to buy masonary nails and finishing nails for his project is $36
If Masonry nails sell for $5.50 per box
Finishing nails cost $3.50 per box.
Now, Only full boxes are available for purchase.
If Ray buys 3 boxes of masonry nails
i.e 3 × $5.50 = $16.5
what is the maximum number of boxes of finishing boxes he can buy?
To determine the number of finishing nails boxes he can buy. we will subtract the expense spent on the prior 3 masonary nails from his total amount
i.e $36 - $16.5
= $19.5
Let's not forget that, only full boxes are available for purchase and not half or quarter.
SO since 1 finishing nail box cost $3.50
then let x finishing nail box cost $19.5
∴ (x) × $3.50 =1 × $19.5
(x) = [tex]\frac{1*19.5}{3.50}[/tex]
(x) = 5.57 boxes
Since full boxes are available for purchase then (x) ≅ 5 boxes, then Ray will be left with $2 at his pocket.
Therefore, the maximum number of boxes of finishing boxes he can buy is 5 boxes
If n is divided by 7 the remainder is 3. What is the remainder if 3n is divided by 7?
Final answer:
If an integer n, when divided by 7, leaves a remainder of 3, then multiplying n by 3 and dividing by 7 will leave a remainder of 2.
Explanation:
Let's solve the problem where n when divided by 7 leaves a remainder of 3 and find the remainder when 3n is divided by 7. According to the information, if n divided by 7 leaves a remainder of 3, we can express n as 7k + 3 for some integer k.
To find the remainder when 3n is divided by 7, substitute 7k + 3 for n: 3n = 3(7k + 3) = 21k + 9. We can further simplify this to 21k + 7 + 2, or 7(3k + 1) + 2. Here, it's evident that when 21k + 9 (or similarly 7(3k+1)+2) is divided by 7, it leaves a remainder of 2.
What is the value of the expression |48÷(-6)|+|-35÷7|
The table shows the profit from a school book fair based on the number of books sold. What is the rate of change for the function represented in the table?
$0.50
$0.67
$1.07
$1.50
Book sold Profit f(x)
(X)
100 ║ $50.00
250 ║ $275.00
300 ║ $350.00
350 ║ $425.00
answer is A-$0.50
You are given a table
[tex]\begin{array}{cc}\text{Number of books sold} & \text{Profit}\\100 & \$50\\250 & \$275\\300 & \$350\\350 & \$450\end{array}[/tex]
The rate of change for the function represented in the table can be calculated using the formula
[tex]\dfrac{y_{i+1}-y_i}{x_{i+1}-x_i},[/tex]
where i=1,2,3.
1. When i=1,
[tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{275-50}{250-100}=\dfrac{225}{150}=1.5[/tex]
2. When i=2,
[tex]\dfrac{y_3-y_2}{x_3-x_2}=\dfrac{350-275}{300-250}=\dfrac{75}{50}=1.5[/tex]
3. When i=3,
[tex]\dfrac{y_4-y_3}{x_4-x_3}=\dfrac{425-350}{350-300}=\dfrac{75}{50}=1.5[/tex]
Then the rate of change is $1.5
Answer: correct choice is D.
The rate of change for the function is [tex]\$ 1.5[/tex]
The rate of change for the function is calculate by the formula
[tex]\frac{y_{n+1}-y_n}{x_{n+1}-x_n}[/tex]
Where [tex]n=1,2,3[/tex].
A) when [tex]n=1[/tex]
[tex]\frac{y_{1+1}-y_1}{x_{1+1}-x_1}=\frac{y_{2}-y_2}{x_{2}-x_2}[/tex]
[tex]\dfrac{275-50}{250-100}=\dfrac{225}{100}[/tex]
Hence Rate of change when [tex]n=1[/tex] is [tex]1.5[/tex]
B)when [tex]n=2[/tex]
[tex]\frac{y_{2+1}-y_2}{x_{2+1}-x_2}=\frac{y_{3}-y_2}{x_{3}-x_2}[/tex]
[tex]\dfrac{350-275}{300-250}=\dfrac{75}{50}[/tex]
Hence Rate of change when [tex]n=2[/tex] is [tex]1.5[/tex]
C) when [tex]n=3[/tex]
[tex]\frac{y_{3+1}-y_3}{x_{3+1}-x_3}=\frac{y_{4}-y_3}{x_{4}-x_3}[/tex]
[tex]\dfrac{425-350}{350-300}=\dfrac{75}{50}[/tex]
Hence Rate of change when [tex]n=3[/tex] is [tex]1.5[/tex]
So the rate of change for function represented in the table is same for different value of [tex]n[/tex] i.e, [tex]\$ 1.5[/tex].
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Jennifer bought a thousand inch roll of ribbon for $21.00. If she cuts the ribbon into 75 equal hair ribbons, how much did she spend per ribbon?
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In a random sample of 160 high school students, 64% of the students participated in summer camp activities. The estimate had a margin of error of 2.5% at a 95% confidence level. Which of the following is a potential percentage of high school students who participated in summer camp activities.
A. 60%
B. 68%
C. 62%
D. 67%
What is the upper quartile of the data represented in the following box-and-whisker plot?
8
12
16
20
Answer:
Step-by-step explanation:
12
write a expression showing the sum of 8 and a number f