Answer:
He paid $6,000 in taxes.
Step-by-step explanation:
His final amount after taxes is $24000. In order to obtain this number we had to tax 20% of the total (Note that 100%-20%=80%). In other words if he was taxed 20% he took home 80% of what he was paid. Therefore mathematically we have:
[tex]0.8A_{pre-tax}=A_{taxed}[/tex]
Since we know he was left with $24000 after taxes then:
[tex]0.8A_{pre-tax}=24000\\\\\frac{0.8A_{pre-tax}}{0.8}=\frac{24000}{0.8}\\\\A_{pre-tax}=\frac{24000}{0.8}\\\\A_{pre-tax}=30000[/tex]
So originally he had $30,000. So how much did he pay in taxes? We can calculate the difference of both pretax and after tax and we get:
$30,000 - $24,000= $6,000 taxed
6 tons 294 lb ÷ 3071
6 tons 294 lb ÷ 3071 is approximately equal to 3.97138
To solve 6 tons 294 lb ÷ 3071, we need to first convert everything to the same unit.
Convert tons to pounds:
1 ton = 2000 pounds
6 tons = 6 * 2000 pounds = 12000 pounds
Combine the weight in pounds:
Total weight = 12000 pounds (6 tons) + 294 pounds
Total weight = 12294 pounds
Divide by 3071:
12294 pounds / 3071 = 3.97138
Therefore, 6 tons 294 lb ÷ 3071 is approximately equal to 3.97138
The expression 1.5t + 20 predicts the height in centimeters of a plant tt days from today. What is the predicted height of the plant 5 days from today?
Answer:
27.5 centimeters.
Step-by-step explanation:
We have been given an expression [tex]1.5t+20[/tex] that predicts the height in centimeters of a plant t days from today.
To find predicted height of the plant 5 days from today we will substitute t=5 in our given expression.
[tex]1.5\times 5+20[/tex]
[tex]7.5+20[/tex]
[tex]27.5[/tex]
Therefore, the predicted height of the plant 5 days from today will be 27.5 centimeters.
To find the predicted height of the plant 5 days from today, substitute 5 for t in the expression 1.5t + 20. Calculating this gives a result of 27.5, so the plant is predicted to be 27.5 centimeters tall after 5 days.
Explanation:
This question involves substitution into a mathematical expression. The expression given in the problem is 1.5t + 20, which predicts the height of a plant t days from now. Here, t represents time in days, and the number you plug in for t is the number of days from today.
To find the height of the plant 5 days from today, you substitute 5 for t in the expression. So the calculation becomes:
1.5 * 5 + 20 = 27.5
Therefore, 5 days from today, the plant is predicted to be 27.5 centimeters tall.
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After recording the pizza delivery times from 2 different shops you concluded that one pizza shop has a mean of 46 minutes with a standard deviation of 3 minutes, The other shop has a mean of 45 minutes with a standard deviation of 19 minutes. Interpret these figures. Which shop would you order fro and why?
Hi There!
Step-by-step explanation:
Standard Deviation - tells you the avearage of how far apart each number in the set values is away from the mean.
Shop 1:
Mean = 46
Standard Deviation = 3
Shop 2:
Mean = 45
Standard Deviation = 19
I would choose shop 1 because even though it has a 1 more minutre of the mean it has a less of a standard deviation. That means that Shop 2 has a set of values that are far apart than shop 1.
Answer:
Shop 1
Hope This Helps :)
in a survey, 16% of the people said they live in a city. if 320 people said they live in a city, how many people were surveyed? show your work. ( question 12 )
Answer: choice B) 2,000 people
=================================
Let x be the number of people surveyed. This is simply a placeholder for the number.
16% of x is going to be equal to 320, so we know that 0.16*x = 320. Recall that 16% converts to the decimal form 0.16 after moving the decimal point two spots to the left.
Divide both sides by 0.16 to isolate x fully
0.16*x = 320
0.16*x/0.16 = 320/0.16
x = 2000
Therefore, 2000 people were surveyed
Answer:
2000 people were surveyed
Step-by-step explanation:
This means that 16 percent of the people surveyed = 320 people surveyed. We need to find the total amount of people, right?
Percentages are always out of 100. And let's say that x is the total amount of people surveyed.
16/100 = 320/x. This is the equation we need to solve.
To solve this, we need to find the denominator of 320/x.
The simplest way to do this is to realize that you can multiply 20 by 16 to get to 320.
Since you multiplied 16 by 20, you also need to multiply 16/100's denominator by 20. 100 times 20 equals 2000.
This means that the answer is 2000 people. There were 2000 people surveyed
Plz tell me the error and what the correct answer is and explain
Answer:
3
Step-by-step explanation:
x÷4 is the expression
Evaluate when x=12
12÷4
12/4
3
He subtracted instead of dividing.
12-4 = 8 12/4 =3
X-3y=3 -x+2y=-3 linear equations by elimination
[tex]\underline{+\left\{\begin{array}{ccc}x-3y=3\\-x+2y=-3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-y=0\to\boxed{y=0}\\\\\text{Put the value of y to the first equation}:\\\\x-3(0)=3\to\boxed{x=3}\\\\Answer:\ \boxed{x=3\ and\ y=0\to(3,\ 0)}[/tex]
If the measure of ab is 134 what is the measure of abc , the tangent-chord angle
The answer is 67 for apex!
Answer:
The measure of ∠ABC is 67°.
Step-by-step explanation:
Consider the provided figure:
Tangent chord angle = [tex]\frac{1}{2}[/tex] intercepted arc
Now consider the provided figure;
Substitute the value of intercepted arc = 134° in the above formula.
Tangent chord angle = [tex]\frac{1}{2}\times134[/tex]
Tangent chord angle = [tex]67[/tex]
Hence, the measure of ∠ABC is 67°.
Classify the sequence (an) =(1,16,31,46,...) as arithmetic, geometric, or neither. If there is not enough information to classify the sequence, choose not enough information.
Answer:
arithmetic
Step-by-step explanation:
It is arithmetic because the terms go up by 15 . That is the common difference is 15.
Answer:
it is an arithmetic sequence
Step-by-step explanation:
general formula of arithmetic progression is
an=a1+(n-1)d
we are given
a1=1
a2=16
we can find d
d=a2-a1=16-1=15
d=a3-a2=31-16=15
d=a4-a3=46-31=15
as we can see that there is a common difference d =15 between successive terms of the this sequence
hence it is a arithmetic sequence
When the quadratic expression is written in standard form, a=1, b=-3 and c=2
The standard form of quadratic equation for given points is x² - 3 x + 2 =0.
What is standard form of quadratic equation?The standard form of quadratic equation is given by ax² + bx + c = 0.
where a , b , c are the constant .
Given,
The value of a, b, c as 1 , -3, 2 respectively.
Putting the value a, b, c in the standard form
we get x² - 3 x + 2 =0.
So, The standard form of quadratic equation for given points is x² - 3 x + 2 =0.
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how to answer this questions
The internal dimension of a cylindrical container has a base area of 20 cm2 and a height of 10 cm. What is the internal volume of the container?
Answer:
As per the statement:
The internal dimension of a cylindrical container has a base area of 20 cm2 and a height of 10 cm.
Volume(V) of a cylinder is given by:
[tex]V =A \cdot h[/tex]
where
A is the area of the base cylinder and
h is the height of the cylinder
Substitute the value A = 20 cm square and h = 10 cm we have;
[tex]V=20 \cdot 10[/tex]
Simplify:
V = 200 cubic cm
Therefore, the internal volume of the container is 200 cubic cm
Answer:
200 cm³
Step-by-step explanation:
In question we have given the area and height of the internal dimension of a cylindrical container.We have to find volume of the container.
From question statement ,we observe that
Area=20 cm² and Height=10 cm
The formula to find volume is :
Volume= Area×Height
putting the values of area and height in above formula,we get
Volume= 20 cm²×10 cm
Volume= 200 cm³
Hence, The internal volume of the container is 200 cm³.
Need help ASAP. MUST be correct. 10 points. Thanks
ΔABC and ΔDBE are similar. Therefore the side are in proportion:
[tex]\dfrac{DE}{DB}=\dfrac{AC}{AB}[/tex]
DE = 3x - 5
DB = a
AC = 20
AB = a + a = 2a
Substitute:
[tex]\dfrac{3x-5}{a}=\dfrac{20}{2a}[/tex] cross multiply
[tex]2a(3x-5)=20a[/tex] divide both sides by 2a ≠ 0
[tex]3x-5=10[/tex] add 5 to both sides
[tex]3x=25[/tex] divide both sides by 3
[tex]x=\dfrac{25}{3}[/tex]
[tex]\boxed{x=8.\overline{3}}[/tex]
Round decimal to the nearest one . Then add 7.91+21.9=
Answer: 29
Step-by-step explanation:
forst you have to round the decimals. 7.91 to 8 and 21.9 to 21. then you add
8+21=29
PLZ MARK AS BRAINIEST I REALLY NEED IT
Mt. Mickey is 14,831 feet tall, whereas Mr. Minnie is 18,940 feet tall. How much taller is Mt. Minnie than Mt. Mickey?
Answer: 4109 feet.
Step-by-step explanation:
You must subtract the height of Mt. Mickey from Mt. Minnie.
18940 - 14831 = 4109
Answer:
4109 is the difference in height.
Step-by-step explanation:
Mount Minnie = 18940Mount Mickey = 14831 SubtractDifference = 4109help me with this problem plzzzz
Answer:
7= 137
6= 43
8=43
Step-by-step explanation:
well 7 would be the same angle as 137
and 6 and 8 are the same angle
so u already know that
7= 137
now to find 6 0r 8 u just need to subtract 137 from 180 to get
6= 43
8= 43
Answer:
see explanation
Step-by-step explanation:
∠7 = 137° ( vertically opposite angle )
∠8 = 180° - ∠7 = 180° - 137° = 43° ( straight angle )
∠6 = ∠8 = 43° ( vertically opposite angles )
Dylan opened a credit card account with $650.00 of available credit. Now that he has made some purchases, Dylan’s account only has $455.00 of available credit. What is the percentage decrease of the amount of available credit in Dylan’s account?
Answer:
32.5%
Step-by-step explanation:
The percentage decrease of available credit in Dylan's account is 30%. This was found by subtracting the new available credit from the original, dividing the difference by the original available credit, and multiplying by 100.
To calculate the percentage decrease of the available credit in Dylan's account, we need to first determine the amount of credit that has been used. The original available credit was $650.00, and it has decreased to $455.00 after some purchases. The difference between the two amounts is $650.00 - $455.00 = $195.00. This value represents the decrease in available credit.
Next, we calculate the percentage decrease by dividing the decrease by the original amount and multiplying by 100. So, the percentage decrease = ($195.00 / $650.00) × 100 = 30%.
Jeff makes 16 quarts of lemonade he then divides the lemonade equally among 5 jigs how many quarts of lemonade are in each jug?
Graph the function rule. Tell whether the the graph is continuous or discrete. The height h, in inches, of the juice in a 20-oz bottle depends on the amount of juice j, in ounces, that you drink. This situation is represented by the function rule h=6-0.3j.
Answer:
The graph of our given function will be continuous.
Step-by-step explanation:
Please find the attached graph of our given function.
Let h represent the height in inches and j represent the amount of juice in ounces.
We have been given that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j in independent variable and h is dependent variable.
The function [tex]h=6-0.3j[/tex] represents the height of juice after drinking j ounces of juice.
As we drink the juice, the height of the juice in bottle will change continuously. The graph of our given function will be continuous as we can drink fractions of an ounce juice.
Since the equation of line in slope-intercept form is [tex]y=mx+b[/tex], where,
m = Slope of line,
b= y-intercept or initial value.
Upon comparing our given function with slope-intercept form of equation we can see that slope of our given function is -0.3 and y-intercept is 6. Negative slope indicates that height of juice in bottle is decreasing after drinking j ounces of juice.
In order to graph our line we need to find x-intercept, which will be at height equals 0 inches.
Upon substituting h = 0 in our given function we will get,
[tex]0=6-0.3j[/tex]
[tex]0+0.3j=6-0.3j+0.3j[/tex]
[tex]0.3j=6[/tex]
[tex]\frac{0.3j}{0.3}=\frac{6}{0.3}[/tex]
[tex]j=20[/tex]
So let us draw a line from points (0,8) to (20,0).
Therefore, the line connecting to these points will be the line representing our given function.
The graph of the given function is a line with a slope of -0.3 and a y-intercept of 6, passing through the points (0, 6) and (20, 0), indicating a continuous decrease in juice height as consumption increases.
We have a function h(j) that represents the height of juice in a 20-oz bottle based on the amount of juice consumed j. The function is given by:
h(j) = -0.3j + 6
Here, j is the independent variable (amount of juice) and h is the dependent variable (height of juice). To analyze the continuity of the graph, we compare the function to the slope-intercept form of the equation y = mx + b, where m is the slope and b is the y-intercept.
Comparing the function to the slope-intercept form:
y = -0.3x + 6
We find that the slope m is -0.3, and the y-intercept b is 6. The negative slope indicates a decrease in juice height as more juice is consumed.
To graph the function, we find the x-intercept by setting h (height) to 0:
0 = -0.3j + 6
Solving for j:
0.3j = 6
j = 20
So, the x-intercept is at j = 20, meaning that when 20 ounces of juice are consumed, the height of juice becomes 0.
Now, we can plot the points (0, 6) and (20, 0) on the graph and draw a line through these points. The line represents the function h(j) = -0.3j + 6. The negative slope indicates a continuous decrease in the height of juice as more ounces are consumed.
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I need help to do this is hard I promise if you answer I will follow you oh and show me the steps plis
Answer:
a. The pattern is that they are getting multiplied by 2 each time.
b. The pattern is they all add to 999.
c. Yes, it is justified because it still equal 999.
Nate has an account that pays 2.76% simple interest per year and wants to accumulate $3,090 in interest from it over the next 15 years. How much money should Nate invest in this account to meet this goal?
a.
$1,279.26
b.
$4,369.26
c.
$4,373.77
d.
$7,463.77
Answer: d. $7,463.77
Step-by-step explanation:
The formula to calculate the simple interest is given by :-
[tex]I=Prt[/tex], where P is the principal amount , r is the rate of interest ( in decimal) and t is time ( in years). (1)
Given : Nate has an account that pays 2.76% simple interest per year and wants to accumulate $3,090 in interest from it over the next 15 years.
i.e. I= $3,090 ; r= 2.76% =0.0276 and t= 15 years
Then, from (1), we have
[tex]3090=P\times0.0276\times15\\\\\Rightarrow\ P=\dfrac{3090}{0.0276\times15}=7463.76811594\approx7463.77[/tex]
Hence, the amount of money Nate should invest in this account to meet this goal = $7,463.77
Simplify 5.4x−1.1−3(x−1.1)
Answer:
2.4x +2.2
Step-by-step explanation:
5.4x−1.1−3(x−1.1)
The first step is to distribute the -3
5.4x−1.1−3(x) -3(−1.1)
5.4x -1.1 -3x +3.3
Now we need to combine like terms
5.4x-3x -1.1+3.3
2.4x +2.2
Answer:
2.4x + 2.2
Step-by-step explanation:
1. Distribute -3 through the parenthesis
2. Combined the like terms
A cell phone provider offers a plan that costs $40 per month plus $0.20 per text message sent or received. A comparable plan costs $60 per month but offers unlimited text messaging. Complete parts a. and b. below.
b. If you send or receive an average of 200 text messages each month, which plan would you choose? Why?
Answer:
x = number of text messages sent
0.2x+40=50
0.2x = 10
5(0.2x) = 5(10)
x = 50
Therefore, 50 text messages would have to be sent or received in order for the plans to cost the same each month.
Step-by-step explanation:
The amount of paint that David needs to cover a cube is directly proportional to the surface area. If David can completely cover a cube of side length 2 feet with exactly 16 quarts of paint, how big a cube (in terms of edge length in feet) can David cover with 169 quarts of paint?
Final answer:
To find the size of a cube that David can cover with 169 quarts of paint, set up a proportion and solve for the edge length, David can cover a cube with an edge length of approximately 5.31 feet using 169 quarts of paint.
Explanation:
To find the size of a cube that David can cover with 169 quarts of paint, we need to use the direct proportion between the amount of paint and the surface area of the cube. Let x be the edge length of the cube. The surface area of a cube is given by[tex]6x^2[/tex]can set up the proportion:
[tex]16 quarts / 2 feet^2 = 169 quarts / (6x^2)[/tex]
Cross-multiplying and then solving for x, we get:
[tex]x^2 = (2^2 * 169) / 16[/tex]
[tex]x^2 = 28.1875[/tex]
x = sqrt(28.1875)
x ≈ 5.31 feet
Therefore, David can cover a cube with an edge length of approximately 5.31 feet using 169 quarts of paint.
Last week Jonah spend
6 1/2 hours on homework Jan spent 3/4 as many hours on homework as Jonah. How many hours did they both spend on homework in all ?
Answer:
They spent 7 1/4 hours on homework
Step-by-step explanation:
you can take out 2/4 from 3/4 and make it into 1/2 and 1/2 + 1/2 = 1
1 + 6 = 7
the only fraction left is 1/4 so,
Jonah and Jan spent a total of 7 1/4 hours on homework.
or
you can make 1/2 into 2/4 and add 3/4 and 2/4 together which gives you the same answer:
7 1/4 hours on homework
make brainliest pls
Final answer:
Jonah and Jan spent a total of 16 1/4 hours on homework.
Explanation:
To find the total number of hours Jonah and Jan spent on homework, we need to first calculate Jan's homework hours. Jan spent 3/4 as many hours on homework as Jonah, which means Jan spent (3/4) x (6 1/2) = 3/2 x 13/2 = 39/4 = 9 3/4 hours on homework.
To find the total hours they both spent on homework, we add Jonah's and Jan's hours together: 6 1/2 + 9 3/4 = 13/2 + 39/4 = (26 + 39)/4 = 65/4 = 16 1/4 hours.
Therefore, Jonah and Jan spent a total of 16 1/4 hours on homework.
if he bought 215 lbs of cement and his son brought another 137 lbs how much cement did he have orinally if he now has 450.
Answer: 98
450-215-137=98
Step-by-step explanation:
The perimeter of a rectangular campsite is 64 cm and its area is 207 cm. Find the length and the breadth of the rectangle.
Answer: w = 9 cm, L = 23 cm
Step-by-step explanation:
P (Perimeter) = 2L(length) + 2w(width)
A (Area) = L (length) x w (width)
Use the formulas above to create a system of equations, then solve using the substitution method.
P = 2L + 2w
64 = 2L + 2w
32 = L + w
32 - w = L ←←← use this to substitute for L in the Area equation
A = L · w
207 = (32 - w)w
207 = 32w - w²
w² - 32w + 207 = 0
(w - 23)(w - 9) = 0
w - 23 = 0 w - 9 = 0
w₁ = 23 w₂ = 9
Now, solve for L:
L₁ = 32 - w₁ L₂ = 32 - w₂
= 32 - 23 = 32 - 9
= 9 = 23
We have 2 sets of solutions (w₁ , L₁) and (w₂ , L₂)
(23, 9) and (9, 23)
Notice that they are the same values but in reverse order. These are the dimensions of the rectangle. We generally consider width (w) to have the smaller value. So, w = 9 and L = 23
what is the value of x and y
X is equal to 15 and y is equal to 17
So the answer to this is A .x=15, y=17
Ellen is playing a video game in which she captures butterflies.there are 3 butterflies on screen, but the number of butterflies doubles every minute.after 4 minutes, she was able to capture 7 of the butterflies.
part A. Write an expression for the number of butterflies after 4 minutes. Use a power of 2 in your answer. part B. Write an expression for the number of butterflies remaining after Ellen captured the 7 butterflies. Simplify the expression.
Answer.... 32
when a number doubles, it is simply a higher power of 2
so there are 3 butterflies in the beginning, which can also be written as 3 * (2^0) where the 0 is the initial power, since anything to the 0 power is 1 (except for 0)
so the expression would be 3 * (2^n)
after 4 minutes, it would be 3 * (2^4) or 3 * 16 or 48
to find out how many are remaining, we know that she captured 7 of them, so it would be 3 * (2^4) - 7
for question 2, Jeff texts 4 classmates, and then they each text 4 classmates, so that would be 4^2 or 16, but since 2 people do it, it would be
32
i saw this on yahoo hope it helps
The number of butterflies after 4 minutes is represented by the expression 3 * 2^4. The number of butterflies remaining after Ellen captures 7 can be expressed as 3 * 2^4 – 7.
Explanation:Part A. We start with 3 butterflies and the number doubles every minute for 4 minutes. Therefore, the number of butterflies after 4 minutes is represented by the expression 3 * 2^4. In this expression, 2 is the base that is raised to the power of 4, representing the four times the initial number of butterflies doubles.
Part B. Ellen was able to capture 7 of the butterflies after 4 minutes. To find out the number of butterflies remaining, we subtract the number of butterflies captured by Ellen from the total number of butterflies after 4 minutes. This can be expressed as 3 * 2^4 - 7. Simplifying this expression will give us the number of butterflies remaining after Ellen's capture.
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−4(m+3)=24 What is M? Please answer.
Answer:
m = -9
Step-by-step explanation:
-4(m+3)=24
You must distribute first.
-4m - 12 = 24
+12 +12
-4m = 36
--- = ---
-4 -4
m = -9
Find the value of x in each of the following proportions. a. 6 : 9 = x : 72 b. 8⁄3 = 40⁄x c. x : 55 = 3 : 5 d. 33⁄x = 11⁄5 A recipe calls for 5 cups of flour for every 6 teaspoons of salt. If you wanted to make a larger batch of the same recipe with 15 cups of flour, how much salt would you need? A 20-foot flagpole casts a 6-foot shadow. How tall is a nearby building that casts a 30-foot shadow (assume the shadows are measured at the same time of the day and both the flagpole and the building face the sun at approximately the same angle)? For every 15 columns of news stories in a newspaper, 4 columns of ads are required. If a newspaper contains 300 columns of news stories, how many columns of ads must it have? A certain color paint should have a mix of blue and green in a ratio of 5 : 2. If a house painter needs to use 8 gallons of green paint, how many gallons of blue paint should he mix with it in order to obtain the right color?
QUESTION 1a
We want to find the value of [tex]x[/tex] in the proportion,
[tex]6:9=x:72[/tex]
We rewrite the ratio on each side of the equation as fractions to obtain,
[tex]\frac{6}{9}=\frac{x}{72}[/tex]
We now multiply both sides of the equation by [tex]72[/tex] to get,
[tex]\frac{6}{9}\times 72=\frac{x}{72}\times 72[/tex]
This simplifies to
[tex]\frac{6}{1}\times 8=\frac{x}{1}\times 1[/tex]
[tex]\therefore 48=x[/tex]
[tex]x=48[/tex]
QUESTION 1b
The given proportion is,
[tex]\frac{8}{3}=\frac{40}{x}[/tex]
We cross multiply to obtain,
[tex]8x=3\times 40[/tex]
We divide both sides by 8 to get,
[tex]x=\frac{3\times 40}{8}[/tex]
[tex]\Rightarrow x=\frac{3\times 40}{8}[/tex]
[tex]\Rightarrow x=\frac{3\times 5}{1}[/tex]
[tex]\therefore x=15[/tex]
QUESTION 1c
The given proportion is
[tex]\frac{x}{55}=\frac{3}{5}[/tex]
We multiply both sides by 55 to get,
[tex]\frac{x}{55}\times 55=\frac{3}{5}\times 55[/tex]
This simplifies to
[tex]x=\frac{3}{1}\times 11[/tex]
[tex]\therefore x=33[/tex]
QUESTION 1d
The given proportion is,
[tex]\frac{33}{x}=\frac{11}{5}[/tex]
We cross multiply to get,
[tex]33\times 5=11x[/tex]
We now divide both sides by 11 to get,
[tex]\frac{33\times 5}{11}=x[/tex]
[tex]\Rightarrow x=15[/tex]
QUESTION 2
Since the recipe calls for 5 cups of flour for every 6 teaspoons of salt, we can write the ratio,
[tex]5:6[/tex]
Let a larger recipe of 15 cups of flour correspond to [tex]x[/tex] teaspoons of salt,
Then the proportion becomes,
[tex]5:6=15:x[/tex]
This implies that,
[tex]\frac{5}{6}=\frac{15}{x}[/tex].
We cross multiply to get,
[tex]5x=6\times 15[/tex]
We divide through by 5 to get,
[tex]x=\frac{6\times 15}{5}[/tex]
[tex]\therefore x=18[/tex]
Hence you will need 18 teaspoons of salt.
QUESTION 3
We were given that a 20-foot flagpole casts a 6-foot shadow.
We write this as a ratio to get,
[tex]20:6[/tex]
Let the nearby 30-foot building cast an x-foot shadow.
We can also write this as a ratio to get,
[tex]30:x[/tex]
The proportion now becomes,
[tex]20:6=30:x[/tex]
We cross multiply to get,
[tex]20x=6\times 30[/tex]
This implies that
[tex]x=\frac{6\times 30}{20}[/tex]
[tex]\Rightarrow x=9[/tex]
QUESTION 4
If 15 corresponds to 4, we write the ratio,
[tex]15:4[/tex]
We want to find what number of ads corresponds to 300 columns. Let that number be x.
Then we have the ratio,
[tex]300:x[/tex]
The proportion is
[tex]15:4=300:x[/tex]
This implies that,
[tex]15x=300\times 4[/tex]
[tex]x=\frac{300\times 4}{15}[/tex]
[tex]x=80[/tex]
It must have 80 ads.
QUESTION 5
The given ratio is [tex]5:2[/tex],
Let the gallons of blue paint be [tex]x[/tex]
We can write the ratio [tex]x:8[/tex]
The required proportion is
[tex]5:2=x:8[/tex]
This implies that,
[tex]\frac{5}{2}=\frac{x}{8}[/tex]
We multiply both sides by 8
[tex]x=\frac{5}{2}\times 8[/tex]
[tex]x=20[/tex]
8 gallons of blue paint is needed