Need some help with table 2.Fill up tables of proportional relationships with missing Values.
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Proportional Relationships
If the variables x and y are in a proportional relationship, then:
y = kx
Where k is the constant of proportionality that can be found as follows:
[tex]k=\frac{y}{x}[/tex]If we are given a pair of values (x, y), we can find the value of k and use it to fill the rest of the table.
For example, Table 1 relates the cost y of x pounds of some items. We are given the pair (2, 2.50). We can calculate the value of k:
[tex]k=\frac{2.50}{2}=1.25[/tex]Now, for each value of x, multiply by this factor and get the value of y. For example, for x = 3:
y = 1.25 * 3 = 3.75
This value is also given and verifies the correct proportion obtained above.
For x = 4:
y = 1.25 * 4 = 5
For x = 7:
y = 1.25 * 7 = 8.75
For x = 10:
y = 1.25 * 10 = 12.50
Now for table 2, we are given the pair (3, 4.5) which gives us the value of k:
[tex]k=\frac{4.5}{3}=1.5[/tex]Apply this constant for the rest of the table.
For x = 4:
y = 1.5 * 4 = 6
For x = 5:
y = 1.5 * 5 = 7.50
For x = 8:
y = 1.5 * 8 = 12
The last column doesn't give us the value of x but the value of y, so we need to solve for x:
[tex]y=k\cdot x\text{ }=>\text{ }x=\frac{y}{k}[/tex]For y = 15:
[tex]x=\frac{15}{1.5}=10[/tex]Related Questions
help meeeeeeeeee pleaseee !!!!!
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The composite functions are evaluated and simplified as:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3x² + 15
How to Evaluate a Composite Function?To evaluate a composite function, the inner function is evaluated first using the given input. After then, the output of the inner function is used as the input to evaluate the outer function.
Given the following:
f(x) = x² + 5g(x) = 3xTherefore:
a. (f o g)(x) = f(g(x))
Substitute g(x) for x into f(x) = x² + 5
f(g(x)) = (3x)² + 5
Simplify the function
f(g(x)) = 9x² + 5
b. (g o f)(x) = g(f(x))
Substitute f(x) for x into g(x) = 3x:
g(f(x)) = 3(x² + 5)
Simplify the function
g(f(x)) = 3x² + 15
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A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 65%pure antifreeze. The company wants to obtain 260 gallons of a mixture that contains 45% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be
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Answer:
80 gallons of water
180 gallons of premium antifreeze solution.
Explanation:
Let's call X the number of gallons of water and Y the number of gallons of the premium antifreeze solution.
The company wants to obtain 260 gallons of the mixture, so our first equation is:
X + Y = 260
Additionally, the mixture should contain 45% of pure antifreeze and the premium antifreeze solution contains 65% pure antifreeze. So, our second equation is:
0.45(X + Y) = 0.65Y
Now, we need to solve the equations for X and Y. So, we can solve the second equation for X as:
[tex]\begin{gathered} 0.45(X+Y)=0.65Y \\ 0.45X+0.45Y=0.65Y \\ 0.45X=0.65Y-0.45Y \\ 0.45X=0.2Y \\ X=\frac{0.2Y}{0.45} \\ X=\frac{4}{9}Y \end{gathered}[/tex]Then, we can replace X by 4/9Y on the first equation and solve for Y as:
[tex]\begin{gathered} \frac{4}{9}Y+Y=260 \\ \frac{13Y}{9}=260 \\ 13Y=260\cdot9 \\ 13Y=2340 \\ Y=\frac{2340}{13} \\ Y=180 \end{gathered}[/tex]Finally, replacing Y by 180, we get that X is equal to:
[tex]\begin{gathered} X=\frac{4}{9}Y \\ X=\frac{4}{9}\cdot180 \\ X=80 \end{gathered}[/tex]Therefore, the solution should have 80 gallons of water and 180 gallons of premium antifreeze solution.
You borrow 200 from a friend you repay the loan in two weeks and agreed to pay eight dollars for interest what is the annual percentage rate? Round your answer to the nearest 10th of a percent
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Rhombus EfGH is shown in the diagram the measure of angle HEF =64 degrees. What is the measure of angle EJF.
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Diagonals of a rhombus bisect each other at right angles, This means that
[tex]m\measuredangle EJF=90\text{ degre}es[/tex]Write the sentence as an equation. 136 is equal to 194 times b Type a slash (/) if you want to use a division sign.
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Given the sentence 136 is equal to 194 times b, we are to write this statement as an equation.
Let us take it one after the other.
For 194 times b, this can be written as;
= 194 * b
= 194b .
Since 136 is equal to the exxpression, the final equation will be gotten by simply equationf 136 to 194b as shown;
136 = 194b
You can then re-arrange
194b = 136
Hence the reuired equation is 194b = 136
For each equation, choose the statement that describes its solution. If applicable, give the solution.
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w=2
All real numbers are solutions
1) In this question, let's solve each equation, and then we can check whether there are solutions, which one would be.
2) Let's begin with the first one, top to bottom
[tex]\begin{gathered} 2(w-1)+4w=3(w-1)+7 \\ 2w-2+4w=3w-3+7 \\ 6w-2=3w+4 \\ 6w-3w=4+2 \\ 3w=6 \\ \frac{3w}{3}=\frac{6}{3} \\ w=2 \end{gathered}[/tex]Note that we distributed the factors outside the parenthesis over the terms inside.
So for the first one, we can check w=2
3) Moving on to the 2nd equation, we can state:
[tex]\begin{gathered} 6(y+1)-10=4(y-1)+2y \\ 6y+6-10=4y-4+2y \\ 6y-4y-2y=4-4 \\ 6y-6y=0 \\ 0y=0 \end{gathered}[/tex]So, there are infinite solutions for this equation, or All real numbers are solutions
11. (04.02 LC) Saving all the money in a safe at home most likely means (5 points) being stingy being dishonest being untrusting O being thrifty
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Saving all the money in a safe at home most likely means D. being thrifty
What is money?Money is any commodity or verifiable record that is widely accepted in a given country or socioeconomic environment as payment for products and services and repayment of debts, such as taxes.
Money enables us to meet our most basic requirements, such as purchasing food and shelter and paying for healthcare. Meeting these demands is critical, and if we don't have enough money to do so, our personal well-being and the community's overall well-being suffer considerably.
In this case, saving the money means that the person is careful with spending and doesn't want to waste the money. This implies thrifty.
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Answer:
Being thrifty
POSSIBLE POINTS: 1One-half of a number increased by 16 is 4 less than two-thirds of the number. What is the number?
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Let the number be x.
[tex]\begin{gathered} \frac{1}{2}x+16=\frac{2}{3}x-4 \\ \\ \frac{2}{3}x-\frac{1}{2}x=20 \\ \frac{4-3}{6}x=20 \\ \frac{1}{6}x=20 \\ x=120 \end{gathered}[/tex]The number is 120
in which quadrant is the given point located (2,-4)
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Answer: 4th Quadrant
Step-by-step explanation:
When plotted, the point (2, -4) lies in the 4th quadrant.
Find g(x), where g(x) is the translation 4 units left of f(x)=|x|.
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The equation for the translated function is:
g(x) = |x + 4|
How to find g(x)?
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left.if N < 0, the translation is to the right.Here we have:
f(x) = |x|
And the translation is of 4 units to the left, so the translated function is:
g(x) = f(x + 4) = |x + 4|
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solve on a map. 1 inch equals 14.7 miles. if two cities are 3.5 inches apart on the map, how far are they actually apart? (round to a decimal)
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On a map. 1 inch equals 14.7 miles
1 inch = 14.7 miles
Two cities are 3.5 inches apart on the map
Distance between two cities = 3.5 inches
[tex]\begin{gathered} \text{ 1 inch = 14.7 miles} \\ \text{ Then for 3.5 inches in miles : Multiply 3.5}\times14.7\text{ } \\ 3.5\text{ inches=3.5}\times14.7\text{ miles} \\ 3.5\text{ inches=}51.45\text{ miles} \end{gathered}[/tex]So, the distance between two cities is 51.45 miles
Answer : 51.45 miles
9. In 1621, the remaining settlers from the Mayflower and Native Americans gathered for a
harvest feast. There were 140 people at the feast and 40 more Native Americans than settlers.
How many people were from each group?
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In order to solve this, we have to formulate some equations describing the number of people. The total number of people can be calculated by adding the number of natives to the number of settlers, like this:
Total = N + S
Where N is the number of natives and S is the number of settlers. We already know that there were 140 people in total, then we can rewrite the above expression to get:
140 = N + S
We are also told that there were 40 more native Americans than settlers, then the number of natives can be calculated by adding 40 to the number of settlers like this:
N = S + 40
By replacing S + 40 for N into 140 = N + S, we get:
140 = N + S
140 = (S + 40) + S
140 = S + 40 + S
140 = S + S + 40
140 = 2S + 40
140 - 40 = 2S + 40 - 40
100 = 2S
100/2 = 2S/2
50 = S
S = 50
By replacing 50 for S into N = S + 40, we get:
N = S + 40
N = 50 + 40 = 90
N = 90
Then, there were a total of 90 natives and 50 settlers
On a particular college campus, 22% of the students belong to a fraternity or sorority. If 56 college students are randomly chosen:a. What is the probability that 16 are members of a fraternity or sorority?Round to at least three decimal places.Incorrectb. What is the mean of this distribution? Round to at least one decimal.Incorrectc. What is the standard deviation of this distribution? Round to at least one decimal
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Explanation
Part A
From the question,
[tex]\begin{gathered} p=\frac{22}{100};q=1-\frac{22}{100} \\ p=0.22;q=0.78 \\ Also,n\text{ =56} \end{gathered}[/tex]Using the binomial probability distribution formula;
[tex]undefined[/tex]what is its base of the parallelogram is72 meters²
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The area of a parallelogram is computed using the formula base x height.
Here we have a parallelogram with an area of 72 square meters and a height of 9 meters. Using the formula, we can solve for the base.
[tex]\begin{gathered} A=bh \\ 72=b(9) \\ \\ \frac{72}{9}=\frac{b(9)}{9} \\ \\ 8=b \end{gathered}[/tex]The base is 8 meters long.
Which region labeled in the graph below would represent the solution (the final shaded area) to the system of linear inequalities:≤12−3<−23+1
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Since both inequalities include the less than symbol, <, the shaded region must be below the two lines.
The intersection (common) of the shaded regions, which are both below the two lines, is region D.
I need help with this practice problem solving. It is trigonometry It asks to graph the function, if you can.. use Desmos to do so..
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Notice that f(x) is
[tex]h(x)=\cos (x)[/tex]translated π/6 to the left.
Now, recall that the period of the cotangent is
[tex]\pi\text{.}[/tex]Since f(x) is just a translation, both functions have the same period.
Answer:
What are the coordinates of point B (3,-2) after a 90° clockwise rotation about the origin?
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Polly surveyed 850 teenagers to find out their favorite type of music she found that 32% of teenagers to Vader like hard rock how many Teenage evade light Hard Rock
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The survryed was on 850 teenagers
Number of teenage that evade light hard rock = 32% of 850
=32/100 x850
=272
I am creating a study guide and need step by step explanation for this question please
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After other workers taken 1 banana, 2 oranges and 1 pear then total fruits left in the basket
[tex]11[/tex]Now the number of oranges left is 4.
So the probability of picking an orange from the basket is
[tex]\frac{4}{11}[/tex]After she took 1st orange then the number of oranges left 3
So the probability of picking an orange for the 2nd time is
[tex]\frac{3}{10}[/tex]Now the number of oranges left is 2, and the total number of fruits is 9. So the probability of picking third fruit also orange is
[tex]\frac{2}{9}[/tex]From the origin of the coordinate plane, how many units does one travel along the y-axis to find the point with the coordinates (1,8)?
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Solution:
Let's recall that in a coordinate plane, we consider (0, 0) as the origin because this is the point where the x and y-axes intersect.
Therefore, the unit you travel along the y-axis from the origin is:
8 - 0 = 8 (Value of y given - Value of y at the origin)
The answer is 8 units
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The function gives the cost to manufacture x items. C(x) = 15,000 + 8x - x2 -; X = 20,000 20,000 Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated a smaller values of h to check your estimates. Round your answers to five decimal places.) h 10 1 Cave 5.99950 5.9995 x Estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. c' (20,000) = 6 $/item A Need Help? Read It Watch It
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We can replace x=20000 in the function so:
[tex]c(20000)=15000+8(20000)-\frac{20000^2^{}}{20000}[/tex]and we simplify:
[tex]c(20000)=15500[/tex]now h=1 is the cost of one more item so we evaluate for 20001
[tex]\begin{gathered} c(20001)=15000+8(20001)-\frac{20001^2}{20000} \\ c(20001)=195010 \end{gathered}[/tex]So for h=1 will be :
[tex]C=0.599950[/tex]Help math help math
What is the answer
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The ratio 25 : 15 as a fraction in the simplest form can be written as 5/3.
What is ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. Ratio are represented in the following way - a : b, c : d etc
Given is 25 to 15.
We can express this ratio as a fraction in the simplest form as -
25 : 15 = 25/15
Now, we have to ensure that only whole numbers are their in the numerator and denominator. So in simplest form, we can write -
25 : 15 = 25/15 = (5 x 5)/(5 x 3) = 5/3
Simplest form in fraction will be 5/3
Therefore, the ratio 25 : 15 as a fraction in the simplest form can be written as 5/3.
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Enrique takes out a student loan to pay for his college tuition this year. Find the interest on the loan if he borrowed $2500 at an annual interest rate of 6% for 3 years.Simple interest
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Answer:
$450
Explanation:
The interest of the loan can be calculated using the following equation:
[tex]I=P\cdot r\cdot t[/tex]Where P is the amount that he borrowed, r is the interest rate and t is the number of years.
So, replacing P by 2500, r by 0.06, and t by 3 years, we get:
[tex]\begin{gathered} I=2500^{}\cdot0.06\cdot3 \\ I=450 \end{gathered}[/tex]Then, the interest of the loan is $450.
Steel bars shrink 8% when cooled from furnace temperature to room temperature. If a cooled steel bar is 46 in. long, how long was it when it was formed?The steel bar was __ in. long when it was formed.(Round to the nearest whole number as needed.)
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Answer:
50 inches
Explanation:
Let the length of the steel bar when it was formed = y
Steel bars shrink 8% when cooled from furnace temperature to room temperature.
[tex]\begin{gathered} \text{Room Temperature Length}=(100-8)\%\text{ of y} \\ =92\%y \\ =0.92y \end{gathered}[/tex]Given that a cooled steel bar is 46 in. long, then:
[tex]0.92y=46[/tex]Divide both sides by 0.92.
[tex]\begin{gathered} \frac{0.92y}{0.92}=\frac{46}{0.92} \\ y=50\;in. \end{gathered}[/tex]The steel bar was 50 in. long when it was formed.
The surface area of a cell phone screen is 4900 mm². Use the fact that 10 mm = 1 cm to convert this area to cm². Round your answer to the nearest whole number. Do not type the units in the space below.
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Answer:
49 cm²
Step-by-step explanation:
10 mm = 1 cm
1 mm = 1/10 cm
4900 mm² = 4900 × mm × mm
4900 mm² = 4900 × 1/10 cm × 1/10 cm = 49 cm²
help me pleaseeeeeeeee
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Answer:
x = -2
Step-by-step explanation:
f(x) = y
f(x) represents the y-axis
f(x) = -3 or y = -3 or y = (0, -3)
When y = -3, x = -2
x = -2
I hope this helps!
Graphed the dilated image of quadrilateral MNOP using a scale factor of 3 and the origin as the center of dilation
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To dilated the figure by a scale factor 3 and center origin
Multiply the coordinates of each point by 3
The image of the point (x, y) is (3x, 3y)
Ex) The function f(x) is shown on the graph. Plot two points on this grid to create the graph of the line that would represent f(x) - 2.
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ANSWER and EXPLANATION
We have the graph of the function f(x) given.
We want to find 2 points that will represent f(x) - 2.
This (f(x) - 2) is a transformation of the function f(x).
It is called a vertical translation. It means that the function moves on the y axis.
It is generally represented as:
f(x) + b
Comparing the required translation with the general form, we can conclude that there is a -2 shift on the y axis.
Therefore, to find two points for the new function, we have to simply pick two points from the given graph and subtract 2 from their y coordinates.
Let the two points be:
(0, 1) and (-4, 4)
Therefore, the two points will be:
(0, 1) => (0, 1 - 2) = (0, -1)
(-4, 4) => (-4, 4 - 2) = (-4, 2)
Plotting them:
The green line is the line of the new function.
LE Answer two questions about Systems A and B: System A System B 3.7 +12y = 15 x+4y=5 10y = -2 73 - 10y = -2 1) How can we get System B from System A? Choose 1 answer: A Replace one equation with the sum/difference of both equations B Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations C Replace one equation with a multiple of itself D Replace one equation with a multiple of the other equation 2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution? Choose 1 answer: А Yes B No
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The first equation from System A is what is called a linear combination of the first equation of System B: the equation are equivalent.
System A equation is equal to the System B equation multiplied by a factor of 3 on both sides, so they contain the same information.
Answer: Yes. The systems are equivalent as their equations are equivalent.
A convention center is in the shape of the rectangular pyramid with a height of 444 yd. Its base measures 348 yd by 418 yd. Find the volume of the convention center. If necessary, round your answer to the nearest tenth.
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Given:
Length of the base = 418 yd
Width of the base = 348 yd
Height of the pyramid = 444 yd
Find: Volume of the rectangular pyramid
Solution:
The formula to get the volume of the rectangular pyramid is:
[tex]V=\frac{1}{3}\text{Area of the base}\times height[/tex]Since the base is rectangular, we can replace the "area of the base" into "length x width" since that is the formula for the area of a rectangle.
[tex]V=\frac{1}{3}l\times w\times h[/tex]Let's plug in the given data to the formula above.
[tex]V=\frac{1}{3}418yd\times348yd\times444yd[/tex]Then, solve for V or volume.
[tex]\begin{gathered} V=\frac{1}{3}\times64,586,016yd^3 \\ V=21,528,672yd^3 \end{gathered}[/tex]Answer: The volume of the convention is 21, 528, 672 yd³.