Part B

Here’s a different way to partition the same function. Write a description of the partitioned function using known function types. Include function transformations in your description

4 cups of mayonnaise should be used if 1 cup of pecans is used.

As per the given data:

A recipe calls for  [tex]$1\frac{1}{2}[/tex] cups of mayonnaise and [tex]$\frac{3}{8}[/tex] cups of pecans.

First, convert the mixed fraction to an improper fraction.

[tex]$1\frac{1}{2}[/tex] cups of mayonnaise = [tex]$\frac{3}{2}[/tex]

Here we have to determine how much mayonnaise should be used if 1 cup of pecans is used.

This can be determined by using the unitary method.

We may determine the value of one unit from the value of many units and the value of many units from the value of one unit using the unitary technique.

The ratio of the amount of pecans comparing reality and the recipe is:

[tex]$= \frac{1}{\frac{3}{8} }[/tex]

= [tex]$\frac{8}{3}[/tex]

To find the amount of mayonnaise that should be added:

= [tex]$\frac{8}{3}[/tex] × [tex]$\frac{3}{2}[/tex]

= 4

Therefore 4 cups of mayonnaise is required.

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A graph of the ordered pairs (time, distance) for the rows in the ratio table is shown in the image attached below.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/10

Constant of proportionality, k = 0.2

When time x = 20, the distance (y) is given by:

y = 20(0.2)

y = 4 miles.

When time x = 30, the distance (y) is given by:

y = 30(0.2)

y = 6 miles.

When time x = 40, the distance (y) is given by:

y = 40(0.2)

y = 8 miles.

Next, we would use an online graphing calculator to plot the ordered pairs as shown in the graph attached below.

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Answer:

The gravitational force acting on the 6-kg bowling ball at the top of the 120-meter tall building is approximately 58.64 Newtons.

Step-by-step explanation:

The equation of the line in slope intercept form is y = -2.65x + 25.

The x-intercept means when the gift card has a balance of zero dollars.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore. let's find the slope of the line using (2, 19.7) and (4, 14.4).

Hence,

m = slope = 14.4 - 19.7 / 4 - 2

m = - 5.3 / 2

m = - 2.65

Therefore, let's find the y-intercept using (2, 19.7).

y = -2.65x + b

19.7 = -2.65(2) + b

b = 19.7 + 5.3

b = 25

Therefore, the equation of the line is y = -2.65x + 25.

The x-intercept is the value of x when y = 0.

Hence,

0 = -2.65x + 25

-25 = -2.65x

x = -25 / -2.65

x = 9.4

The x-intercept means the gift card has zero balance. At this point the medium cup of coffee is 9.4 .

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The linear equation parallel to y=(2/3)x+1 that passes through (3, 0) is:

y = (2/3)*x - 2

A general linear equation can be written in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Particularly, two linear equations are parallel only if both equations have the same slope and different y-intercepts.

Then a line parallel to:

y = (2/3)*x + 1

Is of the form:

y = (2/3)*x + b

And we want this line to pass through the point (3, 0), replacing these values we will get:

0 = (2/3)*3 + b

0 = 2 + b

-2 = b

Then the linear equation is:

y = (2/3)*x - 2

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According to the equation of the trend line the population will reach 52900 in 27831 years.

A mathematical statement known as an equation is a combination of two expressions joined together by the equal sign.

The equation of the trend line is:

y = 1.9x + 21

where, y is the population and x indicate the year.

To find the number of years in which the population reach 52900, substitute y = 52900.

y = 1.9x + 21

52900 = 1.9x + 21

52900 - 21 = 1.9x

52879/ 1.9 = x

x = 27831

Hence, according to the equation of the trend line the population will reach 52900 in 27831 years.

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The number of student tickets sold are 109.

As per the given data a high school drama department sold 238 tickets for their performance.

An adult ticket cost $6. 75.

A student ticket cost $3. 50.

Let the number of adult tickets be x.

Let the number of student tickets be y.

Then we know that the total number of tickets is 238.

x + y = 238 ... (1)

If we multiply the cost of a ticket by the number of tickets we can also get the total.

6. 75x + 3. 50y = 1252. 25(....... (2))

Now we have two equations and two unknowns and we can find the value for these unknowns

Lets use substitution method.

x + y = 238

x = 238 - y

Substitute x = 238 - y in equation (2)

6. 75(238 - y) + 3. 50y = 1252. 25

1606.5 - 6.75y + 3. 50y = 1252. 25

- 3.25y = - 354.25

3.25y =  354.25

y = 109

Substitute y = 109 in equation (1)

x + 109 = 238

x = 129.

Therefore number of student tickets are 109.

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The expression that shows John's score will be 2x + 9.

It is vital to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, Mai has a score of x while John has 9 more than twice mai's score.

The expression for this relationship will be:

= (2 × x) + 9

= 2x + 9

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Complete question

Mai has a score of x. John has 9 more than twice mai's score. Illustrate the expression for Johnsc score.

The system of equations are:

15 + x = y

13 + 2x = y

The weight of the package is 2 pounds.

The delivery cost for both services is 17$.

Here is a system of equations you can use to represent the cost of the two courier services:

First courier: 15 + x = y

Second courier: 13 + 2x = y

Where x is the weight of the package in pounds and y is the total cost of delivery.

We know that the two courier services are equivalent in terms of cost, so we can set the two equations equal to each other:

15 + x = 13 + 2x

then we can subtract 15 from both sides

x = 13 + 2x -15

x = -2 + 2x

then we can subtract x from both sides

-x = -2

then we can divide both sides by -1

x = 2

The package weighs 2 pounds, and the delivery cost for both services is 15 + 2 = 17$.

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Answer: To solve the equation -3(x+2)^2-4 = 5 by factoring, we can follow these steps:

Move all the terms to one side of the equation by adding 3(x+2)^2 and 4 to both sides: -3(x+2)^2-4+3(x+2)^2+4 = 5+3(x+2)^2

Combine like terms: 3(x+2)^2 = 5

Take the square root of both sides of the equation: (x+2)^2 = 5/3

Isolate x+2 on one side of the equation by taking the square root of both sides: x+2 = ±sqrt(5/3)

Solve for x by subtracting 2 from both sides of the equation: x = ±sqrt(5/3) - 2

So the solutions to the equation -3(x+2)^2-4 = 5 by factoring is x = ±sqrt(5/3) - 2.

It's important to note that the square root of a fraction is a positive and negative solution, so the solutions are x = sqrt(5/3) - 2 and x = -sqrt(5/3) - 2

Step-by-step explanation:

You can "find algebraically" if a function is even, odd, or neither by taking it, substituting -x for x, simplifying it, and then comparing the results to what you had initially.

The function is even if it is exactly the same as what you started with (that is, if f(-x) = f (x), with all the signs remaining the same. The function is odd if it is exactly the opposite of what you started with (that is, if f(-x) = -f(x), with all the signs switched.

The function is neither even nor odd if the outcome is neither exactly the same nor exactly the opposite (that is, neither having all the same words but with all the signs reversed).

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She needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

To determine how many times you need to go to the swimming pool to make the membership fee worth paying, you can use the following formula:

Number of visits = membership fee / (cost without the membership - cost with membership)

Plugging in the values, we get:

Number of visits = $50 / ($5 - $3.50)

The savings from the membership's lower entrance price will have surpassed the cost of the membership after 14 visits.

Hence, she needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

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According to the information in the table, the value of B is 50 (option B)

To find the value of B we must calculate the constant, for that we have to perform the following operation:

In this case, we use the values of another column to identify the constant that applies to all the values in the table and the result is the following:

Additionally, to find the value of B we must perform the following operation:

According to the above, the correct answer would be 50 (option B).

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The probability that a death will result from an accident is 0.105, or 10.5%.

Given:

In foggy conditions, 25% of accidents result in fatalities.

Rain-related accidents result in fatalities in 12.5% of cases.

In sunny weather, 5% of accidents result in fatalities.

To find : The probability that a death will result from an accidents

The likelihood that a death will ensue from an accident

5% of 60%(sunny) (sunny)

25% of 20%(foggy) (foggy)

12.5% of 20%(rainy) (rainy)

Probability = 0.05 x 0.6 x 0.25 x 0.125 x 0.22

Chance is 0.105

Chance is 10.5%.

There is a 10.5% chance that a fatal accident may occur.

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Work Shown:

|x - 5| < 3

-3 < x-5 < 3

-3+5 < x-5+5 < 3+5

2 < x < 8

The graph will have open circles at 2 and 8, then shade between the open circles. The open circles indicate "do not include this endpoint". This is why choice A is the final answer.

The transformation represented by the figure is (c) translation

From the question, we have the following parameters that can be used in our computation:

The figure

On the figure, we have the following

A figure and its translated image

When a shape is translated to form another, then the transformation is a translation

Hence, the transformation is translation

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A list that shows the possible outcomes of one day one method of travel:

Monday, bus,

Monday, subway,

Monday, taxi,

Tuesday, bus,

Tuesday, subway,

Tuesday, taxi

The correct answer is an option (B)

Let A represents the set of days.

A = {Monday, Tuesday}

And set B represents the method of transportaion/travel.

B = {bus, subway,  taxi }

To find the list of possible outcomes of one day one method of travel we find the product of set A and set B.

We know that for non-empty sets A and B the Cartesian Product is given by AxB = {(a,b) | a ∈ A and b ∈ B}.

It is a set of all ordered pairs (a, b)

For above sets A and B,

A × B = {(Monday, bus), (Monday, subway), (Monday, taxi), (Tuesday, bus), (Tuesday, subway), (Tuesday, taxi)}

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Find the complete question below.

The relative frequencies for the car riders are given as follows:

A relative frequency is obtained with the division of the number of desired outcomes by the number of total outcomes.

The total number of car riders is given as follows:

78.

The number in each grade is given as follows:

Hence the relative frequencies are given as follows:

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Heat loss, according to Newton's cooling curve, is exponential. Like a half-life, it operates.

Cake temperature and ambient temperature varied by 140 F. The cake has lost half of that difference after 30 minutes, thus that is the half-life. It will shed another half or 35 F in the next 30 minutes, bringing the temperature to 105 F. It will shed 17.5 F in about 30 minutes, leaving 87.5 F.

The temperature is between the last two, at 100 F, so it will be between an hour and an hour and a half. You get an interpolated result of about an hour and ten minutes.

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Answer:

Step-by-step explanation:

X =90

Answer: 12/48 = 25%

Step-by-step explanation: If the unit rate that characterizes my juice reflects its concentration, then there are 36 + 12 = 48 ounces of matter in total. The orange juice mix that we add is 12 ounces of mix, therefore the concentration is 12/48 = 25%.

The standard deviation of the household income will be increased by $5,000.

The standard deviation is a measure of variation from the mean that takes spread, dispersion, and spread into account. The standard deviation reveals a "typical" divergence from the mean. It is a popular measure of variability since it retains the original units of measurement from the data set.

standard deviation is increased by 5x/100 = 0.05x

Change in standard deviation = $5000

There is little variety when data points are near to the mean, and there is a lot of variation when they are far from the mean. How much the data differ from the mean is determined by the standard deviation. Standard deviation, which is based on all data, is the most often used metric for measuring dispersion. As a result, the standard deviation's value can be affected by even a slight change in one number.

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Correct option is D, the fraction of area of square region ABCD is 1/4.

A + B + C = D + E + F since diagonal QS divides the square into two equal portions.

We can see that the areas of regions A and F must be equal because they have the exact same measurements and form. Similar reasoning leads us to the conclusion that the areas of regions D and C are equal.

As a result, it follows that the size of regions E and B must likewise be equal. Due to the fact that URPT is a parallelogram, its area equals (base)(height)=(1)(2)=2.

Area of region E = Area of region B = 1 as a result.

The percentage of the square PQRS's area is represented by the darkened region 1/4 is a fraction.

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Complete question -

The correct answer is Non-existent. If the Earth's spin axis were perpendicular to the Earth's orbital plane, the seasons and seasonal variation would be greatly reduced or eliminated.

This is because the tilt of the Earth's axis (currently at 23.5 degrees) causes the change in the amount of sunlight received at different latitudes during the year, leading to the seasons we experience.

After all, it causes our seasons in the first place. If the Earth's axis were vertical to its orbital airplane, there would be no seasons. Still, there would be minor variations in temperatures and rush throughout each time as Earth moves slightly closer and further down from the sun If the earth and ringed in an upright position around the sun.

If the Earth's spin axis were perpendicular to the ecliptic plane, the Northern and Southern hemispheres would receive roughly the same amount of sunlight throughout the year, and there would be little temperature variation, thus leading to little or no seasonal changes.

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The right response is Nonexistent. Seasons and seasonal fluctuation would be significantly diminished or completely gone if the Earth's spin axis were parallel to its orbital plane.

This is so that the seasons we experience may be attributed to the tilt of the Earth's axis, which is now 23.5 degrees, which affects the quantity of sunlight received at various latitudes throughout the year.

After all, it is the primary cause of our seasons. Seasons wouldn't exist if the Earth's axis were vertical to its orbital plane. If the earth were circled in an upright position around the sun, there would still be modest fluctuations in temperature and rush throughout each period as Earth travels a little closer to and further away from the sun.

The Northern and Southern hemispheres would get nearly the same amount of sunshine throughout the year, and there would be no temperature difference, which would result in little to no seasonal variations if the Earth's spin axis were perpendicular to the ecliptic plane.

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The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

A line is known as a perpendicular bisector when it divides a specified line segment in half, by creating a 90° angle at the intersection.

The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler.

On both sides of the line segment being divided, it forms a 90° angle.

Here we have

On the grid below segment AB is shown with endpoints A(-1,-1) and B(7,5). It's midpoint M. The coordinates of M (3, 2).  

Slope from A(-1,-1) and B(7,5)  

=> [ 5 + 1]/[7 + 1 ] = 6/8 = 3/4

When we draw a perpendicular bisector of AB on the grid. It will pass through the point (0, 6)  

The slope of the perpendicular bisector i.e from (0, 6) to (3, 2)  

=> [2 - 6]/[3 - 0] = - 4/3

Let the equation of the bisector is y = mx + c

=> y = (-4/3)x + c

=> 3y = - 4x + 3c           [ ∵ Slope = -4/3 ]

As we know the bisector will pass through (3, 2)

=> 3(2) = -4(3) + 3c

=> 3c = 12 + 6

=> 3c = 18

Hence, the required equation of the line is 3y = - 4x + 18  

Therefore,

The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

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The z score that corresponds to the 90th percentile is 1.28. Option D

A z-score (also called a standard score) gives you an idea of how far from the mean a data point is. But more technically it’s a measure of how many standard deviations below or above the population mean a raw score is.

The 90th percentile refers to the value above 90 percent of the data. This is illustrated in the figure.

Therefore, using a z-table (also attached) or a technology, we can solve that  getting the  z=1.28.

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keeping in mind that since a year is 12 months, then 4 months is really 4/12 of a year, so

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 20\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ 20 = (1000)(\frac{r}{100})(\frac{1}{3})\implies 20=\cfrac{1000r}{300} \implies 6000=1000r \\\\\\ \cfrac{6000}{1000}=r\implies \stackrel{\%}{6}=r[/tex]

A geometric sequence begins with 72, 36, 18, 9, is Of(n) is 72(2)+1.

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Answer:

f(n) = 72(0.5)n−1

Step-by-step explanation:

Got right.

Answer:

55°

Step-by-step explanation:

For the line including the 110°, the angle of the supplementary angle is 70° which is the 'non-equivalent' length of the isosceles triangle. Then do:

(180°-70°)/2 = 55° to get x

Answer:

Supplementary angles, x = 55

Step-by-step explanation:

Supplementary angles: straight line means both angles add up to 180, this if the outside angle is 110 then the inside angle is 180° - 110° = 70°

Since it is an isosceles triangle, it means both angles are equal to x therefore

[tex]180 - 70 = 2x\\110 = 2x\\\frac{110}{2} = x\\x = 55[/tex]

The frequency table has been created in the attachment

Given that 56 respondents did not belong to any clubs, we know that the number of 7th graders who belong to zero clubs is 56.

Given that twice as many 7th graders belonged to one club as no clubs, we can set up the equation:

x = 2 * 56

Given that 10 fewer 7th graders belonged to more than one club than no clubs, we can set up the equation:

y = 56 - 10

Given that twice as many 8th graders belonged to one club as more than one club, we can set up the equation:

z = 2*w

Now we have the following system of equations:

x = 2 * 56

y = 56 - 10

z = 2*w

x+z = 150

y+w = 150

By solving the above system of equations we get:

x = 112

y = 46

z = 112

w = 56

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