To celebrate its grand opening a store is giving customers gift certificates which customer is the first to get two gift certificates every 8th gets a $50 gift certificate and every 6th person gets a $10 gift certificate

Answer:

4x + 3x = 42

Step-by-step explanation:

The required equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours is 4x + 7y = 56.

To write the equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours, we can use the given information that there are 4 rooms left to clean after 7 hours.

Let's start with the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

We have the point (x₁, y₁) = (7, 4), which represents the number of rooms left after 7 hours.

Substituting the values into the point-slope form, we get:

y - 4 = m(x - 7)

Now, we need to find the slope (m) of the line.

The slope of a line can be determined by the change in y divided by the change in x. In this case, the change in y is -4 (4 rooms left to clean) and the change in x is 7 hours.

m = Δy / Δx = -4 / 7

Now, let's substitute the value of m into the equation:

y - 4 = (-4/7)(x - 7)

To eliminate fractions, we can multiply through by 7:

7y - 28 = -4(x - 7)

7y - 28 = -4x + 28

4x + 7y = 56

So, the equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours is 4x + 7y = 56.

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Final answer:

To express the relationship between the number of rooms left to clean and the hours spent cleaning in a linear equation, we use the slope of -4/7 and a y-intercept of 4, assuming 4 rooms are cleaned in 7 hours. This leads to the slope-intercept form y = -4/7x + 4. Multiplying by 7 and rearranging gives us the standard form 4x + 7y = 28.

Explanation:

To find the equation of the line that represents the number of rooms, y, Martin has left to clean after x hours, we start with the information that 4 rooms take 7 hours to clean. This means that every hour, a fraction of the total rooms are cleaned. To express this situation as a linear equation, we can use the slope-intercept form, which is y = mx + b. In this context, the slope (m) will be negative since the number of rooms left to clean decreases over time, and b is the y-intercept representing the initial number of rooms before any cleaning has started. Since there are 4 rooms to begin with and it takes 7 hours to clean all, the slope is -4/7 (the change in rooms left per hour).

The equation in slope-intercept form is y = -4/7x + 4. To convert this to standard form, we multiply the entire equation by 7 to eliminate the fraction: 7y = -4x + 28. Then we add 4x to both sides of the equation to get: 4x + 7y = 28. This is the equation in standard form, representing the number of rooms left (y) after x hours of cleaning.

Answer:

12 (5x - 2)

Step-by-step explanation:

First to know if we can get a common factor we have to find a number by which it is divisible on 24 and 60

first we will try with 2

60/2 = 30            both are divisible by 2

24 /2 = 12

then we will take common factor 2

60x - 24

we multiply and divide by 2

2 (60x - 24)/2

we distribute the 2

2(60x/2 - 24/2)

and solve

2(30x - 12)

Now we continue with the same procedure until there is no more number in common to divide

we will try with 2

30/2 = 15            both are divisible by 2

12 /2 = 6

then we will take common factor 2

2(30x - 12)

we multiply and divide by 2

2*2 (30x - 12)/2

we distribute the 2

4(30x/2 - 12/2)

and solve

4(15x - 6)

continue with the same procedure

we will try with 2

15/2 = X            only one is divisible by 2

6 /2 = 3

we will try with 3

15/3 = 5          both are divisible by 3

6 /3 = 2

then we will take common factor 3

4(15x - 6)

we multiply and divide by 3

4*3 (15x - 6)/3

we distribute the 3

12(30x/3 - 6/3)

and solve

12(5x - 2)

there is no number other than 1 by which we can divide 5 and 2

12(5x - 2)

Part 1:

Replace "v0" in the given equation with the given velocity of 15 ft/sec:

y = -16t^2 + 15t +6.5

Part 2:

Now set the equation to 0 which would be when the basketball hits the ground:

-16t^2 +15t +6.5 = 0

A quadratic equation is solved using the formula:

t = -b +/- sqrt(b^2-4ac)/2a

Using the given equation: a = -16, b = 15 and c = 6.5

Replace the values and solve:

t = -(15)+/- sqrt(15^2 -4(-16)(6.5))/2(-16)

This solves to get both -0.32 and 1.26 seconds.

The time has to be a positive value so t = 1.26 seconds.

Part3:

Using the quadratic form at^2 + bt + c

The maximum is found using t = -b/2a = -15/2(-16) = = 0.47 seconds

The maximum height would be at 0.47 seconds

Part 4:

Replace t with 0.47 and solve for maximum height:

y = -16(0.47)^2 + 15(0.47) +6.5

Maximum height would be 3.52 feet

Step-by-step explanation:

[tex]m \angle \: C = \frac{1}{2} (m \: arc \: AB)\\(By\:inscribed \:\angle\:theorem) \\ \\ \therefore \: (x + 5) \degree =\frac{1}{2} (4x)\degree \\ \\ \therefore \: x + 5=\frac{1}{2} \times 4x \\ \\ \therefore \: x + 5=2x \\ \\ \therefore \: x - 2x = - 5 \\ \\ \therefore \: - x = - 5 \\ \\ \: \: \: \: \: \huge \purple{ \boxed{\therefore \: x = 5}}[/tex]

Answer:

Hurricanes

Step-by-step explanation:

We are given the following in the question:

Scientists are studying hurricanes to determine the number of hurricanes in the past 50 years that have caused greater than $1 million in damages.

Population:

Thus, for the given scenario

Population of interest:

Hurricanes

From this population a sample of hurricanes that have caused greater than $1 million in damages is taken.

Answer:

A)Hurricanes

Step-by-step explanation:

Answer:

$261

Step-by-step explanation:

The team hopes to earn three times more than it did last year

Last year the team earned $ 87

We are required to determine the team's goal this year.

Therefore;

Since they hope to raise three times than last year;

Then;

Goal this year = 3 × last year's earnings

                        = 3 × $ 87

                        = $261

Therefore, the team's goal this year is $261

Answer:

  d.  about 9 years​

Step-by-step explanation:

There is a "rule of thumb" for doubling time* that says the product of the percentage rate of change per year and the doubling time in years is about 72. Here, that means the doubling time is about ...

  72/8 = 9 . . . . years

_____

You can write the exponential equation ...

  multiplier = (1 +.08)^n

and solve for multiplier = 2:

  2 = 1.08^n

  log(2) = n·log(1.08) . . . . . take logs

  log(2)/log(1.08) = n . . . . . divide by the coefficient of n

  9.00647 ≈ n

It will take about 9 years for the participation to double.

_____

* The farther away from 8% the rate of change is, or the more times per year it is compounded, the less accurate is the "rule of 72." When compounding is continuous, the "rule of 72" becomes the "rule of 69.4". For this problem, answer choices are sufficiently far apart that the rule of thumb is adequate for making a correct choice.

Answer:

Step-by-step explanation:

Why shouldn't classes overlap when one summarizes continuous data? If classes overlap, then some observations will be counted in more than one class. This means that certain observations will end up in more than one bar of a histogram, which will misrepresent the data!

Yo sup??

Since there is an x^2 term therefore this equation is of a parabola

By taking LCM and then cross multiplying it.

6y=x^2-9x+26

6y=x^2-9x+(9/2)^2+23/4

6y-23/4=(x-9/2)^2

we see that this is of the form

X^2=4AY

(x-9/2)^2=4(3y/2-23/16)

Hope this helps.

Answer:

[tex]f(x) =- \sqrt{x-1}+3[/tex]

Step-by-step explanation:

This looks like a square root function [tex]f(x) = \sqrt{x}[/tex]  but symmetric with respect to the x axis and shifted to the right for 1 and up for 3:

Lets take  [tex]f(x) = \sqrt{x}[/tex] . The function symmetric with respect to the x axis would be [tex]-f(x)[/tex], so now we have:

                                                [tex]f(x) = -\sqrt{x}[/tex]

Lets take [tex]f(x) = -\sqrt{x}[/tex] and shift it up for y = 3. Now we have:

                                               [tex]f(x) =- \sqrt{x}+3[/tex]

Lets take [tex]f(x) = -\sqrt{x}+3[/tex] and shift it right for x = 1. That means that instead of x we will have x-1:

                                            [tex]f(x) =- \sqrt{x-1}+3[/tex]

Answer:

Step-by-step explanation:

Let t = flying time in seconds for each plane

Descending rate = 40 ft/s

Ascending rate = 60 ft/s

Descending height, hd= 19200 - 40t

Ascending height, ha = 60t

Equating hd = ha, therefore:

60t = 19200-40t

60t + 40t = 19200

100t = 19200

t = 19200/100

t = 192 seconds

h = 19200 - 192(40)

h = 19200 - 7680

= 11,520 ft.

After 192 seconds, the two airplanes will be at the same height, which is 11,520 feet.

To find the time it takes for the two airplanes to be at the same height, we need to set up an equation based on their rates of ascent and descent. Let's assume the height of the descending airplane is given by h1 and the height of the ascending airplane is given by h2. The descending airplane is descending at a rate of 40 feet per second, so its height after t seconds can be represented by the equation h1 = 19,200 - 40t. The ascending airplane is ascending at a rate of 60 feet per second, so its height after t seconds can be represented by the equation h2 = 60t. To find the time at which the two airplanes are at the same height, we can set h1 equal to h2 and solve for t: 19,200 - 40t = 60t. Simplifying this equation, we get 100t = 19,200, so t = 192 seconds. Therefore, after 192 seconds, the two airplanes will be at the same height.

To find the height at which the two airplanes are at, we can substitute the value of t into either the equation for h1 or h2. Let's use the equation for h1: h1 = 19,200 - 40(192) = 19,200 - 7,680 = 11,520 feet. Therefore, after 192 seconds, the two airplanes will be at a height of 11,520 feet.

Answer:

(1, -2)

(-8, -2)

Step-by-step explanation:

(1 , -6) and (-8 , -6)

1 - (-8) = 9

we know that the length of the side that we know the vertices is 9

from there we make an equation with the sum of the sides equal to the perimeter

we will have 2 times 9 and 2 times x beacause it is a rectangle

x + x + 9 +9 = 26

2x + 18 = 26

2x = 26 - 18

2x = 8

x = 8/2

x = 4

Now that we know the missing side we just have to add or subtract this value to the coordinate in and of the vertices we have and we will obtain the missing vertices

(1, -6 + 4)

(1, -2)

( -8, -6+4 )

(-8, -2)

The coordinates of the other two vertices of the rectangle are (1, -2) and (-8, -2), found by calculating the length of one side using the given vertices and then applying the rectangle's perimeter to find the length of the adjacent sides.

The subject of the question is to find the other two vertices of a rectangle given two of its vertices and the perimeter. We know that the opposite sides of a rectangle are equal in length. So, to solve this, we can use the distance formula to find the length of one side with the two given points (1, -6) and (-8, -6). The length of this side is the absolute value of the difference in the x-coordinates, which is 9 units. Since the perimeter is 26, and this length is 9, the sum of the lengths of the other two sides is 26 - 2*9 = 8 units. Therefore, each of these sides is 4 units long. Because the given points have the same y-coordinate, they lie on a horizontal side of the rectangle, so the other two vertices will have the same x-coordinates as the given ones and will be 4 units vertically away. If we add and subtract 4 units from the y-coordinate of the given points, we get the other two vertices: (1, -6 +4) and (-8, -6 +4). So the coordinates of the other two vertices are: (1, -2) and (-8, -2).

See the explanation

I have corrected your diagram so ∅ is the angle at the top of the diagram. In order to solve this problem we have to use Pythagorean theorem and the law of sines. Moreover, I have named two sides as w and z so those variables will help us to solve this problem. So:

The triangle at the bottom is right, so by Pythagorean theorem is true that:

[tex]w^2=4^2+(2\sqrt{2})^2 \\ \\ w^2=24 \\ \\ w=\sqrt{24} \\ \\ w=2\sqrt{6}[/tex]

By law of sines:

[tex]\frac{z}{sin\theta}=\frac{w}{sin60^{\circ}} \\ \\ z=\frac{wsin\theta}{sin60^{\circ}} \\ \\ z=\frac{2\sqrt{6}sin\theta}{\sqrt{3}/2} \\ \\ z=4\sqrt{2}sin\theta[/tex]

By law of sines again:

[tex]\frac{y}{sin45^{\circ}}=\frac{z}{sin\phi} \\ \\ y=\frac{zsin45^{\circ}}{sin\phi} \\ \\ y=\frac{4\sqrt{2}sin\theta \sqrt{2}/2}{sin\phi} \\ \\ \\ Finally: \\ \\ \boxed{y=\frac{4sin\theta}{sin\phi}}[/tex]

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Answer:

There are 3120 chocolate eggs.                                

Step-by-step explanation:

We are given the following in the question:

Total number of eggs = 4680

Number f chocolate eggs =

[tex]\dfrac{2}{3}[/tex]  the number of real eggs

We have to find the number of chocolate eggs.

Number of chocolate eggs =

[tex]\dfrac{2}{3}\times \text{Total number of eggs}[/tex]

[tex]=\dfrac{2}{3}\times 4680\\\\=3120[/tex]

Thus, there are 3120 chocolate eggs.

Answer:

Like terms are numbers with or without variables that have the same variables.

Step-by-step explanation:

5x and 3x are like terms because they have the same variable.

5x and 3y are not like terms because the variables are different.

To combine them, just add or subtract them. You cannot combine non-like terms!

Answer:

Definition: Like terms - Term in math that have the same variables or powers.

Ex. 2x, -5x, and 7x.

Combine Them: 2x + 7x = 9x - 5x = 4x

Step-by-step explanation:

Question:

A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units.

Which equation can be used to solve for x, the side length of the original square?

x2 − 2x − 120 = 0

x2 + 2x − 120 = 0

x2 − 2x + 120 = 0

x2 + 2x + 120 = 0

Answer:

Option a: [tex]x^{2} -2x-120=0[/tex] is the equation

Explanation:

It is given that the area of the square paper is [tex]x^{2}[/tex] square units.

The area of the remaining piece of paper is 120 square units.

It is also given that the area of the remaining piece of paper is [tex]x^{2}-2 x[/tex]

Thus, equating the area of the remaining piece of paper, we have,

[tex]x^{2} -2x=120[/tex]

Subtracting 120 from both sides of the equation, we have,

[tex]x^{2} -2x-120=0[/tex]

Thus, the equation [tex]x^{2} -2x-120=0[/tex] can be used to solve for x.

Hence, Option a is the correct answer.

Answer:

19 wrong answers.

Step-by-step explanation:

Given:

Sahil got 28 questions right.

Angelina got 7 more wrong answers than Sahil.

There where 40 questions on the test.

Question asked:

How many answers did Angelina get wrong on the math test ?

Solution:

Total questions on the test = 40

Number of right answers, Sahil got = 28

Number of wrong answers, Sahil got = 40 - 28 = 12

As Angelina got 7 more wrong answers than Sahil,

Number of wrong answers, Sahil got = 12

Then, number of wrong answers, Angelina got = 12 + 7 = 19

Therefore, 19 answers did Angelina get wrong on the math test out of 40.

Angelina got 35 wrong answers on the math test.

To find the number of wrong answers Angelina got on the math test, we need to know how many questions she got right. Since Sahil got 28 questions right and there were 40 questions on the test, we can subtract Sahil's score from the total number of questions to find Angelina's score. Sahil got 28 questions right, so Angelina would have gotten 40 - 28 = 12 questions right. And since Angelina got 7 more wrong answers than Sahil, we can subtract Sahil's wrong answers from Angelina's total wrong answers to find the specific number. If Sahil got 12 questions right, then he must have gotten 40 - 12 = 28 questions wrong. And since Angelina got 7 more wrong answers than Sahil, we can add 7 to Sahil's wrong answers to find Angelina's total wrong answers. Therefore, Angelina got 28 + 7 = 35 wrong answers on the math test.

Answer: $13,114

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 9000

r = 3.8% = 3.8/100 = 0.038

n = 2 because it was compounded 2 times in a year.

t = 10 years

Therefore,.

A = 9000(1+0.038/2)^2 × 10

A = 9000(1+0.019)^20

A = 9000(1.019)^20

A = $13114

The final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B:  $13114 approx.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]

For this case, we are given that:

Thus, the final amount at the end of 10 years is given by:

[tex]A = P(1 +\dfrac{1.9}{100})^T\\\\A = 9000(1 + \dfrac{1.9}{100})^{20} = 9000(1.019)^{20} \approx 13114 \text{\: \: (in dollars)}[/tex]

Thus, the final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B:  $13114 approx.

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Answer:

There are 18 Sedans in the dealership shop.

Step-by-step explanation:

Let x represent the number of Sedans in the dealership shop.

Let y represent the number of SUV's in the dealership shop.

If there are a combined 24 sedans and SUVs, it means that

x + y = 24 - - - - - - - - - - - -1

At a car dealership, there are three times as many sedans as SUVs. This means that

x = 3y

Substituting x = 3y into equation 1, it becomes

3y + y = 24

4y = 24

y = 24/4 = 6

x = 3y = 6 × 3

x = 18

Answer:

C

Step-by-step explanation:

In the first instance, he wanted buying euros in exchange for his dollars. He had $540 and wanted to buy euros. The conversion factor here is that for every 1 euro, he pays $1.80

Now at the second instance, he wanted buying dollars with his left over euros. This means for every 1 euro, he gets $1.4

Since, he is having 40 euros, the total amount in dollars he would get will be 40 * $1.4 = $56

Answer:

[tex]d = 670,616,629h \ mi[/tex]

Step-by-step explanation:

Given:

Speed of the light = 670,616,629 mi\hr

We need to find the direct variation equation represents given situation.

Solution:

Speed is defined as the ratio of distance and time. So, the equation of the speed is as follows:

[tex]Speed = \frac{Distance}{Time}[/tex]

And also written as.

[tex]S = \frac{d}{h}[/tex]

Now, we write the above equation for distance.

[tex]d = S\times h[/tex] ------------(1)

Where:

d = distance travel by object.

S = speed of the object.

h = Total time taken

Substitute S = 670,616,629 mi\hr in equation 1.

[tex]d = 670,616,629h \ mi[/tex]

Therefore, direct variation equation to represents the given situation

[tex]d = 670,616,629h \ mi[/tex]

Answer:

7y²

Step-by-step explanation:

First u group them like 4+3+y+y=7y²

Answer: he open the account 9 years ago.

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount deposited.

P represents the principal or amount deposited.

R represents interest rate

T represents the time for which the amount deposited was left in the account.

From the information given,

P = 400

R = 7.5%

I = 670 - 400 = $270

Therefore,

270 = (400 × 7.5 × T)/100 = 30T

T = 270/30

T = 9 years

Step-by-step explanation:

9 years thank you yw bubye

Answer:

At 7 hours from the visit telling the joke, everyone in town would have heard of it

Step-by-step explanation:

Exponential Grow

This is a good example of exponential growth, where the speed at which a rumor is spread out depends on the actual number of persons who already know it.

The visitor told the mayor a new joke at 10:00 am.

Total people who heard the joke=1

This person tells the joke to 3 people in one hour, so at 11:00 am, 1+3=4 persons heard the joke

Total people who heard the joke=4

Those persons take one hour to tell the joke to every 3 persons each. Thus at 11:00  

4 + 4*3 = 16 persons heard the joke. This succession grows very quickly. At 12:00

16 + 16*3 = 64 persons heard the joke

We can note the number of persons hearing the joke is an even power of 2, that is

[tex]2^0=1[/tex]

[tex]2^2=4[/tex]

[tex]2^4=16[/tex]

[tex]2^6=64[/tex]

We can predict the result for each hour since the exponent is double the number of hours passed since the joke started to spread. The number of persons who have heard the joke after t hours is

[tex]N=2^{2t}[/tex]

We can iterate until we find the value of t so that

[tex]2^{2t}<9800[/tex]

Let's better find the limit value of t

[tex]2^{2t}=9800[/tex]

Taking logarithms

[tex]log(2^{2t})=log9800[/tex]

[tex]2tlog(2)=log(9800)[/tex]

Thus

[tex]\displaystyle t=\frac{log(9800)}{2log 2}[/tex]

[tex]t=6.6[/tex]

So at 7 hours from the visit telling the joke (between 16:00 and 17:00), everyone in town would know it

Note that

[tex]2^{12}=4096[/tex]

[tex]2^{14}=16384[/tex]

The coordinates of A'  after rotation  of 270 counterclockwise and then shifted down 3 units are (2, 4).

To find the coordinates of point A' after a 270-degree counterclockwise rotation around the origin and then shifting down 3 units, we first perform the rotation.

A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. So, when we rotate point A(-7, -2) 90 degrees clockwise, we swap the coordinates and change the sign of the former x-coordinate, which gives us the new point A''(2, 7). Next, we shift A'' down 3 units, which means we subtract 3 from the y-coordinate, resulting in A'(2, 4).

Answer: the shipping and handling fee is 8 percent of the cost of the order.

Step-by-step explanation:

Shipping and handling fee of $35 is charged to all furniture orders over $250.

If the order is $437.50, it means that there would be a handing and shipping fee of $35 because the price of the order is above $250.

The percentage of the original price of the order that is the shipping and handling fee would be

35/437.5 × 100 = 0.08 × 100

= 8%

Final answer:

To find the percent that the shipping and handling fee is of the total order, divide the fee by the order amount and multiply by 100. For an order of $437.50 with a fee of $35, the shipping fee is 8% of the total order.

Explanation:

The question asks us to determine what percent the shipping and handling fee is of the total furniture order.

To calculate this percentage, we can use the formula:

Percentage = (Part / Whole)  imes 100

In this case:

Now, we insert the values into the formula:

Percentage = ($35 / $437.50)  imes 100

Percentage = 0.08  imes 100

Percentage = 8%

Therefore, the shipping and handling fee is 8% of the total order.

Answer:

There were 180 voters for blue color.

Step-by-step explanation:

Let the total number of voters be 'x'.

Given:

Number of Voters for blue color = [tex]\frac{5}{8}x[/tex]

Number of Voters for green color = [tex]\frac{5}{9}(x-\frac58x)=\frac59x(1-\frac58)[/tex]

Now we will use LCM to make the denominator common we get;

Number of Voters for green color = [tex]\frac59x(\frac88-\frac58)=\frac59x(\frac{8-5}{9})=\frac59x(\frac38)=\frac{15x}{72}[/tex]

Number of Voters for red color = 48

We need to find the number of voters for blue color.

Solution:

Now we can say that;

total number of voters is equal to sum of Number of Voters for blue color, Number of Voters for green color and Number of Voters for red color.

framing in equation form we get;

[tex]x=\frac58x+\frac{15x}{72}+48[/tex]

Combining like terms we get;

[tex]x-\frac58x-\frac{15x}{72} = 48[/tex]

Now we will make denominators common using LCM we get;

[tex]\frac{72x}{72}-\frac{5x\times9}{8\times9}-\frac{15x\times1}{72\times 1} = 48\\\\\frac{72x}{72}-\frac{45x}{72}-\frac{15x}{72} = 48[/tex]

Now denominators are common so we will solve the numerators we get;

[tex]\frac{72x-45x-15x}{72}=48\\\\\frac{12x}{72}=48\\\\\frac{x}{6}=48[/tex]

Now multiplying both side by 6 we get;

[tex]\frac{1}{6}x\times6=48\times6\\\\x = 288[/tex]

Number of voters for blue color = [tex]\frac{5}{8}x=\frac{5}{8}\times 288= 180[/tex]

Hence There were 180 voters for blue color.

Answer: String variables

Step-by-step explanation:

SPSS means Statistical Package for Social Sciences.

The SPSS has only two variables namely:

1. String variables which includes numbers,letters and other characters.

The string variables cannot perform calculations. It is basically used to type names of people, age,occupation,home addresses,email addresses e.t.c Which is what is what the researcher was trying to do.

2. Numeric variables which include only numbers. It can perform calculations too using mathematical operations like addition,multiplication,division and subtraction.

Answer:

P (Cheese) = 0.199, P (Sausage) = 0.259, P (Pepperoni) = 0.181,

P (Supreme) = 0.130, P (Another Kind) = 0.144

and P (Does not like any kind) = 0.088

Step-by-step explanation:

Given:

Number of students who prefer cheese = 43

Number of students who prefer sausage = 56

Number of students who prefer pepperoni = 39

Number of students who prefer supreme = 28

Number of students who prefer another kind = 31

Number of students who did not like any kind = 19

∴ The total number of students surveyed = [tex]43+56+39+28+31+19=216[/tex]       The number of students who prefer pizza = [tex]43+56+39+28+31=197[/tex]

The probability that a students likes pizza is,

[tex]P(Student\ likes\ pizza)=\frac{No.\ of\ students\ who\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]

                                     [tex]=\frac{197}{216} \\=0.912[/tex]

The probability that a students does not likes pizza is,

[tex]P(Student\ does\ not\ likes\ pizza)=\frac{No.\ of\ students\ who\ does\ not\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                   [tex]=\frac{19}{216} \\=0.088[/tex]

The probability distribution of students who prefer different kinds of pizza is:

       [tex]P(A\ Student\ prefers\ cheese)=\frac{No.\ of\ students\ who\ prefer\ cheese}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                       [tex]=\frac{43}{216}\\=0.199[/tex]

        [tex]P(A\ Student\ prefers\ sausage)=\frac{No.\ of\ students\ who\ prefer\ sausage}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                           [tex]=\frac{56}{216}\\=0.259[/tex]

       [tex]P(A\ Student\ prefers\ pepperoni)=\frac{No.\ of\ students\ who\ prefer\ pepperoni}{Total\ no.\ of\ students\ surveyed}[/tex]  

                                                             [tex]=\frac{39}{216}\\=0.181[/tex]

       [tex]P(A\ Student\ prefers\ supreme)=\frac{No.\ of\ students\ who\ prefer\ supreme}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                           [tex]=\frac{28}{216}\\=0.130[/tex]

        [tex]P(A\ Student\ prefers\ another\ kind)=\frac{No.\ of\ students\ who\ prefer\ another\ kind}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                                   [tex]=\frac{31}{216}\\=0.144[/tex]

Thus, the probability distribution table is displayed below:

The velocities of particles are given by the derivatives of their displacement functions. Equating the velocity functions of the two particles and solving numerically, we find that they have the same velocity for the first time at about t = 1.569 seconds.

The velocity of an object is given by the derivative of its displacement function. So, we need to first find the derivatives of the given displacement functions to find the velocities of the particles.

The derivative of e^(4cos(t)) is [tex]-4e^{(4cos(t))sin(t)[/tex]. The derivative of [tex]-(t^3)/(3) - (t^2)/(2) + 2 is -t^2 - t.[/tex] Now, we equate the two velocities and solve for t[tex].-4e^(4cos(t))sin(t) = -t^2 - t[/tex]

Unfortunately, this equation does not have a simple algebraic solution. However, it can be solved numerically using, for example, a graphing calculator or numerical software. By using these tools, we find the first positive time at which the particles have approximately the same velocity to be about t = 1.569 seconds. Therefore, the correct answer is A.) t = 1.569 seconds.

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