Wenona sketched the polynomial P(X) as shown on the axes below.

Which equation could represent P(X)
A.P(X)=(x+1)(x-2)^2
B.P(X)=(x-1)(x+2)^2
C.P(X)=(x+1)(x-2)
D.P(X)=(x-1)(x+2)

The probability that the student, who ran out of time on a multiple choice exam and randomly guessed the answers for two problems, answered both of the problems correctly is ⁹/₂₅.

Probability refers to the likelihood of an expected outcome occurring out of many possible outcomes.

Probability is computed as the quotient of expected outcome over total outcomes.

The number of questions left = 2

The number options of for each question = 5

Since there are 5 options for each question, 4 of which are wrong, the probability of getting both wrongs is:

⁴/₅ x ⁴/₅ = ¹⁶/₂₅ = 0.64 or 64%

Therefore, probability of getting both questions correct is 36% (1 - 64%) or ⁹/₂₅ (1 -  ¹⁶/₂₅).

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The coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate of the original triangle's vertices).

To find the coordinates of the vertices of the dilated triangle A''B''C'' after two successive dilations, first with a scale factor of 4 and then with a scale factor of 3/4.

Firstly, Apply the first dilation with a scale factor of 4 to the original triangle ABC, with a center of dilation at the origin. This can be done by multiplying each coordinate of the original triangle by 4.

The coordinates of the dilated triangle A'B'C' after the first dilation would be;

A' = (4 × x-coordinate of A, 4 × y-coordinate of A)

B' = (4 × x-coordinate of B, 4 × y-coordinate of B)

C' = (4 × x-coordinate of C, 4 × y-coordinate of C)

Now, we apply the second dilation with a scale factor of 3/4 to the dilated triangle A'B'C', again with a center of dilation at the origin. This can be done by multiplying each coordinate of A'B'C' by 3/4.

The coordinates of the dilated triangle A''B''C'' after the second dilation would be;

A'' = ((3/4) × x-coordinate of A', (3/4) × y-coordinate of A')

B'' = ((3/4) × x-coordinate of B', (3/4) × y-coordinate of B')

C'' = ((3/4) × x-coordinate of C', (3/4) × y-coordinate of C')

Plugging in the values of A', B', C' obtained from the first dilation, we get;

A'' = ((3/4) × 4 × x-coordinate of A, (3/4) × 4 × y-coordinate of A)

B'' = ((3/4) × 4 × x-coordinate of B, (3/4) × 4 × y-coordinate of B)

C'' = ((3/4) × 4 × x-coordinate of C, (3/4) × 4 × y-coordinate of C)

Simplifying further, we get;

A'' = (3 × x-coordinate of A, 3 × y-coordinate of A)

B'' = (3 × x-coordinate of B, 3 × y-coordinate of B)

C'' = (3 × x-coordinate of C, 3 × y-coordinate of C)

Therefore, the  coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate.

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Answer: B) their preferences for recreation

Step-by-step explanation:

We can see here that the difference in the areas of the polygons shown is: 3x + 1.

A polygon is a two-dimensional geometric object that is made up of a finite number of sides that are connected end to end to create a closed shape.

We can find the difference in the areas of the polygons shown in the following way:

Area of Polygon 1: A = x + 5

Area of Polygon 2: A = 4x - 6

Finding their difference, we have:

(4x - 6) -  (x + 5)

= 4x + 6 - x - 5

Collecting like terms, we have:

= 4x - x + 6 - 5

= 3x + 1

Thus, we see here that the difference in the areas of the polygon is =  

3x + 1

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Answer:

  y = -x +3

Step-by-step explanation:

You want the slope-intercept equation of the line with the same intercept as -3y = -9 +3x, and the same slope as -2x -2y = -8.

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . where m is the slope, and b is the y-intercept

For the given equations, we can put them in this form to find the desired parameters.

  -3y = -9 +3x

  y = -x +3 . . . . . . . . . . divide both sides by -3

We observe that the y-intercept is +3, which we will need for our answer.

The slope-intercept form of the second equation is ...

  -2x -2y = -8

  x + y = 4 . . . . . . . . . . divide by -2

  y = -x +4 . . . . . . . . . . subtract x

We observe that the slope (coefficient of x) is -1, which we will need for our answer.

We want the equation of the line with slope -1 and y-intercept 3. It is ...

  y = -x +3 . . . . . . . . . . same as the equation of the first line

__

Additional comment

The slope-intercept equation (green) is plotted using dots, so that you can see it is coincident with the line described by the first equation (red). Parallel lines have the same slope, so our desired line must be parallel to the blue line. (It is.)

Answer:

10. x=82 11.x=25 9. p=225

Factor of the equation are,

⇒ p (p + 2) - q (q + 6) - 8

We have to given that;

The expression is,

⇒ p² + 2p - 8 - q² - 6q

Now, We can factor as;

⇒ p² + 2p - 8 - q² - 6q

⇒ p (p + 2) - 8 - q (q + 6)

⇒ p (p + 2) - q (q + 6) - 8

Thus, Factor of the equation are,

⇒ p (p + 2) - q (q + 6) - 8

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Based on the information in the equation, y = -24x + 648, the TRUE statement is B) Before practice, there are 648 ounces of sports drinks in the cooler.

An equation is an algebraic statement showing that two or more mathematical expressions are equal or equivalent.

The equality or equivalence of an equation is depicted using the equal symbol (=).

Mathematical expressions do not use the equal symbol, but they combine variables with constants, numbers, and values using mathematical operands.

Let the number of ounces in the cooler after practice = y

Let the number of players at the practice who take drinks from the cooler = x

y = -24x + 648

Thus, 648 represents the number of drinks before practice while -24x represents the number of drinks taken by players, making Option B true.

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The probability of correctly guessing which pies were sold on the first day is  near to 2/3.

The Fundamental Counting Principle states that if there are m number of ways to do an activity and n number of ways for a second activity, then there are m x n ways to do the two activities together.

In this case, there are 7 pies and 4 of them were sold on the first day. Therefore, the probability of correctly guessing which pies were sold on the first day is 4/7.

This can be written in simplest form as 2/3.

In conclusion, the probability of correctly guessing which pies were sold on the first day is 2/3.

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Step-by-step explanation:

2,36,53,58

Two place value system:

Twenty-three lakh, sixty-five thousand, three hundred and fifty-eight

Three place value system:

Two crore, thirty-six lakh, fifty-three thousand, three hundred and fifty-eight

3,42,82,627

Two place value system:

Thirty-four million, twenty-eight thousand, six hundred and twenty-seven

Three place value system:

Three crore, forty-two lakh, eighty-two thousand, six hundred and twenty-seven

8,70,13,569

Two place value system:

Eighty-seven million, thirteen thousand, five hundred and sixty-nine

Three place value system:

Eight crore, seventy-one lakh, thirty-five thousand, five hundred and sixty-nine

9,01,50,028

Two place value system:

Ninety million, one lakh, fifty thousand, twenty-eight

Three place value system:

Nine crore, one lakh, fifty thousand, twenty-eight

8,15,52,101

Two place value system:

Eighty-one million, five hundred and fifty-two thousand, one hundred and one

Three place value system:

Eight crore, fifteen lakh, fifty-two thousand, one hundred and one

9,91,60,001

Two place value system:

Ninety-nine million, one lakh, sixty thousand, one

Three place value system:

Nine crore, ninety-one lakh, sixty thousand, one

Answer: X=3

Step-by-step explanation:

The probability that she will hire a woman for the two positions is given as follows:

1/4.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

From the last node, the total number of outcomes is given as follows:

4.

The desired outcomes are Women on the first node and women on the second node, which is one outcome. (the last outcome).

Hence the probability is given as follows:

p = 1/4.

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The required, we can put 125 bottles of water or 8 cans of food in each box, and each box will contain the same number of items.

To find the largest number of relief supplies that can be put in each box, we need to find the greatest common factor (GCF) of 2250 and 144. We can do this by listing the prime factors of each number:

2250 = 2 * 3 * 3 * 5 * 5 * 5 * 2

144 = 2 * 2 * 2 * 2 * 3 * 3

To find the GCF, we need to find the highest power of each common prime factor that appears in both numbers. In this case, the common prime factors are 2 and 3, so we take the highest power of each:

2 * 3 * 3 = 18

So the largest number of relief supplies that can be put in each box is 18. We can check that this works by dividing each quantity by 18:

2250/18 = 125

144/18 = 8

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The equation of the ellipse is:

x²/64 + y²/289 = 1

The standard form of the equation of an ellipse with centered at the origin and major axis parallel to the vertical is:

x²/b² + y²/a² = 1

Coordinates of covertices are ( ±b, 0) = (±8, 0)

Coordinates of foci are (0, ±c) = (0, ±15)

Also c²= a²-b²

a² = b² + c²

a² = 8² + 15²

a² =289

a = √289

a = 17

Using x²/b² + y²/a² = 1:

x²/8² + y²/17² = 1

x²/64 + y²/289 = 1

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Complete Question

Write an equation for an ellipse centered at the origin, which has foci at (0,±15) and co-vertices at (±8,0)

Working out the expression 320.041 - 47.96 gives 272.081

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

320.041 - 47.96

The above expression is a difference or subtraction expression that can be done using a calculator

Using the above as a guide, we have the following:

320.041 - 47.96

Evaluate using a calculator

So, we have

320.041 - 47.96 = 272.081

Hence, teh solution of 320.041 - 47.96 is 272.081

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The concept of Statistical significance as well as practical significance are known to be two different concepts in statistics.

Statistical significance refers to unlikely results not due to chance. P-values are utilized for ascertaining the statistical importance of a particular result by gauging the likelihood of procuring exceptional outcomes under the assumption that the null hypothesis holds true. A significance level of 0.05 or less for the p-value is deemed as statistically meaningful.

Since the Psychology instructor found SAT scores and amount of money carried had a correlation coefficient of r = 0.07 with a p-value of 0.001, showing a significant correlation. The chance of getting a correlation coefficient of 0.07 or greater, if no correlation exists in the population, is very low.

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The answers are A = 46% and B = 20%.

Given that, a table of data, each cell in the table shows the number of cars in that category.

A) The probability that the car's total repair cost is less than $10000 =

86 / (86+35+67) x 100 = 86/188 x 100 = 46%

B) The probability that the car's purchase was more than $40,000 =

40 / (40+86+71) x 100 = 40/197 x 100 = 20%

Hence, the answers are A = 46% and B = 20%.

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a) The number of weeks that she has been saving when she needs $277 is given as follows: 17 weeks.

b) The amount she will need after 5 weeks is given as follows: $505.

The function for this problem is defined as follows:

A(w) = 600 - 19w.

The output of the function is the amount remaining after w weeks.

Hence the number of weeks that she has been saving when she needs $277 is obtained as follows:

277 = 600 - 19w

19w = 600 - 277

w = (600 - 277)/19

w = 17 weeks.

The amount that she needs after 5 weeks is given as follows:

A(5) = 600 - 19 x 5

A(5) = $505.

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Answer: ∠EBJ

Step-by-step explanation:

Starting Angle: ∠EBH

Possible Supplement: ∠EBJ

The correct option- B. the subtraction property of equality is used to arrive at the conclusion. If x + 8 = 10, then x = 2.

According to the equality's feature of subtraction, equality is unaffected when the same amount is subtracted from both sides of an equation.

Given data:

x + 8 = 10

To find the value of x, subtract 8 from both sides:

x + 8 -8 = 10 - 8

x = 2

Thus, the subtraction property of equality is used to arrive at the conclusion. If x + 8 = 10, then x = 2.

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Correct question:

Select the property of equality used to arrive at the conclusion. If x + 8 = 10, then x = 2.

A. the multiplication property of equality

B. the subtraction property of equality

C. the division property of equality

First, you need to find out how much ribbon she has total. Because there are two spools, you multiply 24 x 2. The answer for that is 48. Then you have to figure out how many bows she can make. Each bow uses 1/8 of a piece of yard of ribbon, so you can divide 48 by 8. Your answer would then be 6 bows.

Here are the equations.

[tex]24\times2 = \text{X}[/tex]

[tex]\dfrac{\text{X}}{8} =\text{B}[/tex]

Where X represents the yards of ribbon available and B represents the number of bows that Mari can make.

Complete Question:

Mari makes bows for floral arrangements. She uses 1/8 of a yard ribbon for each bow. How many bows can she make from 2 spools that each has 24 yards ribbon?

The area of the forest after 13 years is  1990.08 [tex]km^2[/tex].

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b[tex])^x[/tex], where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

Here initial area a = 3500[tex]km^2[/tex] ,

Rate of decay = 4.25%= 4.25/100 = 0.0425

Now using exponential decay formula then,

=> [tex]y=a(1-b)^x[/tex] where x=13 years .

=> y = [tex]3500(1-0.0425)^{13}[/tex]

=> y = [tex]3500(0.9575)^{13}[/tex]

=> y = 1990.08 [tex]km^2[/tex]

Hence the area of the forest after 13 years is  1990.08 [tex]km^2[/tex].

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Answer:

a) $299.60

b) $337.05

c) Nicole would pay more at the store

Step-by-step explanation:

a) 10% of $749 = $74.90

60% = ($74.90 x 6) = $449.40

$749 - $449.40 = $299.60

b) 10% = $74.90

50% = $374.50

$749 - $374.50 = $374.50

10% of $374.50 = $37.45

$374.50 - $37.45 = $337.05

Using the laws of multiplication, we can find that after the 4th day the unicorn population of the park is 405.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors.

In the question,

Let the unicorn population be = x.

Now as per the question,

It triples every day.

The function will be = 3x.

The starting unicorn population is 5.

After the 1st day it will get tripled and become 3 × 5 = 15.

After the 2nd day the unicorn population will be 3 × 15 = 45.

After the 3rd day, 3 × 45 = 135.

Finally, after the 4th day, the unicorn population will be = 3 × 135 = 405.

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The statement that best supports the information in the box plots is: D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.

The interquartile range of a data set is the difference between the values that are located on both edges of the rectangular box that is displayed in a box plot.

Interquartile range for the men between 20 - 40 years old = 150 - 110 = 40

Interquartile range for the men between 50 - 70 years old = 125 - 95 = 30

This shows that, D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.

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The average speed of the bike is calculated as: 15.67 mph

The formula for the average speed is:

Average speed = Distance/Speed

We are given the parameters as:

Time = 180 minutes = 3 hours

Distance = 47 miles

The average speed is defined as the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.

Thus:

Average speed = 47/3

= 15.67 mph

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Our calculated t-value of [tex]4.22[/tex] is greater than the critical t-value of 1.684, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.

We can use a one-sample t-test to test the claim that the mean starting salary for college graduates who major in Statistics has increased.

The null hypothesis is that the mean starting salary is still $[tex]54000[/tex], while the alternative hypothesis is that the mean starting salary is greater than $[tex]54000[/tex].

We can calculate the t-statistic as:

t = (sample mean - null hypothesis value) / (standard error of the mean)

= [tex](63500-54000)/(10540/\sqrt{40}[/tex]

= [tex]4.22[/tex]

where [tex]\sqrt{40}[/tex] is the sample size.

The degrees of freedom for the t-test is [tex](n-1) = 39[/tex], where n is the sample size.

Using a t-table or calculator with [tex]39[/tex] degrees of freedom, a one-tailed test, and a significance level of [tex]0.05[/tex], we find the critical t-value to be [tex]1.684[/tex]

Since our calculated t-value of [tex]4.22[/tex] is greater than the critical t-value of [tex]1.684[/tex], we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.

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3.2 x 10^3  is considered to be a rational number.

A rational number is a numerical value expressed as a ratio between two non-zero integers. If any given number can be appropriately displayed in the form of 'a/b,' where both 'a' and 'b' guarantee integer input, it would signify that this specified number adheres to the classification of being labeled as rational.

As we can see from the given number of 3.2 x 10^3, when we write the number after solving it, we have:

3.2 x 10 ^ 3 = 3 .2 x 1, 000

= 3, 200

This can be expressed as 3, 200 / 1 so this is a rational number.

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