r to the nearest whole number.
12) Huong enlarged the size of a painting to a
width of 12 cm. What is the new height if
it was originally 4 cm wide and 3 cm tall?
14) Bill enlarged the size of a photo to a
height of 6 cm. What is the new width if
it was originally 2 cm tall and 4 cm wide?

Answer: 27

Step-by-step explanation:

Mean = Sum of data/Number of data = (2 + 7 + x)/3 = 12

(x+9)/3 = 12

x+9 = 36

x = 27

The probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]

The given parameters are

The total number of people is

n = 20

2 of the 20 people are to be selected.

So, the number of selection is

[tex]n = ^nC_r[/tex]

This gives

[tex]n = ^{20}C_2[/tex]

The expression that represents both students being sophomore is

[tex]n = ^{6}C_2[/tex] --- i.e. 2 students selected from 6

The probability is then represented as:

[tex]\frac{^{6}C_2}{^{20}C_2}[/tex]

Hence, the probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]

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Answer:

a

Step-by-step explanation:

edge 2023

Using the given recipe, he will need 6 cups of milk to make 18 servings.

We know that the recipe for 6 servings, calls for 2 cups of milk.

Miguel wants to do 18 servings, Then he needs to use the recipe:

18 = x*6

Solving the linear equation for x:

x = 18/6 = 3

So he needs to use his recipe 3 times.

And we know that for 6 servings he needs 2 cups of milk, then for 18 he needs:

3*(2 cups) = 6 cups of milk.

Using the given recipe, he will need 6 cups of milk to make 18 servings.

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Answer:

2

Step-by-step explanation:

• Multiplying two numbers with same bases is the same as adding their powers:

∴ [tex](\frac{4^{\frac{5}{4} } \cdot 4^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](\frac{4^{\frac{5}{4} } ^ + ^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

• Dividing two numbers with same bases is the same as subtracting their powers:

∴  [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](4^{{\frac{6}{4} - \frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒  [tex](4^{1})^{\frac{1}{2} }[/tex]

⇒  [tex]4^{\frac{1}{2}[/tex]

• Raising anything to the power of  [tex]\frac{1}{2}[/tex] is the same as square-rooting it:

∴  [tex]4^{\frac{1}{2}[/tex]

⇒ [tex]\sqrt{4}[/tex]

⇒ 2

Answer:

9a^3b^3

Step-by-step explanation:

The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number

Find the prime factors of each term in order to find the greatest common factor (GCF).

The diagram where angles 1 and 2 form a linear pair is option D which is that a horizontal line has 1 line extending from it. Angles 1 and 2 are formed.

Given that angle 1 and 2 form a linear pair.

We know that a linear pair is an angle that are formed when two lines intersect each other at a single point.

In our case when a horizontal line has 1 line extending from it and when angles 1 and 2 are formed shows a linear pair.

In first part when two lines intersect they donot form 4 angles.

In second part when 3 lines extend from a point they don't form right angle between the lines.

Hence the linear pair angles are shown by the statement that a horizontal line has 1 line extending from it. Angles 1 and 2 are formed.

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Answer:

ray

Step-by-step explanation:

Rays only have one endpoint, so it continues infinitely in one direction. Segments have TWO endpoints.

The solutions are { -1,-11}

Lets solve the given equation:

x^2 + 11x + 121/4 = 125/4

Subtracting 125/4 from both sides:

=>x^2 + 11x + 121/4-125/4= 125/4 -125/4

=> x^2 + 11x - (-4/4) = 0

=> x^2 +11x -(-1) = 0

=>x^2 + 11 x + 1 = 0

This is a quadratic equation so we will use the determinant (b^2-4ac)

a = 1

b = 11

c = 1

b^2-4ac = 11^2-4*1*1 = 117

So this equation has two solutions:

x = (-b -/+ √(b^2-4ac) ) / 2a

x = (-11 -/+ √(117) ) / 2

x = (-11 -/+ 3√(13))/ 2

x = -0.91 or x = -10.9

x = -1 or x = -11 ( rounding off)

hence the solutions are { -1,-11}.

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The data of the customer responses would be classified as ordinal data.

Ordinal data is a category of categorical data that has a predetermined order or scale. Ordinal data, for instance, is said to have been gathered when a respondent rates their level of financial contentment on a scale from 1 to 10. There is no established scale for measuring the variance of each score in ordinal data.

Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. On an ordinal scale, these data are available. By having a ranking, the ordinal scale differs from the nominal scale.

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Performing subtraction operations on the given vectors gives;

u - v = <-2 - 3, -7 - (-4) > = <-5, -3>

Therefore;

u - w = <-2 - 5, -7 - 1> = <-7, -8>

u - w = <-7, -8> which corresponds with graph 2

Therefore;

w - v = <5 - 3, 1 - (-4)> = <2, 5>

w - v = <2, 5> which corresponds with graph 3

Therefore;

v - u = <3 - (-2), -4 - (-7)> = <5, 3>

v - u = <5, 3> which corresponds with graph 4

Therefore;

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Answer:

(x+9) (x-8)

Step-by-step explanation:

Edmentum/Plato

Answer:

Step-by-step explanation:

B is the answer

The standard deviation is 0.1243, given the variance to be 0.01545, making option B the right choice.

Dispersion is measured by variance. A metric called a "measure of dispersion" is used to assess how variable data are concerning an average value. There are two sorts of data: grouped and ungrouped. Data is referred to as grouped data when it is presented as class intervals. On the other hand, it is referred to as ungrouped data if it comprises just individual data points. For both types of data, the sample and population variances may be calculated.

The variance of the provided data is obtained by taking the square of the standard deviation. The standard deviation is used to determine how widely distributed the data points are about the mean. In other words, the standard deviation is used to determine how observations in a data collection deviate from the mean. While the standard deviation has the same unit as the population or the sample, variance is represented in square units.

In the question, we are asked to find the standard deviation, if the variance is 0.01545.

We know that Variance = (Standard Deviation)².

This gives us:

Standard Deviation = √Variance,

or, Standard Deviation = √0.01545,

or, Standard Deviation = 0.12429802894 ≈ 0.1243.

Thus, the standard deviation is 0.1243, given the variance to be 0.01545, making option B the right choice.

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Answer:

1) (x-6)^2=49

2) C

Step-by-step explanation:

Subtract 12 x and you get

-x^2-12x+13=0

You will be left with, after making a perfect square

(x-6)^2=49

To get rid of the squared/2nd power, add plus or minus to the opposite side and square root both sides. You will be left with

x-6=plus or minus 7

Your answer comes out to the to problem. Setting both to 0, you get -13, and 1. -6 plus 7 is 1, and -6 plus a -7 is -13.

There are 2 people are stepping onto the roller coaster per minute at peak time

According to statement

Given Flow time = 10 minutes.

Given Inventory = 20.

We use the formula then

I = R × T,

Therefore R = I / T.

Substitute the values in formula then

Flow rate = 20 / 10 = 2 people per minute.

So, There are 2 people are stepping onto the roller coaster per minute at peak time

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Answer:

x = - 1

Step-by-step explanation:

- 15 = 22x + 7 ( subtract 7 from both sides )

- 22 = 22x ( divide both sides by 22 )

- 1 = x

Answer:

Step-by-step explanation:

the third one is correct

[tex]6 \times 3 - \frac{18}{9} \\ (6 \times 3) - (18 \div 9)[/tex]

The rate at which Sean drank the slushy is 5 milliliters  per second.

The time it would take to drink all the slushy is 55 seconds.

In order to determine the speed at which the slushy was drank, divide the slushy drank in 13 seconds by 13 seconds.

Speed = slushy drank in 13 seconds / time

(275 - 210) / 13

65 / 13 = 5 milliliters  per second

Time it would take to drink all the slushy =total milliliters of the slushy / speed

275 / 5 = 55 seconds.

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The surface area of the square pyramid is: 220 units².

Surface area of a square pyramid = 1/2(base perimeter)(slant height) = 1/2(P)(l).

Given the following:

Perimeter of base (P) = 4(10) = 40 units

Slant height (l) = 11 units

The surface area of the square pyramid = 1/2(40)(11)

Surface area of the square pyramid = 220 units²

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Option D. What we can conclude is that  If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

An operation is done on a first column of numbers. When this operation is repeated on the second column, we would have option D.

If the sum of the numbers that are in the third can be seen to be greater than three, then the sums are not going to be seen as equal

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One column of numbers consists of 28, 42, and 14. When the digits of the numbers are added together, the result is 2 + 8 + 4 + 2 + 1 + 4 = 21, and when the digits of 21 are then added together, the end result is 2 + 1 = 3. If the same process is performed on the numbers in a second column, what can be concluded?

A. If the end result from the second column is also 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

B. If the end result from the second column is not 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.

C. If the end result from the second column is also 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.

D. If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

Answer:

Step-by-step explanation:

hello :

the perimeter of triangle is : P= (x-z+yx)+( z+x+xz)+A

given  P=x+y+xy  calculate the third side  A

x+y+xy = (x-z+yx)+( z+x+xz) so :  A=x+y+xy -x+z-yx-z-x-xz....continu

a=

If the perimeter of the triangle park is x + y + xy meter. Then the third length of the triangle will be y - x - xz meters.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The perimeter of the triangle is determined by adding together all of its sides.

The perimeter of the triangle park is x + y + xy meter. The length of the two sides are x - z + yx meter and z + x + xz meter.

Let the third side be 'A'. Then the third length of the triangle is given as,

x + y + xy = (x - z + xy) + (z + x + xz) + A

x + y + xy = x - z + xy + z + x + xz + A

y = x + xz + A

A = y - x - xz

If the perimeter of the triangle park is x + y + xy meter. Then the third length of the triangle will be y - x - xz meters.

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The length of hypotenuse when the value of legs of a right angled triangle are 7 and 7 feet is 9.9 feet.

Given that a and b are legs and c is the hypotenuse. length of legs of a right angled triangle  are 7 feet and 7 feet.

We have to find the value of c in the right angled triangle.

In this we have to apply pythagoras theorem because it says tat the square of hypotenuse is equal to the sum of squares of base and perpendicular of that right angled triangle.

[tex]H^{2} =P^{2} +B^{2}[/tex]

H=c

P=7 feet

B=7 feet.

Put the values in the above rule:

[tex]c^{2} =7^{2} +7^{2}[/tex]

[tex]c^{2}[/tex]=49+49

[tex]c^{2}[/tex]=98

c=9.899

After rounding off to nearest tenth we will get c=9.9.

Hence the value of c is 9.9 which is the length of hypotenuse.

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(C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.

To find what fraction of the marbles now in the bag is blue:

Therefore, (C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.

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Complete question:

A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?

(A) 1/5

(B) 1/4

(C) 1/3

(D) 2/5

(E) 1/2

Answer:

Q₂ = 10

Step-by-step explanation:

Given data set:  3, 9, 12, 4, 6, 40, 25, 14, 10

Q₂ is the median (the middle value) of the given data set when the data set is ordered from smallest to largest.

Order the values in the data set:

3, 4, 6, 9, 10, 12, 14, 25, 40

As the number of values is odd, the middle value is the 5th value.

Therefore, the median (Q₂) of the given data set is 10.

If the number of data values is even, and therefore there are two middle values, the median is halfway between them.

Answer:

Find the rate of sales tax

R= 9000/120000

=0.075

=7.5%

So, the rate is 7.5%

Between 48% and 54% believe that their health is extremely important.

According to the statement

Given that a random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important.

Here

Sample size n =1001

sample proportion p = 0.51

By these values we calculate the Standard error of proportion.

So, Standard error of proportion = 0.0158.

Since sample size is sufficiently large we can take Z critical value for confidence interval

Z critical value for 95% = 1.96

Margin of error = ±1.96*std error

= ±0.0310

confidence interval = 0.51 ±0.0310

= (0.48, 0.54)

So, Between 48% and 54% believe that their health is extremely important.

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More than 93 percent of all blank coupons are distributed as freestanding inserts in newspapers.

What is percent?

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Answer: -4, 0, 2

Step-by-step explanation:

The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].