the table below shows the soft drinks preferences of people in three age groups. cola root beer lemon-lime under 21 years old 40 25 20 between 21 and 40 35 20 30 over 40 years old 20 30 35 if one of the 255 subjects is randomly selected, find the probability that the person drinks lemon-lime given that they are between 21 and 40.

The variables x and y vary directly will be "y = one-third x".

Option (b)  is the correct answer.

The relationship between two variables that vary directly can be expressed mathematically using an equation.

In this case, we are given the values of x and y, and we need to write an equation that relates them.

To determine the correct equation, The definition of direct variation. When two variables vary directly, it means that if one variable increases by a certain factor, the other variable also increases by the same factor. In other words, their ratio remains constant.

Let's apply this concept to the given values of x and y. We know that x = 18 and y = 6. If we divide x by y, we get:

x / y = 18 / 6 = 3

Since this ratio is constant, we can write an equation that expresses this relationship as y = kx

where k is the constant of proportionality. To find the value of k, we can substitute the given values of x and y:

6 = k(18)

k = 1/3

Therefore, the equation that relates x and y in this case is:

y = (1/3)x

Option (b) "y = one-third x" is the correct answer.

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Answer:

Step-by-step explanation:[tex]2\frac{4}{3}.a\frac{4}{3}[/tex]

The volume of the prism will be reduced to 1/512 of its original size

The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. If the dimensions of a prism are multiplied by 1/8, then the new dimensions are 1/8 of the original dimensions. Therefore, the new base area is 1/64 of the original base area, and the new height is 1/8 of the original height.

Substituting these values into the formula for the volume of a prism, we get:

V' = (1/64)Bh(1/8)

Simplifying, we get:

V' = (1/512)Bh

Therefore, the new volume of the prism is 1/512 of the original volume of the prism.

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Answer:

7

Step-by-step explanation:

if 4 people equals 24 then 7 is your answer

174 of the 300 students in school chose pizza or hamburgers as their favorite meal.

We know that from the definition of Probability that,

Probability of an Event = (The favorable number of incidents under that Event)/(Total number of incident)

Here given that the total number of classmates in first = 50

Number of students whose favorite meal is pizza = 12

Number of students whose favorite meal is hamburgers = 17

So the probability of a student has pizza or hamburger as his favorite meal is = (12 + 17)/50 = 29/50

So for 300 such students, the number of students choose pizza or hamburger as their favorite meal is = 300*(29/50) = 6*29 = 174.

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The triangles ΔABC and ΔDEF are similar triangles and DE = 1.52

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔDEF

And , they are similar triangles

Now , the measure of sides of the triangle ABC are

AB = 11

BC = 7.9

AC = 7.6

And , the measure of side ED = 2.2

Now , corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their

So , AB / DE = k

k = 11 / 2.2 = 5

So , the measure of length of side DF = AC / ( 5 )

DF = 7.6 / 5

DF = 1.52

Hence , the measure of length DF of triangle is 1.52

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The first transformation for this composition is a reflection across line n followed by a 270° rotation about point P.

When we convert a point across a line y = x then x-coordinate and y-coordinate change.

Also when we reflect a point across the line y = -x then signs exist changed and both coordinates change places.

When transformation maps X"Y" Z" .Then the first transformation for this composition exists, and the second exists at 90° rotation about point X'.

Therefore, the correct answer is option B. first transformation across the line n.

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The expression for  a and b of AM, fully simplified, is:

AM = x/2 = √(64a² + 116b² - 64ab)/2

The perimeter of an equilateral triangle is the sum of its three sides. P = 3a is the basic formula for calculating the perimeter of an equilateral triangle, where "a" means one side of the triangle. The sum becomes a + a + a = 3a, because all three sides of an equilateral triangle are equal. Height = √3a/ 2.  Since M is the midpoint of AC, we have:

To find AM, we can use the midpoint formula, which states that the coordinates of the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) are:

M = ((x1 + x2)/2, (y1 + y2)/2)

In this case, we know that M is the midpoint of AC, so we can use the coordinates of A and C to find the coordinates of M. Let's assume that A has coordinates (0, 0) and C has coordinates (x, 0), where x is the length of AC. Then, we can find the coordinates of M as follows:

M = ((0 + x)/2, (0 + 0)/2) = (x/2, 0)

Now, we can use the distance formula to find the length of AM. The distance formula states that the distance between two points with coordinates (x1, y1) and (x2, y2) is:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, we want to find the length of AM, so we can use the coordinates of A and M to find the distance between them. Using the coordinates we found for A and M, we get:

d = √((x/2 - 0)² + (0 - 0)²)

Simplifying this expression, we get:

d = √(x²/4) = x/2

Therefore, the length of AM is x/2. To find x, we can use the fact that BC has length 10b and that the triangle ABC is a right triangle (since AC is the hypotenuse). Using the Pythagorean theorem, we can write:

AC² = AB² + BC²

Substituting the given values, we get:

x²= (8a - 4b)² + (10b)²

Simplifying, we get:

x² = 64a² - 64ab + 16b² + 100b²

x² = 64a² + 116b² - 64ab

Taking the square root of both sides, we get:

x = √(64a² + 116b² - 64ab)

Therefore, the length of AM is:

AM = x/2 = √(64a² + 116b² - 64ab)/2

This is the fully simplified expression for AM in terms of a and b

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The height of the tree was 4.8 m after 2 years its height increased by 12.5 percent then 5.1m is the  height after 1 year if its height is increased with the same ratio.

Given that the height of the tree was 4.8 m

After 2 years the height increased by 12.5 %

Let us find the 12.5% of the tree height

12.5% of 4.8

12.5/100×4.8

0.125×4.8

0.6m

In two years the height is increased by 0.6m

In one year 0.3m is increased.

Now the total height of tree after one years is 4.8+0.3 which is 5.1 m

Hence, the height of the tree was 4.8 m after 2 years its height increased by 12.5 percent then 5.1m is the  height after 1 year if its height is increased with the same ratio.

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The height of the tree was 4.8 m after 2 years its height increased by 12.5 percent. What is its height after 1 year if its height is increased with the same ratio

Answer:

The quadratic equation that represents this problem is

4x² + 56x - 165 = 0

Step-by-step explanation:

The dimensions of the picture are 16 length and 12 width both in inches

The area of the picture without frame = 16 x 12 = 192 square inches

Let the frame have a width of x inches. The frame surrounds the picture on both sides of the length and both sides of the breadth

Then the length with the frame = x + 16 + x = 2x + 16  inches

The width of the frame = x + 12 + x = 2x + 12 inches

The area of the painting with the frame
= (2x + 16)(2x + 12)

Using the FOILmethod to multiply these two expressions we get
(2x + 16)(2x + 12) = (2x)(2x) + 2x(12) + 16(2x) + 16 x 12

= 4x² + 24x + 32x + 192

= 4x² + 56x + 192

The area of the frame by itself is the area with frame - area of picture alone

Area of frame = 4x² + 56x + 192 - 192

=>  4x² + 56x

We are given the area of frame is 165 square inches
Hence we get
4x² + 56x = 165

To represent as a quadratic equation move 156 from the right side to the left side to get 0 on the right side

4x² + 56x - 165= 0

ANSWER

It would take Max and Jan 30 minutes to mow the lawn together.

It will take Max 45 minutes to mow the lawn alone, and it will take Jan twice as long, so it will take her 90 minutes to mow the same lawn alone. Working together, we can use the equation 1/45 + 1/90 = 1/t to solve for t, where t is the number of minutes it would take to mow the lawn together.

First, we need to simplify the equation:

1/45 + 1/90 = 1/t

2/90 + 1/90 = 1/t

3/90 = 1/t

1/30 = 1/t

Now we can solve for t by cross-multiplying:

1/30 = 1/t

t = 30

So, it will take Max and Jan 30 minutes to mow the lawn together.
To find how long it would take Max and Jan to mow the lawn together, we can solve the equation 1/45 + 1/90 = 1/t for t.

First, find a common denominator for the fractions, which in this case is 90. Then, rewrite the equation as: (2/90) + (1/90) = 1/t.

Next, add the fractions on the left side: 3/90 = 1/t.

Now, to solve for t, take the reciprocal of both sides: t = 90/3.

Finally, simplify: t = 30.

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Answer:

The surface area of the square pyramid is approximately 864.2 square centimeters.

Step-by-step explanation:

To solve for the surface area of a square pyramid, you need to find the area of the base and the area of each of the four triangular faces.

The area of the base is simply the square of the length of one side. So, for a base with edge lengths of 15 centimeters, the area of the base is:

15^2 = 225 square centimeters.

To find the area of each of the four triangular faces, you need to use the formula:

(area of triangle) = 1/2 x (base of triangle) x (height of triangle)

For a square pyramid, the height of each triangular face is equal to the slant height of the pyramid, which can be found using the Pythagorean theorem:

(hypotenuse)^2 = (height)^2 + (1/2 x base)^2

In this case, the height is given as 20 centimeters and the base is half of the base edge of the pyramid, or 7.5 centimeters. So, the slant height is:

hypotenuse = sqrt(20^2 + 7.5^2) = 21.3 centimeters

Now you can use this slant height to find the area of each triangular face:

(area of triangle) = 1/2 x (base of triangle) x (height of triangle)

= 1/2 x (15) x (21.3)

= 159.8 square centimeters

So, the total surface area of the square pyramid is:

225 (area of base) + 4 x 159.8 (area of each triangular face)

= 225 + 639.2

= 864.2 square centimeters.

Therefore, the surface area of the square pyramid is approximately 864.2 square centimeters.

The notation for the given compositions of transformations is R180∘[tex]R_x[/tex]=2.

The composition of a reflection across the line x=2, followed by a rotation of 180 degrees about the origin, can be represented using function notation as follows:

                                        R180∘[tex]R_x[/tex]=2

Where:

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Solving a system of equations we can see that she has 6 $50 bills and 5 $100 bills.

Let's define the variables.

x = number of $50 bills.

y = number of $100 bills.

We know that there are 11 in total, and the value in total iis $800, then we can write the system of equations:

x + y = 11

x*50 + y*100 = 800

Let's isolate x in the first equation:

x = 11 - y

Replace that in the second one:

(11 - y)*50 + y*100 = 800

550 - y*50 + y*100 = 800

550 + y*50 = 800

y*50 = 800 - 550

y*50 = 250

y = 250/50 = 5

And then:

x = 11 - y = 11 - 5 = 6

These are the numbers.

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To find the limit of (x + x²)/(6 − 5x²) as x approaches infinity, we can first simplify the expression and then apply l'Hospital's Rule if necessary.

1. Factor x out of the numerator: x(1 + x)/(6 - 5x²).

2. Divide both the numerator and the denominator by x²: lim (x→∞) (1 + x)/(6/x² - 5x²/x²) lim (x→∞) (1/x + 1)/(6/x² - 5)

3. Now apply the limit: lim (x→∞) (1/x) = 0 and lim (x→∞) (6/x²) = 0.

So, we have: lim (x→∞) (0 + 1)/(0 - 5) = 1/(-5)

The limit of the function as x approaches infinity is -1/5.

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Answer:

3y

Step-by-step explanation:

Answer:

The answer is 60

Step-by-step explanation:

Solution:

Complete the ratio

[tex] \frac{4}{?} = \frac{1}{15} \\ [/tex]

Hope you understand

The real zeros of the polynomial function P(x) = x⁵ − 50x³ + 49x are -1, 0, and 1.

To find the zeros of this function, we can factor it by first factoring out an x to get P(x) = x(x⁴ − 50x² + 49). Then, we can factor the quadratic expression inside the parentheses using the difference of squares formula, which gives us P(x) = x(x² − 1)(x² − 49). Simplifying further, we have P(x) = x(x − 1)(x + 1)(x - 7)(x + 7).

Therefore, the zeros of P(x) are the values of x that make each factor equal to zero. This gives us x = -7, -1, 0, 1, and 7. Since all of these values are real, we conclude that the number of real zeros of P(x) is 5.

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Answer:

see explanation

Step-by-step explanation:

1

since Δ ABT is a 45- 45- 90 then it is isosceles with ∠ A = ∠ T and

legs are congruent, that is

BT = AB = x = 8

using the sine ratio and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AT}[/tex] = [tex]\frac{8}{y}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

y = 8[tex]\sqrt{2}[/tex]

so x = 8 and y = 8[tex]\sqrt{2}[/tex]

2

using the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex] , then

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{a}{8}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 8 )

a = 8[tex]\sqrt{3}[/tex]

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{b}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

b = 8 × 2 = 16

so a = 8[tex]\sqrt{3}[/tex] and b = 16

Answer:

1.  x = 8,  y = 8√2

2.  a = 8√3,  b = 16

Step-by-step explanation:

The interior angles of a triangle sum to 180°.

From inspection of triangle ABT, angle B is 90° and angle T is 45°. Therefore, angle A is also 45°. This means that this triangle is a special 45-45-90 triangle.

The measures of the sides of a 45-45-90 triangle are in the ratio 1 : 1 : √2.

Therefore, the formula for the ratio of the sides is b : b : b√2 where:

From inspection of triangle ABT, sides AB and BT are the legs of the triangle, and side AT is the hypotenuse. Therefore, as leg AB measures 8 units, then b = 8.

The side labelled "x" is the other leg of the triangle (side opposite the 45° angle). Therefore:

[tex]\rm \implies x = b=8[/tex]

The side labelled "y" is the hypotenuse of the triangle (side opposite the right angle). Therefore:

[tex]\implies \rm y=b\sqrt{2}=8\sqrt{2}[/tex]

[tex]\hrulefill[/tex]

From inspection of the interior angles of the given triangle, it is a special 30-60-90 triangle.

The measures of the sides of a 30-60-90 triangle are in the ratio 1 : √3 : 2.

Therefore, the formula for the ratio of the sides is c: c√3 : 2c where:

The side opposite the 30° angle is 8 units. Therefore, c = 8.

The side labelled "a" is the side opposite the 60° angle. Therefore:

[tex]\rm \implies a = c\sqrt{3} = 8\sqrt{3}[/tex]

The side labelled "b" is the side opposite the 90° angle. Therefore:

[tex]\implies \rm b = 2c = 2 \cdot 8 = 16[/tex]

The answer is none, as there is no overtime worked in this scenario. The Option D is correct.

In this scenario, you have worked 40 hours in one week. Overtime means any hours worked beyond the standard or regular hours of work which is usually 40 hours per week for full-time employment in many countries.

Here, you have worked 40 hours in this week, this means there are no hours that exceed the standard work hours, and so, there is no overtime worked.

As a result, there would be no additional pay for overtime in this case, and the total earnings would be based on the regular hourly wage multiplied by 40 hours of work.

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Answer:

Step-by-step explanation:

0.99

The weight of Bill's pack is a quantitative variable, so the weight can take on any numerical value within a certain range (in this case, likely between 0 and 100 lbs or so).

The type of variable for the weight of Bill's pack is a continuous variable, and the corresponding level of measurement is the ratio level of measurement.

Continuous variable: A continuous variable is a variable that can take on any value within a given range. In this case, the weight of Bill's pack can take on any value within a certain range (e.g., from 0 lb to 100 lb or more), making it a continuous variable.
Ratio level of measurement: The ratio level of measurement has a true zero point and allows for meaningful comparisons and calculations, such as multiplication and division. Since the weight of Bill's pack has a true zero point (0 lb) and allows for meaningful comparisons (e.g., one pack can be twice as heavy as another), it falls under the ratio level of measurement.

Hence,  The weight of Bill's pack (48.3 lb) is a continuous variable, and its corresponding level of measurement is the ratio level of measurement.

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The third root of 20 would give a result of

Radical numbers, are also called roots or surds.

These are mathematical expressions that represent the inverse operation of exponentiation.

They are used to find the value that, when raised to a certain power, results in a given number.

The most common types of radical numbers are

The cube root of 20 also written as ∛20 is solved using calculator to give 2.714417617 and to four decimal place will give 2.7144

This means that 2.714417617 x 2.714417617 x 2.714417617 is approximately equal to 20

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The temperature indoors and outdoors the same after 16 minutes

The function is given as

f(x) = -5log4 (x-15)

When the temperatures are equal, we have

f(x) = 0

So, the equation becomes

-5log4 (x-15) = 0

Divide by -5

So, we have

log4 (x-15) = 0

Take the exponent of both sides

x - 15 = 4^0

So, we have

x - 15 = 1

Evaluate

x = 16

Hence, the time is 16 minutes

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The term is called an identity element. In multiplication, the identity element is one because any number multiplied by one results in the same number. In addition, the identity element is zero because any number added to zero results in the same number.

The term in mathematics for the operation or number that leaves others unchanged when combined with them is called the identity element.

It is also known by the name of neutral element.

In multiplication, the identity element is one (1) because when you multiply a number by one the result remains the same as the original number. For any number a,

a1=1a=a.

While in addition, the identity element is zero (0) because when you add zero to a number, the result remains the same as the original number. For any number a,

a+0=0+a=a.

There is no identity element for subtraction, and division only has an identity element for certain sets.

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The coefficient of determination for a linear regression model fitting with bivariate dataset ( scatterpot present in above figure) is equals to the 90.097.

When we study about linear regressions, usually analyze two coefficients that help us to know about the quality of the regression model and strength of linear relationship between the variables. One is called the coefficient of determination, denoted by R². Consequently, by observing a scatter plot, we can estimate the value of these coefficients. We have a scatterpot for a linear model fitting of the bivariate dataset is present in above figure. Coefficient of determination is always positive. When data are very closely arranged along a approximate line, then coefficient of determination is more near to 1 (In percentage it is 100). Here points are almost closely arranged . So percentage should be near to 100. So possible answer is 90.097. Hence, the answer is 90.097.

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Complete question :

The above figure complete the question.

What is the coefficient of determination for a linear model fitting the following bivariate dataset?

Answer:

The surface area of a cube is given by the formula:

SA = 6s^2

where SA is the surface area and s is the length of one side.

In this case, we know that the surface area is 96 square meters, so we can set up an equation:

96 = 6s^2

Solving for s, we get:

s^2 = 16

s = 4

So the length of one side of the cube is 4 meters.

The volume of a cube is given by the formula:

V = s^3

where V is the volume and s is the length of one side.

Plugging in s = 4, we get:

V = 4^3 = 64 cubic meters

So the volume of the cube is 64 cubic meters.

Step-by-step explanation:

gg

The probability they are both seniors is 0.194

There are a total of 22 possible options to select.

The probability of ranomly selectinga senior is equal to the quotient between the number of seniors and the total number of options, so for the first selection the probability is:

P = 10/22

For the second selection there are 9 seniors and 21 options, so the probability here is:

Q = 9/21

The joint probability is the product of these two, so we get:

p = 10/22*9/21 = 0.194

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