Teresa surveyed 100 students about whether they like pop music or country music. Out of the 100 students surveyed, 41 like only pop, 35 only like country, 11 like both pop and country, and 13 do not likeeither pop or country. Complete the two-way frequency table.

Answer: Undefined

Step-by-step explanation:

There is not enough information to complete the task.

Answer:

Jonathan and Seth

Step-by-step explanation:

multiple the laps by 2 youll get the minutes

Answer:

y = [tex]\frac{-4}{3}[/tex] x + [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

-8x - 6y = -8   Add 8x to both sides

-6y = 8x  - 8   Divide all the way through by -6

y = [tex]\frac{-8}{6}[/tex] c + [tex]\frac{8}{6}[/tex]  Simplify

y = [tex]\frac{-4}{3}[/tex] x + [tex]\frac{4}{3}[/tex]

A negative times a negative is a positive.

A negative times a positive is a negative.

Answer: A. 100/x^2 = h, B. v(x) = x^2*h

Step-by-step explanation:

A. Volume = b * h

100 cm^2 = x^2 * h

100/x^2 = h

B. v(x) = x^2*h

Answer:

y = [tex]\frac{-5}{2}[/tex] x + 6

Step-by-step explanation:

We want the form

y = mx + b

5x + 2y =12   Subtract 5x from both side of the equation

2y = -5x + 12  Divide all the way by 2

y = [tex]\frac{-5}{2}[/tex] x + 6

Using the normal distribution, the probabilities are given as follows:

a) Between 210 and 220 for a single egg: 0.2586 = 25.86%.

b) Between 210 and 220 for the average of 25 eggs: 0.8164 = 81.64%.

c) Third quartile for the average of 25 eggs: 213 milligrams.

d) Less than 220 if less than 210: 0.1011 = 10.11%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the cholesterol levels are given as follows:

[tex]\mu = 215, \sigma = 15[/tex]

For item a, the probability is the p-value of Z when X = 220 subtracted by the p-value of Z when X = 210, hence:

X = 220:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (220 - 215)/15

Z = 0.33

Z = 0.33 has a p-value of 0.6293.

X = 210:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (210- 215)/15

Z = -0.33

Z = -0.33 has a p-value of 0.3707.

Hence the probability is:

0.6293 - 0.3707 = 0.2586.

For item b, we are dealing with a sample of 25, hence we apply the Central Limit Theorem as follows:

n = 25, s = 15/sqrt(25) = 3.

X = 220:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (220 - 215)/3

Z = 1.33

Z = 1.33 has a p-value of 0.9082.

X = 210:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (210 - 215)/15

Z = -1.33

Z = -1.33 has a p-value of 0.0918.

Then the probability is:

0.9082 - 0.0918 = 0.8164 = 81.64%.

The third quartile is X when Z has a p-value of 0.25, so X when Z = -0.675, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

-0.675 = (X - 215)/3

X - 215 = -0.675 x 3

X = 213.

The conditional probability in item d is calculated as follows:

P(X < 210)/P(X < 220) = 0.0918/0.9082 = 0.1011 = 10.11%.

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We will solve as follows:

*First: We find out the value of the product:

Now, we find out from the other expressions:

*First:

[No]

*Second:

[Yes]

*Third:

[Yes]

*Fourth:

[No]

*Fifth:

[Yes]

The area of the given flag is 1187.5 square inches.

Given that, the United States flag has a height : width ratio of 10 : 19.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Let the sum of Height and width of flag be x.

Now, 10+19=29

⇒ 10/29 ×x = 25

⇒ 10x=29 × 25

⇒ x=72.5

So, width = 72.5-25 =47.5

Area of flag = Length × Width

= 25 × 47.5

= 1187.5 square inches

Therefore, the area of the given flag is 1187.5 square inches.

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Answer:

10.5

Step-by-step explanation:

The 5 chicken wings will cost $10.5 to Enola.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Price of 14 chicken wings bought by Enola = $29.40.

To find the price of 5 wings,

Use ratio property,

Price of 14 chicken wings = $29.40

Price of 1 chicken wing = 29.40 / 14

                                       = 2.1

Price of 5 chicken wings = 2.1 x 5 = 10.5

The price of the 5 chicken wings is $10.5.

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The given triangle is a right angled triangle having the follwoing sides;

Hypotenuse = x (longest side)

Opposite = 14 (side facing the given acute angle)

Theta = 15 degrees

Using the SOH trigonometry identity;

sin 15 = opposite/hypotenuse

sin15 = 14/x

x = 14/sin15

x = 14/0.2588

x = 54.09

x is approximately equal to 54.1. Option B is coorect

EXPLANATION:

1.The first thing we must do is use a suitable method that allows us to find the value of y for the two equations of the line

2. The correct and most appropriate method is the matching method.

The exercise is as follows:

Answer:

solve for what? x or y? or anything another

Step-by-step explanation:

if x

1.

[tex] - \sqrt[4]{2} \sqrt[4]{2} [/tex]

2.

[tex]x = (2 \: or \: \infty )[/tex]

so hope it help

Answer:

B

Step-by-step explanation:

[tex]f(x) = 7( { \frac{1}{2} })^{3x} \\ f(x) = 7 ({ \frac{1 \times 1 \times 1}{2 \times 2 \times 2} })^{x} \\ f(x) = 7 ({ \frac{1}{8} })^{x} [/tex]

Answer:

Step-by-step explanation:

    2

3x + y =-12x

Answer:

Step-by-step explanation:

y= 2

45−6x

2−3 y=

2− 45−6x

2 −3 , ∣x∣≤ 2

30

​

​

Equation in the form of f(x) for the solutions of x=-4 and x=3 and a point (0,-60) is equal to f(x) = 5(x+4)(x-3) .

As given in the question,

For the function f(x):

Standard form of the equation with solution x =a and x=b is:

f(x) = k(x-a)(x-b)

Solutions for the given function f(x) is x =-4 and x=3 and a point (0,-60)

is given by:

f(x) = k(x-(-4))(x-3)

     = k(x+4)(x-3)

Point at (0,-60) we get,

-60 = k ( 0+4)(0 -3)

⇒-60 = -12k

⇒ k =5

Required equation is :

f(x) = 5(x+4)(x-3)

Therefore, equation in the form of f(x) for the solutions of x=-4 and x=3 and a point (0,-60) is equal to f(x) = 5(x+4)(x-3) .

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Here, we want to drop a box plot on the number line given the listed numbers

We have the box plot as follows

The listing of the numbers is the actual way the numbers on the box plot will be listed from left to right

We have this as follows;

Given the system of equations:

x + y - z = 4 eq.(1)

3x + 2y + 4z = 17 eq.(2)

-x + 5y + z = 8 eq.(3)

Add the equations 1 and 3

so,

x + y - z + ( -x + 5y + z ) = 4 + 8

x + y - z - x + 5y + z = 12

6y = 12

y = 12/6 = 2

Substitute with y at eq. (1)

So,

x + 2 - z = 4

x - z = 4 - 2

x - z = 2 eq. (4)

Substitute with y at eq.(2)

3x + 2 * 2 + 4z = 17

3x + 4 + 4z = 17

3x + 4z = 17 - 4

3x + 4z = 13 eq.(5)

solve the equations (4) and (5) together

x - z = 2

3x + 4z = 13

Multiply [ x - z = 2 ] by 4

4x - 4z = 8

3x + 4z = 13

Add the last two equations

4x - 4z + 3x + 4z = 8 + 13

7x = 21

Divide both sides by 7

x = 21/7 = 3

So, x = 3 and y = 2

Substitute with the values of x and y at the equation [ -x + 5y + z = 8 ]

So,

-3 + 5 * 2 + z = 8

solve for z

-3 + 10 + z = 8

z = 8 + 3 - 10

z = 11 - 10 = 1

So,

x = 3 , y = 2 and z = 1

Answer:

a=1

Step-by-step explanation:

Angles 1 and 2 are remote interior angles while angle 3 exists as a remote exterior angle. The required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.

The triangle exists a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

Angles 1 and 2 are remote interior angles while angle 3 exists as a remote exterior angle. So there exists a property of a triangle in that the sum of the remote interior angles exists equivalent to the remote exterior angle.

∠1 +∠2 = ∠3.

Therefore, the required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.

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The slope of the line parallel to y = 4  / 7 x + 7 is 4  /7.

The slope of the line perpendicular to y = 4  / 7 x + 7 is - 7 / 4.

The equation of a line can be described as follows:

y = mx + b

where

The equation of the line given is y = 4  / 7 x + 7.

Parallel lines have the same slope.

Therefore, the slope of the line parallel to the given equation of the line is 4 / 7.

A line perpendicular to each other follows the rule below:

m₁ m₂ = -1

where

Therefore, let's find the slope of the line perpendicular to the given equation.

4 / 7 m₂ = -1

cross multiply

4m₂ = -7

m₂ = - 7 / 4

Therefore, the slope of the line perpendicular to the equation is - 7/4

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We are given a rectangle with the following dimensions;

Also, placed inside the large rectangle, is a smaller shaded rectangle which has the dimensions;

The ratio of both figures can be expressed as follows;

Substituting for the values of both figures, we now have;

Answer:

Explanation:

The angular coefficient is also referred to as the slope of the line.

Given that the slope of the lining joining these pair of points are the same:

• (-2, 1) and (1, 4)

• (1, -2) and (3, p)

Then:

We solve the equation for p:

The sentence that properly uses semicolons in a serial list is B. There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.

A semicolon is a punctuation mark consisting of a period put on top of a comma.

Semicolons can be used for the following purposes:

Thus, the proper use of semicolons in a serial list is Option B.

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Answer:

B. There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.

Step-by-step explanation:

Step 1

Find the equation of both lines using

Where,

Hence,

For the second line we will have

Step 2

Hence expressed the graphed solution as a piecewise function

Answer:

[tex](f \circ g)(2)=2[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=-2x+8\\g(x)=\sqrt{x+7}\end{cases}[/tex]

The composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x).  

Therefore (f o g)(2) means to substitute the result of g(2) in place of the x in the function f(x).

[tex]\begin{aligned}\implies (f \circ g)(2) &=f[g(2)]\\&=f(\sqrt{2+7})\\&=f(\sqrt{9}) \\& = f(3)\\& = -2(3)+8\\&=-6+8\\&=2\end{aligned}[/tex]

t(x) = x² + 8x - 20

Coordinate(s) of the solutions/roots

x² + 8x - 20 = 0 ==> (x -2)(x + 10) = 0

roots: x= 2 and x = -10

coordinate of the y-intercept

y-intercept is when x = 0 ==> t(x) = x² + 8x - 20 when x = 0: t(0) = -20

y-intercept: y = -20

location of the line of symmetry

x = -4

y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36) and line of symetry x = -4

coordinate of the vertex

(-4, -36)

y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36)

whether the graph opens up or down and how you know

Opens up

Because the coefficient of x² is positive

   Translation is defined as an interpretation into another language or context. The Spanish word "bueno," which translates to "good," serves as an illustration. A translation can involve explaining to a parent the significance of their teen's expression.

The translation equation or formula is written as g(x) = f(x+k) + C.

Example

(x -3, y - 2)

x - 3 y - 2 ;

x-3 y-2

x-3y - 2

x² -  x - 6 =0

-x + 3 > 2x + 1

line(1, 2),(3 ,1)

f(x) = x³

prove tan²(x) - sin ²(x) = tan²(x) sin²(x)

d /dx(3x + 9/2 -x)

(sin²(0))

sin (120)

lim(x -> 0 (xln(x))

= 0 3/2n.

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Answer:

183 miles per hour.

Explanation:

The estimated velocity(v) at the end of a drag race is modeled using the formula below:

Given:

• The horsepower, p = 1311

• The weight (in pounds), w = 2744 pounds.

Substitute into the formula above:

The velocity is approximately 183 miles per hour.