gwen is interested in the effect of bananas on the speed and endurance of high school cheerleaders. she recruits 20 cheerleaders from high schools in california. each cheerleader was asked to run as many laps as they could in 20 minutes on a standard 100m track. two weeks later the same cheerleaders were asked to run as many laps as they could in 20 minutes, but were asked to eat a banana 10 minutes prior to starting. the number of laps completed (to the nearest quarter lap) was recorded. what is the sample of this study?

The coordinates of the vertices after a reflection over the line x = 2.

D = (8, 5)

E = (6, 5)

F = (4, 8)

G = (7, 8)

There are two ways of translation.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The coordinates:

D = (-4, 5)

E = (-2, 5)

F = (0, 8)

G = (3, 8)

The line x = 2.

We count the units from the line x = 2.

After the reflection, the number of units of each coordinate from the line

x = 2 must be equal to the number of units from the line x = 2 before the reflection.

Thus,

The reflected coordinates of the vertices are:

D = (8, 5)

E = (6, 5)

F = (4, 8)

G = (7, 8)

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Answer:

  f(x) = x³ -10x² +28x +104

Step-by-step explanation:

You want a cubic polynomial f(x) with real coefficients, and its graph, such that one root is -2, another is 6+4i, and f(2) = 128.

A polynomial with real coefficients will have complex (or radical) roots that are conjugate pairs. That means the root 6+4i will be paired with a root 6-4i. The factored form of the required polynomial will be ...

  f(x) = a(x -(-2))(x -(6 +4i))(x -(6 -4i))

  f(x) = a(x +2)(x² -12x +52)

We can use the given value of f(2) to find the scale factor, a.

  f(2) = 128 = a(2 +2)(2² -12·2 +52) = a(4)(32) = 128a

  a = 1 . . . . . divide by 128

The required polynomial is ...

  f(x) = (x +2)(x² -12x +52)

  f(x) = x³ -10x² +28x +104

Answer:

they will probably contact them orrr charge late  fees

The first thing a lender might do if a borrower is late with a payment is to send a reminder.

This reminder will usually be a phone call, email, or letter. The reminder will typically state the amount that is due, the due date, and any late fees that may be charged.

If the borrower does not make the payment after receiving the reminder, the lender may then contact the borrower directly. This contact may be made by a phone call, email, or letter. The lender may also try to work with the borrower to come up with a payment plan.

If the borrower still does not make the payment, the lender may then report the borrower to the credit bureaus. This will have a negative impact on the borrower's credit score. The lender may also start legal proceedings to collect the debt.

The specific steps that a lender will take if a borrower is late with a payment will vary depending on the lender's policies and the borrower's situation. However, sending a reminder is usually the first step.

Here are some additional things that a lender might do if a borrower is late with a payment:

Charge late fees.

Terminate the loan.

Sue the borrower.

Foreclose on the borrower's property.

It is important to note that the lender's actions will also depend on the terms of the loan agreement. The loan agreement will typically specify what happens if a borrower is late with a payment.

If you are a borrower who is late with a payment, it is important to contact your lender as soon as possible. You should try to work out a payment plan with the lender. If you do not make the payment, the lender may take legal action against you.

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The area of the given triangle will be A = 4.52 units².

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

As per the given,

P(4,6), Q(8,5), and R(5,9)

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

PQ = [tex]\sqrt {\left( {4 - 8 } \right)^2 + \left( {6 - 5 } \right)^2 }[/tex]

PQ = √17 = 4.12

PR = [tex]\sqrt {\left( {4 - 5 } \right)^2 + \left( {6 - 9 } \right)^2 }[/tex]

PR = √5 = 2.25

QR = [tex]\sqrt {\left( {8 - 5 } \right)^2 + \left( {5 - 9 } \right)^2 }[/tex]

QR = √18 = 4.25

The area will be as, √(S(S - PQ)(S - QR)(S - PR)

Where, S = (4.12 + 2.25 + 4.25)/2 = 5.31

Area = √(5.31(5.31 - 4.12)(5.31 - 4.25)(5.31 - 2.25)

A = 4.52 units²

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Answer:

6.5 square units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7cm}\underline{Area of a triangle}\\\\$A=\dfrac{x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}{2}$\\\\where:\\ \phantom{ww}$\bullet$ $(x_1,y_1), (x_2,y_2)$ and $(x_3,y_3)$ are \\ \phantom{ww}\;\;\; vertices of the triangle. \\\end{minipage}}[/tex]

From inspection of the given diagram, the vertices of the triangle are:

Substitute the vertices into the formula to solve for area:

[tex]\implies A=\dfrac{4(5 - 9) + 8(9 - 6) + 5(6 - 5)}{2}[/tex]

[tex]\implies A=\dfrac{4(-4) + 8(3) + 5(1)}{2}[/tex]

[tex]\implies A=\dfrac{-16 + 24 + 5}{2}[/tex]

[tex]\implies A=\dfrac{13}{2}[/tex]

[tex]\implies A=6.5 \; \sf units^2[/tex]

Therefore, the area of triangle PQR is 6.5 square units.

Parallel slope intercept form is a form of linear equation that describes a line parallel to a given line with slope m.

It is written as y = mx + b, where m is the slope of the line and b is the y-intercept of the line. This form is useful for finding equations of lines that are parallel to a given line.

y = mx + b

y = mx + b is an equation in the form of a straight line, where m is the slope of the line and b is the y-intercept of the line. This form can be used to determine the equation of a line that is parallel to a given line. The equation can be re-arranged to solve for x, if needed. To solve for x, the equation can be rewritten as x = (y - b) / m.

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Answer:

Below

Step-by-step explanation:

30%   is   .3 in decimal

So the family used 100 %  of last month PLUS .3 of last month MORE

 12 000 = 100 %      now add  .3 (12 000) more =

    12 000  + .3 ( 12 000) = 15600 gallons this month

Step-by-step explanation:

1.6a+4 when a=1/3 is 6

2.5a-2/3=0.133

RIP BRO

it's A

Step-by-step explanation:

i can feel the changes... i am going to gorge my eyes out :)

The completed two-column table used to prove that ΔSUV ≅ ΔTVU, can be completed as follows;

        Statements         [tex]{}[/tex]                        Reasons

1.    [tex]\overline{SU}[/tex] ≅ [tex]\overline{TV}[/tex]                                         Given

2.   ∠TSU ≅ ∠STV [tex]{}[/tex]                               Given

3.   [tex]\overline{UV}[/tex]║[tex]\overline{ST}[/tex]        [tex]{}[/tex]                                  Given

4.   ∠TSU ≅ ∠SUV[tex]{}[/tex]                               Alternate Interior Angles Theorem

5.   ∠TVU ≅ ∠STV[tex]{}[/tex]                               Alternate Interior Angles Theorem

6.   ∠STV ≅ ∠SUV [tex]{}[/tex][tex]{}[/tex]                              Transitive Property of Congruence

7.   ∠TVU ≅ ∠SUV[tex]{}[/tex]                               Transitive Property of Congruence

8.    [tex]\overline{UV}[/tex]    ≅ [tex]\overline{UV}[/tex]                               [tex]{}[/tex]    Reflexive Property of Congruence

9.    ΔSUV ≅ ΔTVU         [tex]{}[/tex]                    SAS                            

Two triangles such  as ΔSUV and ΔTUV are congruent when the three sides of triangle ΔSUV are congruent to the three sides of triangle ΔTUV.

The details of the reasons used to prove the congruency of the triangles are as follows;

Alternate Interior Angles Theorem

The alternate interior angles theorem states that the alternate interior angles formed by two parallel lines, such as [tex]\overline{UV}[/tex] and [tex]\overline{ST}[/tex] and their common transversals, [tex]\overline{TV}[/tex] and [tex]\overline{SU}[/tex], are congruent.

Transitive Property of Congruence

The transitive property of congruence states that two shapes are congruent to themselves if both shapes are congruent to a third shape.

Reflexive Property of Congruence

The reflexive property of congruence states that a shape, line, or angle is congruent to itself.

SAS

SAS, is an acronym for Side-Angle-Side congruency postulate, which states that, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

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(a) The balance after first transaction is, $162.66.

(b) The balance after second transaction is, $109.63.

(c) The balance after third transaction is,  $2.33.

What is transaction?

An agreement that has been fulfilled between a buyer and a seller to exchange goods, services, or financial assets in exchange for cash is referred to as a transaction.

The following are a few examples of transactions: paying a supplier after receiving goods or services from them. acquiring ownership of a property the seller previously owned by paying the seller with cash and a note. remuneration for hours worked.

Given:

Mac Valent opened a new checking account and deposited his paycheck for $209.81.

We have to find the balance after each transactions.

The first transaction is of electric cooperative for $47.15.

So, the balance after first transaction is, $209.81 - $47.15 = $162.66.

The second transaction is of Sharp's Groceries for $53.03.

So, the balance after second transaction is, $162.66 - $53.03 = $109.63.

The third transaction is of Gimbles Auto Repair for $107.30.

So, the balance after third transaction is, $109.63 - $107.30 = $2.33.

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Complete question:

Complete question is attached below.

Answer: c≈44°

Step-by-step explanation:

cos(c)=0,7193

c=arccos(0.7193)

c≈44°

Answer: The blimp is 82% full

Step-by-step explanation:

To find the percentage of the blimp that is filled with gas, we need to divide the volume of the gas that is in the blimp by the total volume of the blimp and then multiply the result by 100%.

The blimp is filled with 28,700 cubic feet of gas, and it has a total volume of 35,000 cubic feet when fully expanded, so the percentage of the blimp that is filled with gas is 28,700 / 35,000 = 0.82.

To express this as a percentage, we need to multiply the result by 100%, so the blimp is 82% full.

Here's the complete solution:

The blimp is filled with 28,700 cubic feet of gas.

The blimp has a total volume of 35,000 cubic feet when fully expanded.

Therefore, the percentage of the blimp that is filled with gas is 28,700 / 35,000 = 0.82.

To express this as a percentage, we multiply the result by 100%, so the blimp is 82% full.

Answer:

588

Step-by-step explanation:

Answer: The ratio of the breadth to the height of the hall is 7:8

Step-by-step explanation:

The ratio of the length to the height of the hall is 7:6, which means that if the length of the hall is represented by 7, the height is represented by 6. We can write this as a proportion as follows:

7/6 = L/H

We know that the length of the hall is 28 meters, so we can substitute this value for L in the proportion to find the height:

7/6 = 28/H

Solving for H, we get:

7/6 = 28/H

7H = 168

H = 168/7 = 24

The height of the hall is 24 meters.

The ratio of the breadth of the hall to its height is the same as the ratio of 21 to 24, which simplifies to 7:8. Therefore, the ratio of the breadth to the height of the hall is 7:8.

The Piecewise function is

f(x) = [tex]\left \{ \right.[/tex] 0,    x<5

          5,     5<x<11

          7,      11<x< 16

A function that is defined piecemeal is one that has numerous subfunctions, each of which applies to a distinct interval in the domain. Instead of being a property of the function itself, piecewise definition is a means to express the function.

A piecewise function is a function that is constructed from bits of various functions across various time intervals.

Given:

let x be the age of person.

We have,

let f(x) represents the piecewise function

f(x) = [tex]\left \{ \right.[/tex] 0,    x<5

          5,     5<x<11

          7,      11<x< 16

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Answer:

No

Step-by-step explanation:

The square of given expression √1 ( square root of 1 ) is equal to 1.

As given in the question,

Given expression is equal to √1 ( square root of 1 )

To calculate the square of √1 we have,

Let us consider variable x is equal to √1

x = √1

Now take square on both the sides of the given expression we get,

x² =  (√1 )²

⇒ x² = √1  × √1

Multiplying square root of 1 to square root of 1 is equal to 1 we get,

or use law of exponent :

√1 × √1 = [tex]1^{\frac{1}{2} + \frac{1}{2} }[/tex]

            = 1

⇒ x² = 1

Therefore, the square of the given expression √1 ( square root of 1 )is equal to 1.

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$15 = 1.25x + 2.50y

x number of games, y = number of rides

Graphing this will show a line with coordinates (x, y) on it who 'fit' in this equation to make it = 15

I graphed points where both x and y are whole numbers.

These are answers to the equation that make it = 15.

Graph the line 2x = y   (2 times the number of games is the number of rides)

Where the lines intersect is where number of rides is twice taht of games, and the price is 15.

Visually, we can determine that they intersect at (2.4, 4.8)

To verify that this is correct, plug them into the first function to see if this gives you 15.

It does equal 15.

While these are not whole numbers, they do make the equations true, but in the real world we would not have numbers like this.

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

At least Eight yards need to raked to earn minimum $52. The equation of model is $6.50 Y≥ $52. So, the correct answer is option(C).

The total earned income by rake leaves in your neighborhood after school is $6.50 per yard. The Minimum amount that you want to earn = at least $52

We have determined a equation of model for the given situation.

Let Y be the number of yards raked to earn at least $52. We have one yard raked which implies to earn $6.50

So,for Y yards raked it implies to earn $6.50× Y. But Y has to rake in atleast $52 , here the minimum is to earn either $52 or more than $52. So,Y($6.50 ) ≥ $52

dividing both sides by $6.50 we get,

Y ≥ 52/6.50

=> Y ≥ 52/6.50 = 8

Hence , at least 8 yards must be raked to earn minimum $52.

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Complete question:

You rake leaves in your neighborhood after school and earn $6.50 per yard you rake. How many yards do you need to rake to earn at least $52? What equation models this situation?

A. at least 45 yards; y + 6.5 ≥ 52.00,

y = number of yards raked

B. at most 8 yards; 6.50y 52.00,

y = number of dollars earned

C. at least 8 yards; 6.50y ≥ 52.00,

y = number of yards raked

D. at most 52 yards; y − 6.5 > 52.00,

y = number of dollars earned

Answer:

33

Step-by-step explanation:

All triangle angles together add up to 180

So we can set up this equation to find angle z:

98 + 49 + z = 180

Now solve:

98 + 49 + z = 180

147 + z = 180

-147        -147

z = 33

Null Hypothesis: The actual mean is equal to the company's claim of 5 hours.Alternative Hypothesis: The actual mean is less than the company's claim of 5 hours.

Null and alternative hypotheses are applied for evaluating statistical theories. In contrast to the null hypothesis, which is a test's default assumption, the alternative hypothesis indicates how your research anticipates an effect or link between variables.

Null hypothesis: The null hypothesis states the expected outcome. In the given situation, the expected outcome is that the actual mean is equal to the company's claim of 5 hours.The alternate hypothesis conveys the null hypothesis' complete opposite.In this case, the alternative hypothesis is that the actual mean is less than the company's claim of 5 hours.

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The equation of the circle if diameter has endpoints (-3,-1) and (1,2) is x² + 2x + y² - y = 5.

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).

Given:

The endpoints of the circle diameter are (-3,-1) and (1,2),

Calculate the coordinates of the center of the circle as shown below,

Center = (-3 + 1 / 2, -1 + 2 / 2)

Center = (-2/2, 1/2)

Center = (-1, 1/2)

Calculate the length of diameter as shown below,

Diameter = [tex]\sqrt{[1- (-3)]^2+[2-(-1)]^2}[/tex]

Diameter = √(4² + 3²)

Diameter = 5

Thus, radius = 5 / 2 =

Calculate the equation of the circle as shown below,

[x - (-1)]² + [y - 1/2]² = (5/2)²

Simplify the above equation as shown below,

x² + 2x + y² - y = 5

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Answer:

not a solution

Step-by-step explanation:

2x-3=2x+5

-2x.  -2x

-3=5

not a solution because -3 does not equal 5

Answer:

3X−9=

4

6⋅6

​

Multiply both sides of the equation by 4.

12X−36=6×6

Multiply 6 and 6 to get 36.

12X−36=36

Add 36 to both sides.

12X=36+36

Add 36 and 36 to get 72.

12X=72

Divide both sides by 12.

X=

12

72

​

Divide 72 by 12 to get 6.

X=6

In the given triangle, length of side AD is 5 unit and length of side AB is 7 unit.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

In triangle ABC,

BC is perpendicular bisector or side AC.

The length of side AC = 10, BC = 7,

Since, BD is a perpendicular bisector of AC,

Therefore, D will be midpoint of AC.

AD = DC = AC /2 = 10/2 = 5.

By angle bisector property,

AB/BC = AD / AC

AB / 7 = 5/5

AB = 7

The length of side AB is 7 and Side AD is 5.

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The length of the radius of a circle with the equation x² + y² = 121 is 11 units  .

In the question ,

it is given that ,

the equation of the circle is ⇒ x² + y² = 121 ,

we know that the general equation of the circle is given as x² + y² = d² ;

and "d" is the radius of circle ,

On comparing both the equations ,

we get ,

d² = 121

Simplifying the above equation further ,

on taking square root on both the sides ,

we get ,

d = √121 = √(11 × 11)

the radius "d" is

d = 11 units .

Therefore , the radius of the circle is = 11 units .

The given question is incomplete , the complete question is

What is the radius of a circle with equation x² + y² = 121 ?

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With the help of simple mathematical operations, we know that the publisher can sell a maximum of 12 yearbooks.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

The order of operations refers to the rules that govern how to solve an expression with several operations.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, the maximum number of books that can be sold are:

24 + 475 = 499

Now, the publisher can receive not more than $6100. Then,

6100/499 = 12.22

Therefore, with the help of simple mathematical operations, we know that the publisher can sell a maximum of 12 yearbooks.

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Answer:

420 calories

Step-by-step explanation:

Multiply 140 by 3 because there are three servings in a can, and each serving is 140 calories, so the number of calories in the can is the product of the numbers.