A cross-country sprint skier keeps track of how his practice times compare to a
qualifying time for a race. A negative number means he skied faster than the qualifying
time. His results are shown in the table.
Practice Run
1
2
3
st
4
5
6
Difference between Practice Time
and Qualifying Time (seconds)
1.25
-5.38
-0.92
2.19
-6.74
-2.46
1 of 5
What is the mean difference between the skier's practice times and the qualifying
time?
Use the number pad to enter your answer in the box.
second(s)
Finish Later
Submit

Answer:

-5

Step-by-step explanation:

The expression for the composition of functions t and s, (t*s)(x), is obtained by substituting the output of s(x) into t(x). So,

(t*s)(x) = t(s(x)) = t(4x) = 3(4x) + 3 = 12x + 3.

The expression for the difference of functions t and s, (t - s)(x), is obtained by subtracting the output of s(x) from t(x). So,

(t - s)(x) = t(x) - s(x) = (3x + 3) - (4x) = -x + 3.

To evaluate (t + s)(-2), we need to add the outputs of t(-2) and s(-2).

t(-2) = 3(-2) + 3 = 3

s(-2) = 4(-2) = -8

So, (t + s)(-2) = t(-2) + s(-2) = 3 + (-8) = -5.

Answer:

small number=3 while Big number is, 13

Step-by-step explanation:

X+y=14

3x+2y=31

3(x+y=14)

3x+3y=42 + 3x+2y=31

X=3,y=11

The perimeter of the figure is 30.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure,

Number of sides = 5

Each side = 6

So,

The perimeter.

= 5 x 6

= 30

Thus,

30 is the perimeter.

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31 people chose Petra as leader in the student council elections.

Percentage is used to represent a fraction of 100.

Percent is represented by the sign "%".

Mathematically, we can write the percentage as -

A% of B

(A/100) x B

AB/100

Given is that in the student council elections, 39% of the 80 voters chose Petra.

We can find the total number people who chose Petra as leader as -

{x} = 39% of 80

{x} = (39/100) x 80

{x} = 31.2

{x} = 31

Therefore, 31 people chose Petra as leader in the student council elections.

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{Question in English -

In the student council elections, 39% of the 80 voters chose Petra. How many optical votes Petra?}

The price of medium pizza paid by both the science and maths clubs found using linear equations is $9.50.

What is meant by equation?

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Given,

Cost of 5 large pizzas and 2 medium pizzas paid by the science club = $79.00

Cost of  4 large pizzas and 4 medium pizzas paid by the math club = $86.00

Let the cost of medium pizza = x

Cost of large pizza = y

Now using the above equation we can write two linear equations.

2x + 5y = 79

4x + 4y = 86

Solving the above system of linear equations.

We are making the coefficient of the x variable the same.

Multiplying the first equation by 2.

4x + 10y = 158

4x + 4y = 86

Subtracting the equations.

6y = 72

y = 12

Now substituting in any one equation, we get the value of x.

2x + 5 * 12 = 79

2x = 19

x = 9.5

Therefore the price of medium pizza found using linear equations is $9.50.

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The expressions that show the number of students for each activity are;

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.

A set is a mathematical model for a collection of various things.

We are given;

Total number of students in the middle school = z

A) From the given table, we can deduce that;

B; Now, the expression to show the students that like either drama or dance is;

(1/7)z + 26 + (1/7)z + 22

>> (2/7)z + 48

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A middle school with z students ran a survey to determine the students' favorite activities. The table indicates the number of students who enjoy each activity. Answer parts A and B.

Table:

Activity:

Dance- 22 more than one-seventh of the students

Baseball- 24 fewer than four-sevenths of the students

Drama- 26 more than one-seventh of the students.

The probability that Omar randomly selects a sugar cookie from the bag eats it, then randomly selects an oatmeal cookie is 0.06.

Omar buys a bag of cookies that contains,

5 chocolate chip cookies,9 peanut butter cookies, 6 sugar cookies, and 7 oatmeal cookies,

We have to find the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie

Total number of cookies in bag = 27

the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie

[tex]=\frac{6}{27}.\frac{7}{26}\\\\=0.0598 =0.06[/tex]

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As per unitary method, it will take 9 years for the man to be three times as old as his son.

The unitary method is a mathematical technique that involves finding the value of a single unit, and then using that unit to find the value of a larger quantity.

First, let's define our variables:

Let the man's age be M

Let the son's age be S

According to the problem, we know that:

M = 42

S = 12

We want to find out how many years it will take for the man's age (M) to be three times his son's age (S). Let's call this number of years "y".

Using the unitary method, we can set up the following equation:

M + y = 3(S + y)

Here's what this equation means:

M + y represents the man's age after y years

S + y represents the son's age after y years

3(S + y) represents three times the son's age after y years

We can simplify this equation by distributing the 3:

M + y = 3S + 3y

Next, we can isolate the variable y (which represents the number of years we're trying to find) by moving all the other terms to the opposite side of the equation:

y - 3y = 3S - M

Simplifying this, we get:

-2y = 3S - M

Finally, we can solve for y by dividing both sides by -2:

y = (M - 3S) / -2

Plugging in the values we know, we get:

y = (42 - 3(12)) / -2

y = 9

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Complete Question:

A man's age is 42 years and his son's age is 12 years. After how many years will the man be thrice as old as his son?

Answer: 1.5 inches

Step-by-step explanation:

Students should be able to solve problems related to similar triangles on the Unit 6 test.

Triangle is a 3×3 sided only going with three angles and three side it is one of the most basic fundamental safe in the geometry and is used in many different area of Mithun science triangle are also after used in the architecture art in other area of the designing triangle came in many other different form.

Unit 6 tests on similar triangles require students to apply the knowledge they have learned in geometry class in order to solve problems related to similar triangles. The main topics covered in this test are the various theorems and properties that apply to similar triangles.

The first theorem students should understand is the AA Theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. This theorem can be used to solve problems that involve similar shapes.

The second theorem students should understand is the SAS Theorem, which states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between those two sides is the same, then the two triangles are similar. This theorem can be used to solve problems in which two triangles have the same angles and sides that are in proportion to one another.

The third theorem students should understand is the SSS Theorem, which states that if three sides of one triangle are proportional to three sides of another triangle, then the two triangles are similar. This theorem can be used to solve problems in which two triangles have the same angles and sides that are in proportion to one another.

Finally, students should also understand the properties of similar triangles. These properties state that the sides of similar triangles are proportional to one another, the angles of similar triangles are congruent to one another, and the corresponding angles of similar triangles are equal.

By understanding these theorems and properties, students should be able to solve problems related to similar triangles on the Unit 6 test.

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The values of the x are:

1) x = 2,

2) x =11.

3) x = 51

4) x = 7

What is the Angle Bisector theorem?

the angle bisector of a triangle bisects the opposite side in such a way that the ratio of the two line segments is proportional to the ratio of the other two sides.

18)

Given:

Two parallel lines intersecting horizontally the three vertical line,

So, Their ratios are in proportion.

9/4 = 13.5 / x + 4

x + 4 = (13.5*4)/9 = 6

x = 6-4 = 2.

So,  the value of the x is 2.

19)

Given:

Two parallel lines intersecting horizontally the three vertical line,

So, Their ratios are in proportion.

12.8/x-3 = x+5/10

12.8 * 10 = (x-3) * (x+5)

128 = x²+2x -15

So, by solving this quadratic equation we get:

x =11.

21)

Given:

VT bisects the ∠STU

By using the Angle Bisector theorem,

9/33 = 12 / 3x+2

9(3x+2) = 33 * 12

27x + 18 = 1396

x =  1396 - 18 / 27

x = 51

22)

Given:

LM bisects the ∠JLK

By using the Angle Bisector theorem,

4/ (x-4) = (x +3) / 8

(x - 4) * (x + 3) = 8 * 4

x² - x - 12 = 32

x = 7.152

x = 7

Hence, the values of the x are:

1) x = 2,

2) x =11.

3) x = 51

4) x = 7

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The profit generated from selling x boxes of pencils is a linear function of x, with a slope of $0.80 and a y-intercept of -$12.60

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range) with the property that each input is related to exactly one output.

Let us first define the demand function as D(x), where x is the number of boxes of pencils sold. We know that the manager can sell 10 boxes of pencils at a price of $2.19 per box, which means that the revenue generated from this sale is:

10 * $2.19 = $21.90

Similarly, when the price is $1.70, she can sell 24 boxes of pencils, which gives a revenue of:

24 * $1.70 = $40.80

Now, we can use these two data points to find the equation of the demand function. Since we assume that the demand is linear, we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept. In our case, y represents the revenue generated by selling x boxes of pencils.

To find the slope, we use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the two data points we have.

m = ($40.80 - $21.90) / (24 - 10)

m = $18.90 / 14

m = $1.35

To find the y-intercept, we can use either of the two data points and solve for b:

$21.90 = $1.35 * 10 + b

b = $7.40

Therefore, the demand function for the pencils is:

D(x) = $1.35x + $7.40

This means that for each additional box of pencils sold, the revenue generated increases by $1.35. The y-intercept of $7.40 represents the revenue generated when no pencils are sold, which includes fixed costs such as rent, utilities, and wages.

We also have the cost function C(x) = 0.55x + $20, which represents the total cost of buying x boxes of pencils. The profit function P(x) is defined as the difference between the revenue and the cost:

P(x) = D(x) - C(x)

Substituting the expressions for D(x) and C(x), we get:

P(x) = ($1.35x + $7.40) - (0.55x + $20)

Simplifying this expression, we get:

P(x) = $0.80x - $12.60

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She has to be at the airport at least 100 minutes before the flight. She must arrive at the airport at least two hours and 120 minutes before the flight.

Which ensures that she has time to check in, go through security and passport control, and board the flight. the amount f time a passenger needs to arrive before the flight can vary depending on the airline and airport. Generally, most airlines recommend that passengers arrive at the airport at least two hours before domestic flights and three hours before international flights.

In order it gives the passenger enough time to get to the airport depending on the location and traffic, check in and drop off any luggage, go through security and passport control, then at last board the flight

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The answer is 10.5

First you need to subtract the ending cost (25.50) giving you $52.5

With that 52.5 just divide by the amount of shirts bought (5) and you get 10.5 per shirt.

Answer:

10.50

Step-by-step explanation:

you take 78 and subtract that by 25.50 which gives you how much money he spends on the 5 t-shirts. that will 52.50

now you know that he spends 52.50 on 5 t-shirts, so you divide that by 5 which gives you 10.50

hope it helps

please mark brainliest

The amount that was paid by Ashley is $ 28.05.  

To find the discount on a given price, multiply the discount that is given by the original price and divide the result by 100.
To find the amount that can be paid by the consumer, subtract the resultant discount from the original price.

Final price of item = Original price - Discount  

Here we have

An item is regularly priced at $33.  

The discount that Ashley bought it = 15% off the regular price.  

The amount that Ashely paid for it = $ 33 - 15% of $ 33  

=> $ 33 - $ (15/100 × 33)

=> $ 33 - $ (0.15 × 33)

=> $ 33 - $ 4.95  

=> $ 28.05  

Therefore,

The amount that was paid by Ashley is $ 28.05.

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The work done in pulling the rope up 10 ft is 864 ft-lbs, calculated by multiplying the rope's weight (72 lbs) by the distance (10 ft) it was lifted.

Work done = Weight x Distance

Work done = 72 lbs x 10 ft

Work done = 720 ft-lbs

Additional work done for weight of rope = Weight of rope x Distance

Additional work done for weight of rope = 90 x 10

Additional work done for weight of rope = 900 ft-lbs

Total work done in pulling the rope up 10 ft = 720 ft-lbs + 900 ft-lbs

Total work done in pulling the rope up 10 ft = 864 ft-lbs

The work done in pulling the rope up 10 ft is calculated by multiplying the weight of the rope (72 lbs) by the distance (10 ft) it was lifted. This gives us a result of 720 ft-lbs. However, since the rope is 90 ft long, we must also take into account the additional weight of the rope beyond the 10 ft that was lifted. So, we multiply the weight of the rope (90 lbs) by the distance (10 ft) to get an additional work done of 900 ft-lbs. Adding the two results together gives us 864 ft-lbs of work done in pulling the rope up 10 ft. This shows that the heavier a rope is, the more work must be done to lift it.

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The required measurement of the ingredient has been shown below for half a batch of cookies.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
When making 1/2 a batch of the cookie recipe, you will need to halve the amount of each ingredient.

Here is the list of ingredients for half a batch:

1 7/8 cups flour

5/8 cup brown sugar

1 egg

1/8 teaspoon salt

1/6 teaspoon baking soda

5/8 cup butter

3/4 cup white sugar

Thus, the required measurement of the ingredient has been shown above for half a batch of cookies.

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The mean of a sample is the average of all values in the sample. The mean of a sample is generally always smaller than the mean of the population from which the sample was taken, since the sample is only a small subset of the population.

The mean of a sample can never be zero or negative, since it is an average of all the values in the sample. The mean of a sample can also never be greater than the mean of the population. None of these alternatives is correct.

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The measure of exterior angle ACD is 132°

The exterior angle theorem states that whenever a triangle's side is extended such that it creates another exterior(outside angle), the resultant exterior angle created is equal to the sum(addition) of the other two opposite (inner) interior angles of the triangle.

From the information given:

Angle A = 50; Angle B = 4x + 2, Angle ACD = 6x + 12

Therefore;

50 + 4x + 2 = 6x + 12

52 + 4x = 6x + 12

4x - 6x = 12 - 52

-2x = - 40

x = 20

Since x = 20, angle ACD = 6x + 12

The measure of angle ACD = 6(20) + 12 =132°

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The correct answer choices for Z and X are $25.08 and $3.72, respectively.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

How to solve for this

To solve for Z and X simultaneously, you can use the following equation: Z + X = 59.5

You can then compare the four given answer choices for Z and X to determine which ones satisfy the equation.

For example, $1.51 + $22.35 = $23.86, which is not equal to 59.5, so neither of these answer choices is correct.

However, $25.08 + $3.72 = $28.80 which is equal to 59.5, so the correct answer choices for Z and X are $25.08 and $3.72, respectively.

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Answer:

D. 3/7, 3:7, or 3 to 7

Step-by-step explanation:

The expression √a²√a² when simplified is (d) a * a

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

√a²√a²

Express as product expression

So, we have the following representation

√a²√a² = √a² *√a²

Evaluate the exponents

This gives

√a²√a² = a * a

Hence, the expression is (d) a * a

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Complete question

Simplify √a²√a²

Which expression is equivalent to √a²√a²

a².aº

aª.a

a³ a

a a

Answer:

why and why not why .I have no idea wish I did

The correct option regarding when Chicago first exceeded Phoenix in the percentage of calls answers within 10 seconds is given as follows:

C. Between September and October.

The output of the graph represents the percentage of calls answered within 10 seconds.

Chicago and Phoenix are represented as follows:

At the beginning of September, the red line was above the green line, but at the beginning of October, the green line was above the red line, hence the correct option is given by option C.

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The value of the function f(a + 1) - f(a) is 2a - 2

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

In the given problem;

f(x) = x² - 3x

f(a + 1) - f(a) = ?

f(a + 1) = a² - a - 2

f(a) = a² - 3a

f(a + 1) - f(a) = a² - a - 2 -(a² - 3a)

f(a + 1) - f(a) = 2a - 2

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The population of the city has decreased by 15%.

Percentage refers to a way of expressing a number as a fraction of 100, and is often represented by the symbol (%).

To find the percent decrease, we need to determine the difference between the original population and the new population. We can do this by subtracting the new population from the original population:

322,000 - 273,700 = 48,300

This means that the population has decreased by 48,300. To find the percentage decrease, we need to express this as a percentage of the original population. We can do this by dividing the decrease by the original population and then multiplying by 100:

(48,300 / 322,000) x 100 = 15%

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it's A and D good luck

Answer:

A., D.

Step-by-step explanation:

Let t = number of two-point questions.

Let f = number of four-point question.

First we deal with the number of questions.

There are 42 questions. All the questions are either 2-point questions or 4-point questions.

t + f = 42

Now we deal with the number of points.

t two-point questions are worth 2t points.

f four-point questions are worth 4f points.

Altogether, they are worth 2t + 4f points.

The total number of points is 100, so

2t + 4f = 100

The system of equations has the equations:

t + f = 42

2t + 4f = 100

Answer: A., D.

Answer:

NO

Step-by-step explanation:

no she cannot. you do not need to do any math for this, none of these measurements are equal to or greater than 6 feet, and i dont think lily's gonna snap her fishing pole in half 6>4, 4=the longest thing about this box, aka the length

Answer: No, she can not store the fishing pole in the box.

No, Lily can not store the fishing pole into the box. The pole is 6 feet long, while the box is 4 feet long. Even if you tried to insert the pole into the box vertically it would not fit. Therefore, no Lily cannot fit the box.

I hope this helped & Good Luck <3 !!!

Answer:

56 cola flavored gumboils

Step-by-step explanation:

Bob's 40 count of gumballs has 16 cola gumballs

Therefore the probability of a gumball being cola based on the sample size of Bob's purchase = 16/40 = 2/5

There are 140 gumballs left in the machine so we can expect that, on an average, 2/5 of them should be cola gumballs

So number of cola gumballs left is expected to be  2/5 x 140 = 56

This is only a prediction based on Bob's sample of 40 cola gumballs