In gym class, a student can do 40 sit-ups in 60 seconds and 100 sit-ups in 150 seconds.

Graph the proportional relationship.

graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 30
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 50
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30
Question 6 (Essay Worth 4 points)

Let A be the event "person under 18" and B be the event "employed part-time". So, we need to find the following probability

which is given by

Since the total number od people in the table is equal to n=4089, we have that

and

and

we have that

which gives

Therefore, the answer the searched probability is: 0.296

Given:

Cost of book = $24

Total cost of book (shipping charge inclusive) = $27

The shipping charge is:

Total cost - cost of book = $27 - $24 = $3

The shipping charge is $3

To find the percentage markup charged for shipping, use the formula:

Therefore, the percent of markup charged for shipping is 11.1%

ANSWER:

11.1%

The standard equation of a vertex is given by:

where (h,k) is the vertex.

Comparing with the given equation after re-arranging:

The vertex of the function is (-1, 4)

Answer

The maximum number of boxes that one can buy with 30 dollars is 6 boxes of strawberries.

Explanation

One box of strawberries cost 5 dollars.

If one buys x boxes of strawberries, the cost would be (5x) dollars.

So, if one has 30 dollars, we want to find the maximum number of boxes that the person can buy, that is, the maximum value of x

5x ≤ 30

Divide both sides by 5

(5x/5) ≤ (30/5)

x ≤ 6

The number of boxes that one can buy is less than or equal to 6.

Hence, the maximum number of boxes that one can buy with 30 dollars is 6 boxes of strawberries.

Hope this Helps!!!

Explanation

Step 1

Domain:The domain of a function is the complete set of possible values of the independent variable, by the graph is it a continuous line, so the domain is

Step 2

Range:The range is the set of all second elements of ordered pairs (y-coordinates), by the graph is it a continuous line, so the range is

Step 3

x-intercept

it is when y= 0 , by the graph :

Step 4

y-intercept

it is when x= 0 m by the graph:

Step 5

rate of change

Let

P1(-2,0) P2(0,4)

rate of change:2

x will be equal to 24.

Given,

There are 4 numbers:
13, 15, 20, and x.

Average of all numbers = 18.

We know that,

Average = ( sum of all numbers) / ( total numbers)

In this case,

Average = ( 13 + 15 + 20 + x) / 4

According to the question,

18 = (48 + x) / 4

=> 72 = 48 + x

=> x = 72 - 48

=> x = 24.

So, in order to make the average equal to 18, x should be equal to 24.

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We have to translate the expression "The product of v and the difference of c and 10".

We know that the expression is a product of two factors: v and a difference. The difference is between the terms c and 10, so it can be written as (c-10).

Then, the product can be written as:

Answer: the expression is v*(c-10)

1. Let D be price of desktop

let L be price of a Laptop

• we know that the laptop cost $400 less than the desktop

L = D -400

• for desktop D, Maya paid interest of 7.5% per year: 7.5/100 = 0.075

• For Laptop L , Maya paid interest of 8 % per year : 8/100 = 0.08

• We know that total charges for finance was $ 371,

therefore :

0.075 D + 0.08L = 371, (remember from the above , L = D-400 , lets substitute this value for L)

0.075 D + 0.08( D-400) = 371

0.075D + 0.08 D -32 = 371

0.155D = (371 +32)=403

D = 403/0.0155

D = $26 000

and L = D-400

= 26000-400

= $25600

• This means that Desktopcost $26000 and Laptop cost $25600,

Percent is given by the expression:

So, he is paying 74% more using the quarterly rate

step 1

Find out the circumference of the outer edge

Find out the radius

r=(650/2)+4

r=329 ft

so

step 2

Find out the circumference of the inner edge

r=650/2=325 ft

substitute

Find out the difference

2,066.12-2,041=25.12 ft

therefore

The correct statements regarding the numeric values of the piece-wise function are given as follows:

B. f(3) = 9.

D. f(2) = 4.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

A piece-wise function means that the definition of the input is different based on the input of the function. In this problem, all the numeric values we are calculating are for positive numbers, hence the definition of the function is given by:

f(x) = x².

Then the numeric values of the function are given as follows:

Meaning that options B and D are correct.

The options are given by the image at the end of the answer.

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Answer:

Explanation:

Answer:

a²+13a+40

Step-by-step explanation:

Now the x in the function has been replaced into (a+5) :

(a+5)²+3(a+5) =

(a²+10a+25)+(3a+15) =

a²+13a+40

Hope this helped and have a good day

ANSWER

$3100

EXPLANATION

Sally deposits $2500 at 8% interest for 3 years.

We want to find the amount she can withdraw at the end of the period.

To know this, we have to first find the interest.

Simple Interest is given as:

Therefore:

Therefore, after 3 years the interest will be $600.

The amount she can withdraw after this period is therefore the sum of the principal and the interest:

$2500 + $600 = $3100

She can withdraw $3100 at the end of the period.

The bar graph is attached below.

The heights of the rectangular bars in a bar graph, which displays complete data, are proportionate to the values they indicate. The graph's bars can be displayed either vertically or horizontally. Bar graphs, commonly referred to as bar charts, are a visual depiction of groups of data. It is one method of processing data. A bar graph is a great tool for representing data that are unrelated to one another and do not need to be displayed in any particular sequence. The bars provide a visual representation for comparing amounts in several categories. The x and y axes, commonly known as the horizontal and vertical axes, the title, labels, and a bar graph are all included.

Hence we frame the desired bar graph.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

triangle diagram

Step 02:

angles:

we must analyze the diagram to find the solution

angle 1:

angle 1 = 180° - 155° = 25°

angle 2:

angle 2 = angle 1 = 25°

angle 3:

angle 3 = 180° - 25° - 25° = 130°

angle 4:

angle 4 = 155°

angle 5:

angle 5 = 180° - 25° = 155°

That is the full solution.

Given data:

The 17 maths problem finish by Laney in 51 minutes.

The 6 maths problem finish by Hayden in 18 minutes.

The time taken by Laney to finish 1 problem is,

17 prob=51 minutes

1 prob=3 minute.

Simmiarly, the time taken by Hayden to finish 1 problem is,

6 prob=18 minutes

1 prob=3 minute.

As, the time taken by the Laney and Hayden to solve one problem is same .

Thus, the given relationship is proportional one.

n²+1 where n is the position of the sequence

1) Considering the sequence (2,5,10,17,26,...) corresponding to 1,2,3,4,5,...

Let's figure out how that sequence grows:

5 -2 = 3

10 -5 = 5

17-10= 7

26-17= 9

And examining the differences from each difference we have:

5-3 =2

7-5 = 2

9-7 =2

2) So we can write the following table, where the first line is the sequence, then the positions, then the subtraction between them.

As it is a quadratic formula, we can write in the general form and then plug x=0

3) Hence, to find the 6th term, for instance, we plug n=6 so

6²+1 = 31. So the formula to find the nth term is n² +1

3) Finally, the sequence is given by n² +1 where n is the position of the term.

Given the coordinate: A(-16, 8), let's perform the following:

First step:

A dilation with a scale factor of 1/2.

Here, we are to multiply the coordinates by 1/2.

A(-16, 8) ==> A'(-16*½, 8*½) = A'(-8, 4)

Second step:

Perform a rotation of 90 degrees clockwise.

(x, y) will change to (y, -x)

A'(-8, 4) ==> A''(4, 8)

Third step:

A reflection over the x axis.

To perform a reflection over the x axis, (x, y) becomes (x, -y)

A''(4, -8) ==> A'''(4, -8)

Therefore, the coordinates of A''' are:

A'''(4, -8)

SOLUTION

Given the question in the question tab, the following are the solution steps to get the ratio of Trumpets to violins

Step 1: Write the given data

40 trumpets

39 clarinets

24 violins

51 flutes

16 trombones

Step 2: Write the ratio of trumpets to violins

Trumpets=40

Violins=24

Hence, the ratio of trumpets to violin in its simplest from is:

Consider that you have a population greater than 30, then, you can use the normal distribution to determine the margin of error.

Use the following formula:

where:

x: mean = 33

s: standard deviation = 2

n = 31

Z: z-value for 98%

The value of Z can be found on a table for the normal distribution. For a margin of error at 98%, you get for Z:

Z = 2.326

Replace the previous values of the parameters into the formula for the margin of error (confidence interval):

Then, the margin of error is:

(33.00 - 0.83 , 33.00 + 0.83) = (32.17 , 33.83)

I must earn at least $625 (or more) per week before tax to pay my bills.

Given,

To make $500 per week after tax in order to pay all my bills.

and, The income tax is 20%

To find the  smallest pre-tax weekly .

Now, According to the question:

Let x be the amount to earn pre - tax.

The income tax is 20% = 20/100 = 0.2

Set up an inequality:

x - 0.2x > = 500

0.8 > = 500

x >= 500/0.8

x >= 625

Hence, I must earn at least $625 (or more) per week before tax to pay my bills.

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According to the problem, the principal is $1,000, the interest is 3% compounded monthly and the time is 8 years.

We have to use the compounded interest formula

Replacing the given information, we have

Now, we solve for A

ANSWER:

A. 15%

STEP-BY-STEP EXPLANATION:

We can determine the percentage using the following formula:

Therefore, the correct answer is A. 15%

We are asked to determine wheater 6/10 in decimal form is repeating or terminating. To do that we need to divide 6 over 10. To do that, we proceed as follows:

We need to find a number that when multiplied by 10 gives 6. That number is 0.6, because:

Therefore 6/10=0.6 Since the numbers after the radix point do not repeat, this is a terminating decimal.

From the trignometric ratio of right angle triangle :

The ratio for the tangent of any angle of right angle triangle is the ratio of the side Opposite to that angle to the adjacent side of that angle :

In the given triangle :The side opposite to the angle A is BC and the adjacent side AC

So,

In the figure : we have AC = 76, BC = 31 and AB = 82.1

Substitute the value and simplify :

Thus, tan A = 0.41

Now, the side opposite to the angle B is AC and the adjacent side is BC

thus :

In the figure : we have AC = 76, BC = 31 and AB = 82.1

Substitute the value and simplify :

tan B = 2.451

Answer :

tanA = 0.41

tanB = 2.45

The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).

What is transforming coordinates?

Polar coordinates (r,θ) are transformed into Cartesian coordinates (x, y) using the formulas x = r cos(θ), and y = r sin(θ).

This problem is under the concept of transforming polar coordinates (r,θ) to cartesian coordinates  (x, y).

For this problem the polar coordinates  are r = 18 and θ = 190°.

Convert these polar coordinates into a cartesian coordinates as,

x = r cos(θ) = 18 cos(190°) = -17.73

y = r sin(θ) = 18 sin(190°) = -3.13

The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).

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Answer: I believe it is representing the angular position of a vector

In short, it is a symbol to represent a measured angle.

The number of hours (time) after which both Remi and Pam would be exactly 15 miles apart is 3 hours.

First of all, we would have to determine the amount of distance (d) covered by both Remi and Pam.

Mathematically, the distance covered (traveled) by a physical body (object) can be calculated by using this formula:

Distance = speed × time

For the distance covered (traveled) by Remi, we have:

r = 3 × t

r = 3t.

For the distance covered (traveled) by Pam, we have:

p = 4 × t

p = 4t.

Also, the amount of distance (d) covered by both Remi and Pam forms a right-angled triangle as they both jogged East and South respectively. Therefore, there distances can be modeled by Pythagorean theorem:

d = r² + p²

Substituting the parameters into the formula, we have;

15² = 3t² + 4t²

225 = 9t² + 16t²

225 = 25t²

Dividing both sides by 25, we have:

t² = 225/25

t² = 9

t = √9

Time, t = 3 hours.

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This is an exponential growth. We would apply the exponential growth formula which is expressed as

y = a(1 + r)^t

Where

a represents the imitial number of subscribers

r represents the growth rate

t represents the number of years

y represents the number of subscribers after t years

From the information given,

a = 750

r = 80/100 = 0.8

t = 9 (number of years between 2000 and 2010)

Thus,

y = 750(1 + 0.8)^9

y = 750(1.8)^9

y = 148769.48

Rounding to the nearest whole number, the number of cell phone subscribers in 2010 is

148769