A child sitting 1.70 m from the center of a merry-go-round moves with a speed of 1.65 m/s.

Calculate the centripetal acceleration of the child

Calculate the net horizontal force exerted on the child

With respect to the linear function, the monthly cost for 68 minutes of calls is $19.28 if 51 minutes and 95 minutes cost $17.24 and $22.52 respectively.

The slope of the cost function which is the same as the variable charge per minute of call is determined by:

(the total costs of the highest activity - the total cost at the lowest activity) /the difference between the number of call minutes slope (cost per minute)

= ($22.52-$17.24)/(95-51)

Slope (cost per minute) =$0.12y

=a+bxy

=total cost

=$22.52

Note that:

a = fixed charge = unknown

b = slope = $0.12x = number of minutes = 9522.52

= a+(0.12*95)22.52

= a+11.40a =22.52-11.40a

=11.12y

= 11.12+0.12x

when x = 68y

= 11.12+(0.12*68)y

= total cost for 68n minutes

=$19.28

Find out more about cost on:

https://brainly.com/question/24516871

#SPJ1

The monthly cost for 68 minutes of calls is $19.28

What is the equation of straight-line?

The equation of straight-line considers the fixed charge of using phone plan per month plus the total variable cost of minutes of call, I mean the cost per minute of the plan can be determined by computing the slope of the straight-line equation

slope=(total cost for 95 minutes-total cost of 51 minutes)/(95-51)

total cost for 95 minutes=$22.52

total cost of 51 minutes=$17.24

slope=($22.52-$17.24)/(95-51)

slope= variable cost per minute=$0.12

We can determine the fixed charge per month using the straight-line equation and cost for 95 minutes

y=a+bx

y=total cost=$22.52

a=fixed charge per month=unknown

b=cost per minute=$0.12

x=number of minutes=95

$22.52=a+($0,12*95)

$22.52=a+$11.40

a=$22.52-$11.40

a=$11.12

total cost(68 minutes)=a+bx

a=$11.12

b=$0.12

x=68

total cost=$11.12+($0.12*68)

total cost=$19.28

Find out more about linear function on:https://brainly.com/question/14115882

#SPJ1

Answer:5.05y

Step-by-step explanation:

Therefore, the expanded form of the expression y (0.5 + 8) is 0.5y + 8y

Using this example we can find out that 0.5y+5 y=5.05 y thats the answer

please kindly give me brainiest thank you

Check the picture below.

The quarterly payment that the ski resort owner must make in 5 years to have the cost of the ski lift is $277,076.57.

The quarterly payment can be computed by determining the ski lift's total cost (future value).

Dividing the future cost or value by the number of periods (quarters) results in quarterly payments.

N (# of periods) = 20 quarters (5 x 4)

I/Y (Interest per year) = 4%

PV (Present Value) = $5,000,000

FV (Future Value) = $0

Results:

PMT = $277,076.57

Sum of all periodic payments = $5,541,531.49

Total Interest = $541,531.49

Thus, the quarterly payment that the ski resort owner must make in 5 years to have the cost of the ski lift is $277,076.57.

Learn more about periodic payments at https://brainly.com/question/13031679

#SPJ1

If by eating 2 eggs and 1​ cupcake, a child consumes 571 mg of cholesterol. The amount of cholesterol that is in each​ item are; 19 mg, 276mg, 8 mg.

E + C + P = 303

Where:

Egg=E

Cupcake=C

Pizza=P

Hence,

3C + 4P =89

4P = 89-3C

P = (89-3C)/4

2E + C = 571

2E = 571-C

E = (571-C)/2

(571-C)/2 + C + (89-3C)/4 = 303

(571-C)2 + 4C + 89-3C = 303×4

(571-C)2 + 4C + 89-3C = 1212

1142 -2C + 4C + 89-3C = 1212

-C = 1212-89-1142

C =19mg (1 cupcake)

E = (571-C)/2

E= (571-19)/2

E=552/2

E= 276mg  (1 egg)

P = (89-3C)/4

P = (89-3(19))/4

P = (89-57)/4

P=32/4

P=8 mg (1 pizza)

So,

Egg=E=19 mg

Cupcake=C=276 mg

Pizza=P=8 mg

Check:

19+276 + 8 = 303 mg

Therefore If by eating 2 eggs and 1​ cupcake, a child consumes 571 mg of cholesterol. The amount of cholesterol that is in each​ item are; 19 mg, 276mg, 8 mg.

Learn more about cholesterol here:https://brainly.com/question/19941388

#SPJ1

Answer:

8.391

1. Compare the first digit. If they are the same, move on to the next digit. In this case, we have to look at the hundredths place.

2. Check to see which number is bigger. We are looking at 9 and 7. 9 is the bigger number. this means that 8.391 is bigger.

The five number summary are as follows:

The range of the data sets is 25.

The interquartile range of the sets is 12.

The five number summary describes where data values occur, their central tendency, variability, and the general shape of their distribution.

The five number summary includes minimum number, maximum number, median(Q₂), first quartile(Q₁) and third quartile(Q₃).

Therefore, the five number summary are as follows:

27, 30, 41, 27, 20, 22, 36, 37, 44, 45, 29, 29

Arrange the data in ascending order.

20, 22, 27, 27, 29, 29, 30, 36, 37, 41, 44, 45

There are as follows;

Therefore,

Range of the data sets = 45 - 20 = 25

Interquartile range (IQR) = Q₃ - Q₁ = 39 - 27 = 12

learn more on five number summary here: https://brainly.com/question/11203575

#SPJ1

Answer:

y=35, z=111

Step-by-step explanation:

By the same-side interior angles theorem, z=111.

By the alternate interior angles theorem,

[tex]111=4y-29 \\ \\ 140=4y \\ \\ y=35[/tex]

From the temperatures given, we have that:

a) The regression equation is: y = 2.91x + 64.61.

b) The predicted temperature at 2 pm is of 88 ºF.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

In the context of this problem, the input and the output are given as follows:

We have that an hour is 60 minutes, hence:

Thus the points are given as follows:

(0, 65), (0.75, 67), (1.5, 68), (2.5, 72), (3, 74), (3.75, 75), (4.5, 77), (5,80).

Inserting these points into the calculator, the equation is:

y = 2.91x + 64.61.

2 pm is 8 hours after 6 am, hence x = 8 and the predicted temperature, in ºF, is given by:

y = 2.91(8) + 64.61 = 88 ºF.

More can be learned about regression equations at https://brainly.com/question/22992800

#SPJ1

Answer:

Triangle B is a dilation of A with approximately what scale factor

Triangle B is a dilation of A with approximately a scale factor of 8.

Triangle A is a dilation of B with approximately a scale factor of 1/8.

Triangle B is a dilation of C with approximately a scale factor of 3/4.

We have,

In mathematics, dilation refers to the transformation of a shape, object, or figure by uniformly scaling it up or down.

When the constant factor is greater than 1, the dilation results in an enlargement of the shape, making it larger.

Conversely, when the constant factor is between 0 and 1, the dilation leads to a reduction of the shape, making it smaller.

Now,

Triangle B is a dilation of A with approximately by a scale factor of:

Since triangle B is greater than A.

The scale factor is greater than 1.

Triangle B looks 8 times of triangle A.

So,

The scale factor is 8.

And,

Triangle A is a dilation of B with approximately by a scale factor of:

Since triangle B is smaller than A.

The scale factor is less than 1.

Triangle A looks like 12.5 % of triangle C.

12.5% = 1/8

So,

The scale factor is 1/8.

Triangle B is a dilation of C with approximately by a scale factor of:

Since triangle B is smaller than A.

The scale factor is less than 1.

Let's say,

Triangle B looks 75% of triangle C.

So,

The scale factor is 3/4.

Thus,

Triangle B is a dilation of A with approximately a scale factor of 8.

Triangle A is a dilation of B with approximately a scale factor of 1/8.

Triangle B is a dilation of C with approximately a scale factor of 3/4.

Learn more about scale factors here:

https://brainly.com/question/20759556

#SPJ7

Function g (x) horizontal shift left with 5 units.

What is Transformation?

The act or process of changing completely is called transformation.

Given that;

The parent function is;

f (x) = |x|

and , After transformed the function is g(x) = |x + 5|

Now, Compare the function to the parent function we get;

The transformation occur from f (x) = |x| to g (x) = |x + 5|.

Function g (x) = |x + 5| horizontal shift left with 5 units.

So, Function g (x) horizontal shift left with 5 units.

Learn more about the parent function visit:

https://brainly.com/question/26397691

#SPJ1

According to the solving the percent Larsons pay to the high school district 63.8%.

A % is a relative figure that represents one-tenth of a quantity. One percent (symbolized 1%) is the hundredth part; consequently, 100 percent denotes the complete amount and 200 percent specifies twice the supplied number.

In scientific and engineering writing, use the symbol% to denote percent, except when expressing numerals at the beginning of a phrase. When writing the word, use the form percent as opposed to the archaic version percent. During the test period, just 3% of the systems crashed.

Bill included $401 for local schools

$145 went to the high school district

Amount Remaining = $ 401 - $145

= $ 256

Percent Larson's pay to the high school district is:

256/401

.638 x 100

= 63.8%

According to the solving the Larsons pay to the high school district 63.8%.

To know more about percent visit:

https://brainly.com/question/14699403

#SPJ9

Answer:

99%

Step-by-step explanation:

The total number of servings is equal to the product of 5, 4 and 3. Thus, the required number of servings is 60.

A product is something that has undergone one or more multiplications. For instance, the mathematical formula "times equals" would be written with the terms "times," "multiplicand," and "product," respectively.

A number can be multiplied by another number to determine each of its products. For instance, 9 x 3 equals 27, so 27 is a product of 9 and 3. Each number has an infinite number of possible products because it can be multiplied by an infinite number of different numbers to produce an infinite number of results. When considering how to find the product of a number, there are some simple facts to understand. For instance, any whole number multiplied by two will always result in an even number.

Learn more about product here

https://brainly.com/question/10873737

#SPJ9

The estimated area of the circular watch face is: 8 cm².

The formula to use in determining or estimating the area of any shape that is circular is expressed as:

Area = πr², where the radius of the circular shape is represented as r.

Given the following:

Diameter of the circular watch face = 3.2 centimeters

The radius = 1/2(diameter) = 1/2(3.2)

Radius (r) = 1.6 centimeters

Plug in the value into πr² to find the estimated area of the watch face:

Area of the watch face = π(1.6²)

Area of the watch face ≈ 8 cm²

Therefore, the estimated area of the circular watch face is: 8 cm².

Learn more about the area of circle on:

https://brainly.com/question/12269818

#SPJ1

25 percent of the original price was saved during the purchase of the futon bed

The percent of the original price that is saved can be calculated as follows

The original price is $700

The new price is $525

The first step is to calculate the percentage change

= 700-525

= 175

Therefore the percent saved can be calculated as follows

= 175/700 × 100

= 0.25 × 100

= 25

Hence 25 percent of the original price was saved

Read more on percent here

https://brainly.com/question/12090131

#SPJ1

The time taken depends upon velocity and distance so the time taken by both balls to reach the same height will be 30 seconds.

Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.

Units of velocity are given by ⇒ meter/second

For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.

Difference between their initial height = 40 - 25 = 15 feet

It means if baseball cover x feet distance then football will cover x + 15 feet.

Now,

Time = distance covered / velocity

Since the time will be the same for both balls to meet them.

So,

Distance covered by baseball/velocity of baseball = Distance covered by football/ velocity of football

x/2.5 = (x + 15)/3

3x = 2.5x + 37.5

0.5x = 37.5

x = 75

So,

Time taken = 75/2.5 = 30 seconds.

Hence "After 30 seconds both balls will go to reach the same height".

To learn more about velocity,

brainly.com/question/18084516

#SPJ1

5x + 13y is prime ,  it cannot be factored.

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial .

Some trinomials cannot be factored. If none of the pairs total b, then the trinomial cannot be factored.

Given equation is 5x + 13y

If a polynomial is prime, then it cannot be factored. 5x + 13y is prime.

In this regard,

The law of detachment states that

1) If p happens, then q happens;

2) p is true;

Then, a there is a third statement that is

3) q is also true.

In this question,

If a polynomial is prime, then it cannot be factored.

The statements in the question can be represented as:

(1) If 5x + 3y is a polynomial and is prime then it cannot be factored

(2) It cannot be factored

Using the above representations of p and q, as an illustration; the third statement would be:

(3) 5x + 3y is a polynomial and is prime then we can conclude that

5x + 13y cannot be factored.

To learn more about law of detachment

visit - brainly.com/question/13966470

#SPJ9

Answer:

-1020

Step-by-step explanation:

-17 x - 5 x - 12 =

- 17 x 60 =

- 1020

these are the only ones i can find

26 37 40 48

Answer:

If they all had to equal 360 when put together then the answer would be 22. If they All had to equal 180 when put together, then the answer would be 2.

Step-by-step explanation:

The directions are not quite clear but I have two answers just in case.

The average time taken by workers to complete the repairing of the road is about the 4 and half weeks.

According to the statement

We have to find that the Time taken by the workers.

So, For this purpose, we know that the

Average time is a measurement that evaluates how long a works spends on repairing roads.

From the given information:

A 13 km stretch of road needs repairs. Workers can repair 3 km of road per week.

Then

If worker complete 3 km of the road in the 7 days

Then

Workers complete 13 km in the days = Total distance / Average distance

Then

Workers complete 13 km in the days = 13 / 3

Workers complete 13 km in the days = 4.33 weeks.

So, The average time taken by workers to complete the repairing of the road is about the 4 and half weeks.

Learn more about Average time here

https://brainly.com/question/1476828

#SPJ9

The given statement fraction numerator 6 y plus 2 x over denominator 5 end fraction in numerical form 18 is 6y + 2x = 90.

A linear equation in two variables has the highest degree of 1 and contains two variables generally in x and y.

Given in numerator we have 6y + 2 and in the denominator, we have 5 and this fraction equals to 18, This can be numerically represented as

(6y + 2x)/5 = 18.

6y + 2x = 90.

This is a linear equation in two variables x and y and for every value of x we get a corresponding value of y or vice-versa and all (x,y) ∈ R.

learn more about linear equation here :

https://brainly.com/question/11897796

#SPJ1

A coefficient in the algebraic expression is: 5

The constant is: 12

A variable is: x

A term in the algebraic expression can be: 5x or 12.

An algebraic expression consist of terms, which can be:

Thus, given the algebraic expression, 5x + 12, the following parts of the algebraic expression can be identified as shown below:

A coefficient in the algebraic expression is: 5 (tis is the number multiplied by the variable x)

The constant is: 12 (this is the number standing alone)

A variable is: x (this is the alphabet in the algebraic expression)

A term in the algebraic expression can be: 5x or 12.

Learn more about algebraic expression on:

https://brainly.com/question/2164351

#SPJ1

Answer:

32°

Step-by-step explanation:

Angles 2 and 4 are vertical angles, so they are congruent. That means that their measures are equal.

First, we set their measures equal to each other.

Then we solve the equation for x.

Then, we use the value of x to find the angle measure.

m<2 = 6x + 5

m<4 = 4x + 14

Set the measures equal.

6x + 5 = 4x + 14

Subtract 4x from both sides.

2x + 5 = 14

Subtract 5 from both sides.

2x = 9

Divide both sides by 2.

x = 4.5

m<2 = 6x + 5

m<2 = 6 × 4.5 + 5

m<2 = 27 + 5

m<2 = 32

Answer: 32°

(2,3) is a solution to the system of equations.

A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).

Consider the system of equations,

2x - 3y = - 5                                                                                 --------(1)

4x - 4y = - 4                                                                                 --------(2)

Multiplying equation (1) with 2.

4x - 6y = - 10

4x - 4y = - 4

Now, subtracting the above equations:

4x - 6y - ( 4x - 4y) = - 10 + 4

4x - 6y - 4x + 4y = - 6

- 2y = - 6

2y = 6

y = 3

Then,

4x - 4y = - 4

4x - 4 × 3 = - 4

4x - 12 = - 4

Adding 12 on both sides of the equation,

4x - 12 + 12 = - 4 + 12

4x = 8

x = ( 8/4 )

x = 2

Therefore, (x, y) = ( 2, 3) is a solution to the system of equations.

Learn more about system of equations here:

https://brainly.com/question/25976025

#SPJ9

Answer:

Yes

Step-by-step explanation:

Answer: Bill weighs 230 pounds and he needs to carry boxes that weigh 75 pounds each. Use the equation 75b+230&lt; =1805 to find the greatest number of boxes Bill can carry in the elevator in one trip.

Step-by-step explanation: