Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
32 kg to 56 kg

a) The new principal (principal + capitalized interest) when Rich begins making loan payments will be $9,425.10.

b) The total interest that Rich will pay over the life of the loan is $4,914.20.

The interest on student loans is based on simple interest.

The only interest capitalized is the interest during the non-payment period if the student does not pay the interest.

Some students elect to pay the interest during the non-payment period to reduce the capitalized interest and principal during the payment period.

Capitalization refers to the addition of interest to the principal amount.

Period of student loan = 10 years

The amount of the federal unsubsidized student loan = $7,900

Interest rate = 4.29%

Capitalized interest during the non-payment time = $1,525.10 ($7,900 x 4.29% x 4.5)

New principal when Rich begins making loan payments = $9,425.10 ($7,900 + $1,525.10)

Total interest for loan = $4,914.20 ($7,900 x 4.29% x 14.5)

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1. Therefore, the sequence is geometric.

2. Therefore, the sequence is arithmetic.

3. Therefore, the sequence is neither arithmetic nor geometric.

4. Therefore, the sequence is geometric.

5. Therefore, the sequence is neither arithmetic nor geometric.

For the arithmetic, geometric, and harmonic sequences, a collection of sequences and series formulas is provided below. The sequence and series formulas presented here contain formulas for determining the sum of the n terms in a series as well as the nth term of the sequence.

A common difference exists between two succeeding terms in an arithmetic series. There is a typical ratio between succeeding terms in a geometric series.

1. Given sequence is 27, 9, 3, ...

As the difference between the number is large.

So, we will check for geometric sequence.

[tex]r = \frac{27}{9} = \frac{3}{3} = \frac{1}{3}[/tex]

Therefore, the sequence is geometric.

2. Given sequence is 4, 8, 12, ...

As we can see there is uniform difference of 4

Therefore, the sequence is arithmetic.

3. Given sequence is 50, 56, 60, ...

As the difference between the number is not uniform.

So, we will check for geometric sequence.

[tex]r = \frac{50}{56} \neq \frac{56}{60}[/tex]

There, the sequence is neither arithmetic nor geometric.

4. Given sequence is 36, 12, 4, ...

As the difference between the number is large.

So, we will check for geometric sequence.

[tex]r = \frac{36}{12} = \frac{12}{4} = 3[/tex]

Therefore, the sequence is geometric.

5. Given sequence is 4, 24, ...

The number of terms is very less and hence we can't decide.

There, the sequence is neither arithmetic nor geometric.

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There is a 0.97541 or 97.541% probability that at least one student will choose a president who passed away in office.

Take into account the details offered.

43 US presidents are listed by Mr. Bray, 8 of them passed away while in office.

Consequently, p= 8/43.

If 8 of the 43 presidents died while in office, then 43-8=35 presidents survived.

q= 35/43

Let X represent how many presidents have passed away while in office.

The probaility that at least one student will choose a president who passed away in office is:

P(X[tex]\geq[/tex]1 ) = 1 -P(X=0)

P(X[tex]\geq[/tex]1 ) = 1 -¹⁸c₀(8/43)⁰(35/43)¹⁸

By using  Combinations Formula,

By solving we get,

P(X[tex]\geq[/tex]1 ) = 0.97541

As a result, there is a 0.97541 or 97.541% chance that at least one student will choose a president who passed away in office.

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The size of the angle x = 54 degrees

The regular pentagon is given

Number of sides of the pentagon = 5

O is the center  of the pentagon

The sum of all the angle around a point is 360 degrees

From the figure we can see that the it equally divided by 5 parts

The measure of each angle = 360/5

= 72 degrees

Consider the corresponding triangle

Sum of all the interior angles of the triangle is 180  degrees and the two sides of the triangle is equal, therefore it is an isosceles triangle

Then,

x + x+ 72 = 180

2x + 72 = 180

2x = 180- 72

2x = 108
x = 108/2

x = 54 degrees

Hence, the size of the angle x = 54 degrees

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Answer: he will be left with 31.74 dollars

Step-by-step explanation:

i first put 55.00 - 4.50 = 50.5

then you subtract 50.5 with 6.25  3 times so the and is 31.74

hope this helped !!

The probability for Jacie or Robyn would consume cheese on a random day is 0.15.

The likelihood of Jacie eating cheese on any particular day is 0.6.

The likelihood of Robyn eating cheese on any particular day is 0.25.

Both events are independent.

As a result, the probability for Jacie or Robyn would consume cheese on a random day is;

P(Jacie or Robyn)  = P(Jacie). P(Robyn)

P(Jacie or Robyn)  = 0.6 x 0.25

P(Jacie or Robyn)  = 0.15

Thus, the probability for Jacie or Robyn would consume cheese on a random day is 0.15.

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The old monthly payment was =  9.27 x 50 = 463.5

The new monthly payment is = 11.10 x 50 = 555

The percent increase in his monthly payment is 1.947%

Given,

Sandra Williams bought a home with a 10.25% adjustable rate mortgage for 25 years. She paid $9.27 monthly per thousand on his original loan

According to the question:

So, per thousand value of $65000 is 50000/1000 =50

Now, the old monthly payment was =  9.27 x 50 = 463.5

She decides to renew and will now pay $11.10 monthly per thousand on his loan.

So, the new monthly payment is = 11.10 x 50 = 555

The percent increase in his monthly payment is= 11.10 /9.27 - 1 x 100

19.7411 % and to nearest tenth it is 1.947%

Hence, the old monthly payment was =  9.27 x 50 = 463.5

the new monthly payment is = 11.10 x 50 = 555

The percent increase in his monthly payment is 1.947%

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The equation of line having a slope of 1/4 which passes through point (8,-3) is y = (1/4)x - 5.

The equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point (8, -3 )

Determine the y-intercept 'b'.

Substitute the point and slope into the equation of line formula and solve for b.

y = mx + b

-3 = (1/4)(8) + b

-3 = 8/4 + b

-3 = 2 + b

b = -3 - 2

b = -5

Now, substitute slope and y-intercept into y = mx + b to determine the equation of the line.

y = mx + b

y = (1/4)x + (-5)

y = (1/4)x - 5

Therefore, the equation of the line is y = (1/4)x - 5.

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Answer:

y=2x+9

Step-by-step explanation:

Fill in the equation

5=2(-2)+b

Solve for b

5 = -4+b

9 = b

Put the original equation

y=2x+9

Each section of a highway has length of 1.5 miles.

In this question, Ms. Galindo’s class has adopted two equal sections of a highway to keep clean.

We need to find the length of each section.

Let each section measures x mile.

The combined length of the two sections is 6/8 of a mile.

So, we get an equation x + x = 6/8

We solve above equation to find the value of x.

2x = 6/8

x = (6/8) / 2

x = 6/4

x = 1.5

Therefore, each section of a highway has length of 1.5 miles.

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The number of days that the food will last when an average of 18 people are at the shelter everyday is 50 days.

From the information given, the shelter has enough food to feed an average of 45 hungry people a day for 20 days.

Let the number of days that the people can be fed when 18 people come be Illustrated as x.

Therefore, this will be illustrated as x. This will be:

x = (45 × 20) / 18

x = 900 / 18

x = 50

The number of days is 15 days.

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Complete question

A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 people are at the shelter everyday, how long will the food last?

Bruce paid $17 and $55 respectively for each of the books

From the question, we have the following statements:

Represent the books with the variables x and y

So, we have the following equations

x = 4 + 3y

x + y = 72

To start with;

We can substitute 4 + 3y for x in the equation x + y = 72

So, we have the following representation

4 + 3y + y = 72

Evaluate the like terms

4 + 4y = 72

Collect the like terms in the above equation

So, we have the following equation

4y = 72 - 4

Evaluate the like terms

4y = 68

Divide both sides by 4

So, we have

y = 17

Recall that x = 4 + 3y

Substitute 17 for y in the equation x = 4 + 3y

x = 4 + 3 * 17

Evaluate the products

x = 4 + 51

Evaluate the sum

This gives

x = 55

Hence, the cost of the books are $17 and $55

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Possible question

Bruce bought two books, one book costs $4 more than three times than the other. They both equal $72.

What is the cost of each book

Answer:

(- 25, 5 )

Step-by-step explanation:

- 3x - 6y = 45 → (1)

- 5y = x → (2)

substitute x = - 5y into (1)

- 3(- 5y) - 6y = 45

15y - 6y = 45

9y = 45 ( divide both sides by 9 )

y = 5

substitute y = 5 into (2)

- 5(5) = x , then

x = - 25

solution is (- 25, 5 )

Answer: 63 inches

Step-by-step explanation:

Answer:

63 inches

Hope this helps :)

If  he has 7 more nickels than dimes. The number of quarters that Warren have is 7.

Let coins be:

n + d + q = 40

Where;

n = nickels

d =dimes

q = quarters

Hence,

.05n + .10d + .25q = 4.05

n = d + 7

Substitute (d+7) for n

(d+7) + d + q = 40

2d + q = 40 - 7

2d + q = 33

q = (33-2d)

So,

.05(d+7) + .10d + .25q = 4.05

.05d + .35 + .10d + .25q = 4.05

15d + .25q = 4.05 - .35

.15d + .25d = 3.70

Substitute (33-2d) for q

.15d + .25(33-2d) = 3.70

.15d + 8.25 - .5d = 3.70

.15d -.5d = 3.70 - 8.25

-.35d = -4.55

Divide both side by -/35d

d = -4.55 / -.35

d = 13 dimes

Nickels

n = d+7 where d is 13

n = 13 + 7

n = 20 nickels

Quarters

q = (33-2d)

q = 33 - 2(13)

q = 33 - 26

q = 7 quarters

Therefore 7 is the quarters.

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As a result of using all values in the data set to calculate an average, the mean is the most widely used measure of central tendency.

A measure of central tendency, also known as a measure of center or a measure of central placement, is a summary statistic that seeks to summarize an entire collection of data by using a single number that corresponds to the middle or center of the distribution.

You are probably most familiar with the central tendency measure known as the mean, which is the arithmetic average. It is fairly easy to determine the mean. Simply add up all the values then divide by the dataset's observation count.

The teacher can get a mathematical breakdown of how well the children are doing through measures of central tendency.

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Step-by-step explanation:

so, after clarification from your side, we know

f(x) = 12500 × (0.82)^x

so, with every new year we are multiplying the value of the previous year by 0.82.

in other words

f(n) = f(n-1) × 0.82

with f(0) = 12500

because anything to the power of 0 equals 1.

A

so, the price is decreasing every year, because any multiplication with a positive value smaller than 1 decreases the original number.

multiplying an amount by a decimal number like 0.82 creates exactly 82% of the original amount because 1 represents 100%.

that means the value decreases every year by 100 - 82 = 18% compared to the value of the previous year.

B

1 5600

2 3136

3 1756.16

4 983.45

remember, Part A showed always an 18% decrease over the previous year.

from 5600 to 3136, this was a change of

100% = 5600

1% = 100%/100 = 5600/100 = $56

the price difference was 5600 - 3136 = 2464

how many % was that decrease ?

as many as how often 1% fits into 2464 :

2464 / 56 = 44%

that was much more than Part A.

from 3136 to 1756.16, this was a change of

100% = 3136

1% = $31.36

the price difference was 3136 - 1756.16 = $1,379.84

how many %

1,379.84 / 31.36 = 44%

again.

from 1756.16 to 983.45, this was a change of

100% = 1756.16

1% = $17.5616

the price difference was 1756.16 - 983.45 = 772.71

hire many %

772.71 / 17.5616 = 43.99997722...%

and again 44% (just a little rounding uncertainty).

so, product B recorded a much greater percentage change in value over the previous year than product A :

44% to 18%

Answer:

Is this an arithmetic sequence?

Yes.

Is there a common difference and if so, what is it?

Yes, there is a common difference : 1

The common difference is 1

Answer:

The answer is –3 < 1

Step-by-step explanation:

-3 is below zero. 1 is above zero. therefore, -3 less than 1

The equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

Given:

(1,-5) with slope m = -1

The standard slope intercept form is y = mx + c.

substitute m = -1 and (1,-5)

-5 = -1(1) + c

-5 = -1 + c

c = -4.

y = mx + c

y = -1(x) + (-4)

y = -x - 4.

Therefore the equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

Therefore equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

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5 days does it take to sell 640 cupcakes.

Given:

A bakery sells 4 dozen cupcakes every 3 hours.

If the bakery is open 8 hours each day.

4 dozen cupcakes = 4*12 cupcakes

= 48 cupcakes

48 cupcakes = 3 hours

divide by 3 on both sides

3hours/3 = 48/3 cupcakes

1 hour = 16 cupcakes

Number of cupcakes for 8 hours = 8 * 16 = 128 cupcakes.

128 cupcakes sells in one day.

To sell 640 cupcakes = 640/128

= 5 days.

Therefore 5 days does it take to sell 640 cupcakes.

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Answer:

The red symbol drawn over ∠2 and ∠3 indicates that the two angles total 90°. Therefore:

[tex]m\angle{2}+m\angle{3}=90^{\circ}[/tex]

The measure of angle1 in the given rectangular figure is 64° .

In the question ,

it is given that ,

the one of the angle is 116° .

From the figure below ,

we can see that

the dashed line is a transversal to AB and CD ,

the angles on the line AB form a linear pair ,

So , angle2 + 116° = 180°

angle2 = 180° - 116°

angle2 = 64°

Since the side panel of the podium is cut from rectangular piece

the figure is representing two parallel lines , cut by the transversal .

By the property of transversal that alternate interior angles are equal in measure ,

angle 1 = angle 2

hence , angle 1 = 64° .

Therefore , The measure of angle1 in the given rectangular figure is 64° .

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The quadratic function has only maximum value :

[tex]F(x)_{min}[/tex] = 30

x = 3

There is no minimum value of the quadratic function.

Given,

In the question:

The quadratic function is given as:

F(x) =  [tex]-3x^2+18x +3[/tex]

Determine whether the following quadratic function has a maximum or a minimum value. Then find  the maximum and minimum value of the function.

Now, According to the question:

The quadratic function is given as:

F(x) =  [tex]-3x^2+18x +3[/tex]

Take out the leading coefficient

F(x) = -3[tex](x^2-6x)+3[/tex]

Complete the square:

F(x) = [tex]-3(x^2+(2(-3))x + (-3)^2)+(3-(-3)^2))[/tex]

Express the function in vertex form

F(x) = [tex]-3(x-3)^2+30[/tex]

To  find the maximum value

[tex]F(x)_{min}[/tex] = 30

x = 3

For Minimum value:

F(x) = [tex]-3x^2 +18x +3[/tex]

Rewrite the function by completing the square

F(x) = [tex]-3(x-3)^2+30[/tex]

The graphs always open downwards

So, There is no minimum value of the quadratic function.

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Answer:

1022

Step-by-step explanation:

360+600+12+45+9=1022

Answer:

25

Step-by-step explanation:

First, we add 50, 12, and 16, which gives us 78. Then, we remove 3 from the answer, giving us 75. Then, divide 75 by 3.

Answer = 25.

(ps: sorry for any spelling mistakes, i dont really type answers alot)

If you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, You win 50 tickets, 12 tickets, and 16 tickets at an arcade. You are able to buy 3 of the same item with 3 tickets left over.

Number of tickets won,

= 50 + 12 + 16

= 78 tickets

Number of items bought = 3 items

Let the cost of 1 item be 'x' tickets.

The cost of 3 items = 3x

By the amount, we can buy 78 tickets as,

3x = 78

x = 26

Thus, if you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.

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Answer:

x = 3.5units

Step-by-step explanation:

Congruent means the same length, so set the given lengths equal to each other.

8x - 17 = -2x + 18

Add 2x to both sides.

10x -17 = 18

Add 17 to both sides.

10x = 35

Divide by 10

x = 3.5

When x is 3.5, KL and ST are the same length. Check.

8(3.5) - 17 = 11

and

-2(3.5) + 18 = 11

The total amount of water Karla drank before and after the tennis practice is 5 cups and 9 fluid ounces.

The correct answer option is option C.

Convert fluid ounces to cups:

1 fluid ounces = 0.125 cups

15 fluid ounces = 1.875 cups

Total volume of water Kayla drank = Volume of water Karla drank before tennis practice + Volume of water Karla drank after tennis practice

= 1.875 cups + 4 cups

= 5.875 cups

Approximately,

5 cups and 9 fluid ounces

Therefore, the total volume of water Karla drank is approximately 5 cups and 9 fluid ounce

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