Henry wants to avoid interest capitalization on his $7,800 unsubsidized Stafford loan. Henry will graduate in four years, and the loan has a duration of ten years. The loan has an interest rate of 5.6%, compounded monthly. How much must Henry pay every month to avoid interest capitalization?
a.
$14.56
b.
$43.68
c.
$36.40
d.
$31.20

Hi!

Your answer is "Multiplicative Inverse Property".

We can see that it's multiplying both sides by [tex]\cfrac{5}{4}[/tex] to get [tex]x[/tex] by itself.

This is known as the "multiplicative inverse" because the numerator and the denominator are swapped.

When a number is multiplied by its multiplicative inverse, it equals 1.

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For another example, see:

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Answer:

Step-by-step explanation:

to get the area of the given figure,

we need to split it in to two (see attached)

then area of a rectangle = length x width

A1 = 15 cm x 4 cm = 60 cm²

A2 = 5 cm x 4 cm = 20 cm²

Area = A1 + A2

        = 60 + 20

        = 80 cm²

Area in this figure will be 80cm².

The area of the rectangle can be calculated by the product of length and breadth of the rectangle.

A=l*b

where l is length and b is the breadth.

So according to asked question in the drawn figure,

connect the point B and G.

now this figure will give two rectangle i.e. ABGH and CDEF

Rectangle ABGH has length l=5cm

breadth b=4cm

area of the rectangle ABGH= length * breadth=l*b=5*4=20cm²

Now CF=CB+BG+GF=5+5+5=15

Rectangle CDEF has length l=CF=15cm

breadth b=4cm

area of the rectangle ABGH= length * breadth=l*b=15*4=60cm²

Area of the figure= area of the rectangle ABGH+area of the rectangle CDEF

=20cm²+60cm²

=80cm²

Therefore area in this figure will be 80cm².

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Answer:

241 units² (nearest whole number)

Step-by-step explanation:

**Assuming the clock is a circular shape**

Area of a circle = [tex]\pi r^2[/tex]

Given:

⇒ area = [tex]\pi[/tex] × 8.75²

            = 240.5281875...

            = 241 units² (nearest whole number)

Answer:241

Step-by-step explanation:

Divide by 2 to find the unit rate and multiply by 7 to find the cost of 7 units.

20.5/2 = 10.25.

10.25 times 7 = 71.75

It will cost $71.75 to buy 7 tickets.

Answer:

=2x-4

Step-by-step explanation:

Answer:

The fully simplified form is2x-4

Step-by-step explanation:

Use Distributive property

5(x-2)=5x-10

3(2-x)=6-3x

5x-10+6-3x

Combine like terms

2x-4

Answer:

f(x) = -5/3 x +44/3

Step-by-step explanation:

helo :   let  f(x)= ax+b

f(4) = 8   means : a(4)+b=8 and f(7) = 3   means : a(7)+b=3

you have this system :  4a +b = 8....(*)

                                      7a+b = 3 ....(**)

solve this system  use (*) : b = 8 -4a   and use (**) : b = 3-7a

so : 8-4a = 3-7a

-4a+7a = 3-8

3a = -5   so a = -5/3

but b =8-4a     so : b= 8-4(-5/3) =8+20/3  =44/3

f(x) = -5/3 x +44/3

Answer:

4

Step-by-step explanation:

6 - (-12) / (-6)

6 + 12 / (-6) (because subtracting a negative is the same as adding)

6 + (-2)

4

I hope this helps! Have a lovely day! :)

(Give brainliest to the other person bc they got it right first)

Answer:

Evaluate 6-(-12) / (-6)

6+12 / -6(The minus change to plus because when 2 minuses meet they make +(plus))

6-2(This is 6-2 because 12 /-6 is -2 because the negative takes over it like dividing 12  by 6 but with not negative)

4

The answer is 4

Answer:

D) Graph Z

Step-by-step explanation:

Convert from point-slope to slope-intercept form

[tex]y-6=4(x-4)\\\\y-6=4x-16\\\\y=4x-10[/tex]

This tells us that the line intersects the y-axis at (0,-10) and that our slope is 4. Therefore, the best choice given the options is D, graph Z.

The linear equation y = 4x - 10 represents the graph z. Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y - 6 = 4(x - 4)

Convert the equation into slope-intercept form. Then we have

y - 6 = 4(x - 4)

y - 6 = 4x - 16

y = 4x - 16 + 6

y = 4x - 10

The slope of the line is 4 and the y-intercept of the line is negative 10. Then the equation represents the graph z, then option D is correct.

More about the linear equation link is given below.

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Answer:

1)23/20

2)14/5

3)47

4)27/56

5)10/7

6)23/14

7)73/35

8)7/4

Step-by-step explanation:

1)multiply both fractions to get 20 as a common denominator

15/20+8/20=23/20

2)make 1 be 5/5

5/5+9/5=14/5

3)multiply both fractions to get 14 as a common denominator

26/14+21/14=47

4) multiply both sides to get 56 as a common denominator

35/56-8/56=27/56

5)make one 7/7

7/7+3/7=10/7

6)make 14 as the common denominator

2/14+21/14=23/14

7)make 35 the common denominator

28/35+45/35=73/35

8)make 1/2 be 2/4

5/4+2/4=7/4

Answer:

1.[tex]1\frac{3}{20}[/tex]
2.[tex]2\frac{4}{5}[/tex]
3.[tex]3\frac{5}{14}[/tex]
4.[tex]\frac{27}{56}[/tex]
5.[tex]1\frac{3}{7}[/tex]
6.[tex]1\frac{9}{14}[/tex]
7.[tex]2\frac{3}{35}[/tex]
8.[tex]1\frac{3}{4}[/tex]

Step-by-step explanation:

Given the following questions:

In order to add or subtract fractions we must find the common denominator, and then add the numerators. To subtract we complete the same steps but subtract the numerators instead of adding them. Of course, converting the improper fraction into a mixed number if needed.

Question one:

[tex]\frac{3}{4} +\frac{2}{5}[/tex]
[tex]CD=20[/tex]
[tex]\frac{3}{4} \times5=\frac{15}{20}[/tex]
[tex]\frac{2}{5} \times4=\frac{8}{20}[/tex]
[tex]\frac{15}{20} +\frac{8}{20}[/tex]
[tex]15+8=23[/tex]
[tex]=\frac{23}{20}[/tex]

Convert into mixed number:
[tex]\frac{23}{20}[/tex]
[tex]=\frac{23}{20}=23\div20=1\frac{3}{20}[/tex]
[tex]=1\frac{3}{20}[/tex]

Your first answer is indeed "1 3/20."

Question two:

[tex]1+\frac{9}{5}[/tex]
[tex]1=\frac{1}{1}[/tex]
[tex]\frac{1}{1} +\frac{9}{5}[/tex]
[tex]CD=5[/tex]
[tex]\frac{1}{1} \times5=\frac{5}{5}[/tex]
[tex]\frac{9}{5} \times1=\frac{9}{5}[/tex]
[tex]\frac{5}{5} +\frac{9}{5}[/tex]
[tex]5+9=14[/tex]
[tex]=\frac{14}{5}[/tex]

Convert into mixed number:
[tex]\frac{14}{5}[/tex]
[tex]\frac{14}{5}\di=14\div5=2\frac{4}{5}[/tex]
[tex]=2\frac{4}{5}[/tex]

Your second answer is indeed "2 4/5."

Question three:

[tex]\frac{13}{7} +\frac{3}{2}[/tex]
[tex]CD=14[/tex]
[tex]\frac{13}{7} \times2=\frac{26}{14}[/tex]
[tex]\frac{3}{2}\times7=\frac{21}{14}[/tex]
[tex]\frac{26}{14} +\frac{21}{14}[/tex]
[tex]26+21=47=\frac{47}{14}[/tex]
[tex]=\frac{47}{14}[/tex]

Convert into mixed number:
[tex]\frac{47}{14}[/tex]
[tex]\frac{47}{14}=47\div14=3\frac{5}{14}[/tex]
[tex]=3\frac{5}{14}[/tex]

Your third answer is indeed "3 5/14."

Question four:

[tex]\frac{5}{8} -\frac{1}{7}[/tex]
[tex]CD=56[/tex]
[tex]\frac{5}{8} \times7=\frac{35}{56}[/tex]
[tex]\frac{1}{7} \times8=\frac{8}{56}[/tex]
[tex]\frac{35}{56} -\frac{8}{56}[/tex]
[tex]35-8=27[/tex]
[tex]=\frac{27}{56}[/tex]

Your fourth answer is indeed "27/56."

Question five:

[tex]1+\frac{3}{7}[/tex]
[tex]1=\frac{1}{1}[/tex]
[tex]CD=7[/tex]
[tex]\frac{1}{1}\times7=\frac{7}{7}[/tex]
[tex]\frac{3}{7} \times1=\frac{3}{7}[/tex]
[tex]\frac{7}{7} +\frac{3}{7}[/tex]
[tex]7+3=10[/tex]
[tex]=\frac{10}{7}[/tex]

Convert into mixed number:
[tex]\frac{10}{7}[/tex]
[tex]\frac{10}{7} =10\div7=1\frac{3}{7}[/tex]
[tex]=1\frac{3}{7}[/tex]

Your fifth answer is indeed "1 3/7."

Question six:

[tex]\frac{1}{7} +\frac{3}{2}[/tex]
[tex]CD=14[/tex]
[tex]\frac{1}{7} \times2=\frac{2}{14}[/tex]
[tex]\frac{3}{2} \times7=\frac{21}{14}[/tex]
[tex]\frac{2}{14} +\frac{21}{14}[/tex]
[tex]2+21=23[/tex]
[tex]=\frac{23}{14}[/tex]

Convert into mixed number:
[tex]\frac{23}{14}[/tex]
[tex]\frac{23}{14}=23\div14=1\frac{9}{14}[/tex]
[tex]=1\frac{9}{14}[/tex]

Your sixth answer is indeed "1 9/14."

Question seven:

[tex]\frac{4}{5} +\frac{9}{7}[/tex]
[tex]CD=35[/tex]
[tex]\frac{4}{5} \times7=\frac{28}{35}[/tex]
[tex]\frac{9}{7} \times5=\frac{45}{35}[/tex]
[tex]\frac{28}{35} +\frac{45}{35}[/tex]
[tex]28+45=73[/tex]
[tex]=\frac{73}{35}[/tex]

Convert into mixed number:
[tex]\frac{73}{35}[/tex]
[tex]=\frac{73}{35}=73\div35=2\frac{3}{35}[/tex]
[tex]=2\frac{3}{35}[/tex]

Your seventh answer is indeed "2 3/35."

Question eight:

[tex]\frac{5}{4} +\frac{1}{2}[/tex]
[tex]CD=8[/tex]
[tex]\frac{5}{4}\times2=\frac{10}{8}[/tex]
[tex]\frac{1}{2} \times4=\frac{4}{8}[/tex]
[tex]\frac{10}{8}+\frac{4}{8}[/tex]
[tex]10+4=14[/tex]
[tex]=\frac{14}{8}[/tex]

Simplify by reducing:
[tex]\frac{14}{8}[/tex]
[tex]\frac{14}{8}\div2=\frac{7}{4}[/tex]
[tex]=\frac{7}{4}[/tex]

Convert into mixed number:
[tex]\frac{7}{4}[/tex]
[tex]\frac{7}{4} =7\div4=1\frac{3}{4}[/tex]
[tex]=1\frac{3}{4}[/tex]

Your final answer is indeed "1 3/4."

Hope this helps.

Answer:

Power Set = {{1,9,11,14},{1,11,14},{1,9,11},{1,9,14},{9,11,14},{1,11},{1,14},{1,9},{11,14},{9,11},{9,14},{1},{11},{14},{9},{}}

Step-by-step explanation:

The power set of a set S is the set of all subsets of S. The first subset will be set S itself. Next, find all subsets that contain one less element (in this case 3 elements). Continue with this process until finding all subsets including the empty set.

Answer:

43°

Step-by-step explanation:

supplementary angles sum to 180° , then

second angle + 137° = 180° ( subtract 137° from both sides )

second angle = 43°

Answer:

Its answer B!

Step-by-step explanation:

Answer:

The width of the fence measures 6 feet

Step-by-step explanation:

Firstly, we assign variables.

Let the width of the fence be represented by w and the length by l

Now let’s get what the length would be. width is 2 less than half length

w = l/2 - 2

or simply l/2 = w + 2

which is same as l = 2(w + 2)

Now the perimeter of the fencing is 44. The perimeter of a rectangle can be calculated using the formula

P = 2(l + w)

Now let’s insert what we have:

P = 44 and l = 2(w + 2)

44 = 2(2(w+2) + w)

44 = 2(2w + 4 + w)

44 = 2(3w + 4)

44 = 6w + 8

6w = 44-8

6w = 36

w = 36/6

w = 6 feet

Step-by-step explanation:

Answer:

Tanisha = 14 years

Ana = 7 years

Elicia = 16 years

Step-by-step explanation:

Let T = age of Tanisha

Let A = age of Ana

Let E = age of Elicia

Tanisha is twice as old as Ana:  

T = 2A

⇒ A = (1/2)T

Elicia is 2 years older than Tanisha:

E = 2 + T

Sum of all their ages is 37:

A + E + T = 37

Substitute A = (1/2)T and E = 2 + T into A + E + T = 37 and solve for T:

⇒ (1/2)T + 2 + T + T = 37

⇒ (5/2)T = 35

⇒ T = 14

If T = 14, then

A = (1/2)T = (1/2) 14 = 7

If T = 14, then

E = 2 + T = 2 + 14 = 16

Answer:

Rectangular prism X

Step-by-step explanation:

For rectangular prism X:

7*3*6=126 cm³
For rectangular prism Y:
5*2*11=110 cm³
Rectangular prism X holds more because 126 is greater than 110
Hope this helps :)

After Assuming a tax percentage of 3.5%, the tax amount gotten is $0.7

and the  total cost of a double room, including tax is $20.7

Given Data

Amount of Tax paid = 3.5/100 * 20

= 0.035* 20

= $0.7

The total cost of a double room, including tax

= Cost of double + Amount of Tax

= 20+0.7

= $20.7

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Answer:

[tex]m = \frac{4}{3} = 1.3334[/tex]

Step-by-step explanation:

To find the slope of a line, all you have to do is determine 2 points that pass through this line;

for example, in this case,

(-4,-2) (4,4)

Use the equation;

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{4 - ( - 4)}{4 - ( - 2)} = \frac{4 + 4}{4 + 2} [/tex]

[tex]m = \frac{8}{6} = \frac{4}{3} [/tex]

This line passes through the point (1,0) and that is your y-intercept.

[tex]y = \frac{4}{3} x + 1[/tex]

The requried slope of the given line is m = 3/4.

The slope of the line is defined as the ratio of the rise and run of the straight line on the curve is given as;

m = (y₂ - y₁) / (x₂ - x₁)

Here,
From the graph, we have (-4, -2) and (4, 4).

The slope of the line is given as:

m = (y₂ - y₁) / (x₂ - x₁)

m = (4+2)/(4+4)
m = 6/8
m = 3/4

Thus, the requried slope of the given line is m = 3/4.

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Answer:

Step-by-step explanation:

Directions

You cut a pizza cut into 2 equal slices and eat 1 slice, or 1/2

of the pizza. You cut another pizza of the same size cut into 4

equal slices, but you still only eat 1 slice. This time you've

eaten only 1/4 of the pizza, which is less than 1/2.

As you divide the pizza into more slices, the bottom number

(the denominator) gets bigger, but the size of each slice gets

smaller.

Drag the fractions in order from least to greatest.

1/3

1/4

1/2

1/8

-------------------

1/3 = 0.33

1/4 = 0.25

1/2 = 0.5

1/8 = 0.125

so

1/8

1/4

1/3

1/2

Step-by-step explanation:

IN ORDER OF INCREASING ORDER OR FROM LEAST TO GREATEST =1/8, 1/4, 1/3 ,1/2

Answer:

Step-by-step explanation:

a) 0.6406; b) 1.000; c) C. The probability from part​ (a) is more relevant because it shows the proportion of male passengers that will not need to bend; d) B. Since men are generally taller than​ women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

Answer:

A

...................

Answer:

7^9

Step-by-step explanation:

when dividing you take away powers.

Answer:

7 to the power of 9

Step-by-step explanation:

7 by it self is 7 to the power of 1, and when you are dividing a power to subtract the power on top, so 10-1=9 and the answer is 7 to the power of 9 or 7^9

Answer:

Step-by-step explanation:

x + x + 2x + 3 + 2x + 3 = 360

6x + 6 = 360

Divide by 6

x + 1 = 60

x = 60 - 1 = 59

Answer:

question 1 : That symbol in question 1 represents 10 houses because 20/2 = 10 I.e it half (1/2) of the first one

question 2 : They built more than 100 houses In the following months:

January 2009

August 2009

December 2009

Answer:

I'm not sure of the exact term in the blank, but a^3 and a^7 are both exponents with the same base meaning you can add the exponents to create one.

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

The correct option is  C

Step-by-step explanation:

From the question we are told that

    The number of outcome is  3 (rock paper and scissors)

     The number of game you and the first friend played is  a = 400

      The number of times friend A chose scissors is b = 100

      The number of game you and the second friend played is c= 120

       The number of times friend B chose scissors  is  d =  20

        The number of game you and the third friend played is e =  300

        The number of times friend B chose scissors  is f = 65

Generally the probability of success of each outcome is  

        [tex]p = \frac{1}{3} = 0.33[/tex]

Generally the probability of failure of each outcome is  

      [tex]q = 1-p[/tex]

=>   [tex]q = 1-\frac{1}{3}[/tex]

=>    [tex]q = \frac{2}{3} = 0.67[/tex]

Generally the proportion of  scissors chosen by friend A is  mathematically represented as

        [tex]p_1 =  \frac{b}{a}[/tex]

=>       [tex]p_1 =  \frac{100}{400}[/tex]

=>       [tex]p_1 = 0.25[/tex]

Generally the proportion of  scissors chosen by friend B is  mathematically represented as

        [tex]p_2 =  \frac{d}{c}[/tex]

=>       [tex]p_2 =  \frac{20}{120}[/tex]

=>       [tex]p_2 = 0.167[/tex]

Generally the proportion of  scissors chosen by friend B is  mathematically represented as

        [tex]p_3 =  \frac{f}{e}[/tex]

=>       [tex]p_3 =  \frac{65}{300}[/tex]

=>       [tex]p_3 = 0.2167[/tex]

Generally the standardized value  for  friend A is mathematically represented as

          [tex]z_1 =  \frac{p_1 - p}{\sqrt{\frac{p* q}{a} } }[/tex]

     => [tex]z_1 =  \frac{0.25- 0.33}{\sqrt{\frac{0.33* 0.67}{400} } }[/tex]

      =>  [tex]z_1 = -3.4[/tex]      

Generally the standardized value  for  friend B is mathematically represented as

          [tex]z_2 =  \frac{p_2 - p}{\sqrt{\frac{p* q}{c} } }[/tex]

     => [tex]z_2 =  \frac{0.167- 0.33}{\sqrt{\frac{0.33* 0.67}{120} } }[/tex]

      => [tex]z_2 =  -3.8 [/tex]      

Generally the standardized value  for  friend C is mathematically represented as

          [tex]z_3 =  \frac{p_3 - p}{\sqrt{\frac{p* q}{e} } }[/tex]

     => [tex]z_3 =  \frac{0.2167- 0.33}{\sqrt{\frac{0.33* 0.67}{300} } }[/tex]

      => [tex]z_3 =  -4.17 [/tex]            

Answer: C

reason: There are special rules to follow when an expression is raised to the power of 0 or 1. Remember these rules when using numerical expressions involving the exponents 0 and 1:

Any number raised to the power 0 is equal to 1. For example, 120 is equal to 1 and 300 is equal to 1. However, this rule does not apply when 0 is the base: 0 raised to any power other than 0 is equal to 0, and 00 is not defined.

Any number raised to the power 1 is equal to the number itself. For example, 121 is equal to 12, 301 is equal to 30, and 01 is equal to 0

A numerical expression contains numbers and operations but not the equality symbol (=). Here are some examples of numerical expressions:

15 + 4 − 2

56 ÷ 7 + 5 × 5 × 5

32 × 5 + 7

Numerical expressions can also be written in words, such as "nine times six minus seven" and "five divided by ten plus two."

Look at the expression 56 ÷ 7 + 5 × 5 × 5. Instead of writing 5 three times in the expression, we can replace it with a whole-number exponent. For that, we write 5 × 5 × 5 as 53:

56 ÷ 7 + 5 × 5 × 5

56 ÷ 7 + 53.

Let's write 2 × 3 × 3 × 3 × 3 × 3 × 3 with a whole-number exponent. Here, 3 is multiplied by itself and occurs 6 times in the expression. Instead of writing 3 six times, we can write 3 × 3 × 3 × 3 × 3 × 3 as 36. So, 2 × 3 × 3 × 3 × 3 × 3 × 3 is the same as 2 × 36.

Answer:

250 km/h

Step-by-step explanation:

5x50=250

Hope it helps!

brainliest, ty!

Answer:

y=-1/2x-1

Step-by-step explanation:

4-0     =      4     =         1

-6-2    =     -8     =       -2

4=-6(-1/2)

4=    3

-4    -4

b= -1

y=mx+b

y=-1/2x-1