Ethan borrowed $1,200 from a loan company at 15% simple interest for 6 months. How much did he have to pay each month on the installment plan?

Answer:

The Radius of circle is 7.15 cm  

Step-by-step explanation:

Given as :

A Triangle is inscribed into circle

The center of circle is O

The Diameter of circle = AK = d

The hypotenuse of triangle being the diameter of circle

The Area of triangle = 50 cm²

Let The radius of circle = r cm

The Triangle is right angle at c

So , ∠ACK = 90°

∠CAK = 42°

∠AKC = 180° - (90° + 42°)

So, ∠AKC = 48°

Now, ∵ Area of triangle ACK = 50 cm²

So, [tex]\dfrac{1}{2}[/tex] × AC × CK = 50

Or, AC × CK = 50 × 2

i.e , AC × CK = 100        ..........1

From figure

Sin 48° =  [tex]\dfrac{AC}{AK}[/tex]

Or, 0.74 =  [tex]\dfrac{AC}{d}[/tex]

∴ AC = 0.74 d             ..........2

Similarly

Sin 42° =  [tex]\dfrac{CK}{AK}[/tex]

Or, 0.66 =  [tex]\dfrac{CK}{d}[/tex]

∴ CK = 0.66 d               .............3

Putting eq 2 and 3 value into eq 1

i.e  AC × CK = 100  

Or, 0.74 d  × 0.66 d = 100  

Or, 0.4884 × d² = 100  

∴ d² = [tex]\dfrac{100}{0.4884}[/tex]

Or, d² = 204.75

Or, d = [tex]\sqrt{204.75}[/tex]

Or, d = 14.30

So, The diameter of circle = d = 14.30 cm

Now, Radius of circle = [tex]\dfrac{\textrm diameter}{2}[/tex]

Or, r =  [tex]\dfrac{\textrm 14.30 cm}{2}[/tex]

i.e r = 7.15 cm

So, The Radius of circle =  r = 7.15 cm

Hence, The Radius of circle is 7.15 cm  Answer

Let's solve this problem step by step.
1. We are given the total number of hippos, which is 3.
2. We are also given the total number of pumpkins, which is 5.
3. We want to find out how many pumpkins each hippo gets if the pumpkins are distributed evenly among the hippos.
To find out the number of pumpkins per hippo, we divide the total number of pumpkins by the total number of hippos.
4. Performing the division, we have:
  \( \frac{5 \, \text{pumpkins}}{3 \, \text{hippos}} = 1.666... \)
5. Each hippo gets approximately 1.666... pumpkins.
To express the number with a finite number of decimal places, we can round it to the desired precision. For example, rounding to two decimal places, we get 1.67 pumpkins per hippo. This is a simplification, as the fraction actually represents a repeating decimal with the digit 6 repeating indefinitely (i.e., 1.\(\overline{6}\) pumpkins per hippo).

Answer:

[tex]x=12[/tex]

Step-by-step explanation:

we know that

A linear pair is two angles that are adjacent and form a line. The angle measure of a line is 180 degrees

In this problem we have that

[tex](10x-20)^o+(6x+8)^o=180^o[/tex] --- by supplementary angles (form a linear pair)

solve for x

[tex](16x-12)=180[/tex]

[tex]16x=180+12[/tex]

[tex]16x=192[/tex]

[tex]x=12[/tex]

The required polynomial that should be subtracted from the polynomial [tex]y^2-5y+1[/tex] to get the difference equal to 5  is [tex]y^2-5y-4[/tex]

Step-by-step explanation:

We need to find polynomial that should be subtracted from the polynomial [tex]y^2-5y+1[/tex] to get the difference equal to 5

Let the required polynomial be x

We are given:

[tex]y^2-5y+1-(x)=5[/tex]

We need to find the value of x

[tex]-x=5-y^2+5y-1\\-x=-y^2+5y+4[/tex]

Divide both sides by - 1

[tex]x=y^2-5y-4[/tex]

So, the required polynomial that should be subtracted from the polynomial [tex]y^2-5y+1[/tex] to get the difference equal to 5  is [tex]y^2-5y-4[/tex]

Keywords: Solving Polynomials

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The unit price per pair of insulated gloves is found by dividing the total cost of the package by the number of pairs. For a package costing $35.34 containing 6 pairs of gloves, the unit price is $5.89 per pair.

The question asks us to calculate the unit price of a pair of insulated gloves when given the total cost for a package containing multiple pairs. To find the unit price, you would divide the total cost of the package by the number of units (pairs of gloves) in the package. If a package of 6 pairs of gloves costs $35.34, then the unit price per pair of gloves is calculated as follows:

Total cost of package: $35.34

Number of pairs in the package: 6

The unit price per pair of gloves = Total cost of package
/ Number of pairs

Unit price per pair of gloves = $35.34 / 6

Calculating this, we get the unit price per pair of gloves:

Unit price per pair of gloves = $5.89

Answer:

x=-8 y=-2

Step-by-step explanation:

substitute x for 2y-4

7(2y-4)+5y=-66

factor

14y-28+5y=-66

add 28 on both sides

14y+5y=-38

19y=-38

divide by 19 on both sides

y=-(38/19)

y=-2

Plug -2 into the first equation for y

x=2(-2)-4

x=-4-4

x=-8

By looking at the graph, we can see that the shape is a quarter of a circle.

The area of a circle is:

[tex]a = \frac{1}{2} \pi {r}^{2} [/tex]

So, this "quarter circle" is:

[tex]a = \frac{1}{4} \times \frac{1}{2} \pi {r}^{2} [/tex]

R is the radius (the diagram shows the radius is 8), so we can now find the area:

[tex]a = \frac{1}{4} \times \frac{1}{2} \pi \times {8}^{2} \\ a = \frac{1}{8} \pi \times 64 \\ \\ a = \frac{64\pi}{8} \\ a = 8\pi[/tex]

The area is 8π.

Answer:

Step-by-step explanation:

r = 8 units

Area of the shape = 1/4 area of circle

=1/4 * πr²

= 1/4 * 3.14 * 8*8

= 3.14 * 2* 8

= 50.24 sq.units

43 pounds is a reasonable range for the total weigh of 6 packages.

Step-by-step explanation:

Given,

Number of packages shipped = 6

Weight of lightest = 24 pounds

Weight of heaviest = 67 pounds

Let,

a, b, c, d be the weight of other four packages.

24, a, b, c, d, 67 (written in lighter to heavier weight order)

Range is defined as the difference between the lowest and highest values.

Range = Highest weight - Lowest weight

Range = 67 - 24 = 43 pounds

43 pounds is a reasonable range for the total weigh of 6 packages.

Keywords: range, difference

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The reasonable range for the total weight of the 6 packages is 24 pounds to 67 pounds.

The reasonable range for the total weight of the 6 packages is 24 pounds to 67 pounds.

Since the lightest package weighs 24 pounds and the heaviest package weighs 67 pounds, any total weight between these two values would be reasonable.

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Answer:

Step-by-step explanation:

marked down by 1/4 of the original price.

let x represent original price

original price - 1/4 of original price = sales price

x - 1/4x = 128

4/4x - 1/4x = 128

3/4x = 128

x = 128/(3/4)

x = 128 * 4/3

x = 512/3

x = 170.666 rounds to 170.67 <== original price

==============================

I hope I am understanding this one correctly...

let x = price the store paid

x + 1/2x = 170.67

2/2x + 1/2x = 170.67

3/2x = 170.67

x = 170.67 / (3/2)

x = 170.67 * 2/3

x = 341.34/3

x = 113.78 <=== what the store paid

===========================

the difference between the discount price..I am assuming this is the $ 128 from part A.....and what the store paid....113.78...from part B..

128 - 113.78 = $ 14.22 <==

I am not completely sure about B and C......B confused me.....and if B is wrong, so is C.

Answer:

Option A) no solution

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The solution of the system of equations is the intersection point both graphs

In this problem the lines are parallel

so

The lines do not intersect

Therefore

The system has no solution ( Is an inconsistent system)

Answer:

b

Step-by-step explanation:

i just did the usa test prep

Explanation:

To do long division, follow the method pattern "DMS down".

D for divide.

M for multiply.

S for subtract.

Down is to bring down.

Use an example:

52 ÷ 2?

Divide 2 by the first digit of 52.

  2          Whenever you divide, put the answer at the top.

2∫52

Multiply answer by number you are dividing by.

  2

2∫52

   4      When not dividing, put the work under the question.

Subtract.

   2

2∫52

   4  

   1

Bring down the next digit.

   2

2∫52

   4  

   12

Divide into the new difference 12.

   26

2∫52

   4  

   12

Multiply the new digit.

   26

2∫52

   4  

   12

   12

Subtract.

   26

2∫52

   4  

   12

   12

    0    You stop when you get to 0. If you ran out of digits to bring down, write this as a remainder.

Answer:

Step-by-step explanation:

1. Put into bar

8(456

2. How many times does 8 go into 45 ( 8*?=45)

8*5=40

057

8(456

-40 45-40=5

56. Bring down the 6

-56 How many times does 8 go into 56

0 8*7=56

LAST STEP:

CHECK

8*57=456

Answer:

4.178×10 to the second power

Step-by-step explanation:

Move the decimal twice to the Left

Answer: The answer is 4.178 × 10^2

Step-by-step explanation: you move the point to the the space immediately after the first digit and multiply the resulting figure by ten raised to the power of number of times the point was moved.

Answer:

The measure of arc AC is [tex]136^o[/tex]

Step-by-step explanation:

Notice that angle BAC (whose measure is given as 34 degrees) is an inscribed angle, and according toe the inscribed angle theorem, the measure of an inscribed angle is half the measure of the central angle that subtends the same chord.

Then, the central angle that subtends the cord BC, is twice 34 degrees ([tex]2\,*\,34^o = 68^o[/tex])

Then, since they give us also the measure of the arc AB which is [tex]156^o[/tex], then the measure of arc AC can be estimated as the needed measure to complete [tex]360^o[/tex] as the sum of all three arcs. That is:

[tex]AC + AB+ BC = 360^o\\AC + 156^o+2\,*\,34^o = 360^o\\AC + 156^o+68^o = 360^o\\AC=360^o-156^o-68^o\\AC=136^o[/tex]

Answer:

Option A. 5.25 units

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

[tex]\frac{PR}{XZ}=\frac{QR}{YZ}[/tex]

substitute the given values

[tex]\frac{7}{XZ}=\frac{4}{3}[/tex]

solve for XZ

[tex]XZ=7(3)/4\\XZ=5.25\ units[/tex]

The measure of XZ from the figure is 5.25

In order to determine the measure of XZ, we need to take the ratios of the similar sides of the triangles as shown:

QR/YZ = RP/XZ

Substitute the equivalent parameters:

4/3 = 7/XZ
4XZ = 21

XZ = 21/4
XZ = 5.25

Hence the measure of XZ from the figure is 5.25

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Answer:

$13,685.69

Step-by-step explanation:

A = P (1 + r)ⁿ

A = $10,000 (1 + 0.04)⁸

A = $10,000 x 1.368569

A = $13,685.69

Answer:

use the distributive property to distribute the 8

-16+16n+3n=40+5n

-16+19n=40+5n

-16=40+5n-19n

-16=40-14n

-14n+40= -16

-14n= -16-40

-14n= -56

n= -56/-14

n= 4

Answer: n=4

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helps you out! If you need anymore help with math, let me know and I will be more than happy to help you! ☺

-Karleif Jonsi-

Answer:

h=2A/b

Step-by-step explanation:

A=1/2bh

bh=A/(1/2)

bh=(A/1)(2/1)

bh=2A/1

bh=2A

h=2A/b

Answer:

The Total cost of 2 coats of paint in the room is 73.508 pounds

Step-by-step explanation:

Given as :

The length of the room = L = 6.8 meters

The breadth of the room = B = 9.2 meters

The cost of paint to cover 20 meters² area = 11.75 pounds

Let The cost painting the room = x pounds

Now, According to question

The Area of rectangular room = Length × breadth

Or, Area = L×B

Or, A = 6.8 meters × 9.2 meters

Or, Area = 62.56 meters²

∵ cost of paint to cover 20 meters² area = 11.75 pounds

∴ cost of paint to cover 62.56 meters² area = [tex]\dfrac{11.75}{20}[/tex] × 62.56 pounds

Or, x = 0.5875 × 62.56 pounds

Or, x = 36.754 pounds

So, cost painting the room = x = 36.754 pounds

Now, Since 2 coats of paints is allowed in the room

And The cost of 1 coats of paints = 36.754 pounds

So, The cost of 2 coats of paints = 36.754 × 2 pounds

i.e The cost of 2 coats of paints = 73.508 pounds

Hence, The cost of 2 coats of paint in the room is 73.508 pounds Answer

Answer:

[tex]10\pi\ cm[/tex] or [tex]31.4\ cm[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=15\ cm[/tex]

substitute

[tex]C=2\pi (15)[/tex]

[tex]C=30\pi\ cm[/tex]

step 2

Remember that the circumference of the circle subtends a central angle of 360 degrees

so

using proportion

Find the length of an arc by a central angle of 120 degrees

[tex]\frac{30\pi}{360^o}=\frac{x}{120^o}\\\\x=30\pi(120^o)/360^o\\\\x= 10\pi\ cm[/tex]

The exact value of the length of the arc is [tex]10\pi\ cm[/tex]

assume

[tex]\pi=3.14[/tex]

[tex]10(3.14)=31.4\ cm[/tex] ---> approximate value

Answer:

Step-by-step explanation:

About 31.4 based on the other answers I have seen.

Complete Question:

Read the following excerpt from Winston Churchill's "Their Finest Hour" speech presented during World War II.

Of this, I am quite sure, that if we open a quarrel between the past and the present, we shall find that we have lost the future. Therefore, I cannot accept the drawing of any distinctions between Members of the present Government. It was formed at a moment of crisis in order to unite all the Parties and all sections of opinion. It has received the almost unanimous support of both Houses of Parliament. Its Members are going to stand together, and, subject to the authority of the House of Commons, we are going to govern the country and fight the war.

What is most likely the intended effect of beginning the speech this way?

A. The audience will be convinced that Churchill will accept criticism.

B. The audience will decide to be subject to authority of the House of

Commons.

C. The audience will realize that past mistakes of the government led

to the war.

D. The audience will perceive the government as strong and united.

Answer:

"The audience will perceive the government as strong and united" is most likely the intended effect of beginning the speech this way

Step-by-step explanation:

The importance of speech “Their Finest Hour” delivered by Winston Churchill was to show his feeling or thoughts towards French and German countries. France has just been defeated by the German country. Winston talked because he thought, Britain should keep continuing their fight to defeat the evils of Hitler.

Here, Finest Hour refers a period or a relatively short period during which an extremely vivid, charming or effective group of action had been performed. So, from this, concluding that the audience who received his speech recognized the united and strong governance.

Answer: D

Step-by-step explanation:

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is hte y-intercept.

In this case, given the linear function:

[tex]f(x)= -\frac{2}{3}x +2[/tex]

You can rewrite it as:

[tex]y= -\frac{2}{3}x +2[/tex]

You can identify in the graph that the y-intercept is:

[tex]b=2[/tex]

Now, in order to find the x-intercept, you can substitute [tex]y=0[/tex] and solve for "x". This is:

[tex]0= -\frac{2}{3}x +2\\\\(-2)(3)=-2x\\\\\frac{-6}{-2}=x\\\\x=3[/tex]

Finally, knowing the y-intercept and the x-intercept, you can graph the function (See the graph attached)

The house will be 10.9 inches high on the blueprint.

Step-by-step explanation:

Given,

Scale on blue print;

6 inch = 11 feet

We will find unit rate in terms of foot.

1 foot = [tex]\frac{6}{11}\ inches[/tex]

Therefore;

20 feet = [tex]\frac{6}{11}*20 = \frac{120}{11}[/tex]

20 feet = 10.9 inches

The house will be 10.9 inches high on the blueprint.

Keywords: unit rate, division

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The house would be approximately 10.91 inches tall on the blueprint to represent a 20-foot actual height.

The student asked how many inches high a house would be on a blueprint if the actual home is to be 20 feet tall, and a blueprint states that a 6-inch line represents 11 feet on the actual home. To solve this, we set up a proportion to determine the blueprint's height. The proportion is 6 inches/11 feet = x inches/20 feet, where x represents the height on the blueprint. First, write the proportion as 6 inches/11 feet = x inches/20 feet. Then, cross-multiply to get 11 feet * x inches = 6 inches * 20 feet. To find x, divide both sides of the equation by 11 feet, getting x = (6 inches * 20 feet) / 11 feet. After calculating, we find that x ≈ 10.91 inches. Therefore, on the blueprint, the house would be approximately 10.91 inches tall to represent an actual height of 20 feet.

Answer:

35 hotdogs and 52 sodas were sold.

Step-by-step explanation:

Create equations to represent the problem.

let "d" be the number of hotdogs sold

let "a" be the number of sodas sold

1.5d + 0.5a = 78.50     Equation for money made

d + a = 87                    Equation for items sold

Rearrange d + a = 87 to isolate one of the variables.

a = 87 - d

Substitute a for 87-d into the other equation. Isolate using reverse operations.

1.5d + 0.5a = 78.50

1.5d + 0.5(87 - d) = 78.50     Distribute over brackets by multiplying

1.5d + 43.5 - 0.5d = 78.50    Collect like terms

43.5 + d = 78.50          1.5d - 0.5d is 1d. You don't need to write "1".

43.5 + d - 43.5 = 78.50 - 43.5   Isolate d, subtract 43.5 from both sides

d = 35    Number of hotdogs sold

Substitute d for 35 in the simpler equation

d + a = 87

35 + a = 87     Subtract 35 form both sides to isolate "a".

a = 87 - 35

a = 52      Number of sodas sold

Therefore 35 hotdogs and 52 sodas were sold.

Answer:

D

Step-by-step explanation:

The law of sines is

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] ( cross- multiply )

a sinC = c sinA ( divide both sides by sinC )

a = [tex]\frac{csinA}{sinC}[/tex] → D

Option d: "a = c * sin(A) / sin(C)" is the correct representation of the law of sines.

The law of sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Mathematically, it can be expressed as:

a/sin(A) = b/sin(B) = c/sin(C)

Where:

- a, b, and c are the lengths of the sides of the triangle.

- A, B, and C are the measures of the angles opposite to sides a, b, and c respectively.

So, in terms of the side lengths:

a/sin(A) = c/sin(C)

Rearranging gives:

a = c * sin(A) / sin(C)

So, option d: "a = c * sin(A) / sin(C)" is the correct representation of the law of sines.

[tex]\text{Solve:}\\\\-5(1+5p)=7p-5\\\\\text{Distribute the -5 to the variables inside the parenthesis}\\\\-5 - 25p=7p-5\\\\\text{Add 5 to both sides}\\\\-25p=7p\\\\\text{Subtract 7p from both sides}\\\\-32p=0\\\\\text{Divide both sides by -32}\\\\\boxed{p=0}[/tex]

Answer: 2 bookcases.

Step-by-step explanation:

Let be "x" the number of bookcases that the custodian will be able to repaint completly with 5 gallons of paint.

According to the data given, the custodian needs 2 gallons of paint to repaint one bookcase. Since all the bookcases are equal, you can set up the following proportion:

[tex]\frac{2}{1}=\frac{5}{x}[/tex]

Now you must solve for "x" in order to find its value:

[tex](x)(\frac{2}{1})=5\\\\2x=5\\\\x=\frac{5}{2}\\\\x=2.5[/tex]

Notice that the custodian will be able to repaint 2 bookcases completely, then you can say that:

[tex]x\approx2[/tex]

The custodian will be able to repaint 2 bookcases with 5 gallons of paint.

To determine the number of bookcases the custodian will be able to repaint with 5 gallons of paint, we need to divide the total amount of paint by the amount of paint required for each bookcase. Each bookcase requires 2 gallons of paint, so we divide 5 gallons by 2 gallons per bookcase:

5 gallons ÷ 2 gallons/bookcase = 2.5 bookcases

Since we cannot have 0.5 of a bookcase, the custodian will be able to repaint 2 bookcases with 5 gallons of paint.

Answer:

15! I hope this helped!

Step-by-step explanation:

You add 8+7

Answer:

0/15

Step-by-step explanation:

I'd like to apologize for the person before me who answered this question completely incorrectly.

Next, I'd be happy to help you.

Start with the second y value, which in this case is 7, and subtract -8 from it.

7 - (-8) = 15

Then, subtract the second x value, from the first x value.

2-2 = 0.

The distance between the 2 points is 0/15.

Answer:

Choice B and Choise C.

Step-by-step explanation:

Equivalent expressions are those expressions that have the same value but they look different.

Given the following expression provided in the exercise:

[tex]6.53 - (-4.11) + 7.92[/tex]

You need to remember the multiplication of signs in order to find the equivalent expressions:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]

Then:

- Eliminating the parentheses, you get this equivalent expression:

[tex]6.53 +4.11 + 7.92[/tex]

- Since the mulplication of two negative signs gives yous a positive sign, you can rewrite the original expression in this form:

[tex]-(-6.53)+4.11-(-7.92)[/tex]

This is an equivalent expression to [tex]6.53 - (-4.11) + 7.92[/tex]

Answer:

b & c

Step-by-step explanation:

I did it on khan academy and it was right

Option A: d(t) = 360-60t is the right answer

Step-by-step explanation:

We will write the given problem in terms of function to find the correct answer.

Let d(t) be the function and t be the number of hours.

Total distance is 360 miles and with each passing hour the distance will reduce 60 miles

So,

The function is:

[tex]d(t) = 360-60t[/tex]

Hence,

Option A: d(t) = 360-60t is the right answer

Keywords: Functions, word problems

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