Joshua borrowed $2,200 for one year and paid $132 in interest. The bank charged him a service charge of $21. What is the finance charge on this loan?

Answer:

0.7 is the decimal equivalent to 70/100.

Step-by-step explanation:

You can just do the numerator (70) divided by the denominator (100): 70÷100 = 0.7

Answer:

[tex]-\frac{11}{12}[/tex]

Step-by-step explanation:

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Answer:

surface area=2816 m² & volume =205.33m³

Step-by-step explanation:

here

diameter of base (d) -28 m

radius(r) = d/2=14 m

vertical height of cone (h)-48 m

slant height of cone (l)-50 m

surface area (TSA)-?

volume (v)-?

we know

TSA=(pie*r*l)+pie*r*r

=pie*r(l+r)

=22/7* 14(50+14)

=22*2(64)

=22*128

=2816 m²

again

v=1/3 pie*r*r

=1/3*22/7*14*14

=1/3*22*2*14

=205.33 m³

Answer:

a. to accuse a public official, before an appropriate tribunal. of misconduct in office

Answer: There are no solutions.

Step-by-step explanation:

1/4(8x - 4) = 2x + 1

2x - 1 = 2x + 1

-1 = 1

Answer:

620. 0.25 x 620 = 155

Answer:

[tex]w=\dfrac{8x^2-2y}{y}[/tex]

Step-by-step explanation:

[tex]\textsf{When}\:\dfrac{2x^2}{y}=\dfrac{w+2}{4}\:\textsf{is solved for}\:w,\:\textsf{one equation is}\:w=\dfrac{8x^2}{y}-2[/tex]

Which of the following is an equivalent to find w?

[tex]w=\dfrac{8x^2+2y}{y}[/tex]

[tex]w=\dfrac{8x^2-2y}{y}[/tex]

[tex]w=8x^2-3y[/tex]

[tex]w=8x^2-y[/tex]

[tex]\textsf{Given}: \quad w=\dfrac{8x^2}{y}-2[/tex]

[tex]\implies w=\dfrac{8x^2}{y}-\dfrac{2y}{y}[/tex]

[tex]\implies w=\dfrac{8x^2-2y}{y}[/tex]

The solution for w is [tex]w=\frac{2(4x^2-y)}{y}[/tex] in the equation [tex]\frac{2x^2}{y} = \frac{w+2}{4}[/tex] obtained by isolating the variable term w.

The given equation is[tex]\frac{2x^2}{y} = \frac{w+2}{4}[/tex]

We need to solve for w:

To do this we have to isolate the term with w.

Apply cross multiplication:

[tex]8x^2 = y(w+2)[/tex]

Divide both sides by y:

[tex]\frac{8x^2}{y}=w+2[/tex]

Subtract 2 from both sides:

[tex]\frac{8x^2}{y}-2=w[/tex]

[tex]\frac{8x^2-2y}{y}=w[/tex]

[tex]\frac{2(4x^2-y)}{y}=w[/tex]

Hence, the solution for w is [tex]w=\frac{2(4x^2-y)}{y}[/tex].

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Complete question:

Find the solution for w in the equation  [tex]\frac{2x^2}{y} = \frac{w+2}{4}[/tex] ?

Answer:

16x^2 - 9 = 0

(4x)^2 - 3^2 = 0

a^2 - b^2 = (a - b) (a + b)

Hence, (4x - 3) (4x + 3) = 0

Either (4x - 3) = 0 or (4x + 3) = 0

4x = 3 or 4x = -3

x = 3/4 or x = -3/4

Step-by-step explanation:

You’ll need a clean, microwave-safe container (a quart-sized bowl works great) to mix the agar with water and then boil it. These proportions make enough nutrient agar to prepare two Petri dishes. Stir these together well:

• ½-teaspoon agar (about 1.2 grams)

• ¼ cup (60 mL) of hot water

Bring this mixture to a boil for three minutes to completely dissolve the agar. CAUTION: Adult supervision is required to boil water. If you are using a microwave oven to boil the mixture, be careful not to let it boil over. The mixture should be clear with no particles floating in it after boiling.

Remove the mixture from the microwave and allow it to cool for 3 to 5 minutes before moving on to the next step.

Take the lid off of the Petri dish (the lid is larger than the dish) and carefully cover the bottom-half of the Petri dish with warm  nutrient agar mixture.

Loosely cover the bottom portion (set the lid ajar so excess moisture can escape) and allow the mixture to cool and harden for at least an hour.

It’s time to collect some bacteria on the end of a cotton swab! The classic test is to roll a clean cotton swab in your mouth and then to lightly draw a squiggle with it on the gelled agar. However, many people like to test something even more gross like the keys on a computer, a cell phone case, the pump handle of a soap dispenser, or the TV remote control. Unless someone recently cleaned the buttons on the remote, you may be seeing some real goobers in a short time. Dampen a cotton swab and roll it in your fingers as you pull it across the surface of your choice.

Lift the lid off the Petri dish and LIGHTLY draw a squiggly line in the agar with the end of the cotton swab. Roll the swab in your fingers as you draw the line. Replace the lid and label the dish with the date and the name of the item you tested.

Use a sanitizing wipe to thoroughly clean one of the surfaces you tested in Step 6, e.g. Cellphone

With a clean swab, redo the squiggle test in the other half of the Petri dish from Step 6 to confirm your cleaning efforts.

Before growing anything, some people place each Petri dish into a separate zipper-lock bag. Place the upside down dishes into a warm – about 98°F (37°C) is fine – and totally dark place to grow. In a closed box on a cable box is a great place. In a short time, you’ll be greeted by an amazing variety of bacteria, molds, and fungi. You likely see more and larger colonies over the next few days. You shouldn’t see too much growth where the disinfectants (hand sanitizers) were used. You might even see a “halo” around each location. This halo is called the “kill zone.” Measure and compare the size of the kill zone to determine the effectiveness of different antibacterial agents.

Remember: Do NOT open the dishes once things begin to grow. You could be culturing some serious goobers and not even know it. The comfort is that they were around you all the time anyway and now you can see them. Just be careful!

Goobers like you’re growing will often stink and make their presence known after a short time. These are not toys or curiosities you’re growing. Proper disposal is essential for both safety and sanitation. Seal all the Petri dishes into larger zipper-lock plastic bags. You can add a generous shot of chlorine bleach to the bag before sealing it to add another level of destruction. Remember: do NOT open the zipper-lock bags… ever! When you’re finished analyzing the cultures, dispose of the entire sealed bag in the trash.

Golly, Mom is right! It IS important to wash your hands with soap and warm water whenever you can!

Answer: The sample might not be a representative of the population because it only included lunch customers.

Step-by-step explanation:

Answer:

The sample might not be representative of the population because it only included lunch customers.

Step-by-step explanation:

Since she is only picking lunch customers and not breakfast and dinner it doesn't show all the people only the people who order lunch

Answer:

20 cubic feet

Step-by-step explanation:

First divide the figure into 3 rectangular prisms like in the screen shot provided below.

Volume of the prism on the left:

l×w×h=v

1×2×3=6 cubic feet

Since the volume of the right prism and the left prism are the same, we can multiply the volume (6cubic feet) by 2. Therefore, the volume of both the prisms outlined in purple is 12 cubic feet.

Volume of the rectangular prism in the middle:

2×1×(7-3)

2×1×4=8 cubic feet

Now we add all the volumes together:

8+12=20 cubic feet.

Hope this helps! :)

Answer:

Exponential model

[tex]y=Ae^{rt}[/tex]

where:

Given:

Substituting given values into the formula and solving for A:

[tex]\begin{aligned}y & =Ae^{rt}\\\implies 100 & = Ae^{r \times 0}\\100 & = Ae^0\\100 & = A(1)\\A & = 100\end{aligned}[/tex]

Given:

Substituting the given values into the equation and solving for r:

[tex]\begin{aligned}y& =Ae^{rt}\\\\\implies 50 & =100e^{30.17r}\\\\\dfrac{1}{2} & = e^{30.17r}\\\\ln \dfrac{1}{2} & = \ln e^{30.17r}\\\\\ln 1-\ln2 & =30.17r \ln e\\\\0-\ln 2 & =30.17r(1)\\\\-\ln 2 & =30.17r\\\\r & = \dfrac{-\ln 2}{30.17}\end{aligned}[/tex]

Therefore, the final equation is:

[tex]y=100e^{\left(-\dfrac{\ln 2}{30.17}\right)t}[/tex]

Part (a)

Q:   From 100g how much remains in 80 years?

[tex]\begin{aligned}t=80 \implies y & =100e^{\left(-\dfrac{\ln 2}{30.17}\right)80}\\& = 15.91389949 \: \sf g\end{aligned}[/tex]

Part (b)

Q:  How long will it take to have 10% remaining?

10% of 100 g = 10 g

[tex]\begin{aligned}y=10 \implies 10 & =100e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\dfrac{1}{10} & =e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\ln \dfrac{1}{10} & =\ln e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\ln 1 - \ln 10 & =\left(-\dfrac{\ln 2}{30.17}\right)t\ln e\\\\0 - \ln 10 & =\left(-\dfrac{\ln 2}{30.17}\right)t(1)\\\\-\ln 10 & =\left(-\dfrac{\ln 2}{30.17}\right)t\\\\t & = \dfrac{- \ln 10}{\left(-\dfrac{\ln 2}{30.17}\right)}\\\\t & = 100.2225706\: \sf years\end{aligned}[/tex]

Part (a)

Q:   How much remains after 50 years (time)?

[tex]\begin{aligned}t=50 \implies y & =100e^{\left(-\dfrac{\ln 2}{30.17}\right)50}\\& = 31.70373153 \: \sf g\end{aligned}[/tex]

Part (b)

Q:   How long to reach 20 g (amount remaining)?

[tex]\begin{aligned}y=20 \implies 20 & =100e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\dfrac{1}{5} & =e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\ln \dfrac{1}{5} & =\ln e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\ln 1 - \ln 5 & =\left(-\dfrac{\ln 2}{30.17}\right)t\ln e\\\\0 - \ln 5 & =\left(-\dfrac{\ln 2}{30.17}\right)t(1)\\\\-\ln 5 & =\left(-\dfrac{\ln 2}{30.17}\right)t\\\\t & = \dfrac{- \ln 5}{\left(-\dfrac{\ln 2}{30.17}\right)}\\\\t & = 70.05257062\: \sf years\end{aligned}[/tex]

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

[tex]\large \sf \underline{Problem:}[/tex]

Solve the system of equations by substitution

====================================.

[tex]\large \sf \underline{Answer:}[/tex]

x = - 5y + 4

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

[tex]\large \sf \underline{Explanation:}[/tex]

x + 5y = 42x + 10y = 8

2(- 5y + 4) + 10y = 8

substituted in the equation for x - 10y - 8 + 10y = 8

distributed

8 = 8

combined like terms 0 = 0(- 10y + 10y)

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

The third angle of the triangle will be ∠B = 69°.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given that:-

The third angle will be calculated as:-

∠A   + ∠C + ∠B = 180

43  +  68  +  ∠B = 180

∠B = 180 - 43 - 68

∠B = 69°

Therefore the third angle of the triangle will be ∠B = 69°.

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Answer:

[tex]slope=-\frac{1}{4}[/tex]

Step-by-step explanation:

To find the slope of the two points (-9,-3) and (7, -7) w have to use the slope formula

[tex]slope=\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]             [tex]slope=\frac{(-7)- (-3)}{7 -(-9) }[/tex]      

[tex]slope=\frac{-4 }{16}=-\frac{1}{4}[/tex]  can also be written as a decimal  [tex]slope=-0.25[/tex]

we get - 1/4 because -4 divided by -4 is 1 and -4 divided by 16 is -4

Answer:

b

Step-by-step explanation:

bc solutions are the zeros or the x intercepts of the graph which would be (-3,0) and (3,0)

Answer:

38.50

Step-by-step explanation:

thirty-eight dollars and fifty cents

Answer: 12

Step-by-step explanation:

By the corresponding angles theorem, [tex]4x-5=97-2x \longrightarrow x=17[/tex].

So, this means that [tex]97-2x=63[/tex].

Now, by the same-side interior angles theorem, we know that [tex]10y-3+63=180 \longrightarrow y=\boxed{12}[/tex]

Answer:

∠A = 22°

Step-by-step explanation:

complementary angles is either of two angles whose sum is 90°

∠A + ∠B = 90°

m∠B = 68°

∠A + 68° = 90°

subtract 68 from both sides

∠A + 68° - 68 = 90° - 68

∠A = 22°

Answer:

22°

Step-by-step explanation:

M<A+M<B= 90° ( complementary angles)

M<A+ 68° = 90°

M<A = 90-68= 22°

M<A= 22°

Answer:

2/9

Step-by-step explanation:

First, square the fraction 5/6 to get 1/2 * 25/36 - 1/8. Next, multiply 1/2 and 25/36 to get 25/72. Finally, subtract 1/8 to get the answer 2/9.

Answer:

2/9

Step-by-step explanation:

=> 1/2 (5/6)^2 - 1/8

=> 1/2 (25/36) - 1/8

=> 25/72 - 1/8

=> make 1/8 to have a denominator of 72.

=> multiply the numerator and denominator by 9/9

=> 1/8 becomes 9/72

soo

=> 25/72 - 9/72

=> 16/72

^the greatest common factor is 8

=> 2/9

2/9 is your answer :)

Answer: x = 20

Step-by-step explanation:

     Let's add what it tells us to the picture. See attached. Since the angles boxed in green are congruent, we can set them equal to each other and solve for x.

3x - 10 = 2x + 10

3x - 20 = 2x

-20 = -x

20 = x

x = 20

Answer:

A

Step-by-step explanation:

Compound Interest Formula :

Here, we are given :

Substituting the given values and taking x in place of t :

If the total number of lunch items is 117, there will be 39 hamburgers there

Fractions are written as a ratio of two numbers

Given

Total items = 117

If the ratio of hot dogs to hamburgers is 26:13, then the total hamburgers that are there is given as:

Hamburgers = 13/39 * 117
Hamburgers = 39

This shows that if the total number of lunch items is 117, there will be 39 hamburgers there

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The expression that represents the constant of variation, k, in this scenario is StartFraction z Over x y EndFraction.

When a quantity varies directly with one variable and inversely with another, it means that the quantity is directly proportional to one variable and inversely proportional to the other. In this case, x varies directly with y and inversely with z.

To represent the constant of variation, k, we need to find the expression that combines the variables x, y, and z in the correct way.

If x varies directly with y, we can represent this relationship as x = ky, where k is the constant of variation.

If x varies inversely with z, we can represent this relationship as x = k/z.

Combining these two expressions, we can write x = ky = k/z.

Simplifying this equation, we get xz = ky.

To isolate k, we divide both sides of the equation by xy, resulting in StartFraction x z Over y EndFraction = k.

Therefore, the expression StartFraction z Over x y EndFraction represents the constant of variation, k.

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Answer:I think It may be B 4.2%

Step-by-step explanation:

The composition of two translations could describe the taxicab’s final position are (1, -2 + 16) and (1, -2 - 16)

The initial position is given as:

Cab = (1, -2)

Assume the cab travel in one direction, the possible translations are:

(x, y + 16)

(x, y - 16)

(x  + 16, y)

(x  - 16, y)

Using the first two translations, the final positions are:

(1, -2 + 16) = (1, 14)

(1, -2 - 16) = (1, -18)

Hence, the composition of two translations could describe the taxicab’s final position are (1, -2 + 16) and (1, -2 - 16)

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