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Valentin [98]
2 years ago
15

To get your car repaired at a certain dealership in Woodstock, the rate charged is $90 per hour worked on your car, plus a $50 d

iagnostic fee.
1) Create an equation to find the (C)harge to fix the car:

2) If your car was worked on for 4.6 hours what would be the total charge?

3) If the total cost was $800, how many hours was the car in the shop?

Mathematics
1 answer:
kakasveta [241]2 years ago
4 0
C- charge
H- hours
D- diagnostic fee

C= #H(90)+ D

C= 4.6(90)+50
=414+50
=$464

C-$800
H-?
D-50

C= #H(90)+50

800=H(90)+50

H(90)=800-50

H(90)=750

H(90)/90=750/90

H=750/90

H= 8.33333333
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Assume that a sample is used to estimate a population proportion p. Find the 98% confidence interval for a
Vikki [24]

Answer:

0.81 - 2.326 \sqrt{\frac{0.81(1-0.81)}{131}}=0.730

0.81 + 2.326 \sqrt{\frac{0.81(1-0.81)}{131}}=0.890

And the confidence interval would be:

0.730 \leq \p \leq 0.890

Step-by-step explanation:

Information given:

n=131 represent the sample size

\hat p=0.81 represent the estimated proportion

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 98% confidence interval the value of \alpha=1-0.98=0.02 and \alpha/2=0.01, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.326

And replacing into the confidence interval formula we got:

0.81 - 2.326 \sqrt{\frac{0.81(1-0.81)}{131}}=0.730

0.81 + 2.326 \sqrt{\frac{0.81(1-0.81)}{131}}=0.890

And the confidence interval would be:

0.730 \leq \p \leq 0.890

6 0
4 years ago
A large tank is filled to capacity with 600 gallons of pure water. brine containing 4 pounds of salt per gallon is pumped into t
nignag [31]
If A(t) is the amount of salt in the tank at time t, then the rate at which the amount of salt in the tank changes is given by

\dfrac{\mathrm dA(t)}{\mathrm dt}=\dfrac{4\text{ lbs}}{1\text{ gal}}\dfrac{6\text{ gal}}{1\text{ min}}-\dfrac{A(t)\text{ lbs}}{600\text{ gal}}\dfrac{6\text{ gal}}{1\text{ min}}
\dfrac{\mathrm dA}{\mathrm dt}=24\dfrac{\text{lb}}{\text{min}}-\dfrac{A(t)}{100}\dfrac{\text{lb}}{\text{min}}

Let's drop the units for now. We have

\dfrac{\mathrm dA(t)}{\mathrm dt}+\dfrac{A(t)}{100}=24
e^{t/100}\dfrac{\mathrm dA(t)}{\mathrm dt}+e^{t/100}\dfrac{A(t)}{100}=24e^{t/100}
\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/100}A(t)\right]=24e^{t/100}
e^{t/100}A(t)=\displaystyle24\int e^{t/100}\,\mathrm dt
e^{t/100}A(t)=2400e^{t/100}+C
A(t)=2400+Ce^{-t/100}

We're given that the water is pure at the start, so A(0)=0, giving

A(0)=0=2400+Ce^{-0/100}\implies C=-2400

So the amount of salt in the tank (in lbs) at time t is

A(t)=2400\left(1-e^{-t/100}\right)
4 0
3 years ago
**Yoxelt buys 4 1/ 2 gallons of soda. One-fourth of the soda he bought was Pepsi and the rest was Sprite. How many gallons of Pe
dusya [7]

Answer:

1 1/8

Step-by-step explanation:

1/4 of 4 1/2 is Pepsi.

1/4 * 4 1/2 = (1/4) * 4 + (1/4) * (1/2) = 1 1/8

7 0
4 years ago
C is the midpoint of AB . AC=2x +2 and AB=8x. Set up an equation and showing all steps, solve for x and length CB.
olga55 [171]

See the attached drawing for a visual.

Since we know that AC = CB is half the length of AB, we can write that in equation form. The goal is to determine the length of CB = AC = 2x+2

2x+2 =\frac{1}{2} (8x)

2x+2 = 4x

2x = 2

x=1

Now that we know the value of x, we can find the value of CB = 2x+2:

CB = 2x+2

CB = 2(1)+2

CB = 4


8 0
4 years ago
1. A rectangular tile has a decorative
Akimi4 [234]

Answer:

  216

Step-by-step explanation:

Each of the 36 tiles has 3×2 = 6 triangles, so there are a total of ...

  36×6 = 216 . . . triangles

6 0
4 years ago
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