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2 years ago

12

The price of a bungalow in 1990 was $850000. If there was a 125% increase in 2000, followed by a 30% decrease in 2013, what was

the price in 2013?

1 answer:

astra-53 [7]2 years ago

6 0

Answer:

1,338,750$

Step-by-step explanation:

1990 price was 850,000

in 2000

850,000 + 125% = 1,062,500

850,000 + 1,062,500 = 1,912,500

in 2013

1,912,500 - 30% = 573,750

1,912,500 - 573,750 = 1,338,750

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A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op

Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, $\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h$

Volume of cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3$

By differentiating with respect to time t, we get that

$\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}$

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie $\dfrac{dv}{dt}=-4\ in^3$

and h = 2 inches deep.

$-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}$

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

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3 years ago

Find the value of x when 6-4x = 6x-8x-2.

mestny [16]

Answer:

4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

6−4x=6x−8x−2

6+−4x=6x+−8x+−2

−4x+6=(6x+−8x)+(−2)(Combine Like Terms)

−4x+6=−2x+−2

−4x+6=−2x−2

Step 2: Add 2x to both sides.

−4x+6+2x=−2x−2+2x

−2x+6=−2

Step 3: Subtract 6 from both sides.

−2x+6−6=−2−6

−2x=−8

Step 4: Divide both sides by -2.

−2x−2=−8−2

x=4

here is a link:

https://www.mathpapa.com/algebra-calculator.html?q=6-4x%3D6x-8x-2.

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4 years ago

At Silver Gym, membership is $30 per month, and personal training sessions are $45 each. At Fit Factor, membership is $90 per mo

pshichka [43]

S(x)=30x+45
F(x)=90x+35

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3 years ago

While conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modem

Kitty [74]

Answer:

We conclude that this is an unusually high number of faulty modems.

Step-by-step explanation:

We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.

The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.

Let p = <em><u>population proportion</u></em>.

So, Null Hypothesis, $H_0$ : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}

Alternate Hypothesis, $H_A$ : p > 0.013 {means that this is an unusually high number of faulty modems}

The test statistics that would be used here <u>One-sample z-test</u> for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion faulty modems= $\frac{10}{367}$ = 0.027

n = sample of modems = 367

So, <u><em>the test statistics</em></u> = $\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }$

= 2.367

The value of z-test statistics is 2.367.

Since, we are not given with the level of significance so we assume it to be 5%. <u>Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.</u>

Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u><em>we reject our null hypothesis</em></u>.

Therefore, we conclude that this is an unusually high number of faulty modems.

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3 years ago

If f(x) =2x+3 then the point (1,5) is on the graph of f true or false

ss7ja [257]

F(x)=y=2x+3
P (1,5)
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3 years ago