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4 years ago

I don’t understand how I’m supposed to do this problem!

Mathematics

1 answer:

sasho [114]4 years ago

8 0

Answer:

$36.75

Step-by-step explanation:

We can determine that 7% is also 0.07 (if we convert a percent to a decimal).

We can find the sales tax for the pool by multiplying the sale price and the sales tax rate.

$525*0.07=36.75$

So the sales tax is $36.75

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Please help i have been trying to figure this out for like an hour

KengaRu [80]

Answer:

Step-by-step explanation:

Since x varies directly as y, the ratio of x to y remains the same. Let the value of x when y=4 be a. Then we have

$\dfrac {7 \frac12} {10} = \dfrac a4$

We can cross multiply to get that

$10a = 30, \text{so } \boxed{a=3}$

7 0

3 years ago

Evaluate the integral Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole ofradius 1 is d

algol13

You want to find the volume inside the hemisphere $x^2+y^2+z^2=4$ (i.e. inside the sphere but above the plane $z=0$ ) and outside the cylinder $x^2+y^2=1$ . Call this region $R$ .

In cylindrical coordinates, we have

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_1^2\int_0^{\sqrt{4-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$

$\displaystyle=2\pi\int_1^2 r\sqrt{4-r^2}\,\mathrm dr$

$\displaystyle=-\pi\int_3^0\sqrt u\,\mathrm du$

(where $u=4-r^2$ )

$\displaystyle=\pi\int_0^3\sqrt u\,\mathrm du$

$=\dfrac{2\pi}3u^{3/2}\bigg|_0^3=2\sqrt3\,\pi$

7 0

4 years ago

Suppose you just received a shipment of seven seven televisions

Alchen [17]

Then I'd be watching 14 different Netflix shows at once

5 0

4 years ago

The mean length of 7 childrens' index finger is 9.4cm. The mean length of 5 adults' index finger is 10.2cm. What is the mean len

Deffense [45]

Answer:

9.73 cm to 2 DP

Step-by-step explanation:

Total of the lengths involved = 7*9.4 + 5*10.2

= 116.8 cm

So the mean of the 12 fingers

= 116.8/12

= 9.73 cm to 2 DP.

3 0

2 years ago

Read 2 more answers

The heights of a random sample of 50 college students showed a mean of 174.5 centimeters and a standard deviation of 6.9 centime

Minchanka [31]

Answer:

Step-by-step explanation:

Hello!

For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.

In this example the variable is:

X: height of a college student. (cm)

There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.

The option you have is to apply the Central Limit Theorem.

The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:

X[bar]~~N(μ;σ2/n)

Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:

98% CI

1 - α: 0.98

⇒α: 0.02

α/2: 0.01

$Z_{1-\alpha /2}= Z_{1-0.01}= Z_{0.99} =2.334$

X[bar] ± $Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }$

174.5 ± $2.334* \frac{6.9}{\sqrt{50} }$

[172.22; 176.78]

With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].

I hope it helps!

4 0

3 years ago