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2 years ago

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An artist forms a spherical glass ornament that has a diameter of 6 cm. What is the volume of the ornament? Use 3.14 for π.

1 answer:

Mrrafil [7]2 years ago

7 0

Answer:

1st option: 113.04 cm³

Step-by-step explanation:

Volume of sphere= $\frac{4}{3} \pi {r}^{3}$

Volume of ornament

$= \frac{4}{3} (3.14)( {3}^{3}) \\ = 113.04 \: cm^{3}$

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Rewrite each expression as a product of two or quotient of two powers

Paul [167]

Answer:

The product is $5^{40}*3^{70}$

Step-by-step explanation:

To do this we must understand how the basic operations apply to powers. If the power has the same base and we multiply them, the base remains the same while we sum the powers, if we divide them the base remains the same and we subtract the powers, if we try to make a power of a power the two powers multiply. Applying this rule we have:

$(\frac{5^8*3^7}{5^4})^{10}\\(\frac{5^8}{5^4}*3^7)^{10}\\(5^4*3^7)^{10}\\5^{40}*3^{70}$

6 0

2 years ago

Joel maps his house and his school on a coordinate grid where each unit is 1 block. His school is at (-7, -2). His house is at (

zhenek [66]

Answer:

10 blocks

Step-by-step explanation

check the image attached, the y coordinate of his school and house are the same that is, -2 so all we have to do is check the distance between x coordinates

that is , -7 and 3

distance between school and his house = 3 - (-7) = 10 blocks

3 0

2 years ago

Read 2 more answers

Michael earns $21 per hour and works 40 hours per week. How many overtime hours would he have to worky in a week for his time-an

Alex73 [517]

Answer:

27 hours

Step-by-step explanation:

The regular hours are paid normally, 21/hr hence working for 40 hours, Michael earns 40*21=$840

To work x hours paid overtime as 1.5 of the normal rate, the rate would be $21*1.5=$31.5/hr

X hours multiplied by rate of $31.5/hr should be at least equal to $840

31.5x>=840

X>=840/31.5>=26.6667 hours and when rounded off

X is 27 hours

6 0

2 years ago

Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage ea

garik1379 [7]

Answer:

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

Step-by-step explanation:

We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.26.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26*0.74}{160}}\\\\\\ \sigma_p=\sqrt{0.0012}=0.0347$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.0347=0.068$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.26-0.068=0.192\\\\UL=p+z \cdot \sigma_p = 0.26+0.068=0.328$

The 95% confidence interval for the population proportion is (0.192, 0.328).

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

3 0

2 years ago

A portfolio consisting of four stocks is expected to produce returns of minus9%, 11%, 13% and 17%, respectively, over the next f

anastassius [24]

Answer:

standard deviation of these expected returns = 0.0295 or 2.95%

Step-by-step explanation:

The detailed step is shown in the attachment

8 0

2 years ago