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FromTheMoon [43]
3 years ago
8

Mary has a cone that has a radius of 5cm and height of 10cm. James has a square pyramid with base length of 10cm and height of 5

cm. Which solid has a larger volume? Explain.
Mathematics
1 answer:
lukranit [14]3 years ago
5 0

Answer: The cone has a larger volume.

Step-by-step explanation:

Volume of a cone = ⅓πr²h

where, radius = 5cm

height = 10cm

Volume = ⅓ × 3.142 × 5² × 10

Volume of cone = 261.83cm³

Volume of square pyramid = A(h/3)

where, A = 10 × 10 = 100cm²

Volume = 100 × (5/3)

Volume of square pyramid = 166.67cm³

Therefore, the cone has a larger volume.

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In a warehouse, boxes have been stacked in 4 layers as shown. The workers make other stacks according to the same pattern. If a
FromTheMoon [43]

Answer:

7n

Step-by-step explanation:

6 0
3 years ago
A circle is divided into 8 equal parts. What is the total<br>angle measure of 4 parts?<br>​
snow_lady [41]

Answer:

Step-by-step explanation:

A circle is divided into 8 equal parts means : 360°/8 = 45°

the total  angle measure of 4 parts is :

45°×4=180°

4 0
3 years ago
Which expression is m times m times m times m times m rewritten in exponential form? m Superscript 5 5 m 5 Superscript m m 5.
sukhopar [10]

The expression which is equal to the m times, m times, m times, m times, m rewritten in exponential form as,

m^5

<h3>What is the exponent or power?</h3>

The exponent or power of a number represent the multiplication of the that number to the power times.

Let suppose a number 2 has the power 2. Then it will be equal to,

2^2=2\times2

Similarly, 3 times of number 2 equal to the number 2 with exponent 3.

2\times2\times2=2^3

The expression is m times, m times, m times, m times, m. It can be written as,

m\times m\times m\times m\times m\\

The number m is total 5 time multiply by itself. Thus, the exponential form of the above equation is,

m^5

The expression which is equal to the m times, m times, m times, m times, m rewritten in exponential form as,

m^5

Learn more about the exponents power here;

brainly.com/question/18324331

5 0
2 years ago
Ava is saving for a new computer that coat 1,218 she already has half saved of the money. Ava earns $14.00 per hour. How many ho
ollegr [7]

Answer:

43.5

Step-by-step explanation:

First

1218 divided by 2

= 609

Second

609 divided by 14 is =43.5

43.5 is the answer

4 0
3 years ago
Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology ex
Nataly [62]

Answer:

(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942  

(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978  

And the 90% confidence interval would be given (0.0942;0.09978).  

We are confident at 90% that the difference between the two proportions is between 0.0942 \leq p_A -p_B \leq 0.09978

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p_A represent the real population proportion female for Biology

\hat p_A =\frac{84199}{144796}=0.582 represent the estimated proportion female for biology

n_A=144796 is the sample size for A

p_B represent the real population proportion female for calculus AB

\hat p_B =\frac{102598}{211693}=0.485 represent the estimated proportion female for Calculus AB

n_B=211693 is the sample size required for B

z represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})  

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}  

For the 90% confidence interval the value of \alpha=1-0.90=0.1 and \alpha/2=0.05, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.64  

And replacing into the confidence interval formula we got:  

(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942  

(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978  

And the 90% confidence interval would be given (0.0942;0.09978).  

We are confident at 90% that the difference between the two proportions is between 0.0942 \leq p_A -p_B \leq 0.09978

5 0
3 years ago
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