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Brilliant_brown [7]
2 years ago
8

A bakery offers a small circular cake with a diameter of 8 inches. It also offers a large circular cake with a diameter of 24 in

ches. Complete the explanation for whether the top of the large cake has three times the area of that of the small cake.
Mathematics
2 answers:
drek231 [11]2 years ago
8 0
Large cake:
24÷2=12
12 is the radius of the large cake.
12×12×3.14=452.16

Small cake:
8÷2=4
4 is the radius of the small cake.
4×4×3.14=50.24

452.16÷3=150.72
So, The area of the large cake is not three times the area of the small cake.
Elanso [62]2 years ago
7 0
We must find the area of each cake's top.

Formula for area of a circle:

A =  \pi  r^{2} where r is the radius.

<span>small cake:
</span>Plug in 4 for r because the radius is 4. (They give us the diameter, which is 8, and the radius is half that)

A =  \pi  4^{2}

A = 16π

<span>big cake:
</span>Repeat the process: 
Plug in 12 for r because the radius is 12. (They give us the diameter, which is 24, and the radius is half that)

A = \pi 12^{2}

A = 144π

So our two radii are 144π and 16π. 
The large cake's top is not 3 times the area of the small cake's.

This makes sense because you are squaring the radius, which makes the fact that the larger cake's diameter is triple the smaller cake diameter irrelevant. 

Hope this helped! ^-^
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Alekssandra [29.7K]

Answer:

None on the above.

Step-by-step explanation:

Here’s what I got:

1/5^-1.

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Andru [333]

You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression

<h3>What is an extraneous solution?</h3>

An extraneous solution is a solution that in obtained after completely solving an equation but it does not  work in the original given equation.

You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression (Option D).

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2 years ago
Which expression is the best estimate of the product of 7/8 and 8 1/10
gtnhenbr [62]

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8

Step-by-step explanation:

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4 0
3 years ago
5. Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312.
Mekhanik [1.2K]

Answer:

The actual SAT score is 2024.

The equivalent ACT score is 29.49.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

SAT score that is in the 95th percentile

Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that \mu = 1511, \sigma = 312

95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:

Z = \frac{X - \mu}{\sigma}

1.645 = \frac{X - 1511}{312}

X - 1511 = 1.645*312

X = 2024

The actual SAT score is 2024.

Equivalent ACT score:

The equivalent ACT score is the 95th percentile of ACT scores.

Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that \mu = 21.1, \sigma = 5.1. So

Z = \frac{X - \mu}{\sigma}

1.645 = \frac{X - 21.1}{5.1}

X - 21.1 = 1.645*5.1

X = 29.49

The equivalent ACT score is 29.49.

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2 years ago
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