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2 years ago

8

Edgar builds a sand castle with a rectangular base. The side lengths of the base are 25 in. And 16 in. He wants to surround the

castle's base with a moat that is w inches wide. Write a quadratic function A in standard form to represent the combined area taken up by the castle and the moat.

1 answer:

STALIN [3.7K]2 years ago

7 0

Answer:

$A=4w^2+32w+400$

Step-by-step explanation:

-Given the castle dimensions is 25in by 16 in.

-And the moat's width is w:

The moat's width will increase the castle's dimension bytwice it's width, 2w:

#The castles area is thus calculated as:

$A=lw\\\\=(25+2w)(16+2w)\\\\=400+80w+32w+4w^2\\\\=4w^2+32w+400$

Hence, the combined area of the boat is given as $A=4w^2+32w+400$

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Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random

yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums, we have that the mean is $\mu*n$ and the standard deviation is $s = \sigma \sqrt{n}$

In this problem, we have that:

$\mu = 100*35 = 3500, \sigma = \sqrt{100}*16 = 160$

This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.

X = 4000

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{4000 - 3500}{160}$

$Z = 3.13$

$Z = 3.13$ has a pvalue of 0.9991

X = 3000

$Z = \frac{X - \mu}{s}$

$Z = \frac{3000 - 3500}{160}$

$Z = -3.13$

$Z = -3.13$ has a pvalue of 0.0009

0.9991 - 0.0009 = 0.9982

So the correct answer is:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

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2 years ago

Rewrite in simplest rational exponent form √x • 4√x. Show each step of your process.

pantera1 [17]

Multiplying these together, we get:

$4 \sqrt{x^2}$

The square root of x^2 is x, so we have a final expression of 4x.

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1 year ago

Drew earns money washing cars for his neighbors on the weekends. Drew charges a set rate for each car he washes.

statuscvo [17]

Answer:

30

Step-by-step explanation:

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2 years ago

Read 2 more answers

*NO 194 39% 13:08 Pilih jawaban yang paling tepat Segitiga PQR dan segitiga XYZ 5 poin merupakan dua segitiga yang kongruen. Bes

Illusion [34]

Answer:

Option d. PQ = YZ

Step-by-step explanation:

<u><em>The question in English is</em></u>

Choose the most appropriate answer. The PQR triangle and the XYZ triangle are two congruent triangles. The angle P = the angle Y and PR = YX. Side pairs of the same length are ... a. PQ = XZ b. QR = YZ c. QR = XY d. PQ = YZ

we know that

If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent

Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement

so

we have that

$m\angle P=m\angle Y$

$PR=YX$

so

Triangle PQR is congruent with Triangle YZX

That means

<em><u>Corresponding angles</u></em>

$m\angle P=m\angle Y$

$m\angle Q=m\angle Z$

$m\angle R=m\angle X$

<u><em>Corresponding sides</em></u>

$PQ=YZ\\QR=ZX\\PR=YX$

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2 years ago

Drag the cards to create a two-digit number that matches these rules. Note: Not all cards will be used 6 is one of the digits 20

Greeley [361]

Answer:

As i understand this:

We have cards with the values:

0, 1, 2 and 6.

We want to create a two digit number such that:

Not all the cards are used.

6 is one digit of our number.

When we round to the nearest ten, we get 20.

Now, first remember how rounding works.

If we have a number like ab, where a and b are single digits (a is in the tens place and b is in the units place), then:

if b is 5 or more, we round up

if b is less than 5, we round down.

Now in this case we want to have a digit equal 6, if we use this in the units place, then when rounding, we will round up.

Then the other digit can be 1, such that we use the cards:

1 and 6.

then our number is 16:

When rounding, 6 > 5, then we round up to 20.

So this number meets all the conditions.

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1 year ago