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2 years ago

Need help pls solve Find the area of the figure.

Mathematics

1 answer:

vampirchik [111]2 years ago

5 0

Answer:

32 ft²

Step-by-step explanation:

Given the right angle and equal sides, we have a square. The diagonal is the hypotenuse of a right triangle, so we can use the Pythagorean Theorem to calculate the side lengths, or realize that the side lengths Squared will be the area of the square.

c² = a²+b² Since a² equals b², the equation becomes c² = 2a²

8² = 2a²

64/2 = a²

32 = a², the area of the square.

The side lengths of the square are √32

about 5.657 feet. If we square that square root, we get the area of the square, 32 square feet.

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Can anyone help me with this math test heres another question on it!!

stira [4]

Answer:

31 1/2, or answer D

Step-by-step explanation:

Because you have three countertops which all have an area of 10 1/2 meaning you multiply 10.5x3 getting 31.5

8 0

3 years ago

Mary scored 10 points less than Judy in the game. Lucy scored twice as many points as

kodGreya [7K]

The answer for this is 10

6 0

3 years ago

Consider that ΔDEF is similar to ΔGHI and the measure of ∠E is 58°. What is the measure of ∠H?

spayn [35]

Answer:

58 degrees

Step-by-step explanation:

If figures are similar to each other, it means that they have the same measures. Therefore, D has the same measure as G, E has the same measure as H, and F has the same measure as I.

6 0

3 years ago

At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine

Tresset [83]

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

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 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.

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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

The machine is known to have 99 green balls and 78 red balls.

This means that $p = \frac{99}{99+78} = 0.5593$

Mean and standard deviation:

$\mu = p = 0.5593$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373$

a. Calculate the probability of getting more than 61% green balls.

This is 1 subtracted by the pvalue of Z when X = 0.61. So

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

By the Central Limit Theorem

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

$Z = \frac{0.61 - 0.5593}{0.0373}$

$Z = 1.36$

$Z = 1.36$ has a pvalue of 0.9131

1 - 0.9131 = 0.0869

0.0869 = 8.69% probability of getting more than 61% green balls.

8 0

2 years ago

If the principal is $300 rate 3% time 4 years then what is the interest earned and the new balance

Tomtit [17]

Answer:

a) Interest earned = $36

New Balance = $336

b) Interest rate = 0.05 or 5%

New Balance = $517.5

c) time t = 5

New Balance = $612.5

d) Principal Amount = $675

New Balance = $783

Step-by-step explanation:

We are given:

a) Principal (P) = $300

Rate (r) = 3% or 0.03

Time (t)= 4 years

Interest earned = ?

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding interest

$Simple \ Interest (I)= P\times r\times t\\Simple \ Interest (I)= 300\times 0.03\times 4\\Simple \ Interest (I)= 36$

So, Interest earned = $36

New Balance = Principal + Interest = 300+36 = $336

b) a) Principal (P) = $300

Rate (r) = ?

Time (t)= 3 years

Interest earned = 67.50

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding rate

$Simple \ Interest (I)= P\times r\times t\\67.50= 450\times r\times 3\\67.50=1350\times r\\r=\frac{67.50}{1350}\\r=0.05 \ or \ 5\%$

So, Interest rate = 0.05 or 5%

New Balance = Principal + Interest = 450+67.50 = $517.5

c) Principal (P) = $500

Rate (r) = 4.5% or 0.045

Time (t)= ?

Interest earned = $112.50

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding time

$Simple \ Interest (I)= P\times r\times t\\112.50= 500\times 0.045\times t\\112.50=22.5 \times t\\t=\frac{112.50}{22.5}\\t=5$

So, time t = 5

New Balance = Principal + Interest = 500+112.50 = $612.5

d) Principal (P) = ?

Rate (r) = 8% or 0.08

Time (t)= 2 years

Interest earned = 108.00

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding Principal

$Simple \ Interest (I)= P\times r\times t\\108=P\times 0.08 \times 2\\108=P\times 0.16\\P=\frac{108}{0.16}\\P=675$

So, Principal Amount = $675

New Balance = Principal + Interest = 675+108 = $783

8 0

3 years ago