All categories

3 years ago

Find the area of the composite shape

Mathematics

1 answer:

Contact [7]3 years ago

4 0

Answer:

Step-by-step explanation:

We can simply subtract the area of the small square from the area of the rectangle

A=8(12)-4(4)

A=96-16

A=80cm^2

You might be interested in

3(-4n - 9) = 21 plc solve

erma4kov [3.2K]

<h3>Answer:</h3>

$\huge{\boxed{n=-4}}$

<h3>Explanation:</h3>

$\begin{array}{cc}\begin{flushright}\text{Divide both sides of the equation by 3.}\end{flushright}&\begin{flushleft}-4n-9=7\end{flushleft}\\\begin{flushright}\text{Add 9 on both sides.}\end{flushright}&\begin{flushleft}-4n=16\end{flushleft}\\\begin{flushright}\text{Divide both sides by -4.}\end{flushrigh}&n=-4\end{array}$

7 0

3 years ago

Read 2 more answers

I’m stuck I need help

arlik [135]

Answer:

X=6

Step-by-step explanation:

First step isolate the variable;2x=12

Simplify;x=12/2=6

8 0

3 years ago

–4(5² – 3) +6² I need help solving that

Marat540 [252]

Answer:

-52

Have a great day! Brainliest?

4 0

2 years ago

Read 2 more answers

A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat

zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

In this question, we have that:

$\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5$

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

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

X = 205

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

$Z = \frac{205 - 200}{5}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

X = 195

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

$Z = \frac{195 - 200}{5}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

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

$Z = \frac{210 - 200}{5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

X = 195

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

$Z = \frac{190 - 200}{5}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0

3 years ago

You and a friend are playing a best-of-three series (first to win 2 games wins the series). You are a stronger player and have a

mariarad [96]

Answer and Step-by-step explanation:

Given that probability of you winning each game = 0.68

And probability of you winning next game = 0.81

Your friend's chance of winning/you losing would be = 1-0.68= 0.32

also his chance of winning next game = 0.73

To find probability that you would win the series given that you need to win two games to win the series

= probability that you win first game and second game+ probability that you win first game, lose second game and win third game + probability that you lose first game, win second game and win third game

= 0.68*0.81+0.68*0.32*0.68+0.32*0.68*0.81

=0.8750

Therefore probability that you would win the series = 0.8750

Note: here we found the probability of winning by adding(or) up the three possible combinations that would result in a win

6 0

3 years ago