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3 years ago

A rectangle's length is three times its breadth x metres. Write an expression

Mathematics

1 answer:

MA_775_DIABLO [31]3 years ago

3 0

Answer:

1. Perimeter = 8x m

2. Area = 3x² m²

Step-by-step explanation:

From the question given above, the following data were obtained:

Breadth (B) = x m

Length (L) = 3B = 3x m

Perimeter (P) =?

Area(A) =?

1. Determination of the perimeter of the rectangle.

Breadth (B) = x m

Length (L) = 3x m

Perimeter (P) =?

P = 2(L + B)

P = 2(3x + x)

P = 2(4x)

P = 8x m

Thus, the perimeter of the rectangle is 8x m

2. Determination of the area of the rectangle.

Breadth (B) = x m

Length (L) = 3x m

Area(A) =?

A = L × B

A = 3x × x

A = 3x² m²

Thus, the area of the rectangle is 3x² m²

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A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work pro

olchik [2.2K]

Answer:

0.756

Step-by-step explanation:

It is given that a machine has four components, A, B, C, and D.

$P(A)=P(B)=0.93, P(C)=0.95,P(D)=0.92$

If these components set up in such a manner that all four parts must work for the machine to work properly.

We need to find the probability that the machine works properly. It means we have to find the value of $P(A\cap B\cap C\cap D)$ .

If two events X and Y are independent, then

$P(X\cap Y)=P(X)\times P(Y)$

Assume the probability of one part working does not depend on the functionality of any of the other parts.

$P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)$

Substitute the given values.

$P(A\cap B\cap C\cap D)=0.93\times 0.93\times 0.95\times 0.92$

$P(A\cap B\cap C\cap D)=0.7559226$

$P(A\cap B\cap C\cap D)\approx 0.756$

Therefore, the probability that the machine works properly is 0.756.

7 0

3 years ago

(1 point) The cost of unleaded gasoline once followed an unknown distribution with a mean of $4.59 and a standard deviation of $

marin [14]

Answer:

a) unknown

b) 1.43% probability that the average price for 30 gas stations is less than $4.55.

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.

In this problem, we have that:

$\mu = 4.59, \sigma = 0.1$

a) What's the approximate probability that the average price for 16 gas stations is over $4.69?

Sample size less than 30 and unknow distribution. Therefore, the central limit theorem cannot be applied and the answer is unknown.

b) Find the probability that the average price for 30 gas stations is less than $4.55.

Now $n = 30, s = \frac{0.1}{\sqrt{30}} = 0.0183$

This probability is the pvalue of Z when X = 4.55. So

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

By the Central Limit Theorem

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

$Z = \frac{4.55 - 4.59}{0.0183}$

$Z = -2.19$

$Z = -2.19$ has a pvalue of 0.0143

1.43% probability that the average price for 30 gas stations is less than $4.55.

5 0

4 years ago

“A patchwork blanket is made up of 10 identical squares. Liam has made 14 squares,Raj has made 12 squares and Gemma has made 15

steposvetlana [31]

Well, assuming that Liam, Raj, and Gemma all have squares identical to each other, then you would first add them all up. 14+12+15=41. Then, you would divide the total number of squares by the number of squares in a quilt. 41/10=4.1, or 4 1/10.
Hope this helps!

8 0

3 years ago

Read 2 more answers

What is an equation in point slope form for the line that passes through the points (-1, 4) and (3, -4)

Nezavi [6.7K]

So the point-slope form looks like (y-y1) = m(x-x1)
So the first thing we should do is solve for m. We can do this using the slope formula (y1-y2)/(x1 - x2)

(-4 - 4)/(3 - -1) = -2

So our slope is -2. Then plug in any order pair for y1 and x2

So a possible solution is y - 4 = -2(x + 1)
Hopes this helps!

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3 years ago

What is 4 to the -2 power divided by 4 to the 4th power

igomit [66]

Answer:

4 to the -2 power divided by 4 to the 4th power

$\frac{ {4}^{ - 2} }{ {4}^{4} } = \frac{1}{( {4}^{2} \times {4}^{4} ) } = \frac{1}{ {4}^{(2 + 4)} } = \frac{1}{ {4}^{6} } = \frac{1}{4096}\\$

<h3>(1/4096) is the right answer.</h3>

7 0

3 years ago