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Lina20 [59]
3 years ago
13

Solve the following for p: 4(1-p)=-4p+4

Mathematics
1 answer:
Digiron [165]3 years ago
5 0
4(1-p)=-4p+4
distribute to get: 4-4p=-4p+4
Add 4p on both sides to get: 4-4p+4p=-4p+4p+4
Simply to get: 4=4
Therefore there are infinite solutions for p.

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Find the area of the sector
Setler [38]

Answer:

10:

7/4π = 5.5(1decimql place)

11:

50π = 157.1(1 decimal place)

Step-by-step explanation:

the equation is (angle/360) X πr^2

6 0
2 years ago
The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points. What is the probabilit
Korolek [52]

Answer:

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

Step-by-step explanation:

To solve this question, we have 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 random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 159, \sigma = 13, n = 60, s = \frac{13}{\sqrt{60}} = 1.68

What is the probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled?

This is the pvalue of Z when X = 159+1 = 160 subtracted by the pvalue of Z when X = 159-1 = 158. So

X = 160

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

By the Central Limit Theorem

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

Z = \frac{160 - 159}{1.68}

Z = 0.6

Z = 0.6 has a pvalue of 0.7257

X = 150

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

Z = \frac{158 - 159}{1.68}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

7 0
3 years ago
Kevin is 4 times as old as Daniel and is also 6 years older than Daniel
MAXImum [283]

Answer:

Part a) Daniel's age is 2 years

Part b) Kevin's age is 8 years

Step-by-step explanation:

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

Part a) How old is Daniel?

Part b) How old is Kevin?

Let

x ----> Kevin's age

y ----> Daniel's age

we know that

x=4y-----> equation A

x=y+6 ----> equation B

Equate equation A and equation B

4y=y+6

solve for y

4y-y=6

3y=6

y=2

therefore

Daniel's age is 2 years

<em>Find the value of x</em>

substitute the value of y in any of the two equations

x=4(2)=8\ years

x=2+6=8\ years

therefore

Kevin's age is 8 years

6 0
3 years ago
-16. What are the roots of<br> (x - 4)(x + 1)(x +9)
sammy [17]

Answer:

4,-1,-9

Step-by-step explanation:

If you set the factorise to equal zero you can solve for the answer

5 0
3 years ago
A climber who is 6 feet tall, casts a shadow that is 20 feet tall, at the same time that a tree casts a shadow which is 90 feet
Agata [3.3K]
The tree is about 27.3 ft. tall.
8 0
3 years ago
Read 2 more answers
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