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Juli2301 [7.4K]
3 years ago
7

2 questions here:

Mathematics
2 answers:
solmaris [256]3 years ago
6 0
<span>1. Make y the subject 
a) 4y=12x+18
y = 3x + 4.5

b) 2x=7-3y
3y = -2x + 7
y = -2/3x + 7/3

2.
a) what is the equation of the line which passes through both (-2,-4) and (6,16)

slope = (16 + 4)/(6 +2) = 20/8 = 2.5
y = mx + b
-4 =2.5(-2) +b
-4 = -5 +b
b = 1

equation
y = 2.5x + 1


b) what is the equation of the line perpendicular to y= 1/2X + 7 passing through point (3,9)

</span>y= 1/2X + 7
slope = 1/2

slope of line perpendicular = -2

passing through point (3,9)

y = mx + b
9 = -2 (3) + b
b = 15

equation

y = -2x + 15

Bingel [31]3 years ago
4 0
Hello here is a solution : 

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kykrilka [37]
To find the area of the trapezoid you add the two bases then multiply by the base and divide by 2. 

B1+b2= 24+16=40
40*h=40*12=480
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D. 240 square feet.
8 0
3 years ago
A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40
bezimeni [28]

Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using 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.

a. How large was the sample used in this survey?

We have that s = 25, \sigma = 400. We want to find n, so:

s = \frac{\sigma}{\sqrt{n}}

25 = \frac{400}{\sqrt{n}}

25\sqrt{n} = 400

\sqrt{n} = \frac{400}{25}

\sqrt{n} = 16

(\sqrt{n})^2 = 16^2[tex][tex]n = 256

A sample of 256 was used in this survey.

b. What is the probability that the point estimate was within ±15 of the population mean?

15 is the bounds with want, 25 is the standard error. So

Z = 15/25 = 0.6 has a pvalue of 0.7257

Z = -15/25 = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

45.14% probability that the point estimate was within ±15 of the population mean

3 0
3 years ago
Pls help me guys! This is super hard
zheka24 [161]
This explanation shall help you, To find a mean you first need to add
25 + 21+36+16+32 and then divide by 5  and then you will get your answer. Hope this helps!
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3 years ago
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