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3 years ago

Help me im absotootley verytootley megatootely stoopid.

Mathematics

1 answer:

Whitepunk [10]3 years ago

3 0

Answer:

The graphs are posted.

Step-by-step explanation:

the method to solve such inequalities is assume the line and then draw the line then search for the inequality

The y < 0.5x-3

First plot the line y=0.5x-3

Now all the values of y which are below the line satisfies the inequality.

similarly for the second question x+y ≥ 5.

Now assume the line x+y=5

All the values of (x , y) above the line satisfies the equation including the points on the line .

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A publisher wants to estimate the mean length of time (in minutes) all adults spend reading newspapers. To determine this estima

liq [111]

Answer:

a) $\bar X=9.07$

b) The 95% confidence interval is given by (8.197;9.943)

c) $m=2.14 \frac{1.580}{\sqrt{15}}=0.873$

d) 3 possible ways

1) Increasing the sample size n.

2) Reducing the variability. If we have more data probably we will have less variation.

3) Lower the confidence level. Because if we have lower confidence then the quantile from the t distribution would belower and tthe margin of error too.

Step-by-step explanation:

Notation and definitions

n=15 represent the sample size

$\bar X= 9.07$ represent the sample mean

$s=1.580$ represent the sample standard deviation

m represent the margin of error

Confidence =95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a: Find the point estimate of the population mean.

The point of estimate for the population mean $\mu$ is given by:

$\bar X =\frac{\sum_{i=1}^{n} x_i}{n}$

The mean obteained after add all the data and divide by 15 is $\bar X=9.07$

Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . The degrees of freedom are given by:

$df=n-1=15-1=14$

We can find the critical values in excel using the following formulas:

"=T.INV(0.025,14)" for $t_{\alpha/2}=-2.14$

"=T.INV(1-0.025,14)" for $t_{1-\alpha/2}=2.14$

The critical value $tc=\pm 2.14$

Part c: Calculate the margin of error (m)

First we need to calculate the standard deviation given by this formula:

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$

s=1.580

The margin of error for the sample mean is given by this formula:

$m=t_c \frac{s}{\sqrt{n}}$

$m=2.14 \frac{1.580}{\sqrt{15}}=0.873$

Part b: Calculate the confidence interval

The interval for the mean is given by this formula:

$\bar X \pm t_{c} \frac{s}{\sqrt{n}}$

And calculating the limits we got:

$9.07 - 2.14 \frac{1.580}{\sqrt{15}}=8.197$

$9.07 + 2.14 \frac{1.580}{\sqrt{15}}=9.943$

The 95% confidence interval is given by (8.197;9.943)

Part d: How can we reduce the margin of error?

We can reduce the margin of error on the following ways:

1) Increasing the sample size n.

2) Reducing the variability. If we have more data probably we will have less variation.

3) Lower the confidence level. Because if we have lower confidence then the quantile from the t distribution would belower and tthe margin of error too.

3 0

3 years ago

The lengths of nails produced in a factory are normally distributed with a mean of 5.02 centimeters and a standard deviation of

zaharov [31]

Answer:

The length that separates the top 6% is 5.1 centimeters.

The length that separates the bottom 6% is 4.94 centimeters.

Step-by-step explanation:

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.

In this question, we have that:

$\mu = 5.02, \sigma = 0.05$

Find the two lengths that separate the top 6% and the bottom 6%.

Top 6%:

The 100-6 = 94th percentile, which is X when Z has a pvalue of 0.94. So X when Z = 1.555.

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

$1.555 = \frac{X - 5.02}{0.05}$

$X - 5.02 = 1.555*0.05$

$X = 5.1$

So the length that separates the top 6% is 5.1 centimeters.

Bottom 6%:

The 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.555.

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

$-1.555 = \frac{X - 5.02}{0.05}$

$X - 5.02 = -1.555*0.05$

$X = 4.94$

The length that separates the bottom 6% is 4.94 centimeters.

7 0

3 years ago

Select the correct answer.

joja [24]

Answer:

D. 21/2

Step-by-step explanation:

We simply have to evaluate the first three terms based on the progression's formula:

t= 1, the first term is 8, as we see:

$8(\frac{1}{4})^{t-1} = 8(\frac{1}{4})^{1-1} = 8 * 1 = 8$

t=2, the second term is 2, as we see:

$8(\frac{1}{4})^{t-1} = 8(\frac{1}{4})^{2-1} = 8 * \frac{1}{4} = 2$

t=3, the third term is 1/2, as we see:

$8(\frac{1}{4})^{t-1} = 8(\frac{1}{4})^{3-1} = 8 * \frac{1}{16} = \frac{1}{2}$

The sum of the first 3 terms is then: 8 + 2 + 1/2 = 10 1/2

Among the answer choices, D. 21/2, which is 10 1/2.

3 0

3 years ago

if Lylah completes the square for f(x)=x squared -12x+7 in order to find the minimum she must write f(x) in the general form f(x

abruzzese [7]

Answer:

A. 6

Step-by-step explanation:

f(x) = x² − 12x + 7

To complete the square, we first factor the leading coefficient to make it 1 (which it already is).

Then, we take half the second coefficient, square it, and then add to both sides. So (-12/2)² = (-6)² = 36.

f(x) + 36 = x² − 12x + 36 + 7

Then we factor the perfect square:

f(x) + 36 = (x − 6)² + 7

Then solve for f(x) by subtracting and simplifying:

f(x) = (x − 6)² + 7 − 36

f(x) = (x − 6)² − 29

So the value of a is 6.

6 0

3 years ago

A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue). a. 9 c. One-fourth b. Four-thirds d. three-f

gayaneshka [121]

In order to find the probability of drawing a marble that is NOT BLUE, we must find the ratio of non-blue marbles to the total amount of marbles

Let's count how many marbles total there are first

8 red + 3 blue + 1 green = 12 marbles total

Now, how many marbles are there that ARE NOT BLUE

8 red + 1 green = 9 marbles THAT ARE NOT BLUE

Now let's create a ratio to find a probility

9/12

This can be simplified to 3/4 by taking out the common factor of 3

Your answer is D! "three-fourths"

7 0

3 years ago