An engineer wants to know if the average amount of energy used in his factory per day has changed since last year. The factory used an average of 2,000 megawatt hours (mwh) per day prior to last year. Since last year, the engineer surveyed 400 days and found the average energy use was 2,040 mwh per day. Assume that the population standard deviation is 425 mwh per day.
a. Specify the null and alternative hypotheses to determine whether the factory's energy use has changed.
b. Calculate the value of the test statistic and the p-value.
c. At the 5% significance level, can you conclude that the energy usage has changed? Explain.

Answer:

Step-by-step explanation:

145 mm hg

Answer:

The slope of the line is 0, that is, it is a horizontal line.

Step-by-step explanation:

Slope of a line:

The slope of a line having two points in the format (x,y) is given by the change in y divided by the change in x.

(-4,-5) and (3,-5).

Change in y: - 5 - (-5) = -5 + 5 = 0

Change in x: 3 - (-4) = 3 + 4 = 7

0/7 = 0

The slope of the line is 0, that is, it is a horizontal line.

Answer:

The answer is 13.005

Step-by-step explanation:

Answer:

13.005

Step-by-step explanation:

Answer:

The 80% confidence interval for the population proportion of oil tankers that have spills each month is (0.199, 0.257).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Suppose a sample of 333 tankers is drawn. Of these ships, 257 did not have spills.

333 - 257 = 76 have spills.

This means that [tex]n = 333, \pi = \frac{76}{333} = 0.228[/tex]

80% confidence level

So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.228 - 1.28\sqrt{\frac{0.228*0.772}{333}} = 0.199[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.228 + 1.28\sqrt{\frac{0.228*0.772}{333}} = 0.257[/tex]

The 80% confidence interval for the population proportion of oil tankers that have spills each month is (0.199, 0.257).

Answer:

0.065 metric tons

Step-by-step explanation:

Given

65 kg

To find

Convert 65 kg to metric tons

Then, the answer is 0.065 metric tons

Answer:

39 sq inches

Step-by-step explanation:

Answer: Compound probability is equal to the probability of the first event multiplied by the probability of the second event

HOPE THIS HELPS

Answer:

a) 0.0526 = 5.26% probability that more than 40 babies weigh less than 25 pounds.

b) 0.409 = 40.9% probability that 34 or more babies weigh less than 25 pounds.

c) 0.6249 = 62.49% probability that the number of babies who weigh less than 25 pounds is between 28 and 38 exclusive.

Step-by-step explanation:

The binomial approximation to the normal is used to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

A government agency reports that 22% of baby boys 6-8 months old in the United States weigh less than 25 pounds.

This means that [tex]p = 0.22[/tex]

A sample of 147 babies is studied.

This means that [tex]n = 147[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 147*0.22 = 32.34[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{147*0.22*0.78} = 5.02[/tex]

(a) Approximate the probability that more than 40 babies weigh less than 25 pounds.

Using continuity correction, this is P(X > 40 + 0.5) = P(X > 40.5), which is 1 subtracted by the pvalue of Z when X = 40.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{40.5 - 32.34}{5.02}[/tex]

[tex]Z = 1.62[/tex]

[tex]Z = 1.62[/tex] has a pvalue of 0.9474

1 - 0.9474 = 0.0526

0.0526 = 5.26% probability that more than 40 babies weigh less than 25 pounds.

(b) Approximate the probability that 34 or more babies weigh less than 25 pounds.

Using continuity correction, this is [tex]P(X \geq 34 - 0.5) = P(X \geq 33.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 33.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33.5 - 32.34}{5.02}[/tex]

[tex]Z = 0.23[/tex]

[tex]Z = 0.23[/tex] has a pvalue of 0.591

1 - 0.591 = 0.409

0.409 = 40.9% probability that 34 or more babies weigh less than 25 pounds.

(c) Approximate the probability that the number of babies who weigh less than 25 pounds is between 28 and 38 exclusive.

Exclusive means that we dont count 28 and 38, so, using continuity correction, this is [tex]P(28 + 0.5 \leq X \leq 38 - 0.5) = P(28.5 \leq X \leq 37.5)[/tex], which is the pvalue of Z when X = 37.5 subtracted by the pvalue of Z when X = 28.5. So

X = 37.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{37.5 - 32.34}{5.02}[/tex]

[tex]Z = 1.03[/tex]

[tex]Z = 1.03[/tex] has a pvalue of 0.8485

X = 28.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{28.5 - 32.34}{5.02}[/tex]

[tex]Z = -0.76[/tex]

[tex]Z = -0.76[/tex] has a pvalue of 0.2236

0.8485 - 0.2236 = 0.6249

0.6249 = 62.49% probability that the number of babies who weigh less than 25 pounds is between 28 and 38 exclusive.

Answer:

110.068181818

Step-by-step explanation:

Answer:

circumference of circle = 2×pi×r

circumference of circle =2×3.14×2.8 mi

circumference of circle =17.584 mi

Answer:

80-40=40

40-30=10

he only has $10 remaining in savings

Step-by-step explanation:

Answer:

$10 or 12.5%

Step-by-step explanation:

80-(80/2)-30

80-40-30

80-70

$10

10 is 12.5% of 80

Hope this helps!

Answer:

[tex] \frac{5}{2} \times \frac{3}{4} \\ \frac{15}{8} [/tex]

Answer:

15/8

Step-by-step explanation:

2.5/2 = 1.25

1.25/2 = 0.625

2.5 - 0.625 = 1.875

1.875 = 75/40 = 15/8

Answer:

a1=4-2(1)

=4-2

a1=2

a2=4-2(2)

=4-4

a2=0

a3=4-2(3)

=4-6

a3=-2

a4=4-2(4)

=4-8

a4=-4

Answer:

Disagree

Step-by-step explanation:

[tex]3.67 = c - 2.13 \\ 3.67 + 2.13 = c \\5.8 0 = c[/tex]

Answer:

A.

Step-by-step explanation:

Recall, SOHCAHTOA.

Reference angle = Z

Opposite = 35

Adjacent = 12

Hypotenuse = 37

Sin Z = Opp/Hyp

Therefore,

Sin z = 35/37

Answer:

152 cm^2

Step-by-step explanation:

To calculate the surface area of this figure, we just need to calculate the surface area of each side and add the total.

Surface area of rectangle = length times width

4 * 8 = 32

Now, we need to multiply 32 by 4 because there are 4 of these rectangles. This yields a value of 128, and we can now find the surface area of the other rectangles:

Surface area of rectangle = length times width

4 * 3 = 12

Now, we need to multiply 12 by 2 because there are 2 of these rectangles. This yields a value of 24 and we can add 24 to 128 to get the total surface area of the prism. This means that the surface area of the prism is 152 cm^2

Answer:

Step-by-step explanation

Answer:

[tex] \boxed{ m \overset{\huge\frown}{EFC} \: = \: 237°} [/tex]

Explanation:

Assuming that [tex] \overline{CF} [/tex] is a diameter, and that the angle of an arc subtending the central angle is congruent, [tex] m \overset{\Large\frown}{CGF} \: = \: 180° [/tex].

And according to the arc addition postulate, [tex] \overset{\Large\frown}{CG} + \overset{\Large\frown}{GF} \: = \: \overset{\huge\frown}{CGF} [/tex].

Using the substitution property:

[tex] \overset{\Large\frown}{CG} + \overset{\Large\frown}{GF} \: = \: 180° [/tex].

Given that [tex] m\overset{\Large\frown}{CG} \: = \: 140° [/tex].

Using the substitution property and that the measures apply to the arc addition postulate, [tex] 140° + m\overset{\Large\frown}{GF} \: = \: 180° [/tex].

[tex] 140° – \: 140° + m\overset{\Large\frown}{GF} \: = \: 180° – \: 140° [/tex].

[tex] m\overset{\Large\frown}{GF} \: = \: 40° [/tex].

Since [tex] \overset{\Large\frown}{GF} [/tex] and [tex] \overset{\Large\frown}{CD} [/tex] are subtending the center of the circle, they form vertical angles and are therefore congruent.

[tex] \overset{\Large\frown}{GF} \: \cong \: \overset{\Large\frown}{CD} [/tex]

According to the definition of a vertical angle, [tex] m \overset{\Large\frown}{CD} \: = \: 40° [/tex].

Using the arc addition postulate again,

[tex] \overset{\Large\frown}{CD} + \overset{\Large\frown}{DE} + \overset{\Large\frown}{EF} \: = \:\overset{\huge\frown}{CDF}/\overset{\huge\frown}{CEF} [/tex]

Using substitution, as well as how we are given that the central angle subtended by [tex] \overset{\Large\frown}{DE}[/tex] = 83°, we can find that:

[tex] 40° + 83° + \overset{\Large\frown}{EF} \: = \:\overset{\huge\frown}{CDF}/\overset{\huge\frown}{CEF} [/tex]

Answer:

r=7

Step-by-step explanation:

Work it backwards

1436.6=4/3pir^3

multiply both sides by the reciprocal, 3/4

1077.45=pir^3

divide by pi (3.14)

342.96

take the cube root of the number

7

Answer:

$78.37 ÷7

Step-by-step explanation

im not smart

Answer:

x < -8

Step-by-step explanation:

−3x>24

Divide each side by negative 3, remembering to flip the inequality

-3x/-3 < 24/-3

x < -8

Answer:

x<-8

Step-by-step explanation:

−3x>24

Multiply both sides by (-1) (reverse the inequality)

(-3x)(-1)<24(-1)

Simplify;

3x<-24

Divide both sides by 3

3x/3<-24/3

Simplify

3x/3<-24/3

Simplify; 3x/3

=x

Simplify; -24/3

Divide the numbers;24/3=8

=-8

x<-8

Hope this helped!!!

1.)1/6

2.)1 5/10

3.)2 6/7

4.)2

5.)1 7/12

6.)2 4/5

7.)1/12

with like denominators you can just add or subtract freely just the top numerators

Answer:

1.)1/6

2.)1 5/10

3.)2 6/7

4.)2

5.)1 7/12

6.)2 4/5

7.)1/12

Step-by-step explanation:

Answer:

$10,213.34

Step-by-step explanation:

Using the compound interest formula;

A = P(1+r/n)^t

Given that;

P = $7,200

rate r = 6% = 0.06

Time t = 6years

n = 1

Substitute into the formula

A = 7200(1+0.06)^6

A = 7200(1.06)^6

A = 7200(1.4185)

A = 10,213.34

Hence the final amount is $10,213.34

Answer:

65000

Step-by-step explanation:

Just round the number

Answer: ~31.3

first use the pythagorean theorem. a^2+(40)^2=50^2.

simply. a+1600=2500. subtract 1600 from both sides. a^2=900.

square root both sides to get a= 30

then find how far the top of the ladder is from the ground once in its new position.

a^2+(39)^2=50^2.

simplify. a^2+1512=2500. subtract 1512 from both sides to get a^2=979.

square root both sides to get a=31.288975. round to the nearest tenth to get a=31.3

Answer:

Step-by-step explanation: iT'S 31.3

Answer:

its 5 I think, good luck

Step-by-step explanation:

Answer:

$506.25.

Step-by-step explanation:

Answer:

31.50

Step-by-step explanation: