A professor at a university wants to estimate the average number of hours of sleep students get during exam week. On the first day of exams, she asked 20 students how many hours they had slept the night before. The average of the sample was 5.88 with a standard deviation of 1.942. When estimating the average amount of sleep with a 95% confidence interval, what is the margin of error?a) 0.3463b) 0.4893c) 0.6344d) 0.6336e) 0.3725

Answer:

862 books

Step-by-step explanation:

You have to divide

Answer:

point T only.

Step-by-step explanation:

for more info see the attachment.

Answer:15.5

Step-by-step explanation:you can use the sin rule so set up x(height)/sin54.1 = 19.1/sin90 then times 19.1/sin90 by sin 54.1 to get 15.5

Answer:

20 Times larger

Step-by-step explanation:

8 * 10^3 = 8000

4 * 10^2 = 400

8000/400 = 20

Answer:

For maximum area: Its a square of dimensions 7.25 * 7.25.

Step-by-step explanation:

We can use calculus to solve this:

Let the length of the rectangle be L and the width be W then we have

2L + 2W = 29

L + W = 14.5

W = 14.5 - L

Area = WL

A = L(14.5 - L)

A = 14.5L - L^2

We need this to be a maximum.

Finding the derivative:

dA/dW = 14.5 - 2L = 0   for a maximum

2L = 14.5

L = 7.25

Also W = 14.5 - L

= 14.5 - 7.25 = 7.25.

So the dimensions for maximum area are 7.25 * 7.25.

The  figure is a SQUARE.

The perimeter of a rectangle, is the sum of its side lengths.

The rectangle that has the maximum area when the length is 7.25 and the width is 7.25

The perimeter is given as:

\(\mathbf{P = 29}\)

Let the dimensions be l and w.

So, we have:

\(\mathbf{2( l + w) = 29}\)

Divide both sides by 2

\(\mathbf{l + w = 14.5}\)

Make l the subject

\(\mathbf{l = 14.5 - w}\)

The area of a rectangle is:

\(\mathbf{A = lw}\)

Substitute \(\mathbf{l = 14.5 - w}\)

\(\mathbf{A = (14.5 - w)w}\)

Open brackets

\(\mathbf{A = 14.5w - w^2}\)

Differentiate

\(\mathbf{A' = 14.5 - 2w}\)

Set to 0

\(\mathbf{14.5 - 2w = 0}\)

Collect like terms

\(\mathbf{2w = 14.5}\)

Divide both sides by 2

\(\mathbf{w = 7.25}\)

Recall that: \(\mathbf{l = 14.5 - w}\)

So, we have:

\(\mathbf{l = 14.5 - 7.25 = 7.25}\)

Hence, the rectangle that has the maximum area when the length is 7.25 and the width is 7.25

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Answer:

8 divided by two equals the radius 4

3.14*4^2=50.24

Hope This Helps!!!

The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.

First, let's calculate the margin of error:

Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055

Next, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%

Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%

Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

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3/5 and -3/4 are the x and y-intercept of the line respectively

Given the coordinate points (−1, −2) and (3, 3), we need to determine the x and y-intercept

The equation of a line in slope intercept form is y = mx + b where:

m is the slope

b is the intercept

For the slope:

slope = 3-(-2)/3-(-1)
Slope = 5/4

For the y- intercept

3 = 5/4(3) + b

3 = 15/4 + b

b = 3 - 15/4

b = -3/4

Hence the equation of the line is. y = 5/4 x - 3/4

For the x-intercept

The x-intercept is the point where y = 0

0 = 5/4 x - 3/4

5/4 x = 3/4

5x = 3

x = 3/5

Hence the x- and y-intercepts of the line are 3/5 and -3/4 respectively.

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Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

You're answer is (A) The cosine law only

Law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle.

Answer:  The correct answer is (#1) the cosine law only.

Step-by-step explanation:  Confirmed correct.

Answer:

HJ > PK

Step-by-step explanation:

Notice that the side PL in one triangle has the same length as side GJ in the other, and side GH has the same size as side LK of the other triangle. Now what is different is the angle subtended between these sides in the case of the triangle on the lower left, the subtended angle is \(90^o\) , which is larger angle than that subtended between equal sides on the other triangle (\(85^o\))

Therefore, if the angle subtended by the equivalent sides in the triangle on the left is larger than the angle subtended on the right hand side triangle, then the sides associated with such angle aperture must keep the inequality. That is:

Since \(\angle\,G\,\,\,>\,\,\,\angle \,L\), then   HJ > PK

Answer:

44,000

Step-by-step explanation:

The number 43,761 rounded to its nearest thousands is 4400.

The place value of a number is given as:

Example:

1234.567

1 = thousand place value

2 = hundred place value

3 = tens place value

4 = ones place value

5 = tenths place value

6 = hundredths place value

7 = thousandths place value

We have,

43,761

3 is in the thousand place.

So,

We will round 3761 to its nearest thousand value.

There are two options:

3000 or 4000

If It is greater than 3499 it will round to 4000.

If it is less than 3500 it will round to 3000.

Now,

3761 > 3499.

So,

The number is rounded to 4000.

Thus,

43,761 is rounded to 4400.

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The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

The confidence interval formula is \(\bar x\pm t\frac{s}{\sqrt{n}}\).

Where, \(\bar x\) is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.

Here,

\(\bar x\) =1.267, s=1.23, n=30

The standard error is Se= 1.23/√30

= 0.2246

Item a:

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

Item b:

Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.

\(\bar x\pm tS_c\)

\(\bar x+ tS_c\) =1.267-2.7564(0.2246) =0.6479

\(\bar x- tS_c\) =1.267+2.7564(0.2246) =1.8861

Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.

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Answer:

-50

Step-by-step explanation:

If the drink is descending by 50 feet, hypothetically I would say that the drinks at 0 ft. so it would be -50

Answer:

-50

Step-by-step explanation:

Drink descended 50 fifty feet, "descended" in this case means subtraction or negative

The scientific notation of the given number is 1.24×10⁻⁶.

The given number is 0.00000124.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Here, 0.00000124=1.24×10⁻⁶.

Therefore, the Scientific notation of the given number is 1.24×10⁻⁶.

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Answer:The diffrence is 11

Answer:

4. 84.82 6. 7238.23 5. 1415.81 7. 1570.8

Step-by-step explanation:

Answer:

4. 254.47ft^3

5. 4247.43yd^3

6. 21714.69 in^3

7. 4712.39 ft^3

hope this helps

have a good day :)

Step-by-step explanation:

We start by writing the expression in ax^b form:

Now, we have the expression is 16x^(-28), so a = 16 and b = -28.

If we add them, we get:

Answer: the sum of a and b is -12.

The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

The actual dimensions of the patio are 20 feet by 16 feet.

The scale factor is 1 inch to 4 feet,

This means that 1 inch on the scale drawing represents 4 feet in reality.

So the dimensions of the scale drawing are:

20 feet x (1/4) = 5 inches (length on scale drawing)

16 feet x (1/4) = 4 inches (width on scale drawing)

The area of the actual patio is:

= 20 feet x  16 feet

= 320 square feet

The area of the scale drawing is:

= 5 inches x 4 inches

= 20 square inches

The ratio of the area of the scaled drawing to the actual area of the patio is: 20 square inches : 320 square feet

To simplify this ratio, we need to convert both values to the same units.

Converting the area of the scale drawing to square feet:

= 20 square inches x  (1/144) square feet/square inch

= 0.1389 square feet

So the ratio of the area of the scaled drawing to the actual area of the patio is:

0.1389 square feet : 320 square feet

Or, in simplified form:

1 : 2306.56

Thus,

The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

B is the correct one. Second.

Answer:

B

Step-by-step explanation:

The approximate sum of the values to the nearest thousand is 117000

Any number of digits after that number becomes zero and this is known as rounding down. If the digit in the smallest place is greater than or equal to 5, then the digit is added with +1.

Given the expression below;

24,687 +38,403 +53,628 = 116718

Hence the approximate sum of the values to the nearest thousand is 117000

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Answer:

I believe the answer is a=58

Step-by-step explanation:

a=1+25+8+24

a=26+8+24

a=34+24

a=58

Step-by-step explanation:

Just :    5,8374

Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)