suppose that based on a random sample, a 95% confidence interval for the mean hours slept (per day) among graduate students was found to be (6.5, 6.9). what is the margin of error of this confidence interval? responses

0.1116 is the area under the standard normal curve using the given z-score.

The standard score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed.

Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

The 90th percentile's z-score is 1.2816, as calculated by the Percentile to Z-Score Calculator.

Therefore, a student's z-score would be deemed "excellent" if it was greater than or equal to 1.2816.

So, the area under the standard normal curve will be:

Find the z-scores by looking at the table's intersection of the 0.9 down and 0.07 across columns, which is 0.1660.

Similarly, find -0.5 down and 0.09 across to get 0.2776.

Add them together now: 0.2776 - 0.1660 = 0.1116

Therefore, 0.1116 is the area under the standard normal curve using the given z-score.

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The profit increased at an average pace of $600 between Hour 5 to Hour 10.

An indicator of the how one dimension changes in proportion to another is a rate of change.

The table for the price is given as;

Hour                Profit

0                        $0

2.5                     $500

5                        $900

7.5                     $1200

10                        $1500

After 5 hours, the profit is 900, and after another 5 hours, the profit is 1500.

In order to determine that average rate of change, we must take 900 away from 1500.

1500-900 = 600

Thus, an average rate of change for profit during Hour 5 to Hour is therefore $600.

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The type of study was cross-sectional study.

An example of an observational study design is the cross-sectional study design. In a cross-sectional study, the researcher simultaneously assesses the participants exposures and outcomes.

After choosing the study subjects, the researcher conducts the study in order to evaluate the exposure and results.

For population-based surveys and to determine the prevalence of illnesses in clinic-based samples, cross-sectional designs are employed.

These studies are typically affordable and reasonably quick to carry out.

An illustration of a cross-sectional study might be a medical investigation into the incidence of cancer in a particular community.

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Answer:

  NK = 26

Step-by-step explanation:

You have a triangle with the centroid identified and all medians drawn. You are given IK = 52 and want NK, where point N is the intersection of median JN with side IK.

The centroid of a triangle is the point where the medians intersect. It divides each median in the ratio 2:1.

A median of a triangle joins a vertex with the midpoint of the opposite side. Here, that means point N is the midpoint of side IK.

IK is given as length 52, so each half of that segment is 52/2 = 26.

  IN = NK = 26

Answer:

p(x)=x^2 -17 x + 84

Step-by-step explanation:

p(x)=(x-7)(x-12)

 = x^2-17x+84

It will take 112.5 minutes to mow a lawn that measures 6000 sq ft .

In the question ,

it is given that ,

the time taken to mow 800 sq ft of the given lawn is = 15 minutes ,

So , the time taken to mow 1 sq ft of lawn is = 15/800 minutes .

to find the time taken to mow 6000 sq ft , we multiply by 6000 ,

We get ,

time taken to mow 6000 sq ft of the lawn is = 6000*(15/800)

on solving , we have

= 90000/8000

Simplifying further ,

we get ,

= 112.5 minutes

Therefore , 6000 sq ft lawn will be mowed in 112.5 minutes .

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The correct option d. 0.109, for the probability of the event: exactly 6 heads out of 8.

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The probability of getting one head = 1/2.

p = 0.5.

Thus, the probability of getting one tail = 1/2

q = 0.5

Thus, for exactly 6 heads

P(X = 6) =  ⁸C₆. (0.5)⁶ (0.5)²

P(X = 6) = 0.109

Thus, the probability of the event: exactly 6 heads on flipping coin 8 times is 0.109.

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Answer:

36

I looked it up on

Kevion and Samantha like to collect stamps and if Kevion has 45 stamps then Samantha has 45*3-2= 129 stamps.

The fundamental methods for mixing numbers or algebraic expressions to carry out mathematical computations are known as mathematical operations. These operations include multiplication, division, exponentiation, multiplication, and subtraction. More complex operations, such square roots, logarithms, and trigonometric functions, are available in addition to these fundamental operations. Mathematical operations are employed in a wide collection of disciplines, from elementary arithmetic to intricate computations in engineering and physics. We can use these operations to resolve issues and generate predictions based on mathematical models. We may better comprehend the world around us and make more precise predictions about what will happen in the future by applying mathematical procedures.

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The possible values of (m,n) are (1,2) and (-17,14).

A system having more than two equations is known as a system of equations.

Given that, the solution of the simultaneous equations is x = 2 and y = 3.

The given equations are:

mx + ny = 8

m²x - n²y = -10

Substitute x = 2 and y = 3 into the above equations:

2m + 3n= 8       (1)

2m² - 3n² = -10     (2)

Rewrite equation (1):

2m + 3n= 8

2m = 8 - 3n

m = (8 - 3n)/2          (3)

Substitute it into equation (2):

[tex]2\frac{(8-3n)^2}{4}-3n^2 = -10\\\\2(64 +9n^2-48n)-12n^2+40 =0\\\\128 +18n^2-96n-12n^2+40=0\\\\6n^2-96n+168=0\\\\n^2-16n+28=0\\\\n^2-14n-2n+28=0\\\\n(n-14)-2(n-14)=0\\\\(n-2)(n-14)=0[/tex]

n = 2 or n =14

Now, substitute n = 2 into equation (3):

m = (8-3×2)/2

m = 1

Further, substitute n = 14 into equation (3):

m = (8-3×14)/2

m = -17

Hence, the possible values of (m,n) are (1,2) and (-17,14).

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Derivative of six inverse trigonometric functions are as follow:

d/dx(sin⁻¹x) = 1 / √1 - x²

d/dx(cos⁻¹x) = -1 / √1 - x²

d/dx(tan⁻¹x) = 1 / √1 + x²

d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1

d/dx(sec⁻¹x) = 1 / |x|√ x² -1

d/dx(cot⁻¹x) = -1 / √1 + x²

As given in the question,

Explanation of the derivative of six inverse trigonometric functions are as follow:

1. y = sin⁻¹x

⇒ x = siny

⇒d/dx(x) = d/dx(siny)

⇒ 1 = cosy dy/dx

⇒dy/dx = 1/cosy

⇒dy/dx = 1/√1-sin²y

⇒dy/dx = 1/√1-x²

⇒d/dx( sin⁻¹x) = 1/√1-x²

2. y = cos⁻¹x

⇒ x = cosy

⇒d/dx(x) = d/dx(cosy)

⇒ 1 =-siny dy/dx

⇒dy/dx = -1/siny

⇒dy/dx = -1/√1-cos²y

⇒dy/dx = -1/√1-x²

⇒d/dx( cos⁻¹x) = -1/√1-x²

3. y = tan⁻¹x

⇒ x = tany

⇒d/dx(x) = d/dx(tany)

⇒ 1 =sec²y dy/dx

⇒dy/dx = 1/sec²y

⇒dy/dx = 1/√1+ tan²y

⇒dy/dx = 1/√1 + x²

⇒d/dx( tan⁻¹x) = 1/√1+x²

4. y = cosec⁻¹x

⇒ x = cosecy

⇒d/dx(x) = d/dx(cosecy)

⇒ 1 =-cosecy coty dy/dx

⇒dy/dx = -1/cosecy coty

⇒dy/dx = -1/cosecy√cosec²y-1

⇒dy/dx = -1/|x|√x²-1

⇒d/dx( cosec⁻¹x) = -1/|x|√x²-1

5.   y = sec⁻¹x

⇒ x = secy

⇒d/dx(x) = d/dx(secy)

⇒ 1 =secy tany dy/dx

⇒dy/dx = 1/secy tany

⇒dy/dx = 1/secy√sec²y-1

⇒dy/dx = 1/|x|√x²-1

⇒d/dx( sec⁻¹x) = 1/|x|√x²-1

6. y = cot⁻¹x

⇒ x =coty

⇒d/dx(x) = d/dx(coty)

⇒ 1 =-cosec²y dy/dx

⇒dy/dx = -1/cosec²y

⇒dy/dx = -1/√1+ cot²y

⇒dy/dx = -1/√1 + x²

⇒d/dx( cot⁻¹x) = -1/√1+x²

Therefore, the derivative of the six inverse trigonometric functions are given below:

d/dx(sin⁻¹x) = 1 / √1 - x²

d/dx(cos⁻¹x) = -1 / √1 - x²

d/dx(tan⁻¹x) = 1 / √1 + x²

d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1

d/dx(sec⁻¹x) = 1 / |x|√ x² -1

d/dx(cot⁻¹x) = -1 / √1 + x²

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Answer:

Step-by-step explanation:

1) The equation of a line passing through the point (5, 9) in point slope form is;  (y - 9) = 3(x - 5)

2) The equation that is parallel and passing through (0, 4) is; y = ¹/₂x + 4

3) The equation of the line parallel to y - 7 = 7(x - 3) and passing through the point (4, 2) is; (y - 2) = 7(x - 4)

4) Thus, the equation of the line parallel to y = -7x - 2and passing through (-9, -12) is; y = -7x - 75

The general equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

1) We are given the equation of a line as;

y = 3x + 5

where;

slope = 3

y-intercept = 5

Thus, the equation of a line passing through the point (5, 9) in point slope form is;

(y - y₁) = m(x - x₁)

Thus; (y - 9) = 3(x - 5)

2) Equation of a line is given as;

y = (1/2)x

Thus, the equation that is parallel and passing through (0, 4) is;

y - 4 = (1/2)(x - 0)

y - 4 = ¹/₂x

y = ¹/₂x + 4

3) We are given the equation;

y - 7 = 7(x - 3)

y - 7 = 7x - 21

y = 7x - 14

Thus, equation of the line passing through the point (4, 2) is;

(y - 2) = 7(x - 4)

4) We are given the equation;

y = -7x - 2

Thus, the equation of the line parallel and passing through (-9, -12) is;

y + 12 = -7(x + 9)

y = -7x - 63 - 12

y = -7x - 75

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Answer: 2.12 miles.

Step-by-step explanation: To find the width of Hardee County, we need to determine the length of one of its sides. We can use the fact that the area of a rectangle is equal to its length times its width to find the length of one of its sides.

The area of Hardee County is 637 square miles, and we know that its width is 30 miles. We can use this information to write the following equation: 637 square miles = 30 miles * length

We can solve this equation for the length by dividing both sides by 30: 637 square miles / 30 miles = length

This simplifies to: 21.2 square miles = length

Since the length of a rectangle is one of its sides, the width of Hardee County is 21.2 miles.

Answer:

2.91666667 dozen marbles can be purchased.

Step-by-step explanation:

To get this answer, you divide $140, by how much it costs per dozen, so $48.

Thus, you can purchase 2.91666667 dozen marbles, with $140.

If each side of a square is increasing at a rate of 7 cm/s, then the rate of increasing the area of the the square when the area of the square is 64 cm square is 112 centimeter square per second

The rate of change of length with respect to the time = 7 cm per second

That is

dl / dt = 7 cm per second

The area of the square = l^2

Where l is the length of the square

The rate of change area with respect to the time is

dA / dt = 2l dl/dt

The area is given that 64 centimeter square and the side will be 8 cm

Substitute the values in the equation

dA / dt = 2 × 8 × 7

= 112 centimeter square per second

Therefore, the rate of increasing the area is 112 centimeter square per second

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The logarithmic expression as a single logarithm is [tex]log_{2}[/tex](a[tex]b^{2}[/tex]/[tex]c^{3}[/tex])

A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction.

[tex]log_{2}a + 2log_{2}b - 3log_{2}c[/tex]

[tex]2log_{2}b[/tex] may be simplified as [tex]log_{2}b^{2}[/tex]

[tex]3log_{2}c[/tex] may be simplified as [tex]log_{2}c^{3}[/tex]

Which reduces the expression as

[tex]log_{2}a[/tex] +  [tex]log_{2}b^{2}[/tex] -  [tex]log_{2}c^{3}[/tex]

factor out log2 since it is common

and replace addition sign with multiplication and subtraction sign with division

[tex]log_{2}(\frac{a * b^{2} }{c^{3} })[/tex] which finally becomes [tex]log_{2}(ab^{2} /c^{3})[/tex]

In conclusion, the simplified form of the logarithmic expression is  [tex]log_{2}(ab^{2} /c^{3})[/tex]

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Answer:

Step-by-step explanation:

ben

Making b the subject in the formula for area of a trapezium, A, given by A = (a+b)÷2 h is found to be b = 2A/h - a

The given expression for area of trapezium is A = (a+b)÷2*h

b is solved for as follows

A = (a+b)÷2*h

A = h * (a+b)/2

divide through by h

A/h = (a+b)/2

multiply through by 2

2A/h = (a + b)

2A/h = a + b

b = 2A/h - a

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The value of n in 1:n is 4.5 in the given equivalent ratio.

What is equivalent ratio?

The concept of a ratio in mathematics is the divisional comparison of two quantities, the antecedent and consequent. As an illustration, each ingredient must be added according to a ratio during cooking. So, we may argue that a ratio is employed to represent one quantity as a portion of another. The ratio can be written as a fraction as well. If the ratio a:b is a fraction, its form is a/b. As a result, it is simple to compare two or more equivalent ratios expressed as equivalent fractions.

The given ratio is 8:36.

In fraction form = 8/36

= 1 / 4.5

=1:4.5

Hence, the value of n in 1:n is 4.5.

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Answer: 27.1875 pounds

Step-by-step explanation:

To find out how many pounds are in 435 ounces, we need to divide the number of ounces by the number of ounces per pound. Since 1 pound is equal to 16 ounces, we can divide 435 ounces by 16 ounces per pound to get the number of pounds. This gives us 435 ounces / 16 ounces/pound = 27.1875 pounds.

Therefore, there are approximately 27.1875 pounds in 435 ounces.

Answer:

27.1875 pounds

Step-by-step explanation:

1 pound = 16 ounces,

x pounds = 435 ounces

x = 435 ounces * 1 pound / 16 ounces

x = 27.1875 pounds

Answer:

The mass of the 30,000 molecules is 1.59\times 10^{-18}1.59×10

−18

Given that,

There are 30,000 molecules.

And, the mass of one molecule of oxygen i.e. 5.3\times 10^{-23}5.3×10

−23

gram.

Based on the above information, the calculation is as follows:

\begin{gathered}= 30,000 \times 5.3\times 10^{-23}\\\\= 3\times10^4 \times 5.3\times 10^{-23}\\\\= 15.9\times 10^{-23+4}\\\\= 15.9\times 10^{-19}\\\\= 1.59\times 10^{-19}\times 10\\\\= 1.59\times 10^{-18}\end{gathered}

=30,000×5.3×10

−23

=3×10

4

×5.3×10

−23

=15.9×10

−23+4

=15.9×10

−19

=1.59×10

−19

×10

=1.59×10

−18

Therefore we can conclude that the mass of the 30,000 molecules is 1.59\times 10^{-18}1.59×10

−18

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A repeated-measures test's null hypothesis is that the population as a whole will have a mean difference of μD = 0.

What is Null Hypothesis?

In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening.

The t statistic is calculated from the difference between the sample parameter in question and the value of the corresponding population parameter assumed under the null hypothesis. If the hypothesis is true, the difference between the values (and the corresponding t statistic) is expected to be zero.

A repeated-measures test's null hypothesis is that the population as a whole will have a mean difference of μD = 0.

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Answer:

Interval notation to inequality notation

95% confidence interval for true average degree of polymerization is  [430.87 ; 446.07] and this interval suggest that 441 is a plausible value for true average degree of polymerization and also this interval does not suggest that 451 is a plausible value.

Given :

The total number of values given is, n = 17

Mean, μ₀ = 438.47

Standard Deviation, σ = 14.79

The normal distribution is given by: N (438.47 ; 14.79)

If Cl  is 95% then  is 5% and  is 2.5%

α/2 = 0.025

Now, use t-statistics distribution with (n -1) degree of freedom

                         df = 16

So, the t score for 0.025 and 16 s from t-table 2.120.

CI = [ μ₀ ± [tex]t_{\alpha /2}[/tex] ; (n-1) × σ/ √n]

⇒ CI = [μ₀ ± 2.120 × 14.79/√17

⇒ CI = [ μ₀ ± 7.60]

⇒ CI = 430.87 ; 446.07]

Yes, the interval suggests that 441 is a plausible value for true average degree of polymerization.

No, the interval does not suggest that 451 is a plausible value.

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The false statement out of given four option is (a)conserves around 9 cubic yards in landfill space.

Area is characterized as the complete space taken up by a level (2-D) surface or state of an item. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Region. Presently, envision your square is comprised of more modest unit squares

That's what first explanation expresses "conserves around 9 cubic yards in landfill space "

Yet, here unit of landfill space is off-base. Since landfill space is an amount that in every case express in region. Unit of region in the proclamation articulation ought to be square yards not cubic yards

The excess amounts units are reliable with what they address.

Subsequently, When 500 telephone directories are reused, then, at that point,  false statement is option  (a) Monitors around 9 cubic yards in landfill space.

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Answer:Y=6

Step-by-step explanation:

I will be using the substitution method:

x+y=9 y=x+3

X + (x + 3) = 9

2x + 3 = 9

*subtract 3 from both sides*

2x = 6

*divide by 2 on each side of the equal sign*

X = 3

find y:

y = 3 + 3

y = 6

check:

3 + 6 = 9

9 = 9 (correct)

The value of x is 3 and the value of y is 6