To investigate whether or not people tend to marry spouses of similar ages or whether husbands tend to be older than their wives, a student gathered age data from a sample of 24 couples, taken from marriage licenses filed in Cumberland County, PA, in June and July 1993.
Diff(H-W)
1
-4
-4
18
2
2
1
1
2
1
0
4
2
-5
7
6
7
2
4
1
-6
1
2
-7
1
16
3
13
2
-1
-1
10
-1
1
0
-4
1
8
-1
-7
1
4
5
3
9
-5
3
-7
2
1
2
-4
0
12
4
13
-1
3
5
3
-2
2
0
2
0
2
13
-1
1
1
2
-3
6
1
1
-5
2
7
-2
-7
-1
1
9
1
-2
-1
3
5
-5
8
1
1
0
2
-2
-7
1
5
7
15
1) Define, in words.
A. The total difference in husband and wife marriage ages in Cumberland County; μd.
B. Average age of men and average age of women; μm and μw.
C. The average difference in husband and wife marriage ages in Cumberland County; μd.
2) Select the appropriate null and alternative hypotheses in the context of the study.
A. Null: The average difference in marriage ages in Cumberland County is 0. Alt: The average difference in marriage ages is not 0.
B. Null: The average difference in marriage ages in Cumberland County is not 0. Alt: The average difference in marriage ages is 0.
C. Null: The average difference in marriage ages in Cumberland County is 0. Alt: The average difference in marriage ages is less than 0.
D. Null: The average difference in marriage ages in Cumberland County is 0. Alt: The average difference in marriage ages is greater than 0.
3) Select the appropriate null and alternative hypotheses in the context of the study depicted using symbols
A. Null: μd = 0, Alt: μd > 0
B. Null: μd = 0, Alt: μd ≠ 0
C. Null: μd > 0, Alt: μd = 0
D. Null: μd = 0, Alt: μd < 0
4) For the 24 couples, the husbands are, on average, 1.875 years older than their wives (SD = 4.812). Use these statistics and the Theory-Based Inference applet to conduct a test of significance and report the resulting p-value to four decimal places.​
5) Based on the p-value, do you have strong evidence that, on average, husbands are older than their wives in Cumberland County?

The presence of the coefficient "a" in ax^2 + bx + c requires that we look for numbers that have a product of ac

Here we have to determine the difference

From the question, we have the following parameters that can be used in our computation:

ax^2 + bx +c and x^2 + bx +c

The presence of the coefficient "a" in the first expression makes a difference in the factoring process.

When factoring x^2 + bx + c, we are looking for two numbers that multiply to give c and add up to b.

For ax^2 + bx +c , we look for the product of ac and sum of b

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Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Answer:

\(\large \boxed{\sf \text{The rate of the boat is } 53 \ km/h \text{, the rate of the current is }8\ km/h \ \ }\)

Step-by-step explanation:

Hello, let's note v the rate of the boat and r the rate of the current. We can write the following

\(\dfrac{135}{v-r}=3=\dfrac{183}{v+r}\)

It means that

\(135(v+r)=183(v-r)\\\\135 v + 135r=183v-183r\\\\\text{ *** We regroup the terms in v on the right and the ones in r to the left***}\\\\(135+183)r=(183-135)v\\\\318r=48v\\\\\text{ *** We divide by 48 both sides ***}\\\\\boxed{v = \dfrac{318}{48} \cdot r= \dfrac{159}{24} \cdot r}\)

But we can as well use the second equation:

\(3(v+r)=183\\\\v+r=\dfrac{183}{3}=61\\\\\dfrac{159}{24}r+r=61\\\\\dfrac{159+24}{24}r=61\\\\\boxed{r = \dfrac{61*24}{183}=8}\)

and then

\(\boxed{v=\dfrac{159*8}{24}=53}\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Hi there

Your answer is:

13i

Step-by-step explanation:

Find the square root of √-169

We do i as coefficient to get rid of negatives

√169 is 13

Hope this helps

Correct.

9/5c+32

substitute c to 5

multiply 9/5 to 5

then add 32

Done

(A) There's a 90% chance the population value is between 7.2 and 8.9 oz.

You should know that In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used

The confidence interval is the probability that the population value would fall within a range of values for a number of times. The confidence interval are calculated by adding and subtracting the margin of error to/from the mean.

A 90% confidence interval of (7.2, 8.9) means that their is a 90% confidence or chance that the population value is between 7.2 and 8.9 oz

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ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

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

Simplifying the equation:

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

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

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

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

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

Simplifying this equation, we get:

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

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

x = 11

Step-by-step explanation:

The two angles measuring (7x + 14)° and (9x - 8)° are corresponding angles, which are always congruent to each other and thus equal to each other.  

Step 1:  Thus, we can find the value of x by setting the two angles equal to each other:

7x + 14 = 9x - 8

7x + 22 = 9x

22 = 2x

11 = x

Optional Step 2:  We can check that we've found the correct answer by plugging in 11 for x in both (7x + 14) and (9x - 8) and checking that we get the same number:

7(11) + 14 = 9(11) - 8

77 + 14 = 99 - 8

91 = 91

If "t" number of years the study started and "y" denote the forest cover area, then the exponential-function representing the relation between "y" and "t" is y = 1500 × \((0.9225)^{t}\).

An "Exponential-Function" is a mathematical expression in which a constant (called the base) is raised to a variable power.

In this case, we want to find an exponential function that relates the area of a forest (y) to the number of years since the start of an environmental study (t).

We know that the forest is decreasing by 7.75% each year, which means that the area of the forest after "t years" will be some percentage of its original area.

The formula for an exponential function is y = a × \(b^{t}\), where "a" = initial value and "b" = growth or decay factor.

In this case, the initial area of the forest is = 1500 km², and

The forest is decreasing by 7.75% each year.

So, the "decay-factor" is = 1 - 0.0775 = 0.9225,

The exponential function that relates the area of the forest (y) to the number of years since the start of the study (t) is:

⇒ y = 1500 × \((0.9225)^{t}\),

Therefore, the required "exponential-function" is y = 1500 × \((0.9225)^{t}\).

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Answer:

Tallahassee's Range: 6

Key West's Range: 4

Step-by-step explanation:

To calculate range, you'd subtract the lowest value from the highest value

Tallahassee:

Highest Value: 90

Lowest Value: 84

Range: 90 - 84 = 6

Key West:

Highest Value: 87

Lowest Value: 83

Range: 87 - 83 = 4

Answer:

W=3

Step-by-step explanation:

(6w + 4w)/48=5/8(taking lcm)

6w+4w=5/8*48

10w=30

W=3

Thanks for putting qsn, makes me remember this againa

Answer:

Step-by-step explanation:

Quadratic means squared equation so

the first one is your answer.

y= 4x²

Answer:

32

Step-by-step explanation:

53 - 11 is 21, so they each gave 21, but vace gave 11 more so you add 11 to get 32

Answer:A= 24.5

B=0

Step-by-step explanation:

Answer:

The missing value in the table of the projectile motion since it assumes a parabolic curve is A = 4, B = 3

Step-by-step explanation:

sorry its late but here it is

Choosing a blue marble does not represent the complement event of choosing a red marble because 2/5 ≠ 4/5.

There are 2 blue marbles, 1 red marble, and 2 purple marbles.

The total number of marbles ⇒ 2 blue + 1 red + 2 purple = 5 marbles.

To find the probability of choosing a blue marble :

P (blue) = No.of blue marbles / Total marbles

⇒ 2 / 5

To find the complement event of choosing a red marble?

Complement of an Event is defined as all the outcomes that are NOT the event.

So the Complement of an event is all the other outcomes (not the ones we want).

Complement of choosing red ⇒ P (not getting red marble)

P (not getting red marble) = No.of marbles other than red / Total marbles

⇒ 4 / 5

Therefore, P(blue) is not equal to P(not getting a red).

⇒ 2/5 ≠ 4/5

So, choosing a blue marble does not represent the complement event of choosing a red marble.

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Choosing a blue marble does not represent the complement event of choosing a red marble because 2/5 ≠ 4/5.

There are 2 blue marbles, 1 red marble, and 2 purple marbles.

The total number of marbles ⇒ 2 blue + 1 red + 2 purple = 5 marbles.

To find the probability of choosing a blue marble :

P (blue) = No.of blue marbles / Total marbles

⇒ 2 / 5

To find the complement event of choosing a red marble?

Complement of an Event is defined as all the outcomes that are NOT the event.

So the Complement of an event is all the other outcomes (not the ones we want).

Complement of choosing red ⇒ P (not getting red marble)

P (not getting red marble) = No.of marbles other than red / Total marbles

⇒ 4 / 5

Therefore, P(blue) is not equal to P(not getting a red).

⇒ 2/5 ≠ 4/5

So, choosing a blue marble does not represent the complement event of choosing a red marble.

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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4x + 32

All u need to do is simplify, 4 * x + 4 * 8 = 4x + 32

Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle

Answer: A

Step-by-step explanation:

Volume= LxWxH so we get 20x28x24 as given.

Volume= 13,440 which is the volume of the box given. ANd so if the box is 10,500cubic inches, we subtract to find the difference.

13,440-10,500= 2,940 Cubic Inches

Option A

Answer:

Part A:  13440 cubic inches.

Part B: A - 2940 cubic inches.

Step-by-step explanation:

The volume of the box = 24x20x28 = 13440 cubic inches.

The problem tells us that his gift is 10,500 cubic inches. So subtract that from the volume of the box.

13440-10500 = 2940 cubic inches. The answer is A.

The solution of the triangle have been shown below.

To solve a triangle means to find the values of all its angles and sides. The method for solving a triangle depends on the given information.

Given that;

a/Sin A = b/SinB

Sin B = bSin A/a

B = Sin-1(bSin A/a)

B = Sin-1 (23Sin 40/17)

B = 60.4 degrees

Then we have that

C = 180 - (40 + 60.4)

= 79.4 degrees

Then;

a/sinA = c/Sin C

c= aSin C/Sin A

c = 17 * Sin 79.4/Sin 40

c =   16.71/0.643

c = 25.9

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\(7x(x^2-5)\)

Step-by-step explanation:

\(7x^3-35x\)

Factor Greatest Common Factors out

\(7x(x^2-5)\)

I hope this helps you

:)

The parts of the graph when labelled are :

There is the origin which is where the line starts from. The x-axis represents the independent variable, which is the variable that is being manipulated or changed in the experiment.

The y-axis represents the dependent variable, which is the variable that is being measured or observed. A trend line is a line drawn on the graph that shows the overall pattern or trend of the data. The x and y - intercepts are the points where the trend line crosses the x and y - axis.

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The rate at which the volume of the cube is changing is 1200 in³/seconds.

Volume is the space occupied by a solid object.

To calculate the rate at which the volume of the cube is changing, we use the formula below.

Formula:

Where:

From the question,

Given:

If, the volume of a cube is V = L³,

Then,

Substitute these values into equation 1

Hence, the rate at which the volume is changing is 1200 in³/seconds.
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well, once you take in all the Revenue from sales, and subtract all the costs that went in for the product, what's leftover is the Profit.

so then, profit P(x), is simply the revenue minus costs, namely P(x) = R(x) - C(x)

\(R(x)=100x-2x^2\hspace{5em}C(x)=500+9x \\\\\\ P(x)=(100x-2x^2)~~ - ~~(500+9x)\implies P(x)=91x-2x^2-500 \\\\\\ \stackrel{\textit{at a production of 25 units, x =25}}{P(25) = 91(25)-2(25)^2-500}\implies P(25)=\stackrel{2275-1250-500}{525}\)

Answer: 3000 square feet

Step-by-step explanation: 21x10=210 .     300x10=3000

Answer:

3

Step-by-step explanation: