we are interested in whether there is a difference in the mean age at which men marry and the age at which women marry. we collect data from a random sample of 24 couples and record the age of the man and the age of the woman in the couple. note the data is matched by couple. are the samples dependent or independent? independent samples dependent samples

The type of error that explains the variability in the results between groups is "random error."Explanation:Random error is the variability between the groups' results due to the imprecision of the measuring instrument or technique.

It is caused by minor differences in the experimental conditions that are unpredictable and can not be controlled or accounted for in the experiment. Random error can lead to imprecise results that fluctuate from the main answer, which means that it is not biased towards one particular direction.The other type of error that is commonly known is "systematic error" which is characterized by consistent errors that occur in a specific direction due to the method or instrument used.

Systematic error is due to the inaccuracy of the measuring instrument or incorrect experimental design, and it can affect the accuracy of the main answer. Mistakes or human errors, on the other hand, are due to human error, such as incorrect calculations or transcriptions, and are not part of the sources of errors.

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The angle of depression to a given point on the lobby floor changes as the elevator rises. The depression's angle widens.

the bend that the line of sight makes as it descends from the horizon. The angle created between the horizon and the observer's line of sight when an item is observed below the observer's height is known as the angle of depression. The angle between the horizontal line of sight and the line of sight gazing down on the object is known as the depression angle. You can determine the slope, for instance, if you are on a hill or building and are gazing down at an item. A theodolite or an inclinometer can be used to measure these angles.

The angle of depression to a given point on the lobby floor changes as the elevator rises. The depression's angle widens.

∠x = 65° ≤ ∠XYZ

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Answer:

As the elevator rises, the angle of depression increases.

Step-by-step explanation:

The one-time administration fee is (d) $60

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

12 months costs $660.

15 months costs $810.

This means that

(x, y) = (12, 660) and (15, 810)

For the one-time administration fee, we have

(x, y) = (0, y)

So, we calculate the slope using

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(y - 660)/(0 - 12) = (810 - 660)/(15 - 12)

This gives

(660 - y)/12 = 50

So, we have

660 - y=600

This gives

y = 60

Hence, the administration fee is $60

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Answer:

17.a)  See below.

17.b)  x = 34.3 cm, y = 34.3 cm

18.a)  See below.

18.b)  r = 8 m

Step-by-step explanation:

Given information (see attachment 1):

According to the Similar Triangles Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.  Therefore, triangles ABC and ADE are similar (refer to attachment 1).

As corresponding sides of similar triangles are always in the same ratio, the ratio of the base to height of the smallest triangle is equal to the ratio of the base to height  of the largest triangle:

\(\implies \sf DE:AD=BC:AB\)

\(\implies y:80-x=60:80\)

\(\implies \dfrac{y}{80-x}=\dfrac{60}{80}\)

\(\implies 80y=60(80-x)\)

\(\implies y=\dfrac{60(80-x)}{80}\)

\(\implies y=\dfrac{3(80-x)}{4}\)

The maximum area of a rectangle is when the length and height are equal:

\(\implies x=y\)

Therefore, to find the value of x when the area of the rectangle is at its maximum, substitute x = y into the equation from part (a) and solve for x:

\(\implies x=\dfrac{3(80-x)}{4}\)

\(\implies 4x=3(80-x)\)

\(\implies 4x=240-3x\)

\(\implies 7x=240\)

\(\implies x=\dfrac{240}{7}\)

\(\implies x=34.3\; \sf cm\;\;(nearest\;tenth)\)

Therefore, the dimensions of the rectangle of maximum area to the nearest tenth are:

--------------------------------------------------------------------------------------------

Given information:

The formula for the volume of a cone is:

\(V=\dfrac{\pi r^2 h}{3}\)

If the sum of the base radius r and the height h is 12 metres then:

\(\implies r + h = 12\)

\(\implies h=12-r\)

Substitute the expression for h into the volume of a cone formula to create an equation for V in terms of r:

\(\implies V=\dfrac{\pi r^2 (12-r)}{3}\)

\(\implies V=\dfrac{12\pi r^2-\pi r^3}{3}\)

\(\implies V=\dfrac{12\pi r^2}{3}-\dfrac{\pi r^3}{3}\)

\(\implies V=4\pi r^2-\dfrac{1}{3}\pi r^3\)

To find the radius of the cone that yields the maximum volume, differentiate V with respect to x:

\(\implies \dfrac{\text{d}V}{\text{d}x}=2 \cdot 4\pi r^{2-1}-3 \cdot \dfrac{1}{3}\pi r^{3-1}\)

\(\implies \dfrac{\text{d}V}{\text{d}x}=8\pi r-\pi r^2\)

\(\implies \dfrac{\text{d}V}{\text{d}x}=\pi r(8-r)\)

Set the differentiated equation equal to zero and solve for x:

\(\implies \pi r(8-r)=0\)

\(\implies 8-r=0\)

\(\implies r=8\)

(Note: r is also equal to zero, but we can discard that solution since the radius has to be more than zero).

Therefore, the radius of the cone that yields the maximum volume is 8 m.

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

-5 - x = 25

add -5 to both sides

-x=-20

x=20

Answer:

Step-by-step explanation:

-5 - z = 25               Add 5 to both sides of the equation

-5+5 - x = 25 + 5

-x = 30                    Multiply both sides by -1

-x*-1 = 30*-1

x = - 30

The number of people died from aids in U.S. in 2005 are 2,30,68,96,671

Given, diseases tend to spread according to the exponential growth model.

In the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9.

In 1983, about 1700 people in the U.S. died of aids.

we have to find the number of people died from aids in 2005.

Let the exponential function, be

P(x) = AB^x

where, A is the initial population of people died of aids in U.S.

B is the growth factor of aids in U.S.

as, B = 1.9

In 1983, x = 0

P(0) = AB^0

1700 = A

Now, P(x) = 1700(1.9)^x

and the number of years from 1983 to 2005 are, 22 years

The number of people died from aids in 2005 be,

P(22) = 1700(1.9)^22

P(22) = 2,30,68,96,671

So, 2,30,68,96,671 people died from aids in 2005.

Hence, 2,30,68,96,671 people died from aids in 2005.

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Answer:

-32

Step-by-step explanation:

To find w(-7) we have to substitute x with -7

w(x)=4x-4

w(x = -7) = 4(-7) -4

w(-7) = -28-4

w(-7) = -32

Answer:

Step-by-step explanation:

Use the following formulas:

surface area of rectangular prism: A = 2wl + 2lh + 2hw

volume of rectangular prism: lwh

surface area of cylinder: A=2πrh+2πr^2

volume of cylinder: V=πr^2h

using these formulas, the surface area of the box is 424.3

the volume of the box is about 511.3

the surface area of the cylinder is about 275.77

the volume is 342.12

knowing this, the cylinder uses less material but the box holds more soup.

Change your group will get back from a $100 cost bill = $4

Me and my three friends are going to wonderland water park. Our group decided to ride each water ride two times.

The coaster cost = $4.50

The slide cost = $4.00

The drop cost = $3.50

Number of people = you + your friends = 1+3 =4

Cost of all three rides = The coaster cost + The slide cost + The drop cost

= $4.50 + $4.00 + $3.50 = $12.00

Four people takes all the rides = $12.00 x 4 = $48.00

If they take all rides twice = $48 x 2 = $96

Change will your group get back from a $100 bill = $100 - $96

Change your group will get back from a $100 bill = $4

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Answer:

z-7 is correct

V=30cmx40cmx200cm

V=240000cm

Step-by-step explanation:

Answer: Line C

Step-by-step explanation:

Because when you use the slope formula on it you get a negative slope. Also the line in going down unlike the other lines which are goign up.

Answer:

-8

Step-by-step explanation:

Answer: there are 30 people in choir

Step-by-step explanation:

The width of the frame will be 6 inches.

The area of the rectangle is defined as the space occupied by the rectangle in two dimensional space.

Given that a rectangular picture is 9 inches wide and 12 inches long. the picture has a frame of uniform width. if the combined area of picture and frame is 180 in².

The area of the picture is calculated as:-

Area = L x W

Area =  12 x 9

Area = 108 square inches

The remaining area of the frame is,

Area = 180 - 108

Area = 72 square inches.

The width of the ram is calculated as:-

Area = L x W
72 = 12 x W
W = 72 / 12

W = 6 inches

Therefore, the frame will have a width of 6 inches.

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The total area between the x-axis and the graph of \(y = x^{(1/5)} - x\), -1 ≤ x ≤ 3, is \((5/6)(3)^{(6/5)} - (9/2)\).

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

To find the total area of the region between the x-axis and the graph of y = x^(1/5) - x, we need to integrate the absolute value of the function over the given interval.

First, let's split the interval into two parts where the function changes sign: -1 ≤ x ≤ 0 and 0 ≤ x ≤ 3.

For -1 ≤ x ≤ 0:

In this interval, the graph lies below the x-axis. To find the area, we'll integrate the negated function: ∫\((-x^{(1/5)} + x) dx\).

∫\((-x^{(1/5)} + x) dx\) = -∫\(x^{(1/5)} dx\) + ∫x dx

                     = \(-((5/6)x^{(6/5)}) + (1/2)x^2 + C\)

                     = \((1/2)x^2 - (5/6)x^{(6/5)} + C_1\),

where \(C_1\) is the constant of integration.

For 0 ≤ x ≤ 3:

In this interval, the graph lies above the x-axis. To find the area, we'll integrate the function as is: ∫\((x^{(1/5)} - x) dx\).

∫\((x^{(1/5)} - x) dx = (5/6)x^{(6/5)} - (1/2)x^2 + C_2,\)

where \(C_2\) is the constant of integration.

Now, to find the total area between the x-axis and the graph, we need to find the definite integral of the absolute value of the function over the interval -1 ≤ x ≤ 3:

Area = ∫\([0,3] |x^{(1/5)} - x| dx\) = ∫[0,3] \((x^{(1/5)} - x) dx\) - ∫[-1,0] \((-x^{(1/5)} + x) dx\)

                                 = \([(5/6)x^{(6/5)} - (1/2)x^2]\) from 0 to 3 - \([(1/2)x^2 - (5/6)x^{(6/5)}]\) from -1 to 0

                                 = \([(5/6)(3)^{(6/5)} - (1/2)(3)^2] - [(1/2)(0)^2 - (5/6)(0)^{(6/5)}]\)

                                 = \([(5/6)(3)^{(6/5)} - (1/2)(9)] - [0 - 0]\)

                                 = \((5/6)(3)^{(6/5)} - (9/2\)).

Therefore, the total area between the x-axis and the graph of \(y = x^{(1/5)} - x\), -1 ≤ x ≤ 3, is \((5/6)(3)^{(6/5)} - (9/2)\).

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The complete question is:

Find the total area of the region between the x-axis and the graph of y=x ^1/5 - x, -1 ≤ x ≤ 3.

The solution to the given inequality is:

b≥4 or b≤-5.

We can also write this as the interval notation:

(-∞, -5] ∪ [4, ∞)

A connection between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics. The inequality can be resolved by adding the same amount to each side, subtracting the same amount from each side, multiplying or dividing each side by the same positive integer, and more. If you multiply or divide either side by a negative value, you must flip the inequality sign.

We need to solve the inequality -10b+3≤-37 or 3b - 10 ≤-25.

First, let's solve the first inequality, -10b+3≤-37:

-10b+3≤-37

Subtracting 3 from both sides, we get:

-10b≤-40

Dividing both sides by -10,

b≥4

So the first solution is b≥4.

Now, let's solve the second inequality, 3b - 10 ≤-25.

3b - 10 ≤-25

Adding 10 to both sides, we get:

3b≤-15

Dividing both sides by 3, we get:

b≤-5

So the second solution is b≤-5.

Therefore, the solution to the given inequality is:

b≥4 or b≤-5.

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The complete question:

What is the solution of the composite inequality -10b+3≤-37 or 3b - 10 ≤-25?

Also, write in the interval notation.

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Answer:

\(y=18x+ 12\)

Step-by-step explanation:

Given equation:

\(2+\dfrac{1}{6}y=3x+4\)

Subtract 2 from both sides:

\(\implies 2+\dfrac{1}{6}y-2=3x+4-2\)

\(\implies \dfrac{1}{6}y=3x+2\)

Multiply both sides by 6:

\(\implies 6 \cdot \dfrac{1}{6}y= 6 \cdot3x+ 6 \cdot2\)

\(\implies y=18x+ 12\)

Answer: 4.4

Step-by-step explanation:

it would be 4.4 because 10 x 6.9 = 69

have a great day! (brainliest?)

Answer:

9.7

Step-by-step explanation:

tan 44° = x / 10

x = 10 tan 44°

9.7

Answer:

see explanation

Step-by-step explanation:

(3x - 1)(x + 5)

Each term in the second factor is multiplied by each term in the first factor , that is

3x(x + 5) - 1 (x + 5) ← distribute parenthesis

= 3x² + 15x - x - 5 ← collect like terms

= 3x² + 14x - 5

Answer:

its true. see below

Step-by-step explanation:

\((3x - 1)(x + 5)\)

\(3 {x}^{2} + 15x - x - 5\)

\(3 {x}^{2} + 14x - 5\)

Yes

13 and 13√2 is the value of x and y in the given diagram

The given diagram is a right triangle, we need to determine the value of x and y.

Using the trigonometry identity

tan45 = opposite/adjacent
tan45 = x/13

x = 13tan45
x = 13(1)
x = 13

For the value of y

sin45 = x/y

sin45 = 13/y
y = 13/sin45

y = 13√2
Hence the exact value of x and y from the figure is 13 and 13√2 respectively.

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The equation is given in the question.

To determine the y in terms of x ,

Replace y with f(x),

The value of f(5) is

The value of f(5) is 3/2.

Answer:

42+25n

Step-by-step explanation:

\(7+5(7+5n)\\=7+35+25n\\=42+25n\)

Answer:

I am pretty sure its b -1 1/2 and -1