According to the United States Census Bureau, the average single-family home constructed in 2016 was 2,463 square feet. Carmen wondered if families in her area still want a smaller home in comparison to the average. She randomly selected 49 people and asked what the ideal square footage of a home is for them. From the responses, she calculated the sample mean equals 1,640 square feet with a sample standard deviation of 66 square feet. Calculate the value of the test statistic.

Answer:

Imma say A i'm sorry if it is incorrect

Step-by-step explanation:

I love your pfp btw

To find the combined rate of all the individuals working together, you must add the individual rates.

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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1. Relation 1 is a function

2. Relation 2 is a function

3. Relation 3 is not a function

4. Relation 4 is a function

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

The relations (1) to (4)

Relation (1)

This relation is a function

This is because each range value point to unique domain values

Relation (2)

This relation is a function

This is because each range value point to unique domain values

Relation (3)

This relation is not a function

This is because domain values w have different range values.

Relation (4)

This relation is a function

This is because each range value point to unique domain values

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Answer:

I believe you cancel out values if there are the same ones for the numerator and dominator.

For example:

\(\frac{x^4+x^2+x-3}{x^4+x^3-3}\)

Since both the numerator and dominator have \(x^4\) and -3, you are able to cancel them out.

This would leave you with \(\frac{x^2+x}{x^3}\)

Notes: the exponents have to be the same number in order to cancel out the values.

Answer:

  11.  C) x +1

  12.  B) x -1

Step-by-step explanation:

You want the simplified form of a couple given rational expressions.

Each of the polynomials can be factored by pairs. Common factors can be cancelled.

Factoring numerator and denominator pairwise, we have ...

  \(\dfrac{x^3+2x^2-x-2}{x^2+2x-x-2}=\dfrac{x^2(x+2)-1(x+2)}{x(x+2)-1(x+2)}=\dfrac{(x^2-1)(x+2)}{(x-1)(x+2)}\\\\=\dfrac{x^2-1}{x-1}=\dfrac{(x+1)(x-1)}{(x-1)}=\boxed{x+1}\)

Factoring the numerator pairwise,, we have ...

  \(\dfrac{x^5-x^4+x^3-x^2+x-1}{x^4+x^2+1}=\dfrac{x^4(x-1)+x^2(x-1)+1(x-1)}{x^4+x^2+1}\\\\=\dfrac{(x^4+x^2+1)(x-1)}{(x^4+x^2+1)}=\boxed{x-1}\)

If b > 1 then it's an exponential growth

If b < 1 then it's an exponential decay

Y = 3(1/2)^(x+3) decay

Y = 4^(x-3) + 6 growth

Y = -2^x - 5 decay

Y = (2/3)^(x-2) +1 decay

The y-intercept is found replacing x = 0 into the equation.

Y = 3(1/2)^(0+3)

Y = 3(1/2)^3

Y = 3(1/8)

Y = 3/8

Y = 4^(0-3) + 6

Y = 4^(-3) + 6

Y = 1/64 + 6

Y = 385/64

Y = -2^0 - 5

Y = -1 - 5

Y = -6

Y = (2/3)^(0-2) +1

Y = (2/3)^(-2) +1

Y = (3/2)^(2) +1

Y = 9/4 +1

Y = 13/4

The vertical movement is found identifying k in the equations.

Y = 3(1/2)^(x+3) k = 0 no vertical move

Y = 4^(x-3) + 6 k = 6 vertical move 6 units up

Y = -2^x - 5 k = -5 vertical move 5 units down

Y = (2/3)^(x-2) +1 k = 1 vertical move 1 unit up

If the equation is flipped or not is seen in the a parameter. If a < 0, it's flipped, if a > 0, it isn't flipped

Y = 3(1/2)^(x+3) a > 0 not flipped

Y = 4^(x-3) + 6 a > 0 not flipped

Y = -2^x - 5 a < 0 flipped

Y = (2/3)^(x-2) +1 a > 0 not flipped

The range is found with help of the vertical move and the flip

Y = 3(1/2)^(x+3) no vertical move, not flipped range: [0, ∞]

Y = 4^(x-3) + 6 vertical move 6 units up, not flipped range: [6, ∞]

Y = -2^x - 5 vertical move 5 units down range: [-5, -∞]

Y = (2/3)^(x-2) +1 vertical move 1 unit up, not flipped range: [1, ∞]

The horizontal movement is found identifying h in the equations.

Y = 3(1/2)^(x+3) h = 3 horizontal move 3 units left

Y = 4^(x-3) + 6 h = -3 horizontal move 3 units right

Y = -2^x - 5 h = 0 no vertical move

Y = (2/3)^(x-2) +1 h = -2 horizontal move 2 units right

If the equation is stretched or shrunk is seen in the a parameter. If a > 1, the function stretches, if 0 < a < 1, 1, the function shrinks

Y = 3(1/2)^(x+3) a = 3 stretches

Y = 4^(x-3) + 6 a = 1 doesn't stretch nor shrink

Y = -2^x - 5 a = -1 doesn't stretch nor shrink

Y = (2/3)^(x-2) +1 a = 2/3 shrinks

Answer:

The percentage of 18 people out of 50 is 36 %

Step-by-step explanation:

The percentage refers to the per hundred or hundredths and is ended with the symbol %.  By dividing two amounts, ratios and percentages are both used to compare the two amounts.

so,

Therefore the percentage of 18 people out of 50 people is 36 %.

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Answer:

Step-by-step explanation:

\((3a^{2} + 6b - 4) + (5a^{2} + 8b + 5)\)

\(3a^{2} + 6b - 4 + 5a^{2} + 8b + 5\)

Let's group the terms based on their polynomial:

\(a^{2}(3 + 5) + b(6 + 8) + (-4 + 5)\)

\(8a^{2} + 14b + 1\)

Answer:

1

Step-by-step explanation:

it will add to 180 degrees

∠1  is supplementary to ∠4 in the given line 'r' parallel to 's'.

"A pair of angles are said to be supplementary if the sum of both the angles is equal to 180°."

According to the diagram,

Line 'r' is parallel to line 's' and 't is the transversal

∠1 ≅∠5 ( corresponding angles)

∠5 + ∠4 = 180° ( interior angles on the same side of transversal)

⇒∠1  + ∠4 =180°

Therefore,

∠1 and ∠4 are supplementary angles.

Hence, we conclude that Option (A) is correct answer.

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Answer:

1. 40-p+w

2. $4 left

I'm not sure about the first one, but I'm pretty sure about the second one.

Step-by-step explanation:

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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Answer:

7

Step-by-step explanation:

Answer:

13(rounded) cents per 1/4 yard and 50 cents per yard

Step-by-step explanation:

Step 1:  Convert the mixed fraction into an improper fraction

\(2\frac{3}{4} = \frac{4}{4}+\frac{4}{4}+\frac{3}{4}\)

\(2\frac{3}{4}=\frac{11}{4}\)

Step 2:  Find the unit price per 1/4 yard

\(\frac{11}{4}/22\)

\(0.125 = 13 \ cents\)

Step 3:  Find the unit price per 1 yard

\(12.5\ cents\ per\ 1/4\ yard=50\ cents\ per\ 1\ yard\)

Answer:  13(rounded) cents per 1/4 yard and 50 cents per yard

Answer:  a

Step-by-step explanation: hope it helps.

Answer:

3zx-15z+12x-60

Step-by-step explanation:

first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20

then distribute the 3 to get the answer

Given the general rule for the division of fractions:

in this case, we can use the formula in the following way:

therefore, the answer is 55/48

The amounts invested at each rate of 5%, 9%, and 14% are $2300, $800, and $3900, respectively.

We have,

Annual income refers to the amount of money earned by an individual or a business in a year, typically before taxes and other deductions are taken out.

According to question:

Let x be the amount invested at 5%, y be the amount invested at 9%, and z be the amount invested at 14%.

From the problem, we know that:

x + y + z = 7000 (total amount invested)

0.05x + 0.09y + 0.14z = 733 (total annual income)

z = x + y + 800 (amount invested at 14% is $800 more than at 5% and 9% combined)

Substituting the third equation into the first, we get:

x + y + (x + y + 800) = 7000

2x + 2y + 800 = 7000

2x + 2y = 6200

x + y = 3100

Substituting the third equation into the second, we get:

0.05x + 0.09y + 0.14(x + y + 800) = 733

0.05x + 0.09y + 0.14x + 0.14y + 112= 733

0.19x + 0.23y = 621

19x + 23y = 62100

Multiplying the equation x + y = 3100 by 19, we get:

19x + 19y = 58900

Subtracting this from the equation 19x + 23y = 62100, we get:

y = 800

Substituting y = 800 into x + y = 3100, we get:

x = 2300

Substituting x = 2300 and y = 800 into z = x + y + 800, we get:

z = 3900

Therefore, the amounts invested at 5%, 9%, and 14% are $2300, $800, and $3900, respectively.

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The radius of the pencil is 3.32mm

The formula for determining the volume of a cylinder is expressed as;

V = πr²h

Given that the parameters are;

From the information given, we have that;

The volume of the cylinder = 110 π mm³

The height of the cylinder = 10mm

Now, substitute the values, we get

110π = πr² × 10

Multiply the values

110π = 10πr²

Divide both sides by the coefficient of r², we get;

r² = 110π/10

r² = 11

Find the square root of both sides

r = 3. 32mm

Hence, the value is 3.32mm

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It would take 370 days to build the wall with the given conditions.

If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:

60 men x 40 days = 2400 man-days

However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.

The number of man-days required for the first 10 days is:

60 men x 10 days = 600 man-days

The number of man-days required for the second 10 days is:

5 men x 10 days = 50 man-days

The total number of man-days required for the first 20 days is:

600 man-days + 50 man-days = 650 man-days

The remaining work can be completed by the 5 men in:

2400 man-days - 650 man-days = 1750 man-days

Therefore, the total time needed to build the wall is:

20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days

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Answer:

3/4

Step-by-step explanation:

0.75

multiply the numerator and denominator by 100.

0.75 x 100 / 1 x 100 = 75/100

75/100

Simplify 75/100

=> 3/4

hope this helps!! p.s. i really need brainliest :)

Answer:

9118

Step-by-step explanation:

9.118 x 10 = 9.11800

To the 3rd means to the 3rd decimal place which then equals 9118

Answer:

50% of 108: 54

25% of 108: 27

75% of 108:  81

Step-by-step explanation:

Hope this helps have a nice day

Answer:

50% : 54

25% : 27

75% : 81

Step-by-step explanation:

If you multiply by the decimal version of the precentages, you will get the remaining amount of how much it is. so to find 50% of 108, you do 108 * 0.50 and it will give you the 50% of 108.

Answer:

-1/2

Step-by-step explanation:

We know

The dilation of K(-2,4) equals K'(1,-2)

To get from -2 to 1, we time -1/2

To get from 4 to -2, we time -1/2

So, the scale factor used for the dilation is -1/2

Answer:

m= 0

y^m = x ^8m over z ^5m

x^ 8m = y^m z5^m

z^ 5m = x^8m over y^m

Step-by-step explanation:

x = 85

sum of all the angles must be 540,

105 + 120 + 3x + 35 + 25 = 540

3x = 255

x is 85

The amount of water tank  with water after 10 minutes will be 4950 liters.

To solve this problem, we need to keep track of the net flow of water into the tank over the course of 10 minutes. The tap filling water adds water to the tank, while the tap emptying water removes water from the tank.

Let's calculate the net flow rate of water per minute:

Flow rate = (filling tap flow rate) - (emptying tap flow rate)

Flow rate = 40 L/min - 25 L/min

Flow rate = 15 L/min

Now, we can calculate the net flow of water over 10 minutes:

Net flow of water = (flow rate) * (time)

Net flow of water = 15 L/min * 10 min

Net flow of water = 150 L

Therefore, over the course of 10 minutes, the net flow of water into the tank is 150 liters.

Initially, the tank had 4800 liters of water. Adding the net flow of water, we can determine the final amount of water in the tank:

Final amount of water = (initial amount of water) + (net flow of water)

Final amount of water = 4800 L + 150 L

Final amount of water = 4950 L

After 10 minutes, there will be 4950 liters of water in the tank.

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Answer:

right π/2

Step-by-step explanation:

The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .

Therefore, the correct answer is right π/2

Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!

Answer:

73

Step-by-step explanation:

180-107=73

angle 1 is congruent to angle 3 which is 107 degrees

first invert fraction of the slope from 4/1 to 1/4 and switch sign. then figure out the y-intercept

the algebraic approach would work like this:

-4x + 10 = 1/4x + b

plug in what you got, here: the intersection information

-4*(4) + 10 = 1/4*(4) + b

-16 + 10 = 1 + b

-6 = 1 + b

-7 = b

Answer: 4

Step-by-step explanation:

1 third of 30 is 10 and 2/5s of 10 is 4