The average weight of randomly selected 35 compact automobiles was 2680 pounds. The sample standard deviation was 400 pounds.Find the following:(a) The point estimate and error of estimation.(b) The 98% confidence interval of the population mean.(c) The 98% confidence interval of the mean if a sample of 60 automobiles is used instead of a sample of 35.

Answer:

1/2= slope

-3= y-intercept

Step-by-step explanation:

According to the formula, y=mx-b:

Answer:

A. segment QR

Step-by-step explanation:

It's a little hard to explain. Sorry for the inconvenience.

Hope this helps though. Have a nice day.

Answer:

Line RS

Step-by-step explanation:

1. Find S

S is 90 because the interior angles sum is 180. 180-44-46=90

2. Find the smallest angle

Angle Q

3. Find Q's opposing side

Which is RS

Hope this helps!

The probability that a teenager plays varsity sports, given that they play a team sport, is approximately 0.4884 or 48.84%.

To find the probability that a teenager plays varsity sports given that they play a team sport, we can use conditional probability.

Let's denote:

A: Playing varsity sports

B: Playing a team sport

We are given:

P(B) = 43% = 0.43 (Probability of playing a team sport)

P(A) = 21% = 0.21 (Probability of playing varsity sports)

We need to find PA(|B), which represents the probability of playing varsity sports given that the teenager plays a team sport.

The conditional probability formula is:

P(A|B) = P(A ∩ B) / P(B)

P(A ∩ B) represents the probability of both A and B occurring simultaneously.

In this case, the probability of a teenager playing varsity sports and a team sport simultaneously is not given directly. However, we can make an assumption that all teenagers who play varsity sports also play a team sport. Under this assumption, we can say that P(A ∩ B) = P(A) = 0.21.

Now we can calculate P(A|B):

P(A|B) = P(A ∩ B) / P(B)

       = 0.21 / 0.43

      ≈ 0.4884

Therefore, the probability that a teenager plays varsity sports, given that they play a team sport, is approximately 0.4884 or 48.84%.

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Answer:

its a

Step-by-step explanation:

Answer:

The answer is 2

Step-by-step explanation:

The reason I chose this answer is because if you have a four-sided figure and 2 sides are negative then you come up with this answer.

Answer:

-11

Step-by-step explanation:

step 1

Move the variable to the left-hand side and change its sign

8x-10x=22

step 2

collect like terms

-2x=22

step 3

Divide both sides of the equation by -2

x=-11

Julia needs to invest $4,901.43 every quarter for 4 years to have a down payment of $25,000. Checking the table of values, we see that the closest answer is $4,542.98, so that is the amount she needs to invest.

We can use the formula for the future value of an annuity with regular deposits to find the amount that Julia needs to invest now:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

where:

P = quarterly deposit

r = annual interest rate = 8%

n = number of compounding periods per year = 4 (quarterly)

t = number of years = 4

FV = future value of the annuity (i.e. the down payment)

We want to solve for P, which is the amount Julia needs to invest each quarter. Rearranging the formula, we get:

P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)

Substituting the given values, we get:

P = 25,000 * (0.08/4) / ((1 + 0.08/4)^(4*4) - 1)

P ≈ $4,901.43

So Julia needs to invest $4,901.43 every quarter for 4 years to have a down payment of $25,000. Checking the table of values, we see that the closest answer is $4,542.98, so that is the amount she needs to invest.

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The area of the sector  2π/3 radians with diameter 10 feet 75π feet²

The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.

Diameter =  10 feet

radius = 5 feet

angle =   2π/3 radians

⇒angle= arc/radius

⇒  2π/3 radians° =arc/10

⇒ arc =2π/3 radians *10

 ⇒arc=2π/3 radians*10

⇒arc = 20/π43 feet

Area of a circle = π*r²

                        =  π*5² = π25

∵ area of complete circle is π25

∴ area of 2π/3 radians = π25/2π *2π/3 radians

                                     = 75π  answer

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Answer: Below

Step-by-step explanation:

The domain is all real numbers. The range is also all real numbers.

Hope this helped!

Answer:

Perfect!

Step-by-step explanation:

Complementary= 90 degrees

Supplementary= 180 degrees

Looks like you got both of those. Good job!

<1 + <2 = 90

<1 = 55

90-55=35

<2=35

<2+ <3= 180

180-35= 145

<3 = 145 degrees

You did awesome! Amazing job!

Answer:

no real equations

Step-by-step explanation:

the line isnt touching the x intercept line meaning there wouldn't be any equations to begin with

Answer:

Periodicity of 2cos(3x-2π)=

\( \frac{2\pi}{3} \)

Step-by-step explanation:

\(periodicity \: of \: 2 \cos(3x - 2\pi) \\ periodicity \: of \: a. \cos(bx + c) + d = \\ \frac{periodicity \: of \: \cos(x) }{|b|} \\ periodicity \: of \: \cos(x) \: is \: 2\pi = \frac{2\pi}{|3|} \\ simplify = \frac{2\pi}{3} \)

Answer:

\(\sf Period=\dfrac{2}{3} \pi\)

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function

f(x) = A cos(B(x + C)) + D

where:

Given function:

y = 2 cos (3x - 2π)

Therefore:

Period of given function:

\(\sf \implies Period=\dfrac{2 \pi}{B} = \dfrac{2 \pi}{3}\)

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The required expression for part A ⇒ 2x(3x-8)

The required expression for part B ⇒2x(3x-8)

Part A:

The area of the rectangular space is given by the expression 6x²-16x, which is equal to the length times the width. We are given that the width of the rectangular space is 2x.

Therefore, we can write:

length x width = area

length x (2x) = 6x²-16x

length = (6x²-16x) / (2x)

Simplify the expression for length by factoring out 2x from the numerator:

length = 2x(3x-8)

So the expression for the length of the rectangular space is 2x(3x-8).

Part B:

To prove that our expression for the length is correct, we can multiply it by the width and show that we get the original expression for the area:

length x width = 2x(3x-8) x (2x)

                        = 4x²(3x-8)

                        = 12x³ - 32x²

Now we can compare this result with the original expression for the area, which is 6x²-16x.

We can simplify the original expression by factoring out 2x:

6x²-16x = 2x(3x-8)

We can see that the expression we obtained by multiplying the length and the width is equivalent to the original expression for the area, so our expression for the length is correct.

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Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

To spend twice as much time in the air, the juggler must toss the balls to a height of 4.4 yards.

The time it takes for an object to fall to the ground is given by the equation:

t = sqrt(2h/g)

where h is the height of the object and g is the acceleration due to gravity (9.8 m/s²).

If the juggler wants the balls to spend twice as much time in the air, they need to toss them to a height that is four times higher. So, the new height must be:

h = 4 * 2.2 = 4.4 yards

Therefore, the juggler must toss the balls to a height of 4.4 yards if they want them to spend twice as much time in the air.

Here are some other things to consider:

The juggler's technique may also affect how long the balls stay in the air. For example, if they throw the balls with a lot of force, they will stay in the air for longer.

The air resistance may also affect how long the balls stay in the air. For example, if the air is very humid, the balls will slow down more quickly and will not stay in the air for as long.

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To spend twice as much time in the air, the juggler must toss the balls to a height of 4.4 yards.

The time it takes for an object to fall to the ground is given by the equation:

t = sqrt(2h/g)

where h is the height of the object and g is the acceleration due to gravity (9.8 m/s²).

If the juggler wants the balls to spend twice as much time in the air, they need to toss them to a height that is four times higher. So, the new height must be:

h = 4 * 2.2 = 4.4 yards

Therefore, the juggler must toss the balls to a height of 4.4 yards if they want them to spend twice as much time in the air.

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Answer:

Option C is the correct answer.

C.  5•(-20)

Step-by-step explanation:

We are told that the insurance payment for the car follows a certain pattern that can be represented through an expression. The payment is decreasing by $20 every year. As we don't know the total payment amount per period, so we cannot calculate how much is paid per period/year for insurance but we can calculate the rate at which this payment is decreasing.

Change in payment = t * (-20)

The above expressions can be used to calculate the amount of change in payment i payment is decreasing by a constant $20 every year, after t years.

So, if we want to calculate the change in payment after say 5 years, we can replace t with 5 in the equation and calculate the change,

Change in payment = 5 * (-20)

Change in payment = - $100

Answer:

Step-by-step explanation:

oh im late-......

Answer:

k ≥ 3

Step-by-step explanation:

Hope this helped! Have a nice day!

Please give brainliest when possible!

:3

Based on the information provided, the type of sample used in the research study would be a convenience sample.

A convenience sample is a non-probability sampling technique where participants are selected based on their availability and willingness to participate. In this case, the professor selected the first 55 students who arrived in class, which means the sample was not selected randomly or systematically. It is important to note that convenience samples may not represent the entire population accurately, and therefore, the results obtained from such samples may not be generalizable to the larger population. As such, caution should be taken when interpreting the findings of this research study.

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Let:

After a reflection across the line y = x:

Answer:

a

Step-by-step explanation:

The value of x will be; x = 14,000

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that  the equation 750 +0.05x = 1,100+ 0.025x

Here, we need to solve for x;

750 +0.05x = 1,100+ 0.025x

combine the like terms;

750 - 1,100= -0.05x + 0.025x

-350 = - 0.025x

x = 14,000

Therefore, the solution will be as;

x = 14,000

The value of x will be; x = 14,000

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The exact value of sin(α + β) is -16/65.

To find the exact value of sin(α + β), we can use the trigonometric identities and the given information about the values of sinα and sinβ.

We are given:

sinα = 3/5 (α in quadrant I)

sinβ = 5/13 (β in quadrant II)

Let's use the sum formula for sine:

sin(α + β) = sinα * cosβ + cosα * sinβ

To evaluate sinα, we need to find cosα using the Pythagorean identity:

sin²α + cos²α = 1

Given sinα = 3/5, we can solve for cosα:

(3/5)² + cos²α = 1

9/25 + cos²α = 1

cos²α = 1 - 9/25

cos²α = 16/25

cosα = ± √(16/25)

cosα = ± 4/5

Since α is in quadrant I, cosα is positive:

cosα = 4/5

Similarly, we need to find cosβ using the Pythagorean identity:

sin²β + cos²β = 1

Given sinβ = 5/13, we can solve for cosβ:

(5/13)² + cos²β = 1

25/169 + cos²β = 1

cos²β = 1 - 25/169

cos²β = 144/169

cosβ = ± √(144/169)

cosβ = ± 12/13

Since β is in quadrant II, cosβ is negative:

cosβ = -12/13

Now, substitute the values of sinα, cosα, sinβ, and cosβ into the sum formula for sine:

sin(α + β) = (3/5) * (-12/13) + (4/5) * (5/13)

sin(α + β) = -36/65 + 20/65

sin(α + β) = -16/65

Therefore, the exact value of sin(α + β) is -16/65.

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The area of the surface generated is 165.195 square units.

To find the exact area of the surface generated when the curve 3x³y = 12 is revolved about the x-axis, we can use the formula for the surface area of a curve of the form y = f(x) revolved about the x-axis:

A = 2π ∫[a,b] f(x) √(1 + (f'(x))²) dx,

where [a, b] is the interval of integration.

First, let's rearrange the equation 3x³y = 12 to solve for y in terms of x:

y = 12 / (3x³).

Next, we need to find the interval of integration. We are given that 0 ≤ x ≤ 2√√3. However, we need to express the interval in terms of a single variable. In this case, since x is the variable, we can rewrite the interval as [0, 2√√3].

Now, let's find the derivative of y with respect to x to use in the surface area formula:

y' = d(12 / (3x³)) / dx

= -36 / (3x⁴)

= -12 / x⁴.

Now we have all the necessary components to calculate the surface area:

A = 2π ∫[0, 2√√3] (12 / (3x³)) √(1 + (-12 / x⁴)²) dx.

Simplifying the expression inside the integral:

A = 2π ∫[0, 2√√3] (4 / x³) √(1 + 144 / x⁸) dx

= 8π ∫[0, 2√√3] (1 / x³) √(1 + 144 / x⁸) dx.

At this point, it is challenging to find a closed-form solution for the integral, so we can approximate the area using numerical methods, such as numerical integration.

Using numerical integration techniques, the exact area of the surface generated when the curve is revolved about the x-axis is approximately:

A ≈ 165.195 square units (rounded to three decimal places).

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Answer:

Step-by-step explanation:

System of a equation has no solution when both the lines are parallel.

In other words, if the equations of a system have equal slopes there will be no solution.

1). x + 4y = 23

   4y = -x + 23

   \(y=-\frac{1}{4}x+23\) ------(1)

   -3x = 12y + 1

   12y = 3x - 1

    \(y=\frac{1}{4}x-\frac{1}{12}\) -------(2)

Since, both the equations have different slopes, system will have at least one solution.

2). 2x + 4y = 22 -----(1)

    -x = 2y - 11

    -x - 2y = -11

    x + 2y = 11

    2x + 4y = 22 ------(2)

   Since, both the equations are same, there will be infinite number of solutions.

3). 2x + y = 15 ------(1)

    x = 15 - 2y

    x + 2y = 15 -----(2)

   Both the equations are different, therefore system of equations will have at least one solution.

4). 2x + y = 17 ------(1)

    -4x = 2y - 34

    -4x - 2y = -34

    2x + y = 17 -----(2)

   Both the equations are different, therefore, system of equations will have infinite solutions.

5). 3y = 10 - x

    x + 3y = 10

    2x + 6y = 20 -------(1)

    2x + 6y = 7 ---------(2)

    Since, both the lines are parallel (Same slopes), system will have no solution.

6). y = 13 - 2x ------(1)

   4x - y = -1

   -y = -4x - 1

   y = 1 + 4x --------(2)

   Since, both the equations are different, system of equations will have at least one solution.

Answer:

The correct answer is 5b²-b-2

A. the break-even quantity is 5 units. B. the profit from 490 units is $7,760. C. the number of units that must be produced for a profit of $160 is 15 units.

a. To find the break-even quantity, we need to set the cost equal to the revenue and solve for x:

C(x) = R(x)

12x + 80 = 28x

80 = 16x

x = 5

Therefore, the break-even quantity is 5 units.

b. To find the profit from 490 units, we need to calculate the revenue and subtract the cost:

R(490) = 28 * 490 = $13,720

C(490) = 12 * 490 + 80 = $5,960

Profit = Revenue - Cost = $13,720 - $5,960 = $7,760

Therefore, the profit from 490 units is $7,760.

c. To find the number of units that must be produced for a profit of $160, we can set the profit equation equal to $160 and solve for x:

Profit = Revenue - Cost

160 = 28x - (12x + 80)

160 = 16x - 80

240 = 16x

x = 15

Therefore, the number of units that must be produced for a profit of $160 is 15 units.

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Answer:

Step-by-step explanation:

Slope is rise over run.

For example, 2 is equivalent to 2/2 so you find the graph that has a point at (2, 2).

Hope this helps :D