According to 2015 census data, 40 percent of Colorado residents were born in
Colorado. If a sample of 250 Colorado residents is selected at random, what is
the standard deviation of the number of residents in the sample who were born in
Colorado?
60
12.23
0.24
7.75
10

(a) The size of angle x will be 90°.

(b) The theorem that helped to solve this problem is, the angle between the tangent and the radius at a point on a circle is 90°.

What is a circle's radius?

The radius of a circular is the separation between any two points on its circumference. R or r is typically used to indicate it. This amount is significant in practically all formulae involving circles. A circle's radius may also be used to calculate its surface area and circumference. Circle circumference equals two.

What are diameter and radius?

The circle's center is where a straight line called the diameter lies. Half of the size makes up the radius. It originates with a point circle and finishes at the circle's center.

Due to the fact that the angle between the tangent and the radius at a point on a circle is 90°.

As a result, angle x = 90°.

(b)The circle theorem that allows the calculation of angle is:

The angle between the tangent and the radius at a point on a circle is 90°.

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The length of the rectangular lot is 30m

The formula for calculating the perimeter of a rectangle is expressed as;

P =2(l + w)

Such that the parameters are;

From the information given, we have that;

Length = 5 + w

Now, substitute the values

110 = 2( 5 + w+ w)

collect the like terms

110 = 2(5 + 2w)

expand the bracket

110 = 10 + 4w

4w = 100

Divide both sides by the coefficient of w

w = 25

Then, the length = 30m

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The fοci οf the given ellipse are apprοximately (-0.65, 3) and (-3.35, 3).

An ellipse is a clοsed curve in a plane that is symmetric abοut twο intersecting perpendicular axes, called the majοr axis and the minοr axis.

The given equatiοn represents an ellipse centered at the pοint (-2, 3) with semi-majοr axis οf length 4 and semi-minοr axis οf length 3. Tο find the fοci, we can use the fοrmula [tex]\rm c = \sqrt{(a^2 - b^2)[/tex], where a is the length οf the semi-majοr axis and b is the length οf the semi-minοr axis.

In this case, a = 4 and b = 3, so:

[tex]\rm c = \sqrt{(4^2 - 3^2) }= \sqrt7[/tex]

The foci are located on the major axis of the ellipse, which is parallel to the x-axis and passes through the center (-2, 3).

Therefore, the coordinates of the foci are [tex](-2 + \sqrt7, 3)[/tex] and [tex](-2 - \sqrt7, 3)[/tex].

Hence, the foci of the given ellipse are approximately (-0.65, 3) and (-3.35, 3).

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Answer:

Step-by-step explanation:

The two true statements are:

By evaluating the linear function in different values of x, we will get the complete table:

x         f(x)

-3         -6

-2         -16/3

0            -4

3             -2

6              0

Here we have a table of x and f(x) and we want to complete it, to do so, we only need to evaluate the function in different  values of x and then put that in the correspondent places.

if x = -2

f(-2) = (2/3)*-2 - 4

      = -4/3 - 4 = -4/3 - 12/3 = -16/3

if x = 0

f(0) = (2/3)*0 - 4 = -4

if x = 3

f(3) = (2/3)*3 - 4 = 2 - 4 = -2

if x = 6

f(6) = (2/3)*6 - 4 = 0

Then putting these in the table, we will get:

x         f(x)

-3         -6

-2         -16/3

0            -4

3             -2

6              0

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Simplified withοut using the absοlute symbοl, |x - (-12)| is equal tο -(x + 12) when x is less than -12.

Mathematical expressiοns with inequalities οn bοth sides are knοwn as inequalities. In an inequality, we cοmpare twο values as οppοsed tο equatiοns. In between, the equal sign is changed tο a less than (οr less than οr equal tο), greater than (οr greater than οr equal tο), οr nοt equal tο sign.

If x is less than -12, then x - (-12) = x + 12. Therefοre,

|x - (-12)| = |x + 12| = -(x + 12) (since x + 12 is negative when x is less than -12).

Sο, simplified withοut using the absοlute symbοl, |x - (-12)| is equal tο -(x + 12) when x is less than -12.

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Three and one-half times one and two-thirds is equal to 35/6 or 5 5/6.

Given the statement in the question; "three and one-half times one and two-thirds"

First, we can be written as a fraction:

Three and one-half → 3 1/2 = 7/2

One and two-thirds → 1 2/3 = 5/3

So, we have:

(7/2) × (5/3)

To multiply these fractions, we multiply the numerators together and the denominators together:

( 7 × 5 ) / ( 2 × 6 )

35/6

5 5/6

Therefore, the simplified form is 35/6 or 5 5/6.

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Answer:

Step-by-step explanation:

We are given that Lisa's age plus Sean's age is 17 years and Sean is 11 years old .

We need to find the age of Lisa.

Let's assume age of Lisa be x years.

A/q Lisa's age plus Sean's age is 17

[tex] \longrightarrow \: x + Sean's \: age = 17 \\ \\ \longrightarrow \: x + 11 = 17 \\ \\ \longrightarrow \: x = 17 - 11 \\ \\ \longrightarrow \: x = 6 \\ \\ [/tex]

Hence, Lisa is 6 years old.

Answer:

Step-by-step explanation:

It seems like you have provided the dimensions of a cylinder, not a cone. To calculate the volume of a cylinder with a diameter of 12 meters and a height of 2 meters, we can use the formula:

Volume = πr^2h

where r is the radius of the cylinder (half of the diameter). So first, we need to find the radius:

r = d/2 = 12/2 = 6 meters

Now we can plug in the values and calculate the volume:

Volume = π(6 meters)^2(2 meters)

Volume = π(36 square meters)(2 meters)

Volume = 72π cubic meters

Therefore, the volume of the cylinder is 72π cubic meters.

Answer:

The 99% confidence interval for the population proportion is between (0.4526, 0.4960). The interpretation is that we are 99% sure that the true proportion of adults who have started paying bills online in the last year is between these two values.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\dfrac{\pi (1-\pi )}{n} }[/tex]

In which

z is the z-score that has a p-value of [tex]1-\dfrac{\alpha }{2}[/tex].

For this problem, we have that:

In a survey of 2954 ​adults, 1401 say they have started paying bills online in the last year. This means that [tex]n=2954, \ p=\dfrac{1401}{2954} =0.4743[/tex]

99% confidence level

So [tex]\alpha =0.01[/tex], z is the value of Z that has a p-value of [tex]1-\dfrac{0.01}{2} =0.995[/tex], so [tex]Z=2.575[/tex].

The lower limit of this interval is:

[tex]\pi -z\sqrt{\dfrac{\pi (1-\pi)}{n} } =0.4743-2.575\sqrt{\dfrac{0.4743\times0.4408}{2954} } =0.4526[/tex]

The upper limit of this interval is:

[tex]\pi -z\sqrt{\dfrac{\pi (1-\pi)}{n} } =0.4743+2.575\sqrt{\dfrac{0.4743\times0.4408}{2954} } =0.4960[/tex]

The 99% confidence interval for the population proportion is between (0.4526, 0.4960). The interpretation is that we are 99% sure that the true proportion of adults who have started paying bills online in the last year is between these two values.

Answer:

70% watched less than an hour.

Step-by-step explanation:

Less than 1 hour -- 3 people

Number of people 10

3/10 -- 30% of people watch less than 1 hour.

Answer:

Step-by-step explanation:

Solve for the variable. Determine if there is one solution, infinitely many solutions, or no solution.

-6x – 12 = 5(-2x – 3)

Let's start by simplifying the right side of the equation:

5(-2x – 3) = -10x - 15

Substituting this back into the original equation, we get:

-6x - 12 = -10x - 15

Next, we can simplify this equation by adding 10x to both sides:

4x - 12 = -15

Finally, we can add 12 to both sides:

4x = -3

Dividing both sides by 4 gives us:

x = -3/4

Therefore, there is one solution, and x equals -3/4.

Answer:

To reflect a point over the x-axis, we need to negate the y-coordinate while keeping the x-coordinate the same.

The given point is located 5 units to the left and 6 units up from the origin. So its coordinates are (-5, 6).

To reflect this point over the x-axis, we negate the y-coordinate to get (−5, −6).

Therefore, the ordered pair that is a reflection over the x-axis for the given point is (−5, −6).

Answer:

b

Step-by-step explanation:

 -5, -6

Answer:

Starting unpaid balance = $5942.00

On April 1st: Starting unpaid balance = $5942.00

On April 10th: $124.00 purchase is made, so the new balance becomes $5942.00 + $124.00 = $6066.00

On April 22nd: $1000.00 payment is made, so the new balance becomes $6066.00 - $1000.00 = $5066.00

On April 28th: $628.00 purchase is made, so the new balance becomes $5066.00 + $628.00 = $5694.00

Therefore, the ending balance on Jerry's credit card statement at the end of April is $5694.00.

Step-by-step explanation:

Therefore , the solution of the given problem of angles comes out to be  the detour via Town P is approximately 3.05 km longer .

The largest and smallest walls of a skew are determined by the point at which the lines that make up its ends meet. At a junction, it's possible that two routes will cross. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.

Here,

We can determine the length of the road from B to P using the rule of cosines:

=> BP² = AB² + AP² - 2AB(AP)cos(20°)

=>  BP² = x² + 4² - 2x(4)cos(20°)

We can determine the length of the detour via town P by using the rule of cosines once more:

y² = AP² + BP² - 2(AP)(BP)cos(110°)

y² = 4^2 + BP² - 2(4)(BP)cos(110°)

y² = 16 + BP² + 8BP(0.342)

y² = 16 + x² + 16 - 8x(cos(20°))(0.342) + 8(4)(0.342)(BP)

y²= 32 + x² - 2.75x + 1.368BP

=> BP² = x²+ 4² - 2x(4)cos(20°)

=> BP² = x² + 16 - 8x(cos(20°))

=> BP² = sqrt(x² + 16 - 8x(cos(20°)))

=> y² = 32 + x²- 2.75x + 1.368(sqrt(x^2 + 16 - 8x(cos(20°))))

=>  y - x = √(y²) - x

=>  y - x = √(32 + x² - 2.75x + 1.368(√x² + 16 - 8x(cos(20°))))) - x

With the aid of a computer, we can determine that y - x is roughly 3.05 km.

Consequently, the detour via Town P is approximately 3.05 km longer .

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Answer: B. y= 6x -4 and C. 12x -2y=-4

Step-by-step explanation:

I got it wrong on nearpod. but luckily nearpod shows you the correct answer after submitting the answer choices. So these are the actual answers.

Suppose a pharmaceutical company wants to do a study of the commissions of its sales force. the probability that a simple random sample of 50 members of the sales force will have commissions within $400 of the population mean is 0.5812, or 58.12%.

We can use the following formula to calculate the standard error of the mean:

Standard error = population standard deviation / sqrt(sample size)

In this case, the standard error is:

Standard error = 3500 / sqrt(50) = 494.9747

Next, we can calculate the z-score for a commission value that is $400 above the population mean as follows:

z = (X - mu) / standard error

where X is the commission value, mu is the population mean, and standard error is the standard error of the mean that we calculated above.

For X = $52,800, the z-score is:

z = (52800 - 52400) / 494.9747 = 0.808

Similarly, we can calculate the z-score for a commission value that is $400 below the population mean:

z = (X - mu) / standard error

For X = $52,000, the z-score is:

z = (52000 - 52400) / 494.9747 = -0.808

Using a standard normal distribution table or calculator, we can find the probability that a random sample of 50 members of the sales force will have commissions within $400 of the population mean:

P(-0.808 < Z < 0.808)

= P(Z < 0.808) - P(Z < -0.808)

= 0.7906 - 0.2094

= 0.5812

Therefore, the probability  is 0.5812, or 58.12%.

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Answer: Y=10

Step-by-step explanation: please label me brainiest if I'm right

90 dL times L/dL equals 9 L

To understand why 90 dL times L/dL equals 90L, it's important to understand the units involved and how they cancel out.

First, dL stands for deciliter, which is a unit of volume equal to one-tenth of a liter.

L, on the other hand, stands for liter, which is a unit of volume equal to 1000 milliliters or one cubic decimeter.

So, 90 dL represents a volume of 90 deciliters, while L/dL represents a ratio of liters to deciliters.

Specifically, L/dL means "liters per deciliter," which is a way of expressing a conversion factor between liters and deciliters.

Multiplying 90 dL by L/dL involves multiplying 90 dL by the conversion factor of L/dL, which is 1 liter per 10 deciliters. The deciliter units cancel out, leaving only the liter units.

Therefore, we can rewrite the calculation as follows:

90 dL x (1 L/10 dL) = (90/10) L = 9 L

So, the result is 9 L, which is equivalent to 90 dL times L/dL.

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Theoretically, there is a probability of 23.1%, or about 0.231, chance that a face card will be drawn at random from a deck of playing cards.

Each of the four suits hearts, diamonds, clubs, and spades in a conventional deck of playing cards, which has 52 cards total, has 13 cards (Ace, 2-10, Jack, Queen, and King). Among these 52 cards, there are 12 face cards (Jacks, Queens, and Kings). So the number of face cards is 12, and the total number of cards is 52.

The probability of selecting a face card can be calculated by dividing the number of face cards by the total number of cards:

[tex]P_{face card}[/tex] = [tex]\frac{number of face cards}{total number of cards}[/tex]

= 12 / 52

= 3 / 13

≈ 0.231 or 23.1%

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The complete question is:

Find the theoretical probability of randomly selecting a face card​ (J, Q, or​ K) from a standard deck of playing cards

The area of the given rectangle in simplest fraction form is: 81³/₅ m²

The formula for the area of a rectangle is expressed as:

A = L * W

Where:

A is Area

L is length

W is width

We are given the parameters:

Length = 12³/₄ meters = 51/4 meters

Width = 6.4 meters = 6²/₅ meters = 32/5 meters

Thus:

Area = 51/4 * 32/5

= 408/5 m²

= 81³/₅ m²

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According to your query I am defining you multiply in simple manner.

The term multiply refers to the mathematical operation of repeatedly adding a number to itself a certain number of times. The result of this operation is known as the product. Multiplication is an essential arithmetic operation that is used in various fields, including science, engineering, and economics.

Multiplication is typically represented by the symbol "×" or "*", and the numbers being multiplied are called factors. For example, if we multiply 2 and 3, we get the product 6, which can be written as 2 × 3 or 2 * 3.

Multiplication has several important properties, including the commutative property, which states that the order of the factors does not affect the product. For example, 2 × 3 is equal to 3 × 2.

Another important property of multiplication is the distributive property, which states that the product of a number and the sum of two or more numbers is equal to the sum of the products of the number and each of the individual numbers. For example, 2 × (3 + 4) is equal to (2 × 3) + (2 × 4), which simplifies to 14.

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According to your query when you multiply in simple manner and it simplifies to 7/5.

The term multiply refers to the mathematical operation of repeatedly adding a number to itself a certain number of times. The result of this operation is known as the product. Multiplication is an essential arithmetic operation that is used in various fields, including science, engineering, and economics.

Multiplication is typically represented by the symbol "×" or "*", and the numbers being multiplied are called factors. For example, if we multiply 2 and 3, we get the product 6, which can be written as 2 × 3 or 2 * 3.

For the given question:

11/7 × 49/5

= 539/35

= 7/5

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The complete question is as follows:

Answer:

Step-by-step explanation:

The probability that a worker selected at random makes between $350 and $450 is 68%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

We can start by standardizing the values of $350 and $450 using the formula:

z = (x - mu) / sigma

where x is the value we want to standardize, mu is the mean, and sigma is the standard deviation.

For $350, we have:

z = (350 - 400) / 50 = -1

For $450, we have:

z = (450 - 400) / 50 = 1

Now, we can use the z-score table or calculator to find the probability of a standard normal distribution between -1 and 1, which is approximately 68%.

Therefore, the probability that a worker selected at random makes between $350 and $450 is 68%.

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the first five terms of the sequence are (1, 1, 2, 3, 5). Option (d) correctly identifies this as the answer.

The problem provides a recursive sequence defined by the formula an = an-2 + an-1, where a1 = 1 and a2 = 1. We are asked to find the first five terms of this sequence.

To find the second term, we can use the formula and substitute n = 3:

a3 = a1 + a2 = 1 + 1 = 2

To find the third term, we can use the formula and substitute n = 4:

a4 = a2 + a3 = 1 + 2 = 3

To find the fourth term, we can use the formula and substitute n = 5:

a5 = a3 + a4 = 2 + 3 = 5

To find the fifth term, we can use the formula and substitute n = 6:

a6 = a4 + a5 = 3 + 5 = 8

Finally, to find the sixth term, we can use the formula and substitute n = 7:

a7 = a5 + a6 = 5 + 8 = 13

Therefore, the first five terms of the sequence are (1, 1, 2, 3, 5). Option (d) correctly identifies this as the answer.

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The line should cross over the x-axis at the point (0.5,). The line should cross over the y-axis at the point (0,2). To show this on the graph, like the question is asking, you can place one point at (0,2) and another point at (1,-2).

The answer of the given question is the monthly payment necessary to amortize the loan is $923.98.

Principal refers to the original amount of money that is borrowed or invested, not including any interest or fees that may accrue over time. In the context of a loan, the principal is the amount that the borrower receives and is responsible for repaying to the lender over a specified period of time, usually with interest.

To calculate the monthly payment necessary to amortize the loan, we can use the following formula:

M = P * (r/12) * (1 + (r/12))ⁿ / ((1 + (r/12))ⁿ - 1)

where:

M = monthly payment

P = principal amount borrowed

r = annual interest rate

n = total number of monthly payments

Plugging in the values for the given loan, we get:

P = 140,000

r = 0.02375 (2.375% expressed as a decimal)

n = 15 years * 12 months/year = 180 months

M = 140,000 * (0.02375/12) * (1 + (0.02375/12))¹⁸⁰ / ((1 + (0.02375/12))¹⁸⁰ - 1)

M = 923.98

Therefore, the monthly payment necessary to amortize the loan is $923.98.

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The monthly payment necessary to amortize the loan is $928.52.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To calculate the monthly payment necessary to amortize a loan, we can use the formula:

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

Where:

P = Monthly payment

A = Loan amount

r = Monthly interest rate (annual interest rate / 12)

n = Total number of payments (number of years * 12)

Using the formula and plugging in the values from the problem:

A = 140,000

r = 0.02375/12 (2.375% annual interest rate divided by 12 months)

n = 15*12 = 180

P = (140,000 * (0.02375/12)) / (1 - (1 + (0.02375/12))^(-180))

P = $928.52 (rounded to the nearest cent)

Therefore, the monthly payment necessary to amortize the loan is $928.52.

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