Find the length of each leg of a right triangle given that one angle is 22° and the length of the hypotenuse is 10 inches.

The fire stations should be located in District 1 and District 4.

This will ensure that all districts can be reached within an 8-minute response time, while minimizing the number of stations needed.

To minimize the number of fire stations needed while ensuring an 8-minute response time, follow these steps:
1. Analyze the table and find districts with response times of 8 minutes or less to all other districts.
2. Identify any districts that are not covered by these districts and repeat step 1 for them.
3. Combine the results to determine the optimal locations for fire stations.
From the table:
1. District 1 has a response time of 8 minutes or less to districts 2, 3, 5, and 6.

However, it doesn't cover districts 4 and 7.
2. District 4 has a response time of 8 minutes or less to districts 1, 2, 3, 5, 6, and 7.

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A system of linear equations with more equations than unknowns is called overdetermined system. This system always be consistent. Because it may result in contradictions or inconsistencies.

An overdetermined system of linear equations cannot always be consistent, due to contradictions or inconsistencies. Since there are more equations than unknowns, there are likely to be restrictions and dependencies among the equations, and not all of them may be satisfied simultaneously.

However, in certain cases, an overdetermined system can still be consistent if the equations are compatible and do not contradict each other. In such cases, the system may have a unique solution or a set of solutions that satisfy all of the equations.

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The standard error of the mean is approximately 19.

The standard error of the mean (SEM) can be calculated using the following formula:

SEM = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size, and sqrt() denotes the square root.

Since the population standard deviation (σ) is not given, we can estimate it using the sample standard deviation (s) as follows:

σ ≈ s

Therefore, the formula for SEM can be rewritten as:

SEM ≈ s / sqrt(n)

Substituting the given values, we get:

SEM ≈ 190 / sqrt(100)

= 190 / 10

= 19

So the standard error of the mean is approximately 19.

The standard error of the mean measures the variability of the sample means around the population mean. It is the standard deviation of the sampling distribution of the mean, and it represents the amount of error that can be expected when using the sample mean as an estimate of the population mean.

To calculate the SEM, we need to know the population standard deviation or estimate it using the sample standard deviation. Since we only have the sample standard deviation in this case, we use it as an estimate of the population standard deviation. Then, we apply the formula for SEM and simplify it to obtain the final answer.

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Answer: 12

Step-by-step explanation: Finding area of triangles. To find a triangle's area, use the formula area = 1/2 * base * height. Choose a side to use for the base, and find the height of the triangle from that base. Then, plug in the measurements you have for the base and height into the formula.

Answer:

(n - 3) (n + 7)

Step-by-step explanation:

n² + 4n - 21

Consider the form x² + bx + c. Find a pair of integers whose product is

c and whose sum is b. In this case, whose product is −21 and whose sum is 4.

-3, 7

Write the factored form using these integers.

(n - 3) (n + 7)

So, the answer is (n - 3) (n + 7)

Answer: True.

explanation:  If a person makes a credit card payment earlier in the month versus later in the month, it will result in a lower average daily balance, lower interest owed, and a smaller minimum payment at the end of the billing cycle. Paying off your balance early or making additional payments before the billing cycle ends decreases your credit utilization.

Required function is f(x) = 2x-3.

What is function?

In mathematics, a function is a rule or a set of rules that assigns a unique output value to each input value. In other words, it is a way of relating one quantity to another. Functions are used in a variety of fields, such as engineering, physics, economics, and computer science, to describe relationships between variables.

An example of a function is the quadratic function f(x) = x² + 2x + 1. This function takes an input value x and produces an output value that is the result of squaring x, multiplying it by 2, and adding 1. For instance, if we substitute x = 3 in the function, we get:

f(3) = 3² + 2(3) + 1 = 9 + 6 + 1 = 16

To determine which function represents the data in the table, we need to substitute the given values of x into each function and compare the results with the corresponding values of f(x) given in the table.

If we use the function f(x) = 2x-3, we get:

f(0) = -3

f(1) = -1

f(2) = 1

f(3) = 3

f(4) = 5

f(5) = 7

We can see that these values match with the values given in the table, so the function that represents the data in the table is:

f(x) = 2x-3.

Therefore, we can conclude that the function f(x) = 2x-3 represents the data in the table.

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Probability equation of P(A/B)=  [tex]\frac{0.31}{0.31+0.17}=0.65[/tex]

let say A and B is not empty set then intersection of A and B is  a set of elements which are common in both two sets A and B .

given that A and B are two events and

probability of A= 0.31+0.30=0.61

probability of B= 0.31+0.17=0.48

probability of intersection of A and B is = 0.31

so,

P(A/B)= is the probability of event A occurring, given that event B occurs.

P(A/B) = intersection of A and B / probability of B

P(A/B) = [tex]\frac{0.31}{0.31+0.17}=0.65[/tex]

therefore , probability of PA/B) = 0.65  

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13 is the inequality so that it represents the whole-number values.

What is Triangle Inequality Theorem?

Triangle inequality, in Euclidean figure, theorem that the sum of any two sides of a triangle is lesser than or equal to the third side; in symbols, a b ≥ c. In substance, the theorem states that the shortest distance between two points is a straight line.

the Triangle Inequality Theorem, which states that

the sum of the lengths of two sides of a triangle must always be greater than the length of the third side

      a = c + b

         = 7 + 6

         = 13

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Answer:
the translated point A' has coordinates (1,9).
Explanation:
To translate the point A(2,7) by the rule (x,y) → (x-1, y+2), we can apply the rule to the x-coordinate and the y-coordinate separately. Subtracting 1 from the x-coordinate and adding 2 to the y-coordinate will give us the new coordinates of the translated point.

Using this rule, we have: A'(x,y) = (2-1, 7+2) = (1, 9)

Therefore, the translated point A' has coordinates (1,9).

To get the answer, we applied the given rule to the x and y coordinates of the point, separately. In other words, we substituted x = 2 and y = 7 into the expressions x-1 and y+2, respectively, to obtain the new x-coordinate and the new y-coordinate.

So, the sophisticated answer is that to translate a point by a given rule, you apply the rule to each coordinate separately, and then combine the results to form the coordinates of the translated point.

Answer:

Point A' has coordinates (1,9).

Step-by-step explanation:

I did the test

Hope this helps :)

Answer:

x ≈ 8.0

Step-by-step explanation:

Using the tangent of the angle is equal to the opposite over the adjacent

tan(37º) = 6/x

x = 6/tan(37º)

x=7.96226892972

Answer:

[tex]90 \div 15 = 6[/tex]

Answer:

6

Step-by-step explanation:

We can use the recursive formula to find each term in the sequence.

From the given formula, we start with:

f(1) = 2

Next, we use the formula to find f(2):

f(2) = -3f(1) = -32 = -6

Using the formula again, we find f(3):

f(3) = -3f(2) = -3(-6) = 18

Now, we find f(4):

f(4) = -3f(3) = -318 = -54

Finally, we can find f(5):

f(5) = -3f(4) = -3(-54) = 162

Therefore, the 5th term in the sequence is 162, or answer (C).

we can found it by using algebra.This checks out, so we can conclude that Simone has:
4 $100 bills
5 $50 bills
2 $20 bills
9 $10 bills

And the total amount of money she has is indeed $780.Let's start by using algebra to represent the information given in the problem. Let:

x = 20 (Simone has 20 bills in total)
h = x/5 (One fifth of the bills are hundreds)
f = x/4 (One fourth of the bills are fifties)
t = x/10 (One tenth of the bills are twenties)
n = x - h - f - t (The rest of the bills are tens)
We also know that the total amount of money Simone has is $780. We can use this information to write an equation:
100h + 50f + 20t + 10n = 780

Now we can substitute the values we found for h, f, t, and n in terms of x:

100(x/5) + 50(x/4) + 20(x/10) + 10(x - x/5 - x/4 - x/10) = 780

We can see that the number of bills must be a whole number, and therefore x must be a multiple of 20. Let's try assuming that Simone has 20 bills of each denomination, which would give us:

h = x/5 = 4 (4 hundreds)
f = x/4 = 5 (5 fifties)
t = x/10 = 2 (2 twenties)
n = x - h - f - t = 9 (9 tens)
Using these values in the algebraic  equation we derived earlier, we get:
100(4) + 50(5) + 20(2) + 10(9) = 780.

Simone has 20 bills. One fifth of the bills are hundreds, 1/4 of them are fifties, 1/10 of them are $20s. The rest of the bills are tens.

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Answer:

3,266.53

Step-by-step explanation:

ok so 3 divided by 75.16 so then the answer would be 0.039914848 so then we then have to round to the nearest whatever so i just used a calculator so I think the answer is 3,266.53

The formula to calculate the volume of a cylinder is:

V = πr^2h

where π is a constant equal to 3.14, r is the radius of the cylinder (which is half of the diameter), and h is the height of the cylinder.

To use Maria's expression, we can first calculate the radius of the cylinder:

diameter = 10 1/2 ft

radius = diameter/2 = 5 1/4 ft

Next, we can substitute the values of π and h into the expression 2ℎ:

2ℎ = 2(4 2/5 ft) = 8 4/5 ft

This expression represents the height of the water in the cylinder when it is filled to capacity. To find the volume of water that can fit in the pool, we can substitute the values of π, r, and h into the formula for the volume of a cylinder:

V = πr^2h = 3.14 × (5 1/4 ft)^2 × 8 4/5 ft ≈ 581.8 ft^3

Rounding to the nearest cubic foot, the approximate volume of water that Maria determined can fit into the pool is 582 cubic feet.

According to the given information we can conclude that Richard paid $123.90 for the car rental.

To solve this problem, we need to calculate the total cost of the car rental based on the daily rate and the mileage charge.

First, we can calculate the cost of the rental for two days by multiplying the daily rate by the number of days:

2 days x $34.95 per day = $69.90

Next, we need to calculate the cost of the mileage charge. To do this, we can multiply the number of miles driven by the mileage rate:

300 miles x $0.18 per mile = $54.00

Finally, we can find the total cost of the car rental by adding the cost of the rental and the cost of the mileage charge:

$69.90 + $54.00 = $123.90

Therefore, Richard paid $123.90 for the car rental.

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the probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.0564 rounded to three decimal places. The final answer is 0.056.

The problem given can be solved by using the central limit theorem.

According to the central limit theorem, if the sample size is sufficiently large, then the sample mean will follow a normal distribution with a mean of μ and a standard deviation of σ/√n, where n is the sample size.Using this formula, we can find the probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years. The formula is:

P(Z < (X-μ)/(σ/√n))

where Z is the standard normal distribution, X is the value we want to find the probability for, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, X = 21.8, μ = 22, σ = 2, and n = 100. Plugging these values into the formula, we get:

P(Z < (21.8-22)/(2/√100)) = P(Z < -1.58)

Using Excel or a standard normal distribution table, we can find that the probability of Z being less than -1.58 is 0.0564.

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The value of angle x = 10.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex. The joint vertex is the common terminal of the two beams.

According to our question-

2x+3 + 5x+17= 90°

7x+20=90

7x=70

x=10

Hence, The value of angle x = 10.

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The actual height of the town's bell is 15 feet.

To find the actual height of the town's bell using the given scale and the height of the miniature replica, follow these steps:
1. Identify the scale:

The scale provided is 1 inch to 3 feet, which means that 1 inch on the replica represents 3 feet in reality.
2. Determine the height of the miniature replica:

The replica is 5 inches tall.
3. Apply the scale to find the actual height:

Since 1 inch represents 3 feet, we can multiply the height of the replica (5 inches) by the scale factor (3 feet) to find the actual height of the bell.

Actual height = Replica height × Scale factor.

Actual height = 5 inches × 3 feet/inch
4. Calculate the result:

Multiplying 5 inches by 3 feet/inch will give us the actual height of the bell in feet.
Actual height = 15 feet.

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Shirley Benson earns $611.60 for a week in which she assembles 278 toys.

The correct answer is 611.60.

To answer the student's question, we can use the formula:
Earnings = Rate x Quantity
In this case, Shirley Benson is paid $2.20 for each toy she assembles.

She has assembled 278 toys in a week.

Therefore, her earnings for the week would be:
Earnings = $2.20 x 278
Earnings = $611.60.

The correct answer is 611.60

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The sample size is needed to achieve a margin of error of .05 for a 90% confidence interval for a proportion of interest to be near 0.25 is equals to the 203.

From the above problem we have,

Mardin of error, E = 0.05

confidence interval, α = 90%

proportion of interest, p = 0.25

We have to determine the sample size.

Using the formula for minimum sample size is written as n = (Z² × p(1 -p)]/E² --(1)

Using the Z-distribution table and the z-score value for 90% is equals to 1.645.

Plug all known values in above equation,

=> n = [(1.645)² × 0.25 ( 1 - 0.25)]/(0.05)²

=> n = (1.645)² × 0.25 ×0.75/(0.05)²

=> n = 0.5074/0.0025

=> n = 202.96 ~ 203

Hence, required sample value is 203

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The story based on the distance-time graph is given below:

Once upon a time, there was a daring bird named Ziggy. Ziggy loved to soar high in the sky, feeling the wind rush beneath her wings.

One day, as she flew higher and higher, she spotted a berry bush on the ground below. Without thinking twice, she dove down to snatch a berry.

But as she got closer, she realized the bush was a trap set by a mischievous fox. Ziggy narrowly escaped the trap and soared back into the sky, but not before losing some altitude.

Determined to keep flying, Ziggy flapped her wings with all her might, gradually ascending back up to her previous height. And as she flew onward, she couldn't help but wonder what other surprises lay ahead.

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1. The length of the fence required to enclose the circular pool with 4 feet of space around it is approximately 125.6 feet.

2.  If he runs around the track once he will still can't complete the goal he needs to run 20 more meters to meet his daily goal. Option A is the correct choice.

1.  To find the length of the fence required to enclose a circular swimming pool with a radius of 20 feet and a 4-foot space around it, we need to first calculate the diameter of the pool plus the space around it.

The diameter of the pool is twice the radius, which is 40 feet.

Adding 4 feet of space on both sides of the diameter gives us a total diameter of 48 feet.

The fence will be installed around the perimeter of this circular area, which is the circumference of the circle.

To calculate the circumference, we use the formula

C = 2πr

where C is the circumference, π is approximately 3.14, and r is the radius of the circle.

Plugging in the values, we get:

C = 2 x 3.14 x 20 feet = 125.6 feet.

2.

To calculate the distance around the swimming pool, we first need to find the total length of the semicircles, which is equal to half the circumference of a circle with a diameter of 35 meters.

The formula for the circumference of a circle is

C = πd

where C is the circumference and d is the diameter.

Plugging in the values, we get:

C = π x 35 meters / 2 = 54.99 meters

The total length of both semicircles is twice the length of one semicircle, which is

2 x 54.99 meters = 109.98 meters.

The length and width of the rectangular part of the pool are 80 meters and 35 meters, respectively.

Therefore, the distance around the rectangular part is

2 x (80 + 35) meters = 230 meters.

Adding the length of the semicircles to the length of the rectangle, we get the total distance around the swimming pool, which is

109.98 meters + 230 meters = 339.98 meters.

Therefore, Kevin needs to run at least 340 meters to meet his daily goal of 320 meters.

Since one lap around the high school track is only 320 meters, Kevin will need to run an additional 20 meters to meet his daily goal.

Thus, the correct answer is: option A "No, he will still need to run 20 more meters."

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Question:

1. A circular swimming pool has a radius of 20 feet. A fence is going to be built so that there is a 4-foot space around the entire pool. What is the length of the fence?

2. A swimming pool is comprised of a rectangle and 2 semicircles. The rectangle has length 80 meters and width 35 meters. The semicircles have diameters of 35 meters. Kevin needs to run 320 meters a day for his training program. He plans on running around the high school track shown. If he runs around the track once, will he meet his daily goal?

A. No, he will still need to run 20 more meters.

B. No, he will still need to run 100 more meters.

C. No, he will still need to run 150 more meters.

D. Yes, he met his daily goal.

The correct system of equations that could be used to find x, the cost of a medium drink, and y, the cost of a large popcorn, is:

A) 2x + y = 13.85 3x + 2y = 23.9

To arrive at these equations, you can use the information given in the question to set up a system of linear equations. You know that 2 medium drinks and a large popcorn cost $13.85, so you can write:

2x + y = 13.85

where x is the cost of a medium drink and y is the cost of a large popcorn.

You also know that 3 medium drinks and 2 large popcorns cost $23.90, so you can write:

3x + 2y = 23.9

Then , you can solve the system of equations for x and y using any method you prefer, such as elimination or substitution. For example, one way to solve the system is to multiply the first equation by 3 to eliminate y:

6x + 3y = 41.55

Then you can subtract the second equation from this equation:

6x + 3y - (3x + 2y) = 41.55 - 23.9

Simplifying this equation gives:

3x + y = 17.65

You now have two equations to solve for x and y:

3x + y = 17.65 3x + 2y = 23.9

This system of equations is equivalent to the system shown in answer A.

Answer:

A

Step-by-step explanation:

The answer is (A) because, first off you have 2 medium drinks. So that is 2x. Second you only have 1 large popcorn. So that is just y. Right now the equation is 2x + y =$13.85. The next part of the problem is the same thing. You have only 1 more medium drink this time, so it is 3x. Then you have 1 more large popcorn, so that is 2y. The final part of the equation is 3x + 2y =$23.90. Since 23.90 is just a decimal you can just get rid of the 0. Now the equation should look like this, 2x + y=$13.85

3x + 2y=$23.9

Abοut 68% οf sixth-grade students will have heights between 55.7 inches and 60.3 inches.

Mean is the average value οf the set given. It is calculated as:

Mean = Sum οf all the values οf the set given / Number οf values in the set

We have,

The standard deviatiοn is a measure οf hοw tο spread οut a set οf data frοm its mean.

In this case,

The standard deviatiοn is 2.3 inches, which means abοut 68% οf the data.

(in this case, the heights οf sixth-grade students) falls within οne standard deviatiοn οf the mean.

This is knοwn as the empirical rule οr the 68-95-99.7 rule.

Specifically, abοut 68% οf students will have heights between οne standard deviatiοn belοw the mean.

(58 - 2.3 = 55.7 inches).

And οne standard deviatiοn abοve the mean.

(58 + 2.3 = 60.3 inches).

Thus,

Abοut 68% οf sixth-grade students will have heights between 55.7 inches and 60.3 inches.

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The answer of question no. 3 is the polygon has 18 sides.

A polygon is a two-dimensional geometric figure that is defined by a closed path of straight line segments. The segments, called sides, intersect at their endpoints, called vertices, and the angles formed by adjacent sides are called interior angles.

Polygons can have any number of sides, but they must have at least three sides (and therefore, three vertices). The most common polygons are the triangle (three sides), quadrilateral (four sides), pentagon (five sides), hexagon (six sides), heptagon (seven sides), octagon (eight sides)

For any polygon, the sum of the exterior angles is always 360 degrees. Therefore, if one exterior angle of a polygon is 20 degrees, then the polygon must have:

360 / 20 = 18 sides.

Therefore, the polygon has 18 sides.

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Answer: the answer is B-130

Explanation: it is farther closest to 50 than the other options.

In conclusion Your tax due is $9,096.

How to find?

To find your taxable income, you need to subtract your exemption from your adjusted gross income (AGI):

Taxable income = AGI - Exemption

Taxable income = $60,000 - $8,200

Taxable income = $51,800

To find your tax due, you need to use the tax table for single filers with a taxable income of $51,800. According to the 2021 tax tables, the tax due for a single filer with a taxable income of $51,800 is $9,096.

Therefore, your tax due is $9,096.

Tax is a compulsory financial charge or other type of levy imposed on an individual or a legal entity by a governmental organization in order to fund public expenditures. Taxes are typically calculated as a percentage of income, value of goods or services, or property.

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110,664,000 possible selections for Head Girl, Deputy Head Girl, Head Boy, and Deputy Head Boy from a group of 101 girls and 105 boys.

How to calculate different possible selections could be made?​

To find the number of possible selections that can be made, we need to multiply the number of choices available for each position.

For the Head Girl position, there are 101 girls to choose from. After one girl is selected for Head Girl, there are 100 girls remaining to choose from for the Deputy Head Girl position. So there are a total of 101 x 100 = 10,100 possible combinations of girls that can be chosen for these two positions.

Similarly, there are 105 boys to choose from for Head Boy, and 104 boys remaining to choose from for Deputy Head Boy. So there are a total of 105 x 104 = 10,920 possible combinations of boys that can be chosen for these two positions.

To find the total number of possible selections, we multiply the number of combinations for the girls by the number of combinations for the boys:

10,100 x 10,920 = 110,664,000

Therefore, there are 110,664,000 different possible selections that could be made.

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