Line Segment BD and Line Segment CK are diameters of ⊙ A. Line Segment BP and Line Segment QP are tangents to ⊙ A. Find each of the following. Show your work.

11.) m∠ABP=_________
12.) m∠BAK=_________
13.) m∠AQP=_________
14.) m∠QAK=_________
15.) Measure of Arc BK=__________
16.) Measure of Arc BQ=__________
17.) m∠CAD=_________
18.) m∠CAB=_________
19.) Measure of Arc CB= __________
20.) m∠CDA=_________

The graph of the data from the table is added as an attachment

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

Jerome is a photographer. He earns $125 per hour

This means that the equation of the function is

f(x) = 125x

Where x is the number of hours he works

Using the above as a guide, we have the following table of values

x    f(x)

1     125

2    250

3    375

4    500

5    625

6     750

Next, we plot the graph from the table of values and the function f(x) = 125x

The graph of the function is added as an attachment

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Answer:

Step A: The third quartile is 9.5, choice d.

Step B: The median of the data set is 6.5.

Step C: The IQR of the data set is 6, and we found this value by subtracting the first quartile from the third quartile (9.5 - 3.5 = 6).

Step-by-step explanation:

First, let's analyze the data set.

1 2 3 4 5 6 7 8 9 10 11 12

Since this data set is already sorted in numerical order, we can determine the median by finding the middle value that divides the data set in half. With 12 values in the data set, the median would be between the 6th and 7th numbers, so we can find this by using the calculation (6+7)/2 = 6.5.

                 6.5

{1 2 3 4 5 6} | {7 8 9 10 11 12}

With this median, we split our data set into two halves. Now, we can find the first quartile, or the 25th percentile, by finding the median of the first half. This would be the value between 3 and 4, so (3+4)/2 = 3.5.

       3.5        6.5

{1 2 3} | {4 5 6} | {7 8 9 10 11 12}

We can repeat this step in the second half in order to find the third quartile or the 75th percentile. The median of the second half would be between 9 and 10, so (9+10)/2 = 9.5.

       3.5         6.5        9.5

{1 2 3} | {4 5 6} | {7 8 9} | {10 11 12}

Now we know Q1 (first quartile) and Q3 (third quartile), we can find the IQR which is Q3 - Q1, so Q3 - Q1 = 9.5 - 3.5 = 6.

So now we can answer the question:

Step A: The third quartile is 9.5, choice d.

Step B: The median of the data set is 6.5.

Step C: The IQR of the data set is 6, and we found this value by subtracting the first quartile from the third quartile (9.5 - 3.5 = 6).

a)  $155.61 is deducted from Violet's paycheck for her 401(k).

b) $19.05 is deposited into Violet's retirement plan each day.

A) To calculate how much is deducted from Violet's paycheck for her 401(k), we need to find her biweekly gross income and then calculate 7% of it.

Violet's biweekly gross income can be found by dividing her annual income by the number of biweekly pay periods in a year, which is 26:

Biweekly gross income = $57,903 / 26 = $2,223

Now, we can calculate the amount that is deducted from Violet's paycheck for her 401(k):

401(k) deduction = 7% of $2,223 = 0.07 x $2,223 = $155.61

Therefore, $155.61 is deducted from Violet's paycheck for her 401(k).

B) To calculate how much is deposited into Violet's retirement plan each day, we need to first find out how much is deposited each pay period.

Violet contributes 7% of her biweekly gross income to her 401(k), which is $155.61 as calculated above. Her employer matches up to 5% of her contribution, so the total contribution to her retirement plan each pay period is:

Total contribution = Violet's contribution + employer's contribution

= $155.61 + (5% of $2,223)

= $155.61 + $111.15

= $266.76

There are 14 days in a biweekly pay period, so we can calculate how much is deposited into Violet's retirement plan each day:

Daily deposit = Total contribution / number of days in pay period

= $266.76 / 14

= $19.05

Therefore, $19.05 is deposited into Violet's retirement plan each day.

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95% confidence that the population mean is less than 6 minutes since the upper limit of the confidence interval is below 6 minutes.

95% confidence that the population mean is within the range of 4.897 to 5.763 minutes.

The t-based 95 percent confidence interval for the population mean:

CI =[tex]\bar x\pm t\alpha/2 \times (s/\sqrt n)[/tex]

[tex]\bar x[/tex]  is the sample mean, s is the sample standard deviation, n is the sample size, tα=/2 is the t-value corresponding to the desired level of confidence and (s/√n) is the standard error of the mean.

The sample size is 100, the sample mean is 5.33, and the sample standard deviation is 2.207, the standard error of the mean is:

s/√n

= 2.207/√100

= 0.221

The t-value corresponding to a 95% confidence level with 99 degrees of freedom (100 - 1), look it up in a t-distribution table or use a calculator.

The t-value is approximately 1.984.

The 95% confidence interval for the population mean is:

CI = 5.33 ± 1.984 × 0.221

= [4.897, 5.763]

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A 2-column table titled Balloon Payment Mortgage has 7 rows. The first column has entries mortgage amount, term, interest rate, monthly payment, balloon payment, total interest, total payment. The second column has entries 170,000 dollars, 8 years, 4 percent, 811 dollars and 61 cents for 95 months, 143,152.99, 50,256, 220,256. By the end of year 8, Demarco and Tanya would have to pay a final payout of $143,152.

Hence, the correct option is C.

With the help of the given values, we know that the mortgage amount is $170,000 and the interest rate is 4%. The term of the loan is 8 years, which is equivalent to 96 months.

To calculate the monthly payment, we can use the following formula

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

Where P is the monthly payment, r is the monthly interest rate (which is 4% / 12 = 0.00333), A is the mortgage amount, and n is the total number of months (which is 96).

By putting the values, we get

P = (0.00333 * 170000) / (1 - (1 + 0.00333)^(-96))

P ≈ $811.61

Hence, the monthly payment is $811.61.

The total interest paid over the life of the loan can be calculated as the difference between the total payment and the mortgage amount.

Total interest = Total payment - Mortgage amount

Total interest = $220,256 - $170,000

Total interest = $50,256

Now, we can calculate the balloon payment using the formula

Balloon payment = A * (1 + r)^n - [P * ((1 + r)^n - 1) / r]

Where A is the mortgage amount, r is the monthly interest rate, P is the monthly payment, and n is the number of months until the balloon payment is due (which is 95 in this case).

By substituting the values, we get

Balloon payment = 170000 * (1 + 0.00333)^95 - [811.61 * ((1 + 0.00333)^95    - 1) / 0.00333]

Balloon payment ≈ $143,152.99

Hence, the correct option is C.

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Answer$143,152

Step-by-step explanation:

Answer:

20/8 or 20:8

Step-by-step explanation:

Ok, so we start off with a smaller square with one side being 8.

We then have to go from one side being 8 to one side being 20.

So, the ratio has to be a number larger than 1 to go from smaller to larger, so we can use the ratio of 20/8 (or 2.5).

Check:

2.5x8=20

11/8 cup of the bowl is made up of granola..

What is fraction?

A fraction represents a part of a whole, and it is written in the form of one integer written above another, separated by a horizontal line. The integer on top is called the numerator, and the integer on the bottom is called the denominator.

The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole. For example, the fraction 3/4 represents three parts out of a total of four equal parts.

Fractions can be used to represent values that are not whole numbers, such as halves, thirds, quarters, etc. They are commonly used in everyday life, such as when measuring ingredients in cooking, dividing up a pizza or a cake, or expressing a probability.

To find the amount of granola in the bowl, we need to subtract the total amount of yogurt and blueberries from the total volume of the bowl.

First, let's add up the yogurt and blueberries:

7/8 cup Greek yogurt + 1 1/4 cup blueberries

= 7/8 + 5/4 (we need to find a common denominator)

= 14/16 + 20/16

= 34/16

Next, let's convert the total volume of the bowl to a fraction with a common denominator of 16:

3 1/2 = 7/2 = 56/16

Now we can find the amount of granola:

Amount of granola = Total volume of bowl - Amount of yogurt - Amount of blueberries

= 56/16 - 34/16

= 22/16

Simplifying the fraction, we get:

Amount of granola = 11/8

Therefore, 11/8 cup of the bowl is made up of granola.

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Buddy's answer of 19 feet for the maximum height of his punt is correct, based on the given quadratic function.

How to solve the question?

To determine the maximum height of the punt, we need to find the vertex of the parabolic function h(x) = −.02x² + 1.2x + 4, which represents the height of the football at any given horizontal distance x from the point of impact.

The vertex of a parabola in the form y = ax² + bx + c can be found using the formula x = -b / 2a, which gives the x-coordinate of the vertex, and then substituting that value into the function to find the corresponding y-coordinate.

In this case, we have a = -.02, b = 1.2, and c = 4. So the x-coordinate of the vertex is x = -b / 2a = -1.2 / (2*(-.02)) = 30, and the corresponding maximum height is h(30) = -.02(30)2 + 1.2(30) + 4 = 19 feet.

Therefore, Buddy's answer of 19 feet for the maximum height of his punt is correct, based on the given quadratic function.

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According to the equation, Carmine used 4.7 pounds of almonds in the mixture.

To represent this relationship mathematically, we can use an equation. Let's use "a" to represent the weight of the almonds in pounds. Then, we can write:

2.8 + a = total weight of the trail mix

We can then solve for "a" by subtracting 2.8 from both sides of the equation:

a = total weight of the trail mix - 2.8

We also know that the trail mix is divided into 5 equal portions, each weighing 1.5 pounds. Therefore, the total weight of the trail mix is:

total weight of the trail mix = 5 * 1.5

total weight of the trail mix = 7.5

Substituting this value into the equation we derived earlier, we get:

a = 7.5 - 2.8

a = 4.7

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The normal approximation for the given binomial distribution with p = 0.10 and n = 40 has a mean of 4 and a standard deviation of 1.93.

The binomial probability distribution can be approximated by the normal distribution when certain conditions are met, such as a large sample size and a probability of success not too close to 0 or 1.

In this case, n = 40 and p = 0.10. To determine if the normal approximation is appropriate, we can check if both np and n(1-p) are greater than or equal to 10

np = 40 x 0.10 = 4

n(1-p) = 40 x 0.90 = 36

Both np and n(1-p) are greater than or equal to 10, so the normal approximation is appropriate.

The mean of the binomial distribution is given by μ = np = 4, and the standard deviation is given by σ = √(np(1-p)) = √(40 x 0.10 x 0.90) ≈ 1.93.

To find the mean and standard deviation of the normal approximation, we use the same mean and standard deviation values

μ = np = 4

σ = √(np(1-p)) ≈ 1.93

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The odds of rolling two 6-sided dice and getting a total between the two dice that is a multiple of three are approximately 31%.

To determine the odds of rolling two 6-sided dice and getting a total between the two dice that is a multiple of three,

we first need to identify the possible outcomes. The possible sums of rolling two dice range from 2 to 12. We then need

to find the multiples of three within that range, which are 3, 6, 9, and 12.

Next, we need to find the number of ways that we can roll each of these multiples of three. To do this, we can create a

chart:
Sum | Ways to roll
---|---
3 | 1
6 | 5
9 | 4
12 | 1

So there are a total of 11 ways to roll a multiple of three with two dice.

To find the odds, we need to divide the number of favorable outcomes (11) by the total number of possible outcomes

when rolling two dice (36), and then convert the fraction to a percentage or a ratio.

11/36 = 0.3056 or approximately 31%

Therefore, the odds of rolling two 6-sided dice and getting a total between the two dice that is a multiple of three are approximately 31%.

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The inverse of the graphs are added as an attachment

To plot the inverse of a graph, you can follow these steps:

See attachment for the graphs

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The requried side length of the square is approximately 9.695 units.

To find the side length of a square with an area of 94 square units, we need to take the square root of the area.

a² = 94
a = √94

a ≈ 9.695

Therefore, the side length of the square is approximately 9.695 units.

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Answer:

396 pi mm²

Step-by-step explanation:

The surface area of a cylinder:

The total surface area (A) of a cylinder is calculated by adding the areas of the two bases and the lateral surface area.

A = 2πr^2 + 2πrh

Given:

The surface area of the first cylinder (A1) = 594π mm^2

Height of the first cylinder (h1) = 24 mm

Height of the second cylinder (h2) = 16 mm

We can use the property of similarity and set up the proportion:

A1 / A2 = (h1 / h2)^2

Plugging in the given values, we get:

594π / A2 = (24 / 16)^2

Simplifying, we get:

594π / A2 = 3/2)^2

594π / A2 = 9/4

Cross-multiplying, we get:

A2 = (594π * 4) / 9

A2 = 264π mm^2

So, the correct surface area of the second cylinder is 264π mm^2.

The length of JL is 20.572.

An angle is a geometric figure formed by two rays or lines that share a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians, and they are used to describe the relationships between lines and shapes in geometry.

The size of an angle is determined by the amount of rotation needed to bring one of the rays into coincidence with the other. A full rotation around the vertex is equivalent to 360 degrees or 2π radians. A right angle, which is formed by one ray perpendicular to another, has a measure of 90 degrees or π/2 radians.

Angles can be classified according to their measures as acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (between 90 and 180 degrees), straight angles (exactly 180 degrees), and reflex angles (between 180 and 360 degrees).

Angles also have a number of important properties and relationships, such as vertical angles (formed by two intersecting lines and are congruent), complementary angles (two angles whose measures sum up to 90 degrees), and supplementary angles (two angles whose measures sum up to 180 degrees).

cos  A= (leg adjacent to ∠A)/hypotenuse: cos(∠KLM)= [tex]\frac{LM}{KL}[/tex]

Substitute, LM= 7, KL= 12 : cos(∠KLM)= [tex]\frac{7}{12}[/tex]

Calculate cos(∠KLM)= [tex]\frac{7}{12}[/tex] : ∠KLM= 54.315°

Representing same angles: ∠JLK= ∠KLM

Substitute ∠KLM= 54.315° into ∠JLK= ∠KLM ⇒∠JLK= 54.315°

cos  A= (leg adjacent to ∠A)/hypotenuse: cos(∠JLK)=[tex]\frac{KL}{JL}[/tex]

Substitute, KL= 12, ∠JLK= 54.315°  ⇒ cos(∠JLK)= [tex]\frac{12}{JL}[/tex]

Calculate cos(54.315°)=[tex]\frac{12}{JL}[/tex] ⇒ JL= 20.572

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The complete question is:

Answer:

562496

Step-by-step explanation:

i think

Answer:189504

Step-by-step explanation:

To get the 1.4% of population you need to multiply it like this: 752000 × 1.4% = 10528.

10528 is the population decrease every year, to find the population decrease after 18 years you need to multiply it again like this: 10528 × 18 = 189504.

189504 is the population decrease after 18 years.

When the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.

This is a related rates problem involving a ladder leaning against a wall. Let's denote the distance of the foot of the ladder from the wall as x, and the height that the top of the ladder reaches as y. We are given that dy/dt = -2 ft/s (since the top is slipping down the wall) and we want to find dx/dt (the speed at which the foot of the ladder is moving away from the wall) when y = 16 ft.

Using the Pythagorean theorem, we have:

[tex]x^2 + y^2 = 17^2[/tex]

Differentiating implicitly with respect to time, we get:

[tex]2x(dx/dt) + 2y(dy/dt) = 0[/tex]

Substituting the given values, we get:

[tex]2x(dx/dt) + 2(16)(-2) = 0[/tex]

Simplifying, we get:

[tex]2x(dx/dt) = 64[/tex]

Dividing both sides by 2x, we get:

dx/dt = 64/(2x)

We know that y = 16, so we can use the Pythagorean theorem to solve for x:

[tex]x^2 + 16^2 = 17^2x^2 = 17^2 - 16^2x^2 = 33[/tex]

Taking the square root, we get:

[tex]x = sqrt(33)[/tex]

Substituting this into our expression for dx/dt, we get:

[tex]dx/dt = 64/(2*sqrt(33)) ≈ 3.86 ft/s[/tex]

Therefore, when the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.

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With 82% confidence that the true average weight gain during the December holidays for the sampled adult population is between -1.25 pounds. and 1.47 pounds.

To find the 82% confidence interval for the mean weight gain over the holidays in December, you can use the following formula:

[tex]CI = xd ± t*(SDd/sqrt(n))[/tex]

where:

xd = average weight change of sample (0.11 lb increase)

SDd = standard deviation of weight difference (5.25 lbs)

n = sample size (23)

t = the critical value of the t distribution with n-1 degrees of freedom and the desired confidence level (82% in this case)

You can use a t-table or a calculator to find the critical value of the t-distribution. With 22 degrees of freedom (n-1) and an 82% confidence level, the critical value is approximately 1.319.

Plugging in the given values ​​gives:

[tex]CI = 0.11 ± (1.319*(5.25/sqrt(23))) = (-1.25, 1.47)[/tex]

Therefore, we can say with 82% confidence that the true average weight gain during the December holidays for the sampled adult population is between -1.25 pounds. and 1.47 pounds.

Note that the confidence intervals include zero. This means that we cannot reject the null hypothesis that there is no significant difference in weight between mid-November and he early-to-mid-January.

However, this does not necessarily mean no weight gain during his December vacation, as there is individual variation in weight change within the sample.  

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Answer:

Step-by-step explanation:

I do believe you should most definitly add units

Answer:

160°/360° = area/(π(5^2))

area = 25π(4/9) = 100π/9 square inches

Circumference = (4/9)π(5) = 20π/9 inches

Answer:

20 3/5

Step-by-step explanation:

this is the correct result when 30 9/10 is multipled by 2/3

A four members of the Harrison family save  $896 on airfare by vacationing in Vancouver.

Here, the airplane tickets to Fairbanks Alaska will cost $958 each.

⇒ c₁ = $958

where c₁ represents the airfare to Fairbanks Alaska

and the airplane tickets to Vancouver Canada will cost $734.

⇒ c₂ = $734

Let us assume that s represents the amount of savings per ticket.

⇒ s = c₁ - c₂

⇒ s = 958 - 734

⇒ s = $224

Since there are four members in the family.

So using unitary method the total savings would be,

⇒ t = 4 × s

⇒ t = 4 × 224

⇒ t = $896

Therefore, the total savings =  $896

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The complete question is:

Airplane tickets to Fairbanks Alaska will cost $958 each. Airplane tickets to Vancouver Canada will cost $734. How much can the four members of a Harrison family save on airfare by vacationing in Vancouver?

Answer:

14

Step-by-step explanation:

28 mm is the diameter of the button, so we have to find the radius, which is half of the diameter.

28/2=14

So, the radius of this button is 14 mm

If PQRS are points on a circle with the centre O, PS is a diameter of the circle Angle PQR=136, the measure of angle RPS is 88 degrees.

Since QR is parallel to PS, we can use alternate interior angles to determine that angle QPS is equal to angle PQR. This means that angle QPS is also 136 degrees.

Angle PQR and angle QPS both subtend the same arc, which is the arc between points P and R on the circle. Therefore, the two angles are equal.

We can use this fact to find the measure of angle RPS. First, we know that the sum of angles in a quadrilateral is 360 degrees. Therefore, we can find the measure of angle PSR as follows:

Angle PSR = 360 degrees - Angle PQR - Angle QPS

Angle PSR = 360 degrees - 136 degrees - 136 degrees

Angle PSR = 88 degrees

Next, we use the fact that angles at the circumference of a circle subtended by the same arc are equal. Angle PSR and angle RPS both subtend the same arc, which is the arc between points P and R on the circle. Therefore, the two angles are equal.

Angle RPS = Angle PSR = 88 degrees

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Complete question is:

PQRS are points on a circle with the centre O PS is a diameter of the circle Angle PQR=136 Work out the size of angle RPS

Answer:

49.60

Step-by-step explanation:

she saves 12.40

Let's call the length of the rectangle "l" and the width "w". We know that the diagonal of the rectangle is 60 inches, and that it creates angles of 30 degrees and 60 degrees in the corners of the rectangle.

Using trigonometry, we can relate the sides of the rectangle to its diagonal and the angles formed by the diagonal. Specifically, we can use the sine and cosine functions to relate the sides to the angles:

sin(30) = w/60 and cos(30) = l/60

sin(60) = l/60 and cos(60) = w/60

Simplifying each equation, we get:

w = 30√3 and l = 30

Therefore, the area of the rectangle is:

Area = l x w = (30)(30√3) = 900√3 square inches.

Hence, the area of the rectangle in simplified radical form is 900√3 square inches.

Answer:

Median = 11

Mean = 19.8

Step-by-step explanation:

Arrange data points from small to large - Median will be the number in the middle

4 7 11 36 41

To get the mean add the numbers together and divide by the number of numbers there are.

The total is 99

5 numbers

99/5

= 19.8

Hope this helps

Answer: To answer this question, we need to know the number of individuals in each combination of Hogwarts elective and house. Without this information, we cannot calculate the expected chi-square test statistic value or the standard deviation.

Assuming we have this information, we can calculate the expected chi-square test statistic value as follows:

Set up a contingency table with the observed frequencies in each cell and the row and column totals.

Calculate the expected frequency for each cell by multiplying the row total by the column total and dividing by the total sample size.

Calculate the chi-square test statistic by summing the squared differences between the observed and expected frequencies for each cell and dividing by the expected frequency for each cell.

The formula for the standard deviation of the chi-square test statistic depends on the degrees of freedom, which is equal to the number of rows minus one multiplied by the number of columns minus one. Once we have calculated the expected chi-square test statistic value and degrees of freedom, we can calculate the standard deviation using the formula:

sqrt(2 * df)

where "df" is the degrees of freedom.

Without the necessary information about the frequencies, we cannot provide a numerical answer to this question.

Step-by-step explanation:

The amount of space in a gift box for earrings would typically be measured in cubic inches (C).

how to solve the question?

Cubic inches is a unit of volume that is commonly used to measure the capacity of small, enclosed spaces like boxes, containers, and packaging. It is defined as the volume of a cube that measures one inch on each side.

For a gift box designed to hold earrings, the volume of the box would need to be sufficient to accommodate the size of the earrings and any additional padding or decorative elements. Since earrings are small, the gift box would likely have a small volume, measured in cubic inches.

Other units of measurement, like square meters or yards, are used to measure the area of two-dimensional surfaces like floors, walls, or yards. Square centimeters are also a unit of area measurement, but they are much smaller than square meters or yards, and may be used to measure the surface area of small objects.

Cubic feet is a larger unit of volume measurement that may be used for larger boxes or containers, like shipping crates or storage bins. However, for a gift box designed specifically for earrings, cubic inches is likely the most appropriate unit of measurement.

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