Ken made a scale drawing of a neighborhood park. He used the scale 2 inches : 1 yard. The actual width of a soccer field in the park is 58 yards. How wide is the field in the drawing?

The probability that a randomly selected student's age is more than 18 years old but no more than 21 years old is 0.57.

What is a continuous random variable's probability?

Continuous random variables are defined as having an infinite number of possible values. A continuous random variable hence has no probability of having an accurate value.

a) In order to create a probability distribution, all potential values of the random variable must be listed along with the related probabilities. We may get the relative frequency (or probability) for each value of the random variable from the above frequency distribution:

Age Frequency Probability

16         3              0.03

17         5              0.05

18        10              0.10

19        15              0.15

20       20             0.20

21        22             0.22

22       17               0.17

Total   92              1.00

b) We can use a histogram to see the probability distribution. The likelihood is represented by the vertical axis, while the age is represented by the horizontal axis. The height of each bar in the histogram should represent the likelihood for that age, with bars for each age value.

With a peak at age 20, the distribution's shape looks to be roughly symmetrical.

c) To get the likelihood that a student chosen at random is under 20 years old, we must add the probabilities for the ages 16, 17, 18, and 19:

P(age < 20) = P(age = 16) + P(age = 17) + P(age = 18) + P(age = 19)

= 0.03+0.05+0.10+0.15

= 0.33

Consequently, there is a 0.33 percent chance that a randomly chosen student is under 20 years old.

d) To determine the likelihood that a randomly chosen student is older than 18 but not older than 21, we must add the probabilities for the ages 19, 20, and 21:

P(18 < age ≤ 21) = P(age = 19) + P(age = 20) + P(age = 21)

= 0.15 + 0.20 + 0.22

= 0.57

As a result, there is a 0.57 percent chance that a randomly chosen student will be older than 18 but not older than 21.

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The skater's total score would be 58 points (7.25 x 8 = 58).

Just dividing the total number of values in a data set by the sum of all of the values yields it. A frequency table of data or raw data can both be used for the calculation.

The following equation can be used to determine each skater's overall score, s, assuming that they each receive evaluations from eight judges and have a mean score of 7.25 points:

s = 7.25 x 8

The total score is determined by multiplying the average score by the quantity of judges in this equation. In this instance, the skater would have earned 58 points overall (7.25 x 8 = 58).

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In a skating competition each skater receives scores from eight judges a skater has a mean (average) of 7.25 points. Write an equation to find the skaters total score?

a. 7.25 × 8

b. 7.25⁸

c. 7.25 - 8

d. 7.25/8

Algebraic expressions are useful for solving different and complex equations in mathematics, as well as for modelling real-life situations such as revenue, cost, inference, etc

The algebraic expression is: [tex]6x - 9[/tex].

To represent the sentence as an algebraic expression, we can follow these steps: Identify the variable. In this case, “a number” is x. Identify the operation. In this case, “less than” means subtraction and “times” means multiplication.

An algebraic expression is an expression that contains variables, constants and mathematical operations. Algebraic expressions are useful because they can help us solve different and complex equations.

For example, if you want to calculate the area of a rectangle with length x and width y, you can use the algebraic expression xy to represent the area.

Write the expression using the order of operations. In this case, we need to multiply six by x first, then subtract nine from the result.

Therefore, The algebraic expression is: [tex]6x - 9[/tex]

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The matching word are as follows:- center of dilation - C,corresponding angles - D,dilation - E,scale factor (of a dilation) - A,similar polygons - B respectively.

Corresponding angles are a pair of angles that have the same relative position at the intersection of two lines when one line is crossed by a transversal.

They are located in corresponding (matching) positions in congruent or similar figures, and are congruent if the figures are similar.

center of dilation: C.The fixed point that is parallel to each point on the pre-image and the corresponding point on the picture during a dilatation

corresponding angles: D.a pair of angles in two congruent or similar figures that are in the same relative position

dilation: E. The transformation in which each point on the image lies on the same line as the corresponding point on pre-image and a fixed point called the center of dilation.

scale factor (of a dilation): in a dilation, the constant  rate between the distance from the center of dilation and a point on the image and the distance from the center of dilation and the  matching point on thepre-image

similar polygons: B.two or  further polygons in which corresponding angles are  harmonious and the lengths of corresponding sides are in proportion.

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Answer:

27 cups of oats

Step-by-step explanation:

23
+ 4=27

Step-by-step explanation:

Area of the trapezoid = height x average of bases

                 area = 4 x (8+13)/2) = 42 in^2

Area of triangle  = 1/2 base * height   = 1/2 (13-8) * 4 = 10 in^2

Answer:

0.9973 or 364/365

Step-by-step explanation:

Assuming that every day of the year is equally likely to be someone's birthday, the probability that a randomly selected person has a birthday on the 1st day of the month is 1/365, since there are 365 possible birthdays in a year.

Therefore, the probability that a randomly selected person does not have a birthday on the 1st day of the month is:

P(not on 1st day) = 1 - P(on 1st day)

P(not on 1st day) = 1 - 1/365

P(not on 1st day) = 364/365

So, the probability that a randomly selected person does not have a birthday on the 1st day of the month is 364/365 or approximately 0.9973.

Answer: Sally will earn $4,830.00 in interest over 7 years.

Step-by-step explanation:

If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:

I = P * r * t

where:

I = the interest earned

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the time period, in years

In this case, we have:

P = $9,000 (the initial deposit)

r = 7% = 0.07 (the annual interest rate)

t = 7 (the number of years)

So, plugging in the values:

I = $9,000 * 0.07 * 7

I = $4,830.00

Therefore, Sally will earn $4,830.00 in interest over 7 years.

Step-by-step explanation:

SA = 2πrh + 2πr²

where;

π = 3.14

r = 8

h = 11

Slotting in those parameters, we have;

= (2 x 3 x 8 x 11) + ( 2 x 3 x 8²)

= 528 + 384

= 912 inches²

To the nearest 100th, answer becomes 900inches²

Answer:

585 miles

Step-by-step explanation:

845 miles ÷ 13 hours = 65 mph

645 mph * 9 hours = 585 miles

The sum οf the twο expressiοn is  [tex]\rm 3x^5 \time y^6(5\sqrt{5y} + 3\sqrt{3y}).[/tex]

An algebraic expressiοn is a mathematical phrase that cοntains variables, cοnstants, and mathematical οperatiοns.

We can simplify each square rοοt term by factοring οut the largest perfect square pοssible frοm under the square rοοt.

Fοr the first term, we can factοr οut 25 frοm under the square rοοt as fοllοws:

[tex]\rm 3\sqrt{(125x^{10}y^{13})} = 3\sqrt{(255x^{10}y^{12}y)} = 35x^{5}y^{6} \times \sqrt{(5y)}[/tex]

Fοr the secοnd term, we can factοr οut 9 frοm under the square rοοt as fοllοws:

[tex]\rm 3\sqrt{(27x^{10}y^{13}) }= 3\sqrt{(93x^{10}y^{12}y)} = 33x^5y^6 \times \sqrt{(3y)[/tex]

Therefοre, the sum οf the twο terms is:

[tex]\rm 3\sqrt{(125x^{10}y^{13)}}+ 3\sqrt{(27x^{10}y^{13} )}= 35x^5y^6\sqrt{(5y)} + 33x^5y^6\sqrt{(3y)}[/tex]

Simplifying further, we can factοr οut 3x^5y^6 tο get:

=  [tex]\rm 3x^5 \time y^6(5\sqrt{5y} + 3\sqrt{3y}).[/tex]

Therefore, the sum of the two terms is [tex]\rm 3x^5 \time y^6(5\sqrt{5y} + 3\sqrt{3y}).[/tex]

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Therefore, the measure of the intercepted arc by the inscribed angle of 61 degrees is 122 degrees.

A circle is a closed shape in geometry that is defined as the set of all points in a plane that are at a fixed distance from a given point, called the center of the circle. The distance between any point on the circle and the center is called the radius of the circle.

Given by the question.

In a circle, an inscribed angle is an angle formed by two chords of the circle that have a common endpoint on the circle. The measure of an inscribed angle is half the measure of its intercepted arc.

Let's call the intercepted arc by the inscribed angle "x". Then, the measure of the inscribed angle is 61 degrees, and we can use the formula mentioned above to find the measure of the intercepted arc:

61 = x/2

To solve for x, we can multiply both sides of the equation by 2:

122 = x

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Answer:

To find the interest rate, we can use the formula for simple interest:

I = Prt

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate

t = Time

We are given that P = $100, t = 3 years, and I = $15. Substituting these values, we get:

15 = 100 * r * 3

Solving for r, we get:

r = 15 / (100 * 3) = 0.05

Therefore, the interest rate on the savings account is 5%.

Mr. Brust is standing at a height of approximately 90.6 feet in the tree. When they shoot him, he will fall from this height.

Let's break down the problem and solve it step by step.

First, we'll find the height from which Mr. Brust falls, and then we'll find the total distance he falls considering the tree's height and the height of the shed.

Find the height of the tree where Mr. Brust is standing:

We can use the tangent function to find the height of the tree above the shed where Mr. Brust is hiding.

tan(θ) = opposite/adjacent

We know the angle of elevation (θ) is 65°, and the tree is 40 feet in front of the shed. So, we have:

tan(65°) = height_above_shed / 40 ft

height_above_shed = 40 ft * tan(65°)

Using a calculator, we find:

height_above_shed ≈ 40 ft * 2.14 ≈ 85.6 ft

Find the total height of the tree where Mr. Brust is standing:

Since Mr. Kelly and Mr. Sullivan are 5 feet off the ground, we need to add this height to the height_above_shed we just calculated:

total_height = height_above_shed + height_of_shed

total_height = 85.6 ft + 5 ft = 90.6 ft

So, Mr. Brust is standing at a height of approximately 90.6 feet in the tree. When they shoot him, he will fall from this height.

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The statements that are correct are:

m∠ACB = 44° (Option B)

m∡AC = 156° (Option C)

A) m∠ACB = 44° is correct because the Circle Theorem indicates that the angle at the center is twice or double the one at the circumference.

Since, the one at the center is already 88°, thus, the one at the angle at the circumference = 88°/2 = 44°

Hence, m∠ACB = 44° (Option B) is correct.


B) m∡AC = 156° (Option C)

To get this, we need to state,

360° - 116° - 88° = 156° (Option C)

C) m∡ BAC should be determined using Alternate Segment Theorem.

According to this theorem which states that the angle that lies between a tangent c and a chord is equal to the angle subtended by the same chord in the alternate segment,

∠BAC is supposed to be equal to ∠GAC - ∠GAB

That is:

∠BAC = 90° - 44°
∠BAC = 46°

However, this is questionable because, we have proven that ∠BAO = (180-88)/2 = 46° (Isoceles Δ BOA created by shared Radii)

Thus,

∠BAC = 46°  cannot be equal to ∠BAO.

Thus, the only right answers are:

Option B and

Option C.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See the attached image.

Answer: what shape?

Step-by-step explanation:

More info please

469

do 16.75 x 28 which will equal to 469

Part A: The slope of line p is 4, so when multiplied by the dilation factor of 2, the slope of line q is 8.

Part B: The y-intercept of line p is (0, 4). When multiplied by the dilation factor of 2, the y-intercept of line q is (0, 8).

A slope is a measure of how steep a line is when plotted on a graph. It is calculated by finding the ratio of the "rise" (vertical change) over the "run" (horizontal change). Slopes can be positive, negative, zero, or undefined. A positive slope is one where the line rises from left to right and a negative slope is one where the line falls from left to right.

Part A: The slope of line q can be determined by calculating the slope of line p and multiplying it by the dilation factor. The slope of line p is 4, so when multiplied by the dilation factor of 2, the slope of line q is 8.

Part B: The y-intercept of line q can be determined by calculating the y-intercept of line p and adjusting it for the dilation factor. The y-intercept of line p is (0, 4). When multiplied by the dilation factor of 2, the y-intercept of line q is (0, 8).

Line segment P'Q is created by the two points (8, 5) and (12, 8). Using the distance formula, the length of line segment P'Q can be determined. The formula for the distance between two points is (x2-x1)² + (y2-y1)². Substituting the coordinates for points P and Q into the formula, the length of line segment P'Q is calculated as (12-8)² + (8-5)²= 9. Therefore, the length of line segment P'Q is 9 units.

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Answer:

421.875 ft³

Step-by-step explanation:

Since the length, width, and heigh are equal, this is a cube.

V = s³

V = (7.5 ft)³

V = 421.875 ft³

Answer:421.875 ft^3

Step-by-step explanation:

Answer:

Step-by-step explanation: 12 / 3 = 4, so php100 x 4 = Php400

Answer:

The question you provided is a math problem involving fractions, specifically solving for an unknown quantity using a proportion. Here is how you can solve it:

1/15 = 5/8

To solve for the unknown quantity, you can use cross-multiplication, which means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa:

1 * 8 = 15 * 5

Simplifying this equation, we get:

8 = 75

This is a contradiction, so the given equation has no solution. Therefore, none of the answer choices (A, B, C, D) are correct.

I hope this helps! If you have any further questions, feel free to ask.

The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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Answer:

1. 90 students x (2/9) = 20 sixth graders

2. 27 students x (2/9) = 6 sixth graders

3. 42 sixth graders x (9/2) = 189 students

One artist not working scenario helps determine domain and range. It shows the max hours one needs to work when the other is not working. C' represents Claude's work hours, and P represents Philipe's work hours on the vertical axis.

The scenario where one of the artists is not working is helpful in finding the domain and range of their work hours. This scenario shows the maximum number of hours one artist would need to work when the other artist is not working. For instance, if Philipe is not working, Claude would have to work for 15 hours (60 caricatures ÷ 4 caricatures per hour) to meet their goal. Similarly, if Claude is not working, Philipe would have to work for 20 hours (60 caricatures ÷ 3 caricatures per hour) to meet their goal. On the horizontal axis, we can represent the hours that Claude works (C'), and on the vertical axis, we can represent the hours that Philipe works (P).

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Answer:

correct answer

c. 0.07 × $350

The required of 0.014 and 100,000  product is 1400.

The object being sold is referred to as a product. A service or an object both qualify as products. It could take on a physical, virtual, or cyber shape. Every product has an expense associated with it, and each one has a price. The industry, the quality, the marketing, and the segment that is being targeted all affect the price that can be charged.

We have to numbers

0.014 and 100000

Then;

0.014( 100000)

= 1400

Thus, required product is 1400.

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Since the function is already in standard form (ax^2 + bx + c form) you don't have to change anything and simply rewrite it.

For the vertex, if you have a quadratic function in standard form -b/2a is the x value of the vertex.

-b/2a = -4/(2(2)) = -1

Since we now know the x-value of the vertex we can plug it into the function to find the corresponding y-value.

h(-1) = 2(-1)^2 + 4(-1) - 10 = -12

So, the vertex is at (-1,-12)

The value of x such that x - 4 and 2x + 1 are angles on a line is 61

x - 4 and 2x + 1 are angles on a line.

Using the theorem of sum of angles on a line that states that:

When two angles are on a line, they add up to 180 degrees.

So we have:

x - 4 + 2x + 1 = 180

Simplifying and solving for x:

3x - 3 = 180

So, we have

3x = 183

Divide both sides by 3

x = 61

Therefore, x = 61 is the value that makes x - 4 and 2x + 1 angles on a line.

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