Kathryn owns a video store. She rents games for 4 and moves for 4 She must rent at least 84 to make a profit She does not have anymore than 20 games Write and solve the system

The percentile score of 71 on test score is 27 and the score of victor is 71.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given, the teacher recorded unit 4 test scores from class.

The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.

A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.

The percentile rank of a score of 71 on the test is find by formula

\(R_{100} =\frac{100(N < )+\frac{1}{2} }{N}\)

=100×4+1/2(1)/15

=400+0.5/15

=400.5/15

=26.7=27th

Now we need to find the score of victor who has 60th percentile.

60=Score/15

score=71

Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.

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Answer:

(a) y =  3x + 2; (b) (0,2); (c) y = 3x - 8; (d) (2,-2)

(e) Area of ∆ABC = 30; (f) Area of ABCD = 40

Step-by-step explanation:

(a) Equation of AD

(i) Slope of AB

m₁ = (y₂ - y₁)/(x₂ - x₁) = (6 - 8)/(8 - 2)= -2/6 = -⅓

(ii) Slope of AD

m₂ = 3

(ii) y-intercept

y = 3x + b

8 = 3(2) + b= 6 + b

b = 2

The equation of AD is y = 3x + 2.

(b) Coordinates of D

The coordinates of D are (0,2).

(c) Equation of perpendicular bisector of AB

(i) Mid-points of AB

x = ½(x₂ + x₁) = ½(8 + 2) = ½(14) = 5

y = ½(y₂ + y₁) = ½(6 + 8) = ½(14) = 7

The coordinates of the mid-point are (5,7).

Slope = 3

y = mx + b

7 = 3(5) + b = 15 + b

b = 7 - 15 = -8

The equation of the perpendicular bisector is y = 3x - 8.

(d) Coordinates of C

C is at the intersection of BC and the perpendicular bisector of AD.

 y = 3x -    8

3y = 4x - 14

3y = 9x - 24

 0 = 5x - 10

5x = 10

 x =   2

 y = 3(2) - 8  = 6 - 8 = -2

The coordinates of C are (2,-2).

(e) Area of ∆ABC

A = ½bh = ½ × 10 × 6 = 30

(f) Area of ABCD

Area of ∆ACD = ½bh = ½ × 10 × 2 = 10

Area of ABCD = ∆ACD + ∆ABC =10 + 30 = 40

Answer:

Slope is -2/3

Step-by-step explanation:

rise/run

y/x

-1 - 2 = -3(x)

4 - 2 = 2(y)

2/-3 = -2/3

The margin at a 99% confidence level is approximately 3.446 inches.The 99% confidence interval is approximately (65.694, 72.586) inches.

To calculate the margin at a 99% confidence level, we need to use the formula:

Margin = Z * (Population Standard Deviation / √n),

where Z is the Z-score corresponding to the desired confidence level, n is the sample size, and the population standard deviation is known.

In this case, we have a sample size of 7 (n = 7) and a population standard deviation of 3 inches. The Z-score for a 99% confidence level is approximately 2.576 (obtained from a standard normal distribution table).

Substituting these values into the formula, we get:

Margin = 2.576 * (3 / √7) ≈ 3.446.

Therefore, the margin at a 99% confidence level is approximately 3.446 inches.

To calculate the 99% confidence interval, we use the formula:

Confidence Interval = (Sample Mean - Margin, Sample Mean + Margin).

Given the sample heights of 75, 70, 65, 69, 75, 69, and 64, we can calculate the sample mean:

Sample Mean = (75 + 70 + 65 + 69 + 75 + 69 + 64) / 7 ≈ 69.14.

Substituting the sample mean and the margin into the confidence interval formula, we obtain:

Confidence Interval = (69.14 - 3.446, 69.14 + 3.446) ≈ (65.694, 72.586).

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The measure of angle ZCBD is 90°. Therefore, the correct option is J. 90.

To find the measure of angle ZCBD, we need to examine the given information.

From the figure, we know that angle CDE is 155°.

Since the opposite angles of a rectangle are congruent, angle BCD is also 155°.

In a rectangle, the sum of the interior angles at a vertex is always 90°.

Therefore, angle CBD is 90°.

Hence, the measure of angle ZCBD is 90°.

Therefore, the correct option is J. 90.

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The quotient of (x³+2 x²-x+6) / (x+3) is (B) x²-x+2.

So, find the quotient of (x³+2 x²-x+6) / (x+3) using the Polynomial long division method:

Therefore, the quotient of (x³+2 x²-x+6) / (x+3) is (B) x²-x+2.

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Answer:

5.5

22/4=5.5

5.5 Feet or inches

Answer:

each section will be 5.5ft long. 22/4=5.5

Step-by-step explanation:

The equation of the parabola that intersects the x-axis at points (-1, 0) and (3,0) is y = 0.

Given that a parabola intersects the x-axis at points (-1, 0) and (3,0).We know that, when a parabola intersects the x-axis, the y-coordinate of the point on the parabola is 0. Therefore, the two x-intercepts tell us two points that are on the parabola.Thus the vertex is given by:Vertex is the midpoint of these x-intercepts=(x_1+x_2)/2=(-1+3)/2=1The vertex is the point (1,0).Since the vertex is at (1,0) and the parabola intersects the x-axis at (-1,0) and (3,0), the axis of symmetry is the vertical line passing through the vertex, which is x=1.We also know that the parabola opens upwards because it intersects the x-axis at two points.To find the equation of the parabola, we can use the vertex form:y = a(x - h)^2 + kwhere (h, k) is the vertex and a is a constant that determines how quickly the parabola opens up or down.We have h=1 and k=0.Substituting in the x and y values of one of the x-intercepts, we get:0 = a(-1 - 1)^2 + 0Simplifying, we get:4a = 0a = 0Substituting in the x and y values of the other x-intercept, we get:0 = a(3 - 1)^2 + 0Simplifying, we get:4a = 0a = 0Since a = 0, the equation of the parabola is:y = 0(x - 1)^2 + 0Simplifying, we get:y = 0Hence the equation of the parabola that intersects the x-axis at points (-1, 0) and (3,0) is y = 0.

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What is the standard form of the parabola?

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The percentage of students scoring 84 or more in the exam is 99.18%.

Given, Mean test score = 72,

Standard deviation = 5.

We are supposed to find the percentage of students scoring 84 or more in the exam.

To find the percentage of students scoring 84 or more in the exam, we will use the following steps:

First, we need to find the z-score associated with 84.

Let us assume that z is the z-score corresponding to the value 84, then;

z = (84 - 72) / 5 = 2.4

Now, we have the value of z, we can find the percentage of students scoring 84 or more in the exam using the normal distribution table.

The percentage is the area under the normal distribution curve to the right of the z-score.

To find the area using the normal distribution table, we need to look for the value 2.4 in the z-table. Since 2.4 is not exactly listed in the z-table, we will use the value for 2.4 closest to it.

Using the z-table, the value closest to 2.4 is 0.9918.

Therefore, the percentage of students scoring 84 or more in the exam is;

P(Z > 2.4) = 0.9918 × 100 = 99.18%.

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A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox television takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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Answer:

Assuming that the two line that look like they are parallel are parallel:

x = 5

<(20x) = 100

<(16x) = 80

Step-by-step explanation:

The 2 angles added together equal 180

20x  + 16x = 180  Combine like terms

36x = 180  Divide both sides by 36

x = 5

Substitute 5 for x

20x

20(5) = 100

16x

16(5) = 80

The slope in the context of predicting verbal SAT scores based on math SAT scores indicates the change in the verbal score for each unit increase in the math score.

In this survey of statistics undergraduate students at Prosperity University, the slope represents the rate of change in the verbal SAT score for every one-point increase in the math SAT score. A positive slope suggests that as the math score increases, the verbal score also tends to increase. The magnitude of the slope indicates the strength of the relationship between the two variables. A larger slope indicates a stronger positive association, meaning that a one-point increase in the math score is associated with a larger increase in the verbal score. Conversely, a negative slope would imply an inverse relationship, where an increase in the math score is associated with a decrease in the verbal score.

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What is the interpretation of the slope in the context of predicting the verbal SAT score based on the math SAT score, according to the survey conducted among undergraduate students majoring in statistics at Prosperity University?

Answer:

The circumference of the following circle is 9π (around 28.274)

Step-by-step explanation:

The circumference can be found by using the following formula, where d is the diameter of the circle...

dπ = 9π ≈ 28.274

Answer:

y = 1/6x + 5

Step-by-step explanation:

-x + 6y = 30

6y = x + 30

y = 1/6x + 5

The population density of Philadelphia is approximately 11,761.76 people per square mile, while the population density of Pottstown is approximately 4,672.16 people per square mile.

To compare the densities of Philadelphia and Pottstown, we need to calculate the population density for each city. Population density is typically measured as the number of individuals per unit area.

For Philadelphia:

Population = 1,579,000

Land area = 134.28 sq miles

Population density = Population / Land area

Population density = 1,579,000 / 134.28

Population density \(^\sim_\sim\) 11,761.76 people per square mile

For Pottstown:

Population = 22,670

Land area = 4.85 sq miles

Population density = Population / Land area

Population density = 22,670 / 4.85

Population density \(^\sim_\sim\) 4,672.16 people per square mile

Therefore, the population density of Philadelphia is approximately 11,761.76 people per square mile, while the population density of Pottstown is approximately 4,672.16 people per square mile.

Comparing the two, we can see that Philadelphia has a higher population density compared to Pottstown.

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The numbers of ways that the director fill these positions is  504 ways.

There are a few different ways to approach this problem, but one possible method is to use the combination formula.

To fill the position of soprano, the director has 9 choices. After selecting one soprano, the director is left with 8 singers to choose from for the alto position. Then, the director has 7 singers to choose from for the tenor position.

So, the total number of ways the director can fill these positions is:

9 × 8 × 7

= 504 ways.

Alternatively, One can also use the permutation formula to solve the question. The formula of permutation is (n!/(r!(n-r)!)), where n is the total number of items to choose from, and r is the number of items to be chosen.

For this case n is 9, and r is 3, so the permutation would be:

(9!/(3!(9-3)!)

= (987)/(321)

= 504

Therefore, In both cases, the answer is 504 ways.

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Answer:

The volume of the cube is 21952.

Step-by-step explanation:

V = L x W x H

because a cube's sides are all the same, the length, width, and height are also the same. So we use the formula:

V= S^3

(S standing for side)

we know the height is 28 and as all sides measure the same we use the equation:

V= 28^3

28^3 = 21952

So, V= 21952

Answer:

This problem has been solved! See the answer. Suppose f and g are differentiable functions with the values shown in the table below. For each of the following functions h, find h ' (6). x. f ( x) g ( x) f ' ( x) g ' ( x)v

Step-by-step explanation:

The equation of the amount to be paid by anyone using the ride in slope intercept form is; y = 0.5x + 10

The general form of the equation of a Line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

Now, we are told that;

Amount charge by Winter Wonderland per child = $0.50

We are told that there is a separate entrance fee.

Amount of times todd sled down the hill = 16 times

Amount paid by todd = $18

Thus, using the slope intercept form, we have;

18 = 0.5(16) + b

18 = 8 + b

b = 10

Thus, the equation of this amount to be paid in slope intercept form is;

y = 0.5x + 10

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Answer:

75°

Step-by-step explanation:

I attached a diagram to try and help visualize this.

We are trying to find an unknown angle, x, on this line.

To start, we know we have a 162° angle. The question is a little weird, but it is essentially asking how big the right side would be if the left side is 87°.

simply take 162, and subtract 87. That would be the angle between Malcolm Way and Park Road.

162 - 87 = 75.

So, the angle between Malcolm Way and Park Road is 75°.

Hope this helps!

Answer:

11.0

Step-by-step explanation:

Circumfrence = 2 x pi x r.

making radius, r the subject of relation, you.get 11.003184713

Answer:

Hey!

Your answer is 11cm!

Step-by-step explanation:

So to get the radius from the Circumference we need both the Circumference and the value of pi...3.14

Radius = \(\frac{C}{2\pi }\) ... (that's the formula)

WE SUBSTITUTE IN:

Radius = 69.1/2 x 3.14

69.1/6.28

This equals = 10.99760656765

BUT 11cm when you round it to the next whole number or 2sf

Answer:

B, no, yes, no, no, no, 225

Step-by-step explanation:

Answer:

x=100

Step-by-step explanation:

50/x=10/20 and 10/50=20/x

50/x=10/20

Cross multiplication

50*20=x*10

1000=10x

x=1000/10

x=100

Check:

50/100=

Divide by 5

10/20

10/50=20/x

Cross multiplication

10*x=50*20

10x=1000

x=1000/10

x=100

They are the same because the fraction that has the unknown both have the same ratio

Answer:

The anser is d edge 2020 lol

Step-by-step explanation:

Answer:

False.

Step-by-step explanation:

If you multiply both sides by 1/2, you will get 1/4 at the right side.

So the correct way, to solve h, you have to divide both sides by 1/2.

The probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.

There cannot be a positive or negative association between a categorical and a numerical variable. here the delivery method is a categorical variable.

We cannot determine what the total number for any of the delivery methods was as we are only given the conditional probability of whether they were returned or not.

We can clearly see that the probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.

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Given, b = 17.23 cm, c = 10.86 cm and B = 101°15' (degree and minute)In a triangle ABC, the angle sum property of a triangle states that the sum of all angles in a triangle is 180°. Mathematically, ∠A + ∠B + ∠C = 180°In ΔABC, let A = aApplying the sine law, we have,b/sinB = c/sinC = a/sinA⇒ 17.23/sin101°15' = 10.86/sinC = a/sinAa/sinA = 17.23/sin101°15' = 16.5Using sine formula:

sinA = a/sinAA = sin⁻¹(a/sinA)A = sin⁻¹(16.5/sinA)Putting the values, A = sin⁻¹(16.5/sinA)A = sin⁻¹(16.5/sin⁡(180 - B - C))Now, using the angle sum property of a triangle, we have∠A + ∠B + ∠C = 180°We know that ∠B = 101°15' and now we can substitute the valuesA + 101°15' + ∠C = 180°A + ∠C = 78°45'...(1)Now, using the sine law,sinA/a = sinC/csinC = csinA/a= 10.86 sinA/16.5 (since a = 16.5 from above calculation)sinC = 10.86sinA/16.5sinC = 0.523sinASubstituting the value of sinC in equation (1)A + sin⁻¹(0.523sinA) = 78°45'⇒ sin⁻¹(0.523sinA) = 78°45' - A (2)We will solve equation (2) using graphical method by plotting the graphs of two functions f(A) = A + sin⁻¹(0.523sinA) and g(A) = 78°45' - A and finding the point of using the Newton Raphson method.The value of A at the point of intersection is the solution of the equation.Now, applying Newton Raphson method to f(A) = A + sin⁻¹(0.523sinA) - (78°45' - A), we getA1 = 54.6583°, f(A1) = -0.0005A2 = 57.6975°, f(A2) = 0.0019A3 = 57.7007°, f(A3) = 0.0000Therefore, A = 57.7007°Now that we know A, we can use the sine law to calculate C,sinC/c = sinA/asinc = csinA/a = 10.86 * sin(57.7007°)/16.5sinc = 0.4869C = sin⁻¹(sinc) = 29.0139°Now, using the angle sum property of a triangle∠A + ∠B + ∠C = 180°∠A + 101°15' + 29.0139° = 180°∠A = 49.9851°a/sinA = 16.5/sin49.9851°a = 12.012 cmTherefore, the values of a, A and C in triangle ABC are 12.012 cm, 57.7007° and 29.0139° respectively.

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The values of a, A and C in triangle ABC are:

a ≈ 12.0764cm,

A ≈ 78°45',

C ≈ 48°20'ora ≈ 18.2388cm,

A ≈ 101°15',

C ≈ 44°35'

In a triangle ABC,

b=17.23cm,

c=10.86cm and

B=101°15'.

We need to calculate the values of a, A and C in triangle ABC.
Given that b=17.23cm,

c=10.86cm and

B=101°15'

In any triangle ABC, a/sin(A) = b/sin(B) = c/sin(C)

Now, we have

b=17.23cm,

c=10.86cm and

B=101°15'.

Using the formula, we geta/sin(A) = b/sin(B)

⇒a/sin(A) = 17.23/sin(101°15')

Putting values, we geta/sin(A) = 17.23/1.7377

⇒a/sin(A) = 9.9187

Similarly, we geta/sin(A) = c/sin(C)

⇒a/sin(A) = 10.86/sin(C)

Now, we know that ∠A + ∠B + ∠C = 180°

In ΔABC, ∠B=101°15',

so ∠A and ∠C can be calculated as follows:∠A + ∠C = 180° - ∠B

⇒∠A + ∠C = 180° - 101°15'

⇒∠A + ∠C = 78°45'

Now, we have two equations:a/sin(A) = 9.9187a/sin(A) = 10.86/sin(C)

Using these two equations, we can solve for the values of a and A.

a/sin(A) = 9.9187

⇒a = 9.9187 sin(A)

Similarly,a/sin(A) = 10.86/sin(C)

⇒a = 10.86 sin(A)/sin(C)

We can equate these two values of a:9.9187 sin(A) = 10.86 sin(A)/sin(C)

⇒sin(C) = 10.86/9.9187⋅sin(A)

⇒sin(C) = 1.0948⋅sin(A)

Now, we know that sin(A) = sin(180°-A)

So, we can have two solutions for A:1. sin(A) = sin(78°45') = 0.9762

Using this value in the equation sin(C) = 1.0948⋅sin(A), we get sin(C) = 1.0683

Using the formula a/sin(A) = b/sin(B) = c/sin(C),

we geta = 12.0764cm (approx)C = 48°20' (approx)2. sin(A) = sin(180°-78°45') = sin(101°15') = 0.9837

Using this value in the equation sin(C) = 1.0948⋅sin(A), we get sin(C) = 1.0764

Using the formula a/sin(A) = b/sin(B) = c/sin(C),

we geta = 18.2388cm (approx)C = 44°35' (approx)

Hence, the values of a, A and C in triangle ABC are:

a ≈ 12.0764cm,

A ≈ 78°45',

C ≈ 48°20'ora ≈ 18.2388cm,

A ≈ 101°15',

C ≈ 44°35'

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The probability is 0.0793 that the mean depth in 15 randomly selected Medium Ground Finches is at least 10 millimeters

From the question,

Mean μ = 9.6 millimeters

Standard deviation σ = 1.1 millimeter

We have to determine the probability that the mean depth in 15 randomly selected Medium Ground Finches is at least 10 millimeters.

So n = 15

σ(x) = σ/√n

σ(x) = 1.1/√15

σ(x) = 0.2840

So the probability that the mean depth in 15 randomly selected Medium Ground Finches is at least 10 millimeters is:

P(x ≥ 10) = 1 - P(x ≤ 10)

P(x ≥ 10) = 1 - P[(x - μ)/σ(x) ≤ (10 - 9.6)/0.2840]

P(x ≥ 10) = 1 - P[z ≤ 0.4/0.2840]

P(x ≥ 10) = 1 - P[z ≤ 1.41]

P(x ≥ 10) = 1 - 0.9207

P(x ≥ 10) = 0.0793

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When there were 375 men and 475 women, the simple ratio of men to women clients was 15/19.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Here,

Total customers=850

Total number of men=375

Total number of women,

=850-375

=475

The ratio of men to women customers,

=375/475

Divide both terms by the GCF 25,

375 ÷ 25 = 15

475 ÷ 25 = 19

=15/19

The ratio of men to women customers in its simplest form is 15/19 when there were 375 men and 475 women.

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Answer:

Increases from points 0x,-6y to 2x,-3y.

Step-by-step explanation: