Please help me with this question

The best description of the distribution of points earned is E) Skewed to the right with a gap.

To determine the best description of the distribution of points earned, we need to look at the shape of the distribution.

The shape of the distribution can be described by the presence or absence of peaks, gaps, and tails, as well as whether the distribution is symmetric or skewed.The term "bimodal" means that the distribution has two peaks, while "skewed to the right" means that the tail of the distribution is longer on the right side.

Based on the answer choices given, the best description of the distribution of points earned is E) Skewed to the right with a gap, since it describes a distribution that has a long tail on the right side and a gap between the two groups of scores.

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The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

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Answer:

sec(π/6 - x) = R.H.S = 2/(√3cosx + sinx)  = L.H.S.

Step-by-step explanation:

sec(π/6 - x) = 1/cos(π/6 - x)

Using compound angle formula,

cos(A - B) = cosAcosB + sinAsinB where A = π/6 and B = x.

So, cos(π/6 - x) = cos(π/6)cosx + sin(π/6)sinx , cosπ/6 = √3/2 and sinπ/6 = 1/2

cos(π/6 - x) = cosπ/6cosx + sinπ/6sinx = (√3/2)cosx + (1/2)sinx

sec(π/6 - x) = 1/cos(π/6 - x)

= 1/(√3/2)cosx + (1/2)sinx = 2/(√3cosx + sinx)

= L.H.S

So, sec(π/6 - x) = R.H.S = 2/(√3cosx + sinx)  = L.H.S

A principal gathered data about the distance in miles that his teachers and bus drivers live from the school. then, the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.

Interquartile Range:

In descriptive statistics, the interquartile range (IQR) is a measure of the statistical distribution, the distribution of data. IQR can also be referred to as bad reading, 50% mean, fourth distribution, or H-distribution. It is defined as the difference between the 75th and 25th percentile of the data. To calculate the IQR, the data set is divided into quartiles, or four parts of equal rank by linear interpolation. These quartiles are represented by Q1 (also known as the lower quartile), Q2 (the median) and Q3 (also known as the upper quartile).

The lower quartile is the 25th percentile and the upper quartile is the 75th percentile, so IQR = Q3 − Q1

Basically, the interquartile range represents the width or “spread” of the collection. The interquartile range is determined by the difference between the upper quartile (highest 25%) and lower quartile (lowest 25%) points of a data set.

From the figure, we can find:

The interquartile range of the bus driver is: 20 -10 = 10

The interquartile range of the teacher is: 30 -15 = 15

Therefore,

the interval interquartile distance is bus The driver's distance was 5 miles less than the interquartile range of the teacher's distance.

Complete Question:

A principal gathered data about the distance in miles that his teachers and bus drivers live from the school .The box plots below show these data.

(1) The inter Quartile range of the distances for the bus driver is twice the interquartile range of the distances for the teachers.

(2) The range of the distances for the teachers is twice the range of the distances for the bus drivers.

(3) the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.

(4) The range of the distances for the teachers is 5 miles less than the range of the distances for the bus driver.

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Answer: C. The interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.

The three solutions of the equation y = -2x - 1 are (–2, 3), (1, –3), and (2, –4).

To find the solutions, we substitute different values of x into the equation and solve for y.

For the first solution, when x is –2, we have y = -2(-2) - 1 = 3. Therefore, the first solution is (-2, 3).

For the second solution, when x is 1, we have y = -2(1) - 1 = -3. Thus, the second solution is (1, -3).

For the third solution, when x is 2, we have y = -2(2) - 1 = -4. Hence, the third solution is (2, -4).

These three points satisfy the equation y = -2x - 1, and therefore, they are the solutions of the equation. They represent coordinate pairs (x, y) where the equation holds true.

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The value of the angle ∠ABD is found to be 35°.

An angle is a figure in Plane Geometry consisting of two rays or lines that have a common endpoint.

Now, as per the given question;

The ∠ABC comprises of two angles ∠ABD and ∠DBC.

Thus, it can be written as;

∠ABC = ∠ABD + ∠DBC

We have to estimate the value of the angle ∠ABD.

Thus,

Rearranging the angles;

∠ABD = ∠ABC - ∠DBC

The values of angles are given;

∠ABC = 118° and ∠DBC = 83°.

Substituting the values;

∠ABD = 118° - 83°

∠ABD = 35°

Therefore, the value of the is ∠ABD obtained as 35°.

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Answer:

1. 45

2. 105

3. 95

4. 85

Step-by-step explanation:

For problems 1 and 4:

Consecutive angles are supplementary in a parallelogram, which means they equal 180.

180 - 135 = 45

180 - 95 = 85

For problems 2 and 3:

Opposite angles are congruent or equal each other in a parallelogram,

Answer:

3/4 a pint

Step-by-step explanation:

1/4 + 2/4 = 3/4

Angle of observation is changing at a rate of -1/15 radians per second (or about -3.8 degrees per second).

We can solve this problem using the concept of related rates. Let's call the distance between the person and the hot air balloon "d" and the height of the hot air balloon "h". We are given that:

d = 400 feet (constant)

dh/dt = -20 ft/sec (because the hot air balloon is coming down)

We want to find dθ/dt, the rate at which the angle of observation is changing.

We can start by drawing a right triangle with the hot air balloon at the top, the person at the bottom left, and the ground at the bottom right. The angle of observation is the angle at the person's location between the ground and the line connecting the person to the hot air balloon:

perl

Copy code

         /|

        / |

     h /  | d

      /   |

     /θ   |

    /_____|

       d

We can use the tangent function to relate h, d, and θ:

tan(θ) = h/d

Taking the derivative of both sides with respect to time t, we get:

sec²(θ) dθ/dt = (dh/dt)/d - h/(d²) (dd/dt)

Plugging in the values we know, we get:

sec²(θ) dθ/dt = (-20)/400 - h/(400²) (0)

When the hot air balloon is 300 feet above the ground, we can use the Pythagorean theorem to find h:

h² + d² = (400)²

h² + (300)² = (400)²

h = sqrt(400² - 300²) = 200 sqrt(2)

So, we can plug in d = 400, h = 200 sqrt(2), and dh/dt = -20 into our equation:

sec²(θ) dθ/dt = (-20)/400 - (200 sqrt(2))/(400²) (0)

sec²(θ) dθ/dt = -1/20

To solve for dθ/dt, we need to find sec(θ). We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle:

sqrt(h²+ d²) = sqrt((200 sqrt(2))² + (400)²) = 400 sqrt(3)

So, we have:

tan(θ) = h/d = (200 sqrt(2))/400 = sqrt(2)/2

sec(θ) = sqrt(1 + tan²(θ)) = sqrt(1 + (sqrt(2)/2)²) = sqrt(3)/2

Therefore:

dθ/dt = (-1/20) / (sqrt(3)/2)² = (-1/20) * (4/3) = -1/15

So, the angle of observation is changing at a rate of -1/15 radians per second (or about -3.8 degrees per second).

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Answer:

t=10.50h or also known as y=10.50x

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the quadratic polynomial given as g(x) = x²- 5x + 4, the zeros of the quadratic polynomial occurs at g(x) = 0 such that x²- 5x + 4 = 0.

Factorizing the resulting equation to get the roots

x²- 5x + 4 = 0

(x²- x)-(4 x + 4) = 0

x(x-1)-4(x-1) = 0

(x-1)(x-4) = 0

x-1 = 0 and x-4 = 0

x = 1 and x = 4

Since a and b are known to be the root then we can say a = 1 and b =4

Substituting the given values into the equation  1/a+1/b-2 ab , we will have;

= 1/1 + 1/4 - 2*1*4

= 1 + 1/4 - 8

= 5/4 - 8

Find the Lowest common multiple

= (5-32)/4

= -27/4

Hence the required value is -27/4

The given system of equations is:

5d + 20e - 10% = -85 …………………..(1)

-20d + 394e = 223 ………………...(2)

4d + 13e = -106 …………………….(3)

We can solve this system of equations using the Gaussian elimination method. In this method, we convert the system of equations into an equivalent system of equations that is easy to solve by eliminating one variable at a time.The elimination process starts by multiplying the equations so that one variable cancels out. We can do this by multiplying both sides of an equation with a constant or by adding or subtracting two equations.

Here, the first equation has a percentage sign which we need to remove.

We can do this by dividing both sides of equation (1) by

10.5d/10 + 20e/10 - 1 = -85/10

⇒ 0.5d + 2e - 1 = -8.5

⇒ 0.5d + 2e = -7.5 ……………………..(4)

Now, we can use equations (2) and (4) to eliminate d.

Multiplying equation (2) by 2 and adding it to equation (4), we get,

2(-20d + 394e = 223) + (0.5d + 2e = -7.5)

⇒ -40d + 788e + 0.5d + 2e = -7.5 + 446

⇒ -39.5d + 790e = 438 ……………………...(5)

Multiplying equation (2) by 5 and adding it to equation (3), we get,

5(-20d + 394e = 223) + (4d + 13e = -106)

⇒ -100d + 1970e + 4d + 13e = -106 + 1105

⇒ -96d + 1983e = 999 ……………………(6)

Now, we can use equations (5) and (6) to eliminate d.

Multiplying equation (5) by 2 and adding it to equation (6), we get,

2(-39.5d + 790e = 438) + (-96d + 1983e = 999)

⇒ -79d + 1563e + (-96d + 1983e) = 876 + 1998

⇒ -175d + 3546e = 2874 …………………..(7)

We can simplify equation (7) by dividing both sides by 7,-25d + 506e = 410 ……………………..(8)

Now, we can use equations (4) and (8) to solve for e.

Multiplying equation (4) by 506/4 and adding it to equation (8), we get,

506/4 × (0.5d + 2e = -7.5) + (-25d + 506e = 410)

⇒ 253d + 506e - 1895 - 25d + 506e = 410

⇒ 228d + 1012e = 2305 ……………………(9)

We can simplify equation (9) by dividing both sides by

4,57d + 253e = 576 ……………………(10)

Now, we can use equations (4) and (10) to solve for d.

Multiplying equation (4) by 57/2 and adding it to equation (10), we get,

57/2 × (0.5d + 2e = -7.5) + (57d + 253e = 576)

⇒ 28.5d + 114e - 214.125 + 57d + 253e = 576

⇒ 85.5d + 367e = 790.125 …………………….(11)

We can simplify equation (11) by dividing both sides by 17,5d + 23e = 46.4166667 …………………….(12)

Now, we can use equations (4) and (12) to solve for e.

Multiplying equation (4) by 23/2 and adding it to equation (12), we get,

23/2 × (0.5d + 2e = -7.5) + (5d + 23e = 46.4166667)

⇒ 11.5d + 46e - 86.625 + 5d + 23e = 46.4166667

⇒ 16.5d + 69e = 133.0416667 ……………………..(13)

We can simplify equation (13) by dividing both sides by 3,5.5d + 23e = 44.3472222 ……………………..(14)

Now, we can use equations (4) and (14) to solve for e.

Multiplying equation (4) by 23 and subtracting it from equation (14), we get,

23 × (0.5d + 2e = -7.5) - (5.5d + 23e = 44.3472222)

⇒ 11.5d - 48.5e = -212.0972222 ……………………..(15)

We can simplify equation (15) by dividing both sides by 1.5,7.6666667d - 32.3333333e = -141.3981481 ……………………..(16)

Now, we can use equations (4) and (16) to solve for e.

Multiplying equation (4) by 32 and adding it to equation (16), we get,

32 × (0.5d + 2e = -7.5) + (7.6666667d - 32.3333333e = -141.3981481)

⇒ 16d + 64e - 240 + 7.6666667d - 32.3333333e = -141.3981481

⇒ 23.6666667d + 31.6666667e = 98.60185185 …………………..(17)

We can simplify equation (17) by dividing both sides by 1.6666667,

14.2d + 19e = 59.1611111 ……………………..(18)

Now, we can use equations (4) and (18) to solve for e.

Multiplying equation (4) by 19 and subtracting it from equation (18), we get,

19 × (0.5d + 2e = -7.5) - (14.2d + 19e = 59.1611111)

⇒ 9.5d - 41e = -186.3111111 ……………………..(19)

We can simplify equation (19) by dividing both sides by 1.9,

5d - 21.57894737e = -98.05789474 ……………………..(20)

Now, we can use equations (4) and (20) to solve for e.

Multiplying equation (4) by 21.57894737 and adding it to equation (20), we get,

21.57894737 × (0.5d + 2e = -7.5) + (5d - 21.57894737e = -98.05789474)

⇒ 43.15789474d + 0e = -252.5263158

⇒ 43.15789474d = -252.5263158

⇒ d = -5.85416667

Substituting the value of d in equation (4), we get,

0.5d + 2e = -7.5

⇒ 0.5(-5.85416667) + 2e = -7.5

⇒ e = -6.5

Now, we have the values of d and e, and we can substitute them in any equation to get the value of the remaining variable.

We can use equation (2),

-20d + 394e = 223

⇒ -20(-5.85416667) + 394(-6.5) = 223

⇒ 117.0833334 + (-2561) = 223

⇒ -2443.916667 = 223

This is not true, which means there is no solution to this system of equations. Hence, the system is inconsistent.

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Answer:

Step-by-step explanation:

Comment

This is an arithmetic series. It has the following givens.

a = 27     The first term

d = - 2       The difference between one term and the one behind it.

n = quite small

Tn = a + (n - 1)*d

tn = 27 - 2n  + 2

tn = 29 - 2n

Answer:

D

Step-by-step explanation:

Since 2.7 is closer to 3 and shown in the graph.

You would first use addition and then multiplication

Answer:

Step-by-step explanation:

Scale factor  = 1 : 7

a)Let the length of the house in the scale drawing = x

1:7 :: x : 21

Product of means = Product of extremes

 7*x = 1* 21

     x = \(\frac{1*21}{7}\)

     x = 3

Length of the house in the scale drawing = 3 in

b) Height of the real house =y

1 : 7 :: 4 : y

Product of extremes = product of means

1 * y = 7*4

   y = 7*4

   y = 28

Height of real house = 28 feet

Answer

Check Explanation

Explanation

12) x ≥ -6; 4

This says that x is equal to or greater than -6. So, 4 is greater than -6 and definitely fits this condition. 4 is a solution to the given inequality.

13) n < 8; 11

This says n is less than 8. So, 11 isn't less than 8 and it doesn't fit this condition. 11 is not a solution to this given inequality.

14) k ≤ 2; (4/3)

This says k is less than or equal to 2. So, (4/3) is less than 4 and it fits this condition. (4/3) is a solution to this given inequality.

15) a > 15; 15

This says a is greater than 15. 15 is not greater than 15 and doesn't fit this condition. 15 is not a solution of this inequality.

16) w ≤ -1.6; 1.7

This says w is less than or equal to -1.6. And 1.7 is not less than -1.6 and doesn't fit this condition. 1.7 is not a solution of this inequality.

17) r ≥ (-5/9); (-3/2)

This says r is greater than or equal to (-5/9). And (-3/2) is less than (-5/9) and doesn't fit into this condition. (-3/2) is not a solution of this inequality.

Hope this Helps!!!

Step-by-step explanation:

A college professor has purchased a new car for commuting to class. This bicycle had a purchase price of $25,000 and depreciates at a constant rate of $1550 a year. What is the bicycle's value after 4 years? How long before the bicycle is worth zero?

25,000 - 1,550y

25,000 - 1,550(4)

25,000 - 6,200

= $18,800 after 4 years

0 = 25,000 - 1,550y

-25,000 = - 1,550y

y = 16.129 years (rounded to three places)

Answer:

-8

Step-by-step explanation:

f(1) = -2

g(4)= 6

-8 *(-2) -4 * 6 = 16 -24 = -8

Answer: If you have 10 balls and one of them is defective (either heavier or lighter), you can find the defective ball in a maximum of 3 weighings using a two-pan balance scale.

Here’s how you can do it:

Divide the balls into three groups of three balls each and one group with the remaining ball.

Weigh two groups of three balls against each other. If they balance, the defective ball must be in the third group of three balls or the group with the remaining ball. If they don’t balance, the defective ball must be in one of the two groups being weighed.

Take two balls from the group that contains the defective ball and weigh them against each other. If they balance, the defective ball must be the remaining ball in that group. If they don’t balance, you have found the defective ball.

This method guarantees that you will find the defective ball in a maximum of 3 weighings.

The calculated value of the test statistic is approximately 6.40.

To test the hypothesis that job satisfaction is the same at Baruch College and Brooklyn College, we can use a two-sample t-test.

The null hypothesis (H0) assumes that the means of the two populations are equal, while the alternative hypothesis (Ha) assumes that the means are not equal.

H0: μ1 = μ2 (Mean job satisfaction at Baruch College is equal to mean job satisfaction at Brooklyn College)

Ha: μ1 ≠ μ2 (Mean job satisfaction at Baruch College is not equal to mean job satisfaction at Brooklyn College)

We can calculate the test statistic using the formula:

t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes.

Given the data:

Baruch College: mean job satisfaction score (x1) = 83.0, standard deviation (s1) = 15, sample size (n1) = 150.

Brooklyn College: mean job satisfaction score (x2) = 73.0, standard deviation (s2) = 12, sample size (n2) = 100.

Calculating the test statistic:

t = (83.0 - 73.0) / sqrt((15^2 / 150) + (12^2 / 100))

t = 10 / sqrt(1 + 1.44)

t ≈ 10 / sqrt(2.44)

t ≈ 10 / 1.561

t ≈ 6.40

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Answer:

A graph with a set amount of numbers.

Step-by-step explanation:

Infinite means never ending and that's what most graphs are. But, a finite graph is a graph that doesn't have arrows at the end of the lines. (simplified answer) A better way of saying it is a graph with a fixed starting position and a fixed ending position. You can use this type of graph if you don't want to go over or under a certain value.

Hope this helps!

Answer:

$8 per pound

Step-by-step explanation:

40 ÷ 5 = 8

$40 per 5 pound= 8

$8 per 1 pound = 8

the horizontal distance between the base of the ladder and the wall is approximately 8.034 feet.

To find the horizontal distance between the base of the ladder and the wall, we can use trigonometry.

In this scenario, the ladder forms an angle of 72 degrees with the ground. We can consider this angle as one of the acute angles in a right triangle, where the ladder is the hypotenuse.

Let's denote the horizontal distance between the base of the ladder and the wall as x.

Using the trigonometric function cosine (cos), we can relate the adjacent side (x) to the hypotenuse (26 feet) using the given angle (72 degrees):

cos(72°) = x/26

Now, let's solve for x:

x = 26 * cos(72°)

Using a calculator, we can find the value of cos(72°) to be approximately 0.3090.

x = 26 * 0.3090

x ≈ 8.034

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 8.034 feet.

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Answer:

34,400

Step-by-step explanation:

3.44 * 10^4=34,400

The z-statistics for the given situations are 20, 12.5, 18.4766, 1.7775, and 13.6293 respectively.

To calculate the z-statistic (z), we use the formula: z = (X - μ) / (σ / √N),

where X is the observed value,

μ is the mean,

σ is the standard deviation,

and N is the sample size.

A.) X = 8.00; μ = 5; σ = 0.6; N = 16
z = (8.00 - 5) / (0.6 / √16) = 3 / (0.6 / 4) = 3 / 0.15 = 20

B.) X = 4.00; μ = 2; σ = 0.8; N = 25
z = (4.00 - 2) / (0.8 / √25) = 2 / (0.8 / 5) = 2 / 0.16 = 12.5

C.) X = 11.50; μ = 9.25; σ = 0.75; N = 38
z = (11.50 - 9.25) / (0.75 / √38) = 2.25 / (0.75 / 6.1644) = 2.25 / 0.1218 = 18.4766

D.) X = 0.95; μ = 0.82; σ = 0.31; N = 18
z = (0.95 - 0.82) / (0.31 / √18) = 0.13 / (0.31 / 4.2426) = 0.13 / 0.0731 = 1.7775

E.) X = 8.14; μ = 4.69; σ = 1.29; N = 26
z = (8.14 - 4.69) / (1.29 / √26) = 3.45 / (1.29 / 5.099) = 3.45 / 0.2531 = 13.6293

Therefore, the z-statistics for the given situations are 20, 12.5, 18.4766, 1.7775, and 13.6293 respectively.

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According to the acceleration, the object is at the point (-7, -3e³ + e⁻²) at t = 2.

To find the position of the object at t = 2, we need to integrate the acceleration twice with respect to time to get the position function. The first integration gives us the velocity function v(t) = {2t + c₁, -e⁻ᵃ + c₂}, where c₁ and c₂ are constants of integration.

We can find these constants by using the initial condition that the object is initially at rest at (3,3). This means that v(0) = {0, 0}, which gives us c₁ = -6 and c₂ = e³.

The second integration gives us the position function r(t) = {t² - 6t + C3, e⁻ᵃ - e³t + C4}, where C3 and C4 are constants of integration.

Again, we can find these constants using the initial condition that the object is initially at rest at (3,3). This means that r(0) = {3, 3}, which gives us C3 = 3 and C4 = 2 - e³.

Finally, we can substitute t = 2 into the position function to find the position of the object at t = 2.

This gives us r(2) = {2² - 6(2) + 3, e⁻² - e³(2) + 2 - e³} = {-7, -3e³ + e⁻²}.

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