MATHEMATICS COLLEGE

Consider the point.(4, 5, 6)
What is the projection of the point on the xy-plane?
(x, y, z) =__________.

What is the projection of the point on the yz-plane?
(x, y, z) =________

What is the projection of the point on the xz-plane?
(x, y, z) =___________

Answers

Answer 1
Answer:

Answer:

(4,5,0)

(0,5,6)

(4,0,6)

Step-by-step explanation:

The projection of the point on the plane can be determined as:

xy-plane, z=0.

(x,y,z)=(x,y,0)=(4,5,0)

yz-plane, x=0.

(x,y,z)=(0,y,z)=(0,5,6)

xz-plane, y=0.

(x,y,z)=(x,0,z)=(4,0,6)

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As the saying goes, “You can't please everyone.” Studies have shown that in a largepopulation approximately 4.5% of the population will be displeased, regardless of thesituation. If a random sample of 25 people are selected from such a population, what is theprobability that at least two will be displeased?A) 0.045B) 0.311C) 0.373D) 0.627E) 0.689
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What value of x would make KM ∥ JN?Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.Complete the statements to solve for x.By the converse of the side-splitter theorem, if JK/KL = , then KM ∥ JN.Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x + 4 EndFraction.Cross-multiply: (x – 5)() = x(x – 3).Distribute: x(x) + x(4) – 5(x) – 5(4) = x(x) + x(–3).Multiply and simplify: x2 – x – = x2 – 3x.Solve for x: x = .

What is the square root of 1350÷600

Answers

Step-by-step explanation:

1350÷600

=2.25

√2.25=1.5

Spencer earns $12.25 per hour and $18.30 for each hour over 40. Howmuch does Spencer earn if he works 48 hours in a week.

Answers

Answer:

Spencer would earn $636.4

Step-by-step explanation:

Spencer makes $12.25 per hour we would multiply 12.25 by 40 and then do 8x18.30 for the rest 8 hours and we get 146.4 and when we add them together our total is = 636.4

A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?

Answers

Answer:

8.3%

Step-by-step explanation:

Find the slope and y- of the table​

Answers

Answer:

y = (3/2) x +6

Step-by-step explanation:

The y-intercept is clearly at y = 6 point (0, 6) of the table.

The slope can be calculated using any two pairs, for example (-4,0) and (-2, 3)

slope = (y2 - y1)/(x2 - x1) = (3 - 0) / (-2 + 4 ) = 3/2

Then the equations of the line in slope y-intercept form is:

y = (3/2) x +6
the answer is y=(3/2)x+6

Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed. 51  53  48  62  34  34  51  53  48  30  62  51  46 ​(a) Find the sample mean and sample standard deviation. ​(b) Each employee in the sample is given a ​$5000 raise. Find the sample mean and sample standard deviation for the revised data set. ​(c) Each employee in the sample takes a pay cut of ​$2000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set. ​(d) What can you conclude from the results of​ (a), (b), and​ (c)?

Answers

Answer:

Mean increase or decrease (same quantity) according to the quantity of the increment or reduction

As all elements were equally affected the standard deviation will remain the same

Step-by-step explanation:

For the original set of salaries: ( In thousands of $ )

51, 53, 48, 62, 34, 34, 51, 53, 48, 30, 62, 51, 46

Mean = μ₀ = 47,92

Standard deviation  =  σ = 9,56

If we raise all salaries in the same amount  ( 5 000 $ ), the nw set becomes

56,58,53,67,39,39,56,58,53,35,67,56,51

Mean   =  μ₀´  = 52,92

Standard deviation  =  σ´ = 9,56

And if we reduce salaries in the same quantity ( 2000 $ ) the set is

49,51,46,60,32,32,49,51,46,28,60,49,44

Mean μ₀´´ = 45,92

Standard deviation  σ´´ = 9,56

What we observe

1.-The uniform increase of salaries, increase the mean in the same amount

2.-The uniform reduction of salaries, reduce the mean in the same quantity

3.-The standard deviation in all the sets remains the same.

We can describe the situation as a translation of the set along x-axis (salaries). If we normalized the three curves we will get a taller curve (in the first case) and a smaller one in the second, but the  data spread around the mean will be the same

Any uniform change in the data will directly affect the mean value

Uniform changes in values in data set will keep standard deviation constant

Final answer:

The mean salary is affected by each employee's changes in salary, such as raises and pay cuts, but the standard deviation (the spread of salaries) remains the same provided the change is the same for all individuals.

Explanation:

To answer this question, we need to calculate the sample mean and sample standard deviation in each case. The sample mean is the average of the data, while the sample standard deviation is a measure of the amount of variation or dispersion in the data set.

  • (a) Calculate the sample mean and sample standard deviation of the initial salaries. This involves summing all the salaries and dividing by the total number to get the mean, then calculating the standard deviation using the formula: square root of [sum of (each salary - mean salary)² divided by (total number of salaries - 1)].
  • (b) When each employee is given a $5000 raise, the mean will increase by 5, while the standard deviation will remain the same because raises do not affect the dispersion of the team's salaries.
  • (c) Similarly, when each employee takes a pay cut of $2000, the mean salary will decrease by 2, but the standard deviation will again remain the same because pay cuts do not affect the dispersion of the team's salaries.
  • (d) We can conclude that while the mean is affected by changes in individual salaries (like raises and pay cuts), the standard deviation is not, provided the change is the same for all individuals. Therefore, it shows that while supply changes can affect the central tendency (mean), they do not impact how spread out the salaries are (standard deviation).

Learn more about Mean and Standard Deviation here:

brainly.com/question/34166299

#SPJ3

Find the value of x
(6x+7) (8x-17)

Answers

Answer:

x=12

Step-by-step explanation:

6x+7=8x-17

-6x     -6x

7=2x-17

+17    +17

24=2x

÷2   ÷2

12=x

x=12
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