Find the population mean or sample mean as indicated.
Sample 17, 13, 5, 12, 13

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

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Answer:

1/3

Step-by-step explanation:

Hope this is useful even though there isn't any working

Answer:

y = -3x + 10

Step-by-step explanation:

slope of perpendicular line = -3

y-1 = -3(x-3)

y-1 = -3x + 9

y = -3x + 9 + 1

y = -3x + 10

The magnitude of the car's acceleration when s=100m and x=0 is 3.49 \(m/s^2\) evaluated using the kinematic equation of motion.

We can use the kinematic equation of motion to determine the acceleration of the car at the given distance:

\(s = ut + (1/2)at^2\)

where s=distance traveled, u = initial velocity, a =acceleration, and t =

time taken.

We can rewrite this equation as:

\(t = (2s/u)^(1/2)\)

Substituting the given values, we get:

\(t = (2(100)/20)^(1/2)\) = 2.236 seconds

Now, we can use the kinematic equation:

v = u + at

where v is the final velocity.

We know the initial velocity u is 20 m/s, and the car's acceleration At=0.5 \(m/s^2\). To find the final velocity, we can use the kinematic equation again:

\(s = ut + (1/2)at^2 + vt\)

Rearranging and substituting the given values, we get:

\(v = (s - ut - (1/2)at^2) / t\)

v = (100 - (20)(2.236) - (1/2)(0.5)(2.236)^2) / 2.236

v = 27.839 m/s

Now we can evaluate the acceleration using the equation:

a = (v-u) / t

Substituting the given values, we get:

a = (27.839 - 20) / 2.236

a = 3.49\(m/s^2\) (rounded to two decimal places)

Therefore, the magnitude of the car's acceleration when s=100m and x=0 is 3.49 \(m/s^2.\)

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the length of the pool is 48 feet.we can get this answer by using Pythagorean Theorem .

what is Pythagorean Theorem ?

The Pythagorean Theorem is a mathematical formula that relates to the three sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In the given question,

Let the length of the rectangular swimming pool be denoted by "L". We can use the Pythagorean Theorem to relate the length, width, and diagonal distance of the pool:

(diagonal distance)² = (length)² + (width)²

Substituting the given values, we get:

60² = L² + 36²

Simplifying and solving for L, we get:

L² = 60² - 36²

L² = 3600 - 1296

L² = 2304

L = √(2304) = 48

Therefore, the length  L of the pool is 48 feet.

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The surface area of the rectangular prism in this problem is given as follows:

A. 426 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.

The dimensions for this problem are given as follows:

5 m, 12 m and 9 m.

Hence the surface area of the prism is given as follows:

S = 2(5 x 12 + 5 x 9 + 12 x 9)

S = 426 m².

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To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer: X + 3

Step-by-step explanation:

Sum hints as to an addition statement and it specifies a variable X and the number 3 so the expression would be X + 3.

SUM MEANS ADDITION

HERE IT MEANS THE ADDITION OF x and 3

written as

\(x + 3\)

HOPE THIS HELPS

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

(3/2)x - 2  

hope it helps

original price be x

VAT 10%

So new price is 10% less

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

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The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer: 86

Step-by-step explanation:

14 times 6 = 86

Answer: 9

Step-by-step explanation:

first you would subtract 96 and 60 to get 36. then divide 36 and 4 to get 9! hope this helped

Answer:

D) 56

Step-by-step explanation:

\(\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56\)

Answer:

-5

Step-by-step explanation:

(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5

Answer:

so that you will multiply 15 * 4.

Step-by-step explanation:

15*4 = 60 now you divide 60 by 4 and the answer will be 15.

The value of f(g(1) from the table of functions is given as 1.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

when x = 1

g(x) = 3

or f(g(1) = f(3) = 1

The value of f(g(1) from the table of functions is given as 1.

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a. Let ER denοte the event that a cοmpany uses training fοr emplοyee retentiοn and PI denοte the event that a cοmpany uses training fοr prοcess imprοvement.

We need tο find P(ER and nοt PI). Using the fοrmula fοr cοnditiοnal prοbability, we have: P(ER and nοt PI) = P(ER | nοt PI) P(nοt PI)

We are given that 36% οf the cοmpanies use training fοr bοth emplοyee retentiοn and prοcess imprοvement. Sο, the percentage οf cοmpanies that use training fοr emplοyee retentiοn but nοt prοcess imprοvement is:

56% - 36% = 20%

Alsο, we are given that 64% οf the cοmpanies dο nοt use training fοr emplοyee retentiοn. Sο, the percentage οf cοmpanies that dο nοt use training fοr prοcess imprοvement is:

100% - 36% = 64%

Using these percentages, we have:

P(ER and nοt PI) = (0.20)/(0.64) ≈ 0.3125

Therefοre, the prοbability that the cοmpany uses training fοr emplοyee retentiοn and nοt fοr prοcess imprοvement is apprοximately 0.3125.

b. We need tο find P(PI | ER), the prοbability that the cοmpany uses training fοr prοcess imprοvement given that it uses training fοr emplοyee retentiοn. Using Bayes' theοrem, we have:

P(PI | ER) = P(ER and PI) / P(ER)

We are given that 36% οf the cοmpanies use training fοr bοth emplοyee retentiοn and prοcess imprοvement. Alsο, we calculated in part (a) that 20% οf the cοmpanies use training fοr emplοyee retentiοn but nοt prοcess imprοvement. Sο, the percentage οf cοmpanies that use training fοr emplοyee retentiοn (with οr withοut prοcess imprοvement) is: 56%

Therefοre, we have:

P(ER) = 0.56

P(ER and PI) = 0.36

P(PI | ER) = (0.36)/(0.56) ≈ 0.643

Therefοre, if it is knοwn that the cοmpany uses training fοr emplοyee retentiοn, the prοbability that it uses training fοr prοcess imprοvement is apprοximately 0.643.

c. We are given that 36% οf the cοmpanies replied that they use training fοr prοcess imprοvement and emplοyee retentiοn. Sο, the prοbability that the cοmpany uses training fοr prοcess imprοvement is 36%.

d. We need tο find P(ER οr PI), the prοbability that the cοmpany uses training fοr emplοyee retentiοn οr prοcess imprοvement. Using the fοrmula fοr the uniοn οf twο events, we have:

P(ER οr PI) = P(ER) + P(PI) - P(ER and PI)

We are given that 36% οf the cοmpanies replied that they use training fοr prοcess imprοvement and emplοyee retentiοn. Alsο, we calculated in part (b) that 56% οf the cοmpanies use training fοr emplοyee retentiοn (with οr withοut prοcess imprοvement). Sο, the percentage οf cοmpanies that use training fοr prοcess imprοvement (with οr withοut emplοyee retentiοn) is: 36%

Therefοre, we have:

P(ER) = 0.56

P(PI) = 0.36

P(ER and PI) = 0.36

P(ER οr PI) = 0.56 + 0.36 - 0.36 = 0.56

Therefοre, the prοbability that the cοmpany uses training fοr emplοyee retentiοn οr prοcess imprοvement is 0.56.

e. We need tο find the prοbability that the cοmpany neither uses training fοr emplοyee retentiοn nοr uses training fοr prοcess imprοvement. This is the cοmplement οf the event that the cοmpany uses training fοr emplοyee retentiοn οr prοcess imprοvement, sο we have:

P(neither ER nοr PI) = 1 - P(ER οr PI) = 1 - 0.56 = 0.44

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Answer:

∠E = tan

∠D = tan

Step-by-step explanation:

Common sense, only perpendicular and base is present.

The solution to the inequality expression is n < -9

The inequality expression is given as

4n - 6(n + 1) > 12

Open the bracket in the above inequality expression

4n - 6n - 6 > 12

Evaluate the like terms

-2n > 18

Divide both sides by -2

n < -9

Hence, the solution to the inequality expression is n < -9

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The number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period is \(-8.6+3.15\).

What is formula for slope and intercept is?

\($$\begin{aligned}& b=\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& a=\bar{y}-b \bar{x} \\& \hat{y}=a+b x\end{aligned}$$\)

The slope is

\($$\begin{aligned}b & =\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& =\frac{12 \times 318-(12 \times 4)(12 \times 4)}{12 \times 232-(12 \times 4)^2} \\& =3.15\end{aligned}$$\)

The intercept is

\($$\begin{aligned}a & =\bar{y}-b \bar{x} \\& =4-3.13 \times 4 \\& =-8.6\end{aligned}$$\)

The regression equation is

\($$\begin{aligned}\hat{y} & =a+b x \\& =-8.6+3.15 x\end{aligned}$$\)

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Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

I might be wrong but i'm pretty sure it's right

Answer:

x<100 and look at picture

Step-by-step explanation:

x-19<81

+19  +19

x<100

+100 on number line, opened line to the left

X<100

Step-by-step explanation:

x-19<18

+19   +19

x<100

+100 on number line, opened line to the left

Answer:

A. B. D. NOT C

Step-by-step explanation:

i don't know if you wrote anything wrong but this is correct if you are correct

Answer:

Expression

Step-by-step explanation:

Answer: Expression

Got this right!!!

Hope this helps!!!

The amount that you need to save per month to fund the emergency fund would be $ 861. 58.

The discretionary money left per month would be $ 585. 88.

The gross income for the month :

= 17. 50 x 40 per week x 4 weeks a month

= $ 2, 800

The amount left which is realized funds for the month is:

= Gross income - FICA + Federal tax withholding + State tax withholding

= 2, 800 x ( 1 - 26. 15 %)

= $ 2, 067. 80

Five months of realized income for the emergency fund is:

= 2, 067. 80 x 5

= $ 10, 339

The amount to save per month is:

= 10, 339 / 12

= $ 861. 58

The amount left per month for discretionary expenses ;

= 2, 067. 80 - 861. 58 - 620. 24 rent

= $ 585. 88

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Answer:

\( ME = 1.64 \sqrt{\frac{0.32 (1-0.32)}{150}}= 0.0625\)

Step-by-step explanation:

For this case we have the following info given:

\( n = 150\) represent the sampel size selected

\( X = 48\) represent the number of households who relied strictly on cell phones for their service

The estimated proportion of households who relied strictly on cell phones for their service is given by:

\( \hat p =\frac{X}{n}= \frac{48}{150}= 0.32\)

And the margin of error would be given by:

\( ME = z_{\alpha/2} \sqrt{\hat p(1-\hat p)}{n}\)

The confidence is 90% so then the significance is \(\alpha=1-0.9=0.1\) and \( \alpha/2 =0.05\) the critical value for this case from the normal standard distribution is:

\( z_{\alpha/2}= 1.64\)

And the margin of error would be:

\( ME = 1.64 \sqrt{\frac{0.32 (1-0.32)}{150}}= 0.0625\)

Answer:

10 × $30 = $300

Step-by-step explanation: