what is the answer to this equation?

Answer:

x = 53.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 51 = 66/x

x tan 51 = 66

x = 66/ tan 51

x=53.44574

Rounding to the nearest tenth

x = 53.4

Complete question is;

A trucking company determined that the distance traveled per truck per year in its entire fleet was normally distributed with a mean of 55 thousand miles and a standard deviation of 11 thousand miles.

a)A truck in the fleet traveled 42 thousand miles in the last vear. Calculate the z-score for this truck.

b) Interpret the z-score

c) The trucking company has a policy that any truck with mileage more than 2.5 standard deviations above the mean should be removed from the road and inspected. What is the probability that a randomly selected truck from the fleet will have to be inspected?

d) A randomly selected truck in the fleet traveled 85 thousand miles in the last year. Should this truck be removed from the road and inspected? Explain why or why not.

Answer:

A) z = - 1.18

B) Interpretation of the z-score in A above shows that the distance traveled per truck per year in its entire fleet is 1.18 standard deviations lesser than the distance traveled per truck on average

C) P(z > 2.5) = 0.0062

D) it's value of z is greater than 2.5 minimum and so the truck will be removed from the road and inspected

Step-by-step explanation:

A) We are given;

Population mean; μ = 55000

Sample mean; x¯ = 42000

Standard deviation; σ = 11000

Z-score formula is;

z = (x¯ - μ)/σ

z = (42000 - 55000)/11000

z = - 1.18

B) Interpretation of the z-score in A above shows that the distance traveled per truck per year in its entire fleet is 1.18 standard deviations lesser than the distance traveled per truck on average.

C) since it has a policy that any truck with mileage more than 2.5 standard deviations above the mean should be removed from the road and inspected, then it means that probability that it will be inspected is;

P(z > 2.5) = 1 - P(z < 2.5)

From p-values from z-score table, we have;

P(z > 2.5) = 1 - 0.9938

P(z > 2.5) = 0.0062

D) A randomly selected truck in the fleet traveled 85 thousand miles in the last year. Thus; x¯ = 85000.

Thus;

z = (85000 - 55000)/11000

z = 2.73

This value of z is greater than 2.5 minimum and so the truck will be removed from the road and inspected

Answer:

7 sqrt(2) = c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

7^2 + 7^2 = x^2

49+49 = c^2

98 = c^2

Taking the square root of each side

sqrt(98) = sqrt(c^2)

sqrt(49*2) = c

7 sqrt(2) = c

Answer:

r = 13.33

Step-by-step explanation:

d = k*r*t

Where,

k = constant of proportionality

d = 110 when r = 55 and t = 2

d = k*r*t

110 = k * 55 * 2

110 = 110k

k = 110/110

k = 1

Find r when d = 40 and t = 3

d = k*r*t

40 = 1 * r * 3

40 = 3r

r = 40/3

= 13.333333333333

Approximately,

r = 13.33

Answer:

k=3/2 or 1 1/2

Step-by-step explanation:

Answer  3/2

Step-by-step explanation:

Answer:

HOPE IT HELP YOU . Plz tell me if it is write or wrong .

Answer:

They got 3.00 back

Step-by-step explanation:

Since they both bought a book it means you have to double the price of one book.

3.50+3.50=7.00

Then since you are looking for the difference of 10.00 you would subtract it.

10.00-7.00=3.00

the answer to this question is the slope is 43

Answer:

Therefore, the slope is 3/4

Step-by-step explanation:

An x -intercept is the value of x when y=0 , so an x-intercept of 4 can be written as a coordinate on the graph as (4,0)

Likewise, an

y -intercept is the value of y when x=0 , so an y -intercept of −3can be written as a coordinate on the graph as (0,-3)

Now we have two points(4,0) (0,-3)

To find the slope given two points, we use the formula

rise÷run , or y2−y1÷x2−x1 .

Plug in the given points into the formula

-3-0/0-4

-3/-4

3/4

Therefore, the slope is 3/4

Hope this helps!

Answer:

I think it is -24t+20 if you want to simplify

Step-by-step explanation:

Answer:

-24t + 20

Step-by-step explanation:

First, remove the parentheses

Then, multiply 6 by 5

Then expand 3(2t+4) - 30t + 8

Finally simplify 6t + 12 - 30t + 8

-24t + 20

Hope this helps!

Answer:

x = 126

Step-by-step explanation:

The angles are complementary which means they sum to 180

x+54 =180

x = 180-54

x = 126

Answer:

Step-by-step explanation:

In the equation y = mx + b, which is the form Ingrid's equation is in, the m stands for the rate of change. If the water level is decreasing, the rate at which it is decreasing is what goes in for m. The "b" of that equation indicates the starting height of the water, which is 170. The equation should be:

y = -4x + 170, negative because the water is decreasing.

Answer: X = 86 gallons

Step-by-step explanation:

X-27=59

X=59+27

Answer:

[tex]Expected = 0.09375[/tex]

Step-by-step explanation:

Given

[tex]Balls = 4[/tex]

[tex]n = 4[/tex] --- selection

Required

The expected distinct colored balls

The probability of selecting one of the 4 balls is:

[tex]P = \frac{1}{4}[/tex]

The probability of selecting different balls in each selection is:

[tex]Pr = (\frac{1}{4})^n[/tex]

Substitute 4 for n

[tex]Pr = (\frac{1}{4})^4[/tex]

[tex]Pr = \frac{1}{256}[/tex]

The number of arrangement of the 4 balls is:

[tex]Arrangement = 4![/tex]

So, we have:

[tex]Arrangement = 4*3*2*1[/tex]

[tex]Arrangement = 24[/tex]

The expected number of distinct color is:

[tex]Expected = Arrangement * Pr[/tex]

[tex]Expected = 24 * \frac{1}{256}[/tex]

[tex]Expected = \frac{3}{32}[/tex]

[tex]Expected = 0.09375[/tex]

We know

[tex]\boxed{\sf cos\theta=\dfrac{B}{H}}[/tex]

[tex]\\ \sf\longmapsto cos\theta=\dfrac{8}{16}[/tex]

[tex]\\ \sf\longmapsto cos\theta=\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto cos\theta=cos60[/tex]

[tex]\\ \sf\longmapsto \theta=60[/tex]

Answer:

graph - A

Step-by-step explanation:

Answer:

here you go! with step by step so you can do it next time

Answer:

-7/8

Step-by-step explanation:

cross multiply first then expand the equations when you cross multiply it will be

(3x+3)(x+4)=(3x+2)(x-1)

3x(x+4)+3(x+4)=3x(x-1)+2(x-1)

3x²+12x+3x+12=3x²-3x+2x-2

3x²+15x+12=3x²-x-2

3x²-3x²+15x+x=-2-12

16x/16=-14/16

x=-14/16

simplified to

-7/8

I hope this helps

Answer:

(x,y+4)

Step-by-step explanation:

This shows a translation of 4 units up, so the y coordinate increases by 4. Please mark brainliest as I need 1 more to move up. It would be much appreciated.

Answer:B

Step-by-step explanation:

[tex] \sf \: c = 3 \\ \sf \: d = 4 \\ \\ \sf \: 5cd \: = \: ?\\ \\ \sf \:5 cd \hookrightarrow \\ \sf = 5 \times (3) \times (4) \\ \sf = 5 \times 12 \\ = \underline{ \bf \: 60}[/tex]

-> Just substitute the values given for variables c & d in the equation 5cd & you'll get the answer.

Answer:

1.96 ;

1.216

Step-by-step explanation:

Given the data :

x : __0 _ 1 _ 2 _ 3 _4 _5 Total

P(x) .07 .36 .27 .17 .10 .03 1.00

. The mean, also called the expected value is defined as ;

E(X) = Σx*p(x)

E(X) = (0*0.07) + (1*0.36) + (2*0.27) + (3*0.17) + (4*0.10) + (5*0.03) = 1.96

The standard deviation, ; √var(x)

Var(X) = Σx²*p(x) - E(X)²

Var(X) = [(0² * 0.07) + (1² * 0.36) + (2² * 0.27) + (3² * 0.17) + (4² * 0.10) + (5² * 0.03)] - 1.96²

Var(X) = 5.32 - 3.8416

Var(X) =14784

SD(X) = √1. 4784 = 1.216

Answer:

∠ L ≈ 52°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cosL = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{LM}{LN}[/tex] = [tex]\frac{8}{13}[/tex] , then

∡ L = [tex]cos^{-1}[/tex] ([tex]\frac{8}{13}[/tex] ) ≈ 52° ( to the nearest degree )

Answer:

sqrt(3) /3

Step-by-step explanation:

1 / sqrt(3)

Multiply the top and bottom by sqrt(3)

1/ sqrt(3) * sqrt(3)/ sqrt(3)

sqrt(3) /  sqrt(3)*sqrt(3)

sqrt(3) /3

Answer:

[tex] = { \sf{ \frac{1}{ \sqrt{3} } }} \\ \\ { \sf{ = \frac{1}{ \sqrt{3} } . \frac{ \sqrt{3} }{ \sqrt{3} } }} \\ \\ = { \sf{ \frac{ \sqrt{3} }{ {( \sqrt{3}) }^{2} } = \frac{ \sqrt{3} }{3} }} [/tex]

Answer:

Look down below

Step-by-step explanation:

A.)Net capitalized cost=146,000-3000= $143,000

Net capitalized cost = 143,000

B.)Money factor=8.4/100 over 24=0.084/24=0.0035

Money Factor= 0.0035

C.)Average monthly finance charge= (143,000+75,000)x 0.0035= 218,000 x 0.0035=$763

Average Monthly Finance Charge= $763

D.)Average monthly depreciation= 143,000-75000/5 x 12=68000/60=$1133.33

Average monthly deprecation= $1133.33

E.)monthly lease payment=1133.33/5= $226.66

Monthly lease payment= $226.66

Answer:

abe = ebc

Step-by-step explanation:

bcos both the seperate angels have the same degree

Answer:

The promoters profit would be $46,350 if they sell 850 tickets

Step-by-step explanation:

The value 61 is likely the cost of each ticket, and the value 5,500 is likely the amount the promoter spent in order to promote at the concert since it was being subtracted from his profits

Hope this helps :)

Answer:

Step-by-step explanation:

Let d and r be the diameter and radius, respectively.

d² + 12² = 15²

d² = 15² - 12² = 81

d = √81 = 9

r = d÷2 = 4.5 mm

Answer:

Since this function is definable for all real values of x,

Domain(f(x)) = R = (-∞,∞)

Step-by-step explanation:

Now,

Let 4x-8=y

4x = y+8

x = (y+8)/4

Since x is definable for all real values of y,

Range(f(x)) = R = (-∞,∞)

Answer:

? ≈ 28°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{19}{41}[/tex] , then

? = [tex]sin^{-1}[/tex] ([tex]\frac{19}{41}[/tex] ) ≈ 28° ( to the nearest degree )

Answer:

[tex]{ \sf{( \sec \theta - \csc \theta)(1 + \tan \theta + \cot \theta) }} \\ = { \sf{( \sec \theta + \tan \theta \sec \theta + \cot \theta \sec \theta) - ( \csc \theta - \csc \theta \tan \theta - \csc \theta \cot \theta)}} \\ = { \sf{( \sec \theta + \sec \theta \tan \theta + \csc \theta) - ( \csc \theta - \sec \theta - \csc \theta \cot \theta)}} \\ = { \sf{ \sec \theta \tan \theta + \csc \theta \cot \theta }} \\ { \bf{hence \: proved}}[/tex]

Answer:

B

Step-by-step explanation:

You need a number that when multiplied by itself 3 times gives you 512. So the length and width of the bottom layer must be 8 by 8 which is 64.

The layers are 8 cm high, so that's the third number you multiply together.

Volume = 8*8*8 = 64

But the answer you want is 8*8 which is 64