Solve for x. Round to the nearest tenth of a degree, if necessary.

This question is solved using the central limit theorem, giving an answer of:

Fourth option, approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 140, standard deviation of 20, sample of 4:

By the Central Limit Theorem, the distribution is approximately normal.

Mean is the same, of 140.

[tex]n = 4, \sigma = 20[/tex], thus:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{4}} = 10[/tex]

Thus, the correct answer is:

Fourth option, approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

For another example of the Central Limit Theorem, you can check https://brainly.com/question/15519207

Answer:

10x-4 feet

Step-by-step explanation:

The perimeter is the amount of the sides together so add the three sides together

2x+1+4x-4+4x-1

Combine like terms

10x-4

(You can also factor out 2 but that would not be simplest --> 2(5x-2))

Answer:

2.7*10³=2700

note if power positive you add '0s' to the back eg 10³=1000 if the power is negative e.g10^-3 add to the front and a decimal e.g 0.001

[tex]\\ \sf \longmapsto 2.7\times 10^3[/tex]

[tex]\\ \sf \longmapsto 27\times 10^{-1}\times 10^3[/tex]

[tex]\\ \sf \longmapsto 27\times 10^{-1+3}[/tex]

[tex]\\ \sf \longmapsto 27\times 10^2[/tex]

[tex]\\ \sf \longmapsto 27\time 100[/tex]

[tex]\\ \sf \longmapsto 2700[/tex]

Answer:

90

Step-by-step explanation:

We know that area of ∆BCD = half of the area of rectangle BEFD, since any triangle drawn from taking a side and base and a point on the opposite side as the 3rd vertex has the half area of the rectangle

so, area of ∆BCD = 15×12/2 = 90 (since two legs of the right triangle are 15 and 12)

since area ∆BCD is half the area rectangle BEFD and sum of the area of ∆BEC and ∆CFD will be the rest of the area of rectangle BEFD, which is 90

Answer:

Step-by-step explanation:

A horizontal line is only concerned with the y value. The equation is y = 10 because that is the point that the line must go through.

The x value does not matter as long as the y value is given as 10. The domain is any real value. The range is 10

Answer:it could b phase shift but i think that u would have 2 put it on the axis 2 really get it but that is what is thought n our grade but axis

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number children tickets = c

Number of adult tickets = 75% of c = 0.75c

c + 0.75c = 1750

1.75c = 1750

   c = 1750/1.75 = 1000

Number of children = 1000

Number of adults = 75% of 1000  = 750

Cost of adult ticket = $ x

Cost of child ticket = 75% of x = 0.75x

Cost of 750 adult ticket = 750x

Cost of 1000 children ticket = 1000 * 0.75x = 750x

750x + 750x = 27000

              1500x = 27000

                      x = 27000/1500

x = $ 18

Cost of adult ticket =  $ 18

Cost of children ticket = 75% of 18 = 0.75 * 18 = $ 13.5

Cost of children's ticket = $ 13.50

Answer:

Hours of labor needed  = 8 hour

Step-by-step explanation:

Given:

Amount total charged = $715

Listed amount = $315

Hourly rate for labor = $50

Find:

Hours of labor needed

Computation:

Total amount of labour = Amount total charged - Listed amount

Total amount of labour = 715 - 315

Total amount of labour = $400

Hours of labor needed  = Total amount of labour / Hourly rate for labor

Hours of labor needed  = 400 / 50

Hours of labor needed  = 8 hour

Answer:

(1) question no.1

x<=8

(2) question no.2

5<x<7

Answer:

1. 8≥g

2. A-5≥7

Step-by-step explanation:

Answer:

Step-by-step explanation:

a + 45 + 70 = 180             45 becomes an interior angle by being opposite a given vertically opposite angle.

a + 115 = 180                      Subtract 115 from both sides

a = 65

b + 68 + 65 = 180            A straight line is 180 degrees.

b +  133 = 180

b = 180 - 133

b = 47

In the triangle b + c + 100 = 180

b = 47

47 + c + 100 = 180

147 + c = 180

c = 33

If C is an exterior angle then C + 33 = 180

C = 147

You have to decide whether c is an interior angle ( in which it is 33) or an exterior angle (in which case it is 147).

Answer:

The first line:

y₁ = (2/3)*x + 6

Has the larger y-intercept, by 5 units.

Step-by-step explanation:

Here we need to find the equation for each line.

First, some theory.

A linear relationship can be written as:

y = a*x + b

where a is the slope and y is the y-intercept.

We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ -x₁)

And, if a line is:

y = a*x + b

a perpendicular line to that one must have a slope equal to:

-(1/a).

Now we can answer this question.

We know that the first line, let's call it y₁, passes through the points (3, 8) and (-3, 4), then its slope will be:

a = (8 - 4)/(3 - (-3)) = 4/6 = 2/3

then the line is something like:

y₁ = (2/3)*x + b

to find the value of b, we can use the fact that we know that the line passes through the point (3, 8)

this means that when x = 3, we must have y₁ = 8

replacing these in the above equation, we get:

8 = (2/3)*3 + b

8 = 2 + b

8 - 2 = b = 6

then the equation for this line is:

y₁ = (2/3)*x + 6

Now let's find the equation for the other line, that we will call y₂.

We know that this line is perpendicular to:

y = (1/3)*x - 2

The slope of that line is:

a = (1/3)

then the slope of a line perpendicular to that one will be:

slope = -(1/a) = -(1/1/3) = -3

slope = -3

then we have:

y₂ = -3*x + b

to find the value of b, we can use the fact that our line passes through the point (2, -5)

This means that when  x = 2, we must have y₂ = -5

then:

-5 = -3*2 + b

-5 = -6 + b

-5 + 6 = b = 1

b = 1

then this equation is:

y₂ = -3*x + 1

Now we know both equations:

y₁ = (2/3)*x + 6

y₂ = -3*x + 1

Which equation does have the larger y-intercept?

We can see that the first line has an y-intercept of 6, and the second line has an y-intercept of 1, then the first line has the larger y-intercept, and is larger by 5 units.

Answer:

<ADC=90

therefore AC= 20 using Pytagoras

BAC is a right angle triangle because it belongs to the Pytagoras theorem:25,20,15 i.e 25²=15²+20²

3) I DON'T THINK PQR IS A RIGHT ANGLE TRIANGLE because it doesn't belong to the Pytagoras triple.

Answer:

y= 8x + 5

Step-by-step explanation:

y = 8x + b

5 = 8(0)+b

b = 5

Answer:

sin (a+b)= sina*cosb - sinb*cosa

cos (a+b) = cosa*cosb + sina*sinb

Answer:

sin (A + B) = sin A cos B + cos A sin B

cos (A + B) = cos A cos B - sin A sin B

on:

Answer:

If... 6.4 inches : 16 dollars

Then... 32 inches = 80 dollars.  

And, 1 inch of track = 80/32 dollars.

80/32 = 2.5.

So, the answer is: 1 inch of track costs 2.5 dollars.

The  constant of proportionality is $2,50.

The equation used to represent direct proportionality is: y = kx

Where:

y = dependent variable

x = independent variable

k = constant of proportionality

Here, the dependent variable is the cost of the track. The independent variable is the length of the tracks.

$16 = 6.4k

k = 16 / 6.4 = $2.5

A similar question was answered here: https://brainly.com/question/17033082

Answer:

the amount will 26.7 ......hope this may help you

the sequence is arithmetic because it's incrementing by a constant ratio of -4

The sequence 11,7,3,... is arithmetic because there is a constant increase of (-4)

Must click thanks and mark brainliest

Answer:

If the rate of interest is 12% than the answer is 12000

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Let the original price = x

From X to get the new price you multiply by 1 + the percent of the increase which is 25%

1,25X = 2.00

Divide both sides by 1.25:

X = 1.60

The original price was B. 1.60

Answer:

x=1.60

Step-by-step explanation:

Let x be the original price

We increase by 25%

x+ .25x = new price

1.25x = 200

Divide each side by 1.25

x = 2.00/1.25

x=1.60

Answer:

10. x is 15; y is \sqrt104. 11. \sqrt5

Step-by-step explanation:

for 10:

first we find the face on the left side; which according to the pythagorean theorem x is 144 + 81 =225 = x = 15. and y is 11^2 + y^2 = 225 = 225 - 121 = y^2 = y = the square root of 104.

for 11:

144 + y^2 = 169 = y^2 = 25 = y = 5. because the two sides are equivalent, the base is also 5 for the left part of the triangle. therefore, 5^2 + 5^2 = x^2 which means x is the square root of 5.

Answer:

(-11, -6)

Step-by-step explanation:

Find the distance between the midpoint, (-3, -1) and (5, 4). This can be calculated by finding the difference between the x coordinates and y coordinates.

-3 - 5 = -8 (distance between x coordinates)

-1 - 4 = -5 (distance between y coordinates)

Find the point (x, y) by subtracting 8 from the midpoint's x value, and then subtracting 5 from the midpoint's y value.

-3 - 8 = -11

-1 - 5 = -6

So, the point (x, y) is (-11, -6)

Answer:

37.5 cm^2

Step-by-step explanation:

The area of a parallelogram is

A = bh  where b is the base and h is the height

A = 7.5 * 5

A = 37.5 cm^2

Answer:

A = 37.5 cm²

Step-by-step explanation:

The area of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

Here b = 7.5 and h = 5 , then

A = 7.5 × 5 = 37.5 cm²

Answer:

Rectangular prism- 12 edges

Rectangular pyramid- 8 edges

Triangular pyramid- 6 edges

Triangular prism- 9 edges

I hope this helps!

Answer:

[tex]x - 3[/tex]

Step-by-step explanation:

Given

[tex]Volume = x(x - 3)(x + 4)[/tex]

Required

The shortest side

The volume of a rectangular prism is:

[tex]Volume = Length * Width * Height[/tex]

By comparison, we have:

[tex]Length = x[/tex]

[tex]Width = x-3[/tex]

[tex]Height = x + 4[/tex]

In ascending order, the sides are:

[tex]Width = x-3[/tex]

[tex]Length = x[/tex]

[tex]Height = x + 4[/tex]

This is so because:

Irrespective of the value of x

x - 3 will be less than x

x + 4 will be more than x

Hence, the shortest length is:

[tex]Width = x-3[/tex]

Answer:

b

Step-by-step explanation:

9514 1404 393

Answer:

  A, C, D, E

Step-by-step explanation:

Any relation that is different from a straight line with a defined constant slope will be a relation that is either or both of ...

__

a) degree 3, not linear

b) a linear function

c) a vertical line with undefined slope, not a function

d) a curve opening downward, not linear

e) a line with a bend in the middle, not linear

f) a linear function

[tex]\large\mathcal{\red{ \implies \: 2 \: \pi \: {r}^{2} \: + \: 2 \: \pi \: r \: h}}[/tex]

Option ( C ) is the correct answer.

Answer:

32 ounces

Step-by-step explanation: