Students in MA238 spend on average 3.75 hours a week studying (with a population standard deviation σ = 5.17). (i) Given this fact, describe the sampling distribution of the mean if all possible random samples of size 50 were chosen. (ii) What can you say about the mean of all the possible sample means? (iii) If 250 such samples were chosen at random and for each you calculated a 95% C.I for the mean, how many such intervals would you expect to contain the true mean? (iv) If instead you calculated a 99% C.I. for the mean, how many intervals would you now expect to capture the true mean.

The surface area of a triangular prism with the 3 sides slant height as 14 the base width as 8 and the base height as 6.9 is 155. 705 in²

The surface area of a triangular pyramid is the total area of all it's faces.

The properties of a triangular prism are;

Surface area = Base Area + 1÷2 (perimeter × base height)

But base area = 1÷2 (base side × height)

Base area = 1÷ 2 (8 × 14) = 0.5 × 112 = 56 in²

Perimeter = sum of all the sides = 14 + 8 + 6.9 = 28. 9 in

Base height = 6. 9in

Surface area = 56 + 1 ÷ 2 ( 28.9× 6. 9) = 56 + 0.5 × 199.41 = 56 + 99. 705 = 155. 705 in²

Surface area = 155. 705 in²

Therefore, the surface area of the triangular prism is 155. 705 in²

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It looks like the differential equation is

[tex]\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}[/tex]

Factorize the right side by grouping.

[tex]xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)[/tex]

[tex]xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)[/tex]

Now we can separate variables as

[tex]\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx[/tex]

Integrate both sides.

[tex]\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx[/tex]

[tex]\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx[/tex]

[tex]\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}[/tex]

You could go on to solve for [tex]y[/tex] explicitly as a function of [tex]x[/tex], but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.

Answer:

no solutions

Step-by-step explanation:

Since the two terms have the same base, we are able to use the rule for subtracting logarithms:

[tex]log_{b}(x) - log_{b}(y) = log_{b}(\frac{x}{y} )[/tex]

Therefore, the equation can be written as:

[tex]log_{6}(\frac{x-6}{x+4} )=2[/tex]

By using the definition of a logarithm we can say that:

[tex]\frac{x-6}{x+4} = 6^{2}\\\frac{x-6}{x+4} = 36\\x -6 = 36x+144\\35x = -150\\x =-\frac{30}{7}[/tex]

When plugging this solution in, you find that the term [tex]log_{6}(x-6)[/tex] has x-6 evaluate to a number less than 0. This is not included in the domain of log functions, so [tex]-\frac{30}{7}[/tex] is not a valid solution. This means that there are no solutions.

Answer:

13 and 44

Step-by-step explanation:

let x and y be the 2 numbers with y < x , then

x - y = 31 ( add y to both sides )

x = y + 31 ( subtract 31 from both sides )

x - 31 = y → (1)

4y = x + 8 → (2)

substitute y = x - 31 into (2)

4(x - 31) = x + 8

4x - 124 = x + 8 ( subtract x from both sides )

3x - 124 = 8 ( add 124 to both sides )

3x = 132 ( divide both sides by 3 )

x = 44

substitute x = 44 into (1)

44 - 31  = y , then

y = 13

the 2 numbers are 13 and 44

Answer:

Acute Triangle.

Explanation:

The figure shows an equilateral triangle which has all the angles equal.

Acute Triangles are those who has angles less than 90°

Hence, an equilateral triangle is always an acute triangle.

Additional,

A right angle triangle has 90° angle.

An obtuse triangle has greater than 90° angle.

Using the law of detachment, the conclusion we can draw from the two given statements is: C. m∠E + m∠F = 90°.

The law of detachment states that, if two statements are true, a third statement that is true can be derived also.

From the information given, we have:

First statement: If 2 angles are complementary, then their sum equals 90 degrees (If p, then q).

Second statement: Angles E and F are complementary (p).

The third true statement (q) would be:

m∠E + m∠F = 90°. (option C)

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Answer:

See below

Step-by-step explanation:

4.33 = 3.83 * (1.13)       .13 is decimal for 13%  

Answer:

no thank you sorry 4h he'll be a great day of school and I have been a while ago but it's a good time 44

Answer:

o

Step-by-step explanation:

Answer:

[tex]f^{-1}(x) = (x+7)^2[/tex]

Step-by-step explanation:

[tex]y=f(x) = \sqrt x - 7 \\\\\text{Replace x with y and then solve for y:}\\\\~~~~~~~~x= \sqrt y -7\\\\\implies \sqrt y = x+7\\\\\implies y = (x+7)^2\\\\\implies f^{-1}(x) = (x+7)^2[/tex]

Answer: Maybe when you Grew from a Baby to a toddler because that would be you growing over time

Step-by-step explanation:

I Hope This Helps!

Answer:

(x + 5)^2 + (y + 8)^2 = 6^2

Step-by-step explanation:

A circle formula: (x - h)^2 + (y - k)^2 = r^2

We are given diameter. To find the radius divide diameter by 2.

d = 12

12/2 = r = 6

H and K are given to be (-5 , -8)

(x - (-5))^2 + (y - (-8))^2 = 6^2

(x + 5)^2 + (y + 8)^2 = 6^2

I have plot this equation to confirm my answer is correct where the origin is (-5 , -8) and has a radius of 6.

Answer:

(2.405, 1.537)

Step-by-step explanation:

When you graph these, they intersect at (2.405, 1.537).

You can use desmos as a graphing calculator, it is extremely helpful.

Hope this helps!

Answer: P(A|B) = P(A)

Step-by-step explanation:

If they are independent, one event being given doesn't impact the probability of the other event.

Answer:b

Step-by-step explanation:

b

Answer:

I would say A is the answer.

Answer:

2.25or21/4

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

Expression:

Simplify it in below steps:

Using a geometric sequence, it is found that the maximum height reached after the 5th bounce is of 43.48 feet.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the ball is dropped from a height of 101.00 inches onto a hard flat floor, and after each bounce, the height is 19% less, that is, 81% of the previous height, hence the first term and the common ratio are given by:

[tex]a_1 = 101, q = 0.81[/tex]

Then, the height of the nth bounce is given by:

[tex]a_n = 101(0.81)^{n-1}[/tex]

And the height of the 5th bounce is:

[tex]a_5 = 101(0.81)^{5-1} = 43.48[/tex]

The maximum height reached after the 5th bounce is of 43.48 feet.

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Answer:

3

Step-by-step explanation:

Step-by-step explanation:

To find slope : y2- y1 / x2 - x1

we have ( -5 , 1 ) which is ( x1 , y1 )

and ( -2 , 7 ) is ( x2 , y2 )

so; 7 - 1 / -2 - (-5)

6/3

= 2

It's translation B to B’, is the composition of transformations that would map figure ABCD to figure A'B'C'D".

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.

here, we have,

from the given figure we get,

there is a transformation of ABCD to A'B'C'D".

now,

Reason: choices are translation, reflection, rotation, or dilation, this is translation.

Hence, It's translation B to B’, is the composition of transformations that would map figure ABCD to figure A'B'C'D".

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Answer:

13

Step-by-step explanation:

Divide 12 by 3 first because of (PEMDAS) you get 4 tge add that to the 9 the you get 13.

P = parentheses

E = exponent

M = multiplication

D = division

A = addition

S = subtraction

Using the normal distribution, it is found that 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 33.8, \sigma = 1.2[/tex]

The proportion of full term newborn female infants with a head circumference between 31 cm and 36 cm is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 31, hence:

X = 36:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{36 - 33.8}{1.2}[/tex]

Z = 1.83

Z = 1.83 has a p-value of 0.9664.

X = 31:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{31 - 33.8}{1.2}[/tex]

Z = -2.33

Z = -2.33 has a p-value of 0.0099.

0.9664 - 0.0099 = 0.9565.

0.9565 = 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.

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Answer:

48.57 USD

Step-by-step explanation:

Just subtract 3500 from 1800 you get 1700

then

1700 divided by 35

Answer:

24

Step-by-step explanation:

from the question above,

30+(-6) =

when plus is multiplying minus it's minus

+ × - = -

30-6 = 24

The calculation that will give us the total surface area of the solid figure that is made up of square faces is: B. 6 × 5 × 5

Area of a square = (side length)².

Therefore are six (6) square faces that make up the solid figure.

Area of the 6 square faces = total surface area of the solid figure = 6(5²)

Total surface area of the solid figure = 6 × 5 × 5

Total surface area of the solid figure is: B. 6 × 5 × 5

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The total area with land based on the information given is 3x² + 60x.

Let the width = x

Let the length = (1.5 × x) = 1.5x

Area = 1.5x × x = 1.5x²

The area along with land:

Width = x + 20

Length = 3 × x = 3x

The total area with land:

= Length × Width

= 3x(x + 20)

= 3x² + 60x.

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The original price of the meal deal if they would have exactly enough money to buy two of the meal deal is $4

let

x = cost of the meal

Both = 2x - 3

3/4x + 1/2x = 2x - 3

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

5/4x = 2x - 3

5/4x - 2x = - 3

(5-8)x/ 4 = -3

-3/4x = -3

x = -3 ÷ -3/4

= -3 × -4/3

= 12/3

x = $4

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The number of miles between the two cities is 8.13 miles.

In order to determine  the number of miles between the two cities, we would have to divide 13 kilometers by 1.6 miles. Division is when a number is grouped into equal numbers using another number.

Number of miles = 13 / 1.6 = 8.13 miles

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Answer:

Step-by-step explanation:

Part A

There are 5 odd numbers from 1 to 10. All three of them must be odd when drawn. I have to assume that there is no replacements.

Probability (odd) = (5 *  4 * 3) / (10 * 9 * 8) = 60 / 720

Probability (odd) = 0.083333

Part B

This is a little harder because 1 even number will turn everything even. So the way to handle this is to assume that there is (1 - probability(odd)) *720  that you have even

So the chances of an even result is 1 - odd/ total or

(1 - 1/12) * 720 =   660/720 = 0.917

Answer

Odd: 0.0833

Even: 0.917