A final exam in Math 160 has a mean of 70 with standard deviation 8. If 16 students arerandomly selected, find the probability that the mean of their test scores is less than 77.(hint: Central limit theorem)

Step-by-step explanation:

first Pythagoras to get BD (the height of the main triangle) :

105² = 84² + BD²

11025 = 7056 + BD²

BD² = 3969

BD = 63

second Pythagoras to get AD :

65² = AD² + BD² = AD² + 63²

4225 = 3969 + AD²

AD² = 256

AD = 16

Answer:

X= -2

Step-by-step explanation:

Answer:

See below:

Step-by-step explanation:

Hello my name is Galaxy and I will be helping you today! I hope you are having a nice day!

We can solve this in two steps, one being Algebra and the second being Answer/Checking our answer. I'll start off with Algebra.

Algebra

We can start to solve this problem by using Algebra and simplifying it down. We can also use the distributive property to solve the problem by using the proof it shows. The distributive property states that we can multiply whats inside the paranthesis by the number on the outside and get the same answer.

We can prove it by doing this:

\(2(1+4)=(2*1)+(2*4)?\\2+8=2+8?\\10=10\)

Now that we have the tools we need to begin solving.

Solving

We can start to solve it by simplifying the equation from its distributive state. We can do that by doing the following:

\(-3(x-2)=12\\-3x+6=12\\\)

Now that we've simplified, we can begin solving it.

\(-3x+6=12\\-3x=12-6\\-3x=6\\x=6 \div -3\\x=-2\)

We have gotten our answer of x being -2. We can now double check our answers.

\(-3(-2-2)=12?\\(-3*-2)+(-3*-2)=12?\\6+6=12?\\12=12\)

Remember that if we multiply two negatives it is a positive!

Cheers!

Answer:

C) 40 students

Step-by-step explanation:

The correct percent double 20% is 40% but they want to know what is 40% of the total. Set up a proportion.

x 40%

_____ = _____

800 100  

Cross multiply and divide to get your answer!

Answer:

Equilateral

Step-by-step explanation:

if three medians of a triangle are equal than triangle is called Equilateral

Answer:342.084

Step-by-step explanation:

If the temperature was 87 degrees, the energy consumption would be approximately 341.184.

The equation provided is:

y = 3.317x + 53.505

where:

y represents energy consumption

x represents temperature

You want to determine the energy consumption when the temperature is 87 degrees (x = 87).

Plug the value of x into the equation:

y = 3.317 * 87 + 53.505

Now, perform the calculations:

y = 287.679 + 53.505

y = 341.184

So, if the temperature was 87 degrees, the energy consumption would be approximately 341.184.

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Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).

To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).

In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:

(x₁ + x₂)/2 = 1

(y₁ + y₂)/2 = 3

We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:

(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2

(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6

Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:

x₁ + (2-x₁) = 2 => x₁ = 1

y₁ + (6-y₁) = 6 => y₁ = 3

So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.

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326 divided by 0.24 to the nearest hundredth is 1358.33

To divide 326 by 0.24 and round the result to the nearest hundredth, we can perform the following calculation:

326 ÷ 0.24 = 1358.3333

Rounding to the nearest hundredth means we need to look at the third decimal place.

So 326 divided by 0.24 to the nearest hundredth is 1358.33.

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Answer:

3.5 and -3.5

Step-by-step explanation:

The lines on the outside of n mean the absolute value (the distance from 0)

Answer:

3.5 and -3.5

Step-by-step explanation:

Sense n is absolute value it doesn't matter whether the integer/number is negative or positive.

Answer:

$12

Step-by-step explanation:

First you multiply the amount of times shew went (4) by the amount of tip she left (1.50). You would get $6. Then you subtract that by the total amount (54) and you would get $48. Then you have to divide the total left over cost by the amount of times you went, and you get $12. $12 would be the amount per salad.

C = 54 - ( 1.50 x 4 ) / 4

The amount that they have altogether is $ 76.8.

To convert mixed fractions to improper fractions, multiply the denominator with the whole number and add the numerator.  

For example,

1 (1/2) =  [ 2×1 + 1] /2 = 3/2

2 (2/5) = [ 5×2 + 2] /5 = 12/5    

Here we have

Andreas has $18

Bonnie has 1 2/3 times as much as Andreas.

Here 1 2/3 is a mixed fraction we need to convert to an improper fractions

=>  1 2/3 = (3+2)/3 = 5/3

=> The amount that Bonnie has = 5/3 of (18)

= \(\frac{5}{3} \times 18\) = 5 × 6 = $ 30

Cheryl has 1  3/5 times as much as Bonnie  

=> 1 3/5 = (5 + 3)/5 = 8/5

=> The amount that Cheryl has = 8/5 of 18

=> \(\frac{8}{5} \times 18\) = $ 28.8  

By the above calculations, they all together have

=> $ 18 + $ 30 + $ 28.8 = $ 76.8

Therefore,

The amount that they have altogether is $ 76.8

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One way to show a function is 1-1 is to show that if two outputs are the same, then the inputs had to have been the same as well:

   If f(a) = f(b), then a=b.

If you can show this, you've shown that each output is paired with a unique input, so the function is 1-1.

For this function, we'd first start assuming that f(a) = f(b):

              f(a) = f(b)

         -3a+5 = -3b+5

Now we'll solve this for a:

        -3a + 5 = -3b + 5

   -3a + 5 - 5 = -3b + 5 - 5

               -3a = -3b

      -3a ÷ (-3) = -3b  ÷ (-3)

                   a = b

This shows that the only way the outputs are the same is if the inputs are the same, which means each output comes from a unique input, so the function is 1-1.

Given:

Percentage of free throws last season = 74%

This season he got to shoot 16 free throws in the first two games this season.

Since his free throw percentage holds from last season, this means that the percentage this season will also be 74%.

To find how many free throws Steven made during these two games, we have:

Therefore, Steven made about 12 free throws during these two games.

ANSWER:

D. 12

The value of x in the given figure is 8.

In the given figure there are two lines which are parallel.

We have to find the value of x.

In the straight line the sum of angles is 180 degrees.

8x+1+115=180

8x+116=180

Subtract 116 from both sides:

8x=180-116

8x=64

Divide both sides by 8:

x=64/8

x=8

Hence, the value of x in the given figure is 8.

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The kayak trip would cost an adult $71.43 at a regular cost

In this question, we have the parameters to be

The regular cost is calculated using

The regular cost = Amount paid/(1 - Discount) * 1/Number of adults

Substitute the known values in the above equation

The regular cost = 250/(1 - 30%) * 1/5

Evaluate

The regular cost = $71.43

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Answer:

the correct answer is: c (-3,-6)

Answer:

Step-by-step explanation:

hello :

6x  the greatest common factor from the polynomial.

 12x² + 30x

Answer:

x>_-1

Step-by-step explanation:

x is such that x is greater or equal to -1

Answer:

222,678

Step-by-step explanation:

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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When a man selects 3 items, the probability that they're all defective will be 1/64.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

From the information, bag contains 8items of which two are deffective. The probability of a defective item is:

= 2/8

= 1/4

When a man selects 3 items, the probability that they're all defective will be:

= (1/4)³

= 1 / 64

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Complete question

A bag contains 8items of which two are deffective. A man selects 3 items, what is the probability that they're all defective?

Answer:

7/5

Step-by-step explanation:

rewrite as an equation ..

3 4/5 \ x = 2 5/7

times x to both sides

2 5/7x= 3 4/5

divide 2 5/7 from both sides

x=7/5

The evaluated function values are g(-3) = 11, g(5) = 11, g(a) = 11 and g(a+h) = 11

A composite function is a function that results from combining two or more functions. It is created by using the output of one function as the input of another function.

The function g(x) is defined as g(x) = 11, which means that the output of the function is always 11, no matter what value of x is inputted.

i.e. the function g(x) = 11 always returns the value 11, regardless of the input.

Therefore, we have:

g(-3) = 11

g(5) = 11

g(a) = 11

g(a+h) = 11

So, regardless of the value of a or h, the function g(x) will always return 11.

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Answer:

D is the answer.

Answer:

c

Step-by-step explanation:

assume base 10

-logy = x

\( \frac{1}{ log(y) } = x\)

log base x y = 5 turns into the format x^ 5 = y

implement that to get c

Answer:

Step-by-step explanation:

Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation: