In 1990, the average duration of long-distance telephone calls originating in one town was A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of The hypotheses are:

Answer: turn percentages into decimals then multiply that by the initial number

Step-by-step explanation:

60%

0.60

0.60*40= 24

Answer:

Order of operations tells you to perform multiplication and division first, working from left to right, before doing addition and subtraction. Continue to perform multiplication and division from left to right. Next, add and subtract from left to right.

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Answer:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

Step-by-step explanation:

Rectangular garden    A (r ) =  x * y

Let´s call x the side of the rectangle to be constructed with a rock wall, then only one x side of the rectangle will be fencing with wire.

the perimeter of the rectangle is  p  =  2*x  +  2*y    ( but in this particular case only one side x will be fencing with wire

56   =   x    +  2*y      56   -  2*y  =  x

A(r)   =  ( 56  -  2*y ) * y

A(y ) =  56*y  -  2*y²

Tacking derivatives on both sides of the equation we get:

A´(y )  =  56  - 4 * y        A´(y) = 0     56  -  4*y  =  0    4*y  =  56

y =  14 m

and x  =  56  - 2*y    =  56 - 28  = 28 m

Then dimensions of the garden:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

How do we know that the area we found is a local maximum??

We find the second derivative

A´´(y)  = - 4     A´´(y)  <  0   then the function A(y) has a local maximum at y = 14 m

Step-by-step explanation:

Recall that

[tex] \cos(x + \pi) = \cos x \cos\pi - \sin x \sin\pi[/tex]

and

[tex] \sin(x - \pi) = \sin x \cos \pi - \cos x \sin \pi[/tex]

But we also know that

[tex] \cos \pi = - 1 \\ \sin \pi = 0 \: \: \: \: [/tex]

so the above relations reduce to

[tex] \cos(x + \pi) = - \cos x \\ \sin(x - \pi) = - \sin x [/tex]

Therefore,

[tex] \cos(x + \pi) - \sin(x - \pi) = - \cos x + \sin x [/tex]

answer is -1 you can check it on the calculator

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Step-by-step explanation:

(-)(-)=+

1−(−3)−5

1+3-5

4-5

-1

Answer:

Option A

Step-by-step explanation:

A probability distribution of a statistic that represents a large sample derived from a certain specific population size to  determine a range of possible outcomes of statistics such as Mean, Standard deviation, mode, median etc. in a way that it represents the existing entire population is known as a  sampling distribution

Hence, option A is correct

Answer:

B. 1150

Step-by-step explanation:

14000-5000=9000 sales over 5000

9000 x .10=900 commission

250 (salary)+ 900 (commission)=1150 total

Answer:

[tex]5ab = 5 \times a \times b[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

5a*b

Answer:

It would be 0.41 ft^3

Step-by-step explanation:

Alright, to start, lets get the volume of the entire cinder block and the holes within it.

1.31 * 0.66 * 0.66 ---> 0.5706...

Next with the holes, they are both 0.33 wide, 0.39 long, and just as tall at 0.66 feet.

0.33 * 0.39 * 0.66 ---> 0.0849...

Since there's two of them: 0.1698...

To finish it, subtract the hole volume from the total volume;

0.5806 - 0.1698 = 0.4108

Rounds to 0.41 ft^3

Answer:

P(A and B) = 0.14.

Step-by-step explanation:

Venn probabilities:

Suppose we have two events, A and B. The probability P(A and B) is given by:

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]

In which [tex]P(A \cup B)[/tex] is P(A or B).

In this question:

P(A) = 0.3, P(B) = 0.63, P(A or B) = 0.79. So

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.3 + 0.63 - 0.79 = 0.93 - 0.79 = 0.14[/tex]

So

P(A and B) = 0.14.

Answer: The customer spends 10 minutes at a booth.

Step-by-step explanation:

Let n= number of booths, [tex]\rho[/tex] = utilization, [tex]\lambda[/tex] = arrival rate, [tex]\mu=[/tex]Service rate

We know that

[tex]\rho=\dfrac{\lambda}{\mu\times n}[/tex]

As per given,

[tex]0.5=\dfrac{15}{\mu\times5}\\\\\Rightarrow\ \mu=\dfrac{15}{5\times0.5}\\\\\Rightarrow\ \mu=6[/tex]

Service rate = 6 customers per hour.

Time taken by each customer = [tex]\frac{1}{\mu}[/tex]

[tex]=\frac{1}{6} \ hours \ or\ \dfrac{60}{6}\ minutes\\\\=10 \ minutes[/tex]

Hence, the customer spends 10 minutes at a booth.

Answer:

10/13

Step-by-step explanation:

High. Very High

The total number of cards is 8 + 3 + 2 = 13

There are 3 green ones and 10 others.

P(~G) = 10/13 = 0.769

Answer:

B -5/6

Step-by-step explanation:

Answer:

1/3 or 33.33%

Step-by-step explanation:

A regular dice has 6 sides each with a single number from 1 to 6. Therefore, there are a total of 6 possible outcomes. Out of all of these only two outcomes are actually less than three and those are the numbers 1 and 2. Meaning, that if the dice were rolled only a single time then the probability of rolling a number less than 3 would be 2/6 or 1/3 (simplified). As a percentage, this probability would be 33.33%

=======================================================

Explanation:

There are 18 ways to pick the first topping and 18-1 = 17 ways to pick the next topping. Picking the same topping again doesn't make much sense (though I suppose it could mean that you just want more of that topping than usual?), so that's why we have the 18 drop to 17 when making that second selection.

If the order of toppings mattered, then we'd have 18*17 = 306 permutations. However, the order of toppings doesn't matter. All that matters is the group rather than the individual toppings. When counting out the 306 permutations, we've overcounted by a factor of 2. In other words, we've double counted.  

So we must divide by 2 to fix this double count. That leads to 306/2 = 153 combinations

------------------------

The alternative method involves using the nCr combination formula

Use n = 18 and r = 2 in this formula

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

the exclamation marks indicate factorial.

Answer:

0.721

Step-by-step explanation:

the last digit (the number '1') must be in the thousandths place; then work backward so the '2' would be in the hundredths and the '7' would be in the 'tenths'

Answer:

natural

Step-by-step explanation:

Answer:

Area = 14¹/16 yd² or 14.0625 yd²

Step-by-step explanation:

2. The figure given is a square having equal sides of 3¾ yd each.

Formula for area of the square = a²

Where,

a = 3¾ yd

Plug in the value into the equation:

Area = (3¾)²

Change to improper fraction

Area = (15/4)²

Area = 225/16

Area = 14¹/16 yd² or 14.0625 yd²

Answer:

Step-by-step explanation:

Answer:

your answer is correct. a trapezoid can be defined by it's set of parallel sides

Step-by-step explanation:

If the shape you're looking at doesn't have at least one set of parallel sides, it's not a trapezoid;

Answer:

B. 0< b < 1

Step-by-step explanation:

b is a fraction that less than 1, so 0 < b < 1

Answer:

Step-by-step explanation:

8 is not a function

9 is a function

10 is a function

Answer:

4 1/2 quarts.

Step-by-step explanation:

So 5 1/2 quarts to start. 4 left over.

Theres 4 cups in a quart.

So theres be 4 1/2 quarts used.. as 4 cups left would be a quart and 1 quart taken away from 5 1/2 quarts in 4 1/2.

The value of f(-1) in the graph is 1.

In mathematics, a function is an expression, rule, or law that establishes a relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

The graph leads to the following finding:

The values of f(-1) for x = -1 are -1 and -3.

The function does, however, have a closed circle at f(-1) = 1.

The function has an open circle at f(-1) = -3.

A closed circle represents inclusive principles.

Hence, the graph's value for f(-1) is 1.

Learn more about functions here:

brainly.com/question/13136492

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Step-by-step explanation:

#1 . the minimum height =

443 - 394 = 49 ft

#2. y = (394/2) + 49 = 197+49

=> y =246

#3. the amplitude is ½× diameter

= ½×394 = 197 ft

#4. the period of function is

the time that the wheel takes

one rotation =>30 minutes

Answer:

0.075

Step-by-step explanation:

Answer:

The half-life for the zombie population is of 8 years.

Step-by-step explanation:

Exponential equation:

An exponential equation has the following format:

[tex]N(t) = N(0)(1-r)^t[/tex]

In which N(0) is the initial value and the part [tex](1-r)^t[/tex] is related to the decay.

In this question:

[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]

Thus N(0) = 300, that is, initial population of 300.

What is the half-life for the zombie population?

This is t for which N(t) = 0.5*300 = 150. So

[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]

[tex]150 = 300(0.5)^{\frac{t}{8}}[/tex]

[tex](0.5)^{\frac{t}{8}} = \frac{150}{300}[/tex]

[tex](0.5)^{\frac{t}{8}} = 0.5[/tex]

[tex](0.5)^{\frac{t}{8}} = (0.5)^1[/tex]

Equal exponents, so:

[tex]\frac{t}{8} = 1[/tex]

[tex]t = 8[/tex]

The half-life for the zombie population is of 8 years.

Answer:

Kelly will have to fill the cup 20 times.

Step-by-step explanation:

Volume of the cube:

Rectangular cube, so the volume of the cube is the multiplication of its three dimensions(3.8 inches, 2.5 inches and 7.2 inches).

V = 3.8*2.5*7.2 = 68.4 cubic inches.

If the bucket holds 1,368 cubic inches of water, how many times will Kelly have to fill the cup in order to fill the bucket?

Solved by proportions, using a rule of three.

1 time - 68.4 cubic inches

x times - 1368 cubic inches

Applying cross multiplication:

[tex]68.4x = 1368[/tex]

[tex]x = \frac{1368}{68.4}[/tex]

[tex]x = 20[/tex]

Kelly will have to fill the cup 20 times.

Answer:

When something is inversely proportional it can be solved by using the equation:

y = k/x

where k is the constant.

So using this we can plug in x and y to find the value of k.

3 = k/4.

Next we isolate k and find that k = 12. Now we use this to find the value of y when x = 8. Plug in x and you get y = 12/8 or y = 3/2 or 1.5.

Another way to solve this is to look at how the value of x changes. When the value of x goes up, the value of y goes down.

In other words, when x is multiplied by some number, y is divided by that number. In this equation we can see that x is multiplied by 2 to go from 4 to 8.

Thus, y must be divided by 2.

Thus, y = 3/2 or 1.5.

Answer:

Step-by-step explanation:

y is inversely proportional to tan x means  

                                                            [tex]y \ \alpha \ \frac{1}{tan x}\\\\y = k \times \frac{1}{tanx}[/tex]

Given y = 2 when x =30° . So we will find k.

                            [tex]y =k \times \frac{1}{tanx } \\\\2 = k \times \frac{1}{tan 30}\\\\k = 2 \times tan 30 = 2 \times \frac{1}{\sqrt{3}} = \frac{2}{\sqrt{3} }[/tex]

Now x is doubled, x = 60°, find y

                         [tex]y = k \times \frac{1}{tanx}\\[/tex]

                            [tex]= \frac{2}{\sqrt{3}} \times \frac{1}{tan 60}\\\\= \frac{2}{\sqrt{3}} \times \sqrt{3}\\\\=2[/tex]