If two events are complementary, then we know that: Multiple Choice the sum of their probabilities is one. the joint probability of the two events is one. their intersection has a nonzero probability. they are independent events.

Answer:

1. tan(65) = x/3

x = 3tan(65)

= 6.434

≈ 6.4

(nearest 10th)

2. cos(43) = AB/17

AB = 17cos(43)

= 12.433

≈ 12.43

(nearest 100th)

Answer:

Yeah

Step-by-step explanation:

Answer:

Step-by-step explanation:

1- digit numbers:

2- digit numbers:

3- digit numbers:

This is more than we have, but we know the number of pages is 3-digit.

Let it be x, then we have:

Answer: How are we going to point it?

Step-by-step explanation:

Answer:

What exactly is the question?? u only gave the statement -_-

Step-by-step explanation:

Answer:

625

Step-by-step explanation:

First, you have to convert 0.2 grams to mg.  To do this, multiply 0.2 by 1000.  This yield 200.  Now 200 is what percent of 32.  

200 * 100 / 32

= 625

9514 1404 393

Answer:

  (a) 10

Step-by-step explanation:

Attached is a graphical solution using "substitution." An expression was written for z using the first equation, and it was substituted into the remaining two equations. This gave two equations in x and y, easily solved graphically.

We found x = 10, y = 3, so ...

  z = 3(10) -4(3) -14 = 30 -12 -14 = 4

The whole solution is (x, y, z) = (10, 3, 4).

Answer:

58+-43=15

Step-by-step explanation:

Answer:

Option A. Only Khaled

Step-by-step explanation:

To know which option is correct, we shall use the formula suggested by both Khaled and Wilma to see which will give the sequence given in the question.

For Khaled:

F(n) = 1 • 3ⁿ¯¹

n = 1

F(n) = 1 • 3ⁿ¯¹

F(1) = 1 • 3¹¯¹

F(1) = 1 • 3⁰

F(1) = 1 × 1

F(1) = 1

n = 2

F(n) = 1 • 3ⁿ¯¹

F(2) = 1 • 3²¯¹

F(2) = 1 • 3¹

F(2) = 1 × 3

F(2) = 3

n = 3

F(n) = 1 • 3ⁿ¯¹

F(3) = 1 • 3³¯¹

F(3) = 1 • 3²

F(3) = 1 × 9

F(3) = 9

For Wilma

F(n) = 1 • 3ⁿ

n = 1

F(n) = 1 • 3ⁿ

F(n) = 1 • 3¹

F(1) = 1 × 3

F(1) = 3

n = 2

F(n) = 1 • 3ⁿ

F(2) = 1 • 3²

F(2) = 1 × 9

F(2) = 9

n = 3

F(n) = 1 • 3ⁿ

F(3) = 1 • 3³

F(3) = 1 × 27

F(3) = 27

SUMMARY

Using Khaled's formula i.e F(n) = 1 • 3ⁿ¯¹ we obtained 1, 3, 9,..

Using Wilma's formula i.e F(n) = 1 • 3ⁿ

We obtained 3, 9, 27,..

Now, comparing the sequence obtained using the formula of both Khaled and Wilma, we can see that only the sequence of Khaled is the same with the one given in the question. Therefore, only Khaled's formula is correct.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the image of the polygon is not given.

I will answer this question with the attached image (similar to your question)

The attached polygon is a trapezoid of the following dimensions.

[tex]Height = 4ft[/tex]

Parallel sides

[tex]Side\ 1 = 4ft[/tex]

[tex]Side\ 2 = 4ft+1ft = 5ft[/tex]

So, the area is:

[tex]Area = \frac{1}{2} * (Side\ 1 + Side\ 2) * Height[/tex]

[tex]Area = \frac{1}{2} * (4ft + 5ft) * 4ft[/tex]

[tex]Area = \frac{1}{2} * 9ft * 4ft[/tex]

[tex]Area = 18ft^2[/tex]

Answer:

[tex] - \frac{4}{5}[/tex]

Step-by-step explanation:

Line is passing through the points (-3, 1) & (2, - 3)

Therefore,

Slope of line

[tex] = \frac{ - 3 - 1}{2 - ( - 3)} \\ \\ = \frac{ - 4}{2 + 3} \\ \\ = - \frac{4}{5} [/tex]

Answer:

The total pay would be $50, But there would also be tax to consider in this situation.

Answer:

The trace of the water left on the floor is 566 cm.

Step-by-step explanation:

The bicycle wheel has a circular shape, therefore;

1 revolution is the same as the circumference of the wheel. So that 3 revolutions is the same as multiplying the circumference of the wheel by 3.

circumference = 2[tex]\pi[/tex]r

where r is the radius of the wheel (r = 30 cm).

Thus,

circumference = 2 x [tex]\frac{22}{7}[/tex] x 30

                        = [tex]\frac{1320}{7}[/tex]

circumference = 188.57 cm

3 revolutions = 3 x 188.57

                      = 565.71 cm

Therefore, the trace of the water left on the floor is 566 cm.

Answer:

brainllest if right

2

Step-by-step explanation:

Answer:

I don't know sorry

Step-by-step explanation:

Answer:

3 1/3 each

Step-by-step explanation:

10/3=3 1/3

Answer:

Domain: [tex][3,\infty)[/tex]

Range: [tex][6,\infty)[/tex]

Step-by-step explanation:

I assume you mean [tex]y=\sqrt{x-3} +6[/tex]?

Take note of how x cannot be less than 3 because it would result in a negative number under the radical, which isn't real. However, x CAN be 3 because [tex]\sqrt{3-3}+6=\sqrt{0}+6=0+6=6[/tex] which is real.

Therefore, the domain of the function is [tex][3,\infty)[/tex]

As for the range of the function, we saw previously that the minimum of the domain resulted in the minimum of the range, which was 6.

Therefore, the range of the function is [tex][6,\infty)[/tex]

See attached graph below for a visual.

Answer:

there are 52 cards in a deck so the chance is a red card (or not a red card) is 26 out of 52.

Step-by-step explanation:

The solution is 12/13

The probability that the selected card is not an ace but a red card is 12/13

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

The value of probability lies between 0 and 1

Given data ,

Let the probability of the selected card is not an ace but a red card be P

Now , the equation will be

Mason randomly chooses a card from a standard deck of playing cards

So , the probability that the card is a red card is

There are 26 red cards in the deck of 52 cards

So , the probability of selecting a red card = 26/52

Now , from the 26 red cards , the probability that the card is not an ace would be = 26 - ( Ace of hearts + Ace of diamonds )

And ,

The probability of the selected card is not an ace but a red card P = 24/26

The probability of the selected card is not an ace but a red card P = 12/13

Therefore , the value of P is 12/13

Hence , the probability is 12/13

To learn more about probability click :

https://brainly.com/question/17089724

#SPJ2

Answer:

$1.33

Step-by-step explanation:

Determine the cost per ounce of the larger bottle

cost per ounce = cost of larger bottle / total ounces

$12.99 / 150 = $0.0866

Multiply cost per ounce by 100

$0.0866 x 100 = $8.66

Subtract the above figure from 9.99

9.99 -  $8.66 = $1.33

9514 1404 393

Answer:

  (3)  35·cos(57°)

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

For the given triangle, this is ...

  cos(57°) = QR/QS

Multiplying by QS gives ...

  QS·cos(57°) = QR

Filling in the value of QS, we have ...

  QR = 35·cos(57°)

Answer:

a. 0.008 = 0.8% probability that the person will answer all three questions correctly.

b. 0.096 = 9.6% probability that the person will answer exactly two questions correctly.

c. 0.384 = 38.4% probability that the person will answer exactly one question correctly.

d. 0.512 = 51.2% probability that the person will answer no questions correctly.

e. The expected value of the person’s score for the three questions is -0.2.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the person answers it correctly, or they do not. The probability of a person answering a question correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Each question has five possible answers.

Person has no idea which option is correct, so the probability of answering correctly is:

[tex]p = \frac{1}{5} = 0.2[/tex]

Three questions:

This means that [tex]n = 3[/tex]

a. What is the probability that the person will answer all three questions correctly?

This is [tex]P(X = 3)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.2)^{3}.(0.8)^{0} = 0.008[/tex]

0.008 = 0.8% probability that the person will answer all three questions correctly.

b. What is the probability that the person will answer exactly two questions correctly?

This is [tex]P(X = 2)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{3,2}.(0.2)^{2}.(0.8)^{1} = 0.096[/tex]

0.096 = 9.6% probability that the person will answer exactly two questions correctly.

c. What is the probability that the person will answer exactly one question correctly?

This is [tex]P(X = 1)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{3,1}.(0.2)^{1}.(0.8)^{2} = 0.384[/tex]

0.384 = 38.4% probability that the person will answer exactly one question correctly.

d. What is the probability that the person will answer no questions correctly?

This is [tex]P(X = 0)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.2)^{0}.(0.8)^{3} = 0.512[/tex]

0.512 = 51.2% probability that the person will answer no questions correctly.

e. Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deducted for each incorrect answer. What is the expected value of the person’s score for the three questions?

The expected number of correct answer is:

[tex]E(X) = np = 3*0.2 = 0.6[/tex]

And the expected number of wrong answers is 3 - 0.6 = 2.4. So, the expected score is:

[tex]S(x) = 0.6 - \frac{2.4}{3} = 0.6 - 0.8 = -0.2[/tex]

The expected value of the person’s score for the three questions is -0.2.

9514 1404 393

Answer:

  19

Step-by-step explanation:

The evaluation is easier if we simplify the expression first.

  9(n +2) -5n = 9n +18 -5n = 4n +18

For n = 1/4, this is ...

  = 4(1/4) +18 = 1 +18

  = 19

The value of the expression for n = 1/4 is 19.

Answer:

57639 employees in total.

Step-by-step explanation:

28.8% of X = 16600

X = 16600 / 28.8%

= 16600 / 0.288

= 57638.89

=57639

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the regression line is not given.

However, I will give a general explanation of how to calculate the degree of freedom of a slope of regression line

The degree of freedom is calculated using:

[tex]df = n - k[/tex]

Where

[tex]k \to number\ of\ parameters[/tex]

[tex]n \to sample\ size.[/tex]

For a regression line; there are two parameters that are being estimates;

The intercept and the slope. So:

[tex]k = 2[/tex]

Hence, the degree of freedom of a slope of regression line is:

[tex]df = n -2[/tex]

So; if for example

[tex]n =101[/tex]

the degree of freedom will be:

[tex]df =101 - 2[/tex]

[tex]df =99[/tex]

Answer:

z = 3a + 4

Step-by-step explanation:

Add 4 to both sides

Answer:

$32.50

Step-by-step explanation:

The total amount of candy bars is 26. Half of that is 13. 13 times the $2.50 for each is $32.50.