Find the length of GV¯¯¯¯¯¯¯¯ A. 43.92 B. 33.1 C. 41.45 D. 68.87

Answer:

1) the domain is all real numbers

2) the range is

[tex]y \geqslant 3[/tex]

Answer:

(a) P(E∪F)= 0.8

(b) P(Ec)= 0.4

(c) P(Fc)= 0.7

(d) P(Ec∩F)= 0.8

Step-by-step explanation:

(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.

If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:

P(A∪B) = P(A) + P(B) - P(A∩B)

In this case:

P(E∪F)= P(E) + P(F) - P(E∩F)

Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1

P(E∪F)= 0.6 + 0.3 - 0.1

P(E∪F)= 0.8

(b)  The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A.  The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is  P (Ac) = 1- P (A)

In this case: P(Ec)= 1 - P(E)

Then: P(Ec)= 1 - 0.6

P(Ec)= 0.4

(c) In this case: P(Fc)= 1 - P(F)

Then: P(Fc)= 1 - 0.3

P(Fc)= 0.7

(d)  The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.

As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:

P(Ec intersection F) + P(E intersection F) = P(F)

P(Ec intersection F) + 0.1 = 0.3

P(Ec intersection F)= 0.2

Being:

P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)

you get:

P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)

So:

P(Ec∩F)= 0.4 + 0.3 - 0.2

P(Ec∩F)= 0.8

Answer:

The expression = [tex] \frac{40}{y - 16} [/tex]

Value of the expression = 4 (when y is 20)

Step-by-step explanation:

Quotient simply means the result you get when you divide two numbers. Thus, dividend (the numerator) ÷ divisor (the denominator) = quotient.

From the information given to us here,

the dividend = 40

the divisor = y - 16

The quotient = [tex] \frac{40}{y - 16} [/tex]

There, the expression would be [tex] \frac{40}{y - 16} [/tex]

Find the value of the expression when y = 20.

Plug in 20 for y in the expression and evaluate.

[tex] \frac{40}{y - 16} [/tex]

[tex] = \frac{40}{20 - 16} [/tex]

[tex] = \frac{40}{4} = 10 [/tex]

The value of the expression, when y is 20, is 4.

Answer:

A)0.126775 B)0.000004325376 C) 0.07548

Step-by-step explanation:

Given the following :

A.) a. n = 15, p = 0.4, find P(4 successes)

a = number of trials p=probability of success

P(4 successes) = P(x = 4)

USING:

nCx * p^x * (1-p)^(n-x)

15C4 * 0.4^4 * (1-0.4)^(15-4)

1365 * 0.0256 * 0.00362797056

= 0.126775

B)

b. n = 12, p = 0.2, find P(2 failures),

P(2 failures) = P(12 - 2) = p(10 success)

USING:

nCx * p^x * (1-p)^(n-x)

12C10 * 0.2^10 * (1-0.2)^(12-10)

66 * 0.0000001024 * 0.64

= 0.000004325376

C) n = 20, p = 0.05, find P(at least 3 successes)

P(X≥ 3) = p(3) + p(4) + p(5) +.... p(20)

To avoid complicated calculations, we can use the online binomial probability distribution calculator :

P(X≥ 3) = 0.07548

Answer:

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Step-by-step explanation:

Let be [tex]f(m, b) = m\cdot b - m^{2}[/tex], if [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex], the value of the expression:

[tex]f(3.48,96.52) = (3.48)\cdot (96.52)-3.48^{2}[/tex]

[tex]f(3.48,96.52) = 323.779[/tex]

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Answer: A) 0

P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.

We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.

Answer:

C

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Sequence a

30 - 10 = 20

90 - 30 = 60

270 - 90 = 180

This sequence is not arithmetic

Sequence b

200 - 100 = 100

300 - 200 = 100

400 - 300 = 100

This sequence is arithmetic but is finite, that is last term is 400

Sequence c

300 - 150 = 150

450 - 300 = 150

600 - 450 = 150

This sequence is arithmetic and infinite, indicated by ........ within set

Sequence d

2 - 1 = 1

4 - 2 = 2

8 - 4 = 4

This sequence is not arithmetic

Thus the infinite arithmetic sequence is sequence c

Weight of man and paint = 160 + 5 = 165 total pounds.

Gravitational force is independent of the path taken so we can ignore the radius of the silo.

Work done = total weight x height

The problem says he climbs to the top so overall height is 90 feet

Work = 165 lbs x 90 ft = 14,850 ft-lbs

Answer:

The answer is 216

Step-by-step explanation:

if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.

Answer:

Divide by 30.48: It would be 0.0656168 feet.

Step-by-step explanation:

Answer:

0.0656

Step-by-step explanation:

2.54 cm = 1 in

12 in = 1 ft

2.54 * 12 = 30.48

2/30.48 = 0.0656167979

False!

The answer is: False.

Whomever stated the answer is "true" is wrong.

Answer:

2 * (x + 2) = 50

Step-by-step explanation:

Let's call the unknown number x. "A number and 2" means that we need to add the numbers, therefore it would be x + 2. "Twice" means 2 times a quantity so "twice a number and 2" would be 2 * (x + 2). "Is" denotes that we need to use the "=" sign and because 50 comes after "is", we know that 50 goes on the right side of the "=" so the final answer is 2 * (x + 2) = 50.

Answer:

(7 x 2.85) + 5v = 28.70. 19.95 + 5v = 28.70. 5v = 28.70 - 19.95. 5v = 8.75. v = 8.75/5. v = 1.75. A pint of veggies costs $1.75.

Answer:

x = 200.674

Step-by-step explanation:

tan∅ = opposite/adjacent

Step 1: Find length of z

tan70° = 119/z

ztan70° = 119

z = 119/tan70°

z = 43.3125

Step 2: Find length z + x (denoted as y)

tan26° = 119/y

ytan26° = 119

y = 119/tan26°

y = 243.986

Step 3: Find x

y - z = x

243.986 - 43.3125 = x

x = 200.674

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

Explanation:

Check out the diagram below.

Draw a vertical number line with 0 at the center. The positive values are above it, while the negative values are below it.

Between -15 and -16, closer to -16, plot the value -15.8 to indicate Ben's position. I have done so as the point B.

We move 4.2 units up to arrive at Cam's position

-15.8 + 4.2 = -11.6

So Cam is 11.6 meters below the surface of the water.

Answer:

c/sin C = b/sin C

Step-by-step explanation:

Look at the statement in the previous step and the reason in this step.

c sin B = b sin C

Divide both sides by sin B sin C:

(c sin B)/(sin B sin C) = (b sin C)/(sin B sin C)

c/sin C = b/sin B

Answer:

-36

Step-by-step explanation:

3*12=36

she is going down (negative) so, it is -36

not sure if this is what you are asking for, if not try this

0-12-12-12=-36

Answer:

hello attached is the missing part of your question and the answer of the question asked

answer : 0.2951

Step-by-step explanation:

Given data:

number of persons allowed in the elevator = 15

weight limit of elevator = 2500 pounds

average weight of individuals = 152 pounds

standard deviation = 26 pounds

probability that an individual selected weighs more than 166 pounds

std = 26 ,  number of persons(x) = 15, average weight of individuals(u) = 152 pounds

p( x > 166 ) = p( x-u / std,  166 - u/ std )

                  = p (  z > [tex]\frac{166-152}{26}[/tex] )

                  = 1 - p( z < 0.5385 )

p( x > 166 ) = 1 - 0.70488 = 0.2951

Answer:

C. 329

Step-by-step explanation:

So 28 is 70% of 40

so we know that 70% percent of students have phones

70% of 470

329

Thats how I solved it have a great day :)

Answer:

A. 5:4

Step-by-step explanation:

Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.

Answer:

W = 9 * g

Step-by-step explanation:

W/9 = g

W = 9 * g

The expression W/9 = g can be written as W = 9g after cross multiplication.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

W/9 = g

To solve for W

Make subject as W:

W = 9g

By cross multiplication.

Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.

Learn more about the expression here:

brainly.com/question/14083225

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Answer:

Step-by-step explanation:

[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]

To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F

Let's solve

First expression = x - 2

Second expression = x + x - 6

Here, we have to find the two numbers which subtracts to 1 and multiplies to 6

= x + ( 3 - 2 ) x + 6

Distribute x through the parentheses

= x + 3x - 2x + 6

Factor out x from the expression

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

Factor out -2 from the expression

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

Factor out x+3 from the expression

= ( x + 3 ) ( x - 2 )

Here, x - 2 is common in both expression.

Thus, H.C.F = x - 2

Hope I helped!

Best regards!!!

Answer:

x - 2

Step-by-step explanation:

by factorization method

1) x - 2

2) x^2 + x - 6

by splitting method

x^2 + 3x - 2x - 6

taking separate common from the first two terms and last two terms

x(x + 3) - 2(x + 3)

now writing x+3 once and the other term to get the right answer

(x + 3)(x - 2)

in both parts just see the similar term and write it as HCF

HCF= x - 2

and the second method by which you can get this answer is division method

Answer:

0.065617 ft

Step-by-step explanation:

Answer:

0.0656168 feet.

Step-by-step explanation:

Answer:

32. A

33. B

Step-by-step explanation:

32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is

33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end

Complete Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive

Answer:

Yes the company conclude that the correlation is positive

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  14

    The correlation is  r =  0.65

The  null hypothesis is  [tex]H_o : r < 0[/tex]

The  alternative hypothesis is  [tex]H_1 : r > 0[/tex]

Generally the standard deviation is mathematically evaluated as

       [tex]Sr = \sqrt{1- r}[/tex]

       [tex]Sr = \sqrt{1- 0.65}[/tex]

       [tex]Sr = 0.616[/tex]

The  degree of freedom for the one-tail test is

       [tex]df = n- 2[/tex]

        [tex]df = 14- 2[/tex]

        [tex]df = 12[/tex]

The standard error is evaluated as

        [tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]

        [tex]SE =0.1779[/tex]

The test statistics  is evaluated as

      [tex]t = \frac{r }{SE}[/tex]

       [tex]t = \frac{0.65 }{0.1779}[/tex]

        [tex]t = 3.654[/tex]

The p-value of of  t is obtained from the z table, the value is  

        [tex]p-value = P(t < 3.654) = 0.00012909[/tex]

Given that [tex]p-value < \alpha[/tex]  then we reject the null hypothesis

           Hence the company can conclude that the correlation is positive

Answer:  60°

Step-by-step explanation:

∠UQR = 180°

∠UQR = ∠UQ + ∠QR

  180° =  115° + ∠QR

   65° = ∠QR

∠QRT = 180°

∠QRT = ∠QR + ∠RS + ∠ST

  180° =  65° + ∠RS  +  55°

  180° = 120° + ∠RS

   60° = ∠RS

The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Given that:

Find how many ways the 4 oldest people can be selected from the group.

Since the 4 oldest people are already determined, there is only 1 way to select them.

To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:

Number of ways to choose k items from n items :

C(n,k) = n! / (k!(n-k)!)

Calculate the total number of ways to select 4 people from the group:

Plugging n and k value from given data:

C(11,4 )= 11! / (4!(11-4)!)

On simplifications gives:

C(11, 4) = 330.

Calculate the probability:

Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people

Plugging the given data:

Probability = 1 / 330

Probability ≈ 0.00303 or 0.303%.

Therefore, the  probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Learn more about probabilities here:

https://brainly.com/question/23846068

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Answer:

16.24

Step-by-step explanation:

of means multiply

28% * 58

Change to decimal form

.28 * 58

16.24

Answer:

[tex]\Large \boxed{\mathrm{16.24}}[/tex]

Step-by-step explanation:

[tex]28\% \times 58[/tex]

[tex]\displaystyle \sf Apply \ percentage \ rule : a\%=\frac{a}{100}[/tex]

[tex]\displaystyle \frac{28}{100} \times 58[/tex]

[tex]\sf Multiply.[/tex]

[tex]\displaystyle \frac{1624}{100} =16.24[/tex]

Answer:

The frequency distribution does not appear to be normal.

Step-by-step explanation:

The data provided is as follows:

S = {0.38 , 0 , 0.22 , 0.06 , 0 , 0 , 0.21 , 0 , 0.53 , 0.18 , 0 , 0 , 0.02 , 0 , 0 , 0.24 , 0 , 0 , 0.01 , 0 , 0 , 1.28 , 0.24 , 0 , 0.19 , 0.53 , 0 , 0, 0.24 , 0}

It is provided that the first lower class limit should be 0.00 and the class width should be 0.20.

The frequency distribution table is as follows:

Class Interval  Count

 0.00 - 0.19            21

 0.20 - 0.39             6

 0.40 - 0.59             2

 0.60 - 0.79             0

 0.80 - 0.99             0

  1.00 - 1 . 19             0

  1.20 - 1. 39             1

The frequency distribution does not appear to be normal. This is because the frequencies does not start and end at almost equivalent points and the mid-distribution does not consist of the highest frequency.

Thus, the frequency distribution does not appear to be normal.