Divide 4 and 5 over 6 ÷ negative 2 and 1 over 7.

Using the binomial distribution, the probabilities are given as follows:

a) 0.000041 = 0.0041%.

b) 0.7164 = 71.64%.

c) 0.2836 = 28.36%.

For each person, there are only two possible outcomes, either they have lost a friend, or they have not. The probability of a person having lost a friend is independent of any other person, hence the binomial distribution is used to solve this question.

The formula for the probability of x successes is:

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

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

The parameters are given by:

For this problem, the values of the parameters are:

n = 4, p = 0.08.

The probability of all four is P(X = 4), hence:

P(X = 4) = (0.08)^4 = 0.000041.

0.000041 = 0.0041% probability that all four have lost a friend or relative to murder.

The probability of none is P(X = 0), hence:

P(X = 0) = (0.92)^4 = 0.7164.

0.7164 = 71.64% probability that none have lost a friend or relative to murder.

The probability of at least one is given by:

P(X >= 1) = 1 - P(X = 0)

Then:

1 - 0.7164 = 0.2836.

0.2836 = 28.36% probability that at least one have lost a friend or relative to murder.

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A = 20

Use sine rule to find the other angles,

Answer:THE ANSWER IS NO.

Step-by-step explanation:

As we have given that x=8 and y=7

put theses values in given equations :-

 -x + y= -1

-8+7= -1,true

But, for 6x+y=41

We get 6*8+7=41

55 ≠41

Hence the answer is NO.

Answer:

(8,7)  is not a solution of the systems.

The percent of juniors whose score is at least 71 % is 69.15 %.

We are given that:

Test of the students are normally distributed.

Mean = μ = 71

Standard deviation = σ = 5

We need to find the percent of juniors whose score is at least 71 %.

Now, we know that:

z = ( x - μ) / σ

z = 100 - 71 / 5

z = 29 / 5

z = 5.8

So, percentage = 69.15 %

Therefore, we get that, the percent of juniors whose score is at least 71 % is 69.15 %.

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Answer: Raise

5

to the power of

4

= 625

Answer:

[tex]5^{4} =625..[/tex]

Step-by-step explanation:

[tex]5^{4} = 625[/tex]

[tex]=625[/tex]

hopefully this helps you :)

Answer:

  a. (-12, 14), (6, 2), (-3, 8)

  b. yes; R(-12, 14)

Step-by-step explanation:

Points P(-6, 10), Q(0, -6), and R lie on a line, with one of them being the midpoint of the other two. You want to know the possible locations of R, and its location if RQ=√208.

Point M is the midpoint of AB when ...

  M = (A +B)/2

If M and A are given, then B is ...

  2M -A = B . . . . . . above equation solved for B

There are three choices for the location of R.

P is the midpoint

  R = 2P -Q = 2(-6, 10) -(0, 6) = (-12, 20-6)

  R = (-12, 14)

Q is the midpoint

  R = 2Q -P = 2(0, 6) -(-6, 10) = (6, 12 -10)

  R = (6, 2)

R is the midpoint

  R = (P +Q)/2 = ((-6, 10) +(0, 6))/2 = (-6, 16)/2

  R = (-3, 8)

The possible coordinates of R are (-12, 14), (6, 2), (-3, 8).

The length of the given segment PQ is ...

  d = √((x2 -x1)² +(y2 -y1)²) . . . . . distance formula

  d = √((0 -(-6))² +(6 -10)²) = √(6² +(-4)²) = √(36 +16) = √52

This is half the length of RQ, so we must have P as the midpoint of RQ.

This distance information chooses one of the three points found in part (a), R(-12, 14).

The Isosceles triangle length of a² will be equal to (32 - 16√2).

What is an isosceles triangle?

The triangle in which the two opposite sides are equal and the two opposite angles are equal is called the isosceles triangle.

A triangle that has at least two sides of equal length is said to be isosceles. Sometimes it is stated to have exactly two sides that are the same length, while other times it is stated to have at least two sides that are the same length, with the latter version mentioning the equilateral triangle as an exception.

It is given that in an isosceles triangle abc has a=π/4 and b=c=4. Then the value of a² will be calculated as below:-

Using the cosine formula to calculate the value of a².

a² = b² + c² -2bc cosФ

a² = 16 + 16 - 2(4)(4)cos(π/4)

a² = 32 - ( 32 x {√2/2})

a² = 32 - 16√2

Therefore, the length of a² will be equal to (32 - 16√2).

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Answer:

4^2(2-root2)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

because it most reasonable

also you times the number as much as the exponents

Answer:

A. (5^8)/(5^9)

Step-by-step explanation:

Using the properties of exponents, in this case case the Power of Quotient Rule, can be changed into the one in A.

Answer:

The answer is $21,854. 35

Step-by-step explanation:

rate = 14.2%

Time = 3 years

Value = 34600

V = (1-r)^t

V=34600(1-0.142)^3

V=34600 (0.858)^3

V=$21,854.35

If a sophomore was chosen yesterday, the probability that a sophomore will be chosen again today is 3/10.

Given, number of students name put into the hat = 20

total number of freshmen in the class = 12

total number of sophomore in the class = 6

total number of juniors in the class = 2

we are asked to determine the probability that the sophomore will be selected the second day also = ?

Calculating a situation's probability allows us to determine its likelihood. Absolute certainty in forecasting is challenging in many situations. With its help, we are only able to anticipate the likelihood, or chance, that an event would occur.

from the given data,

n(s) = 20

n(A) = 6 ⇒ as the name selected in the first day is put back in the hat.

⇒ P(A) = n(A)/n(s)

P(A) = 6/20

P(A) = 3/10

hence the probability that the another day again a sophomore will be chosen is 3/10.

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The numbers are -3 and 6

From the information given, let the number be x;

the expression is given as;

(√3x + 2) = x - 4

To determine the number, find the square of both sides, we have;

(√3x + 2) ^2 = (x - 4)^2

Find the square of both sides

3x + 2 = ( x - 4)(x + 4); difference of two squares

expand the bracket

3x + 2 = x^2 + 4x - 4x - 16

collect like terms

x^2 - 3x - 16 - 2

x^2 - 3x - 18

x^2 - 6x + 3x - 18

Factorize the expression

x( x - 6) + 3( x - 6)

(x + 3) or (x - 6)

x = -3 or x = 6

Thus, the numbers are -3 and 6

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Answer: 2/4 cups of oil and 1.4 teaspoons and 1 cup of peanut butter

Step-by-step explanation: 3/4 take one out of it to make 2/4 since there are 2 dozen then to have 3 groups of 2 teaspoons it would be 0.7 but its an inf number so its 0.7 and then 1 cup of peanut butter because we are taking half of it away since you want 2 dozen.

The solution to the inequality is x ≥ 3

Given the inequality;

– 7x + 3 ≥ – 18

To determine the solution , we take the following steps;

collect like terms

-7x ≥ - 18 - 3

Find the difference

- 7x ≥ - 21

Make 'x' the subject of the formula by dividing both sides by its coefficient, - 7

We have;

-7x / -7 ≥ - 21/ -7

x ≥ 3

Thus, the solution to the inequality is x ≥ 3

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Answer:

Hey there i see that you are doing scientific notation things well i will help you

Step-by-step explanation:

so 5.2 X 10 to the 5th power = 520000

3.9 X 10 to the 8th power = 390000000

and 4.7 X 10 to the 5th power  = 470000

so on that info the answer is

4.7 x 10(5), 5.2 x 10(5), 3.9 x 10(8)

hope you have a nice day

Answer and work is all shown in the provided screenshot! I hope this helps! :)

Answer:...

Step-by-step explanation:

Answer:

Step-by-step explanation:

444

Using their concepts, we have that the measures are given as follows:

a) Mean of 1.0126.

b) Average deviation of 0.01632.

c) Percent deviation of 1.6%.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For this problem, the 5 observations are given as follows:

1.040, 0.989, 1.009, 1.026, 0.999.

Hence the mean is given by:

M = (1.040 + 0.989 + 1.009 + 1.026 + 0.999)/5 = 1.0126.

The average deviation of a data-set is given by the sum of the absolute values of the difference between each value and the mean, divided by the number of observations.

Hence:

Ad = (|1.040-1.0126| + |0.989-1.0126| + |1.009-1.0126| + |1.026-1.0126| + |0.999-1.0126|)/5 = 0.01632.

The percent deviation of a data-set is given by the absolute deviation divided by the mean and multiplied by 100%.

Hence:

0.01632/1.0126 x 100% = 1.6%.

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Answer:

1)

D) -5<x≤-2

R) 0<y≤3

2)

D) 1≤x≤5

R)2≤y≤4

Step-by-step explanation:

(Only in 7th so might be wrong)

1)

D) -5<x≤-2

R) 0<y≤3

2)

D) 1≤x≤5

R)2≤y≤4

look at the range of where the x and y is at (1-2 included = 1<x≤2)

Answer:

[tex]\frac{27}{20}[/tex]

Step-by-step explanation:

[tex]\frac{3}{5} + \frac{6}{8}[/tex]

adjust the denominators;

= [tex]\frac{3*8}{5*8} + \frac{6*5}{8*5}[/tex]

[tex]=\frac{24}{40} + \frac{30}{40} \\\\=\frac{24+30}{40} \\\\=\frac{54}{40} \\\\simplify\\\\=\frac{27}{20}[/tex]

Answer:

Step-by-step explanation:

its ''C''

the answer to your question is Ettwice is 45 years old and Mavis is 15 years old. hope this helps

Step-by-step explanation:

15 * 3 = 45

45 + 15 = 60

Answer:

Step-by-step explanation:

Given,

N= 100

Q1=?

We know that,

Q1= N/4

   = 100/4

   = 25

The amount due at maturity on Andres Michael's loan of interest rate of 3.75% is $20,431.75

What is effective monthly loan interest rate?

The loan effective monthly interest rate can be determined as the annual interest rate of 3.75% divided by 12 since there are 12 months in a year

effective monthly interest rate=3.75%/12

effective monthly interest rate=0.003125

loan balance after 4 months=$24,440*(1+0.003125)^4- $4,410

loan balance after 4 months=$20,336.94

loan balance after 12 months=$20,336.94*(1+0.003125)^8-$2,590

loan balance after 12 months=$18,260.96

balance at the 4 year(after another 36 months)=$18,260.96*(1+0.003125)^36

balance at the 4 year(after another 36 months)=$20,431.75

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Answer:

A. tenths

because there's only two digits after a comma

Answer:

The two solutions are

5 and 9

-5 and -9

Step-by-step explanation:

Let x and y be the numbers

x-y = 4

x*y = 45

Using substitution

x = 4+y

(4+y)y =45

4y + y^2 = 45

Subtract 45 from each side

y^2 +4y -45 =0

Factor

(y - 5) ( y+9) = 0

Using the zero product property

y -5 =0    y+9 =0

y=5    y = -9

Now we can find x

y=5

x = 4+y

x =4+5

x=9

y = -9

x = 4+y

x = 4+-9

x = -5

The two solutions are

5 and 9

-5 and -9

The hotel charge in city one is $767 and the hotel charge in city two is $2276.

Let x = the charge in 1st city before taxes and

Let y = the charge in 2nd city before taxes

The equation before taxes:

y = x ₊ 1500 ..eq(1)

The equation for total tax paid:

0.075x ₊ 0.055y = 700 ..eq(2)

Substitute equation 1 that is y value in equation 2.

0.075x ₊ 0.055(x₊1500) = 700

0.075x ₊ 0.055x ₊ 82.5 = 700

add the variables and subtract the constants.

0.805x = 700 ₋ 82.5

0.805x = 617.5

x = 617.5/0.805

x = 767

now substitute x value in equation 1.

y = 767 ₊ 1500

y = 2267

Hence the hotel charge before the tax in the first city was $767 and in the second city was $2267.

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Answer:

a. $2850

b. $6720

Step-by-step explanation:

a.

3000(1-0.05) = $2850

b.

7000(1-0.04) = $6720