What is the value of the x variable in the solution to the following system of equations? (5 points) 2x − 3y = 3 5x − 4y = 4 Select one: a. −1 b. 0 c. x can be any number as there are infinitely many solutions to this system d. There is no x value as there is no solution to this system

Answer:

a) 0.0081 = 0.81% probability that he receives no job offer

b) He expects to get 2.8 job offers.

c) 0.0837 = 8.37% probability that more than half of the firms he applied do not make him any offer.

d) Each job must be independent of other jobs. Additionaly, if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal approximation to the binomial distribution can be used.

e) 0.2401 = 24.01% probability of him securing more than 3 offers.

Step-by-step explanation:

For each application, there are only two possible outcomes. Either he gets an offer, or he does not. The probability of getting an offer for a job is independent of any other job, which 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.

He can expect to receive a job offer from 70% of the firms to which he applies.

This means that [tex]p = 0.7[/tex]

The student decides to apply to only four firms.

This means that [tex]n = 4[/tex]

(a) What is the probability that he receives no job offer?

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_{4,0}.(0.7)^{0}.(0.3)^{4} = 0.0081[/tex]

0.0081 = 0.81% probability that he receives no job offer.

(b) How many job offers he expects to get?

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

In this question:

[tex]E(X) = 4(0.7) = 2.8[/tex]

He expects to get 2.8 job offers.

(c) What is the probability that more than half of the firms he applied do not make him any offer?

Less than 2 offers, which is:

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

So

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

[tex]P(X = 0) = C_{4,0}.(0.7)^{0}.(0.3)^{4} = 0.0081[/tex]

[tex]P(X = 1) = C_{4,1}.(0.7)^{1}.(0.3)^{3} = 0.0756[/tex]

Then

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0081 + 0.0756 = 0.0837[/tex]

0.0837 = 8.37% probability that more than half of the firms he applied do not make him any offer.

(d) What assumptions do you need to make to find the probabilities? To increase the chance of securing more job offers, the student decides to apply to as many companies as possible, he sent out 60 applications to all different accounting firms.

Each job must be independent of other jobs. Additionaly, if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal approximation to the binomial distribution can be used.

(e) What is the probability of him securing more than 3 offers?

Between 4 and n, since n is 4, 4 offers, so:

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

[tex]P(X = 4) = C_{4,4}.(0.7)^{4}.(0.3)^{0} = 0.2401[/tex]

0.2401 = 24.01% probability of him securing more than 3 offers.

Answer:

D

Step-by-step explanation:

RS is a side.

RQ = QS  They are both equal to seven.

That means that the answer is A or D

Since the word side is in D, it must be the answer.

Answer:

0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.

Step-by-step explanation:

The trees are arranged, so the arrangements formula is used to solve this question. Also, a probability is the number of desired outcomes divided by the number of total outcomes.

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

Desired outcomes:

Two cases:

6 redwoods(6! ways) then the 6 pine trees(6! ways)

6 pine trees(6! ways) then the 6 redwoods(6! ways)

So

[tex]D = 2*6!*6![/tex]

Total outcomes:

12 trees, so:

[tex]D = 12![/tex]

What is the probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other?

[tex]p = \frac{D}{T} = \frac{2*6!*6!}{12!} = 0.0022[/tex]

0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.

Answer:

I hope it help and I guess it is correct

Given:

The given expression is:

[tex]6x^2y-3xy-24xy^2+12y^2[/tex]

To find:

Part A: The expression by factoring out the greatest common factor.

Part B: Factor the entire expression completely.

Solution:

Part A:

We have,

[tex]6x^2y-3xy-24xy^2+12y^2[/tex]

Taking out the highest common factor 3y, we get

[tex]=3y(2x^2-x-8xy+4y)[/tex]

Therefore, the required expression is [tex]3y(2x^2-x-8xy+4y)[/tex].

Part B:

From part A, we have,

[tex]3y(2x^2-x-8xy+4y)[/tex]

By grouping method, we get

[tex]=3y(x(2x-1)-4y(2x-1))[/tex]

[tex]=3y(x-4y)(2x-1)[/tex]

Therefore, the required factored form of the given expression is [tex]3y(x-4y)(2x-1)[/tex].

Answer:

Step-by-step explanation:

Given inequality:

Since b is negative, when multiplied by b, the inequality changes to opposite direction:

Answer:

B. ∆LMN ≅ ∆OPQ because of ASA

Step-by-step explanation:

Two triangles are congruent if two angles and an included side of one triangle are congruent to two corresponding angles and a corresponding included side of the other.

From the information given, we have:

Two angles (<L and <M) in ∆LMN that are congruent to two corresponding angles (<O and <P) in ∆OPQ.

Also, included side in both triangles are congruent (ML ≅ PO).

Therefore, ∆LMN ≅ ∆OPQ by the ASA Theorem.

Answer:

68.3 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan I = opp side / adj side

tan I = sqrt(82) / sqrt(13)

tan I = sqrt(82/13)

Taking the inverse tan of each side

tan ^-1 ( tan I) = tan ^-1( sqrt(82/13))

I = 68.2892

Rounding to the nearest tenth

I = 68.3 degrees

Answer:

50%

Step-by-step explanation:

35 is halve of 70 therefore it is 50%

hope it helps u...........

Answer:

15 cups

Step-by-step explanation:

1 quart = 4 cups

3.75 quarts = (3.75 * 4) cups

3.75 quarts = 15 cups

3.75 quarts mean 15 cups

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given

1 quart = 4 cups

3.75 quarts = (3.75 * 4) cups

3.75 quarts = 15 cups

To know more about unitary methods refer to:

https://brainly.com/question/27989833

#SPJ2

Answer:

142

Step-by-step explanation:

If the enrollment is five times as big, then that is six different things. So, take 852 and divide it by 6 to get 142. Or in other words:

852÷6=142

142x6=856

I hope this helps. Cheers^^

Answer: Because they are corresponding angles (second option is the answer).

Answer:

second option...because they are corresponding angles..

STEP BY STEP EXPLANATION: corresponding angles are formed when two parallel lines are intersected by the transversal

the corresponding angles are 2 and 6

Step-by-step explanation:

Recall that

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

Therefore,

[tex]\csc(-x) = \dfrac{1}{\sin(-x)} = -\dfrac{1}{\sin x}[/tex]

so

[tex]\csc(-x)\tan x = \left(-\dfrac{1}{\sin x}\right)\left(\dfrac{\sin x}{\cos x}\right)[/tex]

[tex]\:\:\:\:\:\:\:\:\:= -\dfrac{1}{\cos x} = -\sec x[/tex]

Answer:

-3(z-x) = y

Step-by-step explanation:

Z=x-y/3

Solve for y

Subtract x from each side

z-x = x- y/3 -x

z-x = -y/3

Multiply each side by -3

-3(z-x) = -y/3 * -3

-3(z-x) = y

4. Percent increase

Because Original Value < New Value

5. Percent

6. Whole

Because it's asking what number that means total.

Thanks :)

Answer:

1.46 dollars per pound

Step-by-step explanation:

Take the total cost and divide by the number of pounds

7.30 dollars / 5 pounds

1.46 dollars per pound

Answer:

1.46

Step-by-step explanation:

Unit rate is the amount for only one pound. To do this, divide 7.30 and 5.

Divide:

7.3 / 5 = 1.46

Each pound is $1.46

Hope this helped.

Answer:

the answer is 4

Step-by-step explanation:

the answer will be positive

Answer:

Step-by-step explanation:

Side=AC=9[tex]\sqrt{2}[/tex]

Side AB= x

Hypotenuse =CB= y

Side AB = 9[tex]\sqrt{2}[/tex]

Hypotenuse CB = 36

Answer:

The answer to your question will be the choice "D."

Answer:

Step-by-step explanation:

a) categorical

b) add all of the numbers and divide by how many numbers there were.

c) outliers means any that were far away from the rest of the data

d) not entirely, you can make an estimate based on it, but nat an exact answer.

Answer:

f(1) = -2

f(x) =1 when x=0 or x=-2

Step-by-step explanation:

f(1) is the y value when x=1

f(1) = -2

f(x) = 1 means find the x value when y=1

when y =1, x =0 and -2

9514 1404 393

Answer:

  3×10^8 m/s

Step-by-step explanation:

The desired speed is ...

  [tex]\dfrac{\dfrac{9.45\times10^{15}\text{ m}}{\text{yr}}}{\dfrac{3.15\times10^7\text{ s}}{\text{yr}}}=\dfrac{9.45}{3.15}\times10^{15-7}\text{ m/s}=\boxed{3.00\times10^8\text{ m/s}}[/tex]

__

Your calculator can help you figure this out.

Answer:

5880 ways

Step-by-step explanation:

For selections like this, we solve using the combination theory. Recall that

nCr = n!/(n-r)!r!

Hence given to find the number of ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies,

= 10C6 * 8C4

= 10!/(10-6)!6! * 8!/(8-6)!6!

= 10 * 9 * 8 * 7 * 6!/4 *3 *2 * 6! * 8 * 7 * 6!/2 * 6!

= 210 * 28

= 5880 ways

The arrangement can be done in 5880 ways

Answer:

0.1088 or 10.88%

Step-by-step explanation:

q = 1 - 0.35 = 0.65

P(X=2) = 12C2 × (0.35)² × (0.65)¹⁰

= 0.1088

Answer:

1520.5 in^2

Step-by-step explanation:

Surface area=2*pi*r^2+2*pi*r*h=2*pi*r*(r+h)=2*pi*11*22=1520.5 in^2

Answer:

B

Step-by-step explanation:

The answer can be obtained by simplifying the whole fraction

Answer:

1. x = 20     2. n = 50

Step-by-step explanation:

1/4x - 2 = 3

1/4x = 5

x = 20

2. 8 = 1/5n - 2

10 = 1/5n

n = 50

Answer:

Question 1

Original equation:

1/4x-2=3

Add 2 to both sides:

1/4x=5

Multiply both sides by 4/1:

x=20

Question 2

Original equation:

8=1/5n x 2

Divide both sides by 2

4 = 1/5n

Multiply both sides by 5/1

n=20

Let me know if this helps!