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What is the radius of a circle whose equation is (x - 7)2 + (y - 10)2 = 4?
2 units
ОО
4 units
8 units
16 units

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:

c

Step-by-step explanation:

use the distributive property to expand the expression:

-2(9 + 32n)

-2*9 + (-2*32n)

-18 - 64n

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:

108.82

Step-by-step explanation:

Answer:

No, it is not a function graph, as there are no variables present in this image.

9514 1404 393

Answer:

  (x, y) = (4, -3)

Step-by-step explanation:

The solution is the point on the graph where the lines intersect:

  (x, y) = (4, -3)

9514 1404 393

Answer:

  (x/y)^(m+n)

Step-by-step explanation:

  [tex]\displaystyle\frac{\left(x+\frac{1}{y}\right)^m\left(x-\frac{1}{y}\right)^n}{\left(y+\frac{1}{x}\right)^m\left(y-\frac{1}{x}\right)^n}=\left(\frac{x}{y}\right)^m\left(\frac{x}{y}\right)^n\\\\=\boxed{\left(\frac{x}{y}\right)^{m+n}}[/tex]

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

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

Explanation:

At 95% confidence, the z critical value is roughly z = 1.960

The population standard deviation is given to be sigma = 3.7

The error is E = 2 since we want to be within 2 inches of the population mean mu

The min sample size needed is:

n = (z*sigma/E)^2

n = (1.960*3.7/2)^2

n = 13.147876

n = 14

We always round up to the nearest whole number to ensure that we clear the hurdle (otherwise, the sample is too small). It doesn't matter that we're closer to 13 than to 14.

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:

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

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:

98

Step-by-step explanation:

2, 10, 18, 26, 34, 42, 50... 98

Hope this helps. Have a great day!

Answer: 58

Step-by-step explanation:

its 58 because chickens have two feet each so divide 2 %  166 and its 58

because each chicken has 2 legs count the 2 legs up to 116 then u get ur answer

Answer:

[tex]\displaystyle \frac{1}{9}[/tex]

Step-by-step explanation:

Hi there!

This question is asking us what the value of y is when x is -2, hence the point (-2,y).

[tex]y=3^x[/tex]

To find y, replace x in the equation with -2 and evaluate:

[tex]y=3^-^2[/tex]

When [tex]a^-^n[/tex] where n>0, [tex]a^-^n=\displaystyle \frac{1}{a^n}[/tex]:

[tex]y=\displaystyle \frac{1}{3^2} \\\\y=\displaystyle \frac{1}{9}[/tex]

I hope this helps!

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

Answer:

0

Step-by-step explanation:

We have two points so we can use the sloe formula

m = (y2-y1)/(x2-x1)

   = ( 10-10)/(1-4)

  = 0/ -3

  = 0

Answer:

Slope is 0

explanation:

Slope is the same as gradient.

Formular:

[tex]{ \boxed{ \bf{slope = \frac{y _{2} - y _{1}}{x _{2} - x _{1} } }}}[/tex]

Substitute the variables:

[tex]{ \tt{slope = \frac{10 - 10}{1 - 4} }} \\ \\ = { \tt{ \frac{0}{ - 3} }} \\ = 0[/tex]

Answer:

I hope it help and I guess it is correct

Answer:

[tex]43.13 = 5.25h + 9[/tex]

Step-by-step explanation:

Let's solve this by making an equation.

$9 for the helmet, and $5.25 per hour.

h will stand for hours, C will stand for Amanda's cost.

[tex]C = 5.25h + 9[/tex]

Now, substitute in what we learned from the problem.

[tex]43.13 = 5.25h + 9[/tex]

This is an equation you can use to solve for the hours.

Answer:

[tex]\displaystyle\frac{19,683}{200,000}\text{ or }\approx 9.84\%[/tex]

Step-by-step explanation:

For each planted seed, there is a 90% chance that it grows into a healthy plant, which means that there is a [tex]100\%-90\%=10\%[/tex] chance it does not grow into a healthy plant.

Since we are planting 6 seeds, we want to choose 2 that do not grow and 4 that do grow:

[tex]\displaystyle \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}[/tex]

However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):

[tex]\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15[/tex]

Therefore, we have:

[tex]\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%[/tex]

Answer:

[tex] {?}^{?} However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):

\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15(26)=2!6⋅5=230=15

Therefore, we have:

\begin{gathered}\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%\end{gathered}P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅(26),P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅15,P(exactly 2 don’t grow)=200,00019,683≈9.84%

[/tex]

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:

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^^

Volume = πr²h

Radius = 3yd

Height = 12yd

Take π = 22/7

Volume = 22/7×3×3×12

= 2376/7

= 339.4285714yd³

Rounding off to nearest tenth

= 339.43yd³

Answered by Gauthmath must click thanks and mark brainliest

explainion:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

Use The (Pythagorean Theorem) to find the length of any side of a right triangle. Form it like its shown in picture above. Follow the instructions that also shown in the picture above.

Answer:

Step-by-step explanation:

(-1,7), (0,5), (1,3)

and

(0,-3), (2,5), (4,13)