Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.​

Add boys and girls together for total students:

40 + 16 = 56 total students

Girls to total students is 16/56

Divide both numbers by 8 to get 2/7

The ratio is 2/7

[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]

[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]

[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]

In a class,

boys=40

girls =16

So,

The students of the class =

According to the question,

we have to find the ratio of girls to the total students

⠀⠀⠀⠀

[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]

⠀⠀⠀⠀

Hence,the ratio of girls to students is 2:7

⠀⠀⠀⠀

Answer:

a) By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.

b) Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.

c) 0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less

d) 0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 0.9 and standard deviation 1.1.

This means that [tex]\mu = 0.9, \sigma = 1.1[/tex]

Suppose a television network selects a random sample of 1000 families in the United States for a survey on TV viewing habits.

This means that [tex]n = 1000, s = \frac{1.1}{\sqrt{1000}} = 0.035[/tex]

a. Describe (as shape, center and spread) the sampling distribution of the possible values of the average number of children per family.

By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.

b. What average numbers of children are reasonably likely in the sample?

By the Empirical Rule, 95% of the sample is within 2 standard deviations of the mean, so:

0.9 - 2*0.035 = 0.83

0.9 + 2*0.035 =  0.97

Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.

c. What is the probability that the average number of children per family in the sample will be 0.8 or less?

This is the p-value of Z when X = 0.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]

[tex]Z = -2.86[/tex]

[tex]Z = -2.86[/tex] has a p-value of 0.0021

0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less.

d. What is the probability that the average number of children per family in the sample will be between 0.8 and 1.0?

p-value of Z when X = 1 subtracted by the p-value of Z when X = 0.8.

X = 1

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1 - 0.9}{0.035}[/tex]

[tex]Z = 2.86[/tex]

[tex]Z = 2.86[/tex] has a p-value of 0.9979

X = 0.8

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]

[tex]Z = -2.86[/tex]

[tex]Z = -2.86[/tex] has a p-value of 0.0021

0.9979 - 0.0021 = 0.9958

0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0

Answer:

(-1, -6)

Step-by-step explanation:

This a term in this function is not negative, which would make it be flipped over the x-axis. Therefore this function takes the typical parabola shape, and it will have a minimum point.

To find the x-value of the minimum use the formula -b / 2a.

-12 / 2(6) = -1

Then plug in the x-value and find the y-value for this function

f(-1) = 6(-1)^2 + 12(-1) = -6

Answer:

6 : 24

Step-by-step explanation:

If we are in the ratio of 1 to 4, the total is 1+4 = 5

Divide 30 by 5

30/5 = 6

Multiply each term in the ratio by 6

1  :4

1*6 : 4*6

6 : 24

Answer:

total ratio:

[tex] = 1 + 4 \\ = 5[/tex]

For the portion of 1:

[tex] = 30 \div \frac{1}{5} \\ = 30 \times 5 \\ = 150[/tex]

For the portion of 4:

[tex] = 30 \div \frac{4}{5} \\ = 30 \times \frac{5}{4} \\ = 37.5[/tex]

= 30 : 7.5

Hi there!  

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I believe your answer is:  

[tex]V=1000\text{mm}^3[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

I am assuming by the infomation given that the figure is a cube.

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the volume of the cube...}}\\\\S = 10mm; V= s^3\\--------------\\\rightarrow V = 10^3\\\\\rightarrow V = 10 * 10 * 10\\\\\rightarrow \boxed{V=1000\text{mm}^3}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

1/4 *1/4*1/2 =0.03125

which as a fraction is 1/32

so the minimuim number of passes that will get him a goal is 1 since he could get it on the first try

Hope This Helps!!!

Answer:

-4 ≤ x ≤ -2, 4 ≤ x ≤ 7

Step-by-step explanation:

A function shows the relationship between two or more variables. A function is said to be constant over an interval if its output value is same for every input value within that interval.

As seen in the question, the x variable is the input while the y variable is the output. The function is constant from x = -4 to x = -2. Also, the function is constant within the interval from x = 4 to x = 7. Hence, the interval is:

-4 ≤ x ≤ -2, 4 ≤ x ≤ 7

Answer: A.

Step-by-step explanation:

Hope this helps!

Answer:

[tex]y = \frac{5ct}{3b}[/tex]

Step-by-step explanation:

[tex]\frac{5t}{4y} =\frac{3b}{4c}[/tex]

1. start by multiplying y to both sides:

y × [tex]\frac{5t}{4y} =\frac{3b}{4c}[/tex] × y

[tex]\frac{5t}{4} =\frac{3b}{4c}y[/tex]

2. divide both sides by [tex]\frac{3b}{4c}[/tex]

[tex]\frac{5t}{4}/\frac{3b}{4c} =\frac{3b}{4c}y/\frac{3b}{4c}[/tex]

[tex]y = \frac{5ct}{3b}[/tex]

Answer:

B. 0.41

Step-by-step explanation:

Binomial experiment:

In a binomial experiment, the probability of the success on each trial is always the same.

The probability of success on trial 4 is 0.41.

This means that the probability of success on trial 8, and all the other 10 trials, is of 0.41, and thus the correct answer is given by option B.

Answer:

Below.

Step-by-step explanation:

22-8 = 14x2 = 28.

Answer:

Step-by-step explanation:

Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.

The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.

The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).

The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320

(0+4)^3*(0-1)*k = 320

-64k = 320

k = -5

Combining all three conditions, f(x)

= -5(x+4)^3*(x-1)

= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)

= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)

= -5(x^4 + 11x^3 + 36x^2 + 16x -64)

= -5x^3 -55x^3 - 180x^2 - 80x + 320

Answer:

Step-by-step explanation:

-4 is a root for 3 times and 1 is root for once

so (x+4)^3 * (x-1) is part of f(x)

the constant term there is 4^3*(-1)=-64

so there is a multiplier of 320/-64=-5

f(x) = -5 * (x+4)^3 * (x-1)

Answer:

Circumference =10 pi yard

Area =25 pi yard squared

Step-by-step explanation:

C=2*pi*r

Circumfrance =10 pi

A=pi r^2

Area =25 pi

For the estimate just sub in pi on the calculator for pi, then round to the hundreth.

Circumfrence= just the unit

Area= squared

Answer:

first thing is y - 35 = 5

then y = 35 + 5 because when = come here - will be + and

then we should do+ y=40 answer

Answer:

a) {3,5}{3,10}{5,10}

b) [tex]P(A)=\frac{1}{3}[/tex]

c) [tex]P(B)=\frac{2}{3}[/tex]

d) [tex]P(C)=\frac{1}{3}[/tex]

e) [tex]P(A and C)=0[/tex]

f) [tex]P(A or B)=1[/tex]

g) [tex]P(B and C)=\frac{1}{3}[/tex]

h) [tex]P(A or C)=\frac{2}{3}[/tex]

i) [tex]P(C given B)=\frac{1}{2}[/tex]

j) [tex]P(C given A)=0[/tex]

k) [tex]P(not B)=\frac{1}{3}[/tex]

l) [tex]P(not C)=\frac{2}{3}[/tex]

Yes, events A and B are mutually exclusive. Because the results can either be even or odd, not both. No, events B and C are not mutually exclusive because the result can be both, odd and prime.

Step-by-step explanation:

a)

In order to solve part a of the problem, we need to find the possible outcomes, in this case, the possible outcomes are:

{3,5}{3,10} and {5,10}

We could think of the oppsite order, for example {5,3}{10,3}{10,5} but these are basically the same as the previous outcomes, so we will just take three outcomes in our sample space. We can think of it as drawing the two chips at the same time.

b)

Now the probability of the sum of the chips to be even. There is only one outcome where the sum of the chips is even, {3,5} since 3+5=8 the other outcomes will give us an odd number, so:

[tex]P=\frac{#desired}{#possible}[/tex]

[tex]P(A)=\frac{1}{3}[/tex]

c) For the probability of the sum of the chips to be odd, there are two outcomes where the sum of the chips is odd, {3,10} since 3+10=13 and {5,10} since 5+10=15 the other outcomes will give us an even number, so:

[tex]P(B)=\frac{2}{3}[/tex]

d) The probability of the sum of the chips is prime. There is only one outcome where the sum of the chips is prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:

[tex]P(C)=\frac{1}{3}[/tex]

e) The probability of the sum of the chips to be even and prime. There are no results where we can get an even and prime number, since the only even and prime number there is is number 2 and no outcome will give us that number, so:

P(A and C)=0

f) The probability of the sum of the chips is even or odd. We can either get even or odd results, so no matter what outcome we get, we will get an odd or even result so:

[tex]P(A or B)=1[/tex]

g) The probability of the sum of the chips is odd and prime. There is only one outcome where the sum of the chips is odd and prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:

[tex]P(B and C)=\frac{1}{3}[/tex]

h) The probability of the sum of the chips is even or prime. There are two outcomes where the sum of the chips is even or prime, {3,10} since 3+10=13 and {3,5} since 3+5=8 so:

[tex]P(A or C)=\frac{2}{3}[/tex]

i) The probability of the sum of the chips is prime given that the sum of the chips is odd. There are two possible results where the sum of the chips is odd {3,10} and {5,10} and only one of those results is even, {3,10}, so

[tex]P(C given B)=\frac{1}{2}[/tex]

j) The probability of the sum of the chips is prime given that the sum of the chips is even. There is only one possible even result: {3,5} but that result isn't prime, so

[tex]P(C given A)=0[/tex]

k) The probability of the sum of the chips is not odd. There is only one outcome where the sum of the chips is not odd (even), {3,5} so:

[tex]P(not B)=\frac{1}{3}[/tex]

l) The probability of the sum of the chips is not prime. There are two outcomes where the sum of the chips is not prime, {3,5} and {5,10} so:

[tex]P(not C)=\frac{2}{3}[/tex]

Are events A and B mutually exclusive?

Yes, events A and B are mutually exclusive.

Why or why not?

Because the results can either be even or odd, not both.

Are events B and C mutually exclusive?

No, events B and C are not mutually exclusive.

Why or Why not?

Because the result can be both, odd and prime.

Answer:

They are both 42 cm

Step-by-step explanation:

Answer:

3b^2 + 2b -8

Step-by-step explanation:

* means multiply

^ means exponent

3b * b = 3b^2

3b * 2 = 6b

-4 * b = -4b

-4 * 2 = -8

3b^2 + 6b -4b -8

3b^2 + 2b -8

Answer:

9.5hrs

Step-by-step explanation:

since they are working together you have to take the average time since is the same order

Answer:

$402.700 capital gain

Step-by-step explanation:

Answer:

1437.3 cm^3 is the volume of sphere whose radius is 7cm

Answer:

[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]k = 2[/tex] --- scale factor

Required

Relationship between ABC and A"B"C"

[tex]k = 2[/tex] implies that the sides of A"B"C" are bigger than ABC

i.e.

[tex]A"B" = 2AB[/tex]

[tex]A"C" = 2AC[/tex]

[tex]B"C" = 2BC[/tex]

In [tex]A"B" = 2AB[/tex]

Divide both sides by A"B"

[tex]1 = \frac{2AB}{A"B"}[/tex]

Divide both sides by 2

[tex]\frac{1}{2} = \frac{AB}{A"B"}[/tex]

Rewrite as:

[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]

(a) is correct

Answer:

40 degrees un edge

Step-by-step explanation:

Answer:

The person above me got this correct, so the answer to this is 40! I just did the Unit Test and got a 100%!

Answer:

Q9: x = 27, Q10: x = 17

Step-by-step explanation:

Answer:

y = -4/3x -46/3

Step-by-step explanation:

The question tells us to write an equation that is:

- parallel to the given line

- goes through the point (-7, -6)

Parallel lines will have the same slope, because if the slope was different, they would eventually intersect and not be parallel lines anymore.

We are going to use the point-slope form to find the other line.

Point-slope form uses a point that the graph will cross through and the slope of the graph to find the graph in y = mx + b form (also called slope-intercept form).

(I attached the point-slope form as an image below)

m = slope

x1 = x coordinate of the point

y1 = y coordinate of the point

We are going to substitute our slope into the form first:

y - y1 = (-4/3)(x - x1)

Next let's put in our point (-7, -6):

(Remember! -7 is our x coordinate & -6 is our y coordinate :-) )

y - (-6) = -4/3(x - (-7))

(cancel out the negatives to make them positive)

y + 6 = -4/3 (x +7)

Now solve for x using basic algebra:

y + 6 = -4/3 (x +7)

(distribue the -4/3)

y + 6 = -4/3x - 28/3

(subtract 6 from both sides)

y = -4/3x -46/3

That's your answer!

Hope it helps (●'◡'●)

Answer:

Step-by-step explanation:

y + 6 = -4/3(x + 7)

y + 6 = -4/3x - 28/3

y + 18/3 = -4/3x - 28/3

y = -4/3x - 46/3

Answer:

The next number is going to be 21

Answer:

19

Step-by-step explanation:

4 even number

3,5,7 odd numbers

14 even

17, 19, 21 even

Answer:

They can buy up to 240 drinks.

Step-by-step explanation:

Let x = number of drinks

The price of 1 drink is 75¢ = $0.75

The price of x drinks is 0.75x

The store gives a discount of $100.

The rice of x drinks is

0.75x - 100

The total price of the drinks must be less than or equal to $80.

0.75x - 100 ≤ 80

Add 100 to both sides.

0.75x ≤ 180

Divide both sides by 0.75

x ≤ 240

Answer: They can buy up to 240 drinks.

Answer:

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