At a game show, there are 7 people (including you and your friend) in the front row.

The host randomly chooses 3 people from the front row to be contestants.

The order in which they are chosen does not matter.

There are 7C3=35 ways to choose the 3 contestants.

What is the probability that you and your friend are both chosen?

A. 2/3
B. 5/35
C. 2/35
D. 3/35

Answer: 3 7/20

Step-by-step explanation:

5 3/5 - 2 1/4

Find GCD.

5 12/20 - 2 5/20

3 7/20 more boxes of raspberries than strawberries

Answer:

The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8.

This means that:

[tex]\mu_A = 85, s_A = \frac{9.8}{\sqrt{22}} = 2.09[/tex]

An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6.

This means that:

[tex]\mu_N = 77, s_N = \frac{10.6}{\sqrt{47}} = 1.55[/tex]

Distribution of the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.

Mean:

[tex]\mu = \mu_A - \mu_N = 85 - 77 = 8[/tex]

Standard deviation:

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{2.09^2 + 1.55^2} = 2.6[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = zs[/tex]

So

[tex]M = 1.645*2.6 = 4.3[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 8 - 4.3 = 3.7

The upper end of the interval is the sample mean added to M. So it is 8 + 4.3 = 12.3

The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).

Answer:

-6,-2 is the answer!!

Step-by-step explanation:

The coordinate of A' would be (-6, -2)

Dilation is a transformation technique that changes the size of an object by a scale factor "k"

From the diagram shown, the measure of the coordinate point is given as (-3, -1).

If the coordinate A is dilated by a factor of 2, the resulting coordinate A' will be given as:

A' = (2(-3), 2(-1)) = (-6, -2)

Hence the  coordinate of A' would be (-6, -2)

Learn more on dilation here: https://brainly.com/question/3457976

Answer: 292

Step-by-step explanation:

Given

There are 240 members in a labor union

The number increases by 5% each year

After 1 year it is

[tex]\Rightarrow 240+5\%\times 240\\\Rightarrow 240(1+0.05)[/tex]

After 2 years

[tex]\Rightarrow 240(1+0.05)+5\%\times 240(1+0.05)\\\Rightarrow 240(1+0.05)(1+0.05)=240(1+0.05)^2[/tex]

Similarly, after 4 years

[tex]\Rightarrow 240(1+0.05)^4\\\Rightarrow 291.72\approx 292[/tex]

Answer:

friend alone could do it in 13 hours and 1/3

Step-by-step explanation:

Your rate = room/8

friends rate = room/x

combined rate = room/8 + room/x

= room(x+8)/(8x)

then

5 = room / [room(x+8)/(8x)]

5 = 8x/(x+8)

8x = 5x + 40

3x = 40

x = 40/3 = 13 1/3

friend alone could do it in 13 hours and 1/3

Answer:

Hence the carnival game gives you better chance of winning.

Step-by-step explanation:

Let the event of win be given by 1/10 in the game of rifle then the event of loose is given by 9/10

the

Odds in favor of a game are given by  = P(Event)/ 1- P(Event)

Odds in favor of winning a rifle are given by = 1/10/ 1- 1/10

                                                                         =1/10/9/10

                                                                          =1/9

                                                                             = 0.111

The probability of winning aa rifle game is 0.111

The probability of winning the carnival game is 0.15

Comparing the two probabilities   0.111:0.15

The probability of  winning carnival game is greater than winning a rifle game

0.15>0.11

Hence the carnival game gives you better chance of winning.

Answer: C

Step-by-step explanation:

Answer:

4+3+6+2 = 15

Step-by-step explanation:

selecting a yellow marker 4/15

selecting a red marker 2/15

Answer:

2option is the correct answer

Answer:

the answer is 3 hours

Step-by-step explanation:

it just makes sense

Answer:

90,000

Step-by-step explanation:

As an estimate

200 * 450

which is 90,000

9514 1404 393

Answer:

  no; √4 = 2

Step-by-step explanation:

If an integer is the square of another integer, its square root is rational. For example, 9 = 3², so √9 = 3, a rational number.

The square root of an integer is irrational if and only if the integer is not a perfect square.

Answer:

[tex]g(x) = 4[/tex]

Step-by-step explanation:

Given

[tex]g(x) = 3\frac{x}{2}[/tex]

Required

Find g(2)

This is calculated as:

[tex]g(x) = 3\frac{x}{2} \\[/tex]

Substitute 2 for x

[tex]g(x) = 3\frac{2}{2}[/tex]

[tex]g(x) = 3+1[/tex]

[tex]g(x) = 4[/tex]

Answer:

17.5

Step-by-step explanation:

35÷y = 140 ÷ 70

or, 35 = 2y

or, y= 17.5

Answer:

19

i hope this is the correct answer.

From the equation, the smaller number is 67/4.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x = smaller number and

y = bigger number

Then we can formulate an equation

x +y = 64 and y = 3x-3

Substituting y into

x+y = 64, we get the equation

[tex]x + 3x -3 = 64\\\\4x = 67\\\\x = \frac{67}{4}[/tex]

To learn more about equation: https://brainly.com/question/10413253

#SPJ2

Answer:

60,000

Step-by-step explanation:

Answer:

60,000

Step-by-step explanation:

Answer:

[tex]-6x^{3} + 322-7x - \frac{b}{x}[/tex]

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

Answer:

95% Confidence Interval = (611.81 ppm, 696.51 ppm)

Step-by-step explanation:

The formula for Confidence Interval is given as:

Confidence Interval = Mean ± z × s /√n

Mean = the sample mean/average = 654.16

s = the sample standard deviation = 164.55

z = z score of 95% confidence interval = 1.96

Confidence Interval =

654.16 ± 1.96 × 164.55/√58

= 654.16 ± 42.348

Hence,

654.16 - 42.348

= 611.812

Approximately to two decimal places = 611.81 ppm

654.16 + 42.348

= 696.508

Approximately to two decimal places = 696.51 ppm

Therefore, the 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected is (611.81 ppm, 696.51 ppm).

Answer:

24

Step-by-step explanation:

I just did it in class. it was hard but you just have to think about the question

Answer:

v = 2

Step-by-step explanation:

You can start by distributing -6:

7v - 20 = -6v + 6

To combine the like x terms, you can add 6v to both sides:

7v - 20 = -6v + 6

+6v          +6v

13v - 20 = 6

Now add 20 to both sides to isolate the x term:

13v - 20 = 6

      +20   +20

13v = 26

You can divide by 13 on both sides to find v,

13v = 26

÷13    ÷13

v = 2

Answer:

v= 2

Step 1: Simplify both sides of the equation.

7v−20=−6(v−1)  

7v+−20=−6v+6

7v−20=−6v+6

Step 2: Add 6v to both sides.

7v−20+6v=−6v+6+6v

13v−20=6

Step 3: Add 20 to both sides.

13v−20+20=6+20

13v=26

Step 4: Divide both sides by 13.

13v/13   = 26/13  

v=2

Answer:

17 ft

Step-by-step explanation:

The triangle on the bottom left is a right triangle.

a² + b² = c²

(8 ft)² + (15 ft)² = (RQ)²

64 ft² + 225 ft² = (RQ)²

(RQ)² = 289 ft²

RQ = 17 ft

Answer:

y = 1

Step-by-step explanation:

since its a horizantal line

if u take any 2 points and find the slope, for example if we take points (1, 1) and (4, 1) the slope will be 0/3 which is zero

y = 0x + b

so there is basically no x in this case

so y = b

now plug in a point from the line, (1, 1)

y = mx + b

y = 0x + b

1 = 0(1) + b

1 = 0 + b

1 = b

b = 1

final equation:

y = 0x + 1

Answer:

y = 10(½)^(x)

Step-by-step explanation:

In writing exponential functions passing through points, we will just substitute the x and y values in each case into y = ab^(x).

Now, for point (-1, 20), the exponential function is; 20 = ab^(-1)

20 = a/b

For the point (1, 5), the exponential function is; 5 = ab^(1)

5 = ab

From 20 = a/b, we have; a = 20b

Thus, putting 20b for a in 5 = ab, we have;

5 = 20b(b)

b² = 5/20

b² = 1/4

b = √(1/4)

b = 1/2

Since a = 20b, then;

a = 20 × 1/2

a = 10

Thus, from y = ab^(x), we have;

y = 10(½)^(x)

1. Use sharpie to cover up private information before throwing it away (because people can look through your trash for your info). For example: credit card information, your address, etc.

2. Secure your mail box. Get a lock to make sure that people won't steal your credit card information.

3. Never ever leave your receipts behind.

4. Don't lose your credit card!! People can steal it can spend your money!

5. Just don't give random people or friends your credit card information...

Well, I hope this helped! Be careful and stay safe!

Answer:

Each notebook cost $3 and each binder cost $4.

Step-by-step explanation:

Do some trial and error when plugging in certain numbers for each notebook and each binder.  You should get $3 and $4 when plugging it in.

Answer:

The population density of India in 2016 was of 1042.8 habitants per miles squared.

Step-by-step explanation:

Population density:

Number of habitants divided by land area.

In 2010 the population of India was 1,231,000,000. By 2016, the population had increased by 7.5%.

This means that India's population in 2016 was given by:

1,231,000,000*1.075 = 1,323,325,000

The land area of India is 1, 269,000 miles squared:

1,323,325,000/1,269,000 = 1042.8 habitants per miles squared.

The population density of India in 2016 was of 1042.8 habitants per miles squared.

Step-by-step explanation:

24-12x,and 2(12-6x)

hope it helps

Answer:

1/6 = 1/6 (already simplified) 1 3/8 = 11/8

Step-by-step explanation: