There are 7 students in a class: 5 boys and 2 girls.
If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a boy?

Answer:

  (0, -5)

Step-by-step explanation:

You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).

That would be ...

  (x, f(x) -5) = (0, 0 -5) = (0, -5)

Answer:

1/90 = 1.11%

Step-by-step explanation:

We have that the number of ways of total selections and assignments possible is a permutation.

We know that permutations are defined like this:

nPr = n! / (n-r)!

In our case n = 10 and r = 2, replacing:

10P2 = 10! / (10 - 2)! = 10! / 8!

10P2 = 90

In addition to this, there will only be one way to randomly select the two members currently holding the positions of President and Vice President and reassign them to their current positions. Thus,

Probability would come being the following:

P = 1/90 = 1.11%

Answer:

the value of x=12

Step-by-step explanation:

d) the answer is d on edg.

Answer:

[tex]P(\bar X>3.4) = 0.385[/tex]

Step-by-step explanation:

Relevant Data provided according to the question is as follows

[tex]\mu[/tex] = 3.2

[tex]\sigma[/tex] = 0.8

n = 4

According to the given scenario the calculation of probability that the sample means will be more than 3.4 pounds is shown below:-

[tex]z = \frac{\bar X - \mu}{\frac{a}{\sqrt{n} } }[/tex]

[tex]P(\bar X>3.4) = 1 - P(\bar X\leq 3.4)[/tex]

[tex]= 1 - P \frac{\bar X - \sigma}{\frac{a}{\sqrt{n} } } \leq \frac{3.4 - \sigma}{\frac{a}\sqrt{n} }[/tex]

Now, we will solve the formula to reach the probability that is

[tex]= 1 - P \frac{\bar X - 3.2}{\frac{0.8}{\sqrt{4} } } \leq \frac{3.4 - 3.2}{\frac{0.8}\sqrt{4} }[/tex]

[tex]= 1 - P (Z \leq \frac{0.2}{0.4})[/tex]

[tex]= 1 - P (Z \leq 0.5})[/tex]

[tex]= 1 - \phi (0.5)[/tex]

= 1 - 0.6915

= 0.385

Therefore the correct answer is

[tex]P(\bar X>3.4) = 0.385[/tex]

So, for computing the probability we simply applied the above formula.

Answer:

its  21

Step-by-step explanation:

its not 21 i really dont know

Equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.

Two or more expressions with an Equal sign is called as Equation.

The given equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex]

We need to check whether the left hand side is equal to right hand side.

These are in the form pf mixed fraction we can convert them to the improper fraction.

[tex]7\frac{1}{2}=15/2[/tex]

[tex]4\frac{2}{3}=\frac{14}{3}[/tex]

So Let us subtract 24/3 from 15/2

15/2-14/3

LCM of 2 and 3 is 6

45-28/6

17/6

This can be written as mixed fraction [tex]2\frac{5}{6}[/tex]

Hence, equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.

To learn more on Equation:

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Answer:

4

Step-by-step explanation:

We are told that figure B is a scaled copy of B, which means figure A was enlarged by a certain scale factor to get a similar figure as A, now referred to as figure B.

The scale factor = ratio of any two corresponding sides of both similar figures.

Thus,

Scale factor of the similar figures given = 40/10 = 4.

This means that, figure A was scaled up by 4 times its original size to get figure B. Each side of figure B is 4 × the corresponding side in figure A.

Scale factor = 4

Your answer would be 76.2% to the nearest tenth.

We can find this by first dividing 16 by 21 to get 0.7619. which is the proportion as a decimal. To convert this into a percentage, we need to multiply it by 100 to get 76.19% = 76.2% to the nearest tenth.

I hope this helps! Let me know if you have any questions :)

Answer:

b. 1.15

Step-by-step explanation:

The z statistics is given by:

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

In which X is the found proportion, p is the expected proportion, and s, which is the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.

This means that [tex]X = \frac{13}{53} = 0.2453[/tex]

She find that the proportion of satisfied teachers nationally is 18.4%.

This means that [tex]p = 0.184[/tex]

Standard error:

p = 0.184, n = 53.

So

[tex]s = \sqrt{\frac{0.184*0.816}{53}} = 0.0532[/tex]

Z-statistic:

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

[tex]Z = \frac{0.2453 - 0.184}{0.0532}[/tex]

[tex]Z = 1.15[/tex]

The correct answer is:

b. 1.15

Answer:

99.48% probability that the sample mean would be greater than 64.8 kilograms.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

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.

In this question:

[tex]\mu = 67, \sigma = \sqrt{121} = 11, n = 164, s = \frac{11}{\sqrt{164}} = 0.86[/tex]

What is the probability that the sample mean would be greater than 64.8 kilograms?

This is 1 subtracted by the pvalue of Z when X = 64.8.

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

By the Central Limit Theorem

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

[tex]Z = \frac{64.8 - 67}{0.86}[/tex]

[tex]Z = -2.56[/tex]

[tex]Z = -2.56[/tex] has a pvalue of 0.0052

1 - 0.0052 = 0.9948

99.48% probability that the sample mean would be greater than 64.8 kilograms.

Answer:4541(Rounded) 4541.99779(Unrounded)

Step-by-step explanation:

A= P(1 + r)^T

A= answer

P=principle(amount of money)

r=Rate(percent / 100)

T=Time(Annually)

1030(1 + .077)^20

Brainliest would be appericiated!

Answer:

A sample of 385 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample:

We need a sample of n.

n is found when M = 0.05.

We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]

[tex]n = 384.16[/tex]

Rounding up

A sample of 385 is needed.

Answer: Evaluate the Function, right?

Hello!

~~~~~~~~~~~~~~~~~~

A) 4x = -4 [x=-1] =

4x = -4 =

x = -1 = x = -1

( The steps : Substitute the given value into the function and evaluate.)

B) 2(x-3) =-12 [x=3] =

2 ( x - 3) = -12 = x = -3

x = 3 = x = 3

( The steps : Substitute the given value into the function and evaluate.)

C) 8x - 4x = 24 [x = 1/2] =

8x - 4x = 24 = x = 6

x = 1/2 = x = 1/2

( The steps : Substitute the given value into the function and evaluate.)

D) 9x - 4x = 24 [x=18] =

9x - 4x = 24 = x = 24/5

x = 18 = x = 18

( The steps : Substitute the given value into the function and evaluate.)

~~~~~~~~~~~~~~~~~~

Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.

Hope this helped you!

Answer:

y = x² + 6x + 16

= (x² + 6x + 9) - 9 + 16

= (x + 3)² + 7 ← vertex form

Therefore, vertex is (-3, 7) and since the coefficient of (x + 3)² is positive the vertex is a minimum.

Answer:

minimum (3,7)

Step-by-step explanation:

Answer:

The best point estimate for the mean monthly car payment for all residents of the local apartment complex is $624.

Step-by-step explanation:

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].

In this question:

We apply the inverse Central Limit Theorem.

The mean monthy car payment for 123 residents of the local apartment complex is $624.

So, for all residents of the local apartment complex, the best point estimate for the mean monthly car payment is $624.

Step-by-step explanation:

input x , output y

if x= x1 then y=y1 and y1 is the only value then it is a function

if we get multiple values of y then it is not a function

Answer:

QIII

Step-by-step explanation:

Answer:

134,596 diffrent ways.

Step-by-step explanation:

Combination has to do with selection. When n object is to be selected from n objects, this can be achieved using the combination formula as shown; \

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

If an election ballot asks voters to select six city commissioners from a group of 24 candidates, then the selection can be done in 24C6 different ways.

Applying the formula above:

24C6 = 24!/(24-6)!6!

24C6 = 24!/18!6!

24C6 = 24*23*22*21*20*19*18!/18!*6*5*4*3*2

24C6 = 24*23*22*21*20*19/24*30

24C6 = 23*22*21*20*19/30

24C6 = 134,596 different ways.

Hence, Six city commissioners can be selected from a group of 24 candidates in 134,596 different ways

Answer:

paper = $4 and stapler = $7

Step-by-step explanation:

let p represent paper and s represent stapler, then

3p + 4s = 40 → (1)

5p + 6s = 62 → (2)

Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p

15p + 20s = 200 → (3)

- 15p - 18s = - 186 → (4)

Add (3) and (4) term by term to eliminate p

2s = 14 ( divide both sides by 2 )

s = 7

Substitute s = 7 into either of the 2 equations and evaluate for p

Substituting into (1)

3p + 4(7) = 40

3p + 28 = 40 ( subtract 28 from both sides )

3p = 12 ( divide both sides by 3 )

p = 4

Thus package of paper costs $4 and stapler costs $7

Answer:

a) If interest rates go up, share prices go down : this will be assigned p→q

b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r)

c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q)

d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park.  P → (q∨r)

e) My sister wants a black and white cat. p∧q

Step-by-step explanation:

A statement  is said to be propositionally logical if the statement that can be assigned either true or false.

∧and

∨or

¬not

→implies

a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.

b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur

c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive

d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park.  P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur

e) My sister wants a black and white cat. p∧q : both events can only occur together

Answer:

2

Step-by-step explanation:

firstly...you have to find the number of students wearing blue and white shirt and subtract from the total number of students to get the number if students that neither wears blue or white shirt as follows :

no wearing blue = 1/6 × 12 = 2

no.wearing white = 2/3 × 12 = 8

total number wearing blue and white = 8+2 =10

number of students not putting on either of the two colours include...= 12-10 = 2

.....

.....

.....

MARK BRAINLIEST will be appreciated please...thanks in advance

The point that is a solution to the inequality shown in the graph is:

A. (0,5).

The points that are on the region shaded in blue are solutions to the inequality.

(3,2) and (-3,-6) are on the dashed line, hence they are not solutions. Point (5,0) is to the right of the line, hence it is not a solution, and point (0,5) is a solution, meaning that option A is correct.

More can be learned about inequalities at https://brainly.com/question/25235995

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Answer:

216 cm³

Step-by-step explanation:

The volume of a cube is denoted by V = s³, where s is the side length.

Here, the side length is 6 centimetres, so plug this into the formula to find V:

V = s³

V = 6³ = 6 * 6 * 6 = 216

The answer is thus 216 cm³.

~ an aesthetics lover

Answer:

216

Step-by-step explanation:

6³ = 216

Answer: 18 (b)

Step-by-step explanation:

3x6=18

Answer:

18

Step-by-step explanation:

you can use a visual for a short answer or organize 3 dots in six groups, count in total

Answer:

p = 2

Step-by-step explanation:

p + 4/p - 4

multiplying through by p,

p×p + 4/p ×p - 4×p

p² + 4 - 4p = 0

p² - 4p + 4 = 0

factorizing,

p(p - 2) -2(p - 2) =0

(p -2)(p -2) =0

p-2 =0

p=2

Answer:

9

Step-by-step explanation:

p^2 -4p +4

Let p = -1

(-1)^1 -4(-1) +4

1 +4+4

9

Answer:(x-5)(x+9)

Step-by-step explanation:

You want two numbers that can give you -45 in multiplication and two numbers that can add to 4 and that is -5 and 9.

Answer:  (x - 5)(x + 9)

If you have to solve, x=5 or x= -9

Step-by-step explanation: You need two numbers that multiply to be 45.

(could be 3 × 15 or 5 × 9) . The difference between the two factors needs to be 4, the coefficient of the middle term.

9 - 5 =4, so use those.  -45 has a negative sign, so one of the factors must be + and the other -  Since the 4 has the + sign, the larger factor has to be + so the difference will be positive.

So (x -5)(x + 9) are your factors. You can FOIL to be sure

x × x += x² . x × 9 = 9x .  -5 ×  x = -5x . -5 × 9 = -45 .

Combine the x terms: 9x -5x = +4x  

Answer:

2{3[9+4(7-5)-4]}

2{3[9+4(2)-4]}

2{3[13(2)-4]}

2{3[26-4]}

2{3[22]}

2{66}

132

Step-by-step explanation: