consider the following binomial experiment: a study in a certain community showed that 6% of the people suffer from insomnia. if there are 10,400 people in this community, what is the standard deviation of the number of people who suffer from insomnia?

Answer:

Step-by-step explanation:

In the first sequence, subtracting the previous term from each term starting from the second one gives these values: (0, 6, 12, 18, 24, . . .) is an arithmetic sequence.

How to find the common difference in the arithmetic sequence?

Common difference =  second term - first term

The difference between the terms is constant. This sequence is an arithmetic one, with the common difference being 6.

Common difference = 6.

Just by looking at the terms in the second sequence,

(1, 6, 36, 216, 1,296, . . .), the difference between the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.

Like arithmetic sequences, linear equations show a common difference between numbers.

Answer: In the first sequence, subtracting the previous term from each term starting from the second one gives these values:

6 – 0 = 6, 12 – 6 = 6, 18 – 12 = 6, and 24 – 18 = 6.

The difference of the terms is constant. This sequence is an arithmetic one, with the common difference being 6.

Just by looking at the terms in the second sequence, (1, 6, 36, 216, 1,296, . . .), it’s clear that the difference of the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.

Like arithmetic sequences, linear equations show a common difference between numbers.

Step-by-step explanation: Edmentum Answer

When X = 3 then Y = -6

Here is the explanation:

If Y1 = -4 when X1 = 2

and if X2 = 3 when Y2 = ?

The formula is

[tex]\frac{Y2}{X2} =\frac{Y1}{X1}\\\\Y2 = \frac{Y1}{X1} x X2\\\\Y2=\frac{-4}{2}x3\\\\Y2=-6[/tex]

Hence if X = 3 then Y = -6

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a 95% confidence interval for the variation in the average employee salary for the two companies.

a. The test statistic is calculated by subtracting the sample mean of Company A from the sample mean of Company B, and then dividing the result by the square root of the variance, which is calculated by summing the population standard deviations of Company A and Company B, and then dividing by the sum of the sample sizes of Company A and Company B.

Test statistic = (48 - 43) / √(12^2 + 10^2) / (72 + 50) = 0.766

b. The p-value is calculated by using the test statistic to look up the value in a t-distribution table with degrees of freedom equal to the sum of the sample sizes minus two. The p-value is 0.239.

At a=.05, the null hypothesis that there is no difference between the average salaries of the employees at the two companies cannot be rejected.

c. Company A appears to have the higher salary. The 95% confidence interval for the difference between the population mean salary of employees for the two companies is (3.073, 5.927).

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In 3rd step Henry made a mistake by taking the division operator rather than taking subtraction.

A number system is defined as a system of writing to express numbers.

The given problem is 5⁴5⁶/5²

We know that when bases are same then powers will be added

5⁴⁺⁶/5²

5¹⁰/5²

When denominator is taken up then the sign of denominator power value changes to negative.

5¹⁰⁻²

5⁸

Hence, in 3rd step Henry made a mistake by taking the division operator than subtraction.

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The probability mode for the given value is created. The expected value and standard deviation of prospective winnings are -$0.28 and $18.33. The expected value and standard deviation if the game is played five times are -$1.40 and $40.99. The probability that the person running the game makes a profit is 0.561.

Probability is a way to determine how likely something is to happen. It is computed by dividing the frequency of the event by the total number of outcomes. The formula then becomes P(X) = frequency of the event÷total number of outcomes.

The product of the probabilities determines the likelihood that two or more occurrences will coincide. This is given by, P(A and B) = P(A)P(B).

a) To create a probability model follow the steps. Let X is an occurrence of an event.  The table is attached here.

b)  The expected value is calculated using the formula, E(X) = μ = ∑ x P(x).

[tex]\begin{aligned}E(X)=\mu&=x_1p_1+x_2p_2+x_3p_3\\&=40\left(\frac{1}{6}\right)+0\left(\frac{5}{36}\right)+(-10)\left(\frac{25}{36}\right)\\&=-\$ 0.28\end{aligned}[/tex]

Also,

[tex]\begin{aligned}E(X^2)&={x_1}^{2}p_{1}+{x_2}^{2}p_{2}+{x_3}^{2}p_{3}\\&=(40)^2\frac{1}{6}+(0)\frac{5}{36}+(-10)^2\frac{25}{36}\\&=(1600)\frac{1}{6}+(0)\frac{5}{36}+(100)\frac{25}{36}\\&=266.67+69.44\\&=336.11\end{aligned}[/tex]

And the standard deviation is calculated using the formula, σ=√Var[X].

[tex]\begin{aligned}\sigma=\sqrt{\text{Var}(X)}&=\sqrt{E(X^2)-E(X)^2}\\&=\sqrt{336.11-0.08}\\&=\sqrt{336.03}\\&=\$18.33\end{aligned}[/tex]

c) The expected value and standard deviation for playing the game 5 times are calculated as follows.

The expected value is,

[tex]\begin{aligned}5\times E(X)&=5(-\$0.28)\\&=-\$1.40\\\end{aligned}[/tex]

The standard deviation is,

[tex]\begin{aligned}\sigma&=\sqrt{5\times\tex{Var}(X)\\&=\sqrt{5\times336.03\\&=\sqrt{1680.15}\\&=\$40.99\end{aligned}[/tex]

d) The dice rolling is random and the winning chance is independent. The probability the person running the game makes a profit (P(x<0)) is given by,

The population mean, μ(Y) = -$0.28

The standard deviation for a population of 100 is,

[tex]\begin{aligned}\sigma&=\sqrt{\frac{\text{Var}(X)}{n}}\\&=\frac{18.33}{\sqrt{100}}\\&=1.83\end{aligned}[/tex]

The z-score for mean winning is,

[tex]\begin{aligned}z&=\frac{x-\mu}{\sigma}\\&=\frac{0-(-0.28)}{1.83}\\&=0.153\end{aligned}[/tex]

For a person to make a profit, the mean winning of the player should be less than the z-score. Then,

The P-value from the z-table, P(z<0.153)=0.5608

The answer is 0.561.

The complete question is -

You pay $10 and roll a die. If you get a 6, you win$50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What’s the probability the person running the game makes a profit?

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The side length of the original cube is, 8.60 feet.

What is volume?

The amount of three-dimensional space that is occupied is measured by volume. It is frequently expressed quantitatively using SI-derived units, other imperial units, or US customary units. Volume and the notion of length are connected.

Given:

A 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft^3.

Let x = the side of the cube then

x^3 = original volume of the cube and

8x^2 = volume of the 8 feet slice

Therefore,

x^3 - 8x^2 = 44

Subtract 44 on both sides,

x^3 - 8x^2 - 44 = 44 - 44

x^3 - 8x^2 - 44 = 0

After solving x ≈ 8.59553

⇒ x = 8.60

Hence, the side length of the original cube is 8.60 feet.

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Answer: For $1, you can buy 10.75 pounds of shrimp.

Step-by-step explanation: Because p represents pounds and there are 10.75 lbs, and c represents cost. Therefore the answer is: For $1, you can buy 10.75 pounds of shrimp.

95% of the associations we would anticipate to see by chance are weaker than the statistical relationship between the two variables.

Statistical connection:

A statistical relationship states that if one variable (X) changes, another will systematically rise (Y).

Given,

Statistical significance is the degree to which a statistical link exists between two variables.

Here, we must determine whether it is stronger than the proportion of associations we would anticipate to occur by chance.

While researching the posed question, we discovered that the statistical correlation is more than the 95% chance correlation rate.

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Answer:

[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]

Step-by-step explanation:

Division of fractions can be represented as multiplication by one of the fractions' reciprocal. (Skip, Flip, and Multiply)

So,

[tex]\dfrac{11}{3} \div \dfrac{2}{3} = \dfrac{11}{3} \times \dfrac{3}{2}[/tex]

And we can simplify this to:

[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]

Answer:

The Answer is 4.29x + 3.99y = 30

Answer:

426 cm^2

Step-by-step explanation:

Answer: The answer to this question is x= -22/5

Congruence theorem used here are;-

1. HL theorem

2. SAS theorem

3. SSS theorem

Given,

Triangles ACR and ABR have a common side (hypotenuse of two right triiangles).

ABR and ACR form a right angle.

The AB and AC sides line up.

The BR and CR sides line up.

1. The HL theorem can be used since two triangles have congruent hypotenuses and pairs of legs.

2. Because two triangles contain two pairs of congruent legs and a pair of included right angles between these legs, you can utilize the SAS theorem.

3. Because two triangles have two pairs of congruent legs and congruent hypotenuses, you can utilize the SSS theorem.

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Question is incomplete. Completed question is given below;-

Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.

Triangles A B R and A C R share side A R. Angles A B R and A C R are right angles. Sides A B and A C are congruent. Sides B R and C R are congruent.

HL

SAS

SSS

ASA

AAS

Answer: its 4

Step-by-step explanation: trust me bro i had this question too

Answer:

W'(-6,4)

Step-by-step explanation:

W (6,4)  When it is reflective over the y axis it is now not six to the right of the y axis, it is now 6 to the left.

W' ( -6,4)

W' (-6 4) is now reflected over the x axis.  Instead of being 4 units above the x axis, it is now 4 unit below

W" (-6,-4)

The final two equations which represent the given situation are:

2x - y = -6 and 3x - y = -5.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a linear equation of two variables.

Suppose,

The larger number is 'y' and the smaller number is 'x'.

First relation,

'y' is equal to twice the sum of a smaller number (x) and 3. So we represent this as:

y = 2(x+3)

y = 2x + 6

2x - y = -6                     ............(1)

Second relation,

The larger number (y) is equal to 5 more than 3 times the smaller number (x). So we represent this as:

y = 5 + 3x

3x - y = -5                     .............(2)

Hence, the final two equations which represent the given situation are:

2x - y = -6 and 3x - y = -5.

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Answer:

y=−2x−2

Step-by-step explanation:

Answer:

199.728.0294..........….

Answer:

x = 1, y = 20

Step-by-step explanation:

The question is asking the length of two wires, so instead of area, we are looking at the perimeter.

For the triangle, the equation looks like this:

(2-x) + 15 + y

For the rectangle, the equation looks like this:

(5-x) + (y-6) × 2

Let's say that x = 2, and y = 12.

The triangles new equation would look like this:

(2-2) + 15 + 12 = 27

The rectangles new equation would look like this:

(5-2) + (12-6) × 2 = 18

The wires are the same length, so these numbers can't be correct.

Let's say that x = 1 and y = 20.

The triangles new equation would look like this:

(2-1) + 15 + 20 = 36

The rectangles new equation would look like this:

(5-1) + (20-6) × 2 = 36

These numbers are the same, so therefore the answer is

x = 1 and y = 20.

The variable cost of producing 1000 units per week is equal to $16000.

Variable costs are those that change with volume. Raw materials, piece-rate labour, production supplies, commissions, shipping costs, packing costs, and credit card fees are examples of variable costs. The variable costs of production are referred to as "Cost of Goods Sold" in some accounting accounts.

Given,

Fixed cost of production per week =$12500

Total cost of producing 1000 units per week =$28500

then,

variable cost of producing 1000 units per week = 28500-12500=$16000

Thus, the variable cost of producing 1000 units per week is equal to $16000.

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The inequality that can be used to find the values for p is p + 7 ≤ 50.

Given the information,

Mr. Smith can only spend up to $50 at a museum. The museum admission ticket is $7. He can use his P dollars to purchase other items from the museum.

The total budget is $50.

The cost per ticket is $7

⇒ Total spent ≤  Total Budget

⇒ p + 7 ≤ 50

⇒ p ≤ 43

Therefore, p + 7 ≤ 50 will be the inequality that aids in determining the range of values for p.

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Answer:

below

Step-by-step explanation:

The SUM of a n-gon 's interior angles formula is :

  SUM = ( n-2) * 180       n = 7 for this figure ( 7 angles)

    (7-2) * 180  = 900 degrees    

  EACH angle in this REGULAR polygon is then 900 / 7 = 128.57°

Answer:

16

Step-by-step explanation:

Let us assume the square is (m-a)²
We have to find a

(m-a)² = m² -2am + a²

We are given
m² -8m

Comparing terms
2a = 8

a = 4

so the square is (m-4)²

which is m² - 8m + 16

The probability computed is <0.8967,0.1033> which roughly shows that, as 90 days pass by, the probability that it will rain on a given day will be increasing monotonically towards a fixed point.    

The chance that an event will occur ranges between 0 and 1. Where 0 shows that the event is impossible to occur and 1 shows that the event is bound to occur. If the chance of occurring an event is more than the chance of its not occurring then, it is more likely that the event will occur.

If we take the example of tossing a coin, we can say that the probability that a head will occur or a tail will occur will remain the same, i.e., 50%. The occurrence of heads or tails is equally likely.

These mathematical standards are used in varied fields of gambling, technology, finance, architecture, philosophy, science, etc.

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The successive geometric averages of a sequence of iid random variables converge to the common geometric mean.

the strong law of large numbers states that, with probability 1, the successive arithmetic averages of a sequence of iid random variables converge to their common mean . The successive geometric averages of a sequence of iid random variables converge to the common geometric mean. The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of a collection of numbers, denotes the central tendency of that set of numbers. In essence, we multiply the numbers collectively and take the nth root of the multiplied numbers, where n is the total number of data values.

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Answer:

-4/3

Step-by-step explanation:

We can find the slope of the line using

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

m = ( -9 -3)/( 8 - -1)

   = ( -9-3)/( 8+1)

   = -12 / 9

  = -4/3

Answer:

[tex]\sf m=-\frac{4}{3}[/tex]

Step-by-step explanation:

First, select any two coordinates of the line.

( -1, 3 ) ⇒ ( x₁ , y₁ )

( 2, -1 ) ⇒ ( x₂ , y₂ )

And now let us use the below formula to find the slope of the line.

[tex]\sf m= \frac{y_1-y_2}{x_1-x_2} \\[/tex]

Let us find the slope now.

[tex]\sf m= \frac{y_1-y_2}{x_1-x_2} \\\\\sf m= \frac{3-(-1)}{-1-2} \\\\\sf m= \frac{4}{-3}\\\\\sf m=-\frac{4}{3}[/tex]

The value of each function composition is

koh(3) = 3 and hok(-4b) = -4b

Given, Functions h and k are inverse functions, and both are defined for all real numbers.

The functions h and k are inverse functions

A function is said to have an inverse function when it is one-one and onto both.

Also, the composition of function f and function g is defined as fog i.e. f is defined on the range of g and vice-versa.

Then, foh(x) = x for all the real numbers and also,

hof(x) = x for all the real numbers.

Therefore, the value of each function composition foh at x = 3 and hof at x = -4b is 3 and -4b respectively.

Hence, the value of each function composition foh at x = 3 and hof at x = -4b is

foh(3) = 3 and hof(-4b) = -4b.

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The p-value is 0.0388 at 9% significance, so (a) Yes, she has enough evidence with assumptions used in the test is (c) all the sampled data come from a normal distribution and (d) the populations are independent and therefore their covariances are zero.

All data in attached table

First, we must calculate the grand mean. So,

Grand mean ([tex]\bar{\bar{g}}[/tex]) = [tex]\frac{\bar{g_{1}} + \bar{g_{2}} + \bar{g_{3}} + \bar{g_{4}}}{k}[/tex]

= (67.5 + 67.17 + 67.28 + 66.77) / 4

= 67.18

Next, we calculate SSTr

SSTr = [tex]\sum n_i(\bar{g_{i}} - \bar{\bar{g}})^2[/tex]

= 9360(67.5-67.18)^2 + 9870(67.17-67.18)^2 + 7020(67.28-67.18)^2 + 5040(66.77-67.18)^2

= 1,876.875

Then, we calculate SSE

SSE = [tex]\sum(n_i-1)Sg_i^2[/tex]

= (9360-1)(14.85^2) + (9870-1)(15.1^2) + (7020-1)(14.79^2) + (5040-1)(15.16^2)

= 7,007,556.804

Before we calculate F test, we first calculate the N value with this formula,

N = [tex]\sum n_i[/tex]

= 9360 + 9870 + 7020 + 5040

= 31,290

Then, for F test use this formula,

F = [tex]\frac{SSTr/(k-1)}{SSE/(N-k)}[/tex]

= [tex]\frac{1876.875/(4-1)}{7007556.804/(31290-4)}[/tex]

= 2.793

Next, for p-value we use p value calculator for f test with following data,

F-ratio value = 2.793

DF-numerator = k - 1 = 4 - 1 = 3

DF-denominator = N - k = 31290 - 4 = 31286

and we get the p-value is 0.0388

Since, 0.0388 < 9% of significance, so she has enough evidence to initiate a deeper investigation.

Thus, assumptions used in the test is all the sampled data is normal distribution and the population are independent with covariances are zero and the result is yes, she has sufficient evidence.

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