In a state pick 4 lottery​ game, a bettor selects four numbers between 0 and 9 and any selected number can be used more than once. Winning the top prize requires that the selected numbers match those and are drawn in the same order.
Do the calculations for this lottery involve the combinations rule or either of the two permutations​ rules? Why or why​ not? If​ not, what rule does​ apply?

A. The permutation rule (with different items) applies to this problem because repetition is allowed. The permutation rule (with some identical items) and the combination rule cannot be used with repetition.
B. The combination and permutations rules do not apply because repetition is allowed and numbers are selected with replacement. The factorial rule applies to this problem.
C. The combination and permutations rules do not apply because repetition is allowed and numbers are selected with replacement . The multiplication counting rule applies to this problem.
D. The combination rule applies to this problem because the numbers are selected with replacement. Neither of the permutations rules allows replacement.
E. The permutation rule (with some identical items) applies to this problem because repetition is allowed The permutation rule (with different items) and the combination rule cannot be used with repetition.

Answer:

option C

Step-by-step explanation:

[tex]\dfrac{3}{5}[/tex] class left [tex]\dfrac{2}{5}[/tex] of the class left.

now,

[tex]\dfrac{1}{3}[/tex] of stayed did not want to go so,  [tex]\dfrac{2}{3}[/tex] of the student wanted to go.

[tex]\dfrac{1}{2}[/tex] of the stayed student join the trip.

number of student that stayed and wanted to go are

     =[tex]\dfrac{2}{5}\times \dfrac{2}{3}\times \dfrac{1}{2}[/tex]

     =[tex]\dfrac{2}{15}[/tex]

fraction of class on the field trip

= [tex]\dfrac{3}{5}+\dfrac{2}{15}[/tex]

= [tex]\dfrac{11}{15}[/tex]

Hence, the correct answer is option C

Answer:

The store must sell 35 bikes to break even.

Step-by-step explanation:

115-65 = 50. 1750 divided by 50 = 35.

Answer:you must sell 35 bikes each month to break even

Step-by-step explanation:

The point at which you break even is the point when there is neither profit nor loss. It mean that

Revenue - cost = 0

Revenue = cost

The cost of operating the bicycle per month is ​$1750

The store pays an average of ​$65 per bike. Let x represent the number of bikes that the store gets in a month. The total cost of x bikes would be

1750 + 65x

The average selling price of each bicycle is ​$115. Total revenue from x bikes would be

115 × x = 115x

Therefore, to break even,

1750 + 65x = 115x

115x - 65x = 1750

50x = 1750

x = 1750/50 = 35

Answer:

89.6%

Step-by-step explanation:

The probability a random person shares your birthday is 1/365, or 0.27%.  That means the probability that they don't share your birthday is 364/365, or 99.73%.

So the probability that you meet 40 people who don't share your birthday is:

P = (364/365)^40

P = 89.6%

The probability that it takes meeting more than 40 people before you meet someone who shares the same birthday as you is roughly 10.13% given that the probability of meeting a random person who has the same birthday as you is approximately 0.27%. This is calculated as the complement of the probability that we don't encounter a matching birthday in 40 people.

The probability of meeting a random person who shares the same birthday as us is 1/365, approximately a 0.27% chance. Now, to calculate the probability that it requires meeting more than 40 people before finding someone who has the same birthday is essentially the complement of the probability that we find someone with the same birthday in 40 people or less.

We can start by calculating the probability of not meeting someone with the same birthday in one encounter which is 364/365 (approximately 0.9973). The probability that we don’t encounter a matching birthday in 40 people is (364/365)^40 (approximately 0.8987). Subsequently, The probability that it takes meeting more than 40 people before you meet someone who has the same birthday is the complement of this probability, which is 1 - 0.8987 = 0.1013 or approximately a 10.13% chance.

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Answer:

B. $337.50

Step-by-step explanation:

1.5% of $22,500 is 337.5

Answer:

B. $337.50

Step-by-step explanation:

Answer:

x=4.8473 cups

Step-by-step explanation:

Concentration of Liquids

It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by

[tex]\displaystyle C=\frac{x}{y}[/tex]

It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.

Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is

x-1 cups of juice.

The new concentration is

[tex]\displaystyle \frac{x-1}{x}[/tex]

The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is

[tex]\displaystyle x-1-\frac{x-1}{x}[/tex] cups of juice.

Simplifying, the cups of juice are

[tex]\displaystyle \frac{\left (x-1\right)^2}{x}[/tex]

The new concentration is

[tex]\displaystyle \frac{\left (x-1\right)^2}{x^2}[/tex]

For the third time, we now have

[tex]\displaystyle \frac{\left (x-1\right)^2}{x}-\frac{\left (x-1\right)^2}{x^2}[/tex] cups of juice.

Simplifying, the final amount of juice is

[tex]\displaystyle \frac{\left (x-1\right)^3}{x^2}[/tex]

And the final concentration is

[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}[/tex]

According to the conditions of the question, this must be equal to 50% (0.5)

[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}=0.5[/tex]

Taking cubic roots

[tex]\displaystyle \sqrt[3]{\frac{\left (x-1\right)^3}{x^3}}=\sqrt[3]{0.5}[/tex]

[tex]\displaystyle \frac{\left (x-1\right)}{x}=\sqrt[3]{0.5}[/tex]

Operating and joining like terms

[tex]\displaystyle x-\sqrt[3]{0.5}\ x=1[/tex]

Solving for x

[tex]\displaystyle x=\frac{1}{1-\sqrt[3]{0.5}}[/tex]

[tex]x=4.8473\ cups[/tex]

Let's test our result

Final concentration:

[tex]\displaystyle \frac{\left (4.8473-1\right)^3}{4.8473^3}=0.5[/tex]

Answer: it will take 14 years

Step-by-step explanation:

A savings account is started with an initial deposit of $600. This means that the principal P is

P = 600

It was compounded annually. This means that it was compounded once in a year. Therefore,

n = 1

The rate at which the principal was compounded is 2.1%. So

r = 2.1/100 = 0.021

The duration of time that for which the money stayed in the account is t years. So

Time = t

The formula for compound interest is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years. Therefore,

a) the equation to represent the amount of money in the account as a function of time in years would be

A = 600 (1+0.021/1)^1×t

A = 600 (1.021)^t

b) the amount of time it takes for the account balance to reach $800 would be

800 = 600 (1.021)^t

Dividing both sides of the equation by 600, it becomes

1.33 = (1.021)^t

t = 14

Answer:

B) -3/2

Step-by-step explanation:

If [x/2]=0 then x/2 is a number such that the least integer greater than or equal to x/2 is 0. We can rewrite this as the inequality x/2≤0. Then, the value of x in C, D and E is wrong because they are positive numbers, then x/2 would be a positive number which contradicts this inequality.

Now, 0 is the least integer that satisfies this inequality, therefore we cannot have that x/2≤-1 since -1 is an integer and -1<0. Then x/2>-1. This discards A as wrong, because for x=-2, x/2=-1, contrary to x/2>-1.

Thus B is the right answer. To verify, if x=-3/2, then x/2=-3/4 and we have that -1<-3/4≤0 as required.

Answer:

The answer to your question is letter A

Step-by-step explanation:

Process

1.- Find two points of the line

A (1, 4)    B ( -1, 5)

2.- Find the slope of the line

     [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

     [tex]m = \frac{-5 - 4}{-1 - 1}[/tex]

     [tex]m = \frac{-9}{-2} = \frac{9}{2}[/tex]

3.- Find the equation of the line

     y - y1 = m(x - x1)

    y - 4 = 9/2(x - 1)

    2y - 8 = 9x - 9

    9x - 2y = - 9 + 8

    9x - 2y = - 1

4.- Convert the equation to a inequality,

    9x - 2y ≤ -1

Answer:

35

Step-by-step explanation:

Use the combination formula:

[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]

Substitute known values:

[tex]C(7,3)=\frac{7!}{3!(7-3)!}=35[/tex]

We don't use the permutation formula since the order of the drawn marbles does not matter.

Answer: 35

Step-by-step explanation:  

He can choose 3 marbles from 7 distinct marbles in (7/3) ways

C(7/3) = 7!/(3!-(7-3)!)

= 7*6*5*4/4*3*2

= 35

Answer:

It takes 16 days to quadruple its population.

Step-by-step explanation:

The population of the virus can be represented by the following exponential function.

[tex]A(t) = A_{0}e^{rt}[/tex]

In which A(t) is the population after t days, [tex]A_{0}[/tex] is the initial population and r is the growth rate.

In this problem, we have that:

[tex]A(8) = 2A_{0}[/tex]

So, we use this to find the value of r.

[tex]A(t) = A_{0}e^{rt}[/tex]

[tex]2A_{0} = A_{0}e^{8r}[/tex]

[tex]e^{8r} = 2[/tex]

Applying ln to both sides

[tex]8r = 0.6931[/tex]

[tex]r = 0.0867[/tex]

How long will it take to quadruple its population?

This is t when [tex]A(t) = 4A_{0}[/tex]

[tex]A(t) = A_{0}e^{rt}[/tex]

[tex]4A_{0} = A_{0}e^{0.0867t}[/tex]

[tex]e^{0.0867t} = 4[/tex]

Again we apply ln to both sides.

[tex]0.0867t = 1.39[/tex]

[tex]t = 16[/tex]

It takes 16 days to quadruple its population.

The number of days it takes to quadruple it's population is; 16days

According to the question;

Therefore;

8days = 2A.

We are required to determine how long it will take to quadruple it's population;

Let no. of days required = x days.

By cross multiplication; we have;

By dividing through by 2A; we have;

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Answer:

a) Monetary values corresponding to the two events are:

-In case of surviving the year = -166$

-In case of a death in the year = 89834$

b) Expected value of the purchasing the insurance is -85 $

c) Yes, insurance company can make a profit with this policy.

Step-by-step explanation:

a) The man need to pay 166$ first to enroll the insurance policy. If he survives within a year, he will lose 166$. Otherwise, if he dies within a year he will profit 89834$.

b) Expected value of the purchasing the insurance as following:

-In case of surviving the year:

Value: -166$

Probability: 0,9991

-In case of death in a year

Value: 89834$

Probability: 0,0009

Expected value is E(x) = -166×0,9991 + 89834×0,0009 = -85 $

c) Lets consider that 10000 different 31 year old man enrolled to this insurance policy. According to probability of death, 9 out of 10000 man expected to be dead within the year. Therefore, company need to pay 9*90000 = 810000$ to their costumers. But, company will collect 10000*166=1660000$ from their costumers in the beginning of the year

So, it is expected that company is going to profit 1660000-810000=850000$ per year.

The monetary values corresponding to surviving or not surviving for a 31-year-old male are $166 and $90,000 respectively. The expected value for the male purchasing the policy is $83.75. The insurance company can expect to make a profit from many such policies.

a. From the perspective of the 31-year-old male, the monetary value of surviving the year is $166 (the cost of the insurance). The monetary value of not surviving is $90,000 (the death benefit).

b. To find the expected value, we multiply the probability of each outcome by its corresponding monetary value and sum them. The expected value is calculated as: (0.9991 * $166) + (0.0009 * (-$90,000)) = $164.75 + (-$81) = $83.75.

c. The insurance company can expect to make a profit from many such policies. This is because the expected value for the 31-year-old male is positive ($83.75), meaning that on average the insurance company will earn more in premiums than it pays out in benefits.

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Answer:Area of shaded region is 454.97

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area of circle = πr^2

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

r = 14

Area of the circle = 3.14 × 14^2 = 615.44

The shaded area is a sector

Area of a sector is expressed as

Area = #/360 × πr^2

Where

# = 94 = central angle

Area of sector = 94/360 × 3.14 × 14

= 160.68

Area of shaded region would be

615.44 - 160.68

= 454.97

Answer:

454.97 unit^2.

Step-by-step explanation:

The area of the whole circle = pi r^2

= 14^2 pi.

As there are 360 degrees in a circle the area  of the shaded region , by proportion = [ (360 - 94) / 360  ] * 14^2 pi

= 454.972 unit^2.

Answer:

[tex]10|y|[/tex]

Step-by-step explanation:

We have been given that the vertices of a triangle are A (5, 0), B (x, y) and C (25, 0). We are asked to find the area of the given triangle.

We will use area formula for triangle with vertices A, B and C as given below:

[tex]|\frac{A_x(B_y-C_y)+B_x(C_y-A_y)+C_x(A_y-B_y)}{2}|[/tex]

Upon substituting the given coordinates of points A, B and C in above formula, we will get:

[tex]|\frac{5(y-0)+x(0-0)+25(0-y)}{2}|[/tex]

[tex]|\frac{5(y)+x(0)+25(-y)}{2}|[/tex]

[tex]|\frac{5y+0-25y}{2}|[/tex]

[tex]|\frac{-20y}{2}|[/tex]

[tex]|-10y|[/tex]

[tex]10|y|[/tex]

Therefore, the area of the given triangle would be [tex]10|y|[/tex].

Answer:

Step-by-step explanation:

[tex]E=\frac{1}{2}mv^2[/tex]

All the variables on the right are being multiplied together then the whole mess is being divided by 2.  Let's get rid of the 2 first.  The undoing of division is multiplication, so we will begin by multiplying both sides by 2 to get

[tex]2E=mv^2[/tex]

Next we will move the m. The undoing of multiplication is division.  So we divide both sides by m to get

[tex]\frac{2E}{m}=v^2[/tex]

The undoing of a square is to take the square root, so we will do that to both sides giving us, finally

[tex]\sqrt{\frac{2E}{m} }=v[/tex]

Answer:

d

Step-by-step explanation:

Answer:

(c) [tex]\left\ ({{4} \atop {1}} )\right.[/tex] [tex]0.25^{1} 0.75^{3}[/tex]

Step-by-step explanation:

As given in the statement, we have:

Out of 4 games pieces, 1 is winner.

Probability to win =p= [tex]\frac{1}{4}[/tex]

Jeff has game pieces = n = sample size = 4

As we need to find the probability that he wins exactly 1 prize, we will use binomial probability here :

[tex]P (X = k) = \left\ ({{n} \atop {k}} )\right. p^{k} (1-p)^{n-k} \\[/tex]

Evaluating at k=1, (k=1 as we need to find probability for exactly 1 prize won)

put n = 4, p =[tex]\frac{1}{4}[/tex]

P (X = 1) =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (1-0.25)^{4-1}[/tex]

P =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (0.75)^{3}[/tex]

Which is the probability that he wins exactly 1 prize and is option c.

Probability (Jeff wins 1 price in 4 game pieces) = C] [tex](4 c 1)(0.25)^1(0.75)^3[/tex]

Important Information : Probability (Winning a price) = 1 / 4 = 0.25

Probability (Not winning price) = 1 - Pr (Winning Price) = 1 - 0.25 = 0.75

Using Binomial Probability : Pr (X = r) = [tex]N c r . P^r . Q^(n-r)[/tex] .

Here N = number of trials (4 game pieces here) , P = Probability of Success (of winning price = 0.25) , R = Number of Success (1 price) , Q = Probability of failure (of not winning price = 0.75) ,

So, Probability = [tex]4 c 1 (0.25)^1 (0.75)^3[/tex]

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Number of dimes are 18 and number of quarters are 31

Solution:

Let "d" be the number of dimes

Let "q" be the number of quarters

value of 1 dime = $ 0.10

value of 1 quarter = $ 0.25

A collection of dimes and quarters is worth $9.55

value of 1 dime x number of dimes + value of 1 dime x number of quarters = 9.55

0.10d + 0.25q = 9.55 ---------- eqn 1

If the quarters were dimes and the dimes were quarters, the total value would be 7.60

quarters were dimes means , q = d

dimes were quarters means d = q

0.25d + 0.10q = 7.60 ----- eqn 2

Let us solve eqn 1 and eqn 2 to find "d" and "q"

Multiply eqn 1 by 2.5

0.25d + 0.625q = 23.875 ---- eqn 3

Subtract eqn 2 from eqn 3

0.25d + 0.625q = 23.875

0.25d + 0.10q = 7.60

( - ) ----------------------

0.525q = 16.275

q = 31

Substitute q = 31 in eqn 1

0.10d + 0.25q = 9.55

0.10d + 0.25(31) = 9.55

0.10d + 7.75 = 9.55

0.10d = 1.8

d = 18

Thus dimes are 18 and number of quarters are 31

Answer:

i needed the answer to this too!! have a good life

Answer:

Part 1: N(x) = 50,000 - 300(x-19)

Part 2: R(x) =-300x² + 55700x

Step-by-step explanation:

Given,

The original price of each ticket = $ 19,

The original attendance = 50,000

Part 1 :

∵ For the each​ $1 increase in the ticket​ price, attendance decreases by 300.

Let x represents the price of each ticket after increment,

Thus, if price increment = (x-19) dollars,

New attendance, N(x) = 50,000 - 300(x-19)

Part 2 :

Since, revenue = price of each ticket × attendance

Thus, the revenue from the football​ game,

R(x) = x(50,000 - 300(x-19))

R(x) = 50000x - 300x²+ 5700x

⇒ R(x) =-300x² + 55700x

Final answer:

For a 229-pound individual, they should receive approximately 11947 mg of the drug every 6 hours.

Explanation:

The student is asking how to calculate the appropriate dosage of a medication based on a person's weight. Specifically, the problem is determining how many milligrams of a drug should be administered every 6 hours when the dosage calls for 460 mg per kg per day and the person weighs 229 pounds.

First, we convert the person's weight from pounds to kilograms, knowing that 1 pound is approximately 0.453592 kg. So, 229 pounds is equal to 229 × 0.453592 kg = 103.890648 kg.

Next, we calculate the daily dosage in milligrams using the provided dosage requirement of 460 mg per kg per day:

103.890648 kg × 460 mg/kg = 47789.09808 mg per day.

Since the medication is divided into four doses, we divide the daily total by 4 to find the amount per dose:

47789.09808 mg ÷ 4 = 11947.27452 mg per dose.

Therefore, the individual should receive approximately 11947 mg of the drug every 6 hours.

Answer:

Number of week day hours purchased  is 5

Step-by-step explanation:

Total number of Parking hours purchased = 26 parking hours

Parking cost on weekdays = $2 per hour

Parking costs on weekends = $10 per hour

Total amount spent on parking =  $220.

To Find:

Number of week days purchased = ?

Solution:

Let  

The number of week days purchased be x

The number of weekends purchased be  y

We know that the total hours purchased is 26

So,

x+y = 26

y = 26-x------------------------------------------------------(1)

Now the total cost is 220

(Total number of weekdays X cost per weekday ) +(Total number of weekends + cost per weekend) =220

Substituting the values

=>[tex]x\times 2 + y \times 10[/tex] = 220

=>[tex]x \times 2 + (26-x) \times 10 =220[/tex]

=>2x + 260 -10x =220

=>260 -8x = 220

=>260 -220 =8x

=>40 = 8x

=>x=[tex]\frac{40}{8}[/tex]

x= 5-------------------------------------------(2)

Now substituting (2) in (1) we get

y= 26-5

y= 21

Answer:

  no

Step-by-step explanation:

The ratio is ...

  boys : girls = 42 : 56 = (14·3) : (14·4) = 3 : 4 . . . . not 5:6

Emma is not correct.

The overall width of the path and garden is 12 feet.

The area of the entire garden and path is 12 x 12 = 144 square feet.

The path is 1 foot wide, so the garden would be 12 - 2 = 20 feet wide.

The area of the garden only would be 10 x 10 = 100 square feet.

The area of the path only = 144 - 100 = 44 square feet.

1 bag covers 9 square feet:

44 / 9 = 4.88

You would need 5 bags.

Answer:

Step-by-step explanation:

1. ∠PQR is an alternate interior angle with the one marked 40°, so it has the measure 40°.

∠PRQ is an alternate interior angle with the one marked 60°, so it has the measure 60°.

Among the answer choices, the one describing ∠PQR as 40° is the only correct one.

__

2. ∠BAD = 2×∠BAE

  130 = 2(9x + 2) . . . substitute the given expressions

  65 = 9x + 2 . . . . . divide by 2

  63 = 9x . . . . . . . . .subtract 2

  7 = x . . . . . . . . . . . .divide by 9

__

3. Think again. Anything being rotated follows a circular path. Circular paths with different radii and the same center are concentric circles.

Straight lines connecting the pre-image and image points will be parallel (and different lengths), but the question is concerned with paths, not endpoints.

Why the path is described as "concentric circles," we're not sure. The path for a 90° rotation will be a 90° arc. It is perfectly reasonable to describe the paths of the two points as concentric arcs, rather than concentric circles. See the attachment.

__

4. Correct. The triangle inequality requires the sum of the two shortest side lengths exceed the longest side length. Here, that means 2+5 > 5 (true). The "toothpicks" meet the requirements of the triangle inequality, so will make a triangle.

The "triangle sum theorem" has to do with angles, not side lengths.

Tom has 29 points in the video game whereas mitch has 79 points.

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. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, Tom and Mitch are engaged in video game gaming. Tom has eight more points than Mitch does, but not by much. Let points of mitch be y and points of tom be x.

Based on the given conditions, formulate y = 3x -8

Rearrange unknown terms to the left side of the equation: 3x = 79 + 8

Calculate the sum or difference: 3x = 87

Divide both sides of the equation by the coefficient of the variable: x = 87/3

Cross out the common factor: x = 29

Therefore, Tom has 29 points in the video game.

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By solving the equation 3T - 8 = 79, we find that Tom has 29 points.

The student is asking a mathematical word problem that involves forming and solving an equation. To find how many points Tom has, we need to work with the information given: Mitch has eight less than triple the points that Tom has, and Mitch has 79 points.

Let's define Tom's points as 'T'. The problem tells us that Mitch's points are eight less than triple Tom's points, which can be written as the equation: 3T - 8 = 79.

Now we solve for 'T':

Tom has 29 points.

Answer:

  20%

Step-by-step explanation:

If there are 4 adults, 2 are female, and 1 of those has 1 child. Then the population is 4 adults and 1 child. The children make up 1/5 = 20% of the population.

Answer

20%

Step-by-step explanation:

Aops Question

After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa. Thus mom gave $ 320 to each girl

Solution:

Given that Lily and Elsa are both college students

Before mom gave them this months allowance lily had $750 and Elsa had &215

Amount (in dollars) with Lily and Elsa already is given as:

amount with Lily = $ 750

amount with Elsa = $ 215

After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa

Let "x" be the equal amount of money which mom gave to Lily and Elsa

Now amount with Lily and Elsa after mom gave equal amount is:

amount with Lily = amount with Lily already + x

amount with Lily = 750 + x

amount with Elsa = amount with Elsa already + x

amount with Elsa = 215 + x

Given that lily had twice as much money as Elsa

Amount with lily = 2(amount with elsa)

750 + x = 2(215 + x)

750 + x = 430 + 2ax

2x - x = 750 - 430

x = 320

Therefore mom gave $ 320 to each girl

Answer: 38.41 minutes

Step-by-step explanation:

The standard error for the difference in means is given by :-

[tex]SE.=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma^2_2}{n_2}}[/tex]

where , [tex]\sigma_1[/tex] = Standard deviation for sample 1.

[tex]n_1[/tex]= Size of sample 1.

[tex]\sigma_2[/tex] = Standard deviation for sample 2.

[tex]n_2[/tex]= Size of sample 2.

Let the sample of Latino name is first and non -Latino is second.

As per given , we have

[tex]\sigma_1=82[/tex]

[tex]n_1=9[/tex]

[tex]\sigma_2=101[/tex]

[tex]n_2=14[/tex]

The standard error for the difference in means will be :

[tex]SE.=\sqrt{\dfrac{(82)^2}{9}+\dfrac{(101)^2}{14}}[/tex]

[tex]SE.=\sqrt{\dfrac{6724}{9}+\dfrac{10201}{14}}[/tex]

[tex]SE.=\sqrt{747.111111111+728.642857143}[/tex]

[tex]SE.=\sqrt{1475.75396825}=38.4155433158\approx38.41[/tex]

Hence, the standard error for the difference in means =38.41 minutes

Answer:

The probability the number of heads will be even is 0.4922.

Step-by-step explanation:

Consider the provided information.

It is given that coin flip seven times.

Thus, the total number of possible outcomes are: [tex]2^7[/tex]

We want heads will be even.

Even numbers are 2, 4, 6.....

Thus, the possible case are: 2 heads, 4 heads or 6 heads.

The required probability is:

[tex](^7C_2+^7C_4+^7C_6)\times\frac{1}{2^7}=\left(\frac{7!}{2!5!}+\frac{7!}{4!3!}+\frac{7!}{6!1!}\right)\frac{1}{128}\approx 0.4922[/tex]

Hence, the probability the number of heads will be even is 0.4922.

Answer:

  14.5 m

Step-by-step explanation:

Let x represent the length of the diagonal. Then the length of the rectangle is (x-3) and its width is (x-8). The area is the product of these, so is ...

  (x -3)(x -8) = 74

  x^2 -11x +24 = 74 . . . . eliminate parentheses

  x^2 -11x = 50 . . . . . . . .subtract 24

  x^2 -11x +30.25 = 80.25 . . . . add 30.25 to complete the square

  (x -5.5)^2 = 80.25 . . . . . . write as square

  x - 5.5 = √80.25 ≈ 8.958 . . . . take the square root

  x = 8.958 + 5.5 = 14.458 . . . . .add 5.5

The length of the diagonal is about 14.5 meters.

Answer:

Step-by-step explanation:

The diagram of the rectangle, ABCD is shown in the attached photo. The diagonal of the rectangle forms a triangle, ABC

Applying Pythagoras theorem,

d^2 = (d - 8)^2 + (d - 3 )^2

d^2 = d^2 - 16d + 64 + d^2 - 6d + 9

d^2 = 2d^2 - 22d + 73

d^2 - 22d + 73 = 0

d^2 = 22d - 73 - - - - - - 1

If the area is 74 m^2, it means that

(d- 8)(d- 3) = 74

d^2 - 11d + 24 = 74

d^2 = 74 - 24 + 11d

d^2 = 50 + 11d - - - - - - - -2

Equating equation 1 and 2, it becomes

22d - 73 = 50 + 11d

22d - 11d = 50 + 73

11d = 123

d = 123/11 = 11.182

diagonal = 11.2 m to the nearest tenth.

Answer: Averages less than 2litres per day

Step-by-step explanation:

The normal range of urine excreted per day is between 1 to 2 litres, but the kidney must produce a minimum urine volume of 500mL per day, to get rid of body waste, anything below that is abnormal, and not good for the body

Answer:

The real roots are

[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]

The sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]

Step-by-step explanation:

The given quadratic equation is [tex]8x^2+12x-14[/tex] has two real roots.

To find the roots .

[tex]8x^2+12x-14=0[/tex]

Dividing the above equation by 2

[tex]\frac{1}{2}(8x^2+12x-14)=\frac{0}{2}[/tex]

[tex]4x^2+6x-7=0[/tex]

For quadratic equation [tex]ax^2+bx+c=0[/tex] the solution is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Where a and b are coefficents of [tex]x^2[/tex] and x respectively, c is a constant.

For given quadratic equation

a=4, b=6, c=-7

[tex]x=\frac{-6\pm\sqrt{6^2-4(4)(-7)}}{2(4)}[/tex]

[tex]=\frac{-6\pm\sqrt{36+112}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{148}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{37\times 4}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{37}\times\sqrt{4}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{37}\times 2}{8}[/tex]

[tex]=2\frac{(-3\pm\sqrt{37})}{8}[/tex]

[tex]=\frac{-3\pm\sqrt{37}}{4}[/tex]

[tex]x=\frac{(-3\pm\sqrt{37})}{4}[/tex]

The real roots are

[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]

Now to find the sum of the squares of these roots

[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3+\sqrt{37}-3-\sqrt{37}}{4}[/tex]

[tex]=\frac{-6}{4}[/tex]

[tex]=\frac{-3}{2}[/tex]

[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3}{2}[/tex]

Therefore the sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]