A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchases 85 yogurt cups, and records whether each was a winner. After consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. He performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). What conclusion can the customer draw about the yogurt company’s claim?

a) The probability of drawing all kings from a shuffled deck of cards without replacement is approximately 0.0000014, or 1.4 in 1 million.

b) The probability of drawing all red cards from a shuffled deck without replacement is approximately 0.000000103, or 1.03 in 10 million.

a) Probability of drawing all kings:

To calculate the probability of drawing all kings, we need to determine the total number of possible outcomes and the number of favorable outcomes. Let's break it down step by step:

Step 1: Total number of possible outcomes

In a standard deck of 52 playing cards, there are four kings. When we draw one card, there are 52 cards to choose from. For the second draw, only 51 cards remain, and so on. Therefore, the total number of possible outcomes for drawing four cards without replacement is:

52 × 51 × 50 × 49 = 649,740

Step 2: Number of favorable outcomes

Since we want all four cards to be kings, there are only four kings in the deck. When we draw the first card, there is a 4/52 chance of it being a king. For the second card, the probability reduces to 3/51 since there are three kings remaining out of 51 cards. Similarly, for the third and fourth cards, the probabilities become 2/50 and 1/49, respectively. Therefore, the number of favorable outcomes is:

(4/52) × (3/51) × (2/50) × (1/49) = 1/270,725

Step 3: Calculating the probability

Finally, we can calculate the probability of drawing all kings by dividing the number of favorable outcomes by the total number of possible outcomes:

P(all kings) = (1/270,725) / (649,740) ≈ 0.0000014

b) Probability of drawing all red cards:

Similarly, let's calculate the probability of drawing all red cards from the deck. We follow the same steps:

Step 1: Total number of possible outcomes

When we draw the first card, there are 26 red cards in a deck of 52. For the second draw, there are 25 red cards remaining out of 51, and so on. Hence, the total number of possible outcomes for drawing four cards without replacement is:

26 × 25 × 24 × 23 = 358,800

Step 2: Number of favorable outcomes

Since we want all four cards to be red, there are 26 red cards in the deck. The probability of drawing a red card for the first draw is 26/52. For the second draw, the probability becomes 25/51, for the third draw it is 24/50, and for the fourth draw, it is 23/49. Thus, the number of favorable outcomes is:

(26/52) × (25/51) × (24/50) × (23/49) ≈ 0.037

Step 3: Calculating the probability

The probability of drawing all red cards is the ratio of the number of favorable outcomes to the total number of possible outcomes:

P(all red cards) = (0.037) / (358,800) ≈ 0.000000103

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Two particles are traveling along space curves defined by the equations r₁(t) = (t, t², t³) and r₂(t) = (1/6t, 1/30t, 1/126t). We need to find the points at which their paths intersect.

To find the points of intersection, we need to solve the system of equations formed by equating the components of the two space curves.

Comparing the x-components, we have:

t = 1/(6t) => t² = 1/6 => t = ±√(1/6).

Comparing the y-components, we have:

t² = 1/(30t) => t³ = 1/30 => t = ±∛(1/30).

Comparing the z-components, we have:

t³ = 1/(126t) => t⁴ = 1/126 => t = ±∜(1/126).

Combining all the solutions, we have four possible values for t: √(1/6), -√(1/6), ∛(1/30), and -∛(1/30). However, we need to check if these values are valid for all components of the curves.

By substituting these values of t into the equations, we find that only the value t = √(1/6) yields valid points of intersection: (√(1/6), 1/6, 1/√6) and (-√(1/6), 1/6, -1/√6).

Therefore, the points at which the paths of the particles intersect are (√(1/6), 1/6, 1/√6) and (-√(1/6), 1/6, -1/√6).

Please note that the other values of t do not yield valid points of intersection, so they are not considered as solutions in this case.

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Answer:

42 inches

Step-by-step explanation:

1 FT=12 inches

One half FT=6 inches

12×3=36

36+6=42

Answer:

42 inches

Step-by-step explanation:

The question is basically asking you to convert 3 1/2 ft into inches. Since there are 12 inches in a feet you have to multiply 3 1/2 by 12. It easier to do it when you turn 3 1/2 into a decimal, which would be 3.5. So then, you multiply 3.5 by 12, to get 42 inches.

12 inches = 1 feet

3 1/2 = 3.5

3.5 x 12 = 42

The house will be 42 inches tall.

Answer:

The last two.

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

Step-by-step explanation:

Radius = Half of Diameter

r = 8/2

= 4 in.

Area of Circle =

[tex]\pi {r}^{2} \\ = \pi( {4}^{2} ) \\ = 16\pi \: {in}^{2} [/tex]

Answer:

Jackson's opponents planned to use the bank to defeat him in the 1832 presidential campaign. Senators Henry Clay and Daniel Webster were friends of Biddle. ... They thought that if Jackson tried to veto, or reject, the renewal of the charter, he would lose support.

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Given the expression x^2 - 10x + 8 = 0.

According to completing the square method

Subtract 8 from both sides

x^2 - 10x + 8 - 8 = 0 - 8

x^2 - 10x = -8

Complete the square

Add the square of half of coefficient of x to both sides

Coefficient of x = -10

Half of Coefficient of x = -10/2

Half of Coefficient of x = -5

Square of Half of Coefficient of x = (-5)^2

Square of Half of Coefficient of x = 25

Add (-5)^2 to both sides

x^2 - 10x + (-5)^2 = -8 + (-5)^2

(x-5)^2 = -8 + 25

(x-5)^2 = 17

Hence the required constant that was added is 25

Answer:

50

Step-by-step explanation:

180-(65+65)

Answer:

<C = 50

Step-by-step explanation:

<c = x

x + 65 + 65 = 180

x + 130 = 180

x = 50

Answer:

s + r = 60 and 12s + 3r = 90

Step-by-step explanation:

I just took the quiz and it said this is correct

Answer:

67

Step-by-step explanation:

no

Answer:

-6

Step-by-step explanation:

To find the slope, you do y₂ - y₁ / x₂ - x₁

y₂ - y₁ / x₂ - x₁

= -35 - 11 / 5 - 1

= -24 / 4

= -6

The slope is -6

Answer:

-6

Step-by-step explanation:

Hi,

To find the slope when given a table, just pick two points, subtract the y values, and then divide them by the x values after you subtract them as well. Here's what I mean...

Let's use 1, -11 and 5, -35

So...

-35 - (-11)

This is the change in y. -35 - (-11) is the same thing as -35 + 11 (subtracting  negative switches to adding it)

You get -24

Now, the change in x.

5 - 1 = 4

So, -24/4 and you get the slope of : -6

I hope this helps :)

Answer:

tee shirt:4

sleeve shirt:3

Step-by-step explanation:

we are given two conditions

we want to figure out how many each type of shirt he bought

let tee and sleeve shirts be t and s respectively

according to the first condition

[tex] \displaystyle t + s = 7[/tex]

according to the second condition

[tex] \displaystyle5t + 6s = 38[/tex]

therefore

our system of linear equation is

[tex] \displaystyle\begin{cases}t + s = 7 \\ 5t + 6s = 38 \end{cases}[/tex]

so

now we need our algebra skills to figure out t and s

to do so we can use substitution method

cancel s from both sides of the first equation:

[tex] \displaystyle t = 7 - s \: \cdots \: i[/tex]

now substitute the value of i equation to the second equation:

[tex] \displaystyle 5(7 - s) + 6s = 38[/tex]

distribute:

[tex] \displaystyle 35 - 5s+ 6s = 38[/tex]

collect like terms:

[tex] \displaystyle s + 35 = 38[/tex]

cancel 35 to both sides:

[tex] \displaystyle \therefore s = 3[/tex]

now substitute the value of s to the i equation:

[tex] \displaystyle t = 7 - 3 \\ \therefore \: t = 4[/tex]

hence,

he bought tee shirt 4 and sleeve shirt 3

Answer:

hi!

Step-by-step explanation:

Answer:

option A

Step-by-step explanation:

thats the answer!!!

Answer: 829.44 ft²

Step-by-step explanation:

Correction - The walkway is 31.2 feet wide.

To solve this, first find the area of the fountain:

Area of a square = Length * Width

= 12 * 12

= 144 ft²

The find the area of the walkway including the fountain:

= 31.2 * 31.2

= ‭973.44‬ ft²

To find the area of the walkway alone, subtract the area of the square from the area of the rectangle:

= 973.44 - 144

= 829.44 ft²

Answer:

3.3/2 = 1.65² x 3.14 = 8.54865

Rounding the cutoff score to the nearest whole number, the cutoff score that will make a student eligible for the reading program is approximately 108.

To find the cutoff score that will make a student eligible for the reading program, we need to determine the score below which the bottom 14% of students fall.

Since the variable is normally distributed and we know the average score and standard deviation, we can use the Z-score formula to find the cutoff score.

The Z-score formula is:

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

Where:

Z is the Z-score,

X is the raw score,

[tex]\mu[/tex] (mu) is the mean, and

[tex]\sigma[/tex] (Sigma) is the standard deviation.

We want to find the Z-score that corresponds to the bottom 14% of students, which means the area to the left of the Z-score is 0.14.

Using a standard normal distribution table or calculator, we can find the Z-score that corresponds to an area of 0.14, which is approximately -1.08.

Now we can rearrange the Z-score formula to solve for X, the cutoff score:

[tex]\[X = Z \cdot \sigma + \mu\][/tex]

Substituting the values we have:

[tex]\[X = -1.08 \cdot 15 + 124.5\][/tex]

Calculating the expression:

[tex]\[X = -16.2 + 124.5\]\\X = 108.3[/tex]

Rounding the cutoff score to the nearest whole number, the cutoff score that will make a student eligible for the reading program is approximately 108.

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Answer:

Tasha has the greater balance at the end of the week.This balance is $381

The account balance is the remaining amount after the deduction of withdrawals from the deposits.

Tasha has the greater balance at the end of the week. This balance is $1 greater than the other balance.

It is the remaining amount after the deduction of withdrawals from the deposits.

We have,

Tasha:

Initial deposits = $250

Withdrawals = $20

Deposits = $65

Debit card purchases = $46

Balance = $250 - $20 + $65 - $46 = $249

Jamal:

Initial deposits = $200

Withdrawals = $60

Deposits = $135

Debit card purchases = $27

Balance = $200 - $60 + $135 - $27 = $248

We see that Tasha has a greater balance than Jamal and Tasha's balance is greater than Jamal's by $1.

Thus,

Tasha has the greater balance at the end of the week. This balance is $1 greater than the other balance.

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a) The probability that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg=0.016

b) The expected value of N=86.6

c) The probability that Day N is also Sunday=1/7.

Explanation:

a)

For 1 day, 1 tray must contain no spoiled eggs: 0.999^12,

1 tray must have at least 1 spoiled egg: 1 - 0.999^12,

and the probability that Miss Ang has 2 trays, each containing at least 1 spoiled egg in one day:

(1 - 0.999^12) * (1 - (0.999^12 + 11 * 0.001 * 0.999^11)) = 0.00245

For 7 days, the probability that Miss Ang has at most 2 trays, each containing at least 1 spoiled egg:

= 0.00245 * C(7,0) * 1^0 * (1 - 1)^7 + 0.00245 * C(7,1) * 1^1 * (1 - 1)^6 + 0.00245 * C(7,2) * 1^2 * (1 - 1)^5

= 0.01622 ≈ 0.016

b)

Let X be the number of trays that Miss Ang has to buy to get the first tray containing at least 1 spoiled egg. Then X follows a geometric distribution with parameter

p = 1 - 0.999^12 and

E(X) = 1/p = 1/0.011543 ≈ 86.6 (rounded to the nearest 0.1).

c)

Since Miss Ang buys one tray of eggs a day, the probability that Day N is Sunday is 1/7. Therefore, the probability that Day N is Sunday given that it is the first day that Miss Ang bought a tray of eggs containing at least one spoiled is also 1/7.

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a) The probability of that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg:

              P(X ≤ 2) = 0.2966763801

b) The expected value of N = 83.8059327318 days

c) The probability that Day N is also Sunday= 0.1406909760

(a)

For each egg produced by HS Farm, there is a 0.001 chance that it is spoiled. Therefore, the probability that an egg is not spoiled is

1-0.001 = 0.999.

Since Miss Ang buys one dozen eggs every day, the probability that all 12 eggs in a tray are not spoiled is

(0.999)¹² = 0.98806738389.

Therefore, the probability that there is at least one spoiled egg in a tray is

1 - 0.98806738389 = 0.01193261611.

The probability that Miss Ang buys at most 2 trays of eggs with each having at least one spoiled egg in one week (7 days) can be found using the Poisson distribution with a mean of λ = 1.19574793916.

Therefore,

P(X ≤ 2) = 0.2966763801

(b)

Let N be the first day that Miss Ang bought a tray of eggs containing at least one spoiled.

Since Miss Ang buys one tray of eggs every day, the probability that N = n is the probability that the tray she buys on day n has at least one spoiled egg, and all the trays she buys on days 1, 2, ..., n - 1 have no spoiled eggs.

This probability is given by

[tex]P(N = n) = (0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]

The expected value of N can then be found by taking the sum of nP(N = n) over all possible values of n.

This gives

[tex]E(N) = Σn=1∞nP(N = n)[/tex]

[tex]= Σn=1∞(0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]

n= 83.8059327318 days.

(c)

Suppose Day 1 is Sunday. Since Miss Ang buys one tray of eggs every day, Day N is also Sunday if and only if N ≡ 1 (mod 7).

Using the same method as in part (b), we get

[tex]P(N ≡ 1 (mod 7)) = Σk=0∞P(N = 7k + 1)[/tex]

                         =[tex]Σk=0∞(0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]

                         = 0.1406909760

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Answer:

-3 for the first box and -69 for the second one.

Step-by-step explanation:

Answer:

162 caps.

Step-by-step explanation:

Let x be the number of caps.

We have been given that cost of one cap is $6, so cost of x caps will be equal to 6x.

We are also told that the company charges an amount of $25 for shipping, so total cost of buying x caps will be equal to the cost of x caps plus shipping charges ().

Since Laura has a budget of $1,000, so cost of x caps will be less than or equal to 1,000. We can represent this information in an equation as:

Now let us solve for x.

Let us divide both sides of our inequality by 6.

Answer:

1/3

Step-by-step explanation:

If you're talking about a 6-sided die, then there are 6 sides.  Rolling a 2 or a 3 would be a 2/6 chance.  To simplify if from there, you can also say that there is a 1/3 chance.

Answer:7

+

7

(

5

)

+

7

5

(

2

)

+

7

5

(

3

)

+

7

5

(

4

)

Step-by-step explanation:

Answer: 5473+7x^5

Step-by-step explanation:

Try Photo Math! Gives step by step explanations!

Hope this helps!!

Answer:

9

Step-by-step explanation:

Hello There!

The circumference is equal to the diameter times π

The diameter given is 9m

NOTE: it says "leave answer in terms of π" meaning that we do not apply π to the diameter

So the answer would be just 9π

Answer:

9

Step by step:

C= 2 x pi x r

c = 2 x pi x 4.5

c=  9 x pi

For the goodness-of-fit test with data collected from 55 subjects, the degrees of freedom for the chi-square distribution will be 4.

In a goodness-of-fit test, the degrees of freedom for the chi-square distribution determine the critical values and the interpretation of the test statistic. For a multinomial distribution with k categories, the degrees of freedom are calculated as (k - 1).

In this specific case, we have a multinomial distribution with 5 categories. Therefore, the degrees of freedom for the chi-square distribution will be (5 - 1) = 4.

Having 4 degrees of freedom means that the chi-square test statistic will be evaluated against the chi-square distribution with 4 degrees of freedom to determine the p-value and assess the significance of the test. The critical values at the chosen significance level will also depend on these degrees of freedom.

In summary, when conducting a goodness-of-fit test for a multinomial distribution with 5 categories and collecting data from 55 subjects, the chi-square test will have 4 degrees of freedom. These degrees of freedom play a crucial role in determining the validity and interpretation of the test results.

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Answer:

0 slope

Step-by-step explanation:

flat horizantal line

no increase in y-value