A basket contains four red apples and an unspecified number of green apples. Four apples are randomly selected. What is the smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent?

Answer:

|Z| = √((-6)^2 + 12^2) = √(36 + 144) = √180

= (√36)(√5) = 6√5

1. The 99% confidence interval is from 877.094 to 942.906.

2. The 99% confidence interval is from 883.267 to 936.733.

3. The 99% confidence interval is from 838.437 to 981.563.

What is interval?

In statistics, an interval refers to a range of values in which a population parameter, such as the mean or proportion, is estimated to lie with a certain level of confidence.

Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.

The 99% confidence interval for the population mean is:

lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(20/√21) = 877.094

upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(20/√21) = 942.906

Therefore, the 99% confidence interval is from 877.094 to 942.906.

Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.

The 99% confidence interval for the population mean is:

lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(40/√21) = 883.267

upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(40/√21) = 936.733

Therefore, the 99% confidence interval is from 883.267 to 936.733.

Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.

The 99% confidence interval for the population mean is:

lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(80/√21) = 838.437

upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(80/√21) = 981.563

Therefore, the 99% confidence interval is from 838.437 to 981.563.

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Answer: x + 10` is **not** a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`.

Step-by-step explanation: To determine if `x + 10` is a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`, we can use the Factor Theorem. The Factor Theorem states that if `f(a) = 0`, then `x - a` is a factor of `f(x)`.

In this case, we want to determine if `x + 10` is a factor of `f(x)`, so we can let `a = -10` and evaluate `f(-10)`:

`f(-10) = 5(-10)^3 + 60(-10)^2 + 109(-10) + 90`

`= -5000 + 6000 - 1090 + 90`

`= -1000`

Since `f(-10) ≠ 0`, we can conclude that `x + 10` is **not** a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`.

[tex]{\Large \begin{array}{llll} \cfrac{x^{-\frac{1}{2}}}{x^{\frac{2}{3}}x^{\frac{3}{2}}}\implies \cfrac{1}{x^{\frac{2}{3}}x^{\frac{3}{2}}x^{\frac{1}{2}}}\implies \cfrac{1}{x^{\frac{2}{3}+\frac{3}{2}+\frac{1}{2}}}\implies \cfrac{1}{x^{\frac{2}{3}+2}}\implies \cfrac{1}{x^{\frac{8}{3}}} \end{array}}[/tex]

There is no correlation between age and the cost of a used car

From the question, we have the following parameters that can be used in our computation:

The scatter plot

Where

x = Age

y = cost of used car

From the graph, we can see that

The points on the graph are scattered and they do not follow a definite pattern

This means that the scatter plot shows no correlation

And as such the correct option is (d)

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The appropriate intervals to use when creating a histogram of the data are:

0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74.

Given information:

The following is a list of movie tickets sold each day for 10 days.

7, 18, 23, 41, 34, 12, 48, 65, 57, 52.

When creating a histogram, you want to group the data into intervals or bins.

The intervals should be chosen so that they are of equal size, and they should also include all the data values.

In this case, the data values range from 7 to 65, so we need to choose intervals that cover this range.

The appropriate intervals to use when creating a histogram of the data are:

0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74

These intervals capture the range of values in the data set and have equal widths, making it easy to create a histogram.

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Answer:

Answer: 9,924.966.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sorry it is hard to explain the process by typing!

The swap rate for a two-year deferred, three-yearinterest rate swap with settlement at the end of the year is 3.7%

Implied forward rate = (1+Present year rate)^Present year /(1+Previous year rate)^Previous year -1

The swap rate for a two-year deferred, three-yearinterest rate swap with settlement at the end of the year=

= [(1 +0.034)2 / (1+0.031)1 ] -1

= [1.069156 / 1.031] -1

= 1.037 - 1

= 0.037

= 3.7%

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Using a system of equations, the number of different rolls of yarn that Laura bought is as follows:

A system of equations refers to simultaneous equations.

Simultaneous equations are two or more equations solved concurrently.

The total number of rolls of yarn bought = 25 rolls

The unit cost of multi-colored yarns = $4

The unit cost of solid-colored yarns = $3

The total cost paid for the 25 rolls of yarn = $88

Let the number of rolls of multi-colored yarns = x

Let the number of rolls of solid-colored yarns = y

Equation 1: x + y = 25

Equation 2: 4x + 3x = 88

Multiply Equation 1 by 3:

3x + 3y = 75 ... Equation 3

Subtract Equation 3 from Equation 2:

4x + 3x = 88

-

3x + 3y = 75

x = 13

Substitute x = 13 in either equations 1 or 2:

x + y = 25

13 + y = 25

y = 12

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Answer:  The sum of the integers is equal to $\frac{14}{3}$ times the largest of the seven integers. What is the smallest integer that pearl wrote down?.

Step-by-step explanation:

Possible strategic initiatives for the strategic objective to satisfy clients:

• Implement additional training course on serving and interacting with clients

a. client review and client growth percentage metrics likely relate to a strategic objective to satisfy and increase clients. The market share and profit margin metrics likely relate to a strategic objective to increase profits.

b.

New clients during the month

7

Lost clients during the month

(4)

Increase in clients

3

Total clients at the beginning of last month

÷ 72

Client growth percentage last month

4.17%

target met

c.

Number of 5-star reviews

55 × 5 =

275

Number of 4-star reviews

10 × 4 =

40

Number of 3-star reviews

3 × 3 =

9

Number of 2-star reviews

1 × 2 =

2

Number of 1-star reviews

1 × 1 =

1

Sum total of stars

327

Total number of reviews

÷ 70

Average online client satisfaction rating

4.67

stars, target

not met

d.

Possible strategic initiatives for the strategic objective to satisfy clients:

• Implement additional training course on serving and interacting with clients

• Invite clients to provide additional feedback through a brief online survey

• Have the company owner send a personal apology to any clients providing a review of 2 stars or less, and offer them some kind of compensation; also ask for their feedback regarding what caused them dissatisfaction

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The nth term of the sequence 4/5, 1/5, 1/20. 1/80..... is an = 4/5(1/4)^(n - 1)

The definition of the function is given as

4/5, 1/5, 1/20. 1/80.....

The above definitions imply that we simply multiply 1/4 to the previous term to get the current term

Using the above as a guide, we have

First term, a = 4/5

Ratio, r = 1/4

So, we have the following equation

an = 4/5(1/4)^(n - 1)

Hence, the value of the nth term is an = 4/5(1/4)^(n - 1)

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a) Point estimate = 10/19 = 0.526

b) The sample should be randomly selected from the population.

The sample size should be large enough such that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the proportion of students who have a job in the population.

The sampling distribution of the sample proportion should be approximately normal.

c) confidence interval = (0.259, 0.793)

d) confidence interval = (0.176, 0.876)

e) n = 365 students

Given data ,

a)

The point estimate for the proportion of GSU students who have a job is simply the proportion of students in the class who have a job, which is:

point estimate = 10/19 = 0.526 (rounded to three decimal places)

b)

To create a confidence interval for the proportion of GSU students who have a job, the following conditions must be met:

The sample should be randomly selected from the population.

The sample size should be large enough such that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the proportion of students who have a job in the population.

The sampling distribution of the sample proportion should be approximately normal.

c)

Assuming the conditions for a confidence interval are met, a 95% confidence interval for the proportion of GSU students who have a job can be calculated as follows:

margin of error = z√(p(1-p)/n)

where z is the z-score corresponding to a 95% confidence level (z = 1.96), p is the point estimate of the population proportion (0.526), and n is the sample size (19).

margin of error = 1.96 √(0.5260.474/19) = 0.267 (rounded to three decimal places)

confidence interval = point estimate ± margin of error = 0.526 ± 0.267

confidence interval = (0.259, 0.793)

Therefore, we can say with 95% confidence that the true proportion of GSU students who have a job is between 0.259 and 0.793.

d)

A 99% confidence interval for the proportion of GSU students who have a job can be calculated using the same formula as above, but with a z-score of 2.576 (corresponding to a 99% confidence level):

margin of error = 2.576sqrt(0.5260.474/19) = 0.350 (rounded to three decimal places)

confidence interval = 0.526 ± 0.350

confidence interval = (0.176, 0.876)

Therefore, we can say with 99% confidence that the true proportion of GSU students who have a job is between 0.176 and 0.876.

e)

To determine the sample size needed to be within 3 percentage points of the true proportion with the point estimate of 0.526, we can use the formula:

n = (z² * p * (1-p)) / E²

where z is the z-score corresponding to the desired confidence level (z = 1.96 for a 95% confidence level), p is the point estimate of the population proportion (0.526), and E is the desired margin of error (0.03).

n = (1.96^2 * 0.526 * 0.474) / 0.03^2

n = 364.16

Hence , we would need a sample size of at least 365 students to be within 3 percentage points of the true proportion using the point estimate from the class data.

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The exponential function that passes through the points (0,19) and (2,1539) is y = 19(9)ˣ.

We can use the two given points to form a system of two equations in two unknowns (a and b) to find the exponential function in the form y = abˣ that passes through those points.

Using the point (0,19), we get

19 = ab⁰

19 = a

Using the point (2,1539), we get

1539 = ab²

Substituting a = 19 from the first equation, we get

1539 = 19b²

Solving for b, we get

b² = 81

b = 9 or b = -9

Since we are dealing with an exponential function that models a growth, we will choose the positive value for b. Thus, b = 9.

Now that we know a and b, we can write the exponential function in the form y = abˣ

y = 19(9)ˣ

Therefore, the exponential function is y = 19(9)ˣ

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--The given question is incomplete, the complete question is given

" Write an exponential function in the form y=ab^x that goes through points ( 0 , 19 ) (0,19) and ( 2 , 1539 ) (2,1539)."--

Answer:

[tex]\frac{1}{3}[/tex] product per minute

Step-by-step explanation:

We Know

A factory worker can make 15 products in 45 minutes.

What is the worker's unit rate of completion?

We Take

15 / 45 = [tex]\frac{1}{3}[/tex] product per minute

So, the workers unit rate of completion is  [tex]\frac{1}{3}[/tex] product per minute

Answer:

The equation of the circle is (x + 7)^2 + (y - 13)^2 = 25.

Step-by-step explanation:

The equation of a circle with a center (a,b) and radius r is given by:

(x - a)^2 + (y - b)^2 = r^2

So, for the center (-7, 13) and a radius of 5 units, the equation of the circle is:   (x - (-7))^2 + (y - 13)^2 = 5^2

Simplifying this equation, we get:

(x + 7)^2 + (y - 13)^2 = 25

Therefore, the equation of the circle with center (-7,13) and radius 5 units is (x + 7)^2 + (y - 13)^2 = 25.

The value of the expression when j=-2 and k=-1 is 8.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.

Let's substitute j=-2 and k=-1 in the given expression and simplify it:

(jk⁻²/j⁻¹k⁻³)³

= ((-2)(-1)⁻²)/((-2)⁻¹(-1)⁻³))³ // Substitute j=-2 and k=-1

= ((-2)/(1/(-1)²))/((-1/(-1)³)))³

= ((-2)/1)/(-1/1))³

= (-2)/(-1))³

= 8

Therefore, the value of the expression when j=-2 and k=-1 is 8.

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Tally's probability of being on the red team is 1/4, or 0.25 when represented as a decimal.

Each team has four students because there are four equal-sized teams.

So Tally's chances of being on the red team are 4 (the number of students on the red team) divided by 16 (the total number of students):

4/16 = 1/4

As a result, Tally's likelihood of being on the red team is 1/4, or 0.25 when represented as a decimal.

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The range of the cosine function is [-1, 1], there are no real solutions for θ in the given range.

We have,

We can solve the given quadratic equation for cos(θ) using the quadratic formula:

cos(θ) = (-b ± sqrt(b^2 - 4ac)) / 2a

Here, a = 1, b = 7, and c = 4.

Substituting these values, we get:

cos(θ) = (-7 ± √(7² - 4(1)(4))) / 2(1)

cos(θ) = (-7 ± √(41)) / 2

Since 0 ≤ θ < 2π, we need to consider only the solutions that lie in this range.

Using a calculator, we get:

cos(θ) ≈ -3.03 or -0.65

Since the range of the cosine function is [-1, 1], there are no real solutions for θ in the given range.

Therefore,

None of the given options (4.03, 2.65, 1.65, 2.25, 1.43) is correct.

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Answer:

3

Step-by-step explanation:

By using distance formula

√(x2-x1)^2+(y2-y1)^2

√(5-5)^2+(4-1^2

√0+(3)^2

√9

=3

Answer:

  D.  5 +9i

Step-by-step explanation:

You want to simplify the expression ...

  √(-16) +√(-25) +5

We know that the value of √(-1) is represented by the constant i. This means we can simplify the expression like this:

  [tex]\sqrt{-16}+\sqrt{-25}+5\\\\=\sqrt{-1(4^2)}+\sqrt{-1(5^2)}+5\\\\=4i+5i+5\\\\=\boxed{5+9i}\qquad\text{matches choice D}[/tex]

<95141404393>

The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively.

Length is a concept used to describe the magnitude of a particular object or distance between two points. It is typically measured in units such as feet, inches, meters, miles, and kilometers. Length is often used to describe the size of an object and the distance between two points. Length can also be used to measure the time required to travel between two points. Length is a fundamental concept in mathematics, physics, and engineering.

The first dotted line shown at the top of the chart is 23.39.

b. With Overall Mean selected, what is the length of the second dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)

The second dotted line shown at the top of the chart is 23.28.

c. With Overall Mean selected, what is the length of the third dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)

The third dotted line shown at the top of the chart is 24.17.

Conclusion: The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively. This data can be used to analyze the age of respondents in Market Research.

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The equation's usable range is 6.6 km d 13.2 km.

Expression is the relation of the numbers and the variables written by the use of mathematical signs.

Kellen exercises for a minimum of an hour and a maximum of two hours. As a result, the equation's useful domain is 1 t 2. Since that time can take on any positive or negative value, the theoretical scope of the equation d = 6.6t is all real numbers.

Substitute the values of the practical domain into the equation.

t = 1, d = 6.6(1) = 6.6 km.

t = 2, d = 6.6(2) = 13.2 km.

Therefore, the equation's usable range is 6.6 km d 13.2 km.

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The area of the composite figure is 136 sq. units.

Given that a composite figure we need to find it area,

The figure is composed of a triangle and a rectangle,

So to find its area we will simply calculate the areas of both the polygons and add them,

So, the area of a triangle = 1/2 x base x height

The area of a rectangle = length x width

So,

The required area = 1/2 x (16-8)(13-7) + 7 x 16

= 1/2 x 8 x 6 + 112

= 24 + 112

= 136

Hence, the area of the composite figure is 136 sq. units.

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The quadratic equation shown in the graph is:

y = (x + 2)*(x - 1)

Remember that if h and k are the zeros of a quadratic equation of leading coefficient a, we can write it as:

y = a*(x - h)*(x - k)

Here we can see that the zeros are:

x = -2

x = 1

Then we can write it as:

y = a*(x + 2)*(x - 1)

And the y-intercept is -2, then we can write:

-2 = a*(0 + 2)*(0 - 1)

-2 = a*-2

-2/-2 = a

1 = a

The quadratic equation is:

y = (x + 2)*(x - 1)

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Answer:

Area of shaded portion= (θ/360º) × πrr

32/360°×22/7×3cm×3cm

(Simplify)

=2.514cm×cm

To nearest tenth= 2.500cm×cm

Answer: 22√3

Step-by-step explanation:

When finding perimeter you take l+l+w+w, or 2l + 2w.

Answer:

[tex]22\sqrt{3}[/tex]

Step-by-step explanation:

To find the perimeter, we have to add up all four sides.

[tex]5\sqrt{3} +3\sqrt{12} +5\sqrt{3} +3\sqrt{12}[/tex]

write this on your calculator then you'll get [tex]22\sqrt{3}[/tex]

Hope this helps

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