How many different simple random samples of size 4 can be obtained from a population whose size is 50?

We have shown that the equation x^3 + bx^2 + cx = 2022 has exactly one real solution.

To show that the equation x^3 + bx^2 + cx = 2022 has exactly one real solution, we will use the discriminant (∆) of the equation. The discriminant helps us determine the nature of the solutions of a polynomial equation.

For a cubic equation, the discriminant is given by the following formula:

∆ = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2

In our case, the equation is x^3 + bx^2 + cx - 2022 = 0, so a = 1, b = b, c = c, and d = -2022.

Now, let's calculate the discriminant:

∆ = 18(1)(b)(c)(-2022) - 4b^3(-2022) + b^2c^2 - 4(1)c^3 - 27(1)^2(-2022)^2

∆ = -36444bc + 8088b^3 + b^2c^2 - 4c^3 - 109222392

We are given that b^2 < 3c. This inequality implies that the first three terms of the discriminant will be negative, as b^2c^2 will be smaller than 3c^2. The negative terms will dominate the discriminant, making ∆ < 0.

When the discriminant of a cubic equation is negative (∆ < 0), it means that the equation has exactly one real solution. Thus, we have shown that the equation x^3 + bx^2 + cx = 2022 has exactly one real solution.

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The dealer should have sold the article for 103,500 naira to make a profit of 15%.

Let C be the cost price of the composition.  According to the problem, the dealer  vended the composition at a loss of 10, so he  entered 90 of the cost price.  thus, 90 of C is equal to 81,000 naira.

C =  81,000

C =  81,000/0.9

 C =  90,000  

So, the cost price of the composition is 90,000 naira.

  Now, let's find out the selling price  needed to make a profit of 15   Let S be the  needed selling price to make a profit of 15.  We know that profit chance is equal to( profit/ cost price) × 100.

Thus,(15/100) × 90,000 =

S- 90,000 , 500

=  S- 90,000  

S =  90,000 13,500

S =  103,500

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All the Bruces together weigh a total of 154 pounds.

If each Bruce weighs 11 pounds and there are 14 Bruces, we can calculate the total weight by multiplying the weight of each Bruce by the number of Bruces.

Weight of each Bruce: 11 pounds

Number of Bruces: 14

To find the total weight, we multiply 11 pounds by 14 Bruces:

Total weight = 11 pounds/Bruce * 14 Bruces

           = 154 pounds

Therefore, all the Bruces together weigh a total of 154 pounds.

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The area of the composite figure is approximately 2447.43 square millimeters to the nearest hundredth.

To find the area of the composite figure, we need to divide it into simpler shapes and then find their areas separately. The composite figure is made up of a rectangle and two semicircles.

First, let's find the area of the rectangle. The length of the rectangle is 55 mm and the width is 32.5 mm, so the area of the rectangle is:

[tex]$$A_{rect} = length \times width = 55 \text{ mm} \times 32.5 \text{ mm} = 1787.5 \text{ mm}^2$$[/tex]

Next, let's find the area of each semicircle. The diameter of each semicircle is equal to the width of the rectangle, which is 32.5 mm. Therefore, the radius of each semicircle is:

[tex]$$r =[/tex] [tex]\frac{32.5 \text{ mm}}{2} = 16.25 \text{ mm}$$[/tex]

The formula for the area of a semicircle is:

[tex]$$A_{semicircle} = \frac{1}{2} \pi r^2$$[/tex]

So, the area of each semicircle is:

[tex]$$A_{semicircle} = \frac{1}{2} \pi (16.25 \text{ mm})^2 \approx 329.97 \text{ mm}^2$$[/tex]

To find the total area of the composite figure, we add the area of the rectangle to the area of the two semicircles.

[tex]$$A_{total} = A_{rect} + 2 \times A_{semicircle} \approx 2447.43 \text{ mm}^2$$[/tex]

Therefore, the area of the composite figure is approximately 2447.43 square millimeters to the nearest hundredth.

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The quotient of 4.082 and 10,000 is 0.000004082.

To find the quotient of 4.082 and 10,000, we need to divide 4.082 by 10,000. However, dividing a decimal by another decimal can be tricky, so we need to move the decimal point of the dividend (4.082) and the divisor (10,000) to make the division easier.

We can move the decimal point of 4.082 four places to the left to obtain 0.04082. This is because moving the decimal point to the left makes the number smaller. For example, moving the decimal point in 4.082 one place to the left gives us 0.4082, which is ten times smaller than 4.082. Moving the decimal point four places to the left gives us a number that is 10,000 times smaller than 4.082.

Similarly, we can move the decimal point of 10,000 four places to the right to obtain 100,000,000. This is because moving the decimal point to the right makes the number larger. For example, moving the decimal point in 10,000 one place to the right gives us 1,000, which is ten times larger than 10,000. Moving the decimal point four places to the right gives us a number that is 10,000 times larger than 10,000.

Now we can divide 0.04082 by 100,000,000, which gives us the quotient of 0.000004082. Therefore, to find the quotient of 4.082 and 10,000, we need to move the decimal point in 4.082 four places to the left and move the decimal point in 10,000 four places to the right, and then divide the resulting numbers.

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Answer:

16.6666 hours.

Step-by-step explanation:

This conversion of 1,000 minutes to hours has been calculated by multiplying 1,000 minutes by 0.0166 and the result is 16.6666 hours.

Answer:

16,666.67 hours

Step-by-step explanation:

A minute is a unit of time equal to 60 seconds.

Answer:

A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9}

Step-by-step explanation:

We can find the union of two sets by including all of the numbers in both sets, but without repeating any numbers.

For example:

if A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8},

then A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8}

We can apply this concept to the problem at hand, but first we need to represent set A as a list of numbers:

They all have to be odd numbers between 0 and 10.

    [tex]\implies A[/tex] = {1, 3, 5, 7, 9}

We are given that B = {2, 3, 4, 5, 6}. So, to find the union of A and B, we can combine both sets of numbers and get rid of copies:

A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9}

The given equation, a = v²/r, solved for r is:

r = v²/a

From the question, we are to solve the given equation for r

From the given information,

The given equation is

a = v²/r

To solve the equation for r means we should isolate the variable r

Solving the equation for r

a = v²/r

Multiply both sides of the equation by r

a × r = v²/r × r

ar = v²

Divide both sides of the equation by a

ar/a = v²/a

r = v²/a

Hence, the equation solved for r is:

r = v²/a

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Answer:

10 outcomes

Step-by-step explanation:

if 2 coins were selected with replacement=10×10=100

number of outcomes if 2 coins were selected without replacement=10×9=90

Finally, 100-90= 10 outcomes!

The box plot that would represent the data recorded by Mr. Larson would be B. Second box plot.

To find the correct box plot of the data recorded by Mr. Larson, the math teacher, first order the grades from lowest to highest :

70, 71, 73, 75, 77, 80, 84, 86, 87, 92, 95, 96, 97, 100

There are 14 grades which means that the median position would be the 7th and 8th grades average :

= ( 84 + 86 ) / 2

= 170 / 2

= 85

The position of Q3 would be:

= ( n + 1 ) x 75 %

= ( 14 + 1 ) x 75 %

= 11 th position which is 95

The correct box plot is therefore the second box plot which shows the Q3 as 95.

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The equation of the downward opening parabola with the given vertex and vertical compression is y = 0.5(x + 5)^2 + 2

The equation of a downward opening parabola with vertex (h, k) and vertical compression a is given by:

y = a(x - h)^2 + k

In this case, the vertex is (-5, 2) and the vertical compression is 0.5. Therefore, we have:

h = -5

k = 2

a = 0.5

Substituting these values into the equation above, we get:

y = 0.5(x + 5)^2 + 2

This is the equation of the downward opening parabola with the given vertex and vertical compression.

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In a case whereby Zelda has 8 rabbits with which to start an animal farm. If the rabbit population doubles each month, the number of  months that the rabbit population will be 5,800 is 9.5 months.

In order to calculatre the month then we can use the expression y = abⁿ

a = starting number ( 8 rabbits)

b = rate of change = (2)

n = number of months that we need to calculate

y = rabbit population = 5800

The we can substitute to have

5800 = 8 × 2ⁿ

5800 / 8 = 2ⁿ

725 = 2ⁿ

n = 9.5 months.

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We can use the Pythagorean theorem to find the distance between the game store and the skate park.

Let's call the distance between the game store and the skate park "d". Then we have:

d^2 = (distance between school and game store)^2 + (distance between school and skate park)^2

d^2 = 7.3^2 + 8.7^2

d^2 = 106.18

d ≈ 10.3

Therefore, the game store is approximately 10.3 kilometers from the skate park.

Answer:

The graph on the top right

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

The equation is y = 1/2x + 2

The y-intercept in this equation is 2, meaning the graph has a point (0,2) on it.  Looking at the options, the only graph that has a point (0,2) is the map on the top right, and that is the answer.

Answer:

The unit  in a volume are always cubic meter

Step-by-step explanation:

Chain of Thought Reasoning: Volume is a three dimensional space, which is measured in three dimensions (length, width, and depth). The SI unit for length is meters, so the SI unit for volume is cubic meters (m^3).                        I hope this helps you

It will take about 387.3 months (or about 32.3 years) to triple the balance of the account.

What is Compound Interest ?

Compound interest refers to the process of earning interest on both the initial principal amount as well as any accumulated interest from previous periods. In other words, it is the interest that is earned on the interest that has been accumulated over time.

We can use the formula for compound interest to solve this problem.

Where:

A = the final amount

P = the initial amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this problem, we have:

P = $250

r = 0.06% = 0.0006 (as a decimal)

n = 12 (since the interest is compounded monthly)

A = 3P = $750

Substituting these values into the formula, we get:

750 = 250[tex](1 + 0.0006/12) ^{12t}[/tex]

Dividing both sides by 250, we get:

3 =[tex](1 + 0.0006/12) ^{12t}[/tex]

Taking the natural logarithm of both sides, we get:

㏒(3) = 12t ㏒(1 + 0.0006÷12)

Solving for t, we get:

t = ㏒(3)/(12 ㏒(1 + 0.0006÷12))

Plugging this into a calculator, we get:

t ≈ 387.3 months

Therefore, it will take about 387.3 months (or about 32.3 years) to triple the balance of the account.

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Out of 25 students in the class, 40% are male is: Descriptive statistics.

Descriptive statistics is the process of summarizing and organizing data from a sample or population in order to provide an overview of the main characteristics. In this case, the data provided tells us that out of 25 students in the class, 40% are male.

This information is a summary of the gender distribution within this specific class, rather than making any predictions or generalizations about a larger population.

In contrast, inferential statistics is the process of using data from a sample to make predictions or draw conclusions about a larger population. If we were given data about a sample of classes and asked to estimate the proportion of male students in all classes, that would be an example of inferential statistics.

To summarize, the situation you provided, which states that out of 25 students in the class, 40% are male, is an example of descriptive statistics as it only provides a summary of the data for that specific class.

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Trevor spent a mean amount of $0.85 per day on snacks during

Week 1.

We have,

To determine during which week Trevor spent a mean amount of $0.85 per day on snacks, we need to calculate the mean (average) amount spent per day for each week and find the week that matches $0.85.

Let's calculate the mean amount spent per day for each week:

Week 1:

= (0.50 + 0.75 + 0.50 + 1.00 + 1.25 + 1.25 + 0.75 + 0.25 + 1.00) / 9

= $0.86 (approximately)

Week 2:

= (1.00 + 0.50 + 0.75 + 0.25 + 0.25 + 1.25 + 0.25) / 7

= $0.61 (approximately)

Week 3:

= (0.75 + 1.00) / 2

= $0.88

Week 4:

= (1.25 + 1.00 + 1.00 + 1.25 + 0.50) / 5

= $1.00

From the calculations, we can see that the mean amount spent per day for Week 1 is closest to $0.85.

Therefore,

Trevor spent a mean amount of $0.85 per day on snacks during

Week 1.

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Answer:

$9.50

Step-by-step explanation:

Divide the total earnings by total hours.

Answer:

75°

Step-by-step explanation:

Arc length LM is 108°, meaning that angle <K is half of the arc length, 54°.

*REMEMBER* all 3 angles inside a triangle must add up to 180° to make it a triangle.

We have angle <L, <K, and we are looking for angle <M.

51+54+?=180

105+?=180

?=75

Angle <M is 75°

Hope this helps :)

We are given that IQ scores are normally distributed with mean μ = 100 and standard deviation σ = 15. We want to find the probability of a random person on the street having an IQ score of less than 96.

To do this, we need to standardize the IQ score using the z-score formula:

z = (x - μ) / σ

where x is the IQ score we're interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

Plugging in the given values, we get:

z = (96 - 100) / 15 = -0.267

Now, we look up the probability of getting a z-score less than -0.267 in a standard normal distribution table or using a calculator. The probability is approximately 0.3944.

Therefore, the probability of a random person on the street having an IQ score of less than 96 is 0.3944 (rounded to 4 decimal places).

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I believe credit cards tend to be the entry point for establishing credit for so many consumers because they provide an easy and accessible way for individuals to begin building their credit history. Credit card companies report to credit bureaus on a regular basis, which helps establish a credit score and credit history.

Additionally, credit cards offer a convenient way for individuals to make purchases and build their credit at the same time. However, it is important for individuals to use their credit cards responsibly and make timely payments in order to maintain good credit standing.

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Answer:

12.5 ft

Step-by-step explanation:

x/10=5/4

4x=5(10)

4x=50

x=12.5

The height of the flagpole is approximately 23.7 feet.

We can use the tangent function to solve this problem. Let's call the height of the flagpole "h". From the ground, we have a right triangle with the flagpole height as the opposite side, the distance to the flagpole as the adjacent side, and the angle of elevation as the angle opposite the flagpole height.

Using the tangent function, we can write:

tan(39°) = h/32

Solving for h, we get:

h = 32 * tan(39°)

h ≈ 23.7 feet

Therefore, the height of the flagpole is approximately 23.7 feet when viewed from a distance of 32 feet at an angle of elevation of 39°.

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The value of angle LQ in the intersected arc is 34 degrees.

If two secants intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.

Therefore, let's find the arc angle LQ as follows:

let

x = arc angle LQ

m∠U = 1 / 2 (108 - x)

37 = 54 - 0.5x

subtract 54 from both sides of the equation

37 = 54 - 0.5x

37 - 54 = 54 - 54 - 0.5x

-17 = -0.5x

divide both sides by -0.5

x = -17 / -0.5

x = 34 degrees

Therefore,

arc angle LQ = 34 degrees

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Answer: B

Step-by-step explanation:

x + 3 + 5x - 8 + 2x + 1 = 180

8x - 4 = 180

8x = 184

x = 23

23 + 3 = 26, 5(23) - 8 = 107, 2(23) + 1 = 47

the smallest is 26

The probability of sample mean less than 3.1 pounds: 0.266. The correct option is C.

The weights of roasts are normally distributed with a mean of 3.2 pounds and a standard deviation of 0.8 pounds. In a sample of 25 roasts, we want to find the probability that the sample mean is less than 3.1 pounds.

First, we need to calculate the standard error of the mean, which is the standard deviation divided by the square root of the sample size:

Standard error = 0.8 / √25 = 0.8 / 5 = 0.16

Now, we need to calculate the z-score for the sample mean of 3.1 pounds:

Z = (Sample mean - Population mean) / Standard error = (3.1 - 3.2) / 0.16 = -0.1 / 0.16 = -0.625

Using a z-table or calculator, we find the probability associated with a z-score of -0.625:

P(Z < -0.625) ≈ 0.266

Therefore, the probability of the sample mean being less than 3.1 pounds is approximately 0.266, which corresponds to option C.

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Complete question:

The owner of a meat market has an assistant who has determined that the weights of roasts are normally distributed, with a mean of 3.2 pounds and a standard deviation of 0.8 pounds. For a sample of 25 roasts, what is the probability of sample mean less than 3.1 pounds?

a. 0.495

b. 0.450

c. 0.266

d. 0.521

The original price of the laptop was $600 because $492 is 82% of the original price (100% - 18% = 82%).

The concept of percentage decrease. A percent decrease is the amount by which a quantity decreases, expressed as a percentage of its original value. In this case, the laptop is being sold for 18% less than its original price, so we can represent the percent decrease as 18%.

To find the original price of the laptop, we need to work backwards from the sale price. We can use the formula:

Sale price = Original price - Percent decrease of original price

where "Percent decrease of original price" is the percentage decrease of the original price, expressed as a decimal. In this case, the percent decrease is 18%, which we convert to a decimal by dividing by 100: 18/100 = 0.18.

Plugging in the values we know, we get:

$492 = Original price - 0.18 * Original price

Simplifying this equation, we get:

$492 = 0.82 * Original price

To isolate Original price, we can divide both sides by 0.82:

Original price = $492 / 0.82

Simplifying this expression, we get:

Original price = $600

the original price of the laptop was $600.

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Answer: To determine the percent of birds in Forest A that are robins, we need to know the number of robins and the total number of birds in Forest A. Let's assume that we have conducted a bird survey and found the following information:

Number of robins in Forest A = 50

Number of other birds in Forest A = 150

Total number of birds in Forest A = 50 + 150 = 200

To calculate the percentage of birds in Forest A that are robins, we can use the following formula:

Percentage = (Number of robins / Total number of birds) x 100%

Plugging in the values, we get:

Percentage = (50 / 200) x 100% = 25%

Therefore, 25% of the birds in Forest A are robins.

Step-by-step explanation:

The fraction value of 0.64 is 16/25 using the greatest common factor method to represent. There are no repeating digits in value.

The given decimal value = 0.64

There are no repeating numbers in the given decimal number 0.64.

To convert the given number into a fraction, we need to multiply the value with 10 on both sides to move the decimal point two places to the right.

0.64 × 100/100 = 64/100

Now simply this value by dividing both the numerator and denominator with the greatest common factor of both values. The greatest common factor is 4.

64/100 = 16/25

Therefore, we can represent the fraction value of 0.64 as 16/25.

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