Use the Intermediate Value Theorem to show that P(x) = x^5 +
4x^3−10x−6
has a root on [0, 2].

Answer:

OPTION C: 2 < x < 6

Step-by-step explanation:

3.5x - 10 > -3

Adding 10 to both sides:

3.5x > 7

Dividing by 3.5:

x > 2

8x - 9 < 39

Adding 9 to both sides:

8x < 48

Dividing by 8:

x < 6

Therefore, the solution set of the compound inequality is:

2 < x < 6

the combined mean and standard deviation for these exams will be Mean, 5. 66; standard deviation, 2. 055.

Combined mean=5.66

Combined standard deviation = 2.06

Combined mean= (MXa+ n×Xb)/(m+n)

Combined mean =2.80+2.86=5.66

Combined mean= sqrt(1.55)^2+(1.35)^2)

Combined deviation = 2.06

The mean is the number you get by separating the amount of a bunch of values by the quantity of values in the set.

Conversely, the middle is the center number in a bunch of values when those values are organized from littlest to biggest.

The mode of a bunch of values is the most often rehashed esteem in the set.

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The correct answer is (c) Ali has a monthly net income of $2,088 after paying 28% in taxes.

.

To calculate Ali's net monthly income, we first need to find out the amount of tax she pays, and then we can subtract it from her annual income to get her net annual income. We'll then divide it by 12 to get her monthly net income.

Calculations: Ali's tax rate is 28%. 28% of 29,000 is 8,12029,000 - 8,120 = 20,88020,880 / 12 = 1,740

Therefore, Ali's net monthly income is $1,740. The correct answer is option D, $1,740. ($29,000 salary x 28% taxes = $8,120 in taxes annually; $8,120 / 12 months = $677 in taxes per month; $29,000 - $677 = $2,088 net monthly income).

Net income refers to the amount of money that a company or an individual has earned after deducting all the expenses and taxes from their gross income. In the context of a company, net income is also called profit, and it is an important measure of a company's financial performance.

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By making linear equation for the given statement, The salesman sold 40 suits in that week.

What is a linear equation, exactly?

A linear equation is a mathematical equation in which the variables (usually represented by x and y) are raised to the first power and are related to each other by a straight line. In other words, a linear equation represents a straight line on a graph. The general form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Now,

Let "x" the number of suits the salesman sells in that week.

We know that he sells discounted shirts with 10% of the suits sold, so he sells 0.1x discounted shirts.

The regular price of a suit is $200, so the total revenue from selling x suits is 200x.

The discounted price of a shirt is $20, so the revenue from selling 0.1x discounted shirts is 20(0.1x) = 2x.

Now we can set up an equation based on the total revenue:

200x + 2x = 8080

Simplifying this equation, we get:

202x = 8080

Dividing both sides by 202, we get:

x = 40

Therefore,

               the salesman sold 40 suits in that week.

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There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.

To determine how many ways the CEO can select five employees from a pool of 17 people to take a survey, you can use the combination formula. The combination formula is nCr = n!/r!(n-r)! where n is the total number of items to choose from, and r is the number of items to choose.

In this case, n = 17 and r = 5.Using the combination formula: n Cr = 17C5= 17!/5!(17-5)!= 6188 There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.

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As per the concept of unitary method, Linda read 5/6 of the book.

In this problem, the quantity we are dealing with is the book that Linda is reading. Let's call the total number of units in the book "x". Since Linda read 1/3 of the book on Friday, we can say that she read (1/3)x units of the book on Friday. Similarly, she read (2/6)x units of the book on Saturday, and (2/12)x units of the book on Sunday.

Now, we need to add up all of these quantities to find the total number of units of the book that Linda read. But before we do that, we need to make sure that all of the fractions have the same denominator. The smallest common multiple of 3, 6, and 12 is 12. So, we will convert all of the fractions to twelfths.

(1/3)x = (4/12)x

(2/6)x = (4/12)x

(2/12)x = (2/12)x

Now, we can add up all of these quantities:

(4/12)x + (4/12)x + (2/12)x = (10/12)x

So, Linda read (10/12)x units of the book in total. But we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

(10/12)x = (5/6)x

Therefore, the resulting value of x is 5/6

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The expression that represents the number of days until only 5% of Technetium-99m remains is approximately 3.79 days.

The given function [tex]T(d) =[/tex]  [tex]100 \cdot 2^{-2d}$[/tex]represents the percent of Technetium-99m remaining d days after the test.

To find the number of days until only 5% remains, we need to solve the following equation:

[tex]$100 \cdot 2^{-2d} = 5$[/tex]

Dividing both sides by 100, we get:

[tex]$2^{-2d}$[/tex] [tex]= 0.05[/tex]

Taking the natural logarithm of both sides, we get:

[tex]$\ln{(2^{-2d})}$[/tex] = [tex]ln(0.05)[/tex]

Using the logarithmic identity log(base a)(bⁿ) = nlog(base a)(b), we can simplify the left side as:

[tex]-2d \cdot ln(2) = ln(0.05)[/tex]

Dividing both sides by -2 ln(2), we get:

[tex]d = ln(0.05) / (-2 \cdot ln(2))[/tex]

Using a calculator, we get:

[tex]d = 3.79[/tex]

Therefore, the expression that represents the number of days until only 5% of Technetium-99m remains is approximately 3.79 days.

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0.68 is a rational number because it can be expressed as a ratio of two integers (17/25).

0.68 is a rational number because it can be expressed as a ratio of two integers.

To see this, we can convert 0.68 to a fraction by placing the decimal value over a denominator of 1 followed by the number of decimal places (two in this case):

0.68 = 68/100

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor,

which is 4:

68/100 = 17/25

Thus, 0.68 can be expressed as the ratio of two integers (17 and 25) and is therefore a rational number.

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The tank will be filled in 6 minutes with the new pipes.

Let the capacity of the tank be C.

Then the rate at which the first pipe can fill the tank is C/12 per minute, and the rate at which the second pipe can fill the tank is C/15 per minute.

If the first pipe is changed with a pipe having twice of its radius, then the rate at which the new pipe can fill the tank is (2C)/12 = C/6 per minute.

If the second pipe is changed with a pipe having half of second’s radius, then the rate at which the new pipe can fill the tank is (1/2)C/15 = C/30 per minute.

Let t be the number of minutes it takes to fill the tank with the new pipes. Then we have:

(C/6 + C/30)t = C

Simplifying this equation, we get:

5Ct/30 = C

Multiplying both sides by 30/5C, we get:

t = 6 minutes

Therefore, the tank will be filled in 6 minutes with the new pipes.

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We can say that after answering the offered question Therefore, the equation constant of proportionality in this scenario is 11.25.

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

As a result, the proportionality constant in this scenario is 11.25.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

Therefore, the constant of proportionality in this scenario is 11.25.

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A radical equation is √(x + 2) = 4 - x and the extraneous solution is x = 7

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

The solution to a radical equation

In step 4 and 5, we have

x = ∛5 * 5 * 5 * 5

x = 5∛5¬ * 5¬ * 5¬ * 5

The above steps are carried out because it would simplify the radical expression to its simplest form

The reason it is done is to have the value of x in its simplest form

Here's an example of a radical equation:

√(x + 2) = 4 - x

Square both sides

x + 2 = 16 - 8x + x^2

Evaluate the like terms

x^2 - 9x + 14 = 0

Factor the quadratic equation

(x - 2)(x - 7) = 0

Solve for x:

x = 2 or x = 7

For x = 2:

√(2 + 2) = 4 - 2

√4 = 2

2 = 2

This is true, so x = 2 is a valid solution.

For x = 7:

√(7 + 2) = 4 - 7

√9 = -3

3 = -3

This is not true, so x = 7 is not a valid solution.

So, there is an extraneous solution

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Answer:

5x+120

Step-by-step explanation:

5(x) + 5(24)

5x+120

The answer of the given question based on the inequality equation the answer is given below,

An equation is mathematical statement that asserts equality of two expressions. It typically includes of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division

The situation that can be represented by 11+ 6.5p ≤ 89 is:

a) Napoleon is the buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at most $89. What is p,

To solve for p, we can follow these steps:

11 + 6.5p ≤ 89 (subtract 11 from both sides)

6.5p ≤ 78 (divide both sides by 6.5)

p ≤ 12

Therefore, Napoleon can buy at most 12 shirts if he wants to spend at most $89.

b) None of the given situations can be represented by the inequality 11 + 6.5p ≤ 89 when p represents the number of shirts Napoleon can buy. This is because the inequality implies that the total cost of buying p shirts at $11 each and mailing them for $6.50 is no more than $89, which is not consistent with the given information about the cost of the shirts and mailing.

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To calculate Daniel's weekly pay, add his regular pay and overtime pay: Weekly pay = $1038.31.

To calculate Daniel's weekly pay, we need to determine his regular hours and his overtime hours.

Regular hours = 37 hours

Overtime hours = Total hours worked - Regular hours

Total hours worked = 9.5 + 8.5 + 10 + 10 + 10.75 = 49.75 hours

Overtime hours = 49.75 - 37 = 12.75 hours

Daniel's regular pay for 37 hours is:

$18.50/hour x 37 hours = $684.50

Daniel's overtime pay for 12.75 hours is:

$18.50/hour x 1.5 = $27.75/hour (time-and-a-half rate)

$27.75/hour x 12.75 hours = $353.81

Therefore, Daniel's weekly pay is the sum of his regular pay and overtime pay:

Weekly pay = $684.50 + $353.81 = $1038.31

Therefore, Daniel's weekly pay is $1038.31.

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Complete question:

Daniel earns $18.50 an hour, with time-and-a-half for hours worked over 37 a week. His clock hours for a week are 9. 5, 8. 5, 10, 10, and 10.75. How much is his weekly pay?

Answer: Using the multiple angle formula for cosine, we have:

cos 4x = 2cos^2 2x - 1

Now we need to rewrite cos 2x in terms of cos x. Again, using the multiple angle formula for cosine, we have:

cos 2x = 2cos^2 x - 1

Substituting this expression into the previous equation, we get:

cos 4x = 2(cos^2 x)^2 - 1

Simplifying the expression further, we have:

cos 4x = 2(cos^4 x) - 1

Therefore, cos 4x can be written in terms of cos x as 2(cos^4 x) - 1.

Step-by-step explanation:

Answer:

a) The Total Expenses y (in dollars) of the College or University for t years can be modeled by an exponential function of the form:

y = ab^t                

Where "a" is the initial amount and "b" is the growth rate.

b) Using the given data, we can find the value of "a" by plugging in the first year's data into the equation:

y = ab^t

21211 = a * b^0

a = 21211

Thus, the function representing the Total Expenses y (in dollars) of the College or University after t years is:

y = 21211b^t

c) The graph of the exponential function will be an upward-sloping curve that starts at the point (0, 21211) and grows at a rate determined by the value of "b".

d) The y-intercept of the graph is (0, 21211), which represents the initial expense at the start of the first year. The function has no asymptotes. The domain of the function is all real numbers, while the range of the function is y > 21211. As t approaches infinity, the function grows without bound, which means the end behavior is that the expenses continue to increase exponentially over time.

Answer:

Multiple of 2

Step-by-step explanation:

There are six possible outcomes when rolling a standard number cube labeled 1 through 6. Out of these six possible outcomes, there are three outcomes that are multiples of 2 (2, 4, and 6) and two outcomes that are multiples of 3 (3 and 6).

Therefore, it is more likely that the cube will show a multiple of 2 than a multiple of 3. The probability of rolling a multiple of 2 is 3/6 or 1/2, while the probability of rolling a multiple of 3 is 2/6 or 1/3.

Answer:

buy a maximum of 31.83 yards of fabric

The cup of water reaches a temperature of 173 F after 5 minutes.

Temperature is a measure of the average kinetic energy of particles in a system. It is an important physical quantity used to describe the state of a system, and is widely used in science, engineering, and everyday life. Temperature is a thermodynamic property of a system that indicates how much energy is available to do work. In everyday terms, temperature is a measure of how hot or cold something is.

k = -0.2416
The equation for the cooling rate of the cup of water is:
T(t) = 207 - 0.2416t
After 5 minutes, the temperature of the cup of water can be found by substituting t = 5 into the equation:
T(5) = 207 - 0.2416(5) = 173.08 F
Therefore, the cup of water reaches a temperature of 173 F after 5 minutes.

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The two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.

Total income of person: $1800 per month.

Rent amount = 1/3 * income

Remaining amount : 1 - 1/3 = 2/3 of income

So,

Remaining amount = 2/3*1800

Remaining amount = 1200

Thus, the two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.

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A box-and-whisker plot is the appropriate data display for Jace's electric-vehicle data and gas-powered vehicle data, and it will give him a visual representation of the difference between the two datasets.

The appropriate data displays for Jace's electric-vehicle data and gas-powered vehicle data would be a box-and-whisker plot. This type of plot is a graphical representation of the five-number summary of a dataset. The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. It can be calculated using the following formulas:

Minimum = smallest value

Q1 = 25th percentile (the value below which 25% of the data lies)

Median = 50th percentile (the value below which 50% of the data lies)

Q3 = 75th percentile (the value below which 75% of the data lies)

Maximum = largest value

Using these formulas, Jace can calculate the five-number summary for his electric-vehicle data and his gas-powered vehicle data. He can then use these values to create a box-and-whisker plot that compares the range and shape of each dataset. The box-and-whisker plot will give him a clear visual representation of the difference between the two datasets. By comparing the range and shape of the two datasets, Jace can get a better understanding of the difference between the electric-vehicle data and the gas-powered vehicle data. From there, he can draw conclusions about the differences between the two vehicle types.

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The inequality represented by the graph is 10 ≤ x ≤ 20.

Inequality is the unequal distribution of resources or opportunities among individuals or groups in a society. It can be measured in multiple ways, including income, wealth, access to education, health care, and political power. It is a major social problem, as it can lead to poverty, lack of opportunity, and even violence. The root causes of inequality are complex, but can include discrimination, unequal access to resources, and social and cultural norms. In order to address inequality, governments must create policies that provide access to resources for all individuals, regardless of their social, economic, or other backgrounds. Additionally, it is important to recognize that the effects of inequality are not limited to one group of people – everyone is affected by it in some way.

The graph shows that x must be a number between 10 and 20 (inclusive). This means that the value of x must be at least 10, but it cannot be greater than 20. This is because the graph shows that the values of x between 50 and 59 are not included in the range.

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The circumference of the circular swimming pool is approximately 245.04 inches.

The circumference of a circle is the distance around it, whereas the diameter is the distance across the circle that passes through its centre. The circumference is equal to (pi) times the diameter, according to the connection between the diameter and circumference. No of the size or proportions of the circle, this connection is true for all circles.

The circumference of the circle is given as:

C = 2πr

We know that, D = 2r = 6 1/2 feet.

6 ½ feet = 6.5 × 12 inches = 78 inches

Substituting the values we have:

C = π × 78 inches = 245.04 inches

Hence, the circumference of the circular swimming pool is approximately 245.04 inches.

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Answer:

a)  $324,000

b)  $291,600

c)  $259,200

Step-by-step explanation:

The percentage of the replacement value represents how much of the house will be insured.

a)  100% of 324000 = 1.00 * 324000 = $324,000

b)  90% of 324000 = 0.9 * 324000 = $291,600

c)  80% of 324000 = 0.8 * 324000 = $259,200

Answer:

Step-by-step explanation:

7x+19=0

7x=-19

x=-19/7 ---> This is your final answer!

Plug in the x we found to see if the expression is correct:

7(-19/7)+19=0

-19+19=0

So our x value is correct!

Corey has saved $24 and Jasper has saved $54.

Let x be the amount of money Corey has saved.

Then, we know that Jasper has saved $6 more than twice as much as Corey, which can be expressed as:

J = 2x + 6

We also know that the total amount saved by both Jasper and Corey is $78, so we can set up another equation:

J + x = 78

Now we can use these equations to solve for x, which will give us the amount of money Corey has saved:

J + x = 78 (substitute J = 2x + 6)

(2x + 6) + x = 78

3x + 6 = 78

3x = 72

x = 24

Therefore, Corey has saved $24.

To check this answer, we can substitute x = 24 into the equation we found for J:

J = 2x + 6

J = 2(24) + 6

J = 54

So Jasper has saved $54.

We can verify that $24 + $54 = $78, which matches the total amount saved by both Jasper and Corey.

In summary, Corey has saved $24 and Jasper has saved $54. It's important to remember to set up equations to represent the given information in a problem and to check our answers to make sure they are reasonable and match the given information.

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Proportionately, if 32% represent students who played football, and the total number of them is 180, the total students in the group is 563.

Proportion is the ratio of two quantities equated to each other.

Proportion is a fractional value and we represent proportional values as between zero and one.

                     Basketball    Tennis     Cricket      Football

Percentage       30%             3%          35%            32% (100 - 30 - 3 - 35)

The number of

 students         169               17           197              180 (32% of 563)

The number of students who played football = 180

Proportionately, if 32% = 180, 100% representing the total number of students in the group = 563 (180/0.32).

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If Theo takes the loan R9000 that is payable over 48 months monthly installment =R 318,92, the total amount that Theo has to pay back for the loan is R15,307.16.

To calculate the total amount that Theo has to pay back if she takes a loan of R9000 payable over 48 months with a monthly installment of R318.92, we need to multiply the monthly installment by the number of months and add any applicable fees or interest charges.

First, let's calculate the total amount that Theo will pay for the loan over the 48-month period:

Total amount = Monthly installment x Number of months

Total amount = R318.92 x 48

Total amount = R15,307.16

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Complete question is:

Calculate the total amount that Theo has to payback if she takes the loan R9000 that is payable over 48 months monthly installment =R 318,92

The information that could be used to determine the number of fluid ounces of lotion in a small bottle and the number of fluid ounces in a medium bottle is given as follows:

b) The number of fluid ounces in 8 small and 4 medium bottles of lotion.

The amounts are obtained with a system of equations, for which the variables are given as follows:

Six small and four medium bottles of lotion give a combined total of 93 fluid ounces of lotion, hence:

6x + 4y = 93.

With 8 small and 4 medium bottles, the equation is given as follows:

8x + 4y = t.

Hence we can subtract the first equation by the second to obtain the value of x, then we replace and obtain the value of y, meaning that the correct option is given by option b.

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