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For each of the three expressions, rationalize the denominator and simplify. Show all steps needed to get the answer.

1)
5/4- srt3


a) What is the conjugate of the denominator?

b) Use the conjugate to rationalize the denominator. What is the simplified answer after rationalizing? Use ‘sqrt’ for square root as needed.



2.

a) What is the conjugate of the denominator?

b) Use the conjugate to rationalize the denominator. What is the simplified answer after rationalizing? Use ‘sqrt’ for square root as needed.



3.

a) What is the conjugate of the denominator?

b) Use the conjugate to rationalize the denominator. What is the simplified answer after rationalizing? Use ‘sqrt’ for square root as needed.

The scatter diagram for the data with college GPA as the independent variable is illustrated as follows.

In this case, we have a dataset that includes the GPA and salary of graduates ten years after graduation. We can use GPA as the independent variable (or x-axis) and salary as the dependent variable (or y-axis). We can then plot each data point on the graph, where the x-coordinate represents the GPA and the y-coordinate represents the salary.

To create the scatter plot, we first need to organize the data into pairs of GPA and salary values. For example, the first pair is (2.22, 72,000), where 2.22 is the GPA and 72,000 is the salary. We can then plot this point on the graph by locating 2.22 on the x-axis and 72,000 on the y-axis.

We repeat this process for each data point, and then connect the points with a line or a curve. The resulting scatter plot shows us the overall pattern of the relationship between GPA and salary. If there is a positive relationship between the two variables, we would expect to see the points cluster around a line that slopes upwards from left to right.

Overall, the scatter plot provides a useful visual tool for exploring the relationship between college GPA and salary. While it suggests that there is a positive relationship between the two variables, it also reminds us that there are many other factors that contribute to earnings.

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Complete Question:

Do students with higher college grade point averages (GPs) earn more than those graduates with lower GPAs?

Consider the following hypothetical college GPA and salary data (10 years after graduation). GPA Salary (S)

72,000 2.22

48,000 2.29

72,000 2.57

64,000 2.59

86,000 2.77

98,000 3.12

133,000 3.35

130,000 2.85

157,000 3.66

162,000 3.68

Develop a scatter diagram for these data with college GPA as the independent variable

The following system of equations has no solutions, the correct option is A.

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

We have given that;

system of equations are

x+y=-4.....1

-x-y=4......2

Now,

Rearranging the equation 2

-4=x+y

Its equal to equation 1

Therefore, the system of equations will have no solution.

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Answer:

give the diagram please

The total length of the two welded together is 26ft.

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. Division and multiplication are the other two fundamental mathematical operations. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).

Given that the length of the two pieces of the pipe is 23ft and 3ft.

The total length of the two welded together is:

23 + 3 = 26ft

Hence, the total length of the two welded together is 26ft.

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Answer:

900

Step-by-step explanation:

5% of 18,000

The percent error in the specified situation is 2%.

The actual length of the metal is 30 centimeters, and the measured length is 29.4 centimeters. The difference between the actual and measured lengths is:

30 - 29.4 = 0.6 centimeters

The absolute error is the magnitude of this difference:

|0.6| = 0.6 centimeters

To find the percent error, we divide the absolute error by the actual value and multiply by 100:

percent error = (absolute error / actual value) x 100%

= (0.6 / 30) x 100%

= 2%

Therefore, the percent error is 2%.

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The corresponding graph for the given data is  a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27), (1,25), (3,21), (4,19) and (7,13)

What is a linear function?

A linear function is a polynomial function whose degree is utmost zero or one. It is represented as a straight line in the graph.

A Girl scout is selling cookies to raise money for her troop.

She is given a certain number of cookies to sell and is tracking the number of boxes remaining each day.

This result is shown in the table:

       Time(in days)         Number of boxes

                 1                                   25

                 3                                   21                                

                 4                                   19

                 7                                   13

The graph for the given data is attached below.

This forms a straight line.

By critically observing the graph and relationship between the time and number of boxes, we determine a function for the graph.

That is y=-2x+27.

Hence, the corresponding graph for the given data is  a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27), (1,25), (3,21), (4,19) and (7,13)

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Answer: Its D.

Step-by-step explanation:

Answer:4 mph

Step-by-step explanation:

The statement which is not true is a. Passive political risk management discourages managers from fully or partially hedging their bets against exposure to political hazards

Passive political risk management does not deter managers from fully or partially hedging their bets against political risk exposure. This management describes a strategy for controlling political risk that involves altering how a firm carries out a business to reduce political risk. This is generally performed without necessarily using financial instruments to safeguard against any degree of political risk.

It may entail taking necessary steps to spread the firm's operations across other geographies and regions, choosing joint venture partners with strong political influence, determining local contacts, and preserving strong ties with local individuals associated with politics. Even if a firm doesn't use active hedging tactics, these activities can efficiently assist it to lessen its exposure to political risk.

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The weighted average grade of the student is 85.6% calculated by multiplying the weight of each category with the average score of that category, and summing up the results.

To find the weighted average grade of the student, we can use the following formula:

Weighted average = (weight of category 1 x average of category 1) + (weight of category 2 x average of category 2) + ... + (weight of category n x average of category n)

where n is the number of categories being considered.

Using this formula and the information given in the question, we can calculate the weighted average as follows:

Weighted average = (0.30 x 85%) + (0.40 x 83%) + (0.20 x 89%) + (0.10 x 91%)

= 25.5% + 33.2% + 17.8% + 9.1%

= 85.6%

Therefore,

The weighted average grade of the student is 85.6%.

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The sampling distribution of the mean price of 30 houses is a normal distribution with a mean of $383,500 and a standard deviation of $52,823 is the correct description among the following given for sampling distribution.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

This can be calculated as:

Standard Deviation of Sampling Distribution =

(Standard Deviation of Population) / (√Number of Samples)

= $289,321 / √30

= $289,321 / 5.4772

= $52.823

Therefore, the sampling distribution of the mean price of 30 houses is a normal distribution with a mean of $383,500 and a standard deviation of $52,823.

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Answer:       is 1 of them 31(2760)q -d)

its b is true I just took it

The number of movies on the shelf is given as follows:

36 movies.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For this problem, the parameters are given as follows:

Hence the total number of outcomes, representing the number of movies on the shelf, is obtained as follows:

1/4 = 9/x

x = 9 x 4

x = 36 movies.

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The probability of having more than the expected number of failures (i.e., at least five failures) in a set of nine Bernoulli trials is 0.2461, assuming that the probability of failure is 0.5.

In the field of probability, it is essential to understand the expected number of successes or failures in a given set of trials. However, what happens when we observe more or fewer outcomes than expected? In this scenario, we need to calculate the probability of observing a specific number of failures in a set of Bernoulli trials.

Let's assume that the probability of failure is denoted by "p," and the probability of success is denoted by "q." Thus, the expected number of failures in nine Bernoulli trials is given by:

E(X) = np

where n is the number of trials, and p is the probability of failure. In this case, n = 9, and we need to determine the probability of having more than the expected number of failures. This means we are interested in finding the probability of observing at least five failures since the expected number of failures is given by:

E(X) = 9p

If we assume that the probability of failure is 0.5 (i.e., p = 0.5), then the expected number of failures is 4.5 (i.e., E(X) = 9 * 0.5 = 4.5). Therefore, we are interested in finding the probability of observing at least five failures in nine Bernoulli trials.

To calculate this probability, we need to use the binomial distribution formula, which is given by:

[tex]P(X = k) = (^n_k) \times p^k \times q^{n-k}[/tex]

where P(X = k) is the probability of observing k failures in n trials, (n choose k) is the binomial coefficient, which is calculated as n! / (k! (n-k)!), p is the probability of failure, q is the probability of success (i.e., q = 1 - p), and k is the number of failures we are interested in observing.

Using this formula, we can calculate the probability of observing at least five failures in nine Bernoulli trials as follows:

P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)

= (9 choose 5) x 0.5⁵ x 0.5⁴ + (9 choose 6) x 0.5⁶ x 0.5³ + (9 choose 7) x 0.5⁷ x 0.5² + (9 choose 8) x 0.5⁸ x 0.5¹ + (9 choose 9) x 0.5⁹ x 0.5⁰

= 0.2461

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The correct answer for each of the math expressions is given below:

The graph of a function f in mathematics is the collection of ordered pairs where displaystyle f(x)=y.

These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

Hence, given that in the graph,

f(x) = 4x + 3

g(x) = [tex]\frac{5}{3} ^x[/tex]

Over the interval (4,5), the average rate of change of g is greater than the average rate of change of f.

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The statement, coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.

When a coin is flipped the probability of getting a heads and a tail is 50%.

Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.

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Answer:  30% less than 40 is 28

Step-by-step explanation:

Answer:

The answer is 28.

Step-by-step explanation:

I'm bad at proving stuff but that's the answer I promise. (quick tip, you are more likely to get answers if you give more points. :D)

The number of balls that he can make is given as follows:

249 balls.

The volume of a sphere of radius r is given by the equation presented as follows:

V = 4πr³/3.

Considering the radius of 3 inches, the volume of each ball is given as follows:

V = 4π x 3³/3

V = 113.1 in³.

He has a total of 28,260 in³ of material, hence the number of balls that he can make is given as follows:

28260/113.1 = 249 balls.

(rounding down, as there will not be enough material for the 250th ball).

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The number of years to grow the amount from $8,000 to $10,000 will be 6.25 years.

Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,

The formula for interest is written as,

I = (PRT)/100

The equation is given below.

10000 = 8000(1 + .04t)

Where 't' represents the number of years. Then solve the equation for 't', then we have

10000 = 8000(1 + 0.04t)

1.25 = 1 + 0.04t

0.04t = 0.25

t = 0.25 / 0.04

t = 6.25 years

The number of years to grow the amount from $8,000 to $10,000 will be 6.25 years.

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Answer:

56 crickets

Step-by-step explanation:

Suppose x is the number of times a woman is selected when 3 people are randomly chosen from a group of 2 women and 2 men, the possible values of x are 0, 1, 2, and 3.

When 3 people are randomly chosen without replacement from a group of 2 women and 2 men, there are a total of 4C₃ = 4 possible outcomes, which we can list as follows:

WWx (two women and one of either gender)

WMx (one woman, one man, and one of either gender)

MWx (one man, one woman, and one of either gender)

MMx (two men and one of either gender)

In each of these outcomes, x represents the number of times a woman is selected. We can see that the possible values of x are 0, 1, 2, and 3, depending on which outcome occurs.

In outcome 1 (WWx), a woman is selected twice, so x = 2.

In outcomes 2 (WMx) and 3 (MWx), a woman is selected once, so x = 1.

In outcome 4 (MMx), no women are selected, so x = 0.

Therefore, the possible values of x are 0, 1, 2, and 3.

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The height of the portion AB of the lamppost is approximately 27.8 feet, as calculated using the tangent function with angle 55 degrees and length BC 20 feet.

Based on the given information, we can use trigonometry to find the height of the portion AB of the lamppost.

Let's call the height of AB "x". We can use the tangent function to solve for x:

tan(55) = x/20

Multiplying both sides by 20:

x = 20 tan(55)

Using a calculator, we get:

x ≈ 27.8 feet

Therefore,

The height of the portion AB of the lamppost is approximately 27.8 feet.

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Answer: 20 tan 55

Step-by-step explanation:

took test and got it right

Answer:R(d)=0.30d+75

Step-by-step explanation:

Note:  This equation, as requested, only shows the cost of

rental on a daily basis.  In order to solve for more than 1

day the equation should be:  Cost = .3r+ 100d or something

similar... with r representing miles driven, d representing

total number of days for the rental.

The measure of m∠A is 27.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

m∠A = (2x + 5) and m∠B = (4x + 19)

∠A and ∠ B are complementary angles.

So,

Solve for x.

(2x + 5) + (4x + 19) = 90

2x + 5 + 4x + 19 = 90

6x + 24 = 90

6x = 90 - 24

6x = 66

x = 11

Now,

m∠A.

= (2x + 5)

= 2 x 11 + 5

= 22 + 5

= 27

Thus,

m∠A = 27

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Answer:

[tex]10x^2+28x+15[/tex]

Step-by-step explanation:

[tex](2x^2+3)(4x+5)-8x(x^2-2)\\\\=(2x^2)(4x)+(2x^2)(5)+(3)(4x)+(3)(5)-8x^3+16x\\\\=8x^3+10x^2+12x+15-8x^3+16x\\\\=10x^2+28x+15[/tex]

Answer: 1/8

Step-by-step explanation: 3/4 is the same as 6/8

7/8- 6/8 = 1/8

The area and perimeter of the figures are( 15a³b⁴ and 10a²b⁴ + 6ab²), (6m³n² and 4m² + 10mn²) and (8m³n and 4√[m(m+2y²)] + 8mn)

1.

The area of the rectangle can be calculated using the formula;

A = l * w

A = 5a²b⁴ * 3ab²

A = 15a³b⁴

The perimeter of the rectangle is

P = 2(l + w)

P = 2[(5a²b⁴) + (3ab²)

P = 10a²b⁴ + 6ab²

2.

The area of a triangle is given by

A = 1/2 b * h

A = 0.5 * 4m² * 3mn²

A = 6m³n²

The perimeter of the triangle is calculated as

P = 4m² + 7mn² + 3mn²

P = 4m² + 10mn²

3.

The area of the triangle is given as;

A = 1/2 * b * h

A = 0.5 * 4mn * 4m²

A = 8m³n

The perimeter of the triangle is

Using Pythagoras theorem to find the hypothenuse side

The third side is 2√[m(m + 2n²)]

The perimeter of the triangle is = 4√[m(m+2y²)] + 8mn

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