(01. 04 MC)Simplify the following expression: (-3)(-2) -2) 0-12 0 12 0-18 0 18

The distance, relative to mile marker 45, to the nearest mile when passing mile marker 112 on a straight highway is 67 miles.

When you pass mile marker 112 on a perfectly straight highway between marker 45 and marker 112, the distance covered is 112 - 45 = 67 miles. This means that you have traveled a total of 67 miles from mile marker 45 to mile marker 112.

To determine the distance relative to mile marker 45, we consider the distance remaining from mile marker 112.

Since you have passed mile marker 112, the remaining distance to cover until you reach the nearest mile relative to marker 45 is the difference between 112 and the nearest mile greater than 112.

Let's assume the nearest mile greater than 112 is 113.

Therefore, the remaining distance is 113 - 112 = 1 mile.

In conclusion, when passing mile marker 112 on the straight highway, the distance relative to mile marker 45 to the nearest mile is 67 miles.

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Answer:

30

Step-by-step explanation:

Answer:

B) 2(3x^2+10x+15

Step-by-step explanation:

Answer:

let common ratio between them be x

So, 5x,3x

5x-3x=18

2x=18

2x/2=18/2

x=9

Step-by-step explanation:

I hope it helps you☺️

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The area of the irregular shape is 84 ft square.

The diagram is a trapezium. A trapezium is a quadrilateral. Therefore, the area of the trapezium can be found as follows:

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

a = 10 ft

b = 18 ft

c = 6 ft

area of the trapezium = 1 / 2 (10 + 18)6

area of the trapezium = 1 / 2 (28)6

area of the trapezium = 168 / 2

area of the trapezium = 84 ft²

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Answer: c

Step-by-step explanation: 54% of people with internet access prefer text messaging, while only 31% of people without internet access prefer text messaging.

Based on the data, Option (c) statements must be true. "A person with internet access is more likely than a person without internet access to prefer text messaging to communicate with their friends."

It is Mbps or kbps of data packets that can be transferred within a specified time.

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The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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The probabilities in each case:

A. P(student does not drink coffee) = 143/495 ≈ 0.2889

B. P(student is male) = 116/495 ≈ 0.2343

C. P(student is a female who prefers regular coffee) = 22/495 ≈ 0.0444

D. P(student prefers decaffeinated coffee | male student) = 18/116 ≈ 0.1552

E. P(male student | student prefers decaffeinated coffee) = 18/69 ≈ 0.2609

F. P(female student | student prefers regular coffee or does not drink coffee) = 165/495 ≈ 0.3333

Let's calculate the probabilities based on the provided information:

(a) Probability that the student does not drink coffee:

Number of students who do not drink coffee = 143

Total number of students surveyed = 495

P(student does not drink coffee) = 143/495 ≈ 0.2889

(b) Probability that the student is male:

Number of male students = 116

Total number of students surveyed = 495

P(student is male) = 116/495 ≈ 0.2343

(c) Probability that the student is a female who prefers regular coffee:

Number of female students who prefer regular coffee = 22

Total number of students surveyed = 495

P(student is a female who prefers regular coffee) = 22/495 ≈ 0.0444

(d) Probability that the student prefers decaffeinated coffee, given that the student is selected from the male students:

Number of male students who prefer decaffeinated coffee = 18

Total number of male students = 116

P(student prefers decaffeinated coffee | male student) = 18/116 ≈ 0.1552

(e) Probability that the student is male, given that the student prefers decaffeinated coffee:

Number of male students who prefer decaffeinated coffee = 18

Total number of students who prefer decaffeinated coffee = 69

P(male student | student prefers decaffeinated coffee) = 18/69 ≈ 0.2609

(f) Probability that the student is female, given that the student prefers regular coffee or does not drink coffee:

Number of female students who prefer regular coffee or do not drink coffee = 22 + 143 = 165

Total number of students who prefer regular coffee or do not drink coffee = 495

P(female student | student prefers regular coffee or does not drink coffee) = 165/495 ≈ 0.3333

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The complete question :

A university cafeteria surveyed the students who ate breakfast there for their coffee preferences. The findings are summarized as follows: Do not Prefer drink regular decaffeinated coffee coffee coffee Total Prefer Female22 Male18 Total 40 143 196 339 69 42 116 234 261 495 A student is selected at random from this group. Find the probability of the following. (Round your answers to four decimal places.) (a) The student does not drink coffee. (b) The student is male. (c) The student is a female who prefers regular coffee. (d) The student prefers decaffeinated coffee, given that the student being selected from the male students (e) The student is male, given that the student prefers decaffeinated coffee. (f) The student is female, given that the student prefers regular coffee or does not drink coffee

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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Answer:

- 2(t - 1)² + 32

Step-by-step explanation:

Given

- 2t² + 4t + 30

Use the method of completing the square to express in vertex form.

The coefficient of the t² term must be 1, so factor out - 2 from the first 2 terms.

= - 2(t² - 2t) + 30

To complete the square

add/subtract ( half the coefficient of the t- term)² to t² - 2t

= - 2(t² + 2(- 1)t + 1 - 1) + 30

= - 2(t - 1)² + 2 + 30

= - 2(t - 1)² + 32

comparing with:

Then a = 1 and b=3

To find the y-intercept, substitute x=0

The y-intercept is 1

Comparing with

The value of a =-1 and the value of b is 3

To find the y-intercept, substitute x=0 into the equation

y=-1

The y-intercept is -1

he equation of the linear function represented by the table in slope-intercept form is y = 3x - 8.

The slope of the line can be calculated using the formula:

slope = (change in y) / (change in x)

to find the equation of the linear function represented by the table in slope-intercept form, we need to first find the slope and the y-intercept of the line.

Using the points (0, -8) and (1, -5), we have:

slope = (-5 - (-8)) / (1 - 0) = 3/1 = 3

Therefore, the slope of the line is 3.

To find the y-intercept, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the point (0, -8) and the slope we just calculated, we have:

y - (-8) = 3(x - 0)

y + 8 = 3x

y = 3x - 8

Therefore, the equation of the linear function represented by the table in slope-intercept form is y = 3x - 8.

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To fully answer this question, I would need the information presented in Figure 3.14 that provides the computer solution. Unfortunately, I cannot access or view specific figures or external sources. However, I can explain the general approach to solving such a problem and provide a LaTeX code snippet to format the question.

To solve the given problem, it appears to be a linear programming problem where the goal is to optimize the total annual return subject to certain constraints. The decision variables are the number of shares of US Oil (U) and Huber Steel (H) to be purchased.

a. The optimal solution would provide the values of U and H that maximize the total annual return while satisfying the given constraints. The value of the total annual return would be the objective function value at the optimal solution.

b. The binding constraints are those that are active and determine the solution. These constraints limit the risk index, the total investment amount, and the maximum number of shares of US Oil. Interpretation of these constraints would depend on the specific problem and its context.

c. The dual values for the constraints represent the marginal values or shadow prices associated with each constraint. They indicate the rate of change in the objective function value for a small change in the right-hand side of the constraint. Interpretation of dual values would also depend on the specific problem and its context.

d. The impact of increasing the maximum amount invested in US Oil would depend on the objective function and the constraints. It could lead to a higher total annual return if US Oil has a higher return rate and the constraint on the risk index or total investment amount allows for it. However, if the maximum number of shares of US Oil is already binding, increasing the maximum investment amount would not be beneficial.

Please provide any additional information or specific values from Figure \(3.14\) if you have access to it, and I can assist further.

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Answer:

5/2

Step-by-step explanation:

10 multiplied by 5/2 gives us 25, so the scale factor is 5/2.

The series ∑ₙ=₁ to ∞ (n/n² + 6) is divergent.

To determine whether the series ∑ₙ=₁ to ∞ (n/n² + 6) is convergent or divergent, we can use the Integral Test.

The Integral Test states that if f(x) is a continuous, positive, and decreasing function on the interval [1, ∞) and f(n) = aₙ for all positive integers n, then the series ∑ₙ=₁ to ∞ aₙ and the integral ∫₁ to ∞ f(x) dx either both converge or both diverge.

In this case, let's consider the function f(x) = x/(x² + 6). We can check if it meets the conditions of the Integral Test.

Positivity: The function f(x) = x/(x² + 6) is positive for all x ≥ 1.

Continuity: The function f(x) = x/(x² + 6) is a rational function and is continuous for all x ≥ 1.

Decreasing: To check if the function is decreasing, we can take the derivative and analyze its sign:

f'(x) = (x² + 6 - x(2x))/(x² + 6)² = (6 - x²)/(x² + 6)²

The derivative is negative for all x ≥ 1, which means that f(x) is a decreasing function on the interval [1, ∞).

Since the function f(x) = x/(x² + 6) satisfies the conditions of the Integral Test, we can evaluate the integral to determine if it converges or diverges:

∫₁ to ∞ x/(x² + 6) dx

To evaluate this integral, we can perform a substitution:

Let u = x² + 6, then du = 2x dx

Substituting these values, we have:

(1/2) ∫₁ to ∞ du/u

Taking the integral:

(1/2) ln|u| evaluated from 1 to ∞

= (1/2) ln|∞| - (1/2) ln|1|

= (1/2) (∞) - (1/2) (0)

= ∞

The integral ∫₁ to ∞ x/(x² + 6) dx diverges since it evaluates to ∞.

According to the Integral Test, since the integral diverges, the series ∑ₙ=₁ to ∞ (n/n² + 6) also diverges.

Therefore, the series ∑ₙ=₁ to ∞ (n/n² + 6) is divergent.

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Incomplete question:

Use the Integral Test to determine whether the series is convergent or divergent.

∑ₙ=₁ to ∞ = n/n² + 6

Evaluate the following integral ∫₁ to ∞ x/x²+6 . dx

To use Theorem 4.6 and find the values of k for which the matrix A is invertible, we first need to know the elements of the matrix A. Please provide the matrix so I can help you determine the values of k.

Theorem 4.6 states that a square matrix A is invertible if and only if its determinant is nonzero. Therefore, to find all values of k for which A is invertible, we need to find the determinant of the matrix and set it equal to zero.

Let A be the given matrix. We have:

det(A) = (k-2)(-1)(k-1) + (-1)(k-1)(2k-3) + (k-2)(2k-3)(k-1)
det(A) = -k^3 + 5k^2 - 5k + 3

Setting det(A) equal to zero and solving for k, we get:

-k^3 + 5k^2 - 5k + 3 = 0

Using synthetic division or factoring, we can find that k = 1 is a root of this equation. Dividing by (k-1), we get:

-(k^2 - 4k + 3) = 0

Factoring again, we get:

-(k-1)(k-3) = 0

Therefore, the values of k for which A is invertible are k = 1 and k = 3.

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To estimate the cost of a new 3000-ft² heat exchange system for a plant retrofit, we can use the price index and the information about the cost of a previous heat exchanger. Given that the price index 7 years ago was 1360 and is now 1478, and assuming a power-sizing exponent of 0.55, rough estimate for the cost of the new heat exchanger system is $77,700.

To estimate the cost, we need to account for the change in the price index over the years. The price index ratio is calculated as (new price index)/(old price index), which in this case is 1478/1360 = 1.085. Since the power-sizing exponent is 0.55, we raise the price index ratio to the power of 0.55, resulting in \(1.085^{0.55 {\)≈ 1.036.

Next, we multiply the cost of the previous heat exchanger by this factor to estimate the cost of the new system. The cost of the previous heat exchanger was $75,000, so the rough estimate for the cost of the new heat exchanger system is approximately $75,000 × 1.036 ≈ $77,700.

It's important to note that this estimate is a rough approximation and does not account for other factors such as inflation or changes in technology. It serves as a starting point for estimating the cost of the new heat exchanger system based on the given information and assumptions.

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Number of ways to form four letters strings formed using a, b, c, d, e with the given conditions is equal to 150ways.

As given in the question,

Given letters are a, b, c, d, e has

Number of vowel = 2

Number of consonant= 3

Number of letter strings to be formed = 4

Condition:

First letter must be vowel

Last letter must be consonant

First place filled in 2 ways

Second and Third place filled in 5ways

Last place filled in 3 ways

Total number of ways to form four letters strings

= 2 × 5 × 5 × 3

= 150

Therefore, number of ways to form four letter string is 150 ways.

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Answer:

9 is how many people can attend

Let the number to be added = x

so the equation will be

-9.46+x=7.489

x=7.489+9.46

as the sign changes on the other side of the equals sign

x=16.949

To check: -9.46+16.949

                =7.486

So the number to be added is 16.949

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Answer:

11 1/3 ounces of ranch dressing.

Step-by-step explanation:

Answer:

it would be 39t for the extra 8s

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Looking at the graph below, the dot (1,2) does not cross through the line and as a result it is not one of the points on the line.

Answer: no

Step-by-step explanation:

Answer:

The range of the graph is:

-3 ≤ y ≤ 3

Hence, option (B) is correct.

Step-by-step explanation:

We know that the range of a function is the set of values of the dependent variable 'y' for which a function is defined.

From the given graph, it is clear that the graph goes down at y=-3 and then goes up to y=3  and then goes down again.

In fact, this indicates that the range of the graph lies between y=-3 to y=3

Therefore, the range of the graph is:

-3 ≤ y ≤ 3

Hence, option (B) is correct.

Answer:

2000

Step-by-step explanation:

If there is only one signiciant figure without a decimal point, then the left-most figure is when counting begins.

Answer:

2000

Step-by-step explanation:

Answer:

(x, y ) → (x + 5, y - 3 )

Step-by-step explanation:

5 units right means add 5 to the x- coordinate

3 units down means subtract 3 from the y- coordinate

the translation rule is

(x, y ) → (x + 5, y - 3 )