Which of the following is the correct translation for the expression x-6?
A.a number subtracted from 6
B.a negative number added to 6
C.the product of a number and -6
D.the difference between a number and 6

The resultant force must be equal and opposite to Betty's force for equilibrium. Hence, FN = - (FA + FC)

(a) If Charles pulls in the direction indicated in the picture, we can use vector addition to find the resultant force. By adding Alex's and Charles' forces as vectors, the resultant force must be equal and opposite to Betty's force for equilibrium. Hence, FN = - (FA + FC).

(b) If Charles pulls in the other possible direction for equilibrium, we again use vector addition. In this case, the resultant force must be equal and opposite to the vector sum of Alex's and Charles' forces. Therefore, FN = - (FA - FC).

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The credit to interest revenue on the loan when the note becomes due will be $412.5

Interest revenue is the amount of money earned when money is learnt to others at an interest rate.

The amount Mike Co loaned the employee for 9 months = $11,000

The annual interest rate of the loan = 5%

The amount the employee will pay when the loan comes due in 2018 = The interest and the amount loaned

The interest on the loan can be calculated using the simple interest formula, which is;

Interest, I = Principal × Rate × Time

The principal on the loan = $11,000

The interest rate on the loan per annum = 5% = 0.05

The duration of the loan = 9 months = (9/12) = 3/4 of a year

Therefore; I = 11,000 × 0.05 × (3/4) = 412.5

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Answer:

B

Step-by-step explanation:

The unit rate changes throughout the table.

Answer:

A x<1125

Step-by-step explanation:

Answer:

57

Step-by-step explanation:

...........................

If you add 2 to 55 it’s going to equal 57

95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.

What is proportional limit?

The maximum stress at which stress and strain are directly proportional and the stress-strain graph is a straight line with a gradient equal to the elastic modulus of the material is known as the proportional limit.

To calculate the 95% lower confidence bound for the true average proportional limit stress of all such joints, we can use the following formula:

lower confidence bound = sample mean - (t-value * standard error)

The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:

              \(standard\ error = sample\ standard\ deviation / \sqrt{(sample \ size)}\\\\= 0.78 / \sqrt{(20)}\\\\= 0.19\)

To find the t-value, we can consult a t-distribution table or use a t-distribution calculator. At a 95% confidence level with a sample size of 20, the t-value is approximately 1.725.

Substituting these values into the formula for the lower confidence bound, we get:

lower confidence bound = 8.52 - (1.725 * 0.19)

= 8.52 - 0.327

= 8.19

So the 95% lower confidence bound for the true average proportional limit stress of all such joints is approximately 8.19 mpa.

Hence,  95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.

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The equation of the tangent plane to the surface y = x^2 - z^2 at the point (10, 36, 8) is 32x + 16z - y = 380.

To find the equation of the tangent plane to the surface y = x^2 - z^2 at the point (10, 36, 8), we need to find the gradient of the surface at that point. The gradient is a vector that points in the direction of the maximum rate of change of the surface, and its components are the partial derivatives of the surface with respect to x, y, and z.

Taking the partial derivatives of the surface with respect to x, y, and z, we get:

∂/∂x (y) = 2x

∂/∂y (y) = 1

∂/∂z (y) = -2z

Evaluating these partial derivatives at the point (10, 36, 8), we get:

∂/∂x (y) = 2(10) = 20

∂/∂y (y) = 1

∂/∂z (y) = -2(8) = -16

So the gradient at the point (10, 36, 8) is the vector:

grad(y) = (20, 1, -16)

This vector is perpendicular to the tangent plane at the point (10, 36, 8). We can use this fact and the point-normal form of the equation of a plane to find the equation of the tangent plane. The point-normal form is:

n · (r - r0) = 0

where n is the normal vector to the plane, r0 is a point on the plane, and r is any point on the plane.

Substituting the values we found earlier, we have:

(20, 1, -16) · ([x, y, z] - [10, 36, 8]) = 0

Simplifying this equation gives:

20(x - 10) + (y - 36) - 16(z - 8) = 0

which can be rearranged to:

32x + 16z - y = 380

Therefore, the equation of the tangent plane to the surface y = x^2 - z^2 at the point (10, 36, 8) is 32x + 16z - y = 380.

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a) The feasible set can be represented as a straight line with a negative slope on a graph.

b) The preferred choice point is (15, 15).

c)  With an entrance fee of $9, the new feasible set shifts vertically upwards.

d)  The change in entrance fee reduced the amount of leftover cash in the feasible set.

a) The x-axis represents the number of pizza slices, and the y-axis represents the leftover cash. The line starts at the point (0, 60) and intersects the x-axis at (20, 0). This means that you can buy a maximum of 20 pizza slices with $60, and if you don't buy any pizza, you will have $60 left.

b) This point represents buying 15 slices of pizza, which costs $45, and having $15 left. It is the preferred choice because it allows for a balance between enjoying pizza and not exhausting all the cash. It provides both a substantial amount of pizza and a reasonable amount of leftover cash.

c) The line now starts at (0, 51) and intersects the x-axis at (20, 9). This means that with the entrance fee, you can buy a maximum of 20 pizza slices and have $9 left.

d) It means that you have less cash available after buying pizza slices. The new preferred choice would likely shift downwards to a point that allows for a reasonable number of pizza slices while still leaving enough money to cover the entrance fee.

The change in entrance fee makes it necessary to consider the balance between the number of pizza slices and the available cash more carefully to ensure you can afford the entrance fee and still enjoy a satisfying amount of pizza.

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a) Every Engineer loves to solve some problem.

x ∀ y(E(x) ∧ A(y) → ~L(x, y))

b) There is a smallest positive integer.

∀ x   y(N(x) ∧ M(y) → x < y)

c) All obtuse triangles have one angle that measures larger than 90°.

x(A(x)  → ~B(x) ∨ ~E(x))

d) There is a student in the class who helps all classmates.

∀x ∀y(C(x) ∧ A(y, x) → ~B(x, y))

a) Every Engineer loves to solve some problem.

The statement using multiple quantifiers and variables.

Let E(x) = x is an engineer

A(x) = x is a problem.

L(x, y) = x loves to solve probability

The negation of the given statement in words.

Negation: There exists at least one engineer who does not love to solve any problem.

The negation using multiple quantifiers and variables.

x ∀ y(E(x) ∧ A(y) → ~L(x, y))

b) There is a smallest positive integer.

The statement using multiple quantifiers and variables.

Let M(x) = x is a negative integer.

x ∀ y(M(x)  ∧ M(y) → x ≥ y)

The negation of the given statement in words.

There exists no longer negative integer.

The negation using multiple quantifiers and variables.

∀ x   y(N(x) ∧ M(y) → x < y)

c) All obtuse triangles have one angle that measures larger than 90°.

The statement using multiple quantifiers and variables.

Let A(x) = x is healthy.

B(x) = x follow diet plan.

C(x) = x follows exercise plan.

∀ x (A(x) → B(X) ∧ C(x))

The negation of the given statement in words.

There exists at least one healthy man who does not follow either diet plan or exercise plan.

The negation using multiple quantifiers and variables.

x(A(x)  → ~B(x) ∨ ~E(x))

d) There is a student in the class who helps all classmates.

The statement using multiple quantifiers and variables.

Let A(y, x) = y is classmate of x.

B(x, y) = x helps y.

C(x) = x is a student in the class.

x ∀ y (C(x) ∧ A(y, x) → B(x, y))

The negation of the given statement in words.

There is no student in the class who helps all classmates.

The negation using multiple quantifiers and variables.

∀x ∀y(C(x) ∧ A(y, x) → ~B(x, y))

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The complete question is:

For each of the statements in a, b, c, and d do the following:

(i) Rewrite the statement using multiple quantifiers and variables.

(ii) Write the negation of the given statement in words.

(iii) Rewrite the negation using multiple quantifiers and variables.

a) Every Engineer loves to solve some problem.

b) There is a smallest positive integer.

c) All obtuse triangles have one angle that measures larger than 90°

d) There is a student in the class who helps all classmates.

Answer:

Step-by-step explanation:

Given

When video is posted 5 people watched it

Next day number of viewers doubled

Suppose this trend continues i.e. No of viewers doubled each day

So on 2 nd day no of viewers is \(2\times 5\)

On 3rd day , viewers \(2^2\times 5\)

on n th day , viewers is \(2^{n-1}\times 5\)

So no of viewers in 1 year i.e. on 365 day

\(=2^{365-1}\times 5\)

\(=2^{364}\times 5\)

(ii)Day on which 640 people seen the video

\(2^{n-1}\times 5=640\)

\(2^{n-1}=128\)

\(2^{n-1}=2^7\)

Therefore

\(n-1=7\)

\(n=8\ days\)

Slope-intercept form

The firm 4's efficient scale occurs at 4

In this question, we have been given a table of long-run total cost and the quantity.

We need to find the quantity at which the firm 4's efficient scale occurs.

We know that the efficient scale occurs at the quantity of output where average total cost is minimum.

For the firm 4 the average total cost would be,

(210 + 340 + 490 + 660 + 850 + 1060 + 1290) / 7

= 4900 / 7

= 700

This value is clsoe to 660.

Therefore, the firm 4's efficient scale occurs at quantity 4.

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Given question is incomplete.

Step-by-step explanation:

You dont have to just wait.

Youll figure out what you like

Answer:

ask what would you like to do or do you make enough money simple questions

Answer:

I believe that your answer is a

Step-by-step explanation:

I remember that the exponent would be multiplied by both sides.

Answer: A

Step-by-step explanation:

the answer is b because if you

multiply it inside and get the exponents the answer

so the answer is A

Hope this helps :)

The complex number in A + Bi form is 3(Cos(3Cos(5)) + iSin(3Cos(5))). We need to express the answer in exact values only for a. Since a = 3cos(5), we can use the cosine of 5 degrees in exact form, which is (sqrt(10) + sqrt(2))/4. Therefore, the final answer is 3[(sqrt(10) + sqrt(2))/4] + 3i sin(5) in the form a + bi with exact values only for a.

Let's understand the given complex number. We have 3 as the magnitude or modulus of the complex number, and the argument is 3(cos(5) + i sin(5)). This argument can be simplified using Euler's formula: e^(ix) = cos(x) + i sin(x). Hence, 3(cos(5) + i sin(5)) = 3e^(i5). Therefore, the given complex number is 3e^(i5) with modulus 3 and argument 5. To convert the complex number to the form a + bi, we need to find the real and imaginary parts of the complex number. Using Euler's formula, we can write the complex number as 3(cos(5) + i sin(5)) = 3cos(5) + 3i sin(5). The real part is 3cos(5) and the imaginary part is 3sin(5). Therefore, the complex number can be written as a + bi, where a = 3cos(5) and b = 3sin(5).

Evaluate the trigonometric functions: Cos(5) and Sin(5) are exact values, so we'll leave them as they are. The expression becomes 3(Cos(3(Cos(5) + iSin(5)))). Apply the De Moivre's theorem, which states (Cos(x) + iSin(x))^n = Cos(nx) + iSin(nx). In our case, n = 3, and x = Cos(5) + iSin(5). So, (Cos(3(Cos(5) + iSin(5)))) = Cos(3Cos(5)) + iSin(3Cos(5)).
Multiply the result by 3: Finally, we multiply the expression by 3 to get 3(Cos(3Cos(5)) + iSin(3Cos(5))). This is now in the A + Bi form.

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The property of determinants illustrated in this equation. |2 2 2 4 -8 4 8 1 -2| = - |4 -8 4 2 2 2 8 1 -2| is  If two rows of A are interchanged to produce B, then det B = - det A. The correct option is D.

In the given equation, the determinant of matrix A is equal to the negative determinant of matrix B. This means that matrix B is obtained by interchanging two rows of matrix A.

According to the property of determinants, if two rows of a matrix are interchanged, then the determinant of the resulting matrix is equal to the negative of the determinant of the original matrix. Therefore, the given equation illustrates this property of determinants. So, The correct option is D that is  If two rows of A are interchanged to produce B, then det B = - det A. The correct answer is D.

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B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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Answer:

Step-by-step explanation: 1/4

Answer:

4.2 gallons

67.2 cups

Step-by-step explanation:

He had 3 gallons of punch.

He added another 1.2 gallons.

The number of gallons of punch he has now is:

3 + 1.2 = 4.2 gallons

1 gallon = 16 cups

=> 4.2 gallons = 4.2 * 16 = 67.2 cups

He has 67.2 cups

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The graphs can be described as shown below.

A.) The first graph has the y-intercept at 2. Therefore, the first graph can be described by the equation, y =5x + 2.

B.) For the second graph, the graph passes through the point (-1,0). Therefore, if we substitute the value of y as 0 in the equation y=3x+3, we will get x=-1.

Hence, the equation of the second graph is y=3x+3.

C.) For the third graph, the graph passes through the point (-1.5,0). Therefore, if we substitute the value of y as 0 in the equation y=2x+3, we will get x=-1.5.

Hence, the equation of the second graph is y=2x+3.

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The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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Answer:

Answer is 70%

Step-by-step explanation:

I hope it's helpful!

Answer:

60%of x=42

x=42×100/60=70 is your answer

Answer:

the answer should be x= -7 hope this helps!

Answer:

w + w

Step-by-step explanation:

w + w   * 1 is the coefficent of w *

1w + 1w

(1+1) w

2w

Answer:

w+w

Step-by-step explanation:

Since Desean sets up his zero based budget and has $175 left after he assigns all of his expenses to each category. Therefore, a good category for him to put that money in is money for bills.

In Economics, a budget can be defined as a financial plan that is typically used for the estimation of revenue and expenditures (expenses) of an individual, business organization or government in the form of money, especially for a specified period of time, often one year.

In this context, we can reasonably infer and logically deduce that Desean should put the remaining money ($175) in the money for bills category.

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Answer:

The slope is 6/7

Step-by-step explanation:

The slope is equal to (y₂ - y₁)/(x₂ - x₁)

Point 1 is (-2,1)

Point 2 is (5,7)

((7) - (1))/((5) - (-2))

(7 - 1)/(5 + 2)

6/7

The slope is 6/7

Answer:

16^10, 4^20 y 2^40

Step-by-step explanation:

Para expresar el producto

16^7 ×16^3  16 ^7 ×16^3

como una potencia de 16, podemos sumar los exponentes y mantener la base:

16^7 × 16^3 = 16^7 + 3=16^10  16^7 ×16^3  =16^7+3  =16 ^10

Para expresar el resultado como una potencia de 4, podemos utilizar la relación

16

=

4

2

16=4

2

:

1

6

10

=

(

4

2

)

10

=

4

2

×

10

=

4

20

16

10

=(4

2

)

10

=4

2×10

=4

20

Finalmente, para expresar el resultado como una potencia de 2, utilizamos la relación

4

=

2

2

4=2

2

:

4

20

=

(

2

2

)

20

=

2

2

×

20

=

2

40

4

20

=(2

2

)

20

=2

2×20

=2

40

Por lo tanto, el producto

1

6

7

×

1

6

3

16

7

×16

3

 puede ser expresado como

1

6

10

16

10

,

4

20

4

20

 y

2

40

2

40

.

Answer:

I hope it will help you dear

Answer:

Step-by-step explanation:

from cosines theorem:

t² = 11² + 14² - 2•11•14•cos87°

t² = 121 + 196 + 308•0.05236

t² = 333.12688

t = √333.12688

t = 18.2517... ≈ 18.3