Evaluate each function.
g(x) = 3x + 4; Find g(-4)
A) 10
B) -2
C) -17
D) -8

Answer:

x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

0.75x+3=6(x−3)

0.75x+3=(6)(x)+(6)(−3)(Distribute)

0.75x+3=6x+−18

0.75x+3=6x−18

Step 2: Subtract 6x from both sides.

0.75x+3−6x=6x−18−6x

−5.25x+3=−18

Step 3: Subtract 3 from both sides.

−5.25x+3−3=−18−3

−5.25x=−21

Step 4: Divide both sides by -5.25.

−5.25x/-5.25    =    -21/-5.25

Answer: x=4

The value of x from the given equation is 4.

The given equation is 0.75x + 3 = 6 (x - 3).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solve for x as follows:

0.75x + 3 = 6x - 18

⇒ 6x-0.75x = 3+18

⇒ 5.25x=21

⇒ x=21/5.25

⇒ x=4

Therefore, the value of x from the given equation is 4.

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The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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If the mpc increases in value, the consumption function will become steeper.

What is MPC ?

MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.

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The missing value of the variable z is 32 degrees. Option A

It is important to note the following;

From the information shown on the diagram, we have that;

4z and 52 degrees are both on a straight line and thus supplementary to each other.

This is then represented as;

4z + 52 = 180

collect the like terms

4z = 180 - 52

subtract the values, we get

4z = 128

Make 'x' the subject of formula, we have;

z = 128/4

divide the values

z = 32 degrees

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The area of each triangle should be rounded to the nearest hundredth.

The area of a triangle can be calculated using the formula A = (1/2)bh, where A represents the area, b represents the length of the base, and h represents the height of the triangle. To find the area, we need to know the values of the base and height.

For example, let's consider a triangle with a base of 5 units and a height of 8 units. Using the formula A = (1/2)bh, we can substitute the given values to calculate the area:

A = (1/2) * 5 * 8

A = (1/2) * 40

A = 20

Therefore, the area of the triangle is 20 square units.

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Answer:

hola, lo puedes colocar en ingles por favor, seria mas facil para mi

Step-by-step explanation:

Answer:

k = - 1

Step-by-step explanation:

13 = -4k + 9

-4k + 9 = 13

subtract 9 from both sides

-4k + 9 - 9 = 13 - 9

simplify

-4k = 4

k = 4 / -4

k = - 1

The critical numbers of the function h(p) = (p - 1) / (p^2 - 5) are "dne" (does not exist).

To find the derivative of h(p), we can apply the quotient rule. Taking the derivative, we have:

h'(p) = \([(p^2 - 5)(1) - (p - 1)(2p)] / (p^2 - 5)^2\)

Simplifying this expression, we get:

h'(p) = \((p^2 - 5 - 2p^2 + 2p) / (p^2 - 5)^2\)

= \((-p^2 + 2p - 5) / (p^2 - 5)^2\)

To find the critical numbers, we set h'(p) equal to zero and solve for p:

\(-p^2 + 2p - 5 = 0\)

However, this quadratic equation does not factor easily. We can use the quadratic formula to find the solutions:

p = (-2 ± √\((2^2 - 4(-1)(-5))) / (-1)\)

p = (-2 ± √(4 - 20)) / (-1)

p = (-2 ± √(-16)) / (-1)

Since the discriminant is negative, the equation has no real solutions. Therefore, the critical numbers of the function h(p) = (p - 1) / (\(p^2\) - 5) are "dne" (does not exist).

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Step-by-step explanation:

you can ask questions for clarification

Answer:

-7

Step-by-step explanation:

-5+|-11|+-13

-5+11+-13

6+-13

= -7

Answer:

-7

Step-by-step explanation:

-5 + |-11| + -13

|-11| = 11

So you have

-5 + 11 + - 13

+ - 13 = -13

Substitute -13 for + - 13

-5 + 11 - 13

6 - 13

-7

Answer:

The better deal is 10 cans of soda for $5.50

Step-by-step explanation:

Therefore, 10 cans of soda for $5.50 is the best deal because you are getting the most cans of soda for the cheapest amount of money.

Hope this helped!

Answer:

10 cans for $5.50

Step-by-step explanation:

3.60/6= $0.60 per can

2.36/4= $0.59 per can

5.50/10= $0.55 per can

Answer:

c

b

Step-by-step explanation:

By evaluating the function in x = -4, we will get:

f(-4) = 12

Here we have the following function:

f(x) = -4 + 4*|x|

So we have an absolute value function.

We want to find f(-4), so we want to evaluate the function in x = -4, to do that, just replace the variable by that number.

We will get:

f(-4) = -4 + 4*|-4|

Remember that the absolute value of a negative number gives the opposite:

|-4| = 4

Then:

f(-4) = -4 + 4*|-4|

f(-4) = -4 + 4*4

f(-4) = -4 + 16 = 12

f(-4) = 12

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Answer:

That is correct

Step-by-step explanation:

To get from a to 2a we multiply by 2, so we also need to multiply -5 by 2:

2(a)=2(-5)

2a=-10

Happy learning!

--Applepi101

The probability of having to try three or more times is = 431/46656.

To find the probability of having to try three or more times to get all three dice to show the same number, we need to consider the probabilities of different outcomes.

On the first roll, all three dice can show any number with equal probability, so the probability of not getting a match on the first roll is 1.

On the second roll, we want to calculate the probability of not getting a match again. There are two cases to consider:

Since we want to calculate the probability of having to try three or more times, we are interested in the event where we do not get a match on the first two rolls.

Therefore, the probability of this event is \((215/216)^2\) = 46225/46656.

Thus, the probability of having to try three or more times is 1 - 46225/46656

= 431/46656.

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A process is in statistical control when only common cause variation is present. In statistical process control (SPC), a process is said to be in statistical control when it exhibits only common cause variation.

Common cause variation, also known as random variation or natural variation, refers to the inherent variability that is present in any process due to factors that are common to the process. These factors include variations in raw materials, environmental conditions, machine performance, and human factors. Common cause variation is considered inherent to the process and is expected to occur within certain limits. When a process is in statistical control, the observed variation can be attributed to the normal functioning of the process and can be predicted within the limits of statistical probability. In this state, the process is stable, and its performance can be characterized using statistical measures such as control charts. The presence of only common cause variation indicates that the process is operating within its designed specifications and is considered to be under control.

On the other hand, if special cause variation is present in a process, it indicates the presence of unusual or assignable factors that are causing the process to deviate from its normal behavior. Special cause variation is characterized by non-random patterns in the data and is typically associated with specific identifiable causes, such as equipment malfunction, operator errors, or external disturbances. When special cause variation is detected, it signifies a departure from the expected process behavior and indicates the need for investigation and corrective actions to eliminate the assignable causes.

In summary, a process is considered to be in statistical control when only common cause variation is present, indicating that the process is stable, predictable, and operating within its normal range of variation.

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Step-by-step explanation:

the answer is xxl in roman number or 21

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

A. Using the distance formula, we can state that the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are equal, AC = BD = √50 units.

C. Based on the slopes of each side, there are 4 right angles on the rectangle.

The distance formula is used to find the distance that exist between tow points that are on a coordinate plane. The formula is: d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

What is the Slope of a Line?

Slope = change in y / change in x.

A. The coordinates of each of the vertices of the rectangle are:

A(1, 2)

B(7, 4)

C(8, 1)

D(2, -1)

Use the distance formula to find AB, CD, BC, and AD.

AB = √[(7−1)² + (4−2)²]

AB = √40

CD = √[(2−8)² + (−1−1)²]

CD = √40

BC = √[(8−7)² + (1−4)²]

BC = √10

AD = √[(2−1)² + (−1−2)²]

AD = √10

Therefore, the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are AC and BD. Find their lengths using the distance formula:

AC = √(8−1)² + (1−2)²]

AC = √50 units

BD = √[(2−7)² + (−1−4)²]

BD = √50 units

Therefore, the diagonals are equal, AC = BD = √50 units.

C. Find the slope of AB, CD, BC, and AD:

Slope of AB = change in y / change in x = rise/run = 2/6 = 1/3

Slope of CD = 2/6 = 1/3

Slope of BC = -3/1 = -3

Slope of AD = -3/1 = -3

-3 is the negative reciprocal to 1/3, this means that, if the two lines that meet at a corner have these two slope, then they will form a right angle because they are perpendicular to each other.

Therefore, there are 4 right angles on the rectangle.

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Answer:

Justin got 51 questions correct

Step-by-step explanation:

I hope this helps!

To perform partial fraction decomposition on the given rational function, we start by factoring the denominator. The denominator

x

4

−

3

x

3

+

x

2

+

3

x

−

2

x

4

−3x

3

+x

2

+3x−2 can be factored as follows:

x

4

−

3

x

3

+

x

2

+

3

x

−

2

=

(

x

2

−

2

x

+

1

)

(

x

2

+

x

−

2

)

x

4

−3x

3

+x

2

+3x−2=(x

2

−2x+1)(x

2

+x−2)

Now, we can express the rational function as a sum of partial fractions:

x

+

2

x

4

−

3

x

3

+

x

2

+

3

x

−

2

=

A

x

2

−

2

x

+

1

+

B

x

2

+

x

−

2

x

4

−3x

3

+x

2

+3x−2

x+2

​

=

x

2

−2x+1

A

​

+

x

2

+x−2

B

​

To find the values of

A

A and

B

B, we need to find a common denominator for the fractions on the right-hand side. Since the denominators are already irreducible, the common denominator is simply the product of the two denominators:

x

4

−

3

x

3

+

x

2

+

3

x

−

2

=

(

x

2

−

2

x

+

1

)

(

x

2

+

x

−

2

)

x

4

−3x

3

+x

2

+3x−2=(x

2

−2x+1)(x

2

+x−2)

Now, we can equate the numerators on both sides:

x

+

2

=

A

(

x

2

+

x

−

2

)

+

B

(

x

2

−

2

x

+

1

)

x+2=A(x

2

+x−2)+B(x

2

−2x+1)

Expanding the right-hand side:

x

+

2

=

(

A

+

B

)

x

2

+

(

A

+

B

)

x

+

(

−

2

A

+

B

)

x+2=(A+B)x

2

+(A+B)x+(−2A+B)

By comparing coefficients on both sides, we obtain the following system of equations:

A

+

B

=

1

A+B=1

A

+

B

=

1

A+B=1

−

2

A

+

B

=

2

−2A+B=2

Solving this system of equations, we find that

A

=

1

3

A=

3

1

​

 and

B

=

2

3

B=

3

2

​

.

Therefore, the partial fraction decomposition of the given rational function is:

x

+

2

x

4

−

3

x

3

+

x

2

+

3

x

−

2

=

1

3

(

x

2

−

2

x

+

1

)

+

2

3

(

x

2

+

x

−

2

)

x

4

−3x

3

+x

2

+3x−2

x+2

​

=

3(x

2

−2x+1)

1

​

+

3(x

2

+x−2)

2

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Answer:

Step-by-step explanation:

The enlargement transformation user to produce the new pentagon is called a dilation.

Dilation or Scaling involves increasing or decreasing the size of an object while maintaining its shape and proportions. In this case, the original pentagon is scaled up or down uniformly to create the new pentagon.

It involves making use of a certain scale factor to make increment or decrease an object. In this case a scale factor greater than 1 was used as the new pentagon was said to be enlarged.

Therefore, the enlargement transformation is a dilation.

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Answer:

False

Step-by-step explanation:

This is right, I did this in my class.

Answer:

I think it's 160...

Step-by-step explanation:

1/4 of 1000 is 250

250

- 90

____

160

Therefore, the correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

Based on the given information, D represents the null hypothesis (H₀) and E represents the alternative hypothesis (Hₐ).

The null hypothesis (H₀) is a statement that there is no significant difference between the observed data and the expected results. In this case, the null hypothesis is that the population mean (μ) is greater than or equal to 1000.

The alternative hypothesis (Hₐ) is a statement that there is a significant difference between the observed data and the expected results. In this case, the alternative hypothesis is that the population mean (μ) is less than 1000.

Correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

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Given:
Let A and B be any sets.
To Prove: (A-B) ∩ B = ∅Proof: (A-B) ∩ B = {x: x ∈ A-B and x ∈ B}Here, A-B is the set of all elements in A that are not in B.
Therefore, x ∈ A-B means x ∈ A and x ∉ B.
Now, (A-B) ∩ B = {x: x ∈ A-B and x ∈ B}= {x: x ∈ A and x ∉ B and x ∈ B}= {x: x ∈ A and x ∈ B and x ∉ B}= A ∩ (B ∩ B') [Intersection of B with its complement B']Now, B ∩ B' = ∅ (As the intersection of a set and its complement is always an empty set)
Therefore, A ∩ (B ∩ B') = ∅ [As intersection with an empty set is always an empty set]
Thus, we have proved that (A-B) ∩ B = ∅ using set laws. The laws used in each line are given below:
(A-B) ∩ B = {x: x ∈ A-B and x ∈ B} - Definition of the intersection(A-B) ∩ B = {x: x ∈ A and x ∉ B and x ∈ B} - Definition of A-B(A-B) ∩ B = {x: x ∈ A and x ∈ B and x ∉ B} - Re-arranging the terms A ∩ (B ∩ B') - Using B' = Universe - B (Complement Law)A ∩ (B ∩ B') = ∅ - Intersection with empty set is always an empty set.

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Answer: 1950 is how many it will hold.

Step-by-step explanation: