What is the equation of the line that passes through the point (3,5) and has a slope
of 2?

Answer:

6,251

Step-by-step explanation:

First you have to multiply 65 by 7 you will get 455

Then you have to multiply 144.9 by 40 you will get 5,796

At last add the two values:

5,796+455=6,251

Using the reflection concept, the function is given by:

\(g(x) = 5x - 2\)

------------------

The function given is:

\(f(x) = -5x + 2\)

The reflection over the x-axis is:

\(g(x) = -f(x)\)

\(g(x) = -(-5x + 2)\)

\(g(x) = 5x - 2\)

Which is the desired function g.

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(a) M(t) = (1 / Γ(a) p^a) ∫[0,∞] x^(a-1) e^((t-p)x) dx

(b) M'(t) = d/dt M(t)

(c) M''(t) = d^2/dt^2 M(t)

(d) If c > 0, the distribution of Y = cX is also a Gamma distribution, specifically a Gamma(a, cp) distribution.

(a) To find the moment-generating function (MGF) of X Gamma(a, p), we use the definition of the MGF:

M(t) = E(e^(tX))

For the Gamma distribution, the MGF is defined for t in the interval (-p, p), where p is the rate parameter.

In this case, the MGF of X is:

M(t) = E(e^(tX)) = ∫[0,∞] e^(tx) f(x) dx

where f(x) is the probability density function (pdf) of the Gamma distribution.

The pdf of the Gamma(a, p) distribution is:

f(x) = (1 / Γ(a) p^a) x^(a-1) e^(-x/p)

where Γ(a) is the gamma function.

Substituting the pdf into the MGF formula, we have:

M(t) = ∫[0,∞] e^(tx) (1 / Γ(a) p^a) x^(a-1) e^(-x/p) dx

Simplifying the expression inside the integral:

M(t) = (1 / Γ(a) p^a) ∫[0,∞] x^(a-1) e^((t-p)x) dx

Now, we can solve this integral to find the MGF My(t) of X.

(b) To compute E(X) using the MGF, we differentiate the MGF with respect to t and evaluate it at t = 0. The first derivative of the MGF is:

M'(t) = d/dt M(t)

(c) To compute var(X) using the MGF, we differentiate the MGF twice with respect to t and evaluate it at t = 0. The second derivative of the MGF is:

M''(t) = d^2/dt^2 M(t)

(d) If c > 0, the distribution of Y = cX is also a Gamma distribution, specifically a Gamma(a, cp) distribution.

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the probability that a bulb lasts longer than the advertised figure of 4100 hours is approximately 0.8413 or 84.13%.

The probability that a bulb lasts longer than the advertised figure can be found using the normal distribution formula. In this case, we have a mean of 4400 hours and a standard deviation of 300 hours. The advertised lifetime is 4100 hours. We will calculate the z-score and then use the standard normal distribution table to find the probability. Here's the step-by-step explanation:
Calculate the z-score: The z-score is a measure of how many standard deviations away from the mean a data point is. To calculate the z-score for the advertised lifetime (4100 hours), use the formula:
z = (X - μ) / σ
where X is the advertised lifetime (4100 hours), μ is the mean (4400 hours), and σ is the standard deviation (300 hours).
z = (4100 - 4400) / 300
z = -300 / 300
z = -1
Use the standard normal distribution table: Now that we have the z-score (-1), we can use the standard normal distribution table to find the probability that a bulb lasts longer than the advertised figure. Look for the value corresponding to -1 in the table, which is 0.1587.
Calculate the probability: The value we found in the standard normal distribution table (0.1587) represents the probability that a bulb lasts less than the advertised figure (4100 hours). To find the probability that a bulb lasts longer, we need to subtract this value from 1:
Probability (bulb lasts longer than advertised figure) = 1 - 0.1587
Probability (bulb lasts longer than advertised figure) = 0.8413

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Answer:

B) Y=-2x+1

Step-by-step explanation:

(-2,5)(2,-3)

M= -8/4 = -2

y = -2x + b

5 = -2(-2)+ b

B= 1

Y=-2x+1

Answer:

AC=CD

Step-by-step explanation:

Just took the test and got it right

Answer:

AC ≅ CD

Step-by-step explanation:

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector, then it is equidistant from the endpoints of the segment.

Mercedes-Benz is a luxury car manufacturer that has been producing high-end cars for many years. The GLA-AMG 35 is a sporty compact crossover that is perfect for people of all ages.

However, the sales manager suggested that it is designed for people between the ages of 18 to 30 years. Therefore, it's important to understand how to sell the GLA-AMG 35 to different age groups.

The first step in selling the GLA-AMG 35 is to understand the needs and preferences of the customer. If the customer is young, then they may be looking for a car that is sporty and stylish. They may also be interested in the latest technology and entertainment features. On the other hand, if the customer is older, they may be more interested in comfort and safety features.

In order to appeal to different age groups, it's important to highlight different features of the car. For younger customers, emphasize the sporty design and performance capabilities. For older customers, emphasize the safety features, such as blind spot assist and lane departure warning.


The GLA-AMG 35 is a luxury car that offers something for everyone. It's important to understand the target audience and tailor the sales pitch accordingly. If the customer is young, then they may be interested in the car's sporty features, such as the turbocharged engine and AMG sport suspension. They may also be interested in the car's advanced technology, such as the 10.25-inch touchscreen display and voice control.

On the other hand, if the customer is older, they may be more interested in the car's safety features, such as the adaptive cruise control and blind spot assist. They may also be interested in the car's comfort features, such as the heated seats and dual-zone automatic climate control.

The GLA-AMG 35 is a car that can appeal to people of all ages. It's important to understand the needs and preferences of the customer in order to tailor the sales pitch accordingly. Highlight the car's sporty features for younger customers, and emphasize the safety and comfort features for older customers. With the right approach, the GLA-AMG 35 can be a great success in the luxury car market.

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Answer:

9

Step-by-step explanation:

s= -1  t= 9

-(-1) * 9 = 1 * 9= 9

two negatives multiplied is a positive

Answer:

B on edge

Step-by-step explanation:

The arrow is counterclockwise so its positive. The person above had the right idea but on edge is B.

Also I took the test and got 100% have a great day :D

Answer:

The answer is B

Explanation:

The arrow is counterclockwise so its positive.

Answer:

inverse variation

Step-by-step explanation:

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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a) let A = {1, 2} and B = {3, 4}. If C = {2, 3}, then A ∪ C = B ∪ C = {1, 2, 3}, even though A and B are not equal.

b) For instance, let A = {1, 2} and B = {3, 4}. If C = {2, 3}, then A ∩ C = B ∩ C = {2}, even though A and B are not equal.

c) If A ∪ C = B ∪ C and A ∩ C = B ∩ C, it follows that A = B.

The conclusion that A = B can only be made when both the union and intersection of sets A and C are equal to the union and intersection of sets B and C, respectively (as stated in statement c).

Let's examine the given statements:

A ∪ C = B ∪ C

This statement implies that the union of sets A and C is equal to the union of sets B and C.

We cannot conclude that A is equal to B solely based on this statement.

It is possible for A and B to have different elements individually, while still having the same union with C.

A ∩ C = B ∩ C

This statement implies that the intersection of sets A and C is equal to the intersection of sets B and C.

Similarly to the previous case, we cannot conclude that A is equal to B based solely on this statement.

It is possible for A and B to have different elements individually, while still having the same intersection with C.

For instance, let A = {1, 2} and B = {3, 4}. If C = {2, 3}, then A ∩ C = B ∩ C = {2}, even though A and B are not equal.

c) A ∪ C = B ∪ C and A ∩ C = B ∩ C

If both the union and intersection of sets A and C are equal to the union and intersection of sets B and C, respectively, then we can conclude that A is indeed equal to B.

The reason is that when the union and intersection of two sets are equal, it implies that the sets have exactly the same elements.

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Step-by-step explanation:

5a + 7+ 3(a_+5) = 70    expand left side

5a + 7 + 3a + 15   = 70       gather 'like terms'

(5a+3a)  +   (7+15)   = 70    simplfy ....and subtract 22 from both sides

  8a = 48         divide through by 8

a = 6

Population  is an entire group under study as specified by the objectives of the research project.

In research methodology, a population refers to the entire group of individuals or elements that are of interest to the researcher and are under study as specified by the objectives of the research project. It represents the larger group from which a sample is drawn. The population is the target group to which the research findings are intended to be generalized.

When conducting research, it is often impractical or impossible to study an entire population due to constraints such as time, cost, and accessibility. Therefore, researchers typically select a subset of the population called a sample. The sample is a smaller representative group that is selected from the population and is used to draw inferences and make generalizations about the population.

The selection of a sample is based on the principle of randomization and aims to ensure that the sample is representative of the population. By studying the sample, researchers can make statistical inferences about the population as a whole.

In summary, the population refers to the entire group under study, while a sample is a subset of the population that is selected for research purposes. The population is the broader target group of interest, and the sample is used to draw conclusions about the population.

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Answer:

The volume of the metal is:

\(V_{t}=548\: cm^{3}\)

Step-by-step explanation:

First, let's find the volume of the front face of the square:

\(V_{1}=12*7*1=84\: cm^{3}\)

The back face is the same, so we have:  

\(V_{2}=84\: cm^{3}\)

The volume of the side faces will be:

\(V_{3}=7*10*1=70\: cm^{3}\)

\(V_{4}=70\: cm^{3}\)

And finally, the volume of the top and bottom side faces of the box will be:

\(V_{5}=12*10*1=120\: cm^{3}\)

\(V_{6}=120\: cm^{3}\)

The total volume of the metal will be:

\(V_{t}=V_{1}+V_{2}+V_{3}+V_{4}+V_{5}+V_{6}\)

\(V_{t}=2(84)+2(70)+2(120)\)

\(V_{t}=548\: cm^{3}\)

I hope it helps you!

Answer:

$4.50

Step-by-step explanation:

6/4=1.5 $1.50 per container. 1.50×3 is $4.50

(check comment)

Answer:

p^15

Step-by-step explanation:

Answer: The independent variable is the number of miles you walked.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

it's right cause I took the quix

That shaded region area we need

Area

Answer:

Step-by-step explanation:

height h=1.2 m

radius r= D/2=4.5=2.25 m

Volume V=πr²h=π(2.25)²×1.2  ≈3.18m³

Any set of n independent vectors in \(R^n\)forms a basis.

To prove this, we will use the following terms: linear independence, linear combination, span, and basis.

Let V be a set of n independent vectors in \(R^n\):

V = {v1, v2, ..., vn}.

Show that V spans \(R^n\).

Since V is a set of n independent vectors, every vector in \(R^n\) can be expressed as a unique linear combination of the vectors in V.

In other words, for any vector x in\(R^n\), there exist scalars a1, a2, ..., an such that:

x = a1×v1 + a2× v2 + ... + an ×vn

Show that V is linearly independent.

By definition, V is linearly independent if for any scalars a1, a2, ..., an, the linear combination:

a1× v1 + a2×v2 + ... + an×vn = 0

implies that a1 = a2 = ... = an = 0.

Since V is given as a set of n independent vectors, this condition is already satisfied.

Combine Steps 1 and 2.

Since V spans \(R^n\) and V is linearly independent, V forms a basis for\(R^n\).

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In solving a system of equations, we look for a point where the two lines intersect. The point of intersection will be a point that is a solution to both equations in the system. We can solve a system of equations by several methods, but one of the most common methods is using substitution or elimination.

To solve a system of equations using substitution, we have to solve one of the equations for one of the variables, and then substitute the result into the other equation. This process eliminates one variable and makes the system easier to solve. Therefore, the best choice that describes a possible first step in solving the system of equations is to solve for y in the second equation. Here is the step-by-step solution:2x - 7y = -14-2x + y = -10Solve for y in the second equation.-2x + y = -10y = 2x - 10Now substitute 2x - 10 for y in the first equation.2x - 7(2x - 10) = -14Simplify:2x - 14x + 70 = -14-12x + 70 = -14-12x = -14 - 70-12x = -84x = -84/-12x = 7Substitute x = 7 into either equation. Let's use the second equation.-2(7) + y = -10-14 + y = -10y = -10 + 14y = 4Therefore, the solution to the system of equations is (x, y) = (7, 4).

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Step-by-step explanation:

According to angles of intersecting chords theorem    ( angle S is also 117):

117 = 1/2 (208 + 2x-4)  

so  x = 15

then 2x-4 = 26 degrees

The area of the polygon is  6. 9m²

From the information given, we have that the regular polygon takes the shape of a triangle.

The formula for calculating the area of a triangle is expressed with the equation;

A = 1/2bh

Such that the parameters in the formula are;

Area of a equilateral triangle is;

= √3/4a²

Then,

= √3/4 (4)²

= √3 × 4

= 6. 9m²

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Answer:

the area of the parallelogram is 120 units

\(\tt Step-by-step~explanation:\)

The two red ticks indicate that those lines are the same length (Isosceles triangle).

Since the two lines are the same length, then that means that both of the angles are the same measure, too. One angle is measured at 71, so that means x = 71.

\(\Large\boxed{\tt Our~final~answer:~x=71^o}\)

Answer:(x+3)2 4+4=( x+3)2=4

Step-by-step explanation:

No, Lydia's assertion that δSTU is a right triangle is not correct.

A right triangle is a triangle in which one of the angles measures 90 degrees (a right angle). To determine if δSTU is a right triangle, we need to examine the angles formed by the given coordinates.

Using the coordinates:

s (-3, 0)

t (0, -3)

u (3, -3)

We can calculate the slopes of the lines formed by connecting these points to see if any of them are perpendicular (indicating a right angle).

The slope of the line connecting points s and t is:

m(st) = (y₂ - y₁) / (x₂ - x₁) = (-3 - 0) / (0 - (-3)) = -3/3 = -1

The slope of the line connecting points s and u is:

m(su) = (y₂ - y₁) / (x₂ - x₁) = (-3 - 0) / (3 - (-3)) = -3/6 = -1/2

The slope of the line connecting points t and u is:

m(tu) = (y₂ - y₁) / (x₂ - x₁) = (-3 - (-3)) / (3 - 0) = 0/3 = 0

None of the slopes calculated are perpendicular to each other, meaning none of the angles formed by the given coordinates are 90 degrees. Therefore, δSTU is not a right triangle.

In summary, Lydia's assertion that δSTU is a right triangle is incorrect because the angles formed by the given coordinates do not include a 90-degree angle.

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Answer:

Gradient =

\(y^{1} - y^{2} \div x^{1} - x^{2} \)

-5-4/-10-q=9

-5-4=9

-10+9=1

Q=-9