which of the following factors is a factor of the expression x^2+5x-6
(x-2)
(x+6)
(x+3)
(x+1)

Answer:

I believe the next numbers would be 13, 29, 61 and it would be a Cube pattern

Step-by-step explanation:

Answer:

Step-by-step explanation:

K

Answer:

2x^6+16x^5+30x^4

Step-by-step explanation:

Answer:

28.27m

Step-by-step explanation:

the formula for area of a circle is

A= π x r^2

A = π x r^2 = π x 3^2 = 28.27433

Credit card limits are included in M2 but not M1. The correct answer is b.

M1 and M2 are measures of the money supply that are used by economists and policymakers to analyze the state of the economy and make monetary policy decisions.

M1 includes the most liquid forms of money, such as physical currency, traveler's checks, demand deposits, and other checkable deposits. M2 includes all of the components of M1, as well as less liquid forms of money, such as savings accounts, money market accounts, and time deposits.

Credit card limits are not included in M1, as they do not represent actual money or funds that are available for immediate spending. Credit cards represent a line of credit, which is a promise by the credit card issuer to lend money to the cardholder up to a certain limit. As such, credit card limits are not considered part of the money supply, and are not included in M1.

However, credit card limits are included in M2, as they represent a potential source of funds that can be used for spending or saving. Even though credit card limits are not immediately available as cash or funds that can be spent, they can be used to obtain loans or other forms of credit that can be used to make purchases or investments.

As such, credit card limits are considered part of the broader definition of the money supply that is included in M2. The correct answer is b.

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the distance from the plane to the radar station is increasing at a rate of approximately 30.84 kilometers per minute.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, A plane flying with a constant speed of 25 km/min passes over a ground radar station at an altitude of 12 km and climbs at an angle of 30 degrees.

We can use the law of cosines to find d:

d² = 12² + (h + 12)² - 2(12)(h + 12)cos(θ)

Since the plane is climbing at an angle of 30 degrees, we can use trigonometry to find h:

sin(30) = h / (25 km/min * 2 min)

h = 25 km/min

Now we can substitute this value of h into the equation for d and simplify:

d² = 12² + (25 + 12)² - 2(12)(25 + 12)cos(θ)

d² = 12² + 37² - 2(12)(37)cos(θ)

d² = 144 + 1369 - 888cos(θ)

d² = 1513 - 888cos(θ)

To find the rate at which d is changing, we can take the derivative of both sides of this equation with respect to time:

2dd/dt = -888(d(cos(θ))/dt)

Since the plane is flying with a constant speed of 25 km/min, we can use trigonometry to find d(cos(θ))/dt:

cos(θ) = 12/d

d(cos(θ))/dt = -(12/d²)(dd/dt)

d(cos(θ))/dt = -(12/d²)(25 km/min)

Now we can substitute these values into the equation for the rate of change of d:

2dd/dt = -888(-(12/d²)(25 km/min))

2dd/dt = (888*12)/(d²)(25 km/min)

dd/dt = (5328)/(d²) km/min

Finally, we can substitute the value we found for d into this equation to get the rate at which d is changing 2 minutes later:

d = sqrt(1513 - 888cos(θ))

θ = 30 degrees

dd/dt = (5328)/(d²) km/min

dd/dt = (5328)/(1513 - 888cos(30)) km/min

dd/dt ≈ 30.84 km/min

Therefore, the distance from the plane to the radar station is increasing at a rate of approximately 30.84 kilometers per minute.

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Valve guides can be measured for roundness and diameter using a micrometer or a bore gauge. Both of these tools are commonly used in the automotive industry to measure the dimensions of engine parts such as valve guides.

A micrometer is a precision measuring tool that uses a calibrated screw to measure the diameter of an object with high accuracy. It can be used to measure the diameter of the valve guide at different points along its length to check for roundness. A bore gauge, also known as an inside micrometer, is a specialized tool used to measure the inside diameter of a cylinder, such as the bore of an engine block or the valve guide. It consists of a probe that is inserted into the cylinder and expands to take a measurement. A bore gauge is particularly useful for measuring the internal dimensions of complex shapes like valve guides, which can have irregular or non-circular profiles. Both micrometers and bore gauges come in various sizes and types, and the specific tool used will depend on the size and shape of the valve guide being measured.

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The difference of a number and 2:  x-2

Twice the difference of a number and 2:  2(x-2)

Is 9.

2(x-2) = 9

2x - 4 = 9

2x = 13

x = 13/2 = 6 1/2

Answer:

i. P(B) =0.12

ii. P(B) = 0.2

Step-by-step explanation:

Note:
Mutually exclusive events:

A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and

P(A AND B) = 0.

P(A ∩ B) =0

Independent events:

Two events A and B are independent events if the knowledge that one occurred does not affect the chance the other occurs.
Two events are independent if the following are true:

For Question:

i) A and B are mutually exclusive events

P((A ∪ B)')=0.48

P(A) = 0.4

Since it is  mutually exclusive events

P(A ∩ B) =0

P(B)=?

We have,

P((A ∪ B)') = 1 - P(A ∪ B)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.4 + P(B) - 0 = P(B) + 0.4

Substituting value

P((A ∪ B)') = 1 - P(A ∪ B)

0.48 = 1 - P(B) - 0.4

1-P(B) - 0.4 = 0.48

Simplifying:

P(B)=1-0.4-0.48

P(B) =0.12

\(\hrulefill\)

ii) A and B are independent events.

P((A ∪ B)')=0.48

P(A) = 0.4

Since A and B are independent events.

P(A ∩ B) =P(A).P(B)

P(B)=?

we have,

P((A ∪ B)') = 1 - P(A ∪ B)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)=  0.4 + P(B) - 0.4 *P(B)

Substitute the values:

P((A ∪ B)') = 1 - P(A ∪ B)

0.48=1-(0.4 + P(B) - 0.4*P(B))

0.48=1-0.4-P(B)+0.4*P(B)

Simplifying:

P(B)-0.4*P(B)=1-0.4-0.48

0.6*P(B)=0.12

Dividing both sides by 0.6:

P(B) = 0.12/0.6

P(B) = 0.2

Answer:

(i)  P(B) = 0.12

(ii) P(B) = 0.2

Step-by-step explanation:

A bar over a set means that we should take the complement of that set. It can also be notated by an apostrophe:

\(\sf P(\overline{A \cup B})=(A \cup B)'\)

A complement of a set refers to the elements that are not included in the set, but are part of the universal set.

The symbol "∪" means the union of sets. It represents the set that contains all the elements that are in either set or in both sets.

P(A ∪ B) represents the probability of the union of sets A and B, which is the event that either A or B or both occur. Therefore, P(A ∪ B)' represents the probability of the complement of P(A ∪ B), so the probability of the event that neither A nor B occurs. Mathematically, it can be defined as:

\(\boxed{\sf P(A\cup B)' = 1 - P(A\cup B)}\)

\(\hrulefill\)

Mutually exclusive events are those that have no common outcomes and therefore cannot occur simultaneously.  When represented using a Venn diagram, mutually exclusive events are depicted as non-overlapping circles.

The addition law for mutually exclusive events is:

\(\boxed{\sf P(A \cup B)=P(A)+P(B)}\)

Therefore, as P(A ∪ B)' = 1 - P(A ∪ B), we can say that:

\(\begin{aligned} \sf P(A \cup B)'&=\sf 1-P(A \cup B)\\ &=\sf 1-[P(A)+P(B)]\end{aligned}\)

Given P(A ∪ B)' = 0.48 and P(A) =0.4, substitute these into 1 - [P(A) + P(B)] and solve for P(B):

\(\begin{aligned}\sf 1-[0.4+P(B)]&=\sf0.48\\\sf1-0.4-P(B)&=\sf0.48\\\sf 1-0.4-0.48&=\sf P(B)\\\sf P(B)&=\sf0.12\end{aligned}\)

Therefore, P(B) = 0.12 if events A and B are mutually exclusive.

\(\hrulefill\)

If the probability of an event B happening doesn’t depend on whether an event A has happened or not, events A and B are independent.

The addition law for independent events is:

\(\boxed{\sf P(A \cup B)=P(A)+P(B)-P(A \cap B)}\)

The product law for independent events is

\(\boxed{\sf P(A \cap B)=P(A)P(B)}\)

Therefore, as P(A ∪ B)' = 1 - P(A ∪ B), we can say that:

\(\begin{aligned} \sf P(A \cup B)'&=\sf 1-P(A \cup B)\\ &=\sf 1-[P(A)+P(B)-P(A \cap B)]\\&=\sf 1-[P(A)+P(B)-P(A)P(B)]\end{aligned}\)

Given P(A ∪ B)' = 0.48 and P(A) =0.4, substitute these into the found expression, and solve for P(B):

\(\begin{aligned}\sf 1-[0.4+P(B)-0.4P(B)]&=\sf0.48\\\sf 1-[0.4+0.6P(B)]&=\sf 0.48\\\sf 1-0.4-0.6P(B)&=\sf 0.48\\\sf 0.6-0.6P(B)&=\sf 0.48\\\sf 0.6P(B)&=\sf 0.12\\\sf P(B)&=\sf 0.2\end{aligned}\)

Therefore, P(B) = 0.2 if events A and B are independent.

Answer:

81

Step-by-step explanation:

using the rule of exponents

• \(a^{0}\) = 1

then

\(3^{4}\) × \(3^{0}\)

= \(3^{4}\) × 1

= 3 × 3 × 3 × 3

= 9 × 9

= 81

Answer: Hello! I'm JK!.....

81

Use the power rule to combine exponents. 3^4+^0

Add 4 and 0. 3^4

Raise 3 to the power of 4.

81

Step-by-step explanation:

 I really hope this helps you! <3 XoXoGoldenMaknae

Chi-squared analysis is used to determine whether there is a significant relationship between two variables. The chi-squared test requires two or more categories of data. The data used in the chi-squared analysis has 200 cases for each location, and the question asks if it is necessary to have the same number of observations from each location for every product.

In the chi-squared test, the null hypothesis is that there is no relationship between the two variables being tested. It is not necessary to have the same number of observations from each location for every product. The null hypothesis is tested against the alternative hypothesis, which states that there is a relationship between the variables. The chi-squared test can be used to test for independence between two categorical variables. In the context of this question, the two variables are location and product. If there is a significant relationship between the variables, it means that the location affects the product. For example, if a company sells two products in two different locations and the sales of one product are significantly higher in one location than in the other location, it means that the location affects the sales of the product. In this case, it is not necessary to have the same number of observations from each location for every product.

Therefore, the answer to the question is no; it is not necessary to have the same number of observations from each location for every product. The chi-squared test can still be used to determine whether there is a significant relationship between the two variables, even if the number of observations is not the same.

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Answer:

A,D

Step-by-step explanation:

I KNOW BECAUSE I KNOW THAT HOW

Answer:

8

Step-by-step explanation:

it is positive 8 because the negative outside the parenthesis cancels out the -3 making it positive now give me brainliest

Answer:   8

Step-by-step explanation: double negative equals a positive... sooo 5 +(- - 3)=

5+3= 8 hope this helps! go answer my question!

The GCD of a and b in the ring of integers is the same as their GCD in the ring of Gaussian integers because both conditions of Gaussian integers are satisfied.

To show that the greatest common divisor (GCD) of integers a and b is the same in the ring of integers and the ring of Gaussian integers, we need to prove two things:

1. GCD(a, b) in the ring of integers divides both a and b.
2. Any common divisor of a and b in the ring of Gaussian integers also divides a and b in the ring of integers.

Let's start with the first point. If GCD(a, b) in the ring of integers divides a and b, it must also divide any linear combination of a and b. Since the ring of Gaussian integers is a subset of the ring of integers, any linear combination of a and b in the ring of Gaussian integers is also a linear combination of a and b in the ring of integers. Therefore, GCD(a, b) in the ring of integers divides any linear combination of a and b in the ring of Gaussian integers.

For the second point, any common divisor of a and b in the ring of Gaussian integers also divides a and b in the ring of integers because the ring of Gaussian integers is a subset of the ring of integers.

In conclusion, the GCD of a and b in the ring of integers is the same as their GCD in the ring of Gaussian integers because both conditions are satisfied.

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The value of the products are;

1. 2.5

2. 6

3. 2.5

4. 10

5.12

6. 5 1/3

7. 2/3

8. 12

We need to know that the value of the product is the number that is determined when two or more numbers are multiplied together.

From the information given, we have that;

1. 5/10 × 5

Multiply the values

25/10

2.5

2. 3/5 × 10

Multiply the values

6

3. 5/6 × 3

Multiply the values

5/2

2.5

4. 5/6 × 12

Multiply the values

10

5. 3/5 × 20

Multiply the values

12

6. 2/3 × 8

Multiply the values

16/3

5 1/3

7. 2/9 × 3

2/3

8. 4/7 × 21

12

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1. The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The Probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

1. The outcomes in the sample space of choosing a letter from the word THANKS are: T, H, A, N, K, S.

  The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. To find the number of outcomes in the sample space, we multiply the number of outcomes for each word.

  Number of outcomes in the sample space = Number of outcomes for the first word × Number of outcomes for the second word

  Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The probability of choosing the letters AA would be the number of favorable outcomes (which is 0 in this case) divided by the total number of outcomes in the sample space.

  Probability of choosing AA = Number of favorable outcomes / Total number of outcomes

  Probability of choosing AA = 0 / 30 = 0.

Therefore, the probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

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According to the use and the fundamental knowledge behind these formulas, The top 5 formulas in mathematics are quadratic, Pythagorean , slope-intercept , exponential and Euler's Formula.

Mathematics is the study of numbers, shapes, and patterns. It is the science of studying the properties and relationships of quantities and shapes using logic, symbols and mathematical operations. It is a way of understanding the world and solving problems using quantitative reasoning.

A mathematical formula is a set of symbols, numbers and mathematical operations that express a relationship or equation. These formulas are used to model, describe and explain phenomena in the natural and physical world, as well as in abstract mathematical theories. Formulas can take many forms, including equations, identities, and inequalities. They allow us to make predictions and calculations, and can be used in various fields of science, engineering and other fields to solve problems.

1. root of \(ax^2+bx+c\) is \(x= \frac {-b+- \sqrt{b^2-4ac}}{2a}\).

2.\(h^2 = p^2 +b^2\)

3. \(y =mx+c\)

4.\(e^x\)

5.\(e^{ix} = cosx+isinx\)

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Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

Answer:

Step-by-step explanation:

This data appears to represent an exponential growth pattern since the y-values are doubling as the x-values increase by 1. Therefore, we can model this data with an exponential function.

One possible exponential function that fits this data is:

f(x) = 2^x

where x is the input variable (independent variable) and f(x) is the output variable (dependent variable).

To check if this function fits the data, we can plug in the x-values and see if the resulting y-values match the given data:

For x = -1, f(-1) = 2^-1 = 1/2, which matches the first given point (-1, 1).

For x = 0, f(0) = 2^0 = 1, which matches the second given point (0, 2).

For x = 1, f(1) = 2^1 = 2, which matches the third given point (1, 4).

For x = 2, f(2) = 2^2 = 4, which matches the fourth given point (2, 8).

For x = 3, f(3) = 2^3 = 8, which matches the fifth given point (3, 16).

Therefore, the function f(x) = 2^x fits the given data.

The exponential function that models the data is the function f(x) = 2ˣ fits the given data.

Here, we have,

This data appears to represent an exponential growth pattern since the y-values are doubling as the x-values increase by 1.

Therefore, we can model this data with an exponential function.

One possible exponential function that fits this data is:

f(x) = 2ˣ

where x is the input variable (independent variable) and f(x) is the output variable (dependent variable).

To check if this function fits the data, we can plug in the x-values and see if the resulting y-values match the given data:

For x = -1, f(-1) = 2⁻¹ = 1/2, which matches the first given point (-1, 1).

For x = 0, f(0) = 2⁰ = 1, which matches the second given point (0, 2).

For x = 1, f(1) = 2¹ = 2, which matches the third given point (1, 4).

For x = 2, f(2) = 2² = 4, which matches the fourth given point (2, 8).

For x = 3, f(3) = 2³ = 8, which matches the fifth given point (3, 16).

Therefore, the function f(x) = 2ˣ fits the given data.

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We can use the Ray tool to graph the absolute value function f(x) = 2|x+2| + 1, which helps us visualize the function by plotting specific points on the coordinate plane.

1. Begin by understanding the structure of the absolute value function f(x) = |x|. The absolute value function takes any input x and returns the positive value of x, making it symmetric concerning the y-axis.

2. In the given function f(x) = 2|x+2| + 1, the "2" in front of the absolute value affects the vertical scale, while the "+2" inside the absolute value causes a horizontal shift of 2 units to the left.

3. Start plotting points on the coordinate plane. To determine the behavior of the graph, consider a few x-values.

  - When x = -4, we have f(-4) = 2|-4+2| + 1 = 2| -2| + 1 = 2(2) + 1 = 4 + 1 = 5. So, we have the point (-4, 5).

  - When x = -2, we have f(-2) = 2|-2+2| + 1 = 2| 0| + 1 = 2(0) + 1 = 1. So, we have the point (-2, 1).

  - When x = -1, we have f(-1) = 2|-1+2| + 1 = 2| 1| + 1 = 2(1) + 1 = 3. So, we have the point (-1, 3).

  - When x = 0, we have f(0) = 2|0+2| + 1 = 2| 2| + 1 = 2(2) + 1 = 5. So, we have the point (0, 5).

  - Continue this process for other values of x to obtain more points.

4. Plot all the points on the graph and connect them smoothly. Remember to maintain symmetry concerning the y-axis due to the absolute value function.

5. The resulting graph will have a "V" shape, with the vertex at the point (-2, 1). The line will extend upward on both sides, following a steep slope with a vertical stretch of 2.

6. Label the axes and any other relevant points to complete the graph.

By following these steps and utilizing the Ray tool, you can accurately graph the given absolute value function f(x) = 2|x+2| + 1.

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Answer:

5x + 6 · x + 3

Step-by-step explanation:

The slope in the context of predicting verbal SAT scores based on math SAT scores indicates the change in the verbal score for each unit increase in the math score.

In this survey of statistics undergraduate students at Prosperity University, the slope represents the rate of change in the verbal SAT score for every one-point increase in the math SAT score. A positive slope suggests that as the math score increases, the verbal score also tends to increase. The magnitude of the slope indicates the strength of the relationship between the two variables. A larger slope indicates a stronger positive association, meaning that a one-point increase in the math score is associated with a larger increase in the verbal score. Conversely, a negative slope would imply an inverse relationship, where an increase in the math score is associated with a decrease in the verbal score.

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What is the interpretation of the slope in the context of predicting the verbal SAT score based on the math SAT score, according to the survey conducted among undergraduate students majoring in statistics at Prosperity University?

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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Answer:

black

black

Step-by-step explanation:

Answer:

1/6

Explain:

The reciprocal of the slope is its perpendicular.

6/1 --> 1/6

Answer: the correct anwser is D square root of 37

Step-by-step explanation:

Answer: It's the first one

Also could you mark my answer as brainliest? It helps and doesnt hurt