4. Find the slope of the line through the
points A(8,7) and B(5,-2).
Explanation:

Answer:

Step-by-step explanation:

To find the class limits for the lowest class, you need to know the class interval, which is the difference between the upper class limit and the lower class limit of each class1. You can find the class interval by subtracting the first two class midpoints: 72.5 - 69.5 = 3.

Then, you can find the lower class limit of the lowest class by subtracting half of the class interval from the first class midpoint: 69.5 - 1.5 = 68.

Similarly, you can find the upper class limit of the lowest class by adding half of the class interval to the first class midpoint: 69.5 + 1.5 = 71.

Therefore, the class limits for the lowest class are 68 and 71.

The direction of the hike from the given vectors represented by the vector C is approximately -26.57° with respect to the positive x-axis.

To find the sum of the displacement vectors A and B, you simply add their respective components.

Vector A = (2.0i + 2.0j) m

Vector B = (2.0i - 4.0j) m

To find the sum (vector C), add the corresponding components,

C = A + B

= (2.0i + 2.0j) + (2.0i - 4.0j)

= 2.0i + 2.0j + 2.0i - 4.0j

= 4.0i - 2.0j

So, the vector representing the sum of A and B is (4.0i - 2.0j) m.

The components of the resulting vector C are 4.0 in the x-direction (i-component) and -2.0 in the y-direction (j-component).

To determine the direction of the hike,

Calculate the angle of the resulting vector with respect to the positive x-axis.

The angle (θ) can be found using the arctan function,

θ = arctan(-2.0/4.0)

θ = arctan(-0.5)

θ ≈ -26.57° (rounded to two decimal places)

Therefore, the direction of the hike represented by the vector C is approximately -26.57° with respect to the positive x-axis.

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Answer:

Step-by-step explanation:

hope this helps!

There are 5,040 different ways that the first seven students in line can be ordered.

An arrangement is a permutation of a set of objects in mathematics where the order of the things is important. An arrangement is specifically an orderly succession of unique elements drawn from a set.

Consider the set "A, B, C," for instance. This set can be arranged in six different ways: ABC, ACB, BAC, BCA, CAB, and CBA. The three components of the set are stated in a precise order in each of these configurations.

The number of ways that 7 students can be arranged in a line is 7! (7 factorial) which is equal to:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

Therefore, there are 5,040 different ways that the first seven students in line can be ordered.

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The transformations to the graph of the quadratic function are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Additionally, when the function is multiplied by |a| > 1, it is said that the function is vertically stretched by a factor of a.

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Answer:

not a polygon

Step-by-step explanation:

The given figure is not a polygon.

A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices.

Given is figure,

We know that, a polygon is made up of straight lines connected with each other in a close circuit.

Here, in the figure, there is no polygon, but two polygons joined by a vertex.

Hence, we can say that the given figure is not a polygon.

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The absolute maximum value of the function f(x) = 5x cos(x) on the interval 0 ≤ x ≤ π, correct to six decimal places, is approximately 5.000000.

To find the absolute maximum value of the function f(x) = 5x cos(x) on the interval 0 ≤ x ≤ π, we can use Newton's method to locate the critical points and evaluate the function at those points.

First, we find the derivative of f(x) with respect to x:

f'(x) = 5 cos(x) - 5x sin(x)

Next, we set the derivative equal to zero to find the critical points:

5 cos(x) - 5x sin(x) = 0

Using Newton's method, we can iteratively approximate the critical points. Let's choose an initial guess x₀ = π/2 and iterate using the formula:

xᵢ₊₁ = xᵢ - f(xᵢ)/f'(xᵢ)

Performing the iterations, we obtain:

x₁ ≈ 1.570796

x₂ ≈ 1.570796

Since both x₁ and x₂ converge to approximately 1.570796, we have a critical point at x = 1.570796.

Next, we evaluate f(x) at the critical point and the endpoints of the interval:

f(0) = 0

f(1.570796) ≈ 5.000000

f(π) ≈ 0.000000

From the above evaluations, we can see that the absolute maximum value of f(x) on the interval 0 ≤ x ≤ π is approximately 5.000000.

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a) The probability of the variable falling between 200 and 5300 is very close to 100%.

b) The probability of the variable being less than 275 is about 88%.

c) The x-values that are in the top 10% of the distribution are those greater than approximately 278.98.

A. To find P(200 X 5300), we need to calculate the probability that our variable falls between the values of 200 and 5300.

This is done using the formula z = (x - mu) / sigma, where x is the value we are interested in, mu is the mean, and sigma is the standard deviation.

So, for the value x = 200, we have z = (200 - 248.3) / 22.8 = -2.12. Similarly, for x = 5300, we have z = (5300 - 248.3) / 22.8 = 229.44.

Now, we need to use a standard normal distribution table or a calculator to find the probability of the variable falling between -2.12 and 229.44. This probability is denoted as P(-2.12 < z < 229.44).

Using a standard normal distribution table or a calculator, we can find that this probability is virtually 1. So, the probability of the variable falling between 200 and 5300 is very close to 100%.

B. To find P(x < 275), we again need to standardize the value of 275 using the formula z = (x - μ) / σ.

For x = 275, we have z = (275 - 248.3) / 22.8 = 1.17.

Now, we need to use a standard normal distribution table or a calculator to find the probability of the variable falling below 1.17. This probability is denoted as P(z < 1.17).

Using a standard normal distribution table or a calculator, we can find that this probability is approximately 0.88. So, the probability of the variable being less than 275 is about 88%.

C. To find the x-values that are in the top 10%, we need to find the z-score that corresponds to the top 10% of the normal distribution.

Using a standard normal distribution table or a calculator, we can find that the z-score that corresponds to the top 10% is approximately 1.28.

Now, we can use the formula z = (x - μ) / σ to find the x-value that corresponds to a z-score of 1.28.

Rearranging the formula, we get x = μ + σ * z = 248.3 + 22.8 * 1.28 = 278.98.

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Complete Question:

Suppose a variable is normally distributed, with mean 248.3 and standard deviation 22.8.

A. What is P(200 X 5300)?

B. What is Plx 2 275)?

C. What x-values are in the top 10%?

Answer:

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

Solve in below steps:

No solutions as we ended up with false equality.

Answer:

no solution

Step-by-step explanation:

0.5 ( -2 + 4d ) - 2d = -13

Solve the brackets.

-1 + 2d - 2d = -13

The term "-2d" cancels out, leaving us with:

-1 = -13

Since this equation is not true (the left side does not equal the right side), there is no solution to the equation.

In other words, there is no value of "d" that satisfies the equation.

The horse's average speed for the race in units of kilometers per hour will be 178.06.

The winning horse in a recent race covered the 5.50-furlong distance in 22.37 seconds.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

The conversion is given as,

1 furlong = 0.201168 km

5.50-furlong = 0.201168 x 5.5 km

5.50-furlong = 1.10642 km

1 second = 1/3600 hour

22.37 seconds = 22.37/3600 hour

22.37 seconds = 0.0062 hour

The average speed is calculated as,

Average speed = 1.10642 / 0.0062

Average speed = 178.06 km per hour

The horse's average speed for the race in units of kilometers per hour will be 178.06.

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Answer:

\(\text{(a) } x=11,\\\text{(b) } \angle C=12^{\circ}\)

Step-by-step explanation:

The sum of the interior angles in a triangle is always equal to 180 degrees. Therefore, we have the following equation:

\((3x+28)+(5x+52)+(2x-10)=180\)

Solving for \(x\):

\((3x+28)+(5x+52)+(2x-10)=180,\\3x+28+5x+52+2x-10=180,\\10x+70=180,\\10x=110,\\x=\boxed{11}\)

Substitute \(x=11\) to solve for angle C:

\(m\angle C=2x-10,\\m\angle C=2(11)-10,\\m\angle C==22-10=\boxed{12^{\circ}}\)

Answer:

it should be the negative repirocal of -2 so 1/2

Answer:

mPerpendicular= 1/2

Step-by-step explanation:

If the parent function \(\sf y=(1.6)^x\) is translated 5 units up and 9 units to the right, then you should subtract 9 from x and add 5 to the whole function. Thus,

1) translation the parent function \(\sf y=(1.6)^x\) 9 units to the right gives you the function \(\sf y=(1.6)^{x-9}\).

2) translation the function \(\sf y=(1.6)^{x-9}\) 5 units up gives you the function \(\sf y=(1.6)^{x-9}+5\)

Therefore, the correct choice is C

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The money invested into the first portion is $78000 while the second is $7000.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year.

Suppose the money invested in the first portion is x while in the second is y.

Total amount  = x + y

x + y = 85000

Now, x is earning 5.5% of interest and y is earning 2.75% of interest.

Total interest = 0.055x + 0.0275y

0.055x + 0.0275y = 4482.50

By substitution,

0.055x + 0.0275(85000 - x) = 4482.50

x = $78000

y = $7000

Hence "The initial investment was $78000, and the subsequent investment was $7000".

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The gamma distribution with parameters $\alpha$ and $\beta$ is a probability distribution that can be derived using the transformation $x = \beta y$.

The probability density function of the gamma distribution is:

f(x; α, β) = \frac{(\beta x)^{\alpha - 1} e^{-\beta x}}{\Gamma(\alpha)}

where $\alpha$ is the shape parameter and $\beta$ is the rate parameter.

The derivation is as follows:

* The gamma function is defined as:

Γ(α) = \int_0^{\infty} x^{\alpha - 1} e^{-x} dx

* Using the transformation $x = \beta y$, we get:

Γ(α) = \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy

* We can then write the probability density function of the gamma distribution as:

f(x; α, β) = \frac{1}{\Gamma(\alpha)} \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy

* This is the same as the probability density function of the gamma distribution with parameters $\alpha$ and $\beta$.

The mean and variance of the gamma distribution can be found using the following formulas:

E(X) = \alpha \beta

Var(X) = \alpha \beta^2

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Answer:

See below

Step-by-step explanation:

If you consider an open circle, it would exclude the value with which we have circled when writing the inequality. Hence the only possible signs with in such an example can be a greater than sign ( > ) or less than sign ( < );

Let us take a look at an example to help. We are given a graph with an open circle on the number say 3. An arrow extends to the right of this number 3;

\(Inequality Sign - <,\\Inequality - x > 3,\\\)

Hope this helps!

Answer:

y = 75°

Step-by-step explanation:

y and 105°

are on a straight line ,

a straight line is 180°

180 - 105 = 75°

y=75 °

I'm not sure about x hope you understand

Answer:

The variable of summation is represented by an index which is placed beneath the summation sign. The index is often represented by i. (Other common possibilities for representation of the index are j and t.) The index appears as the expression i = 1.

Step-by-step explanation:

~Feitan Portor~

Answer:

9) JK = 24.5

10) LM = 24.5

11) m∡L = 51°

12) m∡M = 129°

Step-by-step explanation:

in a parallelogram, adjacent angles are supplementary (add to 180 degrees) and are also congruent

so, ∡K = ∡M and ∡J = ∡L

since ∡'s L and M are adjacent we can add them and set them equal to 180

5z - 6 + 2z - 3 = 180

7z - 9 = 180

7z = 189

z = 27

therefore, m∡M = 5(27)-6 = 129 and m∡L = 180-129, or 51

Also in a parallelogram, opposite sides are equal; so KJ = LM and KL = JM

7x = 3x + 14

subtract 3x from each side to get:

4x = 14

x = 14/4 = 3.5

to find measure of JK, substitute 3.5 for 'x' to get (3.5)(7) = 24.5

to find measure of LM, substitute 3.5 for 'x' to get (3.5)(3)+14 = 24.5

Answer:

Divide each term in

D

C

G

=

145

°

by

C

G

and simplify.

D

=

145

°

C

G

Step-by-step explanation:

ty

Step-by-step explanation:

The given statement " in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables. " is false.

In math chi square test means the process of determine if there is a significant relationship between two nominal (categorical) variables.

Here we have the statement, in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables.

And we need to find the statement is true or not.

According to the definition of chi square test, we know that it checks whether two variables are likely to be related or not.

Here we have counts for two categorical or nominal variables.

So, there is no large value comparision take palce.

Therefore, the statement is false.

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Answer:

5q + 9

Step-by-step explanation:

The Concept in that Question is adding Like-Terms

6q + 4 - q + 5 = ( 6q - q ) + ( 4 + 5 ) = 5q + 9

\( = (x^2 \times x^3)^3 \\ = x {}^{6} \times {x}^{9} \\ = (x) {}^{6 + 9} \\ = {x}^{15} \)

Answer:

Team Blue

Step-by-step explanation:

The reason this is, is because for each day that passes, they make 5 more light bulbs. This is in relation to the days that pass.

EXPLANATION

The area of the figure can be obtained by applying the following relationship:

Where b=base and height=h

In order to find the height, we need to apply the trigonometric relationship:

Multiplying both sides by 6.4:

Solving the argument:

Switching sides:

Now that we have the height, we can compute the area as follows:

The answer is 53.24 squared inches.

Answer:

Sure, what do you need help with?

Step-by-step explanation:

Send whatever you need help with and I'll see if I can explain it.

Answer:

y=-2x+4

Step-by-step explanation:

y=mx+b

m is the slope so the equation looks like this:

y=-2x+b

Now we just need to find b or the y-intercept

so distribute -2 into x and 8 into y (x,y) (-2,8)

8=-2(-2)+b

Multiply -2 and -2 which is 4

8=4+b

Subtract by 4 on both sides:

b=4

So the equation is

y=-2x+4

Hope this helps!

The value of c that makes 3x + c equivalent to 3(x + 7) is 21.

A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions. The equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14, for instance.

We are given that 3x + c is equivalent to 3(x + 7).

To find the value of c, we can expand the right side of the equation using the distributive property:

3(x + 7) = 3x + 21

So we have the equation:

3x + c = 3x + 21

Subtracting 3x from both sides, we get:

c = 21

Therefore, the value of c that makes 3x + c equivalent to 3(x + 7) is 21.

Answer: c = 21

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When an increase in one variable is associated with an increase in a second variable, the two variables are known as positively correlated. The correlation coefficient is the measure of the degree of the relationship between two variables.

The correlation coefficient ranges from -1 to 1. A positive correlation coefficient indicates a positive relationship between two variables, while a negative correlation coefficient indicates an inverse relationship between two variables.

A positive correlation coefficient signifies that as one variable increases, the other variable also increases. For instance, the correlation between a person's height and weight is positive because as their height increases, so does their weight.

In the same way, as a person's income increases, so does their level of expenditure. Positive correlations can be either strong or weak.A strong correlation is indicated by a correlation coefficient close to 1, while a weak correlation is indicated by a correlation coefficient closer to zero.

For example, the correlation between a person's weight and the number of hours they exercise per week is strong. When a person's exercise time increases, so does their weight loss. In conclusion, when an increase in one variable is associated with an increase in a second variable, the two variables are positively correlated.

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