If the slopes of the asymptotes of a hyperbola are ±4/3 , one vertex is at (-2,5), and one focus is at (-4, 5), find the center.

Answer: x<4

Step-by-step explanation:

If we break this down as

-2+4x<14 and we add 2 to both sides

4x+<16 and divide by 4

and you get x<4

In reference to different sampling methods, systematic sampling includes the steps: divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group: [FALSE]

Systematic sampling is a method of sampling where the sample is selected using a fixed interval, rather than using random sampling. The sampling process begins by selecting a random starting point in the population and then selecting every kth element from the population.

For example, if the population has 100 elements and k=10, every 10th element would be selected for the sample.

Dividing the population into groups, and then using simple random sampling to identify a proportionate number of individuals from each group is a method called stratified sampling.

It is important to note that systematic sampling can be vulnerable to sampling bias if the sampling interval is not chosen carefully and the population is not randomly ordered, because in that case, it will not be a truly random sample.

Hence, the correct answer to this is False.

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Answer:

3/4

Step-by-step explanation:

→ 33/44

→ (33 ÷ 11)/(44 ÷ 11)

→ 3/4

So, the simplest term is 3/4.

Answer:

4^x + 6^x = 9^x

9^x=9^x

x=x

The value of y = 3 and x' = -1, y' = -3/7.

Given the equation y² = xy + 6 and knowing that y = 3 and x' = -1, we can use implicit differentiation to find the derivative of y with respect to t, y'.

       d/dt (y²) = d/dt (xy + 6)

       2y * y' = x' * y + x * y' + 0

       2 * 3 * y' = -1 * 3 + x * y'

       6 * y' = -3 + x * y'

        6 * y' - x * y' = -3

        (6 - x) * y' = -3

       y' = -3 / (6 - x)

        y' = -3 / (6 - -1)

        y' = -3 / 7

So, when y = 3 and x' = -1, y' = -3/7.

The specific case we were discussing is finding the derivative of y with respect to t, given the equation y² = xy + 6, and the values of y and x' at a certain time t. This is a problem in calculus, which is a branch of mathematics that deals with the rate of change and slopes of curves. By differentiating both sides of the equation and substituting in known values, we were able to find the value of y' at a specific time t. This method of finding derivatives is called implicit differentiation and it is used to find the derivative of an implicit equation, where one variable is expressed in terms of another.

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Answer:

G

Step-by-step explanation:

the perimeter is the sum of all sides so we have

\(P=a^{2} -ab+a-2a+a^2+ab\\\\P=(a^2-2a^2+a^2)+(-ab+2b)+a\\\\P=(0a^2)+(ab)+a\\\\P=ab+a\)

Answer:

G

Step-by-step explanation:

hope this helps!!!!!!!!!m:)

Answer:

16

Step-by-step explanation:

5x + 2y - 7z    

(x = 2, y = 10, z = 2)

First things first you would want to take the letters that the numbers are equal to and replace them with the numbers.

5(2) + 2(10) - 7(2)

Then you multiply the number that's beside the parentheses, 5(2) is the same as 5 x 2.

5(2) = 10

2(10) = 20

7(2) = 14

so now you have

10 + 20 - 14

10 + 20 = 30

30 - 14 = 16

and 16 is your final answer!

Yes, both triangles are similar.

Similar triangles are two triangles that have the same shape, but may differ in size. In other words, their corresponding angles are congruent and their corresponding sides are proportional. This means that if you were to scale one triangle up or down, it would still maintain the same shape as the other triangle.

In ΔABC,

AC² = 36² +15²

AC² = 1521 = 39²

AC = 39

In ΔXYZ,

XY² = 24² +10²

XY² = 676 = 26²

XY = 26

If the ratio of the sides of both triangles are similar So we can say that the both triangles are similar.

AB/XZ = BC/YZ = AC/XY

15/10 = 36/24 = 39/26

3/2 = 3/2 = 3/2

Here we can see that the ratio of the sides of both triangles are similar So we can say that the both triangles are similar.

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Step-by-step explanation:

Find the sides and perimeter:

Perimeter:

Find the area using shoelace formula:

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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Answer:

the ordered pair is (-2,11)

Answer:

See below ~

Step-by-step explanation:

Equating the system of equations :

When x = -1 :

When x = -2 :

Answer:

See below.

Step-by-step explanation:

The answer would be A and E.

Corresponding angles are angles which are formed in matching corners or corresponding corners .

-hope it helps

Answer:

angles A and D

Step-by-step explanation:

corresponding angles are angle on the same side of one of two lines cut by a transversal

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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With the given equation, the value of m + k is equal to 656 as K is 648 and the value of is 8

We have been given the equation: x² - 4x - 9 = 0

For finding the root, we need to, x = 8² ± 4AC/2A

When we solve for the following equation, we get: x = -10, 26

now we have been given root (m + √K/2) = 26

= (m/2) + (√K/2) = 26

= √2m + √K = 26√2 ......(1)

= m - √K/√2 = -10

= √2m - √K = -10√2 ......(2)

From equation (1) and (2), we get:

2√2m = 16√2

m = 8

therefore, √K = 26√2 - √2m

√K = 18√2

K = 2 × 18² = 648

Now, m + K = 648 + 8 = 656

Therefore, with the given equation, the value of m + k is equal to 656 as K is 648 and the value of is 8

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The sum of four consecutive integers is,

⇒ 4n + 6

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

⇒ n = first integer of the four.

Now, Let four consecutive integers with n is first integer of the four are,

⇒ n, n + 1, n + 2, n + 3

Hence, The sum of four consecutive integers is,

⇒ S = n + (n + 1) + (n + 2) + (n + 3)

      = 4n + 6

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Step-by-step explanation:

how many ways can the coach make out the batting order? 9! = 9 · 8 · 7 · 6 · 5 ·4 · 3 · 2 · 1 = 362,880 .

Answer:

13/14

Step-by-step explanation:

Area of a rectangle = l * b

=> 4 1/3 = 3 1/2 + b

=> (4 1/3) / (3 1/2) = b

=> (13/4) / 7/2  = b

=> 13/4 * 2/7

=> 13/2 * 1/7

=> 13/14

Therefore the width = 13/14

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Answer: 20% of 160 is 32.

Step-by-step explanation:

The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.

To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.

Let us now find the 20% of 160.

20% = 0.2

percentage = 160 × 0.2

= 32

Answer:

Step-by-step explanation:

A = (7 + 4)(24) ÷ 2 = 132 units²

The only solution that is true about the dependent system of equations is "There are infinitely many solutions".

Inconsistent System

For a  system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of equations to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

As discussed above the Dependent consistent system has infinitely many solutions as their line are coinciding, therefore, the only solution that is true about the dependent system of equations is "There are infinitely many solutions".

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Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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The probabilities (rounded to six decimal places) are:

P(all men) = 0.000001

P(all women) = 0.000001

P(8 men and 4 women) = 0.000259

P(6 men and 6 women) = 0.006239

To find the probabilities, we need to determine the total number of possible outcomes and the number of favorable outcomes for each scenario.

Total number of jurors = 23 (men) + 17 (women) = 40

P(all men):

In this case, we need to select 12 men from the pool of 23 men. The number of favorable outcomes is 1, as we want to select all men. The total number of possible outcomes is the total number of ways to select 12 jurors from a pool of 40. Using the combination formula, we have:

P(all men) = (Number of favorable outcomes) / (Number of possible outcomes) = 1 / C(40, 12) ≈ 0.000001

P(all women):

Similar to the previous case, the number of favorable outcomes is 1 (selecting all women), and the total number of possible outcomes is C(40, 12). Therefore:

P(all women) = (Number of favorable outcomes) / (Number of possible outcomes) = 1 / C(40, 12) ≈ 0.000001

P(8 men and 4 women):

For this scenario, we need to select 8 men and 4 women from the respective pools. The number of favorable outcomes is the product of the number of ways to select 8 men from 23 and 4 women from 17. The total number of possible outcomes is C(40, 12). Therefore:

P(8 men and 4 women) = (Number of favorable outcomes) / (Number of possible outcomes) = (C(23, 8) * C(17, 4)) / C(40, 12) ≈ 0.000259

P(6 men and 6 women):

Similarly, we select 6 men and 6 women. The number of favorable outcomes is the product of the number of ways to select 6 men from 23 and 6 women from 17. The total number of possible outcomes is C(40, 12). Hence:

P(6 men and 6 women) = (Number of favorable outcomes) / (Number of possible outcomes) = (C(23, 6) * C(17, 6)) / C(40, 12) ≈ 0.006239

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Answer: (5 × 8) - (5 × 1)

Step-by-step explanation:

When you use the distributive property, you essentially distribute a number to terms it is being multiplied by in order to make the calculation process easier.

When you use the distributive property, you distribute the number outside a multiplication statement to the numbers inside. In this case, 5 is the number outside, and 8 and 1 are the numbers inside.

When you distribute the number 5 to the eight, you are left with (5 × 8). However, you must still include 1, the other number in the parentheses, to finish the equation.

With 1, you go through the same process as you did before. You distribute the number 5 to the 1 and are left with (5 × 1). However, in the original equation, you are subtracting the 8 by the 1, so you must account for the subtraction sign.

You essentially subtract the number you get from (5 × 8) by the number you get from (5 × 1). Therefore, your answer is (5 × 8) - (5 × 1).

B' would now have the following updated coordinates: (-6, 6)

resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.

If ABCD is dilated by a factor of 3

Then To enlarge this by a factor of three...

-2 * 3 = -6

2 * 3 = 6

B' would now have the following updated coordinates:

(-6, 6)

There are a few things to be aware of:

- A "scale factor" is three.

Hence B' would now have the following updated coordinates: (-6, 6)

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The probability that the three randomly selected students will have blood types A, B and AB is given as follows:

0.00164 = 0.164%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

Hence the probability for this problem is calculated as follows:

41/100 x 1/10 x 1/25 = 0.00164 = 0.164%.

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Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Approximately 0.0228 or 2.28% of your yard has more than 5 inches of snow.

Approximately 0.9759 or 97.59% of your yard has between 4 and 5.25 inches of snow.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

z-score = (X-ц )/σ

Standardize the value of 5 using the given mean and standard deviation:

Z = (5 - 4.5) / 0.25 = 2

Using a standard normal distribution table or a calculator, we can find the area to the right of Z = 2.

The area to the left of Z = 2 is 0.9772. Therefore, the area to the right of Z = 2 is:

1 - 0.9772 = 0.0228

This means that approximately 0.0228 or 2.28% of your yard has more than 5 inches of snow.

Standardized the values of 4 and 5.25 using the given mean and standard deviation:

Z_4 = (4 - 4.5) / 0.25 = -2

Z_5.25 = (5.25 - 4.5) / 0.25 = 3

Using a standard normal distribution table, we can find that the area to the left of Z = -2 is 0.0228 and the area to the left of Z = 3 is 0.9987. Therefore, the area between Z = -2 and Z = 3 is:

0.9987 - 0.0228 = 0.9759

This means that approximately 0.9759 or 97.59% of your yard has between 4 and 5.25 inches of snow.

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The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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