Write the equation of the hyperbola with center (1,-3), vertex (1,2), and focus (1,-3+2sqrt10)

Answer:

q = 50

r = 75

s = 115

t = 30

Step-by-step explanation:

The equation of the regression of grades on scores is y = 0.003x + 1.645

The mean of the sat scores = 485

The standard deviation = 85

The average college gpa = 3.1

The standard deviation = 0.4

The correlation between sat scores and college grades = 0.71

The regression equation is

y = mx + b

The value of m = (0.71) × (0.4/85)

= 0.003

Substitute the values in the regression equation and find the value of b

3.1 = 0.003×485 + b

3.1 = 1.455 + b

b = 3.1 - 1.455

b = 1.645

The equation is

y = 0.003x + 1.645

Therefore, the regression equation is y = 0.003x + 1.645

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Answer:4(x+3)

Step-by-step explanation:

8(x + 3)^2 /2(x + 3)

4(x+3)

Answer:

Step-by-step explanation:

Simplify

8(x + 3)^2 divided by 2(x + 3)

8·(x + 3)² : 2·(x + 3) =

8⋅(x²+6x+9):2⋅(x+3) =

(8x²+48x+72):2⋅(x+3) =

(4x²+24x+36)⋅(x+3) =

4x³+36x²+108x+108

The value of interquartile range (IQR) of the data set which is plotted in the dot plot 0 2 4 6 8 10 12 is 6

What is the interquartile range (IQR) of the data?

The interquartile range (IQR) of the data is the middle half of the data, which contains 2nd and 3rd quartiles.

Interquartile range is the difference of third quartile and first quartile.

IQR = Q₃ - Q₁

According to the given question:

In the dot plot below, the data is given as,

0 2 4 6 8 10 12

The first quartile is the medium of the lower half, while the third quartile is the medium of the upper half. For the above data,

Q1 = 3

Q3 = 9

Thus, Interquartile range is,

IQR = Q₃ - Q₁

IQR = 9 - 3

IQR = 6

Hence, the value of interquartile range (IQR) of the data set which is plotted in the dot plot 0 2 4 6 8 10 12 is 6

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Answer:

p=500

Step-by-step explanation:

18/100=90/p

First, set up equation

90x100=18xp

9000=18p

9000/18=18p/18

500=p

Answer:

[tex]p = 500[/tex]

Step-by-step explanation:

Use the cross-multiplication method. Multiply 18 with p, and 90 with 100, respectively:

[tex]\frac{18}{100} = \frac{90}{p} ; \\ 18p = 90 * 100\\ 18p = 9000[/tex]

Isolate the variable, p. Note the equal sign, what you do to one side, you do to the other. Divide 18 from both sides of the equation:

[tex]\frac{(18p)}{18} = \frac{(9000)}{18} \\p = \frac{9000}{18} \\p = 500[/tex]

[tex]p = 500[/tex] is your answer.

~

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Answer:

Step-by-step explanation:

x^2 - 3x + 2x - 6

x^2 - x - 6

The inequality to represent the problem is x + 1.25y ≥ 2000 and it's graph is attached below

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in mathematics. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).

Let;

a) The inequality to represent the situation can be expressed as

1x + 1.25y ≥ 2000

This is further expressed as;

x + 1.25y ≥ 2000

b) The graph of the inequality x + 1.25y ≥ 2000 is attached below.

c) The possible solutions are at (2000, 0) and (0, 1600)

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Answer:

100 is the answer

Step-by-step explanation:

20 people need to be in a group in order for them to save $500.

If there are 15 people or more, people will save $25 on each ticket.

In order to save a total of $500, the number of people who are needed is:

= Amount to be saved / Amount to be saved per ticket

= 500 / 25

= 20 people

In conclusion, if a group of 20 people came, they would save $500.

Answer:

45

Step-by-step explanation:

8 numbers summed and divided by 8 = 41

8numberssummed  / 8 = 41

8numberssummed = 41 * 8 = 328

now taking out two numbers whose mean is 29 is the same as taking out two 29's from the sum ....so now there are SIX numbers

  6numberssummed = 8numberssummed - 29 -29

                                   =   328    -29 -29 = 270

  so to find the mean of the remaining six numbers:

     6numberssummed / 6    is        270/6 = 45

Answer:

mean = 45

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

given the mean of 8 numbers is 41 , then

[tex]\frac{sum_{8} }{8}[/tex] = 41 ( multiply both sides by 8 )

sum₈ = 328

given the mean of 2 of the numbers is 29 , then

[tex]\frac{sum_{2} }{2}[/tex] = 29 ( multiply both sides by 2 )

sum₂ = 58

Then

sum₆ = sum₈ - sum₂ = 328 - 58 = 270

then the mean of the other six numbers is

mean = [tex]\frac{sum_{6} }{6}[/tex] = [tex]\frac{270}{6}[/tex] = 45

Answer:

the right answer is

1,2/9

The width of the photograph is 10 inches if the length of the photograph is 3 inches.

Any arbitrary reference standard for measuring length that has gained acceptance is referred to as a unit of length. The metric system, which is adopted by every nation on earth, is the most prevalent system in use today. The US customary units are also used in the US. The United Kingdom and a few other nations continue to utilize British Imperial units for specific purposes. SI units and non-SI units are subsets of the metric system.

Given,

The expression is:

x(x + 3) = 70

x² + 3x = 70

Now, we have to subtract 70 on both the sides, we get:

x² + 3x - 70 = 0

(x-7)(x + 10) = 0

x-7=0

x=7

x+10=0

x= -10

Since distance cannot be negative, the correct answer is x = 7. We are now plugging in the length (x + 3).

=x + 3

=7 + 3

=10

Therefore, the width of the photograph is 10 inches.

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Congestion management allows for more efficient use of a shared network infrastructure by managing the flow of data packets into the network.

Additive increase and additive decrease (AIAD) This is the policy which follows the below rule

a(i)>0, b(i) =1, a(d)<0 b(d)=1

This policy doesn't converge to fairness which means that it is not stable.

Moreover, this doesn't converges to efficiency and if it is need to be stable then it must satisfy the condition a(d) = a(i)

Multiplicative increase and additive decrease (MIAD) This is the policy which follows the rule of a(i) =0, b(i) >1, a(d)<0, b(d)=1

This policy doesn't converge to fairness which means that it is not stable.

Moreover, this doesn't converges to efficiency and if it is need to be stable then it must satisfy the condition b(i)a(d)/ 1- b(i)

Multiplicative increase multiplicative decrease (MIMD) This is the policy which follows the below rule a(i) =0 , b(i) >1 , a(d)=0, 0<b(d)<1

This policy doesn't converge to fairness which means that it is not stable.

Moreover, this doesn't converges to efficiency and if it is need to be stable then it must satisfy the condition b(i)≥ 1 and 0≤ b(d)<1.

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The value of (1 + i)^8 is 16. De Moivre's describes how the power of a complex number can be calculated using the properties of its modulus and argument.

De Moivre's theorem states that for any complex number z = r * (cos(θ) + i * sin(θ)) and any integer n, we have:

zⁿ = rⁿ * (cos(n * θ) + i * sin(n * θ))

To use this theorem, we need to first express the complex number (1 + i) in terms of its magnitude and angle. We can do this by using the Pythagorean theorem to find the magnitude of the complex number, which is the square root of the sum of the squares of the real and imaginary parts.

In this case, the magnitude is the square root of 1^2 + 1^2, or √2.

The angle of the complex number can be found using the inverse tangent function. In this case, the angle is 45 degrees, since the tangent of 45 degrees is 1. Now that we have the magnitude and angle of the complex number, we can use De Moivre's theorem to find the value of (1 + i)^8. Substituting the values we found into the formula above, we get:

(1 + i)^8 = √2^8 * (cos(8 * 45) + i * sin(8 * 45))

        = 2^4 * (cos(360) + i * sin(360))

        = 16 * (1 + i * 0)

        = 16

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MCN= ACN-ACN-1 is the basis of diminishing marginal utility.

What is marginal utility?

The additional pleasure a consumer has from owning one extra unit of an item or service is known as marginal utility. Economists utilize the idea of marginal utility to estimate the quantity of a good that consumers will buy.

When the overall utility is increased by the consumption of an additional item, positive marginal utility occurs. On the other side, negative marginal utility arises when the overall utility is reduced by the consumption of one extra unit.

According to the law of diminishing marginal utility, as consumption rises, the marginal utility gained from each additional unit decreases, all other things being equal. The incremental improvement in utility brought on by consuming one more unit is known as marginal utility. An economic term for happiness or contentment is "utility."

So

MCN= ACN-ACN-1

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The image of vertex A will be at point (2,-5).

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The perimeter will be P = sum of all three side.

Point A is located at (2, 5), thus you look at the y-coordinate since you are reflecting it across the x-axis.

Given that it is five above the x-axis, you must travel five below it, or you can simply enter the opposite of five, which is -5.

So, A' is at (2, -5).

Hence, The image of vertex A will be at point (2,-5).

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Answer:

3 x - y = 6

Step-by-step explanation:

the equation of a line is

ax + by = c

express the slope initially in the form of y=mx+b

b is the y- intercept (the point where it crosses the y axis)

m is basically the slope, to find m, you have to use a specific formula...

m = (y2 – y1) / (x2 – x1)

(x1, y1) (x2, y2) are 2 coordinate points...

(3,3) and (1, -3)

m = -3 -3 divided by 1 - 3 =  -6/-2 =  3

so your formula for now is .. y = 3x + b (you dont know what b is yet)

Now, substitute the points into the equation.

3 = 9 + b.  b = -6

final formula is,

Y=3x -6

u can also rearrange the formula in a standard form:

3x - y = 6

I REALLY HOPE THIS HELPS U!!

The time required = 4 hours

The time required by the car to move at a speed of 50 mph to reach a distance of 200 miles is 4 hours

What is Speed?

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the distance traveled by the car be = D

Now , the speed S of the car = 40 miles per hour

The time required by the car to travel D distance is T = 5 hours

So , the Distance D is calculated from the formula

Distance D = Speed S x Time T

So , substituting the values in the equation , we get

Distance D = 40 x 5

Distance D = 200 miles

Now , the distance traveled by the car remains the constant

The speed of the car is S = 50 miles per hour

And let the time taken by the car to cover 200 miles at 50 mph be = T

Now to calculate Time T ,

Time T = Distance D / Speed S

Substituting the values in the equation , we get

Time T = 200 / 50

Time T = 4 hours

Therefore , the value of T is 4 hours

Hence , The time required by the car to move at a speed of 50 mph to reach a distance of 200 miles is 4 hours

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(x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.

A quadratic function has the vertex form f(x) = a(x - h)2 + k, where a, h, and k are constants.

Obtain the equation y = ax2 + bx + c.

Determine -b / 2A.

The vertex's x-coordinate is given here.

Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate.

The vertex's y-coordinate is given here.

So, we have the equation:

Y = X² - 2x + 5

Now, calculate as follows:

⇒ y = (x2 - 2x + 1) + 5 -1

⇒ y - 4 = (x -1)2

⇒ (x -1)2 = y - 4

Therefore, (x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.

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1. The weight for 18 tablespoons is 1127.32 grams.

2. The number of tablespoons of the liquid noah needs to add so that the total weight is 1,200 grams is 23 tablespoon.

It's vital to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, Noah placed an empty bowl on a scale and the equation is given as:.

y = 14.75x + 861.82

x = the amount of the liquid, in tablespoons

y = the total weight

The weight for 18 tablespoons will be:

y = 14.75x + 861.82

y = 14.75(18) + 861.82

y = 1127.32

The liquid that Noah needs to add so that the total weight is 1,200 gram will be:

y = 14.75x + 861.82

14.75x + 861.82 = 1200

Collect like terms

14.75x = 1200 - 861.82

14.75x = 338.18

Divide

x = 138.18 / 14.75

x = 23

The tablespoons is 23.

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The difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.

Here, we are given that 13.4% of the population in the US lived in the West in 1950 and 22.5% in 2000.

Thus, the difference in percentage = 22.5 - 13.4 = 9.1%

We observe that the difference is large, this means that the difference in percentages is practically significant.

Now, to determine whether the difference is statistically significant it is appropriate to conduct a two-sample z-test and it is only appropriate to conduct the test of significance when the samples are simple random samples.

In this case, the samples are not simple random samples, because the data given contains information on all individuals in the population. Moreover, it is not appropriate to determine whether the difference in percentages is statistically significant as the samples are not probability samples.

Thus, the difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.

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Answer:

The following statements are true:

A) The equation |-x - 4| = 8 will have two solutions.

D) The equation |2x - 10| = -20 will have two solutions.

E) The equation |0.5x - 0.75| + 4.6 = 0.25 will have no solutions.

The other statements are not true. The equation 3.4|0.5x - 42.1| = -20.6 will not have one solution, as the absolute value of a number cannot be negative. The equation |1/2x - 3/4| = 0 will not have no solutions, as the absolute value of a number cannot be zero. The equation |1/8x - 1| = 5 will not have infinitely many solutions, as the absolute value of a number cannot be negative.

Step-by-step explanation:

The correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."

The relationship between two terms on either side of an equal sign is easily demonstrated using a simple equation.

Additionally, one or more of the four arithmetic operations that simple equations do include addition, fundamental arithmetic, multiplication, and division.

The three possible forms of the equation system are point-slope form, standard form, and slope-intercept form.

So, given equations:

y = 1/2 * x - 3

y = - 1/2 * x - 3

As we are aware, a line's slope-intercept form is:

y = m x + c  

Therefore, it is clear from equations 1 and 2 that:

m1 = 1/2 and c1 = -3

m2 = -1/2 and c2 = -3

Therefore, the correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."

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Complete question:
A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?

a. They have the same slope but different y-intercepts, so they have no solution.

b/. They have the same slope but different y-intercepts, so they have one solution.

c. They have different slopes but the same y-intercept, so they have no solution.

d. They have different slopes but the same y-intercept, so they have one solution.

The expected difference under null hypothesis can be understood by the following :

The required null and alternate hypothesis will be

Null hypothesis :  H0 : μ=μ0

Alternate Hypothesis: H1 : μ<μ0

To determine whether there is a difference in the means of two populations, the z test formula compares the z statistic to the z critical value.

The z critical value in hypothesis testing divides the distribution graph into acceptance and rejection regions. The null hypothesis can be rejected if the test statistic falls within the rejection region; otherwise, it cannot be rejected.

The z test formula  to set up the required hypothesis tests for a one sample and a two-sample z test is

z = (( x−μ) /σ/√n  )x

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The discounted price of an item did the price increased after the weekend by a fraction of 1/5.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. One-fifth is 20 percent of the total five parts of a number, and thus, the price increased by 1/5th after the weekend.

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The time taken by the jet to reach the earth form sun is 3 months

The correct option is option A)

What is speed?

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.

We are given that

Light travels at the speed of 3,00,000 km per second. Light from the sun reaches us in 8 minutes

We first find the distance between sun and earth

to do that we multiply speed of light and time taken by light to reach earth

D = 300000*8

D= 2400000km

Now we are given the speed of the jet which is 1000km/hr

We have to find the time taken by the jet to reach the earth

To do that we divide the distance by speed we get

t = 2400000/1000

t =2400 hr.

3 months

The time taken by the jet to reach the earth form sun is 3 months

The correct option is option A)

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The partial fraction decomposition of the expression with repeated factors is given as follows:

[tex]\frac{1}{x} - \frac{2}{x + 4} - \frac{1}{(x + 4)^2}[/tex]

The function in this problem is defined as follows:

(-x² - x - 16)/(x³ + 8x² + 16x).

The decomposition is made considering the factors of the denominator, which are obtained as follows:

x³ + 8x² + 16x = 0.

x(x² + 8x + 16) = 9

x(x + 4)² = 0.

Hence the denominators are as follows:

Then the decomposition is of:

A/x + B/(x + 4) + C/(x + 4)²

Then the expression will be given as follows:

[tex]\frac{A(x + 4)^2 + Bx(x + 4) + Cx}{x^3 + 8x^2 + 16x} = \frac{-x^2-x+16}{x^3 + 8x^2 + 16x}[/tex]

Then the system of equations, equaling the numerators, is given as follows:

Hence:

16A = 16

A = 1.

B = -1 - A

B = -2.

C = -1 - 8A - 4B

C = -1.

Meaning that the third option is correct.

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The area of the triangle formed by the birdbath, bird feeder and the birdhouse is 15 squared units

Given: the birdbath is at (2,2), the bird feeder is at (8,2), and the birdhouse is at (5,7)

(Consider the image attached)

The distance between the points can be calculated using the formula:

d=√((x2 – x1)² + (y2 – y1)²)

birdbath (5,7) and birdhouse (2,2)

d=√((2 – 5)² + (2 – 7)²) = √34

bird feeder (8, 2) and birdhouse (2,2)

d=√((2 – 8)² + (2 – 2)²) = 6

birdbath (5,7) and bird feeder (8,2)

d=√((8 – 5)² + (2 – 7)²) = √34

The height of the triangle is:

h = √((√34)²-3²) = 5

Area of triangle = 1/2 × base × h

Area of triangle = 1/2 × 6 × 5 = 15 squared units

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Answer:

.321× 50

000

+ 1605X

therefore answer is 1.605

A line plot would be the best data display to highlight every height.

A line plot, also known as a dot plot, is a type of graph that displays data as a series of dots on a number line. Each dot represents a single data point, and the dots are placed above the corresponding value on the number line.

Line plots are useful for displaying small data sets because they provide a simple visual representation of the data. They can quickly show the range of values in the data set, as well as any outliers or clusters of data points. Line plots are commonly used in elementary and middle school classrooms to teach basic data analysis and graphing skills. They are also used in scientific research and statistical analysis to visualize small data sets and identify patterns in the data.

A line plot, also known as a dot plot, displays the data as points on a number line. Each data point is represented by a dot, making it easy to see every height in the data set. Here is an example of a line plot for the given data:

A display that will highlight every height would be a line plot, which would show each individual height as a dot along a number line.

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