find the equation of the hyperbola with vertices (2,5) and (2,−3) and foci (2,10) and (2,−8).

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

The coordinates of the given point; (-1, 0) after a translation of 5 units to the right are; (4, 0).

It follows from the task content that the coordinates of the point (-1, 0) after a translation of 5 units to the right is to be determined.

It is noteworthy to know that a translation of a point (x, y) k units to the right transforms the point to; (x+k, y).

Therefore, the required coordinates of the point (-1, 0) 5 units to the right is; (-1+5, 0) = (4, 0).

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Gasoline costs $3.60 a gallon. Therefore, you spend $2,250 each year on gasoline.

To calculate how much money you spend each year on gasoline, we can use the following steps:

1. Determine the number of gallons of gasoline you need per year:

  Number of gallons = Total miles driven / Miles per gallon

  Number of gallons = 15,000 miles / 24 miles per gallon

  Number of gallons = 625 gallons (rounded to the nearest whole number)

2. Calculate the total cost of gasoline per year:

  Total cost = Number of gallons * Price per gallon

  Total cost = 625 gallons * $3.60 per gallon

  Total cost = $2,250

Therefore, you spend $2,250 each year on gasoline.

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Answer:

80

Step-by-step explanation:

Since the quadrilaterals are similar, corresponding angles are congruent.

m<A = m<F

m<F + 100° + 60° + 120° = 360°

m<F = 80°

z = m<F = 80°

Answer: 80

Answer:

x = -61

Step-by-step explanation:

-  2x - 35 = 87.    

         +35. +35.   Add 35 to both sides

-2x = 122.  

-2/-2 = 122/-2.     Divide by -2 on both sides

     x = -61

Answer:

Step-by-step explanation:

40, because its an arrowhead, its gonna be the same

Answer:

110°

Step-by-step explanation:

<ABC + <ACB = 180 - <BAC

= 180 - 40

= 140°

=> <OBC + <OCB = 140/2 = 70°

=> <BOC = 180 - 70 = 110°

Answer:

the answer is m=19

Step-by-step explanation:

5^(m-7)=5^12

m-7=12(5 is cancelled because it is common in both sides)

m=19

Answer:

b^4 / a

Step-by-step explanation:

I have attached the explanation above. hopefully this will help

Step-by-step explanation:

Amelia got 56% of 75 so

(56/100)*75=(56*75)/100=4200/100=42

Hayden got 8/15 of 75 so

(8/15)*75=(8*75)/15=600/15=40

and Sophie that got 43 out of 75

so we see that Sophie got the highest points.

Given parameters:

  Total test score = 75marks

 Percentage of Amelia score  = 56%

 Fraction  of Hayden's score = \(\frac{8}{15}\)

  Sophie's score  = 43marks

Unknown:

The person with the highest score  = ?

Solution:

  Since total score = 75marks;

Amelia's score = \(\frac{56}{100} x 75\)   = 42marks

 Hayden's score = \(\frac{8}{15} x 75\)   = 40marks

 Sophie's score  = 43 marks

The person with the highest score is Sophie with a mark of 43.

Answer:

18ft

Step-by-step explanation:

6/27= 4.5, 27/4. 4.5x4=18

Answer:

18ft

Step-by-step explanation:

I am taking the test right now and I think this would be the correct answer!

A simple way I found out: 6/4 = 1.5 so I took 1.5 and divided 27 by it.  27/1.5 = 18

Hope this helped!

To calculate the present value of a zero-coupon bond, we can use the formula: Present Value = Future Value / (1 + Interest Rate)^n

where Future Value is the par value of the bond, Interest Rate is the annual market interest rate, and n is the number of years. In this case, the Future Value is $2,000, the Interest Rate is 10% (or 0.10), and the number of years is 5. Using Excel, we can calculate the present value as follows:
1. In cell A1, enter the Future Value: 2000
2. In cell A2, enter the Interest Rate: 0.10
3. In cell A3, enter the number of years: 5
4. In cell A4, enter the formula for calculating the present value: =A1 / (1 + A2)^A3
5. Press Enter to get the result.

The present value of the 5-year zero-coupon bond with a $2,000 par value and an annual market interest rate of 10% is $1,620.97.

The formula for present value calculates the current worth of a future amount by discounting it back to the present using the interest rate. In this case, the future value is $2,000, and we divide it by (1 + 0.10)^5 to account for the effect of compounding over 5 years. The result is the present value of $1,620.97, which represents the amount that is considered equivalent to receiving $2,000 in 5 years at a 10% interest rate.

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We have to write 1,050,200 in scientific notation.

We start doing this as:

The number between 1 and 10: 1.0502

The power of 10: 6

The number in scientific notation: 1.0502 * 10^6

The decimal number 0.4323232323232 can be represented as the fraction 3.8909090909092/9.

To represent the decimal number 0.4323232323232 in the form of p/q, where p and q are integers, we can follow the steps below.

Let x = 0.4323232323232.

Step 1: Multiply x by a power of 10 to eliminate the repeating decimal.

10x = 4.323232323232.

Step 2: Subtract x from 10x to eliminate the non-repeating part.

10x - x = 4.323232323232 - 0.4323232323232

9x = 3.8909090909092.

Step 3: Express 9x as a fraction p/q.

9x = 3.8909090909092

x = 3.8909090909092 / 9.

In summary, 0.4323232323232 in the form of p/q is 3.8909090909092/9.

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The area enclosed between f(x) = 0.2x^2 + 3 and g(x) = x from x = -2 to x = 4 is 28.536 square units.

To find the area enclosed between two curves, we need to find the definite integral of the difference between the two curves. In this case, we need to find:

∫[-2,4] (f(x) - g(x)) dx

Where f(x) = 0.2x^2 + 3 and g(x) = x. Substituting these into the integral, we get:

∫[-2,4] (0.2x^2 + 3 - x) dx

To solve this integral, we need to first distribute the negative sign:

∫[-2,4] (0.2x^2 - x + 3) dx

Then, we can integrate each term separately:

∫[-2,4] 0.2x^2 dx - ∫[-2,4] x dx + ∫[-2,4] 3 dx

Using the power rule of integration, we get:

[0.067x^3]_[-2,4] - [0.5x^2]_[-2,4] + [3x]_[-2,4]

Substituting the limits of integration, we get:

[0.067(4)^3 - 0.067(-2)^3] - [0.5(4)^2 - 0.5(-2)^2] + [3(4) - 3(-2)]

Simplifying, we get:

16.536 - 6 + 18

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Answer:

See below.

Step-by-step explanation:

For 3, we have:

1, 3, 6, ___, 15, 21, _____, 36, _______

Let's try to determine the pattern. From 1 to 3, we added 2.

From 3 to 6, we added 3.

So, it seems that the fourth term would be to add 4, and then add 5. Let's try it:

6+4=10

10+5=15.

So, it seems we're correct. So, we will add 6, then 7, and then 8, etc. Therefore, our correct sequence would be:

1 (+2), 3 (+3), 6 (+4), 10 (+5), 15 (+6), 21 (+7), 28 (+8), 36 (+9), 45

For 4, we have:

100, _____, 64, ______, 36, 25, _______

Notice that these all are perfect squares. 10 squared is 100, 8 squared is 64, etc. Thus, we can rewrite this as:

10², _____, 8², ______, 6², 5², ______

Therefore, our blanks would be:

10², 9², 8², 7², 6², 5², 4².

Evaluated, this woul be:

100, 81, 64, 49, 36, 25, 16.

And we're done!

To determine the 30th and the 75th percentiles for the salaries:

The pth percentile is a data value such that at least p% of the data-set is less-than or equal to this data value and at least (100-p)% of the data-set are more-than or equal to this data value.

Arrange the data set in ascending order as follows:

84 ,224 , 248, 271, 338 , 381, 405 , 428, 452, 495 , 542, 609, 676 , 723 ,767 , 814, 1108

The formula to compute the position of the pth percentile is:

Compute the 30th percentile as follows:

The 5th observation from the arranged data set is 338 .

Thus, the 30th percentile is 338.

Compute the 75th percentile as follows:

The 14th observation from the arranged data set is 814.

Thus, the 75th percentile is 814

Therefore the 30th percentile is 338 and the 75th percentile is 814

Using the concept of conditional probability and the conditions provided, The answer is \(\frac {p^2}{2pq}\) .

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probabilities can be calculated using the ratio of the number of favorable outcomes to the total number of possible outcomes. It helps us to understand the uncertainty of events.

A false positive result is when a test indicates that a particular condition or attribute is present, when in reality it is not. For example, in medical testing, a false positive result would occur when a test for a disease returns a positive result but the person being tested does not actually have the disease. False positives can have serious consequences, as they can lead to unnecessary treatments, further testing, and anxiety for the person being tested.

p=probability of occurrence

q=1-p

P(false positive for both subjects | false positive for one subject) = P(false positive for both subjects and false positive for one subject) / P(false positive for one subject)

P(false positive for both subjects | false positive for one subject) = p^2 / (2pq)

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Answer:

5, -1

with a scale factor of 1, nothing changes

Answer:

10 units

Step-by-step explanation:

Given

(x + 4)(x - 6) = 0

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 6 = 0 ⇒ x = 6

The roots are x = - 4 and x = 6

Use the absolute value to find the distance between them, that is

| - 4 - 6 | = | - 10 | = 10 , or

| 6 - (- 4) | = | 6 + 4 | = | 10 | = 10

The distance between the roots is 10 units

Answer:

75.9

Step-by-step explanation:

Answer:

Ivan took 17/8 hours longer to clean the kitchen

Step-by-step explanation:

The time it took Ivan too long, would be the difference between the time he took to clean the kitchen by the time he took to clean his bedroom.

Then,

Ivan took 17/8 hours longer to clean the kitchen

Answer:

See attached graph

Step-by-step explanation:

The equation is y-3=(x + 6)

Write the equation in a slope intercept form, then graph the equation on a graph tool to see the points that line on the line.

Alternatively , using the coordinates in the answer choices given, input them in the equation of the graph and select the answer choice that has all its coordinates true to the equation.

y-3 = x+6  -----can be written as : y= x+9

Graph  y= x+9 to see the graph and the points that are on the line as attached.

The line passes through points (-5, 4) and (-4, 5).

Hence, option E is correct.

Use the concept of drawing a graph defined as:

Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.

The given equation of a line:

y – 3 = (x + 6)

To plot the graph:

Put x = 0  we get y = 9

put x = 1 we get y = 10

put x = 2 we get y = 11

put x = 2 we get y = 12

proceed similarly.

Now plot the curve by addressing these points.

Hence,

The line passes through points (-5, 4) and (-4, 5) which is option E.

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The complete question is:

Which is the graph of y – 3 = (x + 6)?

A. A coordinate grid with a line passing through the points at (negative 3, 1), (0, negative 1), and (3, negative 3).

B. A coordinate grid with a line passing through the points at (negative 2, 1), (0, 0), and (4, negative 3).

C. A coordinate grid with a line passing through the points at (negative 3, 0), (0, negative 2), and (3, negative 4).

D. A coordinate grid with a line passing through the points at (negative 3, 3), (0, 1), and (3, negative 1).

E. A coordinate grid with a line passing through the points at (negative4, 5)and (negative 5, 4).

Answer:

It is A

Step-by-step explanation:

The square route of 174 is 13.190906. Didn't use a calculator.

Answer:

Phương trình lượng giác cơ bản: lý thuyết, cách giải, bài tập

2. Phương trình cos x = cos α, cos x = a.

3. Phương trình tan x = tan α, tan x = a.

4. Phương trình cot x = cot α, cot x = a. ...

5. Phương trình bậc nhất đối với một hàm số lượng giác. ...

6. Một số điều cần chú ý:

Answer:

36/8 miles which is 4 4/8 or 4 1/2 miles.

Step-by-step explanation:

Hope this helps :)

The answer is a here is proof

Answer:Therefore, the range is 32 and the standard deviation is approximately 10.523 for the given data set.

Step-by-step explanation:To calculate the range and standard deviation for the given data set {40, 65, 33, 46, 55, 50, 61}, we can follow these steps:

Step 1: Find the range.

The range is calculated by subtracting the minimum value from the maximum value in the data set.

Range = Maximum value - Minimum value

Range = 65 - 33

Range = 32

Step 2: Calculate the mean.

The mean is calculated by summing up all the values in the data set and dividing by the total number of values.

Mean = (40 + 65 + 33 + 46 + 55 + 50 + 61) / 7

Mean = 350 / 7

Mean = 50

Step 3: Calculate the deviation for each value.

Deviation is calculated by subtracting the mean from each value in the data set.

Deviation for 40 = 40 - 50 = -10

Deviation for 65 = 65 - 50 = 15

Deviation for 33 = 33 - 50 = -17

Deviation for 46 = 46 - 50 = -4

Deviation for 55 = 55 - 50 = 5

Deviation for 50 = 50 - 50 = 0

Deviation for 61 = 61 - 50 = 11

Step 4: Square each deviation.

Squared deviation for -10 = (-10)^2 = 100

Squared deviation for 15 = 15^2 = 225

Squared deviation for -17 = (-17)^2 = 289

Squared deviation for -4 = (-4)^2 = 16

Squared deviation for 5 = 5^2 = 25

Squared deviation for 0 = 0^2 = 0

Squared deviation for 11 = 11^2 = 121

Step 5: Calculate the variance.

Variance is calculated by summing up all the squared deviations and dividing by the total number of values.

Variance = (100 + 225 + 289 + 16 + 25 + 0 + 121) / 7

Variance = 776 / 7

Variance ≈ 110.857

Step 6: Calculate the standard deviation.

The standard deviation is the square root of the variance.

Standard Deviation ≈ √110.857

Standard Deviation ≈ 10.523