The midpoint of a line with the endpoints (-2, 0) and (-6, 8) is:
(4,4).
(-4,4).
(-4,-4)
(4,-4).

Therefore ,the speed at height 40 feet in the air = 16*40=640 feet/sec

A mathematical function from one set X to another gives each element of X exactly one element of the other. The sets X and Y, respectively, represent the function's domain and codomain.

Here,

the given function is

f(t)=−8[tex]t^{2}[/tex]+25

Therefore, the speed of the ball can be calculated by using derivative of f(t)

f(t)=−8[tex]t^{2}[/tex]+25

Differentiating f(t) w.r.t  t

=> d(f(t)/dt=-8*2t

=> d(f(t)/dt=-16t

Therefore the speed at height 40 feet in the air = 16*40=640 feet/sec

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The solution of the given greatest integer function is found as 3.5.

We have to compute;

f(x) = 1/2[x]

Given what we have; f(7.6).

Enter x = 7.6 in the function provided;

f(7.6) = 1/2[7.6]

As ,the value (7.6) --> 7.0 (greatest integer function)

f(7.6) = 7/2

f(7.6) =  7/2

f(7.6) = 3.5

Thus, the solution of the given greatest integer function is found as 3.5.

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The correct question is-

If f(x) = 1/2[x], what is f(7.6)?

3

3.5

3.8

4

The slope of the line that passes through each pair of points are:

1. -29/3

3. -27/19

5. 2/3

7. -11/3

2. 22/13

4. 1/5

6. 2/3

8. 5/17

The slope of a line that joins two points can be found by using the formula below:

Slope (m) = change in y / change in x

1. Slope (m) of the line that goes through (8, 12) and (11, -17):

Slope (m) = (-17 - 12) / (11 - 8) = -29/3

3. Slope (m) of the line that goes through (-1, -8) and (-20, 19):

Slope (m) = (19 - (-8)) / (-20 - (-1)) = 27/-19

m = -27/19

5. Slope (m) of the line that goes through (2,16) and (8, 20):

Slope (m) = (20 - 16) / (8 - 2) = 4/6

m = 2/3

7. Slope (m) of the line that goes through (11,-6) and (8,5):

Slope (m) = (-6 - 5) / (11 - 8) = -11/3

2. Slope (m) of the line that goes through (2.-11) and (15, 11):

Slope (m) = (-11 - 11) / (2 - 15) = -22/-13

m = 22/13

4. Slope (m) of the line that goes through (5, -18) and (-15, -16):

Slope (m) = (-16 - (-18)) / (-15 - 5) = 2/10

m = 1/5

6. Slope (m) of the line that goes through (9, 10) and (-12,-4):

Slope (m) = (-4 - 10) / (-12 - 9) = -14/-21

m = 2/3

8. Slope (m) of the line that goes through  (11, 8) and (-6, 3):

Slope (m) = (8 - 3) / (11 - (-6)) = 5/17

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Answer:

6

Step-by-step explanation:

it is a8=a1 +(n-1)x d

41=-1+ 7xd

42/7=d

d=6

Answer: 6

Step-by-step explanation:

[tex]a_1=-1\ \ \ \ \ \ \ \ a_8=41\ \ \ \ \ \ \ \ d=?\\\\\boxed{a_n=a_1+d(n-1)}\\\\Hence,\\\\a_8=-1+d(8-1)\\\\41=-1+7d\\\\41+1=-1+7d+1\\\\42=7d\\\\[/tex]

Divide both parts of the equation by 7:

6=d

Thus, d=6

The graphs of these two equations intersect in 4 points.

What is an example of a hyperbola?

A hyperbola is a collection of points in a plane whose separations from two fixed points, known as its foci (plural of focus), differ by an amount that is always the same.

                    Using the figure as an example, a hyperbola with foci at (-3,0) and The point at illustrates its constant distance as being 4. (-3,-2.5).

x²+y²=25

it is a circle with radius=5

x²-y²=3

it is a hyperbola.

x²-y²=3

so, they intersect in four points.

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The complete question is -

The graphs of these two equations intersect in how many points?

x^2+y^2=25

x^2-y^2=3

Answer: [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

The vertex is halfway between the [tex]x[/tex]-intercepts.

So, the answer is [tex]\frac{2+3}{2}=\frac{5}{2}[/tex].

Answer:

Step-by-step explanation:

Graph crosses the x-axis at x = 0 and has zeros at {-5, -5}.Step-by-step explanation: Note that f(x) factors as follows:  f(x) = 4x^5 (x^2 + 10x + 25) …

Answer:

Let's call the length of the long piece x, and the length of each shorter piece y. We can set up the following equation to represent the problem:

x + 2y = 29

Since the long piece is 1 ft longer than twice the length of each shorter piece, we can write this equation as:

x = 2y + 1

Substituting this expression for x in the first equation, we get:

2y + 1 + 2y = 29

Combining like terms on both sides, we get:

4y + 1 = 29

Subtracting 1 from both sides, we get:

4y = 28

Dividing both sides by 4, we get:

y = 7

Substituting this value for y in the expression for x, we get:

x = 2(7) + 1 = 14 + 1 = 15

Thus, the length of the long piece is 15 ft, and the length of each shorter piece is 7 ft.

Answer:

i

Step-by-step explanation:

1. Multiply the Numerator and the Denominator by the Complex Conjugate of the Denominator:

  [tex]\frac{1+i}{1-i}*\frac{1+i}{1+i}=\frac{1+2i+i^{2}}{1-i^{2}}[/tex]

  Remember that i² = -1:

  [tex]\frac{1+2i+i^{2}}{1-i^{2}}=\frac{2i}{2}[/tex]

2. Simplify

find formula for growth of city

y intercept of 300,000 because the function starts here

the slope is 1.08 because it grows by 8 percent each year

population at x year = 300,000(1.08)^x

you can better understand why the x is in the exponent by this example

in one year, it grows 8 percent

300,000 * 1.08 = 324,000

the next year, that previous year grows 8 percent

324,000 * 1.08 = 349,920

300,000 * 1.08 * 1.08 =349,920

300,000 * 1.08^2 = 349,920

in 2 years it grows to that

just do it to the 14th power now

300,000 * 1.08^14 = 881,158

hope this helps :)

if you got any questions just comment

The probability that at least one of them lives more than 87 minutes is 0.87.

Probability

In statistics, the possible way of happening a particular event is called probability.

Given,

Suppose that an experimenter studies the lifespan of members of a colony of bacteria. let t be the lifespan of a randomly chosen member of the colony. suppose the lifespan of the bacteria has an exponential distribution with expected value 100 minutes.

Here we need to find if we choose 5 members of the colony, then what is the probability that at least one of them lives more than 87 minutes.

Here we know that,

Total number of members = 5

Life span = 87 minutes

Expected value = 100 minutes

So, the probability is calculated as,

=> 87 /100

=> 0.87

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Answer:

Step-by-step explanation:

So bill haves 12 quarters and 3 dimes

The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

Twenty-Five Decreased By One-Fifth Of A Number Is Eighteen.

Let the number be 'x'. Then the equation is given as,

25 - (1/5)x = 18

Simplify the equation, then the value of the variable 'x' is calculated as,

25 - (1/5)x = 18

(1/5)x = 25 - 18

(1/5)x = 7

x = 7 (5)

x = 35

The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.

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Answer:  Those both would be 21 with work ....

The final temperature is calculated to be 41.8 degrees Celcius if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa

The final temperature can be calculated by using the combined gas law as follows;

[tex]\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }[/tex]

Here [tex]P_{1}[/tex] and [tex]P_{2}[/tex] represent the initial and final pressure respectively,

[tex]V_{1}[/tex] and [tex]V_{2}[/tex] represent the initial and final volume respectively

[tex]T_{1}[/tex] and [tex]T_{2}[/tex] represent the initial and final temperature respectively

Converting [tex]T_{1}[/tex] to kelvin as follows;

[tex]T_{1}[/tex] = 27 degrees Celcius = 27 + 273 = 300 K

Now the final temperature can be determined by substituting the values in this equation of the combined gas law as follows;

(0.50×10^5)(1.25) / 300 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]

208.333333333 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]

208.333333333 ([tex]T_{2}[/tex]) = (0.82×10^5)(0.80)

[tex]T_{2}[/tex] = (0.82×10^5)(0.80) ÷ 208.333333333

[tex]T_{2}[/tex] = 314.8 K

Converting K to degree Celcius as follows;

[tex]T_{2}[/tex] = 314.8 - 273 = 41.8 degree Celcius

Hence 41.8 degrees Celcius is calculated to be the final temperature.

Although a part of your question is incorrect, you might be referring to this question:

A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?

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CA ⁻¹ is undefined because there are more columns in A ⁻¹ than there are rows in C.

A matrix is a numerical arrangement that is divided into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular array of integers divided into rows and columns. Matrix A, for example, contains two rows and three columns. A matrix is a rectangular organization of a collection of integers into a defined number of rows and columns. When the elements are arranged in a matrix horizontally, it forms the rows of a matrix. When the elements are arranged in a matrix vertically, it forms the columns of a matrix.

CA⁻¹ is undefined because A⁻¹ contains more columns than rows in C.

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The graph of the function square root of the square root of x + 2 in the given domain is given by the image shown at the end of the answer.

The function for this problem is defined as follows:

f(x) = √√x+2

The double square root means that in reality, we have the fourth root of the function, hence the function is then defined as follows:

f(x) = fourth root(x + 2).

The fourth root function is defined for values of x for which the inner term is zero and greater, hence:

x + 2 >= 0

x >= -2.

Then the graph is made over a domain that goes until x = 7, and is given by the image presented at the end of the answer.

(the domain is chosen because it is the domain given by the problem).

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Using the area of the rectangle, we know that the length of the given rectangle is x + 9.

The area is described as the amount of space occupied by a flat (2-D) surface or shape of an object.

Take a marker pen and attract a square on a bit of paper. It is a 2-D figure.

The space the shape occupies on the article is called its Area. Consider your square as being composed of smaller unit squares.

So, we have the area of the rectangle as:

A(x)=2x^2+18x

Area formula: Area = length * width

So, the length of the rectangle will be:

Area = length * width

2x^2+18x = length * 2x

Length = (2x^2 + 18x) / 2x

With the help of long division:

2x√2x² + 18x

Length = x + 9

Therefore, using the area of the rectangle, we know that the length of the given rectangle is x + 9.

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Correct question:
The area of the rectangle is given by the polynomial function A(x)=2x^2+18x. If the width of the rectangle is 2x what is the length?

The relative maxima and minima of the function g(x) are at the point (-4, 22) at the local maxima and at point (4,-124) at the local minima.

Given:

Function g(x) = x^3 - 48x + 4

Take the derivative and set it equal to zero

3x^2 - 48 = 0

x^2 = 48/3 = 16

x = sqr16 = ±4

At x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124

Point (4,-124) is a local or relative minimum

At x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122

The point (-4, 22) is a local or relative maximum

Refer to this complete question:

Find the relative maxima and minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =?

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Answer: 127

Step-by-step explanation: It must add up to 180 degrees

Interior consecutive = congruent

Corresponding = 180

The 95% confidence interval that estimates proportion of 8th graders that are involved in an after school activity (0.745, 0.895) , the correct option is (a) .

In the question ,

it is given that ,

simple random sample of 100 8th graders is taken ,

that means ,

n = 100 ,

also given that , 82% of them are involved with some type of after school activity.

means ; p = 0.82 .

the level of significance (α) = 100 - 95 = 5% = 0.05 .

the critical value=  [tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.025}[/tex] = 1.959964   ......from the Z table .

the lower limit of the 99% confidence interval is = p - [tex]Z_{\alpha /2}[/tex]*SE

and the upper limit for the 99% confidence interval is=  p + [tex]Z_{\alpha /2}[/tex]*SE  .

the standard error is √(p(1-p)/n

= √(0.82(1 - 0.82)/100

= 0.0384

So , the lower limit is ⇒ 0.82 - 1.959964*0.0384

On simplification ,

we get ,

lower limit is = 0.7447006 ≈ 0.745 .

the upper limit is =  p + [tex]Z_{\alpha /2}[/tex]*SE  

= 0.82 + 1.959964*0.0384

On Simplification ,

we get ,

upper limit is = 0.8952994 ≈ 0.895 .

Therefore , the confidence interval is (0.745, 0.895) .

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A triangle can be formed with side lengths 4, 8, 11. Yes, because 4 + 8 > 11

According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.

If the sum of any two sides is greater than the sum of the third, then the difference of any two sides is less than the sum of the third. The sum of any two sides must be greater than the sum of the third. The longest side in a triangle is the side opposite a larger angle.

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Answer: 3(p-5) + 2s

Step-by-step explanation:

Let p represent the henna powder, we know that she has a discount of $5 dollar for every henna powder, and she will buy 3.

So the equation is 3(p-5), plus the two bottles, we get the equation

3(p-5) + 2s

The solution set express the numbers between -5 and 5.

It is a mathematical model contains various elements such as numbers, variables, sign and so on arranged in a sequence order. Different set represents different expression.

The elements of a set that satisfy certain given conditions.

in the question, the set represent the numbers which are > -5 and < 5.

hence, the set indicate the numbers between -5 and 5

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The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

Given that,

In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.

We have to calculate the 95% confidence range for the difference between the two proportions.

We know that,

The 95% confidence interval for difference between two population proportions is given as follows :

[tex]((\bar p_{1} -\bar p_{2})[/tex]±[tex]Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })[/tex]

Here,

p₁ is 0.78

p₂ is 0.68

n₁ is 100

n₂ is 100

Z is 1.96

P is 0.73

Q is 0.27

So,

((0.78-0.68)±[tex]1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })[/tex]

(0.10±0.122)

(0.10-0.122,0.10+0.122)

(-0.022,0.222)

Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

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How you write it is...

m x 10n

The percent of increase in yearly sales is 35%.

A percentage increase means the eventual increase in the quantity in percent form. The percentage increase formula is use to compare growth in a quantity from the initial value to its final value over a period of time.

The formula for getting a percentage increase is "[(Final Value - Initial Value)/Initial Value] × 100"

Initial value = 720,460 pictures

Final value = 972,621 pictures.

The percentage increase:

= [(972,621 - 720,460] / 720,460} * 100

= 0.35 * 100

= 35%

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The rate of change in the profit for the five months earned by the given small business is $2750.

The rate of change explains the relationship between two quantities.

Consider two quantities such profit and time in a small business.

Then, the rate of change in the profit is calculated by the ratio of change in the profit for the particular period to the time. I.e.,

rate of change in the profit = (change in the profit)/time

or

r = (p2 - p1)/(t2 - t1)

Where p1 is the profit gained at time t1 and p2 is the profit gained at time t2.

Given that, a small business earns a profit of $6500 in January (the first month of the year) and $17,500 in May (the fifth month of the year).

So, here p1 = $6500; p2 = $17,500; t1 = 1; and t2 = 5

Then, the rate of change in the profit for this period is

r = (17,500 - 6500)/(5 - 1)

 = 11000/4

 = 2750

Therefore, the rate of change in the profit for the five months is $2750.

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