at a local fitness center, members pay $20 membership fee, and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same.

The average of the 3 points A, B, and C is 1/3

We know that for a set of N values {x₁, x₂, ..., xₙ} the average is:

Average = (x₁ + ... + xₙ)/N

Assuming that all the weights are 1.

Here the values (y values) for the 3 points are:

A = -9

B = 2

C = 8

The average of these 3 points is:

average = (-9 + 2 + 8)/3

average = 1/3

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she sold 2 trays, and each tray contains 12 meat slices and 19 cheese slices

Explanation

Step 1

Let

Each party tray contained the same number of meat slices,so

the total number of party trays and slices of meat and cheese Doris sold is

it means she sold 2 trays, and each tray contains 12 meat slices and 19 cheese slices

I hope this helps you

1.a The probability of throwing at most 2 heads in 5 throws is more probable.

1.b A total of 2^4 = 16 outcomes.

1.c The probability of selecting a black ball, a red ball, and then another black ball is 5/56.

1a. Probability of throwing exactly 15 heads in 20 throws

Probability of getting a head is p = 0.65, and the probability of getting tails is q = 1 - 0.65 = 0.35.

Let X be the random variable which counts the number of heads in 20 throws.

Then X follows the binomial distribution B(20, 0.65).P(X = 15) = 20C15 * 0.65^15 * 0.35^5= 0.16

Probability of throwing at most 2 heads in 5 throws

Let Y be the random variable which counts the number of heads in 5 throws.

Then Y follows the binomial distribution B(5, 0.65).P(Y ≤ 2) = P(Y = 0) + P(Y = 1) + P(Y = 2)

                                                                                                  = 0.01 + 0.08 + 0.25

                                                                                                  = 0.34

Therefore, the probability of throwing at most 2 heads in 5 throws is more probable.

1b. Suppose we flip a fair coin 4 times.

For what combination(s) do there exist exactly 3 permutations?

There are a total of 2^4 = 16 outcomes.

The combinations that exist in exactly 3 permutations are HTTH, HTHT, THHT, THTH, and HHTT.

1c. Probability of selecting a black ball, a red ball, and then another black ball We want to compute the probability of pulling out 3 balls, without replacement, from a box with 5 red balls and 3 black balls.

The total number of ways of pulling out 3 balls is 8C3.

The probability of pulling out a black ball on the first draw is 3/8.

The probability of pulling out a red ball on the second draw is 5/7.

The probability of pulling out another black ball on the third draw is 2/6 = 1/3.

So, the required probability is (3/8) * (5/7) * (1/3) = 5/56.

Therefore, the probability of selecting a black ball, a red ball, and then another black ball is 5/56.

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The coordinates for the local extrema are (0, 0) and (2/3, 4e^(-2)).

To find the coordinates for any local extrema of the function h(x) = 3x^2e^(-3x), we need to find the critical points by taking the derivative of h(x) and setting it equal to zero.

Step 1: Find the derivative of h(x)

h'(x) = d/dx (3x^2e^(-3x))

To differentiate the function, we can use the product rule and the chain rule:

h'(x) = 6xe^(-3x) + 3x^2(-3e^(-3x))

= 6xe^(-3x) - 9x^2e^(-3x)

= e^(-3x)(6x - 9x^2)

Step 2: Set h'(x) = 0 and solve for x

e^(-3x)(6x - 9x^2) = 0

We have two factors: e^(-3x) = 0 and 6x - 9x^2 = 0.

For e^(-3x) = 0, there are no real solutions since the exponential function is always positive.

For 6x - 9x^2 = 0, we can factor out x:

x(6 - 9x) = 0

Setting each factor equal to zero:

x = 0 and 6 - 9x = 0

Solving the second equation:

6 - 9x = 0

9x = 6

x = 6/9

x = 2/3

So the critical points are x = 0 and x = 2/3.

Step 3: Find the corresponding y-values

To find the corresponding y-values, we substitute the critical points into the original function h(x).

For x = 0:

h(0) = 3(0)^2e^(-3(0))

= 0

For x = 2/3:

h(2/3) = 3(2/3)^2e^(-3(2/3))

= 4e^(-2)

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The inverse function is the original function reflected over y=x option (B) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a statement:

The graph of an inverse function compare to the original function:

As we know, every function with domain real numbers can be plotted on graph paper or a coordinate plane.

Let f(x) = ax + b

or

y =ax + b

a and b are the real numbers

To find the inverse of a function interchange the value of x and y

f⁻¹ = x = ay + b

If we plot the above two functions we will see that f(x) is the mirror image of f⁻¹ over the line y = x.

Thus, the inverse function is the original function reflected over y=x option (B) is correct.

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Answer:

13hours and aprox. 15 min

Step-by-step explanation:

199=15*x

199/15=13.26

The equation of the conic section  is x² + y² + 10x + 2y - 20 = 0

The equation of a circle is x^2 + y^2 - 4y - 21 = 0

A circle is a two-dimensional geometric shape that consists of a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius.

A circle can be defined by its center point and radius or by its circumference, which is the distance around the perimeter of the circle. The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14.

The center of the circle is (-5,-1) and its radius is the distance from the center to any point on the circle. Using the distance formula, we can find the radius:

r = √((0 - (-1))² + (-10 - (-5))²) = √(1 + 25) = √(26)

So, the equation of the circle in standard form is:

(x + 5)² + (y + 1)² = 26

Alternatively, in general form, it can be written as:

x² + y² + 10x + 2y - 20 = 0

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The equations are x – y^2 and x – 20y – y^2. The task is to find the volume of the solid generated by revolving the region bounded by the graphs of the equations around the y-axis and the line x = 102. We will consider these cases separately.

Case 1: Revolving the region about the y-axisTo do this, we can make use of the disk method. This means we’ll slice the solid perpendicular to the axis of revolution (y-axis) and integrate over the range of x that intersects both curves. Hence, the volume V1 of the solid is given by:\($$V_1 = \int_{y_1}^{y_2} \pi [R^2(y) - r^2(y)] dy$$\)Where R(y) and r(y) represent the outer and inner radii respectively.

Thus, we can write the volume of the solid as:$$V_2

=\(\int_{100}^{104} \pi \left[\left(\sqrt{102 - x - (x - 102)^2}\right)^2 - \left(\frac{1}{20} [x - (x - 102)^2 - 102]\right)^2\right] dx$$$$= \int_{100}^{104} \pi \left[\frac{20}{441}(x-104)^2\right] dx\)

= \(\frac{4000 \pi}{63}$$\)Hence, the total volume of the solid generated by revolving the region about both lines is given by:\($$V = V_1 + V_2 = \frac{104000 \pi}{3} + \frac{4000 \pi}{63}\)

= \(\frac{437200 \pi}{63}$$\).

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The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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Answer: y =\(\frac{ax - 2}{9x}\)

Step-by-step explanation: look for the lcm

a=\(\frac{9xy + 2}{x}\)

cross multiply

ax =9xy + 2

ax - 2 = 9xy

divide both sides by 9x

\(\frac{ax - 2}{9x} = \frac{9xy}{9x}\)

y=\(\frac{ax - 2}{9x}\)

To calculate the average speed for the time period [1,2], we substitute the value h=1 into the expression v_ave=69−1.86h, and then evaluate it. This will give us the average speed over that specific time interval.

The formula for average speed is given by v_ave = (distance traveled) / (time taken). In this case, we are given the expression v_ave = 69−1.86h, where h represents the time period.

To find the average speed for the time period [1,2], we substitute h=1 into the expression:

v_ave = 69 - 1.86(1)

Simplifying the expression, we get:

v_ave = 69 - 1.86

Evaluating the subtraction, we have:

v_ave = 67.14

Therefore, the average speed for the time period [1,2] is 67.14. This means that, on average, the object traveled at a speed of 67.14 units per unit of time during that interval.

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Answer:

1. 25 cents per ounce

2. 4 ounces.

3. 10x=$2.50 and $2.50x=10

4. I need picture

Step-by-step explanation:

The cost of popcorn per ounce will be $0.25, the amount of popcorn you can buy per dollar will be 4 ounces per dollar, and the equation that represents the cost will be c = 0.25p.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

Elena went to a store where you can scoop your own popcorn and buy as much as you want. She bought 10 ounces of spicy popcorn for $2.50.

The cost of popcorn per ounce will be

⇒ $2.50 / 10

⇒ $0.25

The amount of popcorn you can buy per dollar will be

⇒ 10 / $2.50

⇒ 4 ounces per dollar

Let p for ounces of popcorn and c for cost in dollars. Then the equation is given as,

c = 0.25p

The graph of the equation is attached below.

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In a conditional statement, the statement that immediately follows the word then is generally referred to as a conclusion.

In Mathematics, a conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement typically has the form "if P then Q."

Where:

P and Q represent sentences or statements.

In Science, a hypothesis is primarily considered to be a tentative or an educated guess and it can be defined as a testable explanation for an observation or a specific experimentation (scientific) problem, especially by using the "if . . . then . . . because" format..

In conclusion, an example of a conditional statement is "If the sidewalks are wet, then it is because of an erosion/irrigation."

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Answer:

The cases are when a-b = 0 and when a = b

Step-by-step explanation:

An expression is termed as undefined (not to exist) if the denominator of the expression is zero. Given the expression a/a-b, the denominator of the expression is a-b. For the expression to be undefined, the expression at the denominator must be equal to zero i.e a-b = 0

If a - b = 0, then a = 0+b; a = b

Another case for the function not to exist is if a = b

Answer:

I just need points but sorry I can't help u I'm not smart

The three characteristics of an absolute value:

1) The absolute value of any number is always non-negative.

2) The domain is all real numbers and  range is all whole numbers.

3) The graph is V shaped, symmetric about the y -axis and makes a right angle at the origin.

As we know that an absolute value of any number is nothing but the distance from zero of that a number is on the number line.

The absolute value of any number is always positive.

i.e., for any number p,

|-p| = p and |+p| = p

From definition of absolue value the domain is all real numbers and  range is all real numbers greater than or equal to zero.

The graph of the absolute value function is V shaped and symmetric about the y -axis.

The graph of absolute value function f(x) = |x| makes a right angle at the origin.

The graph lies completely above the x-axis.

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Answer:22.5

Step-by-step explanation:

6/4= 1.5= pages per minute, times 15= 22.5

Answer:

I got the same thing. 22.5

Step-by-step explanation:

6/4 = 1.5

1.5 = pages per minute

1.5(15) = 22.5

Answer:

x = ± 2

Step-by-step explanation:

To find the x- intercepts let y = 0 , that is

4x² - 16 = 0 (add 16 to both sides )

4x² = 16 ( divide both sides by 4 )

x² = 4 ( take the square root of both sides )

x = ± \(\sqrt{4}\) = ± 2

The x- intercepts are x = - 2 and x = 2

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

The value of x is 42.9

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

The ratio of corresponding sides of similar triangles are equal. Therefore:

x/81.9 = 35.2/67.2

= 67.2x = 35.2 × 81.9

67.2x = 2882.88

divide both sides by 67.2

x = 2882.88/67.2

x = 42.9

therefore value of x is 42.9

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Answer:

Least to greatest: (D), 6/25, 0.243, 24.5%,

Step-by-step explanation:

6/25=0.240

0.243=0.243

24.5%=0.245

Answer:

20.4 pounds

Step-by-step explanation:

Given that:

Weight of a coin = 7^-2 pounds

Weight of 1000 coins will be :

Weight per coin * number of coins

7^-2 * 1000

0.0204081 * 1000

= 20.408 pounds

= 20.4 pounds

The correct option is False. The standard formulas for the derivatives of sine and cosine are true when the angle is in radians. These formulas are derived based on the properties of the trigonometric functions in the context of radians. The derivatives of sine and cosine with respect to an angle measured in radians are as follows:

\(\[\frac{d}{dx}(\sin(x)) = \cos(x)\]\)

\(\[\frac{d}{dx}(\cos(x)) = -\sin(x)\]\)

If the angle is measured in degrees, these formulas would not hold true. To differentiate trigonometric functions when the angle is measured in degrees, conversion factors and additional adjustments would be necessary.

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Answer:

24\(x^{2}\) - 2x - 15

Step-by-step explanation:

f(x) = 4x + 3

g(x) = 6x - 5

(4x + 3) (6x - 5)

24\(x^{2}\) - 20x + 18x - 15

24\(x^{2}\) - 2x - 15

Answer:

Statistical inference

Step-by-step explanation:

Answer:

∠KIJ = \(45.8\)°

Step-by-step explanation:

The measure of a straight line is 180°.This means that we simple have to subtract 134.2° from 180°:

\(180-134.2=45.8\)°

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

piggy bank:

quarters and dimes = $5.10

# quarters and dimes = 27

Step 02:

system of equations:

quarters = q

dimes = d

equation 1:

q + d = 27

equation 2:

0.25q + 0.10d = 5.10

The answer is:

q + d = 27 eq.1

0.25q + 0.10d = 5.10 eq.2

Answer:

the fifth number is 70

Step-by-step explanation:

mean (average) of first 5 numbers =50 , Then sum of this 5 numbers = 50*5 =250.

The mean  of 4 numbers = 45 . Sum 4 numbers = 45*4 = 180

the fifth number is 250-180=70

(180 +70)/5=50 which is the mean