f there are 42 boys and 24 girls in a room, fill out all of the possible ratios of boys to girls that could be made.

Answer:

1. 2

2. 7

3. 17

4. 18

5. 83

6. 79

7. 7

8. 7

9. 19

10. 54

11. 26

12. 16

13. 9

14. 4

15. 3

16. 7

17. 5

18. 5

19. 30

20. 14

21. 20

22. 27

Step-by-step explanation:

Hope this helps!

The equations of the osculating circles of the parabola y = (1/2)x^2 at the points (0,0) and (1, 1/2) are x^2 + y^2 = 0 and (x-1/2)^2 + (y-1/4)^2 = 1/16, respectively.

To find the equations of the osculating circles, we need to determine the center and radius of each circle. The osculating circle at (0,0) is tangent to the parabola at that point. Since the radius of the circle is zero, the equation is simply x^2 + y^2 = 0.

At the point (1, 1/2), the osculating circle is tangent to the parabola as well. We can start by finding the slope of the tangent line at this point, which is the derivative of the parabola. Differentiating y = (1/2)x^2 with respect to x, we get dy/dx = x. Evaluating this at x = 1 gives us the slope of the tangent line as 1.

The center of the osculating circle can be found by moving along the normal line from the point (1, 1/2) by a distance equal to the radius of the circle. Since the radius is perpendicular to the tangent line, we can use the slope of the tangent line to find the slope of the normal line, which is -1 (the negative reciprocal of 1).

Using the point-slope form of a line, we have y - (1/2) = -1(x - 1), which simplifies to y = -x + 3/2. Solving this equation simultaneously with the parabola equation, we find the intersection points of the parabola and the normal line.

Substituting y = -x + 3/2 into y = (1/2)x^2, we get (-x + 3/2) = (1/2)x^2. Rearranging this equation, we have (1/2)x^2 + x - 3/2 = 0. Solving this quadratic equation, we find x = 1/2 or x = -3.

Substituting these values back into the normal line equation, we can find the y-coordinates of the intersection points. When x = 1/2, y = -1/2 + 3/2 = 1, and when x = -3, y = 3/2.

Now, we can use the midpoint formula to find the center of the osculating circle, which is the average of the intersection points: (1/2, (1 + 3/2)/2) = (1/2, 5/4) = (0.5, 1.25).

The radius of the osculating circle can be found by the distance formula between the center and one of the intersection points: r = sqrt((1/2 - 1/2)^2 + (5/4 - 1)^2) = sqrt(1/16) = 1/4.

Putting it all together, the equation of the osculating circle at (1, 1/2) is (x - 1/2)^2 + (y - 1/4)^2 = 1/16.

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Answer:

342:9, 38 cans per bag

Step-by-step explanation:

Answer:

it is the first answer because if you add them together you will get the answer.

Step-by-step explanation:

and the answer is the first one, make sure to show your work!

The limit of a function as x approaches c does not exist when the function approaches -3 from the left of c and 3 from the right of c.

To understand this, let's go through it step by step:

1. A limit of a function exists if the function approaches a specific value as x approaches a certain point (c).
2. If the function approaches different values from the left and the right of c, the limit does not exist.
3. In your question, the function approaches -3 from the left of c (written as lim(x->c-) = -3) and 3 from the right of c (written as lim(x->c+) = 3).
4. Since these two values (-3 and 3) are different, the limit of the function as x approaches c does not exist.

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Answer:

The class period was 45 minutes long

Step-by-step explanation:

as you can see 5/8 of the class is 25 minutes, meaning that 1 = 5 if we multiply 8 times 5, it gives 45.

Answer: I believe your answer is 40 minutes for Brandi's class period.

Step-by-step explanation: For every 5 minutes she spends in class, it is 1/8 of her total period of class time. For example, she spent 25 minutes and has 15 minutes or 3/8 left of class.

Answer:

10

Step-by-step explanation:

30/3 = 10

If all bags have the same number of apples, then each bag has 10 apples.

Answer: 10

Answer:

10 apples

Step-by-step explanation:

Given:

30 apples Total

3 Bags

Note:

Hence, Apples/Bags = Solution

Solve:

30/3 = 10

Thus, Aiden have 10 apples in each bag.

[RevyBreeze]

Answer:

m=15/14

Step-by-step explanation:

y2-y1

x2-x1

(3, 0) (-11, -15)

x1 y1   x2   y2

-15-0

-11-3          = -15/-14 m=-15/-14 = 15/14

Answer:

Ms. Cohen can buy 12 poxes of crayons.

Step-by-step explanation:

Ms. Cohen can buy 12 boxes of crayons with the rest of her money. In the question it states she only wants to buy 1 poster not more than one so if she buys 1 poster that's

30-5-25

and than you can just count up by 2 till you get the closest to 25

25-24=1$

24/2 = 12

Hope this helps.

The number of boxes of crayons that can be bought is needed.

The number of boxes that can be bought at most is 12.

Let \(x\) be the number of boxes of crayons

Total amount of money = $30

Cost of one box = $2

Cost of poster = $5

The linear inequality will be

\(2x+5\leq 30\\\Rightarrow x\leq\dfrac{30-5}{2}\\\Rightarrow x\leq 12.5\)

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Answer:

-21

Step-by-step explanation:

(m*n)/p + ( -n )

4(9)/-3 + (-9) = (36/-3) - 9

-12 - 9 = -21

Answers

The zeros of a function represent the x-intercept(s) when the function is graphed. The zeros of a function represent the root(s) of a function.

Answer:

(-4,-52)

(1/12,-3)

(1/3,0)

(0,-4)

(3,32)

Step-by-step explanation

i think thats right

The expression for the area under the graph of f(x) = 9 + sin²(x) using the right endpoints as a limit is

\(A = lim(n → ∞) Σ[i = 1 to n] (9 + sin²(x_i))Δx.\)

To find the area under the graph of a function using the right endpoints, we divide the interval into smaller subintervals and approximate the area of each subinterval with a rectangle. The width of each subinterval is determined by (b - a)/n, where n is the number of subintervals. The right endpoint of each subinterval is used to determine the height of the rectangle, which corresponds to the function value at that endpoint. Taking the limit as the number of subintervals approaches infinity gives us the exact area under the curve. In this case, the expression for the area under the graph of f(x) = 9 + sin²(x) would involve summing the areas of all the rectangles formed by the right endpoints and taking the limit as n tends to infinity.

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Answer:

1 / (x+5)

Step-by-step explanation:

Factor the denominator

(x+1)/ (x+5)(x+1)

Cancel both (x+1)

=1/(x+5)

The point (11,11) will lie on the graph of the function f(x) = IxI

What is coordinate?

The x-coordinate informs us of a point's separation from the y-axis, which is the vertical axis. The abscissa is another term for the x-coordinate. The y-coordinate shows how far a point is from the horizontal axis, or x-axis. The term "ordinate" also applies to the y-coordinate.

the function: f(x) = IxI

The function will have every positive and negative integer contained within itself.

So coordinates of another point with the same y value (11,11) will lies on the graph so as (-11,11).

Hence point (11,11) will lie on the graph of the function f(x) = IxI

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Answer:yes

Step-by-step explanation:

Because x =24 and y=17 are both less than 25

Answer:

AB = 15

BD = 5

Step-by-step explanation:

Statement__________________|          Reason______________

1) m<1 = m<2, AB = AC                    |   Given

2) AD = AD                                      | Reflexive property

3) ΔABD = ΔADC                           | Side - angle - side

4) AB = AC =  15                               | Corresponding part of congruent triangles     .                                                     |  are congruent

5) BD = DC = 5                              | Corresponding parts of congruent triangles   .                                                    |    are congruent

Answer:

Step-by-step explanation:

AB = AC and AC = 15 (both given)

AB≅AC, ∠1≅∠2, AD≅AD (first two given and the last one is the common side)

BD≅DC as corresponding sides

BD = DC and DC = 15

Answer:

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

Step-by-step explanation:

hope this helps you :)

Answer:

a. 6

b. 0.24

c. 0.46

d. 0.86

Answer:

No

Step-by-step explanation:

The biggest is the third side and the other two triangles have to bigger than that side and 8.0 plus 3.5 equals 11.5.

The change in total revenue brought about by a 16 unit increase in Q is -1.5.

(a) (i) To differentiate y = 4x⁴ − 2x² + 28 with respect to x, we apply the power rule of differentiation. We have:
dy/dx = 16x³ - 4x

(ii) To differentiate f(x) = 1/x² + √x³ with respect to x, we can apply the chain rule of differentiation. We have:
f(x) = x⁻² + x³/²
df/dx = -2x⁻³ + 3/2x^(3/2)

(iii)(a) The slope of the function y = 3x² − 4x + 5 at x = 4 and x = 6 can be found by differentiating the function with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
At x = 4,
dy/dx = 6(4) − 4 = 20
At x = 6,
dy/dx = 6(6) − 4 = 32

(b) The second-order derivative of the function y = 3x² − 4x + 5 at x = 4 can be found by differentiating the function twice with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
d²y/dx² = 6
The second-order derivative at x = 4 is 6. The slope of the function at x = 4 is positive, so we would expect the second-order derivative to be positive.

(b) (i) The demand equation is given by: P = aQ⁻² + b
The marginal revenue function is the derivative of the total revenue function with respect to Q. The total revenue function is:
R = PQ
Differentiating both sides with respect to Q gives:
dR/dQ = P + Q(dP/dQ)
Since P = aQ⁻² + b,
dP/dQ = -2aQ⁻³
Substituting into the equation for dR/dQ, we have:
dR/dQ = aQ⁻² + b + Q(-2aQ⁻³)
dR/dQ = aQ⁻² + b - 2aQ⁻²
dR/dQ = (b - aQ⁻²)
Therefore, the marginal revenue function is:
MR = b - aQ⁻²

(ii) To calculate the marginal revenue when Q = 3b, we substitute Q = 3b into the marginal revenue function:
MR = b - a(3b)⁻²
MR = b - ab²/9
To find the change in total revenue brought about by a 16 unit increase in Q, we can use the formula:
ΔR = MR × ΔQ
where ΔQ = 16
ΔR = (b - ab²/9) × 16
To show that ΔR = -1.5, we need to use the given relationship a > 0 and b > 0. Since a > 0, we know that ab²/9 < b. Therefore, we can write:
ΔR = (b - ab²/9) × 16 > (b - b) × 16 = 0
Since the marginal revenue is negative (when b > 0), we know that the change in total revenue must be negative as well. Therefore, we can write:
ΔR = -|ΔR| = -16(b - ab²/9)
Since ΔQ = 16b, we have:
ΔR = -16(b - a(ΔQ/3)²)
ΔR = -16(b - a(16b/3)²)
ΔR = -16(b - 256ab²/9)
ΔR = -16/9(3b - 128ab²/3)
ΔR = -16/9(3b - 16(8a/3)b²)
ΔR = -16/9(3b - 16(8a/3)b²) = -16/9(3b - 16b²/9) = -16/9(27b²/9 - 16b/9) = -16/9(3b/9 - 16/9)
ΔR = -16/9(-13/9) = -1.5

Therefore, the change in total revenue brought about by a 16 unit increase in Q is -1.5.

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Scrooge McDuck would most likely keep punishing his employees when they're late; it's working.

So, the correct answer is D.

Less than Hypothesis testing is a statistical hypothesis test where the alternative hypothesis is formed as <, while the null hypothesis is formed as >=.

Therefore, when Scrooge McDuck utilized the less than hypothesis testing and found that at an alpha of .05 he rejects the null hypothesis, it means that the p-value obtained from the test was less than 0.05, and thus he had enough statistical evidence to reject the null hypothesis and accept the alternative hypothesis.

It indicates that punishing the employees harder when they are late is working and they are more likely to come to work on time. Therefore, he would most likely keep punishing his employees when they're late; it's working.

Hence, the answer is D.

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Answer: 25 rulers

Step-by-step explanation:

19.75/.79=25

Answer:

25

Step-by-step explanation:

Divide the total money, by the cost of each product:

$19.75/$0.79=25

a. the linear equation that expresses the costs (y) in terms of the number of cups (x) is C(x) = 0.25x + 15 b. approximately 430 cups of coffee are produced if the cost of production is $122.50.

A. We are given that the relationship between the costs (y) to produce x cups of coffee is linear. Let's denote the cost as C(x) and the number of cups as x. We can use the information provided to find the equation of the line.

We have two data points: (50, $27.50) and (350, $102.50).

Using the point-slope form of a linear equation, we can determine the equation as follows:

slope = (change in y) / (change in x) = (102.50 - 27.50) / (350 - 50) = 75 / 300 = 0.25

Now, we can choose one of the points to find the y-intercept (b) using the equation y = mx + b. Let's use the point (50, $27.50):

27.50 = 0.25 * 50 + b

b = 27.50 - 12.50

b = 15

Therefore, the linear equation that expresses the costs (y) in terms of the number of cups (x) is:

C(x) = 0.25x + 15

B. We are asked to find the number of cups of coffee produced if the cost of production is $122.50. We can use the linear equation we obtained in part A and substitute the cost (y) with $122.50 to solve for x:

122.50 = 0.25x + 15

Subtracting 15 from both sides:

107.50 = 0.25x

Dividing both sides by 0.25:

x = 107.50 / 0.25

x ≈ 430

Therefore, approximately 430 cups of coffee are produced if the cost of production is $122.50.

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Answer:

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Area of the square = side²

Area

\( = {8}^{2} \\ = 64 \: m {}^{2} \)

✏ The area of the square is D. 64 square metres.

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