Elizabeth won a $300 gift certificate at silver gym. A membership costs $15 a month and has a one- time fee of $50. Complete the equation that models the number of months,x, her gift certificate is will pay for a Silver gym.

Answer:

B

Step-by-step explanation:

half × base × height

height × length

Answer: B

Step-by-step explanation:

Triangle)

25 - 7 = 18

\(A=\frac{1}{2}(b)(h)\\A=\frac{1}{2}(18)(17)\\A=153cm^2\)

Rectangle)

\(A=b(h)\\A=7(17) = 119cm^2\)

Total)

\(153+119=272 cm^2\)

Answer: angle 5 =  55 degrees, angle 6 = 125 degrees, angle 7 = 55 degrees, angle 8 = 125 degrees

Answer:

When x=4, ln x-ln y=y-4, so ln 4-ln 4=4-4, which is true. Therefore, when x=4, y=4, and dy/dx=0.

Step-by-step explanation:

So, when x = 4, the value of the differentiable function dy/dx is 0.

A differentiable function of one real variable is one that has a derivative at each point in its domain. In other words, a differentiable function's graph has a non-vertical tangent line at each interior point in its domain.

Here,

Given the equation ln x - ln y = y - 4, we can rearrange it to get ln(x/y) = y - 4. Taking the derivative of both sides with respect to x using the chain rule:

d/dx (ln(x/y)) = d/dx (y - 4)

(1/x) (dx/dx) - (1/y) (dy/dx) = dy/dx

dy/dx = (1/y) (dx/dx) + (1/x) (dy/dx) = (1/y) + (1/x) (dy/dx)

Rearranging and solving for dy/dx:

(x/y) (dy/dx) = (1/y) - (1/x)

dy/dx = (x/y^2) (1/x - 1/y) = (x/y^2) (1/x - 1/y)

We can substitute x = 4 and y = 4 into the expression to find the value of dy/dx when x = 4:

dy/dx = (4/16) (1/4 - 1/4) = 0

So, the value of differentiable function dy/dx when x = 4 is 0.

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Step-by-step explanation:

f(x + 1) = (5/2)*f(x)

f(x + 1) = 2.5*f(x), f(1) = 3.2

f(2) = 2.5f(1) = 2.5*3.2 = 8

f(3) = 2.5f(2) = 2.5*8 = 20

f(4) = 2.5f(3) = 2.5*20 = 50

f(5) = 2.5f(4) = 2.5*50 = 125

Answer:

Step-by-step explanation:

60 degree, since bd is bisector so ABC and abd value will be same

Answer:

60 degrees

Step-by-step explanation:

A triangle is 180 degrees and there is already 40 and 80 degrees.

So... 180-80-40=60 degrees.

Hope this helps :D

Answer:

2

Step-by-step explanation:

75/8=5

(75/8)/5=5/5

3 3/4=2

Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

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Given: An equation:

Solving for x:

The correct answer is:

scatter plot with points at (1,  6), (2,  4), (3, 2), (3, 6), (4, 1), (5, 4), (6, 2), and (9, 2), with a line passing through the coordinates (1, 6) and (5, 4).

What is the scatter plot?

A scatterplot shows the relationship between two quantitative variables measured for the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.

We have given,

scatter plot with points at

(1,  6), (2,  4), (3, 2), (3, 6), (4, 1), (5, 4), (6, 2), and (9, 2),

The first option shows a line passing through the coordinates (1, 6) and (5, 4) which appears to fit the data.

Therefore, the correct answer is:

scatter plot with points at (1,  6), (2,  4), (3, 2), (3, 6), (4, 1), (5, 4), (6, 2), and (9, 2), with a line passing through the coordinates (1, 6) and (5, 4).

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Answer:

I think its no solution

Step-by-step explanation:

Answer:

x>12

Step-by-step explanation:

i worked it out as quick as possible.. hope this helps :)

The probability that 45 or more people in this sample have consumed alcoholic beverages is 0.0516, or about 5.16 percent.

The probability that 45 or more people in a sample have consumed alcoholic beverages can be determined using normal distribution, as the sample size is sufficiently large. The distribution is also normal because of the large sample size. Using the normal distribution table or a calculator, the probability can be determined. The formula is:

P(X > 44.5) = 1 - P(X ≤ 44.5) = 1 - 0.9484 = 0.0516, approximately.

(Note: We use 44.5 because it is the midpoint of the interval 44.5 to 45.5, which is the one that includes 45.)

Therefore, the probability that 45 or more people in this sample have consumed alcoholic beverages is 0.0516, or about 5.16 percent.

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Answer:

x^2y^-4

Step-by-step explanation:

Answer:

i think the answer is x²y/6

Answer: The highest common factor of 91, 112 and 49 is 7

hope this helps :)

Answer:

The slope is 5/12

Step-by-step explanation:

To find the slope between any two points, we can use the slope formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Where (x₁, y₁) and (x₂, y₂) are our two points.

We have the two points (-9, 1) and (3, 6).

Let’s let (-9, 1) be (x₁, y₁) and let (3, 6) be (x₂, y₂). Substitute appropriately:

\(\displaystyle m=\frac{6-1}{3-(-9)}\)

Evaluate:

\(\displaystyle m=\frac{5}{12}\)

So, the slope of the line that contains the two points (-9, 1) and (3, 6) is 5/12.

Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

\(-\frac{12}{16} + \frac{11}{12}\)

take lcm of the denominator

lcm=48

\(\frac{-12*3 + 11*4}{48}\)

\(\frac{-36 + 44}{48}\)

\(\frac{8}{48}\)

\(\frac{1}{6}\)

Answer:

\(=\frac{1}{6}\)

Step-by-step explanation:

\(-\frac{12}{16}+\frac{11}{12}\)

the lcm of 16 and 12 is 48

\(-\frac{12}{16} =-\frac{36}{48}\)

\(\frac{11}{12} =\frac{44}{48}\)

\(-\frac{36}{48} +\frac{44}{48}=\frac{8}{48}\)

\(=\frac{1}{6}\)

Hope this helps

Answer:

250

Step-by-step explanation:

We can approximate that the scientists counted \(\frac{18}{30}=\frac{3}{5}\) of the elk.

So, the best estimate of the elk population is \(150(5/3)=250\).

Answer:1,250

Step-by-step explanation:

Answer:

evaluate C2 + 4a - b

-2 +4(-5)-3

4=-2-5-3

4=4

=4-4

=0

Answer:

The triangle, square, and trapezoid are the following:

The limit of (f(x) + 1) / sin(x) as x approaches 0 is 0, the approximation for f(1/2) using Euler's method with two steps is 19/32 and the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1.

(a) To find the limit of (f(x) + 1) / sin(x) as x approaches 0, we can first rewrite the given differential equation as:

dy / dx = y²  (2x + 2)

Separating variables, we get:

dy / y²  = (2x + 2) dx

Integrating both sides, we have:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side gives:

-1 / y = x²  + 2x + C1

where C1 is the constant of integration.

Since we have the initial condition f(0) = -1, we substitute x = 0 and y = -1 into the above equation:

-1 / (-1) = 0²  + 2(0) + C1

1 = C1

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Now, to find the limit (f(x) + 1) / sin(x) as x approaches 0, we substitute x = 0 into the particular solution equation:

f(0)(0²  + 2(0) + 1) + 1 = 0

-1(0) + 1 = 0

1 = 0

Therefore, the limit of (f(x) + 1) / sin(x) as x approaches 0 is 0.

(b) Using Euler's method, we approximate the value of f(1/2) starting at x = 0 with two steps of equal size. Let's choose the step size h = 1/4.

First step:

x0 = 0, y0 = f(0) = -1

Using the differential equation, we have:

dy / dx = y²  (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (-1)²  (2(0) + 2) (1/4)

Δy ≈ 1/2

Next, we update the values:

x1 = x0 + Δx = 0 + 1/4 = 1/4

y1 = y0 + Δy = -1 + 1/2 = 1/2

Second step:

x0 = 1/4, y0 = 1/2

Using the differential equation again:

dy / dx = y^2 (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (1/2)²  (2(1/4) + 2) (1/4)

Δy ≈ 3/32

Updating the values:

x2 = x1 + Δx = 1/4 + 1/4 = 1/2

y2 = y1 + Δy = 1/2 + 3/32 = 19/32

Therefore, the approximation for f(1/2) using Euler's method with two steps is 19/32.

c)To find the particular solution to the differential equation dy/dx = y^2 (2x + 2) with the initial condition f(0) = -1, we can solve the separable differential equation.

Separating variables, we have:

dy / y² = (2x + 2) dx

Integrating both sides:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side:

-1 / y = x²  + 2x + C

where C is the constant of integration.

To find the particular solution, we substitute the initial condition f(0) = -1:

-1 / (-1) = 0²  + 2(0) + C

1 = C

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Therefore, the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1

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The probability that all red balls will be selected is 0.0083.

The total number of ways to select 6 balls from the jar is 12C6, which is equal to 495. The number of ways to select only red balls is 4C6, which is equal to 1. So, the probability of selecting all red balls is 1/495 = 0.0083. This means that only a small chance of selecting all red balls exists among all possible selections of 6 balls.

Probability is a mathematical concept that provides a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain to occur.

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Answer:

Step-by-step explanation:

-80

8.6 8.63 8.66 8.611 8.641 8.691

The interval where the product will at least break even is \($\left[\begin{array}{cc}\text { Solution: } & x \leq-5 \\ \text { Interval Notation: } & (-\infty,-5]\end{array}\right]$\)

Given C= 305 x+1350C

R=60 x

To find the interval where the product will at least break even we must have \($R(x) \geq c(x)$\)

\($\Rightarrow \quad 35 x \geq 305 x+1350$\)

\($$35 x \geq 305 x+1350$$\)

Subtract 305 x from both sides

\($$35 x-305 x \geq 305 x+1350-305 x$$\)

Simplify

\($$-270 x \geq 1350$$\)

Multiply both sides by - 1 (reverse the inequality)

\($$(-270 x)(-1) \leq 1350(-1)$$\)

Simplify

\($$270 x \leq-1350$$\)

Divide both sides by 270

\(\frac{270 x}{270} \leq \frac{-1350}{270}$$\)

Simplify

\($$x \leq-5$$\)

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

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To sketch the region enclosed by the curves y = x^3 - 4x and y = 12x and determine the appropriate method of integration. By evaluating the definite integral ∫[-4 to 4] (12x - (x^3 - 4x)) dx, we can calculate the area of the region enclosed by the given curves.

The curves intersect when x^3 - 4x = 12x. Simplifying this equation, we get x^3 - 16x = 0. Factoring out x, we have x(x^2 - 16) = 0, which gives us x = 0 and x = ±4 as the intersection points.

To determine whether to integrate with respect to x or y, we can observe that the region is vertically bounded by the curves. Therefore, we'll integrate with respect to x.

To find the area of the region, we'll integrate the difference of the upper and lower curves within the given bounds, from x = -4 to x = 4.

Now, for a more detailed explanation:

First, let's analyze the curves individually. The curve y = x^3 - 4x represents a cubic function, and y = 12x represents a linear function. By plotting these curves on a graph, we can observe that they intersect at three points: (0, 0), (-4, -48), and (4, 48).

To determine the enclosed region, we need to find the x-values at which the curves intersect. Setting the two equations equal to each other, we have x^3 - 4x = 12x. Rearranging this equation, we get x^3 - 16x = 0. Factoring out x, we have x(x^2 - 16) = 0, giving us x = 0 and x = ±4 as the x-values of intersection.

Since the region is vertically bounded by the curves, we'll integrate with respect to x. To find the area, we'll integrate the difference between the upper curve (y = 12x) and the lower curve (y = x^3 - 4x) within the bounds from x = -4 to x = 4.

By evaluating the definite integral ∫[-4 to 4] (12x - (x^3 - 4x)) dx, we can calculate the area of the region enclosed by the given curves.

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Interest = principal x rate x time

Interest = 8000 x 0.03 x 6

Interest = $1,440

Answer: $1,440

Answer:

3.5 units

Step-by-step explanation:

Base × Height = Area, so 10 Base × 3.5 Height = 35 units^2

Answer:

3.5 units

Step-by-step explanation:

Radius of a circle is the distance from the center of the circle to any point on its circumference. The radius of the circle is 3.2 x 10^8.

The diameter of a circle is twice the length of its radius. So, to find the radius, we divide the diameter by 2.

Given that the diameter is 6.4 x 10^8, we divide it by 2 to get the radius: (6.4 x 10^8) / 2 = 3.2 x 10^8.

To calculate the radius of a circle, you need to know either the diameter or the circumference. If you have the diameter (the distance across the circle passing through the center), you can divide it by 2 to find the radius. If you have the circumference (the distance around the circle), you can use the formula: radius = circumference / (2 * π), where π is a mathematical constant approximately equal to 3.14159.

The radius of the circle is 3.2 x 10^8.

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Answer:

I think it's D, i might be wrong but im pretty sure it's D

Answer:

A. 1206 cm³

Step-by-step explanation:

We have a cone and are asked to find the approximate volume of it.

Keep in mind we are using π for 3.14

The forumla of a cone is V = πr²\(\frac{h}{3}\)

We know the radius = 12

and the height = 8

Substitute :

V = π12²\(\frac{8}{3}\)

Since these are multiplied with each other, we can first start off with multiplying the fraction, including with factoring 12²:

V = \(\frac{2^4*3^2*8\pi }{3}\)

Cancel the common factor - 3 :

V = \(2^4 * 8 * 3\pi\)

Multiply 8 and 3π :

V = \(2^4 * 24\pi\)

Solve the exponent :

V = \(16 * 24\pi\)

Multiply :

V = \(384\pi\)

Multiply for the final answer :

1205.76 cm³

which can be rounded up to

A. 1206 cm³