Consider the following curve. r^2 cos(2 theta) = ___ Write an equation for the curve in terms of sin(theta) and cos(theta). ________
Find a Cartesian equation for the curve. ________
Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 < theta < 2phi.)

By using  1-PsiTarget(H15, 500) we compute the probability of cell H15's value exceeding 500 in a spreadsheet simulation.

PsiTarget is a function commonly used in spreadsheet simulation software to calculate probabilities.

The first argument (H15) specifies the cell you want to calculate the probability for.

The second argument (500) represents the target value you want to compare against.

The PsiTarget function returns the probability of the cell's value being less than or equal to the target value.

By subtracting this probability from 1, you get the probability of the cell's value exceeding the target value.

Therefore, the correct formula to compute the probability of cell H15's value exceeding 500 is 1-PsiTarget(H15, 500).

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Answer:

Scientific notation simply refers to the process of expressing long numbers in decimal.

Answer:

Step-by-step explanation  

Scientific notation is a way of writing numbers that is often used by scientists and mathematicians to make it easier to write large and small numbers. A number that is written in scientific notation has several properties that make it very useful to local scientists. It makes very large numbers into smaller numbers using decimals and exponents.

In the triangle ABC, the value of AC is obtained as 5 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangle ABC is given.

The measure of AB is given as 10 units.

The measure of KB is given as 2 units.

The measure of KM is given as 1 unit.

According to the indirect measurement -

AB / AC = KB / KM

Substitute the values in the equation -

10 / AC = 2 / 1

2 AC = 10

AC = 5  

Therefore, the value of AC is obtained as 5 units.

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In order to multiply two fractions, we can follow the steps below:

0. find the product between the two numerators; ,(3 * 7 = 21)

1. find the product between the two denominators; ,(10 * 2 = 20)

2. the product of the two fractions will be the result of step 1 (the numerator of the final result), divided by the result of step 2 (the denominator of the final result):

Therefore, the answer is:

This problem involves the concept of parametric differentiation. We are given parametric equations:

1. \(\(x(t) = e^{-3t}\)\)

2. \(\(y(t) = e^{3t}\)\)

We are asked to find \(\(\frac{d^2 y}{d x^2}\), the second derivative of \(y\) with respect to \(x\). Here are the steps to solve this problem:

Step 1: Calculate \(\(\frac{dy}{dt}\) and \(\frac{dx}{dt}\)\)

\(\(\frac{dy}{dt} = \frac{d}{dt} e^{3t} = 3e^{3t}\)\)

\(\(\frac{dx}{dt} = \frac{d}{dt} e^{-3t} = -3e^{-3t}\)\)

Step 2: Calculate \(\(\frac{dy}{dx}\)\)

By the chain rule, we can express \(\frac{dy}{dx}\)\) as \(\frac{dy}{dt} / \frac{dx}{dt}\)\).

Hence,

\(\(\frac{dy}{dx} = \frac{3e^{3t}}{-3e^{-3t}} = -e^{6t}\)\)

Step 3: Calculate  \(\(\frac{d^2 y}{dx^2}\)\)

Now, we find the second derivative. Here we have to apply the chain rule again, but now it's a bit trickier because \(\(\frac{dy}{dx}\)\) itself is a function of t, not x So we need to take \(\(\frac{d}{dt}\)\) of \(\(\frac{dy}{dx}\)\) and then divide by \(\(\frac{dx}{dt}\)\)

\(\(\frac{d^2 y}{dx^2} = \frac{d}{dt} (\frac{dy}{dx}) / \frac{dx}{dt}\)\)

Taking the derivative of \(\(\frac{dy}{dx} = -e^{6t}\)\) with respect to t, we get:

\(\(\frac{d}{dt} (\frac{dy}{dx}) = -6e^{6t}\)\)

So,

\(\(\frac{d^2 y}{dx^2} = \frac{-6e^{6t}}{-3e^{-3t}} = 2e^{9t}\)\)

So, the answer is (D)  \(2e^{9t}\)\)

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The second derivative d²y/dx² in terms of t is \(2e^{(9t)\).

Calculus's essential idea of derivatives is how quickly a function changes in relation to its independent variable. They offer details about how a function is altering for a certain input or point.

We must use the chain rule to determine the second derivative of y with respect to x (d²y/dx²) in terms of t.

According to the chain rule, the derivative of y with respect to x is given by dy/dx = (dy/dt) / (dx/dt) if we have a parametric curve defined by x = f(t) and y = g(t).

In this case, we have \(x(t) = e^{(-3t)\) and \(y(t) = e^{(3t)\).

First, we'll find the first derivatives dx/dt and dy/dt:

dx/dt = d/dt \((e^{(-3t)}) = -3e^{(-3t)\)

dy/dt = d/dt \((e^{(3t)}) = 3e^{(3t)\)

Next, we can find dy/dx:

dy/dx = (dy/dt) / (dx/dt)

\(= (3e^{(3t)}) / (-3e^{(-3t)})\\= -e^{(6t)\)

Finally, we differentiate dy/dx with respect to x to find d²y/dx²:

d²y/dx² = \(d/dx (-e^{(6t)})\)

\(= d/dt (-e^{(6t))} \times (dt/dx)\\= -6e^{(6t)} \times (1 / (-3e^{(-3t)}))\\= 2e^{(9t)\)

Therefore, the second derivative d²y/dx² in terms of t is \(2e^{(9t)\).

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Answer:

d

Step-by-step explanation:

Answer:

C. 23

Hope this helps :-D

Answer:

The random process described is a symmetrical random walk.

A symmetrical random walk is a mathematical model that represents a series of steps taken in either a forward (+1) or backward (-1) direction, each with equal probability. Starting from point zero, the process involves taking a certain number of steps. The outcome at each step is independent of previous steps, making it a stochastic process. The key characteristic of a symmetrical random walk is that, on average, the process remains centered around its starting point. This means that over a large number of steps, the expected displacement from the starting point approaches zero.

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Answer:

a 37

Step-by-step explanation:

cant explain bye hope this helps

what is question 10?

The integrating factor to make the given ODE exact is x+y.

To determine the integrating factor for the given ODE, we can use the condition for exactness of a first-order ODE, which states that if the equation can be expressed in the form M(x, y)dx + N(x, y)dy = 0, and the partial derivatives of M with respect to y and N with respect to x are equal, i.e., (M/y) = (N/x), then the integrating factor is given by the ratio of the common value of (M/y) = (N/x) to N.

In the given ODE, we have M(x, y) = 2y² + 3x and N(x, y) = 2xy.

Taking the partial derivatives, we have (M/y) = 4y and (N/x) = 2y.

Since these two derivatives are equal, the integrating factor is given by the ratio of their common value to N, which is (4y)/(2xy) = 2/x.

Therefore, the integrating factor to make the ODE exact is x+y.

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The expected population in an additional 4 years is 15,125.

The expected population can be found by using the formula for uninhibited exponential growth.

Uninhibited exponential growth is modeled by the formula

P(t) = P₀ * e^(rt)

where P₀ is the initial population, e is the base of natural logarithms (approximately equal to 2.718), r is the growth rate, and t is the time elapsed.

We can first find the growth rate by using the formula

r = (ln(P/P₀)) / t

where P is the final population and t is the time elapsed. In this case, P₀ = 8000, P = 12000, t = 7 years, so we have:

r = (ln(12000/8000)) / 7

= 0.4055 / 7

= 0.0579

Next, we can use this growth rate to predict the population in an additional 4 years. Let t' = t + 4, so we have:

P(t') = P₀ * e^(r * t')

= 8000 * e^(0.0579 * (7 + 4))

Using a calculator, we can find that P(t') ≈ 15,125.

So, the expected population in an additional 4 years is approximately 15,125.

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The probability that the first student Mr. Beal selects has a pass or has completed the homework assignment is 23/33.

Let us denote the following:

A  student has a pass =  P

A student has completed the homework assignment =  H.

The given parameters are:

Probability of (P) = 11/33

Probability of (H) = 19/33

Probability of (P and H) = 7/33

We apply the  principle of inclusion-exclusion and have that the  Probability of (P or H) = P(P) + P(H) - P(P and H)

We then substitute values

Probability of (P or H) = (11/33) + (19/33) - (7/33)

= 23/33

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Answer:

Step-by-step explanation:

let us calculate area of pentagon.

it consists of 5 isosceles triangles with base=5 cm

apothem h=3.6 cm

area of pentagon=5×1/2×5×3.6≈45 cm

area of 2 pentagons (top and bottom)=2×45=90 cm²

lateral area of 6 rectangles=2(10×5+10×5+10×5)=2(50+50+50)=300 cm²

Total surface area=90+300=390 cm²

Hello !

Answer:

\(\Large \boxed{\sf x=-11}\)

Step-by-step explanation:

We want to find the value of x that satisfies the following equation :

\(\sf 5x+2=4x-9\)

Let's isolate x !

First, substract 4x from both sides :

\(\sf 5x+2-4x=4x-9-4x\\x+2=-9\)

Now let's substract 2 from both sides :

\(\sf x+2-2=-9-2\\\boxed{\sf x=-11}\)

Have a nice day ;)

Hello!

5x + 2 = 4x - 9

5x - 4x = - 9 - 2

x = -11

Answer:

A

Step-by-step explanation:

just plug in the formula

The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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Answer:

Hey there!

Marked down by 20 percent is equal to 80 percent of the original value.

4.5(0.8)=3.6

9 percent sales tax

3.6(1.09)=3.92

Hope this helps :)

Answer:

$3.92

Step-by-step explanation:

I took the test

The top right graph could show the arrow's height above the ground over time.

The initial and the final height are both at eye level, which is the reference height, that is, a height of zero.

This means that the beginning and at the end of the graph, it is touching the x-axis, hence either the top right or bottom left graphs are correct.

The trajectory of the arrow is in the format of a concave down parabola, hitting it's maximum height and then coming back down to eye leve.

Hence the top right graph could show the arrow's height above the ground over time.

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The measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation if the triangle ABC implies it is bigger than the triangle A'B'C' with a scale factor 1/2 since AC = 10 and A'C' = 5

side A'B' = 8 × 1/2

side A'B' = 4

Therefore, the measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

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Answer:

the answer is B, 4. :)

Answer: 948 grams

Step-by-step explanation:

Kilograms of food purchased = 2.12 kilograms = 2120 grams

Number of grams of food pellets to the rabbits = 177

Number of grams given to the chickens = 276

Number of grams of pellets given to the ducks = 0.1kg = 100 grams

Number of grams given to the goats = 619

Then, grams of food pellets that Allison give to the calves will be:

= 2120 - (177 + 276 + 100 + 619)

= 2120 - 1172

= 948 grams

Therefore, the grams of food pellets that Allison give to the calves is 948 grams.

Note that 1000 grams = 1 kilogram

There is insufficient evidence to reject the null hypothesis, and we cannot conclude that the actual overall mean diameter of the ball bearings is not 4.300 mm.

The standard deviation (s) of the ball bearings' diameters is given as 0.005 mm, indicating the variability in the measurements. The overall mean diameter (µ) is specified as 4.300 mm. A sample of 81 ball bearings (n) has a sample mean of 4.299 mm. To determine whether there's reason to believe that the actual overall mean diameter is not 4.300 mm, we need to conduct a hypothesis test.

We begin with stating the null hypothesis (H₀) as: µ = 4.300 mm, and the alternative hypothesis (H₁) as: µ ≠ 4.300 mm. To conduct the hypothesis test, we can use the Z-test since the sample size is large (n ≥ 30). The Z-test statistic is calculated as:

Z = (sample mean - µ) / (s / √n)

Plugging in the values:

Z = (4.299 - 4.300) / (0.005 / √81) ≈ -1.8

Now, we need to find the p-value associated with this Z-score. The p-value helps us to determine the likelihood of observing a sample mean as extreme as 4.299 mm, given that the null hypothesis is true. A low p-value (typically, p < 0.05) would indicate that there is evidence to reject the null hypothesis in favor of the alternative hypothesis.

In this case, the p-value associated with a Z-score of -1.8 is approximately 0.072, which is greater than 0.05. Therefore, there is insufficient evidence to reject the null hypothesis, and we cannot conclude that the actual overall mean diameter of the ball bearings is not 4.300 mm.

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Answer:

A - 105

Step-by-step explanation:

since the two measurements are supplements, you do x+82+x+112=180. then you get x=-7. then you do 112-7=105

Answer:

105°

Step-by-step explanation:

A line equals 180, so take the two expressions and set them equal to 180:

x+82+x+112=180

simplify:

2x+194=180

2x=-14

x=-7

now plug the x value into the bolded expression

x+112

-7+112 = 105°

Brand A sells their product for 36 dabloons per 6 kg. Brand B sells their product for 4 dabloons per 2 kg. Therefore, Brand B is cheaper than Brand A by 2 dabloons per kg in price.

To determine which brand is cheaper and by how much per kg, we compare the prices of both brands based on the cost per kg.

Brand A sells their product for 36 dabloons per 6 kg. We can simplify this to find the cost per kg:

Cost per kg for Brand A = 36 dabloons / 6 kg = 6 dabloons/kg.

Brand B sells their product for 4 dabloons per 2 kg. We can simplify this to find the cost per kg:

Cost per kg for Brand B = 4 dabloons / 2 kg = 2 dabloons/kg.

Comparing the cost per kg, we find that Brand B has a lower cost per kg than Brand A. Therefore, Brand B is cheaper.

To calculate the difference in price per kg between the two brands, we subtract the cost per kg of Brand B from the cost per kg of Brand A:

Difference in price per kg = Cost per kg of Brand A - Cost per kg of Brand B

= 6 dabloons/kg - 2 dabloons/kg

= 4 dabloons/kg.

Therefore, Brand B is cheaper than Brand A by 4 dabloons per kg.

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17x = 32

x = 1.882

23x = 23 x 1.882 = 43.286 = 43 balls

Answer:

hi

Step-by-step explanation:

you should know that the sum of interior angles of a hexagon is 720 so

\(4x - 10 + 2x + 8 + x - 12 + 7x + 3x + 135 = 720 \\ 17x = 121 \\ x = \frac{121}{17} = 7.11764\)

The correct option  A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.

The statement made by Xavier that the product of two odd integers always results in an even integer should be noticed.

For the given case, conjecture that the sum of two odd integers is always an even integer is -

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The complete question is-

Xavier makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?

Select option;

A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.

B: Look at these different examples: 3 + 5 = 8, 13 + 5 = 18, 23 + 5 = 28. So the sum of two odd numbers must be even.

C: Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.

D: Every time you add two odd numbers, the sum is an even number.

Answer:

(1,-1)

Step-by-step explanation:

-2x-1 = x+2

-3x = 3

x = -1

substitute

y = (-1) + 2

y = 1

point: (1,-1)

The points that lie on the graph of the line after the Transformations are:

C. (0, -7) and D. (1, -6).Therefore, the correct answer is C and D.

To shift the line 3 units to the left and 1 unit up, we need to adjust the x and y coordinates accordingly.

The original line equation is y = x - 5.

1. Shifting 3 units to the left: To shift the line 3 units to the left, we need to subtract 3 from the x-coordinate. The updated equation becomes y = (x - 3) - 5 = x - 8.

2. Shifting 1 unit up: To shift the line 1 unit up, we need to add 1 to the y-coordinate. The updated equation becomes y = x - 8 + 1 = x - 7.

Now, let's check which points lie on the graph of the line after these transformations:

A. (-3, -4):

When we substitute x = -3 into the updated equation, we get y = -3 - 7 = -10, so this point is not on the graph.

B. (1, -3):

When we substitute x = -1 into the updated equation, we get y = -1 - 7 = -8, so this point is not on the graph.

C. (0, -7):

When we substitute x = 0 into the updated equation, we get y = 0 - 7 = -7, so this point is on the graph.

D. (1, -6):

When we substitute x = 1 into the updated equation, we get y = 1 - 7 = -6, so this point is on the graph.

E. (2, 1):

When we substitute x = 2 into the updated equation, we get y = 2 - 7 = -5, so this point is not on the graph.

F. (5, 0):

When we substitute x = 5 into the updated equation, we get y = 5 - 7 = -2, so this point is not on the graph.

G. (6, 5):

When we substitute x = 6 into the updated equation, we get y = 6 - 7 = -1, so this point is not on the graph.

Based on these calculations, the points that lie on the graph of the line after the transformations are:

C. (0, -7) and D. (1, -6).

Therefore, the correct answer is C and D.

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