Help me pls. will pay alot of points

The rectangular equation corresponding to the curve after eliminating theta is y = 5 - 0.5x²

To eliminate the parameter θ, we can use the identity sin²θ + cos²θ = 1, which gives us:

sin²θ = 1 - cos²θ

Substituting this into the equation for x, we get:

x = 5sin2θ

x = 5(2sinθcosθ)

x = 10sinθcosθ

Similarly, substituting the identity into the equation for y, we get:

y = 5cos2θ

y = 5(1 - sin²θ)

y = 5 - 5sin²θ

Now we can eliminate θ by solving for sin²θ and cos²θ in terms of x and y:

sin²θ = (10sinθcosθ/10)²

sin²θ = (x/10)²

cos²θ = 1 - sin²θ

cos²θ = 1 - (x/10)²

Substituting these into the equation for y, we get:

y = 5 - 5sin²θ

y = 5 - 5(x/10)²

y = 5 - 0.5x²

So the rectangular equation corresponding to the curve is y = 5 - 0.5x²

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Andrea bought 6 pounds of cheesecake with her gift card.

Cost price is the amount of money that a seller pays to acquire a product or service, which includes the cost of materials, labor, and overhead expenses. It is also known as the wholesale price or the purchase price.

To determine how many pounds of cheesecake Andrea bought, we can use the following formula:

pounds of cheesecake = (amount spent on cheesecake) / (cost per pound)

First, we need to determine how much Andrea spent on cheesecake. We know that she started with a gift card worth $54 and ended up with $37.56 left over, so she must have spent:

amount spent on cheesecake = $54 - $37.56 = $16.44

Next, we need to determine the cost per pound of cheesecake, which is given as $2.74 per pound.

Now we can plug these values into the formula:

pounds of cheesecake = $16.44 / $2.74 per pound

pounds of cheesecake = 6 pounds (rounded to the nearest hundredth)

Therefore, Andrea bought 6 pounds of cheesecake with her gift card.

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Answer:300pi

Step-by-step explanation:

5*5=25

25pi*12=300pi

Answer:

x ≈ 5.38 meters

Step-by-step explanation:

We are given a right triangle. We know that the length of the hypotenuse (the side opposite of the right angle) is 25.9 m and one of the legs (the sides that make up the right angle) is x, which is what we want to find.

We also know one of the angles is 78°.

In order to find the value of x, we need to use trigonometry.
Recall the three trigonometric ratios:

sine, which is [tex]\frac{opposite}{hypotenuse}[/tex]

cosine, which is [tex]\frac{adjacent}{hypotenuse}[/tex]

tangent, which is [tex]\frac{opposite}{adjacent}[/tex]

These ratios are written in reference to one angle.

We can write our ratios in reference to the 78° angle.

The opposite side will be the other leg (the side that is not labeled), the adjacent side will be the side labeled x, and the hypotenuse will be the side labeled 25.9 m.

Since we have the values of both the adjacent and hypotenuse sides, we can use cosine of 78° to find x.

We set this up as:
cos(78) = [tex]\frac{x}{25.9}[/tex]

Now, multiply both sides by 25.9

25.9 * cos(78) = x

Plug 25.9 * cos(78) into your calculator. Make sure your calculator is on degree mode.

5.38 ≈ x

So, x is about 5.38 meters.

The value of the expression given as 3 + d < 3 - d will be A. d < 0.

An expression consists of one or more numbers or variables along with one more operation.

X + 1 is an example of an expression.

"X" is the variable, "+" is the operation and 1 is a number. Think of "X" as any number that is unknown.

The value of the expression given as 3 + d < 3 - d will be:

= d + d < 3 - 3

= d < 0.

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To solve the inequality g/20 ≤ 5 for g, we can multiply both sides by 20 to get rid of the fraction. This gives us g ≤ 100. So the solution to the inequality is g ≤ 100.

The sum of the series ∑k=1[infinity]1k2 5k is (5π²)/24.

To find the sum of the series ∑k=1[infinity]1k2 5k, we can use the formula for the sum of a geometric series. Let r = 1/5 and a = 1/k², then we have:

S = ∑k=1[infinity]1k2 5k = ∑k=1[infinity] (1/k^2)(1/5)^k

Using the formula for the sum of a geometric series, we get:

S = a/(1-r) = (1/k^2)/(1-1/5) = (5/4)(1/k²)

Therefore, the sum of the series is (5/4) times the sum of the reciprocals of the squares of the natural numbers. This is a well-known series, known as the Basel problem, and its sum is π²/6. So, we have:

S = (5/4) x (π²/6) = (5π²)/24

Therefore, the sum of the series ∑k=1[infinity]1k2 5k is (5π²)/24.

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According to the concept of probability, there is a 40% chance that Gabriel will randomly select a can of chicken soup or beef soup from his kitchen cabinet.

To find the probability of Gabriel choosing a can of chicken soup or beef soup, we need to first determine the total number of cans of soup in Gabriel's kitchen cabinet. From the information given, we know that there are 2 cans of tomato soup, 3 cans of chicken soup, 2 cans of cheese soup, 2 cans of potato soup, and 1 can of beef soup.

The total number of cans of soup is therefore:

2 + 3 + 2 + 2 + 1 = 10 cans of soup

Next, we need to determine the number of cans of chicken soup or beef soup. From the information given, we know that there are 3 cans of chicken soup and 1 can of beef soup.

The total number of cans of chicken soup or beef soup is therefore:

3 + 1 = 4 cans of soup

To find the probability of Gabriel randomly selecting a can of chicken soup or beef soup, we divide the number of cans of chicken soup or beef soup by the total number of cans of soup.

Therefore, the probability of Gabriel selecting a can of chicken soup or beef soup is:

4/10 or 2/5 or 40%.

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Using the Chebyshev’s inequality we prove that limn→∞ Pr(|wn - μ| ≥ ε) = 0.

Chebyshev's Inequality is a theorem in probability theory that states that for any random variable X and for any real number k>0, the probability that the absolute value of X is greater than k is less than or equal to the variance of X divided by k squared. This theorem is useful for determining the probability that a random variable will lie within a certain range.

We will prove that for any ε > 0, limn→∞ Pr(|wn - μ| ≥ ε) = 0.

By Chebyshev's Inequality,

Pr(|wn - μ| ≥ ε) ≤ Var(wn) / ε²

= b / np / ε²

= b / (npε²)

Since p and b are constants, as n approaches infinity, this expression goes to 0. Therefore,

limn→∞ Pr(|wn - μ| ≥ ε) = 0

So wn converges in probability to μ.

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The differential dy of the given function y = csc(6x) is dy = -6csc(6x)cot(6x)dx.

To find the differential dy, we first need to find the derivative of the function y with respect to x. We will use the chain rule and the derivative of the cosecant function in this process.

Step 1: Identify the inner function.
In this case, the inner function is 6x.

Step 2: Identify the outer function.
The outer function is csc(u), where u is the inner function.

Step 3: Find the derivative of the inner function.
The derivative of 6x with respect to x is 6.

Step 4: Find the derivative of the outer function.
The derivative of csc(u) with respect to u is -csc(u)cot(u).

Step 5: Apply the chain rule.
dy/dx = (derivative of outer function) * (derivative of inner function)
dy/dx = (-csc(u)cot(u)) * 6

Step 6: Replace u with the inner function.
dy/dx = (-csc(6x)cot(6x)) * 6

Step 7: Simplify the expression.
dy = -6csc(6x)cot(6x)dx

So, the differential dy of the given function y = csc(6x) is dy = -6csc(6x)cot(6x)dx.

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The value of the given integral is 1/15.

Integration is a fundamental concept in calculus that involves finding the area under a curve.

To evaluate this integral, we can use the substitution method. Let u = 1 − x², then du/dx = -2x, and dx = -du/(2x). We can substitute these expressions for dx and u in the integral:

[tex]\int\limits^1_0[/tex] (x³ √(1 − x²) dx) = [tex]\int\limits^1_0[/tex] [(x²)(-1/u)(√u)(-du/(2x))]

= [tex]\int\limits^1_0[/tex] [(x/2)([tex]u^{(-1/2)}[/tex])(u-1)(-du)]

Now, we can simplify the integral and integrate with respect to u:

[tex]\int\limits^1_0[/tex] [(x/2)([tex]u^{(-1/2)}[/tex])(u-1)(-du)] = -1/2 [([tex]u^{1/2}[/tex]) - ([tex]u^{3/2}[/tex]))] du

= -1/2 [(2/3)[tex](1 - x^2)^{(3/2)}[/tex] − (2/5)[tex](1 - x^2)^{(5/2)}[/tex]] evaluated from 0 to 1

= -1/2 [(2/3) − (2/5)]

= 1/15

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Answer:

65 degrees.

Step-by-step explanation:

To find the measure of angle C you have to add 90+25 and subtract it from 180. The reason for this is a triangle is 180 degrees, so to find the third angle you have to add and subtract. This gives you your answer of 65 degrees

Answer:

65 degrees

Step-by-step explanation:

There are 3 angles in a triangle, and they all add up to 180 degrees.

One angle is 25, and the other one is 90, because we can see a square in the corner, indicating 90 degrees.

If one angle is 25 and the other angle is 90, that makes 115 degrees together.

So we subtract 115 from 180 to get your answer, which is 65 degrees.

May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!

2950 tickets were sold on Friday, 3820 tickets were sold on Saturday and 3450 tickets were sold on Sunday

Here we have the matrix

[tex]\left[\begin{array}{ccc}210&300&270\\360&450&420\\80&110&60\end{array}\right][/tex]

Each row represents the number of people on the Ferris wheel, roller coaster, and merry-go-round respectively. The columns represent the days Friday, Saturday, and Sunday respectively.

Here we are given that each ride requires a different number of tickets. The Ferris wheel requires 3 tickets, the roller coaster requires 6 tickets, and the merry-go-round requires 2 tickets.

Now, the matrix above is a 3 X 3 matrix. We need to use matrix multiplication to find the total number of tickets required for every day.

The days are represented by the colmns, hence we need to make a row matrix with the number of tickets to get

[tex]\left[\begin{array}{ccc}3&6&2\end{array}\right][/tex]

Now multiplying it we will get

[tex]\left[\begin{array}{ccc}3&6&2\end{array}\right]\left[\begin{array}{ccc}210&300&270\\360&450&420\\80&110&60\end{array}\right][/tex]

Multiplying each element of the row in the first matrix to each element in the column of the second matrix we get

[tex]=\left[\begin{array}{cccccc}630+2160+160 && 900+2700+220&&810+2520+120\end{array}\right][/tex]

[tex]=\left[\begin{array}{ccc}2950 & 3820&3450\end{array}\right][/tex]

Hence, 2950 tickets were sold on Friday, 3820 tickets were sold on Saturday and 3450 tickets were sold on Sunday

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Answer:60

Step-by-step explanation:

180-75-60=45

90-45=45

180-45-75=?

The value of function (f o f)(2) = f(f(2)) = 42.

To find (f o f)(2),  we need to first find  f(f(2)) which means we need to apply the function f twice to the input value of 2.

First, we apply the function f to 2 to get:

f(2) = 4(2) + 2 = 10

Now we apply f to the result of the previous step, which gives us:

f(f(2)) = f(10) = 4(10) + 2 = 42

Therefore, (f o f)(2) = f(f(2)) = 42.

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The transformation for which the equation f(x) = g(x) will have two solutions is given as follows:

B. g(x) = -f(x).

The zeros of a function are the values of the input x for which the output y of the function assumes a value of y.

Hence, on the graph of a function, the zeros of a function are the values of x for which the graph either touches or crosses the x-axis.

For the transformation g(x) = -f(x), the zeros of the function remain constant, as the numeric values have the signal exchanged, however zero has no sign, hence the zeros remain the same, giving two solutions to the system of equations f(x) = g(x).

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An equation of an ellipse in standard form with the center at the origin is x^2/9 + y^2/4 = 1.

The standard form equation of an ellipse with center at the origin is:
(x^2/a^2) + (y^2/b^2) = 1 where a and b are the lengths of the major and minor axes respectively.
Using the given characteristics, we can determine that the major axis of the ellipse is horizontal, and has a length of 6 (from (-3,0) to (3,0)). Similarly, the minor axis is vertical, and has a length of 4 (from (0,2) to (0,-2)).
Therefore, we have:
a = 3
b = 2
Substituting these values into the standard form equation, we get:
(x^2/3^2) + (y^2/2^2) = 1
Simplifying:
(x^2/9) + (y^2/4) = 1

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Answer:87

Step-by-step explanation:

Step-by-step explanation:

In the given analogy "6:64::11:?", the two pairs of numbers are related to each other in some way.

To find the missing number, we need to determine the relationship between the first pair of numbers (6 and 64) and then apply the same relationship to the second pair of numbers (11 and ?).

One possible relationship between 6 and 64 is that 64 is the result of squaring 6 and multiplying the result by 2. In other words,

64 = 2 × 6^2

Using this relationship, we can find the missing number as follows:

? = 2 × 11^2

= 2 × 121

= 242

Therefore, the missing number that completes the analogy "6:64::11:?" is 242.

.

The statement "for a second-order homogeneous linear ode, any linear combination of two solutions on an open interval i need not be a solution of the ode on" provided is actually FALSE.

For a second-order homogeneous linear ODE, any linear combination of two solutions on an open interval is indeed a solution of the ODE on that interval.

Let y1(x) and y2(x) be two solutions of a second-order homogeneous linear ODE on an open interval I. Then, the ODE can be written in the form:

[tex]L[y] = y''(x) + p(x)y'(x) + q(x)y(x) = 0[/tex]

where L is a linear differential operator, p(x) and q(x) are continuous functions on I.

Since y1(x) and y2(x) are solutions, we have:

L[y1] = 0 and L[y2] = 0

Now consider any linear combination of y1(x) and y2(x):

y(x) = C1*y1(x) + C2*y2(x)

where C1 and C2 are constants. Let's apply the linear operator L to this linear combination:

L[y] = L[C1*y1(x) + C2*y2(x)]

Using the linearity property of the operator L, we have:

L[y] = C1*L[y1] + C2*L[y2]

Since L[y1] = 0 and L[y2] = 0:

L[y] = C1*0 + C2*0 = 0

Thus, y(x) is also a solution of the second-order homogeneous linear ODE on the open interval I.

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the equation of the level curve passing through P(-2, -3) is 2x² + y² = 17.

To find the equation of the level curve of the function h(x,y)=3-2x^2-y^2 that passes through the point p(-2,-3), we need to first find the value of the constant c such that h(x,y)=c passes through the point p(-2,-3).

Plugging in the values x=-2 and y=-3 into the function, we get:

h(-2,-3) = 3 - 2(-2)^2 - (-3)^2
h(-2,-3) = 3 - 8 - 9
h(-2,-3) = -14

So the level curve that passes through the point p(-2,-3) is given by the equation h(x,y)=-14.

Therefore, the equation of the level curve of the function h(x,y)=3-2x^2-y^2 that passes through the point p(-2,-3) is:

3 - 2x^2 - y^2 = -14
Hi! To find the equation of the level curve of the function h(x, y) = 3 - 2x² - y² that passes through the point P(-2, -3), first substitute the coordinates of the point into the function:

h(-2, -3) = 3 - 2(-2)² - (-3)² = 3 - 2(4) - 9 = 3 - 8 - 9 = -14

Since the level curve represents the points where the function has the same value, the equation of the level curve passing through P(-2, -3) will have h(x, y) = -14:

-14 = 3 - 2x² - y²

Now, rearrange the equation to make it easier to read:

2x² + y² = 3 - (-14)
2x² + y² = 17

So, the equation of the level curve passing through P(-2, -3) is 2x² + y² = 17.

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The value of the given iterated integral after converting to polar coordinates is (1/4)(π/2) or π/8.

Convert the given integral to polar coordinates: Replace x with r*cos(θ) and y with r*sin(θ), and replace dx dy with r dr dθ.

Determine the limits of integration for r and θ: 0 ≤ θ ≤ π/2, and y ≤ r ≤ (2-y^2)^(1/2).

Rewrite the integral in polar coordinates: [tex]∫0^(π/2) ∫y^((2-y^2)^(1/2)) (r*cos(θ)+r*sin(θ)) r dr dθ.[/tex]

Evaluate the inner integral with respect to r: ∫0^(π/2)

[tex]∫0^(π/2) ∫y^((2-y^2)^(1/2)) (r*cos(θ)+r*sin(θ)) r dr dθ.\int\limits^a_b {x} \, dx[/tex] [tex]dθ[/tex]

Evaluate the outer integral with respect to θ: [tex](1/4)[π - (π/2)].[/tex]

So, the value of the given iterated integral after converting to polar coordinates is

[tex](1/4)(π/2) or π/8.[/tex]

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The solutions to the equation e^(2x) - 8e^x + 7 = 0 are x = 0 and x = ln(7).

Step 1: Notice that this equation has the form of a quadratic equation. To see this more clearly, let y = e^x. The equation becomes y^2 - 8y + 7 = 0.

Step 2: Factor the quadratic equation. The factors of 7 that sum up to -8 are -1 and -7. Therefore, we can rewrite the equation as (y - 1)(y - 7) = 0.

Step 3: Solve for y. We have two cases:
- y - 1 = 0 => y = 1
- y - 7 = 0 => y = 7

Step 4: Recall that y = e^x. Replace y with e^x and solve for x:
- e^x = 1 => x = ln(1) = 0 (since the natural log of 1 is 0)
- e^x = 7 => x = ln(7)

So the smaller value is x = 0, and the larger value is x = ln(7). The solutions to the equation e^(2x) - 8e^x + 7 = 0 are x = 0 and x = ln(7).

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Answer: $3090.675

Step-by-step explanation: If you need to round the last number you can but I wasn't sure if I should round it or not.

To count the number of subsets of a set with k elements, we use the recurrence relation sk+1 = 2sk with the initial condition s0 = 1.

For your initial condition, consider a set with 0 elements, which has only one subset - the empty set. Thus, S(0) = 1. Using the recurrence relation and initial condition, you can compute the cardinality of the power set for any set of size k.

To count the number of subsets of a set with k elements, we can set up a recurrence relation.

Let sk be the cardinality of the power set of a set with k elements. When we add one more element to the set, we have two options for each subset: either include the new element or don't include it.

This means that the number of subsets of the set with k+1 elements is twice the number of subsets of the set with k elements. Therefore, we have the recurrence relation: sk+1 = 2sk.

Our initial condition is the number of subsets of an empty set, which is 1 (since the empty set itself is a subset). So s0 = 1.

In this course, when working with counting activities and sets, you can set up a recurrence relation to count the number of subsets of a set with k elements. Let S(k) represent the cardinality of the power set of a set of size k.

When you add one more element to the set, you essentially double the number of possible subsets, as each existing subset can either include or exclude the new element.

Therefore, the recurrence relation can be expressed as:

S(k) = 2 * S(k-1)

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Answer:

Working is attached below with answers.

Answer: b) The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞.

Step-by-step explanation:

The probability of selecting at least one brown one is:

P(at least one brown) = 1 - P(none brown) = 1 - 0.397 = 0.603

a. The probability that a randomly selected peanut M&M is not red is 1 minus the probability that it is red:

P(not red) = 1 - P(red) = 1 - 0.12 = 0.88

b. The probability that a randomly selected peanut M&M is green or orange is the sum of the probabilities of selecting a green one and an orange one:

P(green or orange) = P(green) + P(orange) = 0.15 + 0.23 = 0.38

c. The probability that three randomly selected peanut M&M's are all yellow is the product of the probabilities of selecting a yellow one three times, assuming that the selections are made with replacement:

P(all yellow) = P(yellow) * P(yellow) * P(yellow) = 0.15 * 0.15 * 0.15 = 0.003375 (rounded to 4 decimal places)

d. The probability that none of the six peanut M&M's selected are brown is the probability that each one selected is not brown. Assuming that the selections are made with replacement, the probability of selecting a non-brown one is 1 - 0.12 = 0.88. Therefore, the probability of selecting six non-brown ones is:

P(none brown) = 0.88^6 = 0.397

e. The probability that at least one of the six peanut M&M's selected is brown is equal to 1 minus the probability that none of them are brown. From part (d), we know that the probability of selecting six non-brown ones is 0.397. Therefore, the probability of selecting at least one brown one is:

P(at least one brown) = 1 - P(none brown) = 1 - 0.397 = 0.603

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The time the train takes to travel and the 45 miles distance from Ashford to Bromley indicates that the average speed and the difference between the average speeds are;

a) 30 mph

b) 3 mph

The speed is the rate at which the position of the train is changing with time.

The distance between Ashford and Bromley = 45 miles

The time it takes the train = 20:05 - 18:35 = 1 hour 30 minutes = 1.5 hours

a) The average speed = Total distance ÷ Time taken

Therefore;

Average speed of the train = 45 miles ÷ 1.5 hours = 30 miles per hour

b) The time the train leaves Ashford the following day = Normal time = 18:35

The time the train arrives Bromley = 10 minutes late = 10 + 20:05 = 20:15

The time it takes the train = 20:15 - 18:35 = 1 hours 40 minutes = 1 2/3 hours = 5/3 hours

The average speed of the train the following day is therefore;

Average speed = 45 miles ÷ 5/3 hours = 27 miles per hour

The difference between the average speed of the train on the two days is therefore; 30 mph - 27 mph = 3 mph

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Answer:

To determine the decision, we need to conduct a hypothesis test with the following hypotheses:

Null hypothesis: the mean GPA of honors graduates is not greater than 3.50.

Alternative hypothesis: the mean GPA of honors graduates is greater than 3.50.

We can set up the test using a one-sample t-test with a level of significance of 0.05. The test statistic is calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (3.60 - 3.50) / (0.40 / sqrt(36))

t = 2.25

The degrees of freedom for the t-test is 35 (sample size - 1). Using a t-distribution table with 35 degrees of freedom and a significance level of 0.05, the critical value is 1.690.

Since the calculated t-value (2.25) is greater than the critical value (1.690), we reject the null hypothesis. Therefore, we can conclude that the mean GPA of honors graduates is greater than 3.50 with 95% confidence level.

Step-by-step explanation: