How many solutions does the system have? {y=−2x 2y=x2−3x Enter your answer in the box.

According to the question The volume of the solid obtained by rotating the region about the \($y$\)-axis is \($0$\).

To find the volume of the solid obtained by rotating the region bounded by the curves \(x = 6 - 3y$, $x = 0$, and $y = 3$\) about the \($y$\)-axis, we can use the method of cylindrical shells.

The height of each cylindrical shell is the difference between the two curves, which is given by \($(6 - 3y) - 0 = 6 - 3y$\)

The radius of each cylindrical shell is the distance from the \($y$\)-axis, which is simply \($y$\).

The differential volume of each cylindrical shell is then given by \(dV = 2\pi y(6 - 3y) \, dy$.\)

To find the total volume, we integrate the differential volume from \(y = 0$ to $y = 3$:\)

\($V = \int_{0}^{3} 2\pi y(6 - 3y) \, dy$\)

To solve the integral, let's integrate the expression step by step:

\($V = \int_{0}^{3} 2\pi y(6 - 3y) \, dy$\)

Expanding the expression, we have:

\($V = \int_{0}^{3} 12\pi y - 6\pi y^2 \, dy$\)

Integrating term by term, we get:

\($V = \left[6\pi \left(\frac{1}{2}y^2\right) - 2\pi \left(\frac{1}{3}y^3\right)\right] \bigg|_{0}^{3}$\)

Simplifying further:

\($V = \left[3\pi y^2 - \frac{2}{3}\pi y^3\right] \bigg|_{0}^{3}$\)

Plugging in the limits of integration:

\($V = \left[3\pi \cdot 3^2 - \frac{2}{3}\pi \cdot 3^3\right] - \left[3\pi \cdot 0^2 - \frac{2}{3}\pi \cdot 0^3\right]$\)

Simplifying:

\($V = \left[27\pi - 27\pi\right] - \left[0 - 0\right]$\)

\($V = 0$\)

Therefore, the volume of the solid obtained by rotating the region about the \($y$\)-axis is \($0$\).

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A sample estimator is unbiased if, on average, it gives an estimate of the population parameter that is equal to the true value of the parameter. The correct option is (b) having an unbiased estimator.

An estimator is a statistical function used to estimate an unknown parameter of a population based on a sample of data. A sample estimator is unbiased if, the expected value of the estimator is equal to the true population parameter.

If a sample estimator overestimates the population parameter in some cases and underestimates it in others, the overestimations and underestimations may cancel each other out on average. In this case, the estimator is unbiased, meaning that it provides estimates that are, on average, neither too high nor too low, it means that the estimator does not systematically overestimate or underestimate the true population parameter. The correct answer is (b).

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(1)

[1]   x + 5y - 4z = -10

[2]   2x - y + 5z = -9

[3]   2x - 10y - 5z = 0

Eliminate x by adding -2[1] to [2], and adding -1[2] to [3]:

-2(x + 5y - 4z) + (2x - y + 5z) = -2(-10) + (-9)

-2x - 10y + 8z + 2x - y + 5z = 20 - 9

[4] -11y + 13z = 11

-(2x - y + 5z) + (2x - 10y - 5z) = -(-9) + 0

-2x + y - 5z + 2x - 10y - 5z = 9

[5]  -9y - 10z = 9

Eliminate y by adding -9[4] to 11[5]:

-9(-11y + 13z) + 11(-9y - 10z) = -9(11) + 11(9)

99y - 117z - 99y - 110z = -99 + 99

-227z = 0

z = 0

Plug this solution into either [4] or [5] and solve for y :

[5] -9y - 10(0) = 9

-9y = 9

y = -1

Plug them both into either of [1], [2], or [3] and solve for x :

[1] x + 5(-1) - 4(0) = -10

x - 5 = -10

x = -5

(2)

[1] 2x - y + z = -4

[2] z = 5

[3] -2x + 3y - z = -10

Substitute [2] into [1] and [3]:

2x - y + 5 = -4

[4] 2x - y = -9

-2x + 3y - 5 = -10

[5] -2x + 3y = -5

Solve [4] for y :

2x - y = -9

2x + 9 = y

Substitute this into [5] and solve for x :

-2x + 3(2x + 9) = -5

-2x + 6x + 27 = -5

4x = -32

x = -8

Plug this into either [4] or [5] to solve for y :

[4] 2(-8) - y = -9

-16 - y = -9

y = -5

Answer:

Steps:

SA = 2LW + 2WH + 2LH

SA = 2(9×2) + 2(2×11/2) + 2(9×11/2)

SA = 2×18 + 2×22/2 + 2×99/2

SA = 36 + 22 + 99

SA = 157 in²

Answer:

B : x = - 2

Step-by-step explanation:

8x + 29 + x = 11.

8x + x = 9x

9x + 29 = 11

     - 29    -29

9x = -18

x = -2

Answer:

B. » x => — 2

Step-by-step explanation:

Given : 8x + 29 + x = 11

→ x = - 2

Answer:

28

Step-by-step explanation:

Answer:

26/9

Step-by-step explanation:

whenever you divide fractions, they turn into a multiplication problem and use the second fraction's reciprocal. so it would look something like this:

13/2 * 4/9

just do straight multiplication

numerators: 13*4 = 52

denominators: 2*9 = 18

52/18 = 26/9

Answer:

There is no photo or attachment

Step-by-step explanation:

Attach it and I’ll do it

The ladder touches the wall at a height of approximately 9.2 feet above the ground.

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side, which is the ladder in this case) is equal to the sum of the squares of the lengths of the other two sides (the distance from the wall and the height of the ladder on the wall).

Let's call the distance from the wall "x" and the height of the ladder on the wall "h". Then we have:

\(x^2 + h^2 = 14^2\)

We also know that the bottom of the ladder is placed 3 feet from the wall, so we have:

x + 3 = 14

Solving for x, we get:

x = 11

Substituting this value into the first equation, we get:

\(11^2 + h^2 = 14^2\)

Simplifying and solving for h, we get:

\(h = \sqrt{(14^2 - 11^2)}\)

h ≈ 9.2

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Answer:

the answer of this question is 0

A. First, convert this equation into y-intercept form

y = 2x + 1

B. 2 is the slope: 1 is the y-intercept

Then, plug in 1 for y and solve

C. 1 = 2x + 1

Therefore, x is 0

The area of the triangle is approximately 6.4936 square centimeters.

We can use Heron's formula to find the area of a triangle given the lengths of its sides. Heron's formula states that the area (A) of a triangle with sides a, b, and c is:

A = √[s(s-a)(s-b)(s-c)]

where s is the semi-perimeter of the triangle, defined as:

s = (a + b + c) / 2

Using the values given in the problem, we have:

a = 7 cm, b = 3 cm, c = 5 cm

The semi-perimeter is:

s = (a + b + c) / 2 = (7 + 3 + 5) / 2 = 7.5 cm

Substituting these values into Heron's formula, we get:

A = √[s(s-a)(s-b)(s-c)]

= √[7.5(7.5-7)(7.5-3)(7.5-5)]

= √[7.5(0.5)(4.5)(2.5)]

= √[42.1875]

= 6.4936 cm² (rounded to 4 decimal places)

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Answer:

-22.2222222222%

Step-by-step explanation:

-0.4/1.8×100

I'm not sure if it is dynamic or static equilibrium but if I had to choose I'd say dynamic

Answer:

It is in static equilibrium with a net force of 0 N.

Step-by-step explanation:

EDGE21

Answer:

A = 4.5

Step-by-step explanation:

Area of a triangle:

A = 1/2bh

Given:

b = 3

h = 3

Work:

A = 1/2bh

A = 1/2(3)(3)

A = 1.5(3)

A = 4.5

To calculate the probability that at least 8 participants from one group complete the study while fewer than 8 do so from the other group, we need to use the binomial distribution. The probability can be obtained by summing the probabilities of different combinations of successful and unsuccessful trials.

Let's denote the probability of a participant dropping out before the end of the study as p = 0.28. The probability of a participant completing the study is then q = 1 - p = 0.72.
We can consider two cases: 1) at least 8 participants from group A complete the study and fewer than 8 from group B, and 2) at least 8 participants from group B complete the study and fewer than 8 from group A.
Case 1: At least 8 participants from group A complete the study and fewer than 8 from group B.
The probability of this event can be calculated as the sum of probabilities for 8, 9, and 10 participants from group A completing the study while fewer than 8 do so from group B. For each case, we calculate the probability using the binomial distribution formula:
P(X = k) = C(n, k) * p^k * q^(n-k)
Case 2: At least 8 participants from group B complete the study and fewer than 8 from group A.
We follow the same approach as in Case 1, but now we consider the probabilities for group B instead.
By summing the probabilities from both cases, we obtain the final probability that satisfies the given condition.
To calculate the specific probability, we need additional information, such as the total number of participants in each group (n) or the proportions of participants in the groups. Please provide the necessary information to proceed with the calculation.

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Answer:

  12.903

Step-by-step explanation:

You want the measure of BC in right triangle ABC with A=90°, B=47° and AB=8.8.

The relations between sides and trig functions of the angles in a right triangle are summarized by the mnemonic SOH CAH TOA. Useful here is the relation between the side adjacent to the given acute angle and the hypotenuse:

  Cos = Adjacent/Hypotenuse

  cos(47°) = AB/BC

Solving for BC, we get ...

  BC = AB/cos(47°) = 8.8/cos(47°)

The calculator (2nd attachment) shows this to be ...

  BC = 12.903

Given : A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week . and graph

To Find :  Maximum profit , breakeven point , profit interval

Solution:

The maximum profit the florist will earn from selling celebration bouquets is $ 675

peak of y from Graph

The florist will break-even after  Selling 20     one-dollar decreases.

at breakeven

Break even is the point where the profit p(x) becomes 0

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0 ,20).

after 20 , P(x) is - ve

Answer: EDMENTUM AND PLATO

First Blank: $625

Second Blank: 20

Third Blanks: ( 0, 20 )

Step-by-step explanation:

The value of F for each pair of m&a using Newton's second law is 70N.

We have to find the F for each pair of m&a using Newton's second law which gives F = ma. Since m and a are vectors, we use the vector dot product to calculate F.The formula for the vector dot product is given as

A . B = ||A|| ||B|| cosθ.

Here, θ is the angle between the vectors A and B.

θ = 0° because both the vectors are in the same direction. Therefore, cosθ = 1.

Using the formula for the dot product, we have:

F = m . a= ||m|| ||a|| cosθ= m1a1 + m2a2 + m3a3

where ||m|| = √(52 + 82 + 102) = √189 = 13.75, and

||a|| = √(22 + 52) = √29 ≈ 5.39

Therefore,F = m . a= (5 × 2) + (8 × 5) + (10 × 2)= 10 + 40 + 20= 70 N

Thus, the value of F is 70 N.

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Answer:

4.25c + 3.5p = 36.50

c + 6 = p

c = candies and p = pretzels

Step-by-step explanation:

So for the first equation, the prices will be the coefficients of each variable, since for each candy/pretzel it will be that price. We also know that both of these prices together equal 36.50, so that will be on the other side of the equal sign. So the equation representing this info is 4.25c + 3.5p = 36.50

And for the second equation I saw that Mason bought 6 more pretzels than candies. So no matter what number the candies is, the pretzels should always be 6 more than the candies. So the equation representing this information is c + 6 = p

Lastly I just defined the variables that I used to right the system. That is all! Hope this helps you this should be correct :)

Answer:

i believe it p=5 the first one

Step-by-step explanation:

The net would be 51 feet long to stretch from one side of the court to the other

Scale drawings are drawings that shows a diagram with another proportional dimensions

The scale ratio of the diagram is given as:

Scale = 1 inch = 12 feet

The length of the net is given as:

Length = 4.25 inches

So, the actual length of the net is:

\(Length = 4.25 \times 12 \)

Evaluate the product

\(Length = 51\)

Hence, the net would be 51 feet long, if stretched across the court

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Answer:

Option D

Step-by-step explanation:

According to the image description provided:

Term one starts with one dot. One is an odd number.

If you add two to an odd number, the sum would be another odd number. This is what's happening with the pattern.

For example:

\(3+2 =5\)

Three is an odd number. If you add two to it, you would get five, which is another odd number.

Term two has 3 dots, term three has 5 dots, term four has 7 dots.

So, all terms should be odd.

Option D should be the correct answer.

Answer:

13.25×5+13, cost per day with a helmet.

Step-by-step explanation:

Numerical Expressions • Practice

Answer:

13.25×5+13, Per day without a helmet

Step-by-step explanation:

Answer: When students register online, the question appears in a pop-up window that must be answered in order to proceed with registering. If students register in person, make them answer the question before their registration is processed.

Step-by-step explanation:

There are 26 letters in the English alphabet, so there are 26 choices for each of the 3 letters in the call letters. However, the call letters must begin with either a "k" or a "w", so there are only 2 choices for the first letter. Therefore, the number of sets of call letters having 3 letters is:

2 x 26 x 26 = 1,352

There are 1,352 possible sets of call letters that could be used for radio stations. It is important to note that not all of these sets of call letters may be available or in use, as some may already be assigned to other radio stations or not allowed by regulations.
Hello! I understand that you need help with calculating the possible sets of call letters for radio stations. Here's the answer:

There are two options for the first letter: K or W. For the second and third letters, there are 26 options each, as there are 26 letters in the alphabet. To find the total number of possible sets of call letters, we can use the multiplication principle:

2 (options for first letter) * 26 (options for second letter) * 26 (options for third letter) = 2 * 26^2 = 2 * 676 = 1,352 sets of call letters.

So, there are 1,352 possible sets of 3-letter call letters for radio stations.

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Answer: A straight angle

Step-by-step explanation:

90 + 90 = 180

Answer:

the final answer I combine is 10 combine terms

Answer:

2

Step-by-step explanation:

Turn 3 2/3 into improper fraction: 11/3

11/3-5/3=6/3=2