Use the distributive property to rewrite each algebraic expression 7(y+2) + (8+r) + 8(x + 9)

Let V be the volume of the conical vessel and r and h be the radius and height of the vessel respectively. Given that: V = (1/3)πr²hLet V' be the volume of the water that is added to the vessel. The volume of the water in the vessel with a depth of 12 cm is given by: V₁ = (1/3)πr₁²h₁where h₁ = 12 cm. We know that 23 cubic meters of water are poured into the vessel, which is equivalent to 23,000 liters or 23,000,000 cubic centimeters.

Thus:23,000,000 = (1/3)πr₁²(12)Simplifying and solving for r₁, we get: r₁ = 210.05 cm Using similar triangles, we know that :r/h = r₁/h₁ where r is the radius of the water surface when the depth is 18 cm. Thus: r/h = 210.05/12Therefore:r = (210.05/12)·18 = 3,152.5/6 ≈ 525.4 cm The new volume of the water with a depth of 18 cm is given by: V₂ = (1/3)πr²h₂where h₂ = 18 cm.

Therefore: V₂ = (1/3)π(525.4)²(18) ≈ 21,154,116.9 cubic centimeters The additional volume of water needed is therefore: V' = V₂ - V₁ = 21,154,116.9 - 23,000,000 ≈ -1,845,883.1 cubic centimeters.

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Answer:

C

Step-by-step explanation:

y=5x reads "y equals (5 times x)", which we can rephrase to "the value of y is 5 times the value of x"

y=x+5 reads "y equals (x plus 5)", which we can rephrase to "the value of y is 5 more than the value of x".

Ergo, answer C is what we're looking for.

Answer: C

Step-by-step explanation:

in y=5x, we can see a 5 placed in front of x. If there is no addition, subtraction, or division sign between a number and a variable, it always means it's multiplication.

We know now that this is 5 times x.

In y=x+5, we see that 5 is being added to x. Therefore, y is 5 more than x.

So there you have it.

Answer:

2x+25/12

Step-by-step explanation:

Hope this helps and have a great day!!!!!

Our assumption that the average of four real numbers is less than all of the numbers is false. By contradiction, we conclude that the average of four real numbers is greater than or equal to at least one of the numbers.

To prove the statement using a proof by contradiction, we assume the opposite, namely, that the average of four real numbers is less than all of the numbers. Let's denote the four numbers as a, b, c, and d. We assume that the average of these numbers, which we'll denote as avg, is less than a, b, c, and d.

Now, let's consider the sum of these four numbers: a + b + c + d. The average of these numbers, avg, is calculated by dividing the sum by 4. Therefore, we have avg = (a + b + c + d)/4.

If avg is less than a, b, c, and d, then (a + b + c + d)/4 < a, (a + b + c + d)/4 < b, (a + b + c + d)/4 < c, and (a + b + c + d)/4 < d.

Now, let's consider the sum of these inequalities: (a + b + c + d)/4 + (a + b + c + d)/4 + (a + b + c + d)/4 + (a + b + c + d)/4 < a + b + c + d.

Simplifying the left-hand side, we have (a + b + c + d) + (a + b + c + d) + (a + b + c + d) + (a + b + c + d) < 4(a + b + c + d).

This simplifies to 4(a + b + c + d) < 4(a + b + c + d), which is a contradiction. The left-hand side is greater than the right-hand side, which contradicts our initial assumption.

Therefore, our assumption that the average of four real numbers is less than all of the numbers is false. By contradiction, we conclude that the average of four real numbers is greater than or equal to at least one of the numbers.

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Answer:

Hi! The answer to your question is A. [tex]y=-x-1[/tex]

Step-by-step explanation:

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Answer:

a

Step-by-step explanation:

The Laplace transform of [tex][f(t) = \sin{\sqrt{24}} + te^{-t}\sin{t} \implies L{f(t)} = \frac{\sqrt{24}}{s^2 + 24} + \frac{1}{(s + 1)^2 + 1}][/tex] . However, F(s) = 1 + 1 cannot be the Laplace transform of any valid function f(t) because it does not satisfy the properties and rules of Laplace transforms.

To determine the Laplace transform of the function [tex]\[f(t) = \sin{\sqrt{24}} + te^{-t}\sin{t}\][/tex], we need to apply the properties and formulas of Laplace transforms.

1. Laplace Transform of sin(√24):

The Laplace transform of sin(at) is given by [tex]\[F(s) = \frac{a}{s^2 + a^2}\][/tex]. In this case, a = √24.

So, the Laplace transform of [tex]\[\sin{\sqrt{24}} \implies F(s) = \frac{\sqrt{24}}{s^2 + 24}\][/tex].

2. Laplace Transform of [tex]\[te^{-t}\sin{t}\][/tex]:

To find the Laplace transform of this term, we can use the product rule and the Laplace transform of each component.

The Laplace transform of t is given by [tex]\[F(s) = \frac{1}{s^2}\][/tex], and the Laplace transform of e^(-t)sin(t) can be found using the table of Laplace transforms.

Using the table, the Laplace transform of [tex]\begin{equation}\mathcal{L}(e^{-t}\sin(t)) = \frac{1}{(s + 1)^2 + 1}[/tex].

3. Adding the Laplace transforms:

Since the Laplace transform is a linear operator, we can add the individual Laplace transforms of [tex]sin(\sqrt{24})[/tex] and [tex]te^{-t}\sin(t)[/tex] to obtain the Laplace transform of the whole function f(t).

Therefore, [tex]L\{f(t)\} = \frac{\sqrt{24}}{s^2 + 24} + \frac{1}{(s + 1)^2} + 1[/tex]

Now, to address the second part of the question:

Is it possible for F(s) = 1 + 1 to be the Laplace transform of some function f(t)?

No, it is not possible for F(s) = 1 + 1 to be the Laplace transform of a valid function f(t). The Laplace transform is a mathematical operation that converts a function of time (f(t)) into a function of the complex variable s (F(s)). The Laplace transform must follow specific properties and rules, and it is not possible for F(s) = 1 + 1 to satisfy these properties and correspond to a valid function f(t).

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The Laplace transform of

L {f(t)} for f (t) = sin (V24) + te- T sin (T) => Lf(t) = √24/s²+24 + 1/(s+1)²+1 .

However, F(s) = 1 + 1 cannot be the Laplace transform of any valid function f(t) because it does not satisfy the properties and rules of Laplace transforms.

Here, we have,

To determine the Laplace transform of the function

f (t) = sin (V24) + te- T sin (T) , we need to apply the properties and formulas of Laplace transforms.

1. Laplace Transform of sin(√24):

The Laplace transform of sin(at) is given by F(s)= a/s²+a².

In this case, a = √24.

So, the Laplace transform of sin(√24) => F(s)= √24/s²+24 .

2. Laplace Transform of te- T sin (T):

To find the Laplace transform of this term, we can use the product rule and the Laplace transform of each component.

The Laplace transform of t is given by F(s)=1/s², and the Laplace transform of e^(-t)sin(t) can be found using the table of Laplace transforms.

Using the table, the Laplace transform of L(e^(-t)sin(t)) = 1/(s+1)²+1.

3. Adding the Laplace transforms:

Since the Laplace transform is a linear operator, we can add the individual Laplace transforms ofsin(√24) and e^(-t)sin(t) to obtain the Laplace transform of the whole function f(t).

Therefore,

Lf(t) = √24/s²+24 + 1/(s+1)²+1

Now, to address the second part of the question:

Is it possible for F(s) = 1 + 1 to be the Laplace transform of some function f(t)?

No, it is not possible for F(s) = 1 + 1 to be the Laplace transform of a valid function f(t). The Laplace transform is a mathematical operation that converts a function of time (f(t)) into a function of the complex variable s (F(s)). The Laplace transform must follow specific properties and rules, and it is not possible for F(s) = 1 + 1 to satisfy these properties and correspond to a valid function f(t).

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Answer:

Step-by-step explanation:

horizontal line segment: B (-10, 0) and (-10, 1)

Answer:

QT=8 VQ=17 this is what i came up with because i myself have ur question and i don't know what it is?

The number of edges in the complete bipartite graph is 36

From the question, we have the following parameters that can be used in our computation:

K = (4, 9)

The above means that

The vertices in the sets of the bipartite graph are

Set 1 = 4

Set 2 = 9

The number of edges in the complete bipartite graph is then calculated as

Vertices = Set 1 * Set 2

So, we have

Vertices = 4 * 9

Evaluate

Vertices = 36

Hence, there are 36 edges in the bipartite graph

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The length of the curve y = tan x, -7/3 ≤ x < 0 is approximately 4.481 units.

To calculate the length of the curve, we can use the arc length formula. For a function y = f(x) on the interval [a, b], the arc length is given by the integral:

L = ∫[a,b] √(1 + (f'(x))²) dx,

where f'(x) represents the derivative of f(x) with respect to x.

In this case, the function is y = tan x and the interval is -7/3 ≤ x < 0. To find the derivative, we differentiate y = tan x with respect to x, which gives:

y' = sec² x.

Now we can substitute these values into the arc length formula:

L = ∫[-7/3,0] √(1 + (sec² x)²) dx.

Simplifying the expression under the square root gives:

L = ∫[-7/3,0] √(1 + tan⁴ x) dx.

To evaluate this integral, we can make a substitution. Let u = tan x. Then du = sec² x dx. Using this substitution, the integral becomes:

L = ∫[tan(-7/3),tan(0)] √(1 + u⁴) du.

Now we need to find the limits of integration. Since -7/3 ≤ x < 0, we can evaluate the tangent function at these values to get:

L = ∫[tan(-7/3),0] √(1 + u⁴) du.

Finally, we can use numerical methods or a calculator to evaluate this integral. The result is approximately 4.481 units.

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Answer:

3 2/5

Step-by-step explanation:

Add the distance she already ran, and subtract the sum from the total she needs to run.

Add two distances she ran:

3 1/2 + 2 1/2 = 3 + 2 + 1/2 + 1/2 = 5 + 1 = 6

Subtract sum from total:

9 4/10 - 6 = 3 4/10 = 3 2/5

Answer:

She needs to run 3 4/10 more miles

Step-by-step explanation:

If you add the amount she ran on Monday and the amount she ran on Tuesday you get 6 miles then subtract the 6 miles minus 9 4/10 you will get 3 4/10.

Question:

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.

Type of Crust Number Sold

Thin crust          312

Thick crust          245

Stuffed crust          179

Pan style                  304

Based on this information, of the next  4500 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answer:

1060 thick crusts

Step-by-step explanation:

Given

The above table

Required

Expected number of thick crust for the next 4500

For last week data, calculate the proportion of thick crust sold

[tex]\hat p = \frac{Thick\ crust}{Total}[/tex]

[tex]\hat p = \frac{245}{312+245+179+304}[/tex]

[tex]\hat p = \frac{245}{1040}[/tex]

[tex]\hat p = 0.235577[/tex]

For the next 4500;

[tex]n = 4500[/tex]

The expected number of thick crust is (E(x)):

[tex]E(x) = \hat p * n[/tex]

[tex]E(x) = 0.235577 * 4500[/tex]

[tex]E(x) = 1060.0965[/tex]

[tex]E(x) \approx 1060[/tex]

Answer:

110.92

Step-by-step explanation:

Assuming that the parameters (P), (h), and (B) all represent dimensions of the given prism, then based on the given information, the following can be concluded:

P = 6.6

h = 4.5

B = 2.2

The surface area is the two-dimensional area around a three-dimensional surface. In other words, if one was going to wrap the figure, the surface area is the amount of paper one would need. One can find the surface area by finding the area of each individual side and then adding all the results together. To find the area of a 2-dimensional figure by multiplying the length by the width.

(4.5) * (6.8) = 30.6

(4.5) * (6.8) = 30.6

(2.2) * (6.8) = 14.96

(2.2) * (6.8) = 14.96

(4.5) * (2.2) = 9.9

(4.5) * (2.2) = 9.9

Now add up all of the values,

30.6 + 30.6 + 14.96 + 14.96 + 9.9 + 9.9

= 110.92

Answer: The domain of the function y = (x - 4)(x - 6) is all real numbers, since there are no restrictions on the values that x can take. The range of the function is also all real numbers.

To see why this is the case, we can rewrite the function in standard form by expanding the product: y = (x - 4)(x - 6) = x^2 - 10x + 24. This is a quadratic function with a positive leading coefficient, so its graph is a parabola that opens upwards. The vertex of the parabola is at x = -b/2a = 10/2 = 5, and y = (5 - 4)(5 - 6) = -1. Since the parabola opens upwards, it extends infinitely upwards from its minimum value at the vertex. Therefore, the range of the function is all real numbers greater than or equal to -1.

So, the domain of y = (x - 4)(x - 6) is all real numbers and its range is all real numbers greater than or equal to -1.

Step-by-step explanation:

Answer:

[tex]y = {x}^{2} - 10x + 24[/tex]

Domain: all real numbers

Range: all real numbers > -1

Answer:

36 kilograms

Step-by-step explanation:

Since she made 8 kilograms of dough over the span of 2 hours, you divide 8 by 2 and get 4 then you have to multiply 9 hours by 4 kilograms of dough to get 36 kilograms of dough.

Answer:

25%

Step-by-step explanation:

Answer:

11+3x=68

x=19

Step-by-step explanation:

11+3x=68 is your equation.

subtract 11 from both side to get 3x alone

3x=68-11

3x=57

divide 3 from both sides to get x alone

x=57/3

x=19

19 is your number.

Value of x corresponding to P81 is 59.06.

A normal distribution has a mean u = 67.3 and a standard deviation of o=9.3.

The task is to find P81, which separates the bottom 81% from the top 19%.

For any normally distributed variable z with mean u and standard deviation o, the cumulative distribution function is defined as the probability of a standard normal variable being less than or equal to z.

A standard normal distribution has a mean of 0 and a standard deviation of 1.

That is, the variable z can be calculated as: z = (x - u) / o

The value P(z < z0) can be read off a standard normal table for any value z0.

As the normal distribution is symmetric, we can use the fact that P(z < -z0) = 1 - P(z < z0).

We now calculate z as follows: z0 = (P81 + 1) / 2 = 0.9051

From a standard normal table, we can see that P(z < 0.9051) = 0.8186.

Therefore, P(z < -0.9051) = 1 - P(z < 0.9051) = 0.1814.

Now we calculate the corresponding value of x:

z = (x - u) / o-0.9051 = (x - 67.3) / 9.3x = 59.06

Therefore, P81 corresponds to the value x = 59.06.

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A wardrobe with 3 pants, 5 shirts, and 7 ties, has a possible outcome of 105 outfits and not 15. So the answer is False

False. The number of total possible outfits is not 15. To calculate the number of possible outfits, we need to multiply the number of choices for each item together. In this case, we have 3 choices for pants, 5 choices for shirts, and 7 choices for ties. Therefore, the total number of possible outfits would be 3 x 5 x 7 = 105.

The statement incorrectly states that there are only 15 possible outfits. It's important to consider that when selecting multiple items, the total number of combinations is found by multiplying the number of choices for each item together. In this scenario, with 3 pants, 5 shirts, and 7 ties, there are 105 possible outfits, not 15.

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Answer:

Equation below

Step-by-step explanation:

An equation that represents the relationship between m and n is 2(n - 150) - (m + 150) = 50 .

The expression that represents Malik's score after he gets 150 points = m + 150

The expression that represents Nora's score after she loses 50 points = n - 150

Nora's score after her score is doubled = 2(n - 150)

The difference between Nora and Malik's score is 50. This can be represented as:  2(n - 150) - (m + 150) = 50

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Answer:

The arc length of a circle is 31.5.

Step-by-step explanation:

The arc length can be found as follows:

[tex] arc = r\theta [/tex]

Where:

arc: is the length of the arc of the circle

r: is the radius = 7

θ: is the angle = 4.5 rad        

[tex] arc = r\theta = 7*4.5 = 31.5 [/tex]

Therefore, the arc length of a circle is 31.5.

I hope it helps you!

Answer:

x = 2 or x = 3

Step-by-step explanation:

x = 2 + sqrt(x - 2)

x - 2 = sqrt(x - 2)                  You could divide both sides by sqrt(x - 2)

sqrt(x - 2) = 1                        Square both sides

x - 2 = 1                                Add 2 to both sides

x = 3

There is a second way.

x - 2 = sqrt(x - 2)                 Square

x^2 - 4x + 4 = x - 2             Transfer x - 2 to the left

x^2 - 5x + 6 = 0                   Factor

(x - 2)(x-3)      = 0                 Find the roots.

x - 2 = 0

x = 2

x - 3 = 0

x = 3

We have to check both results.

x = 2 + sqrt(x - 2)

2 = 2 + sqrt(2 -2)

2 = 2 + 0

2 = 2    This seems to work.

x = 2 + sqrt(x - 2)

3 = 2 + sqrt(3 - 2)

3 = 2 + sqrt(1)

3 = 2 + 1

3 = 3  And this works.

edg2021

Answer:

Upper right corner.

Step-by-step explanation:

I took the test and that one was right. Hope this helps!

Answer:

83°

Step-by-step explanation:

WZ is a straight line. Angles at a straight line add up to 180°.

180 - 97 =83°

Answer:

with what? You forget to attach the problem lol

Step-by-step explanation:

Answer: What is the question you need help with??

Step-by-step explanation:

Answer:

slope=2/3

y intercept=4

Step-by-step explanation: