find the volume of a cone of a radius of 6m and height of 5mgive an exact answer or approximate to 3 decimals

The number of hours Melody worked this week was 15.

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Okay so to get this answer u have too Take 17 and subtract 2 This equals 15, So the answer would be 15, This is how I get my answers at least

5th question: \(\frac{-8-4a}{-4} =2 + a\)

6th question: \(11(-4q +3d + 3) = -44q +33d+33\)

7th question: \(\frac{15w +5-35w}{-5} =-3w-1+7w=4w-1\)

8th question: \(4(y-1)+9(y+2) = 4y-4 + 9y+18= 13y+14\)

Hope it helps!

Answer: 790 cm

Step-by-step explanation:

Answer:

790cm

Step-by-step explanation:

10m is equal to 1000cm

let the amount of tread left be x

since she uses 210cm of it, subtract 210 from 1000

x=1000-210

x=790

Mary is left with 790cm of thread.

Answer:

20 feet

Step-by-step explanation:

Height of the student = 68 inches

Length of the student's shadow = 17 inches

Length of the tree's shadow = 60 inches

Let's set up the proportion:

(T / 60) = (68 / 17)

Cross-multiply:

17T = 68 * 60

Simplify:

17T = 4080

Divide both sides by 17:

T = 4080 / 17

Calculate:

T ≈ 240 inches

To convert to feet, divide by 12:

T ≈ 240 / 12

T ≈ 20 feet

Therefore, the tree is approximately 20 feet tall.

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Answer:

25

Step-by-step explanation:

Given,

y = 8

To find : -

9 + 2y = ?

9 + 2y

= 9 + 2 ( 8 )

= 9 + 16

= 25

Answer: you start at point (4,2) x= 4 and y=2

go up one that would be 4,3 but then u go down 2 which your answer should be (4,1)

Step-by-step explanation: you only go up and down here so you only move in Y

Answer:

|-5| > |3|

because the absolute value of -5 is five which is greater than 3

The matrix A can be diagonalized as A = PDP^(-1), where A = [-11 3 -9; 0 -5 0; 6 -3 4], P = [1 -1 1; 0 0 1; 1 2 3], D = [3 0 0; 0 -6 0; 0 0 -9], and P^(-1) is the inverse of P.

1. To diagonalize the matrix A, we need to find an invertible matrix P and a diagonal matrix D such that A = PDP^(-1). In this case, the given matrix A is [-11 3 -9; 0 -5 0; 6 -3 4]. We can find the diagonalized form by calculating the eigenvalues and eigenvectors of A, constructing the matrix P using the eigenvectors, and the matrix D using the eigenvalues.

2. To diagonalize matrix A, we start by finding the eigenvalues λ of A. By solving the characteristic equation |A - λI| = 0, where I is the identity matrix, we can determine the eigenvalues. In this case, the eigenvalues are λ₁ = 3, λ₂ = -6, and λ₃ = -9.

3. Next, we find the corresponding eigenvectors v₁, v₂, and v₃ for each eigenvalue. For each eigenvalue λ, we solve the equation (A - λI)v = 0 to find the nullspace of (A - λI). The eigenvectors are normalized so that ||v|| = 1.

4. For λ₁ = 3, we have the eigenvector v₁ = [1 0 1]. For λ₂ = -6, we have v₂ = [-1 0 2]. And for λ₃ = -9, we have v₃ = [1 1 3].

We construct the matrix P using the eigenvectors as columns: P = [v₁ v₂ v₃] = [1 -1 1; 0 0 1; 1 2 3].

5. To find the diagonal matrix D, we place the eigenvalues on the diagonal of D in the same order as the corresponding eigenvectors in P. Thus, D = [3 0 0; 0 -6 0; 0 0 -9].

6. Finally, we calculate P^(-1) to obtain the inverse of matrix P. Therefore, the matrix A can be diagonalized as A = PDP^(-1), where A = [-11 3 -9; 0 -5 0; 6 -3 4], P = [1 -1 1; 0 0 1; 1 2 3], D = [3 0 0; 0 -6 0; 0 0 -9], and P^(-1) is the inverse of P.

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Answer:

13 because all you need to do is multiply 10 by 3 then subtract 27

Answer:

\((2x+7)(x+3)\)

Step-by-step explanation:

\(2x^2+13x+21\)

To solve, we will need to factor.

\(2x^2+13x+21\)

Now we got an answer!

\((2x+7)(x+3)\)

This is your answer!

Hope this helps!

The first five terms of the given recursively defined sequence. a_n = 3a_n - 1 + 5 and a_1 = 3 are 3, 14, 47, 146, and 443.

To find an expression for the nth term of the sequence 7/8, 8/9, 9/10, 10/11,..., we can observe that the numerator is increasing by 1 and the denominator is also increasing by 1 at each step. The formula for the nth term is:

T_n = (n + 6) / (n + 7)

For the sequence 1/3 × 4, 2/4 × 5, 3/5 × 6, 4/6 × 7,..., we can rewrite each term as a fraction:

1 × 4/3, 2 × 5/4, 3 × 6/5, 4 × 7/6,...

To find the formula for the nth term, observe that the numerator is increasing by 1 and the denominator is increasing by 1 at each step:

T_n = n × (n + 3) / (n + 2)

For the recursively defined sequence a_n = 3a_n - 1 + 5 and a_1 = 3, we will find the first five terms:

a_1 = 3 (given)
a_2 = 3a_1 + 5 = 3(3) + 5 = 14
a_3 = 3a_2 + 5 = 3(14) + 5 = 47
a_4 = 3a_3 + 5 = 3(47) + 5 = 146
a_5 = 3a_4 + 5 = 3(146) + 5 = 443

The first five terms are 3, 14, 47, 146, and 443.

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The first five terms of the given recursively defined sequence. a_n = 3a_n - 1 + 5 and a_1 = 3 are 3, 14, 47, 146, and 443.

To find an expression for the nth term of the sequence 7/8, 8/9, 9/10, 10/11,..., we can observe that the numerator is increasing by 1 and the denominator is also increasing by 1 at each step. The formula for the nth term is:

T_n = (n + 6) / (n + 7)

For the sequence 1/3 × 4, 2/4 × 5, 3/5 × 6, 4/6 × 7,..., we can rewrite each term as a fraction:

1 × 4/3, 2 × 5/4, 3 × 6/5, 4 × 7/6,...

To find the formula for the nth term, observe that the numerator is increasing by 1 and the denominator is increasing by 1 at each step:

T_n = n × (n + 3) / (n + 2)

For the recursively defined sequence a_n = 3a_n - 1 + 5 and a_1 = 3, we will find the first five terms:

a_1 = 3 (given)

a_2 = 3a_1 + 5 = 3(3) + 5 = 14

a_3 = 3a_2 + 5 = 3(14) + 5 = 47

a_4 = 3a_3 + 5 = 3(47) + 5 = 146

a_5 = 3a_4 + 5 = 3(146) + 5 = 443

The first five terms are 3, 14, 47, 146, and 443.

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According to the conventional wisdom, defense-related expenditures in the United States are expected to have a positive skew, with a few states receiving a high amount of spending and most states receiving lower amounts.

The conventional wisdom suggests that a small number of states are well-positioned to influence the allocation of federal defense spending and are successful in securing higher amounts of defense-related expenditures. These states may have influential members of Congress who advocate for their interests, such as by supporting military bases, defense contracts, or research facilities within their constituencies. As a result, these states receive a larger share of the defense budget compared to the majority of states.

In terms of statistical distribution, a positive skew occurs when the tail of the distribution extends towards higher values. In the context of defense-related expenditures, a positive skew would indicate that there are relatively few states with a disproportionately high amount of spending, while the majority of states have lower levels of defense expenditures. This distribution pattern aligns with the conventional wisdom mentioned in the question. Therefore, the answer is (c) a positive skew.

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Answer:

15 people are able to be at the charity gala because 77:55 divided by 5:17.

Answer:

1. 8-10

2. oven

3. 200-220

4 dampen the surface of the bread

5. no allow it to cool

Answer:

6%

Step-by-step explanation:

Answer:

The change in temperature is -6.64

The average hourly rate of change is

6 hours or -3.32

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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(e) The complex number 5+2i in exponential form is (\sqrt{29}e^{i\text{tan}^{-1}\left(\frac{2}{5}\right)}\).
(f) The new period is \(0.31\sqrt{\frac{m}{1.6k}}\) when the spring constant is increased by 60%.

(e) To convert a complex number to exponential form, we need to determine its magnitude and argument. For the complex number 5+2i, the magnitude is given by the formula \(A = \sqrt{{\text{Re}}^2 + {\text{Im}}^2}\) where Re and Im represent the real and imaginary parts, respectively. In this case, the magnitude is \(\sqrt{5^2 + 2^2} = \sqrt{29}\).

The argument, \(\theta\), can be found using the formula \(\theta = \text{tan}^{-1}\left(\frac{{\text{Im}}}{{\text{Re}}}\right)\). For 5+2i, the argument is \(\text{tan}^{-1}\left(\frac{2}{5}\right)\).

Thus, the complex number 5+2i in exponential form is \(Ae^{i\theta} = \sqrt{29}e^{i\text{tan}^{-1}\left(\frac{2}{5}\right)}\).



(f) The period of a spring-mass system is determined by the mass and the spring constant. If the spring constant is increased by 60%, we can calculate the new period using the formula \(T' = T\sqrt{\frac{m}{k'}}\).

Given the original period \(T = 0.31\) seconds and an increase in the spring constant by 60%, we have \(k' = 1.6k\) where \(k\) is the original spring constant.

Substituting the values into the formula, the new period is \(T' = 0.31\sqrt{\frac{m}{1.6k}}\).

Increasing the spring constant causes the spring to become stiffer, resulting in a shorter period. The new period, \(T'\), will be less than the original period \(T\) due to the increased stiffness of the spring.

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Answer:

Step-by-step explanation:

Step 1

Find the height:

Step 2

Find the area:

To apply the Integral Test, we need to find a function f(x) that is continuous, positive, and decreasing such that f(x) = 1/(5√x).

Taking the integral of f(x) from 1 to infinity, we get:

∫1 to infinity (1/(5√x)) dx = 2/5

Since this integral is a finite number, the series is convergent by the Integral Test.
To determine whether the series is convergent or divergent, we will apply the Integral Test as requested. The given series is:

Σ (from n=1 to infinity) of (1 / (5√n))

First, let's consider the function f(x) = 1 / (5√x). This function is positive, continuous, and decreasing for x ≥ 1, which are the necessary conditions for applying the Integral Test.

Now, we evaluate the improper integral:

∫ (from x=1 to infinity) of (1 / (5√x)) dx

To solve this integral, we'll first rewrite the integrand:

1 / (5√x) = 1 / (5x^(1/3))

Now integrate:

∫(1 / (5x^(1/3))) dx = (3/2) * (1/5) * x^(2/3) + C = (3/10) * x^(2/3) + C

Evaluate the improper integral:

lim (t -> infinity) [∫(from x=1 to t) of ((3/10) * x^(2/3)) dx]

= lim (t -> infinity) [(3/10) * (t^(2/3) - 1)]

Since the exponent (2/3) is less than 1, the limit converges to a finite value:

lim (t -> infinity) [(3/10) * (t^(2/3) - 1)] = -(3/10)

Since the improper integral converges, by the Integral Test, the given series is convergent as well.

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Answer:

The domain of a relation is the set of the first coordinates from the ordered pairs.

Explanation: The range is the simple measurement of the difference between values in a dataset. To find the range, simply subtract the lowest value from the greatest value, ignoring the others.

Step-by-step explanation:

Answer:

a^8/256

Step-by-step explanation:

hope this helps!!

Answer:

The percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the formula for the volume of the cylinder is given by:

We have r = 10 inches and h = 5 inches

V = 500π cubic inches

Percent change in volume from cylinder A to cylinder B:

= 50%

Thus, the percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

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Step-by-step explanation:

Answer:

x = 107

Step-by-step explanation:

44+29+107=180

a triangle equals 180 with all the degrees added together :)

Based on the hypothesis test with a 5% significance level, there is sufficient evidence to suggest that the mean cost for auto insurance for teenage boys is significantly greater than that for teenage girls.

To determine if the mean cost for auto insurance for teenage boys is greater than that for teenage girls, we can conduct a two-sample t-test with the following hypotheses

Null hypothesis is the mean cost for auto insurance for teenage boys is equal to that for teenage girls. Alternative hypothesis is the mean cost for auto insurance for teenage boys is greater than that for teenage girls.

At a 5% significance level, the critical t-value for a one-tailed test with 57 degrees of freedom is approximately 1.67.

Using the given sample means and standard deviations, we can calculate the test statistic

t = (x1 - x2 - D) / sqrt(Sp^2 * (1/n1 + 1/n2))

where x1 and x2 are the sample means, n1 and n2 are the sample sizes, Sp^2 is the pooled variance, and D is the hypothesized difference in means under the null hypothesis.

Plugging in the values, we get

t = (677 - 554 - 0) / sqrt(180^2 * (1/36 + 1/23)) = 3.06

Since our test statistic (3.06) is greater than the critical t-value (1.67), we reject the null hypothesis and conclude that there is evidence to suggest that the mean cost for auto insurance for teenage boys is greater than that for teenage girls.

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Answer:

50.24 cm^2

Step-by-step explanation:

The formula for the area of a circle is A = πr^2

The radius is half of the diameter so r = 4

So now you can solve:

A = 3.14(4)^2

= 50.24 cm^2

The x term of the given ordered pairs follow an arithmetic sequence, with common difference of 1.5. The y term of the ordered pairs follow an arithmetic sequence, with common difference of 4.5.

The relationship between the corresponding terms can be described as a linear relationship, where y is a function of x, such that y = 4.5x.

The relationship between the x and y terms can be determined by observing the change in the values between the ordered pairs. For example, the difference in x values between (0,0) and (1.5,4.5) is 1.5, and the difference in y values is 4.5. This pattern continues for all the other pairs, with the x term increasing by 1.5 and the y term increasing by 4.5 for each subsequent pair. This is consistent with an arithmetic sequence, where the difference between each term is constant.

Since the y values increase linearly with the x values, this suggests that the relationship between x and y can be modeled as a linear equation, y = 4.5x. This linear relationship is further confirmed by the fact that the ratio of the increase in the y term to the increase in the x term is constant, and equal to 4.5.

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Answer:

C. Acute

Step-by-step explanation:

Pythagorean theorem can be used to determine the type of triangle any 3 given sides can form.

This,

A right ∆ is formed if a² + b² = c²

An acute ∆ is formed if a² + b² > c²

An obtuse ∆ is formed if a² + b² < c²

Note: c is the longest side of any triangle.

Using the side lengths given:

9.2² + 15.1² ? 17.4²

84.64 + 228.01 ? 302.76

312.65 > 302.76

An acute triangle is formed because a² + b² > c²

Answer:

55 degrees

Step-by-step explanation:

I've found a similar question to this, and the explanation is there.

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m<ABC = 360-250= 110 degrees

"As we know that the measure of angle ABC is equal to half of mADC."

110/2 = 55 degrees.

This should be the answer.