3(2 - b) < 10 - 3(b-6)

Answer:

Step-by-step explanation:

Given Information :

Diameter : 10.2 units

Radius (r) = ?

[tex]r = \frac{d}{2} [/tex]

Input the values

[tex]r = \frac{10.2}{2} \\ \\ r = 5.1[/tex]

If the trace of a 2×2 matrix a is tr(a)=12 and the determinant is det(a)=32, the eigenvalues of matrix a are 4 and 8.

To find the eigenvalues of a 2×2 matrix, we can use the following formula:

λ² - tr(a) * λ + det(a) = 0,

where λ represents the eigenvalues, tr(a) is the trace of the matrix, and det(a) is the determinant.

In this case, we are given that tr(a) = 12 and det(a) = 32. Substituting these values into the formula, we have:

λ^2 - 12λ + 32 = 0.

To solve this quadratic equation, we can factorize it or use the quadratic formula. Factoring the equation, we get:

(λ - 4)(λ - 8) = 0.

Setting each factor equal to zero, we find two solutions:

λ - 4 = 0 => λ = 4,

λ - 8 = 0 => λ = 8.

The trace and determinant of a matrix provide valuable information about its eigenvalues. In this case, by substituting the given trace and determinant into the eigenvalue formula, we were able to find the eigenvalues of the 2×2 matrix a.

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Answer:

7/12

Step-by-step explanation:

Basically to find the boys fraction I subtracted 40 from 96 and got 56. Your answer for the number of boys would be 56/96. I divided 4 from each and got 14/24. lastly I divide by 2 and got 7/12.

Complete question :

The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet. Find length of the ladder.

Answer:

17

Step-by-step explanation:

From Pythagoras :

Hypotenus = sqrt(opposite² + adjacent²)

From the diagram

l = sqrt((l-9)² + 15²)

l² = (l² - 18x + 81 + 225)

Square both sides

l² = l² - 18x + 306

l² - l² = 306 - 18x

18l = 306

l = 306/18

l = 17

Answer:

{7, 13)

Step-by-step explanation:

IR - 31 = 10

IR = 41

7*13 = 41

(-7)*13 = -41

(-13)*13 = -169

Answer: 40 people like song A whereas 20 people like song B. Thus, it is reasonable to say that more people liked Song A .

Step-by-step explanation:

Answer:

250

Step-by-step explanation:

i did cross multiplication 40/100 = 100/x

100*100 and divide by 40

Answer:

C

Step-by-step explanation:

It was right on the quiz

Answer:

It’s B

explanation:

Answer:

Step-by-step explanation:

Answer:

4. 50,000 square miles

5. The office would round to $800,000 instead of $700,000 because they would lose that needed $35,495. If they rounded down, their budget would be cut short, and they won’t have enough money for the office.

6. Five numbers that could also be the population: 577,777; 575,555; 578,999: 578,787; 581,545.

7. 600,000

8.584,000

9. 260,000

Step-by-step explanation:

4. In this question, we’re rounding the number, “54,555” go the nearest ten thousand. When rounding numbers you look at the number next to the digit your rounding. In this case, since the second number is not 5 or higher, we round it to 50,000 as that’s closer than 60,000.

5. Like I stated above: if they round to the lowest amount, they won’t have enough money to but what they need. Therefore, even if according to rounding it needs to be lower, it will not be beneficial to the company.

6. This are all possible numbers cause they can all by round to 580,000 AND 600,000

7. Since the number next to six is not five or higher, we round it to the closest number which is 600,000.

8. Since the number next to 3 is 5, we round it to the higher number. So it’s 584,000

9. Since the number next to the underlined nunber is 6, we round it to the closest number which is 260,000

If you have any more questions, you can ask me :)

[tex]\(\sqrt{k+1}\)[/tex] is irrational.

By the principle of strong induction, we can conclude that the square root of 18 is irrational.

What is irrationality?

In mathematics, irrationality refers to a property of certain numbers that cannot be expressed as a fraction of two integers or as a terminating or repeating decimal.

To prove that the square root of 18 is irrational using strong induction, we need to show that for every positive integer [tex]\(n\), if \(n > 1\) and \(\sqrt{n}\) is irrational, then \(\sqrt{n+1}\)[/tex] is also irrational.

[tex]\textbf{Base Case:}[/tex]

For [tex]\(n = 2\)[/tex], we have [tex]\(\sqrt{2}\).[/tex] It is a known fact that [tex]\(\sqrt{2}\)[/tex] is irrational. Thus, the base case holds true.

[tex]\textbf{Inductive Step:}[/tex]

Assume that for some positive integer k, if[tex]\(2 \leq k\) and \(\sqrt{k}\)[/tex] is irrational, then [tex]\(\sqrt{k+1}\)[/tex] is also irrational.

Now, consider the case for [tex]\(n = k+1\)[/tex]). We want to prove that [tex]\(\sqrt{k+1}\)[/tex] is irrational.

Since [tex]\(k \geq 2\)[/tex], we have [tex]\(k+1 > 2\)[/tex]. Therefore,[tex]\(\sqrt{k+1}\) is greater than \(\sqrt{2}\).[/tex]

Assume, for contradiction, that [tex]\(\sqrt{k+1}\)[/tex] is rational. Then, we can write \[tex](\sqrt{k+1}\)[/tex] as a fraction [tex]\(\frac{p}{q}\),[/tex] where p and q are positive integers with no common factors other than 1.

By squaring both sides, we get [tex]\(k+1 = \left(\frac{p}{q}\right)^2 = \frac{p^2}{q^2}\).[/tex]

Rearranging the equation, we have[tex]\(p^2 = (k+1)q^2\).[/tex]

Since [tex]\(k+1\)[/tex] is a positive integer and [tex]\(q^2\)[/tex] is also a positive integer, [tex]\(p^2\)[/tex]must be a multiple of [tex]\(k+1\)[/tex].

This implies that p must also be a multiple of [tex]\(k+1\).[/tex] Let \(p = m(k+1)\), where m is a positive integer.

Substituting this into the equation, we have [tex]\((m(k+1))^2 = (k+1)q^2\)[/tex].

Simplifying, we get [tex]\(m^2(k+1) = q^2\).[/tex]

This implies that [tex]\(q^2\)[/tex] is a multiple of [tex]\(k+1\)[/tex], which means [tex]\(q\)[/tex] is also a multiple of [tex]\(k+1\).[/tex]

However, this contradicts our assumption that p and q have no common factors other than 1.

Hence, our assumption that  [tex]\(\sqrt{k+1}\)[/tex] is rational must be false.

Therefore, [tex]\(\sqrt{k+1}\)[/tex] is irrational.

By the principle of strong induction, we can conclude that the square root of 18 is irrational.

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Answer:

4 centimetres per hour.

Step-by-step explanation:

Answer:

(3x-2)(2x-3)

Step-by-step explanation:

Good luck!

Answer:

7.1437 is greater

Step-by-step explanation:

Answer:

7.133 < 7.1437

Step-by-step explanation:

Line up the numbers till you find one that is greater

Answer:

A rhombus is a special type of parallelogram

Step-by-step explanation:

Similarities in a rhombus and parallelogram:

A rhombus is a special type of parallelogram in that

The correct answer is c) an outlier and a leverage point.A data point far from the mean of both the x's and y's is both an outlier and a leverage point.

A data point that is far from the mean of both the x-values and y-values can be considered an outlier and a leverage point. An outlier is a data point that significantly deviates from the overall pattern of the data. It lies far away from the majority of the data points and can have a significant impact on statistical analysis.

On the other hand, a leverage point is a data point that has an extreme value in terms of its x-value. It has the potential to influence the regression line and can greatly affect the regression model's fit. Therefore, a data point far from the mean of both x's and y's can be considered both an outlier and a leverage point.

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The estimator V₁ = 1/2(X₁ + X₂) is preferred over V₂ = 1/2(X₁ + 2X₂) because it is unbiased and has a smaller variance.

To determine which estimator to use, consider the properties of unbiased estimators and compare the variances of V₁ and V₂.

Unbiasedness:

For V₁:

E(V₁) = E(1/2(X₁ + X₂)) = 1/2(E(X₁) + E(X₂)) = 1/2(µ + µ) = µ

For V₂:

E(V₂) = E(1/2(X₁ + 2X₂)) = 1/2(E(X₁) + 2E(X₂)) = 1/2(µ + 2µ) = 3/2µ

From the calculations, we can see that V₁ is an unbiased estimator of the population mean µ, while V₂ is biased since E(V₂) ≠ µ

Therefore, V₁ is preferred in terms of unbiasedness.

Variance:

Var(V₁) = Var(1/2(X₁ + X₂)) = 1/4(Var(X₁) + Var(X₂) + 2Cov(X₁, X₂))

Var(V₁) = 1/4(δ² + δ² + 2*0) = 1/2δ²

Var(V₂) = Var(1/2(X₁ + 2X₂)) = 1/4(Var(X₁) + 4Var(X₂) + 2Cov(X₁, 2X₂))

Var(V₂) = 1/4(δ² + 4δ² + 2*0) = 5/4δ²

Comparing the variances, we can see that Var(V₁) = 1/2δ², while Var(V₂) = 5/4δ².

Since Var(V₁) is smaller than Var(V₂), V₁ is preferred in terms of variance as well.

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Answer:

V = 17,371.8

Step-by-step explanation:

V = π r^2 h

V = π (12)^2 (38.4)

V = 17,371.75073729

V = 17,371.8

You have to calculate the area of the base of the cylinder (the circle) by using the formula π r^2, r = the radius of the circle. You are squaring the r because r^2 = diameter. The formula to get the area of a circle is π r ^2. To get the volume you need to multiply the area of the circle by the height of the cylinder. All together the total formula to get the volume of a cylinder is π r^2 h

Answer: -7

Because if y is -7 then the equation would be 4 - 7 = -3 which is true :)

Answer:

1h=20m

60/4

0,25min+1h

1+0,25

=1,2

He will complete the race in 1.2 hours time.

Hence, option B is correct.

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that,

The distance completing in 1 hour = 20 miles

So 1 miles of distance is covered in = 1/20 hours

It is also given that,

The distance of rally = 24 miles.

Therefore,

The time taken to cover 24 miles = 24/20

                                                        = 1.2

Thus,

The required time = 1.2 hours

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Answer:

21900

Step-by-step explanation:

Find 8% of 7500 (600) and multiply it by 24 (amount of months) then add that to 7500

Answer:

X=25

Step-by-step explanation:

y+2=-7+2=5

[tex]5^{2} =25[/tex]

The variable "pounds of popcorn" served at a movie theater is a continuous variable that can take any value within a certain range. It is not restricted to specific discrete values or categories.

A continuous variable is one that can take any value within a certain range. In the case of "pounds of popcorn" served at a movie theater, it can have fractional values and can vary continuously from very small amounts to large amounts.

It is not restricted to specific discrete values or categories. In contrast, discrete variables can only take on specific values, while ratio variables have a meaningful zero point and allow for comparisons of ratios. Since the amount of popcorn served can be measured with any level of precision, it falls under the category of a continuous variable.

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Answer:

32.5 units²

Step-by-step explanation:

We can find the area by dividing the figure into two shapes. If we solve for the area of a square and a triangle, we can add them together.

First, we can solve for the area of the 5x5 square. To find the area, we can multiply the two dimensions.

5 · 5 = 25 units²

Next, we can find the area of the triangle. It has an equal height to the square, so the height of the triangle is 5 units. The width isn't specified. Instead, we are shown that the width of both the square and the triangle equals 8 units. If we subtract the width of the square from the total, we can find the width of the triangle, too.

8 - 5 = 3

So, the height and the width of the triangle are 5x3. To find the area we can multiply these together, and then divide the product by two.

5 · 3 = 15

[tex]\frac{15}{2}[/tex] = 7.5

The area of the triangle is 7.5 units².

Finally, we can add the area of the triangle and the square together.

25 + 7.5 = 32.5

The area of the figure, then, is 32.5 units².

The answer is the last option.

I hope this helps ^^

To evaluate dy/dt given the equation y³ = 2x² + 14, along with dx/dt = 3, x = 5, and y = 4, we can use implicit differentiation and substitute the given values.

dy/dt is approximately equal to 0.51 (rounded to two decimal places).

To explain the solution, let's start by differentiating both sides of the equation implicitly with respect to t:

3y²(dy/dt) = 4x(dx/dt)

Now, we substitute the given values x = 5, y = 4, and dx/dt = 3 into the equation:

3(4)²(dy/dt) = 4(5)(3)

Simplifying this expression, we have:

48(dy/dt) = 60

Dividing both sides by 48, we find:

dy/dt = 60/48 = 1.25

Therefore, dy/dt is approximately equal to 1.25. Rounded to two decimal places, the value is 0.51.

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Answer:

The answer is "320".

Step-by-step explanation:

They have to be 1, 3, 5, 7, and 9 as your final digit. Your middle digit may be anything other than the first digit, and only the last digit or 0, is anything.

Now let us take a look at strange digits ending in 1.

This can start from any digit other than 0, so there are 8 options during the first digit.

Its middle digit could only be 1 digit and 1 digit. Even so, it can also be 0, since it has 8 options.

So, [tex]8\times 8 = 64[/tex] strange number ending in 1.

For other strange amounts, the very same logic is working.

And thus there are 64 possible odd numbers for just about any number ending in any of the five odd digits: 1, 3, 5, 7, or 9.

The answer is [tex]5 \times 64 = 320[/tex].

154 yd ²

the formula is (b • h) / 2 = A

so plug it in (14 • 22) / 2 = 154

Answer:

The angles are adjacent because they have a common side and vertex. Basically, they are both right next to each other.

x = 28

Step-by-step explanation:

When (x + 6)° and 56° are added together, they need to equal 90° since they are both parts of a right angle.

(x + 6) + 56 = 90

x + 62 = 90

x = 28