Question number eight.

Answer:

it's 290

Step-by-step explanation:

\( \frac{290}{29} + 156\)

\(10 + 156 = 166\)

The required probability is  \(\frac{1}{10}\).

This problem is related to probability.

First we have to calculate the number of outcomes and then the number of favorable outcomes.

In this case the numbers are from 1 to 150.

First we have to find the numbers which are perfect square between 1 to 150= {1,4,9,16,25,36,49,64,81,100,121,144}

Now we have to find the numbers which are perfect cube other than those which came in square={8,27,125}

Here the number of favorable outcome is 150 minus number of elements in set of perfect square and perfect cube.

Now the probability of the required problem is = \(\frac{15}{150}\)

                                                                         = \(\frac{1}{10}\)

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The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

How to find the volume of a rectangular prism and pyramid?

The formula for the volume of a rectangular prism is:

Volume = Length * Width * Height

The formula for the volume of a pyramid is:

Volume = (Base Area * Height) / 3

The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

This is because the volume of a rectangular prism is calculated by multiplying its three dimensions together, whereas the volume of a pyramid is calculated by multiplying the base area by the height and dividing the result by 3.

Hence, the volume of the rectangular prism is greater than the volume of the pyramid with the same height and base. This is because the rectangular prism has additional volume in the form of its width, which the pyramid does not have.

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Option d) is correct, i.e. a rotation, then a dilation. Transformation will create a pair of similar but not congruent triangles.

Which composition of transformations will create a pair of similar, not congruent triangles?

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

When triangle is rotated, than position of angles will change. Aftermath the dilation of the triangle would increase the proportion of the sides, but angles remains equal, by which the triangle remain similar but not congruent.

Thus, a rotation, then a dilation transformation will create a pair of siilar but not congruent triangles.

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Answer:

D. a rotation, then a dilation

Step-by-step explanation:

got it right on edge 23

Answer:

(1,2), (2,4), (5,10), (8,16)

Step-by-step explanation:

For the time, the number it land on that would be you x axis and the distance would be your y axis

Answer:

30 min

Step-by-step explanation:

The tank can be filled in 15 min, this means that in one min, 1/15 of the tank can be filled.

The tank can be emptied in 10 min, this means that in one min, 1/10 of the tank can be emptied.

the outflow rate - the inflow rate = rate of emptying the tank

1/10 - 1/15 = 1/x

where x is the time it will take to empty the tank

solving, we'll have

1/30 = 1/x

the reciprocal of the equation gives

x = 30 min

Answer:

Answer = 15

Step-by-step explanation:

since y = 13

replace y with 13 in the given equation (y-6)+8

=(13-6) + 8

=(7) + 8

=15

Answer:

4 and (q − 18 + p)

Step-by-step explanation:

Given:

4(q−18+p)

The factors are

4 and (q − 18 + p)

A factor refers to something which is multiplied by something else. It could be a number, variable, term, or a longer expression.

For example. The factors of the expression 6x(y +2)

are 6, x and (y+2)

After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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The phlebotomist should first collect STAT electrolytes in the ER.

A medical professional who is trained to draw blood samples from patients is known as phlebotomist. The process of taking blood from vein with the help of a needle is known as phlebotomy. An electrolyte test is a blood test that give information about an electrolyte imbalance in the body.

Electrolytes are minerals and salts, such as sodium, Chloride, potassium, and bicarbonate which are found in the blood. These are responsible for conducting electrical impulses in the body. STAT is a short form of a Latin word 'Statim' which means immediately. The phlebotomist should first collect STAT electrolytes in the ER.

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Answer: Greatest common factor (GCF) of 12 and 28 is 4. We will now calculate the prime factors of 12 and 28 then find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12 and 28.

Step-by-step explanation: BRAINLESS PLEASE

The E(X) is 3/2 and the Var(X) is 3/40.Given probability density function (PDF) as:

fX(x) = { cx² for 0 ≤ x ≤ 2, { 0 otherwise To find the value of 'c' we will use the property that the area under the probability density function from 0 to 2 should be equal to 1.

Mathematically,∫fX(x) dx = ∫cx² dx = 1

=> [c (x³/3)]₀² = 1

=> (8/3) c = 1

=> c = 3/8

Thus, the value of c is 3/8.

To compute P(X > 3/2), we need to integrate the PDF from 3/2 to 2, asX> 3/2 for given distribution.

∫3/2² (3/8)x² dx

= [x³/8]₃/₂²

= (1/2) - (27/64)

= 19/64

Hence, P(X > 3/2) = 19/64

To find the cumulative distribution function (CDF), we integrate the PDF from -∞ to x.

FX(x) = ∫ fX(x) dx 0 ≤ x ≤ 2,

= ∫0x 3/8 x² dx 0 < x < ∞

= [x³/24]₀², 0 ≤ x ≤ 2

FX(x) = { 0 for x < 0 { x³/24 for 0 ≤ x ≤ 2 { 1 for x > 2

The expected value or mean of the probability distribution is given as,

E(X) = ∫xfX(x) dx

= ∫₀² x × (3/8) × x² dx

= (3/8) ∫₀² x³ dx

= (3/8) [(x⁴/4)]₂₀

= 3/2

The variance of the probability distribution is given by,

Var(X) = E(X²) - [E(X)]²

= ∫₀² x²(3/8) x² dx - [3/2]²

= (3/8) ∫₀² x⁴ dx - 9/4

= (3/8) [(x⁵/5)]₂₀ - 9/4

= (3/8) (32/5) - 9/4

= 3/40

Hence, the E(X) is 3/2 and the Var(X) is 3/40.

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Yeah, it seems fine so you're doing great so far! ^^

Answer:

7

Step-by-step explanation:

Since 9 and 11 do not factor 35, they are not the answer.

5 is a factor of 35, but not the largest. So, the answer is 7.

Answer:

the largest prime factor of 35 is 5

Step-by-step explanation:

and one of these day I must get straigh and drip all over you

The dot product of the vectors (3,3) and (-5,1) is -12.

The component form of vector g is approximately (-1.5, -3.9).

The magnitude of vector o is 2.

The dot product of the vectors (3,3) and (-5,1) is given by:

(3,3) · (-5,1) = 3(-5) + 3(1) = -12

Therefore, the dot product of the two vectors is -12.

Vector g is from the red jet ski to green, and its magnitude is √26.

The direction angle of vector g is 248.7°.

To write the component form of vector g, we can use the formula:

g = (|g| cos θ, |g| sin θ)

where |g| is the magnitude of vector g, and θ is the direction angle of vector g.

Substituting the given values, we get:

g = (√26 cos 248.7°, √26 sin 248.7°)

Using a calculator, we can evaluate:

g ≈ (-1.5, -3.9)

Therefore, the component form of vector g is approximately (-1.5, -3.9).

Given that the dot product of two vectors o · o is 4, we can use the formula for the magnitude of a vector:

|o| = √(o · o)

Substituting the given value, we get:

|o| = √4 = 2

Therefore, the magnitude of vector o is 2.

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Answer:

x/5+9/5=y or x+9/5=y

Step-by-step explanation:

y= 5x-9

x=5y-9

x+9=5y

x+9/5=y

The correct choice for the given options would be: OA. The point(s) at which the tangent line is horizontal is (approximately) (√(7/3), 3√(7/3)), (-√(7/3), 3√(7/3))

To find the point on the curve y = 8x² + 3x where the slope of the tangent line is equal to 197, we need to find the derivative of the curve and set it equal to 197.

Find the derivative of y = 8x² + 3x:

y' = d/dx (8x² + 3x)

= 16x + 3

Set the derivative equal to 197 and solve for x:

16x + 3 = 197

16x = 194

x = 194/16

x = 12.125

Substitute the value of x back into the original equation to find the corresponding y-value:

y = 8(12.125)² + 3(12.125)

y ≈ 1183.56

Therefore, the point on the curve y = 8x² + 3x where the slope of the tangent line is equal to 197 is approximately (12.125, 1183.56).

To find the point at which the slope of a tangent line is 19 for the function (not specified), we would need the equation of the function to proceed with the calculation.

For the function y = x³ - 7x + 3, to find the points on the graph where the tangent line is horizontal, we need to find the values of x where the derivative of the function is equal to 0.

Find the derivative of y = x³ - 7x + 3:

y' = d/dx (x³ - 7x + 3)

= 3x² - 7

Set the derivative equal to 0 and solve for x:

3x² - 7 = 0

3x² = 7

x² = 7/3

x = ±√(7/3)

Substitute the values of x back into the original equation to find the corresponding y-values:

For x = √(7/3):

y = (√(7/3))³ - 7(√(7/3)) + 3

= 7√(7/3) - 7(√(7/3)) + 3

= 3√(7/3)

For x = -√(7/3):

y = (-√(7/3))³ - 7(-√(7/3)) + 3

= -7√(7/3) + 7(√(7/3)) + 3

= 3√(7/3)

Therefore, the points on the graph where the tangent line is horizontal are approximately (±√(7/3), 3√(7/3)).

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Answer:

Step-by-step explanation:

69

Answer:

y = x - 3

Step-by-step explanation:

Answer:

Y= x-3

Step-by-step explanation:

The distance from our y values is -1.

The distance from our x values is -1.

Rise/ Run = Y/X

-1/-1 = 1 or 1/1

You would rise 1 and run 1!

You can use this strategy if you're using graph paper to eventually get the y intercept which is -3.

Hope this helps! :)

The question isn't well formatted :

From what is obvious, the result of the product are given below :

Answer:

2 × 3 = 6

5 × 6 = 30

4 × 3 = 12

3 × 1 = 3

Step-by-step explanation:

Using calculator :

The product of 2 and 3 : 2 * 3 = 6

Product of 5 and 6 : 5 * 6 = 30

Product of 4 and 3 : 4 * 3 = 12

Product of 3 and 1 : 3 * 1 = 3

The evaluation of the given iterated triple integral is (8/25) * [8√z\(^(5/2)\) - z\(^(5/2)\)].

To evaluate the given iterated triple integral ∫∫∫ x√(x)√(∫zdy)dzdydx, we can start by integrating the innermost integral with respect to y.

∫zdy = zy

Next, we substitute the limits of integration for y, which are y = 0 to y = x.

∫zdy = ∫(zy)dy = 1/2z(x\(^2\) - 0^2) = 1/2zx\(^2\)

Now, we have the expression x√(x)√(∫zdy) = x√(x)√(1/2zx\(^2\)) = x^(3/2)√(1/2z).

Moving to the second integral, we integrate the expression x√(x)√(1/2z) with respect to z.

∫x\(^(3/2)\)√(1/2z)dz

To simplify this integral, we can take out the constants outside the integral:

(1/2)∫x\(^(3/2)\)√(1/z)dz

Now, we can integrate √(1/z) with respect to z:

(1/2)∫x\(^(3/2)\) * 2√z dz = ∫x^(3/2)√z dz = (2/5)x\(^(3/2)\)z\(^(5/2)\)

Finally, we integrate the expression (2/5)x\(^(3/2)\)z with \(^(5/2)\)respect to x over the given limits x = 1 to x = 10.

∫10∫1 (2/5)x\(^(3/2)\)z dx\(^(5/2)\)

Substituting the limits and integrating:

(2/5)∫10∫1 x\(^(3/2)\)z\(^(5/2)\) dx = (2/5) * [(2/5)x\(^(5/2)\)z\(^(5/2)\)] evaluated from x = 1 to x = 10

= (2/5) * [(2/5)(10)\(^(5/2)\))z - (2/5\(^(5/2)\))(1)\(^(5/2)\)z]\(^(5/2)\)

= (2/5) * [(2/5)(100√z - 2/5\(^(5/2)\))z]\(^(5/2)\)

= (2/5) * [40√z\(^(5/2)\) - 2z\(^(5/2)\)]

= (8/25) * [8√z - z]\(^(5/2)\)

Therefore, the evaluation of the given iterated triple integral ∫∫∫ x√(x)√(∫zdy)dzdydx is (8/25) * [8√z\(^(5/2)\) - z].\(^(5/2)\)

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For the number of miles driven, Company A will charge less than Company B if x<y, where x is the number of miles driven for Company A and y is the number of miles driven for Company B. Therefore, the inequality is x<y.

When comparing two companies for their charges for a specific service, it is necessary to obtain a basic understanding of the charges for each company. You can make use of the inequality operator to check when one company will charge less than the other company.

To use the inequality operator, you'll need to calculate the differences between the two companies for the specific mileage. Let's assume that the mileage is represented by "m" and that the charge for company A is "cA" and the charge for company B is "cB".

If the question only provides specific numerical values for these variables, you can substitute them into the inequality formula. If you're given algebraic expressions, you'll need to simplify them before substituting them into the inequality formula.

The inequality formula for comparing the charges is as follows: cA < cB.

To use this formula, substitute the expression for each variable.

For example: 4m + 20 < 3.5m + 35 Now, you'll need to simplify the inequality by performing algebraic operations on both sides of the inequality. Begin by subtracting 3.5m from both sides of the inequality: 0.5m + 20 < 35.

Next, subtract 20 from both sides of the inequality: 0.5m < 15 Finally, divide both sides of the inequality by 0.5: m < 30

Therefore, Company A will charge less than Company B for any mileage less than 30.

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it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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Given that Angelo spends the same amount everyday from the amount in

the lunch card, the function of the amount remaining is a linear function.

Reasons:

The amount Angelo's mother put on the lunch card = $50

A possible table of values to the question is presented as follows;

\(\begin{tabular}{r|c|c|c|c|}Days&0&1&2&3\\Money Remaining&&44.75&39.5&\end{array}\right]\)

Required:

The constant rate of the function that gives the amount remaining from the

amount Angelo's mother put on his lunch card.

Solution:

The two ordered pair that can be used to find the slope or constant rate of change are;

(x₁, y₁) = (1, 44.75), and (x₂, y₂) = (2, 39.5)

With the above two ordered pairs, we have the constant rate of change of the function given as follows;

\(Constant \ rate \ of \ change\ (The \ slope) =\dfrac{39.5-44.75}{2-1} = \mathbf{ -5.25}\)

The constant rate of change for the function that gives the amount remaining in the lunch card is; -5.25

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Answer:

356.53

Step-by-step explanation:

Calculate the semicircle and square areas separately. For the semicircle, A = πr²/2, so 100.53

And for the square, A = a², so 256

Hope this helps

The volume of the solid obtained by rotating the region bounded by the parabola 28y = x² and the square root function y= √28x around the x-axis is 392π/3.

To find the volume of the solid, we use the method of cylindrical shells.

Consider a vertical strip of thickness dx at a distance x from the y-axis. The strip has height (y₂ - y₁) where y₂ is the value of the square root function and y₁ is the value of the parabola.

From the equation of the square root function, we have:

y₂ = √(28x)

From the equation of the parabola, we have:

y₁ = x²/28

Therefore, the height of the strip is:

(y₂ - y₁) = √(28x) - x²/28

The circumference of the cylindrical shell at x is:

2πr = 2πy₁ = 2π(x²/28)

Thus, the volume of the shell is:

dV = 2π(x²/28) * [√(28x) - x²/28] dx

To find the total volume, we integrate dV from x = 0 to x = 28:

V = ∫₀²⁸ 2π(x²/28) * [√(28x) - x²/28] dx

Simplifying and evaluating the integral, we get:

V = 392π/3

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