find the HCF of 18(2x^3-x^2-x)and 20(24x^4 +3x)​

Answer:

\(f(g(x))\)  = \(\sqrt{8x - 4}\)

Step-by-step explanation:

• \(f(x) = \sqrt{x + 8}\)

• \(g(x) = 8x - 12\)

\(f(g(x))\) is the combination of the functions \(f(x)\) and \(g(x)\) such that \(g(x)\) is the input to the function \(f(x)\) .

This means, we have to replace the original input of  \(f(x)\), which is \(x\), with the function  \(g(x)\).

∴  \(f(g(x))\) = \(f(8x - 12)\)

               ⇒ \(\sqrt{8x - 12 + 8}\)

               ⇒ \(\sqrt{8x - 4}\)

Answer:

75 in^2

Step-by-step explanation:

Given data

From the figure

We can see a rectangle and a triangle

The area of the rectangle is

Area= L*W

Area= 13*5

Area= 65 in^2

Area of the triangle

Area= 1/2b*h

Area= 1/2*4*5

Area= 2*5

Area= 10 in^2

Hence the area of the composite figure is

Area= 65+10

Area= 75 in^2

Answer:

Step-by-step explanation:

This is the image of the graph you determine if that's perpendicular.

Perpendicular definition - In elementary geometry, the property of being perpendicular is the relationship between two lines which meet at a right angle. The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle.

Answer:

x = no solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

4x - 5 = x - 1 + 3x

Step 2: Solve for x

Here we see that -5 does not equal -1.

∴ This equation has no solutions.

Answer:

Step-by-step explanation:

\(a_{n}=a_{1}r^{n-1}\\0=848(0.75)^{n-1}\\or~(0.75)^{n-1}=0\\0.75<1\\so~(0.75)^{n-1} \rightarrow 0,if~n-1 \rightarrow ~\infty\)

\(or~n \rightarrow 1+\infty\\or~n \rightarrow \infty\)

Hence lake will never be free of pesticide.

Answer:

- 9 + 12x

Step-by-step explanation:

- 3(3 - 4x) ← multiply each term in the parenthesis by - 3

= - 9 + 12x

Answer:

\( \boxed{\sf b. \ 8(2a + 9)} \)

Step-by-step explanation:

\( \sf Factor \: the \: following: \\ \sf \implies 16a + 72 \\ \\ \sf Factor \: 8 \: out \: of \: 16a + 72: \\ \sf \implies 8 \times 2a + 8 \times 9 \\ \\ \sf \implies 8(2a + 9)\)

The answer of the given question is inferential statistics.

The mathematical procedures used to assume or understand predictions about the whole population, based on the data collected from a random sample selected from the population, are called inferential statistics.

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The mathematical procedures used to assume or understand predictions about the whole population based on data collected from a random sample selected from the population are called statistical inference techniques.

Statistical inference involves drawing conclusions, making predictions, and testing hypotheses about population parameters based on sample data. These techniques include methods such as estimation, hypothesis testing, confidence intervals, and regression analysis.

By using statistical inference, we can generalize findings from the sample to make inferences about the larger population, allowing us to make informed decisions and draw meaningful conclusions based on the available data.

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Answer:

B

Step-by-step explanation:

Answer:

(-5/2,-4)

Step-by-step explanation:

the answer is (x, y) = (-5/2, -4)

The statistics are as follows:

- Test Statistic: The calculated test statistic is approximately 1.02.

- P-value: The P-value associated with the test statistic of 1.02 is approximately 0.154.

- Confidence Interval: The 95% confidence interval for the difference in proportions is approximately -0.0186 to 0.0786.

To solve the problem completely, let's go through each step in detail:

1. Test Statistic:

The test statistic can be calculated using the formula:

z = (p1 - p2) / √[(p_cap1 * (1 - p-cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

Substituting these values into the formula, we get:

z = (0.55 - 0.53) / √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

z = 0.02 / √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

z ≈ 0.02 / √(0.0001386 + 0.0002493)

z ≈ 0.02 / √0.0003879

z ≈ 0.02 / 0.0197

z ≈ 1.02 (rounded to two decimal places)

Therefore, the test statistic is approximately 1.02.

2. P-value:

To find the P-value, we need to determine the probability of observing a test statistic as extreme as 1.02 or more extreme under the null hypothesis. We can consult a standard normal distribution table or use statistical software.

The P-value associated with a test statistic of 1.02 is approximately 0.154, which means there is a 15.4% chance of observing a difference in proportions as extreme as 1.02 or greater under the null hypothesis.

3. Confidence Interval:

To estimate the difference in proportions with a 95% confidence interval, we can use the formula:

(p1 - p2) ± z * √[(p_cap1 * (1 - p_cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

z = 1.96 (for a 95% confidence interval)

Substituting these values into the formula, we get:

(0.55 - 0.53) ± 1.96 * √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

0.02 ± 1.96 * √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

0.02 ± 1.96 * √(0.0001386 + 0.0002493)

0.02 ± 1.96 * √0.0003879

0.02 ± 1.96 * 0.0197

0.02 ± 0.0386

The 95% confidence interval for the difference in proportions is approximately (0.02 - 0.0386) to (0.02 + 0.0386), which simplifies to (-0.0186 to 0.0786).

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The probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19.

The probability of picking a green ball on the first pick, given that at least one red is chosen, can be calculated by finding the total number of possible outcomes and then dividing by the number of outcomes that include at least one red ball. In this bag, there are 11 green balls and 5 red balls, for a total of 16 balls. Since two balls are taken out successively without replacement, the total number of outcomes is 16 choose 2, or 120. Of those, there are 10 outcomes that include at least one red ball, so the probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19. This can be calculated by dividing the number of outcomes that include at least one red ball (10) by the total number of outcomes (120).

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Answer: The answer is net B

Step-by-step explanation: If you look at the net it has one rectangle for the base and four triangles for the side. Then when you look at the completed figure the shapes are the same. Also all the other nets have the wrong shapes.

Hope this helps.

(Edit- was lookin at the wrong stuff answer = d lol sorry

Answer:

Step-by-step explanation:

The mode in a given  set of data is the number that appears the most.

4 appears twice

5 appears twice

3 appears once

1 appears once

6 appears once

Answer:

Step-by-step explanation:

The required solutions of the given system of equations is x = -7 and y = -5.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

Given system of equation

y=x+2 - - - - -(1)

y=4x+23 - - - - (2)

From above equations,
x + 2 = 4x + 23
x = -7

Now,
y = -7 + 2
y = -5

Thus, the required solutions of the given system of equations is x = -7 and y = -5.

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The arc length of the arc intercepted by an angle of 155° of a circle of radius 11.9 cm is 32.2 cm

The arc length is the portion of the circumference of a circle swept by radius by making some angle at the center. If this angle is measured in degrees say some α degrees, then the arc length is given by the formula:

Arc length = (α/360°)*(2πr) ,   where r is the radius of the circle

Given that a circle if of radius 11.9 cm and arc on its circumference is intercepted  by an angle of 155° , r =11.9 and α   = 155°

Then the arc length = (155°/360°)*(2π(11.9)) = (155*2*22*11.9)/(360*7)= 32.2 cm

Therefore, the arc length is 32.2

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The number of calories in stalk of celerystalk and carrot is found as 20 and 7 respectively.

For the given question;

Let the number of calories present in carrot is 'x'.

Let the number of calorie present in celerystalk is 'y'.

Carrot has 13 more calories than celerystalk.

Thus,

x = y + 13   ......eq 1

Now, 5 carrots and 10 celery stalks have total 170 calories.

The equation becomes.

5x + 10y = 170

Substitute the value of x from eq 1.

5(y + 13) + 10y = 170

Simplify the equation;

5y + 65 + 10y = 170

15y = 105

y = 7 (number of calories in stalk of celerystalk)

Put the value of y in eq 1.

x = y + 13

x = 7 + 13  

x = 20 (number of calories in stalk of carrot)

Thus, the number of calories in stalk of celerystalk and carrot is found as 20 and 7 respectively.

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(a) In cylindrical coordinates: (r, θ, z) = (3√2, -π/3, -9). (b) In spherical coordinates: (ρ, θ, φ) = (√91, -π/3, π/2).

(a) The point (-√3, 3, -9) in cylindrical coordinates is (r, θ, z) = (√(9 + 3), arctan(3/(-√3)), -9) = (3√2, -π/3, -9).

In cylindrical coordinates, the conversion from rectangular coordinates is done using the following formulas:

r = √(\(x^{2}\) + \(y^{2}\)),

θ = arctan(y/x),

z = z.

By substituting the given values (-√3, 3, -9) into the formulas, we obtain the cylindrical coordinates (r, θ, z) = (3√2, arctan(3/(-√3)), -9) = (3√2, -π/3, -9).

(b) The point (-√3, 3, -9) in spherical coordinates is (ρ, θ, φ) = (√(9 + 3 + 81), arctan(3/(-√3)), arccos(-9/√(9 + 3 + 81))) = (√91, -π/3, π/2).

In spherical coordinates, the conversion from rectangular coordinates is done using the following formulas:

ρ = √(\(x^{2}\) + \(y^{2}\) + \(z^{2}\)),

θ = arctan(y/x),

φ = arccos(z/√(\(x^{2}\) + \(y^{2}\) + \(z^{2}\))).

By substituting the given values (-√3, 3, -9) into the formulas, we obtain the spherical coordinates (ρ, θ, φ) = (√(9 + 3 + 81), arctan(3/(-√3)), arccos(-9/√(9 + 3 + 81))) = (√91, -π/3, π/2).

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3 hours and 45 minutes = 3.75 hours

\(\frac{100}{3.75}=\boxed{26.\overline{6}}\)

Answer:

Side LM is congruent to side RQ

Angle MNO is congruent to angle RST

Side ON is congruent to side ST

Angle LMN is congruent to angle QRS

Step-by-step explanation:

A way to solve this is to use parchment paper or draw the same shape next to each other, as you will get these:

Side LM is congruent to side RQ

Angle MNO is congruent to angle RST

Side ON is congruent to side ST

Angle LMN is congruent to angle QRS

The volume of the rectangular prism is 8 cubic meters when it takes 8 blocks with a side lengths of one fourths meter to fill a rectangular prism.

If it takes 8 blocks with a side length of one fourths meter to fill a rectangular prism, we can assume that the volume of each block is:

\((1/4)^3 = 1/64m^3\)

To find the volume of the rectangular prism, we need to know its dimensions. We can express its volume as one of the given options:

One eights cubic meters: This means the volume is 1/8 cubic meters. We can find the number of blocks needed to fill this volume by dividing the total volume by the volume of each block:

(1/8) ÷ (1/64) = 8 blocks

This doesn't match the given information, since we were told that it takes 8 blocks to fill the prism, not that the volume of the prism is 8 times the volume of a block.

One fourths cubic meters: This means the volume is 1/4 cubic meters. We can find the number of blocks needed to fill this volume in the same way:

(1/4) ÷ (1/64) = 16 blocks

This also doesn't match the given information.

Half cubic meters: This means the volume is 1/2 cubic meters. We can find the number of blocks needed to fill this volume:

(1/2) ÷ (1/64) = 32 blocks

Since it takes 8 blocks to fill the prism, this option doesn't match either.

One cubic meter: This means the volume is 1 cubic meter. We can find the number of blocks needed to fill this volume:

1 ÷ (1/64) = 64 blocks

This matches the given information, since it takes 8 blocks to fill the prism, which means there are 8 layers of 8 blocks each. Therefore, the dimensions of the prism are:

length = 8 × (1/4) = 2 meters

width = 8 × (1/4) = 2 meters

height = 8 × (1/4) = 2 meters

So the volume of the rectangular prism is:

volume = length × width × height = 2 × 2 × 2 = 8 cubic meters.

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The bearing is the angle measured clockwise from the north direction to a specified direction. To find the bearing of Town Y from Town B, we use the given information that Town B is located south 38 degrees east from Town Y. By subtracting this angle from 180 degrees, we find that the bearing is 142 degrees.

To determine the bearing, we need to find the angle between the north direction and the direction from Town B to Town Y.

Since Town B is located south of Town Y, the bearing will be a southern direction. The bearing angle can be calculated as 180 degrees minus the given angle, which is 38 degrees.

Therefore, the bearing of Town Y from Town B is 180 - 38 = 142 degrees.

In conclusion, the main answer is that the bearing of Town Y from Town B is 142 degrees.

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When x = 90, ΔC = $5.31 and C'(x) = 2.2.
Given the total-cost function C(x) = 0.01x^2 + 0.4x + 50, we'll first find the change in cost (ΔC) and then the derivative of the cost function (C'(x)) when x = 90 and Δx = 1.

To find ΔC when x = 90 and ΔΧΖ = 1, we need to use the formula:
ΔC = C(x + ΔΧΖ) - C(x)
Substituting the values, we get:
ΔC = C(90 + 1) - C(90)
ΔC = C(91) - C(90)
ΔC = [0.01(91)^2 + 0.4(91) + 50] - [0.01(90)^2 + 0.4(90) + 50]
ΔC = 91.31 - 86
ΔC = $5.31
To find C'(x), we need to take the derivative of the total-cost function C(x):
C(x) = 0.01x^2 + 0.4x + 50
C'(x) = 0.02x + 0.4
Substituting x = 90, we get:
C'(90) = 0.02(90) + 0.4
C'(90) = 1.8 + 0.4
C'(90) = 2.2
Therefore, when x = 90, ΔC = $5.31 and C'(x) = 2.2.
Given the total-cost function C(x) = 0.01x^2 + 0.4x + 50, we'll first find the change in cost (ΔC) and then the derivative of the cost function (C'(x)) when x = 90 and Δx = 1.
1. To find ΔC, evaluate C(x + Δx) - C(x) when x = 90 and Δx = 1:
ΔC = C(90 + 1) - C(90) = C(91) - C(90)
2. Now, let's find the derivative of the cost function C(x):
C'(x) = d(0.01x^2 + 0.4x + 50)/dx = 0.02x + 0.4
3. Evaluate C'(x) when x = 90:
C'(90) = 0.02(90) + 0.4 = 1.8 + 0.4 = 2.2
So, ΔC = C(91) - C(90), and C'(x) when x = 90 is 2.2.

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Lemma 1 states that in a weighted, directed graph with a designated root, if we create a new set of edges E' by removing edges from the root to each vertex except itself.

Lemma 1 introduces the concept of an RDMST (Rooted Directed Minimum Spanning Tree) in a weighted, directed graph and highlights the relationship between the set of edges E' and the existence of cycles in the resulting graph T. It states that if T is not an RDMST, it must contain a cycle, indicating that removing certain edges from the root to other vertices can lead to cycles.

Lemma 2 focuses on the weight function w' and its impact on determining an RDMST. It states that the resulting graph T is an RDMST rooted at the designated root in the original graph if and only if it is an RDMST rooted at the designated root in the graph with the modified weight function w'. This lemma demonstrates that adjusting the weights of the edges based on the weights of the vertices preserves the property of being an RDMST.

Overall, these two lemmas provide insights into the properties and characteristics of RDMSTs in weighted, directed graphs and offer a foundation for understanding their existence and construction.

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The value of r in the equation is 35.

1 + r / 9 = 4

We have to find the value of r in the expression.

The value of r in the expression can be found by making r the subject of the formula.

Hence,

1 + r / 9 = 4

cross multiply

1 + r = 9 × 4

1 + r = 36

subtract 1 from both sides

1 - 1 + r  = 36 - 1

r = 35

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To determine the minimum required diameter (D) of the cross-section of the beam, we need to consider the maximum bending moment and the maximum allowable bending stress.

The bending stress in a beam is given by the formula:

σ = (M * c) / I

Where σ is the bending stress, M is the maximum bending moment, c is the distance from the neutral axis to the outermost fiber (which is equal to half of the diameter for a circular cross-section), and I is the moment of inertia of the cross-section.

Rearranging the formula, we have:

D = (2 * M) / (σ * π)

Substituting the given values, with M = 80 kNm (converted to Nm) and σ = 500 MPa (converted to N/m²), we can calculate the minimum required diameter (D):

D = (2 * 80,000 Nm) / (500,000,000 N/m² * π)

D ≈ 0.255 meters or 255 mm

Therefore, the minimum required diameter of the cross-section of the beam is approximately 0.255 meters or 255 mm to resist the maximum bending moment of 80 kNm within the allowable bending stress of 500 MPa.

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Answer:

6 hours

Step-by-step explanation:

20 + 65x=410

65x=390

x=6

The expected payback for betting $6 on red in this roulette game is approximately -$0.32. This means, on average, you can expect to lose about $0.32 per $6 wagered.

To calculate the expected payback for the game, we need to consider the probabilities and payouts associated with the bet on red.

In a standard roulette wheel, there are 18 red compartments, 18 black compartments, and two green compartments (neither black nor red) representing the 0 and 00. This means there are 38 equally likely outcomes.

If you bet $6 on red, there are 18 favorable outcomes (the red compartments) and 20 unfavorable outcomes (the black and green compartments). Therefore, the probability of winning is 18/38, and the probability of losing is 20/38.

If the color red occurs, you get to keep your bet of $6 and win an additional $6.

To calculate the expected payback, we multiply the probability of winning by the payout for winning and subtract the probability of losing multiplied by the amount wagered:

Expected Payback = (Probability of Winning * Payout for Winning) - (Probability of Losing * Amount Wagered)

Expected Payback = ((18/38) * $6) - ((20/38) * $6)

Expected Payback = ($108/38) - ($120/38)

Expected Payback = -$12/38

The expected payback for betting $6 on red in this roulette game is approximately -$0.32. This means, on average, you can expect to lose about $0.32 per $6 wagered.

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The volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane is V = xyz, where x, y, and z are the lengths of the sides of the rectangular box.

To find the largest volume, we need to maximize x, y, and z. Since we have three faces in the coordinate planes, one vertex will be at the origin (0, 0, 0). The other two vertices will lie on the coordinate axes.

Let's assume the vertex on the x-axis is (x, 0, 0), and the vertex on the y-axis is (0, y, 0). The third vertex on the z-axis will be (0, 0, z). Since the box is in the first octant, all the coordinates must be positive.

To maximize the volume, we need to find the maximum values for x, y, and z within the constraints. The maximum values occur when the box touches the coordinate planes. Therefore, the maximum values are x = y = z.

Substituting these values into the volume formula, we get V = xyz = x³. Therefore, the volume of the largest rectangular box is V = x³.

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What is the maximum volume of a rectangular box situated in the first octant, with three of its faces lying on the coordinate planes, and one of its vertices located in the plane?