What are the first five multiples of 12 in increasing order

Answer: 3

Step-by-step explanation:

You are solving a system of equations y1 = abx1 and y2 = abx2, so plug the x and y coordinates into the equations to solve for a and b:6 = ab1 & 3/4 = ab-2Since a = 6/b, we can use this in the second equation to solve for b:3/4 = (6/b)b-23/4 = 6/b36/(3/4) = b38 = b32 = b,which means that a = 3.Now we just input our a and b values into y = abx, so our equation is y = 3*2x.                 I hope this helps

Symmetrical balance, also known as bilateral symmetry, is a type of balance in which two halves are mirror images of each other. This type of balance can be found in both visual art and in nature.

In visual art, symmetrical balance is achieved when similar shapes, colors, lines, and textures are repeated on either side of a vertical axis. This creates an even distribution of visual elements and creates a sense of harmony and equilibrium. In nature, symmetrical balance is created when there is a symmetrical arrangement of organs and features in plants and animals.

Symmetrical balance is often used to create a sense of order and balance in visual works of art, as well as to emphasize the balance of nature in landscapes. It can also be used to convey a sense of unity and tranquility, as the repetition of similar elements creates an overall feeling of calmness and symmetry. Symmetrical balance is an important element in many types of artwork, and it is used in all kinds of visual art, including paintings, photographs, sculptures, and more.

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A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, we can be multiply two polynomials step by step.

Distribute each term of the first polynomial to every term of the second polynomial.

Combine like terms by adding the coefficients of the terms that have the same variables raised to the same powers.

Simplify the result by arranging the terms in descending order of the exponent of the variable.

For example, let's say you want to multiply (2x + 3) and (x - 4):

(2x + 3) * (x - 4) = 2x * x - 2x * 4 + 3 * x - 3 * 4

Simplify the terms: 2x^2 - 8x + 3x - 12

Combine like terms: 2x^2 - 5x - 12

Therefore, the product of (2x + 3) and (x - 4) is 2x^2 - 5x - 12.

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Answer:

1. acute

2. Right

3. maybe acute

4. obtuse

5. acute

6. obtuse

7. straight

8. obtuse

9. acute

10. obtuse

11. acute

12. acute

13. obtuse

14. obtuse

Answer:

multiply them.

Step-by-step explanation:

Answer:

d is parallel to e

Step-by-step explanation:

Since b is parallel to e and d is perpendicular to b , then

d is perpendicular to e

Answer:

x = -2

Step-by-step explanation:

3/2 (x-5) - 3/2 = 9x/2

3x/2 - 15/2 - 3/2 = 9x/2 ... alldenominator

are 2 so we can multiply all term by 2

2(3x/2 - 15/2 - 3/2 = 9x/2)

3x - 15 - 3 = 9x ... simplify it

3x - 12 = 9x

-12 = 9x - 3x ... take 3x to the left

-12 = 6x ... simplify

6x/6 = -12/6 ... dividing both side by 6

x = -2 ... simplify and solve x

The right answer is 10 units.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

Step-by-step explanation:

Given a table of values (x, y) = {(5, 6.5), (7, 9.1), (9, 11.7)}, you want to know (a) if the quantities are proportional, and (b) the equation for the relation.

A proportion is a relation that can be described by the equation ...

  y = kx

where k is the constant of proportionality.

To see if the table describes a proportional relationship, we can compute k for each of the ordered pairs.

  k = y/x = 6.5/5 = 9.1/7 = 11.7/9 = 1.3

The value of k is the same for all of the given table values, so ...

  the quantities are proportional.

As we saw above, the equation y = kx can be used with the value k = 1.3 for this relationship:

  y = 1.3x

The amount of material needed to make a can can be calculated by finding the surface area of the can. In this case, we have a soup can with a height of 6 inches and a radius of 2 inches.

To calculate the surface area, we need to find the area of the circular top and bottom, as well as the area of the curved side. The area of each circular top or bottom is given by the formula A = πr^2, where r is the radius. So, the total area of the circular tops and bottoms is 2π(2^2) = 8π.
The area of the curved side can be found using the formula for the lateral surface area of a cylinder, which is given by A = 2πrh, where r is the radius and h is the height. In this case, the curved side of the can forms a rectangle when it is unrolled, so the height of the rectangle is the same as the height of the can, which is 6 inches. Therefore, the area of the curved side is 2π(2)(6) = 24π.
To find the total amount of material needed, we add the areas of the circular tops and bottoms to the area of the curved side. So, the total surface area of the can is 8π + 24π = 32π square inches.
Therefore, in terms of π, the amount of material needed to make each can is 32π square inches.

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Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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The probability that the luggage is on a flight that is not late is 0.4.

To find the probability that the luggage is on a flight that is not late, given that the luggage is not missing, we can use Bayes' theorem.

Let's denote the events as follows:

A = Flight is not late

B = Luggage is not missing

We want to find P(A | B), which is the probability that the flight is not late given that the luggage is not missing.

According to Bayes' theorem:

P(A | B) = (P(B | A) * P(A)) / P(B)

We are given the following probabilities:

P(B | A) = 0.5 (Probability of luggage not missing given that the flight is not late)

P(A) = 0.4 (Probability of the flight being not late)

P(B) = ? (Probability of luggage not missing)

To calculate P(B), we can use the law of total probability. We need to consider the two possibilities: the flight is late or the flight is not late.

P(B) = P(B | A) * P(A) + P(B | A') * P(A')

P(B | A') = 1 - P(B | A) = 1 - 0.5 = 0.5 (Probability of luggage not missing given that the flight is late)

P(A') = 1 - P(A) = 1 - 0.4 = 0.6 (Probability of the flight being late)

Now we can calculate P(B):

P(B) = P(B | A) * P(A) + P(B | A') * P(A')

    = 0.5 * 0.4 + 0.5 * 0.6

    = 0.2 + 0.3

    = 0.5

Finally, we can substitute the values into Bayes' theorem to find P(A | B):

P(A | B) = (P(B | A) * P(A)) / P(B)

        = (0.5 * 0.4) / 0.5

        = 0.2 / 0.5

        = 0.4

Therefore, given that the luggage is not missing, the probability that the luggage is on a flight that is not late is 0.4.

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Answer:

D. X=1

Step-by-step explanation:

It's clear if you work through it just use substitution and you'll get the same answer yourself

We can calculate the percentages according to the amounts provided in the prompt, and then make a number line to illustrate each percentage as follows:

a) The price of the book decreased by 20%.

$15.00             $12.00

  |-----------------|------->

      100%            80%

b) The percentage decrease in the number of students who take the bus to school is 25%.

200               150

  |-----------------|------->

     100%            75%

Calculating percentages involves finding a portion of a whole expressed as a fraction of 100. To calculate a percentage, divide the part by the whole and then multiply the result by 100.

For example, if 20 out of 100 students are absent, the percentage of absent students is:

(20/100) x 100 = 20%.

With that in mind, we can conclude that we have correctly answered this question.

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Answer:

$1,440

Step-by-step explanation:

He withdrew $40 a month for 3 years. First you multiply $40 x 12 since there are 12 months in a year to see how much he spent in a year and multiply that number by 3 since he did it for 3 years.

$40 x 12 = $480

$480 x 3 = $1,440

The minimum diameter required for the tie rod using the LRFD method based on yielding of the gross section using the LRFD method is 23.6 mm.

Given,

Dead load (D) = 95kN

Live load (L) = 110kN

Yield strength of steel (σy) = 315MPa

Factor of safety with respect to yielding (FOS) = 2.4

Using the ASD method, the minimum diameter required for the tie rod is determined as follows; ASD method

Formula: F= ASD = (D + L)/FOS

Where F = allowable stress

D = dead load

L = live load

FOS = factor of safety

ASD = allowable stress design

FOS = 2.4σy = yield strength

We can now substitute the given values as follows:

F = (D + L)/FOS= (95 + 110)/2.4= 79.17 kNF/A = σy

Where A is the cross-sectional area of the rod

We can now substitute the values as follows:

A = F/σy= 79.17 x 10^3/315 x 10^6= 0.00025m^2

We also know that; A = πd^2/4

We can now rearrange to get d;

d = √(4A/π)

= √(4 x 0.00025/π)

= 0.0283m

The minimum diameter required for the tie rod is 28.3 mm.

Using the LRFD method, the minimum diameter required for the tie rod based on yielding of the gross section using the LRFD method is given by; LRFD method

Given; φ1​ = 0.9

D = 1.2L = 1.5σ

y = 315MPa

FOS = 2.4

F = (D + L)

φ1​ = (1.2D + 1.5L)

φ1​= (1.2 x 95 + 1.5 x 110)0.9

= 187.65 kN

ρ = Aγ

where

ρ is the nominal strength

A is the cross-sectional area of the rodγ is the resistance factor

For steel, γ = 1.67 for yielding of gross sections

ρ = φ1​σyA/γ

Now, we can substitute the given values

ρ = φ1​σyA/γ

= 0.9 x 315 x 10^6 x A/1.67

= 1.7A

We know that; ρ = F

Therefore, 1.7A

= 187.65 kNA

= 110.38 x 10^-6 m^2A

= πd^2/4πd^2/4

= 110.38 x 10^-6 m^2πd^2

= 441.52 x 10^-6 m^2d

= √(441.52 x 10^-6/π)

= 0.0236 m

Therefore, the minimum diameter required for the tie rod using the LRFD method based on yielding of the gross section using the LRFD method is 23.6 mm.

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The probability of selecting a green baseball cap from the order of 64 caps is 0.25 or 25%.

To calculate the probability of selecting a green baseball cap from the order of 64 caps, we can use the concept of probability.

Given:

Total number of caps (n) = 64

Number of green caps (k) = 16

The probability (P) of selecting a green cap can be calculated as the ratio of the number of green caps to the total number of caps:

P(green cap) = k / n

Substituting the values:

P(green cap) = 16 / 64

P(green cap) = 0.25

Therefore, the probability of selecting a green baseball cap from the order of 64 caps is 0.25 or 25%.

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Therefore, the least-squares error in the least-squares solution of ax = b is e = ||b - A(A^T A)^(-1) A^T b||^2.

The least-squares solution of ax = b is given by x = (A^T A)^(-1) A^T b, where A is the matrix whose columns are the coefficients of the variables in the system of equations. The least-squares error is the sum of the squares of the residuals, which are the differences between the values of b and the values of ax predicted by the least-squares solution.

The least-squares error can be calculated as follows:

e = ||b - Ax||^2

= ||b - A(A^T A)^(-1) A^T b||^2

where ||.|| denotes the Euclidean norm.

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Answer:

40,924.79

Step-by-step explanation:

To calculate the approximate user base 13 months from now, we need to apply a 4.1% growth rate to the current user base of 25,220 for each month.

First, let's convert the growth rate to decimal form: 4.1% = 0.041.

To find the user base after one month, we can multiply the current user base by the growth rate:

User base after one month = 25,220 + (25,220 * 0.041)

User base after one month ≈ 25,220 + 1,034.02 ≈ 26,254.02

Next, we repeat this process for the subsequent months, compounding the growth each time. After two months:

User base after two months ≈ 26,254.02 + (26,254.02 * 0.041) ≈ 27,309.36

We continue this calculation for a total of 13 months:

User base after three months ≈ 27,309.36 + (27,309.36 * 0.041) ≈ 28,391.16

User base after four months ≈ 28,391.16 + (28,391.16 * 0.041) ≈ 29,500.57

User base after five months ≈ 29,500.57 + (29,500.57 * 0.041) ≈ 30,638.69

User base after six months ≈ 30,638.69 + (30,638.69 * 0.041) ≈ 31,806.89

User base after seven months ≈ 31,806.89 + (31,806.89 * 0.041) ≈ 33,006.55

User base after eight months ≈ 33,006.55 + (33,006.55 * 0.041) ≈ 34,238.09

User base after nine months ≈ 34,238.09 + (34,238.09 * 0.041) ≈ 35,502.95

User base after ten months ≈ 35,502.95 + (35,502.95 * 0.041) ≈ 36,802.57

User base after eleven months ≈ 36,802.57 + (36,802.57 * 0.041) ≈ 38,138.42

User base after twelve months ≈ 38,138.42 + (38,138.42 * 0.041) ≈ 39,511.98

User base after thirteen months ≈ 39,511.98 + (39,511.98 * 0.041) ≈ 40,924.79

Answer:

Sample Response: To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.

Hope this helps. :)

Factors other than independent variables which may act on the dependent variable , when these factors vary systematically with independent variable they are known as confounds variables or extraneous variable.

Therefore, factors which vary systematically with the given independent variable is called  confounds variables or extraneous variable.

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The area under the curve between z = −2.0 and z = −1.0 is 0.1359.

We can use tables to find the area under the normal curve between two values of z.

However, tables give areas from z = 0 to z = 3.9 (beyond which there is literally no change). But as the normal curve is symmetric at z = 0, we can use it to find between any two given z values.

For example, for the area under the curve between z = −2.0 and z = −1.0, we can take values for z = 2.0 and z = 1.0; their difference will give the area between z = −2.0 and z = −1.0.

From tables for z = 1.0, we have 0.8413 and for z = 2.0, we have 0.9772 and

Hence, the Area under the curve between z = −2.0 and z = −1.0 is 0.9772−0.8413 = 0.1359.

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Answer:

\(\sqrt{2} or (1/2)\)

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

\(\displaystyle\\6\div\frac{2}{3}=\\\\ 6*\frac{3}{2}=\\\\ \frac{(6)(3)}{2}=\\\\ \frac{(2)(3)(3)}{2} =\\\\(3)(3)=\\\\9\)

In this case I believe you would add 25 to both sides. The -25 +25 would cancel out and then +25 would be on the right.

Answer:

x = 5 ± \(\sqrt{17}\)

Step-by-step explanation:

Given

x² - 10x + 25 = 17 ← left side is a perfect square, thus

(x - 5)² = 17 ( take the square root of both sides )

x - 5 = ± \(\sqrt{17}\) ( add 5 to both sides )

x = 5 ± \(\sqrt{17}\)

Thus

x = 5 - \(\sqrt{17}\)

x = 5 + \(\sqrt{17}\)

Answer:

no se perdon no entiendo ingles

The graph of the proportional relationship is (c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

From the question, we have

It costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry

This means that

(x, y) = (20.70, 23) and (34.20, 38)

Where

x = Weight and y = Cost

From the question, we understand that

The graph is a proportional graph

This means that the line passes through the origin

So, we have

(x, y) = (0, 0), (20.70, 23) and (34.20, 38)

Remove one of the points

(x, y) = (0, 0) and (34.20, 38)

Hence, the graph of the proportional relationship is (c)

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Answer:

The graph of the proportional relationship is (c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

Step-by-step explanation:

I took the exam and got it right