a population consists of 18 items. the number of different random samples (without replacement) of size 8 that can be selected from the population is . group of answer choices

it's infinitely many bc the equations have the same line

Answer:

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

Step-by-step explanation:

How many solutions does the following system have?

y = -2x – 4

y = 3x + 3

Solution:

Given y = -2x – 4

y = 3x + 3

Rewriting to the general form

-2x – y – 4 = 0

3x – y + 3 = 0

Comparing the coefficients,

(a1/a2) = -⅔

(b1/b2) = -1/-1 = 1

(a1/a2) ≠ (b1/b2)

Hence, this system of equations will have only one

Answer:

C

Step-by-step explanation:

Solution to a system: intersection point.

  —no solution: parallel lines

  —infinite solutions: same lines

Answer:c

Step-by-step explanation:

Answer:

I hope this helps!

The answer is two base cases, using induction.

What is induction ?

Weak induction is when an inductive mathematical proof holds true for all integers in a set of countable proofs. Natural numbers typically use this. The base step and inductive step are used to prove a set, making it the simplest type of mathematical induction.

Two examples make up an induction proof. Without requiring any prior knowledge of other examples, the first, or base case, establishes the claim for n = 0. The induction process, which is used in the second case, demonstrates that if the assertion is true for any particular scenario where n = k, it must also be true for the subsequent case where n = k + 1.

If a statement true  for n= k, accordily to induction it have to hold good for n = k+1,

Hence, base cases does a proof by the weak form of the principle of mathematical induction requires 2 bases.

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Step-by-step explanation:

5a+9=5+3a

2a=-4 is the required value

Answer:

THE QUOTIENT IS 84  BECAUSE 83 +1 =84.

Step-by-step explanation:

Given:

It can be written as follows.

Dividing 5.44 by 6.8, we get

Hence the quotient is

Divide the length of the longest side of triangle AFB by the longest side of triangle DHG to find the scale factor.

Triangle AFB: A=4 cm, B=5 cm, F=7 cm

Triangle DHG: D=2.8 cm, H=3.5 cm, G=4.9 cm

Scale factor = 7/4.9 = 1.43

Step by explanation

Step 1: Draw triangle AFB on a piece of paper.

Step 2: Measure the side lengths of triangle AFB and record them.

Step 3: Draw a second triangle, DHG, on the paper.

Step 4: Measure the side lengths of triangle DHG and record them.

Step 5: Divide the length of the longest side of triangle AFB by the longest side of triangle DHG to find the scale factor.

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Answer:

3

Step-by-step explanation:

Slope = \(\frac{y_2-y_1}{x_2-x_1}\) where the given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the points (1,-12) and (6,3)

\(=\frac{3-(-12)}{6-1}\\=\frac{3+12}{5}\\=\frac{15}{5}\\= 3\)

Therefore, the slope of the line is 3.

I hope this helps!

Answer:

So, the rational number is \(\frac{52}{12}\) .

Step-by-step explanation:

Let x be the other number.

We know ,

\(\frac{7}{36}\) + x = \(\frac{5}{6}\)

To find x, we need to convert both to have a common denominator.

So, if we multiply \(\frac{7}{36}\) by \(\frac{10}{36}\)  ,

\(\frac{10}{1}\) × \(\frac{7}{36}\) + x = \(\frac{56}{10}\)

After multiplication the fraction  \(\frac{7}{36}\) becomes \(\frac{70}{360}\)  .

\(\frac{70}{360}\)+ x =  \(\frac{56}{10}\)

Now we have common denominator of 360in both fraction,

Now,

we can simplify the equation ,

\(\frac{70}{360}\)  + x = \(\frac{56}{10}\)

70 + 360x = 56 × 36

2520 + 360x = 2016

504 + 360x = 2016

360x = 1512

x = \(\frac{1512}{360}\)

   =\(\frac{52}{12}\)

So, the rational number is \(\frac{52}{12}\) .

The inequality solved for y is:

y ≥ 21/25

To solve an inequality for one variable, we need to isolate that variable.

Here we have:

(8/7)y -1 ≥ (3/7)y - 2/5

Move the terms with y to the left side and the others to the right side.

(8/7)y - (3/7)y ≥ -2/5 + 1

(5/7)y ≥ (3/5)

Now multiply both sides by 7/5, we will get:

y  ≥ (3/5)*(7/5)

y ≥ 21/25

That is the solution simplfied.

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The probability that a San Bernardino resident has a commute time less than 45 minutes. Commute time is normally distributed with a mean of 32.1 minutes and a standard deviation of 7.8 minutes.

$z =\frac{45-32.1}{7.8}=1.65$  Using the Z-table, we find that the probability corresponding to a z-score of 1.65 is 0.9505. Therefore, the probability that a San Bernardino resident has a commute time less than 45 minutes is 0.9505.(b) Find the probability that a San Bernardino resident has a commute time between 25 minutes and 45 minutes. To find the probability that a San Bernardino resident has a commute time between 25 and 45 minutes, we first need to calculate the z-scores for 25 minutes and 45 minutes as follows: $z_{1}

=\(\frac{25-32.1}{7.8}=-0.91$ $z_{2}\)

=\(\frac{45-32.1}{7.8}\)

=1.65$ Using the Z-table, we find the probability corresponding to a z-score of -0.91 to be 0.1814 and the probability corresponding to a z-score of 1.65 to be 0.9505. $1.28

=\(\frac{x - 32.1}{7.8}$ Solving for x, we get: $x\)

= 1.28(7.8) + 32.1

= 42.2.$

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The expression is 8n – 3; The 100th term is 797

The nth term of an arithmetic sequence is given by:

an=a1+(100-1)d          ....[1]

where

a1  is the first term

d is the common difference of two consecutive terms.

n is the number of terms.

Given the sequence:

5, 13, 21, 29, 37, 45, …

This is an arithmetic sequence with first term  = 5 and common difference(d) = 8

Since;

13-5 = 8,

21-13 = 8,

29-21 = 8  and so on....

We have to find the 100th term in the sequence

Substitute in [1] we have;

an=a1+(100-1)d

an=5+(n-1)8=5+8n-8 = 8n-3

Substitute the given values and n=100 we have;

a100= 800 - 3 = 797

Therefore, the 100th term in the sequence is, 797 and an expression to describe a rule for the sequence is, 8n – 3;

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Answer:

The greatest common factor of the expression is 25x

Step-by-step explanation:

Here, we are interested in giving the greatest common factor of the expression.

We can do this by factorization till we have no common factors left.

the expression is;

100x^2 -250xy + 75x

we start with the common factor x;

x(100x -250y + 75)

The next thing to do here is to find the greatest common factor of 100,250 and 75.

The greatest common factor here is 25.

Thus, we have;

25x(4x -10y + 3)

There is no more factor to get from the terms in the bracket. This simply means that the terms in the bracket are no longer factorizable

So the greatest common factor we have is 25x

The number line represents an inequality. The inequality is x  ≥ -3.

What is a number line?

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.

If a number line contains a close circle, then the number includes in the inequality.

If a number line contains an open circle, then the number does not include in the inequality.

In the graph, there is a close circle on -3.

The line represents all real numbers greater than -3.

Since there is a close circle on -3, thus -3 include in the inequality.

The given variable is x.

The graph represents all real numbers greater than or equal to -3.

The inequality is x  ≥ -3.

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Answer:

e=7(12)-3

Step-by-step explanation:

Because he needs three more to have 7 groups of 12 (7x12=84) so he has three less than the 7 groups of 12 he needs (84). So subtract 3 from that.

Answer:

y-intercept=8/7

x-intercept=4

Step-by-step explanation:

y=(8-2x)/7

=8/7-2/7x

Therefore y-intercept =8/7,

Subt.y=0,

8/7-2/7x=0

2/7x=8/7

x intercept=4

\(\\ \sf\longmapsto 2x+7y=8\)

\(\\ \sf\longmapsto 2x+7(0)=8\)

\(\\ \sf\longmapsto 2x=8\)

\(\\ \sf\longmapsto x=4\)

\(\\ \sf\longmapsto 2(0)+7y=8\)

\(\\ \sf\longmapsto 7y=8\)

\(\\ \sf\longmapsto y=\dfrac{8}{7}\)

Answer:

1)D

2)A

Step-by-step explanation:

1)\(-7a-2x+5a-6x\\-7a+5a-2x-6x\\-2a-8x\)

The last choice is the correct answer.

2)

\(16bc-8ab=8b(2c-a)\)

The answer is the first choice

PLEASE MARK ME AS BRAINLIEST

The first term of the geometric series is -2 which gives the final value of the sum of the series approximately -36.857. Option C is the correct answer.

To find the first term of a geometric series, we can use the formula for the sum of a geometric series:

Sₙ = a × (1 - rⁿ) / (1 - r),

where Sₙ is the sum of the first n terms, a is the first term, and r is the common ratio.

We are given the following information:

S₆ = -42,

S₇ = 86,

S₈ = -170.

Using the formula, we can set up the following equations:

-42 = a × (1 - r²) / (1 - r), (equation 1)

86 = a × (1 - r³) / (1 - r), (equation 2)

-170 = a × (1 - r⁴) / (1 - r). (equation 3)

From equation 2, we can rearrange it to isolate a:

a = 86 × (1 - r) / (1 - r³). (equation 4)

Substituting equation 4 into equations 1 and 3:

-42 = (86 × (1 - r) / (1 - r³)) × (1 - r²) / (1 - r), (equation 5)

-170 = (86 × (1 - r) / (1 - r³)) × (1 - r⁴) / (1 - r). (equation 6)

Simplifying equations 5 and 6 further:

-42 × (1 - r) × (1 - r²) = 86 × (1 - r³), (equation 7)

-170 × (1 - r) × (1 - r⁴) = 86 × (1 - r³). (equation 8)

Solving equations 7 and 8 simultaneously, we find that r = -2.

Substituting r = -2 into equation 4:

a = 86 × (1 - (-2)) / (1 - (-2)³),

a = 86 × (1 + 2) / (1 - 8),

a = 86 × 3 / (-7),

a = -258 / 7.

The approximate value of a is -36.857.

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The question is -

In a geometric series, S6=−42, S7=86, and S8=−170. Find the first term. Select one: a. 3 b. 2 c. −2 d. −3

The required Domain and range are Domain = {x | 20 ≤ x ≤ 30} and Range = {c | 271.95 ≤ c ≤ 406.95}.

The domain is the set of all possible values for the independent variable, x, in the function. In this case, the domain is the set of all possible numbers of packages of colored pencils that can be purchased by the Math Department. We know that the department purchased at least 20 and no more than 30 packages, so the domain is:

Domain = {x | 20 ≤ x ≤ 30}

The range is the set of all possible values for the dependent variable, c, in the function. In this case, the range is the set of all possible costs for the packages of colored pencils that the Math Department purchased. We can find the range by plugging in the values of x that are in the domain and seeing what values of c we get:

When x = 20: c = 12.95(20) + 7.95 = 271.95

When x = 30: c = 12.95(30) + 7.95 = 406.95

So the range is:

Range = {c | 271.95 ≤ c ≤ 406.95}

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The problem involves maximizing profit in a factory that produces products X and Y. Constraints include labor time, material availability, testing equipment usage, and minimum production requirements.

(a) To maximize profit, we need to define the objective function. Let x be the number of units of product X and y be the number of units of product Y produced. The objective function can be expressed as Z = 6x + 4.5y, representing the total profit.

The constraints can be formulated as follows:

1. Labor time constraint: 30x + 15y ≤ 60 hours (converted to minutes)

2. Material constraint: 2.5x + 2y ≤ 500 kilograms

3. Testing equipment constraint: Testing time for X ≥ 8 hours (converted to minutes)

4. Minimum production requirement: x ≥ 40 units of product X, y ≥ 80 units of product Y

5. Non-negativity constraint: x ≥ 0, y ≥ 0

(b) By graphing the system of inequalities on graph paper, the feasible region can be shaded. The feasible region represents the intersection of all the constraints.

(c) To find the weekly production that maximizes profit, we need to optimize the objective function within the feasible region. This can be done using linear programming techniques.

By solving the problem, we can determine the values of x and y that maximize the objective function Z. The expected maximum profit will be the value of Z at the optimal solution.

Note: The specific calculations and graphical representation will require numerical values and graphing tools to provide an accurate solution.

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The product of the unsigned integers 11010 and 1011 in binary multiplication is 10011110.

Hi! I'd be happy to help you with this binary multiplication problem using unsigned integers. Here's the step-by-step process:
1. First, write down the two binary numbers, with the larger one (11010) on top and the smaller one (1011) on the bottom.
2. Start multiplying each digit of the bottom number (1011) with the entire top number (11010), working from right to left. Write the results below the original numbers, shifting one place to the left for each digit.
  11010
 x1011
 ------
   11010   (11010 * 1)
  00000    (11010 * 0, shifted one place to the left)
11010     (11010 * 1, shifted two places to the left)
11010      (11010 * 1, shifted three places to the left)
 ------
3. Now, add the results together:
  11010
 x1011
 ------
   11010
  00000
 11010
11010
 ------
10011110

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The required characteristic that has a high survival value in a population is likely to become dominant or common.

Statistics is the study of mathematics that deals with relations between comprehensive data.

A characteristic that has a high survival value in a population is likely to become more common over time. This is because individuals with this characteristic are more likely to survive and reproduce, passing the trait on to their offspring. Over generations, this process, known as natural selection, can lead to an increase in the frequency of the advantageous trait in the population. Over time, the characteristic that has a high survival value in a population is likely to become dominant.

Thus, the required characteristic that has a high survival value in a population is likely to become dominant or common.

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The probability that one of the dice has the number 3 or less facing up given that the other has at least the number 3 facing up is 3/16.

To find the probability that one of the dice has the number 3 or less facing up given that the other has at least the number 3 facing up, we can use conditional probability.

First, let's consider the possible outcomes when rolling a pair of fair dice.

There are a total of 36 possible outcomes, since each die has 6 possible outcomes (numbers 1 to 6)

and there are 6 possibilities for the second die for each outcome of the first die.

Next, let's consider the outcomes where one of the dice has the number 3 or less facing up and the other has at least the number 3 facing up.

If the first die has the number 3 or less, there are 3 possible outcomes:

(1,3), (2,3), (3,3). If the second die has at least the number 3 facing up, there are 16 possible outcomes:

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,3), (5,3), (6,3), (4,4), (4,5), (4,6), (5,4), (5,5), (5,6), (6,4), (6,5), (6,6).

Out of these 16 outcomes, 3 outcomes also satisfy the condition that the first die has the number 3 or less facing up: (3,3), (4,3), (5,3).

Therefore, the probability that one of the dice has the number 3 or less facing up given that the other has at least the number 3 facing up is 3/16.


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The overflow rate of the tank is 0.0006 m³/m².s and the detention time is 5333.33 seconds or 1.48 hours or 1 hour 29 minutes and 17.99 seconds.

The given primary settling tank receives an average flow rate of 0.540 m³/s, has a tank surface area of 900 m² and depth of 3.2 m.

We can compute the overflow rate and detention time using the formulas as follows;

Overflow rate formula:

Overflow rate = Flow rate / Surface area

Overflow rate = 0.540 / 900Overflow rate = 0.0006 m³/m².s

Detention time formula:

Detention time = Volume of tank / Flow rate

Volume of tank = Surface area × Depth

Volume of tank = 900 × 3.2Volume of tank = 2880 m³

Detention time = 2880 / 0.540

Detention time = 5333.33 seconds or 1.48 hours or 1 hour 29 minutes and 17.99 seconds.

Therefore, the overflow rate of the tank is 0.0006 m³/m².s and the detention time is 5333.33 seconds or 1.48 hours or 1 hour 29 minutes and 17.99 seconds.

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Scale drawings are a useful tool for representing real-life objects or structures on paper or in digital form. They allow us to create a proportionate, smaller version of the original, which can be useful in a variety of contexts, such as architecture, engineering, and design.

To create a scale drawing, we need to choose a scale, which represents the ratio of the size of the drawing to the actual size of the object. Once we have selected a scale, we can then begin to draw the object, using the appropriate measurements and proportions.

Scale drawings are a way of representing objects or structures in a smaller, proportional size. They can be useful in a variety of contexts, such as in architecture, engineering, and design, where it is important to have an accurate representation of an object or structure. To create a scale drawing, we need to choose a scale, which is the ratio of the size of the drawing to the actual size of the object. For example, if we choose a scale of 1:100, it means that one unit on the drawing represents 100 units in real life.

Once we have chosen a scale, we can begin to draw the object, using the appropriate measurements and proportions. It is important to ensure that the drawing is accurate and proportional, as this will affect the final product. One way to do this is to use a grid, which can help us to keep the proportions consistent. Another way is to use a ruler or compass to ensure that the measurements are precise.

In conclusion, scale drawings are an important tool for representing objects or structures in a smaller, proportional size. By choosing an appropriate scale and using accurate measurements and proportions, we can create a detailed and accurate representation of the original object.

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Secant can be defined as the reciprocal of cosine. Secant of angle A will be hypotenuse/adjacent.

There are three basic trigonometric ratios. Sin, Cos and Tan.

Sin = opposite side/ hypotenuse

Cos = adjacent side/ hypotenuse

Tan = opposite side/ adjacent side

Here in the give image, Sin(A) = a/c

                                        Cos(A) = b/c

                                        Tan(A) = a/b

There are reciprocals for each trigonometric functions

Cosecant is the reciprocal of sine. Cosec(A) = c/a

Secant is the reciprocal of  Cosine. Sec(A) = c/b

Cotangent is the reciprocal of Tangent . Cot(A) = b/a

So secant is one of inverse trigonometric functions.

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Finding the union of the sets A and C is the first step in solving P(A U C). Since set C only contains the number 6, the union of A and C has the elements 1, 2, 3, 4, and 6. A U C thus equals 1, 2, 3, 4, and 6.

The power set of A U C, which comprises all conceivable subsets of 1, 2, 3, 4, and 6, must then be located. If all conceivable subsets are listed, the power set of A U C, designated as P(A U C), will be discovered.

P(A U C) = { {}, {1}, {2}, {3}, {4}, {6}, {1,2}, {1,3}, {1,4}, {1,6}, {2,3}, {2,4}, {2,6}, {3,4}, {3,6}, {4,6}, {1,2,3}, {1,2,4}, {1,2,6}, {1,3,4}, {1,3,6}, {1,4,6}, {2,3,4}, {2,3,6}, {2,4,6}, {3,4,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,6}, {1,3,4,6}, {2,3,4,6}, {1,2,3,4,6}}.

There are 31 subsets in the power set P(A U C) that result from the union of sets A and C.

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The probability that the team will win the sport is 77%.

Given that an area kicker in pro football incorporates a 77% probability of creating a field goal over 40 yards and every attempt field goal is independent.

Probability is how something is likely to happen. The probability of a happening is calculated by the probability formula by simply dividing the favorable number of outcomes by the overall number of possible outcomes.

So, his team will win the sport if he makes a goal otherwise loses.

Therefore, the Probability that his team will win the sport P[E] =P[making a field goal]

P[E]=77%

Hence, the probability that the team will win the sport when making a field goal is 77%.

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We have shown that the row sum s is an eigenvalue of the matrix A with eigenvector x = (1, 1, ..., 1)T.

To show that s is an eigenvalue of the nxn matrix A, we need to find a nonzero vector x such that Ax = sx, where s is the row sum of A. One way to find such a vector is to take the vector x = (1, 1, ..., 1)T, where T denotes transpose.

Using this choice of x, we have

Ax = (s, s, ..., s)T = sx,

which shows that s is indeed an eigenvalue of A with eigenvector x.

To see why this works, consider the kth entry of Av for any nonzero vector v in R^n. We have

(Av)_k = ∑ A_ki v_i, i=1 to n

where A_ki denotes the entry in the kth row and ith column of A. Since the row sums of A all equal s, we can write

(Av)_k = ∑ A_ki v_i = s ∑ v_i

where the sum on the right-hand side is taken over all i such that A_ki is nonzero.

If we take v = x, then we have ∑ v_i = nx, and hence

(Ax)_k = s(nx) = (ns)x_k,

which shows that x is an eigenvector of A with eigenvalue s.

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