stem of Equations
Substitute (2, 1) into x + 3y = 5 to get
=

Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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3 hours to take second tap alone empty the tank.

Given data :

Time taken by tap A to empty the tank = 4 hours

Work done by tap A in 1 hour = \(\frac{1}{4}\)

Time taken to empty the tank by both taps = 1 hours

Time taken to empty the tank by tap B = Total time taken - time taken by A

=4 - 1 = 3

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Answer:

1.34 units.

Step-by-step explanation:

The line y = 2x - 5 has a slope of 2 so the line passing through the given point will be perpendicular to y= 2x - 5 and will have a slope of -1/2.

Let this line be y = -1/2x + c.

Its passes through (4, 6) so:

6 = -1/2*4 + c

6 = -2 + c

c = 6 + 2 = 8

So, equation of this line is y = -1/2x + 8.

Now we find the point where the 2 lines intersect:

y = 2x - 5

y = -1/2x + 8

2x - 5 = -1/2x + 8

2x + 1/2 x = 5 + 8

(5/2)x = 13

x = 26/5

  = 5.2.

and y = 2(5.2) - 5

          = 5.4.

So, the point of intersection is (5.2, 5.4)

and the distance between the point (4,6) and the line y = 2x - 5

= √((6 - 5.4)^2 + (4-5.2)^2)

= √(0.36 + 1.44)

= √1.8

= 1.34

There is a formula you can use directly to solve this.

In the next generation, the observed genotype frequencies in these two populations will differ due to random genetic drift. The smaller population is more susceptible to the effects of genetic drift.

Genetic drift is a random process that can lead to changes in allele frequencies over time in a population. It is particularly impactful in small populations where chance events can have a larger effect. In the given scenario, the population with 50 individuals is significantly smaller compared to the population with 10,000 individuals.

Due to the effects of genetic drift, the observed genotype frequencies in the next generation will likely differ between the two populations. The smaller population is more prone to fluctuations in allele frequencies, resulting in greater variability in genotype frequencies. In contrast, the larger population is less affected by genetic drift and is more likely to maintain relatively stable genotype frequencies.

It's important to note that genetic drift is a random process, and while we can make predictions based on population size and initial allele frequencies, the actual outcomes may still vary. Therefore, the observed genotype frequencies in the next generation will be subject to chance and random fluctuations driven by genetic drift.

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The possible angles between two unit vectors u and v if ||u x v|| = 1/2 are either 30 degrees or 150 degrees.

The magnitude of the cross product between two vectors u and v is equal to the area of the parallelogram formed by the two vectors. Since the magnitude of the cross product is ||u x v|| = 1/2, it means that the area of the parallelogram formed by u and v is 1/2.

The area of a parallelogram is given by the formula A = ||u|| ||v|| sin(theta), where theta is the angle between the two vectors. Since both u and v are unit vectors, their magnitudes are 1. Thus, we can simplify the formula to A = sin(theta)/2.

Therefore, sin(theta) = 1, which implies that theta is either 30 degrees or 150 degrees. So the possible angles between u and v are either 30 degrees or 150 degrees.

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Answer:

B

Step-by-step explanation:

(f – g)(x) = f (x) – g(x)=

\(3 {x}^{2} - 4x + 3 \\ - 2 {x}^{2} + 6x + 4 \\ = 5 {x}^{2} - 10x - 1\)

The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and y vary directly and y is 44 when x is 11.

Let, y ∝ x.

y = kx.

44 = 11k.

k = 44/11.

k = 4.

Now x = 9.

y = 4×9.

y = 36.

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Answer:

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Step-by-step explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3

Answer:

3/4 books per month

Step-by-step explanation:

12/16=3/4

So she reads 3/4 of a book each month

The slope of the line of best fit in the scatterplot below can be determined using the formula for the slope of a line:
Slope = (y2-y1)/(x2-x1)

In this case, x1 = 3, y1 = 12, x2 = 6, y2 = 19. So, the slope of the line of best fit is (19 - 12) / (6 - 3), which equals 7/3 or 2.33.
The line of best fit is the line that best represents the data on a scatterplot. It is the line that is closest to all the data points in the graph. The slope of the line of best fit helps to indicate whether the data points are moving in a positive or negative direction. If the slope is positive, the data points are increasing, and if the slope is negative, the data points are decreasing.
A positive slope, like the one in this example, means that as x increases, y also increases. This means that in this case, as the x-values (3 and 6) increase, the y-values (12 and 19) also increase.

The slope of the line of best fit can also be used to make predictions about values of y, given values of x. For example, if x = 8, then y = 26, because the slope of the line of best fit is 2.33, and 8*2.33 = 19.8, which is approximately equal to 26.
Overall, the slope of the line of best fit on this scatterplot is 2.33, which is a positive number. This indicates that as the x-values increase, the y-values also increase, and it can also be used to make predictions about y-values, given x-values.

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An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the "equally likely" or "classical" probability approach

The equally likely or classical probability approach assumes that each possible outcome of an experiment is equally likely to occur. This approach is based on the principle of symmetry and assumes that there is no inherent bias or preference towards any particular outcome

This approach is used for situations where there is no inherent bias or preference towards any particular outcome, and each outcome is considered equally likely to occur.

Therefore, the approach is classical probability approach

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it’s 12

Step-by-step explanation:

Answer:ontinuing this process shows that for 16 teams, there are 8 + 4 + 2 + 1, or 15 total games. Using brackets can be done for any number of teams.

Step-by-step explanation:

To find the probability that at least 2 of the comments are positive, we can use the concept of complementary probability. We'll find the probability that fewer than 2 comments are positive and then subtract it from 1 to get the desired probability.

Let's consider the following scenarios:

1. No comments are positive (all 10 comments are negative).

2. Exactly 1 comment is positive.

Let's calculate the probability of each scenario:

1. Probability of no comments being positive:

P(No positive comments) = (0.9)^10 = 0.3487 (rounded to four decimal places)

2. Probability of exactly 1 comment being positive:

P(Exactly 1 positive comment) = 10 * (0.1)^1 * (0.9)^9 ≈ 0.3874 (rounded to four decimal places)

To find the probability that at least 2 comments are positive, we subtract the sum of the above probabilities from 1:

P(At least 2 positive comments) = 1 - P(No positive comments) - P(Exactly 1 positive comment)

                             = 1 - 0.3487 - 0.3874

                             ≈ 0.2639 (rounded to four decimal places)

Therefore, the probability that at least 2 of the comments are positive is approximately 0.2639 or 26.39%

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Answer:

Step-by-step explanation:

Step one:

Given data

the initial salary is = $42,360

the raise in percentage is =3.4%

To know the raise we need to calculate what the amount of 3.4% of $42,360 is

Step two:

=(3.4/100)*42,360

=0.034*42360

=1440.24

therefore thr raise is $1440.24

Step three:

the new salary is given as

new salary= old salary+ raise

New salary= $42,360+$1440.24

New salary= $43,800.24

The probability of her having coffee and a yoghurt is 0.25

We can approach this problem using the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

Let's denote the event of Felicity having coffee as C and the event of her having a yoghurt as Y. Then, according to the problem statement, we know:

P(C) = probability of Felicity having coffee = 0.5 (since she always drinks either fruit juice or coffee, and there are only two options)

P(Y) = probability of Felicity having a yoghurt = 0.5 (since she will eat either cereal or a yoghurt, and there are only two options)

To find the probability of Felicity having both coffee and a yoghurt, we need to calculate

P(C and Y) = probability of Felicity having coffee and a yoghurt

If we assume that the events of having coffee and having a yoghurt are independent (i.e., having coffee does not affect the probability of having a yoghurt, and vice versa), then we can use the multiplication rule to find:

P(C and Y) = P(C) x P(Y) = 0.5 x 0.5 = 0.25

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Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

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Answer:

Step-by-step explanation:

2X + 1 + 3X - 2 + 4X - 5 = 180

9X - 6 = 180

9X = 174

9   =   174

ـــــــــــــــــــــ

9         9

X = 19.333

The perimeter of the triangle in terms of x given the three side lengths is  9x - 6.

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees.

The perimeter of a triangle = sum of the side lengths

(2x + 1) + (3x - 2) + (4x - 5) = 9x - 6

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Answer:

37.68 is the correct answer

Step-by-step explanation:

diameter of the given circle is 12ft

circumference of a circle = pi x diameter.

= 3.14 x 12 ft

= 37.68 ft

Answer:

A

Step-by-step explanation:

because use the equation circumference of a circle

\(2 \times \pi \times r\)

so 12 is diameter half it will be 6 which is radius. Then insert the number in the equation. hope this helps:)

The measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation if the triangle ABC implies it is bigger than the triangle A'B'C' with a scale factor 1/2 since AC = 10 and A'C' = 5

side A'B' = 8 × 1/2

side A'B' = 4

Therefore, the measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

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Answer:

the answer is B, 4. :)

Answer:

A.

Step-by-step explanation:

D: there is no square root

for both C and B there is no decimal.

A should end up being y=-8x+5 which is in y=mx+b form

The population of the town after 10 years will be, 5933

The decrease rate of a value measures its change from one period to another (month, quarter, year). It is very generally expressed as a percentage.

Given that, the population of a small town is decreasing at a rate of 7% per year. If the town's population is 12,259 now,

The decrease rate =

A = P(1-r)ⁿ

A = final population

P = initial population

r = rate

n = time

A = 12259(1-0.07)¹⁰

A = 5933

Hence, the population of the town after 10 years will be, 5933

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Answer:

Step-by-step explanation:

8(2+3)

We need to know the total earnings and total expenses for the day. Without this information, we cannot accurately determine Leo's profit. If you can provide additional details or the complete notebook entries, I would be happy to assist you in calculating the profit.

To determine Leo's profit for the first day, we need more information than what is provided in the question. The notebook shows the money earned and spent, but the given information stops at "10," without specifying whether it represents money earned or money spent. Additionally, we don't have any other earnings or expenses mentioned in the question.

To calculate the profit, we need to know the total earnings and total expenses for the day. Without this information, we cannot accurately determine Leo's profit. If you can provide additional details or the complete notebook entries, I would be happy to assist you in calculating the profit.

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Answer: BC=3

Step-by-step explanation: Set the two side lengths equal to each other and solve.

Answer:

BC = 20 units.

Step-by-step explanation:

This triangle has 3 equal sides.

so: -y + 23 = 6y + 2

23 - 2 = 6y + y

21 = 7y

y = 3.

So each side is 6(3) + 2 = 20 units long.

The inequality equation for the length of the pipe is |x - 3.36| ≤ 0.09, and the range varies from 3.27 ≤ x ≤ 3.45.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given the length of the pipe = 3.36 meters

The pipe must be within 0.09 meters

Let x represent the length of the pipe,

inequality equation,

|x - 3.36| ≤ 0.09

case 1: x - 3.36 ≤ 0.09

x ≤ 3.45

Case 2: x - 3.36 ≥ -.09

x ≥ 3.27

range varies from 3.27 ≤ x ≤ 3.45.

Hence the equation is |x - 3.36| ≤ 0.09 and range is 3.27 ≤ x ≤ 3.45.

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The last number on a synthetic division represents the remainder of the division.

The true statements are:

From the question, we have the dividend to b 2x^2 + 9x - 7, the last number to be 11, and the zero of the divisor to be -6.

This means that:

\(x = -6\) --- the divisor

Set to 0

\(x+6 = 0\)

So, when the dividend 2x^2 + 9x - 7 is divided by divisor x + 6, the remainder is 11.

This also means that, when -6 is substituted for x in the dividend, the remainder is 11

Hence, the true statements are (a) and (e)

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Step-by-step explanation:

3/4 * 24

=>72/4

=> 18

7 * 2 1/7

=> 7×15/7

=> 105/7

=> 15

17 * 1/3 =

=> 17/3

=> 5.666666666

=> 5.7

9 * 4 1/3

=> 9 × 13/3

=> 117/3

=> 39

1/2 * 2 1/4

=> 1/2 × 9/4

=> 9/8

=> 1.125

7 1/2 * 1 1/3

=> 15/2 × 4/3

=> 60/6

=> 10

6 2/3 * 2 1/4

=> 20/3 × 9/4

=> 180/12

=> 15

2 2/3 * 3 1/8

=> 8/3 × 25/8

=> 200/24

=> 8.333333333333333

3/7 * 5 1/4

=> 3/7 × 21/4

=> 63/28

=> 2.25

Answer:

The number of softballs that would fill the room is 221796 softballs

Step-by-step explanation:

First we will determine the Volume of the room.

The volume of a room is given by

\(Volume = lwh\)

From the question, the given dimension of the room is  10 by 12 by 24 foot

Hence the volume of the room = 10 × 12 × 24

= 2880 cubic feet (ft³)

Convert to cubic inches

To do this, multiply the answer in cubic feet by (12 × 12 × 12)

(NOTE: 1 foot = 12 inches)

Hence, 2880 cubic feet = 2880 × 12 × 12 × 12 cubic inches

= 4976640 cubic inches

This is the volume of the room.

To estimate the number of softballs that would fill the room, we will determine the number of softballs which would give a total volume that is equal to the volume of the room.

First, we will find the volume of one softball

Diameter of softball = 3.5 inches

∴ Radius of softball, r = 3.5/2 inches = 1.75 inches

∴ r = 1.75 inches

Now, for the volume of one softball

From,

V = 4/3 (3.14)r^3

\(V = \frac{4}{3}(3.14)r^{3}\)

\(V = \frac{4}{3}(3.14)\) × \(1.75^{3}\)

\(V = 22.43791667\) cubic inches

This is the volume of one softball

The number of softballs that would fill the room will be

= Volume of the room / Volume of one softball

= 4976640 cubic inches / 22.43791667 cubic inches

=221795.9926

≅221796

Hence, the number of softballs that would fill the room is 221796 softballs