Use the substitution method to solve the system of equations choose the correct ordered pair

x+y=3

y=8

A. (-11,8)

B. (11,8)

C. (-5,8)

D,(5,8)

The given triangles AOB and triangle OCB are proved congruent by using the property - angle side angle congruency.

Of three sides, three angles, plus three vertices, a triangle is a two-dimensional shape. If the matching sides or angles of two or more triangles match, the triangles are said to be congruent. Congruent triangles are identical in terms of their dimensions and shape.

Two triangles belong together if whose corresponding two angles but one included side are equivalent, according to the Angle- Side- Angle rule (ASA).

Given data:

As, AB || CD, ∠ABO ≅ ∠OCD (alternate interior angles)

∠AOB ≅ ∠COD (vertically opposite angles)

So,

∠AOB ≅ ∠COD

CO = OB

∠ABO ≅ ∠OCD

By using angle side angle congruence:

ΔAOB ≅ ΔCOD

Thus, the given triangles AOB and triangle OCB are proved congruent by using the property - angle side angle congruency.

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The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

In this case, we have two figures, LMNO and HIJK, and we know that LMNO is a reflection of HIJK. This means that there is an axis of reflection that maps HIJK onto LMNO.

When a shape is reflected across a line of symmetry, its angles are preserved. That is, if two angles in the original shape are congruent, then their images in the reflected shape are also congruent.

In this case, ZH is an angle in HIJK, and we want to find the angle in LMNO that corresponds to it. To do this, we need to find the line of symmetry that maps HIJK onto LMNO.

Once we have identified this line, we can draw the perpendicular bisector of ZH and find where it intersects the line of symmetry. The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

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Answer:

Step-by-step explanation:

The students do not spend nmore time reading in April than in July

Find the mean

5 + 2+ 7+23+3+6+3+1+10 / 10

= 64 / 10

= 6.4

standard deviation = √368.4 / 9 = 6.398

test statistic = 6.4 / 6.398/√10

= 3.1633

degree of freedom= 10 - 1

= 9

p v alue = 0.005745

This shows that the students do not spend nmore time reading in April than in July

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Answer:

5.5

Step-by-step explanation:

x＋3＝8.5

or，x＝5.5

I hope it helped you

Please Mark me brainliest

Answer:

x > 12

Step-by-step explanation:

3x + 18 > 54

The odds ratio of 5.91 suggests that vaccination significantly increases the likelihood of remaining healthy and not developing COVID-19 symptoms compared to no vaccination.

Calculate the odds of staying healthy for each vaccination status based on the data provided:

Unvaccinated:

Number of individuals who stayed healthy = 44

Number of individuals who developed COVID-19 = 25

Odds of staying healthy = Number of individuals who stayed healthy / Number of individuals who developed COVID-19 = 44/25 = 1.76

Vaccinated:

Number of individuals who stayed healthy = 52

Number of individuals who developed COVID-19 = 5

Odds of staying healthy = Number of individuals who stayed healthy / Number of individuals who developed COVID-19 = 52/5 = 10.4

Next, let's calculate the odds ratio from the odds of staying healthy for each vaccination status:

Odds ratio = Odds of staying healthy for vaccinated / Odds of staying healthy for unvaccinated

= 10.4 / 1.76

= 5.91

Now, let's interpret the odds ratio and answer the research question. An odds ratio of 5.91 indicates that the odds of staying healthy among vaccinated individuals is 5.91 times higher compared to unvaccinated individuals.

This suggests that vaccination is associated with a significantly higher likelihood of staying healthy and not developing COVID-19 symptoms. Therefore, the data collected by the researcher suggests that the vaccine is effective in preventing the development of COVID-19 symptoms.

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The IQR (Interquartile Range) of 13 is the most accurate measure of variability to use for this data since the data is skewed and contains outliers. The IQR is less sensitive to outliers than the range and provides a better representation of the spread of the middle 50% of the data.

Variability refers to the extent to which data points in a dataset differ from each other. It is a measure of how spread out or dispersed a set of data is.

In statistics, measures of variability are used to describe how spread out or clustered a set of data is. There are several measures of variability, but the two most common ones are the range and the interquartile range (IQR).

The range is the difference between the maximum and minimum values in a set of data. It is a simple measure of variability that gives an idea of how much the data varies. However, it can be affected by outliers, which are values that are much larger or smaller than the other values in the data set.

The IQR is a more robust measure of variability that is less affected by outliers. It is the difference between the third quartile (the value above which 75% of the data falls) and the first quartile (the value below which 25% of the data falls). The IQR describes the range of the middle 50% of the data and gives an idea of how spread out the data is around the median.

In the case of the charity's donations, the data is skewed towards the higher end, with most of the donations falling between $16 and $20. This means that the range of 13 (20-5) would be affected by the outliers at the high end, and would not accurately represent the variability of the data.

On the other hand, the IQR of 13 (the difference between the third quartile at $20 and the first quartile at $7) would give a more accurate representation of the variability of the data, as it is less affected by the outliers.

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The total vertical change after travelling horizontal distance 516 feet is equal to 370 feet.

Monongahela Incline slope is equal to = 18.5 / 25.8

This implies that after traveling a horizontal distance of 25.8 it rise upto 18.5.

To ride up the funicular total travelling at the top is equal to,

25.8 Horizontal change = 18.5 vertical change

⇒ 1 horizontal change = ( 18.5 / 25.8 ) vertical change

⇒ 516 feet horizontal change = 516 feet × ( 18.5 / 25.8 ) vertical change

                                                  = 370 feet.

Therefore, the total vertical distance while travelling at the top of the funicular is equal to 370 feet.

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The average value of the function f(x,y) = sin(x+y) over the rectangle 0 ≤ x ≤ π/3, 0 ≤ y ≤ 5π/3 is -27√(3) / (40π^2).

To find the average value of the function ​f(x,y)=sin(x+y) over the given rectangle, we need to integrate the function over the rectangle and then divide by the area of the rectangle.

So, we have:

average value of f(x,y) = (1/Area of rectangle) × double integral of f(x,y) over the rectangle

where the limits of integration are

0 ≤ x ≤ π/3

0 ≤ y ≤ 5π/3

The area of the rectangle is

Area = (π/3 - 0) × (5π/3 - 0) = 5π^2 / 9

Now, we can integrate the function f(x,y) over the rectangle

double integral of f(x,y) over the rectangle = integral from 0 to π/3 of integral from 0 to 5π/3 of sin(x+y) dy dx

= [tex]\int\limits^{\pi /3}_0[/tex] [-cos(x+y)] evaluated from y=0 to y=5π/3 dx

= [tex]\int\limits^{\pi /3}_0[/tex] [-cos(x+5π/3) + cos(x)] dx

= [tex]\int\limits^{\pi /3}_0[/tex]  [-1/2cos(x) - 1/2cos(x+π/3)] dx

= [-1/2sin(x) - 1/4sin(x+π/3)] evaluated from x=0 to x=π/3

= [-1/2sin(π/3) - 1/4sin(2π/3)] - [-1/2sin(0) - 1/4sin(π/3)]

= (-√(3)/4) - (1/4 × √(3)/2) = -3sqrt(3)/8

Therefore, the average value of f(x,y) over the rectangle is

average value of f(x,y) = (1/Area of rectangle) × double integral of f(x,y) over the rectangle

= (-3sqrt(3)/8) / (5π^2 / 9)

= -27sqrt(3) / (40π^2)

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The given question is incomplete, the complete question is:

Find the average value of ​f(x,y)=sin(x+y) over the rectangle 0≤x≤π/3​, 0≤y≤5π/3.

To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.

We define the actual score, theoretical score, and explain how to calculate the percent success on an exam.
Actual score:

The actual score refers to the number of points a student has earned on an exam.

It represents the student's performance on the test, taking into account the correct and incorrect answers.
Theoretical score:

The theoretical score is the maximum number of points a student can earn on an exam.

This represents a perfect performance, where the student answers all questions correctly.
Calculating percent success:

To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.
a. Divide the actual score by the theoretical score: (actual score) / (theoretical score)
b. Multiply the result by 100: (result from step a) * 100
c. The final value is the percent success.

For example, if a student has an actual score of 80 and the theoretical score is 100, the percent success would be calculated as follows:
a. 80 / 100 = 0.8
b. 0.8 * 100 = 80
c. The percent success is 80%.

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The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is 91%. Option A is the correct answer.

To calculate the coefficient of variation, first, we need to calculate the standard deviation and mean of the sample.

The mean of the sample is (3 + 5 + 12 + 3 + 2)/5 = 5.

To find the standard deviation, we first need to calculate the variance. The variance can be found by taking the sum of the squared differences between each data point and the mean, dividing by the sample size minus one, and then taking the square root.

The variance is ((3-5)² + (5-5)² + (12-5)² + (3-5)² + (2-5)²)/4 = 20.5.

The standard deviation is the square root of the variance, which is approximately 4.53.

Finally, we can calculate the coefficient of variation by dividing the standard deviation by the mean and multiplying by 100%.

Coefficient of variation = (4.53/5) x 100% = 90.6%.

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The question is -

A researcher has collected the following sample data. The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is?

a. 91%

b. 72.66%

c. 330%

d. 264%

The minimum number of tiles required to cover the kitchen floor is approximately 71 tiles.

The dimension of the square tiles are 6inches L and W

Hence the area = 6 x 6 = 36inches

In ft this would be:

36/12 = 3ft

since 1 ft = 12 inches.

The dimension of the rectangular floor is 12.5ft by  17ft

Hence it's area = L x W = 12.5ft x  17ft = 212.5ft

So recall that the area of the tile = 3f, hence the minimum number of tiles required = 212.5ft/3ft

= 70.8333333333

The minimum number of tiles requires is [tex]\approx[/tex] 71 tiles.

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Full Question:

Although part of your question is missing, you might be referring to a similar question:

A carpenter is going to install square tiles on a living room floor. T?he living room florrs is in the shape of a 12.5ft x 17ft  rectangle as shown.

The side length of each square tile is 6 inches. What is the minimum number of the tiles the carpenter needs to completely cover the living room?

So, the area of the figure is 54.5 square miles.

In mathematics, the area is the measurement of the size of a two-dimensional surface or region, usually expressed in square units. It is a quantity that expresses the extent of a two-dimensional shape or figure in a plane. The area of a figure is calculated by multiplying the length and width of the shape, in the case of a rectangle, or by using the appropriate formula for other shapes such as triangles, circles, or irregular polygons.

Here,

The area of rectangle R1 is:

Area of R1 = 5 mi x 2 mi

= 10 square miles

The area of rectangle R2 is:

Area of R2 = 2 mi x 14 mi

= 28 square miles

The area of the triangle TRI is:

Area of TRI = (1/2) x base x height

           = (1/2) x 11 mi x 3 mi

           = 16.5 square miles

Therefore, the total area of the figure is:

Area of figure = Area of R1 + Area of R2 + Area of TRI

              = 10 + 28 + 16.5

              = 54.5 square miles

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The slope of the second line is also positive, as it is parallel to the first line which has a positive slope.

Slope is a measure of how steep a line is, and is defined as the ratio of the change in the y-coordinate (vertical change) to the change in the x-coordinate (horizontal change) between any two points on the line. It represents the rate at which the line is rising or falling as it moves from left to right. Slope can be positive, negative, or zero. A positive slope indicates that the line is increasing as it moves from left to right, a negative slope indicates that the line is decreasing as it moves from left to right, and a zero slope indicates that the line is horizontal.

Here,

When two lines are parallel, they have the same slope. In this case, the first line has a positive slope of "a," which means that it is increasing as it moves from left to right. Since the second line is parallel to the first line, it will also have the same slope as the first line. Therefore, the slope of the second line will also be positive, indicating that it is increasing as it moves from left to right.

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The total area of the space is given as 1729 sq ft.

We can make use of engineered wood because it fits the budget

A mathematical model is a representation of a real-world system, process, or phenomenon using mathematical concepts, equations, and symbols. The purpose of creating a mathematical model is to understand and analyze the behavior of the system under different conditions and to make predictions about its future behavior.

Mathematical models can be used in various fields, including physics, engineering, economics, biology, and social sciences. They can range in complexity from simple algebraic equations to sophisticated computer simulations and can incorporate various factors such as time, space, and multiple variables.

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Answer:

Step-by-step explanation:

it is -2

Answer: -2

Step-by-step explanation:

So this is asking for the cube root of -8.

This is the same as asking what is multiplied by itself 3 times to get -8.

-2 * -2 *-2 = -8

You can also use a calculator.

Another way to solve it is to write -8^(1/3).

Hope this helps!!!

The number of envelopes left to address by Sani is at most 51 .

And Messages > 10 to have unlimited plan cheaper than paying for each messages.

At least numbers of envelopes Sani has = 68

Number of envelops he addressed = 17

Let x be the number of envelopes that Sani has left to address.

Then we have,

x ≤ 68 - 17

Simplifying this inequality, we get,

x ≤ 51

Sani has at most 51 envelopes left to address.

Cost per text message send or received by Nadine = $0.5

Cost pf unlimited number of text message send or received = $5

Let m be the number of messages Nadine sends or receives.

Then the cost of paying for each message is,

0.5m

The cost of the unlimited plan is $5.0.

The number of messages m such that,

5.0 ≤ 0.5m

Simplifying this inequality, we get,

⇒ 10 ≤ m

If Nadine sends or receives more than 10 messages, the unlimited plan is cheaper than paying for each message.

So the solution to the inequality is m > 10.

Therefore, number of message Sani left to address is at most 51 envelopes .

And to have unlimited plan cheaper than paying for each messages for Nadine is m > 10.

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The expected winning is $2.

To calculate the expected winning, we need to find the probability of each outcome and multiply it by the amount we will win in that outcome.

There are 2 possible outcomes for each coin flip: heads or tails. Therefore, there are 2x2x2=8 possible outcomes for flipping a coin three times.

Here are all the possible outcomes with the number of heads in each outcome:

The probability of each outcome can be calculated using the formula: probability = (number of favorable outcomes) / (total number of possible outcomes)

For example, the probability of getting 3 heads (HHH) is 1/8 because there is only one favorable outcome out of 8 possible outcomes.

Using this formula, we can calculate the probability and expected winning for each outcome:

To calculate the overall expected winning, we need to add up the expected winning for each outcome multiplied by its probability:

(1/8) x $6 + (1/4) x $4 + (1/4) x $4 + (1/4) x $4 + (3/8) x $2 + (3/8) x $2 + (3/8) x $2 + (1/8) x $0 = $2

Therefore, the expected winning is $2.

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Answer:

x >-15

Step-by-step explanation:

Please here is it.

where x >-15

Answer:

f -1

Step-by-step explanation:

the inverse of a function (f) is denoted by f -1 and exsists only when f is both one to one and onto function.

All four zeros are real solutions in the polynomial equation.

What are polynomials in equations?

A polynomial is an expression that consists of one or more variables, coefficients, and non-negative integer exponents of the variables. An equation is a mathematical statement with an equal sign between two algebraic expressions with equal values. 

x⁴ – 41 x² = – 400

Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get

       x⁴ - 41x² + 400 = -400 + 400

     x⁴ - 41x² + 400 = 0

Factoring by product sum rule.

We need product of 400 and sum upto -41.

We can see that 400 = -25 × -16 = 400 and -25-16 = -41.

Therefore,

         x⁴ - 25x² - 16x²  + 400 = 0

Making it into two groups, we get

  (x⁴ - 25x²) + (-16x² + 400) = 0

Factoring out GCF of each group, we get

  x²(x² - 25) (x² - 16) = 0

(x² - 25) = x² - 5²  = (x - 5) (x + 5)

x² - 16 = x² - 4² = (x - 4)(x + 4)

(x - 5) (x + 5) (x - 4)(x + 4) = 0

Applying zero product rule,

x-5=0

x+5=0

x-4=0 and

x+4=0.

Therefore,

x = -5, -4, 4 and 5.

All four zeros are real solutions.

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To find the equation for the line of best fit, we can use linear regression. Based on the given data:

x: 2, 5, 7, 12, 16

y: 9, 10, 5, 3, 2

The equation for the line of best fit would be in the form: y = mx + b, where m is the slope and b is the y-intercept.

Using a calculator or statistical software, we can calculate the slope and y-intercept for the line of best fit.

The result is:

Slope (m): -0.580 (rounded to three decimal places) Y-intercept (b): 10.671 (rounded to three decimal places)

So, the correct answer is:

A. y = -0.580x + 10.671

The inequality is simplified as 0 ≤ x ≤ 4

In mathematics, inequality refers to a mathematical expression that indicates that two values or quantities are unequal. An inequality is represented by the symbols "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

For example, the inequality "x > 5" means that the value of x is greater than 5, and the inequality "y ≤ 10" means that the value of y is less than or equal to 10.

To graph the conjunction, we first need to solve for x:

-4 ≤ x - 4 ≤ 0

Add 4 to all parts of the inequality:

0 ≤ x ≤ 4

Image of graph is attached below.

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Comparing the rates of change, we can see that Function 2 has a greater rate of change than Function 1. Therefore, the answer is (B) Function 2.

What is the rate of change?

The rate of change is the amount of change in the output (dependent variable) for a given change in the input (independent variable).

In this case, the input is the number of days ridden, and the output is the cost of transportation for a month.

For Function 1, the cost is $5.50 per day. Therefore, the rate of change is $5.50 per day.

For Function 2, the equation E = 8.25 + 1.50d represents the cost of transportation for a month, where d is the number of days ridden. The rate of change is the coefficient of d, which is $1.50 per day.

Hence, Comparing the rates of change, we can see that Function 2 has a greater rate of change than Function 1. Therefore, the answer is (B) Function 2.

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Answer: 102 miles.

Step-by-step explanation:

You divide 17 by 5 and then multiply by 30.

It is important for researchers to carefully consider these factors when designing studies and analyzing data to ensure that their results are accurate and reliable.

Small Sample Size: With only 40 participants remaining in the experimental group after 6 months, the sample size may have been too small to detect any significant differences between the experimental and control groups.

Sampling Error: Even with random assignment to groups, there is always a chance that the groups will differ on some important characteristic that could affect the results.

Statistical Power: The statistical power of a study refers to its ability to detect a true effect if one exists. With a small sample size, the statistical power of the study may have been too low to detect any real differences between the groups.

Data Analysis: The way in which the data was analyzed could have influenced the results. For example, if the researchers used an inappropriate statistical test or did not correct for multiple comparisons, it could have led to faulty results.

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The value of the missing angles are:

w = 109°

x = 39°

y = 141°

z = 109°

In geometry, we know that the sum of angles on a straight line is 180 degrees. Thus:

w = 180 - 71

w = 109°

We know that alternate angles are formed when two parallel lines are cut by a transversal. Thus:

x = 39°

y = 180 - 39

y = 141°

Similarly:

z = 180 - 71

z = 109°

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Answer:

Step-by-step explanation:

Medium is 28

Mean is 29

Range is 11

Midrange is 29.5