Which sets of angles add to equal 180°?
a.
Linear Pair Angles
c.
Parallel Lines with Alternate Interior
Angles
b. Parallel Lines with Consecutive Interior d. Interior Angles of a Triangle
Angles

The point (-2, 8) is a solution of the first system of equations:

y - 2x = 12

x - 2y = -18

To see this, we need to evaluate that point on all the equations and see for which system that point solves both equations.

For the first system:

y - 2x = 12

x - 2y = -18

Replacing the values x = -2 and y = 8 we get:

8 - 2*-2 = 12

2 - 2*8 = -18

12 = 12

-18  = -18

Both are true, then the first option is the correct one.

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Answer:

Hint: 0 is x1, -2 is y1, 10 is x2, and -6 is y2.

Step-by-step explanation:

I'm not sure how to explain it, but that's how you can label your coordinates to  make it easier to substitute it into the formula. The first number at the beginning of the coordinate is x and the other is y. For example, (3, 7). The three is x and the seven y. If you have two coordinates, then one group has a 1 underneath it while the other has a 2. Simply put, (x1, y1) and (x2, y2). The only thing left is to find the midpoint of segment AB (or line, not sure) by using the midpoint formula.

(If you still need help, you can always reply back)

Answer:

the simplest form of 15/20 is 3/4

The solution to the system of equations y = -6x - 3 and y = -x^2 can be found by finding the point(s) of intersection between the two graphs.

To solve the system, we can set the two equations equal to each other:

-6x - 3 = -x^2

Rearranging the equation, we get:

x^2 - 6x - 3 = 0

Using the quadratic formula, we can find the solutions for x:

x = (6 ± √(36 + 12))/2

x = (6 ± √48)/2

x = (6 ± 4√3)/2

x = 3 ± 2√3

Substituting these x-values back into either equation, we can find the corresponding y-values:

For x = 3 + 2√3, y = -6(3 + 2√3) - 3 = -18 - 12√3 - 3 = -21 - 12√3

For x = 3 - 2√3, y = -6(3 - 2√3) - 3 = -18 + 12√3 - 3 = -21 + 12√3

Therefore, the solutions to the system of equations are (3 + 2√3, -21 - 12√3) and (3 - 2√3, -21 + 12√3).

To know more about  systems of equations click here:   brainly.com/question/20067450

#SPJ11

The probability in a normal distribution is approximately 90% percent.

According to the statement

we have given that the

Probability of the more three standard deviations and we have to find the percentage  in a normal distribution.

We know that the

A normal distribution is a type of continuous probability distribution for a real-valued random variable.

So,  In the presence of a more than three standard deviations the normal distribution is about 95%.

Because in the normal distribution is 95% due to the empirical rule.

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.

So, The probability in a normal distribution is approximately 90% percent.

Learn more about normal distribution here

https://brainly.com/question/4079902

#SPJ1

Answer:

34.58$

Step-by-step explanation:

TO find the answer we must first find 1% of 38$, which would be .38. so now multiply by 15 and 15% of 38 is 5.7$ so now the cost is 32.3$. Now we find the 6% of sales tax. .38 x 6 = 2.28, now add it all together and you get 34.58$

(っ◔◡◔)っ ♥ Hope It Helps ♥

The solution of the initial value problem Dy(t)/dt + 8y(t) = 1 + e-6t is option (c) y(t) = (1/8) - (1/8) * e^(-8t).

To solve the given initial value problem, we can use the method of integrating factors.

The given differential equation is:

\(dy(t)/dt + 8y(t) = 1 + e^(-6t)\)

First, we write the equation in the standard form:

\(dy(t)/dt + 8y(t) = 1 + e^(-6t)\)

The integrating factor (IF) is given by the exponential of the integral of the coefficient of y(t), which is 8 in this case:

IF = \(e^(∫8 dt)\)

=\(e^(8t)\)

Now, we multiply both sides of the differential equation by the integrating factor:

\(e^(8t) * dy(t)/dt + 8e^(8t) * y(t) = e^(8t) * (1 + e^(-6t))\)

Next, we can simplify the left side by applying the product rule of differentiation:

\((d/dt)(e^(8t) * y(t)) = e^(8t) * (1 + e^(-6t))\)

Integrating both sides with respect to t gives:

\(∫(d/dt)(e^(8t) * y(t)) dt = ∫e^(8t) * (1 + e^(-6t)) dt\)

Integrating the left side gives:

\(e^(8t) * y(t) = ∫e^(8t) dt\)

\(= (1/8) * e^(8t) + C1\)

For the right side, we can split the integral and solve each term separately:

\(∫e^(8t) * (1 + e^(-6t)) dt = ∫e^(8t) dt + ∫e^(2t) dt\)

\(= (1/8) * e^(8t) + (1/2) * e^(2t) + C2\)

Combining the results, we have:

\(e^(8t) * y(t) = (1/8) * e^(8t) + C1\)

\(y(t) = (1/8) + C1 * e^(-8t)\)

Now, we can apply the initial condition y(0) = 0 to find the value of C1:

0 = (1/8) + C1 * e^(-8 * 0)

0 = (1/8) + C1

Solving for C1, we get C1 = -1/8.

Substituting the value of C1 back into the equation, we have:

\(y(t) = (1/8) - (1/8) * e^(-8t)\)

Therefore, the solution to the initial value problem is:

\(y(t) = (1/8) - (1/8) * e^(-8t)\)

The correct answer is option (c) \(y(t) = (1/8) - (1/8) * e^(-8t).\)

To know more about initial value problem

https://brainly.com/question/30503609

#SPJ11

Answer:

\((0,-1)\)

Step-by-step explanation:

\((x^{2} -x^{1} )(y^{2} -y^{1} )\)- the formula

\((-1 - -1) = 0\)

\((-8 - -7) =-1\)

So, the answer is:

\((0,-1)\)

or

\(0=-1\)

  ^

this is the swiggly line

Answer:

9

Step-by-step explanation:

How to solve your question

Your question is

|

−

9

|

|-9|

∣−9∣

Solve

1

Find the absolute value

|

−

9

|

9

Solution

9

(a) The time series plot shows an increasing non-linear trend pattern in the data.

(b) The parameters for the line that minimizes MSE for this time series are:

\(b_o = 2.4376\\b_i = 2.434\)

(a)

t      1    2    3    4    5

\(y_t\)    7  12    8   15   16

Plotting the data points on a graph with time (t) on the x-axis and the observed values (\(y_t\)) on the y-axis, we obtain the following time series plot.

From the time series plot, we can observe an increasing trend in the data. The values of \(y_t\) generally rise over time, indicating a non-linear positive trend pattern.

(b) To find the parameters for the line that minimizes the Mean Squared Error (MSE) for the given time series data, we can use simple linear regression analysis.

The equation for simple linear regression is given by:

\(Y_t = b_o + b_i * t\)

\(\sum Y_t = n * b_o + b_i * \sum t\\\sum Y_t * t = b_o * \sum t + b_i * \sum t^2\)

where n is the number of observations.

Let's calculate the required values:

n = 5 (number of observations)

\(\sum Y_t = 5 + 12 + 8 + 15 + 16 = 56\\\sum t = 1 + 2 + 3 + 3 + 4 + 5 = 18\\\sum Y_t * t = (5 * 1) + (12 * 2) + (8 * 3) + (15 * 3) + (16 * 4) = 117\)

Now, we can substitute these values into the equations:

\(n * b_o + b_i * \sum t = \sum Y_t\\5 * b_o + 18 * b_i = 56 ---(1)\\b_o * \sum t + b_i * \sum t^2 = \sum Y_t * t\\18 * b_o + 30 * b_i = 117 ---(2)\)

To solve this system of equations, we can multiply equation (1) by 18 and equation (2) by 5 to eliminate bo:

\(90 * b_o + 324 * b_i = 1008 ---(3)\\90 * b_o + 150 * b_i = 585 ---(4)\)

Subtracting equation (4) from equation (3):

\(174 * b_i = 423\)

Dividing both sides by 174:

\(b_i = 423 / 174 = 2.434\)

Now, substitute the value of \(b_i\) back into equation (1):

\(5 * b_o + 18 * 2.434 = 56\)

Simplifying:

\(5 * b_o + 43.812 = 56\\5 * b_o = 56 - 43.812\\5 * b_o = 12.188\\b_o = 12.188 / 5 = 2.4376\)

Therefore, the parameters for the line that minimizes the MSE for this time series data are approximately:

\(b_o = 2.4376\\b_i = 2.434\)

So, the equation for the line is:

\(Y_t = 2.4376 + 2.434 * t\)

Complete Question:

Consider the following time series data. t 1 2 3 3 4 5 Yt 5 12 8 15 16

(a) Construct a time series plot. What type of pattern exists in the data?

(b) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.

To know more about time series plot, refer here:

https://brainly.com/question/28481310

#SPJ4

Answer:

It might be C if im wrong sorry

Step-by-step explanation:

Answer:

$36 dollars

Step-by-step explanation:

Answer:

To get the result we have to find 4/5 of 45$. To do this we have to just multiply 4/5 by 45, so

- 36 is the answer

Answer:

I hope this helped!

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

To learn more about cash : brainly.com/question/31754110

#SPJ11

Answer:

Answer: -⅔ and ⅔

Step-by-step explanation:

\( - \frac{2}{3} \times \frac{2}{3} = - \frac{4}{9} \\ \)

a. We have shown that α + 1 = β.

b. We have shown that α² = β.

A substance that cannot be broken down into another substance is referred to as an element. Because each element is made up of its own type of atom, each element is distinct and distinct from the others.

Since K is a field with 4 elements, the nonzero elements of K form a cyclic group of order 3 under multiplication. Let us call this group G. Since G is cyclic, it has a unique generator, say g. Then we can write G = {1, g, g²}.

Now, since α and β are both in K but not in Z2, they must be elements of G. Moreover, since K contains Z2 as a sub-field, α and β must be roots of the polynomial x² + x + 1 over Z2. Therefore, we have the following possibilities for α and β:

α = g

β = g²

or

α = g²

β = g

a. Let us first consider the case where α = g and β = g². Then we have:

α + 1 = g + 1

= g² + g + 1 (since g³ = 1)

= β + α + 1 (since β = g² and α = g)

= β

Therefore, we have shown that α + 1 = β.

b. Next, we will show that α² = β. Using the same assumption that α = g and β = g², we have:

α² = g²

= β

Therefore, we have shown that α² = β.

Learn more about polynomials on:

https://brainly.com/question/4142886

#SPJ11

The statement "The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is 1/(a-b)" is False.

In a uniform distribution, the probability density function (PDF) is constant within the interval [a, b]. The height of the PDF represents the density of the probability distribution at any given point within the interval. Since the PDF is constant, the height remains the same throughout the interval.

To determine the height of the PDF, we need to consider the interval length. In a uniform distribution defined on the interval [a, b], the height of the PDF is 1/(b - a) for the PDF to integrate to 1 over the entire interval. This means that the total area under the PDF curve is equal to 1, representing the total probability within the interval [a, b].

Therefore, the correct statement is that the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is not 1/(a - b), but rather it is a constant value necessary for the PDF to integrate to 1 over the interval, i.e., 1/(b - a).

Learn more about  uniform distribution here:

https://brainly.com/question/32291215

#SPJ11

Answer:

The answer should be $31.99

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

for such more question on Hexadecimal numbers

https://brainly.com/question/28280312

#SPJ8

Answer:

Step-by-step explanation:

50(0.975)^30

= 23.39 Round if necessary to 23.40

The amount of Ib of chromium will be 23.40 if one type of chromium has a radioactive decay rate of 2.5% per day.

It is defined as the factor that represents the increase and decrease in value by that factor. For the growth add one as a decimal and for the decay subtract one as a decimal.

It is given that:

One type of chromium has a radioactive decay rate of 2.5% per day.

y = 50(0.975)×

y = 50(0.975)³⁰

= 23.39

= 23.40

Thus, the amount of Ib of chromium will be 23.40 if one type of chromium has a radioactive decay rate of 2.5% per day.

Learn more about the growth and decay factor here:

brainly.com/question/4098905

#SPJ2

Answer:

3x5−4x4−x2+5

Simplify the expression.

Answer: did you make that up ??

Step-by-step explanation:

Answer:

A. Alternate interior

B. Transitive property

C. Converse alternate interior angles theorem.

The commission the salesperson would receive is $490.

What is a commission?

A commission is a payment made to an individual, such as a salesperson or agent, for services rendered or a good sold. The commission is typically a percentage of the sale or revenue generated. This percentage is known as the commission rate.

To find the commission a salesperson would receive from selling a car, we need to multiply the commission rate (5%) by the car's value ($9,800).

The commission rate is given as a percentage, so we need to convert it to a decimal to do the calculation. We can do this by dividing the percentage by 100.

So 5% = 5/100 = 0.05

Then to find the commission the salesperson would receive we multiply:

Commission = 0.05 * $9,800

Commission = $490

Hence, the commission the salesperson would receive is $490.

To learn more about the commission, visit:

https://brainly.com/question/24951536

#SPJ1

The prevalence of sampling errors can be reduced by increasing the sample size. As the sample size increases, the sample gets closer to the actual population, which decreases the potential for deviations from the actual population.

When studying the incidence of rare phenomena, researchers should use "relatively large samples". Using a large sample corrects for bias. If bias has been eliminated, it is safe to assume that the sample is free of sampling errors." The effects of random sampling errors are predictable in the long run.

One of the most effective methods that can be used by researchers to avoid sampling bias is simple random sampling, in which samples are chosen strictly by chance. This provides equal odds for every member of the population to be chosen as a participant in the study at hand.

The prevalence of sampling errors can be reduced by increasing the sample size. As the sample size increases, the sample gets closer to the actual population, which decreases the potential for deviations from the actual population.

Non-probability sampling often results in biased samples because some members of the population are more likely to be included than others.

To avoid non-response bias, researchers should keep surveys as simple as possible, with clear wording and instruction and seek respondents who are relevant to the survey topic.

Therefore,

The prevalence of sampling errors can be reduced by increasing the sample size. As the sample size increases, the sample gets closer to the actual population, which decreases the potential for deviations from the actual population.

To learn more about Sampling bias visit :

brainly.com/question/29153663

#SPJ4

(a) correctly describes the relationship between a parameter and a statistic.

The correct description is:

a) A statistic is calculated from sample data and is generally used to estimate a parameter.

In statistics, a parameter refers to a characteristic or measure that describes a population, while a statistic is a characteristic or measure calculated from sample data. Statistics are often used to estimate or infer the corresponding parameters of the population. Therefore, option (a) correctly describes the relationship between a parameter and a statistic.

To know more about Statistic related question visit:

https://brainly.com/question/31538429

#SPJ11

Answer:

4a+6

Step-by-step explanation:

a+2+3a+4

4a+6

Histograms are used to graph the frequency of data, where the length of the bar represents the frequency.

The number of students that drank the recommended amount of water are 125

Given that

\(Recommended = 40\ or\ more\)

The number of students who drank the recommended amount are students whose frequency (i.e. length of bars) is 40 or more

From the histogram (see attachment), only 2 bars are above the frequency of 40.

And the number of students in these bars are: 50 and 75

\(Total =50 + 75\)

\(Total =125\)

Hence, the number of students that drank the recommended amount of water are 125

Read more about histograms at:

https://brainly.com/question/14421716

L = 1.3245 is  the legnths of the pen's sides .

What is area and perimeter?

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

The equation for perimeter is 2L + W = 30 ( I'm assuming that the shed takes up one of the Widths, but you can use the Length if you want, it doesn't matter.)

So W = 30 - 2L.

Area = L x W = L (30 - 2L) = 30L - 2L^2.

This is a quadratic equation, easily graphed as a parabola, with a maximum point at L = 1.3245 .

Learn more about perimeter

brainly.com/question/11957651

#SPJ4