8. Write the equation of the line in slope-intercept form that has:
points: (3, 5) and (-1,-3)

Answer:

Step-by-step explanation:

resources. This includes fostering the wisest use of our land and water resources, ... Back Cover: Geologist John B. Mertie exploring the Brooks Range, April 1924. ... I would like to thank Lynn Horvath for her wise counsel and ... focuses more broadly on exploration as a his- ... he paused several times to meet with Eskimo.

The measure of each exterior angle of a regular 90-gon is 4 degrees.

To find the measure of each interior angle of a regular polygon, we can use the formula:

Interior Angle = (180 × (n - 2)) / n,

where 'n' is the number of sides of the polygon.

For a regular 90-gon, we substitute n = 90 into the formula:

Interior Angle = (180 ×(90 - 2)) / 90 = 178 degrees.

Therefore, the measure of each interior angle of a regular 90-gon is 178 degrees.

To find the measure of each exterior angle of a regular polygon, we can use the relationship:

Exterior Angle = 360 / n,

where 'n' is the number of sides of the polygon.

For a regular 90-gon, we substitute n = 90 into the formula:

Exterior Angle = 360 / 90 = 4 degrees.

Therefore, the measure of each exterior angle of a regular 90-gon is 4 degrees.

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Answer:

An acute triangle is a triangle with three acute angles. An obtuse triangle is a triangle with one obtuse angle and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry

Answer:

25%

Step-by-step explanation:

The (not mentioned in the question) set is: 6 7 8 9.

There are 4 total outcomes and only 1 favorable outcome, then the probability to pick a 9 is:

P(9) = favorable outcome/total outcomes

P(9) = 1/4 = 0.25 or 0.25*100 = 25%

The total amount of revenue generated by the store's CD sales on April 18 is 21,144.2.

To find the total amount of revenue generated by the store's CD sales on April 18, we need to calculate the product of the number of CDs sold and the price per CD on that day.

First, let's find the number of CDs sold on April 18. We are given the function n(d) = 12d + 35, where d represents the number of days since April 8. Since we want to find the number of CDs sold on April 18, we substitute d = 18 into the function:

n(18) = 12(18) + 35
n(18) = 216 + 35
n(18) = 251

So, the store sold 251 CDs on April 18.

Next, we need to find the price per CD on April 18. We are given the function p(d) = 0.3d^2 - d + 5. Substituting d = 18 into the function:

p(18) = \(0.3(18)^2 - 18 + 5\)
p(18) = 0.3(324) - 18 + 5
p(18) = 97.2 - 18 + 5
p(18) = 84.2

So, the price per CD on April 18 is $84.2.

To find the total amount of revenue generated, we multiply the number of CDs sold by the price per CD:

Revenue = Number of CDs sold * Price per CD
Revenue = 251 * 84.2

Calculating this product, we find that the total amount of revenue generated by the store's CD sales on April 18 is 21,144.2.

In conclusion, the total amount of revenue generated by the store's CD sales on April 18 is 21,144.2.

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Answer:

See below

Step-by-step explanation:

Horizontal lines have ZERO slope

Vertical lines have 'undefined' slope

for this example  x = 1/2    includes the point and has undiefined slope

The value of the indicated trigonometric ratio.

cosβ is equal to 0.9167

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

the side CA = 22 is adjacent to the angle β while BA = 24 is the hypotenuse, so:

cosβ = 22/24 {adjacent/hypotenuse}

cosβ = 11/12

cosβ = 0.9167

Therefore, the cosine of the angle β is equal to 0.9167 using the trigonometric ratio.

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Answer:

Step-by-step explanation:

In this problem, we have to find the area of an square adjacent to the third side of the right triangle.

To solve this problem, we need to use Pythagorean's Theorem, beacuse it's about a right triangle. Also, this theorem is about square areas, that's the geomtrical meaning of it.

\(h^{2} =32 \ u^{2} + 32 \ u^{2} = 64\ u^{2} \\h=\sqrt{64 \ u^{2} } =8u\)

Therefore, the area of a square adjacent to the third side is 64 square units.

Answer:the answer is 8

Step-by-step explanation:

I'll do problem 1 to get you started

First sort the values from smallest to largest and you should end up with this set

{1, 6, 7, 11, 13, 16, 18, 21, 22, 23}

The smallest value is 1 and the largest value is 23, so the min and max are 1 and 23 in that order.

We have ten values in this set. The middle-most number is going to be between the 10/2 = 5th slot and the 6th slot. The numbers 13 and 16 are in the fifth and sixth slots respectively. Average those values to get (13+16)/2 = 29/2 = 14.5

The median is 14.5 which is another name for the second quartile (Q2).

Now split the data set into two halves

L = lower half of values smaller than the median

U = upper half of values larger than the median

In this case,

L = {1, 6, 7, 11, 13}

U = {16, 18, 21, 22, 23}

sets L and U have five items each

Find the median of set L and U to get 7 and 21 respectively. These medians of L and U represent the values of Q1 and Q3 in that order.

Q1 = first quartile = 7

Q3 = third quartile = 21

===================================================

Answer:

The five number summary for problem 1 is

To find the rate at which the diameter of a sphere is changing when the volume is 4000π/3 cm3, you can use the formula for the volume of a sphere, which is given by the equation V = (4/3)πr3, where V is the volume, π is the constant approximately equal to 3.14, and r is the radius of the sphere.

You can rearrange this formula to solve for the radius of the sphere:

r = (3V/(4π))^(1/3)

Plugging in the known values, you get:

r = (3(4000π/3)/(4π))^(1/3)

= (4000/4)^(1/3)

= 100^(1/3)

= 10

The diameter of the sphere is twice the radius, so the diameter is 2r = 2 * 10 = 20 cm.

To find the rate at which the diameter is changing, you can use the formula for the rate of change of a function, which is given by the equation rate of change = (change in y)/(change in x). In this case, the change in y is the change in the diameter of the sphere and the change in x is the change in the volume.

Since the volume is increasing at a rate of 50π cm3/min and the diameter is changing at the same time, you can use the formula to solve for the rate of change of the diameter:

rate of change = (change in y)/(change in x)

= (change in diameter)/(50π cm3/min)

To find the change in the diameter, you would need to know the initial and final diameters of the sphere. Without this information, it is not possible to determine the rate of change of the diameter.

Answer:

Marcus; 1.25 km

Step-by-step explanation:

Marcus ran farther than Cindy because 3.2 km is greater than 1.95 km.

How much farther is:

3.2 - 1.95 = 1.25 km

He ran 1.25 km farther than Cindy.

The person who ran further is the person who ran more kilometers.

The person who ran more kilometers is Marcus which means that Marcus ran farther.

The distance he ran farther by is:

= Distance Marcus ran - Distance Cindy ran

= 3.2 - 1.95

= 1.25 km

In conclusion, Marcus ran farther by 1.25 km.

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To solve this problem, we need to use the transition matrix P50 provided in the file data6.mat. This matrix tells us the probabilities of moving from one state to another, where each state represents a different number of coins that you and your friend have.

First, we need to define the initial state vector Xo as [0, ...,1,...,0], where 1 is at index 26 to represent the starting state where both you and your friend have 25 coins. We can use this vector to calculate the probability distribution after 201 rolls of the dice.

To do this, we can use the formula Xn = P^n * Xo, where P^n is the transition matrix raised to the power of n, and Xn is the resulting state vector after n rolls of the dice.

Using MATLAB, we can calculate X201 as follows:

load data6.mat
P = P50;
Xo = zeros(1,50);
Xo(26) = 1;
X201 = (P^201)*Xo;

We can store the resulting vector as Ex1Avec and visualize it as a bar plot using the following code:

Ex1Avec = X201;
bar(Ex1Avec)
xlabel('State')
ylabel('Probability')
title('State Vector: 201 Rolls')

This will give us a bar plot showing the probability distribution for each state after 201 rolls of the dice. We can see which state has the highest probability of occurring, which will tell us the most likely outcome of the game after 201 rolls.
To find the probability distribution after 201 rolls of the dice, you can follow these steps:

1. Load the transition matrix P50 from the data6.mat file.
2. Initialize the initial state vector X0 with 1 at index 26 (representing you and your friend having 25 coins each) and all other entries 0.
3. Raise the transition matrix P50 to the power of 201 (the number of turns).
4. Multiply the initial state vector X0 by the raised matrix to obtain the state vector X201.
5. Store the vector X201 as Ex1Avec and visualize it using the provided bar plot code.

Here's the MATLAB code for these steps:

```MATLAB
load('data6.mat'); % Load the transition matrix P50
X0 = zeros(1, 51); % Initialize the initial state vector X0
X0(26) = 1; % Set the initial state with you and your friend having 25 coins each

P201 = P50^201; % Raise the transition matrix P50 to the power of 201
Ex1Avec = X0 * P201; % Multiply the initial state vector X0 by the raised matrix to obtain X201

% Visualize the state vector as a bar plot
bar(Ex1Avec);
xlabel('State');
ylabel('Probability');
title('State Vector: 201 Rolls');
```

The output will be a bar plot of the state vector after 201 rolls of the dice, representing the probability distribution of the game at that point.

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According to the output analysis, the model presented above is of Discrete-event simulation (DES) type.

What is Discrete-event simulation (DES)?

Discrete-event simulation (DES) is indeed a type of computer-based simulation where events occur at specific points in time. In DES, a system's behavior is modeled by specifying the sequence of events that occur during the system's lifespan.

In a discrete-event simulation, the state of the system changes only when events occur, rather than continuously evolving over time. Events represent significant occurrences or activities within the system, such as customer arrivals, service completions, or resource allocations. Each event is associated with a specific time or occurrence point, and the simulation progresses by processing events in chronological order.

DES is particularly useful for modeling complex systems where the timing of events and their interactions play a crucial role. It allows for capturing the dynamic nature of the system, simulating the flow of entities (such as customers, vehicles, or messages) through the system, and observing the effects of event sequencing and resource allocation on system performance.

By simulating the system and observing the events and their consequences, DES enables analysts to evaluate different scenarios, study the impact of various parameters, and optimize system design or operation. It provides insights into system performance measures, such as throughput, waiting times, resource utilization, or customer satisfaction.

Overall, discrete-event simulation is a powerful technique for modeling and analyzing complex systems with discrete changes, events, and interactions over time.

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The model above is known as a discrete-event simulation model according to the output analysis.

A discrete event simulation is a type of computer-based modeling where a series of discrete events in a system are simulated.

In such models, the system under consideration evolves through a series of discrete events that are instantaneous.

For example, in the retail establishment model, each customer arriving at the store would be considered a separate, discrete event.

The simulation would model the sequence of events that occur between the time the store opens at 9 am and when the last customer leaves before closing time at 5 pm.

The objective of the simulation would be to estimate some measure of the quality of customer service during this time period.

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Answer: c

Step-by-step explanation:

In order to be parallel, the slope must be the same. This means slope is 2

Now one of the point is 5,-1, so do 2x5 + x = -1, so x = -11

meaning b is -11

so the equation should be y=2x-11

a). The distance between A and C is derived to be 42° to the nearest degree.

b). The bearing of the point C with respect to A is equal to 72°

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

Let ∆ABC be the triangle formed with bearings so that:

angle B = 30° + 90° + 15°

angle B = 135°

AB = 20km

BC = 25km

a). The distance between A and C is calculated using the cosine rule as follows:

AC² = 20² + 25² - 2(20)(25)cos135° {cosine rule}

AC² = 1025 + 707.1068

AC = √1732.1068 {take square root of both sides}

AC = 41.6186 approximately 42°

b). The bearing of the point C with respect to A is the angle from the north of A to the line AC, so;

bearing of the point C with respect to A = 30° + 42° = 72°

Therefore, the distance between A and C is derived to be 42° to the nearest degree and the bearing of the point C with respect to A is equal to 72°

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The sunfish adds around 2% to its present mass each day, which is the daily percent change in mass.

Based on the provided model, the daily percent change in the mass of the ocean sunfish is an addition of around 2% to its mass. By calculating the derivative of the function M(t) with respect to t, the following may be calculated:

\(M'(t) = \frac{ln(1.35)}6 * (1.35)^t\)

This indicates that the constant factor is ln(1.35)/6, or around 0.02, and therefore the rate of change of the sunfish's mass with respect to time is proportionate to the sunfish's present mass.

As a result, the sunfish's daily percent change in mass is around a 2% increase over its present mass.

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Answer:

J=12 + 19 ; 31 + 19 =50

Step-by-step explanation:

50-12 =38

38÷2 =19

therefore 19+12 = 31yrs is Jodarns age

Anna is 19yrs

Answer:

This is my best explanation

Step-by-step explanation:

3y-y=2y

2y+4y=6y

Now you need to divide 12 by 6 to get the value of y

That will be 12/6=2

So, y=2

Have a nice day.

Answer:

Step-by-step explanation:

12 = 3y - y + 4y

combine ys

3- 1 = 2

12 = 2y +4y

12 = 6y

divide,

12/6

y=2

Inferences can be made for these types of plants, and the conclusion can be drawn that the fertilizer will help these types of plants grow taller.

A scientific experiment known as a randomised controlled trial (RCT) includes randomly allocating participants or subjects to various groups, often a treatment group and a control group. The intervention or therapy under test is administered to the treatment group while being withheld from the control group. Researchers can isolate the impact of the intervention on the desired outcome and reduce the impacts of confounding variables by randomly allocating individuals to these groups. To evaluate the effectiveness of therapies and treatments, RCTs are often employed in the medical, psychological, and other domains.

In the given experiment, the fertiliser appeared to be helpful in boosting plant development for this specific type of seedling since the plants that got it grew noticeably taller than the ones that did not.

Hence, option 4 is correct.

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Answer:

32

Step-by-step explanation:

12 * (3 + 2²) / 2 - 10

12(3 + 4) / 2 - 10

12(7) / 2 - 10

84 / 2 - 10

42 - 10

32

Best of Luck!

Answer:

Step-by-step explanation:

\(12\times (3+2^2)\div 2-10\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Calculate\:within\:parentheses}\:\left(3+2^2\right)\:\\:\quad 7\\\\=12\times \:7\div \:2-10\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:12\times \:7\div \:2\:\\:\quad 42\\\\=42-10\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:42-10\:\\:\quad 32\)

Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

<95141404393>

The product of 3x(x^2+ 4) is 3x^3 + 12x.

To find the product of 3x(x^2+ 4), we distribute 3x to both terms inside the parentheses:

3x * x^2 = 3x^3

3x * 4 = 12x

Combining these terms, we get 3x^3 + 12x as the final product.

In the expression 3x(x^2+ 4), we multiply the coefficient 3x by each term inside the parentheses. This is known as the distributive property of multiplication. By multiplying 3x with x^2, we get 3x^3. Similarly, multiplying 3x with 4 gives us 12x.

So the correct answer is 3x^3 + 12x.

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Answer:

a) To determine the common difference of the sequence, subtract the 17th term (-10) from the 8th term (17) to get a common difference of 27.

b) To find the first term, subtract the common difference (27) from the 8th term (17) a total of 7 times to get the first term of -144.

17th term (-10)

- (common difference of 27)

- -144

c) To find the 77th term, take the first term (-144) and add the common difference (27) a total of 76 times to get the 77th term of 1062.

-144

+ (common difference of 27)

+ 1062

2. To find the number of multiples of 7 between 250 and 340, begin by finding the greatest multiple of 7 which is less than 250. This would be the multiple of 7 with the value of 245. Next, Find the least multiple of 7 between 250 and 340. This would be the multiple of 7 with the value of 336. Finally, to get the number of multiples of 7 between 250 and 340, subtract 245 from 336 and then add 1 to get the answer.

336 - 245 + 1 = 92

Step-by-step explanation:

The null hypothesis would not be rejected and the researcher would fail to find statistical significance at the chosen alpha level of .05.

If a researcher sets the alpha level at .05 and obtains a p-value of .06, it means that the p-value is greater than the chosen significance level. The alpha level, also known as the significance level, represents the threshold for determining whether the results are statistically significant or not.

In hypothesis testing, the null hypothesis assumes that there is no significant difference or relationship between variables.

If the p-value is less than or equal to the alpha level, it suggests that there is enough evidence to reject the null hypothesis and conclude that there is a significant difference or relationship.

However, if the p-value is greater than the alpha level, as in this case with a p-value of .06, it means that the observed data does not provide sufficient evidence to reject the null hypothesis.

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To find the radius of the spinner, we'll first find the total area of the spinner and then use the formula for the area of a circle. Radius is defined as the length between the center and the arc of circle.

Here are the steps:
1. Determine the proportion of the sectors that do not move the token: There are 3 such sectors (remaining sectors) out of a total of 9 sectors. So, the proportion is 3/9 = 1/3.

2. Calculate the total area of the spinner: Since 1/3 of the spinner has an area of 14.6 square inches, we can find the total area by multiplying the area of non-moving sectors by 3.
Total area = 14.6 * 3 = 43.8 square inches.

3. Use the formula for the area of a circle to find the radius: The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. We'll solve for the radius (r) in this formula:
43.8 = πr^2

4. Divide both sides of the equation by π:
r^2 = 43.8 / π

5. Calculate r:
r = √(43.8 / π)

6. Round the result to the nearest tenth of an inch:
r ≈ 3.7 inches

So, the radius of the spinner is approximately 3.7 inches.

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The correct option is (a) connectors. The elements that give data on the network a way to move between nodes. This covers network media, connectors, and network interface cards (NIC).

A message is a piece of data sent over the internet, but before a message is sent, it is divided up into smaller pieces called packets. Using Transport Control Protocol (TCP) and Internet Protocol (IP), these messages and packets move between sources (TCP).

The cables (coaxial, twisted pair, fiber optic, and telephone lines) connecting the various network hardware components, the network adapters used by computers connected to the network (hosts), and any concentrators, repeaters, routers, or bridges employed in the network make up the physical network. The term "physical connection" refers to the total number of trunk lines, complete circuits, and connections—including those made by wire, optics, radio signal, or other means—necessary to provide reasonably adequate telecommunications service among telecommunications providers.

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Answer:10

Step-by-step explanation:

Divide 12.75 by 1.25

you get 10.2

She can cut 10 strings but has 0.2 string leftover

Angles p and q are complementary, which means that their sum is equal to 90 degrees. Let's assume the size of angle q is x degrees. Since p is four times the size of q, we can write the equation p = 4q.

To find the size of q, we need to substitute the value of p in terms of q into the equation for the sum of the angles: p + q = 90.

Substituting 4q for p, we get:

4q + q = 90

Combining like terms:

5q = 90

To solve for q, we divide both sides of the equation by 5:

q = 90/5

Simplifying:

q = 18

Therefore, the size of angle q is 18 degrees.

when angles p and q are complementary and p is four times the size of q, the size of angle q is 18 degrees.

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