In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game

Answer

To find the slope of a line parallel

1. Calculate the line slope

The slope m = ( y2 - y1 ) / ( x2 - x1 )

You can select two different point

For example,

(x1 , y1 ) = (-4, 0)

(x2, y2 ) = (0, 6)

_______________________________

So then, the slope,

m = ( y2 - y1 ) / ( x2 - x1 )

Replacing with the two points chosen

m = ( 6 - 0) / ( 0 - (-4) )

m=6/4

m= 3/2

___________

The parallel lines have the same slope.

_____________

The slope of a line parallel to the given line is 3/2

Answer:

Answer:

  6.  (a)  -9 < x ≤ 2

  7.  (c)  All real numbers

Step-by-step explanation:

You want the domains of the two function graphs.

The domain of a function is the set of x-values for which it is defined. It is the horizontal extent of the graph.

The line segment graph has an open circle at x = -9. This is sufficient to tell you the correct answer choice is ...

  -9 < x ≤ 2

The arrows on the ends of the curve tell you the curve extends horizontally to -∞ and to +∞. The curve is defined on a domain of ...

  All real numbers

__

Additional comment

The right end of the segment in problem 6 has a solid dot at x=2. This tells you that x=2 is right end point of the domain. This, too, is sufficient to tell you that the first answer choice is the correct one.

Answer:

B, C, E

Step-by-step explanation:

The solution of the inequality is x ≤ -7

The graph would have a closed circle because it's less than or equal to

-7 is a part of the solution because it's less than or equal to -7

Answer:

Step-by-step explanation:

Subtract 22 from both sides to get \(x\leq -7\). So the 2nd one is correct

The sign is less than or equal to, so the graph does indeed have a closed circle. So the 3rd one is also correct

The answer is x is less than or EQUAL to -7, so -7 is included in the asnwer. So the 5th one is also correct

Answer:

Is there a question?

Step-by-step explanation:

If it is, by the way I look at it, To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

The centre height of Sam's tent to the nearest tenth = 7.8 feet.

The length of both sides of the tent (a) = 5ft

The base of the tent is (b)= 6ft

The centre height (c) = ?

Using the Pythagorean theorem

c² = a² + b²

c² = 5² + 6²

c² = 100 + 36

c² = √136

c² = 7.8 feet

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The outward flux of the vector field F across the boundary of the region D, which is the cube bounded by the planes x = ±1, y = ±1, and ±1, can be found using the divergence theorem.

The outward flux is the integral of the divergence of F over the volume enclosed by the boundary surface.The first step is to calculate the divergence of F. The divergence of a vector field F = P i + Q j + R k is given by div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z. In this case, div(F) = ∂/∂x(5y - 4x) + ∂/∂y(-4z - 5y) + ∂/∂z(-3y - 2x). Simplifying these partial derivatives, we have div(F) = -4 - 2 - 3 = -9.

Applying the divergence theorem, we can relate the flux of F across the boundary surface to the triple integral of the divergence of F over the volume enclosed by the surface. Since D is a cube with sides of length 2, the volume enclosed by the surface is 2^3 = 8.

Therefore, the outward flux of F across the boundary of D is given by ∬S F · dS = ∭V div(F) dV = -9 * 8 = -72. The negative sign indicates that the flux is inward.

In summary, the outward flux of the vector field F across the boundary of the cube D, as described by the given vector components, is -72. This means that the vector field is predominantly flowing inward through the boundary of the cube.

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Answer:

2 looks good  I & IV

Step-by-step explanation:

Answer:

m= -1/26

Step-by-step explanation:

plug into the formula and solve

The solution to the inequality in this problem is given as follows:

d. x > 2.

The graphical solution to the inequality is given by the image shown at the end of the answer.

The inequality for this problem is defined as follows:

5 - x < 2(x - 3) + 5.

Applying the distributive property, we have that:

5 - x < 2x - 6 + 5

5 - x < 2x - 1.

Hence the solution set is composed by the region in which the line 2x - 1 is greater than the line 5 - x.

The numerical solution set is obtained as follows:

5 - x < 2x - 1.

-3x < -6

3x > 6. (the leading coefficient is negative, hence the multiplication by -1 also changes the sign).

x > 6/3

x > 2.

Meaning that option d is correct.

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Answer:

85

Step-by-step explanation:

The interior angles of any triangle always add up to 180. You have a 75 degree angle and a 20 degree angle, so you will subtract those from 180 to find the missing angle, which is 85 degrees.

Answer:

x = 7

Step-by-step explanation:

Let the number added to the numerator is x.

ATQ,

\(\dfrac{3+x}{7+2x}=\dfrac{10}{21}\)

Cross multiplying each side,

\(\dfrac{3+x}{7+2x}=\dfrac{10}{21}\\\\63+21x=70+20x\\\\21x-20x=70-63\\\\x=7\)

Hence, the person that is added is 7.

Answer:

2 and 8

Step-by-step explanation:

Well. Boy A gets 1 orange, so the other must get 4. So say boy A gets 2 oranges now, so the other must get also double the amount of oranges, which is 8.

1:4

If you changed the 1 to a 2, you have x2 (you can only x or ÷, in ratio) on the other side. Whatever you do to this side, you do to the other side. So it becomes

2:8

Add the numbers together to find the total number of parts. You get 10 in this ratio, so it must be the answer.

Answer:3 or 3/10

Step-by-step explanation:

The radical expressions when evaluated are √15/3x, [4√(3b) + 4b]/[3 - b²] and √(3a)/2a

From the question, we have the following parameters that can be used in our computation:

√5 ÷ √3x²

So, we have

√5 ÷ x√3

Rationalize

√5/x√3 * √3/√3

Evaluate

√15/3x

Next, we have

4√b ÷ (√3 - b)

Rationalize

4√b/(√3 - b) * (√3 + b)/ (√3 + b)

So, we have

[4√(3b) + 4b]/[3 - b²]

Next, we have

[3√(a²)/√3 ÷ 2a³⁺²]

So, we have

[a√3 ÷ 2a³⁺²]

This gives

[a√3 ÷ 2a√a]

Rationalize

[a√3 ÷ 2a√a] * [√a ÷ √a]

So, we have

[a√3a ÷ 2a²]

Divide

√(3a)/2a

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Answer: 4/3 ft long, or  1  1/3ft

Step-by-step explanation:

Answer:

£160

Step-by-step explanation:

Ammount he receives per year times 4.

800 x 0.05 x 4

= £160

The values of the variables in the parallelogram are x = 26 and y = 11. Option C

It is important to note the properties of a parallelogram;

From the information shown in the diagram, we have that;

x - 2 and 24 are opposite sides

y and 11 are opposite sides

Then, we can say that;

y = 11

x - 2 = 24

collect the like terms

x = 24 + 2

add then values

x = 26

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A ratio is the number of one item compared to the number of another item. It can be written as a fraction or with a colon between the numbers.

The question wants the ratio of red to blue, so the number for red would be first.

They have 64 red and 31 blue

The ratio would be 64/31

64 and 31 do not have any common multipliers so cannot be simplified.

The answer would be 64/31

Answer:

64/31

Step-by-step explanation:

I just know

The probability of  4 in the tens place is \(\frac{1}{9}\), the probability of  at least one 4 in the tens place or the units place is \(\frac{1}{5}\), the probability no 4 in either place is \(\frac{4}{5}\).

(a) total number of 2-digit terms =(99 - 10) + 1 = 90

n(s) = 90

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

number of 2 digits that have 4 in tens place = 40, 41, 42 ......49

n(a) = 10

P(A) =\(\frac{ n(a)}{n(s)}\)

Substituting the values

P(A) = \(\frac{10}{90}\)

P(A) = \(\frac{1}{9}\)

Therefore, P(A) = \(\frac{1}{9}\)

(b) From the previous one, we know the P(A) = \(\frac{1}{9}\)

Number of 4's in units place = 14, 24, 34.....94 = 9

n(b) = 9

P(B) = \(\frac{ n(b)}{n(s)}\)

Substituting the values

P(B) = \(\frac{9}{90}\)

P(B) =\(\frac{1}{10}\)

P(A and B) = \(\frac{1}{10}\)

Using OR probability, we have

P(A or B) = P(A) + P(B) - P(A and B)

P(\(\frac{1}{9}\) or \(\frac{1}{10}\)) = \(\frac{1}{9}\) + \(\frac{1}{10}\) - \(\frac{1}{90}\)

P(\(\frac{1}{9}\)or \(\frac{1}{10}\)) = \(\frac{1}{5}\)

Therefore, P(\(\frac{1}{9}\)or \(\frac{1}{10}\)) = \(\frac{1}{5}\)

(c) Probability of no 4 in either place = 1 - ( probability of 4 in either place)

= 1 - \(\frac{1}{5}\) = \(\frac{4}{5}\)

Therefore, probability of no 4 in either place = \(\frac{4}{5}\)

Therefore, the probability that the integer chosen has a 4 in the tens place is \(\frac{1}{9}\), P(\(\frac{1}{9}\) or \(\frac{1}{10}\)) = \(\frac{1}{5}\), and probability of no 4 in either place = \(\frac{4}{5}\).

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We can prove that the statement is true using the definition of Θ.

The given function is: f(n) = (2n + 2n + log2 n)2

Using the definition of Θ, we need to prove or disprove the following statement:

f(n) is Θ(n2).

Now, we need to find positive constants c1, c2, and n0 such that: c1n2 ≤ f(n) ≤ c2n2 for all n ≥ n0.Let's simplify the given function:

f(n) = (2n + 2n + log2 n)2

     = (4n + log2 n)2

     = 16n2 + 8n log2 n + (log2 n)2

Here, we can observe that the highest degree term in the polynomial expression is 16n2.

Therefore, we can set c2 = 16.

Let's consider the lower bound:

16n2 ≤ f(n)≤ 16n2 + 8n log2 n + (log2 n)2≤ 16n2 + 8n2 + n2= 25n2

Now, we can set c1 = 1/25.

Let's check if the conditions hold for n0 = 1.

For n ≥ 1:16n2 ≤ 16n2 + 8n log2 n + (log2 n)2 ≤ 25n2

⇒ c1n2 ≤ f(n) ≤ c2n2

Therefore, f(n) = (2n + 2n + log2 n)2 is Θ(n2).

Hence, we can prove that the statement is true using the definition of Θ.

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Answer:

2

Step-by-step explanation:

(0, 2) & (3, 8)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(8 - 2) / (3 - 0)

Simplify the parentheses.

= (6) / (3)

Simplify the fraction.

6/3

= 2

This is your slope.

The measure of angle ADC, based on the definition of similar triangles is determined as: 80 degrees.

Two triangles are similar to each other if their corresponding pairs of angles have angle measure that are equal or congruent to each other.

In the image shown above, side ED and side CB are parallel to each other, thus, this means that angle ADE and angle ABC are corresponding angles. Since corresponding angles are equal to each other, therefore, measure of angle ADC and measure of angle ABC are equal.

Thus, we have:

m<ADC = 80 degrees.

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(a) The expected number of board-feet of timber next year is 102.9. (b) The interest rate at the bank matters in deciding to cut the trees down now or in the future due to the opportunity cost of waiting and potential earnings from investing the proceeds. (c) In order for cutting the trees down next year to be a better choice than cutting them down now, the interest rate at the bank has to be lower.

(a) To calculate the expected number of board-feet of timber next year, we multiply the probabilities of each outcome by the corresponding timber quantity and sum them. With a 98% probability of growth and a 5% increase in timber, and a 2% probability of fire and no timber, the expected number of board-feet of timber next year would be: (0.98 * 100 * 1.05) + (0.02 * 0) = 102.9 board-feet.

(b) The interest rate at the bank matters in deciding to cut the trees down now or in the future because it represents the opportunity cost of waiting. By cutting the trees down now and selling the timber, you can invest the proceeds in the bank and earn interest over time. If the interest rate is high, the present value of the future timber may be lower compared to the immediate cash flow from selling the timber now, making it more favorable to cut the trees down earlier.

(c) In order for cutting the trees down next year to be a better choice than cutting them down now, the interest rate at the bank has to be lower. A lower interest rate implies that the present value of future cash flows (from selling the timber next year) is higher relative to the immediate cash flow (from selling the timber now). Therefore, a lower interest rate makes it more advantageous to delay cutting the trees and wait for them to grow, maximizing the forester's profit.

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To find the new price of the picture frame, we need to use the information that the shop increases all their prices by 9% and the fact that the picture frame increased by £621.

We can start by using the following formula:

New Price = Original Price + (Original Price x Percentage Increase)

Let's let the original price of the picture frame be P. We know that the percentage increase is 9%, which can be written as 0.09 in decimal form. We also know that the picture frame increased by £621, so we can set up the equation:

P + (P x 0.09) = P + £621

Now we can solve for P:

P + 0.09P = P + £621

0.09P = £621

P = £621 ÷ 0.09

P = £6,900

Therefore, the new price of the picture frame is £6,900.

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From the given data, we say a definite integral is improper if one endpoint is infinite, or if the integrand is infinite.

One endpoint is infinite, or if the integrand is infinite, the definite integral cannot be evaluated using the usual techniques. Instead, we must use the concept of a limit to find the value of the integral, if it exists. In the case where one endpoint is infinite, we take a limit as a variable approaches infinity. In the case where the integrand is infinite, we may need to split the integral into pieces or use some other method to deal with the singularity.

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Answer:

x/2 + 7 = -4

Step-by-step explanation:

7 more just means plus 7

a quotient of a number and blank basically is 'a number' (usually x) over a the number given if that makes sense. so in our scenario its x/2

'is' basically means is equal to

put it all together and you get x/2 + 7 = -4

hope this helps <3

This question is about understanding and applying the Mean Value Theorem in calculus to numerous contexts. According to the Mean Value Theorem, for a differentiable function on an interval, there exists a point in that interval where the slope of the tangent line equals the average slope of the secant line. The question gives many claims about the function and asks whether or not they can be deduced from the Mean Value Theorem.

The Mean Value Theorem states that if a function f is differentiable on the interval (-♾,♾), then there exists at least one value c in the interval such that f'(c) = (f(b)-f(a))/(b-a), where a and b are any two values in the interval. From this, the following statements are true:

(a) If f(3) = f(7), then f'(x)= 0 for some c in (3, 7)

- True. If f(3) = f(7), then (f(7)-f(3))/(7-3) = 0. Therefore, there exists some value c in the interval (3,7) such that f'(c) = 0.

(b) If f(3) < f(7), then f’(x) > 0 for some c in (3, 7).

- True. If f(3) < f(7), then (f(7)-f(3))/(7-3) > 0. Therefore, there exists some value c in the interval (3,7) such that f'(c) > 0.

(c) If f has a tangent line of slope 0, then f has a secant line of slope 0.

- False. The slope of the secant line may or may not be equal to the slope of the tangent line.

(d) If f'(x) > 0 for every x, then every secant line has positive slope.

- True. If the derivative of a function is greater than 0 for all x, then the secant line will have a positive slope.

(e) If every secant line has a positive slope, then f'(x) > 0 for all x.

- False. The derivative may be greater or less than 0 for any given x.

(f) If f'(x) < 0 for every x, then f has no global minimum. - True. If the derivative of a function is less than 0 for all x, then the function will not have a global minimum.

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