What is the equation of the line passing through the points (4,8) and (-1,-12)

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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It is important in the definition of logarithm that the base of the logarithm does not equal 1 because log base 1 is undefined and leads to mathematical inconsistencies.

The logarithm of a number is defined as the exponent to which a specific base must be raised to obtain that number. However, when the base of the logarithm is equal to 1, the definition becomes problematic.

If the base of the logarithm is 1, we have log₁(x) = y, where 1^y = x. Since any number raised to the power of 0 equals 1, we would have 1^0 = x, which implies that x equals 1 for all values of x. This creates a contradiction, as it would suggest that all numbers are equal to 1, which is not true.

To avoid this inconsistency, the definition of logarithms excludes the base 1. By excluding 1 as a possible base, logarithmic functions maintain their essential properties, such as the logarithmic identities and the relationship between exponentiation and logarithms.

Therefore, the restriction that the base of the logarithm cannot equal 1 is necessary to ensure mathematical consistency and clarity in the definition of logarithmic functions. It helps prevent mathematical contradictions and allows logarithms to be defined in a meaningful and consistent manner.

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Answer:

f(x)=320(1.16)^x

Step-by-step explanation:

This is an exponential equation with an initial population at x=0 of 320 (because 1.16^0=1, and 320*1=320) After the first year, there are 371 bunnies. After two years, there are 431, etc etc.

Answer:

f(x)=320(1.16)^x

This is an exponential equation with an initial population at x=0 of 320 (because 1.16^0=1, and 320*1=320) After the first year, there are 371 bunnies. After two years, there are 431, etc etc.

Answer:

x=20

Step-by-step explanation:

There are (n + 2ⁿ- 1) * 2ⁿ different ways to select talks for inclusion in the book, given that at least one talk is selected.

We know that at least one talk must be selected, so we have two cases to consider: either one or more than one talk is selected.

Case 1: If only one talk is selected, then there are n possible talks to choose from since any participant could have given the selected talk.

Case 2: If more than one talk is selected, then we need to consider the number of talks that could have been selected. There are a total of 2ⁿ - 1 possible non-empty subsets of talks that could have been selected. However, we need to subtract 1 from this number to exclude the case where no talks are selected.

So the total number of ways to select talks for the book is n + 2ⁿ - 2.

Now we need to consider the number of ways to assign talks on Saturday and Sunday. There are 2ⁿ possible ways to assign talks since each participant can give their talk on Saturday or Sunday.

(n + 2ⁿ - 2) * 2ⁿ

However, we need to subtract the case where no talks are selected and included in the book, which is simply 2^n since each talk can be assigned to either Saturday or Sunday. So the final answer is:

(n + 2ⁿ - 2) * 2ⁿ - 2ⁿ = (n + 2ⁿ - 1) * 2ⁿ.

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Answer:

Proved

Step-by-step explanation:

See attachment for the given parameters.

Required

Prove that  turkey sandwiches and 9-grain wheat are  independent events

From the attachment, we have:

\(P(T) = 23.6\%\)

\(P(W) = 51.7\%\)

The intersection between both is:

\(W\ and\ T = 36\)

So:

\(P(W\ and\ T) = \frac{36}{300}\)

\(P(W\ and\ T) = 0.12\)

\(P(W\ and\ T) = 12\%\)

For both events to be independent, the following must be true.

\(P(W\ and\ T) = P(W) * P(T)\)

\(P(W\ and\ T) = 23.6\% * 51.7\%\)

\(P(W\ and\ T) = 12.2\%\)

The calculated values of P(W and T) are estimates

\(12.2\% \approx 12\%\)

Hence, both events are independent

Answer:

d = 3

Step-by-step explanation:

2d + 1 = 7

7 -1

2d = 6

2 divided by 2(cancels out), 6 divided by 2 is 3.

d = 3

The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

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Note that the rational numbers represented on points- P, Q, R, and S are given as follows:  7/3, 8/3, -4/3, -5/3 respectively. See the explanation below.

A rational number is defined in mathematics as the proportion or fraction p/q of two integers, a numerator p, and a non-zero denominator q. 3/7, for example, is a rational number, as is every integer.

For the solution above:
Each section in between two numbers is broken into three sections.

Thus, we have a = (6/3), P = (7/3), Q = (8/3) and B = (9/3)

In the same way,

T = = -3/3,

R = -4/3

S = -5/3 and

U = -6/3

Therefore, the rational numbers represented - P, Q, R, and S are given as follows:  7/3, 8/3, -4/3, -5/3.

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Answer:

A. and B. are true.

Step-by-step explanation:

For a, -4 + 3(-5) = -19, and 18 is obviously greater.

For b, -7 - 2(-5) = 3, and 3 is greater than 1.

the solution w = -36 is correct

The given equation is w/4 + 16 = 7.The main objective here is to solve for the variable w. Let us see the step-by-step process to solve for w:

Step 1: Simplify the left side of the equation by subtracting 16 from both sides. w/4 + 16 = 7 ⇒ w/4 = -9The justification for subtracting 16 from both sides is the additive inverse property of equality, which states that if a = b, then a - c = b - c for any real number c.

Step 2: Multiply both sides of the equation by 4 to isolate w. w/4 = -9 ⇒ (4)(w/4) = (4)(-9) ⇒ w = -36The justification for multiplying both sides of the equation by 4 is the multiplication property of equality, which states that if a = b, then ac = bc for any real number c.

Step 3: Check the solution. Substitute -36 for w in the original equation to make sure it satisfies the equation. w/4 + 16 = 7 ⇒ (-36)/4 + 16 = 7 ⇒ -9 + 16 = 7 ⇒ 7 = 7Since 7 = 7 is a true statement, . The justification for this step is that it ensures that the solution obtained in the previous step is valid.

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Answer:

To find the number of feet the pipe was lifted, divide the total work (72 foot-pounds) by the weight of the pipe (24 pounds). This gives you 3 feet, which is the answer to your question.

Answer:

Step-by-step explanation:

A line segment forms when it has two end points

Answer:

Two

Step-by-step explanation:

A segment has two endpoints, since it is not connected to anything. Hopefully this image can help you understand the types of lines there are in mathematics.

Hope this helped.

A parallelogram with vertices O, A, B, and C can be represented as O + a = B, and O + b = A.

a) MT is the midpoint of BT, which can be represented as (O + b + B)/2 = (O + B)/2 + (b/2). Therefore, MT = (b/2).

b) TN is the midpoint of AT, which can be represented as (O + A)/2 + (a/2). Therefore, TN = (a/2).

c) MN can be represented as B - A = a - b. Therefore, MN = a - b.

d) P is the midpoint of MN, which we already found to be a - b. Therefore, the position vector of P is (a - b)/2.

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The probability that the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35% is approximately 82.38%.

Assuming the sample of 30 Americans is representative of the population, we can calculate the sample proportion as the number of individuals in the sample who agree divided by the total sample size. Let's assume that the sample proportion is p'.

To calculate the probability of the proportion exceeding 35%, we need to find the z-score of the value 0.35 using the formula:

z = (p' - p) / √[p * (1 - p) / n]

where p is the population proportion (which we don't know), and n is the sample size (30 in this case). We can use p' as an estimate of p.

Once we find the z-score, we can use a standard normal distribution table or a calculator to find the probability that the z-score is greater than the value we calculated. This probability is the probability that the proportion of Americans who agree that climate change is an immediate threat to humanity exceeds 35%.

For example, if p' = 0.4, then the z-score is:

z = (0.4 - 0.35) /√ [0.35 * (1 - 0.35) / 30] = 1.03

Using a standard normal distribution table, we can find that the probability of a z-score being greater than 1.03 is approximately 0.8238, or about 82.38%.

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Answer:

parallelogram is the answer

Answer:

Step-by-step explanation:

The quadrilateral is a parallelogram ( more precisely is the rhombus )

e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

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Answer:

3654.7

Step-by-step explanation:

isbssnsbscTag c z agajama

Answer:

if rounding to the nearest 10 :

3650

if rounding to the nearest tenths :

3654.7

Answer:

8x-8

Step-by-step explanation:

10x-2x=8x

-3-5=-8

Answer:

11ft

Step-by-step explanation:

The equation for circumference is 2pi x radius

2 x pi x radius = 22 pi

2 x 22/7 x radius = 22 pi

44/7 x radius = 22 pi

radius = 22 pi x 7/44

radius = 11ft

The total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

To find the total amount of money earned by Nora over 21 years, we need to calculate the salary for each year and then sum them up.

In the first year, Nora's salary is $40,000.

In the second year, her salary will be increased by 3%, so it will be:

$40,000 + 3% of $40,000 = $40,000 + $1,200 = $41,200.

In the third year, her salary will again increase by 3%, so it will be:

$41,200 + 3% of $41,200 = $41,200 + $1,236 = $42,436.

We can continue this process for each year, adding 3% of the previous year's salary to calculate the next year's salary.

To calculate the total amount of money earned over the 21 years, we need to sum up the salaries for each year. Here's the calculation:

Total = $40,000 + $41,200 + $42,436 + ... (21 terms)

To simplify the calculation, we can use the formula for the sum of an arithmetic series:

Total = (n/2) * (2a + (n - 1)d)

where:

n = number of terms (21 in this case)

a = first term ($40,000)

d = common difference (3% of the previous year's salary)

Plugging in the values:

Total = (21/2) * [2(40,000) + (21 - 1)(0.03)(40,000)]

Simplifying further:

Total = (21/2) * [80,000 + 20(0.03)(40,000)]

= (21/2) * [80,000 + 2,400(40,000)]

= (21/2) * [80,000 + 96,000]

= (21/2) * 176,000

= 21 * 88,000

= 1,848,000

Therefore, the total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

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To find the inverse of a Laplace transform, one typically uses partial fraction decomposition and partial fraction expansion. Partial fraction decomposition involves breaking down a Laplace transformed function into simpler terms, each with a corresponding inverse Laplace transform. Partial fraction expansion involves using known formulas to find the inverse Laplace transform of these simpler terms.

The "inverse of a Laplace transform" is a mathematical operation that transforms a Laplace transformed function back into its original time domain form. It is a useful tool for solving linear differential equations, as well as for analyzing signals and systems.

The process of finding the inverse of a Laplace transform can also involve using convolution theorem, which states that the inverse Laplace transform of the product of two Laplace transformed functions is equal to the convolution of their respective inverse Laplace transforms. This theorem can be useful for solving systems of differential equations and for understanding the response of linear systems to different inputs.

It's also important to note that not all Laplace transformed functions have an inverse Laplace transform, as some functions may have poles in the right half of the complex plane, meaning they do not converge. In such cases, the inverse of a Laplace transform cannot be found using these methods.

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After 4 more minutes, the reading on the thermometer will be 9°C. It will take approximately 10 minutes for the thermometer to read -4°C after being taken outdoors.

The thermometer initially dropped from 19°C to 13°C in 1 minute when taken outdoors. This indicates a temperature decrease of 6°C in 1 minute. Therefore, after 4 more minutes, the thermometer would experience a further decrease of 6°C per minute for a total of 24°C (6°C × 4 minutes). Subtracting this from the initial reading of 13°C, we get 13°C - 24°C = -11°C. However, since the lowest temperature outdoors is -5°C, the reading will stabilize at -5°C after 4 more minutes.

(b) To determine when the thermometer will read -4°C, we can calculate the time it takes for the temperature to decrease by 9°C (-5°C - (-4°C) = -1°C) from the initial reading of 13°C. Since the temperature decreases by 6°C per minute, it will take approximately 9/6 = 1.5 minutes to reach -4°C from 13°C. Therefore, the thermometer will read -4°C approximately 1.5 minutes after being taken outdoors.

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x = # of minutes

$6 + $0.08x = $20.64. Subtract 6 from both sides

$0.08x = $14.64. Divide each side by $0.08

x = 183

Goran was billed for 183 minutes

Answer:

c ≤ 6

Step-by-step explanation:

Lets make our equation!

2.5 per chore thats our slope

+3 she starts with 3 dollars

y = 2.50x +3

Substitute y for 17!

17 = 2.5x +3

Subtract 3!

14 = 2.5x

Divide both sides by 2.5!

x = 5.6

5.6 --> 6

x = 6

Turn it into an inequality!

c ≤ 6

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The equation of the ellipse with focus at (-2,0) and vertices at (±7, 0) is given as follows:

x²/49 + y²/45 = 1.

The equation of an ellipse of center (h,k) is given by the equation presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

The center of the ellipse is given by the mean of the coordinates of the vertices, as follows:

Hence:

x²/a² + y²/b² = 1.

The vertices are at x + a and x - a, hence the parameter a is given as follows:

a = 7.

Considering the focus at (-2,0), the parameter c is given as follows:

c = -2.

We need the parameter c to obtain parameter b as follows:

c² = a² - b²

b² = a² - c²

b² = 49 - 4

b² = 45.

Hence the equation is given as follows:

x²/49 + y²/45 = 1.

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Answer:

C

Step-by-step explanation:

2 * 3 is 6

4 * 3 is 12

8 * 3 is 24

Answer:

C

Step-by-step explanation:

2,6 4,12 and 8,24 are all simplified to the fraction 1/3 so the relationship is proportional.

Also in each of the x column every number is always three times the amount.

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Answer:

12

Step-by-step explanation:

12 - 4 = 8

The square of 8 is 64

Answer:

6

Step-by-step explanation:

(n + 4)^2 = n^2 + 64

n^2 + 8n + 16 = n^2 + 64

8n = 48

n = 6