Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

(a) 2/3
(b) 3/2
(c) 25/36
(d) 12/13​

Step-by-step explanation:

3x - 2x² = 7

2x² - 3x + 7 = 0

or

f(x) = 2x² - 3x + 7

a = 2

b = -3

c = 7

5 - 2x² = 6x

2x² + 6x - 5 = 0

or

f(x) = 2x² + 6x - 5

a = 2

b = 6

c = -5

(x+3)(x+4) = x² + 4x + 3x + 12 = x² + 7x + 12 = 0

f(x) = x² + 7x + 12

a = 1

b = 7

c = 12

(2x + 7)(x - 1) = 2x² - 2x + 7x - 7 = 2x² + 5x - 7 = 0

f(x) = 2x² + 5x - 7

a = 2

b = 5

c = -7

2x(x - 3) = 15

2x² - 6x = 15

2x² - 6x - 15 = 0

or

f(x) = 2x² - 6x - 15

a = 2

b = -6

c = -15

Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope.

To ascertain whether a table of values is a linear function, follow these steps:

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Answer:

8) 2.5 meters

9) 56 fluid ounces

Step-by-step explanation:

You need to know all the conversion factors.

Answer:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. Since the line given in the question is parallel to y = 1/4x + 7, we know that the line has a slope of m = 1/4.

To find the equation of the line that passes through (4,-1), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).

Therefore, the equation of the line passing through (4,-1) and parallel to y = 1/4x + 7 is:

y - (-1) = 1/4(x - 4)

y + 1 = 1/4x + 1

This is the equation of a line passing through (4,-1) and parallel to y = 1/4x + 7.

Answer:

in math volume is the amount of space in a certain 3D object.

Step-by-step explanation:

For instance, a fish tank has 3 feet in length, 1 foot in width and two feet in height. To find the volume, you multiply length times width times height, which is 3x1x2, which equals six.

Answer:

neither an Euler path or Euler circuit

So, it takes Hillary and Bill approximately 4.35 hours to complete 1 puzzle together and the speed of the boat in still water is approximately 12 mph.

a. Let's call the time it takes for Hillary and Bill to complete the puzzle together "t." We know that in 5 hours, Hillary can do 1 puzzle, so her rate is 1/5 puzzles per hour. Bill can do 1 puzzle in 7 hours, so his rate is 1/7 puzzles per hour. When they work together, their combined rate is (1/5 + 1/7) puzzles per hour. To find the time it takes them to complete 1 puzzle together, we set up an equation: t = 1 / (1/5 + 1/7). Solving for t, we find that it takes them approximately 4.35 hours to complete 1 puzzle together.

b. Let's call the speed of the boat in still water "s." When the boat is going against the current, its speed is s - 3 mph, and when it is going with the current, its speed is s + 3 mph. We know that it takes the same amount of time for the boat to go 10 miles against the current and 15 miles with the current, so we can set up an equation: 10 / (s - 3) = 15 / (s + 3). Solving for s, we find that the speed of the boat in still water is approximately 12 mph.

Therefore, it takes Hillary and Bill approximately 4.35 hours to complete 1 puzzle together and the speed of the boat in still water is approximately 12 mph.

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it is seen that if the number of people in the group is n = 23, the probability that at least two people will have the same birthday is at least 1/2.

Let P(A) be the probability that in a randomly selected group of n people, at least two people have the same birthday.

If we assume that the year has 365 days, then the number of ways to select n people with different birthdays is n x (n-1) x (n-2) x ... x (n-364).

the probability of selecting n people with different birthdays is P(A') = n(n - 1)(n - 2)...(n - 364)/365nThen, the probability that at least two people in a group of n have the same birthday is given by P(A) = 1 - P(A').

We need to find the smallest value of n such that P(A) ≥ 1/2.Let's solve for this.Let us find n such that P(A) ≥ 1/2.

By using the complement rule, 1-P(A') = P(A).Then:1 - n(n - 1)(n - 2)...(n - 364)/365n ≥ 1/2n(n - 1)(n - 2)...(n - 364)/365n ≤ 1/2(2)n(n - 1)(n - 2)...(n - 364) ≤ 365n/2Now, take the natural logarithm of both sides and simplify as follows:ln[n(n - 1)(n - 2)...(n - 364)] ≤ ln[365n/2]nln(n) - ln[(n - 1)!] - ln[(n - 2)!] - ... - ln[2!] - ln[1!] ≤ ln[365n/2]

Therefore, we need at least 23 people in the group for the probability of two or more people having the same birthday to be at least 1/2.

This is because n = 23 is the smallest number for which the inequality holds, and therefore, it is the smallest number of people required to ensure that the probability of two or more people having the same birthday is at least 1/2.

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A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

f(1)= 5

so x=1

f(5)= 5(5-1) = 20

The value of f(5) is 3125.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(1) = 5 and f(n) = 5f(n − 1)

Now, for finding the the 5 th term we have to find the remaining four term before the 5th term.

So, n=2

f(2) = 5f(1)

f(2)=  5(5)

f(2)=  25

Now, n=3

f(3) = 5f(2)

f(3)=  5(25)

f(3)=  125

Now, n=4

f(4) = 5f(3)

f(4)=  5(125)

f(4)=  625

Now, n=5

f(5) = 5f(4)

f(5)=  5(625)

f(5)=  3125

Hence, the value of f(5) is 3125.

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What I did was I took the $1000 and subtracted the percent off (35% equals 350)

\(1000 - 350 = 650\)

The total cost of the sale price is $650 (C)

Thank you! btw can i please get brainly :3

Answer:

650

Step-by-step explanation:

1000-350=650

Answer:

For n = 1, 2, 3, ...

\({a}(n) = - 3 + 4(n - 1)\)

Answer:

11

Step-by-step explanation:

you can find the area of the cube and convert it to liters, if the area if the cube is more than the amount of soil then the soil is less, if the amount of soil is more than area of the cube then u have more soil and if they're both the same u have the perfect amount of soil

The values for numbers #21 through #26 are as follows:

#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397

#21: 2.33% (arithmetic mean as a fraction: 0.0233)

#22: $56.4842 (result of the calculation)

#23: 1.85% (geometric mean as a fraction: 0.0185)

#24: $56.4148 (result of the calculation)

#25: 3.64% (continuous mean as a fraction: 0.0364)

#26: $57.4397 (result of the calculation)

To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.

#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.

#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.

#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.

#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.

#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.

#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.

Hence, the values for numbers #21 through #26 are as calculated above.

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a) Build the probability distribution of X =  0.125.  b) Find the mean value of X= 1.875.  c) Find the standard deviation of X = 1.0533

a)

For a fair coin,

P(H) = P(T) = 0.5

Outcome X Probability

T 1 0.5

HT 2 0.5*0.5 = 0.25

HHT 3 0.5*0.5*0.5 = 0.125

HHHT 4 0.5*0.5*0.5*0.5 = 0.0625

HHHH 4 0.5*0.5*0.5*0.5 = 0.0625

So, the probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X P(X) X*P(X) X2*P(X)

1 0.5 0.5 0.5

2 0.25 0.5 1

3 0.125 0.375 1.125

4 0.125 0.5 2

\(\sum\) 1 E(X) = 1.875 E(\(x^{2}\)) = 4.625

Mean = \(\sum\)X* P(X) = 1.875

c)

Variance = E(\(x^{2}\)) - E\((x^{2} )\)= 4.625 – \(1.875^{2}\)  = 1.1094

Standard Deviation = \(\sqrt{variance} = \sqrt{1.1094} = 1.0533\)

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Answer:a=20 b=16 c=18

Step-by-step explanation:

the ration 4/3 , a=15*4/3=20 b=12*4/3=16. C=24/4/3=18

1. x + y = 8 would be x= -y+8

2. x - y = 6 would be x= y+6

Hope this helps

The Probability that all four of the light bulbs work is 0.004 approx.

The probability that all four light bulbs work can be calculated by taking the product of the probability that each individual light bulb works. If each light bulb works independently of the other light bulbs, then the probability that all four light bulbs work is:

P(all 4 bulbs) = P(bulb 1) * P(bulb 2) * P(bulb 3) * P(bulb 4)

P(all 4 bulbs) = 0.25 * 0.25 * 0.25 * 0.25

P(all 4 bulbs) = 0.25^4

P(all 4 bulbs) = 0.00390625

So, the probability that all four light bulbs work is 0.00390625 or approximately 0.004.

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Antivirus software can use techniques called Heuristic analysis to detect malware by analyzing the characteristics and behavior of suspicious files

Heuristic analysis, which is similar to signature analysis, which looks for certain strings to identify potential risks, seeks unique instructions or commands that are not often encountered in antivirus software.

By finding unidentified viruses and offering defense against recently developing malware that hasn't been included in virus definition files yet, antivirus heuristic analysis helps software manufacturers and their clients remain ahead of the competition.

Heuristic antivirus software uses a range of scanning techniques, such as file emulation, file analysis, and genetic signature identification.

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A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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To put fractions in order from least to greatest, you need to compare their values by finding the common denominator.

Step 1: Find a common denominator for all the fractions.

Step 2: Convert each fraction to an equivalent fraction with the common denominator.

Step 3: Compare the numerators of the equivalent fractions. The fraction with the smallest numerator is the smallest fraction, and the fraction with the largest numerator is the largest fraction.

Step 4: If two or more fractions have the same numerator, compare their denominators. The fraction with the smallest denominator is the smallest fraction, and the fraction with the largest denominator is the largest fraction.

Step 5: Write the fractions in order from least to greatest.

For example, let's say you need to put the fractions 1/3, 2/5, and 3/8 in order from least to greatest.

Step 1: The common denominator for 3, 5, and 8 is 120.

Step 2: Convert each fraction to an equivalent fraction with a denominator of 120.

1/3 = 40/120

2/5 = 48/120

3/8 = 45/120

Step 3: Compare the numerators of the equivalent fractions: 40 < 45 < 48

Step 4: Since 40 is not equal to 45 or 48, we don't need to compare the denominators.

Step 5: Write the fractions in order from least to greatest: 1/3 < 3/8 < 2/5.

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Answer:

Step-by-step explanation:

1)

2) x/y=8

3) x*1/4 + x

4) 6w = 4L

5) 3x-2 = 5*y

Answer:

x = 874

Step-by-step explanation

Set up your equation like this: Part/whole = percent/100

Assign the variable x to the unknown part of the equation and add in the known numbers:

So in this situation it would be: x/920 = 95/100

Solve for x:

100 times X = 920 times 95. (cross multiply)

That leaves you with 100x = 87,400

Divide both sides by 100:

x = 874

The expression becomes:

∫[0 to 1] (t)(t²)(\(e^{t^{3} }\)) dy

To evaluate the expression `[₂ C xy ez dy C: x = t, y = t², z = t³, 0 ≤ t ≤ 1]`, let's break it down step by step.

1. Start with the integral sign `[₂ C ... dy C]`, which indicates that we're evaluating a definite integral.

2. Next, we have `xyez dy` as the integrand. Since `x = t`, `y = t²`, and `z = t³`, we can substitute these values into the integrand: `(t)(t²)(\(e^{t^{3} }\))dy`.

3. The limits of integration are given as `0 ≤ t ≤ 1`.

Putting it all together, the expression becomes:

∫[0 to 1] (t)(t²)(\(e^{t^{3} }\)) dy

To solve this integral, we need to determine if `y` is an independent variable or a function of `t`. If `y` is an independent variable, then we can't perform the integration with respect to `y`. However, if `y` is a function of `t`, we can proceed with the integration.

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The expected value of buying one ticket in this charity raffle is $0.42. This means that, on average, a person can expect to win approximately $0.42 if they purchase a single ticket.

To calculate the expected value, we need to consider the probability of winning each prize multiplied by the value of the prize. Let's break it down:

- There is a 1/5000 chance of winning the $600 prize, so the expected value contribution from this prize is (1/5000) * $600 = $0.12.

- There are 3/5000 chances of winning the $300 prize, so the expected value contribution from these prizes is (3/5000) * $300 = $0.18.

- There are 5/5000 chances of winning the $40 prize, so the expected value contribution from these prizes is (5/5000) * $40 = $0.04.

- Finally, there are 20/5000 chances of winning the $5 prize, so the expected value contribution from these prizes is (20/5000) * $5 = $0.08.

Summing up all the expected value contributions, we get $0.12 + $0.18 + $0.04 + $0.08 = $0.42.

Therefore, if you buy one ticket in this raffle, the expected value of your winnings is $0.42.

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From the question, we can find the expression for the money Isabella needs to pay, as follows:

Where k is the amount of miles. We know that she paid $14.00, so we can find the amount of miles:

So the taxi drove 39 miles.

Answer: the common number is 8 for 151 and 152

Step-by-step explanation: hope this helps