4. State all reasons why Rolle's Theorem does not apply to the function on the interval (– 2,0]. (2 points) 4. 2 f(x) = (x+1) 3. Find the absolute maximum and the absolute minimum off on the given interval. (2 points) f(x) = x + sin x ; [0,21] = 3.

Answer:

-29/35

Step-by-step explanation:

Answer:

its the second one

Step-by-step explanation:

Answer:

- 64

Step-by-step explanation:

\((-4)^{3}\)

= - 4 × - 4 × - 4

= 16 × - 4

= - 64

The probability of selecting a white-tailed deer that carries the Lyme disease bacteria is 1 in 10,000, or 0.0001. This means that out of every 10,000 white-tailed deer on the east coast, only one is expected to carry the Lyme disease bacteria.

If we assume that each deer in the population has an equal chance of carrying the bacteria, then the probability of selecting a deer that carries the bacteria can be calculated using the formula for probability:

Probability = Number of desired outcomes / Total number of possible outcomes

In this case, the number of desired outcomes is one (since we want to select a deer that carries the bacteria), and the total number of possible outcomes is the total number of white-tailed deer in the population. Since we don't know the exact number of deer in the population, we can assume that it is very large, so we can use an approximation:

Probability ≈ 1 / (Very large number)

Therefore, the probability of selecting a white-tailed deer from the east coast population that carries the Lyme disease bacteria is very close to 0.0001 or 1 in 10,000.

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The closest answer choice to this value is option 1, 33. Therefore, the best estimate for the unicity distance for an affine cipher is 33.

To find the best estimate for the unicity distance for an affine cipher, we can use the following formula:

Unicity Distance  (U) = (keyspace / entropy) × log2(1 / redundancy).

Given the answer choices:
1. 33
2. 35
3. 33
4. 26
5. 17.5

For an affine cipher, the keyspace is 26^2 (since there are 26 possibilities for both 'a' and 'b' in the equation

y = (ax + b) mod 26).

The entropy of English text is roughly 1.5 bits/character, and the redundancy is approximately 0.7.

Using the formula, we have:

U = (26^2 / 1.5) × log2(1 / 0.7)

U ≈ 33.49

Therefore, the best estimate for the unicity distance for an affine cipher is 33.

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For question 1, we are asked to solve the integral 3e^-x(1+e^-(1+e^-x)^2)dx. This integral requires substitution, where u=1+e^-x and du=-e^-x dx. After substituting, we get the integral 3e^-x(1+u^2)du.

Solving this integral, we get the final answer of 3(e^-x-xe^-x+x+1/3e^-x(2+u^3)+C). For question 2, we are asked to solve the integral 4∫(10³dx)/(x²+3x-5)(x+2)²(x-1). This integral requires partial fraction decomposition, where we break the fraction down into simpler fractions with denominators (x+2)², (x+2), and (x-1). After solving for the coefficients, we get the final answer of 4(7/20 ln|x+2| - 9/8 ln|x-1| + 13/40 ln|x+2|^2 - 1/8(x+2)^(-1) + C). In summary, for question 1 we used substitution and for question 2 we used partial fraction decomposition to solve the given integrals.

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The total amount of interest paid along with annual rate is $163.80 at 16.08%.

The annual percentage rate refers to the yearly rated interest which is taken from when the individual takes a loan. It is also considered a measure of the cost of credit or borrowing expense which involves a interest and fees concerning the transaction.

And an annual percentage yield is helpful in the effective annual rate which includes the points of compounding given in that year.

For the given loan of $1000 with a 15% APR compounded monthly,

The evaluated monthly interest rate would be

15%/12 = 1.25%.

The total evaluated amount of interest paid on the course of a year will be $163.80.

The current effective annual rate will be 16.08%.

The total amount of interest paid along with annual rate is $163.80 at 16.08%.

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Answer:

here is the ananswer

Step-by-step explanation:

red go to red and black to black

Answer:

0.19 50% 15/20 9/10 95%

Step-by-step explanation:

I know

The probability that at least one of the next four people surveyed works for a small business is 0.9375 or 93.75%.

To determine the probability that at least one of the next four people surveyed works for a small business, we can first examine the possible outcomes of the random number generator for each person surveyed.

Since 50% of the people surveyed work for a small business, we can assign the numbers 0 to 4 to represent those who work for a small business, and the numbers 5 to 9 to represent those who do not work for a small business.

Now, let's look at the simulated results:

Person 1: 8 (does not work for a small business)

Person 2: 1 (works for a small business)

Person 3: 7 (does not work for a small business)

Person 4: 3 (works for a small business)

Out of the four people surveyed, two work for a small business (person 2 and person 4) and two do not work for a small business (person 1 and person 3).

To calculate the probability that at least one of the next four people surveyed works for a small business, we can use the complementary probability. That is, the probability that none of the next four people surveyed work for a small business is:

(5/10) * (5/10) * (5/10) * (5/10) = 0.0625

Therefore, the probability that at least one of the next four people surveyed works for a small business is:

1 - 0.0625 = 0.9375

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Answer:

Rotational Symmetry

Step-by-step explanation: It stays the same when rotated

The correct answer is 63c9.  To simplify the expression (9c) (7c8), we need to multiply the coefficients (numbers) and combine the variables with the same base.

In this case, we have:

(9c) (7c8) = 9 * 7 * c * c8

Multiplying the coefficients gives us 9 * 7 = 63.

Multiplying the variables with the same base, 'c' in this case, means adding their exponents. Here, we have c * c8, which equals c^(1+8) = c^9.

Putting it all together, (9c) (7c8) simplifies to 63c^9.

Therefore, the expression equivalent to (9c) (7c8) is 63c^9.

So, the correct answer is 63c9.

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8 cot(x) sec(x) can be simplified to 8 csc(x) - 8 sin(x) by converting the left side into sines and cosines.

How can the expression 8 cot(x) sec(x) be simplified using trigonometric identities?

To verify the identity by converting the left side into sines and cosines, we'll simplify each step.

Starting with the left side of the equation:

8 cot(x) sec(x)

First, let's express cot(x) and sec(x) in terms of sines and cosines:

cot(x) = cos(x) / sin(x)

sec(x) = 1 / cos(x)

Substituting these values back into the equation:

8 (cos(x) / sin(x)) (1 / cos(x))

Next, we can cancel out the common terms of cos(x):

8 (1 / sin(x))

Finally, we can rewrite 1 / sin(x) as csc(x):

8 csc(x)

Therefore, the left side of the equation simplifies to 8 csc(x).

The right side of the equation is already in the desired form:

8 csc(x) - 8 sin(x)

Thus, we have successfully shown that the left side of the equation, after converting to sines and cosines, simplifies to the right side of the equation. The identity is verified.

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After conducting some mathematical operations, we know that Brent earned $28.75.

So, the amount Brent will earn when there are 7 children:

Brent earns $7.25 per hour and he watched kids from 9:00 am to noon which is 3 hours.

He earns $1 per child and there are 7 children present, then:

Total amount he earned: $21.75 + $7 = $28.75

Therefore, after conducting some mathematical operations, we know that Brent earned $28.75.

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The correct question is given below;
ON SATURDAY MORNINGS FROM 9:00 UNTIL NOON, BRENT WATCHES A GROUP OF PRESCHOOLERS WHILE THEIR PARENTS WORK OUT IN THE GYM. BRENT EARNS $7.25 PER HOUR PLUS $1.00 PER CHILD. TODAY THERE ARE 7 CHILDREN…HOW MUCH WILL BRENT EARN?

Answer:

2.5 years/2 years 6 months

Step-by-step explanation:

Half year = 6 months

One year = 12 months

Two years = 24 months

30-24=6 months

2 Years + 6 months = 2.5 years/30 months/2 years 6 months

Answer:

volume is equal to ratio

Answer:

This is your answer. If I'm right so,

Please mark me as brainliest. thanks!!!

The price of the computer if the discount is applied before the rebate is $1225. The composite function is (g.f)(x) = g(f(x))

(g.f)(x) = g(f(x))

f(1500) = 0.95(1500)

= 1425

g(1425) = 1425-20

= 1225

= $1225

Therefore, The price of the computer if the discount is applied before the rebate is $1225. The composite function is (g.f)(x) = g(f(x))

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To go from the first town to the second town, you must drive 137.5 miles.

What is an proportion?

A proportion is a mathematical equation that compares two ratios. It is usually written as two equal fractions or ratios, one on each side of the equation. A proportion can be used to compare the relationship between different quantities, such as measurements, rates, or even time.

We can use proportion to solve this problem. The proportion relates the map scale to the actual distance:

0.75 inch / 50 miles = x / distance

where x is the actual distance we want to find.

We can cross-multiply and solve for x:

0.75 inch * distance = 2.75 inches * 50 miles

x = (2.75 inches * 50 miles) / 0.75 inch

x = (137.5 miles)

To go from the first town to the second town, you must drive 137.5 miles.

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The total number of different entertainment centers Madelyn can make is 7 × 7 × 2 = 98. Answer: 98.

Madelyn is creating a media center.

There are 7 televisions and 7 sets of speakers to choose from. For the DVD player, Madelyn has 2 options.

We are supposed to determine how many different entertainment centers Madelyn can make.

Therefore, we need to use the multiplication principle of counting.

According to the multiplication principle of counting, if an event can occur in m ways and a second event can occur in n ways, then the two events can occur in m x n ways.

Let's use the multiplication principle of counting to solve this problem.

The number of ways Madelyn can choose a TV is 7.

The number of ways Madelyn can choose a set of speakers is 7.

The number of ways Madelyn can choose a DVD player is 2.

Therefore, the total number of different entertainment centers Madelyn can make is 7 × 7 × 2 = 98. Answer: 98.

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The standard deviation of McDonovan, Inc.'s stock returns is approximately 19.54%.

To calculate the standard deviation for McDonovan, Inc.'s stock returns using the provided information, we can use the following steps:

1. Assign weights to each return based on their respective probabilities.

Boom: Probability = 0.20, Return = 0.40

Normal: Probability = 0.60, Return = 0.15

Recession: Probability = 0.20, Return = -0.20

2. Calculate the expected return by taking the weighted average of the returns.

Expected Return = (0.20 × 0.40) + (0.60 × 0.15) + (0.20 × -0.20) = 0.09 or 9%

3. Calculate the squared difference between each return and the expected return.

Boom: (0.40 - 0.09)² = 0.1296

Normal: (0.15 - 0.09)² = 0.0036

Recession: (-0.20 - 0.09)² = 0.0736

4. Calculate the variance by taking the weighted average of the squared differences.

Variance = (0.20 × 0.1296) + (0.60 × 0.0036) + (0.20 × 0.0736) = 0.03808

5. Take the square root of the variance to obtain the standard deviation.

Standard Deviation = √(0.03808) = 0.1954 or 19.54%

Therefore, the standard deviation of McDonovan, Inc.'s stock returns is approximately 19.54%.

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Step 1

The number of pieces for 5 cuts is

Step 2

The general formula Tn, for the number of rope pieces is

Step 3

How many rope cuttings will make up 153 rope pieces

Step 4

How many ropes pieces will result from 11 cuttings

The 90% confidence interval for the given sample is (7.58, 8.60).

To calculate the 90% confidence interval for the given sample assuming normality of the data, we need to use the formula as follows;Confidence interval = X ± Z α/2(σ/√n)Where, X is the sample meanZ α/2 is the Z-score for the desired level of confidenceσ is the population standard deviationn is the sample sizeFirst, we need to calculate the sample mean and standard deviation.Sample mean,

X= (7.9 + 8.3 + 8.4 + 9.6 + 7.7 + 8.1 + 6.8 + 7.5 + 8.6 + 8 + 7.8 + 7.4 + 8.4 + 8.9 + 8.5 + 9.4 + 6.9 + 7.7) / 18

= 8.09

Sample standard deviation,

σ = √[Σ(xi - X)² / (n - 1)]σ = √[(7.9 - 8.09)² + (8.3 - 8.09)² + (8.4 - 8.09)² + (9.6 - 8.09)² + (7.7 - 8.09)² + (8.1 - 8.09)² + (6.8 - 8.09)² + (7.5 - 8.09)² + (8.6 - 8.09)² + (8 - 8.09)² + (7.8 - 8.09)² + (7.4 - 8.09)² + (8.4 - 8.09)² + (8.9 - 8.09)² + (8.5 - 8.09)² + (9.4 - 8.09)² + (6.9 - 8.09)² + (7.7 - 8.09)² / (18 - 1)]σ = 0.761

Now, we need to find the Z α/2 value from the standard normal distribution table.

Z α/2 = 1.645 (for 90% confidence level)Putting the values in the formula,Confidence interval =

X ± Z α/2(σ/√n)

= 8.09 ± 1.645(0.761/√18)

= 8.09 ± 0.511

= (8.09 - 0.511, 8.09 + 0.511)

= (7.58, 8.60).

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hope it helped jwgwhwfhwgwjwh

Answer:

21

Step-by-step explanation:

I took the k12 quiz

Answer:

7) 8.94

8) 6.71

Step-by-step explanation:

for both questions, use pythagorean theorem

\(a^{2} + b^{2} = c^{2}\)

Question 7:

\(4^{2} + 8^{2} = c^{2}\)

16 + 64 = \(c^{2}\)

80 =  \(c^{2}\)

\(\sqrt{80} = \sqrt{c^{2}}\)

c = 8.94

Question 8:

\(6^{2} + 3^{2} = c^{2}\)

36 + 9 = \(c^{2}\)

45 = \(c^{2}\)

\(\sqrt{45} = \sqrt{c^{2} }\)

c = 6.71

In the video game Rebecca is playing using only addition the expression that represents Rebecca's score after these three turns is  

= 4 + (-6) + (8) + (-1)

Rebecca's energy level after Turn 1 = -2

Rebecca's energy level after Turn 2 = 6

Rebecca's energy level after Turn 3 = 7

Following the rule of the video game the expression is written in steps below

Rebecca is currently at energy level 4

= 4

Turn 1: 6 trees cut

= 4 + (-6)

= 4 - 6

= -2

Turn 2: 8 trees planted

= 4 + (-6) + (8)

= -2 + 8

= 6

Turn 3: 1 tree cut

= 4 + (-6) + (8) + (-1)

= 6 - 1

= 7

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Answer:

y = 60x + 20

Step-by-step explanation:

The number of hours that we ski is a variable cost where each hour costs $60. On top of that, we have a fixed cost of $20 which stays the same no matter how long we ski.

So we can use an equation to find the totla cost C given the number of hours t as follows:

C(t) = 60t + 20

We can use this equation to find the cost of a skiing session by plugging in some value for t. For example, if we ski for 3 hours:

C(3) = 60(3) + 20 = $200

The equation can also be written using x and y and mean the same thing.

Given:

The expression is

\(x^3(2x-6)+x^2(2x-6)\)

To find:

The factors of the given expression.

Solution:

We have,

\(x^3(2x-6)+x^2(2x-6)\)

First taking \((2x-6)\) common, the given expression can be written as

\(=(2x-6)(x^3+x^2)\)

Taking \(x^2\) common from \((x^3+x^2)\), we get

\(=x^2(2x-6)(x+1)\)

Therefore, the factors of the given expression are \(x^2(2x-6)(x+1)\).

Answer:

the first one

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

it is going to be answer 2 because he put more in at the end

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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