Find the following limits. You may or may not need L'Hospital's rule. 3-8 1. lim 1-2 2 tan(4x) 2. lim sin3 1+cos 3. lim cos() In 22 lim lim 1 6 arctan( 7. lim

When converting a larger unit to a smaller one, we multiply; when we convert a smaller unit to a larger one, we divide

The built-in functions for multiply, divide, and subtract can also be used to specify arithmetic operations.

If we need to go from a bigger to a smaller unit, multiply. If we need to get from a smaller to a larger unit, we should divide. We will do so since division is all about bringing down numbers, as we well know.

As a result, we multiply when translating a larger unit to a smaller one and divide when converting a smaller unit to a larger one.

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If x is the largest of the three consecutive integers, then the three consecutive integers can be represented as x-1, x, and x+1.

The sum of these three consecutive integers is:

(x-1) + x + (x+1)

Simplifying the expression, we get:

3x

Therefore, the expression in terms of the given variables that represents the sum of three consecutive integers when x is the largest is 3x.

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Finding a line segment parallel to another segment and passing through a given point is true.

A line segment is a finite portion of a line that is bounded by two distinct points.

The statement is asking whether the following method is true or false for finding a line segment parallel to another segment and passing through a given point:

This method is called the "fold-and-copy" method, and it is a valid way to construct a segment parallel to another segment and passing through a given point. The reason this works is because when the paper is folded along the given point, the fold line is perpendicular to the original segment. When the segment is copied onto the paper on both sides of the fold, the resulting segments are also perpendicular to the fold line. Since two lines that are both perpendicular to the same line are parallel, the resulting segment is parallel to the original segment. The resulting segment also passes through the given point, since it was copied from the original segment which passes through the given point. Therefore, the statement is true.

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If 74 amplifiers are sampled, the probability that the mean of the sample would differ from the population mean by less than 2.8 watts is approximately 0.

The question is asking for the probability that the mean of the sample would differ from the population mean by less than 2.8 watts. We are given that the mean output of the amplifier population is 321 watts with a variance of 144, and that 74 amplifiers are sampled.

To find the probability, we can use the standard deviation, which is the square root of the variance. Therefore, the standard deviation is √144 = 12 watts.

Since we are dealing with a sample mean, we can use the formula for the standard error of the mean, which is the standard deviation divided by the square root of the sample size. In this case, the sample size is 74.

The standard error of the mean is 12 / √74 ≈ 1.3922 watts.

To find the probability that the mean of the sample would differ from the population mean by less than 2.8 watts, we can use the standard normal distribution. We can calculate the z-score using the formula: (x - μ) / σ, where x is the difference in means (2.8 watts), μ is the population mean (321 watts), and σ is the standard error of the mean (1.3922 watts).

The z-score is (2.8 - 321) / 1.3922 ≈ -231.0971.

To find the probability, we need to find the area under the standard normal curve to the left of the z-score. Using a standard normal table or a calculator, the probability is essentially 0 (rounded to four decimal places).

Therefore, the probability that the mean of the sample would differ from the population mean by less than 2.8 watts is approximately 0.

Complete Question: The mean output of a certain type of amplifier is 321 watts with a variance of 144. If 74 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 2.8 watts? Round your answer to four decimal places.

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Answer:

x=1

Step-by-step explanation:

4.3x + 0.7 = 5

Subtract .7 from each side.

4.3x + 0.7.-.7 = 5-.7

4.3x = 4.3

Divide each side by 4.3

4.3x /4.3 = 4.3/4.3

x =1

The amount paid for different weights of oranges at a farmer's market are shown below (A) is the relationship between the price and the weight of the oranges proportional?

Oranges (lb) Price ($)

2--------- $3

3--------- $4.50

5--------- $7.50

Answer:

proportional relationship. Exist

Step-by-step explanation:

To check for propottionality:

2 = 3k

Solve for k = constant of proportionality

2/3 = 3k/3

2/3 = k

Quantity at price = 4.50

Price * k = quantity

4.50 * 2/3 = 3

Quantity at price = 7.50

Price * k = quantity

7.50 * 2/3 = 5

Hence, proportional relationship. Exist

The value of k for which P(X > k) = 0.75 is approximately 4.696. Option D

To find the value of k for which P(X > k) = 0.75, we need to use the properties of the standard normal distribution.

Given that X has a normal distribution with a mean of 2 and a standard deviation of 4, we can standardize the variable X using the z-score formula:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation.

Substituting the given values, we have:

z = (X - 2) / 4

To find the value of k, we need to determine the z-score that corresponds to a cumulative probability of 0.75.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.75 is approximately 0.674.

Setting the standardized value equal to 0.674, we have:

0.674 = (k - 2) / 4

Solving for k, we find:

k - 2 = 0.674 * 4

k - 2 = 2.696

k ≈ 4.696

Therefore, the value of k for which P(X > k) = 0.75 is approximately 4.696.

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Answer: 348

Step-by-step explanation: y is going to be 2x

Answer:

A. 10:2, simplifies to 5:1

B. 2:6, simplifies to 1;3

C. 5 cars there are 3 trucks

D. Motorcycle

Step-by-step explanation:

Statements (1) and (4) are consistent, while statements (2) and (3) are contradictory.

Let's analyze the given statements:

1. f(x) < 0 over the interval (-∞, -4):

This means that for any value of x between negative infinity and -4, the function f(x) yields a negative value.

2. f(x) < 0 over the interval (-∞, -3):

This statement is a subset of the previous one. It implies that for any value of x between negative infinity and -3, the function f(x) yields a negative value.

3. f(x) > 0 over the interval (-∞, -3):

This contradicts the previous statement (2). If f(x) is greater than 0 for any value of x between negative infinity and -3, it means that the function yields positive values in that interval.

4. f(x) > 0 over the interval (-∞, -4):

This statement is a subset of statement (3). It implies that for any value of x between negative infinity and -4, the function f(x) yields positive values.

Therefore, statements (1) and (4) are consistent, while statements (2) and (3) are contradictory.

It's important to note that without specific information about the function f(x), we cannot provide a precise interpretation of these statements. The analysis is based solely on the given conditions.

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Answer: C -  square root of 74

Step-by-step explanation: took the test and got it right. hope this helps.

have a good day :)

Answer:

\(\sqrt{74}\)

Step-by-step explanation:

Answer:126

Step-by-step explanation:

Answer: B. C(n)=0.75n-0.25

Hope these helped u :)

Step-by-step explanation:

Answer: I believe it's B because 1 candy bar=0.75 but there's a $0.25 percent off so I think 0.75n-0.25 would be the right answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

a.)

\(4880.76=4000(1+.04/4)^{4x}\\\\1.22019=1.01^{4x}\\\frac{\ln{1.22019}}{\ln{1.01}}=4x\\x= 4.999999= 5\)

b.)

\(5395.4=4000(1+x/12)^{12*5}\\1.34885=(1+x/12)^{60}\\\sqrt[60]{1.34885} =1+x/12\\x= 0.0599999772677= .06\)

c.)

\(\i)\\100*(1+.1255)= 112.55\\\\2)\\100*(1+.1218/2)^2= 112.550881= 112.55\)

Answer:

C is the answers for the question

Step-by-step explanation:

please give me brainlest

Answer:

The height of the flagpole is approximately 33.16 ft.

Step-by-step explanation:

Use ratio and proportion

Let h be the height of the flagpole

\(\frac{h}{43ft} =\frac{64 in}{83in}\\ h = \frac{43ft(64in)}{83in} \\h = 33.16ft\)

Examples of perpendicular lines include the sides of a square, the edges of a cube, and the sides of a right triangle.

Perpendicular is a mathematical term that describes a relationship between two lines or planes that intersect at a right angle, or 90 degrees.  It is also used to describe a line or plane that is perpendicular to a given line or plane.

The term "perpendicular to all points in the plane" or "perpendicular to each line it intersects" is used to describe a line that is perpendicular to the plane. If the dihedral angle at which two planes intersect is a right angle, then the two planes are said to be perpendicular in space.

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Answer:

the answer should be 3....this is not right btw

the probability of having a winning raffle ticket is 15%.

The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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Answer:

1, 4                    2, -3                        3, 5.5                          4, -2.5

Step-by-step explanation:

Answer:

Step-by-step explanation:its 27

E, "As I was saying, . . .". The salesperson should use this statement if they wished to ignore the objection.

Option E is the best choice to ignore the objection because it allows the salesperson to redirect the conversation back to their main point without directly addressing the objection. The statement implies that the objection is not important enough to interrupt the flow of the conversation.

Ignoring objections is not always the best approach in sales, but if the salesperson chooses to do so, they should use a statement like option E to redirect the conversation back to their main point.


When a salesperson wants to ignore an objection, they should choose a response that does not address the concern raised and instead redirects the conversation back to the topic they were discussing. Option e does this effectively by not acknowledging the objection and continuing with the original discussion.

To ignore an objection, a salesperson should use a statement like option e, which allows them to refocus the conversation without addressing the concern raised.

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The condition on the sides of a triangle is that the sum of any two side lengths must be greater than the third side.

So, if there is any pair of numbers that sum up to less than the third number, those three numbers cannot be measures of the sides of a triangle.

Notice that, for the three numbers given in option d (11, 6, 3), we have:

11 + 6 > 3

11 + 3 > 6

but

6 + 3 = 9

6 + 3 < 11

Therefore, those numbers in option d cannot be measures of the sides of a triangle.

With 95% confidence that the true population mean weight of the sardine cans is between 7.813 oz and 7.887 oz.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

here, we have,

In this scenario, we have a cannery that claims their sardine cans have a net weight of 8 oz. We want to test this claim by taking a simple random sample of 30 cans and measuring their weights

From our sample of 30 cans, we calculated a sample mean of 7.85 oz and a standard deviation of 0.1 oz. The sample mean is an estimate of the population mean, and the standard deviation tells us how much the weights in our sample vary from the mean.

To determine the cutoff values for the middle 95% of the mean weights in this distribution based on the sample data, we can use the t-distribution with n-1 degrees of freedom. The degrees of freedom in this case are 29, which is one less than the sample size.

Using a t-distribution table or calculator, we can find the t-value for a 95% confidence level with 29 degrees of freedom, which is approximately 2.045. We can use this t-value to calculate the margin of error for the sample mean as:

margin of error = t-value * (standard deviation / square root of sample size)

= 2.045 * (0.1 / √(30))

= 0.037

The margin of error tells us how much the sample mean is likely to vary from the true population mean. To find the cutoff values for the middle 95% of the mean weights, we add and subtract the margin of error from the sample mean as follows:

lower cutoff value = sample mean - margin of error

= 7.85 - 0.037

= 7.813

upper cutoff value = sample mean + margin of error

= 7.85 + 0.037

= 7.887

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The percentage of decrease in calories is  33 % .

What is percentage ?

A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given:

Initial caloric intake = 3000 per day

Final  caloric intake =  2010 per day

Therefore percent of decrease in calories = 3000 - 2010 / 3000 x 100

= 33 %

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Answer:

3/8

Step-by-step explanation:

3/5 × 5/8

Multiply the numerators and denominators respectively

15/40

Simplify

3/8

The value of b for which ∫b0cos(ex)dx is minimum is π/2e..

To find the value of b for which the definite integral ∫b0cos(ex)dx is a minimum, we can find the critical points (i.e. local extrema) of the integrand cos(ex) in the interval [0, 2].

Since cos(ex) is a periodic function with period 2π/e, it suffices to consider the interval [0, 2π/e]. In this interval, cos(ex) has its maximum value of 1 at x = 0, and its minimum value of -1 at x = π/2e and x = 3π/2e.

Since e is positive, the function cos(ex) is increasing on the interval [0, π/2e) and decreasing on the interval (π/2e, π/e].

Therefore, if b is in the interval [0, π/2e), the integral is minimized when b = 0. If b is in the interval [π/2e, π/e], the integral is minimized when b = π/2e.

Since the maximum value of b is 2, and 2 < π/e, it follows that the integral ∫b0cos(ex)dx is minimized when b = π/2e.

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