Suppose a cone and a cylinder both have congruent circular bases and congruent heights. How may times larger is the cylinder than the cone?

F is continuous at every point x₀ ∈ I. Thus, f is continuous on an interval I.

Regarding the converse, the statement "if f is continuous on an interval I, then it is uniformly continuous on I" is not always true. There exist functions that are continuous on a closed interval but not uniformly continuous on that interval. A classic example is the function f(x) = x² on the interval [0, ∞). This function is continuous on the interval but not uniformly continuous.

To prove that if a function f is uniformly continuous on interval I, then it is continuous on I, we need to show that for any ε > 0, there exists a δ > 0 such that for any x, y ∈ I, if |x - y| < δ, then |f(x) - f(y)| < ε.

Since f is uniformly continuous on I, for the given ε, there exists a δ > 0 such that for any x, y ∈ I, if |x - y| < δ, then |f(x) - f(y)| < ε.

Now, let's consider an arbitrary point x₀ ∈ I and let ε > 0 be given. Since f is uniformly continuous, there exists a δ > 0 such that for any x, y ∈ I, if |x - y| < δ, then |f(x) - f(y)| < ε.

Now, choose δ' = δ/2. For any y ∈ I such that |x₀ - y| < δ', we have |f(x₀) - f(y)| < ε.

Therefore, for any x₀ ∈ I and ε > 0, we can find a δ' > 0 such that for any y ∈ I, if |x₀ - y| < δ', then |f(x₀) - f(y)| < ε.

This shows that f is continuous at every point x₀ ∈ I. Thus, f is continuous on interval I.

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The average number of customers visiting the dealership daily, the appropriate hypotheses are HA: µ < 800

The hypotheses are:

H0: µ = 800

HA: µ < 800 (claim)

The mean number of daily customers was 800.  She feels the number of customers has decreased, so the alternate is mu is less than 800.

for the given values we can find test statistics:

A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.

The general form of  test statistics:

         \(Z=\frac{x-u}{\frac{sd}{\sqrt{n} } } --------(1)\)

we have all values

x=750 u= 800 sd=350  n=100

substitute in equation(1)

\(Z=\frac{750-800}{\frac{350}{\sqrt{100} }}=-1.43\)

Z=-1.43

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Answer: x= 7191.509 ft

Step-by-step explanation:

Sin9/1 = 1125/x

X/1 = 1125/sin9

Answer:

x(x-2)

Step-by-step explanation:

X^2-2x

x(x-2)

Answer:

-4

Step-by-step explanation:

that is the nth termmmmm

Answer:

64

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

5) 2     7) 4

Step-by-step explanation:

3/5 x 25 = 15

15 - 1 = 14 / 7 = 2 = x

25     20

---  =  ----

40    7x+4

25 x 4/5 = 20

40 x 4/5 = 32

32 - 4 = 28 / 7 = 4 = x

Answer:

5/3

Step-by-step explanation:

Take the cube root of each of the numbers on the right

This inequality indicates that -35 is less than -22, confirming that -35 is positioned to the left of -22 on a horizontal number line.

To represent the statement "On a horizontal number line, -35 is located to the left of -22" as an inequality, we can use the less than symbol (<).

Since -35 is to the left of -22, it means that -35 is a smaller number than -22.

Therefore, the inequality that represents this statement is:

-35 < -22

This inequality indicates that -35 is less than -22, confirming that -35 is positioned to the left of -22 on a horizontal number line.

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The one mean Z test can be used for small samples of size less than 15 when the population standard deviation is known.

The one-mean z-test is a hypothesis test that is used to test a hypothesis about the mean of a population when the population standard deviation is known, and the sample size is large (typically greater than 30).

When the sample size is small (less than 15), the one-mean z-test is not appropriate because the assumptions of the test may not be met.

When the sample size is small, we typically use a t-test instead of a z-test to test a hypothesis about the population mean.

Specifically, we use a one-sample t-test when the population standard deviation is unknown, and the sample size is small (typically less than 30).

The one-sample t-test uses a t-distribution to calculate the p-value and test the null hypothesis about the population mean.

It is important to note that the sample size of 15 is not a hard and fast rule for when to switch from the z-test to the t-test.

The decision of which test to use depends on the specific context and the assumptions of the test.

In general, if the population standard deviation is unknown and the sample size is small (less than 30), then we use the t-test. If the population standard deviation is known and the sample size is large (greater than 30), then we use the z-test.

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To write the inequality we will start by defining "a number" as n.
Then, "twice a number" can be written as 2n.

increased by 3 becomes: 2n + 3 is less than" turns it into" 2n + 3 < the number decreased by 4 is:  n − 4

Step-by-step explanation:
To solve, first, subtract 3 and n from each side of the inequality to solve for n while keeping the inequality balanced:
− n + 2n + 3 − 3 < − n + n − 4 − 3
− 1n + 2n + 0 < 0 − 7

(−1 + 2)n < −7

1n < − 7
n < − 7

The compound interest earned on an account with $700 invested at 4.5% for 2 years is $64.42.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

To calculate the compound interest earned, we use the formual below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the compound interest earned is $64.42.

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In the given argument, "No swimmers fear water. Some bathers are swimmers.

Therefore, some bathers do not fear water," it is a deductive argument.

A deductive argument is an argument in which the premises provide complete and conclusive support for the conclusion. This means that if the premises are true, then the conclusion must also be true.

In this argument, the first premise is "No swimmers fear water," which is a universal negative statement. The second premise is "Some bathers are swimmers," which is a particular affirmative statement.

The conclusion "Therefore, some bathers do not fear water" follows logically from the two premises, and is a particular negative statement.

Therefore, it is a deductive argument.

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Answer:

13 weeks

Step-by-step explanation:

Add 590 and 60 together and then divide by 50 and you'll get 13

Answer:

20 feet

Step-by-step explanation:

35 - 15 = 20

not sure what you mean by "order matters" but

sea level is 0

the owl is 35 feet above

the dolphin is 15 feet below

35 + 15 = 50

The midpoint between two co-ordinate points is the point between them.

To find the midpoint M between S and T, we use the formula below.

Formula:

From the question,

Given:

Substitute these values into equation 1

To calculate the distance between S and T, we use the formula below.

Formula:

Substituting into equation 2

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Answer:

the correct answeria A.pretest sensitization

This method is used when the population has distinct subgroups.

The plan to conduct a survey by randomly selecting 20 students from each of the freshman, sophomore, junior, and senior classes is an example of stratified random sampling.

In stratified random sampling, the population is first divided into subgroups or strata based on some characteristic, such as class level (freshman, sophomore, junior, senior), and a random sample is then selected from each stratum.

This method is used when the population has distinct subgroups and it is important to ensure that the sample is representative of each subgroup. In this case, by taking random samples of 20 students from each class level, the statistics class can ensure that the survey results accurately reflect the views of each class level and not just one particular group.

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Answer:

a c and d

Step-by-step explanation:

lmk if you need work

and remember that when it is negative, the value that is closer to 0 is greater

Answer: The probability is 0.083

Step-by-step explanation:

First, let's find the individual probabilities:

The probability that the outcome of the red number cube is even:

This will be equal to the quotient between the number of outcomes that are even (3) and the total number of outcomes for this dice (6)

Then the probability is:

p = 3/6 = 1/2.

The probability that the outcome of the blue number cube is a 5.

Similar to the above case, here the probability will be the quotient between the number of outcomes that are 5 (only one) and the total number of outcomes.

q = 1/6

And the joint probability will be equal to the product of the individual probabilities, then he probability that the outcome of the red number cube is even and the outcome of the blue number cube is a 5 is equal to:

P = p*q = (1/2)*(1/6) = 1/12 = 0.083

Answer:

its addittion cus ur adding 73

Step-by-step explanation:

just got taught this in clas

The appropriate methods for analyzing the variables Birth Rate and Death Rate at the same time would be scatterplot, two-way table, and stacked bar chart.

Scatterplot: A scatterplot can be used to visually display the relationship between two quantitative variables, such as Birth Rate and Death Rate. Each point on the scatterplot represents a pair of values for the two variables, making it easy to identify patterns or trends in the data.

Two-way table: A two-way table can be used to display the distribution of two categorical variables, such as Birth Rate and Death Rate, and how they relate to each other. It can help identify the joint frequency or relative frequency of different categories.

Stacked bar chart: A stacked bar chart can be used to show how two categorical variables, such as Birth Rate and Death Rate, are related to each other. Each bar represents the total frequency for each category, and the bars are divided into sections representing the subcategories of the other variable. This makes it easy to compare the distribution of the two variables across each category.

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Answer:

reflected image shown in red on attached diagram

Step-by-step explanation:

When reflecting an object in the line x = a:

So when reflecting in the line x = 1

(2, 7) → (0, 7)

(2, 4) → (0, 4)

(4, 4) → (-2, 4)

The expected time for completion of Activity "X" on a PERT chart is 9 hours.

PERT analysis is a project management technique that is used to evaluate and analyze the tasks involved in finishing a project. It makes use of 3 duration estimates: optimistic, pessimistic, and most likely times to calculate the expected duration of each activity. These estimates are used to analyze the critical path, slack time, and schedule of the project.

Let's calculate the expected time for completion of Activity "X" on a PERT chart using the given estimates:

Optimistic time (O) = 6 hours

Most likely time (M) = 9 hours

Pessimistic time (P) = 12 hours

Expected time (TE) = [O + 4M + P] ÷ 6= [6 + 4(9) + 12] ÷ 6= [6 + 36 + 12] ÷ 6= 54 ÷ 6= 9

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Answer:

8x^2 + 6x + 36xy^2 + 24y^2

Step-by-step explanation:

First, multiply the two terms inside the second set of parentheses by-2x; we get 8x^2 + 6x.

Next, multiply the same two terms by -9y^2; we get 36xy^2 + 24y^2.

Now add these products together:  

8x^2 + 6x + 36xy^2 + 24y^2    This is the desired product.

Answer:

w = \(\frac{P-2h}{2}\)

Step-by-step explanation:

Given

P = 2w + 2h ( subtract 2h from both sides )

P - 2h = 2w ( divide both sides by 2 )

\(\frac{P-2h}{2}\) = w

The domain of the function f(x) = 3x^2 - 6x - 13 is (-∞, ∞).

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes.

To determine the domain of the function f(x) = 3x^2 - 6x - 13, we need to consider any restrictions on the values of x that would make the function undefined.

In this case, since x represents the velocity of the boat relative to land, there are no inherent limitations or restrictions on the possible values of x. The domain of the function is therefore all real numbers, or (-∞, ∞).

Therefore, the domain of the function f(x) = 3x^2 - 6x - 13 is (-∞, ∞).

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

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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