write an iterated integral for over the region r described to the right using a) vertical cross-sections, b) horizontal cross-sections.

The best interpretation is that the sum of 2.1 and –1.2 times a number is greater than or equal to 8.

Inequality are expressions not separated by an equal sign, Given the inequality;

2.1 + (-1.2x) ≥ 8

The sign ≥ means greater than or equal to

The expression 2.1 + (-1.2x) ≥ 8 can also be expressed as 2.1 - 1.2x ≥ 8

The best interpretation is that the sum of 2.1 and –1.2 times a number is greater than or equal to 8.

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Answer:

The 1st, 4th, and 5th

Step-by-step explanation:

if the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph., then the visitor  would run 14 .45 miles  before swimming to minimize the time it takes to reach the island .

we are given that an island is 1 mi due north of its closest point along a straight shoreline., where the visitor is staying at a cabin on the shore that is 15 mi west of that point, in some point the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph. Considering x be the distance the visitor runs. so the total time will be :

Time (T)= x/6 + √((15-x)²+1²)/2.5

Differntiating both sides respect to  x , we get

dT/dx = 1/6 -(15-x)/√(15-x)²+1)/2.5

=>1/6 = (15-x)/√(15-x)²+1)/2.5

=>6(15-x) = 2.5√(15-x)²+1)

Now considering   15 - x = y, we get  

=>6y = 2.5√(y²+1)

=>36y² = 6.25y² + 6.25

=>29.75y² = 6.25

y = √(25/119),  therefore ,x = 15 - √(25/119) = 14 .45

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Answer:

The function that models the total amount of money Julio has after weeks is:

f(x)=150+10x, where:

x is the number of weeks

Step-by-step explanation:

With the information provided,  you can say that the total amount of money Julio has would be equal to the initial amount he has plus the result of multiplying the $10 that he saves every week for the number of weeks, which can be expressed as:

f(x)=150+10x, where:

x is the number of weeks

Answer: f(x)=150+10x,

Step-by-step explanation:

Answer:

The first option.... The one with the blue dot I guess you have chosen that

\(E=\{0,1,2,3,4,5\}\)

The remainders from dividing a natural number by a natural number \(n\) are \(0,1,2,3,\ldots,n-1\).

The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when other data value is increased or decreased respectively.

The pertinent data are:

Period Fertilizer Sales Number of Mowers Sold

1 1.6 12.0

2 1.3 10.0

3 1.8 13.0

4 2.0 15.0

5 2.2 15.0

6 1.5 11.0

7 1.6 12.0

8 1.4 10.0

9 1.8 13.0

10 1.4 10.0

11 1.9 15.0

12 1.4 11.0

13 1.7 14.0

14 1.4 13.0

To determine the correlation between the two variables

Regression equation ( y ) = a + bx

y = dependent variable ( mower )

x = independent variable ( fertilizer)

a = intercept point ( y-axis and regression line )

b = slope ( regression line )

From the given data;

N = 14 ,    Σ x = 22.8,  

Σy = 131,   Σy^2 = 1269,

Σx^2 = 38.18,      (Σx)^2 = 519.84

Σxy = 219.8,       (Σy)^2 = 17161

Hence, The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.

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Option A: defined quantities, option C: integers that are part of a mathematical equation, and option D: measurements that can be counted, are all kinds of numbers that are exact.

A value that is known with 100 percent confidence is called an exact number. In other terms, an exact integer has an infinite number of significant digits and zero uncertainty. It is impossible to simplify or reduce an exact number. Defined quantities like volume in liters, integers that are a part pf mathematical equation like 4π\(r^{3}\), and countable measurements such as the number of students is exact number that can be quantified.

Determining if a particular unit is an exact number can be challenging because not all units and their conversions have clear definitions. Since the SI base units have all been specified, they are all precise integers. Imperial units that are defined in accordance with the SI base units are likewise precise numbers.

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Complete question is:

What kinds of numbers are exact?

Check all that apply.

A) Defined quantities (e.g., 1000 mL in 1 liter).

B) The readings of the thermometer.

C) Integers that are part of a mathematical equation (e.g., 4πr33)

D) Measurements that can be counted, such as the number of students in class.

The derivative of y = (5x6 − 3x4 + 2x2 − 1)(4x9 + 3x7 − 5x2 + 4x) is (30x^5 - 12x^3 + 4x)(4x^9 + 3x^7 - 5x^2 + 4x) + (5x^6 - 3x^4 + 2x^2 - 1)(36x^8 + 21x^6 - 10x + 4).

Using the product rule of differentiation, we have:

y' = (5x^6 - 3x^4 + 2x^2 - 1)'(4x^9 + 3x^7 - 5x^2 + 4x) + (5x^6 - 3x^4 + 2x^2 - 1)(4x^9 + 3x^7 - 5x^2 + 4x)'

Taking the derivative of the first term using the power rule, we get:

(5x^6 - 3x^4 + 2x^2 - 1)' = 30x^5 - 12x^3 + 4x

Taking the derivative of the second term using the product rule, we get:

(4x^9 + 3x^7 - 5x^2 + 4x)' = 36x^8 + 21x^6 - 10x + 4

Therefore, we have:

y' = (30x^5 - 12x^3 + 4x)(4x^9 + 3x^7 - 5x^2 + 4x) + (5x^6 - 3x^4 + 2x^2 - 1)(36x^8 + 21x^6 - 10x + 4)

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Given:

Mark has only used 8.5% of a 34-oz bottle of shampoo.

To find:

How many ounces has he used?​

Solution:

According to the question,

Shampoo used by Mark =  8.5% of a 34-oz

                                        \(=\dfrac{8.5}{100}\times 34\text{-oz}\)

                                        \(=0.085\times 34\text{-oz}\)

                                        \(=2.89\text{-oz}\)

Therefore, he used 2.89-oz of shampoo.

Therefore, Bryan filled 2 smaller bottles.

Bryan divided 3/4 of a liter of plant fertilizer evenly among some smaller bottles.

He put 3/8 of a liter into each bottle. We need to find how many smaller bottles Bryan filled.

To find the number of smaller bottles filled by Bryan, we need to divide the total amount of fertilizer by the amount in each bottle.

Dividing 3/4 by 3/8 is equivalent to multiplying 3/4 by 8/3:(3/4) × (8/3) = 24/12 = 2

Since 3/4 of a liter was divided evenly among some smaller bottles, and each bottle received 3/8 of a liter, Bryan filled 2 smaller bottles (24/12 = 2).

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The height of the tree stump is 2.48 feet.

To find the height of the tree stump, we can use the formula for the volume of a right cylinder: \(V = \pi r^2h\), where V represents the volume, r represents the radius, and h represents the height.

Given that the circumference of the tree stump is measured as 197 inches, we can use the formula for the circumference of a circle: C = 2πr, where C represents the circumference.

From the given circumference, we can solve for the radius, r, by dividing the circumference by 2π: r = C / (2π).

Plugging in the given circumference of 197 inches, we have: r = 197 / (2π) ≈ 31.416 inches.

Now, we can substitute the known values of the volume and radius into the volume formula: 92650 = π(31.416)^2h.

To solve for the height, h, we divide both sides of the equation by π(31.416)^2: h = 92650 / (π(31.416)^2) ≈ 29.74 inches.

Since we want to convert the height from inches to feet, we divide the height by 12: h = 29.74 / 12 ≈ 2.48 feet.

Therefore, the height of the tree stump is approximately 2.48 feet.

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Answer:

If the line RS has been rotated 90 degrees, then VU will be perpendicular to RS and the two slopes must be opposite and reciprocal, i.e. product of the two slopes will equal -1.

As a verification, we find the locations of V and U from rotations of R & S.

(actually, the triangle had been rotated -90°, 90 ° clockwise)

Step-by-step explanation:

Slope RS, m1:

Slope VU, m2

Hence m1*m2=1*-1=-1, meaning that m1 and m2 are opposite (in sign) and are reciprocal to each other, as expected

The lines RS and VU have the opposite and reciprocal slopes because                               Slope of QRS is 1, where as Slope of TVU is -1

Slope of a triangle represents the angle that are formed between positve X-axis moving anticlockwise towards y-axis.

RQ=3

SQ=3

 slope (Tan∅)=\(\frac{perpendicular}{base}\)

                       =RQ/SQ

                        =3/3 =1

           TanФ=45°

UT=3

VT=-3

 slope (Tan∅)=\(\frac{perpendicular}{base}\)

                       =UT/VT

                        =3/-3 =-1

           TanФ=135°

Slope of QRS is 1, where as

Slope of TVU is -1

∴ RS and VU have the opposite and reciprocal slopes.

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The actual area of the logo 1 is 24ft²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The actual sides of the logo 1 will be;

base = 1/2 in

= 1/2 × 8 = 4ft

small base = 1/4 × 8 = 2ft

The logo can be sub divided into two equal trapezoid.

area of trapezoid = 1/2 (a+b)h

= 1/2( 4+8) 2

= 12 ft²

area of the logo = 2 × 12 = 24ft²

Therefore the area of the logo is 24ft²

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Answer:

\(x^{2}\) + 3x - 8 = 0

Step-by-step explanation:

ax² + bx + c = 0 (standard form)

Answer:

x² + 3x = 8

Step-by-step explanation:

No, we cannot use the binomial probability formula with x counting the number who are left-handed in this case

This is because the adults surveyed were selected without replacement. The binomial distribution requires that the samples are independent and identically distributed (i.e., the probability of success remains constant for each trial).

However, when we sample without replacement, the probabilities are not constant because the population size changes with each selection. This means that the probability of selecting a left-handed person for the first selection is not the same as the probability of selecting a left-handed person for the second selection, and so on. Therefore, we cannot use the binomial distribution to calculate the probability of at least 30 left-handed adults among 100 selected without replacement from the US population.

Instead, we can use the hypergeometric distribution to calculate the probability of at least 30 left-handed adults among 100 selected without replacement from the US population. The hypergeometric distribution takes into account the changing probabilities as each selection is made without assuming that the selections are independent.

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Answer:

x equals 14, y equals 19.8

Step-by-step explanation:

The 74th percentile of the sample mean for the number of pets per household is approximately 3.08.

To find the 74th percentile of the sample mean when the mean number of pets per household is 2.96 with a standard deviation of 1.4 and a sample size of 52 households, you can follow these steps:

1. Determine the standard error of the sample mean.

The standard error (SE) is calculated by dividing the population standard deviation by the square root of the sample size:
SE = σ / √n
SE = 1.4 / √52
SE ≈ 0.194

2. Determine the z-score associated with the 74th percentile.

You can use a z-table or a calculator to find the z-score that corresponds to a cumulative probability of 0.74. The z-score is approximately 0.63.

3. Calculate the sample mean associated with the 74th percentile by using the z-score, the population mean, and the standard error:
Sample mean = μ + z * SE
Sample mean = 2.96 + 0.63 * 0.194
Sample mean ≈ 3.08

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The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.

∫3e^x dx = 3∫e^x dx = 3e^x + C₁

∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂

∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃

∫1 dx = x + C₄

Now, we can combine these results to obtain the final answer:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

where C is the constant of integration.

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Refer to the attachments!!~

\(\rule{300pt}{3pt}\)

The exact value is found by making use of order of operations. The

functions can be resolved using the characteristics of quadratic functions.

Correct responses:

\(\displaystyle i. \hspace{0.1 cm} \underline{ f(x) = 2 \cdot \left(x - 1.25 \right)^2 + 4.875 }\)

ii. The function has a minimum point

iii. The value of x at the minimum point, is 1.25

iv. The equation of the axis of symmetry is x = 1.25

First part:

The given expression, \(\displaystyle \mathbf{ 1\frac{4}{7} \div \frac{2}{3} -1\frac{5}{7}}\), can be simplified using the algorithm for arithmetic operations as follows;

Second part:

y = 8 - x

2·x² + x·y = -16

Therefore;

2·x² + x·(8 - x) = -16

2·x² + 8·x - x² + 16 = 0

x² + 8·x + 16 = 0

(x + 4)·(x + 4) = 0

y = 8 - (-4) = 12

Third part:

(i) P varies inversely as the square of V

Therefore;

\(\displaystyle P \propto \mathbf{\frac{1}{V^2}}\)

\(\displaystyle P = \frac{K}{V^2}\)

V = 3, when P = 4

Therefore;

\(\displaystyle 4 = \frac{K}{3^2}\)

K = 3² × 4 = 36

\(\displaystyle V = \sqrt{\frac{K}{P}\)

When P = 1, we have;

\(\displaystyle V =\sqrt{ \frac{36}{1} } = 6\)

Fourth Part:

Required:

Solving for x in the equation; 2·x² + 5·x  - 3 = 0

Solution:

The equation can be simplified by rewriting the equation as follows;

2·x² + 5·x - 3 = 2·x² + 6·x - x - 3 = 0

2·x·(x + 3) - (x + 3) = 0

(x + 3)·(2·x - 1) = 0

Fifth part:

The given function is; f(x) = 2·x² - 5·x + 8

i. Required; To write the function in the form a·(x + b)² + c

The vertex form of a quadratic equation is f(x) = a·(x - h)² + k, which is similar to the required form

Where;

(h, k) = The coordinate of the vertex

Therefore, the coordinates of the vertex of the quadratic equation is (b, c)

The x-coordinate of the vertex of a quadratic equation f(x) = a·x² + b·x + c,  is given as follows;

\(\displaystyle h = \mathbf{ \frac{-b}{2 \cdot a}}\)

Therefore, for the given equation, we have;

\(\displaystyle h = \frac{-(-5)}{2 \times 2} = \mathbf{ \frac{5}{4}} = 1.25\)

Therefore, at the vertex, we have;

\(k = \displaystyle f\left(1.25\right) = 2 \times \left(1.25\right)^2 - 5 \times 1.25 + 8 = \frac{39}{8} = 4.875\)

a = The leading coefficient = 2

b = -h

c = k

Which gives;

\(\displaystyle f(x) \ in \ the \ form \ a \cdot (x + b)^2 + c \ is \ f(x) = 2 \cdot \left(x + \left(-1.25 \right) \right)^2 +4.875\)

Therefore;

ii. The coefficient of the quadratic function is 2 which is positive, therefore;

iii. The value of x for which the minimum value occurs is -b = h which is therefore;

iv. The axis of symmetry is the vertical line that passes through the vertex.

Therefore;

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a. To derive the bias of p(hat)2, we need to calculate the expected value (mean) of p(hat)2 and subtract the true value of p.

Bias(p(hat)2) = E(p(hat)2) - p

Now, p(hat)2 = (Y+1)/(n+2), and Y has a binomial distribution with parameters n and p. Therefore, the expected value of Y is E(Y) = np.

E(p(hat)2) = E((Y+1)/(n+2))

          = (E(Y) + 1)/(n+2)

          = (np + 1)/(n+2)

The bias of p(hat)2 is given by:

Bias(p(hat)2) = (np + 1)/(n+2) - p

b. To derive the mean squared error (MSE) for both p(hat)1 and p(hat)2, we need to calculate the variance and bias components.

For p(hat)1:

Bias(p(hat)1) = E(p(hat)1) - p = E(Y/n) - p = (1/n)E(Y) - p = (1/n)(np) - p = p - p = 0

Variance(p(hat)1) = Var(Y/n) = (1/n^2)Var(Y) = (1/n^2)(np(1-p))

MSE(p(hat)1) = Variance(p(hat)1) + [Bias(p(hat)1)]^2 = (1/n^2)(np(1-p))

For p(hat)2:

Bias(p(hat)2) = (np + 1)/(n+2) - p (as derived in part a)

Variance(p(hat)2) = Var((Y+1)/(n+2)) = Var(Y/(n+2)) = (1/(n+2)^2)Var(Y) = (1/(n+2)^2)(np(1-p))

MSE(p(hat)2) = Variance(p(hat)2) + [Bias(p(hat)2)]^2 = (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

c. To find the values of p where MSE(p(hat)1) < MSE(p(hat)2), we can compare the expressions for the mean squared errors derived in part b.

(1/n^2)(np(1-p)) < (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

Simplifying this inequality requires a specific value for n. Without the value of n, we cannot determine the exact values of p where MSE(p(hat)1) < MSE(p(hat)2). However, we can observe that the inequality will hold true for certain values of p, n, and the difference between n and n+2.

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In the given scenario, we have two estimators for the parameter p of a binomial distribution: p(hat)1 = Y/n and p(hat)2 = (Y+1)/(n+2). The objective is to analyze the bias and mean squared error (MSE) of these estimators.

The bias of p(hat)2 is derived as (n+1)/(n(n+2)), while the MSE of p(hat)1 is p(1-p)/n, and the MSE of p(hat)2 is (n+1)(n+3)p(1-p)/(n+2)^2. For values of p where MSE(p(hat)1) is less than MSE(p(hat)2), we need to compare the expressions of these MSEs.

(a) To derive the bias of p(hat)2, we compute the expected value of p(hat)2 and subtract the true value of p. Taking the expectation:

E(p(hat)2) = E[(Y+1)/(n+2)]

          = (1/(n+2)) * E(Y+1)

          = (1/(n+2)) * (E(Y) + 1)

          = (1/(n+2)) * (np + 1)

          = (np + 1)/(n+2)

Subtracting p, the true value of p, we find the bias:

Bias(p(hat)2) = E(p(hat)2) - p

             = (np + 1)/(n+2) - p

             = (np + 1 - p(n+2))/(n+2)

             = (n+1)/(n(n+2))

(b) To derive the MSE of p(hat)1, we use the definition of MSE:

MSE(p(hat)1) = Var(p(hat)1) + [Bias(p(hat)1)]^2

Given that p(hat)1 = Y/n, its variance is:

Var(p(hat)1) = Var(Y/n)

            = (1/n^2) * Var(Y)

            = (1/n^2) * np(1-p)

            = p(1-p)/n

Substituting the bias derived earlier:

MSE(p(hat)1) = p(1-p)/n + [0]^2

            = p(1-p)/n

To derive the MSE of p(hat)2, we follow the same process. The variance of p(hat)2 is:

Var(p(hat)2) = Var((Y+1)/(n+2))

            = (1/(n+2)^2) * Var(Y)

            = (1/(n+2)^2) * np(1-p)

            = (np(1-p))/(n+2)^2

Adding the squared bias:

MSE(p(hat)2) = (np(1-p))/(n+2)^2 + [(n+1)/(n(n+2))]^2

            = (n+1)(n+3)p(1-p)/(n+2)^2

(c) To compare the MSEs, we need to determine when MSE(p(hat)1) < MSE(p(hat)2). Comparing the expressions:

p(1-p)/n < (n+1)(n+3)p(1-p)/(n+2)^2

Simplifying:

(n+2)^2 < n(n+1)(n+3)

Expanding:

n^2 + 4n + 4 < n^3 + 4n^2 + 3n^2

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Without specific information about the content of reports B05 and B06, it is difficult to determine their exact purpose.

However, based on the given statement that the reports contain a lot of information and may require practice to use effectively, we can make some general assumptions about their purpose.

1. Information analysis and decision-making: Reports B05 and B06 likely provide detailed data and analysis on a particular subject or topic. They may present information in a structured and organized manner, allowing users to make informed decisions based on the fractions data provided.

2. Performance evaluation and improvement: The reports may contain performance metrics, statistics, or feedback on a specific process, project, or system. The purpose could be to assess performance, identify areas for improvement, and track progress over time.

3. Research and exploration: Reports B05 and B06 may serve as a resource for research purposes, providing comprehensive information and analysis on a specific subject. Researchers or analysts may refer to these reports to gain insights or support their own studies.

4. Communication and documentation: The reports may act as a means of communication and documentation, conveying information to stakeholders, clients, or team members. They could summarize findings, highlight key points, and serve as a reference for future discussions or actions.

It's important to note that the actual purpose of reports B05 and B06 can vary depending on the specific context, industry, or organization involved.

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The method-of-moments estimator for λ is simply the sample mean, which is, λ_hat = (1/n) * ∑yi, where i = 1 to n, where λ_hat is the estimator of λ, yi are the observed values of the random sample, and n is the sample size.

The Poisson distribution is used to model the probability of a certain number of events occurring in a fixed interval of time or space when these events occur independently and at a constant rate.

In the method-of-moments, we equate the sample moments to their corresponding population moments and solve for the unknown parameter. For the Poisson distribution, the mean and variance are both equal to λ.

Thus, the method-of-moments estimator for λ is simply the sample mean, which is:

λ_hat = (1/n) * ∑yi, where i = 1 to n

Where λ_hat is the estimator of λ, yi are the observed values of the random sample, and n is the sample size.

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We will ahve the following:

So, the common ratio for the geometric sequence is 3. [Option B]

Answer:

Regression is a statistical technique or method that evaluates the relationship between one dependent variable (usually denoted by Y) and a set of other variables (known as independent variables or regressors)

Step-by-step explanation:

The probability that a randomly selected Christian living in the United States would identify as Catholic can be calculated by dividing the number of Catholics in the US by the total number of Christians in the US.

To do this calculation, we need to know the accurate data on the number of Catholics and the total number of Christians in the US. Let's assume that there are X Catholics and Y total Christians in the US.

The probability of a randomly selected Christian being Catholic would be:

P(Catholic) = X/Y

Without the accurate data on the number of Catholics and total Christians in the US, it is not possible to calculate the exact probability. However, if we assume that the data provided is accurate and stable, we can use the formula above to calculate the probability.

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Answer:

2278

Step-by-step explanation:

(3.9×10−5)(7×10−3)

= (39 - 5)(7 x 10 -3)

= (39 - 5)(70-3)

= 34(70-3)

= 34 x 67

= 2278

Answer:

Please see below :)

Step-by-step explanation:

The slope is just what's in front of the x!

So:

1.) slope = -1/4

2.) slope = undefined

3.) slope = -9

4.) slope = 9/2

Hope this helps!

Answer:

1. -1/4

2. undefined

3. zero

4. 6/5

Step-by-step explanation:

Answer: 3 lessons

Step-by-step explanation:

Matt starts swimming lessons on Day 5.

He then goes to swimming lessons every 10 days. The dates he went on lessons are therefore:

First lesson = Day 5

Second lesson = Day 5 + 10 days = Day 15

Third lesson = Day 15 + 10 days = Day 25

Fourth lesson = Day 25 + 10 days= Day 35

He therefore only went for 3 lessons because the 4th lesson was after Day 30.

We can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

A 95% confidence interval for the population mean can be constructed using the t-distribution when the sample size is small (<30) or the population standard deviation is unknown.

In this case, we have a random sample of 46 people with a mean body mass index (BMI) of 27.2 and a standard deviation of 6.0.

Thus, we need to use the t-distribution to construct the confidence interval.

The formula for the confidence interval is as follows:

Upper limit of the confidence interval:27.2 + (2.013) (6.0/√46) = 29.032Lower limit of the confidence interval:27.2 - (2.013) (6.0/√46) = 25.368

Therefore, the 95% confidence interval for the population mean BMI is (25.368, 29.032).

This means that we can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

To learn more about true population visit:

https://brainly.com/question/32979836

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