When we do a confidence interval for the mean, we use the following distribution to determine the number of standard deviations needed for our confidence:t-distribution z-distributionskewed distribution Chi Square distribution

Answer:

D. (3x^2-3x+27)^1/3

Step-by-step explanation:

dy/dx=2x−1/y^2

Cross multiply to get Y's and X's on different sides.

(y^2)dy = (2x-1)dx

Take the integral of each side

∫(y^2)dy = ∫(2x-1)dx

y^3/3 = 2x^2/2 - x + C

Multiply both sides by 3

y^3 = 3x^2 - 3x + C

Plug in (0,3) and solve for C

27 = 0 - 0 + C

C = 27

Plug in C to the equation

y^3 = 3x^2-3x+27

Cube root both sides to get just y

y = √(3x^2-3x+27)

y = (3x^2-3x+27)^1/3

D.

The particular solution of the equation will be "\((3x^2-3x+27)^\frac{1}{3}\)".

According to the question,

→    \(\frac{dy}{dx}\) = \(\frac{2x-1}{y^2}\)

By applying cross-multiplication,

(y²)dy = (2x - 1)dx

By integrating both sides, we get

→ ∫(y²) dy = ∫(2x - 1) dx

           \(\frac{y^3}{3}\) = \(\frac{2x^2}{2}\) - x + C

By multiplying "3" both sides, we get

           y³ = 3x² - 3x + c

By substituting "(0,3)" in above equation,

          27 = 0 - 0 + C

            C = 27

By substituting value of C in the above equation,

         y³ = 3x² - 3x + 27

By cubing both sides,

y = √(3x²-3x+27)

  = \((3x^2-3x+27)^\frac{1}{3}\)        

Thus the above answer i.e., "Option D" is correct.

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The rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute

From the question, we are to determine the rate which is equivalent to the rate Paula walked

Using the formula,

\(Rate = \frac{Distance}{Time}\)

From the given information,

Distance = 1/12 mile

Time = 5/3 minutes

Putting the parameters into the formula, we get

\(Rate =\frac{\frac{1}{12} }{\frac{5}{3} }\)

\(Rate = \frac{1}{12} \div \frac{5}{3}\)

\(Rate = \frac{1}{12} \times \frac{3}{5}\)

\(Rate = \frac{3}{60}\)

\(Rate = \frac{1}{20}\) mile/minute

Hence, the rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute

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The given relation in table shows the direct proportion of the values.

One kind of proportionality relationship is the direct proportion.

For direct proportion:

y/x=k

k = 31 / 217 = 0.412

k = 20/140 = 0.412

.

.

.

k = 12/ 84 = 0.412

All value of k are same.

Thus, relation is of direct proportion.

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The correct question is 11.

Answer:

720ft= 8640in => 18/8640 =0.002083 = 2083/1000000

Step-by-step explanation:

Answer: A variable is an object, event, idea, feeling, time period, or any other type of category you are trying to measure.

A variable is a characteristic that can be measured and that can assume different values. Height, age, income, province or country of birth, grades obtained at school and type of housing are all examples of variables. Variables may be classified into two main categories: categorical and numeric

Answer:

a variable (as the letters a, b, c, y, etc.) is considered a missing number within a mathematical problem

The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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No, we cannot measure 3 gallons of water using 2 jugs of size 100 and 98 gallons. But, we can measure 4 gallons of water using these jugs.

Let's call the two jugs A and B, with A being the 100-gallon jug and B being the 98-gallon jug.

To measure 3 gallons of water, we need to have one jug that is smaller than 3 gallons and another jug that is larger than 3 gallons.

However, both of these jugs are larger than 3 gallons.

This means that it is impossible to measure 3 gallons of water using these jugs.

To measure 4 gallons of water, we can follow these steps:

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 2 gallons of water in jug A.

Pour the water from jug B down the drain, then pour the 2 gallons from jug A into jug B.

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 96 gallons of water in jug B, with 4 gallons of water in jug A.

Thus, we can measure 4 gallons of water using these jugs.

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Answer:

Проведите линию через форму, чтобы каждая сторона была зеркальным отражением. Когда фигура складывается пополам по оси симметрии, две половинки совпадают. На этой фотографии белая линия по центру представляет собой вертикальную ось симметрии.

Step-by-step explanation:

The value of u is not provided, we cannot determine the exact value of y. None of the given options (a, b, c, d) can be chosen as the approximate value of y.

For the first question, you are given the model yhat = 2.1 + 1.0x^2 and you want to find the estimated marginal effect of x on y when x = 1.3. To find the estimated marginal effect, you need to take the derivative of yhat with respect to x. In this case, the derivative would be 2.0x.

Now, substitute x = 1.3 into the derivative:

2.0(1.3) = 2.6.

Therefore, the estimated marginal effect of x on y when x = 1.3 is 2.6.

For the second question, you are given the model \(lny = β₁ + β₂x^2 + u\), with parameter estimates

β₁ = 2 and

β₂ = 1.

To predict the value of y when x = 2, substitute the given values into the model:
\(lny = 2 + 1(2^2) + u\)
lny = 2 + 1(4) + u
lny = 2 + 4 + u
lny = 6 + u

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David can best improve his investigation by including a control group. A control group is a group that does not receive any treatment or intervention and is used as a benchmark to compare the results of the experimental group. In this case, the control group would be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well.

In scientific research, it is important to include a control group to ensure that the results of the experimental group are due to the treatment or intervention and not due to other factors. In this case, David is investigating the factors that affect plant growth, and he is manipulating the amount of water and fertilizer that the two elm trees receive. However, there could be other factors that affect plant growth, such as soil quality, sunlight exposure, temperature, and pests. If David only measures the height and trunk girth of the two elm trees that receive water and fertilizer, he cannot be sure if any changes in their growth are due to the treatment or due to other factors.

To improve his investigation, David can plant a third young elm tree near the other two and not give it any water or fertilizer. This third tree will serve as the control group, and David can measure its height and trunk girth every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

David can best improve his investigation by including a control group, which will serve as a benchmark to compare the results of the experimental group. The control group should be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

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Answer:

n=6

Step-by-step explanation:

(n-18)/3 = -4

multiply by 3

n-18 = -12

add 18

n = 6

Answer:

53°

Step-by-step explanation:

As we can see that ∠3 and ∠7 are corresponding angles. Therefore,

Now calculate the angles of ∠3 and ∠7.

Now we can see that ∠3 and ∠1 are alternate angles and ∠7 and ∠1 are alternate exterior angles. Thus, we can say that

Hence the measure of ∠1 is 53°.

♦♦♦♦♦Hope it helps♦♦♦♦♦

Answer:

The answer is 64

Step-by-step explanation:

128 divided by 2 and that is the answer

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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Answer:

7/4- 39/10=

-8.6 = -8 3/5

Step-by-step explanation:

Answer:

Choice C

Step-by-step explanation:

The Equation of a circle is (x-h)^2+(y-k)^2=r^2, where h and k are the x and y coordinates respectively of the center of the circle, and r is the radius. Because the center here is (2, -5), we have (x-2)^2+(y- - 5)^2, and the two minuses become (y+5)^2. This eliminates A and B. The radius is 4, so r^2=16, and thus, we get C.

Answer:

30. $25.42

31.  $21.48

32. $23.06

Step-by-step explanation:

30.  8.54+7.50+9.38 = 25.42

31.  6.99+5.99+8.50 = 21.48

32.   8.50+5.33+9.23 = 23.06

From linear function data, we have

From exponential function data, we have

The major distinction between linear and exponential functions is the rate of their growth.

Linear growth is always at the same rate, whereas exponential growth increases exponentially over time.

The standard form for a linear equation is: ax + by + c = 0

Once we move all the variables and constants to one side, we get the standard form for a linear equation

\(y = \frac{2}{5} x - 7\\y -\frac{2}{5}x = -7\\ y - \frac{2}{5}x + 7 = 0\\\)

Hope that helps!

The values that represent the possible distance, d, in miles, between Lincoln, NE, and the third city are given as follows:

300 < d < 699.

A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.

The measurements for this problem are given as follows:

Then if 500 miles is the largest distance, we have that:

x can be between 300 and 500.

If x is the largest distance, we have that:

x can be between 501 and 699.

Then the range of possible distances is given as follows:

300 < d < 699.

(which are the distances for each case).

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Answer:

see picture

Step-by-step explanation:

Answer:

Statement A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

i dont know how to explain it but its b

1. The graphs and table that represent functions include the following: B, C, and E.

2. The set of ordered pairs that does not represent a function are:

A. {(-4, 9), (-4, 7), (1, -5), (7, -7)}.

C. {(-2, 0), (0, -2), (1, 1), (2, 0)}.

D. {(-5, 4), (-3, 4), (-1, 4), (2, 4)}.

In Mathematics and Geometry, a function is used for defining and representing the relationship that exists between two or more variables in a relation, table, ordered pairs, or graph.

Part 1.

Based on the given graphs and tables, we can logically deduce that the graph of a circle represent a relation because it does not have an inverse function. Also, tables D and F does not represent a function because the input values (domain) are not uniquely mapped to the output values (range).

Part 2.

Based on the given set of ordered pairs, we can logically deduce that only set A represent a function because the input values (domain) its uniquely mapped to the output values (range).

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Answer:

It's the first option 5%

Step-by-step explanation:

The probability of a premature baby girl being born at this hospital is,

⇒ 5%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

Now, If the likelihood of boys being born is 56%,

Then, the complement of that is the likelihood of girls being born which is,

⇒ 100% - 56% = 44%.

Since, we are given that of the baby girls born, 12% are premature, the probability of a premature baby girl  being born is:

⇒ (0.44)(0.12)

= 0.0528

⇒ 5.28%

Thus, The probability of a premature baby girl being born at this hospital is,

⇒ 5%

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Answer:

\(\frac{4^{5}}{4^{2}}\\\)

Step-by-step explanation:

\(\frac{1}{4^{3}} =4^{-3}\\\\4^{-3}\\\\\frac{4^{2}}{4^{5}}=4^{2-5}=4^{-3}\)

But 4^5/4^{2} = 4^3

Answer:

Step-by-step explanation:

Without a specific graph, it's difficult to give three specific observations. However, I can provide three general observations that can be made from a graph showing the average time a student spends playing a sport in the fall:

The average time spent playing a sport in the fall varies by sport: Depending on the graph, different sports may show different average times spent playing. For example, if the graph shows the average time spent playing soccer, football, and volleyball, we may see that soccer has the highest average time, followed by football, then volleyball.

The average time spent playing a sport in the fall may be influenced by factors such as school policies or regional climate: School policies may dictate the length of a sport's season or the number of practices and games per week, which can impact the average time spent playing. Regional climate can also impact the average time spent playing certain sports, such as outdoor sports that may be less popular in colder climates.

There may be a correlation between the average time spent playing a sport and other factors such as academic performance or overall physical activity levels: Depending on the data presented in the graph, there may be a correlation between the average time spent playing a sport and factors such as GPA or the amount of time spent on other physical activities outside of sports.

The inverse of the linear equation is y = x/58 - 12/29. After an evaluation of the inverse function at an input of 227, the output is equal to 223/58 or 3.85.

An inverse function is a type of function that is created by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of the given function y = 58x + 24, we would interchange both the input value (x) and output value (y) as follows:

y = 58x + 24

x = 58y + 24

Subtracting 6 from both sides of the function, we have the following:

x - 24 = 58y + 24 - 24

x - 24 = 58y

Dividing both sides of the function by 58, we have:

y = (x - 24)/58

y = x/58 - 24/58

y = x/58 - 12/29

At an input value of 227, we have:

y = 227/58 - 12/29

y = (227 - 24)58

y = 223/58 or 3.85.

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One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

As we know;-

1 meter is 100 cm so 0.2 meters will be calculated as:-

1 meter = 100 cm

0.2 meter = 0.2 x 100 = 20 centimeters.

Therefore One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.

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