Suppose the distance an athlete throws a hammer follows a normal distribution with mean 50 feet and standard deviation 5 feet. What is the probability he throws it between 50 feet and 60 feet? Give your answer to 4 decimal places.?

The indefinite integral is: ∫(1/(x^2+1))dx = ln|x^2 + 1| + c, where c is the constant of integration

To find the indefinite integral by making a change of variables, we can use the substitution method. Let u be the denominator of the integrand, so we can write:

∫(1/(x^2+1))dx = ∫(1/u) * (du/dx) dx

To find du/dx, we differentiate both sides of u = x^2 + 1 with respect to x:

du/dx = 2x

Substituting this into our integral, we get:

∫(1/u) * (du/dx) dx = ∫(1/u) * (2x) dx

Now we can make a change of variables by letting f(u) = ln|u|. Using the chain rule, we have:

df/du = 1/u

Substituting this into our integral, we get:

∫(1/u) * (2x) dx = 2∫(df/du) * x dx

Integrating with respect to x, we get:

2∫(df/du) * x dx = x * ln|u| + c

Substituting u = x^2 + 1, we get:

x * ln|u| + c = x * ln|x^2 + 1| + c

Therefore, the indefinite integral is:

∫(1/(x^2+1))dx = ln|x^2 + 1| + c, where c is the constant of integration.

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Answer:

b) 70 feet

Step-by-step explanation:

let me know if you want an explanation please :)

Answer:

the answer will be a 375

Step-by-step explanation:

Answer:

Step-by-step explanation:

Question

Find the perimeter of a triangle with vertices A(2,5) B(2,-2) C(5,-2). Round your answer to the nearest tenth and show your work.​

perimeter of a triangle = AB+AC+BC

Using the distance formula

AB = sqrt(-2-5)²+(2-2)²

AB = sqrt(-7)²

AB =sqrt(49)

AB =7

BC = sqrt(-2+2)²+(2-5)²

BC = sqrt(0+3²)

BC =sqrt(9)

BC =3

AC= sqrt(-2-5)²+(2-5)²

AC= sqrt(-7)²+3²

AC =sqrt(49+9)

AC =sqrt58

Perimeter = 10+sqrt58

each child plays for 45 minutes.

To determine the number of minutes each child plays, we can divide the total playing time (90 minutes) by the total number of children (5). Since only two children can play at a time, we need to divide the playing time equally among the pairs of children.

Let's calculate:

Number of pairs of children = Total number of children / 2 = 5 / 2 = 2 pairs

Minutes each child plays = Total playing time / Number of pairs of children

Minutes each child plays = 90 minutes / 2 pairs = 45 minutes

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Answer:

Step-by-step explanation:

Answer:

sdsgsdfes

Step-by-step explanation:

Answer:

Infinite

Step-by-step explanation:

if we take any no. instead X gives same equivalent equation

The relation S={(a,b)∈R×R:a²+b²=1} is not an equivalence relation on the set of real numbers R.

To show that S is not an equivalence relation, we need to demonstrate that it fails to satisfy one or more of the properties of an equivalence relation: reflexivity, symmetry, and transitivity.

Reflexivity: For a relation to be reflexive, every element of the set should be related to itself. However, in the case of S, there are no real numbers (a, b) that satisfy the equation a² + b² = 1 for both a and b being the same number. Therefore, S is not reflexive.

Symmetry: For a relation to be symmetric, if (a, b) is related to (c, d), then (c, d) must also be related to (a, b). However, in S, if (a, b) satisfies a² + b² = 1, it does not necessarily mean that (b, a) also satisfies the equation. Thus, S is not symmetric.

Transitivity: For a relation to be transitive, if (a, b) is related to (c, d), and (c, d) is related to (e, f), then (a, b) must also be related to (e, f). However, in S, it is not true that if (a, b) and (c, d) satisfy a² + b² = 1 and c² + d² = 1 respectively, then (a, b) and (e, f) satisfy a² + b² = 1. Hence, S is not transitive.

Since S fails to satisfy the properties of reflexivity, symmetry, and transitivity, it is not an equivalence relation on the set of real numbers R.

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The probability of obtaining numbers greater or equal to four and head is 0.25 or 25%. The restaurant can offer 24 different meals.

When two dice and one coin are rolled, there are 6 possible outcomes for the dice (1, 2, 3, 4, 5, 6) and 2 possible outcomes for the coin (head, tail). To find the probability of getting numbers greater or equal to four and head, we need to count the favorable outcomes.

Favorable outcomes: {(4, head), (5, head), (6, head)}

Total outcomes: 6 (for dice) * 2 (for coin) = 12

Probability = Favorable outcomes / Total outcomes = 3 / 12 = 1/4 = 0.25

Therefore, the probability of obtaining numbers greater or equal to four and head is 0.25 or 25%.

The number of different meals the restaurant can offer can be calculated by multiplying the number of options for each category: pie, salad, and drink.

Number of different meals = Number of pie options * Number of salad options * Number of drink options

= 2 (types of pie) * 4 (types of salad) * 3 (types of drink)

= 24

Therefore, the restaurant can offer 24 different meals.

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By using a sampling technique  we ensure that we choose a sample of students that is representative of all 8:00 am classes.

There are  varieties of sampling strategies: chance sampling includes random selection, permitting you to make sturdy statistical inferences approximately the complete organization. Non-opportunity sampling entails non-random selection primarily based on convenience or different standards, permitting you to without problems gather records.

Random sampling is part of the sampling technique wherein every sample has an same possibility of being chosen. A sample chosen randomly is meant to be an unbiased representation of the overall population.

explanation;

we conclude the

Since the students' lecture hallsare on different building the samples are

Dividing the students into groups, the students will be grouped by the buildings of their lecture halls.

The number of students in each building is:

There are 100 students in each building

Then select at random an equal proportion of student from each building let 20 students in each building.

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Answer:

1/24

Step-by-step explanation:

20) 1/6 / 4 = 1/6 * 1/4 = 1/24

Answer:

\(\:\frac{1}{5}\div 2=\frac{1}{5}\cdot \:\frac{1}{2}=\frac{1}{10}\)

\(\:\frac{1}{6}\div \:4=\frac{1}{6}\cdot \frac{1}{4}=\frac{1}{24}\)

Step-by-step explanation:

Question 18

We know that the fraction rule is:

\(\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\)

Thus,

\(\:\frac{1}{5}\div 2=\frac{1}{5}\cdot \:\frac{1}{2}=\frac{1}{10}\)

Question 20

We know that the fraction rule is:

\(\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\)

Thus,

\(\:\frac{1}{6}\div \:4=\frac{1}{6}\cdot \frac{1}{4}=\frac{1}{24}\)

The function u(x, y) = ex cos(ky) is a solution of Laplace's equation Uxx + Uyy = 0.
b. The function u(x, y) = ekxek²y is a solution of the heat equation Uxx - Uy = 0.
c. The function u(x, y) = ekxe-ky is a solution of the wave equation uxx - Uyy = 0.
d. The function u(x, y) = x² + (1 - k) is a solution of Poisson's equation Uxx + Uyy = 1.

a. To show that u(x, y) = ex cos(ky) is a solution of Laplace's equation Uxx + Uyy = 0, we calculate the second partial derivatives Uxx and Uyy with respect to x and y, respectively, and substitute them into the equation. By simplifying the equation, we can see that the terms involving ex cos(ky) cancel out, verifying that the function satisfies Laplace's equation.
b. For the heat equation Uxx - Uy = 0, we calculate the second partial derivatives Uxx and Uy with respect to x and y, respectively, for the function u(x, y) = ekxek²y. Substituting these derivatives into the equation, we observe that the terms involving ekxek²y cancel out, confirming that the function satisfies the heat equation.
c. To show that u(x, y) = ekxe-ky is a solution of the wave equation uxx - Uyy = 0, we calculate the second partial derivatives Uxx and Uyy and substitute them into the equation. After simplifying the equation, we find that the terms involving ekxe-ky cancel out, indicating that the function satisfies the wave equation.
d. For Poisson's equation Uxx + Uyy = 1, we calculate the second partial derivatives Uxx and Uyy for the function u(x, y) = x² + (1 - k). Substituting these derivatives into the equation, we find that the terms involving x² cancel out, leaving us with 0 + 0 = 1, which is not true. Therefore, the function u(x, y) = x² + (1 - k) does not satisfy Poisson's equation for any constant k.

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Answer:

y=90 degrees

Step-by-step explanation:

x+y+70=180 degrees  ==> these three angles make up a triangle, and the

                                         the total sum of angles in a triangle is 180 degrees

Notice that y is on a straight line?

Straight lines are 180-degree angles called straight angles.

Hence:

(180-y)+x+70=180  ==>  these three angles also make up a triangle, and the

                                        the total sum of angles in a triangle is 180 degrees

180-y+x+70=x+y+70  ==> since both expressions equal 180, they both are

                                         equal to each other

180-y+x+70 + y = x+y+70 + y ==> add y on both sides to isolate y to one side

180 - y + y + x + 70 = x + y + y + 70  ==> simplify

180 + x + 70 = x + 2y + 70

180+x+70 - x = x+2y+70 - x  ==> subtract x on both sides to eliminate x

180 + x - x + 70 = x - x + 2y + 70  ==> simplify

180 + 70 = 2y + 70

180 + 70 - 70 = 2y + 70 - 70 ==> subtract both sides by 70 to simplify the equation

180 = 2y

y = 180/2

y = 90 degrees

The volume of the right prism with a base area of 10 square feet and a height of 6 feet is 60 cubic feet.

A prism is a polyhedron that has a base and a top face that are the same in size and shape, with sides connecting them that are rectangles in a right prism.

A right prism is a prism in which all of the side faces are perpendicular to the base.

Therefore, the height of the right prism is perpendicular to the base as well.

A right prism has a volume equal to the product of the base area and the height.

This formula can be represented as:

V = Bh

Here, B represents the area of the base, and h represents the height.

The volume of the right prism can be found by multiplying the area of the base by the height of the prism, according to the formula:

V = Bh.

In this problem, the area of the base of the prism is given to be 10 square feet.

The height of the prism is 6 feet.

We can simply substitute these values into the formula to obtain the volume of the right prism as follows:

V = BhV

   = 10 × 6V

   = 60

Therefore, the volume of the right prism is 60 cubic feet.

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Answer:

x = 21

y = 65

Step-by-step explanation:

L = Z = 44

J = W

4x - 13 = 71

4x = 84

x = 21

J + K + L = 180

71 + K + 44 = 180

115 + K = 180

K = 65

Y = K

Therefore, y = 65

P(X = 2) is not equal to P(X = 3)

To show that P(X = 2) = P(X = 3) in a binomial distribution with n = 5 and p = 0.5, we need to use the formula for the probability mass function (PMF) of a binomial distribution.

The PMF of a binomial distribution is given by the formula:

P(X = k) = C(n, k) *\(p^k * (1-p)^{(n-k)}\)

where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) represents the binomial coefficient.

In our case, n = 5 and p = 0.5. Let's calculate P(X = 2) and P(X = 3) using the formula:

P(X = 2) = \(C(5, 2) * (0.5)^2 * (1-0.5)^{(5-2)}\)

        = 10 * 0.25 * 0.125

        = 0.3125

P(X = 3) = C(5, 3) * \((0.5)^3 * (1-0.5)^{(5-3)}\)

        = 10 * 0.125 * 0.125

        = 0.125

As we can see, P(X = 2) = 0.3125 and P(X = 3) = 0.125.

Therefore, P(X = 2) is not equal to P(X = 3) in this specific case of a binomial distribution with n = 5 and p = 0.5.

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"Study smart one triangle has vertices a,b, and c. another has vertices t, r, and i, are the 2 triangles similar?"

It is not possible to determine if the two triangles are similar based on the information provided.

In order for two triangles to be similar, they must have the same shape but not necessarily the same size. The sides of the two triangles must be in proportion and corresponding angles must be congruent.

Similarity between two triangles can be determined by using the criterion of AAA similarity or SAS similarity, which states that two triangles are similar if:

without knowing the measures of the angles and sides of the triangles, it is impossible to determine if the two triangles are similar.

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The equation of the line passing through the points (−5,5) and (8,5) will be y = 0x + 5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation is passing through the points  (−5,5) and (8,5). The equation of the line will be written below,

Y = mx + c

Slope = m  = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = m  =( 5 -5  ) / ( 8 + 5)

Slope = m  = 0

The y-intercept will be calculated as,

Y = 0x + c

5 = 0 + c

C = 5

The equation of the line is,

Y = mx + c

Y = 0x + 5

Therefore, the equation of the line passing through the points (−5,5) and (8,5) will be y = 0x + 5

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Answer:

put a dot on the following points ( -1, -3) (0, -2) (1, -1) and (2, 0)

Step-by-step explanation:

Answer:

B 2 hours of 130 miles is the 60th term of the y intercept!

Step-by-step explanation:

Have a great day

Hopefully this helped if not HMU and I will get u a better answer!

:) <3

Answer: Samantha will pass Herbert after 2 hours, and they each will have traveled 130 miles.

Step-by-step explanation:

\({ \bold{ \sqrt[3]{V}}} \)

Step-by-step explanation:

\({ \green{ \sf{V = s³}}}\)

Cube on both sides, then

\({ \green{ \sf{s = \sqrt[3]{V}}}} \)

Answer:  3√2

Step-by-step explanation:

The middle line is also 3 so if you use a^2 + b^2 = c^2 you can find the hypotenuse

Answer:

\(x = \frac{57}{29} \ , \ y = \frac{12}{29}\)

Step-by-step explanation:

                            2x + 5y = 6     --------( 1 )

                            5x - 2y = 9     --------( 2 )

                        _____________

     ( 1 ) x 5 =>     10x + 25y = 30   -----------( 3 )

     ( 2 ) x 2 =>    10x - 4y = 18       ----------- ( 4 )

                       ______________

    ( 3 ) - ( 4 ) =>    0 +  29y = 12

                                   \(y = \frac{12}{29}\)

Substitute y in ( 1 ) =>

                            \(2x + (5 \times \frac{12}{29}) = 6\\\\2x + \frac{60}{29} = 6\\\\2x = 6 - \frac{60}{29}\\\\2x = \frac{174 - 60}{29}\\\\x = \frac{114}{29 \times 2}\\\\x = \frac{57}{29}\)

Answer:

74 feet

Step-by-step explanation:

24^2 + 70^2 = 74^2

Pythagorean Theorem

To solve the equation -2.5(e + 17.4) = -50, we can use algebraic techniques to isolate the variable e on one side of the equation.

First, we can simplify the left-hand side of the equation by distributing the -2.5 to the expression inside the parentheses:

-2.5e - 2.5(17.4) = -50

Next, we can simplify the expression on the left-hand side by multiplying:

-2.5e - 43.5 = -50

To isolate the variable e, we can add 43.5 to both sides of the equation:

-2.5e = -6.5

Finally, we can solve for e by dividing both sides of the equation by -2.5:

e = 2.6

Therefore, the solution to the equation -2.5(e + 17.4) = -50 is e = 2.6.

Answer:

x + y = 150

x = 80 + y

Step-by-step explanation:

x (guitar) + y (piano) = total 150 min

x (guitar) = 80 min + y (piano)

Answer:

If I am understanding this correctly you are asking that "A computer costs $400.000 (rounded) and is given a 15% discount if it is paid by cash?" then the sale price of the computer with the discount would be $60.00

Step-by-step explanation:

It can be easily calculated by dividing 15 by 100 and multiplying the answer with 1400 to get 60.