The diameter of ball bearing are ditributed normally. The mean diameter i 81 millimeter and the variance i 16. Find the probability that the diameter of a elected bearing i greater than 85 millimeter. Round your anwer to four decimal place

The value of people in this proportion is equal to 165/10 or 10.67.

In Mathematics, a proportion can be defined as an equation which is typically used to represent (indicate) the equality of two ratios. This ultimately implies that, proportions can be used to establish that two ratios are equivalent and solve for all unknown quantities.

By applying direct proportion to the given information, we have the following mathematical expression:

3/10/p = 4/5/1/4

3/10 × p = 4/5 × 4

3p/10 = 16/5

Cross-multiplying, we have the following:

15p = 160

People, p = 160/15

People, p = 10.67

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Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

The amount of milk Jonah bring is 8 quarts of milk

From the question, we have the following parameters that can be used in our computation:

Jonah brought 16 pints of milk to share with his soccer teammates at halftime.

This means that

Milk = 16 pints of milk

By the metric units of conversion, we have

1 pint of milk = 0.5 quart of milk

Substitute the known values in the above equation, so, we have the following representation

Milk = 16 quarts of milk * 0.5

Evaluate

Milk = 8 quarts of milk

Hence, the amount of milk is 8 quarts of milk

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Answer:

1). Other line is, y = \(\frac{1}{3}x+5\)

2). Solution of the system is (3, 6)

Step-by-step explanation:

From the table (1),

Let the equation of the line from the given table is,

y - y' = m(x - x')

Where m = slope of the line

(x', y') is a point lying on the line.

Choose two points from the table which lie on the line.

Let the points are (0, 5) and (3, 6)

Slope = m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

                 = \(\frac{5-6}{0-3}\)

                 = \(\frac{1}{3}\)

Therefore, equation of the will be,

y - 5 = \(\frac{1}{3}(x-0)\)

y = \(\frac{1}{3}x+5\) -------(1)

Let the other line from the table (2) is,

y - y" = m'(x - x")

Two points taken from this table are (0, 7) and (3, 6)

m' = \(\frac{7-6}{0-3}\)

    = \(-\frac{1}{3}\)

Equation of the line will be,

y - 7 = \(-\frac{1}{3}(x-0)\)

y = \(-\frac{1}{3}x+7\) -------(2)

Therefore, equation of the other line will be, y = \(\frac{1}{3}x+5\)

By adding equations (1) and (2),

y + y = \(-\frac{1}{3}x+\frac{1}{3}x+5+7\)

2y = 12

y = 6

From equation (1),

6 = \(\frac{1}{3}x+5\)

\(\frac{1}{3}x=7-6\)

x = 3

Therefore, solution of the system is (3, 6).

Answer:

The first line is 1/3x and 5. For the second line the answer is (3,6).

Answer:

FH = 6.0

FG = 3.6

m<H = 31°

Step-by-step explanation:

sin Θ = opp/hyp

cos Θ = adj/hyp

sin 59° = FH/GH

sin 59° = FH/7

FH = 7 × sin 59°

FH = 6.0

cos 59° = FG/GH

cos 59° = FG/7

FG = 7 × cos 59°

FG = 3.6

m<F + m<G + m<H = 180°

90° + 59° + m<H = 180°

m<H = 31°

The histogram representing the data is attcwhwd in the picture below.

Answer:

C On exactly 25% of these days, Shane drank 3 to 4 glasses of water.

Step-by-step explanation:

The number of 8 - ounce glasses is represented on the x - axis and the number of days on the y - axis.

From the histogram ;

Shane drank 1 - 2 glasses on exactly 1 day

Shane drank 3 - 4 glasses on exactly 3 days

Shane drank 5 - 6 glasses on exactly 6 day

Total number of days = 12

60% of 12 = 7.2

On exactly 60% of the days, which is 7.2 days, number of glasses drunk isn't covered by the histogram

25% of 12 ; 0.25 * 12 = 3 days

From the histogram, number of glasses consumed is 3 - 4 glasses ; which is the only true statement about the histogram in the options given.

Solid A has five(5) rectangular blocks that are co-joined. The dimension of each, is 45miles by 90miles.

Thus,

Solid B has five(5) rectangular blocks that are co-joined. The dimension of each, is 30mi by 60mi.

Thus,

The ratio of the T.S.A of the similar solids is given below:

Hence, the correct option is Option A

Answer:

OPTION A is correct

39 ounces

Step-by-step explanation:

Given:

The amount of water in the pitcher= 32 ounces

The amount of lemon juice in the pitcher = 7.15 ounces

We were to calculate the most reasonable estimate for the amount of liquid in the pitcher

To do this we need to sum up the Amount of water and Amount of lemon juice in the pitcher because the water is a liquid as well as the lemon juice which is

32 ounces + 7.15 ounces

=39.15 ounces

Therefore, the Estimated amount of liquid in the pitcher is approximately 39 ounces

Step-by-step explanation:

3x + 4 + 2x +7

= 3x + 2x + 4 + 7

= 5x + 11

the probability of at least two 6's appearing is: P(B) = 1 - [P(rolling one 6) + P(rolling zero 6's)]

To compare the probabilities of the given events, let's analyze each one separately:

Event A: At least one 6 appears when 6 fair dice are rolled.

To calculate the probability of this event, we can consider the complement event, which is the probability of no 6 appearing when rolling 6 dice.

The probability of not rolling a 6 on a single fair die is 5/6 (since there are 6 possible outcomes, and only 1 is a 6). Since we have 6 dice, the probability of not rolling a 6 on any of them is (5/6)^6.

Therefore, the probability of at least one 6 appearing is:

P(A) = 1 - P(no 6 on any die) = 1 - (5/6)^6

Event B: At least two 6's appear when 12 fair dice are rolled.

Similarly, we can consider the complement event, which is the probability of rolling one or zero 6's when rolling 12 dice.

The probability of rolling one 6 on a single fair die is 1/6, and the probability of not rolling a 6 is 5/6. Using the binomial distribution, we can calculate the probability of rolling one 6 and eleven non-6's in 12 dice rolls:

P(rolling one 6) = (12 choose 1) * (1/6)^1 * (5/6)^11

The probability of rolling zero 6's is:

P(rolling zero 6's) = (12 choose 0) * (1/6)^0 * (5/6)^12

Therefore, the probability of at least two 6's appearing is:

P(B) = 1 - [P(rolling one 6) + P(rolling zero 6's)]

To determine which event has the higher probability, we compare P(A) and P(B). Whichever probability is higher, the corresponding event has the higher probability.

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After one year, the club had approximately 123123 members. After two years, the club had approximately 149149 members. After three years, the club had approximately 180180 members.To calculate the number of members after three years, multiply the initial number of members (101010) by the factor of 1.21.21 three times

1. To calculate the number of members after one year, multiply the initial number of members (101010) by the factor of 1.21.21:

101010 x 1.21.21 = 12312

2. To calculate the number of members after two years, multiply the initial number of members (101010) by the factor of 1.21.21 twice:

101010 x 1.21.21 x 1.21.21 = 149149

3. To calculate the number of members after three years, multiply the initial number of members (101010) by the factor of 1.21.21 three times:

101010 x 1.21.21 x 1.21.21 x 1.21.21 = 180180

After one year, the club had approximately 123123 members. After two years, the club had approximately 149149 members. After three years, the club had approximately 180180 members.

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The value of x using Pythagorean theorem is 14.05 units

An equation shows how two or more numbers and variables are related to each other.

Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:

hypotenuse² = adjacent² + opposite²

In the diagram, using Pythagoras theorem:

22² = (x + 1)² + (x + 2)²

484 = x² + 2x + 1 + (x² + 4x + 4)

2x² + 6x + 5 = 484

2x² + 6x - 479 = 0

x = 14.05

The value of x is 14.05 units

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Therefore, the dimensions of the pool are 30 meters in length, 12 meters in width, and 3 meters in depth.

To find the dimensions of the rectangular pool, we first need to determine the ratio of the length, width, and depth. We are given that the ratio is 10:4:1. We can represent this ratio as:
Length = 10x
Width = 4x
Depth = x

Where x is a common factor that we will use to determine the actual measurements of the pool.
Now, we are given that the volume of the pool is 1,080 cubic meters. We can use the formula for the volume of a rectangular prism, which is:
Volume = Length x Width x Depth
Substituting the values we have for the length, width, and depth, we get:
1,080 = (10x) x (4x) x (x)
Simplifying the equation, we get:
1,080 = 40x^3
Dividing both sides by 40, we get:
27 = x^3
Taking the cube root of both sides, we get:
x = 3

Now that we know x is equal to 3, we can find the actual measurements of the pool by substituting x back into the original ratio we were given.
Length = 10x = 10(3) = 30 meters
Width = 4x = 4(3) = 12 meters
Depth = x = 3 meters

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The amplitude of vibrations after a very long time is 0.

Given data: Mass attached to a spring = 4 kg. Spring constant = 100 N/m.\(Force = f(t) = 12e^(-2t)cos7t\) .In the absence of damping.(a) Find the position of the mass when \(t = π\). (b) What is the amplitude of vibrations after a very long time?

Solution: (a) The differential equation of motion of the given system is,\(mx'' + kx = f(t)\).

Here, m = Mass attached to the spring. k = Spring constant.\(f(t) = 12e^(-2t)cos7t\)

Differentiating w.r.t. t, we get,\(mx' + kx = f'(t)\) Differentiating f(t), we get,\(f'(t) = -24e^(-2t)cos7t - 84e^(-2t)sin7t\). Substituting the given data in the above equation, we get,\(mx' + kx = -24e^(-2t)cos7t - 84e^(-2t)sin7t\) ……(1)

Here,x is the displacement of the spring from its equilibrium position at any time t.

Now, the complementary function of equation (1) is,\(mx_c'' + kx_c = 0\). The characteristic equation of equation (2) is,\(mr² + k = 0\)

On solving the characteristic equation, we get,\(r = ±√(k/m) = ±√(100/4) = ±5i\). Let the complementary function of equation (1) is,\(x_c = A cos5t + B sin5t\) Putting \(x_c\) in equation (1), we get\(,A = 0 and B = -3/13\). Position of mass when \(t = π\) is given by x = x_p + x_c ,Where,x_p = Particular integral of equation (1).

mx_p'' + kx_p = f(t)

mx_p'' + kx_p = 12cos7t

Comparing coefficients, we get,

x_p = (3/170)(3cos7t + 4sin7t).

Thus, the position of the mass when t = π is given by,

x = x_p + x_c = (3/170) \(e^{(-2\pi)}\)(3cos7π + 4sin7π) + (-3/13)sin5π= (3/170) \(e^{(-2\pi)}\) × (-3) + 0= (9/170) \(e^{(-2\pi)}\)

(Ans)(b) The amplitude of vibrations after a very long time is given by,

A = (f(t) / k)\(\frac{1}{2}\). Putting the given data in the above equation, we get,A = (12\(e^{(-2t)}\)cos7t / 100)\(\frac{1}{2}\)For a very long time t, we know that the amplitude of vibrations will be maximum when cos7t = 1So,A = (12\(e^{(-2t)}\) / 100)\(\frac{1}{2}\) = (3/5)\(e^{(-t)}\) . On substituting t = ∞ in the above equation, we get,

A = 0 (Ans)Therefore, the amplitude of vibrations after a very long time is 0.

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Answer: awnser is m= 1/6

Step-by-step explanation: m = add the terms which is  -1 -5m-4+6 m= 1-5m

step 2 then rerange the terms  to m= 1-5m to m = 5m + 1

step 3  add 5m to both sides m= -5m+1 to m + 5m= -5m + 1  + 5m

step 4  simplify and combine like terms 6m= 1

step 5 divide both sides by the same factor 6m= 1  6m/6 =  1/6

step 6 simplify Cancel terms that are in both the numerator and denominator so it is m= 1/6 is the correct awnser mark me brainliest please

we write the iterated integral of a continuous function f over the region using the order dy dx. Since the region is symmetric with respect to the x-axis, we can integrate over the top half of the region and then multiply by 2.
Here, "region" refers to the part of the circle of radius 5 centered at the origin that lies in the first quadrant, "integral" refers to the calculation of the area or volume under a curve or surface, and "quadrant" refers to one of the four regions obtained by dividing a plane into four equal parts by the x- and y-axes.

Step 1: Sketch the region
The region (R) is in the first quadrant, which means x ≥ 0 and y ≥ 0. The region is bounded by a circle with radius of 5 centered at the origin (0,0). This circle can be represented by the equation x^2 + y^2 = 25.

Step 2: Write the iterated integral
To find the iterated integral of a continuous function f over the region R using the order dy dx, we first need to find the bounds for y and x.
The limits of integration for y are from 0 to the y-coordinate of the top half of the circle, which is √(25-x^2). The limits of integration for x are from 0 to 5. Therefore, the iterated integral is:
∫ from 0 to 5 ∫ from 0 to √(25-x^2) f(x,y) dy dx

For y: Since R is in the first quadrant and bounded by the circle, the lower bound for y is y = 0. The upper bound for y, given x, is the equation of the circle's top half, solving for y: y = sqrt(25 - x^2).

For x: Since R is in the first quadrant, the lower bound for x is x = 0, and the upper bound is x = 5 (the radius of the circle).

Now we can write the iterated integral using these bounds:
∫(from x=0 to x=5) ∫(from y=0 to y=sqrt(25-x^2)) f(x,y) dy dx

This iterated integral represents the continuous function f over the specified region R in the first quadrant, using the order dy dx.

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total spent is = 45$

let money spent on snack is x

let money spent on rides is y

so the equation of the expenses is ,

x + y = 45

thus, the answer is

x + y = 45

Answer:

It's 111 degrees

Step-by-step explanation:

The unknown angle is alternating with the 111 degrees angle

The amount he had to pay if he have to purchase a laptop today that is the same value as the one he saw in the ad is $ 390.24.

Given that:-

Price of the laptop after 1 year = $ 400.

Inflation rate = 2.5 %

We have to find the amount he had to pay if he have to purchase a laptop today that is the same value as the one he saw in the ad.

Let the price he had to pay be x.

Hence, we can write,

x + (x*(2.5)*1)/100 = 400

x(1 + 1/40) = 400

x(41/40) = 400

x = 400*40/41 = $ 16000/41 = $ 390.24.

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Answer:

Step-by-step explanation:

(-4 + 2)/2 =-2/2 = -1

(3 - 1)/2= 2/2 = 1

(-1, 1)

Based on the given side lengths of 8, 11, and 12, none of them are equal. Therefore, we can classify the triangle as a Scalene Triangle.

To classify a triangle by its angles and sides, we can use the properties and definitions of different types of triangles. Let's analyze the given triangle with sides measuring 8, 11, and 12 and angles measuring 45 degrees, 65 degrees, and 70 degrees.

Classification by angles:

Acute Triangle: An acute triangle has all three angles less than 90 degrees.

Obtuse Triangle: An obtuse triangle has one angle greater than 90 degrees.

Right Triangle: A right triangle has one angle exactly 90 degrees.

Based on the given angles of 45 degrees, 65 degrees, and 70 degrees, none of them are greater than 90 degrees, so we can classify the triangle as an Acute Triangle.

Classification by sides:

Equilateral Triangle: An equilateral triangle has all three sides of equal length.

Isosceles Triangle: An isosceles triangle has two sides of equal length.

Scalene Triangle: A scalene triangle has all three sides of different lengths.

Based on the given side lengths of 8, 11, and 12, none of them are equal. Therefore, we can classify the triangle as a Scalene Triangle.

In summary, based on the given measurements, the triangle can be classified as an Acute Scalene Triangle. We determined this by comparing the angles to the definitions of acute, obtuse, and right triangles, and comparing the side lengths to the definitions of equilateral, isosceles, and scalene triangles.

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Answer:

Q is not a function

Step-by-step explanation:

In this case the answer is very simple . .

We must apply the distributive property of multiplication.

That is the solution. .

O sin(0.0005) ≈ 0.0005. The line tangent to the graph of f(x) = sin x at (0,0) is y = x.

The line y = x touches the graph of f(x) = sin x at exactly one point, (0,0). This means that the point (0,0) is on the line y = x and the slope of the line y = x is equal to the derivative of the function f(x) = sin x evaluated at x = 0. The slope of the line y = x is 1, so the derivative of f(x) = sin x evaluated at x = 0 is 1.

The line y = x is the best straight line approximation to the graph of f(x) = sin x for x near 0. This is because the first derivative of sin x evaluated at x = 0 is 1, which is the same as the slope of the line y = x. Therefore, the tangent line to the graph of f(x) = sin x at (0,0) is y = x.

Finally, O sin(0.0005) ≈ 0.0005. This is because sin x is approximately equal to x for small values of x. When x = 0.0005, sin x is approximately equal to 0.0005. Therefore, O sin(0.0005) ≈ 0.0005.

In summary, the line tangent to the graph of f(x) = sin x at (0,0) is y = x. The line y = x touches the graph of f(x) = sin x at exactly one point, (0,0). The line y = x is the best straight line approximation to the graph of f(x) = sin x for x near 0. O sin(0.0005) ≈ 0.0005.

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Answer:

13.9 ft

Step-by-step explanation:

Answer:

\(a_{n}\) = 5n + 5

Step-by-step explanation:

The nth term of an arithmetic progression is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and d = a₂ - a₁ = 15 - 10 = 5 , then

\(a_{n}\) = 10 + 5(n - 1) = 10 + 5n - 5 = 5n + 5

Answer:

192 divided by 44 = 4.36

So 5 baskets

Step-by-step explanation:

Answer:

75 cu in

Step-by-step explanation:

the formula for volume is V = l w h (volume equals length times width times height) and can also be written V = B h (volume equals the area of the base times the height). Notice that the version, V = l w h is only true for rectangular prisms and cubes.

V = L x W x H

V = 5 x 5 x 3

V = 75

Answer: 75 in³

Step-by-step explanation:

    We will use the given formula to solve for volume by substituting and multiplying.

V = LWH

V = (5 in)(5 in)(3 in)

V = 75 in³