The diameter of the ball bearings varies according to a distribution that is approximately Normal
with mean 11.5 mm and standard deviation 0.05 mm. Two ball bearings are randomly selected. Find the probability that the difference in the diameters of the two ball bearings is less than 0.06 mm.

The final value of the iterated integral is 945[tex]\sqrt{10}[/tex].

To calculate the iterated integral, we need to evaluate the inner integral with respect to y first and then the outer integral with respect to x.

The inner integral is to be integrated with respect to y is:

∫(6xy[tex]\sqrt{(x^2 + y^2)}[/tex])dy from 0 to 1 = [3y([tex]x^2 + y^2[/tex][tex])^{(3/2)}[/tex])] from 0 to 1

= [3y*[tex](x^2 + y^2[/tex][tex])^{(3/2)}[/tex]] from 0 to 1

= 3(1)*([tex]x^2[/tex] + 1[tex])^{(3/2)}[/tex]

= 3([tex]x^2[/tex] + 1[tex])^{(3/2)}[/tex]

Now, we can use this result as the inside function to evaluate the outer integral with respect to x.

The outer integral is to be integrated with respect to x is:

∫(3([tex]x^2[/tex] + 1[tex])^{(3/2)}[/tex])dx from 0 to 3

= [x([tex]x^2[/tex] + 1[tex])^{(5/2)}[/tex]] from 0 to 3

= [3[tex](3^2 + 1[/tex] [tex])^{(5/2)}[/tex] - 0(0^2 + 1[tex])^{(5/2)}[/tex]]

= [3(10 - 0]

= [945[tex]\sqrt{10}[/tex])]

So the final value of the iterated integral is 945[tex]\sqrt{10}[/tex].

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The complete question is -

Calculate the iterated integral. Integral from 0 to 3 integral from 0 to 1 of 6xy[tex]\sqrt{(x^2 + y^2)}[/tex] dy dx

The value of sum of squared deviations is 12.

The given population is 1,1,1,5

First find the mean:

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Mean = (Sum of all the observations/Total number of observations)

Mean=[tex]\frac{1+1+15}{4}=\frac{8}{4}=2[/tex]

The Mean is 2.

The symbol of mean is usually given by the symbol [tex]\bar x[/tex]. The bar above the letter x, represents the mean of x number of values.

[tex]\bar X[/tex] = (Sum of values ÷ Number of values)

Subtract the mean from each observation and square the resulting difference. Then add the differences to get SS:

SS=[tex](1-2)^{2}+ (1-2)^{2}+ (1-2)^{2}+ (5-2)^{2}[/tex]

[tex]=1+1+1+(3)^{2} \\=3+9\\=12[/tex]

Therefore, the value of SS is 12.

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Therefore  , solution of ratio problem is 5760 m & 5.76 km, respectively, are the distances covered per hour for the two halves.

As a/b, a ratio shows the  variable relationship between two numbers. When two ratios are equal, as when a/b = c/d, we get a proportion. Mathematical issues involving the unit numbers of the quantities can be resolved using ratio and proportion.

Here,

The ratio approach can be used to solve the above problem as follows:

(A) A 1.6 m/s walking speed is typical.

The calculation for the speed in meters per hour is

1/3600 of an hour is equal to one second.

Take the following 1.6:3600 ratio as an example:

1.6 ÷ 1/3600

= 3600 × 1.6

= 5760

The typical walking speed is 1.6 m/s.

It implies a speed of 1.6 meters per second.

Now, 1 m equals 1/1000 km.

=> 1.6 m = 1.6/1000 km

Moreover, one second is equal to three thousand six hundredths of an hour.

As a result, the distance traveled in kilometers per hour can be calculated by using the following ratio:

1.6/1000 ÷ 1/3600

= (3600 × 1.6)/1000

= 5.76

Therefore, 5760 m and 5.76 km, respectively, are the distances covered per hour in meters and kilometers.

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The ratio of people in its simplest form is 1 : 3

The ratio of benches in its simplest form is 1 : 4

A ratio is the number representing a comparison between two named things.

It also refers to the relative magnitudes of two quantities usually expressed as a quotient.

For instance, if there are 12 students in a class which includes 8 girls and 4 boys,

The ratio of girls to all students = 8 : 12

= 8/12

= 2/3

= 2 : 3

The ratio of boys to girls = 4 : 8

= 4/8

= 1/2

= 1 : 2

The ratio of all students to boys = 12 : 4

= 12/4

= 3/1

= 3 : 1

Hence,

People = 6 : 18

= 6 / 18

= 3 / 9

= 1/3

= 1 : 3

Benches = 3 : 12

= 3 / 12

= 1 / 4

= 1 : 4

Therefore, the ratio of people and benches in its simplest form is 1 : 3 and 1 : 4 respectively.

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The completed statement would be

12ft/sec = 7.2 yd/min.

What is the unit conversion?

Unit conversion is the process of changing a measurement from one unit to another, while maintaining the same numerical value. It is used to convert measurements from one system of units to another, such as from metric units to imperial units, or from feet to meters.

To convert feet per second to yards per minute, we need to multiply the value in feet per second by the conversion factor of 1 yard/3 feet and then divide the result by the conversion factor of 1 minute/60 seconds.

12 ft/sec = (12 ft/sec) * (1 yard/3 feet) * (1 min/60 sec) = (12*1/3) * (1/60) = 4/5 = 0.8.

So, 12 ft/sec is equal to 0.8 yards per minute. Rounded to the nearest hundredth, this is 7.2 yards per minute

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The left page number is 180 and the right page number is 181.

What is consecutive integers?

Consecutive integers or consecutive numbers are the terms used to describe the sequence of numbers. In this case, the integers are arranged in ascending order from smallest to highest. The following are a few examples: -4, -3, 2, 1, 0, 1, 2, 3, 4.

Given:

The left and right page numbers of an open book are two consecutive interfere whos sum is 361.

We have to find the page numbers.

Let

The left page number is n.

The right page number is n + 1.

As the sum of numbers is 361.

⇒ n + (n + 1) = 361

         2n + 1 = 361

              2n = 360

                n = 180

Hence, the left page number is 180 and the right page number is 181.

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The system of equations that can be used to find the price in dollars of each pencil, x, and each folder, y that Sally and Henry bought is D.

6x + 3y = 3.90

2x + 5y = 3.30.

A system of equations is also known as a simultaneous equation.

Simultaneous equations are equations solved concurrently.

                            Sally     Henry

Units of pencils     6            3

Units of folders     3            2

Total costs         $3.90    $3.30

Let pencils = x and folders = y

Sally's total cost = 6x + 3y = $3.90

Henry's total cost = 3 x + 2y = $3.30

In this situation, to find the price of each pencil and each folder, the system of equations that can be used is from Option D.

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Yes, for every 6 duck decoys big lake bob carves he must give up 20 fishing lures.

Production possibility schedule:-

Fish lures:

Fish lures in one week = 100

lures in a day = 20

So, 100-20 = 80

80 - 20 = 60

60 - 20 = 40

40 - 20 = 20

20 - 20 = 0

Duck decoys:

Duck in one day = 0

So, 0 + 6 = 6

6 + 6 = 12

12 + 6 = 18

18 + 6 = 24

24 + 6 = 30

number of duck decoy in a week = 30

Hence, For every 6 duck decoys Bob carves 20 lures.

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A point-to-point graph, also called a line graph

To establish if a graph reflects a function, use the vertical line test. If a vertical line is dragged across the graph and only touches the graph at one location at any time, the graph is a function. If the vertical line intersects the graph more than once, the graph is not a function.

A line graph, also known as a point-to-point graph, is a visual representation of data in which precise values of a function are represented as dots on a coordinate plane. Straight lines link adjacent pairs of dots.

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Answer: 0.25 30% 1/3  

Step-by-step explanation:

1/3 is the largest because when made in a decimal it would be 3.3 reapeting, 30 % is 0.3 and 0.25 . So the order will be 0.25 30% and 1/3.

Answer:

B. 18

Step-by-step explanation:

Given that f = 2.5,

8 + 4f

=8 + 4(2.5)

8 + 10 = 18

The number of meters that the truck could go given the energy provided by the students combined, would be 800, 000 meters

To find the distance the truck would go, first find the number of meters the truck would go with the energy your heart provides :

= 32 x 1, 000 meters per kilometer

= 32, 000 meters

There are 25 people in the math class so the distance the truck would go is:

= Number of students x Distance per person

= 25 x 32, 000

= 800, 000 meters

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While calculating the measurements given.The correct answer is 384 ft.

Given,

Inches when drawing =1/4

Actual feet according to the drawing =12 ft

To calculate the The mesurement of 8 inch

8 ÷ 1/4 = 8/1 x 4/1 = 32

32 x 12 = 384

Sometimes we find the value in feet and inches rather than converting the amount to decimals. For instance, 71 inches is equivalent to 5 feet, 11 inches. It's because we get 5 as the quotient and 11 as the remainder when we divide 71 by 12. The residual value will be expressed as the number of inches it is. This is known as converting inches to feet and feet to inches. Let's examine a few of the instances below.

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The evaluation of the arithmetic series  gives 4545

An arithmetic progression ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.

From the given information, we can get the first term (a) and  last term (l) of the sequence by substituting n = 1  and n = 45 respectively into the given expression, (4n + 9). That is:

a = 4(1) + 9 = 13

l = 4(45) + 9 = 189

Sum of all terms in a finite AP with the first term (a) and last term (l) is given by:

S = n/2(a + l)

S = 45/2 (13+189) = 4545

Thus, the arithmetic series evaluates to

[tex]\sum_{n}^{45}(4n + 9) = 4545[/tex]

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An Experimental study is used. As subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. after months, the numbers of respiratory tract infections each group had were compared.

Experimental investigations or study involve introducing an intervention and observing its results. Typically, volunteers in experimental research are grouped randomly, or by chance.

During a randomized controlled trial (RCT), participants are divided into two or more groups at random. While the control group is given nothing or a placebo, the intervention group is given the new drug, for example. The outcome of each group is then investigated by the researchers. The intervention can thus be blamed for any variations in the results.

Whereas, Observational study is the Studies in which researchers look at how a risk factor, diagnostic test, treatment, or other intervention affects a population without attempting to alter who is or is not exposed to it.

Hence, it is experimental study.

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Answer:

54

Step-by-step explanation:

[tex]f(x)=x^2+10x+29 \\ \\ f(x)=(x^2+10x+25)+29+25 \\ \\ f(x)=(x+5)^2+54 \\ \\ \therefore (x+5)^2 \geq 0 \implies (x+5)^2+54=f(x) \geq 54[/tex]

The equation formed by the sentence is 9b - 7 = 8.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Let the variable be b

By the given sentence we get the equation

9b - 7 = 8

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As a set of inputs with one output for each, a function is defined as a relationship between them.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

When examining a graph, one method is to perform a "vertical line test" to see if a relationship is indeed a function. Anywhere on the graph where a vertical line can be created to cross the relation twice indicates that the relationship is not a function.

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Therefore , the solution to the given problem of unitary method comes out to be Henry uses the scooter for 143 minutes after that.

In order to solve an issue, one can use the unit technique, which involves first multiplying the worth of one unit by the number of units needed. Simply said, the unit function is used to extract a single entity number from a given many. 40 needle would cost 400 rupees, or the price of one pen. There may be a standard method for checking this out. one country only. anything has a distinctive element. Mathematical analysis, algebra, matrix logic, and its interpellation and inverse are all equivalent.

Here,

Start the scooter for $7.00

$0.07 for each minute

$17.01 in total.

1. Subtract the cost of starting the scooter from the total bill:

The price for Henry's entire ride is $10.01.

2. Subtract the price for each minute to get the price per minute:

=> 10.01/0.07 * 100/100

=> 1001/7

=> 143

Henry uses the scooter for 143 minutes after that.

Therefore , the solution to the given problem of unitary method comes out to be Henry uses the scooter for 143 minutes after that.

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The equation of the perpendicular line is y = -5

We have to recall that the general form of the equation of a line can be given by the expression that is written as y = mx + c. m is the slope of the graph while c is the intercept of the graph.

We would then have;

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

We can see that m = 0 from the first line that has been given the we have;

y - (-5) = 0(x - 4)

y + 5 = 0

y = -5

This is the equation that has been required in the problem above.

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The equation of the line that passes through the point (5, 3) and has a slope of - 6/5 is y = -6/5x - 3.

What is Slope?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

What is Equation of line?

The equation for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

Given that ;

point passes through is (5,3)

and has slope of (-6/5)

We have equation of line;

y = mx+c

3 = -6/5(-5)+b

3 = 6 + b

Eliminate 6 by using the equality's subtraction property, then isolate b. (subtract 6 from 6 to cancel it out and to 3).

b = -3

So, the equation of the line that passes through the point (5, 3) and has a slope of - 6/5 is y = -6/5x - 3.

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Answer:

Step-by-step explanation:

j7yu8iol9ololololol

The histogram for the stickers from the small package is distributed as follows:

Normally.

To obtain the distribution of the histogram, we must correctly identify the mean and the median of the distribution.

Hence the distribution is defined as follows:

The ordered distribution is given as follows:

13, 15, 18, 19, 22, 24.

Hence the median is of:

(18 + 19)/2 = 18.5.

The mean is of:

(13 + 15 + 18 + 19 + 22 + 24)/6 = 18.5.

They are equal, hence the histogram is normal = symmetric;

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Answer:

2x² + 7x + 2

Step-by-step explanation:

f(x) = 3x² + 5

g(x) = 4x - 2

h(x) = x² - 3x + 1

f(x) + g(x) — h(x) =

(3x² + 5) + (4x - 2) - (x² - 3x + 1) = ==> plugin the values of f(x), g(x), and h(x)

3x² + 5 + 4x - 2 - (x² - 3x + 1) =

3x² + 5 + 4x - 2 - x² + 3x - 1 =  ==> distribute the negative sign to x², -3x, 1

                                                     x² ==> -x², -3x ==> 3x, 1 ==> -1

3x² - x² + 4x + 3x + 5 - 2 - 1 =  ==> combine like terms

2x² + 7x + 2 = ==> simplify

The probability that all 4 computers with the critical file fail in this incident is given as follows:

0.0046 = 0.46%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of these parameters for this problem are given as follows:

N = 30, k = 4, n = 9.

The probability that all fail is P(X = 4), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,30,9,4) = \frac{C_{4,4}C_{26,5}}{C_{30,9}} = 0.0046[/tex]

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The final solution is -sin(1).

To evaluate the iterated integral, we need to integrate with respect to the outer variable first, then integrate with respect to the inner variable.

The given iterated integral is:

[tex]∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds[/tex]

To evaluate this, we need to integrate with respect to t first, and then integrate with respect to s.

[tex]∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds = ∫(1 to 0) [∫(s^4 to 0) cos(s^5) dt] ds= ∫(1 to 0) (-1/s^5 * sin(s^5)) \\ds= [-1/s^5 * sin(s^5)] \\evaluated at s = 1,0= (-1/1^5 * sin(1^5)) - (-1/0^5 * sin(0^5))= (-1/1 * sin(1)) - (0)= -sin(1)[/tex]

So the final solution is -sin(1)

Note that the integral is not defined for s=0, [tex]s^5=0[/tex] , as the function is not defined there.

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This is $20,330.08 more than the total cost of the bank loan.

Payment is the transfer of money from one party to another in exchange for goods, services, or to fulfill a legal obligation. Payment is an important part of any transaction, as it is the final step that completes the exchange of goods or services.

Therefore, the lowest monthly payment would be the credit card payment of $511.11. Paying with a credit card at 15% compounded monthly would be the least expensive option for Genesis. With this option,  would pay a total of $36,330.08 over the 7 years, including the interest. This is $20,330.08 more than the total cost of the bank loan.

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