Inclusions are defects in poured metal caused by contamitants. The number of (large) inclusions in cast iron follows a Poisson distribution with a mean of 2 per cubic millimeter. Deter mine the following:

a. Probability of at least one inclusion in a cubic millimeter.
b. Probability of at least 3 inclusions in 4.0 cubic millimeters.
c. Volume of material to inspect such that the probability of at least one inclusion is 0.98
d. Determine the mean inclusion per cubic millimeter such that the probability of at least one inclusion is 0.98.

[tex] - 6 \leqslant x \leqslant 6[/tex]

[tex] - 5 \leqslant y \leqslant 5[/tex]

Answer:

A and E

Step-by-step explanation:

the answer is 200, hope it helps

~Shoto Todoroki here~

Colin's mean score of his 10 runs is 18.8.

Colin's new mean score after the game on Sunday is 20.

Mean is a measure of central tendency. It is used to describe a data set. It is the sum of a set of observations divided by the number of observations. It is also known as average.

Mean = sum of scores / total number of scores.

Colin's mean scores can be determined by dividing the sum of scores by total number of scores.

Sum of scores = (20 + 29 + 34 + 19 + 8 + 12 + 0 + 23 + 29 + 14) = 188

Number of scores = 10

Mean of scores = 188 / 10 = 18.8

Colin's new mean score can be determined by adding 32 to the sum of scores already determined and dividing the sum by the total number of scores.

New sum of scores = 188 + 32 = 220

Number of scores = 11

Mean scores = 220 / 11 = 20

hope this helps :D

The value of k in the function f(x) = 2x-k is 6.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

f(x) = 2x + 4

f(x) = 2x-k

Now,

To shift a linear function to the right, we subtract a constant from the input variable x. For example, f (x) = 2x + 4 shifts to the right by 2 units when it is replaced with f (x) = 2 (x - 2) + 4.

In this case, f (x) = 2x + 4 shifts six units to the right when it is replaced with f (x) = 2 (x - k) + 4. To find the value of k, we can equate the expressions inside the parentheses and solve for k:

x - k = x - 6 k = 6

Therefore, by the given functions the answer will be 6.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ7

Answer:

There are 30 apples left!

Step-by-step explanation:

81-

51

-----

30

Answer:

Step-by-step explanation:

The computation of triangle ABC and ACD which are both isosceles shows that the value of x will be 36°.

It should be noted that the sum of angles in a triangle is 180°. In this situation two of the three angles have been given.

Therefore, the value of the third angle will be:

86° + 58° + x = 180°

144° + x = 180°

x = 180° - 144°

x = 36°

In conclusion, x is 36°.

Learn more about triangles on:

https://brainly.com/question/17335144

Answer:

x = 3,75

Step-by-step explanation:

x/3 = 15/12

x/3 = 5/4

4x = 3 × 5

4x = 15

x = 15/4

x = 3,75

Answer:

22

Step-by-step explanation:

Answer:

0.02 tons per cubic foot

Step-by-step explanation:

delt math

The density of the material is, 106.36 tons per cubic foot.

Density is the mass of a material substance per unit volume.

d = M/V, where d is density, M is mass, and V is volume, is the formula for density.

Grams per cubic centimeter are a typical unit of measurement for density.

Given, The density of a certain material is such that it weighs 1 pound for every 3.5 cups.

Therefore, d = 1/3.5 per cubic cup.

d = 0.29 pounds per cubic cup.

Now, We know 1 ton is equal to 2000 pounds and 1 foot is equal to 119688.

Therefore, The density of the material per cubic foot is,

= 119688/(2000×0.29) tons per cubic foot.

= 106.36 tons per cubic foot.

learn more about density here :

https://brainly.com/question/29775886

#SPJ3

Answer:

The inverse is  5±sqrt(x+25)

Step-by-step explanation:

y = x^2 - 10x

To find the inverse, exchange x and y and solve for y

x = y^2 -10y

Complete the square

x+25 = y^2 -10y +25

x+25 = (y-5)^2

Take the square root of each side

±sqrt(x+25) = y-5

Add 5 to each side

5±sqrt(x+25) = y

The inverse is  5±sqrt(x+25)

Answer:

[tex]y=\pm\sqrt{x+25}+5[/tex]

Step-by-step explanation:

Given function:

[tex]y=x^2-10x[/tex]

Rearrange to make [tex]x[/tex] the subject.

First, complete the square by adding 25 to both sides and factoring:

[tex]y+25=x^2-10x+25[/tex]

[tex]y+25=(x-5)^2[/tex]

Square root both sides:

[tex]\pm\sqrt{y+25}=x-5[/tex]

Add 5 to both sides:

[tex]x=\pm\sqrt{y+25}+5[/tex]

Finally, swap [tex]x[/tex] and [tex]y[/tex] (since the inverse of a function is its reflection in the line [tex]y = x[/tex])

[tex]y=\pm\sqrt{x+25}+5[/tex]

Answer:

B no wrok needed

Step-by-step explanation:

Answer:

1,2,4

Step-by-step explanation:

all are positive intergers

Answer:

-19x

Step-by-step explanation:

to make this equation easier, remove the variables (-8-11) which equals -19. You can then say the answer is -19x

Answer:

4(x+5)

Step-by-step explanation:

Answer:

x = 2.6, x = -1.6

Step-by-step explanation:

If we compare the graph to points (-1, 2) and (2, 2) [see blue lines on attachment], we can determine that the scale of the y-axis is 1 square per 1 unit.  (This is different from the scale of x-axis, which is 2 squares per unit).

Therefore, to use the graph to estimate the x-value when y = 4, count 4 square up the y-axis from 0, then trace along the horizontal line until you meet the curve.  Then trace down to the x-axis and read the values of x. (shown by the red lines on the attachment).

So the approximate value of x is -1.6 and 2.6 when y = 4.

The actual answer can be calculated as follows:

   x² - x = 4

⇒ x² - x - 4 = 0

Use the quadratic formula:

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\implies x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(1)(-4)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{1\pm\sqrt{17}}{2}[/tex]

[tex]\implies x=2.6,x= -1.6 \sf \ (1 \ dp)[/tex]

Answer:

x=-1.56,2.56

Answer:

8.5

Step-by-step explanation:

because the hundredths place is not above 5

Answer:1.694

Step-by-step explanation:

You take away the decimal from 3.54 and make the 6 the same number place

Ex. 1 ÷ 1.20

1=100

1.20=120

600 ÷ 354 = 1.694

Answer:

38.5

D

Step-by-step explanation:

5.5x7=38.5

The probability that the winning three numbers match the date on any given​ day is the likelihood of the winning number

Start by calculating the number of possible outcomes

Each of the three digits can take any of 0 - 9 i.e. 10 digits.

So, the number of possible outcomes is:

[tex]n =10^3[/tex]

[tex]n =1000[/tex]

There can be only one winning date.

So, the probability (p) is:

[tex]p = \frac 1n[/tex]

This gives

[tex]p = \frac 1{1000}[/tex]

[tex]p = 0.001[/tex]

Hence, the probability that the winning three numbers match the date on any given​ day is 0.001

In a calendar year, there are 65 days, where the whole year passes without matching the winning numbers.

The dates are:

This means that the matching numbers can occur on the remaining 300 days.

The probability that the winning date does not occur on a date is calculated using the following complement rule

[tex]p' = 1 - p[/tex]

So, we have:

[tex]p' = 1 - 0.001[/tex]

[tex]p' = 0.999[/tex]

For the 300 days, we have:

[tex]p = 0.999^{300}[/tex]

[tex]p = 0.7407[/tex]

Hence, the probability that a whole year passes without this​ happening is 0.7407

This is calculated using the following complement rule

[tex]p' = 1 - p[/tex]

So, we have:

[tex]p' = 1 - 0.7407[/tex]

[tex]p' = 0.2593[/tex]

Hence, the probability that the date and winning lottery number match at least once during any​ year is 0.2593

In (b), we have:

[tex]p' = 0.999[/tex]

So, the probability is calculated as:

[tex]p =1 - (p')^n[/tex]

Where n is the number of states i.e. n = 27.

So, we have:

[tex]p = 1 - 0.999^{27}[/tex]

[tex]p = 0.0267[/tex]

Hence, the probability that at least one of them will come up 1-1-4 on January 14​ is 0.0267

Read more about probability at:

https://brainly.com/question/25870256

Using an exponential function, the recursive formula that describes the fraction of contaminants still remaining in the liquid sample after passing through n filters is given by:

[tex]A[n] = (0.052)^n[/tex]

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, considering an initial fraction of A(0) = 100% = 1, the decay rate is of r = 0.948, hence the formula is:

[tex]A[n} = (1 - r)^n[/tex]

[tex]A[n] = (0.052)^n[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

Using proportions, it is found that there are 22 stones in the circle.

A proportion is a fraction of a total amount.

In this problem, the sixth stone was directly opposite the seventeenth stone, hence over half the circle, there was 11 stones.

Then, we apply the proportion, and get that:

0.5n = 11

n = 22.

There are 22 stones in the circle.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

The area is 155 ft.

Step-by-step explanation:

To find the area if a trapezoid, you have to add the number on top( in this case 13 ft) and then add that with the bottom number(18 ft.) Then, you take that answer and divide it by 2. After that, multiply it with the height(10.) Thus, the answer is 155 ft.

Answer:

D  5y + 29x = 500

Step-by-step explanation:

Slope-intercept form of a linear equation:  y = mx + b

(where m is the slope/rate of change, and b is the y-intercept)

Given:  

⇒ when x = 0, y = 100

Therefore,  b = 100

Given:

Note that the water is decreasing in volume as time goes by.  Therefore, the rate of change is negative, so m = -5.8

Inputting these values into the equation gives:

y = -5.8x + 100

Multiply the equation by 5:

5y = -29x + 500

Rearrange:

5y + 29x = 500

Therefore, D is the solution.

The probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.

Given that the probability Kayla will score above 70% on a mathematics test is 0.60, and Kayla will take four tests this semester, and we want to find the probability she will score above 70% on exactly three out of the four tests, to determine what is the probability of Kayla scoring above 70% on exactly three out of the four tests, the following calculation must be performed:

Therefore, the probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.

Learn more about probability in https://brainly.com/question/26684125

Answer:

No

Step-by-step explanation:

(2,-2)

2 is the x coordinate

-2 is the y coordinate

3x - y = 4

3(2) -(-2) = 6 + 2

6 + 2 = 8, not 4

Hope this helps :)

Have a nice day!

Answer:

No, it is not in the line.

Step-by-step explanation:

Let's plug the coordinates of the point and find out

[tex]3(2) -(-2) = 4\\6+2 = 8\ne 4[/tex]

Answer:

C. [tex] y = 3.50 + 2.75x [/tex]

Step-by-step explanation:

Initial fee charged by the taxi driver = $3.50

Fee charged per kilometer = $2.75

Number of kilometers of travel = x

Total cost charged for a trip = y = initial fee charged for renting a taxi + fee paid based on the number of kilometers travelled

Total cost of the trip can be expressed by the following equation:

[tex] y = 3.50 + 2.75x [/tex]

The answer is C. [tex] y = 3.50 + 2.75x [/tex].