in a shipment of 54 vials, only 16 do not have hairline cracks. if you randomly select one vial from the shipment, what is the probability that it has a hairline crack?

Number of ways , two contaminated and 8 non- contaminated farms be choosen is 3,304,845,180.

Permutation and Combination

Combination is a mathematical way to arranging the set of values randomly.

ⁿCᵣ = n! / r! (n-r)!

we have given that ,

total number of farms for lead contamination = 50

Number of farms have dangerously high level of lead = 8

so, number of non- containmated farms ( no high level of lead ) = 50-8 = 42

We have to find the number of ways to choose two contaminated farms and eight non- contaminated farms. Two containmated farms are selected from 8 containated farms and 8 non- contaminated farms are selected from 42 farms .

Number of ways for selecting two containmated farms = ⁸C₂ = 8!/2!×6! = 8×7/2 = 28

Number of ways for selecting eight non-containmated farms from 42 farms = ⁴²C₈

= 42! / 8! 34! = 42×41×---×35/8×7×----×1

= 118013185

The total number of ways to obtain 2 containmated farms and 8 non- contaminated farms in 10 farms selected is then product of number of ways to select the 2 containmated farms and number of ways to select 8 non-containmated farms .

= 118030185× 28 = 3,304,845,180

To learn more about Combination and Permutation, refer:

https://brainly.com/question/28065038

#SPJ4

Answer:

6 hours.

Step-by-step explanation:

Subtract initial fee from total. (67 - 19 = 48).

Divide by the hourly rate. (48 / 8 = 6).

The bike was rented for 6 hours.

Answer:

The answer is x^{3}-2x^{2}-5x+6

Step-by-step explanation:

This is because only a Cubic Function would have such a shape. That leaves x^3 functions from there just substitute points and check

Part A: The formula 5d-13 indicates the distinction between the quantity of basic arrangements and deluxe arrangements sold.

Part B: The difference between the money the store made from basic arrangements and deluxe arrangements is $158.

An expression, also known as a mathematical expression, in mathematics is a finite combination of symbols that are well-formed in accordance with principles that depend on the context. Mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, grouping, and integers (constants) to help with logical grammar and operation ordering.

Part A: (8d-7)-(3d+6)

=8d-7-3d-6

=5d-13

Part B: For 7 days, d=7

              Cost        No. of sold

Basic       17          8(7)-7=49

Deluxe     25         3(7)+6=27

Therefore, Basic=17*49=$833

Deluxe=25*27=$675

Difference=833-675=158

To know more about expression, visit:

https://brainly.com/question/13947055

#SPJ1

Answer:

[tex]\frac{17}{76}[/tex]

Step-by-step explanation:

expressing the ratio in fractional form

[tex]\frac{11\frac{1}{3} }{50\frac{2}{3} }[/tex] ← change mixed number to improper fractions

= [tex]\frac{\frac{34}{3} }{\frac{152}{3} }[/tex] ( multiply numerator and denominator by 3 )

= [tex]\frac{34}{152}[/tex] ( divide numerator and denominator by 2 )

= [tex]\frac{17}{76}[/tex] ← in simplest form

Answer:

x = [tex]\frac{3}{8}[/tex]

Step-by-step explanation:

[tex]\frac{3}{2}[/tex] = 4x ( multiply both sides by 2 to clear the fraction )

3 = 8x ( divide both sides by 8 )

[tex]\frac{3}{8}[/tex] = x

The maximum and minimum measurements are 5 and -3 respectively.

f ( x ) = -x^3 +3x^2+ 45 x + 10

f' l x ) = 0

0 = - 3x^2 +6x +45

x = 5,- 3.

f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174

f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58

f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1

+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185

Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}

                        = 185 at x=5

Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}

                      = - 71 at x= -3

In light of this, the maximum and minimum values are 5 and -3, respectively.

Learn more about Absolute maximum  :

brainly.com/question/28767824

#SPJ4

The cost of covering the field with grass pallets is $40996.58.

Given that the rectangular field measures 90 m and 162 m.

Hence, the area of the field is 90 X 162 m²

The grass pallets are sure in shape with an area covering 90 square yards.

1 m = 1.09 yards

Hence,

1 m² = 1.09² square yards

Hence,

90 X 162 m² = 90 X 162 X 1.09² square yards

Hence the number of pallets to be used is

(90 X 162 X 1.09²) / 90

= 162 X 1.09² pallets.

= 192.4722 pallets.

1 pallet costs $213

Hence,

192.4722 pallets cost

192.4722 X 213

= $40996.58

Therefore we get the cost of covering the field with grass is  $40996.58.

To learn more about Areas visit

https://brainly.com/question/14356835

#SPJ4

Answer:

-------------------------------

Let the sides of the old rectangle are l and w.

Answer: Hence the answer is 27 square feet.

Please look at the images for more details.

Using the concept of percentage we get 16-inch pizza is 43.75% larger than a 12-inch pizza.

Percentage means out of hundred. A number that is expressed as a fraction of a hundred is called a percentage. Percentage change = Change in the value / Initial value.

Area of circle = π R²,

Where R is the radius of circle.

Given that size of a pizza is measured by its diameter and surface area.

Diameter of the first pizza = 16 inch

So its radius = 8 inch

Hence area = π×8²

= 64π

And the diameter of the other pizza = 12 inch

So, its radius = 6 inch

Hence its area = π×6²

= 36π

Now the difference in areas of Both the pizza = 64π - 36π

= 28π

Now percentage difference in areas of both pizzas = 28π×100)/64π%

= 2800/64

=43.75%

Hence, 16-inch pizza is 43.75% larger than a 12-inch pizza.

To know more about the percentage, visit:

https://brainly.com/question/15043030

#SPJ4

its 4 cause i have done this

First, we isolate the variable on one side of the inequality by subtracting 15 from both sides:

15 - 2x - 15 ≤ 11 - 15

Simplifying the left side, we get:

-2x ≤ -4

Next, we divide both sides by -2. Since we are dividing by a negative number, we need to flip the inequality sign:

-2x/-2 ≥ -4/-2

Simplifying, we get:

x ≥ 2

Therefore, the solution to the inequality 15-2x ≤ 11 is x ≥ 2.

add me cuties

The star asterisk in the fraction 12*/23* is being replaced by all the possible values as outlined

1 to be 11/21

2 to be 61/116

4 to be 62/117

5 to be 25/47

6 to be 63/118

8 to be 64/119

0 to be 12/23

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a chunk or section taken from a whole, which can be any number, and can represent any amount.

The fractions with different numerators and denominators when compared with another fraction but the same value with the fraction are said to be equivalent fractions.

The asterisk value is replaced with digit in each case, and the fraction formed is reduced to their equivalent forms as below

12*/23* * replaced by 1 and reduced to be 11/21

12*/23* * replaced by 2 and reduced to be 61/116

12*/23* * replaced by 4 and reduced to be 62/117

12*/23* * replaced by 5 and reduced to be 25/47

12*/23* * replaced by 6 and reduced to be 63/118

12*/23* * replaced by 8 and reduced to be 64/119

12*/23* * replaced by 0 and reduced to be 12/23

Learn more about fractions:

https://brainly.com/question/29321903

#SPJ1

Answer:

All answers other than {7, 11, 15, 19}

Step-by-step explanation:

If we have a Set A, it is a subset of Set B if every element in A is also in B. Set A is a proper subset of Set B if it is a subset of Set B but not equal to Set B.

Using the above information, we know that the proper subset of {7, 11, 15, 19} cannot be itself, so we can rule out the second option.

All of the other options are sets where every element of that set is also an element of {7, 11, 15, 19}. The 3rd option is an empty set, which is a proper subset of any set other than itself, so it is a proper subset of {7, 11, 15, 19}.

Therefore, all of the options except for {7, 11, 15, 19} are valid.

i came back home now....

The volume of the rectangular prism is the 75 ft cube.

The prism below is a rectangular prism.

A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that all the pairs of the opposite faces are congruent.

The volume of a rectangular prism can be express as follows:

Volume of a rectangular prism = base area × height

Therefore,

base area of the prism = 25 ft²

height of the prism = 3 ft.

Hence,

Volume of the rectangular prism = 25 × 3

Volume of the rectangular prism = 75 ft³

learn more on volume here: https://brainly.com/question/318504

#SPJ1

The solution for x in the expression given as 15 + ax/5 =  10 is x = -25/a

From the question, the algebraic expression is given as

15 + ax/5 =  10

There is a constant to add to or subtract from the expression

So, the we subtract 15 from both sides

- 15 + 15 + ax/5 =  10 - 15

Evaluate

ax/5 = -5

Multiply both sides of the equation by 5

This gives

5 * ax/5 = -5 * 5

Evaluate the products

So, we have the following equation

ax = -25

Multiply both sides of the equation by 1/a

This gives

1/a * ax = -25 * 1/a

Evaluate the products in the above expression

x = -25/a

Hence, the solution is x = -25/a

Read more about equations at

brainly.com/question/2476251

#SPJ1

Answer: 16

Step-by-step explanation:

The page is in landscape mode with a width : height is 3: 2

Given that,

The printable area is should be 42 square inches on a rectangular page. The margins at the top and bottom of the page are each one inch, while the margins on one side are one inch and two inches, respectively.

x = length of the horizontal side of the printable area

y = length of the vertical side of the printable area

XY = 42 inch²

y = 42/x

page height = y + 1 + 1

page width = x + 1 + 2

A = area of an entire sheet of paper

  = (x+3)(y+2)

  = (x+3)(42/x+2)

  = x(42/x+2)+3(42/x+2)

  = 42+2x+126/x+6

A = 2x+126/x+48

Extremes occur when A' = 0:

A' = 0 = 2 – 126/x²

1 = 63/x²

x² = 9*7

x = 3√(7), x has to be positive

y = 42/x = 42/(3√(7)) = 14√(7)/7 = 2√(7)

What should the dimensions of the page be so that the least amount of paper is used?

page width = x + 3 = 3√(7) + 3 = 3(√(7) + 1)

page height = y + 2 = 2√(7) + 2 = 2(√(7) + 1)

So, the page is in landscape mode with width: height is 3: 2.

To learn more about dimensions click here:

braihttps://brainly.com/question/28815550

#SPJ4

The table showing the possible value of S and their possibilities is attached below,

The probability that a player moves their counter forward more than 2 spaces is 0.5.

The Probability is the ratio of favorable outcomes to total number of outcomes. The probability of an event must be less than 1 as the sum of all probabilities of events is equal to 1.

Here, If the number on the dice is even, S is half that number; if it is not even, S is double that amount. The table showing the possible value of S and their possibilities is attached below,

Now, finding the probability that a player moves their counter forward more than 2 spaces,

As seen from the table, the number of favorable outcomes where the player moves the counter more than 2 spaces is 3.

The total number of outcomes is 6. so, the probability will be,

Probability [tex]=\frac{3}{6}[/tex]

[tex]=\frac{1}{2} \\\\=0.5[/tex]

Hence, the probability that a player moves their counter forward more than 2 spaces is 0.5.

To learn more about the Probability visit here:

https://brainly.com/question/25870256

#SPJ1

The correct property of equality to solve each equation. 3 + x = 27 and x + 6 = 5 is subtraction property of equality.

The property of equality defines an equivalence relationship between two variables. The subtraction property of equality refers to the property that two sides of the equation remain equal when the same number is subtracted from both sides of an equation. According to the subtraction property of equality, if two quantities a and b are equal, and if c is subtracted from both a and b, then the difference of a and c and the difference of b and c are equal. Hence, if a = b, a – c = b – c. Using the subtraction property of equality:

3 + x = 27

3 + x -3 = 27 - 3

x = 24

Similarly,

x + 6 – 6 = 5 – 6

x = -1

Learn more about Subtraction property of equality:

https://brainly.com/question/1601404

#SPJ4

Answer:

3+x=27

✔ subtraction property of equality with 3

x/6 = 5

✔ multiplication property of equality with 6

Step-by-step explanation:

The probability that of getting more than two heads is 0.9537.

The probability of precisely x successes per n repeated trials is known as a binomial probability, and X has only two possible outcomes.

P(X = x) = Cn,ₓ.pˣ(1 - p)ⁿ⁻ˣ   ...eq 1

Where  Cn,ₓ represents the number of distinct combinations of x items drawn from a group of n elements, as determined by the formula below.

Cn,ₓ = n!/x!(n - x)!

Where p is the likelihood that anything will happen.

10 appeals are necessary; n = 10.

Because 40% of appeals are successful; p = 0.4.

For the probability of getting at least two heads.

P(X ≥ 2) = 1 - P(X < 1)

P(X < 2) = P(X = 0) + P(X = 1)

Put the values in eq 1 and get the values for X.

P(X < 2) = 0.006 + 0.0403  = 0.0463

Now,

P(X ≥ 2) = 1 -  0.0463

P(X ≥ 2) = 0.9537

Thus, the probability that of getting more than two heads is 0.9537.

To know more about the binomial probability, here

https://brainly.com/question/9325204

#SPJ4

The rational numbers are -√25, -√25, √100, √0.36, √0.0144 and -√36/49. Select them

A rational number is a number that can be expressed as a fraction where both the numerator and the denominator in the fraction are integers e.g 2/3, 7/1, √100 = 10/1, etc.

An irrational number is any real number that cannot be expressed as the quotient of two integers. This is the opposite of rational numbers. They are usually of roots that cannot give integers e.g 3√5, √8, etc.

√75 = √(25 x 3) = √25 x √3 = 5 x √3 = 5√3    (This is not rational)

-√25 = -5 = -5/1   (This is rational)

2*√7 = 2√7        (This is not rational)

√100 = 10 = 10/1  (This is rational)

√0.36 = √(36/100) = 6/10   (This is rational)

√0.0144 = √(144/10000) = 12/100  (This is rational)

√3/7 = √3/7  (This is not rational)

-√36/49 = -6/7  (This is rational)

Therefore, -√25, -√25, √100, √0.36, √0.0144 and -√36/49 are rational numbers. They should be selected

Learn more about rational numbers on:

https://brainly.com/question/12088221

#SPJ1

The solution to the inequality is x > 0

Inequality in mathematics differentiate two values,  if one is less than, greater than, or not equal to another value

Evaluate the equation by letting the unknow to be on one side

−1 − 10x < −1

-10x < -1+1

Add +1 to both sides

= -1-10x+1 < -1+1

= -10x < 0

Divide both sides by -10 same factor and flip the relation because  of negative factor

=  -10x /-10 > 0/-10

= x > 0

Therefore the solution to the inequality is x>0

Learn more about inequality here: https://brainly.com/question/24372553

#SPJ1

The number of yards of ribbon Isabel bought is 41 yards.

It is given in the question that:-

Money in prepaid debit card = $ 20

Price of ribbon = 7 cents per yard

Money left on the card after buying the ribbon = $ 17.13

We have to find the number of cards of ribbon Isabel bought.

Money used in buying the ribbon = 20 - 17.13 = $ 2.87

We know that,

$ 1 = 100 cents

Hence, according to the data given in the question, we can write,

$ 2.87 = 287 cents

Yards of ribbon bought = 287/7 = 41 yards.

To learn more about Price, here :-

https://brainly.com/question/19091385

#SPJ1

Looking at the triangles, the information needed to prove that ABC∼△DEF is AC = 10

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

AB and DE, BC and FE, then AC and DF

The solution is worked out using sides BC and FE, then AC and DF

BC / AC = FE / DF

8 / AC = 16 / 20

reducing the fraction 16/20 gives

8 / AC = 8 / 10

hence  AC = 10

Learn more about similar triangles here:

https://brainly.com/question/14285697

#SPJ1

It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.

A lawn can be mowed by Wilma in 40 minutes. In one hour, Vanessa can cut the same lawn in 120 minutes.

1/120 + 1/40 = 1/T

multiply by 40T;

3T = 40

T = 40/3

  = 13 1/3 minutes

  = 13 minutes 20 seconds

It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.

To learn more about minutes click here:

brainly.com/question/15600126

#SPJ4

Answer:9x>6=76

Step-by-step explanation:9x>6=76

Answer:

plsssssssssssssssssssssssssssssssssss

It will take 33.33 years for the account to reach $5500

What is simple interest?

Simple interest is defined as the direct crediting of cash flows related to an investment or deposit.

We know,

Victoria deposited  into a savings account $5000

Annual simple interest rate of 0.3%.

Formula of Simple Interest

                        A = P(1 + rt)

                       5500 = 5000(1 + 0.003t)

                       5500 = 5000 + 15t

                        15t = 500

                         [tex]t = \frac{500}{15} = 33.33[/tex]

It will take 33.33 years for the account to reach $5500

To learn more about simple interest visit,

https://brainly.com/question/25793394

#SPJ13