The area A, in square meters, of a rectangle with a perimeter of 140 meters is given by the equation A = 70w - w², where w is the width of the rectangle in meters. What is the width of a rectangle if its area is 600 m²?

As a seismologist, Janet understands the devastating effects that earthquakes can have. so, she keeps her basement stocked with canned food, like chili. This table shows the relationship between the number of cans of chili Janet buys, x, and the total cost (in dollars), y.

[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]

According to the values in the table, x and y have not a proportional relationship.

Table

[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]

Specifies the gradient (m) in rows 1 and 2

m₁ = [tex]\displaystyle \frac{56.80 - 26.40}{44-12}[/tex]

m₁ = [tex]\displaystyle \frac{30.40}{32}[/tex]

m₁ = [tex]\displaystyle \frac{19}{20}[/tex]

Specifies the gradient (m) in rows 2 and 3

m₂ = [tex]\displaystyle \frac{77.70 - 56.80}{66-44}[/tex]

m₂ = [tex]\displaystyle \frac{20.9}{22}[/tex]

Because the values of m₁ and m₂ are not the same [tex]\displaystyle \frac{19}{20}[/tex] ≠ [tex]\displaystyle \frac{20.9}{22}[/tex], then x and y have not a proportional relationship.

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The required radius of given circle is 30 units.

A circle is a shut two-layered figure wherein the arrangement of the multitude of focuses in the plane is equidistant from a given point called "focus". Each line that goes through the circle shapes the line of reflection evenness. Likewise, it has rotational evenness around the middle for each point.

Picture result for What is circle and region of its area?

The equation for the region of the area of a circle is(r2) /360where r is the span of the circle and is the point of the area.

Angle of sector = 100 degree, area= 250π

Let radius of circle be r

Then,

area of sector = (r^2) /360

250π =  (r2) 100/360

r^2 = 250×360/100

r = √25×36 = 30 units

Thus, radius of the circle is 30units.

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If p = 6, he will not meet his goal.

If p = 7, he will meet his goal.

If p = 8, he will meet his goal.

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

Here, we have

Jerome has already read 50 pages of a novel and read p pages each day from Monday to Friday.

If Jerome read at least 85 pages by the end of Friday, inequality will be,

50 + 5p ≥ 85

If Jerome reads 6 pages each day,

If p = 6,

Inequality will be,

50 + 5(6) ≥ 85

80 ≥ 85

It's not true.

Hence, he will not meet his goal.

If p = 7,

Inequality will be,

50 + 5(7) ≥ 85

85 ≥ 85

It's true.

Hence, he will meet his goal.

If p = 8,

Inequality will be,

50 + 5(8) ≥ 85

90 ≥ 85

It's true.

Hence, he will meet his goal.

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The storage bin can hold 5477 bushels.

We have total capacity of the storage bin which is given to us in mixed fraction form.

If we convert this into improper fraction, it is equivalent to =27385/4

Now, in the same way ,we have also given that  some amount of wheat already fills which is also given in mixed fraction form.

If we convert this into improper fraction form, it is equivalent to

=5/4

Now, to find the the number of bushels storage bin maximally hold is =(total volume of storage bin)/(Volume of wheat fills)

=>N = (27385/4)/(5/4)

=>N=27385/5

=>N=5477

Hence, total number of bushels which storage bin can hold is 5477.

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Answer:

130 mi/ per quart

Step-by-step explanation:

260 mi/8 gallons =32.5 mi/gallon

1 gallon = 4 quarts, so 32.5 gallons is 130 quarts

Option (d)- No, because the events are not independent. Hence we can not conclude that because (0.26)(0.15) = 0.039 about 4% of the labor force are college-educated labors or operators.

We have given that government data show that 26% of the civilian labor force has at least 4 years of college and that 15% of the labor force works as laborers or operators of machine or vehicle.

So here,

event A = 26% of civilian labor force hast at least 4 years of college

event B = 15% of the labor force works as laborers or operators of machines or vehicles

Therefore it is observe that both the events are not independent.

Hence we cannot conclude that because (0.26)(0.15) = 0.039 about 4% of the labor force are college-educated laborers or operators.

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If no box has a card with the same letter as the box, then count the number of elements as 24 ways.

Given that,

Four randomly selected cards with the letters A, B, C, and D are placed in the corresponding boxes. There is exactly one card in each box.

We have to find If no box has a card with the same letter as the box, then count the number of elements.

We know that,

A permutation is a mathematical calculation that establishes the number of possible arrangements for a given set, taking into account the arrangement's order.

From the given information:

The permutation approach can be used to represent the four cards that are randomly placed in the four boxes and can be used to express the following:

=⁴P₄

Since no box contains a card that begins with the same letter as the box, it follows that

Card A can be inserted into a box four different ways,

Card B three different ways,

Card C two ways, and

Card D one way.

The four cards' permutation can then be calculated as follows:

⁴P₄=4!/0!=4×3×2×1/1=24.

Therefore, If no box has a card with the same letter as the box, then count the number of elements as 24 ways.

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The sum of given equation is 96/13.

Given equation is sum from n equals 1 to infinity of 12 times negative five eighths end quantity to the power of n that means

∑ n=1 to ∞ [12(-5/8)ⁿ]

This is in the form of geometric expression

that is an = ar^(n-1)

therefore we get

a = 12 and r = - 5/8

We have to find the sum.

Sum of infinity of the sequence is expressed as

Sum = a / (1-r)

where a  = first term of the series

and r = common ratio between two consecutive terms

Now we will substitute values of a and r in the above equation

Sum = [tex]\frac{12}{1-(-5/8)}[/tex]

        = [tex]\frac{12}{1 + 5/8}[/tex]

        = [tex]\frac{12}{13/8}[/tex]

Sum = [tex]\frac{96}{13}[/tex]

Hence the sum of given equation is 96/13.

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The number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.

In the given question, if the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, then we have to find the collections of 30 coins can be chosen.

Number of coins only of quarters = 15

Number of coins only of dimes = 20

The number of ways to choosing coins with at least 15 quarters and 20 dimes= Total- [tex](^{18}C_{3}+^{13}C_{3})[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]^{33}C_{3}-(^{18}C_{3}+^{13}C_{3})[/tex]

Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33!}{3!(33-3)!}-(\frac{18!}{3!(18-3)!}+\frac{13!}{3!(13-3)!})[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33!}{3!30!}-(\frac{18!}{3!15!}+\frac{13!}{3!10!})[/tex]

Simplifying

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33\times32\times31\times30!}{3\times2\times1\times30!}-(\frac{18\times17\times16\times15!}{3\times2\times1\times15!}+\frac{13\times12\times11\times10!}{3\times2\times1\times10!})[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 11×16×31-(3×17×16+13×2×11)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-(816+286)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-1102

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 4354

If the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, the number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.

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Lacy's blue fish tank has now 3 2/3 gallons of water.

If Lacy has 10 gallons of water and she pour an equal number of gallons of water into each of her 3 fish tanks, then the amount of water each tank will have is equal to the quotient of 10 divided by 3.

amount of water poured in each tank =  10 gallons / 3

amount of water poured in each tank = 10/3 gallons

If Lacy's blue fish tank already has 1/3 gallon of water in it, then the total amount of water the blue fish tank has is the sum of the two fractions.

Add the initial amount and the amount poured in after.

1/3 + 10/3 = 11/3 =  3 2/3 gallons

Simplifying the fraction, Lacy's blue fish tank has now 3 2/3 gallons of water.

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The depth of the juice in the glass is 5.30cm

Given in the question,

length of juice box = 5cm

width of juice box = 3cm

Height of juice box = 10cm

Volume of juice box = volume of cuboid = length× width× height

= (5)(3)(10)

=(15)(10)

= 150 cm³

This juice then poured into a glass with radius of 3 cm

Glass is of cylindric shape

So, volume of cylinder = πr²h

= π(3)²h

Volume of juice should be equal to volume of glass

=>  π(3)²h = 150 cm³

=> (3.14)(9)h=150

=> h = 150 / (3.14)(9)

h = 150/28.26

h = 5.30cm

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After doing a hypothesis test the conclusion is reject [tex]H_0[/tex] .

Given:

tom is a big green bay packers and aaron rodgers fan. he claims that aaron rodger's average number of touchdowns per game is 2.45. dave (a hardcore bears fan) believes that tom might be inflating rodgers's statistics. from his debut until november 18, 2019, aaron rodgers has played 175 games! dave does not want to look at all of them. he randomly selects 52 games that rodgers played and finds the sample average number of touchdowns to be 1.942 with a standard deviation of 1.42.

here n = 52

σ = 1.42

x = 1.942

μ = 2.45

z = x - μ / σ/√n

= 1.942 - 2.45 / 1.42/√52

= -2.58

p value = 0.0049

[tex]H_0:mean = 2.45[/tex]

[tex]H_a:mean < 2.45[/tex]

Rejection rule:Reject [tex]H_0[/tex] if p value < 0.05

Conclusion Reject [tex]H_0[/tex]

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We can determine which table represents a function by, verifying each input value's pairing with a single output value.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given,

We can determine which table represents a function by,

Determine whether a table of input and output values constitutes a function. Determine the values for the input and output. Verify each input value's pairing with a single output value. In that case, the table is a function.

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If the firm increases its production and sales from 3 to 4 units per day, the profit margin increases.

The correct answer option is option B

Total profit = Total revenue - Total cost

Total revenue = number of units × price of each Units

At 3 units:

Total profit = Total revenue - Total cost

= (3 × 2500) - $3000

= $7,500 - $3000

Total profit = $4,500

At 4 units:

Total profit = Total revenue - Total cost

= (4 × $2,500) - $4,100

= $10,000 - $4,100

= $5,900

In conclusion, the profit margin when production is increased from 3 to 4 units will also increase.

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If the data collection contains the given following numbers: 1, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 87 , Here 1 and 87 represents the outlier.

The important characteristics of the Statistics that are given as follows:

Statistics have always been numerically expressed.

For instance, if the data collection contains the following numbers: 1, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 87

The display of all data and outliers

The numbers 1 and 87, which are at the extreme and are hence outliers in the number line above, may be seen to be at these extremes.

The group outliers are a part of it, but they are not always close to the other group members.

Outliers are a concern as they cause an imbalance in the data set, which is why they are typically eliminated. Furthermore, an error can sometimes cause an outlier to appear in a data collection.

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Exactly one unique triangle exists with the given side lengths, option B is correct.

Here, we are given that the three sides of triangle are- 12, 15 and 18.

According to the triangle inequality theorem- “The sum of the length of any two sides of a triangle should be greater than the third side”. Let us see if this holds in this case-

(12 + 15) > 18

(15 + 18) > 12

(12 + 18) > 15

Thus, we see that the triangle inequality theorem is satisfied. So there is only one triangle possible with the sides of given lengths.

Hence, exactly one unique triangle exists with the given side lengths, option B is correct.

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Your question was incomplete. Check for full content below-

How many triangles exist with the given side lengths?

12 in, 15 in, 18 in

A) No triangle exists with the given side lengths.

B) Exactly one unique triangle exists with the given side lengths.

C) More than one triangle exists with the given side lengths.

Answer:

In explanation down below.

Step-by-step explanation:

So if the boat was able to travel 27 miles in 2 hours that means that it traveled 13.5 miles an hour. I think that you want to know how many miles the boat will travel in 1/2 an hour. Which is 6.75.  

1 hour: 13.5 miles

1/2 hour the boat has traveled 6.75 miles.

I hope this helps!!!

Please mark brainliest :)

The solution to the system of equation is [tex](\frac{14}{3},-\frac{16}{3})[/tex]

A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.

Differentiate between substitution and elimination method.

The major difference between the substitution and elimination method is that the substitution method is the process of replacing the variable with a value, whereas the elimination method is the process of removing the variable from the system of linear equations.

The system of equations are :

y = x - 10 and

2x + y = 4

On solving two equations by using substitution method ,we get

By substituting the value of y in another equation ,we obtain the equation in terms of one variable :

Now, according to the question

⇒ 2x + (x - 10) = 4

⇒ (2x + x) = (4 + 10)

⇒ 3x = 14

⇒ x = 14/3

Further for y ,we substitute obtained value of x in the equation

y = x - 10

Now,

[tex]y = \frac{14}{3}-10[/tex]

  [tex]=\frac{(14-30)}{3}[/tex]

  [tex]= (\frac{-16}{3})[/tex]

  [tex]= - (\frac{16}{3})[/tex]

Hence ,the solution is (x,y) : [tex](\frac{14}{3},-\frac{16}{3})[/tex]

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By using the concept of probability, it can be calculated that

a) State space S(x) = {-1, 0, 1, 2}

b) The required probability mass function is

    P(X = -1) = [tex]\frac{125}{216}[/tex]

    P(X = 0)  [tex]= \frac{25}{72}[/tex]

    P(X = 1)  [tex]= \frac{5}{72}[/tex]

    P(X = 2)  [tex]= \frac{1}{216}[/tex]

c) Expected value of X  = -0.5

d) the stake of the gambler in  order to make this a fair game is $0.5

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

a) Let a number n be chosen between 1 and 6

Three fair six sided dice are thrown

The following cases can occur

1) Number n occur on none of the three dice

2) Number n occur on one dice

3) Number n occur on two dice

4) Number n occur on three dice

Let X denote your net win after one round of gambling (i.e., the payment received from the casino minus your stake)

1) X = 0  -1 = -1

2) X = 1 - 1 = 0

3) X = 2 - 1 = 1

4) X = 3 - 1 = 2

State space S(x) = {-1, 0, 1, 2}

b) P(X = -1) = [tex]{3 \choose 0}(\frac{1}{6})^0(\frac{5}{6})^3 = (\frac{5}{6})^3 = \frac{125}{216}[/tex]

    P(X = 0) = [tex]{3 \choose 1})(\frac{1}{6})(\frac{5}{6})^2 = \frac{25}{72}[/tex]

    P(X = 1) = [tex]{3 \choose 2}(\frac{1}{6})^2\frac{5}{6} = \frac{5}{72}[/tex]

    P(X = 2) = [tex]{3 \choose 3}(\frac{1}{6})^3(\frac{5}{6})^0 = \frac{1}{216}[/tex]

    The required probability mass function is

    P(X = -1) = [tex]\frac{125}{216}[/tex]

    P(X = 0)  [tex]= \frac{25}{72}[/tex]

    P(X = 1)  [tex]= \frac{5}{72}[/tex]

    P(X = 2)  [tex]= \frac{1}{216}[/tex]

c) Expected value of X = [tex]-1 \times \frac{125}{216} + 0 \times \frac{25}{72} + 1 \times \frac{5}{72} + 2\times \frac{1}{216}[/tex]

                                      = [tex]\frac{-125 + 0 + 15 +2}{216}\\[/tex]

                                      = [tex]-\frac{108}{125}[/tex]

                                      = -0.5

d) The gambler looses $0.5 on a average

   So this is not a fair game

   Let the stake of the gambler in  order to make this a fair game be t

   By the problem,

   -0.5 + t = 0

     t = 0 + 0.5

     t = $0.5

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These are the preposition for the given conditions:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).

The domain of the propositional P(x, y) consists of pairs x and y, where x is 1, 2, 3 and y is 1, 2, 3.

What are the disjunction and conjunction?

In logic functions, there are two kinds of compound statements. These are referred to as conjunction and disjunction. A conjunction implies that both statements are correct, whereas a disjunction implies that at least one of the statements is correct. A conjunction connects statements with the word "and," whereas a disjunction connects statements with the word "or."

By using disjunction and conjunction we get,

a) ∀x∀y P(x, y) is written as:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).

b) ∃x ∃y P (x, y) is written as:

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

c) ∃x∀y P(x, y)  is written as:

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

d) ∀y∃x P(x, y)  is written as:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).

Hence, these are the preposition for the given conditions:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).

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Answer:

(8,2), (12,2),(10,10)

Step-by-step explanation:

any coordinate that means the two sides will have the same length

first, we know that the length is twice the amount of the width

so any coordinate we pick must be twice the length

pick a coordinate that is quite high up ( so we don't get into negatives)

so let's say (10,10)

then we want to go a positive number down - don't want to deal with fractions.

so e.g 8

so 6 down would be (10,2)

then the width is half the length so it has a 4cm wide base

and put an equal amount on each side to the left and the right to get the base co-ordinates

to the left : (8,2)
plus to the right: (12,2)

2+2= make a 4cm base

put these coordinates together and presto! you have coordinated proofs!

Answer:

$14

Step-by-step explanation:

since there are 2 halves in a pound we just need to multiply 7 by 2

7x2

14

Hopes this helps please mark brainliest

It's $7 for 1/2 a pound so we have to double it to get our answer so...

$14 would be our answer.

[tex]1/2+1/2=1[/tex]

The equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

According to the question,

We have the following information;

Point thorough which line is passing = (8,2)

Equation of the line:

x+4y = 28

Now, we will convert this equation into the slope-intercept form:

4y = -x+28

Dividing by 4 on both sides of the equation:

y = -x/4+28/4

y = -x/4+7

Slope of the line = -1/4

We know that the following formula is used to find the equation of the line:

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

(y-2) = -1/4(x-8)

y-2 = -x/4+2

Adding 2 on both sides:

y = -x/4+4

Hence, the equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

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Answer:

Step-by-step explanation:

8.5

The answer to the given question is 4096-fold. If it assumed that each cycle in the PCR process takes 5 minutes, then total 4096-fold amplification could be accomplished in an hour.

PCR is based on 3 simple steps needed for any DNA synthesis reaction. Those steps are: denaturation of the template to the single strands; annealing of the primers to every original strand for a new strand synthesis; and development of the new DNA strands from the primers.

In this case, each cycle takes 5 minutes and doubles the DNA.

Thus, in one hour, there would be 60 / 5 = 12 cycles.

So, the DNA would be amplified 212 = 4096-fold.

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Chance is also referred to as probability and the probability that one is blue and one is red is 4/19

probability = Number of event/Total samples space

If there are 10 black socks,20 white socks,2 red socks, and 6 blue socks in a drawer, the total number of socks will be the sample space

Sample space = 10+20+2+6

Sample space = 38

Total number of blue and red socks is the event

Number of event one blue and one red = 8 blue socks

Chance that the socks is blue = n(E)/n(S)

Chance that the socks is one red and one blue  = 8/38

Chance that the socks is red and blue = 4/19

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The line segment i rotated 270 degree clockwise about the origin to form P'Q' the statement describe P'Q'. The accurate alternative is (B) P'Q' is same in period to PQ.

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The allowable child and dependent care credit considering their pre-credit tax liability is $0

The following chart illustrates how their authorized child and dependent care credit was calculated:

If the revenue is less than $22,000, the full 22% would be permitted.

However, the eligible kid expense would only be allowed up to $7,000.

Consequently, the sum would be

= $7,000 × 22%

= $1,540

Since there is already a pre-credit tax liability, $0 should be taken into account because there would be no credit.

Due to their pre-credit tax liability, the available child and dependent care credit is therefore $0.

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