A wall shaped like a trapezoid needs to be painted. The height of the wall is 16 feet and the bases are 20 feet and 24 feet. If one can of paint covers 20 square feet, how many whole cans of paint will the painter need to buy to paint the wall with one coat

A and B are independent events if the probability of getting a red convertible is 0.08

The given parameters are:

P(A) = 0.20

P(B) = 0.40

The events are independent, if

P(A and B) = P(A) * P(B)

So, we have:

P(A and B) = 0.20 * 0.40

Evaluate

P(A and B) = 0.08

Hence, A and B are independent events if the probability of getting a red convertible is 0.08

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Complete question

A video game randomly chooses your car color and type. The probability of getting a red car is 0.20, and the probability of getting a convertible is 0.40.

Event A = You get a red car.

Event B = You get a convertible.

A and B are independent events if _____.

A.The probability of getting a red car or a convertible is 0.60.

B.The probability of getting a red car or a convertible is 0.08.

C.The probability of getting a red convertible is 0

D.The probability of getting a red convertible is 0.08

A square is a plane shape that has an equal length of sides. The required answers to the questions are;

i. Yes, the area of a square and its length of sides are directly proportional.

ii. Yes, the perimeter and length of the side of a square are directly proportional.

A square is a plane shape that has an equal length of sides, with four internal right angles. The area of a square can be determined as:

Area = length x length

        = [tex](length)^{2}[/tex]

This implies that the value of area of a given square depends on the value of its length. So that the area and length of sides of a square are directly proportional.

If the value of its length increases, then the value of its area increases, viz-a-viz. Then the area and length of the sides of a square are directly proportional.

The perimeter of a square is the sum of the length of its individual sides. Thus, the perimeter of a square can be determined by:

perimeter = 4 x length

Thus the value of the length determines the value of its perimeter. If the length of its sides increases, so is that of the perimeter. Therefore, the length and perimeter of a square are directly proportional.

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The value of 2+8+32+128…..,n=9 is 174762

The series is given as:

2+8+32+128…..,n=9

Start by calculating the common ratio (r)

r = 8/2

r = 4

The sum of the series is then calculated as:

[tex]S_n = \frac{a *(r^n - 1)}{r -1}[/tex]

This gives

[tex]S_9 = \frac{2 *(4^9 - 1)}{4 -1}[/tex]

Evaluate the difference

[tex]S_9 = \frac{2 *( 262143)}{3}[/tex]

Evaluate the quotient

[tex]S_9 = 174762[/tex]

Hence, the value of 2+8+32+128…..,n=9 is 174762

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Answer:

2/3

Step-by-step explanation:

1/3 cup powdered sugar

2/6 cup brown sugar

Reduce 2/6 to 1/3.

1/3 + 1/3 = 2/3

Using linear function concepts, it is found that the volume of each marble is of 0.05 liters.

A linear function is modeled by:

y = mx + b

In which:

The linear function that gives the volume of water, when n marbles are inserted into the tank, is given by:

w = 32 - 0.05n

The slope of -0.05 means that for each marble inserted, there are 0.05 liters less for water, hence the volume of each marble is of 0.05 liters.

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Answer:

.05 liters

Step-by-step explanation:

Using it's concept, the domain of the function represented by the graph is all real numbers.

The domain of a function is the set that contains all possible input values for the function.

In this problem, a parabola is used, which has no restriction such as an even root or a fraction, hence the domain is all real values.

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Quarts of detergent 1208

First, we convert each unit to its pint equivalent.

1 gallon =eight US Pint

114 gallons =114 X eight =912 Pint

34 gallon =34 X 8 =272 Pint

further, 1 quart =2 Pint

12 quart = 12 X 2 Pint =24 Pint

including the three values

912+272+24=1208 Pint

therefore, Meredith will want 1,208 Pint boxes.

The unitary technique is a way of solving trouble by way of first finding the fee of a single unit, and then finding the essential value with the aid of multiplying the unmarried unit price.

The system of the unitary technique is to locate the fee of an unmarried unit after which multiply the fee of a single unit to a wide variety of devices to get the vital fee.

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The length of the triangle will be equal to 2.7.

It should be noted that that sin will be the opposite divided by the hypothenuse.

The measure of angle L is 20°.

This will be:

sin 20 = LN/8

NM = 8 sin 20

NM = 2.7

In conclusion, NM is 2.7.

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Answer:   2.7

Step-by-step explanation:  TRUST ME!!!  Answer is correct on Edge!!!  :)

Answer:

a) x = 1.5 and x = -0.3

b) x = -8 and x = 5

Step-by-step explanation:

a)

The given equation follows the general structure: ax² + bx + c = 0.

Therefore, if a = 5, b = -6, and c = -2, you can substitute the values into the quadratic formula and solve for "x".

b)

Another way of solving polynomials is through factorization. After rearranging the equation to fit the general structure of a quadratic (as seen above), you can factor by asking yourself the question, which 2 numbers multiply to "c" (-40) and add to "b" (3)? The answers will make up your factors.

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\huge\textbf{Equation \#1. }[/tex]

[tex]\mathsf{5x^2 - 6x - 2 = 0}[/tex]

[tex]\huge\textbf{Use the quadratic formula to solve:}[/tex]

[tex]\mathsf{x = \dfrac{-(-6)\pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}}[/tex]

[tex]\huge\textbf{Simplify it: }[/tex]

[tex]\mathsf{x = \dfrac{6 \pm \sqrt{76}}{10}}[/tex]

[tex]\huge\textbf{Simplify that as well:}[/tex]

[tex]\mathsf{x = \dfrac{3}{5} + \dfrac{1}{5}\sqrt{19}\ or\ x = \dfrac{3}{5} + (-\dfrac{1}{5})\sqrt{19}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x \approx 1.5 \ or\ x\approx -0.3{}\ }}\huge\checkmark[/tex]

[tex]\huge\textbf{Equation \#2.}[/tex]

[tex]\mathsf{x^2 + 3x = 40}[/tex]

[tex]\huge\textbf{Subtract 40 to both sides:}[/tex]

[tex]\mathsf{x^2 + 3x - 40 = 40 - 40}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x^2+ 3x - 40 = 0}[/tex]

[tex]\huge\textbf{Factor the left side of the equation:}[/tex]

[tex]\mathsf{(x - 5)\times (x + 8) = 0}[/tex]

[tex]\mathsf{(x - 5)(x + 8) = 0}[/tex]

[tex]\huge\textbf{Set the factors to equal to 0:}[/tex]

[tex]\mathsf{x - 5 = 0 \ or\ even\ x + 8 = 0}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = 5\ or\ x = -8}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 5\ or \ x = -8}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The probability that two of three football games will go to into overtime is 0.08

From the question, we have the following parameters about the probability

Sample size, n = 3

Proportion that goes to overtime, p = 18%

Number that goes into overtime, x = 2

The probability that two of three football games will go to into overtime is calculated using the following binomial probability

P(x) = nCx * p^x * (1 - p)^(n -x)

Substitute the known values in the above equation

P(2) = 3C2 * (18%)^2 * (1 - 18%)^(3 -2)

Express 18% as decimal

P(2) = 3C2 * (0.18)^2 * (1 - 0.18)^(3 -2)

Evaluate the difference

P(2) = 3C2 * (0.18)^2 * (0.82)^1

Evaluate the combination expression

P(2) = 3 * (0.18)^2 * (0.82)^1

Evaluate the exponent

P(2) = 3 * 0.0324 * (0.82)

Evaluate the product

P(2) = 0.079704

Approximate

P(2) = 0.08

Hence, the probability that two of three football games will go to into overtime is 0.08

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Answer:

[tex]\frac{23}{90}[/tex]

Step-by-step explanation:

we require 2 equations with the recurring digit placed after the decimal point.

let x = 0.2555.. ( multiply both sides by 10 and 100 )

10x = 2.555... (1)

100x = 25.555.... (2)

subtract (1) from (2) thus eliminating the recurring digits

90x = 23 ( divide both sides by 90 )

x = [tex]\frac{23}{90}[/tex]

Answer:

[tex]\sf \dfrac{23}{90}[/tex]

Step-by-step explanation:

  x = 0.25555.....  --------------(I)

Number of non-recurring digits is 1. So, multiply equation (I) by 10.

10x = 2.5555.... --------------(II)

Number of recurring digits is 1. So, multiply equation (II) by 10.

 100x = 25.5555...... (III)

Subtract equation (II) from (III)

     100x = 25.5555........

       10x =    2.5555.......

    -             -                      

         90x = 23

             x = 23/90

The centre angle of circular sector is n = 90 degrees (approximately).

A sector is referred to as a component of a circular made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radius of the circle at its ends.

A piece of pizzas can be used as an analogy for the form of a circle's sector.

The formula for finding the angle formed at the circular sector in radian is;

Let 'n' be the centre angle.

Let 'l' be the slant height of the cone which is equal to radius of circular sector.

Let 'r' be the radius of the cone.

First, calculate the total length of the circular sector say 'L' which is equal to the circumference of the circular base of the cone.

circumference = 2[tex]\pi[/tex]r

                        = 2×3.14×1

                        = 6.28

Now,

centre angle = length of circular sector/radius of circle

n = L/l

n = 6.28/4

n = 1.57 radian

Convert radian in degree as;

n = (1.57×180)/[tex]\pi[/tex]

n = 89.95

n = 90 degrees (approximately)

Therefore, the angle made by the circular sector is 90 dergees.

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The correct question is-

The slant height and radius of a cone are 4 and 1, respectively. Unrolling the curved surface gives a circular sector with center angle n degrees. Find n.

Answer:

I don't know.i don't know

Answer:

Step-by-step explanation:

The graph is widest when the coefficient of [tex]x^2[/tex] has the smallest absolute value.

The graph is narrowest when the coefficient of [tex]x^2[/tex] has the largest absolute value.

By comparing the graphs of the functions, function 1: y = 0.25x2 is the widest and function 4: y = -16x2 is the narrowest.

The graph is widest when the coefficient of [tex]x^{2}[/tex] has the smallest absolute value.

The graph is narrowest when the coefficient of [tex]x^{2}[/tex] has the largest absolute value.

The answer lies in the coefficient for the [tex]x^{2}[/tex] term. When the absolute value of the coefficient gets bigger, the graph gets narrower (positive and negative simply show the direction the parabola is pointing, with positive opening up and negative opening down).

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Answer:

the 4th answer option. W = 153°, P = 71°

Step-by-step explanation:

PQRS ~ TUVW

that means both figures are similar.

and that means that the angles at the corresponding vertexes are the same, and all 4 corresponding sides (and any other pair of corresponding lines like diagonals) have the same scaling factor.

we see due to the proportions of the different parts of the shapes

U corresponds to Q.

T corresponds to P.

W corresponds to S.

V corresponds to R.

therefore, as the angle at S = 153°, so is W.

and as the angle at T = 71°, so is P.

As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution whenever the sample size is large.

Thus, as a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution when the sample size is large and each element is selected independently from the same population.

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Answer:

15.78°

Step-by-step explanation:

Let the angle be x.

From the x, the known sides are the opposite side, O(13) and the adjacent side, A(46)

Therefore, The trigonometric ratio is the tangent ratio.

tan x = O/A

tan x =13/46

x = 15.78°

The age of the father is 57 years old

Total age = Average age x Population

Average of the four children = 15

Population = 4

Total age of the four children = 15 x 4

Total age of the four children = 60 years

If the parents are added:

Population = 6

Average age = 25

Total age = 25 x 6

Total age = 150 years

Total age of the parents = 150 - 60

Total age of the parents = 110 years

The father is 4 years older than his wife

Let the age of the father be x

The age of the wife = x - 4

x + x - 4 = 110

2x = 114

x = 114/2

x = 57

Therefore, the age of the father is 57 years old

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The rewritten equation for the given equation is [tex]x=\frac{h+g}{-f}[/tex]. So, option C is correct.

A linear equation given in the form ax + b = c can be rewritten to solve for x as below:

ax + b = c

⇒ ax = c - b

∴ x = (c - b)/a

So, here the basic operations such as addition, subtraction, multiplication, and division are used on both sides to rewrite the given equation for solving x.

Given equation is -fx - g = h

Step 1: Adding 'g' on both sides

-fx - g + g = h + g

⇒ -fx = h + g

Step 2: Dividing by '-f' on both sides

-fx = h + g

⇒ -fx/-f = (h + g)/-f

∴ x = (h + g)/-f

Therefore, the rewritten equation to solve for x is x = (h + g)/-f.

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Disclaimer: The given question was incomplete in the portal. Here is the complete question.

Question: Select the correct answer. which equation is correctly rewritten to solve for x?

Equation: -fx = h + g

A. x = (g - h)/f

B. x = (h - g)/-f

C. x = (h + g)/-f

D. x = (h + g)/f

Answer:

12, 14, 16, 18

Step-by-step explanation:

(x + (x+2) + (x+4) + (x+6))/4 = 15

^ solve algebraically

you'll get (4x+12)/4 = 15

then: 4x + 12 = 60

then 4x = 60-12

then 4x = 48

then x = 12

x is 12 so then do substitution

so you get

12 + (12+2) + (12+4) + (12+6)

12, 14, 16, 18

Answer:

  3 1/2 quarts

Step-by-step explanation:

The fraction of the lemonade that is water can be determined from the ratio of water to lemon juice. That fraction of a gallon is the quantity of interest.

Of the 7+1 = 8 parts that make up the lemonade, 7 of those are water. That is, water is 7/8 of the lemonade.

Of the 4 quarts of lemonade, the quantity that is water will be ...

  (7/8)(4 quarts) = 7/2 quarts = 3 1/2 quarts . . . of water

Answer:

x-2

Step-by-step explanation:

The formula for area of rectangle is length x width
And we know that width is x-16
And we know that the area is [tex]x^{2} -18x +32[/tex]

So we know that when x-2 is multiplied with  x-16, it gives off [tex]x^{2} -18x +32[/tex]

The value of x is 17/12

The equation is given as

2 (3/4 - x/3) = 1 1/4

Express as improper fractions

2 (3/4 - x/3) = 5/4

Divide through by 2

3/4 - x/3 = 5/9

Collect like terms

x/3 = 3/4 - 5/9

Multiply through by 3

x = 9/4 - 15/9

Evaluate

x = (81 - 30)/36

Evaluate

x = 51/36

Simplify

x = 17/12

Hence, the value of x is 17/12

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The value is J = 1.71*10^-6 kmol/m^2.s

According to the given conditions we get,

The length the tube l= 0.20m

The diameter of the tube d= 0.01m

The total pressure inside the tube P= 101.32kPa

The partial pressure of CO2 at the first end is

P1= 456mm Hg = 60794.832 Pa

The partial pressure of CO2 at the other end is

P2= 76mm Hg = 10132.472 Pa

The temperature is T = 298 K

The diffusion coefficient D= 1.67* 10^-5 m^2/s

Generally the molar flux of CO2 is mathematically represented as

J= D{p1-p2} / R.T

Here R is the gas constant with value R= 8.314 j/kmol

So we get J= 1.71 * 10^-3 mol/m^2.sec

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Answer:

f[g(4)] = 4

Step-by-step explanation:

Given table:

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} x & -6 & -4 & 1 & 3 & 4\\\cline{1-6} f(x) & 4 & -1 & -6 & 1 & 3 \\\cline{1-6} g(x) & 1 & 4 & 3 & -4 & -6 \\\cline{1-6}\end{array}[/tex]

f[g(4)] is a composite function.

When calculating composite functions, always work from inside the brackets out.

Begin with g(4):  g(4) is the value of function g(x) when x = 4.

From inspection of the given table, g(4) = -6

Therefore, f[g(4)] = f(-6)

f(-6) is the value of function f(x) when x = -6.

From inspection of the given table, f(-6) = 4

Therefore, f[g(4)] = 4

As we can see

So

Answer:

A=P(1+in)

A=13000(1+6/100×9)

A=press calculator

The quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2

The statement is given as:

Divide 24x2y + 8xy2 + 8xy by -4xy

The quotient is represented as:

Quotient = (24x^2y + 8xy^2 + 8xy)/(-4xy)

Factor out -4xy

Quotient = (-4xy)(-6x - 2y - 2)/(-4xy)

Evaluate the quotient

Quotient = -6x - 2y - 2

Hence, the quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2

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Answer:

? = 120°

Step-by-step explanation:

the central angle is the same as the arc that subtends it , that is

? = 120°

The equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.

Slope of the line KL = (8 - 0)/(-6 - 6) = 8/(-12) = -2/3.

Using the formula of the slope of the line passing through the points (x₂, y₂) and (x₁, y₁), as m = (y₂ - y₁)/(x₂ - x₁).

The slope of the line parallel to the line KL will be equal to the slope of KL.

Thus, the slope of the required line is m = -2/3.

The required line also passes through point M (-4, -2).

Thus, the equation of the required line will be,

y - (-2) = (-2/3)(x - (-4)) {Using the equation of the line passing through the point (x₁, y₁) and a slope m, as y - y₁ = m(x - x₁)},

or, y + 2 = (-2/3)(x + 4),

or, 3(y + 2) = -2x - 8,

or, 2x + 3y = -6.

From the given points, only the point (-6, 2) satisfies the equation.

Thus, the equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.

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The provided question is incomplete. The complete question is:

"On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M?

(–10, 0)

(–6, 2)

(0, –6)

(8, –10)"