Solve.

2/13−1/2x=−2/3

Enter your answer in the box.

x =

(a) The mean of Y is 100 meters, and the standard deviation of W is approximately 0.7348 meters.

(b) The mean of W is 100 meters, and the standard deviation of W is approximately 0.6935 meters.

a) To find the mean and standard deviation of Y, where Y = (X₁ + X₂) / 2, we use the properties of the mean and variance of a sum of independent random variables.

Mean of Y:

The mean of Y is simply the average of the means of X₁ and X₂, as the measurements are independent and have the same true height of 100 meters.

Mean(Y) = (Mean(X₁) + Mean(X₂)) / 2 = (100 + 100) / 2 = 100 meters

The standard deviation of Y:

When adding or subtracting independent random variables, the variances add up. Since the measurements are independent, we can use the formula:

Var(Y) = Var((X₁ + X₂) / 2) = (Var(X₁) + Var(X₂)) / 4

Now, calculate the variance of Y:

Var(Y) = (1.2² + 0.85²) / 4 ≈ 0.54

Standard deviation(Y) = √Var(Y)
                                    ≈ √0.54
                                      ≈ 0.7348 feet

b) Now, let's find the mean and standard deviation of W, where W = (1/3)X₁ + (2/3)X₂.

Mean of W:

Mean(W) = (1/3) * Mean(X₁) + (2/3) * Mean(X₂)
               = (1/3) * 100 + (2/3) * 100
               = 100 meters

The standard deviation of W:

To calculate the standard deviation of W, we need to find the variance of W and then take its square root.

Var(W) = (1/3)² * Var(X₁) + (2/3)² * Var(X₂)
            = (1/9) * 1.2² + (4/9) * 0.85²

Now, calculate the variance of W:

Var(W) = 0.0181 + 0.1956 =0.481

Standard deviation(W) = √Var(W)
                                     ≈ √0.481
                                      ≈ 0.6935 meters

So, the mean of W is 100 meters, and the standard deviation of W is approximately 0.6935 meters.

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The variety of arrangements we can make for the 2n people to stand in a line such that nobody is next to their spouse;

(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

The step for the simplification are-

Finally, on a broad note:

(2n)! - (2(ⁿC₁)(2n - 1)! - 2²(ⁿC₂)(2n - 1)! + .....2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

On further simplifying;

(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

Thus, the variety of arrangements we can make for the 2n people to stand in a line such that nobody is next to their spouse;

(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

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Answer:

1 = 45

2 = 75

3 = 60

4 = 41

5 = 71

6 = 109

Step-by-step explanation:

This may seem tricky at first, but if you follow the order of the numbers, you can find them fairly quickly using the values already given.

For angle 1:

The angle above it of 45 degrees is similar to angle 1, so that it automatically going to be 45

For angle 2:

The same concept for angle 1 applies for angle 2, so it will be 75 degrees.

For angle 3:

All triangles add up to 180 degrees. So, since we have angles 1, and 2, solve to find 3:

180 - 45 - 75 = 60

For angle 4:

All straight lines add up to 180 degrees. So solve to find angle 4 using the value we found for angle 3:

180 - 60 - 79 = 41

For angle 5:

Angle 5 is part of another triangle and we have two of the angles already. So solve to find angle 5 using the logic used to find angle 3:

180 - 41 - 68 = 71

For angle 6:

angles 5 and 6 are part of a straight line, so use the same logic for angle 4 and solve for angle 6:

180 - 71 = 109

The area is 120 [tex]cm^{2}[/tex].

Area is the size of a two-dimensional surface, usually expressed in square units, such as square feet or square meters. It is the amount of two-dimensional space enclosed within a given set of boundaries. Area can be calculated for various shapes, including squares, rectangles, triangles, circles, and more complex shapes. Area is also a measure of the amount of space an object occupies. In mathematics, area is used to measure the size of a shape or region in a plane. It can also be used to calculate the size of a figure, such as the area of a triangle, or to measure the area of an enclosed space, such as a garden or a room.

Given:

AB = CD = 8cm

AD = BC = 12cm

EF = DH = 4cm

So, the required area is A = Area (ABCEFD) = Area (ABCD) + Area (CEFD)

Area of ABCD = Area (ABCD) = AB × BC

⇒ 12 × 8 = 96 [tex]cm^{2}[/tex]

Area of CEFD = Area (CEFD) = 0.5 (CD + EF) × HD

⇒ 0.5 × (8 + 4) × 4 = 24[tex]cm^{2}[/tex]

Now, the required area is

⇒ A = 96 [tex]cm^{2}[/tex] + 24 [tex]cm^{2}[/tex] = 120 [tex]cm^{2}[/tex]

Hence, the required area of the figure is 120 [tex]cm^{2}[/tex].

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Answer:

correct answer is D) $1.94.

Step-by-step explanation:

To solve this problem, we first need to calculate the total cost of the candy bars and the sodas. The candy bars cost $0.84 each, so 3 candy bars cost 3*$0.84=$2.52. The sodas cost $1.80 each, so 2 sodas cost 2*$1.80=$3.60. The total cost of the candy bars and sodas is $2.52+$3.60=$6.12.

Since you are going to split the cost with your friend, you will pay for half, which is $6.12/2=$3.06. You pay for your half with a five dollar bill, so you will receive $5-$3.06=$1.94 in change.

I hope it helps, let me know if you have another questions.

Answer:

Step-by-step explanation:

First, we need to find the total cost of the candy bars by multiplying the number of candy bars by the price per candy bar: 3 candy bars * $0.84/candy bar = $3*0.84=2.52Next, we need to find the total cost of the sodas by multiplying the number of sodas by the price per soda: 2 sodas * $1.80/soda = $2*1.8=3.60Then, we need to add the cost of the candy bars and the sodas to find the total cost: $2.52 + $3.60 = $<<2.52+3.6=6.12>>6.12Since you are paying for half of the total cost, you need to pay half of $6.12, or $3.06.If you pay for your half with a five dollar bill, you will receive $5 - $3.06 = $5-3.06=1.94 in change. Answer: 1.94.

Answer:

A

(will be continued)

Step-by-step explanation:

this is an exponential graph

The original mass is 7.71 because it is being multiplied by the percentage.

0.9333 in percentage form is 93.33

Since it is being multiplied, by the original mass this means that 93.33% of it is the amount being left over.

100% - 93.33% = 6.67%

this is the decrease in the amount of the thing

***tell me if i explained it clearly i'm not sure if i did

Answer: 1 3/8

Step-by-step explanation:

6 - 4 5/8 = 1 3/8

Since you are missing a part to the sum, you use subtraction to find the missing part.

3.7261×10¹⁵ seconds  is the time it would take you to empty the lake

Given that:

Lake Eric can hold 116 cubic miles of water

One cup has a diameter of 2 and 3/4 inches and a height of 4 inches

Volume of cone cup = 1/3 πr²h

Volume of cone cup = 1/3×π×(11/8)²×4 = 7.92 cubic inches

Volume of Lake Erie = 116 cubic miles

To convert to cubic inches multiply by 2.544×10¹⁴:

Volume of Lake Erie = 116×2.544×10¹⁴ = 2.95104×10¹⁶ cubic inches

Time taken = 2.95104×10¹⁶ / 7.92 = 3.7261×10¹⁵ seconds

Therefore, it would take you 3.7261×10¹⁵ seconds to empty the lake

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Answer:

x=36

Step-by-step explanation:

The length of a secant segment and a tangent segment drawn to a circle drawn from an external point is:

whole secant * external secant = tangent^2

(12+x)*12=24^2

144+12x=576

12x=432

x=36

Answer:

68 cm^2

Step-by-step explanation:

A = ((a+b)/2) x h

A = ((6+11)/2) x 8

A = 68 cm^2

I hope my answer helps you.

Answer:

Area of the trapezium is 68[tex]cm^{2}[/tex]

Step-by-step explanation:

[tex]Given[/tex],

[tex]Parallel side\\[/tex] [tex]A[/tex]= 6cm

[tex]Parallel[/tex][tex]sideB=11cm[/tex]

[tex]Height = 8[/tex]

Formula to find the area of the trapezium

[tex]Area[/tex] [tex]of[/tex][tex]Trapezium[/tex]=[tex]\frac{1}{2}(a+b)h[/tex]

[tex]\frac{1}{2}[/tex][tex](6+11)8[/tex]

[tex]\frac{1}{2}[/tex] X[tex]136\\[/tex]

[tex]68[/tex]

Hence the area of the trapezium is 68

After solving the quadratic equation, the value of k will be equal to 71.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given equation in the question,

4x² - 5x = -6

4x² - 5x + 6 = 0

k = b² - 4ac

⇒ (-5)² - 4(4)(6)

k = 25- 96

k = -71 or,

k = i(71)

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The solution for this system of equation will be [tex]x=4, y=-3.[/tex]

We will solve the given system of equation by the method of substitution. Now we label the equations as  [tex]2x+y=5....(i)[/tex] and [tex]-3x-5y=3....(ii)[/tex].

Now from equation [tex](i)[/tex] we will find the value of [tex]y[/tex] which is [tex]5-2x[/tex]. Then we will substitute the value of [tex]y[/tex] in equation [tex](ii)[/tex].

So, [tex]-3x-5\times(5-2x)=3[/tex]

⇒ [tex]-3x-25+10x=3[/tex]

⇒ [tex]7x-25=3[/tex]

⇒ [tex]7x=28[/tex]

[tex]\therefore x =\frac{28}{7}=4....(iii)[/tex]

Now we will take the value of [tex]x[/tex] from equation equation [tex](iii)[/tex] and substitute in equation [tex](i)[/tex] to get the value of [tex]y[/tex].

So, [tex](2 \times 4)+y=5[/tex]

⇒ [tex]8+y=5[/tex]

⇒ [tex]y=8-5[/tex]

[tex]\therefore y=3[/tex]

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Answer:

22, and -22

Step-by-step explanation:

22x22=484

-22x(-22)=484

The number of players the team can bring to the tournament would be = 24 players

The softball game is the type of game that involves two teams which is made up of 9. - 10 players.

The total amount of money raised by a softball team=

$2089.50

The amount of money spent on rented bus = $1087.50

The amount left after rent deductions= 2,089.50 - 1,087.50 = 1,002

The amount budgeted for meals for each player= $41.75

The number of players that would be brought for tournament= 1,002/41.75

= 24 players.

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Answer:

4/5

Step-by-step explanation:

The number of dark chocolate AJ sold is 75

Simultaneous equations are two or more algebraic equations that share variables e.g. m and d . They are called simultaneous equations because the equations are solved at the same time.

If the number of Milk chocolate candy is m and the number of dark chocolate candy is d, then

m+d= 200 equation 1

3m+4d= 675 equation 2

to eliminate m we multiply both equations by 3

3m+3d= 600 equation 3

3m+ 4d=675 equation 4

subtract equation 3 from 4

d = 675-600

d= 75

Therefore the number of dark chocolate candy AJ sold is 75.

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The probability of the card being an ace, given that it is a non-face card will be 0.1 or 10%

There are total 52 cards.

Out of 52, 26 are red and 26 are black.

Each of the four French suits—clubs (♣), diamonds (♦), hearts (♥) and spades (♠).—has 13 ranks in a regular 52-card deck. King, Queen, and Jack are the three court cards (face cards) in each suit, and their pictures are reversed (double-headed). The ten numerical cards, or pip cards, in each suit range in value from one to 10.

Out of 52 cards, (Kings, Queen, Ace) are faced card.

And each set of cards have 4 different colour and shades.

So, total number of faced card will be = 4*3 = 12

So, total number of not a faced card = 52-12 = 40

So, the value of P (It is an ace and it is not a face card) =4/52

So, the value of P(It is not a face card)=40/50

[tex]P\left(\frac{\text { It is a ace }}{\text { It is not a face curd }}\right) =\frac{P(\text { It is an ace and it is not aface carl) }}{P(\text { It is not a face card) }} \\\\ =\frac{\frac{4}{52}}{\frac{40}{52}}\\\\=\frac{4}{40}\\\\=0.1=10\% }[/tex]

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Answer: $18.30

Step-by-step explanation:

The sprinkler cost 9.23, and the change is 9.07, so adding both of them equal $18.30

Answer 18.3

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Answer: 11.5

Step-by-step explanation:

[tex]\sin 35^{\circ}=\frac{x}{20}\\\\x=20 \sin 35^{\circ}\\\\x=11.5[/tex]

Answer: $1,504,000

Step-by-step explanation:

First, take 800,000 divided by 100% = $8000

So we know that 1% is $8000

We are missing 88%, so take 8000 times 88 = $704,000

Then we add 800,000 with 704,000 = $1,504,000

So the total sales are $1,504,000

Answer: $14.18

Step-by-step explanation:

Because total change is the amount the cashier is giving back to us,

we can do

$ amount given - $ price of order = $ total change

So:

50 - 35.82 = $14.18

The cashier will give us $14.18 back in change.

The width of the prism is x+2. The smallest dimension of an item or figure on a planar surface is its width.

When calculating the volume of a rectangular prism, we multiply the prism's length, width, and height.

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism. It is referred to as a prism because of the length of its cross-section.

Given, the volume of the prism

= x³ + 2x²+ 20x - 24

length = (x- 6 )

height and width are equal then

h * w = x³ + 2x²+ 20x - 24 / (x - 6)

= (x + 2 ) (x + 2)

h = (x +2 )and

w = (x+2)

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Answer:

0

Step-by-step explanation:

          x

f(x) = ------  -  3

          7

           21

f(21) = ------  -  3

            7

f(21) = 3  -  3

f(21) = 0

I hope this helps!

The average rate of change in the stock from hour 1 to hour 6 is -$0.20/hr.

What is average rate of change in stock?

We need to find the average rate of change of stock from 1 hour to 6 hours.

The value of stock was $11 in hour 1 and $10 in hour 6.

Average rate of change = Δy/ Δx

= $10 - $11 / 6-1

= - $1/5

= -$0.20 /hr

Hence, the average rate of change in the stock from hour 1 to hour 6 is -$0.20/hr.

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The inequality that represents all possible combinations of x, the number of monitors, and y, the number of keyboards, the university can buy for the computer lab is 250x + 50y <= 4500

Which inequality represents all possible combinations?

The given parameters are:

Spending = At most $4,500

Cost of monitor (x) = $250 per unit

Cost of keyboard (y) = $50 per unit

The total spending is represented as

Total = 250 * x + 50 * y

This gives

Total = 250x + 50y

The spending is at most $4,500 i.e less than or equal to

So, we have

250x + 50y <= 4500

Hence, the inequality that represents all possible combinations of x, the number of monitors, and y, the number of keyboards, the university can buy for the computer lab is 250x + 50y <= 4500

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The solutions are

a) The smallest possible value of x - y is A = -6

b) The largest possible value of 2x / y is B = 6

c) The largest possible value of x² + y² is C = 100

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the first inequality equation be represented as P

The value of P is

-4 ≤ x ≤ 6

Let the second inequality equation be represented as Q

The value of Q is

2 ≤ y ≤ 8

Now , the smallest value of inequality P is = -4

The largest value of inequality P is = 6

And , the smallest value of inequality Q is = 2

The largest value of inequality Q is = 8

a)

Let the smallest possible value of x - y be = A

The value of x - y is calculated as

The smallest value of P - smallest value of Q

Substituting the values in the equation , we get

A = -4 - 2

A = -6

Therefore ,  The smallest possible value of x - y is A = -6

b)

Let the largest possible value of 2x / y be = B

The value of 2x/y is calculated as

Largest value of x goes in numerator and smallest value of y goes in denominator to get the largest value of 2x/y

So , substituting the values in the equation , we get

B = ( 2 x 6 ) / 2

B = 12 / 2

B = 6

Therefore , The largest possible value of 2x / y is B = 6

c)

Let the largest possible values of x² + y² be = C

The value of x² + y²  is calculated as

The largest value of x squared + the largest value of y squared

Substituting the values in the equation , we get

C = 6² + 8²

C = 36 + 64

C = 100

Therefore , The largest possible value of x² + y² is C = 100

Hence , The solutions are

a) The smallest possible value of x - y is A = -6

b) The largest possible value of 2x / y is B = 6

c) The largest possible value of x² + y² is C = 100

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Only a line that goes from (0, 0) and (3.6, 14.4) satisfy the given relationship.

        y = mx

        m = y/x

        [m] is called constant of proportionality.

Given is a graph as shown in the figure.

The graph represents a proportional relationship. The possible coordinates that can be plotted are (x, y) and not (y, x). Only a line that goes from (0, 0) and (3.6, 14.4) satisfy the given relationship.

Therefore, only a line that goes from (0, 0) and (3.6, 14.4) satisfy the given relationship.

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Answer:

3.75mm

Step-by-step explanation:

4.5/3=1.5

1.5(2.5)=3.75

the ratios are the same

Answer:

176cm

Step-by-step explanation:

therefore r=13÷2 =r=7.5. and pieces =22÷7

then we substitute

22÷7×(7.5 ×7.5)

=3.14×56.25

=176.58

to the nearest whole =176cm