Ken's living room and computer room have the dimensions shown.

What is the total volume of the rooms, in cubic feet?

Answer:

[tex]\mathrm{23cm,19.81cm^2}[/tex]

Step-by-step explanation:

[tex]\mathrm{Solution:}\\\mathrm{Let\ a=5cm,\ b=8cm\ and\ c=10cm}\\\mathrm{Let\ "P"\ denote\ the\ perimeter\ and\ "A"\ denote\ the\ area\ of\ the\ triangle.}\\\mathrm{Then,\ P=a+b+c=5+8+10=23cm}\\\mathrm{Also,\ Semiperimeter(s)=\frac{P}{2}=\frac{23}{2}=11.5}\\[/tex]

[tex]\mathrm{Now,}\\\mathrm{Area\ of\ triangle=\sqrt{s(s-a)(s-b)(s-c)}}\\\mathrm{=\sqrt{11.5(11.5-5)(11.5-8)(11.5-10)}}\\\mathrm{=\sqrt{11.5\times 6.5\times 3.5\times 1.5}}\\\mathrm{=19.81cm^2}\\\mathrm{So,\ the\ perimeter\ of \ the\ triangle\ is\ 23cm\ and\ area\ is\ 19.81cm^2.}[/tex]

He started walking the dog at the time 12:30 p.m.

We know that Dakota completed hera chores at 1:32 p.m. and that she spent a total of 48 minutes doing them.

That means she must have started her chores at:

⇒    1:32 p.m. - 48 minutes = 12:44 p.m.

We know that she walked the dog for 14 minutes.

We want to find out what time she started walking the dog,

so subtract 14 minutes from the time she started doing chores,

⇒ 12:44 p.m. - 14 minutes = 12:30 p.m.

Therefore,  

Dakota started walking the dog at 12:30 p.m.

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Answer:

a is -13

b is 31

c is 24

Step-by-step explanation:

Step-by-step explanation:

Tess's expression is NOT equivalent because she forgot to include the - sign when multiplying -7 and -4.

Bernette's expression is NOT equivalent because she did 2-7 first which is not correct. Since the -7 is connected to the parenthesis, she needs to fully distribute the -7 into the parenthesis before including the 2.

Lucy's expression IS equivalent because she factored it correctly and distributed the -7 into the parenthesis.

Answer:

x = 12.85714286 (as a decimal)

x = [tex]\frac{90}{7}[/tex] (as a fraction)

Step-by-step explanation:

These 2 triangles are similar.

[tex]\frac{20}{x} = \frac{20 + 8}{x + 18}[/tex]

20(x + 18) = x(20 + 8)

20x + 360 = 20x + 8x

20x + 360 = 28x

360 = 28x

x = 12.85714286 or x = [tex]\frac{90}{7}[/tex]

I believe the correct anwser is 45

It is false that for a population of scores, the sum of the deviation scores is equal to expected value.

The sum of deviation scores is not equal to the expected value (EX) of a population of scores. The expected value represents the average value that we expect to obtain if we were to repeatedly sample from the population.

The sum of deviation scores is the sum of the differences between each score and the mean of the population. It provides information about the total variability in the data. While both concepts are related to the distribution of scores, they serve different purposes and are calculated differently.

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To find the image of point Q after applying the given translation rule, we need to apply the rule to the coordinates of point Q(-2, 6).

Using the translation rule (x, y) → (x + 4, y - 5), we can apply the rule to the coordinates of point Q:

Q' = (-2 + 4, 6 - 5)

= (2, 1)

Therefore, the image of point Q after the translation is Q'(2, 1).

The value of the given expression sin(45°) + cos(67°) - 4554 + 97 + 64555 + 755577652 - 6622 is approximately 755,642,129.099.

To find the value of the expression sin(45°) + cos(67°) - 4554 + 97 + 64555 + 755577652 - 6622, we can start by evaluating the trigonometric functions and then simplifying the arithmetic operations.

First, let's find the values of sin(45°) and cos(67°).

sin(45°) is equal to √2/2, approximately 0.7071, and cos(67°) is equal to 0.3919 (rounded to four decimal places).

Now, we can substitute these values into the expression:

0.7071 + 0.3919 - 4554 + 97 + 64555 + 755577652 - 6622

Next, let's perform the arithmetic operations:

0.7071 + 0.3919 = 1.099 (rounded to three decimal places)

1.099 - 4554 + 97 + 64555 + 755577652 - 6622

Simplifying further:

-4554 + 97 + 64555 = 60098

60098 + 755577652 - 6622 = 755642128

Finally, we have:

1.099 + 755642128 = 755642129.099

Note: The answer has been rounded to three decimal places for intermediate steps and provided as an approximate value due to rounding in trigonometric functions.

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The solution of the expression is,

a) 3,724

b) 2,784

We have to given that,

a) Divide 70,756 by 19.

b) Subtract 940 from your answer to part a).​

Now, We can simplify as,

a) Divide 70,756 by 19.

⇒ 70,756 ÷ 19

⇒ 3,724

And, Subtract 940 from your answer to part a).​ that is, 3724

⇒ 3724 - 940

⇒ 2,784

Therefore, The solution of the expression is,

a) 3,724

b) 2,784

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Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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The percent increase of total interest paid between purchasing one point and purchasing no points is approximately [tex]6.9[/tex]%.

To calculate the percent increase of total interest paid between purchasing one point and purchasing no points, we need to find the difference in total interest and then calculate the percentage increase.

For Example 1 (No Points), the total interest paid is $[tex]216,370.00[/tex].

For Example 2 (One Point), the total interest paid is $[tex]201,250.00[/tex].

The difference in total interest is $[tex]216,370.00[/tex] - $[tex]201,250.00[/tex] = $[tex]15,120.00[/tex].

To calculate the percentage increase, we divide the difference by the total interest of Example 1 and multiply by [tex]100[/tex]:

[tex]\[\frac{15,120.00}{216,370.00} \times 100 \approx 6.9\%\][/tex]

Therefore, it can be said that the percent increase of total interest paid between purchasing one point and purchasing no points is approximately [tex]6.9[/tex]% (rounded to the nearest tenth).

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Answer:

Step-by-step explanation:

[tex]P(blue)=\frac{3}{10} \\[/tex]

For sample of 500 jellybeans:

   [tex]E(blue)=\frac{3}{10}\times500=150[/tex]

Solution: 150 blue jellybeans.

Answer:

(x,y)=(2,0)

Step-by-step explanation:

Multiply top equation by 4 and bottom equation by 5

-5y = 10 - 5x --> -20y = 40 - 20x

-2y = 8 - 4x --> -10y = 40 - 20x

Subtract both equations

-10y = 0

y = 0

Substitute y=0 into one of the original equations to find x

-5y = 10 - 5x

-5(0) = 10 - 5x

0 = 10 - 5x

5x = 10

x = 2

Therefore, the solution is (x,y)=(2,0)

In both cases considered below, we have either x = m or m ∉ x. Therefore, m is an ∈-minimal element of X.

Let's consider a nonempty subset X ⊆ ℕ.

To prove that X has an ∈-minimal element, we can follow the given hint: pick an arbitrary n ∈ X and look at the intersection of X with the set {0, 1, 2, ..., n}.

Let's denote this intersection as Y = X ∩ {0, 1, 2, ..., n}.

We can observe the following:

Y is a nonempty subset of ℕ: Since X is nonempty, and we are intersecting it with a nonempty set {0, 1, 2, ..., n}, the resulting set Y = X ∩ {0, 1, 2, ..., n} will also be nonempty.

Y is a finite subset of ℕ: The set {0, 1, 2, ..., n} is finite, and the intersection of any two finite sets is also finite. Therefore, Y is a finite subset of ℕ.

Since Y is a nonempty and finite subset of ℕ, it must have a minimal element with respect to the element hood relation ∈.

Let's denote this minimal element as m, where m ∈ Y.

Now, we need to show that m is an ∈-minimal element of X, i.e., for any x ∈ X, either x = m or m ∉ x.

Consider an arbitrary element x ∈ X. We know that x ∈ Y because Y is defined as the intersection of X with {0, 1, 2, ..., n}. Since m is the minimal element of Y, we have two cases:

Case 1: If x = m, then we have x = m, satisfying the condition.

Case 2: If x ≠ m, then x ∈ Y implies that x ∉ {0, 1, 2, ..., n} \ {m}. In other words, x ∉ {0, 1, 2, ..., n} or x = m. But x ≠ m, so x ∉ {0, 1, 2, ..., n} must hold. Since x ∉ {0, 1, 2, ..., n}, we can conclude that m ∉ x.

In both cases, we have either x = m or m ∉ x. Therefore, m is an ∈-minimal element of X.

Since we picked an arbitrary n ∈ X and showed that X ∩ {0, 1, 2, ..., n} has an ∈-minimal element, we have demonstrated that every nonempty subset X ⊆ ℕ has an ∈-minimal element.

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The producer surplus is approximately $663.772.

To find the producer surplus, we need to calculate the area between the supply curve and the selling price line.

The supply curve is given by the equation:

[tex]s(x) = 180 + 0.3x^{(3/2)[/tex]

where x is the product quantity.

Let's set the selling price to $250.

We want to find the quantity (x) at which the selling price intersects the supply curve. So, we can set:

[tex]250 = 180 + 0.3x^{(3/2)[/tex]

Now, let's solve this equation to find the value of x:

[tex]250 - 180 = 0.3x^{(3/2)[/tex]

[tex]70 = 0.3x^{(3/2)[/tex]

Divide both sides by 0.3:

[tex]x^{(3/2)} = 70 / 0.3[/tex]

[tex]x^{(3/2)} = 233.33[/tex]

Now, we can solve for x by raising both sides to the power of 2/3:

[tex]x = (233.33)^{(2/3)[/tex]

x ≈ 24.88

So, the quantity (x) at which the selling price intersects the supply curve is approximately 24.88.

To calculate the producer surplus, we need to find the area between the supply curve and the selling price line from 0 to x.

The formula for the producer surplus is:

Producer Surplus = ∫[0 to x] (s(x) - Selling Price) dx

Using the given supply curve [tex]s(x) = 180 + 0.3x^{(3/2)[/tex] and the selling price of $250, we can evaluate the integral:

Producer Surplus = ∫[0 to 24.88] ([tex]180 + 0.3x^{(3/2)[/tex]) dx

Calculating the integral we get,

= 663.772

Therefore, the producer surplus is approximately $663.772.

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Answer:

Amanda has 8 cousins

Step-by-step explanation:

Let C be the number of cousins Caleb has, A be the number of cousins Amanda has, and R be the number of cousins Ruby has:

[tex]C=2A\\R=5\\R=C-11\\\\R=C-11\\5=C-11\\16=C\\\\C=2A\\16=2A\\8=A[/tex]

Therefore, Amanda has 8 cousins.

Answer:

Amanda has 8 cousins.

Step-by-step explanation:

Let's use algebraic variables to solve the problem.

Let's assume the number of cousins Amanda has is represented by 'A'.

Since Caleb has twice as many cousins as Amanda, the number of cousins Caleb has is '2A'.

And Ruby has 5 cousins, which is 11 less than what Caleb has, so the number of cousins Caleb has is '5 + 11 = 16'.

Equating the two expressions for the number of cousins Caleb has:

2A = 16

Now we can solve for 'A', the number of cousins Amanda has:

Divide both sides of the equation by 2:

A = 16 / 2

A = 8

Therefore, Amanda has 8 cousins.

To maximize profit, the factory should manufacture 8 bicycles and 12 motorcycles.

Let us assume the number of bicycles as 'x'

Let us assume the number of motorcycles as 'y'.

The time constraint on machine A can be expressed as: 5x + 4y ≤ 120

The time constraint on machine B can be expressed as: 4x + 8y ≤ 144

To maximize profit, we need to maximize the objective function:

P = 40x + 50y

By graphing the constraints and finding the feasible region, we can determine the optimal solution.

Graphing the constraints:

For 5x + 4y ≤ 120:

Let's solve for y in terms of x: y ≤ (120 - 5x) / 4

For 4x + 8y ≤ 144:

Let's solve for y in terms of x: y ≤ (144 - 4x) / 8

The feasible region will be the intersection of the shaded regions:

y ≤ (120 - 5x) / 4

y ≤ (144 - 4x) / 8

Now, we will find the corner points of the feasible region:

When x = 0, y = 0

When x = 24, y = 0

When x = 8, y = 12

Substituting values into objective function P = 40x + 50y:

When x = 0, y = 0:

P = 40(0) + 50(0)

P = 0

When x = 24, y = 0:

P = 40(24) + 50(0)

P= 960

When x = 8, y = 12:

P = 40(8) + 50(12)

P = 1360.

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Answer:

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

Step-by-step explanation:

what is the sum 3/x+9+5/x-9

[tex]\frac{3}{x} + 9 + \frac{5}{x} - 9 =[/tex]     (add [tex]\frac{3}{x}[/tex] and [tex]\frac{5}{x}[/tex])

[tex]\frac{8}{x} + 9 - 9 =[/tex]            (solve 9 - 9 = 0)

[tex]\frac{8}{x}[/tex]                           ( your answer)

Each member should still raise, on average, at least $39.96 to meet the goal.

Answer: 38.4 + 216 = 254.4

Step-by-step explanation: The volume of the block at the top is 38.4 and the volume of the block at the bottom is 216 so add them together to make 254.4

Hope it helped :D

The correct answer is option (C): 0.487

If the typical duration for a customer to receive their food in a dining establishment is 15 minutes, it is possible to utilize the exponential function to estimate the likelihood of obtaining the meal within the initial 10 minutes.

The probability density function (PDF) that characterizes the exponential distribution is expressed as f(x) = (1/µ) * e^(-x/µ), where µ denotes the mean or average value.

The average duration in this scenario is 15 minutes, denoted as µ. Our goal is to determine the probability of X falling between the limits of a and b, where a is set at 0 and b is set at 10.

To calculate this probability, we need to integrate the PDF from a to b:

P(0 ≤ X ≤ 10) = ∫[tex][0 to 10] (1/15) * e^(-x/15) dx[/tex]

Integrating this expression gives us:

P(0 ≤ X ≤ 10) = [tex][-e^(-x/15)] from 0 to 10[/tex]

Plugging in the values, we get:

P(0 ≤ X ≤ 10) = [tex][-e^(-10/15)] - [-e^(0/15)][/tex]

Simplifying further:

P(0 ≤ X ≤ 10) = [tex]-e^(-2/3) + 1[/tex]

Using a calculator, we can evaluate this expression:

P(0 ≤ X ≤ 10) ≈ 0.487

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The final simplified form of the equation using BEDMAS​ is:

76 + (55555co)/12 + TO + 47

To simplify the equation using the order of operations (BEDMAS), we'll follow these steps:

-12 - 11 - 10 - 9 - 8 - 7 + 6 + 5 + (co ÷ 12) × 55555 + 11 + 10 + 9 - 2 - 1 - TO - 9 - 10 - 11 + "12 × (4 ÷ 4) + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Let's simplify this step by step:

-12 - 11 - 10 - 9 - 8 - 7 = -57

-57 + 6 + 5 = -46

co ÷ 12 = co/12

co/12 × 55555 = (55555co)/12

(55555co)/12 + 11 + 10 + 9 = (55555co)/12 + 30

-2 - 1 = -3

TO - 9 - 10 - 11 = TO - 30

"12 × (4 ÷ 4) = 12

12 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 80

Now we can simplify the entire equation:

-46 + (55555co)/12 + 30 - 3 + TO - 30 + 80

To further simplify the equation:

46 + (55555co)/12 + 30 - 3 + TO - 30 + 80

Let's simplify the expression:

46 + (55555co)/12 + 30 - 3 + TO - 30 + 80

= 76 + (55555co)/12 + TO + 47

The final simplified form of the equation is:

76 + (55555co)/12 + TO + 47

Simplifying further depends on the value or expression assigned to "co" and "TO." Without specific values or expressions, we cannot provide a final simplified form of the equation.

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The probability of hitting the black circle as required is closer to 0 than. it is to 1.

The probability of hitting the white portion of the target as required is closer to 1 than it is to 0.

It follows from the task content that the probability of hitting the circle is dependent on the area of the black circle and the square shaped target.

Since the area of the square is; 9² = 81.

The area of the black circle is; π(1.5)² = 7.07.

Since the area of the black circle is less than half the area of the square; it follows that the the probability are as stated in the answer section above.

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Answer:

[tex]9\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]\displaystyle 1\frac{1}{4}+\biggr(3\frac{2}{3}+5\frac{3}{4}\biggr)\\\\1\frac{3}{12}+3\frac{8}{12}+5\frac{9}{12}\\\\(1+3+5)+\biggr(\frac{3}{12}+\frac{8}{12}+\frac{9}{12}\biggr)\\\\9+\frac{20}{12}\\\\9+1\frac{8}{12}\\\\9+\frac{2}{3}\\\\9\frac{2}{3}[/tex]

Again, least common denominator is 3*4=12

Step-by-step explanation:

1 1/4 + ( 3 2/3 + 5 3/4)

First change them from mixed fractions to normal fractions.

= 5/4 + ( 11/3 + 23/4)

Then Find the LCM(lowest common factor) of 4 and 3 which is 12 so we'll multiply both 4 and 3 to the number so the answer would be 12. and also if we multiply the denominator we do the same to the numerator.

= 5/4 + (44/12 + 69/12)

add them.

= 5/4 + (44 + 69/12)

now find their LCM and do the same to them since 4 is a factor of 12 we'll multiply it by 3 to get 12 as a denominator to add.

= 5/4 + 113/12

= 15/4 + 113/12

= 15 + 113/12

add them.

= 128/12

Divide both numerator and the denominator by the LCM.

= 64/6

= 32/3

Answer: 32/3 or in mixed fraction: 10 2/3

Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Answer: C. not buying any phone

The cost of the car is $59,711.4.

Since,  A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100.

Given here:

Price of the car = $46,890.00,

percent down: 26%,

finance cost: $792.00 per month for 60 months

Thus Total cost= $46,890.00×0.26+60×792

                        = $12191.4 + $47520

                        = $59,711.4

Hence, The cost of the car is $59,711.4

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The net present value of the equipment is, $7,564.56.

Now, Based on the information , the net present value (NPV) of the equipment can be calculated using the formula:

NPV = (-Initial Investment) + (CF1 / (1+r)) + (CF2 / (1+r)) + ... + (CFn / (1+r)^n)

Where:

Initial Investment = $150,000

CF₁ - CFn = $22,000

r = 8%

Plugging in these values, we get:

NPV = (-$150,000) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08))

Simplifying the equation, we get:

NPV = -$150,000 + $20,370.37 + $18,828.67 + $17,405.10 + $16,088.71 + $14,871.71

Therefore, the net present value of the equipment is $7,564.56.

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Answer:

Option D

Step-by-step explanation:

       (-5, -2)   ;   x₁ = -5  & y₁ = -2

        (5 , 4)    ;   x₂ = 5   & y₂ = 4

Plugin the points in the below mentioned formula and find the slope.

  [tex]\boxed{\bf slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

             [tex]\sf = \dfrac{4-[-2]}{5-[-5]}\\\\\\=\dfrac{4+2}{5+5}\\\\=\dfrac{6}{10}\\\\=\dfrac{3}{5}[/tex]

Equation of slope-intercept form: y =mx + b

Here, m is the slope and b is the y-intercept.

     [tex]\sf y = \dfrac{3}{5}x + b[/tex]

  The line is passing through (5, 4). So, substitute the points in the equation and find the y-intercept.

           [tex]4 =\dfrac{3}{5}*5 + b\\\\\\4=3+b\\\\[/tex]

      4 - 3 = b

            b = 1

Slope intercept form of the equation:

            [tex]\sf y = \dfrac{3}{5}x + 1[/tex]