Find an equation for the line that passes through the points (-2, -5) and (4, 3).

The expected operational time of the machine is 6.75

For given x , y > 0 , the lifetime of the machine is max{x , y} because it stops when the two component will fail.

The life expectancy if therefore the expectancy of max{x, y}

t = E [ max{x,y} ]

So, the max{x , y} can be x or y

We have three integral

I₁ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{18-x}_{x} y \. dy\)

Solving the integration

=> I₁ =  729 / 162

=> 4.5

I₂ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{x}_{0} y \. dy\)

=> I₂ = 121.5/162

=> 0.75

=> I₃ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{18-x}_{x} x \. dy\)

=> I₃ = 243 / 162

=>  1.5

So . the total is 4.5 + 0.75 + 1.5

=>  6.75 is expected operational time

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Answer:

Answer: B.

I don't know for sure but there are no outliers so B is my best guess put B at your own risk though please

Answer:

Yes

Step-by-step explanation:

Step 1: Define

12x - 10x⁵ - 7 + 3x⁴

-10x⁵ + 3x⁴ + 12x - 7

Step 2: Rearrange both equations into standard form

-10x⁵ + 3x⁴ + 12x - 7

-10x⁵ + 3x⁴ + 12x - 7

We see both are equivalent.

Answer:

\(sum \: of \: one \: exterior \: angle \: is \: \\ \\ equal \: to \: two \: opposite \: angle \: \\ \\ x + (x - 25) = 145 \\ \\x + x - 25 = 145 \\ \\ 2x - 25 = 145 \\ \\ 2x = 145 - 25 \\ \\ 2x = 120 \\ \\ x = 120 \div2 \: \\ \\ x = 70\)

Answer:

x = 85

Step-by-step explanation:

180 - 145 = 35

35 + (x-25) + x = 180  All angles added together should equal to 180

solve for x with calculator:

x = 85

Answer:

9

Step-by-step explanation:

4-x = 5(16-x)

44-x = 80-5x

4x = 36

x = 9

Step 1:

Write the graph of the parent function y = f(x)

Step 2

Given the graph of y=f(x)as shown, sketch y = f(-x).

Step 3

The function y = f(x) will reflect about the y-axis to form the function y = f(-x).

Final answer

y-axis

Answer:

\({x, y} = {-\frac{2}{3}, \frac{5}{3}}\)

Step-by-step explanation:

7x + 4y = 2

x + y = 1

// Solve equation [2] for the variable  y  

 [2]    y = -x + 1

// Plug this in for variable  y  in equation [1]

  [1]    7x + 4•(-x +1) = 2

  [1]    3x = -2

// Solve equation [1] for the variable  x  

  [1]    3x = - 2  

  [1]    x = - 2/3  

// By now we know this much :

   x = -2/3

   y = -x+1

// Use the  x  value to solve for  y  

   y = -(-2/3)+1 = 5/3  

Solution :

{x,y} = {-2/3,5/3}

Timilehin has 40 books

Tomilola has 8 books.

Answer:

C. No solutions

Step-by-step explanation:

5x - 3 = 5 (x - 1)

5x - 3 = 5x - 5

* so they have the same slope but different y-intercepts. So they would be parallel lines and they would never intercept meaning. No Solutions!

Answer:

Volume of a sphere = 4πr³/3

r=10

V = 4πx10³/3

=4000π/3

V= 1333.33π (in terms of pi)

or

V= 4188.79(Nearest Hundredth).

Answer:

25.13

Step-by-step explanation:

by using formula

3.14 × radius²× height

a. The random variable represents the time which takes to completely tune an automobile engine.

b. The probability of tuning an engine is qual to 0.593, or 59.3%.

a. The random variable here is the time it takes to completely tune an engine of an automobile.

b. To find the probability of tuning an engine in 45 minutes or less,

Use the exponential distribution formula.

The exponential distribution is characterized by a rate parameter, which is the reciprocal of the mean.

The mean is 50 minutes,

The rate parameter (λ) can be calculated as λ

= 1/mean

= 1/50.

Using this rate parameter,

The probability of tuning an engine in 45 minutes or less by integrating the exponential probability density function (PDF) from 0 to 45 minutes,

P(X ≤ 45) = \(\int_{0}^{45}\)λ × \(e^{(-\lambda x)\) dx

Substituting the value of λ = 1/50 into the equation,

P(X ≤ 45) = \(\int_{0}^{45}\) (1/50) × \(e^{(-x/50)\) dx

Rewrite the integral:

P(X ≤ 45) = (1/50) ×  \(\int_{0}^{45}\)  \(e^{(-x/50)\) dx

Apply the integral,

P(X ≤ 45) = (1/50) × [-50 × \(e^{(-x/50)\)] evaluated from 0 to 45

Plug in the limits of integration,

P(X ≤ 45) = (1/50) × [-50 ×\(e^{(-45/50)\) - (-50 × \(e^{(-0/50)\))]

Simplify the expression,

P(X ≤ 45) = (1/50) × [-50 × \(e^{(-45/50)\)+ 50 × \(e^0\)]

Simplify further,

P(X ≤ 45) = -\(e^{(-45/50)\) + 1

Evaluate the expression,

⇒P(X ≤ 45) ≈ -\(e^{(-0.9)\) + 1

⇒P(X ≤ 45) ≈ -0.407 + 1

⇒P(X ≤ 45) ≈ 0.593

Therefore, the probability of tuning an engine in 45 minutes or less is approximately 0.593, or 59.3%.

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Demand refers to the quantity of a product or service that buyers are willing and able to purchase at a certain price level. A demand curve is a graphical representation of the relationship between the quantity of a good or service that buyers are willing to purchase at different price levels.

In the market for VCRs, the demand and supply equations are Qd = 1,000 - 6P and Qs = 4P respectively. The government decides to impose a tax of $30 per unit sold on VCRs. This will lead to a shift in the supply curve upwards by $30, resulting in a new equilibrium point.

1. To find the new equilibrium quantity with the tax, we set Qd = Qs + tax. Thus, 1,000 - 6P = 4P + 30. Solving for P, we get P = $105. The equilibrium quantity is therefore Q = 1,000 - 6($105) = 370.

2. The price paid by buyers is the same as the equilibrium price, which is $105.

3. The price paid by sellers is the equilibrium price minus the tax, which is $75.

4. The diagram below illustrates the impact of the tax on the market for VCRs. The original equilibrium point is E0, with a price of $70 and a quantity of 400. With the tax, the new equilibrium point is E1, with a higher price of $105 and a lower quantity of 370. The tax creates a vertical distance between the two equilibrium points, which represents the tax revenue collected by the government.

[Insert Diagram Here]

5. The deadweight loss due to the tax is the reduction in total surplus (consumer surplus + producer surplus) that results from the tax. Using the original equilibrium as a benchmark, the total surplus is (1/2)($70)(400) = $14,000. With the tax, the total surplus is (1/2)($75)(340) = $6,375. Thus, the deadweight loss is $7,625.

6. To calculate the consumer surplus due to the tax, we need to compare the original consumer surplus with the new consumer surplus. Using the original equilibrium as a benchmark, the consumer surplus is (1/2)($70)(400 - 70) = $5,950. With the tax, the consumer surplus is (1/2)($105)(370 - 105) = $12,145. Thus, the consumer surplus due to the tax is $6,195.

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A statement about the data which must be true include the following: A. The spread from the lower quartile to the median is greater than the spread from the median to the upper quartile.

In Mathematics, a box plot is a type of chart that is used for the graphical or visual representation of the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided above, the five-number summary for the given data set include the following:

Spread from lower quartile (first) to median = 7 -4  = 3

Spread from median to upper quartile (third) =  9 - 7 = 2

Therefore, the spread from lower quartile (first) to median is greater than the spread from median to upper quartile (third).

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Answer: The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept.

Answer:

y=-2/3x

Step-by-step explanation:

y=mx+b the m is your slope and the b is your y-intercept, assuming that -2/3 is your slope and you have no y-int, you simply apply it to the formula replacing m giving us the result of y=-2/3x! hope this helped :-)

The equation of the line that is parallel to y = -4 is expressed as: y = -3.

A horizontal line has a slope of 0, therefore, the equation that represents a given horizontal line is expressed as y = b, where b is the value of the point where the horizontal line intercepts the y-axis.

Given the equation, y = -4, this shows that the line is a horizontal line. The line intercepts the y-axis at y = -4.

We are also told that another line that is parallel to y = -4 passes through the point, (-4, -3). This means the parallel line is also a horizontal line. Therefore, the line will intercept the y-axis at -3.

To write the equation of the parallel line, substitute b = -3 into y = b:

y = -3.

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The simple interest rate on the account is 7.5%.

The simple interest rate can be calculated by dividing the interest earned by the principal balance and the time period. In this case, the interest earned is $56.25, the principal balance is $300, and the time period is two and one-half years.

To find the interest rate, we use the formula:

Simple Interest = Principal × Rate × Time

Substituting the given values:

$56.25 = $300 × Rate × 2.5

To solve for the interest rate, divide both sides of the equation by $750:

Rate = $56.25 / ($300 × 2.5)

Simplifying the calculation:

Rate = $56.25 / $750

Rate = 0.075

Therefore, the simple interest rate on the account is 7.5%.

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Answer:

28 = 2 x - 2

Step-by-step explanation:

Better yet, let y = 6 and solve for x.

6 = x^2 –2x + 5

Now solve for x.

Answer:

$1050

Step-by-step explanation:

1=87.5

total is 12

The exact area of each hexagonal shape is 181.5sqrt(3) cm^2. Option B

To determine the exact area of each hexagonal shape formed by the equilateral triangles, we need to calculate the area of one equilateral triangle and then multiply it by the number of triangles that make up the hexagon.

The formula to calculate the area of an equilateral triangle is:

Area = (sqrt(3) / 4) * side^2

Given that the side of each tile measures 11 cm, we can substitute this value into the formula to find the area of one equilateral triangle:

Area = (sqrt(3) / 4) * (11 cm)^2

= (sqrt(3) / 4) * 121 cm^2

= 121sqrt(3) / 4 cm^2

Now, since the hexagon is formed by six equilateral triangles, we can multiply the area of one triangle by 6 to find the total area of the hexagon:

Hexagon Area = 6 * (121sqrt(3) / 4 cm^2)

= 726sqrt(3) / 4 cm^2

= 181.5sqrt(3) cm^2

Therefore, the exact area of each hexagonal shape is 181.5sqrt(3) cm^2.

The correct answer is B: 181.5√3 cm^2.

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Answer:

Yes but not vedanta publication book

Answer:

f(8)=69

Step-by-step explanation:

f(X)= -3 (-3x) -3

f(8)= -3 (-3(8)) -3

= -3 (-24) -3

= 72-3

=69

In 180 rotation (x, y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across  x-axis (x, y) becomes (x, -y).

Now, According to the question:

180° rotation about the origin change the coordinates from (x, y) to (-x,-y). It means if an object having coordinates (3,4) then it will be (-3,-4).

Translation 7 units up change the coordinates from (x, y) to (x, y+7). It means if an object having coordinates (3,4) then it will be (3,4+7).

Reflection across the x-axis change the coordinates from (x, y) to (x, -y). It means if an object having coordinates (3,4) then it will be (3,-4).

Hence we can summarize the above phenomenon as in 180 rotation

(x, y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across  x-axis (x, y) becomes (x, -y).

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The complete question is this:
First, take a look at Preston’s sequence. How does a 180-degree rotation about the origin change the coordinates of a shape?

How does a translation 7 units up change the coordinates of a shape?

Now look at Chanel’s sequence. How does a reflection across the x-axis change the coordinates of a shape?

The total playground area is 280 square meter, if the dome cover an area of 1+2/3 = 5/3 square meter.

The area covered by the dome = 5/3 square meter

The area covered by the dome is 5/840 times of the total playground area.

Let the total area of the playground = A

5/3 = 5/840 × A

A = (5 × 840)/(3 × 5)

A = 280 square meter

--The given question is incomplete, the complete question is " Ben like to go in the covered dome, when he feels overexcited. The dome covers an area of 5/3 square meter, which is 5/840 of the total playground area. What is the total playground's area?"--

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\(\text{Solve for y:}\\\\-4.1=8(y-5)\\\\\text{Use the distributive property}\\\\-4.1=8y-40\\\\\text{Add 40 to both sides}\\\\35.9=8y\\\\\text{Divide by 8}\\\\\boxed{4.4875=y}\\\\\)

Answer:

13

Step-by-step explanation:

You need to use pythagorean theorem (a^2 + b^2 = c^2). In this case 5 is a, 12 is b, and z is c. 5^2 + 12^2 = z^2, this ends up as 169 = z^2. Now you find the square root of 169 which is 13.

Step-by-step explanation:

Maybe it is root 5²time 12²=60