If you earn $560 for working 20 hours during the week. How much did you earn
per hour?
$560
$30
$20
$10

The probability that the lifetime of at least one component exceeds 2 is 0.135.

Given that the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image.

We want to find the probability that the lifetime of at least one component exceeds 2.

The probability that the lifetime of at least one component exceeds 2 is P(X>2).

[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}f(x,y)dydx\end[/tex]

Now, we will substitute the given function, we get

[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}xe^{-x(1+y)}dydx\end[/tex]

Further, we will simplify this, we get

[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\left[-e^{-x(1+y)\right]_{0}^{\infty}dx\\ &=\int_{x=2}^{\infty}e^{-x}dx\\ &=\left[-e^{-x}\right]_{2}^{\infty}\\ &=e^{-2}\\ &=0.135\end[/tex]

Hence, the probability that the lifetime of at least one component exceeds 2 for the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image is 0.135.

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Using mensuration we know that the volume of the square-based pyramid is (1/3)(x^2h) cubic units.

So, if 'B' is the base and 'h' is the height of the pyramid,  its volume is V = (1/3) (Bh) cubic units.

Therefore, using mensuration we know that the volume of the square-based pyramid is (1/3)(x^2h) cubic units.

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Step-by-step explanation:

The total price of 3 pencils and 1 protractor at $3 was 4 times the total price of 1 pencil and 1 eraser at $0.60. What is the price of 1 pencil?​

when pencil = p

3p + 3 = 4(p + 0.6)

expand right side:

3p + 3 = 4p + 2.4

subtract 3 from both sides:

3p + 3 - 3 = 4p + 2.4 - 3

3p = 4p -0.6

subtract 4p from both sides:

3p - 4p = 4p -0.6 - 4p

-p = -0.6

divide both sides by -1:

(-p)/-1 = (-0.6)/-1

p = 0.6

so each pencil costs $0.60

Answer: 3)

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The fraction 1/4th of the animals at the Jackson Zoo are monkeys.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

At the Jackson Zoo, 1/2 of the animals are primates

So if x is the total animals in that zoo, total primates are x/2.

Now out of them, 1/2 are monkeys i.e  1/2 of x/2

= x/4.

Hence 1/4 th fraction of the animals at the Jackson Zoo are monkeys.

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the moment of inertia is [tex]0.405 kgm^{2}[/tex] .

Given :

mass of rod (m) = 1.5kg

length of rod (l) = 1.8m

formula :

We know that moment of inertia of rod about it's center is

      [tex]I = ml^{2}/12[/tex]

I = (1.5)*(1.8*1.8)/12

I = 1.5*3.24/12

I = 4.86/12

I = 0.405  [tex]kgm^{2}[/tex]

hence, the moment of inertia of rod about its center is 0.405 [tex]kgm^{2}[/tex].

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The moment of inertia of the given condition is 0.405 kgm².

Given that,

Mass of the rod = 1.5 kg

Length of the rod = 1.8 m

A thin rod with mass M and length L has an axis running through its center, and the formula for its inertial momentum is given by,

I = ML²/12

I = 1.5*(1.8)²/12

I = 0.405 kgm²

Hence, the moment of inertia of the given condition is 0.405 kgm².

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The smallest possible sum for this series is 20736 = 12^4.

Given:

A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power.

S = a + (a+2) + (a+4) + ... + (a+2*287) = 288(a+(a+574))/2 = 288(a+287)

288 = 2^5 * 3^2

smallest value of (a+287) that will make S = 288(a+287) a perfect fourth power is:

a + 287 = 2^3 * 3^2 = 72

a = −215

Smallest sum = 288*72 = 20736 = 12^4

Smallest odd integer in series = −215

−215 + −213 + −211 + ... + −1 + 1 + 3 + ... + 213 + 215 + ... + 359

= 20736 = 12^4.

Therefore the smallest possible sum for this series is 20736 = 12^4.

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Your answer is in bold below!

8.5 x 3 = 25.5

Answer: Her brother is 25.5 kg.

Step-by-step explanation:

If her brother is 3 times as heavy, we need to multiply 8.5 kg by 3.

8.5 kg times 3 is 25.5 kg.

Answer:

Your answer will be 7

Answer:

7

Step-by-step explanation:

i know

The dimensions of the box are (S-2x)by(S-2x)byS =  2S/3 by 2S/3 S by S/6 to obtain a box with largest possible volume

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

Let S = length of the sides of the square cardboard sheet.  Let x = the side of each square cut from the corners.  The volume, V, of the box when the sheet is folded up is:

V = (S-2x)(S-2x)x = 4x3 - 4Sx2 + S2x

To find the maximum value, take the derivative of V wrt x, set it to zero, and solve for x:

V ' = dV/dx = 12x2 - 8Sx + S2

0 = 12x2 - 8Sx + S2

0 = (6x-S)(2x-S)

x = S/6 and S/2

To determine which is the max and which is the min, take the second derivative of V wrt x.

V'' = d2V/dx2 = 24x - 8S

At x = S/2, V'' = 24(S/2) - 8s = 4S. Since S>0, the point x=S/2 is a minimum. This makes sense because you have cut away the entire cardboard square.

At x = S/6, V'' = 24(S/6) - 8S = -4S < 0, so x = S/6 is the maximum

The dimensions of the box are (S-2x)by(S-2x)byS =  2S/3 by 2S/3 S by S/6

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Answer:

[tex]f(x)=x^3-9x^2+8x+60[/tex]

Step-by-step explanation:

The zeros of a function are the x-values when f(x) = 0.

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).

If the zeros of the polynomial are -2, 5 and 6 then (x + 2), (x - 5) and (x - 6) are factors of the polynomial.

Therefore, the polynomial in factored form is:

[tex]f(x)=a(x+2)(x-5)(x-6)[/tex]

where a is the leading coefficient.

Given a = 1:

[tex]f(x)=(x+2)(x-5)(x-6)[/tex]

Expand the parentheses to express the polynomial in standard form:

[tex]f(x)=(x+2)(x-5)(x-6)[/tex]

[tex]f(x)=(x^2-3x-10)(x-6)[/tex]

[tex]f(x)=x^3-6x^2-3x^2+18x-10x+60[/tex]

[tex]f(x)=x^3-9x^2+8x+60[/tex]

If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, this phenomenon is called random phenomenon.

A phenomenon is random if individual outcomes are uncertain, but there is in spite of that, a regular distribution of outcomes in a great number of repetitions.

The probability of any outcome of a random phenomenon can be

described as the proportion of times the outcome would happen in a very lengthy chain of repetitions.

The outcome of any individual coin toss is random. But the outcome over many tosses is foreseeable, as long as the trials are individualistic (i.e., the outcome of a new coin flip is not impacted by the outcome of the preceding flip).

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The solution for p(-2) in the function when the function p(n) = 2n is -2

From the question, we have the following equation that can be used in our computation:

p(n)=2n

To make the equation legible, we need to rewrite it

So, we have the following representation

p(n) = 2n

Also from the question, we have

p(-1)

This means that the value of n is -1, and we calculate p(n) when n = -1

Substitute the known values in the above equation, so, we have the following representation

p(-1) =  2 * -1

So, we have the following equation

p(-1) =  2 * -1

There is no constant to add or subtract to both sides of the equation

So, we have the following representation

p(-1) =  -2

Hence, the solution is -2

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The value of n for the given exponential function is 5/2.

Exponential function:

Exponential function means the function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Given,

Here we have the exponential function (√7)⁵ = 7ⁿ

Now, we need to find the value of n.

Based on the rule of exponent, we have written the square as 1/2, like the following,

√7 = [tex]7^{\frac{1}{2}}[/tex]

So, when we apply these on the given expression then we get,

(√7)⁵ = [tex](7^{\frac{1}{2}})^5[/tex]

Now, we have to multiply both values on the power then we get,

=> [tex](7^{\frac{5}{2}})[/tex]

When we equate this with the RHS, then we get the value of n as,

[tex]= > (7^{\frac{5}{2}})=7^n[/tex]

Therefore, the value of n is 5/2.

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Answer:

PQR is a right triangle

Step-by-step explanation:

slope of the line that contains PQ = 0

Because the line is parallel to x axis

slope of the line that contains QR

(5-1)/(-6+2) = 4/-4 = -1

slope of the line that contains PR
(1-5)/(-2-2) = -4/-4 = 1

PR and QR are perpendicular so the triangle is right

Answer:

4000 + 400x = 3750 + 450x

Step-by-step explanation:

The number of cars where the offer would be equal is 5 cars.

4000 + 400x = 3750 + 450x  Subtract 400x from both sides of the equation

4000 = 3750 + 50x  Subtract 3750 from both sides of the equation

250 = 50x  Divide both sides by 50

5 = x

If you sell less than 5 cars a month, take job A.  If you sell more than 5 cars a month, take job B.

The given equations, 2x + y = -3 and -2y = 6 + 4x, written in slope-intercept form is y = -2x - 3

From the question, we are to write the equations in slope-intercept form.

The given equations are

2x + y = -3

and

-2y = 6 + 4x

The slope-intercept form of the equation of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

Writing 2x + y = -3 in slope-intercept form

2x + y = -3

Subtract 2x from both sides of the equation

2x - 2x + y = -3 - 2x

y = -3 - 2x

y = -2x - 3

Writing -2y = 6 + 4x in slope-intercept form

-2y = 6 + 4x

Divide through by -2

-2y/-2 = 6/-2 + 4x/-2

y = -3 - 2x

y = -2x - 3

Hence, the equation is y = -2x -3

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The graph of the exponential function f(x) = (3/4)ˣ is attached below and this is also option A in the question given

An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.

In the given function

f(x) = (3/4)ˣ,

we can use a graphing calculator to plot the graph while applying the values from the table of function.

Comparing the graph plotted and the options given, the answer is option A

Kindly find the attached graph below

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Answer:

[tex]r = \dfrac{a}{b - pcos( \theta)} \\ \\ r \times (b - pcos( \theta)) = \dfrac{a}{ \cancel{b - pcos( \theta)}} \times \cancel{b - pcos( \theta)} \\ \\ a = r \times (b - pcos( \theta) \\ \\ a = rb - rpcos( \theta)[/tex]

Put different values of x in the function and find values of g(x). Then plot the points on a graph.

Graphing a function involves tracing the curve on a coordinate plane that corresponds to the function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.

The given function is

g(x) = - 3x

Put x = - 3

g(x) = -3(-3)

g(x) = 9

Put x = - 2

g(x) = -3 (-2)

g(x) = 6

Put x = - 1

g(x) = -3 (-1)

g(x) = 3

Put x = 1

g(x) = - 3 (1)

g(x) = - 3

Put x = 2

g(x) = -3 (2)

g(x) = - 6

Plot the points on a graph, and keep the values of x on the x-axis and g(x) on the y-axis.

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Answer: About 1 to 1.5 ratio. You would use one cup rice to 1.5 cup water.

Step-by-step explanation:

Answer:

1 17/18

Step-by-step explanation:

4 2/3 / 2 2/5 =

= 14/3 / 12/5

= 14/3 × 5/12

= 70/36

= 35/18

= 1 17/18

4 2/3 divided by 2 2/5 results to 35/18.

In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed.

Given:

4 2/3 divided by 2 2/5

So, 14/3 divided by 12/5

= 14/ 3 x 5/ 12

= 7/3 x 5/6

= 35/ 18

Hence, 4 2/3 divided by 2 2/5 results to 35/18.

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Step-by-step explanation:

3900 if by hundreds

If by thousands 4000

Answer:

3 times .. just multiply

The value of trigonometric function sin(x-y) = -44/125

Given ,

cos x = 3/5

sin y = 24/25

Sin( x - y) = sin(x)cos(y) - sin(y)cos(x)

substituting the values,

=> sin(x)cos(y) - sin(y)cos(x)

=> sin(x)cos(y) - (24/25)(3/5) ------(1)

As we know ,

sin(x) = √(1 - cos²x)

sin x = √(1 - (3/5)²)

=> sin x = √1 -9/25

=> sin x = √16/25

=> sin x = 4/5

Again ,

cos y = √(1 - sin²y)

=> cos y = √(1 - (24/25)²

=> cos y = √1 - 576/625

=> cos y = √49/625

=> cos y = 7/25

Substituting the values of sin x and cos y in equation (1)

=> sin(x - y) = (4/5)(7/25) - (24/25)(3/5)

=>  sin(x - y) = (28 / 125) - (72 / 125)

=>  sin(x - y) = -44/125

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For rolling four-sided die and a six-sided die, six-sided die have the lowest probability.

As per the state question-

Sample space for four-sided die = (1, 2, 3, 4).

Sample space for six-sided die = (1, 2, 3, 4, 5, 6).

The each outcome for the four-sided die will be 1/4 .

The each outcome for the six-sided die will be 1/6.

1/6 < 1/4

Thus, six-sided die have the lowest probability.

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Part A:

After adding the meals tax we get the total bill as $27.32

Part B:

After adding the tip the total lunch cost was 432.24, hence the percentage of tip he gave is 18%

Tax

Meal plus tax = 25.3 + 8/100 * 25.3

Meal plus tax = 25.3 + 2.024             Round later. Find the total.

Meal plus tax = 27.324

Meal plus tax = 27.32 rounded to the nearest cent.

Tip

Total cost = $32.242

tip = 32.242 - 27.324

percentage of tip= 4.918

= 18%

Hence we get the required answers.

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