Difference of two exponential random variables

(f + g) (x)= -3 x+ 5

(f + g)(x) = -3x + 5

For given question,

We have been given two functions.

f(x) = x+8 and g(x) = -4x - 3

We need to find the value of (f + g)(x)

This means, we need to find the addition of functions f(x) and g(x)

⇒ (f + g)(x) = f(x) + g(x)

⇒ (f + g)(x) = (x + 8) + (-4x - 3)

⇒ (f + g)(x) = x - 4x + 8 -3

⇒ (f + g)(x) = -3x + 5

Therefore, (f + g)(x) = -3x + 5

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simple it is divisible by both

is the answer is both 2 and 3

Final answer:

The expected value of a transaction decreases by 10% for customers using a rewards points card, going from $500 to $450 per transaction as they receive a 10% discount.

Explanation:

The question pertains to the expected value of a transaction at a shopping mall considering different discounts for customers who use a rewards points card. The expected value takes into account the average (mean) value of transactions and the discounts applied to those transactions. With shoppers using the rewards card receiving a 10% discount, the average transaction value for these customers is $450, compared to $500 for those without the card.

If we calculate the expected value for a transaction without considering the card, it would simply be the average transaction amount of $500. However, when including the rewards card usage, we have to account for the discount. Therefore, the expected value for a transaction from a customer using the rewards card is 10% less than $500, which equals $450. This means the expected value for a transaction with the card has decreased by $50 compared to customers without the card.

To summarize the effect, use of the rewards card reduces the expected value of transactions for the business, given that a discount is provided. On the other hand, it incentivizes customers with savings, potentially increasing customer loyalty and the frequency of visits, which might offset the decrease in expected transaction value in a broader business strategy.

Answer:

No. The expected value can be a value different from the exact value of x.

The width of the rectangle is 4.5 meters, and the length is 6 meters.

Let's denote the width of the rectangle as [tex]\( w \)[/tex] and the length as [tex]\( l \)[/tex].

1. The area [tex]\( A \)[/tex] of a rectangle is given by the product of its length and width, so we have the equation:

[tex]\[ A = l \times w \][/tex]

Since the area is given to be 27 square meters, we can write:

[tex]\[ l \times w = 27 \][/tex]

2. The length of the rectangle is 3 meters less than twice the width.

This relationship can be expressed as:

[tex]\[ l = 2w - 3 \][/tex]

This is our second equation.

Now we have a system of two equations with two variables:

[tex]\[ \begin{cases} l \times w = 27 \\ l = 2w - 3 \end{cases} \][/tex]

We can substitute the expression for [tex]\( l \)[/tex] from the second equation into the first equation:

[tex]\[ (2w - 3) \times w = 27 \][/tex]

Expanding the equation, we get:

[tex]\[ 2w^2 - 3w - 27 = 0 \][/tex]

To solve this quadratic equation, we can factor it:

[tex]\[ (2w - 9)(w + 3) = 0 \][/tex]

Setting each factor equal to zero gives us two possible solutions for [tex]\( w \)[/tex]:

[tex]\[ 2w - 9 = 0 \quad \text{or} \quad w + 3 = 0 \][/tex]

Solving for [tex]\( w \)[/tex], we get:

[tex]\[ w = \frac{9}{2} \quad \text{or} \quad w = -3 \][/tex]

Since the width of a rectangle cannot be negative, we discard [tex]\( w = -3 \)[/tex].

Thus, [tex]\( w = \frac{9}{2} \)[/tex] meters, which simplifies to [tex]\( w = 4.5 \)[/tex] meters.

Now we can find the length [tex]\( l \)[/tex] by substituting [tex]\( w = 4.5 \)[/tex] into the second equation:

[tex]\[ l = 2(4.5) - 3 \][/tex]

[tex]\[ l = 9 - 3 \][/tex]

[tex]\[ l = 6 \][/tex]

Final answer:

To write each equation in slope-intercept form and identify the slope and y-intercept, rearrange the given equations. a) 2x - y = 4: slope = 2, y-intercept = -4. b) 2x - y = 0: slope = 2, y-intercept = 0. c) x + 3y = 0: slope = -1/3, y-intercept = 0. d) 2y - 6 = 0: slope = 0, y-intercept = 3.

Explanation:

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. To write each equation in slope-intercept form and identify the slope and y-intercept, we can rearrange the given equations.

a) 2x - y = 4
First, we rearrange the equation to isolate y: -y = -2x + 4, then we rewrite as y = 2x - 4. Therefore, the slope is 2 and the y-intercept is -4.

b) 2x - y = 0
Rearranging the equation gives y = 2x. The slope is 2 and the y-intercept is 0.

c) x + 3y = 0
Isolating y, we get y = -1/3x. The slope is -1/3 and the y-intercept is 0.

d) 2y - 6 = 0
Solving for y, we find y = 3. The slope is 0 and the y-intercept is 3.

The greatest possible number of club members that we can divide 48 classical CDs and 42 show tune CDs is 6.

HCF is the highest common number or factor that divides two or more than two given numbers completely.

These types of questions can be solved by the concept of HCF.

Given that the glee club has a set of 48 classical CDs and a set of 42 show tune CDs and we have to determine the highest number of club members so that we can distribute these two types of CDs to the club members equally.

∴ The HCF of 42 and 48 is 6, we know 2 and 3 also divides 42 and 48 but they are not the largest number.

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(5y-3) = (3y+27)   -3y from both sides

2y-3 =  27    +3 to both sides

2y= 30   divide both sides by 2

y=15

check

5X15-3 = 3x15+27

72 = 72

correct that y=15 and that each angle is 72

in that shape correlating angles are the same so...

360-72-72= 216

216 divided by 2= 108 degrees

B is equal to 108 degrees

A is equal to 72 degrees

Answer:

A

Step-by-step explanation:

BIG BRAIN

To find the equation of a parabola given the vertex and one point, use the vertex form of a parabola equation: y = a(x - h)² + k.

To find the equation of a parabola given the vertex and one point, you can use the vertex form of a parabola equation: y = a(x - h)² + k. Here's how:

For example, if the vertex is (2, 3) and the point is (4, 5), the equation of the parabola would be y = 1(x - 2)² + 3.

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The total number of trips is x to walk a total of 12 kilometers is 3 trips if Tanner walked a total of 8 kilometers by making 2 trips to school.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Tanner walked a total of 8 kilometers by making 2 trips to school.

Let the total number of trips be x to walk a total of 12 kilometers.

8 km → 2 trips

12 km → x trips

8x = 24

x = 24/8

x = 3 trips

Thus, the total number of trips is x to walk a total of 12 kilometers is 3 trips if Tanner walked a total of 8 kilometers by making 2 trips to school.

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To find the rate of brain growth, we calculate the derivatives of the brain weight and body weight functions. Then, we find the rate by multiplying the derivatives and substituting the average length of 18cm. The rate of brain growth is approximately 0.04 grams/cm.

To find the rate at which the species' brain was growing when the average length was 18cm, we need to find the derivative of the brain weight function with respect to body weight and then multiply it by the derivative of body weight with respect to body length.

First, let's find the derivative of the brain weight function, b = 0.007w^(2/3), with respect to body weight, w.

Taking the derivative, we get db/dw = (2/3) * 0.007 * w^(-1/3).

Next, let's find the derivative of the body weight function, w = 0.12l^(2.53), with respect to body length, l.

Taking the derivative, we get dw/dl = 2.53 * 0.12 * l^(1.53).

Finally, to find the rate of brain growth when the average length was 18cm, we plug in the value 18 for l in the derivative of the body weight function and multiply it by the derivative of the brain weight function:

Rate of brain growth = (2/3) * 0.007 * (18)^(-1/3) * 2.53 * 0.12 * (18)^(1.53).

Rounding to the nearest hundredth, the rate of brain growth when the average length was 18cm is approximately 0.04 grams/cm.

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The form used  to write the equation of a line if you knew the slope and x-intercept y=mx−k/m

The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it

According to the given situation we have given :a slope of 'm' and an x-intercept of 'k'

we can write

y=mx−k/m

and generally, To find the x-intercept, set y = 0 and solve for x.

For example,

Let k be some constant such that

y=mx + k

where

m is the slope.

m=3/4 and the x-intercept is 4

If the x-intercept is 4 this means that x=4 when y=0

So equation:

y=mx + k becomes

0=3/4+ k

k=−3

and our equation is

y=3/4x−3

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New Orleans has the lower elevation at -8 feet compared to Long Beach, which is at -7 feet, since a lower numerical value below zero indicates a further drop below sea level.

To determine which city has the lower elevation, we need to compare the elevations of Long Beach, California and New Orleans, Louisiana. A lower elevation means that it is further below sea level. Long Beach is at an elevation of -7 feet, while New Orleans is at 8 feet below sea level. In numerical terms, New Orleans’ elevation can be considered as -8 feet because the word 'below' indicates a negative elevation.

Comparing the two elevations:

Long Beach, California: -7 feet

New Orleans, Louisiana: -8 feet

Since -8 is less than -7, we determine that New Orleans has the lower elevation compared to Long Beach.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of x is 72.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Let the integer be x and y.

An integer x is divided by an integer y, and the quotient is 24.

This can be written as:

x ÷ y
x/y = 24

x = 24y _____(1)

Now,

The sum of the integer is 75.

x + y = 75

From (1) we get,

24y + y = 75

25y = 75

Divide both sides by 25.

y = 3

Now,

From (2 ) we get,

x + y = 75

x + 3 = 75

Subtracting 3 on both sides.

x = 75 - 3

x = 72

We can also cross-check:

x = 72 and y = 3

= x ÷ y

= 72/3

= 24

Thus,

The value of x is 72.

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 add like terms

 x^3x^4 = x^7

5x^2 + 5x^2 = 10x^2

you end up with x^7 +3x^4 + 10x^2 +x