help me plz ''allen''

The range of C(t), the function of the average monthly cost of owning the cell phone, is (60, 560].

The range of a function is the set of all y-values obtained after substituting all possible x-values.

Steps to find the range of a function:

For the given problem:

The price of the device = $500

Monthly plan = $60

C(t) is defined as the average monthly cost of owning the phone.

Let t = number of months of owning the cell phone.

Then, total cost after t month = 500 + 60 t.

Hence, the average is:

C(t) = (500 + 60t)/t

C(t) =  500/t + 60

For t = 1, C(1) = 500 + 60 = 560

For t > 1, C(t) < 560

Therefore the maximum value of C(t) = 560

For t →∞  then 500/t will approach zero, hence:

C(t) →(0 + 60), or C(t) will approach 60.

Therefore, we can conclude that 60 < C(t) ≦ 560, or the range of C(t) is (60, 560].

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To find the marginal density of X/Y, we need to integrate the joint density function fXY(x, y) over the range of Y. By performing the integration, we obtain the marginal density of X/Y as a function of X. The resulting marginal density provides information about the distribution of the ratio X/Y.

The marginal density of X/Y can be obtained by integrating the joint density function fXY(x, y) over the range of Y. In this case, the joint density function is given by:

fXY(x, y) =

  24xy    if x >= 0, y >= 0, and x + y <= 1

  0       otherwise

To find the marginal density of X/Y, we integrate fXY(x, y) with respect to y, while keeping x as a constant. The integration limits for y can be determined based on the given conditions x >= 0, y >= 0, and x + y <= 1. Since y must be non-negative, the lower limit of integration is 0. The upper limit of integration can be determined by the constraint x + y <= 1, which implies y <= 1 - x.

Integrating fXY(x, y) over the range of y, we obtain the marginal density of X/Y as follows:

fX/Y(x) = ∫[0 to (1 - x)] 24xy dy

Evaluating the integral, we have:

fX/Y(x) = 24x * ∫[0 to (1 - x)] y dy

       = 24x * [(y^2)/2] evaluated from 0 to (1 - x)

       = 12x * (1 - x)^2

The resulting marginal density fX/Y(x) represents the distribution of the ratio X/Y. It provides information about the likelihood of different values of X/Y occurring. The shape of the distribution can be further analyzed to understand the characteristics of the random variable X/Y.

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Answer:

the total cost of the brackets before tax is $89.7

Step-by-step explanation:

The computation of the total cost of the bracket before tax is as follows

Given that

height = 9 feet

length = 10 feet

wall brackets:

48-in costing $12.95

60-in costing $16.95

The distance of brackets from ends is 1 foot

The maximum distance between brackets is 24 inches

Now based on the above information

The brackets are

= 48 ÷ 12

= 4 feet

And

= 60 ÷ 12

= 5 feet

The length of the shelf is  60 inch

Now the 1 could be deducted from each side

= 60 - 2

= 58 in

Now Divide it by 24 inches

= 58 ÷ 24

= 2.41 ~ 3  

Finally, The total cost is

= ($12.95 + $16.95) × 3

= $89.7

Hence, the total cost of the brackets before tax is $89.7

Answer: 2

Step-by-step explanation:

The dimensions of the rectangle has a width = 12cm and length = 5cm.

In calculating the area of a rectangle, we multiply its length and width.

Let us use the letter x to represent the width, so that the length = x - 7

hence we calculate for the unknown x as follows;

x(x - 7) = 60

expand and equate to zero to derive a quadratic equation

x² + 7x - 60 = 0

by factorisation;

x² - 12x + 5x - 60 = 0

x(x - 12) +5(x -12) = 0

(x + 5)(x - 12) = 0

thus for x + 5 = 0

x = -5

and for x - 12 = 0

x = 12

Therefore, x = 12 is true for the quadratic equation and also for the width = 12 and length = 5cm for the rectangle.

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Answer:

19

Step-by-step explanation:

A' represents everything out A

B' represents everything out B

C' represents everything out C

So only the outside is left hope this helps

2/63 as a percentage round to the nearest tenth of a percent can be written as 31.7%

Fractions refer to a part of a whole. The word fraction comes from Latin word Fractus meaning broken. A percentage is a number that can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol %.

Fractions can be converted into percentages by the following steps:

1. Convert the fraction into decimals.

Therefore, on converting 2/63 to decimal we get 0.317

2. Multiply the given decimal by 100 to get a percentage

Hence, the percentage we get after multiplication is 31.7%.

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Answer:

\(\dfrac{l-k}{l}\)

Step-by-step explanation:

The probability that Stephen wins a raffle is given by the expression:  \(\dfrac{k}{l}\)

Given an event A

P(A occurring)+P(A not occurring)=1

Therefore:

P(Stephen wins the raffle)+P(Stephen does not win the raffle)=1

Substituting our given probability, we obtain:

\(\dfrac{k}{l}$ + P(Stephen does not win the raffle)=1\\P(Stephen does not win the raffle)$=1-\dfrac{k}{l}\\$Taking the Lowest common multiple of the right-hand side, we have:\\\\P(Stephen does not win the raffle)$=\dfrac{l-k}{l}\)

Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

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The formula for the distance between point (x_1,y_1) and (x_2,y_2) is,

Determine the distance between points (4,9) and (12,3) by using distance formula.

So distance between the two points is 10.

The value of  is 2. We found this by first determining the relationship between the angles in the triangle and solving for the unknown angle using the sum of angles in a triangle.

Let's label the points as follows:

Given that angle  is a right angle and angle  is twice angle , we can determine the relationship between the angles. Since the sum of the angles in a triangle is 180 degrees, we have:

angle  + angle  + angle  = 180 degrees

Since angle  is a right angle (90 degrees), we have:

90 + angle  + angle  = 180 degrees

Simplifying the equation, we find:

angle  + angle  = 90 degrees

Since angle  is twice angle , we can express angle  as 2x. Substituting this into the equation, we get:

2x + x = 90 degrees

Simplifying further:

3x = 90 degrees

Dividing both sides by 3:

x = 30 degrees

Now we can find the value of angle :

angle  = 2x = 2 * 30 degrees = 60 degrees

Next, we need to find the length of side . We can use the tangent function:

tan(angle ) = side /

tan(60 degrees) = side /

√3 = side /

side = √3

Finally, we need to find the value of . Since we know that , we can use the Pythagorean theorem:

^2 + side^2 = ^2

^2 + (√3 )^2 = ^2

^2 + 3 = ^2

^2 = 4

= 2

Therefore, the value of  is 2.

The value of  is 2. We found this by first determining the relationship between the angles in the triangle and solving for the unknown angle using the sum of angles in a triangle. Then, we used the tangent function to find the length of side . Finally, we used the Pythagorean theorem to find the value of .

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The pitch of the roof is 0.3.

Pitch:

The pitch can be expressed numerically as a fraction. The pitch fraction represents a certain amount of vertical rise over the entire span.

Here it is given that the rise in the roof is 3.6m and a rum of 12m,

We have to find the pitch of the roof.

As is already given in the statement that the slope of a roof is called its pitch.

By this we get the slope:

Slope = 3.6/12

= 3/10

= 0.3

Therefore we get the pitch of the roof at 0.3.

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Answer:

1/4 of the pizza

Step-by-step explanation:

Imagine that the pizza was spilt into fourths. If you dropped 1/2, you dropped 2 pieces out of the 4. If you shared 2/4, which is also 1/2, you shared 1 out 2 pieces left. You now have 1 out of the 4 pieces left.

Answer:

a. 4  b.15  c. 26.   d.30

Step-by-step explanation:

i had this problem and i have the paper and i got it right so if they are wrong then i have no clue

Answer:a. 4  b.15  c. 26.   d.30

Step-by-step explanation:

Hope it helps

Answer:

The approximate weight of 1 student back pack is 7.38 pounds.

Step-by-step explanation:

We have to find the unit rate of one back back. All we need to do is divide the 5 backpacks by the number of pounds, so:

36.90 ÷ 5 = 7.38

Answer: The approximate weight of one back pack is 7.38.

Step-by-step explanation: Divide the combined weight by 5. Hope this helps.

Answer: the answer is -1.

the inverse operation of subtraction is addition so you would add 2 on both sides. now you have -4 + 2= -2. now the opposite of multiplication is division. so -2 divided by 2 is -1. hope this helps. Brainliest please!

Answer:

−1=t

Step-by-step explanation:

−4=2t−2

Simplify

First, add the same terms to both of the sides of this equation.

−4=2t−2

−4 + 2 =2t - 2 + 2

Secondly, simplify.

add the numbers

−4 + 2 =2t - 2 + 2

-2 = 2t - 2 + 2

Then,

-2 = 2t - 2+2

-2 = 2t

v

It's simplified to -2 = 2t

Thirdly, Divide both sides of the equation by the same term.

−2=2t

2  over −2

​ =  

2  over 2t

Simplify

(divide the numbers)

2  over −2

​ =  

2  over 2t

which also equals to

(simplify fraction)

−1 =   2  over 2t

-1 = t

​

​

For the function S(t) = -35t + 30 , the correct interpretation is that the car has an initial speed of 30 units and is slowing down by 35 units per second , the correct option is (c) .

The function S(t) = -35t + 30 represents the changing speed of the car as a function of time.

The coefficient of time "t" is -35, which represents the rate of change of speed with respect to time, also called as acceleration.

The negative sign indicates that the car is slowing down.

The constant term is 30, which represents the initial speed of the car at time t=0.

So, the car starts with an initial speed of 30 units.

Therefore , the correct interpretation is denoted in Option(c) .

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The given question is incomplete , the complete question is

The changing speed of a car is modeled by the function S(t) = -35t + 30, where t is time in seconds. Interpret the model

(a) The car has an initial speed of 0 units and is speeding up to a speed of 30 units by 35 units per second.

(b) The car has an initial speed of 35 units and is speeding up by 30 units per second.

(c) The car has an initial speed of 30 units and is slowing down by 35 units per second.

(d) The car has an initial speed of 30 units and is speeding up by 35 units per second.

Answer: You cannot.

Step-by-step explanation:

3 can be multiplied into an odd number

4 cannot be multiplied into an odd number

6 cannot be multiplied into an odd number

8 cannot be multiplied into an odd number

Overall, you will not be able to get an odd number with the numbers provided.

Answer: 4683

Step-by-step explanation:

To have an odd number, and since the only odd number you have in your list is 3, that would be in the one's place. Then, you have to put the smallest number (except for 3) in the front. Now, you have two more places to fill in (4 _ _ 3). Like the 4, put the 6 after the 4 to have the smallest possible hundreds place. Now place the eight. Your final number should be... 4683.

The given expression produces a different equation that is not the same as the choices made, neither option is correct in this situation.

A whole is made up of a fraction. The numerator is divided by the denominator to express the number as a quotient in mathematics. Both are integers in a straightforward fraction. A fraction in the numerator or denominator makes up a complex fraction. The numerator and denominator are equal in a proper fraction.

here

the expression which is given

13/15 | 2 - x | = 4/15

choices are

| 2- x | = 1/15

isolate the absolute value

13/15 | 2- x | = 1/15

| 2- x | = 4 * 15 / 15 * 13

| 2- x | = 1/13

The correct response is therefore none of the aforementioned, assuming your question is complete. Because the given expression produces a different equation that is not the same as the choices made, neither option is correct in this situation.

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Answer:

i think your answer is two times the sum of x and seven plus ten

if i am wrong than tell me

Step-by-step explanation:

hope this will help :)

Answer:

i cannot understand

Step-by-step explanation:

Answer:  -1 < x < 3

Step-by-step explanation:

\(\dfrac{5}{(x+2)(4-x)}<1\)

Step 1   The denominator cannot equal zero:

x + 2 ≠ 0    and     4 - x ≠ 0

     x ≠ -2                4 ≠ x

Place these restrictive values on the number line with an OPEN dot:

    <----------o-------------------o--------->

                -2                       4

Step 2   Find the zeros (subtract 1 from both sides and set equal to zero):

\(\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1\)

Add the zeros to the number line with an OPEN dot (since it is <):

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 3    Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):

Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive

Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive

Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative

Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive

Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive

          +         +        -          +       +

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 4  Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.

Negative values only occur between -1 and 3

So the solution is:     -1 < x < 3

Answer:

0.73

Step-by-step explanation:

Data obtained from the question include the following:

Length (L) of square = x

Base (b) of triangle = (3x – 2)

Height (h) of triangle = (2x + 4)

Area of square = L²

Area of square = x²

Area of triangle = ½bh

Area of triangle = ½(3x – 2) (2x + 4)

Expand

½ [3x(2x + 4) –2(2x + 4)]

½[6x² + 12x – 4x – 8]

½[6x² + 8x – 8]

3x² + 4x – 4

Area of triangle = 3x² + 4x – 4

Now, to find the value of x which makes the area of the two figures the same, we simply equate both areas as shown below:

Area of triangle = area of square

Area of triangle = 3x² + 4x – 4

Area of square = x²

Area of triangle = area of square

3x² + 4x – 4 = x²

Rearrange

3x² – x² + 4x – 4 = 0

2x² + 4x – 4 = 0

Solving by formula method

a = 2, b = 4, c = –4

x = – b ± √(b² – 4ac) / 2a

x = – 4 ± √(4² – 4×2×–4) / 2×2

x = – 4 ± √(16 + 32) / 4

x = – 4 ± √(48) / 4

x = (– 4 ± 6.93)4

x = (– 4 + 6.93)4 or (– 4 – 6.93)4

x = 0.73 or –2.73

Since the measurement can not be negative, the value of x is 0.73.

The expression which represents either the length or width is (x+3). The correct answer is option (c).

Given that the area of a rectangle which is given as x²+5x+6.

We have to find which expression represents either the length or width.

We are given an expression for the area. But we also know that the area of a rectangle is length times width. So the expression we were given, x²+5x+6 must be equal to the length of the rectangle times its width.

So, will find the factoring the expression we can see expressions for the length and the width.

Factoring x²+5x+6 we get (x+2)(x+3).

One of these factors is the width and the other is the length.

Hence, the expression represents either the length or width of the rectangle when the area of a rectangle is given as x²+5x+6 is (x+3).

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Step-by-step explanation:

let x=8 for a small triangle

y=10 for a big triangle

Answer: The answer is 2.

Step-by-step explanation: 3/15 can be simplified to 1/5. Find 1/5 of 10. You can do that by dividing 10 and 5. Therefore, the answer is 2.

Answer:

rectangle

Step-by-step explanation:

the question is asking what the shape of the cross section would be if it was perpendicular to the base. imagine a cylinder that you could slide a piece of paper into. what would be inside the cylinder? perpendicular to the base, it would be a rectangle. if it was parallel to the base, you'd then have a circle.

There are 9 employees at the smaller location and 12 employees at the larger location.

Let's use the following variables:

Let x be the number of employees at the smaller location.

Let y be the number of employees at the larger location.

We know that the total number of employees is 21, so we can write:

x + y = 21

We also know that "four times the number of employees at the larger location is six less than six times the number of employees at the smaller location". In other words, we can write:

4y = 6x - 6

Simplifying this equation, we get:

2y = 3x - 3

We now have a system of two equations with two variables:

x + y = 21

2y = 3x - 3

We can solve this system using substitution or elimination. Here, we'll use substitution method:

From the second equation, we can solve for x in terms of y:

2y = 3x - 3

3x = 2y + 3

x = (2/3)y + 1

We can now substitute this expression for x into the first equation:

x + y = 21

(2/3)y + 1 + y = 21

(5/3)y = 20

y = (3/5) × 20

y = 12

Substitute y = 12 back into x + y = 21, we get:

x + 12 = 21

x = 9

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Answer:

Step-by-step explanation:

Answer is

(x+4) (2x+9)

(3x+13)

3/13

x =4.3