Suppose x follows a distribution with density function: \begin{equation} f\left(x\right) = \left\{\begin{array}{rl} c\left|x - 2\right|,& 0 \le x \le 3\\ 0, & \text{otherwise}\\ \end{array}\right. \end{equation} (note: for this question you can enter your answer in decimals as well as fractions.) what must the value of c be so that f(x) is a probability density function? tries 0/5 find the cumulative distribution function of f(x) for $ 2 \leq x \leq 3 $. [ the accepted form of answer is an algebraic expression in terms of "x". all algebraically equivalent expressions to the correct answer are accepted. write product as *
e.g 23 or 3x, index/power as superscript,
e.g 2^3 for 2 raised to the power 3, the exponential function as exp(x), the logarithm function as log(x) (and not as ln(x)) ] tries 0/5 find the median of the probability distribution of x tries 0/2 find e(x) tries 0/5 find the cumulative distribution function of f(x) for $ 0 \leq x \leq 2 $. [ the accepted form of answer is an algebraic expression in terms of "x". all algebraically equivalent expressions to the correct answer are accepted. write product as *
e.g 23 or 3x, index/power as superscript,
e.g 2^3 for 2 raised to the power 3, the exponential function as exp(x), the logarithm function as log(x) (and not as ln(x)) ]

Answers

Answer 1

The question is a bit of a mess, so here's an attempt at parsing out the relevant information.

Given the PDF of a random variable [tex]X[/tex]:

[tex]f_X(x)=\begin{cases}c|x-2|&\text{for }0\le x\le3\\0&\text{otherwise}\end{cases}[/tex]

Find [tex]c[/tex], the CDF, the median of [tex]X[/tex], and the expectation of [tex]X[/tex] (in no particular order).

For [tex]f_X(x)[/tex] to be valid PDF, we require

[tex]\displaystyle\int_{-\infty}^\infty f_X(x)\,\mathrm dx=1[/tex]

Note that

[tex]|x-2|=\begin{cases}x-2&\text{for }x\ge2\\2-x&\text{for }x<2\end{cases}[/tex]

We have

[tex]\displaystyle\int_{-\infty}^\infty f_X(x)\,\mathrm dx=c\int_0^3|x-2|\,\mathrm dx=c\int_0^2(x-2)\,\mathrm dx+c\int_2^3(2-x)\,\mathrm dx[/tex]
[tex]\implies\dfrac{5c}2=1\implies c=\dfrac25[/tex]

The CDF is defined by

[tex]F_X(x)=\mathbb P(X\le x)=\displaystyle\int_{-\infty}^xf_X(t)\,\mathrm dt[/tex]

To find the CDF, we compute the integral above for the four possible cases:

[tex]x<0\implies\displaystyle\int_{-\infty}^xf_X(t)\,\mathrm dt=0[/tex]
[tex]0\le x<2\implies\displaystyle\int_{-\infty}^xf_X(t)\,\mathrm dt=c\int_0^x|t-2|\,\mathrm dt=\frac{4x-x^2}5[/tex]
[tex]2\le x<3\implies\displaystyle\int_{-\infty}^xf_X(t)\,\mathrm dt=\frac45+c\int_2^x|t-2|\,\mathrm dt=\frac45-c\int_2^x(2-t)\,\mathrm dt=\frac{8-4x+x^2}5[/tex]
[tex]x\ge3\implies\displaystyle\int_{-\infty}^xf_X(t)\,\mathrm dt=1[/tex]

So the CDF is

[tex]F_X(x)=\begin{cases}0&\text{for }x<0\\\\\dfrac{4x-x^2}5&\text{for }0\le x<2\\\\\dfrac{8-4x+x^2}5&\text{for }2\le x<3\\\\1&\text{for }x\ge3\end{cases}[/tex]

The median is the value [tex]M[/tex] such that [tex]\mathbb P(X\le M)=\dfrac12[/tex]. From the PDF, we can gather that the median must fall somewhere in [tex]0\le x\le2[/tex]. The CDF then tells us that

[tex]\mathbb P(X\le M)=F_X(M)=\dfrac12=\dfrac{4M-M^2}5\implies M=2-\sqrt{\dfrac32}\approx0.775[/tex]

The expected value of [tex]X[/tex] is given by

[tex]\mathbb E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx[/tex]

We have

[tex]\mathbb E[X]=\displaystyle\frac25\int_0^2x(x-2)\,\mathrm dx+\frac25\int_2^3x(2-x)\,\mathrm dx=\frac{16}{15}[/tex]

Related Questions

The formula for the volume of a cube is V(s) = s3 where s is the side length of the cube. In which quadrant(s) is the graph of the function V(s)?

Answers

For this case what you should know is that we are in the presence of a cubic function that could take both positive and negative values.
However, when talking about the volume of a figure, a cube specifically, so that there is a physical sense, it must be fulfilled:
s> 0
Thus:
V (s)> 0
Thus, the function V (s) = s3 belongs to the first quadrant.
Answer:
the graph of the function V (s) is in the first quadrant.

Answer:

The answer is A: Quadrant 1

Step-by-step explanation:

On Edge :)

what is the answer please

Answers

Hey there!

Use The Pythagorean theorem. It’s a^2+b^2=c^2. Plug in 11 and 60. The equation would be 11^2+60^2=c^2. Simplify to get 121+3600=c^2. Simplify again to get 3721=c^2. Sqaure root each side to get c=61. The answer is the last one, c=61.

I hope this helps!

5 quarts =how many fluid ounces

Answers

160 fluid ounces :) hope this helped

1 us liquid quart= 32 us fluid ounces

multiply the number of quarts by 32 ounces per quart

= 5 quarts * 32 oz/qt
= 160 fluid ounces

ANSWER: There are 160 fluid ounces in 5 quarts.

Hope this helps! :)

Complete the square to form a perfect square trinomial x^2-14x+

Answers

Answer: x^2 - 14x + 49

Explanation:

1) Divide the coefficient of x by 2:

14 / 2 = 7

2) so you have to add 7^2 = 49

x^2 - 14x + 49

3) that trinomial is equivalent to:

=> (x - 7)^2

4) prove that using the formula (a - b)^2 = a^2 - 2ab + b^2

(x - 7)^2 = x^2 - 14x + 49

Then you have to add 49 to complete the square. and form a perfect square trinomial.

Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx

Answers

Okay, so we have

[tex] \int\limits { \dfrac{7ln(x)}{x \sqrt{5+ln(x)^2}}} \, dx [/tex].

Substitute [tex]u=ln(x)^2+5[/tex] and differentiate.
[tex]dx= \dfrac{x}{2ln(x)}du[/tex]
[tex] \dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}}} \, du [/tex]

[tex]\int\limits { \dfrac{1}{ \sqrt{u}}} \, du = 2 \sqrt{u} [/tex]

[tex] \dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}} } \, du = 7 \sqrt{ln(x)^2+5}+C [/tex]

The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

Given an integral expression:

[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

This can be written as:

[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

It is required to find the integral value.

Let u = 5 + (ln (x))²

Differentiate.

[tex]du=2ln(x)*\frac{1}{x} dx[/tex]

Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]

Substitute the values.

[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]

[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]

[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]

Substitute back the value of u.

[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]

Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

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PLEASE HELPS NEED THIS DONE BEFORE 3 O CLOCK

1)Jerome noticed the following house numbers on his street:

305, 318, 331, 344

The house numbers follow a pattern. Which expression can be used to determine the nthnth house number on his street?

A) 292 +13n

B) 292n

C) 292n + 13

D) 13(n + 292)

2) A polynomial expression is shown below.

(mx+8)(2x−4)

The expression is simplified to:

−6x2+28x−32-6x2+28x-32

What is the value of m?

A) 3

B) 4

C) -3

D) -4

3) What is the domain of the function shown below? (PICTURE AT BOTTOM)

A) 2
B) −8 ≤ x <3and 4 ≤ x <8

C) −8 ≤ x < 8

D) −7 ≤ x ≤ 7

Answers

1) Put n=2 in each of the offered expressions and see which one gives you 318 (the second house number).
A) 292 + 13*2 = 318 . . . . a good candidate
B) 292*2 = 584 (nope)
C) 292*2 + 13 = 597 (nope)
D) 13(2 + 292) = 3822 (nope)
The appropriate choice is ...
A) 292 +13n

2)The squared term in the product is 2mx^2. The squared term in the given expression is -6x^2. Comparing the coefficients, we have
2m = -6
m = -3
The appropriate choice for the value of m is ...
C) -3

3) The end point of one segment matches up with the beginning of the next except in the region 3 ≤ x < 4.
The appropriate choice is ...
B) -8 ≤ x < 3 and 4 ≤ x < 8

Answer:

Jerome noticed the following house numbers on his street:

Answer 292 +13n

A polynomial expression is shown below. What is the value of m?

Answer -3

What is the domain of the function shown below

Answer −8 ≤ x <3and 4 ≤ x <8

Shondra found large candles on sale at her favorite store. She has a large family and many friends, so she bought as many of the candles she could fit in her trunk to give as gifts. Her trunk is 2 feet deep, 4 feet wide, and 3 feet long. If each candle comes in a cube box with 1 foot edges, how many candles will fit in her trunk?

Answers

The trunk of the car is shaped like a rectangular prism whose volume is length * width * height.

The volume of the trunk is LWH = 3 ft * 4 ft * 2 ft = 24 ft^3

The volume of a cube is the cube of the side (edge)
.
Each cubic box has volume V = s^3 = (1 ft)^3 = 1 ft^3

Now we divide the volume of the trunk by the volume of each cube box.

[tex] \dfrac{24 ft^3}{1 ft^3} = 24 [/tex]

Answer: She can fit 24 boxes in her trunk.

Q.8 What is the tail length?

Answers

If I'm correct you should make a fraction first
5.4 3.6
----- to -----
4.8 ?

Now find the missing number
5.4 to 3.6 would be a difference of ÷ 1.5 so you must do the same for 4.8

÷1.5
5.4 3.6
----- to -----
4.8 3.2
÷1.5

The tail length should be 3.2 feet

The tail length of an alligator with a body length of 3.6 feet is approximately 3.2 feet.

The problem states that the alligator's tail length, [tex]$T$[/tex], varies directly with its body length, [tex]$B$[/tex]. When two quantities vary directly, we can express this relationship using a proportionality constant, often denoted as [tex]$k$[/tex]. In this case, we have:

[tex]$\frac{T_1}{B_1} = \frac{T_2}{B_2}$,[/tex]

where [tex]$T_1$ and $B_1$[/tex] are the initial tail length and body length, and [tex]$T_2$ and $B_2$[/tex] are the final tail length and body length.

Given that an alligator with a body length of 5.4 feet has a tail length of 4.8 feet, we can use this information to find [tex]$k$:[/tex]

[tex]$\frac{4.8}{5.4} = \frac{T_2}{3.6}$.[/tex]

Now, solve for [tex]$T_2$:[/tex]

[tex]$T_2 = \frac{4.8}{5.4} \times 3.6$.[/tex]

[tex]$T_2 \approx 3.2$ feet.[/tex]

So, the tail length of an alligator with a body length of 3.6 feet is approximately 3.2 feet.

The tail length is 3.2 feet. This result confirms the direct variation between tail length and body length, where [tex]$T$[/tex] is proportional to [tex]$B$[/tex] with a proportionality constant of approximately 0.8889 (4.8/5.4).

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PLZZZZZZ HELPPPP

Solve the system of equations using the substitution method.
{2x+8y=4x=−3y+5 Enter your answers in the boxes.

Answers

2x + 8y = 4
x = -3y + 5

plug in the value of x, from the second equation, into the first
2(-3y + 5) + 8y = 4
-6y + 10 + 8y = 4
combine like terms
2y + 10 = 4
subtract 10
2y = -6
divide both sides by 2
y = -3

then, plug what you got for y into one of the equations
x = -3y + 5
x = -3(-3) + 5
x = 9 + 5
x = 14

Hope this helps! And yes, it's correct!

The method of substitution is a three step method to solve the equations. In this method , one equation for one of the variables is solved and in the first step.

The outcome is then substituted to the second equation in the second step for solving the equation.The value is re-substituted to the original equation to find the outcome in the third step.

On solving the equations by substitution method we get x=14 and y=-3

Calculation:

Given equations:

[tex]\rm 2x+8y = 4[/tex] (1)

[tex]\rm x=-3y+5[/tex] (2)

On substituting [tex]x=-3y+5[/tex] in equation 1:

[tex]\begin{aligned}\rm 2(-3y+5)+8y&=4\\\\-6y+10+8y&=4\\\\2y+10&=4\\\\2y&=4-10\\\\ 2y &= -6\\\\y&=\dfrac{-6}{2}\\\\y&=-3\end[/tex]

Substituting [tex]\rm y=-3[/tex] in equation 2:

[tex]\rm x&=-3y+5\\\\x&=-3(-3)+5\\\\x=9+5\\\\x=14[/tex]

Therefore the values of x and y for the given equations is 14 and -3 respectively.

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2x - y + 3z = -9
x + 3y - z = 10
3x + y - z = 8

find the ordered triple

Answers

Try the suggested option, note, that the used method is Gauss' method.

What the complement of 54.6 degree

Answers

complementary angles add up to 90°, if say the angle is "x", then

x + 54.6° = 90°

x = 90° - 54.6°.

how many rootes are in f(x)=(x^2-3x+1)^2
2
5
6
9

Answers

Since there is an x^2 inside the parenthesis, there will be only 2 roots. so A

What is the volume of the figure below if a = 3.9 units, b = 5.7 units, and c = 3 units?

A. 157.95 cubic units
B. 351.351 cubic units
C. 124.605 cubic units
D. 113.49 cubic units

Answers

a x a x c = 3.9 * 3.9 * 3 =45.63
45.63 * 2 = 91.26

a x b x c = 3.9 * 5.7 * 3 = 66.69

66.69 + 91.26 = 157.95 cubic units

Final answer:

The volume of the parallelepiped with sides of lengths a = 3.9 units, b = 5.7 units, and c = 3 units is given by the formula V = a × b × c. After performing the calculation, the volume comes out to be 66.87 cubic units.

Explanation:

To find the volume of the parallelepiped with edges of lengths a, b, and c, you can multiply the length of each edge together. The volume (V) of a parallelepiped (a three-dimensional figure formed by six parallelograms) is given by the product of the lengths of its three dimensions. In this case, the formula to calculate the volume is V = a × b × c.

By plugging in the values provided:

a = 3.9 units

b = 5.7 units

c = 3 units

We get:

V = 3.9 units × 5.7 units × 3 units

Doing the multiplication:

V = 66.87 cubic units

Therefore, the volume of the figure is 66.87 cubic units.

2x+1=3(x+1)-x-2 solve for x

Answers

2x+1=3(x+1)-x-2
2x+1=3x+3-x-2
2x+1=2x+1
2x=2x
x=x

infinite answers

For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?

Answers

for the graph to cross the x axis twice, b²-4ac needs to be larger than 0
b=-k, a=1, c=k²
b²-4ac=k²-4k²=-3k²
-3k² will never be larger than 0.

Determine if the functions are even, odd or neither. f(x) = -5x4 - 2 and g(x) = x3 + 2x

Answers

Try this option:
the rule: if f(-x)=f(x), then the function f(x) is even, if f(-x)=-f(x) then the function is odd.
1. f(x)=-5x⁴-2;
if to substitute x→(-x), then f(-x)=-5*(-x)⁴-2; ⇔ f(-x)=-5x⁴-2, in other words f(x)=f(-x), it means that this function is even.
2. f(x)=x³+2x.
if to substitute x→(-x), then f(-x)=(-x)³+2*(-x); ⇔ f(-x)=-(x³+2x), in other words f(-x)=-f(x), it means that this function is odd.

A basketball player gets 2 free-throw shots when she is fouled by a player on the opposing team. She misses the first shot 40% of the time. When she misses the first shot, she misses the second shot 5% of the time. What is the probability of missing both free-throw shots?

Answers

The probability that the player misses the first shot = 40% = 0.4

When first shot is missed, the probability that she misses the second shot = 5% = 0.05

The probability of missing both shots will be the product of the probabilities of missing individual shots which will be:

Probability of missing both shots = 40% x 5% = 0.4 x 0.05 = 0.02 = 2%

Thus there is a 2% probability that the basketball player misses both free-throw shots.

You were just approved for a $32,000 car loan at an APR of 1.99% for 60 months. As you make payments over time: your payment is , the amount of interest you will pay each month , and the amount of principal you pay each month .

Answers

What it Means...

If you borrow $32,000 at 1.99% for 5 years, your monthly payment will be $560.75.

The payments do not change over time. The loan amortizes over the repayment period, meaning the proportion of interest paid vs. principal repaid changes each month. As the loan amortizes, the amount of monthly interest paid decreases while the amount of principal paid increases.

Loan Amount: $32,000
Term (years): 5 (60 Months)

Annual Interest Rate (%): 1.99% Monthly Payment = $560.75

Check out upload files

Amortization Schedule

Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 55 adult smartphone users are randomly selected, find the probability that at least 22 of them use their smartphones in meetings or classes.

Answers

This is a problem of Binomial Probability.

Success Rate = p = 0.48
Sample Size = n = 55
Number of success = x = 22

We are to find [tex]P(X \geq 22)[/tex] i.e. that probability that atleast 22 adults use the smartphone in meetings or class.

The probability can be calculated using the Binomial Calculators and it comes out to be 0.907.

This means there is 0.907 or 90.7% probability that there are atleast 22 adults among the 55 selected adults who use cell phones in meeting or class.

Shryia read a 480 page long book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 402 pages left to read. Let P(t) denote the number of pages to read P as a function of time t (measured in hours). Write the function's formula.

Answers

The correct answer is P(t)=-52t+480. Hope this helped.

Final answer:

The function representing the number of pages Shryia has left to read at a given time is P(t) = 480 - 52t, considering she reads at a constant rate of 52 pages per hour.

Explanation:

Shryia read a 480-page book in one session at a constant rate. Since P(t) represents the number of pages she has left to read at time t, after 1.5 hours, she had 402 pages left. To find the rate at which she reads, we can see that in 1.5 hours, she read 480 - 402 = 78 pages. Thus, her reading rate is 78 pages per 1.5 hours, or 52 pages per hour.

At time t=0, the book is completely unread, meaning P(0) = 480 pages. Her reading rate is constant, so the function is linear: for every hour that passes, 52 more pages are read. Therefore, the number of pages left, P(t), decreases by 52 for each hour. The function P(t) can then be defined as:

P(t) = 480 - 52t

Suppose a shipment of 140 electronic components contains 3 defective components. to determine whether the shipment should be accepted, a quality-control engineer randomly selects 3 of the components and tests them. if 1 or more of the components is defective, the shipment is rejected. what is the probability that the shipment is rejected?

Answers

Final answer:

To find the probability that a shipment of 140 electronic components, with 3 defects, is rejected upon testing 3 components, calculate the complement (all non-defective) and subtract from 1.

Explanation:

The question involves determining the probability that a shipment containing 140 electronic components, with 3 being defective, is rejected based on a quality-control test of 3 components. To solve, consider the complementary probability - the chance all selected components are non-defective. First, calculate the probability of picking 3 non-defective components: (137/140) * (136/139) * (135/138). Then, subtract this probability from 1 to find the probability of the shipment being rejected.

1 - [(137/140) * (136/139) * (135/138)] equals the probability the shipment is rejected. After performing the calculations, you find that the shipment's rejection probability is determined by the presence of at least one defective component in the tested sample.

Find the inverse of this 3x3 matrix. [1 5 2]
[ 1 1 7]
[0 -3 7]

Answers

Lets say the 3x3 Matrix is

M = [1 5 2 ]
[1 1 7 ]
[0 -3 7 ]

We apply the Gauss-Jordan elimination method (Procedure and result shown in the image below)

Answer:

Step-by-step explanation:

⎡−25 26 −33⎤

⎥ 4 −4 5 ⎥

⎥ 3 −3 4 ⎦

whats the distance between (-8,-7) (8,-4)

Answers

To find the distance between points, use the distance formula.

Distance formula: [tex] \sqrt{ (x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]

Plug in your values for [tex] x_{2}, x_{1}, y_{2}, y_{1}[/tex] using (-8, -7) and (8, -4) and solve.

[tex] \sqrt{(8 - (-8))^{2}+(-4 - (-7))^{2}} [/tex]
[tex] \sqrt{(8+8)^{2}+(-4+7)^{2}} [/tex]
[tex] \sqrt{(16)^{2}+(3)^{2}} [/tex]
[tex] \sqrt{256+9} [/tex]
[tex] \sqrt{265} [/tex] ≈ [tex] 16.28[/tex]

Answer:
Approximately 16.28 units.

Cheryl paid $3 for each pin in her collection. She bought 32 pins in March and 56 pins in April.

How much did Cheryl spend on pins in April?

A.
What is the total amount of money Cheryl spent buying pins?

B.
How many pins did Cheryl add to her collection in March and April?

C.
What is the total cost of the pins that Cheryl bought in April?

D.
What is the difference between the number of pins bought in March and April?

Answers

A) She spent $264 in both March and April
B) She added 88 pins in total to her collection
C) She spent $168 in April
D) The difference is 24 pins
If you want me to explain the answers, just let me know :)

A. As with any purchase, the total cost is the cost of each item multiplied by the number of items.
$3×(32 +56)
= $3×88
= $264

B. From part A, 88 pins.

C. $3×56 = $168

D. 56 -32 = 24
Cheryl bought 24 more pins in April than in March.

(Sometimes, "the difference of M and A" is intended to be strictly interpreted as "M - A". If that is the intent here, then the answer would be -24. More commonly, this wording is interpreted in common English to mean the value that results when the smaller number is subtracted from the larger one.)

A 2 liter drink costs $0.10 per deciliter. How much does the drink cost?

Answers

I liter is ten deciliters
0.1*20=2
2 dollars

The price of drink is given as 0.10 dollars per deciliter.

It says to find the cost of 2 liters of drink.

We need to convert the units from liters to deciliters.

We know 1 liter = 10 deciliters.

then 2 liters = 20 deciliters.

So we need to find the cost of 20 deciliters of drink at rate of 0.10 dollars per deciliter.

1 deciliter of drink cost = 0.10 dollars.

20 deciliter of drink would cost = 20 x 0.10 dollars = 2.00 dollars.

Hence, 2 liters of drink would cost 2 dollars.

Treys online music club charges a monthly rate of $20 plus $0.80 per song download. Debs online music club charges a monthly rate of $21 plus $0.60 per song download. For what number of songs will the monthly charge be the same for both clubs? How much will it cost?

Answers

For this case, the first thing we must do is define variables.
We have then:
x: number of songs.
y: total charge
For Treys online music club:
[tex]y = 0.80x + 20 [/tex]
For Debs online music club:
[tex]y = 0.60x + 21 [/tex]
Equaling both equations we have:
[tex]0.80x + 20 = 0.60x + 21 [/tex]
Clearing x we have:
[tex]0.80x - 0.60x = 21 - 20 0.20x = 1 x = 1 / 0.20 x = 5 songs[/tex]
Substituting the value of x for any of the equations we have:
[tex]y = 0.60 (5) + 21 y = 3 + 21 y = 24 $[/tex]
Answer:
The monthly charge will be the same for 5 songs in both clubs.
the cost will be $ 24

Answer:

For 5 songs the monthly charge be the same for both clubs.

It will cost $ 24.

Step-by-step explanation:

Let, for x songs, the monthly charges are same for both clubs,

Given,

For Treys online music club,

Monthly rate = $ 20,

Additional Charges for a song = $ 0.80,

⇒ Additional Charges for x song = $ 0.80x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 20 + 0.80x

Now, for Debs online music club,

Monthly rate = $ 21,

Additional Charges for a song = $ 0.60,

⇒ Additional Charges for x song = $ 0.60x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 21 + 0.60x

Hence, we can write,

[tex]20 + 0.80x = 21 + 0.60x[/tex]

[tex]0.80x - 0.60x = 21 - 20[/tex]

[tex]0.20x = 1[/tex]

[tex]\implies x = \frac{1}{0.20}=5[/tex]

Hence, for 5 songs the monthly charge be the same for both clubs.

Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24

the sum of two numbera is 122. the second number is 18 less than three times the first number. find the numbers. help please!

Answers

so you can write two equations
x + y = 122
y = 3*x - 18
by substitution:
x + (3x - 18) = 122
now you simplify:
4x - 18 = 122
4x = 140
x = 35
to find y, you can use the first equation
35 + y = 122
y = 87

Robin randomly selects a number between 1 and 20. What is the probability that the number selected is the square of a natural number?

Answers

All of the natural squares from one to twenty are 1,4,9, and 16. This means there is 4 out of 20 which can be reduced to 1 out of 5 or 20%

The probability that the number selected is the square of a natural number will be 0.20.

What is probability?

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Robin randomly selects a number between 1 and 20.

Then the total number of the events will be

Total events = 20 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

The probability that the number selected is the square of a natural number will be

We know that natural numbers 1, 2, 3, 4, 5, and so on.

Then the square of the natural numbers will be

1, 4, 9, 16, 25, ....

Favorable event = 3 {1, 4, 9, 16}

Then the probability will be

P = 4 / 20

P = 1/5

P = 0.20

The probability that the number selected is the square of a natural number will be 0.20.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ5

The hypotenuse of a right triangle is 8 centimeters long. One of the legs of the triangle is 7 centimeters. What is the length of the triangle's other leg?

Answers

Answer:

3.87 centimeters

Step-by-step explanation:

sorry its took 3 years lol :)

Answer:

3.87 centimeters

Step-by-step explanation:

Got it right on Imagine math.

I WILL GIVE U BRAINLY!!!

Which substance has been changed most over time from its original plant material?

A.

peat

B.

anthracite coal

C.

bituminous coal

D.

lignite

Answers

lignite . . . .......... ............. .......... ............. .
.
...

Lignite, is the correct answer hope this helps

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