A bike rental costs $8 per hour. Desiree has a coupon for 2 free hours. To find how many hours she can rent with $40, Desiree sets up the equation 8(x – 2) = 40, where x is the number of hours.

Answer:

1/15

Step-by-step explanation:

For the arrival of both Bob and alice independently at uniformly distributed times on that day. The probability they will meet for lunch that day is equals to the 0.4514.

Let X = arrival time (in minutes past noon) of the first-to-arrive person and

Y = arrival time (in minutes past noon) of the second-to-arrive person. Then, we have X and Y are independent implies their joint probability = product of their individual probabilities .... (1)

Probability density function, Pdf of X is : (1/60)dx [noon to 1 pm is 60 minutes and X ~ Uniform ....(2)

Similarly, Pdf of Y is: (1/60)dy [noon to 1 pm is 60 minutes and Y ~ Uniform] ...(3)

The two will meet for lunch on that day if

Y = X ± 15...(4)

To expand equation (4), further,

P(The two will meet for lunch on that day) = A + B + C, ...(5)

where \(A = \int_{0}^{15}(\frac{1}{60}\int_{0}^{x +15}\frac{1}{60}dy)dx\)

\(B = \int_{15}^{45}(\frac{1}{60}\int_{x- 15}^{x +15}\frac{1}{60}dy)dx \\ \)

\(C= \int_{45}^{60}(\frac{1}{60}\int_{x- 15}^{60}\frac{1}{60}dy)dx \)

Now, we solve the above integrales one by one, \(A = \int_{0}^{15} \frac{1}{3600} (x + 15)dx\)

\(A =\frac{1}{3600}[x^{2}+15x]_{0}^{15}\)

\(= \ \frac{1}{3600}[15^{2} + 15 \times 15 - 0]\)

A = \( \frac{775}{7200} = 0.1076 \)

\(B= \int_{15}^{45} \frac{1}{3600} [(x + 15) - (x - 15)]dx \\ \)

\(= \int_{15}^{45} \frac{1}{3600}[30]dx \)

= \( \frac{1}{3600}[30x]_{15}^{45} \\ \)

\(= \frac{30}{3600} [ 45 - 15 ]\)

\( \frac{900}{3600} \: = 0.25\)

\(C = \int_{45}^{60} \: \frac{1}{3600}(60 - x + 15)dx\)

\(= \int_{45}^{ 60} \: \frac{1}{3600}(75 - x )dx\)

\(= \frac{1}{3600}[75x - \frac{x²}{2}]_{45}^{ 60} \)

\(= \frac{1}{3600}[75 \times 60 - \frac{{60}^{2}}{2} - 75 \times 45 + \frac{ {45}^{2}}{2}] \\ \)

\(= \frac{1}{3600}[ 1125 - 787.5] \)

= \( \frac{337.5}{3600} = 0.0938\)

From Required probability = 0.1076 + 0.25 + 0.0938 = 0.4514

Hence, required probability is 0.4514.

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Answer: Neither of them are solutions.

Step-by-step explanation: Hope this helped!!!!

Answer:

see below

Step-by-step explanation:

We need to write it on vertex form (f(x) = a(x - c)² + d where (c, d) is the vertex) and to do that we will complete the square.

f(x) = x² + 3x - 2

= (x² + 3x + 9/4) - 9/4 - 2

= (x + 1.5)² - 4.25

The vertex is (-1.5, -4.25).

Answer:

it depends if you want them separately it is 20000 and 700 if not it’s 20700

Step-by-step explanation:

Hey there!

(2070)×10

=> 2070 * 10

=> 20,700

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Answer:

v < 2.2

Step-by-step explanation:

0.5v < 1.14 – 0.04

0.5v < 1.1

v < 1.1/0.5

v < 2.2

pls mark as brainliest

Answer:

it needed your to focus on school work , homework and work hard to make yourself feel ready

Answer:

See Below

Step-by-step explanation:

Point A (0,0)

Point B (3,2)

Point C (9,6)

b. x values from A to B: 0 to 3

x values from B to C: 3 to 9

No, AB has a change of 3 and BC has a change of 6 in x

c. y values from A to B: 0 to 2

y values from B to C: 2 to 6

No, AB has a change of 2 and BC has a change of 4 in y

d. Calculate Slope: \(\frac{y{2}-y{1}}{x{2}-x{1}}\)

AB (2-0/3-0) = 2/3

BC (6-2/9-3) = 4/6 = 2/3 simplified

Thus, AB has the same ratio of change as BC

Answer: after 6 years, the account will have approximately $23,394.27, and after 15 years, the account will have approximately $54,765.15.

Step-by-step explanation:

FV = Future value

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of compounding periods per year

t = Number of years

Given that you received $15,000 from your aunt and the interest rate is 7.8% compounded quarterly, we can calculate the future values as follows:

After 6 years:

P = $15,000

r = 7.8% or 0.078 (as a decimal)

n = 4 (quarterly compounding)

t = 6 years

FV = $15,000 * (1 + 0.078/4)^(4*6)

FV = $15,000 * (1 + 0.0195)^24

FV = $15,000 * (1.0195)^24

FV ≈ $15,000 * 1.559618

FV ≈ $23,394.27

After 15 years:

P = $15,000

r = 7.8% or 0.078 (as a decimal)

n = 4 (quarterly compounding)

t = 15 years

FV = $15,000 * (1 + 0.078/4)^(4*15)

FV = $15,000 * (1 + 0.0195)^60

FV ≈ $15,000 * (1.0195)^60

FV ≈ $15,000 * 3.651010

FV ≈ $54,765.15

The line of 305,000 people, with an average distance of 33 inches between them, would be approximately 33.1 miles long.

To calculate the length of the line, we can follow these steps:

1. Convert the average distance between people from inches to miles. Since there are 12 inches in a foot and 5280 feet in a mile, we have 33 inches / (12 inches/foot) / (5280 feet/mile) = 33/12/5280 miles.

2. Multiply the average distance by the number of people minus one to get the total distance between them. In this case, it would be (33/12/5280) * (305,000 - 1) miles.

3. Add the length of one person to the total distance to account for the endpoints. The length of one person can be considered negligible compared to the total distance, but for accuracy, we include it. So the total length of the line is (33/12/5280) * (305,000 - 1) + (1/5280) miles.

4. Simplify the expression and round the result to the nearest tenth of a mile. This will give us the final answer, which is approximately 33.1 miles.

Therefore, the line of 305,000 people, with an average distance of 33 inches between them, would be approximately 33.1 miles long.

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The distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

The distribution of X, representing the IQ of an individual from the ruling species on the faraway planet, is a normal distribution with a mean (μ) of 106 and a standard deviation (σ) of 18. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

In this distribution, the majority of IQ values will cluster around the mean of 106. The standard deviation of 18 indicates the average amount of variation or dispersion from the mean. The normal distribution is symmetric, which means that the probabilities of IQ values being above or below the mean are equal.

The shape of the normal distribution is bell-shaped, with the highest point being at the mean. As we move away from the mean, the probability of observing extreme values decreases. The spread of the distribution is determined by the standard deviation, where a larger standard deviation indicates a wider spread of IQ values.

the distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet.

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On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.  What is the distribution of X? X ~ N( 106 , 18 )  

Answer:

second option

Step-by-step explanation:

The x- intercepts are the values on the x- axis where the graph crosses.

These are

x = - 3, x = - 1 and x = 3

the answer would be forty nine

The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of f and the domain of g which is false.

A statement, opinion, or rule that forms a linking of two variables is characterized as a function. Mathematics has functions, which are necessary for the design of meaningful relationships.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

The denominator of the rational function shouldn't be 0. The function is not defined if the denominator is 0.

Thus, the given statement is false.

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Answer: 2 circles and a rectangle

Step-by-step explanation:

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=12\\ \theta =75 \end{cases}\implies 12=\cfrac{(75)\pi r^2}{360}\implies 12=\cfrac{5\pi r^2}{24} \\\\\\ 288=5\pi r^2\implies \cfrac{288}{5\pi }=r^2\implies \sqrt{\cfrac{288}{5\pi }}=r\implies 4.3\approx r\)

Answer:

-1

Step-by-step explanation:

so -x-6 and x-4 are both = to y so that means they are both = to each

other so -x-6=x-4 add x to both sides -6=2x-4 add 4 to both sides 2x = -2 simplify by divide by 2 so x=-1

Answer:

Take the second equation and add 4 to both sides, this gives you x=y+4. The plug in y+4 on the first equation, so y=-(y+4)-6, distribute the negative to everything inside the parentheses, and you get y=-y-4-6. Combine like terms and you get y=-y-10, then add y to both sides, you get 2y=-10, divide both sides by 2 and you get y=-5.

Then plug -5 into the second equation and you get -5=x-4, add 4 to both sides and you get -1=x.

If you want to check your answer, just plug in x and y to either of the equations and see if it makes a true statement.

we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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..no lo sé, pero como necesito puntos, ¿sí?

Answer:

the first one if you solve it it will be the same and the second one 41/7

Step-by-step explanation:

\(~~~~|2x +0.75| = 5 \dfrac 67\\\\\\\implies \left|2x+\dfrac 34\right| = \dfrac{41}7\\\\\\\implies 2x +\dfrac 34 = \dfrac{41}7~~~~ \text{or}~~~~ 2x + \dfrac 34 =- \dfrac{41}7\\\\\\\implies 2x = \dfrac{41}7- \dfrac 34~~~~ \text{or}~~~~ 2x = -\dfrac 34 - \dfrac{41}7\\\\\\\implies 2x = \dfrac{143}{28}~~~~~~~~ \text{or}~~~~ 2x = -\dfrac{185}{28}\\\\\\\implies x = \dfrac{143}{56}~~~~~~~~~ \text{or}~~~~~ x = -\dfrac{185}{56}\\\\\\\)

\(\implies x = 2\dfrac{31}{56}~~~~~~~~~ \text{or}~~~~~ x = -3\dfrac{17}{56}\\\)

Answer:

hello! :) have a good day!

W = 9

Answer:

\(21y^{2} +4y-1\)

Step-by-step explanation:

Hello!

\((12y^{2} +17y-4)+(9y^{2} -13y+3)\)

For this, we can combine like terms

\(12y^{2} +9y^{2}=21y^{2}\)

17y - 13y = 4y

-4 + 3 = -1

Combine the answers and we get

\(21y^{2} +4y-1\)

Hope this Helps!

Answer:

21y² + 4y -1

Step-by-step explanation:

(12y² + 17y - 4) + (9y² - 13y + 3)  ---- remove parentheses

= 12y² + 17y - 4y + 9y² - 13y + 3

= 12y² + 9y² + 17y - 13y - 4 + 3  -----grouped like terms

= 21y² + 17y - 13y - 4 + 3

= 21y² + 4y - 4 + 3

= 21y² + 4y - 1

Answer:

Volume of a cylinder = 549.5 cm³

Step-by-step explanation:

Volume of a cylinder = πr²h

Where,

π = 3.14

Radius, r = 5 cm

Height, h = 7 cm

Volume of a cylinder = πr²h

= 3.14 * (5 cm)² * 7 cm

= 3.14 * 25 cm² * 7 cm

= 549.5 cm³

Volume of a cylinder = 549.5 cm³

Answer:

D is the answer.

Step-by-step explanation:

What happened to your computer

In trigonometry, it should be noted that the value of sin(-5pi/6) is -0.5.

In order to find the value, we can use the following steps:

Draw a unit circle and mark an angle of -5pi/6 radians.

The sine of an angle is represented by the ratio of the opposite side to the hypotenuse of the triangle formed by the angle and the x-axis.

In this case, the opposite side is 1/2 and the hypotenuse is 1.

Therefore, sin(-5pi/6) will be:

= 1/2 / 1

= -0.5.

We can also use the following identity to find the value of sin(-5pi/6):

sin(-x) = -sin(x)

Therefore, sin(-5pi/6)

= -sin(5pi/6)

= -0.5.

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Answer:

the answer is 8$

Step-by-step explanation:

Suppose that F(x) = \(A0 + A1*x + A2*x^2 + A3*x^3 + A4*x^4 + ....\) If F(x) = 1/(1-x), A1000 = 1000!

The function F(x) can be expressed as a geometric series with a first term of 1 and a common ratio of x. Thus, we can write:

F(x) = \(1 + x + x^2 + x^3 + x^4 + ...\)
To find the coefficients A0, A1, A2, A3, A4, and so on, we can differentiate both sides of the equation with respect to x. This gives:
F'(x) = \(1 + 2x + 3x^2 + 4x^3 + 5x^4 + ...\)
Multiplying both sides by x, we get:
xF'(x) = \(x + 2x^2 + 3x^3 + 4x^4 + 5x^5 + ...\)
Now, we can differentiate both sides of this equation with respect to x again:
xF''(x) + F'(x) = \(1 + 4x + 9x^2 + 16x^3 + 25x^4 + ...\)
Multiplying both sides by x again, we get:
x(xF''(x) + F'(x)) = \(x + 4x^2 + 9x^3 + 16x^4 + 25x^5 + ...\)
Continuing this process, we get:
x^nFn(x) = \(n!x^n + n(n-1)!x^{(n+1)} + n(n-1)(n-2)!x^{(n+2)} + ...\)
Now, we can substitute x = 0 into this equation to find the coefficients. When we do this, all the terms except for the first one on the right-hand side disappear. Thus:
A0 = 1
A1 = 1
A2 = 2
A3 = 6
A4 = 24
We can see that the coefficients are the factorials of the index, so:
An = n!
Therefore, A1000 = 1000!

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