You drive a car that holds 15 gallons of gasoline. Your car uses 0.03 gal per mile. Which equation best represents this information

now, assuming it's asking for its equation.

\((\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{5}{2}}(x-\stackrel{x_1}{(-1)}) \implies y +2 = - \cfrac{5}{2} ( x +1) \\\\\\ y+2=- \cfrac{5}{2}x-\cfrac{5}{2}\implies y=- \cfrac{5}{2}x- \cfrac{5}{2}-2\implies {\Large \begin{array}{llll} y=- \cfrac{5}{2}x- \cfrac{9}{2} \end{array}}\)

Step-by-step explanation:

the correct answer is option a 6a-7

Explanation

Opposite sides are 5 miles each and for each semicircle we have:

Then the lenght of the track is:

Approximately 13.1416 miles

There will be 6.11 acres in a piece of property measuring 620' x 430'

To calculate the number of acres in a piece of property, you need to convert the measurements from feet to acres.

1 acre is equal to 43,560 square feet.

Given that the property measures 620' x 430', you can calculate the area in square feet by multiplying the length by the width: 620' x 430' = 266,600 square feet.

To convert the area from square feet to acres, divide the square footage by 43,560: 266,600 square feet / 43,560 = 6.11 acres (rounded to two decimal places).

Therefore, the piece of property measures approximately 6.11 acres.

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Answer:

1/2

Step-by-step explanation:

options in a 6 sided die= 1,2,3,4,5,6

greater than 3 = 4,5,6

so three  sides  out of a 6 sided die is greater than three

P(not greater than 3) = \(\frac{6-3}{6} = \frac{1}{2}\)

Answer:

1/2 or 0.5

Step-by-step explanation:

The probability of rolling a number greater than 3 on a six-sided die is 3/6 or 1/2, since there are three numbers (4, 5, 6) out of six that are greater than 3.

To find the probability of not rolling a number greater than 3, we can subtract the probability of rolling a number greater than 3 from 1:

P(not greater than 3) = 1 - P(greater than 3)

P(not greater than 3) = 1 - 1/2

P(not greater than 3) = 1/2

Therefore, the probability of not rolling a number greater than 3 is 1/2 or 0.5.

We can write the integral of f(x) as the sum of the integral of the even component, e(x), and the integral of the odd component, o(x). This gives us the following equation:  ∫f(x)dx = ∫e(x)dx + ∫o(x)dx

Integrals can be written as the sum of the integral of an odd function and the integral of an even function. This is because any function can be broken down into its even and odd components. Even functions are those that remain unchanged when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the same as the result for its negative. Odd functions are those that change sign when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the negative of the result for its negative.

The integral of an even function is the same regardless of whether it is written as the sum of the integral of an odd function and the integral of an even function, or if it is written just as an integral of the even function. The integral of an odd function is the negative of the integral of the even function when written as the sum of the two integrals.

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The bonus question asks for the application of the integral test to determine the convergence of the series given by 2n*e^(-a).

The integral test is a method used to determine the convergence or divergence of a series by comparing it to the integral of a related function. In this case, we are given the series 2n*e^(-a), and we can use the integral test because the terms of the series involve the variable 'n', and the function e^(-a) can be integrated.

To apply the integral test, we consider the integral of the function corresponding to the series. In this case, we integrate the function f(x) = 2x*e^(-a) from 1 to infinity. If this integral converges, then the series is also convergent. Conversely, if the integral diverges, then the series is divergent.

By evaluating the integral of f(x) and analyzing its convergence or divergence, we can determine whether the given series 2n*e^(-a) converges or diverges. Showing all the steps in evaluating the integral and discussing the convergence properties of the resulting integral will be necessary to receive full credit for this question.

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Answer:

No

Step-by-step explanation:

Sooooooooooooo no

P.S. The answer is accually (Deleted)

Answer:

it is not correct

Step-by-step explanation:

the answer is instead of 55 its 73

if this is wrong im sryyyyy

The ticket price that would maximize revenue for the baseball team is $10.

To determine the ticket price that maximizes revenue, we need to find the point where the product of the ticket price and attendance is highest. In this case, we have two data points: when the ticket price is $11, the average attendance is 28,000, and when the ticket price is $8, the average attendance is 35,000.

We can start by calculating the revenue at each data point. Revenue is calculated by multiplying the ticket price by the attendance. At $11 per ticket, the revenue is $11 * 28,000 = $308,000. At $8 per ticket, the revenue is $8 * 35,000 = $280,000.

By comparing the revenues at these two data points, we can see that the revenue is higher when the ticket price is $11. However, this is not the ticket price that maximizes revenue. To find the optimal ticket price, we need to determine the point where the revenue is highest.

Since attendance is linearly related to the ticket price, we can assume a linear equation of the form y = mx + b, where y represents attendance, x represents ticket price, m represents the slope of the line, and b represents the y-intercept. Using the two data points, we can calculate the slope:

m = (35,000 - 28,000) / ($8 - $11) = 7,000 / (-$3) = -2,333.33

Now, we can substitute the slope and one of the data points into the equation to calculate the y-intercept (b):

28,000 = -2,333.33 * $11 + b

b = 28,000 + $25,666.63 = $53,666.63

With the equation y = -2,333.33x + $53,666.63, we can find the attendance at any given ticket price. To maximize revenue, we need to find the ticket price that corresponds to the maximum point of the revenue curve.

Revenue = Ticket Price * Attendance

Revenue = x * (-2,333.33x + $53,666.63)

Revenue = -2,333.33x^2 + $53,666.63x

To find the ticket price that maximizes revenue, we can use calculus. By taking the derivative of the revenue function with respect to x and setting it equal to zero, we can find the critical point:

dRevenue/dx = -4,666.66x + $53,666.63 = 0

4,666.66x = $53,666.63

x = $53,666.63 / 4,666.66 ≈ $11.50

However, since the ticket price must be a multiple of $0.50, the closest valid ticket price is $11. Therefore, the ticket price that would maximize revenue for the baseball team is $10.

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To find the equation of the sphere tangent to the plane 2x + 3y - 6z = 5 with center C(-2, 3, 7), we need to find the radius of the sphere. The equation of the sphere is (x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 36.

The distance from the center of the sphere to the plane is equal to the radius. We can use the formula for the distance between a point (x, y, z) and a plane Ax + By + Cz + D = 0:

Distance = |Ax + By + Cz + D| / sqrt(A^2 + B^2 + C^2)

In this case, the plane equation is 2x + 3y - 6z - 5 = 0. Plugging in the coordinates of the center C(-2, 3, 7) into the formula, we have:

Distance = |2(-2) + 3(3) - 6(7) - 5| / sqrt(2^2 + 3^2 + (-6)^2)

= |-4 + 9 - 42 - 5| / sqrt(4 + 9 + 36)

= |-42| / sqrt(49)

= 42 / 7

= 6

So, the radius of the sphere is 6.

The equation of a sphere with center C(-2, 3, 7) and radius 6 is:

(x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 6^2

Simplifying further, we have:

(x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 36

Therefore, the equation of the sphere is (x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 36.

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Answer:

Description

Step-by-step explanation:

.20(8)+4=5.6

on the graph the point is (8,6)

.25(8)+4=6

We need to decide whether the given equations are always or never true for values of x .The given equations are ,

solve out for x,

\(\longrightarrow x -x =12+1\\ \)

\(\longrightarrow 0 =13\\ \)

This can never be true. Hence the equation is never true for any values of x.

solve out for x,

\(\longrightarrow x -x =\dfrac{3}{4}+\dfrac{3}{4}\\ \)

\(\longrightarrow 0=\dfrac{3}{2}\)

This can never be true. hence the equation is never true for any values of x.

solve out for x,

\(\longrightarrow 4x +12=8x+12-4x\\\)

\(\longrightarrow 4x -8x +4x =12-12\\\)

\(\longrightarrow 0=0\)

hence this equation is true for all values of x.

solve out for x,

\(\longrightarrow 2x -x -x =8+8\\ \)

\(\longrightarrow 0=0 \)

hence the equation is true for all values of x.

solve out for x,

\(\longrightarrow 2x +10+3x =5x-25\\ \)

\(\longrightarrow 5x -5x =-25-10\\\)

\(\longrightarrow 0 =-35\)

This can never be true. hence the equation is never true for any values of x.

and we are done!

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer: 3.85714285714=x

Step-by-step explanation:

3x+12=10x-15

-3x      -3x

12=7x-15

+15    +15

27=7x

27/7=7x/7

3.85714285714=x

:)

Answer: x ≥ $30.

Where x is the amount of money that you need to spend if you want to have the 3 free songs.

Step-by-step explanation:

When you spend $45 or more, you get 3 free songs.

You already bought an album that costs $15, then the minimum amount that you need to spend is (when you spend exactly $45):

$45 - $15 = x = $30.

Then the inequality is:

x ≥ $30.

Because if you spend more than $45 you also get the songs.

The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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Answer:

9.102

Step-by-step explanation:

Assuming this means multiply to each other

1.11 x 8.2 = 9.102

The probability that the sample will contain more than 5% defective units is approximately 0.9525 or 95.25%.

To solve this problem, we can use the binomial distribution formula:

P(X > 5) = 1 - P(X ≤ 5)

where X is the number of defective items in a sample of size n = 100, and p = 0.1 is the probability of an item being defective.

To calculate P(X ≤ 5), we can use the binomial cumulative distribution function (CDF) or a binomial probability table. Alternatively, we can use a normal approximation to the binomial distribution, which is valid when np ≥ 10 and n(1-p) ≥ 10, as is the case here (np = 10 and n(1-p) = 90).

Using the normal approximation, we can standardize the distribution of X as follows:

\(z = (X - np) / \sqrt{(np(1-p))}\)

Then, we can use a standard normal table or calculator to find the probability of z ≤ z0, where z0 is the standardized value corresponding to X = 5.

Let's use the normal approximation method to solve the problem:

np = 100 x 0.1 = 10

σ = \(\sqrt{(np(1-p))} = \sqrt{(9)} = 3\)

z0 = (5 - 10) / 3 = -1.67 (rounded to two decimal places)

Using a standard normal table or calculator, we find that P(Z ≤ -1.67) = 0.0475 (rounded to four decimal places).

Therefore, P(X > 5) = 1 - P(X ≤ 5) = 1 - 0.0475 = 0.9525 (rounded to four decimal places).

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Cars with exactly two options = Total cars - Cars with none or one option - Cars with all three options. 8 cars had exactly two of the given options during the month of July.

To determine the number of cars that had exactly two of the given options (air conditioning, automatic transmission, and power steering), we can follow these steps:

1. Find the total number of cars sold in July.
2. Subtract the number of cars with none, one, or all three options to get the number of cars with exactly two options.

Step 1: Find the total number of cars sold in July
- 24 cars had none of the extras
- 24 cars had only air conditioning
- 64 cars had only automatic transmission
- 35 cars had only power steering
- 8 cars had all three extras
Total cars = 24 + 24 + 64 + 35 + 8 = 155 cars

Step 2: Subtract the number of cars with one or all three options
- 87 cars had air conditioning
- 99 cars had an automatic transmission
- 73 cars had power steering
- 8 cars had all three extras

Total cars with at least one option = 87 + 99 + 73 - 8 = 251 cars

Now, subtract the number of cars with none or one option from the total number of cars to find the number of cars with exactly two options:

Cars with exactly two options = Total cars - Cars with none or one option - Cars with all three options
Cars with exactly two options = 155 - (24 + 24 + 64 + 35) - 8 = 155 - 147 = 8 cars
Therefore, 8 cars had exactly two of the given options during the month of July.

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Answer:

the first

Step-by-step explanation:

if it's perpendicular so is the gradient so y= -5/6 + 12

*I'm so sorry if I'm wrong

Answer:

Any value of x makes the equation true.

All real numbers

Interval Notation:

(−∞,∞)

Step-by-step explanation:

Answer:

x=0

Step-by-step explanation:

8x+11=2(4x-7)+25

8x+11=8x-14+25

8x+11=8x+11

8x-8x=11-11

x=0

Answer:jjj

Step-by-step explanation:because

The equation will be written as (42/2) = 21.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the quotient of a number, 2, and 21 is 42. The equation of the quotient will be written as,

42 / 2 = 21

Here the value 42 when divided by 2 will give 21.

Therefore, the equation will be written as (42/2) = 21.

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The value of the double integral is 128/27 - 32/9 + 8ln2/3. From triangular region with vertices (0, 1), (1, 2), (4, 1) d.

To evaluate the double integral, we first need to set up the limits of integration. Since the region D is a triangle, we can use the following limits:

0 ≤ x ≤ 1

1 + x ≤ y ≤ 4 - x

The integral then becomes:

∫0^1 ∫1+x^4-x 8y^2 dy dx

Evaluating the integral with respect to y first, we get:

∫0^1 ∫1+x^4-x 8y^2 dy dx = ∫0^1 [(8/3)(y^3)]1+x^4-x dx

= ∫0^1 [(8/3)(1+x^3)^3 - (8/3)(1+x^2)^3] dx

= 128/27 - 32/9 + 8ln2/3

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The mole percent of hydrogen in the product stream is 84.25%.

Solution:Calculate the number of moles of each component in the feed:

For 100 g of the feed,

Mass of H2 = 72.47 g

Mass of N2 = 15.81 g

Mass of argon = 100 - 72.47 - 15.81 = 11.72 g

Molar mass of H2 = 2 g/mol

Molar mass of N2 = 28 g/mol

Molar mass of argon = 40 g/mol

Number of moles of H2 = 72.47/2 = 36.235

Number of moles of N2 = 15.81/28 = 0.5646

Number of moles of argon = 11.72/40 = 0.293

Number of moles of reactants = 36.235 + 0.5646 = 36.7996

From the balanced chemical equation: 1 mole of N2 reacts with 3 moles of H21 mole of N2 reacts with 3/0.5646 = 5.312 moles of H2

For 0.5646 moles of N2,

Number of moles of H2 required = 0.5646 × 5.312 = 3.0005 moles

∴ Hydrogen is in excess

Hence, the number of moles of ammonia formed = 20.28% of 0.5646 = 0.1144 moles

Number of moles of hydrogen in the product stream = 3.0005 moles (unchanged)

Amount of nitrogen in the product stream = 0.5646 - 0.1144 = 0.4502 moles

Total number of moles in the product stream = 3.0005 + 0.1144 + 0.4502

= 3.5651 mol

Mole fraction of H2 in the product stream: XH2 = 3.0005/3.5651

= 0.8425Mole percent of H2 in the product stream: 84.25%

Therefore, the mole percent of hydrogen in the product stream is 84.25%.

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Answer:

20 hours hope this helps :)

Step-by-step explanation:

Answer:

20 hours :)

Step-by-step explanation:

Sami earns 4.50 per hour and needed 90.00. What I did was I divided 90 by 4.5 to find out how many hours he would need to work.

90/4.5=20

ps can u please give me brainly

The net force acting on the object is 3456 N, the objective with an acceleration.

The net force applied to an object is equal to the product of its mass and acceleration, according to Newton's second law of motion. Mathematically, this can be represented as:

Fnet = ma

Where Fnet is the net force, m is the mass, and a is the acceleration. In your scenario, the net force applied to the object is 125 N, and its acceleration is 24.0 m/s2. Therefore, we can rearrange the formula and solve for the mass of the object as follows:

m = Fnet / a
m = 125 N / 24.0 m/s2
m = 5.21 kg

However, this answer does not match the given mass of the object, which is 144 kg. This suggests that there may be an error in one of the values provided. Assuming the mass of the object is actually 144 kg, we can use the same formula to solve for the net force acting on it as follows:

Fnet = ma
Fnet = 144 kg * 24.0 m/s2
Fnet = 3456 N

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The mass of an object with net force value = 125 Newton and acceleration of 24.0 m/s² is equals to the 5.208 kg. So, option(c) is right one.

The force formula is derived by Newton's second law of motion. The basic formula force applied on object is F = ma, which implies that net force is equals to product of mass and acceleration of an object. We have an object with the following information, Net applied force on object, F = 125 N

Acceleration of an object, a = 24.0 m/s²

We have to determine mass of object. Using the above force formula, F = M× a

where M --> mass in kilograms

a --> Acceleration in m/s²

F --> net force in Newton

Substitute all known values in above formula, 125 N = M × 24.0 m/s²

=> M = = \(\frac{125}{24}\)

=> M = 5.208 kg

Hence, required value is 5.208 kg.

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Complete question:

A net force of 125 N is applied to a certain object. As a result, the object accelerates with an acceleration of 24.0 m/s^2. The mass of the object is ?

a) 144 kg

b) 236 kg

c) 5.208 kg

d) 459 kg

Given sequence is geometric sequence and common ratio between consecutive term is

In Arithmetic sequence , common difference between consecutive terms should be equal.

In Geometric sequence, common ratio between consecutive terms should be equal.

Given sequence, 16, 8, 4, ...

Since, common difference = 8 - 16 ≠ 4 - 8 , this is not arithmetic sequence.

Common ratio = T2/T1 = T3/T2 = 8/16 = 4/8 = 1/2 Because common ratio is are equal. Thus, given sequence is geometric sequence.

Hence the sequence is a geometric sequence and the common ratio = 1/2

Answer:

l think that the answer is 91 degrees because they are corresponding angles , that is what I think.

In ∆JKL and ∆MLK

Hence

∆JKL≅∆MLK(Side-Angle-Side)

by SAS property of congruency of triangles, ΔJKL and ΔMLK are congruent.  

Given that :

JK ≅ ML

∠JKL ≅ ∠MLK

To Prove: △JKL ≅ MLK

Proof:

We know that corresponding angles formed by transversal line are congruent.

Hence ∠JKL = ∠ MLK ...(i)

Now consider triangles ΔJKL and triangles  ΔMLK

JK = LM  {Given}  , This means that Line JK is Congruent to Line LM. Two congruent lines means they are equal. Thus; JK = LM.

∠JKL = ∠ MLK { Using (i) }

KL = KL  {common sides}

Hence by SAS property of congruency of triangles, ΔJKL and ΔMLK are congruent.  

Hence proved.

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