Carolines car used 16 gallons to travel 544 how far can she travel on 9 gallons

The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.

The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.

So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

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Given

Solution

Step 1

Subtract C from both sides

Step 2

Divide both sides by 7

The final answer

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Answer:

see below

Step-by-step explanation:

(-3) ^2

(-3)*(-3)

A negative times a negative

9

If the problem is

- (3) ^2

- (3*3)

- 9

Answer:

3/14

Step-by-step explanation:

This is because 1/2-1/3 is 1/6 and then 1/6 times 6/7 is 3/14

Answer:

here u go

Step-by-step explanation:

Let x, x+2 & x+4 be the 3 integers.

x+2(x+2)=(x+4)+20

x+2x+4=x+4+20

3x+4=x+24

3x-x=24-4

2x=20

x=20/2

x=10 answer for the smallest integer.

10+2=12 for the middle integer.

10+4=14 answer for the largest integer.

Proof:

10+2*12=14+20

10+24=34

34=34

Therefore, the three consecutive integers are 10, 12, and 14.

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The right question is:

Find three consecutive even integers such that the sum of the smallest number and twice the middle number is 20 more than the largest number​.

Step-by-step explanation:

The three methods most commonly used to solve systems of equations are substitution , and augmented matrices.

Answer:

b. False

It is false since lowering the confidence level causes the interval to narrow while raising the confidence level actually widens it.

The chance or degree of assurance that the true population parameter will fall inside the estimated confidence interval is represented by the confidence level. A broader interval is needed to cover a greater range of possible values when the confidence level is raised, say from 90% to 95%. This is because a higher level of assurance is demanded. Conversely, lowering the level of confidence, for example, from 95% to 90%, allows for a lower level of certainty, which, in turn, allows for a narrower interval because it only needs to encompass a smaller range of possible values.

Answer:

see explanation

Step-by-step explanation:

∠ AOB = 360° - 264° = 96°

The altitude OM bisects ∠ AOB and the base AB

(a)

∠ MOB = 0.5 × 96° = 48°

Using the cosine ratio in right triangle MOB

cos48° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{OM}{OB}\) = \(\frac{18}{r}\) ( OB is the radius r of the circle )

Multiply both sides by r

r × cos48° = 18 ( divide both sides by cos48° )

r = \(\frac{18}{cos48}\) ≈ 27 cm ( to the nearest cm )

(b)

Using the tangent ratio in the right triangle MOB

tan48° = \(\frac{opposite}{adjacent}\) = \(\frac{MB}{OM}\) = \(\frac{MB}{18}\) ( multiply both sides by 18 )

18 × tan48° = MB then

AB = 2 × MB = 2 × 18 × tan48° = 36 × tan48° ≈ 40 cm ( to nearest cm )

Answer:

Step-by-step explanation:

Hope this Helps ;)

A random variable Y has a uniform distribution over the interval (θ1, θ2). The variance of Y is (θ2 - θ1)^2 / 12.

The variance of a uniform distribution is given by:

\(Var(Y) = (θ2 - θ1)^2 / 12\)

To derive this, we can use the standard formula for variance:

\(Var(Y) = E(Y^2) - [E(Y)]^2\)

where E(Y) is the expected value of Y.

Since Y is uniformly distributed over the interval (θ1, θ2), we have:

\(E(Y) = (θ1 + θ2) / 2\)

To compute E(Y^2), we have:

\(E(Y^2) = ∫θ1^θ2 y^2 f(y) dy\)

where f(y) is the probability density function of Y, which is constant over the interval (θ1, θ2) and zero elsewhere. Therefore:

\(E(Y^2) = ∫θ1^θ2 y^2 (1 / (θ2 - θ1)) dy\)

\(= [(y^3 / 3) * (1 / (θ2 - θ1))] from θ1 to θ2\)

\(= (θ2^3 - θ1^3) / (3 (θ2 - θ1))\)

Now, we can compute the variance:

\(Var(Y) = E(Y^2) - [E(Y)]^2\)

\(= (θ2^3 - θ1^3) / (3 (θ2 - θ1)) - [(θ1 + θ2) / 2]^2\)

\(= (θ2 - θ1)^2 / 12\)

Therefore, the variance of Y is (θ2 - θ1)^2 / 12.

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Answer:

267.008

Step-by-step explanation:

Answer:

267.008

Step-by-step explanation:

Answer:

\(x > \frac{5}{2} > 2\frac{1}{2}\)

Step-by-step explanation:

group

\(4x-7 > 3\\4x-7+7 > 3+7\\4x > 3+7\\4x > 10\)

isolate "x"

\(4x > 10\\=\frac{4x}{4} > \frac{10}{4}\\x > \frac{10}{4}\\x > \left(\frac{5\cdot 2}{2\cdot 2}\right)\\x > \frac{5}{2}\)

Answer:

x > 2.5 or in fraction form x > 2 1/2

Step-by-step explanation:

4x - 7 > 3

     +7  +7         Add seven to both sides.

4x > 10

÷4     ÷4            Divide both sides by 4.

x > 2.5

Hope this helps!

Answer:

It is - \(\frac{1}{4}\) throughout the line

Step-by-step explanation:

The points O, A and B lie on the line and so the slope will be the same for OA, OB and AB

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = B(- 12, 3) and (x₂, y₂ ) = O(0, 0)

m = \(\frac{0-3}{0+12}\) = \(\frac{-3}{12}\) = - \(\frac{1}{4}\)

Thus the slope is - \(\frac{1}{4}\) throughout the line.

Answer:

A: one pound of spinach is $0.40

B: 10 pounds of spinach for $4

Step-by-step explanation:

X=number of pounds of spinach

Y=price in dollars

(x,y)

(5,2) would be 5 pounds of spinach for $2

(10,4) would be 10 pounds of spinach for $4

2/5 $0.40per pound of spinach

Check: 4/10=0.40

1 pound of spinach would be $0.40

From the logarithmic differentiation, function \(f(x) = \frac{( 1 + 2x)^{\frac{1}{x}}}{ sin(x)}\),

a) \( ln (f(x)) = \frac{1}{x} ln( 1 + 2x) - ln(sin(x))\\ \)

b) \( \frac{f'(x)}{f(x)} = \frac{2}{x( 1 + 2x)} - \frac{1}{x²} ln( 1 + 2x) - cot(x) \\ \)

c ) The derivative of function, f(x) is

\(f'(x) = \frac{( 1 + 2x)^{\frac{1}{x}}}{ sin(x)}( \frac{2}{x( 1 + 2x)} - \frac{1}{x²} ln( 1 + 2x) - cot(x)) \\ \)

A logarithmic differentiation calculator is one of online tool used to calculate the derivative of a function using logarithm.

We have a function, \(f(x) = \frac{( 1 + 2x)^{\frac{1}{x}}}{ sin(x)}\).

We have to use logarithmic differentiation to determine the derivative and other values of the function.

a) Taking natural logarithm both sides in f(x), \(ln (f(x)) = ln( \frac{( 1 + 2x)^{\frac{1}{2}}}{ sin(x)})\)

Now, using the logarithm property,

\(ln(\frac{m}{n}) = ln(m) - ln(n) \)

\(ln (f(x)) = ln( 1 + 2x)^{\frac{1}{x}} - ln(sin(x)) \\ \). Also use power property, ln(p)² = 2ln(p),

\( ln (f(x)) = \frac{1}{x} ln( 1 + 2x) - ln(sin(x)) - - (1) \\ \)

b) Now, we determine the ratio of f'(x)/f(x)

Take a derivative of equation (1), we have

\(\frac{f'(x)}{f (x) } = \frac{2}{x( 1 + 2x)} - \frac{1}{x²} ln( 1 + 2x) - \frac{cos(x)}{sin(x)}\\ \)

\(= \frac{2}{x( 1 + 2x)} - \frac{1}{x²} ln( 1 + 2x) - cot(x) \\ \)

c) Now, we determine the derivative of f(x), Substitute original value of f(x) in previous equation,\( \frac{f'(x)}{ \frac{( 1 + 2x)^{\frac{1}{x}}}{ sin(x)}} = \frac{2}{x( 1 + 2x)} - \frac{1}{x²} ln( 1 + 2x) - cot(x) \\ \)

f'(x) \( = \frac{( 1 + 2x)^{\frac{1}{x}}}{ sin(x)}( \frac{2}{x( 1 + 2x)} - \frac{1}{x²} ln( 1 + 2x) - cot(x)) \\ \). Hence, required value is \( \frac{( 1 + 2x)^{\frac{1}{x}}}{ sin(x)}[ \frac{2}{x( 1 + 2x)} - \frac{1}{x²} ln( 1 + 2x) - cot(x)] \\ \).

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Step-by-step explanation:

mXYZ+mXYW=180°(being straight angle)

mXYW =180-115

mXYW=65

now,

mXWY+mWXY+mXYW=180°(sum of angle of triangle)

mXWY=180-110

mXWY=70°

hope it helps.

The measure of the angle ∠XWY of the triangle is ∠XWY = 70°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔXYZ

And , the measure of ∠XYZ = 115°

Now , the measure of ∠WXY = 45°

So , the measure of ∠XYW = 180° - 115° ( angles on a straight line = 180° )

And , the measure of ∠XYW = 65°

Now , the measure of ∠XWY = 180° - ( 45° + 65° ) ( angles in a triangle = 180° )

On simplifying , we get

The measure of angle ∠XWY = 70°

Hence , the angles of the triangle is solved

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Answer:

18/8 or 9/4 or 2 1/4 inches of rain per hour

Step-by-step explanation:

Since the rain is falling at 9/8 inches per half hour, we can double that to get the inches of rain per hour.

9/8 x 2/1 = 18/8

Simplify

9/4  or  2 1/4

Answer:

x ≥ 21.5/19

Step-by-step explanation:

-1.5(4x + 1) ≥ 45 - 25(x + 1)

-6x - 1.5 ≥ 45 - 25x - 25

-6x + 25x ≥ 45 - 25 + 1.5

19x ≥ 21.5

x ≥ 21.5/19

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Parabolas are used to represent quadratic functions. The x-intercepts of the parabola are -1.969 and 6.01. Vertex of the parabola are 2.02 and 78.002.

A quadratic function is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.

The function is given as:

f(x) = \(4.9x^{2} + 19.8x+58\)

Next, we plot the graph of the function f(x)

From the graph (see attachment), we have the following features

Vertex = (2.02, 78.002)

Line of symmetry, x = 2.02

x-intercepts = -1.969 and 6.01

Hence, the x-intercepts of the parabola are -1.969 and 6.01 and Vertex of the parabola are 2.02 and 78.002.

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Zirinak's patent amortization for 2021, assuming the straight-line method is used is $852,000. The correct answer is B.

To compute Zorinak's patent amortization for 2021 using the straight-line method, we need to determine the annual amortization expense.

The patent was acquired for $4.5 million and has a useful life of five years. Therefore, the annual amortization expense is calculated as:

The Annual amortization expense = (Cost of patent - Residual value) / Useful life

= ($4.5 million - $240,000) / 5

= $4,260,000 / 5

= $852,000

So, Zorinak's patent amortization for 2021, assuming the straight-line method is used, is $852,000.

Therefore, the correct answer is option B) $852,000.

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Answer:

a = -4

b = 3

c = -10

d = -6

Step-by-step explanation:

Plug each value into the equation and solve.

\(a = 3(0)-4\\a=-4\)

\(5=3b-4\\9=3b\\b=3\)

\(c=3(-2)-4\\c=-6-4\\c=-10\)

\(-22=3d-4\\-18=3d\\d=-6\)

Answer:

Amedia =  30 m

Top of the Lighthouse = +45 m

Boat = 0

Fish = - 10 m
The distance between Amelia and the fish  is 40 meter

Step-by-step explanation:

Amelia  = 30 m ( height of the cliff) since Amelia is standing on it's edge

-Top of lighthouse =  lighthouse is located on top of the cliff ;
mean height of cliff + height of light house = (30 + 15) = 45 m

-The boat = 0 (on the surface of water) ; this is the sea level surface or point

-The fish = - 10 m (10 meters below the water surface).

Distance between Amelia  and fish :

30 m - ( - 10 m) = 30 m + 10 m = 40 m

The side lengths of the real object will be 50 inches and 60 inches.

The scale factor is the ratio of the actual size of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.

The given scale factor is 5:1, which means that the dimensions of the scale drawing are 1/5 of the dimensions of the real object.

To find the side lengths of the real object, we can use the ratio of the dimensions in the scale drawing and the real object.

For example, the length of the real object can be found by multiplying the length of the scale drawing by the scale factor:

Real object length = Scale drawing length x Scale factor

Real object length = 10 in x 5

Real object length = 50 in

Similarly, the width of the real object can be found using the same method:

Real object width = Scale drawing width x Scale factor

Real object width = 12 in x 5

Real object width = 60 in

Therefore, the side lengths of the real object are 50 inches and 60 inches.

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To find a second solution, y2(x), for the given differential equation y" + 2y' + y = 0 using the reduction of order or the formula y2 = y1(x)∫e^(-∫P(x)dx)y1^2(x)dx, we will substitute the given solution y1(x) = xe^(-x) into the formula.

The second solution is y2(x) = e^(-2x) (Option C).

To explain the solution, let's start by substituting y1(x) = xe^(-x) into the formula for y2(x):

y2(x) = xe^(-x) ∫e^(-∫(2x)dx)(xe^(-x))^2dx

Simplifying the expression, we have:

y2(x) = xe^(-x) ∫e^(-2x)(x^2e^(-2x))dx

Integrating the expression inside the integral, we get:

y2(x) = xe^(-x) ∫(x^2e^(-4x))dx

Integrating this expression, we find:

y2(x) = xe^(-x) (-1/4) * (x^2e^(-4x) - 2∫xe^(-4x)dx)

Simplifying further, we have:

y2(x) = xe^(-x) (-1/4) * (x^2e^(-4x) - 2(-1/4)e^(-4x))

Finally, simplifying the expression, we obtain:

y2(x) = xe^(-x) (1/4) * (x^2e^(-4x) + (1/2)e^(-4x))

This can be further simplified as:

y2(x) = (1/4) * x^3e^(-5x) + (1/8) * xe^(-5x)

Therefore, the second solution is y2(x) = e^(-2x) (Option C).

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Answer:

4

Step-by-step explanation:

2x2x2x2 = 16

Answer:

2^4 =16

Step-by-step explanation:

Rewriting 16

2^n = 2*2*2*2

2^n = 2^4

2^4 = 16

Thus, choice A is the best one. Vertex is a minimal point at (-3,-2).

An algebraic equation of the second degree in x is a quadratic equation. With a, b, and c being constants and x being the variable, it can be expressed in the conventional form as ax² + bx + c = 0.

The name "quadratic," which refers to the fact that the equation's variable x is squared, is derived from the Latin word "quadratus," which means "square." Or, to put it another way, "the equation of degree 2"." to put it another way.

There are several uses for quadratic equations across many disciplines, including physics, engineering, economics, and more.

A quadratic equation's vertex form is provided by:

y = a(x - h)² + k

where the parabola's vertex is (h, k).

We can see that h = 3 and k = -2 by comparing this to the equation y = 2(x-3)²-2 that is provided.

Hence, the parabola's vertex is (3, -2).

The parabola widens upwards because the value of x² is positive. The vertex is a minimal point as a result.

Thus, choice A is the best one. Vertex is a minimal point at (-3,-2).

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Step-by-step explanation:

For table 1,

x =  20     36    56     80

y =  4        6       8       10

Taking 20/4 = 5

36/6 = 6

56/8 = 7

80/10 = 8

The value of x/y is not same in any of the cases. The constant of proportionality is different. It means x and y for this table is not proportional.

For table 2,

x = 28    42    56    70

y = 20    30    40    50

Taking 28/20 = 1.4

42/30 = 1.4

56/40 = 1.4

70/50 = 1.4

The value of x/y is same in each case. The constant of proportionality is same i.e. 1.4 in each case.

\(\dfrac{x}{y}=1.4\\\\\dfrac{y}{x}=\dfrac{1}{1.4}\\\\\dfrac{y}{x}=\dfrac{5}{7}\\\\y=\dfrac{5}{7}\times x\)

So, y is 5/7 times of the x.