The graph shows the relationship between the distance a truck can travel and the amount of gasoline used.



What is the unit rate for the distance traveled to the amount of gasoline used?

Enter your answer in the box.

{?} mpg

For the table of values gives, the equation of line is obtained as y = 1/3x.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The coordinate points for cups of flour, x and loaves of bread y is given in the table.

The slope-intercept form of an equation is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

(3 - 2)/(9 - 6)

1/3

So, the slope point is obtained as m = 1/3.

The equation becomes - y =1/3 x + b

To find the value of b substitute the values of x and y in the equation -

2 = 1/3(6) + b

2 = 2 + b

b = 2 - 2

b = 0

So, the value for b is 0.

Now, the equation becomes -

y = 1/3x + 0

y = 1/3x

The graph is plotted for the equation.

Therefore, the equation is y = 1/3x.

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To read small font using a magnifying lens with a focal length of 3 in and holding the lens at 1 foot from your eyes, you should place the page approximately 1.09 feet from the magnifying lens.

The thin-lens equation relates the object distance (u), the image distance (v), and the focal length (f) of a lens. The equation is given as:

1/f = 1/v - 1/u

In this case, the focal length (f) of the magnifying lens is 3 in. We want to hold the lens at 1 foot from our eyes, which is 12 inches. Let's assume the distance between the lens and the page is u inches.

We can set up the thin-lens equation as:

1/3 = 1/v - 1/u

Since we want the lens to be 1 foot away from our eyes, the image distance (v) will be 12 inches.

1/3 = 1/12 - 1/u

Simplifying the equation, we get:

1/u = 1/12 - 1/3

    = 1/12 - 4/12

   = -3/12

Taking the reciprocal of both sides, we find:

u = -12/3

  = -4 inches

Since distance cannot be negative, we take the positive value, u = 4 inches.

Therefore, to read small font, you should place the page approximately 1.09 feet (12 + 4 inches) from the magnifying lens

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Answer:

32/52 = 16/26 = 8/13

Step-by-step explanation:

If only Black cards = 26 this includes all black face cards

Face cards = 3 in each suit, 2 red suits so  3 × 2=6

26 + 6 = 32

Answer:

See explanation

Step-by-step explanation:

Mass of  samarium-151  originally present (No) = 5 g

Mass of  samarium-151 discovered (N) = 0.625 grams

time taken = ?

half life of samarium-151 (t1/2) = 96.6 years

From

N/No = (1/2)^t/t1/2

0.625/5 = (1/2)^t/96

0.125 = (1/2)^t/96

1/8 = (1/2)^t/96

(1/2)^3 = (1/2)^t/96

3 = t/96

t = 3 * 96

t = 288 years

The mass of europium-151 when the rock was discovered is obtained from;

Fraction of  samarium-151  left = 1/8

Fraction of  europium-151 formed = 1 - 1/8 = 7/8

Mass of  europium-151 = 7/8 * 5 = 4.375 g

The relationships between the angles x and y are given as follows:

Alternate interior angles. and Alternate exterior angles.

Vertical angles are angles that are on the opposite by the same vertex, and in item 1, the vertex is the intersection of the upper parallel line with the transversal, hence angles x and y are vertical angles.

Alternate Interior angles;

These are the angles that are on the inner side of the two parallel lines but on opposite sides relative to the transversal, therefore, on item 2 x and y are alternative interior angles.

The Corresponding angles are angles that are on the same position relative to the transversal line, but relative to different parallel lines, thus on item x and y are corresponding angles.

Alternate Exterior angles;

There are angles that are on the opposite sides of the transversal line, and one above the upper parallel line and the other below the lower parallel line, shows that angles x and y are alternate exterior angles in item 4.

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The number of tickets sold during the 12 games is 83,100 tickets

The college stadium has 6,925 seats for the baseball games this season.

During the entire 12 baseball games, al the seats were filled up and tickets were sold out.

Therefore the number of tickets sold in the entire 12 games can be calculated by multiplying  6,925 by 12

= 6925 × 12

= 83,100

Hence 83,100 tickets were sold in the entire 12 games

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The inverse Laplace transform of G(s) is \(g(t) = 10e^{-t} - 10e^{-3t}\).

To find the inverse Laplace transform of the given function G(s), we can use partial fraction decomposition and known Laplace transforms. The partial fraction decomposition of G(s) is:

\(G(s) = 10s^2e^{-s} / (s+1)(s+3)\)

To perform the partial fraction decomposition, let's write G(s) in the following form:

G(s) = A/(s+1) + B/(s+3)

To find the values of A and B, we need to find a common denominator for the two fractions on the right-hand side:

\(10s^2e^{-s} = A(s+3) + B(s+1)\)

Expanding the right-hand side:

\(10s^2e^{-s} = As + 3A + Bs + B\)

Now, equating the coefficients of \(s^2\), s, and the constant term:

Coefficient of \(s^2\):

10 = A

Coefficient of s:

0 = A + B

Constant term:

0 = 3A + B

From the first equation, A = 10. Substituting this value in the second and third equations:

0 = 10 + B

0 = 3(10) + B

From the second equation, B = -10. Substituting B = -10 into the third equation:

0 = 3(10) - 10

0 = 30 - 10

0 = 20

Now that we have the values of A and B, we can rewrite G(s) as:

G(s) = 10/(s+1) - 10/(s+3)

To find the inverse Laplace transform of G(s), we can use the known Laplace transform pairs. The inverse Laplace transform of 10/(s+1) is 10e^(-t), and the inverse Laplace transform of \(-10/(s+3) is -10e^{-3t}\). Therefore, the inverse Laplace transform of G(s) is:

\(g(t) = 10e^{-t} - 10e^{-3t}\)

So, the inverse Laplace transform of G(s) is \(g(t) = 10e^{-t} - 10e^{-3t}\).

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Answer:

Object A

Step-by-step explanation:

Usually for these kinds of questions you would look at the steepness of the slope, the steeper it is, the quicker/faster it is.

1. 5a - 8b + 7b + 3a

→ 5a + 3a - 8b + 7b

→ 8a - b ★

2. -5a + 8b - 7b - 3a

→ -5a - 3a + 8b - 7b

→ -8a + b ★

3. 5a + 8b - 7b + 3a

→ 5a + 3a + 8b - 7b

→ 8a + b ★

4. -5a - 8b + 7b - 3a

→ -5a - 3a - 8b + 7b

→ - 8a - b ★

Final answers ;

\( \boxed {\sf { 5a - 8b + 7b + 3a = 8a - b } } \)

\( \boxed {\sf { -5a + 8b - 7b - 3a = -8a + b } } \)

\( \boxed {\sf {5a + 8b - 7b + 3a = 8a + b } } \)

\( \boxed {\sf {-5a - 8b + 7b - 3a = - 8a - b} } \)

5a – 8b + 7b + 3a

5a – 8b + 7b + 3a

= 5a + 3a – 8b + 7b

= 8a – b ( Answer )

________________________________________________

–5a + 8b – 7b – 3a

–5a + 8b – 7b – 3a

= –5a – 3a + 8b – 7b

= –8a + b ( Answer )

________________________________________________

5a + 8b – 7b + 3a

5a + 8b – 7b + 3a

= 5a + 3a + 8b – 7b

= 8a + b ( Answer )

________________________________________________

–5a – 8b + 7b – 3a

–5a – 8b + 7b – 3a

= –5a – 3a – 8b + 7b

= –8a – b ( Answer )

________________________________________________

So, the ratios for the given numbers are:

7/5, 3/1, -13/4, -27/1, and 0/1.

1 2/5 can be expressed as the ratio 1/1 + 2/5 = 7/5

3 can be expressed as the ratio 3/1

-3 1/4 can be expressed as the ratio -13/4

-27 can be expressed as the ratio -27/1

0 can be expressed as the ratio 0/1

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.

For example, if there is 1 boy and 3 girls you could write the ratio as:

So, the ratios for the given numbers are:

7/5, 3/1, -13/4, -27/1, and 0/1.

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Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Hey there!

1/2(8 - 6y) + 1/5(10y - 25)

DISTRIBUTE 1/2 & 1/5 WITHIN the PARENTHESES

= 1/2(8) + 1/2(-6y) + 1/5(10y) + 1/5(-25)

= 4 - 3y + 2y - 5

COMBINE the LIKE TERMS

= (-3y + 2y) + (4 - 5)

= -3y + 2y + 4 - 5

= -1y - 1

≈ -y - 1

Therefore, your answer is: -y - 1

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

By using the method of implicit differentiation, the value of dx/dt is 0 when xy = 5, dy/dt = 1, and x = 3.

Taking the derivative of both sides of the equation xy = 5 with respect to t, we get

d/dt(xy) = d/dt(5)

Using the product rule on the left-hand side, we have:

x(dy/dt) + y(dx/dt) = 0

Substituting the given value of dy/dt = 1 and the given value of xy = 5, we have

3(dx/dt) + y(dx/dt) = 0

Substituting y = 5/x, we get

3(dx/dt) + (5/x)(dx/dt) = 0

Factoring out dx/dt, we have

dx/dt(3 + 5/x) = 0

Solving for dx/dt, we get

dx/dt = 0 when x ≠ -5/3

Substituting the given value of x = 3, we have

dx/dt = 0 when x ≠ -5/3 = 0

Therefore, the value of dx/dt when x = 3 is 0.

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Answer:

8/18 = 44.44%

Answer:

6.2 km x 1000 = 6200 m

Step-by-step explanation:

So, 6.2 kilometers = 6.2 × 1000 = 6200 meters. Conversion of 6.2 kilometers to other length, height & distance units -web

Step-by-step explanation:

let eqn be y = mx + b.

m = (-2 - 8)/(1 - 3) = 5

sub (3, 8):

8 = 5(3) + b

b = -7

therefore equation of the line is y = 5x - 7

Topic: coordinate geometry

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:y = 5x - 7

Step-by-step explanation: /

To find the joint density function, we need to calculate the Jacobian determinant of the transformation from (x, y) to (u, v)

The joint distribution of (u, v), where u and v are defined as

\(u = \frac{x}{{\sqrt{x^2 + y^2}}}\)  and \(v = \frac{y}{{\sqrt{x^2 + y^2}}}\), is given by:

\(f_{U,V}(u,v) = \frac{1}{{2\pi}} \cdot e^{-\frac{1}{2}(u^2 + v^2)}\)

To find the joint density function, we need to calculate the Jacobian determinant of the transformation from (x, y) to (u, v):

\(J = \frac{{du}}{{dx}} \frac{{du}}{{dy}}\)

\(\frac{{dv}}{{dx}} \frac{{dv}}{{dy}}\)

Substituting u and v in terms of x and y, we can evaluate the partial derivatives:

\(\frac{{du}}{{dx}} &= \frac{{y}}{{(x^2 + y^2)^{3/2}}} \\\frac{{du}}{{dy}} &= -\frac{{x}}{{(x^2 + y^2)^{3/2}}} \\\frac{{dv}}{{dx}} &= -\frac{{x}}{{(x^2 + y^2)^{3/2}}} \\\frac{{dv}}{{dy}} &= \frac{{y}}{{(x^2 + y^2)^{3/2}}}\)

Therefore, the Jacobian determinant is:

\(J &= \frac{y}{{(x^2 + y^2)^{\frac{3}{2}}}} - \frac{x}{{(x^2 + y^2)^{\frac{3}{2}}}} \\&= -\frac{x}{{(x^2 + y^2)^{\frac{3}{2}}}} + \frac{y}{{(x^2 + y^2)^{\frac{3}{2}}}} \\J &= \frac{1}{{(x^2 + y^2)^{\frac{1}{2}}}}\)

Now, we can find the joint density function of (u, v) as follows:

\(f_{U,V}(u,v) &= f_{X,Y}(x,y) \cdot \left|\frac{{dx,dy}}{{du,dv}}\right| \\&= f_{X,Y}(x,y) / J \\&= f_{X,Y}(x,y) \cdot (x^2 + y^2)^{\frac{1}{2}}\)

Substituting the standard normal density function

\(f_{X,Y}(x,y) &= \frac{1}{2\pi} \cdot e^{-\frac{1}{2}(x^2 + y^2)} \\f_{U,V}(u,v) &= \frac{1}{2\pi} \cdot e^{-\frac{1}{2}(x^2 + y^2)} \cdot (x^2 + y^2)^{\frac{1}{2}} \\&= \frac{1}{2\pi} \cdot e^{-\frac{1}{2}(u^2 + v^2)}\)

Therefore, the joint distribution of (u, v) is given by:

\(f_{U,V}(u,v) &= \frac{1}{2\pi} \cdot \exp\left(-\frac{1}{2}(u^2 + v^2)\right)\)

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To find the joint density function, we need to calculate the Jacobian determinant of the transformation from (x, y) to (u, v)

The joint distribution of (u, v) is a bivariate normal distribution with mean (0,0) and variance-covariance matrix

\(\begin{bmatrix}2 & 0 \0 & 2\end{bmatrix}\)

The joint distribution of (u, v) can be found by transforming the independent random variables x and y using the following formulas:

\( u = x + y\)
\( v = x - y \)

To find the joint distribution of (u, v), we need to find the joint probability density function (pdf) of u and v.

Let's start by finding the Jacobian determinant of the transformation:

\(J = \frac{{\partial (x, y)}}{{\partial (u, v)}}\)

\(= \frac{{\partial x}}{{\partial u}} \cdot \frac{{\partial y}}{{\partial v}} - \frac{{\partial x}}{{\partial v}} \cdot \frac{{\partial y}}{{\partial u}}\)

\(= \left(\frac{1}{2}\right) \cdot \left(-\frac{1}{2}\right) - \left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right)\)

\(J = -\frac{1}{2}\)

Next, we need to express x and y in terms of u and v:

\(x = \frac{u + v}{2}\)

\(y = \frac{u - v}{2}\)

Now, we can find the joint pdf of u and v by substituting the expressions for x and y into the joint pdf of x and y:

\(f(u, v) = f(x, y) \cdot |J|\)

\(f(u, v) = \left(\frac{1}{\sqrt{2\pi}}\right) \cdot \exp\left(-\frac{x^2}{2}\right) \cdot \left(\frac{1}{\sqrt{2\pi}}\right) \cdot \exp\left(-\frac{y^2}{2}\right) \cdot \left|-\frac{1}{2}\right|\)

\(f(u, v) = \frac{1}{2\pi} \cdot \exp\left(-\frac{u^2 + v^2}{8}\right)\)

Therefore, the joint distribution of (u, v) is given by:

\(f(u, v) = \frac{1}{2\pi} \cdot \exp\left(-\frac{{u^2 + v^2}}{8}\right)\)

In summary, the joint distribution of (u, v) is a bivariate normal distribution with mean (0,0) and variance-covariance matrix

\(\begin{bmatrix}2 & 0 \0 & 2\end{bmatrix}\)

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The Answer is (x+9)^2

Answer:

-81/20

Step-by-step explanation:

Answer:

11 minutes. 1/4 of 44 is 11

Answer:

5 if you round it, or exact answer is 4.63 hours

Answer:

5 hours ( approxemitly)

Step-by-step explanation:

divide 650 (the miles) by 3 (the hours) to see how much miles it travels per hour....

after that make a T-chart where you see how much hours it takes to reach 1000 miles...

like this :

1 hour = 216.6 miles

2 hours = 432 miles

3 hours = 650 miles

And so on...

if you look the exact number per hour is 216.666667

but im asuming your techer would want the approximate answer so i just rounded it for you.

Tho the most exact answer is 4.62 hours.

The process of Visualizing Modernist Poetry involves analyzing the poem for themes and motifs, choosing a visual medium, creating a visual representation that incorporates those motifs etc..

Visualizing modernist poetry can be a creative and subjective process, but here is an example of one approach you could take:

Read and analyze the poem: Before you start visualizing, it's important to understand the themes and imagery of the poem.

Identify key images and motifs: As you read through the poem, take note of recurring images and motifs.

Choose a visual medium: Depending on your preferences and skills, you could use a variety of mediums to create a visualization of the poem.

Create a visual representation: Using your chosen medium, create a visual representation of the poem that incorporates the key images and motifs you identified.

Reflect on your visualization: Once you've created your visualization, take some time to reflect on what you've created and what it reveals about the poem.

Share your work: Finally, if you feel comfortable, share your visualization with others and get feedback.

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The margin of error with 99% confidence is 62.15 (rounded to 2 decimal places).

a. To calculate the margin of error with 99% confidence, we first need to find the sample mean and the sample standard deviation.

The sample mean is: 162.5

where z* is the z-score for 99% confidence level and n is the sample size.

From the z-score table, we find that the z-score for 99% confidence level is 2.576.

Thus, the margin of error is:

ME = 62.15

Therefore, the margin of error with 99% confidence is 62.15 (rounded to 2 decimal places).

b. To construct the 99% confidence interval for the average number of customers served on weekdays,

CI is the confidence interval, x is the sample mean, z is the z-score for 99% confidence level, s is the sample standard deviation, and n is the sample size.

Substituting the values, we get:

CI = = (89.29, 235.71)

Therefore, the 99% confidence interval for the average number of customers served on weekdays is (89.29, 235.71).

The margin of error reported in part a can be reduced by either increasing the sample size or reducing the variability in the data.

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Answer:

The sale this month = 79

Step-by-step explanation:

Let the amount he needs to sell this month = x

\(Average = \frac{sum\ of\ individual\ data\ }{number\ of\ entries}\)

\(Average= \frac{90\ +\ 45\ +\ 103\ +\ 68\ +\ x}{5}\)

Note that number of entries = number of months = 5

To maintain an average sales of 77, the amount of sale in month 5 is determined as follows:

\(77 = \frac{306\ +\ x}{5} \\cross-multiplying\\77\ \times\ 5\ = 306\ +\ x\\385 = 306\ +\ x\\x =385\ -\ 306\\x = 79\)

Answer:

16/4 = 4

1 block = 4 minutes

4 blocks = 16 minutes

to put this into a ratio it would be 1:4

The value of m is 1/3.

To solve the equation 9²m⁻¹ × 9⁵ = 9m², we can simplify the equation and solve for the value of m.

Let's simplify the equation step by step:

9²m⁻¹ × 9⁵ = 9m²

Expanding the exponents:

(9²)(9⁵)(m⁻¹) = 9m²

Simplifying the exponents:

9^(2+5)(m⁻¹) = 9m²

Using the property\(a^{(m+n)\)= \(a^m \times a^n\):

9^7(m⁻¹) = 9m²

Applying the power of 9⁷:

9m⁻¹ = 9m²

Dividing both sides by 9m⁻¹:

1 = 9m²/m⁻¹

Dividing with the same base and different exponents, we subtract the exponents:

1 = \(9m^{(2-(-1))\)

Simplifying the exponents:

1 = 9m³

Now, we can solve for m by isolating it on one side of the equation:

m³ = 1/9

Taking the cube root of both sides:

m = ∛(1/9)

The cube root of 1/9 is the same as raising 1/9 to the power of 1/3:

m = \((1/9)^{(1/3)\)

Simplifying the cube root:

m = 1/3

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value of given expression = 48

The order of operations is a rule that specifies the correct steps for evaluating mathematical expressions. We can remember the order with PEMDAS -

Parentheses, exponents, multiplication and division (left to right), addition and subtraction (left to right).  

Given expression,

9 - 4 ÷ (2 + 2) + 2³ . 5

By PEMDAS rule

First solving parentheses

= 9 - 4 ÷ 4 + 2³ . 5

then solving exponent

= 9 - 4 ÷ 4 + 8 . 5

Now solving multiplication

= 9 - 4 ÷ 4 + 40

Now solving division

= 9 - 1 + 40

Now solving addition

= 49 - 1

Now solving subtraction

= 48

Hence, 48 is the value of the expression.

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The first and third linear systems are possible and the second and the fourth have no solution.

(a) A linear system of 3 equations and 3 unknowns can have infinitely many solutions if the equations are linearly dependent or if the system represents a plane intersecting a line or three planes intersecting at a single point. An example of an augmented row-reduced echelon matrix that satisfies this description could be:

[ 1  0  0 |  3 ]

[ 0  1  0 | -2 ]

[ 0  0  0 |  0 ]

(b) A linear system of 3 equations and 4 unknowns cannot have exactly one solution. This is because there are more unknowns than equations, which leads to an underdetermined system. Therefore, there will be infinitely many solutions or no solutions at all.

(c) A linear system of 3 equations and 2 unknowns can have exactly one solution if the equations represent three lines that intersect at a single point. An example of an augmented row-reduced echelon matrix that satisfies this description could be:

[ 1  0 |  2 ]

[ 0  1 | -3 ]

[ 0  0 |  0 ]

(d) A linear system of 3 equations and 2 unknowns cannot have a unique solution. This is because there are more equations than unknowns, resulting in an overdetermined system. Therefore, there will be either infinitely many solutions or no solutions at all.

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a) The probability that the next student will ask a question within the next 3 minutes  \($P(X \leq 3) = 1 - e^{-3/8}$\)

b) \($P(X \leq 6) = 1 - e^{-6/8}$\)

c) \($P(4 \leq X \leq 8) = (1 - e^{-8/8}) - (1 - e^{-4/8})$\)

d) \($P(X > 18) = 1 - P(X \leq 18) = 1 - (1 - e^{-18/8})$\)

The time between students walking up to the instructor's desk during an exam follows the exponential probability distribution with a mean of 8 minutes.

a) To find the probability that the next student will ask a question within the next 3 minutes, we can use the cumulative distribution function (CDF) of the exponential distribution. The CDF gives the probability that the time is less than or equal to a given value. In this case, we want to find P(X ≤ 3), where X is the time between students asking questions.

Using the exponential CDF formula, we have P(X ≤ 3) = 1 - e^(-3/8).

b) Similarly, to find the probability that the next student will ask a question within the next 6 minutes, we calculate P(X ≤ 6) = 1 - e^(-6/8).

c) To find the probability that the next student will ask a question between 4 and 8 minutes, we subtract the probability of it happening within 4 minutes from the probability of it happening within 8 minutes. Therefore, P(4 ≤ X ≤ 8) = P(X ≤ 8) - P(X ≤ 4) = (1 - e^(-8/8)) - (1 - e^(-4/8)).

d) To find the probability that the next student will ask a question in more than 18 minutes, we use the complement of the CDF. P(X > 18) = 1 - P(X ≤ 18) = 1 - (1 - e^(-18/8)).

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