how many miles can you drive, if your car gets 25.00 miles per gallon and you have 12.00 gallons of gas?

A graph of the relationship modeled by the equation is shown in the image attached below.

If the graph continues, the point (28, 24) will not be on the graph.

The height of a picture when the total height of the picture with the frame is 38.5 cm would be 34.5 cm.

In this scenario, the total height of a picture in its frame (in centimeters) would be plotted on the y-axis of the graph while the height of the picture (in centimeters) would be plotted on the x-axis of the graph.

Based on the ordered pair (28, 24), we would determine if it lies on the graph of the equation:

y = x + 4

24 = 28 + 4

24 = 32 (False).

When the total height of the picture with the frame is 38.5 cm, the height of a picture can be calculated as follows;

y = x + 4

38.5 = x + 4

x = 38.5 - 4

x = 34.5 cm.

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Complete Question:

The equation y = x + 4 models the total height of a picture in its frame, y, in centimeters with respect to the height of the picture, x, in centimeters.

a. Graph the relationship modeled by the equation. Be sure to label the axes.

b. If the graph continues, will the point (28, 24) be on the graph?

c. Determine the height of a picture when the total height of the picture with the frame is 38.5 cm.

the rule for division is:

Then:

you will substract the exponents

The physical characteristics of a landscape and can be used in various applications such as habitat modeling and land-use planning.

A metric that measures terrain ruggedness as the variation in three-dimensional orientation of grid cells within a neighborhood is called Terrain Ruggedness Index (TRI). This index is used to quantify the variation in elevation in a specific area. It measures the difference between the elevation of a central grid cell and the average elevation of the surrounding grid cells. The greater the difference, the higher the ruggedness of the terrain. The TRI is a useful measure for understanding the physical characteristics of a landscape and can be used in various applications such as habitat modeling and land-use planning.

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Answer:

y = -2

Step-by-step explanation:

The horizontal line through this point has a slop of 0

Answer:

Option C

Step-by-step explanation:

Area of a triangle given with measures of 2 sides and angle between these sides will be,

Area of a triangle = \(\frac{1}{2}\text{(a.b)sinC}\)

Here, a and b are two sides of the triangle and C is the angle between these sides.

From the figure attached,

a = 6, b = 9 and m∠C = 110°

Substitute these values in the formula,

Area of ΔQRS = \(\frac{1}{2}\text{(a.b)sinC}\)

                        = \(\frac{1}{2}{(9\times 6)\text{sin}(110^{\circ})}\)

                        = 25.37

                        ≈ 25.4 square units

Therefore, Option C will be the answer.

Answer:

I believe it is 67 degrees

Step-by-step explanation:

Since all the angles in a triangle add up to 180 degrees, you can subtract 78 and 35 from 180 to get 67.

The equation (log(x) - 1) * log(x) = 0 can be solved by considering two cases: when the expression (log(x) - 1) equals zero, or when the expression log(x) equals zero. The solutions for x are x = 1 and x = 10.

To solve the equation (log(x) - 1) * log(x) = 0, we need to consider two cases.
Case 1: (log(x) - 1) = 0
Solving this equation, we find that log(x) = 1. By exponentiating both sides with base 10, we get x = 10.
Case 2: log(x) = 0
For log(x) to equal zero, the base of the logarithm must be raised to the power of zero, resulting in x = 1.
Therefore, the solutions to the equation are x = 1 and x = 10.

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For the proportional relationship, we have found that:

a)  The complete table is:

x        y

14      21

64      96

26      39

1         3/2

b) The equation is:

y = (3/2)*x

A proportional relationship between two variables can be written as:

y = k*x

Where k is the constant of proportionality.

a) If we look at the table we can see the pair (14, 21), replacing that in the proportional relation we have:

21 = k*14

(21/14) = k

(3/2) = k

Then the equation is:

y = (3/2)*x

To complete the table, we need to evaluate the other values in the given equation.

for x = 64 we have:

y = (3/2)*64 = 96

for y = 39 we have:

39 = (3/2)*x

x = (2/3)*39 = 26

For x = 1 we have:

y = (3/2)*1 = 3/2

Then the complete table is:

x        y

14      21

64      96

26      39

1         3/2

b) We already found the equation, it is:

y = (3/2)*x

c) Just graph the above pairs (the ones from the table) and connect them with a line, an example can be seen below.

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The distance between the fountain and the playground is approximately 10.8 yards.

To find the distance between the fountain and the playground, we can use the Pythagorean theorem.

Given:

Coordinates of the center of the park: (0, 0)

Fountain is 4 yards north of the center: (0, 4)

Playground is 10 yards east of the center: (10, 0)

Let's consider the distance between the fountain and the playground as the hypotenuse of a right triangle formed by the fountain, playground, and the center of the park.

Using the Pythagorean theorem, the distance between the fountain and the playground (hypotenuse) can be calculated as follows:

Distance^2 = (Difference in x-coordinates)^2 + (Difference in y-coordinates)^2

Difference in x-coordinates = 10 - 0 = 10 yards

Difference in y-coordinates = 4 - 0 = 4 yards

Distance^2 = (10)^2 + (4)^2

Distance^2 = 100 + 16

Distance^2 = 116

Taking the square root of both sides to find the distance:

Distance = sqrt(116)

Distance ≈ 10.8 yards (rounded to the nearest tenth)

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Answer: the answer is axis of 3

Step-by-step explanation:

Answer:

I think it's (4,4) but I could be wrong

Step-by-step explanation:

The function f(x) = \(10 - 6x - 2x^2\)is strictly decreasing for x < -3/2, has a local minimum at x = -3/2, and is strictly increasing for x > -3/2.

To determine whether the function \(f(x) = 10 - 6x - 2x^2\) is strictly increasing or decreasing, we need to find the first derivative of the function and determine its sign.

\(f(x) = 10 - 6x - 2x^2\)

f'(x) = -6 - 4x

To determine the sign of f'(x), we can set it equal to zero and find its critical points:

f'(x) = -6 - 4x = 0

x = -3/2

When x < -3/2, f'(x) is positive, which means that f(x) is decreasing. When x > -3/2, f'(x) is negative, which means that f(x) is increasing.

At x = -3/2, f'(x) changes sign from negative to positive, which means that f(x) has a local minimum at x = -3/2.

Therefore, the function \(f(x) = 10 - 6x - 2x^2\)is strictly decreasing for x < -3/2, has a local minimum at x = -3/2, and is strictly increasing for x > -3/2.

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Answer:

7 2 + 3 3

Step-by-step explanation:

Answer:

go there

Step-by-step explanation:

yw :)

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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1. The probability that she pulled out a red marble first and a yellow marble second is 0.13 (2nd option)

2. The probability that a black pen is chosen first and then another black pen is chosen is 0.21 (3rd option)

First, we shall obtain the total marbles in the bag. Details below:

Total = 4 + 4 + 12

Total marble = 20

Next, we shall obtain the probability of pulling red marble first. Details below:

P(R) = 4/20

P(R) = 0.2

Next, we shall obtain the probability of pulling yellow marble in the 2nd pull. Details below:

P(Y) = 12/19

P(R) = 0.63

Finally, we shall obtain the probability of pulling red followed by yellow marble. Details below:

P(RY) = P(R) × P(Y)

P(RY) = 0.2 × 0.63

Probability of red followed by yellow = 0.13 (2nd option)

First, we shall obtain the total pen in the bag. Details below:

Total = 1 + 4 + 3

Total pen = 8

Next, we shall obtain the probability of chosen black pen first. Details below:

P(1st B) = 4/8

Next, we shall obtain the probability of chosen another black pen. Details below:

P(2nd B) = 3/7

Finally, we shall obtain the probability of pulling red followed by yellow marble. Details below:

P(1st B and 2nd B) = P(1st B) × P(2nd B)

P(1st B and 2nd B) = 4/8 × 3/7

Probability of black and black pen = 0.21 (3rd option)

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Answer:

Because of cars, and factories making it everyday.

Step-by-step explanation:

The equation has a value less than 2,175 is- one half x 2,175

0.5 x 2,175 = 1087.5

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

The equation has a value less than 2175, let us simplify each option:

A) 1 x 2175 = 2175

B) 2 x 2175 = 4350

C) 2/2 x 2175 = 1 x 2175 = 2175

D) 1/2 x 2175 = 1087.5

From the simplified forms, we see that the equation that has a value less than 2175 is:

The correct answer is Option D

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When using a one-way within-groups ANOVA, the variability due to individual differences is reduced, resulting in a more accurate assessment of the effect of the independent variable on the dependent variable.

To minimize the variation between individuals, their scores are evaluated within the same group rather than comparing them across different groups.

The within-groups ANOVA method utilizes identical individuals in different conditions or treatments to counteract personal variances, thereby enabling a more accurate measurement of the independent variable's impact.

By adopting this method, the analysis gains greater statistical strength, resulting in a more heightened aptitude to identify genuine effects of the independent factor on the dependent element.

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Answer: f(x) = 3

Step-by-step explanation: because if you substitute 2(1) = 2 and 2+1 equals 3.

Answer:

x = 22 y = 113

Step-by-step explanation:

3x-15 = 2x+7

-2x         -2x

x-15 = 7

+15     +15

x = 22

180-51 = 129

y+16 = 129

-16       -16

y = 113

Answer:

x = 22

y = 113

Step-by-step explanation:

The angles marked as (2x+7) and (3x-15) are vertical angles, and therefore are equal to each other.

2x + 7 = 3x - 15 simplifying:

7 = x - 15

22 = x

Angles marked as (3x-15) and (y+16) form a linear pair and are therefore supplimetery. Now that we know the value of x, we can set up the following equation.

3(22) - 15 + y + 16 = 180 simplifying:

66 - 15 + y + 16 = 180

66 + y + 16 = 195

y = 113

option C is the correct answer. sin β = 15 / 17

Given data

Right angled triangle has sides

opposite = 15

adjacent = 8

Hypotenuse = 17

sin β = opposite / hypotenuse

substituting the values gives

sin β = 15 / 17

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Answer:

The answer is D

Step-by-step explanation:

because u need to divide the y and x and when u do it to all of them u will get the same ratio which is 4

To show that X + Y and X - Y are independent if ox = oy, we need to demonstrate that the joint probability density function (pdf) of X + Y and X - Y is bivariate normal with a correlation coefficient of zero.

Let's start by defining the random variables Z1 = X + Y and Z2 = X - Y. We want to find the joint pdf of Z1 and Z2, denoted as f(z1, z2).

To do this, we can use the transformation method. First, we need to find the transformation equations that relate (X, Y) to (Z1, Z2):

Z1 = X + Y

Z2 = X - Y

Solving these equations for X and Y, we have:

X = (Z1 + Z2) / 2

Y = (Z1 - Z2) / 2

Next, we can compute the Jacobian determinant of this transformation:

J = |dx/dz1  dx/dz2|

   |dy/dz1  dy/dz2|

Using the given transformation equations, we find:

dx/dz1 = 1/2   dx/dz2 = 1/2

dy/dz1 = 1/2   dy/dz2 = -1/2

Therefore, the Jacobian determinant is:

J = (1/2)(-1/2) - (1/2)(1/2) = -1/4

Now, we can express the joint pdf of Z1 and Z2 in terms of the joint pdf of X and Y:

f(z1, z2) = f(x, y) * |J|

Since X and Y are bivariate normal with a given joint pdf, we can substitute their joint pdf into the equation:

f(z1, z2) = f(x, y) * |J| = f(x, y) * (-1/4)

Since f(x, y) represents the joint pdf of a bivariate normal distribution, we know that it can be written as:

f(x, y) = (1 / (2πσxσy√(1-ρ^2))) * exp(-(1 / (2(1-ρ^2))) * ((x-μx)^2/σx^2 - 2ρ(x-μx)(y-μy)/(σxσy) + (y-μy)^2/σy^2))

where μx, μy, σx, σy, and ρ represent the means, standard deviations, and correlation coefficient of X and Y.

Substituting this expression into the equation for f(z1, z2), we get:

f(z1, z2) = (1 / (2πσxσy√(1-ρ^2))) * exp(-(1 / (2(1-ρ^2))) * (((z1+z2)/2-μx)^2/σx^2 - 2ρ((z1+z2)/2-μx)((z1-z2)/2-μy)/(σxσy) + ((z1-z2)/2-μy)^2/σy^2)) * (-1/4)

Simplifying this expression, we find:

f(z1, z2) = (1 / (4πσxσy√(1-ρ^2))) * exp(-(1 / (4(1-ρ^2))) * (((z1+z2)/2-μx)^2/σx^2 - 2ρ((z1+z2)/2-μx)((z1-z2)/2-μy

)/(σxσy) + ((z1-z2)/2-μy)^2/σy^2))

Notice that the expression for f(z1, z2) is in the form of a bivariate normal distribution with correlation coefficient ρ' = 0. Therefore, we have shown that the joint pdf of X + Y and X - Y is bivariate normal with a correlation coefficient of zero.

Since the joint pdf of X + Y and X - Y is bivariate normal with a correlation coefficient of zero, it implies that X + Y and X - Y are independent of one another.

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The total arc length AB that the pendulum travels is approximately 13.96 inches.

To find the total arc length traveled by the pendulum, we can use the formula for the arc length of a pendulum given by:

Arc length (s) = θ × r

where θ is the angle in radians and r is the length of the pendulum.

However, in this case, we are given the angle in degrees, so we need to convert it to radians. The formula for converting degrees to radians is:

θ (in radians) = (π/180) × θ (in degrees)

Given that the angle is 80°, we can convert it to radians as follows:

θ (in radians) = (π/180) × 80° = (4π/9) radians

Now, we can calculate the arc length:

Arc length (s) = (4π/9) radians × 10 inches

The total arc length traveled by the pendulum is therefore:

Arc length (s) = (40π/9) inches

To approximate the answer, we can use the value of π as approximately 3.14:

Arc length (s) ≈ (40 × 3.14/9) inches

Arc length (s) ≈ 13.96 inches

Therefore, the total arc length AB that the pendulum travels is approximately 13.96 inches.

Please note that this calculation assumes that the pendulum swings in a perfect arc without any friction or external factors affecting its motion. In reality, there may be slight variations due to factors such as air resistance or imperfections in the pendulum's motion.

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