3. Dimitri's car has a fuel efficiency of 21 miles per gallon. His tank is full with 12 gallons of gas. Does he have
enough gas to drive from Cincinnati to Toledo, a distance of 202.4 miles?
Show your calculations, including at least one use of dimensional analysis. You choose how to round.

Using linear function, the slope of -1 means that when one of the ratio of dimension is increased by 1, the other is decreased by 1.

A linear function is modeled by:

y = mx + b

Here, m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

Also shown as b is the y-intercept, which is the value of y when x = 0.

Given that the lengths and the widths are interchangeable, that is, either can be considered as the input or as the output.

The slope of -1 means that when the input in increased by 1, the output is decreased by -1, that is;

=  length/width

This is increased by 1, and the other is decreased by 1.

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The domain of the function is -6 ≤ x ≤ 6.

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.

A function is defined as the relationship between input and output, Where each input has exactly one output. The inputs are the elements in the domain. The co-domain of the function is the set of output values.

From the graph given the possible input values of x lies from -6 to 6.

Hence, the domain of the function is -6 ≤ x ≤ 6.

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Answer:

L = 4.5

Step-by-step explanation:

You can rewrite the equation as 2L^2 + L - 45 = 0 and then solve using the quadratic formula

L = (-1 plus or minus the sq root of 361) / 4

L = (-1 plus or minus 19) / 4

L = -5 or 4.5 but lengths can't be negative so the length is 4.5

The ideal pie charts should always show both the sum of all the pie elements along with the data that constitute the pie slices. Thus the statement in the question is true.

The circle diagram, often known as a pie chart, pie chart, or pie chart, is used to depict qualitative or discrete information. It is used to display the percentage of each variable's values' constituent parts.

To do this, divide the circle into sections proportionate to the relative frequency. Recognize the area of the circle that corresponds to each possible value of the variable as a component. It is characterized as an "exploded cake graph" because it divides the graph into its many components in order to shift one of the portions.

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Answer:

Step-by-step explanation:

The inequality |3x| >= 0 simply states that the absolute value of 3x must be greater than or equal to zero.

Since the absolute value of any number must always be non-negative, this inequality is always true. That means any real number x satisfies the inequality |3x| >= 0.

Therefore, the solution to the inequality |3x| >= 0 is x ∈ R, where R represents the set of all real numbers.

Answer:

B) Annually

Step-by-step explanation:

If interest is compounded once every 12 months, it is compounded annually.

Answer:

B) Annually

Step-by-step explanation:

Compounded means to calculate interest on the borrowed amount and on previous interest.

Monthly means to be done one every month.

Annually means to be done yearly or every year.

Let's break this down. Semi means half or a partial of something. Annually, as we already discussed, means yearly or every year. Now, when we put it together, it creates half a year. So, semiannually means half a year.

We know a quarter, as in, the coin, is 25 cent. if we multiply 25 cents by four, we get a dollar. So a quarter coin is one fourth, or, a quarter of a dollar. Now, applying that to years, since a year is twelve months and a quarter is one fourth, we can divide twelve by four to get three. Three months is one quarter of a year.

With this in mind, twelve months is equal to a year. So, the interest is compounded every year.

A is incorrect because it says monthly. We have already figured out that the interest is compounded yearly, so it is incorrect.

B is correct because the definition of Annually is yearly or every twelve months.

C is incorrect because semiannually means half or part of a year, not a full year.

D is incorrect because quarterly means one fourth of a year, or, three months.

The coordinates of all the points generated from (x, y, z) by repeatedly applying the operations in the order given are: (a) (x, -y, z); (b) (x, y, -z); (c) (-x, y, -z); (d) (-x, z, y); and (e) (x, -z, -y).

For (a), a mirror perpendicular to the y-axis and passing through the origin reflects the coordinates in the y-axis, so the new coordinates will be (x, -y, z).

For (b), a four-fold rotation whose axis is coincident with the x-axis and passing through the origin rotates the coordinates around the x-axis by 90 degrees, so the new coordinates will be (x, y, -z).

For (c), a 4 roto inversion whose axis is coincident with the x-axis and passing through the origin inverts the coordinates in the x-axis, so the new coordinates will be (-x, y, -z).

For (d), a three-fold rotation whose axis passes through the origin and the point (1,1,1) rotates the coordinates around the axis by 120 degrees, so the new coordinates will be (-y, -z, x).

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If A is a matrix of order m × n, then

Rank of A + Nullity of A = Number of columns in A = n

Now, According to the question:

The rank-nullity theorem states that the dimension of the domain of a linear function is equal to the sum of the dimensions of its range (i.e., the set of values in the codomain that the function actually takes) and kernel (i.e., the set of values in the domain that are mapped to the zero vector in the codomain).

The range null-space decomposition is the representation of a vector space as the direct sum of the range and the null space of a certain power of a given matrix.

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The given question is incomplete,

So, The question is:

What is rank nullity theorem and range and null space ?

When the level of confidence decreases, the margin of error c. Becomes larger

The margin of error is a gauge of how uncertain a sample-based estimate is. It is impacted by the sample size and level of confidence and shows the potential difference between the estimate and the true population value. The user selects a level of confidence, which is commonly given as a percentage, when we want to generate a confidence interval for a population parameter, such as a mean or proportion. By selecting a degree of confidence of 95%, for instance, we are expressing our confidence that the true population parameter falls inside the interval.

Based on the level of confidence, and sample size the margin of error is determined. In order to account for greater uncertainty, a higher level of confidence necessitates a bigger margin of error, whereas a lower level of confidence necessitates a smaller margin of error. As a result, the margin of error rises as the level of confidence declines, indicating a wider range of values within which the true population parameter is expected to fall.

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The number of cups of milk that Minka pours as a mixed number is found in the attached image.

The total number of cups of milk that Minka pours into her oatmeal is calculated as follows:

First day = 1/4

Second day = 1/4 + 1/4

Second day = 2/4

Third day = 1/4 + 2/4

Third day = 3/4

Fourth day = 1/4 + 3/4

Fourth day = 4/4 or 1

Fifth day =  5/4 or 1/4 + 1

Fifth day = 1 1/4

Sixth day = 1/4 + 5/4

Sixth day = 1 1/2

Seventh day = 1/4 + 6/4

Seventh day = 7/4 or 1 3/4

Eight day = 1/4 + 7/4

Eight day = 8/4 or 2

The completed number line is found in the attached image

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The required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

An arrangement of numbers in which the numbers are arranged from smallest to greatest numbers is called ascending order.

Given that, some numbers, 3√2, √3 − 1, √19 + 1, 6, 2√10 ÷ 5 and √14.

We need to order them from least to greatest,

3√2 = 4.24

√3 − 1 = 0.73

√19 + 1 = 5.35

6

2√10 ÷ 5 = 1.26

√14 = 3.74

The order from least to greatest is :-

0.73, 1.26, 3.74, 4.24, 5.35 and 6

i.e.

√3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

Hence, the required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

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The weight of the beagle D. Erin has weighs 35 pounds.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information, Let the weight of the beagle is 'x'.

So, the weight of a Great Dane is (2x + 2) pounds.

Therefore, 2x + 2 = 72.

2x = 70.

x = 35 pounds.

So,  The beagle weighs 35 pounds.

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The required point of the beginning is given as Point A. Option B is correct.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

When you move 5 units north, you increase the y-coordinate by 5. When you move 3 units west, you decrease the x-coordinate by 3. So, if you start at an unknown point and move 5 units north and 3 units west, your final position would be at a point with the coordinates (x - 3, y + 5).

Since you ended at point D, and the final coordinates are not given, we cannot determine the starting point without more information.

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Answer:

Step-by-step explanation:

23x

The probability of the different discrete random variable X are;

a) P(x = 3) = 0.12

b) (P x ≤ 2) =  0.239

c)  P(x ≥ 1) =  0.947

d) P(1 ≤ x ≤ 4) = 0.493

a) The probability expressed as P(x = 3) from the table is;

P(x = 3) = 0.12

b) The probability expressed as (P x ≤ 2) is;

(P x ≤ 2) = P(x = 2) + P(x = 1) + P(x = 0)

= 0.093 + 0.093 + 0.053

= 0.239

c) The probability expressed as P(x ≥ 1) is;

P(x ≥ 1) = P(x = 6) + P(x = 5) + P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1)

P(x ≥ 1) = 0.267 + 0.187 + 0.187 + 0.12 + 0.093 + 0.093

P(x ≥ 1) =  0.947

d) The probability expressed as P(1 ≤ x ≤ 4) is;

P(1 ≤ x ≤ 4) = P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1)

= 0.187 + 0.12 + 0.093 + 0.093

= 0.493

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2. Scale factor of a dilation that maps Circle A onto a circle congruent to Circle B is: 4/3 . 3. Scale factor of a dilation that maps Circle C onto a circle congruent to Circle A is 1/2.

By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made. Transformational geometry, a fresh viewpoint on geometry, was first forth by Felix Klein in the 19th century.

The majority of geometric proofs rely on how objects change. Using transformations, we can change any image in a coordinate plane. By using transformational logic, it is possible to comprehend video game graphics more fully.

From the given figure we see that:

Diameter of A = 8

Diameter of B = 6

Diameter of C= 4

2. Scale factor of a dilation that maps Circle A onto a circle congruent to Circle B is:

8/6 = 4/3

3. Scale factor of a dilation that maps Circle C onto a circle congruent to Circle A is:

4/8 = 1/2

4. When a figure is dilated the new figure is similar to the pre-image. The segments, sides, edges, of the new image is dilated by scale factor.

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The equation from the graph of the function is g(x) = |x - 1|

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the function

The function is an absolute value function

The parent function of an absolute value function is:

y = |x|

The function y = |x| is shifted right by 1 units

Using the above as a guide, we have the following:

g(x) = f(x - 1)

This represents a translation to the right by 1 unit

So, we have

g(x) = |x - 1|

Hence, the translation is g(x) = |x - 1|

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Applying the knowledge of sets, the number of people that have been to Australia but not Europe is calculated as: 2.

Let's call the number of people who have been to Europe "E" and the number of people who have been to Australia "A". We know that:

E = 11

A = 7

We also know that 5 people have been to both Europe and Australia, so they are counted in both E and A:

E = 11

A = 7

E ∩ A = 5

To find the number of people who have been to Australia but not Europe, we can use the formula:

A - (E ∩ A) = A - 5 = 7 - 5 = 2

Therefore, the 2 people have been to Australia but not Europe.

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The correlation coefficient for this set of five students is approximately 0.95.

First we can use the formula:

r = [nΣ(xy) - ΣxΣy] / [√{nΣx^2 - (Σx)^2} √{nΣy^2 - (Σy)^2}]

Where

Using the values given in the table, we can calculate the necessary sums and products:

n = 5

Σx = 173 + 172 + 175 + 176 + 177 = 873

Σy = 62 + 65 + 64 + 66 + 65 = 322

Σx^2 = 173^2 + 172^2 + 175^2 + 176^2 + 177^2 = 150367

Σy^2 = 62^2 + 65^2 + 64^2 + 66^2 + 65^2 = 20410

Σ(xy) = (172)(62) + (173)(65) + (175)(64) + (176)(66) + (177)(65) = 56209

Plugging these values into the formula for r, we get:

r = [5(56209) - (873)(322)] / [√{5(150367) - (873)^2} √{5(20410) - (322)^2}]

Simplifying the numerator and denominator:

r = [281045 - 280506] / [√{5(150367) - (873)^2} √{5(20410) - (322)^2}]

r = 0.95 (rounded to the hundredths place)

Therefore, the correlation coefficient for this set of five students is approximately 0.95.

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The minimum product between the two numbers is 0 and the two numbers are 4 and 0.

here 1st number is x

and 2nd number is y

and the difference between twice a number and another number is 8 so 2x-y = 8

minimum value of

xy

= x(2x-8)

here the eqn is x(2x-8)

and we have to find its minima

If we have a formula expressed as y= ax2+bx+c , we can find the minimum of the quadratic equation according to the following formula: The minimum value is min= c-b2 /4a.

and the minima is at x=4

here the minimum value will be 0

so either value of x=0  or x= 4;

first number is 4 and second is 0

and product of x*y = 0;

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Answer:

Step-by-step explanation:

We can use the formula for a confidence interval for the population mean:

CI = x¯¯¯ ± z*(σ/sqrt(n))

where:

x¯¯¯ is the sample mean, which is 81.

σ is the population standard deviation, which is 11.8 (assuming the sample is drawn from a normally distributed population).

n is the sample size, which is 175.

z is the z-score corresponding to the desired level of confidence, which is 2.33 for a 98% confidence level.

Substituting the known values, we get:

CI = 81 ± 2.33*(11.8/sqrt(175))

Calculating this expression, we get:

CI ≈ (79, 83)

Therefore, a 98% confidence interval for the population mean is approximately (79, 83).

Therefore, the answer is (B) (79, 83).

The equations must intersect at a single point then it have the unique solution and the value of h and k are h = -1 and k = 6

A system has no solution if the equations are inconsistent, meaning there is no way to satisfy both equations simultaneously. It has a unique solution if the equations intersect at a single point, meaning there is only one set of values that satisfies both equations.

Let's take a look at the first system of equations, 19.

Equation 1: x + hx = 2

Equation 2: 4x + 8x = k

For the system to have no solution, the equations must be inconsistent. This means they must be parallel and never intersect. To achieve this, we can set the slopes of the lines to be equal but the y-intercepts different. In other words, we need to choose h and k such that:

h = -2 and k = 5

Substituting these values into the equations, we get:

Equation 1: x - 2x = 2

Equation 2: 4x + 8x = 5

You can see that these two equations do not have a common solution. They are inconsistent, meaning there is no point that satisfies both equations.

For the system to have a unique solution, the equations must intersect at a single point. This means the slopes and y-intercepts must be different. To achieve this, we can choose h and k such that:

h = -1 and k = 6

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Answer:

I'm not sure, but the quotient is divided, so 5016/11

Step-by-step explanation:

5016/11, and then 50/11, and find out the answer.

Assuming that each face is equally likely to come up.

(a) The sample space for this experiment  = {1, 2, 3}

(b) P(odd number) = 2/3

(c) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces:

(i) The probability of the single events, P(3) = 2/7

(ii) P(even number) = 1/3

(a) The sample space for this experiment is the set of all possible outcomes, which are the numbers 1, 2, and 3 that can appear on the face of the die.

Sample space = {1, 2, 3}

(b) To find the probability of getting an odd number, we need to find the probability of getting a 1 or a 3. There are 3 faces with the number 1 and 1 face with the number 3, so there are 3 + 1 = 4 faces that result in an odd number. There are 6 faces total, so the probability of getting an odd number is 4/6 = 2/3.

P(odd number) = 2/3

(c)

(i) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces, then each of the other five faces would have a probability of 1/7 of coming up, and the face with the 3 on it would have a probability of 2/7 of coming up.

P(1) = P(2) = 1/7

P(3) = 2/7

(ii) To find the probability of getting an even number, we need to find the probability of getting a 2. There are 2 faces with the number 2, so there are 2 faces that result in an even number. There are 6 faces total, so the probability of getting an even number is 2/6 = 1/3.

P(even number) = 1/3

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Answer:

No

Step-by-step explanation:

At least two sides will have to be the same.

We can write the equivalent value of the root expression √8√3 as 2√6.

The square root of a number is given by -

y = √x

y² = x

More specifically, we can write -

y = ± √x

Given is the root expression as -

√8√3

We can solve the expression as by finding the square roots of the numbers as -

√8√3 = √8 x √3

√8√3 = √(2 x 2 x 2) x √3

√8√3 = 2√2 x √3

√8√3 = 2√6

So, we can write that -

√8√3 = 2√6

Therefore, we can write the equivalent value of the root expression √8√3 as 2√6.

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Answer:

77

Step-by-step explanation:

(V ∪ C) = V + C - (V ∩ C)
This is the same as: (V or C) = V + C - (V and C)

(V ∪ C) represents the number of people that chose chocolate or vanilla (or possibly both)

(V ∩ C) represents the number of people that chose chocolate and vanilla twist.

(V ∪ C) = V + C - (V ∩ C) ⇔ 200 = 162 + 115 - (V ∩ C)
(V ∩ C) = 162 + 115 - 200 = 77