jamie drove 61 miles jamie car used 4 gallons of gas, how many miles per gallon did jamie car get

The value of P(D OR E) = 0.1 + 0.4 - 0.02 = 0.48, P(D AND E) = 0.1 * 0.2 = 0.02,P(E | D) = 0.02 / 0.1 = 0.2

a. P(D AND E) = P(D) * P(E | D)

P(D) = 0.1 (10% of students have taken a distance learning class)

P(E | D) = 0.2 (20% of part-time students have taken a distance learning class)

Therefore, P(D AND E) = 0.1 * 0.2 = 0.02

b. P(E | D) = P(D AND E) / P(D)

P(E | D) = 0.02 / 0.1 = 0.2

c. P(D OR E) = P(D) + P(E) - P(D AND E)

P(D) = 0.1 (10% of students have taken a distance learning class)

P(E) = 0.4 (40% of students are part-time students)

P(D AND E) = 0.02 (10% of students have taken a distance learning class and that 40% of students are part-time students)

Therefore, P(D OR E) = 0.1 + 0.4 - 0.02 = 0.48

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Answer:

[-23.27 < x]

Step-by-step explanation:

Distribute -15/4 to the numbers in the parenthesis:

[tex]\frac{-15}{4}*2x[/tex] = [tex]-\frac{30}{4}[/tex]

[tex]\frac{-15}{4}*-\frac{2}{3}[/tex] = [tex]\frac{5}{2}[/tex]

[tex]-\frac{30}{4} + \frac{5}{2} < 64 + \frac{11}{4}x[/tex]

Combine like terms:

[tex]-5 < 64 + \frac{11}{4}x[/tex]

Subtract 64 from both sides:

[tex]-64 < \frac{11}{4}x[/tex]

Multiply both sides by 4:

[tex]-256 < 11x[/tex]

Divide both sides by 11:

[tex][-23.27 < x][/tex]

The percentage gain of the company is calculated to be 10%.

The percentage gain is calculated by multiplying the fraction of the gain and the initial amount by 100.

we shall calculate for the percentage gain of the company as follows:

gain = $33 - $30 = $3

initial amount = $30

percentage gain = ($3/$30) × 100

percentage gain = (1/10) × 100

percentage gain = 10%

Therefore, the percentage gain of the company is calculated to be 10%.

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Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

The function of parking in the garage is C(t) = 6 + 2.4t

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

Rate each hour = 2.40

Initial rate = 6.00

The function is then represented as

C(t) = Initial rate + Rate each hour * number of hours

So, we have:

C(t) = 6 + 2.4t

Hence, the function is C(t) = 6 + 2.4t

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Answer:

A = 112

Step-by-step explanation:

Area of rectangle = LW

x = 2

L = x + 6 = 2 + 6 = 8

W = 9x − 4 = 9(2) − 4 = 18 - 4 = 14

A = LW = 8(14) = 112

Answer: A = 112          

Your welcome for the help                                                                                                    

The amount of chicken meat required by the lion to meet his protein diet is 6.66 ounces.

A 120-pound lion need 50 gram of protein a day.

The protein provided by the 4-ounce chicken is 30 grams.

By using unitary method,

We can write,

4 ounce chicken = 30 grams protein

4/30 ounce chicken = 1 grams protein

Now, the required amount of protein is 50 grams.

So, the chicken meat needed is,

50 grams = 4/30 x 50 ounces

50 grams protein = 6.66 ounces.

So, a total of 6.66 ounces of chicken meat is required.

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Answer: y = -4x + 29

Step-by-step explanation:

To find the equation of the line passing through the points (-3, 17) and (2, -3), we can use the slope-point form of a line, which is given by:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line. To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two points, we have:

m = (-3 - 17) / (2 - (-3)) = -20 / 5 = -4

Next, we plug in the coordinates of one of the points and the slope into the slope-point form of a line:

y - 17 = -4(x - (-3))

Expanding the right side:

y - 17 = -4x + 12

Adding 17 to both sides:

y = -4x + 29

So the equation of the line passing through the points (-3, 17) and (2, -3) is: y = -4x + 29

The simplification of the given equation would be = k = 1/2(X+y+z)

Division can be defined as one of the major arithmetic operation which is used to share or distribute a whole value between two or more values.

The equation that is given;

k = x3+y3+z3/6

k =3(X+y+y)/6

Divide through by 3;

k = =X+y+y/2 or

k = 1/2(X+y+z)

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The equivalent fractions are
1.) 5/6 > 4/6

5.) 7/8 > 4/8
9.) 8/10 < 15/10
13.) 6/8 < 7/8

what is a fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity into equal parts. It consists of two parts, a numerator and a denominator. The numerator represents the number of equal parts of the whole and the denominator represents the total number of parts the whole is divided into.

1.) 5/6 ___ 2/3

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 6 and 3 is 6. So, to make the denominator of 2/3 equal to 6, multiply both the numerator and denominator by 2:

2/3 * 2/2 = 4/6

Now, both 5/6 and 4/6 have a common denominator of 6. So, we can easily compare:

5/6 __ 4/6

5/6 is greater than 4/6, so the answer is 5/6 > 4/6

5.) 7/8 ___ 1/2

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 8 and 2 is 8. So, to make the denominator of 1/2 equal to 8, multiply both the numerator and denominator by 4:

1/2 * 4/4 = 4/8

Now, both 7/8 and 4/8 have a common denominator of 8. So, we can easily compare:

7/8 __ 4/8

7/8 is greater than 4/8, so the answer is 7/8 > 4/8

9.) 8/10 ___ 3/4

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 10 and 4 is 10. So, to make the denominator of 3/4 equal to 10, multiply both the numerator and denominator by 5/5:

3/4 * 5/5 = 15/10

Now, both 8/10 and 15/10 have a common denominator of 10. So, we can easily compare:

8/10 __ 15/10

8/10 is less than 15/10, so the answer is 8/10 < 15/10

13.) 3/4 ___ 7/8

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 4 and 8 is 8. So, to make the denominator of 3/4 equal to 8, multiply both the numerator and denominator by 2:

3/4 * 2/2 = 6/8

Now, both 6/8 and 7/8 have a common denominator of 8. So, we can easily compare:

6/8 __ 7/8

6/8 is less than 7/8, so the answer is 6/8 < 7/8

Hence, the equivalent fractions are
1.) 5/6 > 4/6

5.) 7/8 > 4/8
9.) 8/10 < 15/10
13.) 6/8 < 7/8

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Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

Here i attached answer.

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When 14 cm is converted into inches it will be 5.51181 inches.

Here given the value is 14cm.

To convert to inches it is equal to,

14 x 0.393701

= 5.51181 inches.

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By applying the linear equation concept, it can be concluded that:

A. The slope of the line is 15

B. The standard form of the equation is 15x - y + 325 = 0

C. The function notation of the equation is g(x) = 15x + 325

D. The balance in the bank account after 12 days is $505

Linear equation is an equation that contains one or more variables, where each variable has the power of one.

The standard form of a linear equation is y - y₁ = m(x - x₁) or ax + by + c = 0, where m is the slope of the function.

Slope of the function represents the change in y (Δy) over the change in x (Δx). m = Δy / Δx

We have the following table:

x         0       5       10

g(x)   325   400   475

A. To find the slope of the line, we calculate the value of Δy  dan Δx:

Δy = y₂ - y₁

    = 400 - 325

    = 75

Δx = x₂ - x₁

     = 5 - 0

     = 5

m = Δy / Δx

   = 75 / 5

   = 15

B. To find its standard form, we can input the value of one point into y - y₁ = m(x - x₁):

            y - y₁ = m(x - x₁)

        y - 325 = 15 (x - 0)

        y - 325 = 15x - 0

15x - y + 325 = 0

C. function notation changes the y to g(x), so we get:

   15x - y + 325 = 0

15x - g(x) + 325 = 0

                  g(x) = 15x + 325

D. The balance in the bank account after 12 days can be calculated by substituting the value of x = 12 into the function:

g(x) = 15x + 325

      = 15 · 12 + 325

      = 180 + 325

      = $505

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A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.

Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:

1. Enter the lengths of the sides of the right triangle into the calculator.

2. Select the angle for which you want to find the trigonometric ratios.

3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.

Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.

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A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.

Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:

1. Enter the lengths of the sides of the right triangle into the calculator.

2. Select the angle for which you want to find the trigonometric ratios.

3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.

Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.

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The probability of the coach’s basketball team winning the tournament most accurately impossible.

3.03 percent Chance of A

As a result, you could say there is a 3.03% Probability instead of saying there are 1 to 32 Odds.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

A basketball coach determines the team has a 1 32 probability of winning a tournament.

The probability of the coach’s basketball team winning the tournament most accurately impossible.

The complete question is

A basketball coach determines the team has a 1/32 probability of winning a tournament. Which choice describes the probability of the coach's basketball team winning the tournament most accurately?

answer choices

certain

impossible

likely

unlikely

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The solutions of Ax=0 in parametric vector​ form:

[tex]x_2\left[\begin{array}{c}-3&1&0&0\\\\\end{array}\right] +x_3\left[\begin{array}{c}0&0&1&0\\\\\end{array}\right] +x_4\left[\begin{array}{c}4&0&0&1\\\\\end{array}\right][/tex]

we have a matrix where A is the row equivalent to that matrix:

[tex]\left[\begin{array}{cccc}1&3&0&-4\\2&6&0&-8\\\end{array}\right][/tex]

The given matrix can be written in an Augmented form as:

[tex]\left[\begin{array}{ccccc}1&3&0&-4&0\\2&6&0&-8&0\\\end{array}\right][/tex]

Row Reduced Echelon Form can be obtained using the following steps.

Interchanging the rows R₁ and R₂

.[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\1&3&0&-4&0\\\end{array}\right][/tex]

Applying the operation R₂-->2R₂-R₁, to make the second.

[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\1&3&0&-4&0\\\end{array}\right][/tex]  R₂-->2R₂-R₁,

[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\0&0&0&0&0\\\end{array}\right][/tex]

Dividing the first row by 2 to generate 1 at the

[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\0&0&0&0&0\\\end{array}\right][/tex]  R₁--->1/2R₁

[tex]\left[\begin{array}{ccccc}1&3&0&-4&0\\0&0&0&0&0\\\end{array}\right][/tex]

From here the following equation can be deducted:

x₁+3x₂-4x₄=0

Making the subject of the equation:

x₁=-3x₂+4x₄

Hence, the Ax=0 parametric vector form’s solutions can be written as:

[tex]X=\left[\begin{array}{c}-3x_2+4x_4&x_2&x_3&x_4\\\\\end{array}\right] \\\\\\=\left[\begin{array}{c}-3x_1&x_2&0&0\\\\\end{array}\right] +\left[\begin{array}{c}0&0&x_3&0\\\\\end{array}\right] +\left[\begin{array}{c}4x_4&0&0&x_4\\\\\end{array}\right] \\\\\\ =x_2\left[\begin{array}{c}-3&1&0&0\\\\\end{array}\right] +x_3\left[\begin{array}{c}0&0&1&0\\\\\end{array}\right] +x_4\left[\begin{array}{c}4&0&0&1\\\\\end{array}\right][/tex]

Numerical Result:

[tex]x_2\left[\begin{array}{c}-3&1&0&0\\\\\end{array}\right] +x_3\left[\begin{array}{c}0&0&1&0\\\\\end{array}\right] +x_4\left[\begin{array}{c}4&0&0&1\\\\\end{array}\right][/tex]

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The student must earn a 74 on the final exam to pass the course with an average of 70.

The student's current average score is (64 + 69 + 73) / 3 = 66.

To find the score the student needs to earn on the final exam to maintain an average of 70, we can set up an equation:

(64 + 69 + 73 + x) / 4 = 70

Where x is the score the student needs to earn on the final exam.

Solving for x:

(64 + 69 + 73 + x) = 280

x = 280 - 64 - 69 - 73 = 74

So, the student must earn a 74 on the final exam to pass the course with an average of 70.

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The order of the group generated by matrices a and b under matrix multiplication is a process of multiplying the matrices and counting the number of distinct matrices that can be produced.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

The order of a group generated by matrices a and b refers to the number of distinct matrices that can be produced by multiplying a and b a certain number of times.

To find the order of the group, we need to start by multiplying a and b and see if we get any new matrices. If we do, we keep multiplying those matrices until we get back to the original matrices a and b.

The order of the group is the number of distinct matrices we get in this process.

It is important to note that matrix multiplication is associative, which means that the order in which we multiply the matrices does not affect the result. Also, the identity matrix is a special matrix that, when multiplied by any matrix, produces the same matrix.

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To determine the width:

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Answer:

B

Step-by-step explanation:

Matthew's monthly take-home pay is approximately $2,960.69 (47,530 / 12). To calculate the exact amount, we need to subtract the state income tax from his monthly salary:

$47,530 / 12 = $3,961.67

$3,961.67 * 0.0307 = $122.57

$3,961.67 - $122.57 = $3,839.10

Therefore, the correct answer is B) $3,839.24

Answer:

5 hours.

Step-by-step explanation:

280 divided by 56 is 5.

The number of hot dogs will Team A need to sell to reach its goal is 690.

What is the linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form: y = mx + b,where "x" is the independent variable, "y" is the dependent variable, "m" is the slope of the line, and "b" is the y-intercept.

Let the number of dogs be x.

1.48x - 20 = 1000
1.48x = 1020
x = 1020/1.48
x = 690

Hence, the number of hot dogs will Team A need to sell to reach its goal is 690.

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Answer:

The square root of 200 in its simplest radical form is 10√2.

Step-by-step explanation:

If we know the prime factorization of a number, we can write the radical form of the square root of that number.

Answer: 10√2.

Step-by-step explanation: the prime factorization of 200 is 2 × 2 × 2 × 5 × 5. As a result, the square root of 200 in the simplest radical form should be 10√2.

The portion of the parabola from t=-1 to t=1 can be parametrized as x=2t²-4 and y=t.

A parabola is a symmetrical and U-shaped curve that is defined by a mathematical equation.

In this case, we will use the variable t to represent the y-coordinate and find the corresponding x-coordinate. The equation becomes y=t, and substituting this into the original equation, we get

=> x=2t²-4.

To find the portion of the parabola where -1≤t≤1, we can plot the points (x, y) for various values of t in this range.

when t=-1,

=> x=2(-1)²-4 = 0.

And when

t=1, x=2(1)²-4 = -2.

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Answer:

Let x be the amount Pam has, then Dan has x - $3.00 and Sam has x + x - $3.00 + $1.00 = 2x + $1.00

The total amount of money they have is x + x - $3.00 + 2x + $1.00 = 31.00

So, 4x + $1.00 = 31.00

Subtracting $1.00 from both sides gives 4x = 30.00

Finally, dividing both sides by 4 gives x = $7.50

So Pam has $7.50, Dan has $7.50 - $3.00 = $4.50, and Sam has $7.50 + $4.50 + $1.00 = $13.00.

The equation with the given values for pipe length and elapsed time to calculate the initial head needed to achieve the desired velocity.

The velocity of water, v (m/s), discharged from a cylindrical tank through a long pipe can be computed using the equation:

v= √2gH tanh (√2gH/2L. T)

where g = 9. 81 m/s2, H = initial head (m), L = pipe length (m), and t = elapsed time (s).

To plot the velocity function f(H) versus H for H = 0 to 4 m, we can use MATLAB to create a script that uses the equation to calculate the velocity for each value of H. We can then plot the points on a graph, with H on the x-axis and v on the y-axis.

To determine the initial head needed to achieve υ = 5 m/s in 2. 5 s for a 4-m long pipe, we can use the LastNameBisect method with initial guesses of xl = 0 and xu = 4 m. This will use the equation with the given values for pipe length and elapsed time to calculate the initial head needed to achieve the desired velocity.

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Discrete mathematics is a branch of mathematics that deals with objects that can assume only distinct, separated values and can be counted. It has played a significant role in reducing cultural distinctions by providing a unifying language for the field of mathematics and a common understanding for solving problems across cultures.

Through discrete mathematics, people from different backgrounds and cultures can communicate and collaborate more effectively, breaking down cultural barriers and promoting unity.

For example, discrete mathematics has been used to create algorithms that solve complex problems in computer science, cryptography, and optimization, making it possible for people from different cultures to work together to solve these problems.

Additionally, the standardization of mathematical language and symbols through discrete mathematics has made it easier for people to understand and share mathematical ideas across cultures, further promoting unity and reducing cultural distinctions.

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When multiplying decimal numbers, you move the decimal point to the left of the amount of integers in the equation that are to the right of the decimals.25.5 x 0.81 = 20.655

When multiplying decimal numbers, you move the decimal point to the left of the amount of integers in the equation that are to the right of the decimals.

After multiplication, you would move the decimal three places to the left because there is one number after the decimal point in 25.5 and two numbers after the decimal point in 0.81.

25.5 x 0.81 = 20.655

( notice there are 3 numbers to the right of the decimal point) ( note there are 3 numbers to the right of the decimal point)

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Answer:

1/8

Step-by-step explanation:

The coin is flipped three times; the total number of outcomes = 2 × 2 × 2 = 8. P(X) = |X| / |Ω| = 1/8.

Answer: The values that make the denominator equal to zero for a rational expression are known as restricted values. How do you identify restrictions in rational expressions? The restriction is that the denominator can not be equal to zero. So in this problem, since 4x is in the denominator it can not equal zero.