The following table gives the number of drinks and the resulting blood alcohol percent for a man of a certain weight legally considered driving under the influence (DUI) a. The average rate of change in blood alcohol percent with respect to the number of drinks is a constant. What is it? b. Write an equation of a linear model for this data, Number of Drinks 5 6 7 8 10 Blood Alcohol 0.19 0.22 0.25 0.28 0.31 0.34 9 Percent a. What is the rate of change in blood alcohol percent? 0.03% b. What is the equation that models blood alcohol percent as a function of x, where x is the number of drinks?

Answer:

-3 is the coefficient of x here

Step-by-step explanation:

The first thing to do here is to open the brackets.

(x-5)(x + 2) = x(x + 2)-5(x + 2)

x^2 + 2x -5x -10

x^2 -3x -10

When we say the coefficient of x, we mean the value by which x only is multiplied by in the equation. That would be -3

This must not be confused with the coefficient of x^2 which is entirely different from the coefficient of x

Answer:

40m

Step-by-step explanation:

The total distance from Aurora to Clifton through Burlington is: 65 + 72 = 137

137 - 97 = 40

So it is 40 m  closer to travel from Aurora to Clifton directly than from Aurora to Clifton through Burlington.

Answer:

False

Step-by-step explanation:

Inductive reasoning is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion.

Answer:

We move the decimal point to the right by a number of digit places equal to  the power of 10.

Step-by-step explanation:

If we want to multiply a decimal by a power of 10, we move the decimal point to the right by a number of digit places which is the power of the number ten or the number of zeros which are present in the multiplying number 10. If we do not have a digit after the last digit, we put zeros to complete the number of digits until, we have the number of digit places added after the decimal point which are equal to the power of 10.

Using the example given above

8.653 x 10000, we have four zeros. So, in index form it is

8.653 x 10⁴

Since we have the number 10 raised to the power of four or having 4 zeros, we move the decimal point 4 places to the right.

So, 8.653 x 10000 = 8.653 x 10⁴ = 86530

Answer:

B. DC is 14 units.

F. DE can be found by counting.

Step-by-step explanation:

I took the test

Hope this helps :)

out of all the statements given about the line segments only the statement "DE can be found by counting"

The vertices of the polygon are A(5, 7), B(10, -2), C(8, -6), D(-6, -6) and E(-6, 8).

The formula to find the distance is Distance\(=\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^{2}}\).

ED=√(-6+6)²+(8+6)²=14 units.

DC=√(8+6)²+(-6+6)²=14 units.

CB=√(10-8)²+(-2+6)²=√18 units.

EA can not be found by counting.

AB can not be found by counting.

DE can be found by counting.

Therefore, out of all the statements given about the line segments only the statement "DE can be found by counting"

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To solve the given differential equation y" - 9y = 12e^9x + e^3x using the Method of Undetermined Coefficients, we need to find a particular solution for the equation and combine it with the complementary solution.

First, let's find the complementary solution by assuming y = e^(mx), where m is a constant. Substituting this into the differential equation, we get:

m^2e^(mx) - 9e^(mx) = 0

This gives us the characteristic equation:

m^2 - 9 = 0

Solving the characteristic equation, we find two distinct roots: m = ±3. Therefore, the complementary solution is:

y_c = C1e^(3x) + C2e^(-3x)

Next, we find the particular solution for the non-homogeneous part of the equation. For the term 12e^(9x), since the exponent is already in the solution, we assume the particular solution to be of the form:

y_p1 = Ae^(9x)

Substituting this into the differential equation, we get:

81Ae^(9x) - 9Ae^(9x) = 12e^(9x)

Simplifying, we find:

72Ae^(9x) = 12e^(9x)

Therefore, A = 1/6. Hence, the particular solution for the term 12e^(9x) is:

y_p1 = (1/6)e^(9x)

For the term e^(3x), since the exponent is already in the complementary solution, we multiply it by x to ensure linear independence:

y_p2 = Bxe^(3x)

Substituting this into the differential equation, we get:

18Bxe^(3x) - 9Bxe^(3x) = e^(3x)

Simplifying, we find:

9Bxe^(3x) = e^(3x)

Therefore, B = 1/9. Hence, the particular solution for the term e^(3x) is:

y_p2 = (1/9)xe^(3x)

Finally, the general solution is obtained by combining the complementary and particular solutions:

y = y_c + y_p1 + y_p2

 = C1e^(3x) + C2e^(-3x) + (1/6)e^(9x) + (1/9)xe^(3x)

This is the solution to the given differential equation using the Method of Undetermined Coefficients.

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Answer:

14400 words

Step-by-step explanation:

1 hour = 60 minutes

2 hours

= 2 x 60

= 120 minutes

Let the no. of words that he can type in 2 hours is " x ".

1800 : 15 : : x : 120

1800 / 15 = x / 120

1800 * 120 = 15 * x

x = 1800 * 120 / 15

= 120 * 120

x = 14400 words

Therefore,

He can type 14400 words in 2 hours.

Answer:

Xbox One is the better console to buy.

Adding the game console for $150.00 with 7 games costing 24, they will cost you $318.00

While the PlayStation 4 with the 7 games cost a total of $320.00

Step-by-step explanation:

For the given situation, angle of depression is 18 degrees and the horizontal distance from the driver's eyes to the front of the car is 5 feet then the bumpers are 5.26 feet apart from the nearest foot.

As given in the question,

Angle of depression between driver's eye to bottom of 3 foot high back end of car front is equal to 18°

Horizontal distance from the driver's eyes to the front of the car = 5 feet

Let us consider 'x' be the distance between bumper and nearest foot .

For the given situation right angle triangle get formed,

x represents the hypotenuse of the triangle,

5 feet is the base of the triangle

Using cosine rule,

cos 18° = 5 / x

⇒ x = 5 / cos 18°

⇒ x = 5 / 0.9511

⇒ x = 5.26 feet (approximately)

Therefore, for the given situation, angle of depression is 18 degrees and the horizontal distance from the driver's eyes to the front of the car is 5 feet then the bumpers are 5.26 feet apart from the nearest foot.

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Yes, the continuous time complex exponential is always periodic, and it is because complex exponentials can be written using Euler's formula.

Euler's formula, in mathematics, is a formula that links five fundamental mathematical constants:

e, the base of the natural logarithm;

pi, a mathematical constant;

i, an imaginary unit;

1, the multiplicative identity; and

0, the additive identity.

The formula is

\(e^{ix} = cos(x) + i sin(x)\)

In the above formula, x is a real number. cos(x) and sin(x) are the trigonometric functions cosine and sine, respectively. And i is the imaginary unit.

In general, periodic functions are mathematical functions that repeat themselves after a certain period. And when complex exponentials can be written using Euler's formula, they can also be expressed as:

\(cos(x) =\frac{1}{2} (e^{ix} + e^{-ix})sin(x) = 1/2i (e^{ix} - e^{-ix})\)

As a result, it can be concluded that the continuous time complex exponential is always periodic since it can be expressed using Euler's formula, and Euler's formula can also be written in a periodic form.

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Answer:

x is 30 because it is part of a complimentary angle and y is 5 because it is part of the equilateral triangle that has a side length of 40

Answer: C

Step-by-step explanation: The slope of Function A is 6 and the slope of Function B is 5.

The height of the basketball hoop is 13.32'.

What is law of similarity?

The Law of Similarity in mathematics states that if two geometric figures have the same shape but different sizes, then they are considered similar. This means that the corresponding angles of the two figures are congruent, and the corresponding sides are proportional in length.

Formally, if we have two geometric figures A and B, and if every angle of figure A is congruent to the corresponding angle of figure B, and if the ratio of the length of any pair of corresponding sides of A and B is constant, then we can say that A and B are similar figures.

Here we can see two triangle and base of two triangle is given.

Here base of small triangle is 12' and the base of big triangle is (12'+25') = 37'.

It is also given that height of small triangle is 4'3.84".

Now we want to find the height of the basketball hoop which is equal to height of big triangle.

Let the height of the basketball hoop be x.

So, by law of similarity ratios,

12'/37' = 4'3.84"/x

Now, 4'3.84" = 4.32'

So, 12'/37' = 4.32'/x

Therefore, x = 13.32'

Therefore, the height of the basketball hoop is 13.32'.

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Answer:

11 ; 13

Step-by-step explanation:

Let the numbers be :

x and x + 2

x * (x + 2) = 6(x + x + 2) - 1

x² + 2x = 6(2x + 2) - 1

x² + 2x = 12x + 12 - 1

x² + 2x = 12x + 11

x² + 2x - 12x - 11 = 0

x² - 10x + 11 = 0

x² - 11x + x + 11 = 0

x(x - 11) + 1(x - 11) = 0

(x - 11) = 0 or (x + 1) = 0

x = 11 or x = - 1

X cannot be negative

x = 11

x + 2 = 11 +2 = 13

Answer:

Step-by-step explanation:

ill explain How to solve.

A:    

     x+4>15

     15-4=11

      x<11

C:

     6b=>54

     54/6=9

      b=>9

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Expressions, equations, and inequalities are all mathematical sentence forms, but they differ in their structure, purpose, and meaning.

An expression is a mathematical phrase that combines numbers, variables, and operators but does not contain an equals sign. Expressions can be simplified by performing arithmetic operations, but they cannot be solved for a particular value. Examples of expressions include 2x + 5, 3y - 7, and 4z² - 6z + 9.

An equation is a mathematical sentence that states that two expressions are equal. Equations have an equals sign and are used to solve for a particular value of a variable. They can be solved by applying algebraic operations to both sides of the equation until the variable is isolated. Examples of equations include 2x + 5 = 11, 3y - 7 = 2y + 1, and 4z² - 6z + 9 = 0.

An inequality is a mathematical sentence that compares two expressions using inequality symbols such as <, >, ≤, or ≥. Inequalities can be used to represent relationships between quantities that are not necessarily equal. They are solved by isolating the variable on one side of the inequality symbol. Examples of inequalities include 2x + 5 < 11, 3y - 7 > 2y + 1, and 4z² - 6z + 9 ≤ 0.

In summary, expressions are mathematical phrases that cannot be solved for a particular value, equations are mathematical sentences that state that two expressions are equal and can be solved for a particular value, and inequalities are mathematical sentences that compare two expressions using inequality symbols and can be used to represent relationships between quantities that are not necessarily equal.

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Answer:

.25 and 1/4

Step-by-step explanation:

1 - .75 = .25

.25 = 1/4

The best way to interpret this expression, as we did for Consider this expression is the c.r.v X is has an expected value with a mean of mu and standard deviation of sigma. (option c).

The mean, represented by the Greek letter mu (μ), is the expected value of the distribution, and the standard deviation, represented by the Greek letter sigma (σ), is a measure of the spread or variability of the data. In this case, since the standard deviation is zero, it means that all the data points are the same, and there is no variability. This is a degenerate distribution that occurs when all values are constant.

Therefore, the best way to interpret this expression is that the random variable X is normally distributed with a mean of 1 and a standard deviation of 0. This means that X can only take on the value of 1, which is the expected value of the distribution.

Hence the correct option is c).

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The bank routing number on a check is a 9-digit code used to identify a financial institution in a transaction. It is also known as an ABA routing number, an RTN, and a routing transit number.

In order to determine the routing number on a check:

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Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

Answer:

$73.16  (nearest cent)

Step-by-step explanation:

Gross weekly income:

= pay per hour × hours worked per week

= $10 × 13

= $130

Total taxes:

= Federal + FICA + State

= 10% + 7.65% + 3%

= 20.65%

Therefore, total taxes to pay:

= percentage of gross weekly income

= 20.65% of $130

= 0.2065 × $130

= $26.845

Realized income:

= gross weekly income - taxes - retirement plan contribution

= $130 - $26.845 - $30

= $73.155

= $73.16  (nearest cent)

Answer:

x = - 10

Step-by-step explanation:

Given

10 - x = - 2x ( add 2x to both sides )

10 + x = 0 ( subtract 10 from both sides )

x = - 10

The random variable X is not binomial in the given experiment.

To be considered a binomial distribution, a random variable X must satisfy the following conditions:

There must be a fixed number of trials, n.

Each trial must have only two possible outcomes, success or failure.

The probability of success must be the same for each trial.

The trials must be independent.

In this experiment, the number of trials is not fixed since we are selecting cards without replacement. The probability of success changes for each trial, as the number of red cards in the deck decreases with each card drawn. Therefore, X cannot be considered a binomial random variable.

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The measure of reliability of a statistical inference is the significance level. The significance level, also known as alpha, is the probability of rejecting the null hypothesis when it is actually true. It determines the threshold for accepting or rejecting a hypothesis.

A lower significance level indicates a higher level of confidence in the results. A descriptive statistic provides information about the data, but it does not directly measure the reliability of a statistical inference. It simply summarizes and describes the characteristics of the data.

A sample statistic is a numerical value calculated from a sample, such as the mean or standard deviation. While it can be used to make inferences about the population, it does not measure the reliability of those inferences.
A population parameter is a numerical value that describes a population, such as the population mean or proportion.

While it provides information about the population, it does not measure the reliability of inferences made from a sample. In conclusion, the significance level is the measure of reliability in a statistical inference as it determines the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.

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Answer:

Step-by-step explanation:

Let's represent each face of the cube by a number from 1 to 6, where the ant is initially on face 1. We can use a tree diagram to determine all the possible paths the ant can take in 4 minutes:

1-2-3-2-1

| | |

5-6-5

| | |

4-3-4

Each path has a probability of (1/3)^4 = 1/81 of occurring, since the ant has 3 choices for its next move and there are 4 moves in total. We need to find the paths that end on face 1, which are 1-2-3-2-1 and 1-5-6-5-1. Therefore, the probability that the ant is back in its original face after 4 minutes is:

(1/81) + (1/81) = 2/81

So the answer is 2/81 in simplified form.

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Answer:

I believe it would be -2

Step-by-step explanation:

The midpoint of (0,4) and (4,-8) is (2,-2)

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The equation will be...

\(\frac{3x-6}{2} +12\)

I don't know if you need to solve it but here you go anyways...

\(\frac{3}{2}x+9\)