Find a function rule for the line that passes through the origin (0,0) and the point (-6,-18).

The correct answer is B. on average it takes 1.8 beers to increase blood alcohol content by 1%.

The equation implies that for each beer consumed, the blood alcohol content increases by 0.0180, meaning it takes 1.8 beers to increase the blood alcohol content by 1%.

It is important to note that different people metabolize alcohol at different rates, so the number of drinks it takes to reach a 0.08% BAC can vary significantly. Generally, it takes about 1.8 drinks to raise the BAC by 1%. This means that an average person would need to consume 15 drinks in order to reach the legal limit of 0.08%.

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Answer:

nothing

Step-by-step explanation:

Answer:

Step-by-step explanation:

nothing

Answer:6

Step-by-step explanation:

The two numbers are 3 and 7.

Let the two numbers be x and y.

Considering the first statement :

x + y = 10 ...........................(1)

Considering the second statement:

x - y = 4   ............................(2)

Adding equations (1) and (2):

x + y + x - y = 10 + 4

              2x = 14

                x = 7

Substituting the value of x in equation (1):

           7 + y = 10

                 y = 10 - 7

                 y = 3

Therefore, the value of the two numbers is 3 and 7.

For reference:

https://www.cliffsnotes.com/study-guides/algebra/algebra-i/word-problems/number-problems-with-two-variables

Answer:

3 2/5 = 17/5

3 4/6 = 22 / 6 = 11 / 3

17/5 + 11 / 3   need to find and 15 is the least common denominator

51 / 15 + 55 / 15 = 106 / 15

106 / 15 =  7  1 / 15     lowest terms

Note 7 1/15 = 7 2/30      second of 4 answers

Answer:

-5

Step-by-step explanation:

First, find the solutions to the quadratic equation.

[tex]3x^2+15x+9=0\\3(x^2+5x+3)=0[/tex]

Since this is not factorable, use the quadratic formula and simplify.

x = (-5±[tex]\sqrt{(5)^2-4(1)(3)}[/tex])÷2(1)

x = (-5±[tex]\sqrt{13}[/tex])÷2

So x1 = (-5+[tex]\sqrt{13}[/tex])÷2 and x2 = (-5-[tex]\sqrt{13}[/tex])÷2

Now just sub it into the equation and simplify:

(-5+[tex]\sqrt{13}[/tex])÷2 + (-5-[tex]\sqrt{13}[/tex])÷2

= [tex]\frac{-5+\sqrt{13} + (-5)-\sqrt{13}}{2}[/tex]

= [tex]\frac{(-5)+(-5)+\sqrt{13}-\sqrt{13} }{2}[/tex]

= [tex]\frac{-10}{2}[/tex]

= -5

Answer:

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Answer:

1) Given

2) Multiplication Property of Equality

3) 3x + 6 = 24     Distributive Property of Addition

4) 3x = 18     Subtraction Property of Equality

5) x = 6     Division Property of Equality

Step-by-step explanation:

[tex]\begin{array}{|l|l|}\cline{1-2}\vphantom{\dfrac12} \rm Statements & \rm Reasons\\\cline{1-2}\vphantom{\dfrac12}\frac{3(x+2)}{4}=6& \rm Given\\\cline{1-2}\vphantom{\dfrac12}3(x+2)=24&\text{Multiplication Property of Equality}\\\cline{1-2}\vphantom{\dfrac12}3x+6=24&\text{Distributive Property of Addition}\\\cline{1-2}\vphantom{\dfrac12}3x=18&\text{Subtraction Property of Equality}\\\cline{1-2}\vphantom{\dfrac12}x=6&\text{Division Property of Equality}\\\cline{1-2}\end{array}[/tex]

Given:

[tex]\dfrac{3(x+2)}{4}=6[/tex]

Apply the Multiplication Property of Equality by multiplying both sides by 4:

[tex]\implies 3(x+2)=24[/tex]

Apply the Distributive Property of Addition:

[tex]\implies 3 \cdot x + 3 \cdot 2=24[/tex]

[tex]\implies 3x+6=24[/tex]

Apply the Subtraction Property of Equality by subtracting 6 from both sides:

[tex]\implies 3x+6-6=24-6[/tex]

[tex]\implies 3x=18[/tex]

Apply the Division Property of Equality by dividing both sides by 3:

[tex]\implies \dfrac{3x}{3}=\dfrac{18}{3}[/tex]

[tex]\implies x=6[/tex]

--------------------------------------------------------------------------------

For all numbers, a, b, and c:

Multiplying a number by a group of numbers added together is the same as multiplying each number separately:  

For all numbers, a, b, and c:

For all numbers, a, b, and c:

The meer-kitty survey feedback tab has limitations in its data. The survey results must have at least 120 unique responses to be considered useful and aligned with the business objective. The current data, however, only has 40 total responses, with 11 of them coming from one user. This skews the results and makes it difficult to accurately analyze the feedback.

To address these limitations, it is recommended to remove the duplicates, in this case the 11 responses from one user, and focus on the remaining 29 unique responses. This will provide a clearer picture of the survey results and a more accurate representation of the feedback. By doing so, the analysis of the data will be better aligned with the original business objective and provide more valuable insights.

It is important to consider the limitations of the data when conducting any type of analysis, especially when it comes to surveys and feedback. By taking the necessary steps to ensure the data is as accurate and reliable as possible, the results of the analysis will be more meaningful and relevant to the business.

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The length of the bases for the trapezoid are

shorter base is 3 in and the longer base is 7 in

The formula for area of trapezoid is

= 1/2 sum of bases * height

base of the trapezoid

20 = 1/2 sum of bases * 4

1/2 sum of bases = 5

sum of bases = 10

The relationship between the bases

longer base = 2 * shorter base + 1

sum of bases = longer base + shorter base

sum of bases = 2 * shorter base + 1 + shorter base

sum of bases = 3 shorter base + 1

substituting will result to

10 = 3 shorter base + 1

10 - 1 = 3 shorter base

9 = 3 shorter base

shorter base = 3 in

longer base = 2 * shorter base + 1

longer base = 2 * 3 + 1

longer base = 7 in

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The questions that are appropriate for the teacher to ask her population are:

How many hours of sleep do you get per night?

On average, how long does it take you to complete your homework?

What time do you leave for school in the morning?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The survey is conducted among the seventh grade students so the valid question their teacher would have asked them is:

How many hours of sleep do you get per night?

On average, how long does it take you to complete your homework?

What time do you leave for school in the morning?

while the other two questions are invalid as it the students are young and they are not legal to vote also it is not necessary that they would arrive to school by car.

Hence, the questions that are appropriate for the teacher to ask her population are:

How many hours of sleep do you get per night?

On average, how long does it take you to complete your homework?

What time do you leave for school in the morning?

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Step-by-step explanation:

The graph would represent a straight line that slopes downwards and passes through the point (2,1).

The value of h such that the matrix is the augmented matrix of a consistent linear system is -2

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

6 -3 h

-12 6 4

For a consistent system of linear equation, the equations are the equivalent

So, we have

6x - 3y = h

-12x + 6y = 4

Divide the second equation by -2

6x - 3y = -2

By comparing the equations, we have

h = -2

Hence, the solution of h is -2

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The length t of the triangle side is 44 mm

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

according to law of cosines,

t² = 41² +54² - 2 (41)(54) cos x

t² = 41² +54² - 2 (41)(54) ( 3/5)

t² =  1681 + 2916 - (13284/5)

t² =  1681 + 2916 - (13284/5)

t² =  4597 - 2656.8 =1940.2

t = ±√1940.2 = ±44 mm

length is positive

The length t of the triangle side is 44 mm

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Student use simple random sampling method.

There are two types of data sets are collected for the research. They are population and sample. Population includes all the elements from the data set. Sample is a part of population.

A student is researching if people like to study at the city library.

The student stands by the door of the city library and surveys people walking in.

It is type of simple random sampling.

In this simple random sampling every member of an population has an equal chance of being selected.

This is one of the probability sampling methods.

Hence, student use simple random sampling method.

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Answer:

The zero in the equation y = 2x + 8 is when x = -4. When x = -4, y = 0.

So,the value of the 30th percentile of the given data will be =P30=4

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, assessed at x, is the likelihood that X will have a value less than or equal to x in probability theory and statistics.

Using the Cumulative Distribution Function to Calculate Probabilities

F(x) is a cumulative distribution function that calculates the likelihood that the random variable X is smaller than or equal to x:

To get the cumulative probability that X is less than or equal to 1, multiply P(X=0) by P(X = 0) by (P=1):

First, we will determine the value of the cumulative probability P(X<=x):

x         f(x)       P(X<=x)

1       0.02          0.02

2       0.01          0.03

3       0.2          0.23

4       0.17           0.4

5       0.39           0.79

6       0.2           0.99

7 0.01 1

30th percentile will be the x value,

below which less than or equal to 30% of the data falls.

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Confidence interval refer a range of estimates for an unknown parameter and here unknown parameter is percentage of residents support the increase. So, the correct answer is option(c), i.e., More than 40 percent of the residents support the increase.

We have, A random sample of residents in city J, about whether they supported raising taxes to increase bus service for the city and sample is based on survey.

Significance level = 95%

Confidence interval = (0.46,0.52)

Confidence interval: A confidence interval, in statistics, defines to the probability that a population parameter will fall between two set values. Therefore, the population parameter i.e., the proportion lies in range of between 0.46 to 0.52. Therefore the actual population proportion of people who support the increase is surely greater than 40%, but always be less than 52%. So, out of five options, option (c) is that satisfied this condition. That is more than 40% of the residents support the increase, implies the option( C) is the correct answer.

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The solution to the equations are

a) The city will have 231 streetlights at the end of 49 weeks

b) The city will have 191 streetlights at the end of 29 weeks

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The initial number of streetlights in the city = 133 streetlights

The number of streetlights installed per week = 2 streetlights

So , the number of streetlights after 49 weeks = 49 x number of streetlights installed per week

Substituting the values in the equation , we get

The number of streetlights after 49 weeks = 49 x 2 = 98 streetlights

And , the total number of streetlights after 49 weeks = initial number of streetlights in the city + number of streetlights after 49 weeks

Substituting the values in the equation , we get

The total number of streetlights after 49 weeks A = 133 + 98

The total number of streetlights after 49 weeks A = 231 streetlights

Now ,

Let the number of streetlights after n weeks = 191 streetlights

So , the number of weeks n = ( 191 - initial number of streetlights ) / 2

Substituting the values in the equation , we get

The number of weeks n = ( 58 ) / 2

The number of weeks n = 29 weeks

Hence , the equations are solved

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The number of pounds of $9 nuts he must used, 126

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Randall wants to mix 21 lb of nuts worth $2 per lb,

with some nuts worth $9 per lb

He wants to make a mixture worth $8 per lb

The number of pounds of $9 nuts must he use = ?

Suppose, the number of pounds of $9 = x

Then, According to given condition,

Average price in a mixture  =  (9x + 21 x 2)/x +21

                                              =  8

(9x + 21 x 2)/x +21 = 8

9x + 42 = 8(x + 21)

9x + 42 = 8x + 168

9x - 8x = 168 - 42

x = 126

Hence, the number of pounds of $9 nuts is 126

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The total manufacturing cost assigned to Job P is $84,240.

The total manufacturing cost consists of direct material, direct labor, variable overhead, and fixed overhead costs.

The variable manufacturing costs include direct materials, direct labor, and variable overhead while the fixed overhead costs are period costs related to the production process.

                                                              Molding    Fabrication      Total

Machine hours used                                4,200         2,520           6,720

Fixed manufacturing overhead           $16,800    $25,200     $ 42,000

Fixed manufacturing overhead per hr    $4              $10

Variable manufacturing overhead

per machine-hour                               $ 1.40           $ 2.20

                                         Job P       Job Q

Direct materials           $ 21,840    $ 13,440

Direct labor cost        $ 35,280    $ 12,600

Actual machine hours used:

Molding                           2,890          1,340

Fabrication                       1,010          1,480

Total                                3,900        2,820

Actual Manufacturing Costs (Job P):

                                                             Job P

Direct materials                                   $21,840

Direct labor costs                               $35,280

Overheads:                        

Variable                                               $5,460 (3,900 x $1.40)

Fixed:

Molding = $11,560 ($4 x 2,890)

Fabrication = $10,100 ($10 x 1,010)   $21,660

Total manufacturing costs               $84,240

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[tex] \: [/tex]

[tex] \: [/tex]

Then ,

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

The critical F value for a sample of 6 and 4 degrees of freedom at a .10 two-tailed significance level can be found using a F-distribution table. The exact value depends on the specific table used.

For the comparison between Mark and Debbie, we would need to perform an F-test for equality of variances to determine if there is more variation in Mark's data. The null hypothesis is that the variances are equal, and the alternative hypothesis is that the variance of Mark's data is greater. The test statistic would be the ratio of the larger variance to the smaller variance, with the degrees of freedom being the smaller of the two sample sizes minus 1.

A .05 significance level means that we reject the null hypothesis if the p-value is less than .05. The p-value can be found using an F-distribution table or a statistical software.

The conclusion would depend on whether the p-value is less than .05 or not.

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The batter ran a distance of 0.112 kilometers or approximately 112 meters.

A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

A baseball diamond is made up of four bases, and the distance a batter runs for a single is from home plate to first base, then first base to second base, then second base to third base, and finally third base back to home plate.

So the total distance the batter runs is 4 times the distance from home plate to first base, which is 28 meters.

28 meters x 4 = 112 meters

To convert meters to kilometers, divide by 1000:

112 meters / 1000 = 0.112 kilometers

Thus, the batter ran 0.112 kilometers or approximately 112 meters.

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The factor by which g([tex]x[/tex]) grows over the interval from 14 to 16 is 1.1429.

The factor is a number that can be divided evenly into another number. For example, 2, 3, 5 and 10 are all factors of 10. When two or more numbers are multiplied together, each number is a factor of the product.

The factor by which g(x) grows over the interval from 14 to 16 can be determined by calculating the ratio of the values of g(x) at the endpoints of the interval.

At x = 14, g(x) = 4(14) = 56

At x = 16, g(x) = 4(16) = 64

The factor by which g(x) grows over the interval from 14 to 16 is 64/56 = 1.1429.

This means that g(x) grows by a factor of 1.1429 over the interval from 14 to 16.

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y(0.9) ≈ -658.91 using Euler's method with the ODE [tex]dy/dx + 5y^2 = sin x[/tex], initial condition y(0.3) = 5, and step size h = 0.3.

Given that ODE:

[tex]dy/dx + 5y^2 = sin x[/tex]

with the initial condition:

y(0.3) = 5

and step size h = 0.3, the value of y(0.9) using Euler's method can be approximated as follows:

Starting with the initial condition y0 = 5, use the formula:

[tex]y(x + h) = y(x) + hf(x, y(x))[/tex]

where [tex]f(x, y) = (sin x - 5y^2)/(dy/dx) + 5y[/tex] is the right-hand side of the ODE, and h = 0.3.

After two iterations, the approximate value of y(0.9) is y2 ≈ -658.91.

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Using the system of equations we get the values of 3 digit number as:

238

Given:

The sum of the digits of a three-digit number is 13.

The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits.

we are asked to determine each digit of the given number:

we frame the equation as:

tens digit (t) = 1+h

hundreds digit (h) = h

units digit (u) = 3+(t+h)

hence,

h + (1+h) + (3+(t+h)) = 13

open the brackets.

h+1+h+3+(t+h)=13

substitute t value from the above mentioned state.

h+1+h+3+((1+h)+h)=13

h+1+h+3+1+h+h=13

arrange the like terms and add.

4h + 5 = 13

4h = 13-5

4h=8

h = 8/4

h = 2

hence we get the hundreds digit as 2.

now substitute it to get t and u value.

t = 1+h

t = 1+2

t = 3

tens digit = 3

u = 3+(t+h)

u = 3+(3+2)

u = 3+5

u = 8

units digit = 8

The joint probability distribution function for exponential random variables with pdf f(x) = 0.5e^(-0.5x), x ≥ 0, find P(X > 1,Y > 4) is, e^(-5/2).

The X and Y are independent variables, so probability distribution function of X is same as that of Y.

The joint probability distribution function for independent variables is,

[tex]\int \int f(x)f(y) dx dy[/tex]

where f(x) and (y) are the probability distribution function in x and y respectively.

In this question, X>1 and Y>4, so the limits of integration for X goes from 1 to infinity and for Y it goes from 4 to infinity.

[tex]\int_4^\infty \int_1^\infty 0.5 \times 0.5 \times e^{-0.5x} e^{-0.5y} dx dy\\= 0.25\int_4^\infty e^{-0.5y} dy \int_1^\infty e^{-0.5x} dx\\= 0.25 \times [-2e^{-0.5y}]_4^\infty \times [-2e^{-0.5x}]_1^\infty \\= 0.25 \times \dfrac{2}{{e}^2} \times \dfrac{2}{\sqrt{e}}[/tex]

The integral is, e^(-5/2).

The joint probability distribution function is, e^(-5/2).

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--The complete question is, If X and Y are independent exponential random variables with pdf f(x) = 0.5e^(-0.5x), x ≥ 0, find P(X > 1,Y > 4).--

Answer: x ≤ -6 or x > 5

Step-by-step explanation: There are 2 lines so you will need 2 inequalities to define it.

The first line is going to left means the variable (x) will have to be less than the greatest value of the line (the right most point) which is -6. Therefore, x < 6 with < representing less than. However, we also have to consider the a CLOSED dot at -6 meaning the sign of the inequality is going to be ≤ since we including that point in the inequlity saying x can be equal to or less than 6.

The second line going to the right means x has to be greater than the smallest value of the line which is -5 (the left most point of the line). Therefore, x > 5 (> means greater than). In this case, we do not use ≥ because the point at -5 has a OPEN dot meaning x cannot equal 5 and we can not include that point in our inequality so it would just be x > 5.

So we get x ≤ -6 or x > 5

Answer:

Please type or attach a math question to be answered.

Answer:

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