Math question please help

The equation of the required line in slope-intercept form is y = -1/4x + 8.

Here are the steps to find the equation of the line:

Step 1: Find the slope of the given line in slope-intercept form

y = mx + c

-4x + y = 43 ⇒ y = 4x + 43... (1)

Here, the slope (m1) of the given line is 4.

Step 2: Find the slope of the required line as the two lines are perpendicular to each other.

m1 × m2 = -1

[As the given line and the required line are perpendicular to each other]

4 × m2 = -1 ⇒ m2 = -1/4

So, the slope (m2) of the required line is -1/4.

Step 3: Write the equation of the required line in point-slope form.

y - y1 = m(x - x1)

[Using the point-slope formula]

Let (x1, y1) = (-8, 10)m = -1/4

Putting the values in the above formula, we get

y - 10 = -1/4(x - (-8)) ⇒ y - 10 = -1/4(x + 8)... (2)

Step 4: Simplify the above equation to get the required equation of the line in slope-intercept form.

y - 10 = -1/4x - 2 ⇒ y = -1/4x + 8... (3)

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The length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

so by Pythagoras rule we can evaluate for the length RV by considering the following right triangles:

For ∆TVU:

13² = 5² + TV²

TV = √(13² - 5²) {make TV the subject}

TV = √(169 - 25)

TV = √144

TV = 12

For ∆TVS:

15² = 12² + SV²

SV = √(15² - 12²) {make SV the subject}

SV = √(225 - 44)

SV = √81

SV = 9

For ∆RVS:

11² = 9² + RV²

RV = √(11² - 9²) {make RV the subject}

RV = √(121 - 81)

RV = √49

RV = 6.3246

Therefore, the length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.

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Answer:

y = 12

Step-by-step explanation:

if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is

y² = 8(8 + 6 + 4) = 8 × 18 = 144 ( take square root of both sides )

y = [tex]\sqrt{144}[/tex] = 12

An Inequality is a relationship between two expressions or values that aren't equal. The relationship between n and 4 is given by the inequality n> 4.

We want to find a relation between n and 4 similar that

7 *( n/ 4)> 7

still, we get

If we now divide both sides of the former inequality by 7.

7 *( n/ 4)/ 7>7/7

n/ 4> 1

So n/ 4 must be lesser than 1.

A better way to show the relationship is to multiply both sides of the inequality by 4.

4 *( n/ 4)> 4 * 1

n> 4

So the relationship between n and 4 is that n must be lesser than 4.

In mathematics, an inequality is a relationship that results in an unstable comparison of two figures or other fine expressions. It's frequently used to compare two figures on a number line grounded on their size.

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Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.

Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.

The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.

As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.

using the formula no.

Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.

Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

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the complete question is

Write a positive or negative number to represent each change in the high temperature.

1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?

2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?

3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?

4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?

a)The probability that none of the restaurants are in violation of the health code is approximately 0.0482.

b)The probability that one of the restaurants is in violation of the health code is approximately 0.3729.

c)The probability that at least two of the restaurants are in violation of the health code is approximately 0.4681.

(a) Probability that none of the restaurants are in violation of the health code:

Let E be the event that a restaurant is in violation of the health code, and let F be the event that a restaurant is not in violation of the health code. Therefore, probability that a restaurant is in violation of the health code is:

P(E) = 0.30

,then the probability that a restaurant is not in violation of the health code is:

P(F) = 1 - P(E) = 1 - 0.30 = 0.70

The health inspector selects 9 restaurants. The probability that none of the restaurants are in violation of the health code is:

P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) = (0.70)^9 ≈ 0.0482.

Therefore, the probability that none of the restaurants are in violation of the health code is approximately 0.0482.

(b) Probability that one of the restaurants is in violation of the health code:

The health inspector selects 9 restaurants. We want to find the probability that one of the restaurants is in violation of the health code. We can use the product rule of probability for this. Let us assume that the health inspector selects the first restaurant and that it is in violation of the health code. The probability of that happening is:

P(E) = 0.30

Then the probability that the other eight restaurants are not in violation of the health code is:

P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) = (0.70)^8

Then, the health inspector could have selected the restaurant that is in violation of the health code from any of the 9 restaurants. So, we have to multiply by 9.

P(one restaurant in violation of health code) = 9 × P(E) × P(F)^8≈ 0.3729

Therefore, the probability that one of the restaurants is in violation of the health code is approximately 0.3729.

(c) Probability that at least two of the restaurants are in violation of the health code:

Let X be the random variable that denotes the number of restaurants that are in violation of the health code. Then, X can take on values 0, 1, 2, 3, ..., 9.The probability that at least two of the restaurants are in violation of the health code is the same as the probability that two or more are in violation of the health code:

P(X ≥ 2) = P(X = 2) + P(X = 3) + · · · + P(X = 9)

We can use the sum rule of probability for this.Let us calculate the probability that exactly k of the 9 restaurants are in violation of the health code:

P(X = k) = (9Ck) P(E)k P(F)9−k = (9Ck) (0.30)k (0.70)9−k

Then:P(X ≥ 2) = P(X = 2) + P(X = 3) + · · · + P(X = 9)= ∑ (9Ck) (0.30)k (0.70)9−k, where k = 2, 3, ..., 9

= 1 − [P(X = 0) + P(X = 1)]= 1 − [1 × (0.70)^9 + 9 × (0.30)(0.70)^8]≈ 0.4681

Therefore, the probability that at least two of the restaurants are in violation of the health code is approximately 0.4681.

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The initial investment (P) is 19.65205 billion dollars. The annual interest rate (r) is 1.5% expressed as a decimal, which is 0.015 and the time period (t) is 3 years. The amount of money in the investment account on December 31, 2020, will be 21.190 billion dollars. Company Y did not invest any additional money into the account between January 1, 2018, and December 31, 2020 and also Company Y earned 1.538 billion dollars in interest on this investment between January 1, 2018, and December 31, 2020.

Now to calculate the amount of money in the investment account on December 31, 2020, we can use the formula for continuous compound interest:

[tex]A = Pe^{(rt)}[/tex]

Where A is the amount of money in the account at the end of the investment period, P is the initial investment, r is the annual interest rate (APR) expressed as a decimal, and t is the time period in years.

First, let's calculate the total amount of money that Company Y plans to invest over the next three years. We know that they plan to invest 8.5% of their sales amount each year, so the total amount invested will be:

[tex]Investment = 0.085 * Sales * (1 + 1.06 + 1.06^2)[/tex]

[tex]Investment = 0.085 * 78.71 * 3.06[/tex]

[tex]Investment = 19.65205[/tex]billion dollars

So, the initial investment (P) is 19.65205 billion dollars. The annual interest rate (r) is 1.5% expressed as a decimal, which is 0.015. The time period (t) is 3 years.

Using the formula, we get:

[tex]A = Pe^{(rt)}[/tex]

[tex]A = 19.65205e^{(0.0153)}[/tex]

[tex]A = 21.190[/tex] billion dollars

Therefore, the amount of money in the investment account on December 31, 2020, will be 21.190 billion dollars.

To calculate the amount of money that Company Y invested between January 1, 2018, and December 31, 2020, we simply subtract the initial investment from the total investment amount:

Amount invested = Investment - P

Amount invested = 19.65205 - 19.65205

Amount invested = 0 billion dollars

Therefore, Company Y did not invest any additional money into the account between January 1, 2018, and December 31, 2020.

To calculate the interest earned on the investment, we simply subtract the initial investment from the amount of money in the account on December 31, 2020:

Interest earned = A - P

Interest earned = 21.190 - 19.65205

Interest earned = 1.53795 billion dollars

Therefore, Company Y earned 1.538 billion dollars in interest on this investment between January 1, 2018, and December 31, 2020.

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Consequently, C = 17.2° as by the result of the Rule of Cosines , rounded to the nearest tenth.

A geometric figure known as an angle is created by two lines that share an endpoint and are referred to as the angle's sides and vertex, respectively. The quantity of rotation required to align one side with the other side around the vertex is the angle's unit of measurement. Typically, angles are expressed as degrees or radians, where a complete rotation equals 360 degrees or 2 radians. Angles are frequently used to define the position and orientation of lines and shapes in geometry, trigonometry, and other branches of mathematics.

given

As a result of the Rule of Cosines, we have:

A2 Plus B2 - 2ab cos = c2 (C)

Adding the specified values:

c² = 26² + 29² - 2(26)(29) cos(50°)

c² = 676 + 841 - 1508 cos(50°)

c² = 1517 - 1508 cos(50°)

c ≈ √(1517 - 1508 cos(50°))

c ≈ 17.2° (rounded to the closest tenth)

Consequently, C = 17.2° as by the result of the Rule of Cosines , rounded to the nearest tenth.

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Answer:

C= 23.22

This is the answer this question.

Without specific details it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. So, based on the information we can define some data as below.

A graph in x-y axis plot is a visual representation of functions or data points. The dependent or vertical variable represented by y-axis, while the independent or horizontal variable represented by the x-axis.

Without the specific details of the performance review or the names of the employees, I cannot provide an exact answer. However, based on the information given, we can infer the following:

Person 6 : has a perfect score.

Person 3 : not achieved any of their goals.

Person 5 : excellent personality and very good job knowledge.

Person 4: more interested in hanging out at the water cooler.

Given this information, it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. We also do not have enough information to make an informed judgment about the performance of each employee. It is possible that the review could belong to any of the employees, depending on their individual scores and performance.

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Answer: So that means the answer is $112.5

Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.

YES THIS IS RIGHT!!!!

Joe aura 35 pommes.

40-5=35

Answer:

(a) Since there are 428 equally likely pages, the probability of randomly turning to page 45 is 1/428, which is approximately 0.00234 or 0.234%.

(b) There are two possible cases for an even numbered page: either the last digit is 0, 2, 4, 6, or 8, or the page number ends in 00.

For the first case, there are 5 possible digits for the units place, and each of these digits can be followed by any one of the 5 possible digits for the tens place. So there are 5x5 = 25 even numbered pages that end in a non-zero digit.

For the second case, there are 4 possible digits for the hundreds place, and each of these digits can be followed by 00. So there are 4 even numbered pages that end in 00.

Therefore, there are 25 + 4 = 29 even numbered pages in total. Since there are 428 pages in the book, the probability of randomly turning to an even numbered page is 29/428, which is approximately 0.06776 or 6.776%.

Step-by-step explanation:

(a) Оскільки існує 428 рівноймовірних сторінок, ймовірність випадкового переходу на сторінку 45 дорівнює 1/428, що становить приблизно 0,00234 або 0,234%.

(b) Існує два можливих випадки, коли сторінка має парний номер: або остання цифра 0, 2, 4, 6 або 8, або номер сторінки закінчується на 00.

У першому випадку є 5 можливих цифр для позначення одиниць, і за кожною з цих цифр може слідувати будь-яка з 5 можливих цифр для позначення десятків. Таким чином, існує 5x5 = 25 парних сторінок, які закінчуються на ненульову цифру.

У другому випадку є 4 можливі цифри для сотень, і за кожною з цих цифр може стояти 00. Отже, є 4 парні сторінки, які закінчуються на 00.

Таким чином, всього є 25 + 4 = 29 парних сторінок. Оскільки в книзі 428 сторінок, ймовірність випадкового переходу на парну сторінку дорівнює 29/428, що становить приблизно 0.06776 або 6.776%.

The area of the region of overlap between the 8-inch by 10-inch paper and the 8(1/2)-inch by 11-inch paper measures 12 square inches.

The area of the region of overlap between an 8-inch by 10-inch paper and an 8(1/2)-inch by 11-inch paper can be found in the following steps:

Step 1: Calculate the area of each paper. The area of an 8-inch by 10-inch paper is:

[tex]$$\text{Area} = \text{length} \times \text{width} = 8 \text{ in.} \times 10 \text{ in.} = 80 \text{ sq. in.}$$[/tex]

The area of an 8 1/2-inch by 11-inch paper is:

[tex]$$\text{Area} = \text{length} \times \text{width} = \left( 8 \frac{1}{2} \right) \text{ in.} \times 11 \text{ in.} = 93.5 \text{ sq. in.}$$[/tex]

Step 2: Find the horizontal and vertical lengths of the region of overlap.

The horizontal length is the length that is common to both papers, which is 8 inches.

The vertical length is the amount by which the two papers overlap, which is 8(1/2) inches - 10 inches = -1(1/2) inches. However, since the region of overlap cannot have a negative length, we take the absolute value of this result, which is 1(1/2) inches.

Step 3: Calculate the area of the region of overlap.

The area of the region of overlap is the product of the horizontal and vertical lengths:

[tex]$$\text{Area of the region of overlap} = 8 \text{ in.} \times 1 \frac{1}{2} \text{ in.} = 12 \text{ sq. in.}$$[/tex]

Therefore, the area of the region of overlap in square inches is 12 square inches.

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Answer: Quadratic (not 100% sure)

The average number of beads that the girls have is 63

Let's start by using algebra to represent the given information:

Let b be the number of beads that Sally has.

Then, Kelly has 3/4 times as many beads as Sally, which can be expressed as (3/4)b.

Also, we know that Kelly has 18 more beads than Sally, which can be expressed as (b + 18).

Putting these together, we can write the equation:

(3/4)b = b + 18

Solving for b, we get:

b = 72

So, Sally has 72 beads, and Kelly has (3/4) × 72 = 54 beads.

The average number of beads that the girls have is (72 + 54)/2 = 63 beads

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In response to the stated question, we may state that The coefficient equation  of -1.327 indicates that the amount of water in the cistern declines at an exponential rate as time passes.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

The least-squares regression line has the following equation:

2.993 - 1.327 In(Volume)* (Time)

The link between the natural logarithm of water volume and the natural logarithm of time is illustrated by this equation. The coefficient of -1.327 indicates that the amount of water in the cistern declines at an exponential rate as time passes.

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the length of the other leg is 7m and the length of the hypotenuse is 7√2 m.

In the right-angled triangle, the square of the hypotenuse side is equals to the sum of the squares of the other two sides, according to Pythagoras's Theorem. This triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Because to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

The definition yields the following as the Pythagoras Theorem formula:

Hypotenuse² = Perpendicular² + Base²

c² = a² + b²

Length of one leg=7m

Angles of triangle are 45°,45° and 90°

According to Pythagoras theorem,

x²=7²+7²

x=7√2

the length of the other leg is 7m and the length of the hypotenuse is 7√2 m.

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The force equation for the system is F = bV - bF, where F is the force of friction, V is the velocity of the object, and b is the coefficient of viscous friction.

Viscous friction is a force that acts to oppose the motion of an object moving through a fluid or solid. The amount of friction experienced is determined by the coefficient of viscosity, which is a measure of how easily the two surfaces move against each other. In this equation, bV is the force generated by the object's motion, and b

F is the opposing force of friction. Together, these two forces determine the net force acting on the object.

Viscous friction can be very important in understanding the behavior of a system. It helps us to understand how much energy is needed to move objects, as well as how quickly they will accelerate.

Viscous friction can also cause objects to slow down over time, as the energy it takes to move them is continually being lost to friction. Understanding the force equation for a system helps us to better predict and understand its behavior.

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The number of students on the bus is 40.

The first step is to form two equations that represent the information in the question:

a + b = 45 equation 1

375a + 200b = 9875 equation 2

Where:

a = number of adults in the bus

b = number of students in the bus

The elimination method would be used to determine the number of students on the bus.

Multiply equation 1 by 375

375a + 375b = 16,875 equation 3

Subtract equation 2 from equation 3

175b = 7000

Divide both sides of the equation by 175

b = 7000 / 175

b = 40

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Answer:

6.25 minutes

Step-by-step explanation:

So, if there are 96 tests being graded in 2 minutes, the average per minute (using the equation 96/2 = average) would be 48 per minute. Next you would do 300/48 to get the number of minutes that it would take to grade that amount. The answer to that would be 6.25, So it would take approximately 6.25 minutes.

Therefore, the function that matches the mosquito counts is'(w) = 8([tex]1.5^{w}[/tex]).

by the question.

To determine which function matches the mosquito counts, we can plot the given data points on a graph and see which function fits the curve. Here are the counts for the first few weeks:

Week Mosquito Count

0 8

1 20

2 50

3 125

4 312

Plotting these points on a graph with weeks on the x-axis and mosquito count on the y-axis, we get:

mosquito graph

Looking at the graph, we can see that the curve increases rapidly and seems to be exponential. This rule out option A (which is linear), leaving us with options B, C, and D.

To determine which of these options matches the data, we can try plugging in the week numbers and seeing which one gives us values close to the actual counts. We can also use a calculator or graphing technology to help us with this.

Option B gives us the following mosquito counts for the first five weeks:

Week Mosquito Count

0            8

1         19.5

2        47.25

3       114.19

4       276.32

Option C   gives us:

Week Mosquito Count

0       8

1        12

2       18

3       27

4       40.5

Option D is not a function of mosquito counts with weeks as the input variable, so we can rule it out.

Comparing the values from options B and C to the actual counts, we can see that option C is the closest match.

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Answer:

The answer is the standard error is a measure of the accuracy of the sample mean as an estimate of the population mean.

Step-by-step explanation:

The domain of discourse of the propositional function P(x) is {1,2,3,4}, by using negation, disjunction, and conjunction are:

a)  "there does not exist an x in the domain for which P(x) is false."

b) "there exists an x in the domain for which P(x) is false."

c)  "there exist exactly three x's in the domain for which P(x) is true."

d) -(E. P(x)) can be rewritten as “Every x is not P(x)”

We are given that the domain of discourse of the propositional function P(x) is {1, 2, 3, 4}. We need to rewrite each propositional function below using only negation, disjunction, and conjunction.

a) The propositional function "Vx P(x)" means "for all x in the domain, P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:

-(Ex -P(x)), which means "there does not exist an x in the domain for which P(x) is false."

b) The negation of "Vx P(x)" is "there exists an x in the domain for which P(x) is false." Using De Morgan's law again, we can rewrite this as:

Ex -P(x).

c) The propositional function "3x P(x)" means "there exist exactly three x's in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can break it down into two statements:

Using the symbols for negation, disjunction, and conjunction, we can write this as:

(Ex_1 P(x_1) ∧ Ex_2 P(x_2) ∧ Ex_3 P(x_3)) ∧ -(Ex P(x)).

d) The propositional function "-(E. P(x))" means "it is not true that there exists an x in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:

Ax -P(x),

which means "for all x in the domain, P(x) is false."

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The answers of the question number 3 and 4 are given below respectively.

A graph is a visual representation of data or mathematical relationships.

It typically involves plotting points on a coordinate plane and connecting them with lines or curves.

Graphs can help to illustrate patterns, trends, and relationships in data and make it easier to understand complex information.

3.Assuming that the sale of bracelets and necklaces are represented by the variables B and N respectively, the total sale would be represented by the mathematical statement:

Total sale = B + N

Graph of Total Sale = B + N

The x-axis represents the number of bracelets sold (B), and the y-axis represents the number of necklaces sold (N).

4.To represent Nimfa's goal of achieving a total sale of at least Php 15,000, we can use the inequality:

Total sale ≥ Php 15,000

or, using the expression from the previous question:

2B + N ≥ Php 15,000

Graph of Total Sale ≥ Php 15,000

The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000. Any point above the plane is a valid combination of sales that meet Nimfa's goal.

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3. The x-axis represents the number of bracelets sold (B), and the y-axis represents the number of necklaces sold (N).

4. The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000.

A graph is a visual representation of data or mathematical relationships.

It typically involves plotting points on a coordinate plane and connecting them with lines or curves.

Graphs can help to illustrate patterns, trends, and relationships in data and make it easier to understand complex information.

3.Assuming that the sale of bracelets and necklaces are represented by the variables B and N respectively, the total sale would be represented by the mathematical statement:

Total sale = B + N

Graph of Total Sale = B + N

4.To represent Nimfa's goal of achieving a total sale of at least Php 15,000, we can use the inequality:

Total sale ≥ Php 15,000

or, using the expression from the previous question:

2B + N ≥ Php 15,000

Graph of Total Sale ≥ Php 15,000

The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000. Any point above the plane is a valid combination of sales that meet Nimfa's goal.

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The car sticker information indicates a highway average of 27 mpg, while the sample mean's standard deviation is around 1.455 mpg. The mean estimate's margin of error is roughly 3.06 mpg.

The simplest approach to figure out your gas mileage is to simply divide the distance driven by the quantity of petrol your car required to fill up. That amounts to kilometers traveled divided by petrol consumed.

a) The formula for the standard deviation of the sample mean, σx¯, is:

σx¯ = σ / sqrt(n)

where σ is the standard deviation of the population, and n is the sample size. In this case, σ = 6.5 mpg and n = 20. So,

σx¯ = 6.5 / sqrt(20) ≈ 1.455 mpg

b) To find the margin of error for the mean estimate at a 95% confidence level, we can use the following formula:

Margin of error = z* (σx¯)

where z* is the critical value for a 95% confidence interval, which is 1.96.

Therefore, the margin of error = 1.96 * 1.454 = 2.85 mpg.

c) To find the 95% confidence interval for the mean highway mpg for this vehicle, we can use the following formula:

Confidence interval = x¯ ± Margin of error

where x¯ is the sample mean, which can be calculated by adding up all the mpg readings and dividing by the sample size:

x¯ = (37.2+21.0+17.4+29.2+7.4+27.0+36.9+38.8+35.3+32.3+19.0+26.1+25.8+41.4+34.4+32.5+26.5+28.2+22.1) / 20

= 29.231 mpg

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Answer:

0.33

Step-by-step explanation:

To solve this, you first write the problem as an algebra equation as follows: 3x + 4 = 5

Then you solve the equation by subtracting 4 from both sides, and then divide both sides by 3. Here is the math to illustrate better:

3x + 4 = 5

3x + 4 - 4 = 5 - 4

3x = 1

3x/3 = 1/3

x = 0.33

Answer = 0.33

The height of the nearby lemon tree is 8 feet using the property of similar triangles.

Triangles that are similar to one another in shape but differ in size are called similar triangles. Their respective sides are proportional to one another, and their corresponding angles are equal. The ratio of the corresponding sides of two triangles that are comparable is constant across all pairs of corresponding sides. Problems involving unknown lengths or heights in comparable forms can be resolved using this attribute.

The given situation represent two proportional triangles.

We know that the ratio of lengths of similar triangles are equal thus,

height of plum tree / length of plum tree's shadow = height of lemon tree / length of lemon tree's shadow

Substituting the values we have:

12 / 9 = height of lemon tree / 6

Using cross multiplication:

height of lemon tree = 12 * 6 / 9 = 8 feet

Hence, the height of the nearby lemon tree is 8 feet using the property of similar triangles.

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Answer: 2

Step-by-step explanation:

If there are three times as many students when there are 6 students you do 6 divided by three to give you two.

The resulting double-line graph should show the sales data for desktop and laptop computers over the five days, with a line for each type of computer.

A double-line graph is a graph that displays two sets of data on the same graph, using two lines to show how each set of data changes over time or some other variable.

To create a double-line graph of the sales data for desktop and laptop computers over five days, follow these steps:

Draw a graph with two perpendicular axes, the horizontal axis (x-axis) representing the days, and the vertical axis (y-axis) representing the number of computers sold.

Label the horizontal axis with the days from Day 1 to Day 5.

Label the vertical axis with the heading "Number of Computers Sold".

Plot the data points for desktop computer sales. For Day 1, plot a point at (1, 4), for Day 2 plot a point at (2, 1), for Day 3 plot a point at (3, 2), for Day 4 plot a point at (4, 5), and for Day 5 plot a point at (5, 1).

Connect the data points for desktop computer sales with a line.

Plot the data points for laptop computer sales. For Day 1, plot a point at (1, 5), for Day 2 plot a point at (2, 2), for Day 3 plot a point at (3, 3), for Day 4 plot a point at (4, 7), and for Day 5 plot a point at (5, 3).

Connect the data points for laptop computer sales with a line.

Use a different color or style for the line representing desktop sales and the line representing laptop sales.

Add a legend to the graph to indicate which line corresponds to desktop sales and which corresponds to laptop sales.

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If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.

To do this, we can set the coefficients of x and y in the two equations equal to each other:

6 - 4m = 2k(2m - 1)

2n - 7 = 3k

Simplifying these equations, we get:

8m - 6 = 4km

2n - 7 = 3k

We can solve the first equation for k:

k = (8m - 6)/(4m)

Substituting this into the second equation and solving for n, we get:

n = (16m - 29)/(8m - 12)

Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.

We find that the expressions for k and n are the same for m = 3/2.

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Complete Question:

Determine the values of m and n so that the following system of linear equations have infinite number of solutions:

(2m−1)x+3y−5=0

3x+(n−1)y−2=0