Suppose the current cost of gasoline is ​$2.93 per gallon. Find the current price index​ number, using the 1975 price of 56.7 cents as the reference value.

Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.

What is the slope?

In mathematics, the slope is a measure of the steepness of a line.

The solution provided involves three steps to find the slope of the line that passes through two points: (-2, 8) and (4, 6).

Step 1 involves finding the change in y-coordinates, which is the difference between the y-coordinate of the second point and the y-coordinate of the first point. In this case, the second point has a y-coordinate of 6 and the first point has a y-coordinate of 8.

Therefore, the change in y-coordinates is 6 - 8 = -2.

Step 2 involves finding the change in x-coordinates, which is the difference between the x-coordinate of the second point and the x-coordinate of the first point. In this case, the second point has an x-coordinate of 4 and the first point has an x-coordinate of -2.

Therefore, the change in x-coordinates is 4 - (-2) = 6.

Step 3 involves dividing the change in y-coordinates by the change in x-coordinates to find the slope of the line. In this case, the change in y-coordinates is -2 and the change in x-coordinates is 6, so the slope is -2/6 or -1/3.

Since all the steps are correct and properly executed, there is no error.

Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.

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If we cοnsider (x, y) tο be a pοint οn the unit circle, we get:

[tex]x^2 + y^2 = 1[/tex] (because the pοint is οn the unit circle) (since the pοint is οn the unit circle)

All real numbers must be determined in such a way that:

tan(s) = y / x

The trigοnοmetric identity can be applied:

Tan is equal tο Sin / Cοs.

We thus have:

Y/X = Tan(S), Sin(S), and Cοs (s)

Using the identity cοs(s) + sin(s) = 1, we square bοth sides tο οbtain:

[tex](y/x)^2 = sin^2(s) / cos^2(s) = 1 - cos^2(s)[/tex]

Rearranging and applying the equatiοn x2 + y2 = 1 results in:

cοs2(s) equals 1 - (y/x).

[tex]^2 = x^2[/tex]

Given that (x, y) is in the first οr fοurth quadrant and that x is pοsitive, we can take the square rοοt tο get the fοllοwing result:

cοs(s) = ± x

Sο, s is determined by:

S equals arccοs(x) + n, where n is any pοsitive integer.

The range οf x's value is limited tο [-1, 1] because it is οn the unit circle. As a result, the values οf s are prοvided by:

S = arccοs(x) + n, where n is any pοsitive integer and x is within the range [-1, 1].

The pοssible values οf s in exact radian measure in [0, 2] are as fοllοws:

S = arccοs(-1) + = S = arccοs(1) = 0

S is equal tο arccοs(0) + n + (n + 1/2)

where any integer n is used.

As n can be any integer, the pοssible pοssibilities οf s are s = 0,, and (n + 1/2).

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Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

Step-by-step explanation:

x = weeks

Yours    75 + 5x

Friend's 30 + 10x

When are they equal ?

75 + 5x     =     30 + 10x

45 = 5x

x = 9 weeks

Instead of 2.00 as mentioned in the question, the semester GPA is 1.38. Please double-check your calculations or provide more details if you made an error when reporting your grades or computing your GPA.

Students must devote approximately 135 hours (45 x 3) of class, instructional, and independent time to a three credit unit course. Students who enroll in a course for four credit hours must dedicate around 180 (45 x 4) hours to it, split between in-class and out-of-class work.

You must first translate each letter grade using the common 4.0 scale into its equivalent numerical number before you can determine your semester GPA:

A = 4.0

B = 3.0

C = 2.0

D = 1.0

F = 0.0

E = 0.0 (equivalent to F)

Then, you can use the formula:

(Total grade points) / GPA (total credit hours)

Using this formula, we can calculate your semester GPA as follows:

FYE 105: F (0.0) x 3 credit hours = 0.0 grade points

MAT 150: E (0.0) x 3 credit hours = 0.0 grade points

ENG 101: D (1.0) x 3 credit hours = 3.0 grade points

BIO 112: A (4.0) x 3 credit hours = 12.0 grade points

BIO 113: B (3.0) x 1 credit hour = 3.0 grade points

Total grade points = 0.0 + 0.0 + 3.0 + 12.0 + 3.0 = 18.0

Total credits earned is 13 (3 + 3 + 3 + 3 + 1)

GPA = 18.0 / 13 = 1.3846

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Step-by-step explanation:

See Venn diagram below

Using ratios and proportionality, we can find that the length of the missing part is 18 units.

By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.

The part to whole ratio is one, and the part-to-part ratio is another category that exists. The part-to-part ratio illustrates the relationship between two separate entities or groupings.

Here,

Let the missing length be = x.

Given,

The upper segment is 24.

One part of it is 16.

So, the other part is = 24 - 16 = 8

Now as per the ratios,

16/36 = 8/x

⇒ x = 8 × 36/16

⇒ x = 18 units.

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Answer:

11

Step-by-step explanation:

[tex]61 {}^{2} - {60 }^{2} = 121[/tex]

[tex] \sqrt{121} = 11[/tex]

The relation between a point and a circle is relative to the location of the point relative to the circumference of the circle, which can be inside, at the circumference, or outside.

The relationship between a point and a circle can be described as follows:

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Answer:

D. 7/5

Step-by-step explanation:

In right triangle ABC with right angle C,

sinA = 4/5 = cosB

cosA = 3/5 = sinB

sinB + cosB = 3/5 + 4/5 = 7/5

Sure! The general term of a sequence is a formula which describes the nth term of the sequence. In this case, the pattern is that each term is increased by 3 when compared to the previous term. This pattern can be expressed as a formula - an=a1+(n-1)d, where a1 is the first term, n is the term number and d is the common difference.

For the sequence given -2,1,4,7

a1=-2

n=4

d=3

Substituting these values in the formula will give us the general term of the sequence an = -2 + 3(n-1)

Hence, the general term of the sequence -2,1,4,7 is an = -2 + 3(n-1).

If d is not a prime number and n^2 is divisible by d, it does not necessarily mean that n is also divisible by d, example is d = 6 and n = 3, where n^2 = 9 is divisible by 6, but n = 3 is not divisible by 6.

A prime number is a positive integer greater than 1 that has exactly two distinct factors: 1 and itself. For example, 2, 3, 5, 7, 11, 13, and 17 are all prime numbers.

If a number d is not prime, then it has at least one factor other than 1 and itself. Let's assume that d is not prime, and let p be a factor of d such that p is not equal to 1 or d. Then, by definition, p divides d evenly with no remainder.

Consider the case where d = 6 and n = 3.

Here, d is not a prime number, and n^2 = 9, which is divisible by d since 9 is a multiple of 6. However, n = 3 is not divisible by d = 6, as 6 does not divide 3 evenly.

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Answer:

The formula to calculate the amount of loan with flat rate interest is:

Amount = Principal + (Principal x Rate x Time)

Where,

Principal = the amount of loan

Rate = the interest rate per year

Time = the time period in years

Given,

Principal = K40,000.00

Rate = 9% per year

Time = 2.5 years

Substituting the values in the formula, we get:

Amount = K40,000.00 + (K40,000.00 x 0.09 x 2.5)

Amount = K40,000.00 + K9,000.00

Amount = K49,000.00

Therefore, the amount he will pay the bank is K49,000.00.

Answer:

7:42

Explanation: Since, the ratio was 4:24, it equals to 1:6, and the only one with a factor of 6 for the second number is C

Here is the stem and leaf plot:

5  4

6   0, 1, 2, 2

7    1, 2, 4, 6, 8

8    2, 3, 4,  6, 7,

9   0, 2, 5, 5, 9

The range is 45.

A stem-and-leaf plot is a table that is used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. The stem is the tens digit and the leaf is the units digit. For example, in the number 54, 5 is the stem and 4 is the leaf.

Range is used to measure the variation of a dataset by finding the difference between the highest number and the lowest number.

Range = highest value - lowest value

99 - 54 = 45

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Answer:

103%

Step-by-step explanation:

1.03/1 x 100% = 103%

To convert the decimal 1.03 into a percentage, you multiply it by 100 which gives you 103%, so 1.03 is equal to 103%.

To express 1.03 as a percentage, we need to multiply the decimal by 100.

This is because the word percent in terms of mathematics means 'per hundred'. So, 1.03 multiplied by 100 equals 103.

Hence, 1.03 expressed as a percentage is 103%.

Rewrite your decimal as a fraction with a denominator of 100 to change it into a percentage.

For example, 1.03 can be written as 103/100 which translates into 103% in percentage format.

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The equation representing the money or balance (y) in your savings account any time (x) is y = z - 25x.

An equation is an algebraic statement showing the equality of two or more mathematical expressions.

Mathematical expressions combine variables with numbers, values, and constants without the equal symbol (=).

The monthly withdrawals = $25

The number of months (x) = 4

Account balance (y) = $75

Let z = the initial balance in the savings account.

y = z - 25x

75 = z - 25x

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the largest integer [tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]

To find the largest integer[tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$[/tex], we need to count how many factors of 3 are in the product of the odd integers from 1 to 99.

One way to do this is to factor each odd integer into its prime factors and count how many factors of 3 are present. However, this would be quite tedious and time-consuming.

A quicker approach is to use the fact that every third odd integer is a multiple of 3. Thus, we can count how many multiples of 3 are present in the product of the odd integers from 1 to 99.

Let [tex]$m$[/tex] be the number of multiples of 3 in the range from 1 to 99. Then we have:

[tex]m = \left\lfloor \frac{99}{3} \right\rfloor = 33[/tex]

This is because there are 33 multiples of 3 in the range from 1 to 99 (namely, 3, 6, 9, ..., 96, 99).

Each multiple of 3 contributes at least one factor of 3 to the product of the odd integers. However, some multiples of 3 contribute two or more factors of 3, depending on how many factors of 3 they contain.

To count how many multiples of 3 contribute two or more factors of 3, we need to count how many multiples of 9, 27, and 81 are present in the range from 1 to 99.

There are [tex]$\left\lfloor \frac{99}{9} \right\rfloor = 11$[/tex]multiples of 9, namely 9, 18, 27, ..., 81, 90, 99. Each multiple of 9 contributes at least two factors of 3 to the product of the odd integers.

There are [tex]$\left\lfloor \frac{99}{27} \right\rfloor = 3$[/tex] multiples of 27, namely 27, 54, 81. Each multiple of 27 contributes at least three factors of 3 to the product of the odd integers.

There is only one multiple of 81 in the range from 1 to 99, namely 81, which contributes at least four factors of 3 to the product of the odd integers.

Thus, the total number of factors of 3 in the product of the odd integers from 1 to 99 is:

[tex]n = m + 2\times\text{number of multiples of 9} + 3\times\text{number of multiples of 27} + 4\times\text{number of multiples of 81}[/tex]

[tex]n = 33 + 2\times 11 + 3\times 3 + 4\times 1 = 62[/tex]

Therefore, [tex]the $ largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]

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a) The probability the sum is 6 is equals to the 77/144.

b) The probability event that sum is 6 in case of both dice are 6 -sided is equals to the 5/36.

c) The probability event that sum is 6 in case of both dice are 4 -sided is equals to the 3/16.

d) The probability event that sum is 6 in case of one die is 4 -sided and one is 6 sided is equals to 5/24.

There are five fair dice in my pocket, three are 4-sided and two are 6-sided. Randomly select two of the dice, roll them, and record the sum. We have to determine the probabilities for different events. First, When two six-sided dice are rolled, total possible outcomes = 36

= {1,2,3,4,5,6}{1,2,3,4,5,6}

Similarly, When two four-sided dice are rolled, total possible outcomes = 16 = {1,2,3,4}{1,2,3,4}

Also, when one 4-sided and othe 6-sided faire dice are rolled, total possible outcomes = 24 = {1,2,3,4 } {1,2,3,4,5,6}

a) Let the event for sum is 6 be 'E'. The probability the sum is 6, P(E) = 5/36 + 3/16 + 5/24 = ( 20 + 27 + 30)/144

= 77/144

b) The probability that sum of the dice is 6 for both dice are 6 -sided = 5/36

c) Possible outcomes of occurrence of event E in case of both dice are 4 -sided = 3

The probability of occurrence of event E in case of both dice are 4 -sided, P(E)

= 3/16

d) Possible outcomes of occurrence of event E in case of one die is 4 -sided and one is 6 sided = 5

The probability one die is 4 -sided and one is 6 sided = 5/24

Hence, required probability is 5/24.

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The area of the living room is 24.7 m², and the area of the game room is 37.05 m².

Area is the measure of the two-dimensional space occupied by a figure or an object. It is usually expressed in square units such as cm2, m2, or in2. It is used to measure the size of a figure or object, and can also be used to calculate the amount of material required for a project.

The area of a living room measuring 4.75 m by 5.2 m can be calculated using the formula A = l × w, where A is the area, l is the length and w is the width. In this case, A = 4.75 m × 5.2 m = 24.7 m².

To calculate the area of the game room, we must multiply the area of the living room by 1.5. Therefore, the area of the game room is 1.5 × 24.7 m² = 37.05 m².

The area of the living room is 24.7 m², and the area of the game room is 37.05 m².

The area of a room can be used to determine how much furniture can fit in the room or how much floor space is available for activities. Knowing the area of a room is also important for calculating the cost of painting, wallpapering, carpeting, and other flooring materials.

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Answer:

6188 ways

Step-by-step explanation:

there ate 5 objects to be choosen and there is no replacement of the object therefore you got

17 choices for the first selection of the object and 16 objects for the selection of the second object and so on until you get 13 objects for the last selection

totally you have 5 selections also arrangement does not matter there fore you have 17!/12!5! which is 6188

note we used 5! cause there are 5 placed objects and 12! are unplaced objects

note

that you have used one so you have to deduct one every time you use one

According to the given information, the missing side measure is 14.

What is triangle?

A triangle is a polygon with three sides, three angles, and three vertices. It is the simplest polygon and the fundamental shape used in geometry. A triangle can be classified based on the length of its sides and the measure of its angles.

To find the missing side measure, we can set up a proportion between the corresponding sides of the two similar triangles:

(x + 5) / x = 9.5 / 7

We can then solve for x by cross-multiplying:

7(x + 5) = 9.5x

7x + 35 = 9.5x

35 = 2.5x

x = 14

Therefore, the missing side measure is 14.

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Answer:

The total labor charges for the job are P3,500.

Step-by-step explanation:

To find the total labor charges for a job that takes 2 1/2 hours, we need to look at the labor charges for each hour and a half-hour fraction and add them up.

For the first hour, the charges are P1,200. For the second hour, the charges are P1,400. For the third hour (the half-hour fraction), the charges are P1,800 / 2 = P900.

So, the total labor charges for 2 1/2 hours of work are

P1,200 + P1,400 + P900 = P3,500

Therefore, the total labor charges for the job are P3,500.

Therefore, the answers are: (i) ZADB = 48.5 degrees, and (ii) ZEAO = 54 degrees.

An angle is a geometric concept that describes the amount of rotation between two intersecting lines or planes. It is defined as the figure formed by two rays with a common endpoint, called the vertex. The two rays are called the sides of the angle, and they can be measured in degrees or radians.

In the degree measurement system, a full rotation is 360 degrees, and an angle that is one quarter of a rotation (90 degrees) is called a right angle. Angles that are less than 90 degrees are called acute angles, while angles greater than 90 degrees but less than 180 degrees are called obtuse angles. An angle that measures exactly 180 degrees is called a straight angle, and an angle that measures greater than 180 degrees, but less than 360 degrees is called a reflex angle.

by the question.

ZOAB + ZEDA = 32 + 15 = 47 degrees. Since these two angles are opposite each other, they must add up to 180 degrees (straight angle) and therefore, ZAOB + ZEDC = 180 - 47 = 133 degrees.

Angle D is given as 37 degrees, and since ZEDC is a straight line, ZEDD = 180 - 37 = 143 degrees.

ZADB = ZAOB + ZOAB + BAD. Since ZAOB + ZOAB = 180 - ZEDC = 180 - 133 = 47 degrees, we have ZADB + BAD = 37 + 47 = 84 degrees. Also, BAD is an exterior angle of triangle ABD, so it is equal to the sum of the two opposite interior angles, which are ZADB and ABD. Therefore, ZADB + ABD + BAD = 180 degrees. Substituting the value of BAD and simplifying, we get ZADB = 48.5 degrees.

ZEAO = ZEDC - ZEDA - ZOAD. We already know ZEDC and ZEDA, so we need to find ZOAD. Since ZOAB and ZOAD are opposite each other, they must add up to 180 degrees. Also, ZOAB is equal to half the central angle ZODB (since it subtends the same arc), which is equal to 2ZOAD (since it is an inscribed angle subtended by the same arc). Therefore, we have ZOAB + ZOAD = 180 and ZOAB = ZOAD/2. Substituting the value of ZOAB from the given information, we get ZOAD = 64 degrees. Substituting all the values, we get ZEAO = 54 degrees.

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The probability that X takes the value 1 is 1/4 and the probability that X takes the value 2 is 1/12.

The given CDF of a random variable X is F(X)=-*- on the support of X, where the support of X is x = 1,2,3,... The task is to determine P(X = 1) and P(X = 2).

To find P(X = 1), we need to find the probability that X takes the value 1. From the given CDF, we can see that F(1) = 1/4. Therefore, P(X = 1) = F(1) - F(1-) = 1/4 - 0 = 1/4.

To find P(X = 2), we need to find the probability that X takes the value 2. From the given CDF, we can see that F(2) = 7/12. Therefore, P(X = 2) = F(2) - F(2-) = 7/12 - 1/2 = 1/12.

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Question:-

The CDF Of A Random Variable X Is Given The Function F(X)=-*- On The Support Of X, Where The Support Of X Is X = 1,2,3,... Determine P(X = 1) And P(X = 2). 3x + X

Answer:

B. 2.1

Step-by-step explanation:

If you draw a line from C to intersect AB perpendicularly at point D so we have 2 right triangles ACD and BCD.

For △ACD, AC is hypotenuse so sinA = CD/AC

=> CD = 5 x sin(20) = 5 x 0.342 = 1.71

then we have AB = AD + BD

Pythagorean theorem: c^2 = a^2 + b^2

for △ACD, 5^2 = 1.71^2 + AD^2

AD^2 = 5^2 - 1.71^2 = 22.0759

AD = 4.70

BD = AB - AD = 6 - 4.70 = 1.30

for △BCD, BC is hypotenuse

BC^2 = BD^2 + CD^2 = 1.30^2 + 1.71^2 = 4.61

BC = √4.61 = 2.1

The number of lionfish after 6 years will be 85,609. The recursive equation for [tex]f(n)[/tex] will be [tex]f(n) = 4242.42(1.65)^n - 1300n[/tex].

Consider the function:

[tex]y = a (1 \pm r)^x[/tex]

Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

lionfish are considered an invasive species, with an annual growth rate of 65%.

Then the equation will be

[tex]f(n) = P(1.65)^n[/tex]

[tex]\text{P = initial population}[/tex]

A scientist estimates there are 7,000 lionfish in a certain bay after the first year.

[tex]7000 = P(1.65)[/tex]

    [tex]P = 4242.42[/tex]

Then the equation will be

[tex]f(n) = 4242.42(1.65)^n[/tex]

The number of lionfish after 6 years will be

[tex]f(n) = 4242.42(1.65)^6[/tex]

[tex]f(n) = 85608.58[/tex]

[tex]f(n) \cong 85,609[/tex]

If scientists remove 1,300 fish per year from the bay after the first year.

Then the recursive equation for f(n) will be

[tex]f(n) = 4242.42(1.65)^n - 1300n[/tex]

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Answer: C

Step-by-step explanation:

The correct answer is C.

The slope of the line represents the hourly wage, so Hunter's wage is $35 an hour, as given in option A and B. However, the y-intercept of the line represents the starting pay or the pay for zero hours worked. In this case, the y-intercept is 25, which means Hunter received $25 even if he did not work any hours. Hence, option C is correct as it states that Hunter's wage is $25 an hour, but it appears that he received no signing bonus.

The point of intersection of the two lines is (-3.4, -1.2).

Step 1: The slope of a line passing through two points (x1,y1) and (x2,y2) can be found using the formula:

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

Using this formula, we can find the slope of the first line:

m1 = (−2−3)/(-5 -5) = −5/(-10) = 1/2

And the slope of the second line:

m2 = (−4−4)/(2 -(-6)) = -8/4 = -2

Step 2: Find the y-intercept of each line

The y-intercept of a line in slope-intercept form (y = mx + b) is the value of y when x=0. We can use one of the two given points on each line to find the y-intercept:

For the first line passing through points (5,3) and (−5,−2):

y = mx + b

3 = (1/2)(5) + b

b = 3 - 5/2

b = 1/2

So the first line can be written as y = 1/2x + 1/2

For the second line passing through points (−6,4) and (2,−4):

y = mx + b

4 = (-2)(−6) + b

b = 4 - 12

b = -8

So the second line can be written as y = -2x - 8

Step 3: Each line in slope-intercept form (y = mx + b):

First line: y = 1/2x + 1/2

Second line: y = -2x - 8

Step 4: To find the point of intersection of the two lines, we need to solve the system of equations. We can solve for x by setting the two right-hand sides equal to each other:

1/2x + 1/2 = -2x - 8

(x + 1)/2 = -2x - 8

x + 1 = -4x - 16

5x = -16 - 1

5x = -17

x = -17/5

x = -3.4

Now that we know x, we can find y by substituting x=10 into one of the two equations:

y = -2x - 8

y = -2(-3.4) - 8

y = - 1.2

Thus, the point of intersection of the two lines is (-3.4, -1.2).

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