In 1992, Jason bought a gallon of gas for $1.23. Yesterday, he bought a gallon of gas for $2.17. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent. A. 23.6% B. 56.7% C. 76.4% D. 43.3%

Explanation:

The w/4 term is the same as (1/4)w or 0.25w since 1/4 = 0.25

Because a variable is attached to this term, it is not constant. The same can be said about the -7z term as well.

The 12.5 is constant. It never changes. It will always be 12.5 no matter what the other variable terms change to.

For example, if w = 12, then the term w/4 becomes 12/4 = 3. Or if w = 24, then w/4 = 24/4 = 6 is the new value. This shows that term changing depending on the input variable.

Answer:

  -x⁵ +3x² +3x +C

Step-by-step explanation:

You want the indefinite integral of (-5x⁴ +6x +3).

The power rule for integration is the reverse of the power rule for derivatives.

  [tex]\begin{array}{ll}\text{Derivative:}&\dfrac{d(x^n)}{dx}=n\cdot x^{n-1}\\\\\text{Integral:}&\displaystyle\int {x^n}\,dx=\dfrac{x^{n+1}}{n+1}\end{array}[/tex]

An indefinite integral represents a family of functions, each with the same derivative. In general, they may differ by a constant. That constant is necessary to signify the functions that will have the given expression as their derivative.

  [tex]\displaystyle\int {(-5x^4+6x+3)}\,dx=-5\dfrac{x^{4+1}}{4+1}+6\dfrac{x^{1+1}}{1+1}+3\dfrac{x^{0+1}}{0+1}=\boxed{-x^5+3x^2+3x+C}[/tex]

Answer:

2(1/2)(8)(15) + 17(2) + 8(2) + 15(2)

= 200 cm^2

The circle graph would be the best graphical representation for the given scenario as it effectively shows the proportion of students who preferred each subject.

For the given scenario where the teacher gathered data from a random sample of 100 students in a particular school and wants to represent the preferred subject of the students, the most appropriate graphical representation would be a circle graph or a pie chart.

A circle graph is a circular chart that is divided into sectors, where each sector represents a portion of the whole.

In this case, each sector can represent the percentage or number of students who preferred a particular subject. The circle graph is suitable when we want to show the proportion of different categories or data that add up to a whole.

On the other hand, a stem-and-leaf plot, histogram, and box plot are usually used to represent quantitative data, such as measures of central tendency (mean, median, mode), range, and distribution.

They are not ideal for categorical data like the preferred subject of students.

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The circle graph that correctly represents the data in the table is that with:  A. four sections, labeled turkey 30 percent, ham 20 percent, chicken 35 percent, and vegetarian 15 percent correctly represents the data in the table.

To find the percentage for each type of sandwich, we can divide the number of customers who ordered that sandwich by the total number of customers (100) and multiply by 100.

Using the data given in the table, we get:

Turkey: 30/100 x 100% = 30%

Ham: 20/100 x 100% = 20%

Chicken: 35/100 x 100% = 35%

Vegetarian: 15/100 x 100% = 15%

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The solution set for this equation S^2-11s can be expressed as 0, 11.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on. The purpose of an equation is to find the value(s) of the variable(s) that make the equation true.

Given that S^2-11s, which can be written as S^2-11s = 0 We can factor the expression on the left-hand side to get:

S(S-11) = 0

Then this  equation is satisfied when either S = 0 or S-11 = 0. Thus, the solution set is: S = {0, 11}

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Once you have information with two quantitative factors, x, and y, and you watch a common slant that changes heading, one good method to decide in case there's a relationship between x and y and to form a show that permits you to anticipate the anticipated esteem of y based on x is to utilize polynomial regression.

Polynomial relapse may be a sort of relapse investigation in which the relationship between the free variable (x) and the dependent variable (y) is modeled as an nth-degree polynomial. By fitting a polynomial work to the information, you'll be able to capture the common drift of the information even if it changes course and utilizes it. to foresee the anticipated esteem of y based on a given esteem of x.

polynomial relapse can be a valuable method to analyze and show information with a changing drift and give experiences into the relationship between x and y. 

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Using a system of equations, the number of bracelets made and the number of necklaces made are:

A system of equations is two or more equations that can be solved simultaneously or at the same time.

Simultaneous equations can be solved concurrently.

Quantity of gold in each bracelet = 6 grams

Quantity of gold in each necklace = 24 grams

The total number of bracelets and necklaces made = 16

The total quantity of gold used in making the 16 pieces = 258 grams

Let the number of bracelets made = x

Let the number of necklaces made = y

x + y = 16 ...Equation 1

6x + 24y = 258 ...Equation 2

Multiply Equation 1 by 6:

6x + 6y = 96 ...Equation 3

Subtract Equation 3 from Equation 2:

6x + 24y = 258

-

6x + 6y = 96

18y = 162

y = 9

x = 7 (16 - 9)

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The type of error that could have occurred in this scenario is a Type II error. A Type II error occurs when the null hypothesis is not rejected, even though it is false.

In this case, the null hypothesis is that the proportion of defective bulbs in the shipment is greater than or equal to 5%. By not rejecting this null hypothesis, the company is accepting the possibility that the shipment has a high proportion of defective bulbs, when in reality it does not. This can lead to significant costs for the company, such as the cost of returning the shipment or the cost of replacing defective bulbs in the future.

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So, Lena sent 24 messages, Alan sent 32 messages, and Bill sent 48 messages.

Let's denote the number of messages Lena, Alan, and Bill sent as L, A, and B, respectively. We are given the following information:

L + A + B = 104 (Total messages)

L = A - 8 (Lena sent 8 fewer messages than Alan)

B = 2L (Bill sent 2 times as many messages as Lena)

Now, we'll use the second equation to express A in terms of L:

A = L + 8

Next, substitute the expressions for A and B from equations 2 and 3 into equation 1:

L + (L + 8) + 2L = 104

Combine like terms:

4L + 8 = 104

Subtract 8 from both sides:

4L = 96

Divide by 4:

L = 24

Now that we have the number of messages Lena sent, we can find the number of messages Alan and Bill sent:

A = L + 8 = 24 + 8 = 32

B = 2L = 2 * 24 = 48

Answer:

a) m || n

b) p || q, and m must be perpendicular to both p and q.

c) p || q

d) p || q

e) m || n and p || q

Answer:

Step-by-step explanation:

angle L is 106 degrees

x= 2

angle LMK is 37 degrees

its equal, you can check by adding up all the angles to 360 degrees

The Surface Area of wooden box is 432 inch².

We have,

length = 12 inch

width = 8 inch

Height = 6 inch

So, Surface Area of wooden box

= 2 (lw + wh + lh)

= 2 (96 + 48 + 72)

= 2 x 216

= 432 inch²

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Answer:

Yes

Step-by-step explanation:

The definition of dimension is Length, Width, and Height so if he doubles the dimensions it will be double. The volume is 630.

The two consecutive digits whose product is 132 are equals to 11 and 12.

Product of two consecutive digits = 132

Let us consider that the two consecutive digits are y and y+1.

Then we can write the expression as,

⇒y × ( y + 1 ) = 132

Expanding the left side of the expression, we get,

⇒ y² + y = 132

Rearranging the values and solving for y, we get,

⇒ y² + y - 132 = 0

Factorize this quadratic equation to get the value of y we have,

⇒ y² + 12y - 11y - 132 = 0

⇒ y( y + 12 ) -11 ( y + 12 ) = 0

⇒ ( y + 12)(y - 11) = 0

This implies,

The two possible values of y are -12 and 11.

However, choose the positive value of y .

Since we are dealing with digits.

Thus, y = 11, and the consecutive digits are 11 and 12.

Therefore, the two consecutive digits are 11 and 12, and their product is indeed 132.

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The given question is incomplete, I answer the question in general according to my knowledge:

The product of two consecutive digit is equal to 132 . What are the numbers?

Given the above conditions in the word problem above, x is also equal to 6.5°.

The angle x is the angle between this perpendicular line and the Earth's surface. It is also equal to the angle between the tangent line and the horizontal axis.

Since the reentry angle is 6.5°, we know that the tangent line makes an angle of 6.5° with the horizontal axis. We also know that the tangent line and the perpendicular line form a right angle, so the angle between the perpendicular line and the horizontal axis is 90° - 6.5° = 83.5°.

Finally, we can subtract this angle from 90° to find x:

x = 90° - 83.5° = 6.5°

Therefore, x is also equal to 6.5°.

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BMED is a trapezoid and OD is equals to BD/2. Proof of these is given below.

It should be noted that to prove that BMED is a trapezoid, we need to show that either BM || ED or BM || DE. We will show that BM || DE.

Since O is the midpoint of AM, we have OA = OM, and thus triangle ODM is isosceles. Therefore, OD = DM.

Also, since E is the midpoint of DC, we have DE || AB (because AB is also a mid-segment of triangle ADC). Therefore, angle ADE = angle ABC.

Using the fact that angles in a triangle add up to 180 degrees, we have:

angle EDC + angle ADE + angle CED = 180 degrees

Substituting angle ADE = angle ABC, we get:

angle EDC + angle ABC + angle CED = 180 degrees

But angle CED = angle BCD (because they are alternate interior angles formed by transversal BD cutting parallel lines DC and AB). Therefore:

angle EDC + angle ABC + angle BCD = 180 degrees

This means that angles BCD, ABC, and EDC are all on the same line, and thus angle BCD + angle ABC = 180 degrees.

Now, using the fact that angles in a triangle add up to 180 degrees, we have:

angle BAC + angle ABC + angle ACB = 180 degrees

Substituting angle BCD + angle ABC = 180 degrees, we get:

angle BAC + angle BCD + angle ACB = 180 degrees

Since triangle BCD is isosceles (because BD is an angle bisector), we have angle BCD = angle CBD. Therefore:

angle BAC + angle CBD + angle ACB = 180 degrees

But angle ACD = angle ACB + angle CBD, so:

angle BAC + angle ACD = 180 degrees

This means that triangle ABC is similar to triangle ACD.

Now, since BM is a median of triangle ABC, we have:

BM = 1/2 AC

But triangle ADC is similar to triangle ABC, so:

AC = 2 AD

Therefore:

BM = AC/2 = AD

So we have BM || DE, and BM = DE, which means that BMED is a trapezoid.

2. To prove that D is the midpoint of AE, we will use the fact that BMED is a trapezoid. Since BM || DE, we have:

BD/DM = BE/EM

But DM = OD (since triangle ODM is isosceles) and EM = DC/2 = AC/4 (since E is the midpoint of DC and AC is a mid-segment of triangle ADC).

Therefore:

BD/OD = BE/(AC/4)

But we also have:

BE = BD + DE = BD + BM = 2BD

Substituting this into the previous equation, we get:

BD/OD = 2BD/(AC/4)

Simplifying:

BD/OD = 8BD/AC

This means that:

OD = AC/8

But we also know that AC = 2AD, so:

OD = AD/4

Since O is the midpoint of AM, we also have:

OD = OM = AM/2

Therefore:

AD/4 = AM/2

This means that:

AD = 2AM/4 = AM/2 = OD

So D is the midpoint of AE, and CD = 2AD.

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In a triangle ABC. [AM] is the median relative to [BC] and O is the midpoint of [AM]. (BO) cuts [AC] at D. Let E be the midpoint of [DC]. 1) Prove that BMED is a trapezoid. 2) Prove that D is the midpoint of [AE); deduce that CD = 2AD. 3) Prove that OD == BD.

Statements I, II, and III are partially correct, but statement II needs to be corrected to indicate that stem plots are better for small to moderate-sized datasets.

We might choose to display data with a stem plot rather than a boxplot because:

Reveals the shape of the distribution.

Is better for small to moderate-sized datasets.

Displays the actual data.

A stem plot is a type of graph that shows the distribution of data by grouping the observations into stems and leaves.

It allows for the display of the actual data values, which is not possible in a boxplot.

Additionally, stem plots are particularly useful for small to moderate-sized datasets as they provide a detailed view of the distribution, allowing for the identification of patterns such as skewness, multimodality, and outliers.

On the other hand, boxplots are better for large datasets as they provide a more concise summary of the distribution, including information about the median, quartiles, and outliers, while still conveying information about the spread and shape of the distribution.

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Answer:

c = 56°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

120° is an exterior angle of the triangle , then

c + 64° = 120° ( subtract 64° from both sides )

c = 56°

A bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 200 and a standard deviation of 50.

We will find the score that separates the lower 60% of ratings from the top 40% of ratings.

Let x be the score that separates these two portions. We can find the corresponding z-scores using the standard normal distribution, since the ratings are normally distributed with mean 200 and standard deviation 50.

The z-score corresponding to the 60th percentile is the value z such that

P(Z ≤ z) = 0.6

With the help of standard normal tables, we can find that z = 0.25. Therefore, we have

(x - 200)/50 = 0.25

For x, we get

x - 200 = 0.25 * 50

x - 200 = 12.5

x = 212.5

Similarly, the z-score corresponding to the 40th percentile is the value z such that

P(Z ≤ z) = 0.4

With the help of standard normal tables, we can find that z = -0.25. Therefore, we have

(x - 200)/50 = -0.25

For x, we get

x - 200 = -0.25 * 50

x - 200 = -12.5

x = 187.5

Hence, the score that separates the lower 60% from the top 40% is between 187.5 and 212.5.

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The value of k is 20.

An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables and may involve arithmetic operations such as addition, subtraction, multiplication, division, or exponents. The goal of solving an equation is to determine the value of the variable that makes the equation true. Equations are commonly used in algebra and other mathematical fields to model real-world situations and solve problems. They can be written in various forms, including standard form, slope-intercept form, point-slope form, and general form, among others.

Since the sum of two angles on a straight line is always 180 degrees, we can set up an equation:

First angle + Second angle = 180

112 + 3k + 8 = 180

Simplifying the equation, we get:

3k + 120 = 180

Subtracting 120 from both sides, we get:

3k = 60

Dividing both sides by 3, we get:

k = 20

Therefore, the value of k is 20.

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Given the inverse demand function p = 100 - 20q for toasters and a price of $35, we can find the consumer surplus.

First, we'll find the quantity demanded at the given price:

35 = 100 - 20q
20q = 100 - 35
q = (100 - 35) / 20
q = 65 / 20
q = 3.25

Now, to find the consumer surplus, we'll use the formula:

Consumer Surplus = (1/2) × Base × Height

The base represents the quantity (q = 3.25) and the height is the difference between the maximum willingness to pay (p = 100) and the actual price (p = 35).

Consumer Surplus = (1/2) × 3.25 × (100 - 35)
Consumer Surplus = 0.5 × 3.25 × 65
Consumer Surplus = 105.625

So, the consumer surplus is $105.63 when rounded to two decimal places.

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Thus, with 99% confidence, we can say that the proportion of smeared ink in the 200 sheets of paper inspected falls between 1.3% and 15.7%.

To calculate the confidence interval of the proportion smeared in 200 sheets of paper inspected for smeared ink, we can use the formula:

Confidence Interval = sample proportion ± (critical value) x (standard error)

The sample proportion is the number of sheets containing smeared ink divided by the total number of sheets inspected, which is 17/200 = 0.085.

The critical value for a 99% two-sided confidence interval with 200 observations can be found using a t-distribution table or calculator, and is approximately 2.576.

The standard error can be calculated as the square root of [(sample proportion) x (1 - sample proportion) / sample size], which is the square root of [(0.085) x (1 - 0.085) / 200] = 0.028.

Plugging in these values, we get:

Confidence Interval = 0.085 ± (2.576) x (0.028)
Confidence Interval = 0.085 ± 0.072
Confidence Interval = (0.013, 0.157)

Therefore, with 99% confidence, we can say that the proportion of smeared ink in the 200 sheets of paper inspected falls between 1.3% and 15.7%. This means that we are 99% confident that the true proportion of smeared ink in the population of printed sheets falls within this range.

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The LCM of 63 and 42 is 126 where 63 is the required number lying in between 60 and 70.

Let the missing number be x.

The number x lies in between 60 and 70.

The LCM ( Least Common Multiple) refers to the least value that is divisible by any two (or more) numbers.

Here LCM of x and 42 is 126.

Simplifying 126 we can write it as,

126 = 2*3*21

Thus, one of the number having 126 is as multiple is 42  (as already given).

The other number, that is x, having 126 as multiple lying between 60 and 70 is,

x = 3*21 = 63

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There are 60 apples in the bag

Let y represent the total number of apples that is in the bag

36/y= 60/100

cross multiply both sides

60y= 36×100
60y= 3600

Divide both sides by the coefficient of y which is 60

60y/60= 3600/60

y= 60

Hence the total number of apples in the bag is 60 apples

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Answer: C Q

Step-by-step explanation:

You need to Use Q And C In algebra if thats what your going for. Hopefully this help's.

If the base of an isosceles triangle is 50 cm and the length of one of its legs is 65 cm, the height of the isosceles triangle is 60 cm.

To find the height of the isosceles triangle, we need to use the Pythagorean theorem and the properties of isosceles triangles.

First, we draw a diagram of the triangle and label the known values. We know that the base is 50 cm and one of the legs is 65 cm. Since the triangle is isosceles, the other leg is also 65 cm.

Next, we can draw a perpendicular line from the top vertex to the base, which represents the height of the triangle. We can label this height as "h".

Now, we have a right triangle with a base of 50 cm, a hypotenuse of 65 cm, and a height of "h". We can use the Pythagorean theorem to find the value of "h":

h² + 25² = 65²

h² + 625 = 4225

h² = 3600

h = 60

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Answer: y = -5

Step-by-step explanation:

We move the constants to one side to get y^3 = -125.

Then, we cube root both sides to get y = -5.

Based on the medians, we can conclude that Bus 47 typically has a faster travel time than Bus 18. The median travel time for Bus 47 is 16 minutes, which is 3 minutes faster than the median travel time for Bus 18, which is 13 minutes.

To determine which bus typically has the faster travel time, we need to compare the measures of center for each data set. Since the data sets are relatively small and appear to have some outliers, the median is the more appropriate measure of center to use in this case, as it is less affected by extreme values than the mean.

For Bus 47, the median is 16, which means that half of the students take less than 16 minutes to travel to school on that bus, and half take more than 16 minutes.

For Bus 18, the median is 13, which means that half of the students take less than 13 minutes to travel to school on that bus, and half take more than 13 minutes.

Therefore, based on the medians, we can conclude that Bus 47 typically has a faster travel time than Bus 18. The median travel time for Bus 47 is 16 minutes, which is 3 minutes faster than the median travel time for Bus 18, which is 13 minutes.

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