The gas tank on a car holds 13.4 gallons. If the car goes 335 miles on a single tank, how many miles per gallon does the car get? Provide an explanation of what the final answer means, in terms of the given problem. Show all work.

chile..

The growth formula for calculating the future value of an investment or loan, un = uo(1 + i)^n, can be expressed as un = uo[(1 + 1/a)^a]^rt. This equation relates the initial value (uo), the interest rate (r), the number of years (t), and the number of interest payments per year (N).

The growth formula for calculating the future value of an investment or loan is given by the equation un = uo(1 + i)^n. In this equation, r represents the annual interest rate as a percentage, t is the number of years, and N represents the number of interest payments made per year. To find the values of i and n in terms of r and t, we can use the formulas i = r/N and n = Nt.

Using the given formulas, we substitute i and n into the growth formula to get un = uo(1 + r/N)^(Nt). Simplifying further, we can rewrite the expression as un = uo[(1 + 1/N)^N]^t.

Now, to show that un = uo[(1 + 1/a)^a]^rt, we need to equate the expressions for N and a. By setting N = a^(-1), we can rewrite the formula as un = uo[(1 + 1/a)^a]^rt. This demonstrates that the growth formula un is equivalent to uo[(1 + 1/a)^a]^rt, given the relationship between N and a.

In summary, the growth formula for calculating the future value of an investment or loan, un = uo(1 + i)^n, can be expressed as un = uo[(1 + 1/a)^a]^rt. This equation relates the initial value (uo), the interest rate (r), the number of years (t), and the number of interest payments per year (N), showing the growth of an investment or loan over time.

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Answer:

Your answer would be:

\(x=6\)

Step-by-step explanation:

\(5x + 30 = 110\)

\(5x + 30 - 30 = - 30\)

\(5x = 80\)

\(x = 16\)

Hope this helped! UwU

Answer:

what are the questions?

Step-by-step explanation:

Answer:

B) $12.25

Step-by-step explanation:

First, you subtract 8 from 15.5 and have 7.5

Now, you add 7.5 to 4.75 because you need to include the money left over. It’s 12.25

Answer:

9)  3.7 in

10) 12 in²

11) 18 in³

12) V=432π cm³

   TSA= 216π cm²

13)V=448π ft³

   TSA=240π ft²

Step-by-step explanation:

9) Since all side of the trapezium are the same the height = perpendicular line which is 3.7 in

10) 3×4 (the quadrilateral at the bottom)

11)∵ A= Cross-sectional area× height

  ⇒A= Area of the trapezium × 4

  ∴ A=\(\frac{1}{2} \\\) (sum of the parallel sides) × 4

  A=\(\frac{1}{2} \\\) (3+6) × 4

  A= 18 in²

12) V=πr²h

    V=π(6)²(12)

⇒V=432 cm³

   TSA=2(πr²)+2πrh

  TSA=2(π(6)²)+2π(6)(12)

 ⇒TSA=240π cm²

13. V=πr²h

    V=π(8)²(7)

   V=448π ft³

TSA=2(πr²)+2πrh

TSA=2(π(8)²)+2π(8)(7)

TSA=240π ft²

9)  3.7 in

10) 12 in²

11) 18 in³

12) V=432π cm³

   TSA= 216π cm²

13)V=448π ft³

   TSA=240π ft²

A study conducted in 2004 examined the usage of cable television and radio among 10 individuals to determine if there was a significant difference in the average hours spent on each medium. Using a significance level of 0.05, statistical analysis was performed to test for a disparity between the population mean usage of cable television and radio.

The researchers collected data on the number of hours per week spent watching cable television and listening to the radio from a sample of 10 individuals. The objective was to determine if there was a significant difference in the average usage between cable television and radio, considering the increasing competition among various entertainment options.

To test for a difference between the population mean usage for cable television and radio, a statistical hypothesis test was conducted. The significance level (α) of 0.05 was chosen, which means that the results would be considered statistically significant if the probability of obtaining such extreme results by chance alone was less than 5%.

The test compared the means of the two samples, namely the average hours spent watching cable television and listening to the radio. By analyzing the data using appropriate statistical techniques, such as a two-sample t-test, the researchers determined whether the observed difference in means was statistically significant or could be attributed to random variation.

After conducting the hypothesis test, if the p-value associated with the test statistic was less than 0.05, it would indicate that there was a significant difference between the population mean usage of cable television and radio. Conversely, if the p-value was greater than 0.05, there would be insufficient evidence to conclude a significant disparity.

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To plot the stem-and-leaf plot, we need to take the digits of tens in the leaf and the digits of ones in the stem. The final result of the stem-and-leaf plot looks like the table below:

Stem Leaf

100 0 1 3 5

125 0 1 2

137 0 1 8

145 0 1 6

180 0 9

190 0 1 5

210 0 2

In the histogram, the data will be divided into classes. Since the data ranges from 100 to 210, we can create classes that are about 10 units wide. The first class will be from 100 to 109, the second class will be from 110 to 119, and so on. The histogram of the data is shown below:

Histogram of Weight of students in class in lbs. [100-210]

  |    

  |    

  |    

  |    

  |    

  |    

  |    

  |    

  |    

  |    

---+---------------

  100   120   140

The shape of this data is approximately normal, also known as the bell curve.

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Answer: n=3/11

Step-by-step explanation:

1. You want to simplify both sides of the equation.

2n+3/4n=3/4.

(2n+3/4n)=3/4 (combine like terms).

11/4n=3/4.

2. Multiply both sides using 4/11.

(4/11)x(11/4n)=(4/11)x(3/4)

3. You get your answer which is n=3/11.

Hoped I help :)

The correct answer is (a) gas mileage is a response variable, and you expect to find a negative association.

The reason for this is that other things being equal, larger automobile engines require more fuel to operate, which means they are less fuel efficient. Therefore, as engine size (in liters) increases, we would expect fuel efficiency (in mpg) to decrease.

To test this hypothesis, we would need to gather data on the engine size and fuel efficiency of a sample of sport utility vehicles. We could then use regression analysis to determine the strength and direction of the association between engine size and fuel efficiency. If our hypothesis is correct, we would expect to see a negative coefficient for engine size in our regression model, indicating that larger engine sizes are indeed associated with lower fuel efficiency.

In summary, when studying the effect of engine size on fuel efficiency, gas mileage is the response variable and we expect to find a negative association between engine size and fuel efficiency.

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Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

X is many things but B is correct.

Answer:

7.04 × 10⁵

Step-by-step explanation:

Standard form (also called "Scientific notation ") is written in the form of

\(a \times 10^n\) , where \(1\leq a < 10\) and \(n\) is any positive or negative whole number.

To convert a number into standard form, move the decimal point to the left or right until there is one digit to the left of the decimal point.

The number of times you have moved the decimal point is the power of 10 (the value of n).

Seven hundred and four thousand = 704000

To convert 704000 to standard form, move the decimal point 5 places to the left so that the value of "a" is 7.04.  As the decimal point has been moved 5 places the left, we need to multiply 7.04 by 10⁵.

Therefore, 704000 = 7.04 × 10⁵.

Answer:

7.04 × 10⁵

Step-by-step explanation:

We have to convert,

→ Seven hundred and four thousand into standard form.

Now the standard form is,

→ 704000

→ 7.04 × 10⁵

Hence, the answer is 7.04 × 10⁵.

The sum of the remainders is 10. This result is independent of the value of x and holds true for any five consecutive positive integers.

Arbitrary positive integer is any positive integer that is chosen without any particular reasoning or pattern. This can also refer to any number that is randomly chosen or assigned.

Let the original numbers be x, x+1, x+2, x+3, and x+4, where x is an arbitrary positive integer.

Then, their modulo 5 values are x mod 5, (x+1) mod 5, (x+2) mod 5, (x+3) mod 5, and (x+4) mod 5.

Now, let's calculate the sum of these modulo 5 values.

x mod 5 + (x+1) mod 5 + (x+2) mod 5 + (x+3) mod 5 + (x+4) mod 5

= x mod 5 + x mod 5 + 1 + x mod 5 + 2 + x mod 5 + 3 + x mod 5 + 4

= 5x mod 5 + 10

= 0 + 10

= 10

Hence, the sum of the remainders is 10.

This result is independent of the value of x and holds true for any five consecutive positive integers.

This is because when modulo 5 is applied to any set of five consecutive numbers, each number in the set will have an entry in the modulo 5 table, and the sum of the entries in the table is 10.

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Answer:

distance is 5 units

Step-by-step explanation:

plug in values

Answer:

8/12, 6/19 and 9/10!

Step-by-step explanation:

All of them cannot be simplified.

but the rest can like  

4/26 can be simplified by 2

and 10.22 can be simplified by 2

After the transformation defined by the rule T⟨1, 4⟩ B"s coordinates are B(3, 9).

What is Transformation?

In mathematics, a shape is not turned; rather, it is moved left, right, up, or down. If the translated shapes (or the image) appear to be the same size as the original shapes, they are congruent. Only their direction or directions have changed.

Given:

Triangle ABC has vertices A(1, 3), B(2, 5), and C(5, 3).

Now, after applying Translation rule T⟨1, 4⟩

A(1, 3)-------> A( 1+ 1 , 3+ 4 ) = A( 2, 7)

B(2, 5)-------> B( 2+ 1 , 5+ 4 ) = B( 3, 9)

C(5, 3) -------> C( 5+ 1 , 3+ 4 ) = C ( 6, 7)

Hence, the coordinates of B' after the translation described by the rule T⟨1, 4⟩ is B'( 3, 9).

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You should be aware of the fundamental theorem of algebra (FTCoA). If a quadratic has roots at \(r_1\) and \(r_2\), then we can factorize it as

\((x - r_1) (x - r_2)\)

Expanding, this is equivalent to

\(x^2 - (r_1 + r_2) x + r_1 r_2\)

Now, if we can also write this

\(x^2 + bx + c\)

then we must have

\(x^2 + bx + c = x^2 - (r_1 + r_2) x + r_1r_2 \\\\ ~~~~ \implies \begin{cases} b = -(r_1 + r_2) \\ c = r_1r_2 \end{cases}\)

(By the way, these are known as Vieta's formulas.)

We're told that the quadratic,

\(p(x) = 3x^2 - 6x + 8,\)

has roots \(x=\alpha\) and \(x=\beta\), so by the FTCoA, we can write

\(p(x) = 3 (x - \alpha) (x - \beta)\)

Expanding this last form, we have the identity and exact values

\(3x^2 - 6x + 8 = 3 (x^2 - (\alpha + \beta) x + \alpha\beta) \\\\ ~~~~ \implies x^2 - 2x + \dfrac83 = x^2 - (\alpha + \beta) x + \alpha\beta \\\\ ~~~~ \implies \begin{cases} \boxed{\alpha + \beta = 2} \\\\ \boxed{\alpha\beta = \frac83} \end{cases}\)

(i) We want to construct a new quadratic \(p_{\rm i}(x)\) such that its roots are \(x=\alpha^2\) and \(x=\beta^2\). By the FTCoA, we would have

\(p_{\rm i}(x) = (x - \alpha^2) (x - \beta^2)\)

Expanding,

\(p_{\rm i}(x) = x^2 - (\alpha^2 + \beta^2) x + \alpha^2\beta^2\)

Now, notice that

\(\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = 2^2 - 2\cdot\dfrac83 = -\dfrac43\)

\(\alpha^2\beta^2 = (\alpha\beta)^2 = \left(\dfrac83\right)^2 = \dfrac{64}9\)

It follows that

\(p_{\rm i}(x) = x^2 + \dfrac43 x + \dfrac{64}9\)

which we can rewrite with integer coefficients by scaling each term by a factor of 9 to get

\(p_{\rm i}(x) = \boxed{9x^2 + 12x + 64}\)

(ii) Now we want a quadratic \(p_{\rm ii}(x)\) with roots at \(2\alpha\) and \(2\beta\). This means

\(p_{\rm ii}(x) = (x - 2\alpha) (x - 2\beta) \\\\ ~~~~~~~~ = x^2 - 2 (\alpha + \beta)x + 4\alpha\beta\)

\(\implies p_{\rm ii}(x) = x^2 - 4x + \dfrac{32}3\)

or more cleanly, scaling by 3,

\(p_{\rm ii}(x) = \boxed{3x^2 - 12x + 32}\)

(iii) Now the roots are \(x=\frac\alpha2\) and \(x=\frac\beta2\), which gives

\(p_{\rm iii}(x) = \left(x - \dfrac\alpha2\right) \left(x - \dfrac\beta2\right) \\\\ ~~~~~~~~ = x^2 - \dfrac{\alpha + \beta}2 x + \dfrac{\alpha\beta}4\)

\(\implies p_{\rm iii}(x) = x^2 - x + \dfrac8{12}\)

\(\implies p_{\rm iii}(x) = \boxed{12x^2 - 12x + 8}\)

(iv) If the roots are \(x=\frac\alpha{\alpha+1}\) and \(x=\frac\beta{\beta+1}\), we have

\(p_{\rm iv}(x) = \left(x - \dfrac\alpha{\alpha+1}\right) \left(x - \dfrac\beta{\beta+1}\right) \\\\ ~~~~~~~~~= x^2 - \left(\dfrac\alpha{\alpha+1} + \dfrac\beta{\beta+1}\right) x + \dfrac{\alpha\beta}{(\alpha+1)(\beta+1)}\)

Note that

\(\dfrac\alpha{\alpha+1} + \dfrac\beta{\beta+1} = \dfrac{\alpha(\beta+1) + \beta(\alpha+1)}{(\alpha+1)(\beta+1)} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{2\alpha\beta + \alpha + \beta}{\alpha\beta + \alpha + \beta + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{\frac{16}3 + 2}{\frac83 + 2 + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{22}{17}\)

\(\dfrac{\alpha\beta}{(\alpha+1)(\beta+1)} = \dfrac{\alpha\beta}{\alpha\beta + \alpha + \beta + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \dfrac{\frac83}{\frac83 + 2 + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \dfrac8{17}\)

\(\implies p_{\rm iv}(x) = x^2 - \dfrac{22}{17}x + \dfrac8{17}\)

\(\implies p_{\rm iv}(x) = \boxed{17x^2 - 22x + 8}\)

The equation of a line can be expressed in either the general form (Ax + By = C) or the slope-intercept form (y = mx + b). The equation of the line is y = (3/7)x - 3.

Given that the x-intercept is 7 and the y-intercept is -3, we can use this information to find the equation of the line.

The x-intercept is the point where the line crosses the x-axis, meaning the y-coordinate is 0. Therefore, the x-intercept is (7, 0).

The y-intercept is the point where the line crosses the y-axis, meaning the x-coordinate is 0. Therefore, the y-intercept is (0, -3).

To find the equation of the line, we can use the slope-intercept form. The slope (m) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1) = (-3 - 0) / (0 - 7) = -3 / -7 = 3/7

Substituting the slope and the y-intercept (b = -3) into the slope-intercept form, we have:

y = (3/7)x - 3

Therefore, the equation of the line is y = (3/7)x - 3.

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Answer:

x=8, y=4

(8,4)

Step-by-step explanation:

y = x - 4

y = -0.5x + 8

x - 4 = -0.5x + 8

x = -0.5x + 12

1.5x = 12

15x = 120

x = 8

plug x back into one of the first equations, and you get

y = 4.

(8,4)

Answer:

Weight in Kilograms = 0.8 Kilograms

Weight in grams = 800 grams

Step-by-step explanation:

Tyler has a baseball bat that weighs 28 ounces.

a) Weight in Kilograms

From the question:

1 kilogram = 35 ounces

Hence:

35 ounces = 1 kilogram

28 ounces = x kilogram

Cross Multiply

35 × x = 28 × 1

x = 28/35

x = 0.8 kilograms

b) Weight in grams

1 kilogram = 1000 grams

0.8 kilogram = x

Cross Multiply

x = 0.8 × 1000 grams

x = 800 grams

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

21100 minutes or about 351.67 hours

Step-by-step explanation:

First find out how many $10 is in $42200 by dividing. The answer is 4220

This means there is 4220 5 minutes. Multiply to get 21100.

It takes 21100 minutes or about 351.67 hours to get 42200 dollars.

Step-by-step explanation:

13) 4x-22+x+11+10x-4 =180

15x=195

x=13

<P=(10(13)-4)=126

<Q=(4(13)-22)=30

<R=13+11=24

Answer:

Step-by-step explanation:

2(2x +4) - 2x = x + 18

4x +8 -2x = x +18

2x -x = 18-8

X = 10

Put the value of x in both side

Left side *+*+*+*+*+

2 ( 2*10+4)-2*10

48-20 = 28

Right side +*+*+*+*+*

X + 18

10+ 18 = 28

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ANSWER: -1/2

7-9=-2 and -2 divided by 4 is -1/2 therefore the answer is -1/2

Answer: If two forecasters have unbiased forecasts, then they should have the same average error over many forecasts. In that sense, they would be equally good at forecasting.

Step-by-step explanation:

The statement that is true regarding evaluating the quality of a forecast is:

If both forecasters have an unbiased forecast, then they are equally good at forecasting.

Explanation:

A biased forecast can have a zero forecast error if the bias happens to offset the error in the forecast. However, a zero forecast error does not necessarily indicate that the forecast is unbiased.

In the mean squared error (MSE) evaluation, one single observation can make a very large difference because the errors are squared before they are averaged. Therefore, outliers can have a large impact on the MSE.

If we are evaluating the same forecaster, then the mean squared error is not always lower than the mean absolute error. It depends on the specific forecast and the distribution of errors.

However, if two forecasters have unbiased forecasts, then they should have the same average error over many forecasts. In that sense, they would be equally good at forecasting.

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The linear equation representing the amount Zoey owes her friend after t weeks is L + 10t = 190

Given, Zoey borrowed some money from her friend in order to help buy a new video game system. Zoey agreed to pay back her friend $10 per week and originally borrowed $190.

Table of the values :

L     190   180   170   160   150

t       0        1       2       3      4

Using the values of the table,

(L1 - L2)/(t1 - t2) = (L - L2)/(t - t2)

(190 - 180)/(0 - 1) = (L - 180)/(t - 1)

10/-1 = (L - 180)/(t - 1)

10(t - 1) = -1(L - 180)

10t - 10 = 180 - L

L + 10t = 190

Hence, the linear equation representing the amount Zoey owes her friend after t weeks is L + 10t = 190

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By following these steps, organizations can work towards bringing the process back under control and making it capable of producing output within the desired specifications.

Under statistical process control (SPC) and process capability analysis, if a process is determined to be out-of-control and not capable, the logical next step would be to first identify and address the sources of variation and special causes of variation in the process.

Here are the steps to follow:

Identify and eliminate special causes: Special causes are factors that cause unpredictable and non-random variation in the process. These causes need to be identified and eliminated or controlled. This may involve investigating specific factors such as equipment malfunction, operator error, or material defects that are leading to the out-of-control condition.

Stabilize the process: Once special causes have been identified and addressed, efforts should be made to stabilize the process. This involves reducing the sources of common cause variation, which are the inherent and predictable variations present in the process. Techniques such as process standardization, operator training, improved equipment maintenance, and standard operating procedures can be implemented to stabilize the process.

Assess process capability: After stabilizing the process, it is important to evaluate its capability to meet the desired specifications or requirements. Process capability analysis helps determine if the process is capable of consistently producing output within the desired tolerance limits. This analysis involves calculating process capability indices such as Cp, Cpk, or Pp, Ppk, and comparing them to the specified limits or customer requirements.

Implement process improvements: If the process is found to be incapable or not meeting the desired capability targets, process improvements need to be implemented. This may involve redesigning process parameters, adjusting equipment settings, improving material quality, or making other modifications to improve process performance and capability.

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Answer:

5 1/2

Step-by-step explanation:

The calories contained are from grams of carbohydrates and other ingredients

One gram of carbohydrate contains 4 calories

The equation 4c + 5 = 27 represents the relationship between these quantities.

1. 5 from the equation represent calories from other ingredients

2. Neither 8 nor 3 is the solution to the equation

4c + 5 = 27

When 8 is the solution

4(8)+5=27

32+5=27

37=27

When 3 is the solution

4(3)+5=27

12+5=27

17=27

Neither 8 nor 3 is the solution to the equation because 8 gives a higher calories in the granola bite and 3 gives a lower calories in the granola bite.

3. Solution to the equation

4c + 5 = 27

4c= 27-5

4c = 22

Divide both sides by 4

c=22/4

=5 2/4

=5 1/2

The solution to the equation is 5 1/2

Answer:

usage patterns are a variable used in market segmentation.

Step-by-step explanation:

Usage patterns are a variable used in behavioral segmentation.

Behavioral segmentation is a marketing strategy that divides a market into different segments based on consumer behavior, specifically their patterns of product usage, buying habits, and decision-making processes. This segmentation approach recognizes that customers with similar behavioral characteristics are likely to exhibit similar preferences and respond in a similar manner to marketing initiatives.

Usage patterns, as a variable, help marketers understand and classify customers based on how they interact with a product or service. This can include factors such as the frequency of product usage, the amount of product used, the timing of purchases, brand loyalty, product benefits sought, and other behavioral indicators.

By analyzing usage patterns, marketers can identify distinct segments within their target market and tailor marketing strategies to meet the unique needs and preferences of each segment. This enables companies to develop more targeted marketing campaigns, optimize product offerings, improve customer satisfaction, and drive customer loyalty.

Overall, behavioral segmentation, including the consideration of usage patterns, allows companies to better understand and connect with their customers by aligning their marketing efforts with specific behaviors and motivations.

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Answer:

14a-2

Step-by-step explanation: