Cara's new car holds 13.5 gallons of gas. If gas costs $2.98 per gallon, how much would it cost her to fill the gas tank from empty?

The expression when -1/2 is factored out is -1/2(x - 12)

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

-1/2x + 6

The factor is given as

-1/2

So, we divide -1/2x and 6 by -1/2

The results of these divisions are

-1/2x/-1/2 = x

6/-1/2 = -12

So, we have the following results

-1/2x + 6 = -1/2(x - 12)

Hence, the factored expression is -1/2(x - 12)

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Answer:

answer is 28

Step-by-step explanation:

3x=84

x=84/3= 28

If we reject the null hypothesis, it suggests that the test statistic is more extreme than the critical value, the correct answer is b.

When we conduct a hypothesis test, the null hypothesis assumes that there is no significant difference or relationship between the variables being tested. The alternative hypothesis, on the other hand, suggests that there is a significant difference or relationship. In hypothesis testing, we compare the test statistic (calculated from our sample data) to the critical value (determined based on the significance level chosen).

If the test statistic is more extreme than the critical value, it means that the observed data is highly unlikely to occur under the assumption of the null hypothesis. This leads us to reject the null hypothesis in favor of the alternative hypothesis. By rejecting the null hypothesis, we conclude that there is evidence to support the presence of a significant difference or relationship between the variables.

rejecting the null hypothesis indicates that the test statistic is more extreme than the critical value, providing evidence for a difference or relationship between the variables being tested.

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Answer:

Step-by-step explanation:  Hello!

I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent.  This also means that line segments PQ and ST are congruent.  You also know that angles Q and S are congruent which is given.  By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.

Answer:

-5 < x ⩽ 1

Step-by-step explanation:

Given the compount inequality

–2 < x + 3 ⩽ 4

Subtract 3 from all the sides

-2-3 < x+ 3 - 3 ⩽ 4 - 3

-5 < x ⩽ 1

This can be expressed as;

-5 <x and x ⩽ 1

x > -5 and x ⩽ 1

Hence the reqiures set of values of x are values from -4 to 1

S ={-4, -3, -2, -1, 0, 1}

Answer:

can u give the prices for the tickets?

An adult ticket costs $2 more than a child ticket

Let x and (x + $2)represent the cost of the child and adult ticket respectively

2(x+ $2) + 3x = $34

now solving for x

2x+ $4 + 3x = $34

5x = $30

 x = $6 , the cost of the child ticket.

the cost of adult ticket $6+2=$8

Step-by-step explanation:

The symbol that represents the dependent variable in a regression equation is:

a. y

The dependent variable is the variable that is being predicted or explained by the independent variable(s) in the regression analysis. It is typically represented by the symbol "y" in the regression equation. The independent variable(s) are usually represented by the symbol "x" or other appropriate letters.

In a regression equation, the dependent variable is the variable that we are trying to predict or explain based on the independent variable(s). It is the variable whose value is influenced or determined by the independent variable(s). For example, if we are studying the relationship between income (dependent variable) and education level (independent variable), we want to understand how education level affects or predicts income. In this case, income would be represented by the symbol "y" in the regression equation, as it is the variable we are interested in explaining or predicting. The independent variable(s), such as education level, would be represented by the symbol "x".

Therefore, the correct answer is option a. y.

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Given,

The Fibonacci sequence is F(n) = F(n-1) + F(n-2).

F(8) = 21 and F(9) = 34

To find: Which of the following is true.

Solution:

In a Fibonacci series, the sum of first two terms is equal to the third term.

The next term will always be the sum of the previous two terms.

Hence, the given option D is correct.

Answer:

less than

Step-by-step explanation:

you cant add 2x to 12 because of the x.

Answer:

no, more then i think

Step-by-step explanation:

even we don't know what x is x is coud make the number bigger so 14x is bigger then 14

Answer:

Hexagonal Prism

The mathematical equation E(y) = 0 + 1x is known as the regression equation.

In the context of regression analysis, the regression equation represents the relationship between the independent variable (x) and the expected value of the dependent variable (y). The equation is written in the form of y = β0 + β1x, where β0 is the y-intercept and β1 is the slope of the regression line.

The regression equation is the fundamental equation used in regression analysis to model and predict the relationship between variables. It allows us to estimate the expected value of the dependent variable (y) based on the given independent variable (x) and the estimated coefficients (β0 and β1).

The coefficient β0 represents the value of y when x is equal to 0, and β1 represents the change in the expected value of y corresponding to a one-unit change in x. By estimating these coefficients from the data, we can determine the equation that best fits the observed relationship between the variables.

The regression equation is derived by minimizing the sum of squared residuals, which represents the discrepancy between the observed values of the dependent variable and the predicted values based on the regression line. The estimated coefficients are obtained through various regression techniques, such as ordinary least squares, which aim to find the line that minimizes the sum of squared residuals.

Once the regression equation is established, it can be used to make predictions and understand the relationship between the variables. By plugging in different values of x into the equation, we can estimate the corresponding expected values of y. This allows us to analyze the effect of the independent variable on the dependent variable and make predictions about the response variable based on different levels of the predictor variable.

In summary, the mathematical equation E(y) = 0 + 1x is known as the regression equation. It represents the relationship between the independent variable and the expected value of the dependent variable. By estimating the coefficients, the equation can be used to make predictions and analyze the relationship between the variables. The regression equation is a fundamental tool in regression analysis for understanding and modeling the relationship between variables.

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Answer:

Table c mate

Step-by-step explanation:

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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I'll solve each problem separately:

(a) First, we write the equation in standard form:

dy/dt + [2(t-10)/(t-2)]y = cos(t)/(t^3 + t^2 - t - 3)

This is a linear, first-order ODE, and the coefficients are continuous functions of t except at t=2, where the denominator of the coefficient becomes zero. Therefore, the maximal interval of existence of the solution is (-∞, 2) U (2, ∞).

To solve this ODE, we can use an integrating factor of e^(integral [2(t-10)/(t-2) dt]) = e^2ln|t-2| = e^(2ln|t-2|) = (t-2)^2. Multiplying both sides of the ODE by this integrating factor, we get:

[(t-2)^2 dy/dt + 2(t-2)^3(dy/dt)(t-10)]/(t-2)^2 + 2y(t-10)/(t-2) = cos(t)/(t^3 + t^2 - t - 3)(t-2)^2

Simplifying, we get:

d/dt [(t-2)^2 y] = cos(t)/(t^3 + t^2 - t - 3)(t-2)^2

Integrating both sides from 0 to t, we get:

(t-2)^2 y(t) - 4 = ∫[0, t] cos(s)/(s^3 + s^2 - s - 3)(s-2)^2 ds

The integral on the right-hand side exists for all t in the maximal interval of existence of the solution, which is (-∞, 2) U (2, ∞).

(b) This ODE is also a linear, first-order ODE, and the coefficients are continuous functions of t except at t= -5 and t=2, where the denominators become zero. Therefore, the maximal interval of existence of the solution is (-∞, -5) U (-5, 2) U (2, ∞).

To solve this ODE, we can use an integrating factor of e^(integral [(2t+10)/(t-2) dt]) = e^(2ln|t-2| + 10ln|t-2|) = (t-2)^12. Multiplying both sides of the ODE by this integrating factor, we get:

d/dt [(t-2)^12 y] = 2(t-2)^12

Integrating both sides from 3 to t, we get:

(t-2)^12 y(t) - (3-2)^12 y(3) = 2/11 [(t-2)^13 - (3-2)^13]

The right-hand side is finite for all t in the maximal interval of existence of the solution, which is (-∞, -5) U (-5, 2) U (2, ∞).

(c) This ODE is also a linear, first-order ODE, and the coefficients are continuous functions of t except at t= -3 and t=2, where the denominators become zero. Therefore, the maximal interval of existence of the solution is (-∞, -3) U (-3, 2) U (2, ∞).

To solve this ODE, we can use an integrating factor of e^(integral [(2t+10)/(t-2) dt]) = e^(2ln|t-2| + 10ln|t-2|) = (t-2

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b) An approximate value for e is 2.71828,

c) The natural exponential function is eˣ

The number e is a mathematical constant that is closely related to the exponential function. It is one of the most important and widely used numbers in mathematics and science.

The number e is defined as the limit of the sequence of numbers

=> (1 + 1/n)ⁿ

as n approaches infinity.

In other words, it is the unique number that satisfies the equation

=> eˣ = lim(n→∞) (1 + x/n)ⁿ.

This equation states that as n increases, the value of the exponential function of x approaches eˣ.

The approximate value of e is 2.71828, but it can be calculated to an infinite number of decimal places.

The natural exponential function is a mathematical function that is defined by

=> eˣ

It is used to model real-world situations that involve exponential growth or decay, such as the growth of a population or the decay of a radioactive substance.

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On solving the provide outlier question, we can say that The difference between the upper and lower fourth makes up the fourth outlier (h) = 73.7 - 22.2 = 51.5

Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater). For instance, both 3 and 85 are "outliers" when the scores are 25, 29, 3, 32, 85, 33, 27, 28, etc. Move away. Look for values that are significantly larger or significantly smaller than all other values to identify outliers. Because it is significantly smaller range than all other values, Value 4 is an outlier. An observation that differs unusually from other values in a population sample taken at random is referred to as an outlier.

Here,

a) The data values should now be sorted from smallest to largest:

22.2 40.4 16.4 73.7 36.6 109.9

b) The sorted data set's median is its middle value. The median is the sixth data value in the sorted data set because there are 11 data values total:

m = 36.6

c) The median of the data values below the median, or at 25% of the data, is in the lower fourth.

The lower fourth is the third data value because there are 5 data values below the median.

d) The data value 6 + 3 = 9 represents the third quartile.

Q{3} 73.7

The difference between the upper and lower fourth makes up the fourth outlier (h):

73.7 - 22.2

51.5

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The additional information needed to prove both triangles are similar are:

A. ∠B ≅ ∠M

C. △ABC was rotated and dilated by a scale factor between 0 and 1

E. ∠C ≅ ∠L

When a triangle is rotated and dilated by a scale factor, the new triangle formed has the same shape but different size of the original triangle. However, all its corresponding angles remains congruent.

Thus, for triangles ABC and NML to be similar to each other, since we already known each have one congruent right angles, the additional information needed are:

A. ∠B ≅ ∠M

C. △ABC was rotated and dilated by a scale factor between 0 and 1

E. ∠C ≅ ∠L

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Answer:

B

Step-by-step explanation:

Answer:

the answer B

Step-by-step explanation:

Answer: r>13

Step-by-step explanation:

The sign is less than so r +8 has to be 20 or less.

The measure of the angles that is supplementary to the given angles is as follows:

4. 52°

5. 20°

6. 130°

Supplementary angles are those angles that sum up to 180 degrees. In

other words, supplementary angles refer to the pair of angles that always

sum up to 180°. Therefore, let's find the measure of the angles that are

supplementary angles to the following angles.

Therefore,

4.

180 - 128 = 52 degrees

5.

180 - 160 = 20 degrees

6.

180 - 50 = 130 degrees

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Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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Answer:

Answer:

She would have 33 more pages left.

Step-by-step explanation:

You would want to subtract 23 from 56.

Answer:

290

Step-by-step explanation:

30x2 + 20x4 + 50x3

Hope this helps. Please mark brainliest if you would. It would really help me out

Answer:

290

Step-by-step explanation:

30x2+4x20+3x50 multiply first and you get 60+80+150=290

Answer:

x= -8, 9 1/4

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

The probability of selecting a six-person committee as per given condition is equal to 0.1623 or 16.23%.

To calculate the probability of selecting four Democrats

And two Republicans in a six-person committee from a city council consisting of five Democrats and six Republicans,

Use the concept of combinations.

The total number of ways to form a committee of six people from a council of eleven five Democrats and six Republicans is

Using combination formula,

C(n, k) = n! / (k! × (n - k)!)

where n is the total number of items and k is the number of items chosen.

Here, select four Democrats and two Republicans,

Number of ways to choose four Democrats from five

C(5, 4)

= 5! / (4! × (5 - 4)!)

= 5

Number of ways to choose two Republicans from six,

C(6, 2)

= 6! / (2! × (6 - 2)!)

= 15

To find the total number of ways to form the committee with four Democrats and two Republicans, multiply the two results,

Total number of ways

= C(5, 4) × C(6, 2)

= 5× 15

= 75

The total number of ways to form a committee of six people from the city council is,

Total number of ways

= C(11, 6)

= 11! / (6! × (11 - 6)!)

= 462

Finally, calculate the probability by dividing the favorable outcomes (75) by the total number of outcomes (462),

Probability

= 75 / 462

≈ 0.1623

Therefore, the probability of selecting a six-person committee with four Democrats and two Republicans is approximately 0.1623 or 16.23%.

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Answer:

y - 1 = -2(x - 3)

Step-by-step explanation:

Point slope form is y1 - y2 = m(x1 - x2)

We are given a point that we'll label as (x2,y2):  (3,1)

Slope, m, is -2

We then have:

y1 - y2 = m(x1 - x2)

y - 1 = -2(x - 3)

Answer:

Step-by-step explanation:

So I am hoping this is right....

you would take 3790/579

rounded to the thousandths place would be 6.546 rounded

this would be part to whole

so as part to whole for every 100 people 6.546 shop at the local farmers market