Twice last​ month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily​ fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4​ days, she drove 450​ miles, and the rental cost her $264.00. On her second business trip she drove 200 miles in 3​ days, and paid $165.00 for the rental. Find the daily​ fee, and find the mileage charge.

f(n) = (n+1) * (n) * (n-1) * ... * (2) * (1) * 5 / (5^n). This is the function that identifies the nth term of the recursively defined sequence.

The recursively defined sequence is given by an+1 = ((n + 1 )an / 5) for n ≥ 1, with a1 = 5. We need to find a function f(n) that identifies the nth term an of the sequence, as an = f(n).

To do this, we can use the recurrence relation to express an in terms of a(n-1), a(n-2), and so on, until we reach a1. Substituting an-1 = f(n-1), we have:

an = ((n + 1) an-1 / 5)
  = ((n + 1) f(n-1) / 5)

We can simplify this expression by substituting an-2 = f(n-2) into the expression for an-1, and so on, until we obtain:

an = (n+1) * (n) * (n-1) * ... * (2) * (1) * a1 / (5^n)

This expression shows that the nth term an is a function of n, namely f(n) = (n+1) * (n) * (n-1) * ... * (2) * (1) * a1 / (5^n).

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Answer:

$12.31

Step-by-step explanation:

11.62 divided by 2 =0.69

$11.62+$0.69=12.31

Answer: 16x+3x^3−8

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Answer:

2 9/14

Step-by-step explanation:

Answer: None of them

I think your teacher made a typo. See explanation below for details

=================================================

Explanation:

With math problems like this one, it is often very tricky to find integer solutions. Luckily, we're given a list of choices. Let's plug them in one at a time and see what happens.

If y = 5, then

y^2 - 7x^2 = 11

5^2 - 7x^2 = 11

25 - 7x^2 = 11

-7x^2 = 11-25

-7x^2 = -14

x^2 = -14/(-7)

x^2 = 2

But x^2 = 2 does not have any integer solutions. The two solutions are irrational. So we can rule out choice F.

Repeat for y = 4 and you should find that x^2 = 5/7, which also does not have any integer solutions. Choice G can be ruled out.

Choices H through K are even worse. Not only are there no integer solutions, but there aren't any real number solutions either (there are complex or imaginary solutions though). Plugging in y = 3 leads to x^2 = -2/7 which has imaginary solutions due to applying the square root to a negative radicand. Similar situations happen with J and K as well.

In summary, none of these answer choices are valid. We need to have two integers x and y that satisfy the equation. I think your teacher made a typo somewhere.

Since side A = 50 cm, side B = 99 cm, and angle C is a right angle, angle B . must be 63.204° which rounded to two decimal places is 63.2°

Answer: -1/28 gallon

Step-by-step explanation:

divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)

Answer: -1/28 gallon

Step-by-step explanation:

Answer:

  x > -3

Step-by-step explanation:

The function will be increasing where its derivative is positive.

__

  y = x^2 +6x . . . . . given function

  y' = 2x +6 . . . . . . . derivative

The derivative is positive for ...

  2x +6 > 0

  2x > -6

  x > -3 . . . . . domain where the function is increasing

Answer:

54

Step-by-step explanation:

10m +n^2 /4

= 10*5 + 4^2 /4

= 50 + 16/4

= 50 + 4

= 54

Answer:

54

Step-by-step explanation:

The companies being considered are:

The company that is concerned with corded telephones

The company that is concerned with cellphones

Let x represent the number of years since 2002 and y represent the total number of accounts

From the information given,

Considering the first company,

Initial number of accounts = 946 x 10^6

The number of accounts fell by approximately 28 million per year. This means that in x years, the number of accounts that would have been lost is

28 x 10^6 * x

= - 28x x 10^6

It is negative because it is reducing

The slope intercept form of a linear equation is expressed as

y = mx + c

where

m = rate of change

c = y intercept of value of y when x = 0

By comparing with the given scenario,

Answer: low

Step-by-step explanation: because  there are more greens than red or might say 20%

To reduce a fraction, you divide the numerator and denominator by the same number.

This number is the greatest common divisor (GCD) of the numerator and denominator. By dividing both the numerator and denominator by their GCD, you simplify the fraction to its simplest form. The GCD is the largest number that evenly divides both the numerator and denominator without leaving a remainder.

Dividing by the GCD ensures that the fraction is expressed in its lowest terms, where the numerator and denominator have no common factors other than 1. This process eliminates any common factors and reduces the fraction to its simplest representation.

Therefore, To reduce a fraction, you divide the numerator and denominator by the same number. Option c is correct.

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The r chart is used to monitor the dispersion of the process.

The r chart is a statistical tool used in quality control to monitor the dispersion or variability of a process. It is specifically used to track the range (the difference between the highest and lowest values) within subgroups of data. By plotting the ranges on the r chart over time, it becomes easier to identify any patterns or shifts in process variability. This helps in assessing the stability and consistency of the process, allowing for timely adjustments or interventions if needed.

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Answer:

Area of trapezoid is: \(\mathbf{11x^3y^2}\)

Area of triangle is: \(\mathbf{6a^3b^2}\)

Perimeter of triangle is: \(\mathbf{3ab+14a^2b}\)

Step-by-step explanation:

Image 1:

We need to Find area of trapezoid.

The formula used is: \(Area=\frac{1}{2}h(b_1+b_2)\)

where h is height and b₁ and b₂ are parallel sides.

Looking at the figure we get:

h = 2xy

b₁ = 4x²y

b₂ = 7x²y

Putting values and finding area:

\(Area=\frac{1}{2}h(b_1+b_2)\\Area=\frac{1}{2}\times 2xy(7x^2y+4x^2y)\\Area=\frac{1}{2}\times 2xy(11x^2y)\\Area=\frac{1}{2}\times 22x^3y^2\\Area=11x^3y^2\)

So, Area of trapezoid is: \(\mathbf{11x^3y^2}\)

Image 2:

We need to find area and perimeter of triangle.

First we will find area of triangle.

The formula used is: \(Area=\frac{1}{2}\times b \times h\)

where b is base and h is height

Looking at the figure,

b = 3ab

h = 4a²b

Finding area:

\(Area=\frac{1}{2}\times b \times h\\Area=\frac{1}{2}\times 3ab \times 4a^2b\\Area=\frac{1}{2}\times 12a^3b^2\\Area=6a^3b^2\)

So, Area of triangle is: \(\mathbf{6a^3b^2}\)

Now, finding Perimeter of triangle

The formula used is: \(Perimeter = Sum\:of\:lengths\:of\:all\:sides\:of\:triangle\)

Looking at figure:

Length of side 1 = 3ab

Length of side 2 = 4a²b

Length of side 3 = 10a²b

Finding Perimeter

\(Perimeter = Sum\:of\:lengths\:of\:all\:sides\:of\:triangle\\Perimeter = 3ab+10a^2b+4a^2b\\Perimeter=3ab+14a^2b\)

So, Perimeter of triangle is: \(\mathbf{3ab+14a^2b}\)

Answer:

(50^1/2)^4

Step-by-step explanation:

basically if I am comprehending your question correctly, the square root of 50 can also be written as 50^1/2

If you put 50^1/2 to the 4th power, it basically becomes (50^1/2)^4

The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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Explanation:

In this number line the solution set that's graphed is all numbers less than 1. It doesn't include 1 because that point is graphed with an empty circle.

Answer:

x < 1

Answer: The answer is B. It is not a function because the domain(x) is repeating and if the x was not repeating it would have been a function :)

Step-by-step explanation:

The system of linear equations has at least one solution is consistent , whereas a system of linear equations that has no solution is inconsistent

What is a system of linear equations?

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

The subject of linear algebra, which is employed in most areas of contemporary mathematics, is based on the theory of linear systems. Numerical linear algebra includes computational strategies for obtaining the solutions, which are crucial to the fields of engineering, physics, chemistry, computer science, and economics. A helpful strategy when creating a mathematical model or computer simulation of a relatively complex system is to approximate a system of non-linear equations by a linear system (see linearization).

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Answer:

The expression (8-i)/(2+i) in standard form is, 3 - 2i

Step-by-step explanation:

The expression is,

(8-i)/(2+i)

writing in standard form,

\((8-i)/(2+i)\\\)

Multiplying and dividing by 2+i,

\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)

Hence we get, in standard form, 3 - 2i

The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.

The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:

(8-i)/(2+i) * (2-i)/(2-i)

Using the distributive property, we can expand the numerator and denominator:

(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))

Simplifying further:

(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)

Since i^2 is equal to -1, we can substitute -1 for i^2:

(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))

Combining like terms:

(15 - 10i) / (3 + 4i)

Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

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Answer:

x=-2 and y=-1

Step-by-step explanation:

If x = -2 then:

y = -(-2)-3

y = 2-3

so y = -1

I hope this helps! And plz mark me brainliest!!!

Answer:

(-2,-1)

Step-by-step explanation:

Well if x is -2 we can plug it in to find y,

y = -(-2) - 3

y = 2 - 3

y = -1

(-2, -1)

Thus,

the solution is (-2,-1)

Hope this helps :)

The x-intercepts for the expression which is used by Jen and her friends to represent the height of the arch, in inches, at any value of x along the arch are 8,0) and (-3,0).

The factor of a quadratic is the terms in linear form, which are when multiplied together, give the original quadratic equation as a result.

Jen and her friends need to consider the robot’s height and its width at its base. The robot must be short enough and narrow enough to navigate through several arches along the obstacle course.

The expression to represent the height of the arch, in inches, at any value of x along the arch:

\(-x^2 + 5x + 24.\)

Factorize this expression by equating it to zero and changing its sign,

\(\begin{aligned}-x^2 + 5x + 24=0\\x^2 - 5x - 24=0\\x^2 - 8x +3x- 24=0\\x(x - 8)+3(x - 8)=0\\(x-8)(x+3)=0\\x=8,-3\end\)

Thus, the x intercept of the equation is (8,0) and (-3,0)

Hence, the x-intercepts for the expression which is used by Jen and her friends to represent the height of the arch, in inches, at any value of x along the arch are 8,0) and (-3,0).

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Answer: x = 8,0 and x = -3,0

Step-by-step explanation:

Answer:I don’t Knowt Try To Answer it yourself

Step-by-step explanation:

The value of a is 37°, the value of b is 34° and the value of c is 143° in the given triangle.

According to the question,

We have the following information:

We have a triangle with angles given.

We know that angle made on a straight line is 180° and the sum of all three angles of a triangle is 180°.

We also know that vertically opposite angles are equal.

So, a is vertically opposite to 37°.

So, the value of a is 37°.

Now, a and c make a straight line.

c = 180-37

c = 143°

a + b + 109° = 180°

37° + b + 109° = 180°

b+146° = 180°

b = 180-146

b = 34°

Hence, the value of a is 37°, the value of b is 34° and the value of c is 143° in the given triangle.

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The equation of the perpendicular line is y = 3x - 6

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

x + 3y = 21

Make y the subject

y = -1/3x + 7

Also, from the question;

We have the following points

Point = (1, -3) i.e.  (x, y) = (1, -3)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = -1/3

This means that the slope is -1/3

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is 3

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = 3

(x₁, y₁) = (1, -3)

So, we have

y = 3(x - 1) - 3

Evaluate

y = 3x - 6

Hence, the line has an equation of y = 3x - 6

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Answer:

93

Step-by-step explanation: The first term of AP is -5 and second term means -3.  

Common difference(d) = second term - first term

d = (-3)-(-5)

d= 2

Now using the formula of nth T  

n

​

=a  

1

​

+(n−1)d

Here a  

1

​

=−5,n=50,d=2

Puting these values in the formula of of nth term we get  

a  

n

​

=−5+(50−1)2

a  

n

​

=−5+98

a  

n

​

=93

Answer:-42

Step-by-step explanation: