SALES An automobile company sold 2.3 million new cars in a year. If the average price per car was $21,000, how
much money did the company make that year? Write your answer in scientific notation.

Answer:

The value of x is 2.

Step-by-step explanation:

5(2x -1) + 3(x -3) = -(4x - 6) + 2(13 -3x)

Expand both sides of the equation to remove parenthesis

10x - 5 + 3x - 9 = -4x + 6 + 26 - 6x

Transpose all terms with x as the coefficient on the left side of the equation and transpose the constants to the right.

10x + 3x + 4x + 6x = 6 + 26 + 5 + 9

Simplify

23x = 46

Divide both sides of the equation by 23

23x/23 = 46/23

x = 2

It will take John approximately 17 months to pay off the balance.

What is simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

Assuming that John does not use the credit card for any other purchases and that the credit card company uses a simple interest calculation method, we can use the following steps to calculate the number of months it will take John to pay off the balance:

Calculate the monthly interest rate by dividing the annual percentage rate (APR) by 12:

Monthly interest rate = 19% / 12 = 0.01583

Calculate the monthly finance charge by multiplying the outstanding balance by the monthly interest rate:

Monthly finance charge = $2000 x 0.01583 = $31.66

Subtract the monthly payment from the monthly finance charge to get the amount that will be applied to the outstanding balance:

Payment applied to balance = $150 - $31.66 = $118.34

Divide the outstanding balance by the payment applied to balance to get the number of months it will take to pay off the balance:

Number of months to pay off balance = $2000 / $118.34 = 16.9

(rounded up to the nearest whole number)

Therefore, it will take John approximately 17 months to pay off the balance.

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Equation that represents the total number of minutes y Emily studied for the math exam is y = 40 +x.

We can represent the total number of minutes Emily studied for the math exam using the equation,

y = 40 + x

Here, 'y' represents the total number of minutes Emily studied for the math exam, '40' represents the number of minutes she studied in the morning, and 'x' represents the number of minutes she studied later that evening.

By adding the number of minutes studied in the morning to the number of minutes studied later that evening, we can calculate the total number of minutes Emily studied for the math exam.

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In the 8 Axioms, 4 and 6 axioms fails to holds and S is not a vector space. Rest of the axioms try to hold the vector space.

To demonstrate that S is not a vector space, we must demonstrate that at least one of the eight vector space axioms fails to hold. Let us examine each axiom in turn:

Therefore, axioms 4 and 6 fail to hold, and S is not a vector space.

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The correct question:

Let S be the set of all ordered pairs of real numbers. Define scalar multiplication and addition on S by α(x₁, x₂) = (αx₁, αx₂); (x₁, x₂) ⊕ (y₁, y₂) = (x₁ + y₁, 0). We use the symbol ⊕ to denote the addition operation for this system in order to avoid confusion with the usual addition x + y of row vectors. Show that S, together with the ordinary scalar multiplication and the addition operation ⊕, is not a vector space. Which of the eight axioms fail to hold?

The area of Habib's diagram when s = 1/2 is 7.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.

To find the area of Habib's diagram when s = 1/2, we just need to substitute s = 1/2 into the expression for the area:

Area = 6 + 4s²

Area = 6 + 4(1/2)²

Area = 6 + 4(1/4)

Area = 6 + 1

Area = 7

Therefore, the area of Habib's diagram when s = 1/2 is 7.

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Answer:

C

Step-by-step explanation:

3x - 9y = 9 → (1)

- 2x +2y = 8 ( subtract 2y from both sides )

- 2x = - 2y + 8 ( divide through by - 2 )

x = y - 4

substitute x = y - 4 into (1)

3(y - 4) - 9y = 9

3y - 12 - 9y = 9

- 6y - 12 = 9 ( add 12 to both sides )

- 6y = 21 ( divide both sides by - 6 )

y = [tex]\frac{21}{-6}[/tex] = - [tex]\frac{7}{2}[/tex]

Let's use the variable x to represent the list price of the car.

The total cost your cousin paid for the car is the list price plus a 7% sales tax on the list price, plus $450 in additional fees.

We can write this as an equation:

Total cost = List price + 0.07(List price) + 450

We know that the total cost your cousin paid was $12,755, so we can substitute that into the equation:

12,755 = x + 0.07x + 450

Simplifying the right side:

12,755 = 1.07x + 450

Subtracting 450 from both sides:

12,305 = 1.07x

Dividing both sides by 1.07:

x = 11,500

Therefore, the list price of the car your cousin bought was $11,500.

The list price of the car your cousin bought was $11,500.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's start by setting up an equation to represent the total cost of the car:

Total cost = List price + 7% of List price + $450

We know that the total cost is $12,755, so we can substitute that in:

$12,755 = List price + 0.07(List price) + $450

Simplifying this equation, we get:

$12,755 = 1.07(List price) + $450

Subtracting $450 from both sides, we get:

$12,305 = 1.07(List price)

Dividing both sides by 1.07, we get:

List price = $11,500

Therefore,

The list price of the car your cousin bought was $11,500.

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Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.

To calculate the mean absolute deviation (MAD), we first need to find the mean of each sample.

Sample 1:[tex]17/25 = 0.68[/tex]

Sample 2: [tex]12/25 = 0.48[/tex]

Sample 3: [tex]14/25 = 0.56[/tex]

Sample 4: [tex]9/25 = 0.36[/tex]

Next, we calculate the deviation of each observation from its respective sample mean:

Sample 1: |0.68 - x1|, |0.68 - x2|, ..., |0.68 - x25|

Sample 2: |0.48 - x1|, |0.48 - x2|, ..., |0.48 - x25|

Sample 3: |0.56 - x1|, |0.56 - x2|, ..., |0.56 - x25|

Sample 4: |0.36 - x1|, |0.36 - x2|, ..., |0.36 - x25|

where xi is the satisfaction rating (0 or 1) of the Ith customer in the sample.

The MAD is the average of these deviations:

MAD = (|0.68 - x1| + |0.68 - x2| + ... + |0.36 - x25|)/100

Since we don't know the actual ratings of the customers, we cannot calculate the MAD exactly. However, we can say that the MAD is likely to be higher for samples 2 and 4, which have lower satisfaction rates, compared to samples 1 and 3, which have higher satisfaction rates. Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.

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The expression for the problem is:

Total cost = $42 + ($12/hour × 3 hours) × 2 people

Bruce charged David and Ricky a fixed fee of $42 for parts plus an hourly rate of $12 for labor. He spent 3 hours repairing the motorcycle. Since there are two people (David and Ricky), we need to multiply the hourly rate by the number of hours worked (3) and then multiply that by 2. Finally, we add the fixed fee for the parts to get the total cost.

To evaluate the expression using the order of operations, we need to perform the multiplication first and then the addition. So, we have:

Total cost = $42 + ($12/hour × 3 hours) × 2 people

= $42 + ($36) × 2

= $42 + $72

= $114

Therefore, David and Ricky owe Bruce a total of $114 for the motorcycle repair.

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All of these ratios are equal to b, and we have shown that there is a constant ratio between consecutive output values.

The common ratio is the ratio that remains constant between successive function output values. The behaviour of a geometric sequence, which is a series of numbers where each term is produced by multiplying the one before it by a set number (the common ratio), depends on the common ratio. The sequence is rising exponentially if the common ratio is bigger than 1. The sequence decreases exponentially if the common ratio is between 0 and 1.

To show that the function form shows a constant ratio we take:

[tex](x+1) / f(x) = (ab^{(x+1)}) / (ab^x) = b[/tex]

Similarly, we have:

[tex]f(x+2) / f(x+1) = (ab^{(x+2)}) / (ab^{(x+1)}) = b[/tex]

Hence, all of these ratios are equal to b, and we have shown that there is a constant ratio between consecutive output values.

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For a normal distribution ,a positive value of z simply means that the observation or sample mean is above the population mean this implies

none of the options provided is completely accurate.

All the observations must have had positive values,

It is not necessarily true for a positive value of z.

The value of z indicates how many standard deviations away from the mean a particular observation or sample mean is.

A positive value of z simply means that the observation or sample mean is above the population mean.

The area corresponding to the z is either positive or negative,

It is also not accurate.

The area under the normal curve corresponds to probabilities, not positive or negative values.

The area to the right of the mean corresponds to positive z-values, and the area to the left of the mean corresponds to negative z-values.

The sample mean is smaller than the population mean,

It is a possibility when the z-value is negative, indicating that the sample mean is below the population mean.

The sample mean is larger than the population mean,

It is a possibility when the z-value is positive, indicating that the sample mean is above the population mean.

Therefore, the sample mean can be either larger or smaller than the population mean depending on the direction of the z-value.

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The probability that at least one customer arrives at the shop during a one-minute interval is 0.632.

Since the arrival of customers at a Starbucks shop can be modeled as a Poisson process with an average rate of 1/min, the probability of exactly k customers arriving in a one-minute interval is given by the Poisson probability mass function:

P(k arrivals) = (λ^k * e^(-λ)) / k!

where λ is the average rate of arrivals (in this case, 1/min), e is the mathematical constant e, and k! is the factorial of k.

To find the probability that at least one customer arrives during a one-minute interval, we can use the complement of the probability that zero customers arrive (i.e., the probability of at least one arrival is 1 minus the probability of zero arrivals).

Thus, the probability of at least one customer arriving during a one-minute interval is:

P(at least one arrival) = 1 - P(0 arrivals)

P(at least one arrival) = 1 - [([tex]1^{0}[/tex] * [tex]e^{-1}[/tex]) / 0!] = 1 - [tex]e^{-1}[/tex] = 0.632

Therefore, the probability that at least one customer arrives at the shop during a one-minute interval is 0.632.

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Answer:

see the images and explanation

Step-by-step explanation:

for the graph:

the domain 0 < x < 5

the range for each functions:

g(x) = 2x + 1

g(x) = y  ,   1 < y < 11

h(x) = 2x + 2 ,  2 < y < 12

A minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.

Sample size refers to the number of observations or individuals included in a study or experiment. It is the number of subjects or units that are selected from a population to be studied. The sample size is an important consideration in statistical analysis, as it can affect the accuracy and generalizability of the results. A larger sample size generally leads to more precise estimates and stronger statistical power, but it can also be more costly and time-consuming to collect and analyze.

To calculate the minimum sample size required to maintain a margin of error of 0.05 or less with a 99% confidence level, we can use the formula:

n = (Z² * p * (1-p)) / E²

where n is the sample size, Z is the Z-score for the desired confidence level (2.576 for 99% confidence level), p is the estimated proportion of the population that has a certain characteristic (we can use 0.5 for maximum variability), and E is the margin of error.

Plugging in the values, we get:

n = (2.576² * 0.5 * (1-0.5)) / 0.05²

n = 664.3

Rounding up to the nearest whole number, we get a minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.

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To compute the covariance matrix of the variables in the data, the "matrix-operation" which should be used is ([tex]X^{t}[/tex] × X)/n.

The "Covariance" matrix is defined as a symmetric and positive semi-definite, with the entries representing the covariance between pairs of variables in the data.

The "diagonal-entries" represent the variances of individual variables, and the off-diagonal entries represent the covariances between pairs of variables.

Step(1) : Compute the transpose of the centered data matrix X, denoted as [tex]X^{t}[/tex]. The "transpose" of a matrix is found by inter-changing its rows and columns.

Step(2) : Compute the "dot-product" of [tex]X^{t}[/tex] with itself, denoted as [tex]X^{t}[/tex] × X.

The dot product of two matrices is computed by multiplying corresponding entries of the matrices and summing them up.

Step(3) : Divide the result obtained in step(2) by the number of samples in the data, denoted as "n", to get the covariance matrix.

This step scales the sum of the products by 1/n, which is equivalent to taking the average.

So, the covariance matrix "C" of variables in "centered-data" matrix X can be expressed as: C = ([tex]X^{t}[/tex] × X)/n.

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The given question is incomplete, the complete question is

Let X be a matrix of centered data with a column for each field in the data and a row for each sample. Then, not including a scalar multiple, how can we use matrix operations to compute the covariance matrix of the variables in the data?

Answer:

Step-by-step explanation:

· Find the surface area of a cone with a slant height of 8 cm and a radius of 3 cm. SA = B + πrS = (πr2) + πrs = (π(32)) + π(3)(8) = 9π + 24π = 33πcm2 = 103.62cm2. Find the surface area of a rectangular pyramid with a slant height of 10 yards, a base width (b) of 8 yards and a base length (h) of 12 yards.

Answer:

7,000,000÷2000

= 3,500

Step-by-step explanation:

therefore, each worker makes 3500 bikes per year

The cube roots of 216 written in the rectangular (standard) form are 3 + 3√3, -3+3√3, and 6.

In mathematics, the cube root formula is used to represent any number as its cube root, for example, any number x will have the cube root 3x = x1/3. For instance, 5 is the cube root of 125 as 5 5 5 equals 125.

3√216 = 3√(2x2x2)x(3x3x3)

= 2 x 3 = 6

the prime factors are represented as cubes by grouping them into pairs of three. As a result, the necessary number, which is 216's cube root, is 6.

Therefore, the cube roots of 216 are 3 + 3√3, -3+3√3, and 6.

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The length of the given line AB is 6 units and the polygon ABCDEF has been created.

A graph is a mathematical structure made up of a collection of points called VERTICES and a set of lines connecting some pair of VERTICES that may or may not be empty.

There is a chance that the edges will be directed, or orientated.

If the lines are directed or undirected, respectively, they are referred to as ARCS or EDGES.

Make a sequence of bars on graph paper as an example of a graph.

So, in the given situation the polygon ABCDEF has been created:

(Refer to the graph attached below)

Now, the length of the side AB:

Count the units as follows which comes to 6 units.

Therefore, the length of the given line AB is 6 units and the polygon ABCDEF has been created.

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Correct question:

Help Here is your graph of the points on the previous screen.

Connect the points in order to create polygon `ABCDEF`.

1.2 Enter the length of the segment between A and B.

The alternative hypothesis can be written as H₁: pA < pB.

The alternative hypothesis would be that there is a difference in the proportion of Republicans (Group A) and Democrats (Group B) who favor the government investing billions of dollars to improve the country's train system. Expressly, it would state that the proportion of Republicans who favor this investment is less than the proportion of Democrats who favor it:

H₁: pA < pB

where pA denotes the proportion of Republicans who favor the investment and pB denotes the proportion of Democrats who favor the investment.

In the alternative hypothesis, we actually create the relationship between the variables which are being tested in that situation. According to these, we come across the comparison among the variables and how much they differ from each other. The alternative hypothesis is the statement the researcher tries to prove by conducting a statistical analysis.

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Step-by-step explanation:

hope this will help you Thanks

vehicle?

The average delay per vehicle would be 20 minutes. This is calculated by taking the total time the freeway was shut down (40 minutes) and dividing it by the total number of vehicles that would have been on the freeway during that time (2400 vehicles).

Step-by-step explanation:

Again, using similar triangle ratios

7.2 m  is to 2.4 m  

     as   AB is to  12.0 m

7.2 / 2.4  = AB/12.0    Multiply both sides of the equation by 12

12 *   7.2 / 2.4   = AB = 36.0 meters

It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.

The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.

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The logical assumption used is: An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.

An arithmetic sequence is a set of numbers where, with the exception of the first term, each term is obtained by adding a fixed constant to the term before it. Every pair of following terms in the sequence has the same fixed constant, which is known as the common difference. A1 stands for the first term in an arithmetic sequence, while an is used to represent the nth term.

A solid line symbolises continuous numbers, whereas the classmate's logical presumption is that an arithmetic series comprises of discrete values. This presumption is untrue, though, as a line can effectively represent an arithmetic series.

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Answer:

x = 9.0

Step-by-step explanation:

sin E = CD/EC = CD/x

<=>     sin 50 = 6.9/x     <=> x = 6.9/sin 50 ≅ 9.0

1. Mean = 54

2. Standard Deviation = 6.3

3. Probability = 0.077

4. Probability = 0.845

5. Probability = 0.155

6. Probability = 0.323