A dealer paid $10,000 for a boat at an auction. At the dealership, a salesperson sold the boat for 30% more than the auction price. The salesperson received a commission of 25% of the difference between the auction price and the dealership price. What was the salesperson’s commission?

The number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

To calculate the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels, we can use the concept of stars and bars.

First, we need to ensure that we have at least one of each type of bagel. So, we take one bagel of each type, which leaves us with 14 bagels to buy.

Now, we can use stars and bars to distribute the remaining 14 bagels among the 6 types of bagels. We represent the 14 bagels as stars and the 5 possible locations between the types of bagels as bars.

Using this method, we need to distribute 14 stars among 5 bars, which can be done in

(14+5-1) choose (5-1) = 18 choose 4 = 3060 ways.

Therefore, the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

Learn more about ways :

https://brainly.com/question/11823283

#SPJ4

Answer:30%

Step-by-step explanation:

GAIN = 156- 120=$ 36

% GAIN = \(\frac{gain}{old cost price } X 100%\\\)

= \(\frac{36}{120} X 100%\)

=30%

Answer:

54 Words Per Minute

Hope I helped!

yes Step-by-step explanation:

The given relation in the mapping diagram represents a function.

A function in mathematics is an expression with a independent variable (x) in it. The variable is called independent because it is not dependent on any value to get its value. Function also has a dependent variable (y) whose value depend on x. Ex -

y = f(x) = ax + d

We have a relation as shown in the figure.

The given relation is a function as all the values of [x], has independent values of [y]. Two or more values of [x] can have same value of y.

Therefore, the given relation in the mapping diagram represents a function.

To solve more questions on Operations of functions, visit the link below-

brainly.com/question/24114937

#SPJ2

Step-by-step explanation:

5x^2 +5x - x^2 + 3x -7 -12

or, 4x^2 + 8x - 19

This is the solution of this question..

Step-by-step explanation:

1st rearrange like terms

5x^2-x^2+5x+3x-7-12

then add/ subtract the rearranged like terms

4x^2+8x+19

finally there's no similar to simplify

The assumptions for a chi square test for homogeneity are

In statistics, the chi square test is used to determine where there exists a relationship or association between two variables

Amongst other assumptions, the variables are assumed to be categorical variables.

This means that variables can be used as labels

The other assumptions are:

Read more about chi square test at

https://brainly.com/question/4543358

#SPJ1

(a) Two descriptive statistics cited from the survey are: a. Of those investment managers surveyed, 44% were bullish or very bullish on the stock market.

b. Of those investment managers surveyed, 23% selected health care as the sector most likely to lead the market in the next 12 months.

These statistics describe the proportions or percentages of investment managers with certain attitudes or preferences based on the survey results. (b) Inference about the average return expected on equities over the next 12 months for the population of all investment managers: Based on the survey, the average expected return over the next 12 months for equities among the investment managers surveyed was 11.3%. Therefore, we can infer that the estimated average expected 12-month return on equities for the population of investment managers is likely to be around 11.3%. However, it's important to note that this is an inference and not a definitive conclusion, as the survey represents a sample of investment managers and may not perfectly represent the entire population.

(c) Inference about the length of time it will take for technology and telecom stocks to resume sustainable growth: The survey found that the managers' average response for the length of time it would take for technology and telecom stocks to resume sustainable growth was 2.3 years. From this, we can infer that the estimated average length of time it will take for technology and telecom stocks to resume sustainable growth for the population of investment managers is approximately 2.3 years. Again, this is an inference based on the survey data and may not be an exact representation of the entire population.

Learn more about stock here

https://brainly.com/question/31211894

#SPJ11

Answer:

5 blocks

Step-by-step explanation:

Firstly, as both sides of the see saw are equal, we can write an equation for it using k for the number of blocks and g for the number of bags:

6k + 3g = k + 4g

Now we can group both terms on their own to solve for the other using one:

6k - k + 3g - 3g= k-k +4g - 3g

5k = g

One bag = 5 blocks

There are 5 blocks in every bag.

Hope this helped!

Answer:

Step-by-step explanation:

Given equation:

Solve for the answer:

Answer:

Step-by-step explanation:

Given equation:

100x + 20 - (-30)

Solve for the answer:

100x + 20 - (-30)

= 120x - (-30)

= 150x.

Answer: 23 cm(Hope it's Right!)

Step-by-step explanation:

Write Lin as L and Chen as C

So put 25cm+8cm

The greatest common factor (MFC) of 12 and 16 is 4. By both the prime factorization method and the common divisors method.

To find the greatest common factor (MFC) of 12 and 16, we can use different methods, such as the prime factorization method or the common divisors method.

Decomposition into prime factors:

First, we break the numbers 12 and 16 into prime factors:

12 = 2*2*3

16 = 2*2*2*2

Then, we look for the common factors in both decompositions:

Common factors: 2 * 2 = 4

Therefore, the MFC of 12 and 16 is 4.

Common Divisors Method:

Another method to find the MFC of 12 and 16 is to identify the common divisors and select the largest one.

Divisors of 12: 1, 2, 3, 4, 6, 12

Divisors of 16: 1, 2, 4, 8, 16

We note that the common divisors are 1, 2, and 4. The largest of these is 4.

Therefore, the MFC of 12 and 16 is 4.

In summary, the greatest common factor (MFC) of 12 and 16 is 4. By both the prime factorization method and the common divisors method, we find that the number 4 is the greatest factor that both numbers have in common.

for more such question on factorization visit

https://brainly.com/question/25829061

#SPJ8

Answer:

AC = 8 cm,

AD = 3 cm and ∠ACB = ∠CDA

From figure,

∠CDA = 90°

∴ ∠ACB = ∠CDA = 90°

In right angled ∆ADC,

AC2 = AD2 + CD2

⇒ (8)2 = (3)2 + (CD)2

CD2 = 64 – 9 = 55

⇒ CD = √55 cm

In ∆CDB and ADC.

∠BDC = ∠AD [each 90°]

∠DBC = ∠DCA [each equal to 90°-∠A]

∴ ∠CDB ∼ ∆ADC

Then,

Answer: A

Step-By-Step Explanation: if n is greater than or equal to 2 is an add integer then the domain of: f(x)-x^2+8 is the solution to the inequality 2+8 greater than or equal to 0. which of the following statements is true?

Answer:

\(x=\frac{4}{3}\)

Step-by-step explanation:

\(-\left(3x-12\right)=9x-4\)

Distribute the negative sign to both 3x and -12:

\(-\left(3x\right)-\left(-12\right)=9x-4\)

Remove brackets: (Double negative = Positive)

\(-3x+12=9x-4\)

Subtract 12 from both sides:

\(-3x+12-12=9x-4-12\)

\(-3x=9x-16\)

Subtract 9x from both sides:

\(-3x-9x=9x-16-9x\)

\(-12x=-16\)

Divide both sides by -12:

\(\frac{-12x}{-12}=\frac{-16}{-12}\)

\(x=\frac{4}{3}\)

The solution to the inequality is x ≤ 1.

Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.

To solve this inequality, we must first perform the operations on the left side of the equation to get an expression equal to 4. We can start by simplifying the fraction on the left side of the equation. We can multiply both the numerator and denominator by x, which will give us 5x - 3 = x + 2x. We can then add 3 to both sides to get 5x = 3 + 2x, which can then be simplified to 3x = 3. Finally, we can divide both sides by 3 to get x = 1. Therefore, the solution to the inequality is x ≤ 1.

To know more about inequality click-
https://brainly.com/question/24372553
#SPJ1

Step-by-step explanation:

the third option is the correct one

To find the point P on the line y=3x that is closest to the point (50,0), we need to use the formula for the distance between a point and a line. This formula is:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

Where A, B, and C are the coefficients of the equation of the line in the form Ax + By + C = 0.

In this case, the equation of the line y=3x can be written as -3x + y = 0. So we have:

A = -3, B = 1, C = 0

Now we can plug in the values of (50,0) and solve for x and y to find the point P that is closest to it:

distance = |-3x + y| / sqrt((-3)^2 + 1^2)
distance = |-3x| / sqrt(10)

To minimize the distance, we need to minimize |-3x|. This occurs when x = 0. So the point P that is closest to (50,0) is the point (0,0).
To find the point P on the line y = 3x that is closest to the point (50, 0), we need to minimize the distance between P and (50, 0).

Let P(x, y) be a point on the line y = 3x. The distance between P and (50, 0) is given by the distance formula:

D = sqrt((x - 50)^2 + (y - 0)^2)

Since y = 3x, we can rewrite the distance formula as:

D = sqrt((x - 50)^2 + (3x)^2)

To minimize the distance, we can minimize the square of the distance (D^2), as it avoids dealing with the square root:

D^2 = (x - 50)^2 + (3x)^2

Now, we can find the derivative of D^2 with respect to x and set it to 0 to find the critical points:

d(D^2)/dx = 2(x - 50) + 2(3x)^2 * 6x = 0

Solve this equation to find the x-coordinate of the point P. Then, use y = 3x to find the corresponding y-coordinate. Finally, you'll have the coordinates of the point P that is closest to (50, 0).

Visit here to learn more about  derivative : https://brainly.com/question/25324584
#SPJ11

We are given a set \($$B = \{ 1+2x+3x^2,\ 2+3x+x^2,\ 1+4x-x^2\}.$$\) We need to show that the set $B$ spans $\mathcal{P}_2$. In other words, for any \($f(x) = ax^2 + bx + c \in \mathcal{P}_2$.\)

We must show that there exist coefficients \($p, q, r$ such that $$f(x) = p(1+2x+3x^2) + q(2+3x+x^2) + r(1+4x-x^2).$$\)

We can do this by equating the coefficients of\($x^2$, $x$\), and the constant term on both sides.

That is, \($$\begin{aligned} f(x) &= p(1+2x+3x^2) + q(2+3x+x^2) + r(1+4x-x^2)\\ &= (p+q+r)x^2 + (2p+3q+4r)x + (3p+q-r). \end{aligned}$$\)

Equating the coefficients of\($x^2$, we get $p+q+r = a$.\)

Equating the coefficients of \($x$, we get $2p+3q+4r = b$.\)

Equating the constant terms, we get \($3p+q-r = c$.\)

This is a system of three linear equations in three unknowns\($p, q, r$.\)

The coefficient matrix is \($$\begin{pmatrix} 1 & 1 & 1 \\ 2 & 3 & 4 \\ 3 & 1 & -1 \end{pmatrix}.$$\)

We can solve this system using row operations on the augmented matrix \($$\begin{pmatrix}[ccc|c] 1 & 1 & 1 & a \\ 2 & 3 & 4 & b \\ 3 & 1 & -1 & c \end{pmatrix}.$$\)

I will omit the details, but the reduced row echelon form of this matrix is \($$\begin{pmatrix}[ccc|c] 1 & 0 & 0 & \frac13 (2a-b+2c) \\ 0 & 1 & 0 & \frac13 (4a-b-c) \\ 0 & 0 & 1 & \frac13 (a+2b-c) \end{pmatrix}.$$\)

Therefore, we have \($$\begin{aligned} p &= \frac13 (2a-b+2c) \\ q &= \frac13 (4a-b-c) \\ r &= \frac13 (a+2b-c). \end{aligned}$$\)

These are the required coefficients, and hence the set $B$ spans $\mathcal{P}_2$.

To know more about set visit:

https://brainly.com/question/30705181

#SPJ11

Answer:

it's 12

Step-by-step explanation:

when the number is between those boxes whether it's negative or positive, it's automatically a positive.

By answering the above question, we may state that A kite has graphs perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph

The measurements of the numbered angles in each kite cannot be given without a reference image or particular kite. We can, however, offer some general knowledge on kites and their angles.

With two sets of neighboring congruent sides and angles, a kite is a quadrilateral with congruent sides on all four sides. A kite has perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Let's give a generic kite's angles the labels displayed in the accompanying diagram:

  A-------B

 /         \

D-----------C

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

the indicated z-score for the shaded area of 0.090 is approximately 1.34.

To find the indicated z score, we need to use the standard normal distribution table.
First, we need to determine which side of the distribution the shaded area is on. Since the area is less than 0.5, it must be on the left side of the distribution.
Next, we need to find the corresponding z score for the area of 0.090 (since that is the closest value to the shaded area).
Looking at the table, we find that the closest area value is 0.0892, which corresponds to a z score of 1.29.
Since the shaded area is slightly greater than this value, we can estimate the z score to be between 1.26 and 1.34.
Therefore, the answer is b. 1.26 or c. 1.34.
To find the indicated z-score for the standard normal distribution with a mean of 0 and a standard deviation of 1, we can look at the given probabilities (shaded areas) and use a z-score table or calculator to determine the corresponding z-score. Here are the z-scores for each shaded area:
a. 0.090 -> z-score ≈ 1.34
b. 1.00 -> z-score ≈ 0 (because the mean is 0)
c. 1.26 -> z-score ≈ 0.90
d. 1.34 -> z-score ≈ 0.91
e. 1.45 -> z-score ≈ 0.93
So, the indicated z-score for the shaded area of 0.090 is approximately 1.34.

To know more about normal distribution visit:

https://brainly.com/question/15103234

#SPJ11

Answer:

Is the answer 9 .please mark me as brainliest

a) The probability model for rolling two 4-sided dice can be represented as a table or matrix with 16 equally likely outcomes, each with a probability of 1/16.

b) The probability the sum of the numbers is 5 based on the probability model is 25%

a) The probability model for rolling two 4-sided dice can be represented using a table or a matrix, where the rows and columns represent the possible outcomes of the first and second die, respectively. Since each die has four equally likely outcomes, there are 4 x 4 = 16 possible outcomes in total. We can list these outcomes as ordered pairs (blue, yellow), where blue and yellow represent the numbers on the bottom of the blue and yellow dice, respectively

(1,1) (1,2) (1,3) (1,4)

(2,1) (2,2) (2,3) (2,4)

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3) (4,4)

Each outcome has a probability of 1/16, since each die has four equally likely outcomes.

b) To find the probability that the sum of the numbers is 5, we need to count the number of outcomes where the sum is 5 and divide by the total number of outcomes. There are four outcomes where the sum is 5: (1,4), (2,3), (3,2), and (4,1). Therefore, the probability is

4/16 = 1/4 = 0.25 = 25%

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The largest prime factor that always divides the sum of the terms in the sequence is 37.

The sequence is finite and consists of three-digit integers.

The tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term.

From the above property of the sequence, we can see that each digit at the units, tens as well as hundreds place will appear the same number of times in the sequence.

Let "x" be the sum of the digits at unit place in all the terms.

The sum of all the terms is "S".

S = 111*x

S = 3*37*x

We can clearly see that the sum "S" is divisible by 37.

Hence, the largest prime factor that always divides the sum of the terms in the sequence is 37.

To learn more about sequence, visit :

https://brainly.com/question/21961097

#SPJ4

Answer:

1/3

Step-by-step explanation:

The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4).

According to the statement

We have to find that the coordinates after the rotation.

So, For this purpose, we know that the

Rotation means a degree is being moved in clockwise or counterclockwise direction with some angle.

From the given information:

The point is a (0,4)

The rotation is drained 90, 180, 270 degrees.

Given point is:(0,4)

When some extent (x,y) is rotated 180° counter clockwise its coordinates become (-x,-y) the negative of original point.

So for the given point the coordinates will become (-0,-4)

Then,The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4)

So, The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4)

Learn more about rotation here

https://brainly.com/question/2078551

#SPJ9

Answer:

B

Step-by-step explanation:

The value of y for the given right angle triangle by the trigonometric function will be 12.43 ft thus option (B) is correct.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

The trigonometric functions found in the quadrants, as well as their graphs, domains, and differentiation and integration, will all be understood.

As per the given right angle triangle,

By cosine function,

cos43° = y/17

y = 17 cos43° = 12.43 feet

Hence "The trigonometric function will yield 12.43 feet as the value of y for the given right angle triangle".

For more information about the trigonometric function,

https://brainly.com/question/14746686

#SPJ2

A study by a business professor at Arizona State University found that students who missed two classes had grades that were one full letter grade lower than those who attended all classes. This suggests that attending class is essential for academic success.

There are a few reasons why missing class can lead to lower grades. First, students who miss class may miss important information that is covered in lectures. Second, they may miss opportunities to ask questions and get help from the professor. Third, they may fall behind on assignments and readings.

To avoid falling behind, it is important to attend all classes. If you must miss class, be sure to get notes from a classmate and ask the professor for any missed assignments or readings. By attending class and staying on top of your work, you can improve your chances of academic success.

Learn more about Information:

https://brainly.com/question/3282789

#SPJ4

Complete question:

A study by a business professor at Arizona State University showed that, on average, is students' grades wet down one full grade for every _ classes they missed.

a. one

b. two

c. three

d. four

Answer:I don't know.

Step-by-step explanation:You never added an image for the table.