A salesperson earns a commision of $480 for selling $3000 in merchandise. Find the commission rate. Write your answer as a percentage.

The probability that the salesman sells a deluxe and a standard encyclopedia on his two appointments is 0.126.

To calculate this probability, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

Let S1 be the event that the salesman makes a sale on his first appointment, and S2 be the event that he makes a sale on his second appointment. Let D1 be the event that the sale is for the deluxe model, and S1 be the event that the sale is for the standard model.

Then, the probability of selling a deluxe model on the first appointment is 0.3 * 0.5 = 0.15 (since there is a 50% chance of selling a deluxe model). The probability of selling a standard model on the second appointment is 0.4 * 0.5 = 0.3 (since there is a 50% chance of selling a standard model).

Therefore, the probability of selling a deluxe model on the first appointment and a standard model on the second appointment is 0.15 * 0.3 = 0.045. However, this can also occur in reverse order (i.e., selling a standard model on the first appointment and a deluxe model on the second appointment), so we need to double the probability to get the final answer: 0.045 * 2 = 0.09.

Finally, the probability that both events occur (selling a deluxe and a standard encyclopedia on his two appointments) is 0.09 * 2 = 0.126.

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a) A table and a graph for this situation is shown in the image below.

b) You can use the table or graph to predict how many weeks it will take Martha to earn enough money to pay for the new computer by comparing the week when her savings are both equal.

c) Since the x-value and y-value in both the table and the graph increase simultaneously, it is an example of linear growth.

In this scenario, the variable x would represent the number of weeks while the variable y would represent the total amount of savings. Since Martha received $200 for her birthday and makes $150 each week, a linear equation in slope-intercept form that models the situation is given by;

y = mx + c

y = 150x + 200

Next, we would use an online graphing calculator to make a table and a graph for this situation as shown in the image attached below.

Part b.

The table and the graph both have the total amount of savings (y) equal to $1,850 when x is equal to 11 weeks. This ultimately implies that, it would take Martha between 11 weeks to save enough money to buy this new computer.

Part c.

By critically observing the table and the graph, we can logically deduce that there is a linear relationship between the variables because both the x-value and y-value increase simultaneously.

Therefore, this is an example of a linear growth.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Explanation:

Method 1

First, list the multiples of both numbers:

To find the lowest common multiple (LCM) of 6 and 8, first express the numbers as a product of its prime factors.

Next, pick the highest powers for each of the numbers:

The cost of the Bike wholesale after the markup is $236.25

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

Bike wholesale = $189

Markup = 25%

The cost of the bike wholesale after the markup is then calculated as

Cost = Bike wholesale * (1 + markup)

Substitute the known values in the above equation, so, we have the following representation

Cost = 189 * (1 + 25%)

Evaluate the products

Cost = 236.25

Hence, the cost is $236.25

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Answer:

6

Step-by-step explanation:

x-4=2

+4    +4

x=6

Hope this helps!

Answer:

Step-by-step explanation:

You want to identify the given shapes as a regular or irregular polygon, or neither.

A regular polygon is one that has all sides congruent, and all interior angles congruent. Polygon E is marked as having congruent sides and congruent angles.

Polygon E is a regular polygon.

A polygon is a closed figure formed by line segments connected end-to-end. A simple polygon is one that has no intersecting line segments. A convex polygon is one that has all interior angles measuring 180° or less.

Any simple polygon that is not a regular polygon is an irregular polygon.

Polygons A, B, D are irregular polygons.

A circle is not a polygon. Figure C is neither a regular polygon nor an irregular polygon.

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Answer:

  (c)  y = 3^x

Step-by-step explanation:

A function is described as exponential if the independent variable is found in the exponent.

  y = x^(1/2) . . . a square root function, not exponential

  y = 2x^3 . . . . a cubic (polynomial) function, not exponential

  y = 3^x . . . . . an exponential function

Answer:

6x^2+ 19x+8

Step-by-step explanation:

(3x+8)(2x+1) use foil method which gives you,

6x^2+16x+3x+8 then combine like terms which gives you,

6x^2+ 19x+8.

Answer:

20

Step-by-step explanation:

There is 6-2 =4 years between them

24-4 =20

The sister is 20

Answer: 20 years old

Step-by-step explanation: So, we know the girl is 4 years older than the sister...how do we know that? Because...

6 - 2 = 4

She's 4 years older...we know the girl is 24, then the sister must be 20.

24 - 4 - 20...

The sister is 20 years old, I hope this helps

First, let find the equation for one variable using the given information:

1)There were 24 fewer 2 lb boxes of walnuts than 3 lb boxes of pecans.

Set w for the boxes of walnuts.

Set p for the boxes of pecans.

Then, we can write the next equation:

w= p-24

Now, let's find the weight equation:

2)The total weight of the shipment was 462 lb.

(in a shipment of 3 lb boxes of pecans and 2 lb boxes of walnuts)

Therefore, we can write the next equation:

boxes of walnuts + boxes of pecans = 462 lb

2w + 3p = 462 lb

Replace using the first equation w= p-24

2(p -24)+3p = 462 lb

2p - 48 + 3p = 462 lb

Solve for p:

5p - 48 = 462

5p=462 + 48

5p =510

p = 510/5

p = 102

Hence, there are 102 boxes of pecans

and the total weight of pecans is given by "shipment of 3 lb boxes of pecans"

Then , 3p = 3(102)=306

To find the number of walnuts, replace p on the w equation:

w = p - 24

w= 102 - 24

w=78

There are 78 boxes of walnuts.

The weight is given by 2w = 2(78) =156 lb

Answer:

70 students

Step-by-step explanation:

If 40% of all students in Mrs. Well's class got an A, and 28 students got an A, that means that 28 = 40%

To find the total number of students, we need to find 100%

40% = 28

Divide by 4

10% = 7

Multiply by 10

100% = 70

So there are 70 students in Mrs. Well's class.

Hope this helps you! :D

Answer:

A. A

Step-by-step explanation:

In a scatter plot, the value of correlation coefficient is represented by values between -1 to 1. The closer any value of correlation coefficient is to "0", the farther the data points on a scatter plot are from the line of best fit.

Invariably, considering the scatter plot shown in the graph above, the point that will MOST DECREASE the value of correlation coefficient is point A. This is because, if point A is added in the scatter plot, it will cause the value of correlation coefficient to be closer to 0, as point A is the farthest from the line of best fit compared to other points. This will make the data points more spread out and less clustered along the line of best fit.

Answer:

A

Step-by-step explanation:

It's A

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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Answer:

13 is a prime number, not divisible by any number greater than 1 or less than 13. So the prime factorisation of 78 is: 78 = 2 ⋅ 3 ⋅ 13 This can also be represented by a factor tree:

Step-by-step explanation:

Answer:

78 = 2 ⋅ 3 ⋅ 13

Step-by-step explanation:

78  ends with an even digit, so is divisible by  2 and we find:  78 = 2 ⋅ 39

39  ends with an odd digit, so is not divisible by  2 .

The digits of  39  add up to a multiple of  3 , namely  3 + 9 = 12 . So we can tell that  39  is divisible by  3 : 39 = 3 ⋅ 13

13  is a prime number, not divisible by any number greater than  1  or less than  13 .

So the prime factorization of  

78  is:

78= 2 ⋅ 3 ⋅ 13

The volume comparison of the given data is written below:

In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.

Given, The height of the cone and cylinder is twice the radius, while the radius of a sphere is the same.

The volume of the cone =   πr²h

Since, h = 2r

The volume of the cone =   πr² * 2r = 2/3 πr³

The volume of the Cylinder = πr²h

Since, h = 2r

The volume of the Cylinder = πr² * 2r = 2πr³

The volume of the sphere = 4 πr³

Thus, the volume of 3 cones = 2πr³

that is also equal to The volume of one Cylinder.

Thus, the volume of 2 cones = 4/3πr³

that is also equal to The 1/3 volume of the Cylinder.

Thus, the volume of 1 sphere = 4πr³

that is also equal to The volume of 2 cylinders.

Thus, the volume of 1 cone = 2/3πr³

that is also equal to The 1/6 volume of the cone.

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Answer:

Step-by-step explanation:

When moving -18 to the other side, he didn’t do 20 + 18. (Mistake 1)

When dividing 2/-4 he didn’t flip the inequality from > to <. (Mistake 2)

Correct:

\(-18-4y<20\\-4y<38\\y > -9.5 (or -4\frac{1}{2}\)

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ Q(\stackrel{x_1}{-7}~,~\stackrel{y_1}{-5})\qquad J(\stackrel{x_2}{1}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ QJ=\sqrt{(~~1 - (-7)~~)^2 + (~~3 - (-5)~~)^2} \implies QJ=\sqrt{(1 +7)^2 + (3 +5)^2} \\\\\\ QJ=\sqrt{( 8 )^2 + ( 8 )^2} \implies QJ=\sqrt{ 64 + 64 } \implies QJ=\sqrt{ 128 }\implies QJ\approx 11.31\)

Answer:

x=-4 and y=3

Step-by-step explanation:

-3x-3(-5x-17)=3

-3x+15x+51=3

12x=-48

x=-4

y=-5x-17

y=20-17

y=3

Answer: 21.4

Step-by-step explanation:

Answer:

56.32

Step-by-step explanation:

The hundredths place is the second place after the decimal point.

Side note:

All you need to do is if the hundredths is less than 5, you round down. If it's greater than or equal than 5, then you round up.

(A) The rate of making coffee by coffee maker  is 6 mL/second.

(B) The rate of making juice by juice maker is 8 mL/second.

(C) Juice is being made at a faster rate.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The rate of coffee made by coffee maker is represented by,

y = 6x       (1)

Here, y represents the amount of coffee in mL and x represents the time passed in seconds.

Also, The rate of juice made by juice make can be represented by the given table as,

k = 8h     (2)

Here, k represents the amount of juice in mL and h represents the time passed in seconds.

(A)

To find the rate of making coffee, solve the equation (1),

y = 6x

⇒ y/x = 6 mL/second

The rate of making coffee by coffee maker  is 6 mL/second.

(B)

To find the rate of making juice, solve the equation (2),

k = 8h

⇒ k/h = 8 mL/second

The rate of making juice by juice maker is 8 mL/second.

(C)

Since, the juice is made at the rate of 8 mL/second and the coffee is made at the rate of 6 mL/second.

Therefore, juice is being made at a faster rate.

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Okay, let's evaluate each modeling equation candidate based on the r^2 value:

a. y=16.5839•1.0185^x

No r^2 value given, so cannot determine if this is the best fit.

b. y=0.985515x-2.81333

No r^2 value given for this linear model, so cannot determine if it is the best fit.

c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667

This is a 3rd order polynomial model, but no r^2 is given, so cannot determine if it is the best fit.

d. y=0.00182197x^2+0.785098x+1.195

If this model has the highest r^2 value, it would be the best fit.

Based on the information provided, the only option that could potentially be the best fit is choice d, the quadratic model y=0.00182197x^2+0.785098x+1.195, if it has the highest r^2 value. But without the actual r^2 values for each model, a definitive determination cannot be made.

Does this help explain the approach? Let me know if you have any other questions!

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Answer:

The correct answer is,

\(x = \frac{65}{37} \)

Answer:

Prime number are a multiples of 8 because there are multiples of 8

Step-by-step explanation:

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

Answer:1

Step-by-step explanation:between 0&8

It is only 1 that can divide itself

Answer: Function B

Step-by-step explanation: Function A's equation would be y = x + 3 and although they have a greater y-intercept (starting point on x) the rate of change is less than Function B.

Answer:

-8-7x=-5x-10

+8-7x=-5x+8

-7x=-5x-2

Step-by-step explanation:

-8-7x=-5x-10

+8-7x=-5x+8

-7x=-5x-2

+5x=+5x-2

-2x=-2

/-2x=-2

x=1