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3 years ago

QUESTION 9.1 POINT

Mathematics

1 answer:

Rainbow [258]3 years ago

5 0

Answer:

120 different color combinations are possible.

Step-by-step explanation:

The order in which the color are chosen is not important(blue, green and red is the same outcome as red, blue, green), which means that the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

3 colors from a set of 10, so:

$C_{10,3} = \frac{10!}{3!7!} = 120$

120 different color combinations are possible.

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What is the final price of the four-night reservation

AlekseyPX

Answer:

$512

Step-by-step explanation:

Charges at the first hotel are ...

4(168 -40) = 4(128) = 512

Charges at the second hotel are ...

(4-1)(185) = 3(185) = 555

The first hotel offers the better rate: $512 for four nights.

5 0

3 years ago

Read 2 more answers

A company makes t-shirts and their research shows that that price and demand are related linearly: p = m x + b . They know that

allsm [11]

Answer:

The linear equation relating price to demand is Q=-0.5*P + 30

Step-by-step explanation:

The demand for a good is the quantity of that good that the demanders are willing to purchase at a given price.

Then, the Demand Curve relates the quantity that a consumer would be willing to buy as a function of price.

You seek to determine the linear equation that relates the price to the demand Q = m * P + b where Q is the quantity demanded at a price P, and compared with the equation of the straight line y = mx + b, m is the slope and b is the ordinate to the origin.

On a line of the form y = m * x + b, the value of m, having two points, is calculated by:

$m=\frac{y2-y1}{x2-x1}$

And the ordinate to the origin b is calculated, taking the value of m, replacing any of the two points (replacing any of the two because it must give the same value of b) in the expression y = m * x + b and solving its value.

In the case of Q=m*P+b, the value of m, having two points, is calculated by:

$m=\frac{Q2-Q1}{P2-P1}$

Being:

Q1= 5
P1= $50
Q2= 10
P2= $40

and replacing:

$m=\frac{10-5}{40-50}$

you get:

m= -0.5

So, being Q=-0.5*P+b, b is calculated by:

Replacing the point Q1= 5 and P1= 50

5= -0.5*50 + b → 5= -25 + b → 5+25= b → b= 30

Replacing the point Q1= 10 and P1= 40

10= -0.5*40 + b → 10= -20 + b → 10+20= b → b= 30

Then, the linear equation relating price to demand is Q=-0.5*P + 30

8 0

3 years ago

Can someone tell me why this isn’t a function? I thought it was because each input has an output.

aksik [14]

Answer: I think it's because you can't have two of the same numbers in the domain. For example the (5, -3) and the (5,2)

Step-by-step explanation:

6 0

3 years ago

The vertices of a triangle are located at the points A(0, 1), B(2, 4) and C(3, 0). The triangle is translated 5 units down to ob

lyudmila [28]

Answer:

The coordinates of the vertices of triangle A'B'C' are $A'(x,y) = (0,-4)$ , $B'(x,y) = (2,-1)$ and $C'(x,y) = (3,-5)$ .

Step-by-step explanation:

According to this statement, triangle ABC must be translated 5 units in the -y direction to form triangle A'B'C'. We need to use the following operations:

$A'(x,y) = A(x,y) +(0,-5)$ (1)