Evaluate without a calculator: 1.19·5.4·3.12−5.4·1.19^2−1.93·5.4·1.19

A friend of mine is giving a dinner party. His current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabe

Vlada [557]

Answer:

a) 720, b) 475020, c) 69300, d) 0.146, e) 0.001

Step-by-step explanation:

It is given that my friend has 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet.

a)

If he wants to serve 3 bottles of zinfandel and serving order is important, then the total number of ways is

$10\times 9\times 8=720$

Therefore if he wants to serve 3 bottles of zinfandel and serving order is important, then the total number of ways are 720.

b)

The total number of bottles is

$10+8+11=29$

Combination is defined as

$^nC_r=\frac{n!}{r!(n-r)!}$

where, n is total possible outcomes and r is selected outcomes.

we have to select 6 bottles out of 29. so,

$^{29}C_{6}=475020$

Therefore ff 6 bottles of wine are to be randomly selected from the 29 for serving, then the total number of ways are 475020.

c)

If we want to select 2 bottles of each variety, then total number of ways are

$^{10}C_{2}\times ^{8}C_{2}\times ^{11}C_{2}=69300$

Therefore if 6 bottles are randomly selected with two bottles of each variety, then the total possible ways are 69300.

d)

Probability is defined as

$P=\frac{\text{Total outcomes}}{\text{Favorable outcomes}}$

$\frac{^{10}C_{2}\times ^{8}C_{2}\times ^{11}C_{2}}{^{29}C_{6}}=\frac{69300}{475020}\approx 0.146$

Therefore the probability that two bottles of each variety being chosen is 0.146.

e)

If 6 bottles are randomly selected, then the probability that all of them are the same variety is

$\frac{^{10}C_{6}+^{8}C_{6}+^{11}C_{6}}{^{29}C_{6}}=\frac{700}{475020}\approx 0.001$

Therefore if 6 bottles are randomly selected, then the probability that all of them are the same variety is 0.001.

7 0

2 years ago

Two students, Claude and Diane, were asked to use synthetic division and the Remainder Theorem to find the value of f(2) given f

ad-work [718]

Answer:

Step-by-step explanation:

Part A

In applying the synthetic division, the polynomial would be fully expressed as

2x³ + 0x² + 5x - 6

The coefficients are 2, 0, 5 and - 6

The working becomes

2| 2 0 5 -6

4 8 16

2 4 13 10

The student that correctly used synthetic division to find f(2) is Claudia

Part B

The value of f(2) is

2(2)^3+5(2) - 6

= (2 × 8) + 10 - 6

= 16 + 10 - 6 = 20

Part C

x - 2 is not a factor of 2x³ + 5x - 6 because there is a remainder of 20.

Part D

The methods that can be used to find out if x - 2 is a factor of 2x³ + 5x - 6 are synthetic division, long division, remainder theorem

8 0

2 years ago

The average length of time that three lawn-service mowers operate on a given day is 930 minutes. None of the mowers operates for

Zielflug [23.3K]

Answer:

The answer is A. 990.

Step-by-step explanation:

Now, to find the greatest possible length of time any of the mowers operates.

The 3 lawn-service mowers operate at the average length of time = 930 minutes.

So, the total length of time the 3 lawn mowers take = $930\times 30=2790\ minutes.$

The least length a mowers operates = 900 minutes.

Now, to find the greatest possible length of time any of the mowers operates:

Let $x$ be the greatest possible length of time any of the mowers operates.

As, any one of the mowers operates greatest length.

So, rest of the two mowers be least at length.

According to question:

$x+900+900=2790$

$x+1800=2790$

Subtracting both sides by 1800 we get:

$x=2790-1800$

$x=990.$

Thus, the greatest possible length of time any of the mowers operates is 990 minutes.

Therefore, the answer is A. 990.

3 0

2 years ago

a jogger runs 218 meters eastward then 72 meters westard then 62 meters eastward and finally 184 meters westward. For this motio

iris [78.8K]

Answer:

Total distance = 536 m

Total displacement = 24 m

Step-by-step explanation:

Distance and Displacement

A moving object constantly travels for some distance at defined periods of time. The total moved distance is the sum of each individual distance the object traveled. It can be written as:

dtotal=d1+d2+d3+...+dn

This sum is obtained independently of the direction the object moves.

The displacement only takes into consideration the initial and final points of the path defined by the object in its moving. The displacement, unlike distance, is a vectorial magnitude and can be even zero if the object starts and ends the movement at the same point.

For the question at hand, it's not known if the requirement is about the distance or the displacement, so we will compute both.

To compute the distance, we just add all the distances:

dtotal= 218 m + 72 m + 62 m + 184 m = 536 m

To compute the displacement, we must establish a positive direction as desired. Let's choose the east as the positive direction. Any movement eastward is considered positive and any movement westward is negative. We mentioned the displacement is a vector, but since we only have movement in the x-axis, we can only manage the signs. Thus, the total displacement is:

xtotal = 218 m - 72 m + 62 m -- 184 m = 24 m

Since the result is positive, the jogger stopped 24 meters eastward form the original point.

4 0

2 years ago

Chris invested some money at a rate of 5% per year compound interest.

max2010maxim [7]

Step-by-step explanation:

the answer is in the picture ☝️

6 0

2 years ago