Determine if a quadrilateral with the given vertices is an isosceles trapezoid. Show and explain all steps to prove or disprove.

Janet is three years older than her sister Julie Janet's brother is 8 years older than their sister Julie the sum of all their a

seropon [69]

Answer:

Julie is 14.67, Janet 17.67 and Brother 22.66

Step-by-step explanation:

Let Julie age be x

Janet: x+3

Brother: x+8

x+x+3+x+8=55

3x+11=55

3x=44

x=14.7

4 0

2 years ago

You know how to play 21 songs on your guitar. (a) If you want to choose 8 of the songs to make a setlist to play for a small gat

UNO [17]

Answer:

(a) 8,204,716,800

(b) 5,985

Step-by-step explanation:

Combinations and Permutations

Combinatorics is the part of the discrete mathematics that studies the enumeration of groups or sorting of a determined number of elements. The concept of combinations is tied to the different forms to group elements where the order of their arrangements is not important or does not differentiate from the very same set of elements picked in a different order.

The concept of combinations is tied to the differents forms to group elements where the order of their arrangements is not important or does not differentiate from the very same set of elements picked in different order.

On the other hand, permutations or variations are sets selected in a specific order and another set with the same element but in different order is considered a different set.

If we have n elements available to pick from in sets of m elements each, there can be C(n,m) different combinations, and it's given by

$\displaystyle C(n,m)=\frac{n!}{m!(n-m)!}$

Similarly the number of permutations is given by

$\displaystyle P(n,m)=\frac{n!}{(n-m)!}$

(a) I have n=21 songs to pick from and I want to choose m=8 of them where the order matters, so it's a permutation:

$\displaystyle P(21,8)=\frac{21!}{(13)!}=\frac{51,090,942,171,709,440,000}{6,227,020,800}=8,204,716,800$

I can make more than 8 billion different setlists

(b) To choose m=4 songs from n=21 songs where the order does not matter, we compute the combination

$\displaystyle C(21,4)=\frac{21!}{4!(17)!}=\frac{21\cdot 20\cdot 19\cdot 18\cdot 17!}{4\cdot 3\cdot 2\cdot 1(17)!}$

$\displaystyle C(21,4)=\frac{143,640}{24}=5,985$

I can make almost 6,000 sets of 4 songs

5 0

3 years ago

The mean of the commute time to work for a resident of a certain city is 27.3 minutes. Assume that the standard deviation of the

posledela

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Mean commute time (m) = 27.3 minutes

Standard deviation (sd) = 7.1 minutes

a) What minimum percentage of commuters in the city has a commute time within 2 standard deviations of the mean?

Using chebyshev's theorem ;

No more than 1/k² values of a distribution can be

k standard deviations from the mean.

Here k = 2

Hence,

1/k² = 1/2² = 1/4 = 0.25

Hence, minimum percentage of commmuters within 2 standard deviations of the mean :

1 - 0.25 = 0.75 m

B.) What minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the mean?

Here, k = 1.5

1/k² = 1/1.5² = 1/2.25 = 0.444

Hence, minimum commute time within 2 standard deviations of the mean :

1 - 0.444 = 0.56 = 56%

Commute time within 1.5 standard deviation

[27.3 - (1.5 × 7.1), 27.3 + (1.5 * 7.1)

[16.65, 37.95]

C.) What is the minimum percentage of commuters who have commute times between 6minutes and 48.6 minutes?

X - m /sd

X = 6

= (6 - 27.3) / 7.1 = - 3

X = 48.6

= (48.6 - 27.3) / 7. 1 = 3

Hence,

1/k² = 1 / 3² = 1/9

1 - 1/9 = 8/9

= 0.888 = 0.89 = 89%

3 0

4 years ago

In Which set do all of the values make the inequality 2x-1<10 true

Step2247 [10]

X<5.5, x has to be less than 5.5 because you add 1 to both sides and then divided both sides by two and you would get x < 5.5

8 0

4 years ago

Which equation is equivalent to the given equation?

Zolol [24]

Answer:

C.

i guess so

$\\ \\ \\$

7 0

3 years ago

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