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3 years ago

Nancy is 5 years younger than her brother Stan. Last year she was twice as young as he was. How old is each of them now?

Mathematics

2 answers:

otez555 [7]3 years ago

4 0

Nancy: 5 Stan: 10

5 is 5 years
younger then Stan
And 5 is twice as
young as 10

Svetllana [295]3 years ago

4 0

Answer:

Nancy is 6 years old and Stan is 11 years old now.

Step-by-step explanation:

Let the present age of Stan be x.

Then age of Nancy = y

x - y = 5

Last year she was twice as young as he was

Age of Nancy last year = y-1

Age of Stan last year = x-1

2 × (y-1)= x-1

2y -2 = 5 + y -1

y = 6

x = y + 5 = 6 + 5 = 11

Nancy is 6 years old and Stan is 11 years old now.

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2 years ago

Suppose a simple random sample of size nequals81 is obtained from a population with mu equals 79 and sigma equals 18. (a) Descr

Daniel [21]

Answer:

(a) The sampling distribution of $\overline{X}$ = Population mean = 79

(b) P ( $\overline{X}$ greater than 81.2 ) = 0.1357

(c) P ( $\overline{X}$ less than or equals 74.4 ) = .0107

(d) P (77.6 less than $\overline{X}$ less than 83.2 ) = .7401

Step-by-step explanation:

Given -

Sample size ( n ) = 81

Population mean $(\nu)$ = 79

Standard deviation $(\sigma )$ = 18

(a) Describe the sampling distribution of $\overline{X}$

For large sample using central limit theorem

the sampling distribution of $\overline{X}$ = Population mean = 79

(b) What is Upper P ( $\overline{X}$ greater than 81.2 ) =

$P(\overline{X}> 81.2)$ = $P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}> \frac{81.2 - 79}{\frac{18}{\sqrt{81}}})$

= $P(Z> 1.1)$

= $1 - P(Z< 1.1)$

= 1 - .8643 =

= 0.1357

$P(\overline{X}\leq 74.4)$ = $P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}\leq \frac{74.4- 79}{\frac{18}{\sqrt{81}}})$

= $P(Z\leq -2.3)$

= .0107

(d) What is Upper P (77.6 less than $\overline{X}$ less than 83.2 ) =

$P(77.6< \overline{X}< 83.2)$ = $P(\frac{77.6- 79}{\frac{18}{\sqrt{81}}})< P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}\leq \frac{83.2- 79}{\frac{18}{\sqrt{81}}})$

= $P(- 0.7< Z< 2.1)$

= $(Z< 2.1) - (Z< -0.7)$

= 0.9821 - .2420

= 0.7401

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2 years ago

What is the probability of drawing five face cards?

anastassius [24]

Total number of cards = 52
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P( 5 face cards) = (12/52)(11/51)(10/50)(9/49)(8/48) = 33/108290

Answer: 33/108290

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2 years ago

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asambeis [7]

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3 years ago

Please help asap, shehhrhd

Dovator [93]

Answer:

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*Exterior Angle Theorem*

<u><em>Sorry for the lack of explanation. It's midnight, so I didn't have much time.</em></u>

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2 years ago