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Natasha_Volkova [10]

2 years ago

10

Leia cuts congruent triangular patches with an area of 27 square centimeters from a rectangular piece of fabric that is 27 centi

meters long and 9 centimeters wide. How many of the patches can Leia cut from 28 pieces of the fabric?(pls help)

1 answer:

Rama09 [41]2 years ago

6 0

27>28 57 only a praise

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1) Two coins are to be flipped. The first coin will land on heads with probability .6, the second with probability .7. Assume th

ddd [48]

Answer:

(a) P(X=1)=0.46

(b) E[X]=1.3

Step-by-step explanation:

(a)

Let A be the event that first coin will land on heads and B be the event that second coin will land on heads.

According to the given information

$P(A)=0.6$

$P(B)=0.7$

$P(A')=1-P(A)=1-0.6=0.4$

$P(B')=1-P(B)=1-0.7=0.3$

P(X=1) is the probability of getting exactly one head.

P(X=1) = P(1st heads and 2nd tails ∪ 1st tails and 2nd heads)

= P(1st heads and 2nd tails) + P(1st tails and 2nd heads)

Since the two events are disjoint, therefore we get

$P(X=1)=P(A)P(B')+P(A')P(B)$

$P(X=1)=(0.6)(0.3)+(0.4)(0.7)$

$P(X=1)=0.18+0.28$

$P(X=1)=0.46$

Therefore the value of P(X=1) is 0.46.

(b)

Thevalue of E[X] is

$E[X]=\sum_{x}xP(X=x)$

$E[X]=0P(X=0)+1P(X=1)+2P(X=2)$

$E[X]=P(X=1)+2P(X=2)$ ..... (1)

First we calculate the value of P(X=2).

P{X = 2} = P(1st heads and 2nd heads)

= P(1st heads)P(2nd heads)

$P(X=2)=P(A)P(B)$

$P(X=2)=(0.6)(0.7)$

$P(X=2)=0.42$

Substitute P(X=1)=0.46 and P(X=2)=0.42 in equation (1).

$E[X]=0.46+2(0.42)$

$E[X]=1.3$

Therefore the value of E[X] is 1.3.

3 0

3 years ago

Problem 3.2.14a<br><br> Show that 2^2x+1 +1 is divisible by 3.

elena-s [515]

Answer:

The given expression is divisible by 3 for all natural values of x.

Step-by-step explanation:

The given expression is

$2^{2x+1}+1$

For x=1,

$2^{2(1)+1}+1=2^{3}+18+1=9$

9 is divisible by 3. So, the given statement is true for x=1.

Assumed that the given statement is true for n=k.

$2^{2k+1}+1$

This expression is divisible by 3. So,

$2^{2k+1}+1=3n$ .... (1)

For x=k+1

$2^{2(k+1)+1}+1$

$2^{2k+2+1}+1$

$2^{(2k+1)+2}+1$

$2^{2k+1}2^2+1$

Using equation (1), we get

$(3n-1)2^2+1$

$(3n)2^2-2^2+1$

$(3n)2^2-4+1$

$(3n)4-3$

$3(4n-1)$

This expression is also divisible by 3.

Therefore the given expression is divisible by 3 for all natural values of x.

4 0

3 years ago

5. Kal Tire installs automobile tires on a first-come first-served basis. A random sample of 50 customers experienced an average

Rainbow [258]

5.7099 is the margin of error.

<h3>What is standard deviation ?</h3>

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

According to the question,

The standard sampling error of the sample mean is σₓ ,

The sampling distribution is: N (u,σₓ/n)

Therefore,

By using the standard deviation formula:

σₓ = √∑(xi -μ)/N

Where,

∑= population standard deviation

N= the size of the population

xi= each value from the population

μ =the population mean

So ,

σₓ = $\frac{20.6}{\sqrt{50} }$ = 2.913

Since, a = 1- 95% = 0.05

therefore $Z\frac{a}{2}$ = (1-0.005 x 2) = 1.959964

Here, the margin of error for a 95% confidence interval for this sample is given by:

$Z\frac{a}{2}$ * σₓ = 1.959964 x 2.913

= 5.7099

5.7099 is the margin of error for a 95% confidence interval for this sample.

Learn more about standard deviation here:

brainly.com/question/13905583

#SPJ1

7 0

1 year ago

How many groups of of 5/6 are in 1

zysi [14]

Answer:

6/5

Step-by-step explanation:

to find the number of 5/6 's in 1 , divide 1 by by 5/6 . when dividing by a fraction , rewrite it as multiplying by the reciprocal

4 0

2 years ago

Does 1+1=fish??????????

Ahat [919]

No 1+1 does not equal fish.....I thought so too until I looked it up

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3 years ago