AV Can the HL Congruence Property be used? Yes O No O Yes O No

Answer two questions about Systems A and B:System A x+3y=−9 2x+y=4 System B 3x+4y=−9 2x+y=4

Jet001 [13]

Answer:

A=(21/5,-22/5) B=(5,-6)

Step-by-step explanation:

6 0

3 years ago

A report indicated that 37% of adults had received a bogus email intended to steal personal information. Suppose a random sample

fiasKO [112]

Answer:

5.05% probability that no more than 34% had received such an email.

Step-by-step explanation:

We use the binomial approximation to the normal to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 700, p = 0.37$

$\mu = E(X) = np = 700*0.37 = 259$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{700*0.37*0.63} = 12.77$

In a random sample of 700 adults, what is the probability that no more than 34% had received such an email?

34% is 0.34*700 = 238

So this probability is the pvalue of Z when X = 238.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{238 - 259}{12.77}$

$Z = -1.64$

$Z = -1.64$ has a pvalue of 0.0505

5.05% probability that no more than 34% had received such an email.

7 0

4 years ago

Last year at a certain high school, there were 125 boys on the honor roll and 80 girls on the honor roll. This year, the number

Elodia [21]

Answer:

6.8% decrease

Step-by-step explanation:

a drop of 8% means that only 92% of 125 boys remained on honor roll from last year; .92 x 125 = 115

a drop of 5% means that only 95% of 80 girls remained on honor roll from last year; .95 x 80 = 76

total number of students on honor roll last year = 125 + 80 = 205

total number of students on honor roll this year = 115 + 76 = 191

percent of change = (191 - 205) ÷ 205 = -14/205 = -.068

-.068, which represents a 6.8% decrease

3 0

2 years ago

Estimate quotient using multiples, 136÷6

lana66690 [7]

136/6 = 22.6666667......

3 0

3 years ago

Read 2 more answers

A person's heartbeat is 88 beats per minute. If his/her heart beats 3.1e9 times in a lifetime, how long (in whole years) does th

Anit [1.1K]

We can solve this problem by the rule of three.

88 beats-------------------1 minute
3.1*10⁹ beats------------ x

x=(3.1*10⁹ beats * 1 minute) / 88 beats=35227272.73 minutes.

Now, we express this amount of time in years.

1 year=365 days
365 days=365 day*(24 hour/1day)*(24 hour /1day)*(60 minutes /1hour)=
=525600 minutes.

525600 minutes----------------------1year
35227272.73 minutes----------------x

x=(35227272.73 minutes * 1year) / 525600 minutes=67.0229 years
≈ 67 years.

Answer:this person can live 67 years.

5 0

3 years ago