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Paladinen [302]
2 years ago
5

Sarah wants to swim across a 193 m river. Due to the current she is swept 67 m downriver from where she wanted to be. What is th

e length that she actually swam from start to where she ended? Round to the nearest tenth
Mathematics
2 answers:
tatyana61 [14]2 years ago
8 0

Answer:

Step-by-step explanation:

Sarah swam the diagonal length of a right-angled triangle with sides of river width, 193m and how far she was swept downstream, 67m.

By Pythagorean Theorem, distance swam = sqrt(193^2+67^2)

= 204.3 m

VMariaS [17]2 years ago
3 0

Apply Pythagorean theorem

\\ \rm\rightarrowtail H^2=P^2+B^2

\\ \rm\rightarrowtail H^2=193^2+67^2

\\ \rm\rightarrowtail H^2=41738

\\ \rm\rightarrowtail H=204ft(Approx)

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Answer:

8/3

Step-by-step explanation:

i put equations as this:

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where x is galllons of pure mixture and y is the gallons of the new mixture

the other equation i id was:

x+0.2(40) = 0.25y

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y = 4x+32

solve using substitution

(x+40) = 4x+32

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2 years ago
The expression below is the factorization of what trinomial-1(x+5)(x+6)
Nadya [2.5K]

Answer:

-x^2 - 11x -30

Step-by-step explanation:

Solve using foiling. Ignore the -1 to begin with and just look at the part in parenthesis. Do x from the first parenthesis times the stuff in the second parenthesis.

ie: x(x) and x(6)

ie: x^2 + 6x

Then do the 5 times the things in the second parenthesis.

ie: 5(x) and 5(6)

ie: 5x + 30

Then add what you got from multiplying the first value to what you got from multiplying the second.

ie: x^2 + 11x + 30

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4 0
2 years ago
Suppose that administrators at a large urban high school want to gain a better understanding of the prevalence of bullying withi
boyakko [2]

Answer:

lower limit =0.261

upper limit =0.369

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Description in words of the parameter p

p represent the real population proportion of people that have experienced bullying

X= 63 people in the random sample that have experienced bullying

n=200 is the sample size required  

\hat p=\frac{63}{200}=0.315 represent the estimated proportion of people that have experienced bullying

z_{\alpha/2} represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Numerical estimate for p

In order to estimate a proportion we use this formula:

\hat p =\frac{X}{n} where X represent the number of people with a characteristic and n the total sample size selected.

\hat p=\frac{63}{200}=0.315 represent the estimated proportion of people that they were planning to pursue a graduate degree

Confidence interval

The confidence interval for a proportion is given by this formula  

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}  

For the 90% confidence interval the value of \alpha=1-0.90=0.1 and \alpha/2=0.05, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.64  

And replacing into the confidence interval formula we got:  

0.315 - 1.64 \sqrt{\frac{0.315(1-0.315)}{200}}=0.261  

0.315 - 1.64 \sqrt{\frac{0.315(1-0.315)}{200}}=0.369  

And the 90% confidence interval would be given (0.261;0.369).  

We are confident at 90% that the true proportion of people that they were planning to pursue a graduate degree is between (0.261;0.369).  

lower limit =0.261

upper limit =0.369

5 0
3 years ago
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