He figure is rotated counterclockwise. Which rotation could have taken place?
1 answer:
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Roots with imaginary parts always occur in conjugate pairs. Three of the four roots are known and they are all real, which means the fourth root must also be real.
Because we know 3 and -1 (multiplicity 2) are both roots, the last root is such that we can write
There are a few ways we can go about finding , but the easiest way would be to consider only the constant term in the expansion of the right hand side. We don't have to actually compute the expansion, because we know by properties of multiplication that the constant term will be
.
Meanwhile, on the left hand side, we see the constant term is supposed to be 9, which means we have
so the missing root is 3.
Other things we could have tried that spring to mind:
- three rounds of division, dividing the quartic polynomial by , then by
twice, and noting that the remainder upon each division should be 0
- rational root theorem
Answer:
A 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .
Step-by-step explanation:
We are given that a researcher randomly selects records from 60 such drivers in 2009 and determines the sample mean BAC to be 0.16 g/dL with a standard deviation of 0.080 g/dL.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~
where, = sample mean BAC = 0.16 g/dL
s = sample standard deviation = 0.080 g/dL
n = sample of drivers = 60
= population mean BAC in fatal crashes
<em>Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation. </em>
So, a 90% confidence interval for the population mean, is;
P(-1.672 < < 1.672) = 0.90 {As the critical value of t at 59 degrees of
freedom are -1.672 & 1.672 with P = 5%} P(-1.672 < < 1.672) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u>90% confidence interval for</u> = [
,
]
= [ ,
]
= [0.143, 0.177]
Therefore, a 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .
Question is Incomplete;
Complete question is given below;
Tracy had a total of $200 to spend while shopping. She has already spent $122 on clothes. She wants to buy some video games that are on sale for $20 each, including tax. Enter the maximum number of video games Tracy can buy with the remaining money.
Answer:
Tracy can buy maximum of 3 video games with the remaining money.
Step-by-step explanation:
Given:
Total money to spend on shopping = $200
Money spend on clothes = $122
Cost of each video game = $20
We need to find the number of Video games she could buy.
Solution:
Let the number of video games be 'x'.
So we can say that;
Money spend on clothes plus Cost of each video game multiplied by number of Video games should be less than or equal to Total money to spend on shopping.
framing in equation form we get;
Now by subtraction property of Inequality we will subtract both side by 122 we get;
Now dividing both side by 20 using division property of inequality we get;
Hence Tracy can buy maximum of 3 video games with the remaining money.