Which situation can be represented by the expression 1.3x?

__________ is the source error that can be avoided by locating questions sensitive to bias and changing or dropping them.

brilliants [131]

I think the correct answer from the choices listed above is option B. Deliberate bias <span> is the source error that can be avoided by locating questions sensitive to bias and changing or dropping them. Hope this answers the question. Have a nice day.</span>

8 0

2 years ago

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(b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y =

frutty [35]

Answer:

Check attachment for complete question

Step-by-step explanation:

Given that,

y=Coskt

We are looking for value of k, that satisfies 4y''=-25y

Let find y' and y''

y=Coskt

y'=-kSinkt

y''=-k²Coskt

Then, applying this 4y'"=-25y

4(-k²Coskt)=-25Coskt

-4k²Coskt=-25Coskt

Divide through by Coskt and we assume Coskt is not equal to zero

-4k²=-25

k²=-25/-4

k²=25/4

Then, k=√(25/4)

k= ± 5/2

b. Let assume we want to use this

y=ASinkt+BCoskt

Since k= ± 5/2

y=A•Sin(±5/2t)+ B •Cos(±5/2t)

y'=±5/2ACos(±5/2t)-±5/2BSin(±5/2t)

y''=-25/4ASin(±5/2t)-25/4BCos(±5/2t

Then, inserting this to our equation given to check if it a solution to y=ASinkt+BCoskt

4y''=-25y

For 4y''

4(-25/4ASin(±5/2t)-25/4BCos(±5/2t))

-25A•Sin(±5/2t)-25B•Cos(±5/2t).

Then,

-25y

-25(A•Sin(±5/2t)+ B •Cos(±5/2t))

-25A•Sin(±5/2t) - 25B •Cos(±5/2t)

Then, we notice that, 4y'' is equal to -25y, then we can say that y=Coskt is a solution to y=ASinkt+BCoskt

4 0

2 years ago

The mean annual salary for intermediate level executives is about $74000 per year with a standard deviation of $2500. A random s

lidiya [134]

Answer:

11.51% probability that the mean annual salary of the sample is between $71000 and $73500

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 74000, \sigma = 2500, n = 36, s = \frac{2500}{\sqrt{36}} = 416.67$

What is the probability that the mean annual salary of the sample is between $71000 and $73500?

This is the pvalue of Z when X = 73500 subtracted by the pvalue of Z when X = 71000. So

X = 73500

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

By the Central Limit Theorem

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

$Z = \frac{73500 - 74000}{416.67}$

$Z = -1.2$

$Z = -1.2$ has a pvalue of 0.1151

X = 71000

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

$Z = \frac{71000 - 74000}{416.67}$

$Z = -7.2$

$Z = -7.2$ has a pvalue of 0.

0.1151 - 0 = 0.1151

11.51% probability that the mean annual salary of the sample is between $71000 and $73500

8 0

2 years ago

Mr Hughes is competing in the Mr. Legs campaign to raise money for the coral shores high school scholarship fund. On the first d

lakkis [162]

<span>The number of dollars collected can be modelled by both a linear model and an exponential model. To calculate the number of dollars to be calculated on the 6th day based on a linear model, we recall that the formula for the equation of a line is given by (y - y1) / (x - x1) = (y2 - y1) / (x2 - x1), where (x1, y1) = (1, 2) and (x2, y2) = (3, 8) The equation of the line representing the model = (y - 2) / (x - 1) = (8 - 2) / (3 - 1) = 6 / 2 = 3 y - 2 = 3(x - 1) = 3x - 3 y = 3x - 3 + 2 = 3x - 1 Therefore, the amount of dollars to be collected on the 6th day based on the linear model is given by y = 3(6) - 1 = 18 - 1 = $17 To calculate the number of dollars to be calculated on the 6th day based on an exponential model, we recall that the formula for exponential growth is given by y = ar^(x-1), where y is the number of dollars collected and x represent each collection day and a is the amount collected on the first day = $2. 8 = 2r^(3 - 1) = 2r^2 r^2 = 8/2 = 4 r = sqrt(4) = 2 Therefore, the amount of dollars to be collected on the 6th day based on the exponential model is given by y = 2(2)^(5 - 1) = 2(2)^4 = 2(16) = $32</span>

4 0

2 years ago

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Manuel has $600 in a savings account at the beginning of the summer. He wants to have at least $300 in the account at the end of

klasskru [66]

600-28(w)=300
-28(w)=-300
~approximately 10 weeks

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2 years ago

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