Suppose you roll two dice. How many different ways can you roll the dice so that their sum is 2

Suppose u and v are functions of x that are differentiable at x=0 and that u(0)=3, u'(0)= -4, v(0)= 2, v'(0)= -7. Find the value

3241004551 [841]

$\bf \cfrac{d}{dx}[u(x)\cdot v(x)]\implies \cfrac{du}{dx}\cdot v(x)+u(x)\cdot \cfrac{dv}{dx}\quad 
\begin{cases}
u(0)=3\qquad u'(0)=-4
\\\\
v(0)=2\qquad v'(0)=-7
\end{cases}
\\\\
\left[ \cfrac{du}{dx} \right]_{x=0}\cdot v(0)+u(0)\cdot \left[ \cfrac{dv}{dx} \right]_{x=0}$

so.. hmm pretty sure you know what that is

7 0

3 years ago

Read 2 more answers

Omar deposited $4000 into an account with 4.4% interest, compounded quarterly. Assuming that no withdrawals are made, how much w

melamori03 [73]

The formula you want is: fv=p(1+int/c)^(nc)
future value
principal
int
compound
years

7 0

2 years ago

Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame

lbvjy [14]

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

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 problem, we have that:

$\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678$

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

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

By the Central Limit Theorem

$Z = \frac{207.9 - 208}{0.1678}$

$Z = -0.6$

$Z = -0.6$ has a pvalue of 0.2743

2*0.2743 = 0.5486

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

6 0

3 years ago

How do you do this problem 7-r=8-r-r

Oliga [24]

Answer:

r = 1

Step-by-step explanation:

Solve for r

by simplifying both sides of the equation, then isolating the variable.

3 0

3 years ago

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Which is greater 78.61 or78.6

ANTONII [103]

Answer:

78.61 is greater than 78.6.

Step-by-step explanation:

Adding a zero to 78.6, resulting in 78.60, makes it easier to compare 78.6 and 78.61. 78.61 is greater than 78.6.

7 0

3 years ago