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3 years ago

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A line passes through the point (2 comma negative 2 comma 10 ), and is parallel to the vector 9 Bold i plus 7 Bold j plus 10 Bo

ld k. Find the standard parametric equations for the line, written using the components of the given vector and the coordinates of the given point.

1 answer:

lyudmila [28]3 years ago

3 0

Title:

<h2>The standard parametric equation for the line is $\frac{x - 2}{9} = \frac{y + 2}{7} = \frac{z - 10}{10}$ .</h2>

Step-by-step explanation:

The standard parametric equation for a line generally represented as $\frac{x - a}{l} = \frac{y - b}{m} = \frac{z - c}{n}$ ; where (a, b, c) is the point that the line passes through and (l, m, n) is the direction vector of the line.

It is given that the line passes through the point (2, -2, 10).

Hence, here (a, b, c) ≡ (2, -2, 10).

Similarly, the direction vector of the line is given by (l, m, n) ≡ (9, 7, 10).

Putting all the values in the equation of the line, the equation becomes

$\frac{x - 2}{9} = \frac{y + 2}{7} = \frac{z - 10}{10}$ .

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Brand name producers of aspirin claim that one advantage of their aspirin over generic aspirin is that brand name aspirin is muc

11Alexandr11 [23.1K]

Answer:

Step-by-step explanation:

The claim here is that the brand name aspirin is more consistent in the amount of active ingredient used than the generic aspirin.

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean amount of active ingredients in brand name aspirin and μ2 be the mean amount of active ingredients in generic name aspirin

The random variable is μ1 - μ2 = difference in the mean amount of active ingredients between the brand name and generic aspirin

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 ≥ μ2 H0 : μ1 - μ2 ≥ 0

The alternative hypothesis is

H1 : μ1 < μ2 H1 : μ1 - μ2 < 0

This is a left tailed test

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 325.01

x2 = 323.47

s1 = 10.12

s2 = 11.43

n1 = 200

n2 = 180

t = (325.01 - 323.47)/√(10.12²/200 + 11.43²/180)

t = 1.24

1.237877

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [10.12²/200 + 11.43²/180]²/[(1/200 - 1)(10.12²/200)² + (1/180 - 1)(11.43²/180)²] = 1.53233946713/0.00537245359

df = 285

We would determine the probability value from the t test calculator. It becomes

p value = 0.108

Since alpha, 0.025 < than the p value, 0.108, then we would fail to reject the null hypothesis. Therefore, at 2.5% level of significance, these data support the brand name producers claim

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3 years ago

For X a binomial random variable with n=5 and p=1/4, answer the following

mash [69]

Recall that for $X\sim\mathrm{Bin}(n,p)$ , i.e. a random variable $X$ following a binomial distribution over $n$ trials and with probability parameter $p$ ,

$\mathbb P(X=x)=f_X(x)=\begin{cases}\dbinom nx p^x(1-p)^{n-x}&\text{for }x\in\{0,1,\ldots,n\}\\\\0&\text{otherwise}\end{cases}$

So you have

$\mathbb P(X=2)=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac34\right)^{5-2}=\dfrac{135}{512}\approx0.26$

$\mathbb P(2\le X\le4)=\displaystyle\sum_{x=2}^4\mathbb P(X=x)$
$=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac14\right)^{5-2}+\dbinom52\left(\dfrac14\right)^3\left(1-\dfrac14\right)^{5-3}+\dbinom52\left(\dfrac14\right)^4\left(1-\dfrac14\right)^{5-4}$
$=\dfrac{375}{1024}\approx0.37$

The expected value of $X\sim\mathrm{Bin}(n,p)$ is simply $np$ , while the standard deviation is $\sqrt{np(1-p)}$ . In this case, they are $\dfrac54=1.25$ and $\sqrt{\dfrac{15}{16}}\approx0.97$ , respectively.

7 0

3 years ago

N the function y = 12.00x + 50, y represents the cost of carpet by the square yard and x represents the number of square yards.

borishaifa [10]

Answer:

The cost increase for each square of carpet by 12.

Step-by-step explanation:

The given function is

$y=12.00x+50$

It is a slope intercept form of the line

$y=mx+b$

Where m is the slope and b is y-intercept.

Therefore the slope of given function is 12 and the y-intercept is 50.

It means the initial ot fixed cost of the carpet is 50 and the cost increased by 12 for each square of carpet.

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3 years ago

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GrogVix [38]

The answer would be -2! :)

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3 years ago

Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118. If a recent test-taker

LuckyWell [14K]

Answer:

Probability that the student scored between 455 and 573 on the exam is 0.38292.

Step-by-step explanation:

We are given that Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118.

<u><em>Let X = Math scores on the SAT exam</em></u>

So, X ~ Normal( $\mu=514,\sigma^{2} =118^{2}$ )

The z score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean score = 514

$\sigma$ = standard deviation = 118

Now, the probability that the student scored between 455 and 573 on the exam is given by = P(455 < X < 573)

P(455 < X < 573) = P(X < 573) - P(X $\leq$ 455)

P(X < 573) = P( $\frac{X-\mu}{\sigma}$ < $\frac{573-514}{118}$ ) = P(Z < 0.50) = 0.69146

P(X $\leq$ 2.9) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{455-514}{118}$ ) = P(Z $\leq$ -0.50) = 1 - P(Z < 0.50)

= 1 - 0.69146 = 0.30854

<em>The above probability is calculated by looking at the value of x = 0.50 in the z table which has an area of 0.69146.</em>

Therefore, P(455 < X < 573) = 0.69146 - 0.30854 = <u>0.38292</u>

Hence, probability that the student scored between 455 and 573 on the exam is 0.38292.

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3 years ago