Jennet graphs the inequality Negative 6 less-than x on the number line below.

Evaluate the triple integral ∭Tx2dV, where T is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,3,0), and (0,0,3).

bixtya [17]

Answer:

the integral I=81

Step-by-step explanation:

for the integral I

$I=\int\limits^{}_{}\int\limits^{}_{}\int\limits^{}_{T} {x^{2} } \, dxdydz$

where T is the solid tetrahedron , then

$I=\int\limits^{3}_{0}\int\limits^{3}_{0}\int\limits^{3}_{0} {x^{2} } \, dxdydz = \int\limits^{3}_{0}dz\int\limits^{3}_{0}dy\int\limits^{3}_{0} {x^{2} } \, dx = (3-0)*(3-0)*1/3*(3^{3}-0^{3}) = 3^{4} = 81$

the integral is equal to 81

8 0

2 years ago

Ella’s test grades in her history class are 89, 94, 82, 84, and 98. What score must Ella make on her next test to have a mean te

aksik [14]

Mean is same as average

to find average
add up terms
divided that sum by the number of terms you have
example

mean of x,y,z
x+y+z
3 terms
(x+y+z)/3=mean

so
represent next test score as x
89+94+82+84+98+x
count how many terms ther are (6 terms)

mean is 90
(89+94+82+84+98+x)/6=90
add the like terms
(447+x)/6=90
multiply both sides by 6 to clear fraction
447+x=540
subtract 447 from both sides
x=93

she needs a score of 93 on next test

8 0

2 years ago

Read 2 more answers

Is 0.398 a whole number, interger, rational number, irrational number, or a real number

docker41 [41]

It would be a real number

3 0

2 years ago

Read 2 more answers

preliminary sample of 100 labourers was selected from a population of 5000 labourers by simple random sampling. It was found tha

VladimirAG [237]

Answer:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

n=369

Step-by-step explanation:

1) Notation and definitions

$X=40$ number of the selected labourers opt for a new incentive scheme.

$n=100$ random sample taken

$\hat p=\frac{40}{100}=0.4$ estimated proportion of the selected labourers opt for a new incentive scheme.

$p$ true population proportion of the selected labourers opt for a new incentive scheme.

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".

The population proportion have the following distribution

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

2) Solution tot he problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: