If M= {m, a,t} how many subsets of M are there?

A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced.

zzz [600]

Answer:

$CI=(66.54,78.46)$

Step-by-step explanation:

Given : A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed.

To find : A 99% confidence interval for the mean yield when the new catalyst is used ?

Solution :

Let X be the yield of the batches.

We have given, n=10 , $\bar{X}=72.5\%$ , s=5.8%

Since the size of the sample is small.

We will use the student's t statistic to construct a 995 confidence interval.

$\bar X\pm t_{n-1,\frac{\alpha}{2}}\frac{s}{\sqrt n}$

From the t-table with 9 degree of freedom for $\frac{\alpha}{2}=0.005$

$t_{n-1,\frac{\alpha}{2}}=t_{9,0.005}$

$t_{n-1,\frac{\alpha}{2}}=3.250$

The 99% confidence interval is given by,

$CI=72.5 \pm 3.25\frac{5.8}{\sqrt{10}}$

$CI=72.5 \pm 5.96$

$CI=(72.5+5.96),(72.5-5.96)$

$CI=(66.54,78.46)$

8 0

2 years ago

Helppp, graph of function!!

Debora [2.8K]

Yes I will help you but give me point then I will help you

3 0

2 years ago

WITH PICTURE!!3. What is the value of x in the regular polygon below? (3 points)

monitta

Answer: FIRST OPTION.

Step-by-step explanation:

Regular polygons are those polygons whose sides are equal in length and whose angles are all equal.

By definition each interior angle of a Regular polygon,is:

$\frac{180 ( n -2 )}{n}$ (In degrees)

Where "n" is the number of sides of the polygon.

Observe the Regular polygon given in the exercise.

Since it has 6 sides, you can conclude that it is an Hexagon. Then:

$n=6$

Substituting into $\frac{180 ( n -2 )}{n}$ and evaluating, you get:

$\frac{180 ( 6 -2 )}{6}=120\°$

Knowing this, you can write the following equation:

$3x=120$

Finally, you must solve for "x" in order to find its value. This is:

$x=\frac{120}{3}\\\\x=40$

8 0

3 years ago

express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]

Lemur [1.5K]

The limit as a definite integral on the interval $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π , 4π] is $\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$ .

<h3>What is meant by definite integral?</h3>

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$

substitute the values in the above equation, we get

= $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π, 4π],

simplifying the above equation

$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$

To learn more about definite integral refer to:

brainly.com/question/24353968

#SPJ4

8 0

1 year ago

Please help!! Use cube root to solve. Will give brainliest!!

marissa [1.9K]

Answer: x=-17

Step-by-step explanation: Divide by -1 then add 8 to both sides and get (x+9)^3=-512, and the cube root of -512 is -8, so x+9=-8, and subtracting 9 from both sides we get x=-17 as answer.

4 0

2 years ago