Round 69781 to the nearest thousand

Answer:

0.9544 = 95.44% probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons.

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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, 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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

Suppose the mean fill for the shipment is actually 50 gallons. Standard deviation of 0.6 gallons.

This means that [tex]\mu = 50, \sigma = 0.6[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{0.6}{\sqrt{100}} = 0.06[/tex]

What is the probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons?

This is the pvalue of Z when X = 50.12 subtracted by the pvalue of Z when X = 49.88. So

X = 50.12

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{50.12 - 50}{0.06}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 49.88

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{49.88 - 50}{0.06}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons.

Answer:

the first one

the first one Step-by-step explanation:

the first one Step-by-step explanation:from the formula Un =ar^n-1

where a is 2

where a is 2 r = 20/2=10

where a is 2 r = 20/2=10 so Un= 10×2^n-1

that's all.....have fun

Answer:

C.)  an =1/5 * 10n-1

Step-by-step explanation:

D.) is out of the question just at first look.
A.) is irregular to the sequence, giving you the wrong outputs.
B.) is also irregular to the sequence.

Leaveing your answer...

Hi there!

[tex]\large\boxed{\text{At (-1, -2), }\frac{dy}{dx} = -\frac{2}{5}}}[/tex]

[tex]\large\boxed{\text{At (-1, 3), }\frac{dy}{dx} = -\frac{3}{5}}}[/tex]

We can calculate dy/dx using implicit differentiation:

xy + y² = 6

Differentiate both sides. Remember to use the Product Rule for the "xy" term:

(1)y + x(dy/dx)  + 2y(dy/dx) = 0

Move y to the opposite side:

x(dy/dx) + 2y(dy/dx) = -y

Factor out dy/dx:

dy/dx(x + 2y) = -y

Divide both sides by x + 2y:

dy/dx = -y/x + 2y

We need both x and y to find dy/dx, so plug in the given value of x into the original equation:

-1(y) + y² = 6

-y + y² = 6

y² - y - 6 = 0

(y - 3)(y + 2) = 0

Thus, y = -2 and 3.

We can calculate dy/dx at each point:

At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.

At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.

Answer:

wth is this

show the pic of the question

Answer:

im pretty sure its D :) hope this helps you out.

Answer:

The circumference is 45.2yd

Step-by-step explanation:

Given

[tex]d = 14.4[/tex] --- diameter

Required

Determine the circumference

The circumference is calculated as:

[tex]C =\pi d[/tex]

So, we have:

[tex]C =\pi * 14.4[/tex]

Take pi a 3.14

[tex]C =3.14 * 14.4[/tex]

[tex]C =45.216[/tex]

Approximate

[tex]C =45.2yd[/tex]

Answer:

75%

Step-by-step explanation:

The computation of the percent of the professional professors there are tenured is shown below;

Given that

academic professors A = 60%

professors  tenured P = 70%

professors at Paracelsus University = 90%

Based on the above information

As we know that 90% of the professors could be academic professors or tenured or both

so  here we can say that the percent of academic professors  is

= 60 + 70 - 90

= 40

Therefore professors  tenured will be

= 70 - 40

= 30

Now the percentage of professional professor that is tenured is

= 30 ÷ 40 × 100

= 75%

Answer:

angle O is equal to 41°

I hope it's helps you

Answer:

Step-by-step explanation:

Parts + 3($40 labor)=183.30

parts + 120=183.30

parts=63.30 but it includes tax. To find costs of parts before tax you

63.30/1.055=60 so parts are $60

or to solve with one equation:

parts(1.055) + 3($40 labor) = 183.30

parts(1.055) + 120=183.30

parts(1.055)=63.30

Parts = 63.30/1.055

parts = 60

Answer:

24j + 24

Step-by-step explanation:

6(3j + 4 +j)

6(4j + 4)

24j + 24

Answer:

u = v - at

Step-by-step explanation:

v = u + at

v - at = u + at - at

v - at = u

u = v - at

Answer:

4/3 x 5/8 is correct

Step-by-step explanation:

Answer: C 7/10 * 5/8

Step-by-step explanation:

4/3 * 5/8 = 20 / 24 = 5 / 6

3/2 * 5/8 = 15 / 16

7/10 * 5/8 = 35/80 = 7 / 16

9/7 * 5/8 = 45 / 56

5/8  = 10/16

7/16 < 10/16

7/16 < 5/8

Answer:

[tex]Interval = (-2,1.5)[/tex]

[tex]Interval = (-\infty, -2)\ u\ (1.5,\infty)[/tex]

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Increasing interval

To do this, we simply identify the interval at which the value of the graph increases.

The value has an increased interval between -2 and 1.5 (of the x-axis).

Hence, the increasing interval is:

[tex]Interval = (-2,1.5)[/tex]

Solving (b): Decreasing interval

To do this, we simply identify the interval at which the value of the graph decreases.

The value has decreased intervals between - infinity and -2 and also 1.5 and infinity (of the x-axis).

Hence, the decreasing interval is:

[tex]Interval = (-\infty, -2)\ u\ (1.5,\infty)[/tex]

Dilation involves changing the size of a figure

The endpoints of the image are (-2,-1) and (6,1)

The coordinates of the pre-image are give as:

(2,2) and (6,2)

The scale factor is given as:

k = 2

The center of dilation is given as:

(a,b) = (6,5)

The coordinates of the image are then calculated as:

[tex](x,y) \to (k(x -a) + a, k(y -b) + b)[/tex]

For (2,2), we have:

[tex](x,y) \to (2(2 -6) + 6, 2(2 - 5) + 5)[/tex]

[tex](x,y) \to (-2, -1)[/tex]

For (6,2), we have:

[tex](x,y) \to (2(6 -6) + 6, 2(2 - 5) + 5)[/tex]

[tex](x,y) \to (6, -1)[/tex]

Hence, the endpoints of the image are (-2,-1) and (6,1)

Read more about dilation at:

https://brainly.com/question/3457976

Answer:

B

Step-by-step explanation:

Answer:

0.877 but rounded it will be 0.88

Answer:

c. SA = 596 ft²

Step-by-step explanation:

Area of the rectangular pyramid = Base area + area of the 2 equal lateral faces + area of the 2 lateral faces

Base area = length × width

Length = 16 ft

Width = 12 ft

Base area = 16 × 12 = 192 ft²

Area of the 2 lateral faces with the following dimension:

base = 12 ft

height = 15 ft

Area = 2(½bh) = 2(½*12*15) = 180 ft²

Area of the 2 lateral faces with the following dimensions:

base = 16 ft

height = 14 ft

Area = 2(½*14*16) = 224 ft²

✅Total surface area = 192 + 180 + 224 = 596 ft²

Answer:

10

Step-by-step explanation:

Answer:

No  If it would be 10 percent of the total would be the price tag without tax

Step-by-step explanation:

Answer:

3. m<4=101°

4. sum of angle on a straight line

5. m<8= 101°

6.m<3=180-101°

=79°

7.sum =180°

8. alternate angles

9. and m<8

10. 180°

Answer:

3.

m<1=79°

m<4=180-79°=101°(linear pair)

4.

<7+<8=180°(straight line)

5.

m<6=101

m<8=101°[vertically opposite angle]

6.

m<3=180-101=79°

7.

180°

8.

alternate angle

9.

and <8

10.

180°

Answer:

Step-by-step explanation:

hello :

use identity : a²-b²=(a-b)(a+b)

(2x+1) (2x-1)= (2x)²-1 =4x²-1

Answer:

x = 9.4868

Step-by-step explanation:

For this problem we can use the Pythagorean Theorem

Pythagorean theorem = [tex]a^2+b^2=c^2[/tex]

IN THIS CASE C = X

A and B are the side and base lengths of a right triangle.

C is the Hypotenuse side.

[tex]9^2+3^2=c^2[/tex]

Solve...

81 + 9 = [tex]c^2[/tex]

90 =[tex]c^2[/tex]

[tex]\sqrt{90}[/tex] = c

c = 9.4868

Answer:

The correct answer is B.

Step-by-step explanation:

V=whl=1.5·2·5=15

Answer:

B. 15 ft.3

Step-by-step explanation:

multiply all the measurements to find the volume :)

9514 1404 393

Answer:

  9/10

Step-by-step explanation:

(1 1/10) - 1/5 = (1 1/10) -2/10 = 1 + (1/10 -2/10) = 1 -1/10 = 9/10

__

1.1 -0.2 = 0.9 = 9/10

Answer:

6.3

Step-by-step explanation:

99(.07)=6.3

original price was 92.7 + 6.3 gives you 99