Classify each as true or false. if the statement is true, identify the theorem. if the statement is false, give a counter example to show it is false.

Answer:

The expected total amount of time the operator will spend on the calls each day is of 210 minutes.

Step-by-step explanation:

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.

n-values of normal variable:

Suppose we have n values from a normally distributed variable. The mean of the sum of all the instances is [tex]M = n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]

Calls to a customer service center last on average 2.8 minutes.

This means that [tex]\mu = 2.8[/tex]

75 calls each day.

This means that [tex]n = 75[/tex]

What is the expected total amount of time in minutes the operator will spend on the calls each day

This is M, so:

[tex]M = n\mu = 75*2.8 = 210[/tex]

The expected total amount of time the operator will spend on the calls each day is of 210 minutes.

Answer:

[tex]c < 4[/tex]

Step-by-step explanation:

Move the constant to the right-hand side and change its signs:

[tex]c < 16 - 12[/tex]

Subtract the numbers:

[tex]c < 16 - 12 = c < 4[/tex]

Answer:

sum of angles in a triangle = 180°

180-(90+21)

= 69

pls am I correct

Answer:

10.9 %

Step-by-step explanation:

46 - 41 = 5

5/46 * 100% = 10.8695652174%

Rounded

10.9 %

Answer:

So, to fill the tray completely , he needs 3 bags of sand.

Step-by-step explanation:

Tray dimensions,

length = 0.8 m

Width = 0.6 m

height = 0.1 m

Volume of one sand bag = 17000 cm^3

Let the volume of the tray is V.

V = length x idth x height

V = 0.8 x 0.6 x 0.1 = 0.048 m^3

Number of sand bags

[tex]n=\frac{0.048}{17000\times 10^{-6}}\\\\n = 2.82[/tex]

So, to fill the tray completely , he needs 3 bags of sand.

Answer:

25 is A and 26 is B

Step-by-step explanation:

25) a²+b²=c²

missing side can be=b

to find the missing side subtract 6.7² from 12.6²

b²=12.6²-6.7²

b²=158.76-44.89

the square root of b²= the square root of 113.87

b=10.67

the missing side is equal to 10.7(1d.p)

26) a²+b²=c²

c= hypotenuse

10.8²+11²=c²

116.64+121=c²

c²=237.64

the square root of c²= the square root of 237.64

c=15.42(2d.p)

the hypotenuse is=15.4

The places that I have "the square root of" you must replace it with the square root sign. I'm using my phone so I wasn't sure how to insert a square root sign.

Answer:

= 5 * NORMINV(RAND(), 35, 5)

Step-by-step explanation:

From the given information:

The total weekly profit is achieved by the multiplication of the unit profit (5) and the weekly demand.

Here, the weekly demands obey a normal distribution where the mean = 35 and the standard deviation = 5.

Using the Excel Formula:

The weekly profit can be computed as:

= 5 * NORMINV(RAND(), 35, 5)

The values of variables, such as the height of the table can be found by writing equations of their relationships

The height of the table is 105 cm

The reason the above height value is correct is as follows;

Known parameters:

The diagram shows a table, a cat and a mice

Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice

From the given diagram, we have;

Height of the table + Height of the cat - Height of the mice  = 120 cm

∴ x + y - z = 120...(1)

Height of the table + Height of the mice - Height of the cat   = 90 cm

∴ x + z - y = 90...(2)

Adding equation (1) to equation (2) gives;

x + y - z + (x + z - y) = 120 + 90 = 210

x + y - z + (x + z - y) = 210

However;

x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x

∴ x + y - z + (x + z - y) = 2·x = 210

x = 210/2 = 105

Therefore;

The height of the table, x = 105 cm

Learn more about word problems leading on simultaneous equations here:

https://brainly.com/question/16513646

Exact Surface Area = 378pi

Approximate Surface Area = 1186.92

The approximate surface area uses pi = 3.14

The units are cm^2 or "square cm".

=========================================================

Work Shown:

SA = surface area of cylinder

SA = 2*pi*r^2 + 2*pi*r*h

SA = 2*pi*7^2 + 2*pi*7*20

SA = 2*pi*49 + 2*pi*140

SA = 2*49*pi + 2*140*pi

SA = 98pi + 280pi

SA = 378pi ..... exact surface area

SA = 378*3.14

SA = 1186.92 ..... approximate surface area

----------

Side note: The diameter 14 cuts in half to get the radius r = 7

Answer:

1187.52

Step-by-step explanation:

Use the formula [tex]2\pi rh+2\pi r^{2}[/tex].

r= 7 (half of your diameter, which is 14)

h = 20

Fill in your radius and height.

[tex]2\pi (7)(20)+2\pi (7^{2})[/tex]

Enter your equation into a calculator and you'll get 1187.52202.

When rounded to the nearest hundredths, you get 1187.52

Answer:

Step-by-step explanation:

產品 1 14 20 13

產品 2 15 11 18

產品 3 12 15 16

The equation and graph show the cost to rent movies from two different companies. The cost is a function of the number of movies rented.The description best compares the two functions?

here the pic and pls brainly me hege

Answer:

345

Step-by-step explanation:

Answer:

12,10

Step-by-step explanation:

60,50:100x20=12.10

9514 1404 393

Answer:

  (x^(1/2))(x^(1/2)) = x^(1/2 +1/2) = x^1 = x

Step-by-step explanation:

The rule of exponents is ...

  (x^a)(x^b) = x^(a+b)

From which ...

  (x^a)(x^a) = x^(a+a) = x^(2a)

So, if we want two identical factors that have a product of x = x^1, then the exponents of those factors will be such that ...

  x^(2a) = x^1

  2a = 1

  a = 1/2

The square root is defined as one of two identical factors that have a product equal to the specified value. That is ...

  (√x)(√x) = x

Above, we have shown that ...

  (x^(1/2))(x^(1/2)) = x

so, we can conclude ...

  √x = x^(1/2)

_____

Additional comment

In like fashion, we can show that the n-th root of a number is the same as that number to the 1/n power. It's really a matter of definition. Since the square of x^(1/2) is x, we call x^(1/2) the square root. It is used commonly enough that it has its own symbol: √x.

Answer:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

Answer:

[tex]Probability = \frac{4}{15}[/tex]

Step-by-step explanation:

B1 = first bag

B2= second bag

B3 = third bag

Let A = ball drawn is red

Since, there are three bags.

Probability of choosing one bag=  P(B1) = P(B2) = P(B3) = 1/3.

From B1: Total balls = 10

3 red + 7 black balls.

Probability of drawing 1 red ball from it , P(A) = 3/10.

From B2: Total balls = 10

8 red + 2 black

Probability of drawing 1 red ball is, P(A) = 8/10

From B3 : Total Balls = 10

4 red + 6 black

Probability of drawing 1 red ball, P(A) = 4/10 .

To find Probability given that the ball drawn is red, that the ball is drawn from the third bag by Bayes' rule.

That is , P(B3|A)

                     [tex]=\frac{\frac{1}{3} \times \frac{4}{10}} { \frac{1}{3} \times \frac{3}{10} + \frac{1}{3} \times\frac{8}{10} + \frac{1}{3} \times \frac{4}{10}}[/tex]

                    [tex]=\frac{4}{30} \times \frac{30}{15}\\\\=\frac{4}{15}[/tex]

Therefore, the probability that it is drawn from the third bag is 4/15.

Answer:

4/15

Step-by-step explanation:

Solution of conditional probability problem:

Given:

Bags (3R,7B), (8R,2B), (4R,6B)

Let

P(R,i) = probability of drawing a red AND from bag i

P(R, 1) = 3/10 * (1/3) = 3/30

P(R, 2) = 8/10 * (1/3) = 8/30

P(R, 3) = 4/10 * (1/3) = 4/30

Let

Let P(R) = probability of drawing a red from any bag

P(R) = sum P(R,i)  for i = 1 to 3   using the addition rule

= 3/30 + 8/30 + 4/30

= 15/30

= 1 / 2

Conditional Probability of drawing from the third bag GIVEN that it is a red

= P(3 | R)

= P(R, 3) / P(R)

= 4/30 / (1/2)

= 8/30

= 4 / 15

(Since all bags contain 10 balls, by intuition, 4 red from third / 15 total red = 4/15)

Answer:

Step-by-step explanation:

y = 2x-8

2x = y+8

x = 0.5y+4

inverse function: y = 0.5x+4

Answer:

x=41

Step-by-step explanation:

LM =JM

154=4x-10

154+10=4x

164=4x

164/4=4x/4

41=x

hope this is helpful

Given:

A figure of a construction.

To find:

The correct option that represent the given construction.

Solution:

We know that, if a transversal line intersect two parallel lines, then the corresponding angles are equal.

In the given figure, two corresponding angles are constructed by using the compass.

Since the corresponding angles are equal, therefore the construction represents the parallel lines through a point.

Therefore, the correct option is B.

Answer:

When we multiply two number with the same base but different power, the power gets added.

So, the answer is:

5^17*5^2

=5^(17+2)

=5^19

domain is  (- infinity, infinity)

range is (- infinity, infinity)

Answer:

Yes, because they are identical to eachother

Step-by-step explanation:

Answer:

The common denominator of [tex]y + \frac{y-3}{3}[/tex] is 3

Step-by-step explanation:

Given

The complex fraction

Required

The common denominator

To solve this, we need not consider the whole complex fraction.

We only consider

[tex]y + \frac{y-3}{3}[/tex]

Take LCM

[tex]y + \frac{y-3}{3} = \frac{3y - (y-3)}{3}[/tex]

Single out the denominator, i.e. 3

Hence, the common denominator of [tex]y + \frac{y-3}{3}[/tex] is 3

Answer:

9.4

Step-by-step explanation:

The net income for theis company is $216,060

The average total assets is 2,290,000

Therefore the return on total assets is

= 216,060/2,290,000

= 0.0943×100

=9.4

9514 1404 393

Answer:

  2. correct

  3. addition property of equality

  4. substitution property of equality

Step-by-step explanation:

You're asked for the Reasons, so you need to examine the Statements to see how you get from one line to the next.

The first line of Statement 2 differs from Statement 3 in that m∠GHI has been added to both sides of the equation (ignoring the typo in statement 3). The reason you can add the same thing to both sides of an equation is given by the Addition Property of Equality.

Statement 3 differs from Statement 4 in that one of the m∠GHI has been replaced by m∠JKL. We can do this replacement because those measures are equal to each other. Replacement of equals by equals is allowed by the Substitution Property of Equality.

Answer:

a)89

b)89.45

Step-by-step explanation: