Graph the equation. Let x​3, ​2, ​1, ​0, 1,​ 2, and 3. y=3x-1

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)

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:

B) $85,167

Step-by-step explanation:

u got discount 45% so u just have to pay 55% of it

cost = 55% x $154,85 = $85,1675

domain is  (- infinity, infinity)

range is (- infinity, infinity)

Answer:

Y= -x^2+12x-36

Step-by-step explanation:

Answer:

sum of angles in a triangle = 180°

180-(90+21)

= 69

pls am I correct

Answer:

y = -4x+14

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

m = (2-10)/(3-1)

   =-8/2

   = -4

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = -4x+b

Substitute a point into the equation

10 = -4(1)+b

Add 4 to each side

14 = b

y = -4x+14

Answer:

345

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The product of three consecutive numbers is divisible by ​6

Let us say the numbers are x, x+1 , x+2

if x = 1,

Product of the three consecutive numbers,

(1)(2)(3)

=> 6, which is divisible by 6

if x = 2,

Product of the three consecutive numbers,

(2)(3)(4)

=> 24, which is divisible by 6

Similarly if we take any 3 consecutive numbers their product will be divisible by 6.

Answer:

split the other three in half

Step-by-step explanation:

Answer:

10.9 %

Step-by-step explanation:

46 - 41 = 5

5/46 * 100% = 10.8695652174%

Rounded

10.9 %

Answer:

120 times

Step-by-step explanation:

On a dice, there are 6 sides.

Since one of these sides is a 5, the chance of rolling a five is 1/6.

Find how many times Malachy can expect to roll a five by multiplying 720 by 1/6:

720(1/6)

= 120

So, Malachy can expect to roll a five 120 times

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:

a)89

b)89.45

Step-by-step explanation:

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

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.

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:

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

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:

[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:

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.

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:

Yes, because they are identical to eachother

Step-by-step explanation:

Answer:

a) 0.0171 fluid ounces.

b) 0% probability that the average fill volume of 22 bags is below 5.95 ounces

c) The mean should be of 6.153 fluid ounces.

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 establishes 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.

Standard deviation of 0.08 fluid ounces.

This means that [tex]\sigma = 0.08[/tex]

(a)What is the standard deviation of the average fill volume of 22 bags?

This is s when n = 22. So

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]s = \frac{0.08}{\sqrt{22}}[/tex]

[tex]s = 0.0171[/tex]

(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?

We have that [tex]\mu = 6.16[/tex]. The probability is the p-value of Z when X = 5.95. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{5.95 - 6.16}{0.0171}[/tex]

[tex]Z = -12.3[/tex]

[tex]Z = -12.3[/tex] has a p-value of 0.

0% probability that the average fill volume of 22 bags is below 5.95 ounces.

(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?

[tex]X = 6.1[/tex] should mean that Z has a p-value of 0.001, so Z = -3.09. Thus

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

[tex]-3.09 = \frac{6.1 - \mu}{0.0171}[/tex]

[tex]6.1 - \mu = -3.09*0.0171[/tex]

[tex]\mu = 6.153[/tex]

The mean should be of 6.153 fluid ounces.

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:

The answer for thid equation is x = -5/3

Answer:

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