A single die is rolled twice. The 36​ equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is 10 .

Answer:

0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.

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.

Mean of 15.0 ounces and a standard deviation of 0.2 ounces.

This means that [tex]\mu = 15, \sigma = 0.2[/tex]

What is the probability that a randomly chosen bag will weigh more than 15.6 ounces?

This is 1 subtracted by the p-value of Z when X = 15.6. So

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

[tex]Z = \frac{15.6 - 15}{0.2}[/tex]

[tex]Z = 3[/tex]

[tex]Z = 3[/tex] has a p-value of 0.9987.

1 - 0.9987 = 0.0013

0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.

Answer:

24 years

Step-by-step explanation:

total ratio =8

older student=40 years

3/8*40 ÷ 5/8=24

Answer:

9514 1404 393

Answer:

  $313.37

Step-by-step explanation:

The compound interest formula is used to find that value.

  A = P(1 +r/12)^(12t)

P compounded monthly at annual rate r for t years.

  A = $200(1 +0.05/12)^(12·9) ≈ $313.37

The expected value of the distribution of the number of selected red balls is 0.795.

The expected value of the distribution is the mean or average of the possible outcomes.

There are 12 balls in an urn, five of which are crimson. The selection of a red ball is desired and hence considered a success.

In this case, the possible outcomes are 0, 1, 2, or 3 red balls.

To calculate the expected value, we need to find the probability of each outcome and multiply it by the value of the outcome.

The probability of selecting 0 red balls is :

[tex]$\frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$[/tex].

The probability of selecting 1 red ball is :

[tex]$3 \cdot \frac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{315}{660}$[/tex].

The probability of selecting 2 red balls is

[tex]:$\dfrac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$.[/tex]

The probability of selecting 3 red balls is

[tex]$\dfrac{5}{12} \cdot \frac{4}{11} \cdot \frac{3}{10} = \frac{15}{660}$[/tex]

The expected value is then :

[tex]$0 \cdot \frac{105}{660} + 1 \cdot \frac{315}{660} + 2 \cdot \frac{105}{660} + 3 \cdot \frac{15}{660} = \frac{525}{660} = \frac{175}{220} \approx \boxed{0.795}$[/tex]

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Answer:

Step-by-step explanation:

Everything is correct. But you forgot to add

x = 6 - square root of 26. The answer is

x = 6 + square root of 26 or

x = 6 - square root of 26

Answer:

Hence The probability that she is taking a night​ class given that Jane has a​ part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher)    = 0.6999.

Step-by-step explanation:  

Probability(full-time teacher/ day ) = 0.85  

Probability(part-time teacher/ day ) = 1- 0.85 = 0.15  

Probability(full-time teacher/ night) = 0.30  

Probability(part-time teacher/ night) = 1 - 0.30 = 0.70  

total no of section = 4+2 = 6  

P(jane has part time teacher) = P(jane is from day section)*Probability(part-time teacher/ day )+P(jane is from night section)*Probability(part-time teacher/ night)  

= (4/6)(0.15)+(2/6)(0.70) = 0.33  

P(jane has part time teacher and she is taking night class ) = P(jane is from night section)*Probability(part-time teacher/ night) = (2/6)(0.70) = 0.23  

According to Bayes theorem :    

The probability that she is taking a night​ class given that Jane has a​ part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher)  

= 0.23/0.33  

= 0.6999

Answer:

A. 37.39 B. 37.41 C. 37.27

Answer:

(3/2,10)

Step-by-step explanation:

Mid point is ((10-7)/2,(13+7)/2)=(1.5,10)

Answer:

15

Step-by-step explanation:

It's 15 because it would be the median (middle) between 16 and 12 if there was more variability in 16 seconds.

Answer:

Regal Theatre makes 1.6 times more than Player Productions when they have 0.25 hours longer productions

Step-by-step explanation:

Given

[tex]h(t) \to[/tex] player production theatre

[tex]g(t) \to[/tex] regal theatre

Where:

[tex]g(t) = 1.6h(t + 0.25)[/tex]

Required

Compare both functions

We start from the bracket

[tex]t + 0.25[/tex]

The + in [tex]t + 0.25[/tex] means longer hours of production

So:

[tex]t + 0.25[/tex] means 0.25 hours longer that player productions

[tex]g(t) = 1.6h(t + 0.25)[/tex]  can be rewritten as:

[tex]g(t) = 1.6 * h(t + 0.25)[/tex]

The above means 1.6 times player production when they have 0.25 longer hours.

Answer:

Your equation would be

y=4x-12

Step-by-step explanation:

So an easy way to figure this out is graph the points and look at the distance the points are away from each other. In this case it was 12 up and 3 right. This is your slope. Simplify the fraction to 4/1. Then from (2,-4) use the given slope to work back to a point that is on the y axis, which is (0,12). Plug all of the given information you found into y=mx+b and you get the given formula.

Answer: 15

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Set 2x + 3 = 3x - 5

Solve for x

x = 8

Answer:

F(x) = 45*x - (5/2)*x^2 + C

Step-by-step explanation:

Here we want to find the antiderivative of the function:

f(x) = 45 - 5*x

Remember the general rule that, for a given function:

g(x) = a*x^n

the antiderivative is:

G(x) = (a/(n + 1))*a*x^(n + 1) + C

where C is a constant.

Then for the case of f(x) we have:

F(x) = (45/1)*x^1 - (5/2)*x^2 + C

F(x) = 45*x - (5/2)*x^2 + C

Now if we derivate this, we get:

dF(x)/dx = 1*45*x^0 - 2*(5/2)*x

dF(x)/dx = 45 - 5*x

Hi there!

Given the expression below:-

[tex] \large{ - 3 {m}^{2} + 4n - p}[/tex]

We are also given these three values below:

Simply substitute these values in:-

[tex] \large{ - 3 {( - 6)}^{2} + 4(2) - 4}[/tex]

Any negative numbers squared would result in positive.

[tex] \large{ - 3(36) + 8 - 4} \\ \large{ - 108 + 4} \\ \large \boxed{ - 104}[/tex]

Hence, the answer is -104 when substituting values in the expression.

Let me know if you have any questions!

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{-3m}\mathsf{^2}\large\textsf{ + 4n - p}\\\large\textsf{= -3(-6)}\mathsf{^2}\large\textsf{ + 4(2) - 4}\\\\\large\textsf{(-6)}^2\\\large\textsf{= (-6)(-6)}\\\large\textsf{= \bf 36}\\\\\large\textsf{= -3(36) + 4(2) - 4}\\\\\large\text{-3(36)}\\\large\textsf{= \bf -108}\\\\\large\textsf{= -108 + 4(2) - 4}\\\\\large\textsf{4(2)}\\\large\textsf{= \bf 8}\\\\\large\textsf{= -108 + 8 - 4}\\\\\large\textsf{-108 + 8}\\\large\textsf{= \bf -100}\\\\\large\textsf{-100 - 4}\\\large\text{ = \bf -104}[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your answer is: \boxed{\bf -104}}}}\huge\checkmark[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]  

Answer:

Option (D) x≥ 0 is absolutely correct

Step-by-step explanation:

The reason is that the square root function is defined for only non negative numbers.

Answer: x is greater than or equal to 0

Step-by-step explanation:

Answer:

The answer is D cuz two if the corresponding angles are congruent.

Answer:

Z = (42-20)/4 = 5.5

Z = X-μ / σ

Step-by-step explanation:

The z-score for the data value of 42 is 5.5.

A z-score is defined as the fractional representation of data point to the mean using standard deviations.

Formula of z-score = (X - μ) / σ

Given,

μ = 20

σ = 4

X = 42

z-score = (X - μ) / σ

Substitute the values,

z-score =  (42-20)/4

z-score = 22/4

z-score =  5.5

Hence, the z-score for the data value of 42 is 5.5.

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I need more information, comment on my "answer".

Answer:

3.2 hours

Step-by-step explanation:

12 workers * 4 hours = 48 worker hours

15 workers  * x hours = 48 worker hours

48 /15 =3.2 hours

Answer:

3 hours and 12 minutes.

Step-by-step explanation:

12 Workers complete a job in 4 hours

1 worker complete a job 12 × 4 = 48

15 workers complete a job = 48/15 = 3³/¹⁵ = 3¹/⁵

= 3 hours + 1/5 × 60  minutes = 3 hours 12 minutes.

Answer:

a. Relative Growth rate = 10% (6/60 * 100)

b. Number of cells after t hours = 50 * 1.1^t

c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)

d. The number of cells after 6 hours is

= 89 cells

Step-by-step explanation:

A cell divides into two cells every 20 minutes

In one hour, the cell will divide into 60/20 * 2 = 6 cells

Each cell growth 6 cells per hour

Initial population of a culture = 50 cells

t = time in hours

a. Relative Growth rate = 10% (6/60 * 100)

b. Number of cells after t hours = 50 * 1.1^t

c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)

d. The number of cells after 6 hours = initial population * growth factor

= 50 * 1.772

= 88.6

= 89 cells

Answer:

There are 4 questions to answer here and the answers are given below:

1. COMBINATION

2. SET 2  

3. {S2, S3, S4, S5}

4. { }  OR  ∅

Step-by-step explanation:

The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.

The assignment has 5 questions in all. The options for each question are listed below and separated by commas:

1. True, False

2. True, False

3. A, B, C, D

4. A, B, C, D

5. A, B, C, D

Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.

QUESTION 1

If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?

ANSWER TO QUESTION 1

You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only two possible answers (also known as options) while questions 3, 4 and 5 have four possible answers/options to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.

QUESTION 2

Find "Set 1 ∩ Set 2" and explain the notation in the sentence.

ANSWER TO QUESTION 2

First list out relevant information:

- The correct answers to questions 3, 4 and 5 are respectively C, B, A

- The universal set consists of five students: S1, S2, S3, S4, S5 hence

Ц = {S1, S2, S3, S4, S5}

Next, enlist the elements of each defined set

Set 1: {S1, S2, S3, S4, S5}     Set 2: {S2, S3, S4}     Set 3: {S4, S5}

Note: Set 1 is equal to the universal set.

Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.

In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.

If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:

The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.

So the answer to question 2 is

Set 1 ∩ Set 2 = Set 2

QUESTION 3

Find "Set 2 ∪ Set 3" and explain the notation in the sentence.

ANSWER TO QUESTION 3

The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.

So, Set 2 union Set 3 = {S2, S3, S4, S5}

As earlier stated, Student 4 isn't appearing twice in the new set.

QUESTION 4

Find the ' of Set 1 and explain the notation in this sentence.

ANSWER TO QUESTION 4

The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.

Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!

Set 1 ' Ц = { }  or  ∅

where the empty bracket symbol and the slashed zero symbol represent null set.

Kudos!

Answer:

[tex]r'(t) = 298t -850[/tex]

Step-by-step explanation:

Given

[tex]q(t) = 1000t - 150t^2[/tex]

[tex]p(t) = 150t - t^2[/tex]

Required

[tex]r'(t)[/tex]

First, we calculate the revenue

[tex]r(t) = p(t) - q(t)[/tex]

So, we have:

[tex]r(t) = 150t - t^2 - (1000t - 150t^2)[/tex]

Open bracket

[tex]r(t) = 150t - t^2 - 1000t + 150t^2[/tex]

Collect like terms

[tex]r(t) = 150t^2 - t^2 + 150t - 1000t[/tex]

[tex]r(t) = 149t^2 -850t[/tex]

Differentiate to get the revenue change with time

[tex]r'(t) = 2 * 149t -850[/tex]

[tex]r'(t) = 298t -850[/tex]

Answer:

68.3 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan I = opp side / adj side

tan I = sqrt(82) / sqrt(13)

tan I = sqrt(82/13)

Taking the inverse tan of each side

tan ^-1 ( tan I) = tan ^-1( sqrt(82/13))

I = 68.2892

Rounding to the nearest tenth

I = 68.3 degrees

Answer:

9

Step-by-step explanation:

Divide 6 by 2:

3(1+2)

Add 1 and 2:

3 x 3

Multiply 3 by 3:

3 x 3 = 9

Answer:

1

Step-by-step explanation:

6

------

2(1+2)

6

-----

2(3)

6

-----

6

1