you roll two fair dice. find the probability that the first die is a 6 given that the minimum of the two numbers is a 4.

Answer:

  (2)  11

Step-by-step explanation:

You want the area of the triangle with vertices (1, 3), (3, -1), and (-2, -2).

Pick's theorem says the area of a figure drawn on a grid can be found by counting the grid points on the boundary (b) and the interior grid points (i). Then the area is ...

  A = (b/2) +i -1

This figure has a boundary grid point at (2, 1) in addition to the three vertices. So, b = 4.

There are 10 interior grid points, a number that can be arrived at by counting them. The numbers in each row, starting from the bottom, are 4, 3, 2, 1.

Then the area is ...

  A = (4/2) +10 -1 = 11

The area of the triangle is 11 square units.

The area can be computed from the coordinates by the formula ...

  A = 1/2|x1(y2 -y3) +x2(y3 -y1) +x3(y1 -y2)|

  A = 1/2|1(-1 -(-2)) +3(-2 -3) +(-2)(3 -(-1))| = 1/2|1 -15 -8| = 11

The area is 11 square units.

The triangle can be bounded by a square 5 units on a side. The triangle area is smaller than the square area by the sum of the three triangles cut from the corners of the square. Clockwise from left, those triangle areas are ...

  1/2(5·3) +1/2(4·2) +1/2(1·5) = 1/2(15 +8 +5) = 14

Then the area of the triangle of interest is ...

  5² -14 = 11

The area of the triangle is 11 square units.

The angle the bottom edge makes with the horizontal is ...

  arctan(1/5) ≈ 11.3099°

and the length of that edge is ...

  5/cos(11.3099°) ≈ 5.099

The angle the left side makes with the horizontal is ...

  arctan(5/3) ≈ 59.0362°

and the length of that edge is ...

  3/cos(59.0362°) ≈ 5.831

The area of the triangle with sides 'a' and 'b' and angle C between them is ...

  Area = 1/2(ab·sin(C)) = 1/2(5.099·5.831·sin(59.0362° -11.3099°)) = 11

The area of the triangle is 11 square units.

__

Additional comment

Side lengths could also be determined using the Pythagorean theorem, and the angle between any two of them could be found using the Law of Cosines.

Heron's formula could be used to find the area from the three side lengths.

In the gym, there are 100 feet between the opposing corners.

Given,

The length of the rectangular gymnasium = 80 feet

The width of the rectangular gymnasium = 60 feet

We have to find the distance between opposite corners of the gymnasium;

Here,

The distance between opposite corners of the gymnasium is the diagonal of the rectangle;

Diagonal of rectangle = [tex]\sqrt{width^{2} + length^{2} }[/tex]

Then,

Diagonal = [tex]\sqrt{80^{2} +60^{2} }[/tex]

Diagonal = [tex]\sqrt{6400+3600}[/tex]

Diagonal = √10000

Diagonal = 100 feet

That is,

The distance between the opposite corners if the gymnasium is 100 feet.

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For ΔDEF , Length of shorter side = 6, Length of medium side = 8 , Length of longer side = 12.

For ΔGHI , Length of shorter side = 9, Length of medium side = 12 , Length of longer side = 18.

For ΔJKL , Length of shorter side = 3/2, Length of medium side = 2 , Length of longer side = 3.

What are Similar Triangles ?

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

In the given figure below, two triangles ΔABC and ΔXYZ are similar only if,

i)       ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z

ii)       AB/XY = BC/YZ = AC/XZ (Similar triangles proportions)

Hence, if the above-mentioned conditions are satisfied, then we can say that ΔABC ~ ΔXYZ

It is interesting to know that if the corresponding angles of two triangles are equal, then such triangles are known as equiangular triangles. For two equiangular triangles we can state the Basic Proportionality Theorem (better known as Thales Theorem) as follows:

For two equiangular triangles, the ratio of any two corresponding sides is always the same

Given that ,

For ΔABC , Length of shorter side = 3, Length of medium side = 4 , Length of longer side = 6.

Now,

For ΔDEF ,

Scale Factor = 2

Length of shorter side = 2*3 = 6, Length of medium side =2*4 = 8 , Length of longer side =2*6 = 12.

For ΔGHI ,

Scale Factor = 3

Length of shorter side = 3*3 = 9, Length of medium side =3*4 = 12 , Length of longer side =3*6= 18.

For ΔJKL ,

Scale Factor = 1/2

Length of shorter side =3*1/2 = 3/2, Length of medium side =4*1/2= 2 , Length of longer side =6*1/2= 3.

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Answer:

[tex]\boxed{\tt v < 6.8}[/tex]

Step-by-step explanation:

[tex]\tt 0.5v+0.06 < 3.46[/tex]

Multiply both sides by 100:-

[tex]\tt 0.5v\times\:100+0.06\times\:100 < 3.46\times\:100[/tex]

[tex]\tt 50v+6 < 346[/tex]

Subtract 6 from both sides:-

[tex]\tt 50v < 340[/tex]

Divide both sides by 50:-

[tex]\tt \cfrac{50v}{50} < \cfrac{340}{50}[/tex]

[tex]\tt v < \cfrac{34}{5}[/tex]

Or

[tex]\tt v < 6.8[/tex]

Therefore, your answer is v < 6.8!!! :)

______________________

Hope this helps!

Have a great day!

Answer:

640 1/4 lbs

Step-by-step explanation:

The amount which the agency makes on the house as described is; $26,100.

The amount earned in commission by the agent is; $6,525.

It follows from the task content that the house in discuss was sold for $348,000.

Also, since the commission rate for the real estate agency is; 7.5%.

It therefore follows that the commission earned by the real estate agency is;

7.5% of 348,000 = 0.075 × 348,000

= $26,100.

Also, since the commission rate for the agent is 25% of the agency's commission.

Therefore, the amount earned by the agent is;

25% of 26,100 = 0.25 × 26,100

= $6,525.

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Answer:

I'm pretty sure it's 0.625kg

Step-by-step explanation:

There are 1000g in 1kg so 7kg would be 7000g plus 500g which is 7500g.

7500g divided by 12 is 625g. Divide by 1000 to get kg and you get 0.625kg.

Hope this helps!

Answer: The selling price was at first $776 but then the store advertised a 30% markdown on the system. Find the current sale price.

Step-by-step explanation:

$776 - (30% of $776) = $ x :: current sale price

776 - 776 * 0.3 = x

776 * (1 - 0.3) = x

776 * 0.7 = 543.20

Current sale price for the computer system is $543.20.

The remainder will be less than k, when the positive integer n is divided by the positive integer k, where k > 1.

Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers. In this essay, we will learn more about integers, their definition, and their characteristics.

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers.

Hence, The remainder will be less than k, when the positive integer n is divided by the positive integer k, where k > 1.

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Probability that randomly selected audient attend all the concerts is 0.05.

What is probability?

P(A) = 28/100 = 0.28

P(B) = 42/100 = 0.42

P(C) = 30/100 = 0.30

P(A∩B) = 10/100 = 0.10

P(A∩C) = 8/100 = 0.08

P(B∩C) = 7/100 = 0.07

P(A∪B∪C) = 80/100 = 0.80

P(A∩B∩C) = ?

P(A∪B∪C) = P(A) + P(B) + P(C) - P(A∩B) - P(A∩C)  - P(B∩C) + P(A∩B∩C)

P(A∩B∩C) = - 0.28 - 0.42 - 0.30 + 0.10 + 0.08 + 0.07 + 0.80

= 0.05

Probability that randomly selected audient attend all the concerts is 0.05.

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Step-by-step explanation:

easiest example : multiply both (it is important to do it to both) by 2 :

2×2 = 4 cups of yellow

3.5×2 = 7 cups of blue

will make the same shade of green, as the mixing ratio is the same.

just, instead of 5.5 cups, it gives us 11 cups of green paint (surprise, surprise, this is also twice as much) .

Answer:

B.

Process of elimination.

A is incorrect because 6 out of 10 people is 60 percent.

C is wrong because if you consider just half (50 percent) of 65, you'll get 32.5 . In order to get 65 percent, C would have to be over 32.5, and 10 is not.

D is wrong because once again, half (50 percent) of 13 is 6.5 and in order to get 65 percent, D would have to be over 6.5, and 5 is not.

The element of this group is {0, 1, 2, 3, ...., 25}, this group is a cyclic group, and 16 is not a generator for this group but 5 is a generator for this group.

[tex]Z_{26}[/tex] ≡ Group of integers under addition modulo 26

addition modulo is all addition of integer in ordinary way than remove integral multiple. For example, addition modulo a+mb is a+b than remove all integral multiple m and the result is lower than m (residue).

a) The elements of this group is all the integers remainder after mod 26. So,

x = k (mod 26) where 0 ≤ k < 26

or we can write each of them as {0, 1, 2, ..., 23, 24, 25}

b) Cyclic group is a group that is generated by 1 element. Since, the group is integers under addition modulo with all integers can be generated by adding 1 repeatedly, so the group [tex]Z_{26}[/tex] is cyclic group.

c) As 1 ∈ [tex]Z_{26}[/tex] but there is no m ∈ N such that [tex]16^m[/tex] = 1, but for [tex]5^m[/tex] is

{0, 5, 10, 15, 20, 25, 4, 9, 14, 19, 24, 3, 8, 13, 18, 23, 2, 7, 12, 17, 22, 1, 6, 11, 16, 21}

or in simply way, we can say there is m ∈ N for [tex]5^m[/tex] = 1. So, 16 is not generator of this group, but 5 is generator of this group.

Thus, the number of {0, 1, 2, 3, ...., 25} is the element for this group, cyclic group is a type of this group, and 5 is a generator for this group but 16 is not a generator for this group.

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Equation 1 needs to be multiplied with + 2

Equation 2 needs to be multiplied with  + 5.

Step-by-step explanation:

Here, the given system of equation is given as:

Equation 1 : 6 x − 5 y = -4

Equation 2: 4 x + 2 y = 28

Here, in equation 1, the coefficient of y  = - 5

Also, in the equation 2, the coefficient of  y = + 2

Now, in order to eliminate the y coefficients,

Coefficient  of y in  1  =   -  Coefficient of y in  2

Now, to make -5 and  + 2 to eliminate each other,

Multiply -5 with 2, we get            -5 x 2  = -10

And Multiply the coefficient + 2 with 5, we get   +2 x 5  = + 10

The new coefficient of y is equation 1 = - 10 y

The new coefficient of y in equation 2  = + 10 y

They will cancel out each other, when both equations are ADDED.

Hence, equation 1 needs to be multiplied with + 2

and the equation 2 needs to be multiplied with  + 5.

Answer:

Step-by-step explanation:

1 1.5/2

The required distance between the points  (−1, −4) and (−9, −8). is the square root of 80 units. Option D is correct.

Given that,

The distance between points (−1, −4) and (−9, −8) is to be determined.

Distance is defined as the object traveling at a particular speed in time from one point to another.

here,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]

Substitute the value in the above equation,
D = √[[-9 + 1]² + [-8 + 4]²]
D = √[[-8]² + [ 4]²]
D = √[64 + 16]
D = √80

Thus, the required distance between the points  (−1, −4) and (−9, −8). is the square root of 80 units. Option D is correct.

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Answer:

the person above is correct, the answer is D "[tex]\sqrt{80[/tex] units"

Step-by-step explanation:

I took this exam and got this answer right, hope this helps :))

Answer:

  sum = 65

Step-by-step explanation:

You want the sum of the set of 5 consecutive positive integers such that the sum of the even integers in the set is 26.

The sum of even integers will be a multiple of 3 if the middle integer of the set is even. Here, that sum is 26, not a multiple of 3. Hence the middle integer of the set is 26/2 = 13, and the sum of the set is 13·5 = 65.

The sum of the five integers is 65.

__

Additional comment

When working "consecutive integer" problems, it is often useful to think in terms of the average of the integers, the middle one of an odd-length set, or the number halfway between the two middle ones of an even-length set.

A set of 5 integers will have either 3 odds and 2 evens, or 3 evens and 2 odds. The set here obviously does not have 3 even integers (whose sum would be 3 times the middle one).

The set is s = {11, 12, 13, 14, 15}. 10 is not in the set, but 11 is. The sum of evens is 12+14=26.

the standard deviation of the sample means:

σ(x) = σ/[tex]\sqrt{n}[/tex]

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement text annotation indicator, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. In fact, this also holds true even if the population is binomial, provided that min(np, n(1-p))> 5, where n is the sample size and p is the probability of success in the population. This means that we can use the normal probability model to quantify uncertainty when making inferences about a population mean based on the sample mean.

For the random samples we take from the population, we can compute the mean of the sample means:

μ (x) = μ

and the standard deviation of the sample means:

σ(x) = σ/[tex]\sqrt{n}[/tex]

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The standard deviation of the sampling distribution of the average (sample mean) score for the 36 students = 1

What is standard deviation?

The standard deviation of the sampling distribution of mean is given by :- σₓ = σ/√n, where  = population standard deviation and n= sample size.

According to the given question:

The scores of individual students on the American college testing program composite college entrance examination have a normal distribution with mean 18.0 and standard deviation 6.0. at kent roosevelt high.

i.e. μ = 18.0, σ = 6.0

Sample size : n= 36

Then, the standard deviation of the sampling distribution of the average (sample mean) score for the 36 students will be :-

σₓ = 6/√36 = 1

Hence, The standard deviation of the sampling distribution of the average (sample mean) score for the 36 students = 1

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If the bond angle between two adjacent hybrid orbitals is 180 degree then the hybridization  is sp hybridization , it forms linear molecules with an angle of 180°.

Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.

In sp hybridization, the s orbital of the excited state carbon is mixed with only one out of the three 2p orbitals. It is called sp hybridization because two orbitals (one s and one p) are mixed.

The resulting two sp hybrid orbitals are then positioned at 90 degree and 180 degree, respectively, with the two 2p unhybridized orbitals:

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The new width is 4 inches.

Since Jessica reduced one side (the length), that means that she also reduced the other side (the width) by the same number:

Original length:

4

New length:

2

4 ÷ 2 = 2

Original Width:

8

New Width:

4

8 ÷ 2 = 4

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

2/12 = 1/6

24 * 1/6 = 4

or

12/24 = 2/x

12 x = 48

x = 4

or the original width was twice the length

twice 2 is 4

maybe

Answer:

[tex]\frac{2}{13}[/tex]

Step-by-step explanation:

All the sides have equal lengths.  Set the two sides equal to each other and solve for y

[tex]\frac{5}{4}[/tex]y + 1 = [tex]\frac{7}{3}[/tex]y  -2  I am going to clear the fractions by multiplying through by 12

[tex](\frac{12}{1})[/tex][tex]\frac{5}{4}[/tex] y + (12)(-1) = [tex](\frac{12}{1})[/tex][tex]\frac{7}{3}[/tex] y - (12)2

15y - 12 = 28y - 24  Subtract 15y from both sides

-12 = 13y - 24  Add 24 to both sides

12 = 13y  Divide both sides by 13

[tex]\frac{12}{13}[/tex] =  y

Plug 12/13 into the expression for either side to find the length of BC.  All the sides have the same length

[tex]\frac{7}{3}[/tex][tex](\frac{12}{13})[/tex]  -  2

[tex]\frac{28}{13}[/tex] - [tex]\frac{26}{13}[/tex] = [tex]\frac{2}{13}[/tex]

Answer:

8 pounds of oranges for $12.

Step-by-step explanation:

Answer: 0.69

Step-by-step explanation:

0.44 + 0.25 = 0.69

The correct answer is [tex]\boxed{0.69}[/tex]

For this question we will be adding the numbers given.

Given:

[tex]0.44\\0.25[/tex]

Therefore, the equation is:

[tex]\boxed{0.44 +0.25}[/tex]

Therefore, the correct answer is [tex]\boxed{0.69}[/tex]

There is not evidence that the population mean waiting time is different from 3.6 ​minutes.

What is the p-value?

A statistical measurement known as a p-value is employed to check a hypothesis' validity against actual data. A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct. The statistical significance of the difference that was found increases with decreasing p-value.

From the question, we know that the size (n), the mean (x), and the standard deviation (s) of the sample are 81, 3.45 minutes and 0.9 minutes. Additionally, we are going to decide if the waiting time is different or not from 3.6 minutes, so the null and alternative hypotheses are:

H0: m=3.6

H1:  m≠3.6

Where m is the mean of the population.

Then, we don't need to be concerned about the shape of the population distribution because the value of the n is bigger than 30 and we can use the statistic z as:

[tex]z = \frac{x-m}{\frac{a}{\sqrt{n} } }[/tex]

So, replacing the values, the test statistic is:

[tex]z = \frac{3.45 - 3.6}{\frac{0.9}{\sqrt{81} } }[/tex]

= 2.50

On the other hand, the p-value for this test is calculated as:

p-value = 2P(z >2.50) = 2(0.0668) = 0.134

Taking into account that the p-value is bigger than the level of significance 0.01, the null hypothesis is not rejected, and there is not evidence that the population mean waiting time is different from 3.6 ​minutes.

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Answer:

1. 150mi

2. 2&1/2

3. He needs to know how many miles is each city.

Step-by-step explanation:

The correct unit prices are,

1. 20 for $1.56 = A. 7.8 cents each

2. $3.78 for 6 = B. 63 cents each

3. 2 1/2 for one dollar = C. 40 cents each

4. 5 at $3.90 = D. 78 cents each

5. 1 1/2 for $1.58 = E. $1.05 each

From the given cases;

1. Given that 20 things cost $1.56,

So, the price of one item is = $1.56/20

                                             = $0.078.

Cents for every dollar,

So, $0.078 equals $0.078 * 100

                              = 7.8 cents.

2. Since the cost of six products is $3.78, 

The cost of one item is 3.78/6

                                    =  $0.63.

Cents for every dollar,

Thus, $0.63 equals $0.63 * 100

                               = 63 cents.

3. 2 1/2 = 5/2 = 1 as a price

So, the price of one item is equal to 2/5 of a dollar, or 100 cents.

$2/5 equals 2/5 * 100, or 40 cents.

4. Given that the price of 5 things is $3.90

The price of 1 item is 3.90/5, or $0.78.

Cents for every dollar

So, $0.78 = $0.78 * 100 = 78 cents.

5. Cost of 1 1/2 = 3/2 = $1.58

So, cost of 1 item =  1.58/(3/2)

                            = 1.05

Hence, these are the solutions for the given cases.

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The control limits for the x chart for a sample of size 10,

a-Develop the control limits for the $\oveline x$ chart for samples of size 10, 20, and 30

UCL = 359.48

LCL = 340.51

b. What happens to the control limits as the sample size is increased

The control limits for the x chart for a sample of size 20,

UCL = 356.71

LCL = 343.29

c-What happens when a Type I error is made

The control limits for the x chart for a sample of size 30,

UCL = 355.47

d- What happens when a Type II error is made? e. What is the probability of a Type I error for samples of size 10, 20, and 30

LCL = 344.52

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event.

The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Probability generally refers to the degree to which something is likely to occur.

This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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