Identify why this assignment of probabilities cannot be legitimate: P(A) = 0.4, P(B) = 0.3, and P( AB=0.5 (A) A and B are not given as disjoint events (B) A and B are given as independent events (GP(A and B) cannot be greater than either P(A) or P(B) (D) The assignment is legitimate

Complementary angles are two angles whose sum is 90 degrees. Supplementary angles are two angles whose sum is 180 degrees.

If you have an angle x, you can find its complementary angle y by subtracting x from 90 degrees. So the complementary angle is:

y = 90 - x

For example, if you have an angle of 35 degrees, its complementary angle is:

y = 90 - 35 = 55 degrees

If you have an angle x, you can find its supplementary angle y by subtracting x from 180 degrees. So the supplementary angle is:

y = 180 - x

For example, if you have an angle of 65 degrees, its supplementary angle is:

y = 180 - 65 = 115 degrees

It's important to note that complementary and supplementary angles do not have to be adjacent angles. They can be any two angles whose sum is 90 or 180 degrees, respectively.

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Answer:

1.ABC is equilateral triangle because all sides are equal

3.because they are the joined figure of a triangle

Answer:

C

explanation:

x = 4/3πr³

cross multiply

3x = 4πr³

cube root both side

³√3x = ³√4πr³

³√3x = ³√4π x r

divide both side by ³√4π

r = ³√3x/4π

Comparing the articles I, II, and III of the constitution, in the descending order of length and detail, the articles are ranked as I, II, and III. Article I is the longest.

Article I of the constitution created the legislative branch, article II of the constitution created an executive branch, and article III of the constitution created a judicial constitution. Article I is the longest and more detailed part of the constitution as the powers and the duties of the legislative branch are much more varied than the executive branch. Additionally, the legislative branch is composed of more individuals than the executive branch.

Article 1 is the longest as founding fathers believed that a legislative branch is very important in a government that represents the citizens. Article 3 is the shortest part of the constitution as the founding fathers did not expect the judiciary to play a large role.

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(a) E(SD) = E(S)E(D) = 0. (b) S and D are independent.

(a) We can start by computing E(S) and E(D) separately:

E(S) = E(RI + R2) = E(RI) + E(R2) = (1/6)(1+2+3+4+5+6) + (1/6)(1+2+3+4+5+6) = 7

E(D) = E(RI - R2) = E(RI) - E(R2) = (1/6)(1+2+3+4+5+6) - (1/6)(1+2+3+4+5+6) = 0

Now, to find E(SD), we can use the fact that S and D are both linear combinations of independent random variables (RI, R2). Therefore, we have:

E(SD) = E((RI + R2)(RI - R2))

= E(RI^2 - R2^2)

= E(RI^2) - E(R2^2) (because RI and R2 are independent)

= (1/6)(1^2+2^2+3^2+4^2+5^2+6^2) - (1/6)(1^2+2^2+3^2+4^2+5^2+6^2)

= 0

Thus, we have shown that E(SD) = E(S)E(D).

(b) To determine if S and D are independent, we need to check if their joint distribution is equal to the product of their marginal distributions. We know that the joint distribution of S and D is given by:

P(S=s, D=d) = P(RI+R2=s, RI-R2=d)

We can rewrite this as:

P(RI=s1, R2=s-s1, RI-R2=d)

Now, we can express this in terms of the marginal distributions of RI and R2:

P(RI=s1)P(R2=s-s1)P(RI-R2=d)

This shows that the joint distribution of S and D can be factored into the product of their marginal distributions. Therefore, S and D are independent.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

In each empty table square, fill in the value that is computed by replacing 'n' in the rule to the left with the value of 'n' above that square.

For example:

The upper left empty square will be filled with ...

  n -5 . . . . with n replaced by 1

  1 - 5 = -4 . . . . the value that goes in the upper left square.

__

Another example:

The lower right square will be filled with ...

  4n -3 . . . . with n replaced by 100

  4·100 -3 = 400 -3 = 397 . . . . the value that goes in the lower right square

_____

Additional comment

When there are numerous table values to fill, it can be convenient to let a spreadsheet do the calculations. Here, each formula was entered once, then filled to the right.

Answer:

28

Step-by-step explanation:

8÷2/7 = 8 x 7/2 = 56/2 = 28

^Its the same as this^

Hope this helps :D

Answer:

28

Step-by-step explanation:

8÷2/7 = 8 x 7/2 = 56/2 = 28

Hope this answers your question!

Answer:

D

Step-by-step explanation:

Given the root of a quadratic equation x = a then the factor is (x - a)

Here the roots are x = 5 and x = 7 , then the corresponding factors are

(x - 5) , (x - 7)

The equation is then the product of the factors, that is

y = (x - 5)(x - 7) ← expand using FOIL

   = x² - 7x - 5x + 35 ← collect like terms

y = x² - 12x + 35 → D

The quadratic equation has roots of 5 and 7 so, the quadratic equation would be equal to \(y = x^{2} - 12x + 35\).

Suppose that the given quadratic equation is

ax^2 + bx + c = 0

Then its roots are given as:

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

It is Given the root of a quadratic equation x = a then the factor is (x - a)

Here the roots are x = 5 and x = 7 , then the other factors are

(x - 5) , (x - 7)

The equation is then the product of the factors,

\(y = (x - 5)(x - 7)\\y = x^{2} - 7x - 5x + 35 \\y = x^{2} - 12x + 35\)

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The distance covered by the car is 264cm.

Here we have to find the distance covered by the car.

Information provided:

Diameter (d) = 5.6cm

radius(r) = 5.6/2

             = 2.8cm

Rotation = 15 times

Formula to find the circumference of the tire:

Circumference = 2πr

                        = 2 × 22/7 × 2.8

                        = 17.6cm

This is the distance covered by the tire in one rotation.

Distance covered after 15 rotations = 15× 17.6

                                                         = 264 cm

Therefore distance covered is 264 cm.

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Here answer is true that is, a standard normal distribution always has a mean of zero and a standard deviation of 1.

The statement is true. A standard normal distribution, also known as the Z-distribution or the standard Gaussian distribution, is a specific form of the normal distribution. It is characterized by a mean of zero and a standard deviation of 1.

The mean represents the central tendency of the distribution, while the standard deviation measures the spread or variability of the data. In a standard normal distribution, the data points are symmetrically distributed around the mean, with 68% of the data falling within one standard deviation of the mean, 95% falling within two standard deviations, and 99.7% falling within three standard deviations.

This standardized form of the normal distribution is widely used in statistical analysis and hypothesis testing, and it serves as a reference distribution for various statistical techniques. By standardizing data to the standard normal distribution, researchers can compare and analyze data from different sources or populations.

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Answer:

C

Step-by-step explanation:

Here, we want to select the the trigonometric ratio that is positive quadrant iii

The trigonometric ratio positive in quadrant iii is the tangent

This is the ratio of the opposite to the adjacent and it is usually abbreviated as tan theta

Answer:

Step-by-step explanation:

\(\frac{4}{5+6}=\frac{4}{11}\\\\3+\frac{4}{5+6}=3+\frac{4}{11}\\\\=\frac{3*11}{1*11}+\frac{4}{11}\\\\=\frac{33+4}{11}\\\\=\frac{37}{11}\\\\\\\frac{2}{3+\frac{4}{5+6}}=\frac{2}{\frac{37}{11}}\\\\=2*\frac{11}{37}\\\\=\frac{22}{37}\\\\\\\\1+\frac{2}{3+\frac{4}{5+6}}=1+\frac{22}{37}\\\\=\frac{37}{37}+\frac{22}{37}\\\\=\frac{37+22}{37}\\\\=\frac{59}{37}\\\\=1\frac{22}{37}\\\)

Answer

\(59/37\)

Explanation

\(1+\frac{2}{3+\frac{4}{5+6} }\)

\(1+\frac{2}{3+\frac{4}{11} }\)

\(1+\frac{2}{\frac{3}{1} +\frac{4}{11} }\)

\(1+\frac{2}{\frac{33}{11} +\frac{4}{11} }\)

\(1+\frac{2}{\frac{37}{11} } }\)

\(1+2 \times \frac {11}{37}\)

\(1+\frac{22}{37}\)

\(1\frac{22}{37}\)

\(\approx 1.594594594594594594594594594594595\)

Answer:

The answer is 138

Step-by-step explanation:

4:92

1:23

23×6=138

Answer:

138

Step-by-step explanation:

92 divided by 4 = 23

Trevor makes 23 toys per hour

23 x 6 = 138

So, Trevor would make 138 toys in 6 hours.

4y - 56 is the equivalent expression for 8(1/2y - 7)​​

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).

Given: 8(1/2y - 7)​​

In order to write an equivalent expression, clear the parenthesis:

8(1/2y - 7)​​ = 8(1/2y ) -  8(7)

                = 4y - 56

Therefore, the equivalent expression for 8(1/2y - 7)​​ is 4y - 56

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The loads carried by an elevator are found to follow a normal distribution with a mean weight of 1812 lbs, and a standard deviation of 105.3 lbs. The answer is c) [1606, 2018].

To answer this question, we need to use the concept of confidence intervals. A 95% confidence interval means that in 95% of all cases, the true population parameter (in this case, the weight of the elevator load) will fall within the interval.

To find the interval centered about the mean, we need to calculate the margin of error first. The formula for margin of error is:

Margin of Error = z*(standard deviation/square root of sample size)

Since we do not have a sample size here, we will use the population standard deviation instead.

For a 95% confidence level, the z-value is 1.96. So, plugging in the values we have:

Margin of Error = 1.96*(105.3/square root of 1)

Margin of Error = 205.97

Now, we can find the interval by adding and subtracting the margin of error from the mean:

Interval = [1812 - 205.97, 1812 + 205.97]

Interval = [1606.03, 2017.97]

Therefore, the answer is c) [1606, 2018].

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Answer:

RT = 86

Step-by-step explanation:

23x - 6 = 2(15x - 17)

23x - 6 = 30x - 34

23x - 30x = - 34 + 6

-7x = -28 |÷(-7)

x = 4

RT = 23x - 6 = 23 × 4 - 6 = 92 - 6 = 86

To find the number of licorice ropes r that came in the bag, the equation would be r = 27.

A system of equations is two or more equations that can be solved to get a unique solution.

Each student gets 3 licorice ropes to decorate the roof of his or her gingerbread house.

Let the number of licorice ropes that came in the bag be r.

The equation formed:

Therefore, to find the number of licorice ropes r that came in the bag, the equation would be r = 27.

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Answer:

Then your car gets 25 miles to the gallon, Which is pretty good. I don't really see any question content here...You might want to try to re-post your question!  I will then try to answer better. Thanks.

Step-by-step explanation:

A four members of the Harrison family save  $896 on airfare by vacationing in Vancouver.

Here, the airplane tickets to Fairbanks Alaska will cost $958 each.

⇒ c₁ = $958

where c₁ represents the airfare to Fairbanks Alaska

and the airplane tickets to Vancouver Canada will cost $734.

⇒ c₂ = $734

Let us assume that s represents the amount of savings per ticket.

⇒ s = c₁ - c₂

⇒ s = 958 - 734

⇒ s = $224

Since there are four members in the family.

So using unitary method the total savings would be,

⇒ t = 4 × s

⇒ t = 4 × 224

⇒ t = $896

Therefore, the total savings =  $896

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The complete question is:

Airplane tickets to Fairbanks Alaska will cost $958 each. Airplane tickets to Vancouver Canada will cost $734. How much can the four members of a Harrison family save on airfare by vacationing in Vancouver?

Answer:

There is a vertical translation happening here:

- Up 2 units

- Down 4 units

This is the only change that has happened from f(x) to g(x).

Answer:

see explanation

Step-by-step explanation:

using the identity

cos²x = 1 - sin²x

consider the left side

\(\frac{1-cosx}{sinx}\)

multiply numerator/ denominator by (1 + cosx)

= \(\frac{(1-cosx)(1+cosx)}{sinx(1+cosx)}\) ← expand numerator

= \(\frac{1-cos^2x}{sinx(1+cosx)}\)

= \(\frac{sin^2x}{sinx(1+cosx)}\) ← cancel sinx on numerator/ denominator

= \(\frac{sinx}{1+cosx}\)

= right side , thus proven

Answer:

B. 16/25

Step-by-step explanation:

6

10

+

4

100

=  

6 × 10

10 × 10

+

4

100

=  

60

100

+

4

100

=  

60 + 4

100

=  

64

100

=  

64 ÷ 4

100 ÷ 4

=  

16

25

Answer:

\(\huge\boxed{\sf \frac{16}{25} }\)

Step-by-step explanation:

\(\displaystyle \frac{6}{10} +\frac{4}{100}\)

To equalize the denominator, we will have to multiply the fraction 6/10 by 10.

\(\displaystyle =\frac{6 \times 10}{10 \times 10} +\frac{4}{100} \\\\\ =\frac{60}{100} +\frac{4}{100}\)

Now, that the denominator is equal, we can add both the fractions.

\(\displaystyle= \frac{60+4}{100} \\\\=\frac{64}{100}\)

Divide both numerator and denominator by 2.

\(\displaystyle = \frac{64 \div 2}{100 \div 2} \\\\= \frac{32}{50}\)

Divide again.

\(\displaystyle= \frac{32 \div 2}{50 \div 2} \\\\= \frac{16}{25} \\\\\rule[225]{225}{2}\)

Answer:

0.36582

Step-by-step explanation:

(a×b)

= (1.34×0.273)

= 0.36582

Answer:

The answer is $2.14 per pound of apples.

Step-by-step explanation:

7.29/3.4= roughly 2.14.

Answer:

is 24.786

Step-by-step explanation:

multiply the numbers and that's how you get your answer and I use my calculator so I know the answer is 24.786

Answer:

Soccer:3 dollars

Basketball:4dollars

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The average weight of three apples = 118 g

Estimated average weight of 36 apples = 1416 g or 1 kg 416 g

Total weight of 36 apples = 50976 g or 50 kg 976 g

Answer:

Your answer is F

Step-by-step explanation:

Philips amount is more than 200 but less than 300.