HW HELP ASAP PLZZZZZ

Given:

Two dice are thrown.

[tex]E_1[/tex] is the event that the sum of their dots is a prime number

[tex]E_2[/tex] is the event that 5 is the dot on the top of second die.

To find:

Whether [tex]P(E_1\cap E_2)=P(E_1)\cdot P(E_2)[/tex] is true or false.

Solution:

If two dice thrown, then the total possible outcomes are:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).

[tex]E_1[/tex] is the event that the sum of their dots is a prime number.

[tex]E_1=\{(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)\}[/tex]

[tex]P(E_1)=\dfrac{15}{36}[/tex]

[tex]P(E_1)=\dfrac{5}{12}[/tex]

[tex]E_2[/tex] is the event that 5 is the dot on the top of second die.

[tex]E_2=\{(1,5), (2,5),(3,5),(4,5),(5,5),(6,5)\}[/tex]

[tex]P(E_2)=\dfrac{6}{36}[/tex]

[tex]P(E_2)=\dfrac{1}{6}[/tex]

The intersection of these two events is:

[tex]E_1\cap E_2=\{(2,5),(6,5)\}[/tex]

[tex]P(E_1\cap E_2)=\dfrac{2}{36}[/tex]

[tex]P(E_1\cap E_2)=\dfrac{1}{18}[/tex]

Now,

[tex]P(E_1)\cdot P(E_2)=\dfrac{5}{12}\cdot \dfrac{1}{6}[/tex]

[tex]P(E_1)\cdot P(E_2)=\dfrac{5}{72}[/tex]

[tex]P(E_1)\cdot P(E_2)\neq P(E_1\cap E_2)[/tex]

Therefore, the given statement is false because [tex]P(E_1\cap E_2)\neq P(E_1)\cdot P(E_2)[/tex].

Answer:

Kindly check explanation

Step-by-step explanation:

If the null is rejected, then we conclude that the average Consumption of beer and cider by customers who are 21 years and above is greater than 26.1

A type 1 error is committed if the null hypothesis is incorrectly rejected ; this means we will be concluding that customers who are 21 years and older have higher average Consumption when they actually do not. This may lead to a restriction on beer consumption in the city when there actually isn't a need for it.

For type 2 error, a false null is incorrectly accepted, in this scenario, we are saying that the consumption of beer and cider is not beyond the mean value when in actual sense it is.

Answer:

The non-negative zero of the function f(x) is x = 2.

Step-by-step explanation:

For a given function f(x), the "zeros" of the function are the values of x such that:

f(x) = 0

In this case, we have the function:

f(x) = 6*x^2 - 9*x - 6

If we want to find the zeros of this function, we need to solve:

f(x) = 0 =  6*x^2 - 9*x - 6

To solve this, we can use the Bhaskara's formula, which says that for a general quadratic equation:

0 = a*x^2 + b*x + c

The zeros are:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

In this case our equation is:

0 =  6*x^2 - 9*x - 6

then, in the above notation, we have:

a = 6

b = -9

c = -6

Replacing these in our general formula, we get:

[tex]x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4*6*(-6)} }{2*6} = \frac{9 \pm 15 }{12}[/tex]

Then we have two zeros:

x = (9 + 15)/12 = 24/12 = 2

x = (9 - 15)/12 = -6/12 = -1/2

But we want only the non-negative, so we can discard the second one.

Concluding, the non-negative zero of the function f(x) is x = 2.

Answer:

[tex]V=280[/tex] cubic inches

Step-by-step explanation:

Volume formula for triangular prism is  [tex]V=\frac{1}{2} bhl[/tex]

[tex]V=\frac{1}{2} (7)(10)(8)[/tex]

[tex]V=\frac{1}{2}(560)[/tex]

[tex]V=280[/tex]

Hope this helps

Answer:

r(x) = 14x - 18

Step-by-step explanation:

(p×2)(x) = 2×p(x) = 2×(7x - 9) = 14x - 18

Answer:

I'd use A = πr^2

The area is 28.3 if we're using 3.14 as pi (rounded to the nearest tenth)

Answer:

3 gallons of carpet shampoo

Step-by-step explanation:

room area: 16 * 15 = 240 ft

1 gallon carpet shampoo: 80 ft

240/80 = 3

3 gallons of carpet shampoo are needed.

Answer:

2nd one is the answer if it's the question

Answer:

$400 Altogether.

The main half of 4 is 2 , so I think they all collected 400 Dollars

so if it was 200 for Ben and collected 7 time than what he actually did

so 200 × 7

= $1400

Answer:

37

Step-by-step explanation:

In the given figure the angles are vertically opposite angles so ;

4x + 2 = 150

or, 4x = 148

or, x = 37 ans .

Answer:

Step-by-step explanation:

What points were you given to choose from?

Step-by-step explanation:

....

I Dont Known........

Answer:

16 full cases

Step-by-step explanation:

4 quarts to a gallon

50 gallons is 200 quarts (50 x 4)

200 quarts / 12 quarts per case = 16.66667 (.66667 isn't a full case)

so, it's 16

Answer:

1/6 * 1/2 = 1/12

Step-by-step explanation:

1 number on a 6 sided die is 1 out of 6 (1/6) and an even number (2,4,6) on a 6 sided die is 3/6 or 1/2 (always simplify when multiplying fractions)

so 1 times 1 = 1 and 6 times 2 = 12 making it 1/12

Answer:

650 adult tickets and 250 children's tickets.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First of all, I'm having a bit of trouble seeing what the exponent on the leading term in the distance is, but I think its an x-squared so that's what I used to solve this. Keep in mind that you do NOT get a number answer here; you get another expression in terms of x for an "answer".

Let's simplify down the rate first by multiplying. What I did was put the denominator under each of the terms in the numerator and then simplified by dividing each term:

[tex]r=\frac{2x^2}{2x}-\frac{5x}{2x}-\frac{3}{2x}[/tex] which simplifies to

[tex]r=x-2.5-\frac{3}{2x}[/tex] Now let's get rid of that denominator there by multiplying everything by 2x to get

[tex]r=2x^2-5x-3[/tex] and we're ready to solve for time.

If d = rt, then

[tex]t=\frac{d}{r}[/tex] so filling in:

[tex]t=\frac{6x^2+3x}{2x^2-5x-3}[/tex] and we can divide this using the method of long division. It would be impossible to show you how to do that here in this forum, but when you divide, you get

[tex]t=3+\frac{18x+9}{2x^2-5x-3}[/tex] ...as crazy as that seems.

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

Explanation:

Compute the area to get 12*8 = 96 square yards

We can think of it like having 96 squares and each square costs $1. So naturally the total cost is 96*1 = 96 dollars.

Answer:

A: y < -2x - 1

Step-by-step explanation:

First, to figure out which part of the graph to be looking at, you will look at the shaded region as the solution area.

So, the solution area is to the left of the line. Said line is a dotted line which means that the points on the line can not be a solution.

If the points on the line can not be a solution then it eliminates answer choices C and D because y can not equal the other side of the inequality.

Now, we will bring the shaded region back into focus to find out if y is greater than or less than the other side. The shaded area is "below" the line so it is less than -2x - 1.

To ensure this is correct, plug two points into the inequality we just chose, one from the shaded region and one not, just to make sure the answer is correct.

I picked (-3,4) to test. So plug them into the inequality to get:

4 < -2 (-3) - 1

So 4 < 6 - 1 which is correct.

Then from the other side of the line I picked (5,2)

2 < -2 (5) - 1

2 < -10 - 1

2 < -11 is not true so the inequality that we found was correct.

Answer:6

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

Answer:

D. None of the above

Step-by-step explanation:

The two right triangles have different sizes. Therefore, their areas cannot be the same as well.

Congruent triangles have the same three angles that are congruent to each other and three side lengths that are congruent or equal to each other. The two triangles only have equal angles bit different corresponding side lengths. Therefore, they cannot be congruent.

The correct answer is "None of the above".

Answer:

PROPORTIANAL SIDE LENGTHS

Step-by-step explanation:

I JUST TOOK THE TEST

Answer:

x = 2.8

Step-by-step explanation:

sin = opp/hyp

hyp = opp/sin

x = 2.4/sin60

x = 2.771281292110204

rounded

x = 2.8

Answer:

4b mod 12 = 4

Step-by-step explanation:

Since b mod 12 = 7, it implies that there is an integer, m such that

b = 12m + 7.

We desire to find 4b mod 12

So, multiplying b by 4, we have

4b = 4(12m + 7)

4b = 4 × 12 m + 4 × 7

4b = 4 × 12 m + 28

4b = 4 × 12 m + 24 + 4

4b = 4 × 12 m + 12 × 2 + 4

Factorizing 12 out, we have

4b = 12(4m + 2) + 4

Since m is an integer 4m + 2 is an integer since the operation of adding and multiplication is closed for the set of integers.

comparing 4b = 12q + r with 4b = 12(4m + 2) + 4,

q = 4m + 2 and r = 4

So 4b mod 12 = 4, that is the remainder when 4b is divided by 12 is 4.

In this exercise we have to calculate the value of the unknown, so we have:

the value is 4

we know that the equation will be given as:

[tex]b = 12m + 7\\[/tex]

we need to multiply both sides by 4 to become another known equation, like this:

[tex]4b = 4(12m + 7)\\4b = 4 * 12 m + 4 * 7\\4b = 4 * 12 m + 28\\4b = 4 * 12 m + 24 + 4\\4b = 4 * 12 m + 12 * 2 + 4[/tex]

So factoring this equation we will find that:

[tex]4b = 12(4m + 2) + 4[/tex]

Thus, when making a comparison between the two equations, we have that:

[tex]4b = 12q + r \\4b = 12(4m + 2) + 4\\q = 4m + 2\\r = 4[/tex]

See more about factoring at brainly.com/question/6810544

Answer:

100

Step-by-step explanation:

since its collinear it has to be 180 -80 which equals 100.

9514 1404 393

Answer:

  6

Step-by-step explanation:

Any of the three can be in first place.

Any of the remaining two can be in 2nd place.

The remaining swimmer will be in 3rd place.

There are 3 × 2 × 1 = 6 possible orderings of the swimmers.

Answer:

a. 97.72% of the observations are less than 33

b. Approximately 977 observations are less than 33.

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 25 and a standard deviation of 4.

This means that [tex]\mu = 25, \sigma = 4[/tex]

a. Approximately what percentage of the observations are less than 33?

The proportion is the p-value of Z when X = 33. So

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

[tex]Z = \frac{33 - 25}{4}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

0.9772*100% = 97.72%

97.72% of the observations are less than 33.

b. Approximately how many observations are less than 33?

Out of 1000:

0.9772*1000 = 977.2

Approximately 977 observations are less than 33.

Answer:

73.0m

Step-by-step explanation:

see the attachment. Hope it helps.

Answer:

x = 43.7°

Step-by-step explanation:

Reference angle (θ) = x°

Opposite side length = 43

Adjacent side length = 45

Apply the trigonometric function, TOA, which is:

Tan θ = Opp/Adj

Substitute

[tex] Tan(x) = \frac{43}{45} [/tex]

[tex] x = Tan^{-1}(\frac{43}{45}) [/tex]

x = 43.7° (nearesth tenth)