MATHEMATICS COLLEGE

Two number cubes are rolled for two seperate events: Event A is the event that the sum of numbers on both cubes is less than 10. Event B is the event that the sum of numbers on both cubes is a multiple of 3. Complete the conditional-probability formula for event B givem thaf event A occurs first by writing A and B in the blanks:

Answers

Answer 1

Answer:

Answer:

Probability of getting sum less than

10 = \frac{30}{36}= \frac{5}{6}

Probability of getting a multiple of 3= \frac{20}{36}= \frac{5}{9}

(A) P(B|A)= \frac{P(B∩A)}{P(A)} = \frac{15/36}{30/36}= \frac{15}{30}=0.5

(B)P(A|B)= \frac{P(A∩B)}{P(B)}= \frac{15/36}{5/9}=0.75

(D) {A} = {1, 2, 3, 4, 5 ,6, 7, 8, 9}

-Hope this helps-

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Match the correct y=mx+b equation to the graph:

pls show work/explanation!

Answers

Answer:

$y=-3x+2$

$\boxed{m=-3,\ b=2}$

Step-by-step explanation:

Equation of a line

To define the equation of a line, we only need two points through which it passes. The graph shows two clear points to choose: (0,2) and (1,-1)

Set up the equation of the line by using the formula

$\displaystyle y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)$

$\displaystyle y-2=(-1-2)/(1-0)(x-0)$

Operating

$y-2=-3x$

Rearranging

$y=-3x+2$

$\boxed{m=-3,\ b=2}$

Il give brainliest thanks

Answers

Answer:

D) a = 14, b = 6√2

Step-by-step explanation:

The given figure is trapezoid.

When we draw perpendicular to base "a", we get h = 6

From 45, 45, 90 degrees triangle, the ratio of sides 1:1:√2

since h = 6, b = 6√2

a = 8 + 6

a= 14

Therefore, a = 14 and b = 6√2

Thank you.

When are the expressions 5(p + 4) and 5p + 20 equivalent?

Answers

Answer:

yes they are equal

Step-by-step explanation:

5(p+4) when it is distributed it equals 5p+20 which equals to 5p+20

Final answer:

The expressions 5(p + 4) and 5p + 20 are equivalent at all times due to the distributive property of multiplication over addition in mathematics. These two expressions are the same, and their equivalence doesn't depend on the value of 'p'.

Explanation:

The expressions 5(p + 4) and 5p + 20 are equivalent at all times. This is due to the distributive property of multiplication over addition in mathematics.

This means that when you have an expression like 5(p + 4), you multiply each quantity inside the parentheses by the number outside, which gives you 5p + 20.

So these two expressions are actually the same and are equivalent no matter what the value of p is.

Learn more about Distributive Property here:

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The planet Mars has a radius of 3400 km. What is the volume of Mars?Write your answer in scientific notation to three decimal places.

Answers

Answer:

1.646×10¹¹ km³.

Step-by-step explanation:

From the question given, we obtained the following information:

Radius (r) = 3400 km

Volume (V) =.?

The shape of a planet is spherical in nature. Thus, we shall apply the formula for calculating the volume of a sphere to obtain the volume of Planet Mar as illustrated below:

Radius (r) = 3400 km

Pi (π) = 3.14

Volume (V) =.?

Volume of a sphere = 4/3 πr³

V = 4/3 × 3.14 × (3400)³

V = 4/3 × 3.14 × 3.9304×10¹⁰

V = 1.646×10¹¹ km³

From the calculations made above, the volume of Planet Mar is 1.646×10¹¹ km³

What is a3 if an=64(12)n−1

Answers

Answer:

$\huge\boxed{a_3=9,216}$

Step-by-step explanation:

$a_n=64(12)^(n-1)\n\n\text{substitute}\ n=3:\n\na_3=64(12)^(3-1)=64(12)^2=64(144)=9,216$

When the Chili restaurant chain was in ﬁnancial trouble.its CEO directed the managers of each of the chain's restaurant to trim costs without sacriﬁcingcustomer satisfaction.Which of the following did the CEO use to make restaurant managers accountable for cost-cutting measures?A) substitution8) transpositionC) delegation of authorityD) job sharing

Answers

Answer: Option C : delegation of authority

Step-by-step explanation:

the CEO used DELEGATION OF AUTHORITY approach to make restaurant managers accountable for cost-cutting measures in the above case.

Final answer:

The CEO of the Chili restaurant chain used the delegation of authority principle to make restaurant managers responsible for cost-cutting measures without sacrificing customer satisfaction.

Explanation:

In the situation described, the Chili restaurant chain's CEO used delegation of authority to make restaurant managers accountable for cost-cutting measures. Delegation of authority refers to the process of passing down responsibilities and decision-making power from upper to lower levels of management. In this case, the CEO entrusted the restaurant managers with the responsibility of reducing costs, while also maintaining customer satisfaction. Using this strategy, the CEO was able to shift accountability to the managers, who now have the authority to manage their resources and strategize their cost-cutting measures in a manner that would not compromise the level of satisfaction of their customers.

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