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Sliva [168]
2 years ago
12

A fair 6-sided die is rolled 4 times and the resulting sequence of 4 numbers is recorded. How many different sequences consist e

ntirely of even numbers
Mathematics
1 answer:
Charra [1.4K]2 years ago
7 0

Answer:

81

Step-by-step explanation:

Rolling 6-sided fair die you can throw out three even numbers: 2, 4, 6.

If a fair 6-sided die is rolled 4 times, then each of 4 times each of three even numbers can be thrown out. Then the number of different sequences that consist entirely of even numbers is

3\cdot 3\cdot 3\cdot 3=3^4=81.

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When Joseph first starts working at a grocery store, his hourly rate is \$10$10dollar sign, 10. For each year he works at the gr
morpeh [17]

Answer:

R(t)=10+0.50t

Step-by-step explanation:

Let t represent the number of years.

We have been given that When Joseph first starts working at a grocery store, his hourly rate is $10.

For each year he works at the grocery store, his hourly rate increases by $0.50. Increase in hourly rates after t years would be 0.50t

The hourly rates after t years will be 10 plus 0.50t.

We can represent this information in an equation as:

R(t)=10+0.50t

Therefore, the function R(t)=10+0.50t represents Joseph's hourly rates after t years.

3 0
2 years ago
Solve the following logarithmic equations.<br> log2(49x^2) = 4
Mariana [72]

Answer:

x_{1} = \frac{4}{7} \\x_{2} = \frac{-4}{7} \\

Step-by-step explanation:

To solve this equation, one must apply the following logarithmic property:

if

log_{a}(b) = c\\

then

b= a^{c}

Applying it to the problem at hand:

2^{4} = 49x^{2} \\x^{2} = \frac{16}{49} \\x_{1} = \frac{4}{7} \\x_{2} = \frac{-4}{7} \\

The solutions to the problem are 4/7 and -4/7.

*Note that this solution was pretty straight forward because log2(16) = 4 is a known value, otherwise, a change of base to a base ten log would be required.

4 0
2 years ago
Suppose that the exam scores for students in a large university course are normally distributed with an unknown mean and standar
HACTEHA [7]

Answer:

Critical value t-score=2.701.

Step-by-step explanation:

When we calculate a confidence interval with an unknown population standard deviation, we estimate it from the sample standard deviation and use the t-score instead of the z-score.

The critical value for t depends on the level of confidence and the degrees of freedom.

If the sample size is 42, the degrees of freedom are:

df=n-1=42-1=41

For a confidence level of 99% and 41 degrees of freedom, the critical value of t is t=2.701.

6 0
2 years ago
How many ways are there to seat six different boys and six different girls along one side of a long table with 12 seats? how man
GaryK [48]
Q1: 479 001 600 ways

Explanation:
You have 12 people, 12 seats, ¹²P₁₂ ways in arranging them, or essentially 12! ways

Q2: 1 036 800 ways

Explanation:
Let's break it up into two cases.

Case 1: BGBGBGBGBGBG
Case 2:GBGBGBGBGBGB

Let's deal with case 1, because case 2 will pop out. There are ⁶P₆ ways in sorting out the boys and ⁶P₆ ways in sorting out the girls, so for case 1, we'd have (⁶P₆)² ways in sorting out boys and girls in case 1.

This is exactly the same in case 2, so it'd be (⁶P₆)² ways in sorting out girls and boys in case 2.

So, (⁶P₆)² + (⁶P₆)² ways = 1 036 800 ways if they alternate
3 0
2 years ago
ΔABC is similar to ΔAXY by a ratio of 4:3. If BC = 24, what is the length of XY?
pogonyaev

Answer:

18

Step-by-step explanation:

24/4 = 6 so....

4*6 is 24 and 3*6 is 18

6 0
2 years ago
Read 2 more answers
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