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3 years ago

3. Jessica is playing a board game with her mother. The spinner used for

Mathematics

1 answer:

Natali [406]3 years ago

4 0

Answer:

C. 1/25

Step-by-step explanation:

I assume this is a fair spinner and the probability of landing in all colors is equal.

First spin:

p(purple) = 1/5

Second spin:

p(purple) = 1/5

The two spins are independent events, so the probability of landing on purple twice is the product of the two individual probabilities.

p(purple and purple) = 1/5 * 1/5 = 1/25

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53% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the

faltersainse [42]

Answer:

$P(X = 5) = 0.2423$

$P( X \ge 6 )= 0.4516$

$P( X < 4 )= 0.12694$

Step-by-step explanation:

From the question we are told that

The population proportion is p = 0.53

The sample size is n = 10

Generally the distribution of the confidence of US adults in newspapers follows a binomial distribution

i.e

$X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial distribution is

$P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}$

Here C stands for combination hence we are going to be making use of the combination function in our calculators

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is exactly five is mathematically represented as

$P(X = 5) = ^{10}C_5 * 0.53^5 * (1- 0.53)^{10-5}$

=> $P(X = 5) = 252 * 0.04182 * 0.023$

=> $P(X = 5) = 0.2423$

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is at least six is mathematically represented as

$P( X \ge 6 )= P( X = 6) + P( X = 7) + P( X = 8) + P( X = 9) + P( X = 10)$

=> $P( X \ge 6 )= [^{10}C_6 * [0.53]^6 * (1- 0.53)^{10-6}] + [^{10}C_7 * [0.53]^7 * (1- 0.53)^{10-7}] + [^{10}C_8 * [0.53]^8 * (1- 0.53)^{10-8}] + [^{10}C_9 * [0.53]^9 * (1- 0.53)^{10-9}] + [^{10}C_{10} * [0.53]^{10} * (1- 0.53)^{10-10}]$

=> $P( X \ge 6 )= [0.227] + [0.1464] + [0.0619] + [0.0155] + [0.00082]$

=> $P( X \ge 6 )= 0.4516$

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is less than four is mathematically represented as

$P( X < 4 )= P( X = 3) + P( X = 2) + P( X = 1) + P( X = 0)$

=> $P( X < 4 )= [^{10}C_3 * 0.53^3 * (1- 0.53)^{10-3}] + [^{10}C_2 * 0.53^2 * (1- 0.53)^{10-2}] + [^{10}C_1 * 0.53^1 * (1- 0.53)^{10-1}] + [^{10}C_0 * 0.53^0 * (1- 0.53)^{10-0}]$

=> $P( X < 4 )= 0.09051 + 0.03 + 0.0059 + 0.000526$

=> $P( X < 4 )= 0.12694$

5 0

3 years ago

Solve this equation log3X + log3(x-6) = log3 7

ExtremeBDS [4]

Hello!

log₃(x) + log₃(x - 6) = log₃(7) <=>

<=> log₃(x * (x - 6)) = log₃(7) <=>

<=> log₃(x² - 6x) = log₃(7) <=>

<=> x² - 6x = 7 <=>

<=> x² - 6x - 7 = 0 <=>

<=> x² + x - 7x - 7 = 0 <=>

<=> x * (x + 1) - 7 * (x + 1) = 0 <=>

<=> (x + 1) * (x - 7) = 0 <=>

<=> x + 1 = 0 and x - 7 = 0 <=>

<=> x = -1 and x = 7, x ∈ { 6; +∞ } <=>

<=> x = 7

Good luck! :)

3 0

3 years ago

Fission tracks are trails found in uranium-bearing minerals, left by fragments released during fission events. An article report

Harlamova29_29 [7]

Answer:

Mean track length for this rock specimen is between 10.463 and 13.537

Step-by-step explanation:

99% confidence interval for the mean track length for rock specimen can be calculated using the formula:

M± $\frac{t*s}{\sqrt{N}}$ where

M is the average track length (12 μm) in the report
t is the two tailed t-score in 99% confidence interval (2.977)
s is the standard deviation of track lengths in the report (2 μm)
N is the total number of tracks (15)

putting these numbers in the formula, we get confidence interval in 99% confidence as:

12± $\frac{2.977*2}{\sqrt{15}}$ =12±1.537

Therefore, mean track length for this rock specimen is between 10.463 and 13.537

4 0

3 years ago

Please help with this its a little confusing

Molodets [167]

What about it? What is the question?

8 0

2 years ago

$25;300%increse percent change

Korolek [52]

well and 300% increase means you multiply by 3 and then add the original number

in this case 300% of 25 is 75 and its an increase so 25+75=100

the answer is 100

4 0

3 years ago