Factor the trinomial completely. 10x^2+7x-12

You’re about to get on a plane to Seattle. You want to know if it’s raining. You call 3 random friends who live there and ask ea

Lyrx [107]

Answer:

The probability that it is actually raining in Seattle is 26/27

Step-by-step explanation:

Here we have the probability that a friend is telling the truth = 2/3

The probability that a friend is telling a lie = 1/3

Therefore, if all three friends say "Yes" it is raining in Seattle, the probability that is actually raining is given by the probability that one of them is telling the truth. That is the complement that all are messing with their friend.

The probability that all are not telling the truth is;

P(All not telling the truth) = $\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}$

P(One is telling the truth) = 1 - P(All not telling the truth) = $1- \frac{1}{27} = \frac{26}{27}$

Therefore, the probability that it is actually raining in Seattle = 26/27.

3 0

3 years ago

Solve the following equation <br> 2/7x + 2 =<br> 6

Oksi-84 [34.3K]

Answer:

x=1/14

Step-by-step explanation:

2/7x+2=6

left part times 7x = right part times 7x is:

2+14x=42x

2=28x

x=1/14

3 0

3 years ago

Complete the second equation below so that the terms in the system align.

cricket20 [7]

The equation is 3x+2y= -22

3 0

2 years ago

Read 2 more answers

Suppose that scores on a knowledge test are normally distributed with a mean of 60 and a standard deviation of 4.3. Scores on an

Sphinxa [80]

Question:

(c) Boris also took a logic test. His z-score on that test was +0.93 . Does this change the answer to which test Boris performed better on? Explain your answer using z-scores.

Answer:

The answers to the questions are;

(a) Based on the z score, Boris perform better on his aptitude test.

(b) Based on the z score, Callie perform better on his knowledge test .

(c) For Boris since +0.93 = $z_{logic}$ > $z_{knowledge}$ > $z_{aptitude}$

Yes as Boris now performed best on the logic test.

Step-by-step explanation:

The z-score of a score is a measurement of the score withe respect to its distance from the mean as a factor of the standard deviation.

To solve the question, we note that we are required to find the z score as follows.

z score is given by $z = \frac{x -\mu}{\sigma}$

Where:

z = Standard score

x = Score

σ = Standard deviation

μ = Mean

(a) To find out which test did Boris performed better usin z score, we have

Boris scored a

57 on the knowledge test and

106 on the aptitude test

Therefore the z sore for the knowledge test is

$z = \frac{x -\mu}{\sigma}$

Here

x = 57

μ = 60

σ = 4.3

Therefore

$z_{knowledge} = \frac{57 -60}{4.3}$ = -3/4.3 = -30/43 = -0.6977

The z sore for Boris on the aptitude test is

Here

x = 106

μ = 110

σ = 7.1

$z_{aptitude} = \frac{106 -110}{7.1}$ = -40/17 = -0.5634

Based on the z score, Boris perform better on the aptitude test as his z score is higher (on the number line), --0.5634, compared to the z score on the knowledge test , -0.6977

(b) For Callie we have

Callie scored a

63 on the knowledge test and

114 on the aptitude test

Therefore the z sore for the knowledge test is

$z = \frac{x -\mu}{\sigma}$

Here

x = 63

μ = 60

σ = 4.3

Therefore

$z_{knowledge} = \frac{63 -60}{4.3}$ = 3/4.3 = 30/43 = 0.6977

The z sore for Callie on the aptitude test is

Here

x = 114

μ = 110

σ = 7.1

$z_{aptitude} = \frac{114 -110}{7.1}$ = 40/17 = 0.5634

Based on the z score, Callie perform better on the knowledge test as his z score is higher (on the number line), 0.6977, compared to the z score on the aptitude test , 0.5634.

(c) If $z_{logic}$ = +0.93 then sinc for Boris $z_{knowledge}$ = -0.6977 and

$z_{aptitude}$ = - 0.5634 then

$z_{logic}$ > $z_{knowledge}$ > $z_{aptitude}$

Therefore Boris now performed best on the logic test.

6 0

2 years ago

Jaxon has $65 in his savings account. He deposits $15 every week. His father also deposits $25 into the account every time Jaxon

Grace [21]

Part A:
A coefficient can be either '15' or '25'.
A variable can be either 'w' or 'm'.
A constant is 65.

Part B:
Simply substitute, or plug-in, the numbers and solve.
***Step 1:
65+15w+25m --> 65+15(20)+25(3)
You do this because you are substituting the 'w' for the number
of weeks that Jaxon saved up for, which is 20, and the 'm' for the number
of times that Jaxon mowed the lawn, which is 3.
***Step 2:
65+15(20)+25(3) --> 65+300+75
Begin to solve, using PEMDAS, or whichever acronym you learned.
Remember, if you are using PEMDAS, recall that the order is Parenthesis,
Exponents, Multiplication/Division (whichever comes first), and
Addition/Subtraction (whichever comes first). Here, I checked for parenthesis.
I did find parenthesis, however, they do not have any expressions inside of
them, meaning that these parenthesis are for multiplying, and not for stating
order. So, you skip parenthesis. Next, you check for exponents, which you
find none of, so you skip over that. Now, we get to multiplying/dividing, so
you multiply the 15 and the 20 to get 300, and the 25 and 3 to get 75.
***Step 3:
65+300+75 --> 440
Now, we get to addition. You simply add everything up to get your final
answer: $440.

Part C:
If Jaxon had $75, then yes, the coefficients would change.
By subtracting $65 from $75, we can see that the total amount of money
from Jaxon's deposits and his lawn-mowing money is $10. Jaxon already
deposits $15 a week, meaning that, while using the current equation, Jaxon
CANNOT have $75 in his bank account. We can change the equation
so that Jaxon is able to have $75 in his savings account. You can change
the coefficient of 15 to 10, and the other coefficient of 25 to 0.
Now Jaxon is able to have $75 in his savings account.

8 0

3 years ago