Answer:
1. The correct option is 3.
2.The correct option is 3.
3.The correct option is 3.
4.The correct option is 4.
Step-by-step explanation:
1.
Sameera planned a rectangular walkway to be 25 ft long. She decides to change the walkway to be 45 ft long.
The scale factor is
The scale factor is 9/5, it means the change in the scale factor is 5 to 9.
Therefore the correct option is 3.
2.
Total possible outcomes for flipping four coins are
S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}
Possibilities of getting the same number of heads and tails.
A = {HHTT, HTHT, HTTH, THHT, THTH, TTHH} = 6
The probability of getting the same number of heads and tails is
Therefore the correct option is 3.
3.
The given expression is
Therefore the correct option is 3.
4.
The given expression is
Step 1: (–10.2)(–16.4) = (–16.4)(–10.2)
Step 2: = (–16.4)(–10) + (–16.4)(–0.2)
Step 3: = 164 + 3.28
Step 4: = 167.28
Therefore the correct option is 4.
Answer:
The roots of equations are as m = And n =
Step-by-step explanation:
The given quadratic equation is 2 x² + 6 x - 1 = 0
This equation is in form of a x² + b x + c = 0
Let the roots of the equation are ( m , n )
Now , sum of roots =
And products of roots =
So, m + n = = - 3
And m × n =
Or, (m - n)² = (m + n)² - 4mn
Or, (m - n)² = (-3)² - 4 ()
Or, (m - n)² = 9 + 2 = 11
I.e m - n =
Again m + n = - 3 And m - n =
Solving this two equation
(m + n) + ( m - n) = - 3 +
I.e 2 m = - 3 +
Or, m =
Similarly n =
Hence the roots of equations are as m = And n =
Answer
Answer:
1) Randomization: We assume that we have a random sample of students
2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size
3) np = 500*0.66= 330 >10
n(1-p) = 500*(1-0.66) =170>10
So then we can use the normal approximation for the distribution of p, since the conditions are satisfied
The population proportion have the following distribution :
And we have :
Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).
Step-by-step explanation:
For this case we know that we have a sample of n = 500 students and we have a percentage of expected return for their sophomore years given 66% and on fraction would be 0.66 and we are interested on the distribution for the population proportion p.
We want to know if we can apply the normal approximation, so we need to check 3 conditions:
1) Randomization: We assume that we have a random sample of students
2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size
3) np = 500*0.66= 330 >10
n(1-p) = 500*(1-0.66) =170>10
So then we can use the normal approximation for the distribution of p, since the conditions are satisfied
The population proportion have the following distribution :
And we have :
And we can use the empirical rule to describe the distribution of percentages.
The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
• The probability of obtain values within one deviation from the mean is 0.68
• The probability of obtain values within two deviation's from the mean is 0.95
• The probability of obtain values within three deviation's from the mean is 0.997
Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).