Answer:
x=8 and y=3 (So, yes!)
Step-by-step explanation:
I will solve your system by substitution.
(You can also solve this system by elimination.)
−x+4y=4;−x+3y=1
Step: Solve −x+4y=4 for x:
−x+4y+−4y=4+−4y(Add -4y to both sides)
−x=−4y+4
-x/-1 = -4y+4/-1 (Divide both sides by -1)
x=4y−4
Step: Substitute 4y−4 for x in −x+3y=1:
−x+3y=1
−(4y−4)+3y=1
−y+4=1(Simplify both sides of the equation)
−y+4+−4=1+−4(Add -4 to both sides)
−y=−3
-y/-1 = -3/-1 (Divide both sides by -1)
y=3
Step: Substitute 3 for y in x=4y−4:
=4y−4
x=(4)(3)−4
x=8(Simplify both sides of the equation)
<u>Answer:</u>
x=8 and y=3
Answer: 81%
Step-by-step explanation:
From the question, we are informed that a student received the following test scores: 71%, 89%, 72%,
84% and 83% in 5 tests and the student wants to maintain an average of 80%.
The lowest score/grade they can receive on the next test to maintain at least an 80% average first thus:
First, to make it easy we can remove the percent sign. Then we multiply 80 by 6 since we're calculating for 6 tests scores. This will be:
= 80 × 6
= 480
We then add all the 5 test scores. This will be:
= 71 + 89 + 72 + 84 + 83
= 399
We then subtract the values gotten. This will be:
= 480 - 399
= 81
This means the student must get at least 81%
Answer:
First number=6
Second number=14
Step-by-step explanation:
Let the first number be x
So the second number is x+8
So the sum of the two is
X+x+8=20
2x+8=20
2x=20-8
2x=12
X=12/2
=6
The second number will x+8
So 6+8=14
First number=6
Second number=14
The answer is 52.
20+52=72
Given:
n = 20, sample size
xbar = 17.5, sample mean
s = 3.8, sample standard deiation
99% confidence interval
The degrees of freedom is
df = n-1 = 19
We do not know the population standard deviation, so we should determine t* that corresponds to df = 19.
From a one-tailed distribution, 99% CI means using a p-value of 0.005.
Obtain
t* = 2.8609.
The 99% confidence interval is
xbar +/- t*(s/√n)
t*(s/√n) = 2.8609*(3.8/√20) = 2.4309
The 99% confidence interval is
(17.5 - 2.4309, 17.5 + 2.4309) = (15.069, 19.931)
Answer: The 99% confidence interval is (15.07, 19.93)
