Answer:
x=8
Step-by-step explanation:
1
(x+2)=
2
1
(x−4)
Use the distributive property to multiply
5
1
by x+2.
5
1
x+
5
1
×2=
2
1
(x−4)
Multiply
5
1
and 2 to get
5
2
.
5
1
x+
5
2
=
2
1
(x−4)
Use the distributive property to multiply
2
1
by x−4.
5
1
x+
5
2
=
2
1
x+
2
1
(−4)
Multiply
2
1
and −4 to get
2
−4
.
5
1
x+
5
2
=
2
1
x+
2
−4
Divide −4 by 2 to get −2.
5
1
x+
5
2
=
2
1
x−2
Subtract
2
1
x from both sides.
5
1
x+
5
2
−
2
1
x=−2
Combine
5
1
x and −
2
1
x to get −
10
3
x.
−
10
3
x+
5
2
=−2
Subtract
5
2
from both sides.
−
10
3
x=−2−
5
2
Convert −2 to fraction −
5
10
.
−
10
3
x=−
5
10
−
5
2
Since −
5
10
and
5
2
have the same denominator, subtract them by subtracting their numerators.
−
10
3
x=
5
−10−2
Subtract 2 from −10 to get −12.
−
10
3
x=−
5
12
Multiply both sides by −
3
10
, the reciprocal of −
10
3
.
x=−
5
12
(−
3
10
)
Multiply −
5
12
times −
3
10
by multiplying numerator times numerator and denominator times denominator.
x=
5×3
−12(−10)
Do the multiplications in the fraction
5×3
−12(−10)
.
x=
15
120
Divide 120 by 15 to get 8.
x=8
Answer:
The equation representing pounds of apples will has left .
Will has left with 7 pounds of apples.
Step-by-step explanation:
Given:
Total pounds of apple = 20 pounds.
Pounds of apple used for apple sauce = 4 pounds
Pounds of apple used for apple butter = 6 pounds
Pounds of apple used for making juice = 3 pounds
We need to write the equation to represent pounds of apples will has left.
Solution:
Let us assume pounds of apples will has left be 'x'.
So we can say that;
pounds of apples will has left can be calculated by subtracting Pounds of apple used for apple sauce and Pounds of apple used for apple butter and Pounds of apple used for making juice from Total pounds of apple.
framing in equation form we get;
Hence The equation representing pounds of apples will has left .
On Solving the above equation we get;
Hence Will has left with 7 pounds of apples.
Using the <em>normal distribution and the central limit theorem</em>, it is found that there is a 0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation .
In this problem:
- The mean is of 660, hence .
- The standard deviation is of 90, hence .
- A sample of 100 is taken, hence .
The probability that 100 randomly selected students will have a mean SAT II Math score greater than 670 is <u>1 subtracted by the p-value of Z when X = 670</u>, hence:
By the Central Limit Theorem
has a p-value of 0.8665.
1 - 0.8665 = 0.1335.
0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.
To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213