Answer:
- <u>120 pens and 200 pencils.</u>
<u></u>
Explanation:
You can set a system of two equations.
<u>1. Variables</u>
<u />
- x: number of pens
- y: number of pencils
<u>2. Cost</u>
- <em>each pen costs</em> $1, then x pens costs: x
- <em>each pencil costs</em> $0.5, then y pencil costs: 0.5y
- Then, the total cost is: x + 0.5y
- The cost of the whole purchase was $ 220, then the first equation is:
x + 0.5y = 220 ↔ equation (1)
<u>3. </u><em><u>There were 80 more pencils than pens</u></em>
Then:
pencils = 80 + pens
↓ ↓
y = 80 + x ↔ equation (2)
<u>4. Solve the system</u>
i) Substitute the equation (2) into the equation (1):
ii) Solve
iii) Substitute x = 120 into the equation (2)
Solution: 120 pens and 200 pencils ← answer
Answer:
19
Step-by-step explanation:
12-n/7 = -1
Cross multiply
We have 12-n = -7
Collect like terms
12 + 7 = n
Therefore n = 19
Answer:
840,000,0
Step-by-step explanation:
Answer
The line of symmetry x = -4
Step by step explanation
Here we have to use the formula.
The symmetry of a parabola x = -b/2a
Now compare the given equation y = 3x^2 + 24x -1 with the general form y = ax^2 + bx + c and identify the value of "a" and "b"
Here a = 3 and b = 24. Now plug in these values in to the formula to find the line of symmetry.
x = -24/ 2(3)
x = -24/6
x = -4
Therefore, the line of symmetry x = -4.
Thank you.
Answer:
There is a 0.82% probability that a line width is greater than 0.62 micrometer.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. The sum of the probabilities is decimal 1. So 1-pvalue is the probability that the value of the measure is larger than X.
In this problem
The line width used for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micrometer and a standard deviation of 0.05 micrometer, so
.
What is the probability that a line width is greater than 0.62 micrometer?
That is 
So



Z = 2.4 has a pvalue of 0.99180.
This means that P(X \leq 0.62) = 0.99180.
We also have that


There is a 0.82% probability that a line width is greater than 0.62 micrometer.