You can set both equations together
y = -3x + 1
and y = x - 3
we can replace the y of one equation with the other side
-3x+1 = x-3
add 3x on both sides
1 = x + 3x -3
add 3 on both sides
1 + 3 = x+ 3x
simplify
4 = 4x
divide by 4 on both sides
x = 1
y = x - 3
y = 1 - 3
y = 2
So the solution is: (1,2)
Answer:
Explanation:
<u>1) Data:</u>
a) height of the person = opposite-leg to the angle the sun makes with the ground = 5 ft
b) length of the shadow = adjacent-leg to the angle the sun makes with the ground = 12 ft
c) angle, α = ?
<u>2) Solution</u>
- tanα = opposite-leg / adjacent-leg
- tanα = 5 ft / 12 5t = 5/12
- 22.6° rounded to the nearest degree is 23° ← answer
Answer: The roses costed $9
Step-by-step explanation:
3 multiplied by 3 equals 9
1 multiplied by 6 equals 6
9+6=15
Answer:
P-value = 0.0368
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 101.5
Sample mean,
= 106.4
Sample size, n = 30
Alpha, α = 0.05
Population standard deviation, σ = 15
First, we design the null and the alternate hypothesis
We use One-tailed(right) z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
We reject the null hypothesis and accept the alternate hypothesis. Thus, students in Pennsylvania have an IQ that is significantly greater than the state average.
P-value can be calculated with the standard normal table.
P-value = 0.0368
P-value is lower than the significance level.