The inequality described can be written as:
y < 3x + 2.
<h3>How to get the inequality?</h3>
First, we know that we have a dashed line, and the region to the left of that line is shaded, then we will have:
y < line.
The linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:
Here we know that the line passes through (-3, -7) and (0, 2), so the slope is:
And because the line passes through (0, 2), the y-intercept is 2, then the inequality is:
y < 3x + 2.
If you want to learn more about inequalities:
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Answer:
D
Step-by-step explanation:
So you start with $2.65 and a variable y. What we will do is work without the dollar and keep it for the end as it quite disturbs and work our way while keeping the y. So first we have 2.65. Now it rose by y so. The price = 2.65 + y. Then it dropped by 0.15. So 2.65 + y - 0.15. Here you see we have like terms so we reduce and get 2.50 + y. Now it rose by 0.05. So 2.50 + y + 0.05. Again, like terms, reduce. 2.55 + y. There you go with the answer.
I believe it is the second one hope that helped
Answer:
C. with 3000 successes of 5000 cases sample
Step-by-step explanation:
Given that we need to test if the proportion of success is greater than 0.5.
From the given options, we can see that they all have the same proportion which equals to;
Proportion p = 30/50 = 600/1000 = 0.6
p = 0.6
But we can notice that the number of samples in each case is different.
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size
po = Null hypothesized value
p^ = Observed proportion
Since all other variables are the same for all the cases except sample size, from the formula for the test statistics we can see that the higher the value of sample size (n) the higher the test statistics (z) and the highest z gives the strongest evidence for the alternative hypothesis. So the option with the highest sample size gives the strongest evidence for the alternative hypothesis.
Therefore, option C with sample size 5000 and proportion 0.6 has the highest sample size. Hence, option C gives the strongest evidence for the alternative hypothesis
Answer:
∠F ≈ 53°
General Formulas and Concepts:
<u>Trigonometry</u>
- sin∅ = opposite over hypotenuse
- sin inverse evaluates "backward" to find the measure angle
Step-by-step explanation:
<u>Step 1: Define</u>
Looking at ∠F
opposite leg of ∠F = ED = 8
hypotenuse = FE = 10
<u>Step 2: Find m∠F</u>
- Substitute: sin∠F = 8/10
- Simplify: sin∠F = 4/5
- Take sin inverse: ∠F = sin⁻¹(4/5)
- Evaluate: ∠F = 53.1301°
- Round: ∠F ≈ 53°
