In order to make a table, we sample some x values (whichever we want), and we compute the expression for those value. Each x value will yield a unique y value.
If you need this table to graph the function, you'll only need two points, since this is a line, and having two points you just need to connect them.
Here are some samples, feel free to make more if you need to:
So, we have the following table
Answer:
x >>>>>>>> f(x)
–9 >>>>>> 10
–7 >>>>>>> 0
0 >>>>>>>> –35
5 >>>>>>>> –60
Step-by-step explanation:
f(x) = –5(x + 7)
1. x = –9, f(x) =?
f(x) = –5(x + 7)
f(x) = –5(–9 + 7)
f(x) = –5(–2)
f(x) = 10
2. f(x) = 0, x =?
f(x) = –5(x + 7)
0 = –5(x + 7)
Divide both side by –5
0 / –5 = x + 7
0 = x + 7
Collect like terms
x = 0 – 7
x = –7
3. x = 0, f(x) =?
f(x) = –5(0 + 7)
f(x) = –5(7)
f(x) = –35
4. f(x) = –60, x =?
f(x) = –5(x + 7)
–60 = –5(x + 7)
Divide both side by –5
–60 / –5 = x + 7
12 = x + 7
Collect like terms
x = 12 – 7
x = 5
SUMMARY:
x >>>>>>>> f(x)
–9 >>>>>> 10
–7 >>>>>>> 0
0 >>>>>>>> –35
5 >>>>>>>> –60
Answer: The probability in (b) has higher probability than the probability in (a).
Explanation:
Since we're computing for the probability of the sample mean, we consider the z-score and the standard deviation of the sampling distribution. Recall that the standard deviation of the sampling distribution approximately the quotient of the population standard deviation and the square root of the sample size.
So, if the sample size higher, the standard deviation of the sampling distribution is lower. Since the sample size in (b) is higher, the standard deviation of the sampling distribution in (b) is lower.
Moreover, since the mean of the sampling distribution is the same as the population mean, the lower the standard deviation, the wider the range of z-scores. Because the standard deviation in (b) is lower, it has a wider range of z-scores.
Note that in a normal distribution, if the probability has wider range of z-scores, it has a higher probability. Therefore, the probability in (b) has higher probability than the probability in (a) because it has wider range of z-scores than the probability in (a).
Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
<em></em>
Therefore, the angle between their paths is <em>100.8°</em>
Let x = the amount of grapes that can be bought for 0.40.
Note: By 90 I assume you mean 90 cents. The same for 40.
12/x = 0.90/0.40
0.90x = 12(0.40)
0.90x = 4.80
x = 4.80 ÷ 0.90
x = 5.33333
We can round the decimal to the ones place to get 5 grapes.
