What is the measure of ∠XYZ? A. 116° B. 72° C. 64° D. 108°
1 answer:
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Answer:
7
Step-by-step explanation:
The diagonal is the hypotenuse of the right triangle with legs 7
Use Pythagoras' identity to solve for the diagonal d
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
d² = (7)² + (7
)²
= 147 + 147
= 294 ( take the square root of both sides )
d = = 7
≈ 45.37 ( to 2 dec. places )
The transformed function is y = 1/3(log(x/3 + 4)) + 1
<h3>How to transform the logarithmic function?</h3>The parent logarithmic function is
y = log(x)
When shifted left by 4 units, we have:
y = log(x + 4)
When shifted up by 3 units, we have:
y = log(x + 4) + 3
When compressed vertically by 1/3, we have:
y = 1/3(log(x + 4) + 3)
This gives
y = 1/3(log(x + 4)) + 1
When stretched horizontally by 3, we have:
y = 1/3(log(x/3 + 4)) + 1
Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1
<h3>The transformation of function f(x)</h3>We have:
f(x) = log[-(x – 5)] + 4
Set the radicand greater than 0
-(x - 5) > 0
Divide by -1
x - 5 < 0
Add 5 to both sides
x < 5 -- this represents the domain
A logarithmic function can output any real number.
So, the range is
In the domain, we have:
x < 5
This means that the interval of decrease is
Rewrite as an equation
x = 5 --- this represents the equation of asymptote
Read more about logarithmic functions at:
#SPJ1
Answer:
A t-score of 1.701 should be used to find the 95% confidence interval for the population mean
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 29 - 1 = 28
Now, we have to find a value of T, which is found looking at the t table, with 28 degrees of freedom(y-axis) and a confidence level of 0.95(). So we have T = 1.701.
A t-score of 1.701 should be used to find the 95% confidence interval for the population mean