Given:
Square DEFG = SIDE LENGTH = 2 UNITS
Square D'E'F'G' = SIDE LENGTH = 6 UNITS
The question was which scale factor was used to dilate square DEFG to square D'E'F'G'
From a side length of 2 units to a side length of 6 units
The scale factor used is 3.
2 * scale factor = 6
scale factor = 6/2
scale factor = 3
Answer:
A) sin θ = 3/5
B) tan θ = 3/4
C) csc θ = 5/3
D) sec θ = 5/4
E) cot θ = 4/3
Step-by-step explanation:
We are told that cos θ = 4/5
That θ is the acute angle of a right angle triangle.
To find the remaining trigonometric functions for angle θ, we need to find the 3rd side of the triangle.
Now, the identity cos θ means adjacent/hypotenuse.
Thus, adjacent side = 4
Hypotenuse = 5
Using pythagoras theorem, we can find the third side which is called opposite;
Opposite = √(5² - 4²)
Opposite = √(25 - 16)
Opposite = √9
Opposite = 3
A) sin θ
Trigonometric ratio for sin θ is opposite/hypotenuse. Thus;
sin θ = 3/5
B) tan θ
Trigonometric ratio for tan θ is opposite/adjacent. Thus;
tan θ = 3/4
C) csc θ
Trigonometric ratio for csc θ is 1/sin θ. Thus;
csc θ = 1/(3/5)
csc θ = 5/3
D) sec θ
Trigonometric ratio for sec θ is 1/cos θ. Thus;
sec θ = 1/(4/5)
sec θ = 5/4
E) cot θ
Trigonometric ratio for cot θ is 1/tan θ. Thus;
cot θ = 1/(3/4)
cot θ = 4/3
Image is attached below.
If the sum of the digits its divisible by 9,
then the original number is divisible by 9.
Since 18 (the sum of the digits) is divisible by 9,
the number 540,171 is also divisible by 9.
Answer:
3
Step-by-step explanation:
To find the 10 term substitute n = 10 into the rule, that is
f(10) = 
= 
= 3
Answer: (14.4, 17.2)
Step-by-step explanation: We are to construct a 98% confidence interval for mean household usage of electricity.
We have been given that
Sample size (n) = 872
Sample mean (x) = 15.8
Population standard deviation (σ) = 1.8
The formulae that defines the 98% confidence interval for mean is given below as
u = x + Zα/2 × σ/√n...... For the upper limit
u = x - Zα/2 × σ/√n...... For the lower limit
Zα/2 = critical value for a 2% level of significance in a two tailed test = 2.33
By substituting the parameters we have that
For upper tailed
u = 15.8 + 2.33 × (1.8/√872)
u = 15.8 + 2.33 (0.6096)
u = 15.8 + 1.4203
u = 17.2
For lower tailed
u = 15.8 - 2.33 × (1.8/√872)
u = 15.8 - 2.33 (0.6096)
u = 15.8 - 1.4203
u = 14.4
Hence the 98% confidence interval for population mean usage of electricity is (14.4kwh, 17.2kwh)
