Answer:
2
Step-by-step explanation:
greatest common factor means the greatest number we can divide by for each of the number and still get a whole number
14 and 22. they are both even so one factor is 2
if we check, 14 & 22 aren't both divisible by 3,4,5,6,7,8,9,10,11,12,13,14 so the gcf is 2
Answer: Expression for the amount raised by Rachel = x
Expression for the amount raised by Francesca = x+10.50
Step-by-step explanation:
Let x = the amount raised by Kayla.
Since Rachel and Kayla each raised the same amount.
then, expression for the amount raised by Rachel = x
Francesca raised $10.50 more than each of them.
Then, expression for the amount raised by Francesca = x+10.50
Answer:
The calculated value Z = 1.39 <1.96 at 0.05 level of significance
The null hypothesis is accepted
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the mean of the Population = 43
Given that the mean of the sample = 47
Given that the standard deviation of the Population = 25
Given that the sample size 'n' = 76
<u><em>Step(ii):-</em></u>
<u><em>Null hypothesis:H₀: μ = 43</em></u>
<u><em>Alternative Hypothesis: H₁: μ ≠ 43</em></u>
Test statistic
Z = 1.39
Level of significance = 0.05
The critical value = 1.96
<u><em>Final answer:-</em></u>
<em>The calculated value Z = 1.39 <1.96 at 0.05 level of significance</em>
<em>The null hypothesis is accepted </em>
Answer:
388.5yd²
Step-by-step explanation:
We have Triangle TUV
In the question, we are given already
Angle U = 32°
Angle T = 38°
Angle V = ???
Side t = 31yd
Side u = ?
Side v = ?
Area of the triangle= ?
Step 1
We find the third angle = Angle V
Sum of angles in a triangle = 180°
Third angle = Angle V = 180° - (32 + 38)°
= 180° - 70°
Angle V = 110°
Step 2
Find the sides u and v
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle TUV
t/ sin T = u/ sin U = v/ sin V
We have the following values
Angle T = 38°
Angle U = 32°
Angle V = 110°
We are given side t = 31y
Finding side u
u/ sin U= t/ sin T
u/sin 32 = 31/sin 38
Cross Multiply
sin 32 × 31 = u × sin 38
u = sin 32 × 31/sin 38
u = 26.68268yd
u = 26.68yd
Finding side x
v / sin V= t/ sin T
v/ sin 110 = 31/sin 38
Cross Multiply
sin 110 × 31 = v × sin 38
v = sin 110 × 31/sin 38
v = 47.31573yd
v = 47.32yd
To find the area of triangle TUV
We use heron formula
= √s(s - t) (s - u) (s - v)
Where S = t + u + v/ 2
s = (31 + 26.68 + 47.32)/2
s = 52.5
Area of the triangle = √52.5× (52.5 - 31) × (52.5 - 26.68 ) × (52.5 - 47.32)
Area of the triangle = √150967.6032
Area of the triangle = 388.5454973359yd²
Approximately to the nearest tenth =388.5yd²
Answer:
x+9
Step-by-step explanation:
the perimeter of any polygon is the sum of all the sides
