Answer: 109.1 degrees
Step-by-step explanation:
To find the angle between the given vectors, we will use the formula below:
Cos(θ) = (U.V)/ |U|.|V|
Where
U = 13i - 8j
V = 2i + 9j
U.V = (2x13) + (-8×9)
U.V = 26 - 72
U.V = - 46
|U| = sqrt ( 13^2 + 8^2)
= sqrt ( 233) = 15.264
|V| = sqrt( 2^2 + 9^2)
= sqrt ( 85 ) = 9.22
Substitute all the value of the parameters into the formula
Cos ø = -46 / (15.3 × 9.2)
Cos ø = - 46 / 140.72
Cos Ø = - 32687
Find the cos inverse of the value
Ø = cos^-1( -32687)
Ø = 109.079 degrees
Therefore, the angle between the given vectors to the nearest tenth of a degree is 109.1 degrees
Answer:
the sum of exterior angles of a polygon is 360°
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Answer:
--- Variance
Step-by-step explanation:
Given
Solving (a): Calculate the mean.
The given data is a grouped data. So, first we calculate the class midpoint (x)
For 51 - 58.
For 59 - 66
For 67 - 74
For 75 - 82
For 83 - 90
So, the table becomes:
The mean is then calculated as:
-- approximated
Solving (b): The sample variance:
This is calculated as:
So, we have:
-- approximated
a) The expression to find the sale price of pastry = 0.75 x
b) The regular price of the pastry bought by Kimberly = $2.70
Step-by-step explanation:
Step 1 :
Let x be the regular price of the pastry in the bakery
Percentage of discount = 25%
Amount of discount = 0.25 x
The expression to find the sale price of pastry = x - 0.25 x = 0.75 x
Step 2 :
Sale price of the pastry bought by Kimberly = $2.03 = 0.75 x
<u>To find the regular price</u>
0.75x = 2.03
x = = 2.70
Regular price of the pastry bought by Kimberly = $2.70
Step 3 :
Answer :
a) The expression to find the sale price of pastry = 0.75 x
b) The regular price of the pastry bought by Kimberly = $2.70