Answer:
x + y = 90 - - - (1)
y = 1/4x - - - - (2)
Step-by-step explanation:
x = larger acute angle
y = smaller acute angle
Recall:
A right angle measures 90°
Sum of angles in a triangle = 180°
y = 1/4x
Hence :
90 + x + y = 180
x + y = 180 - 90
x + y = 90 - - - (1)
y = 1/4x - - - - (2)
Put y = 1/4x in (1)
x + 1/4x = 90
1.25x = 90
x = 90 / 1.25
x = 72
x + y = 90
72 + y = 90
y = 90 - 72
y = 18
Answer:
95% z-confidence interval for the proportion of all children enrolled in kindergarten who attended preschool is between a lower limit of 0.528 and an upper limit of 0.772.
Step-by-step explanation:
Confidence interval = p + or - zsqrt[p(1-p) ÷ n]
p is sample proportion = 39/60 = 0.65
n is the number of children sampled = 60
Confidence level (C) = 95% = 0.95
Significance level = 1 - C = 1 - 0.95 = 0.05
Divide significance level by 2 to obtain critical value (z)
0.05/2 = 0.025 = 2.5%
z at 2.5% significance level = 1.96
zsqrt[p(1-p) ÷ n] = 1.96sqrt[0.65(1-0.65) ÷ 60] = 1.96sqrt[0.2275 ÷ 60] = 1.96sqrt(3.792×10^-3) = 1.96×0.062 = 0.122
Lower limit = p - 0.122 = 0.65 - 0.122 = 0.528
Upper limit = p + 0.122 = 0.65 + 0.122 = 0.772
95% confidence interval is between 0.528 and 0.772
Answer:
Part 26) 
Part 27) 
Step-by-step explanation:
Part 26)
we know that
The length of Alana's hair was 9 3/4 inches
After her haircut, the length was 6 1/2 inches
To find out how many inches did she have cut subtract 6 1/2 from 9 3/4
but first
Convert mixed number to an improper fraction


Find the difference

Convert to mixed number

Part 27)
we have that
Emeril used a total of 7 1/4 cups of flour to make three pastries
He used 2 1/4 cup of flour for the first and 2 1/3 cups of flour for the second
To find out how much cups of flour Emeril use for the third pastry, subtract the sum of the cups of flour used in the first and second pastry from the total cups of pastry used
Let
x ----> number of cups of flour used in the third pastry

but first
Convert mixed number to an improper fraction



substitute




Simplify

Convert to mixed number

Area of triangle = 24cm
Area of rectangle = 120
therefore, w x 12 = 120
w = 10
Answer:
what grade is this
Step-by-step explanation:
it looks hecka hard