The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
The triangles ΔLNO and ΔLMO have the same leg Lo, therefore you need the equality of hypotenuses LM=LN.
Answer: she still has to cut off 19/16 inches.
Step-by-step explanation:
Olivia wants to cut 3 3/4 inches from a piece of string. Converting 3 3/4 inches to improper fraction, it becomes 15/4 inches.
She has already cut off 2 9/16 inches from the piece of string. Converting 2 9/16 inches to improper fraction, it becomes 41/16 inches.
Therefore, the length of string that is left for her to cut off would be
15/4 - 41/16 = (60 - 41)/16
= 19/16 inches
Answer:
Pr(X>1540.2) = 0.0655
Step-by-step explanation:
Expected value of large bottle,
E(Large) = 1016
Expected value of small bottle,
E(small) = 510
Expected value of total
E(total) = 1016 + 510 = 1526
So the new mean is 1526
Find standard deviation of new amount by variance
Variance of large bottle,
v(large) = 8^2 = 64
Variance of small bottle,
v(small) = 5^2 = 25
Variance of total
v(total) = 64+25 = 89
So the new standard deviation
sd(new) = sqrt(89) = 9.434
Find probability using the new mean and s.d.
Pr(X>1540.2)
Z score, z = (x-mean)/sd
= (1540.2 - 1526)/9.434
= 1.505
value in z score
P(z<1.51) = 0.9345
For probability of x > 1540.2
P(z > 1.51) = 1 - 0.9345 = 0.0655
Good morning ☕️
Answer:
<h3>i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰ =
0</h3>
Step-by-step explanation:
Consider the sum S = i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰
S = i¹ + i² + i³ + . . . + i⁹⁹ + i¹⁰⁰
S = a₁ + a₂ + a₃ +. . . + a₉₉ + a₁₀₀
then, S is the sum of 100 consecutive terms of a geometric sequence (an)
where the first term a1 = i¹ = i and the common ratio = i
FORMULA:______________________
_______________________________
then
or i¹⁰⁰ = (i⁴)²⁵ = 1²⁵ = 1 (we know that i⁴ = 1)
Hence
S = 0
Answer: Total number of bracelet: 235
Step-by-step explanation:
Given:
Total budget= $1,500
Spend on wire = $250
Per braclet beads = $5.30
Find:
Total number of bracelet
Computation:
Total number of bracelet = [1,500 - 250]
Total number of bracelet = [1,250/ 5.30
Total number of bracelet = 235.849
Total number of bracelet = 235 [By round minium]
