Answer:
Step-by-step explanation:
: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
Answer:
4.979044478499338 × 10²⁶
Step-by-step explanation:
Combination can be used to determine the number of ways the mice can be selected for the drugs (A, B) and the control group.
Combination factorial is define by ⁿCr = 
21 group of mice receiving Drug A can be selected in ⁶⁰C₂₁ = 
(60 - 21 = 39 ) mice remained for selection of 21 mice for the second drug
Drug B 21 mice can be chosen with ³⁹C₂₁ = 
( 39 - 21 = 18) remained for control with ¹⁸C₁₈ = 
The number of ways the mice can be chosen for drug A, drug B and the control = ⁶⁰C₂₁ × ³⁹C₂₁ × ¹⁸C₁₈ = × × = 4.979044478499338 × 10²⁶
Answer:
tan−1(StartFraction 6.9 Over 9.8 EndFraction)
Step-by-step explanation:
tan−1(StartFraction 6.9 Over 9.8 EndFraction)
tan = opp/adj = 9.8/6.9
tan -1 = 1 / tan = 1 / (9.8 /6.9) = 6.9 /9.8
<span>Let L be the number of yards on a roll of lace ribbon.
Let S be the number of yards on a roll of satin ribbon.
We can set up two equations.
equation 1: 3L + 2S = 120 yards
equation 2: 2L + 4S = 160 yards
We can multiply (equation 1) by 2 and subtract (equation 2).
equation 1: 6L + 4S = 240 yards
equation 2: 2L + 4S = 160 yards
4L = 80 yards
L = 20 yards
equation 1: 3L + 2S = 120 yards
3(20 yards) + 2S = 120 yards
2S = 60 yards
S = 30 yards
There are 20 yards on a roll of lace ribbon.
There are 30 yards on a roll of satin ribbon.</span>
Answer:
k = 11.
Step-by-step explanation:
y = x^2 - 5x + k
dy/dx = 2x - 5 = the slope of the tangent to the curve
The slope of the normal = -1/(2x - 5)
The line 3y + x =25 is normal to the curve so finding its slope:
3y = 25 - x
y = -1/3 x + 25/3 <------- Slope is -1/3
So at the point of intersection with the curve, if the line is normal to the curve:
-1/3 = -1 / (2x - 5)
2x - 5 = 3 giving x = 4.
Substituting for x in y = x^2 - 5x + k:
When x = 4, y = (4)^2 - 5*4 + k
y = 16 - 20 + k
so y = k - 4.
From the equation y = -1/3 x + 25/3, at x = 4
y = (-1/3)*4 + 25/3 = 21/3 = 7.
So y = k - 4 = 7
k = 7 + 4 = 11.
