Answer:
The number of nickels are 16 and the number of dimes are 14.
Step-by-step explanation:
As given
Let n represent the number of nickels.
let d represent the number of dimes.
As given
Luis is saving money to purchase a new video game.
He has a total of 30 coins consisting of nickels and dimes.
Than the equation becomes
n + d = 30
As the value of the coins is $2.20.
As 1 nickel = 0.05 dollars
1 dimes = 0.1 dollars
Than the equation becomes
0.05n + 0.1d = 2.20
Simplify the above
L.C.M of (10,100) = 100
Than
5n + 10d = 220
Than two equations are
n + d = 30 and 5n + 10d = 220
Multiply n + d = 30 by 5 and subtracted from 5n + 10d = 220 .
5n - 5n + 10d - 5d = 220 - 150
5d = 70
d = 14
Put in the equation n + d = 30
n + 14 = 30
n = 30 - 14
n = 16
Therefore the number of nickels are 16 and the number of dimes are 14.
Answer:
And we can use the following formula:
And replacing the info we got:
Step-by-step explanation:
We define two events for this case A and B. And we know the probability for each individual event given by the problem:
And we want to find the probability that A and B both occurs if A and B are independent events, who menas the following conditions:
And for this special case we want to find this probability:
And we can use the following formula:
And replacing the info we got:
Answer:
The area of the parallelogram is;
32 square units
Step-by-step explanation:
The given parameters are;
The coordinates of the parallelogram RSTU = R(-4, 4), S(2, 6), T(6, 2), and U(0, 0)
We note that the area of a parallelogram = Base length × Height
From the drawing of the parallelogram RSTU, we have;
The base length = The length of = The length of
= √((2 - (-4))² + (6 - 4)²) = 2·√10
The height of a parallelogram is perpendicular to its base length = The line
∴ Where, the slope of the base length = m, the slope of the height = -1/m
The slope, 'm' of = (6 - 4)/(2 - (-4)) = 1/3
Therefore, the slope of the height = -1/(1/3) = -3
We note that a point on the height is the point 'T', therefore, the equation of the line in point and slope form is therefore;
y - 0 = -3·(x - 0)
∴ y = -3·x
Therefore, the coordinates of the point 'V' is given by the simultaneous solution of the equations of and
The equation of the line in point and slope form from the point 'R' and the slope 'm = 1/3' is given as follows;
y - 4 = (1/3) × (x - (-4)) = (1/3) × (x + 4)
y = x/3 + 4/3 + 4 = x/3 + 16/3
y = x/3 + 16/3
We then have the coordinate at the point 'V' (x, y) is given as follows;
-3·x = x/3 + 16/3
-9·x = x + 16
-10·x = 16
x = -16/10 = -1.6
x = -1.6
∴ y = -3·x = -3 × -1.6 = -4.8
y = 4.8
The coordinate at the point, V = (-1.6, 4.8)
The length of the line = The height of the parallelogram = √((-1.6 - 0)² + (4.8 - 0)²) = 8/5·√10
The height of the parallelogram = 8/5·√10
The area of the parallelogram, A = Base length × Height
∴ A = 2·√(10) × 8/5·√(10) = (16/5) × 10 = 32
The area of the parallelogram, A = 32 square units.
Answer: 64
Step-by-step explanation:
256 is thesame thing as 2 raise to power of 8.
We then multiply 2 raise to power 8 by the power of 3/4. We will then be left with 2 raise to power 6.
2 raise to power 6 equals:
= 2 × 2 × 2 × 2 × 2 × 2
= 64
Check the attached file for proper explanation.
