Answer:
x = 6.00 $/kg ----> almond
y = 3.5 $/kg ------> nut
Step-by-step explanation:
To find the price per kg of each product you first write the algebraic equations for the given relations:
x : price per kg of almond
y: price per kg of nut
Then, you have:
5x + 4y = 44.00 (1)
8x + 6y = 69.00 (2)
By using substitution you have from (1):
y = (44.00-5x)/(4) = 11.00 - (5/4)x
you replace this expression for y into (2):
8x+6[11.00-(5/4)x] = 69.00
8x+66.00-(15/2)x = 69.00
8x-(15/2)x = 69.00 - 66.00
(1/2)x = 3.00
x = 6.00 $/kg ----> almond
And for nut:
y = 11.00 - (5/4)x = 11.00 - (5/4)(6.00) = 3.5$/kg
y = 3.5 $/kg ------> nut
Answer:
She will pay $122.85
Step-by-step explanation:
First, find the amount of the percents.
To do that, turn the percents into decimals.
25% --> 0.25
10% --> 0.10
Then, multiply each decimal with the original price.
189×0.25= 47.25
189×0.10= 18.90
Now that you have the amount of the percents, subtract both from the original price.
189- (47.25+18.90)
189-66.15= 122.85
Answer:
The new volume is 1/343 of the old volume or the ratio of the new volume to the old volume is 1 to 343
Step-by-step explanation:
In this question, we are asked to state the effect of multiplying the radius of a sphere by 1/7 on the volume.
Mathematically, the volume of a sphere V can be calculated using the formula
V = 4/3 * π * r^3
Now multiplying the radius by 1/7, the new radius will be r/7
Thus the new volume here will be
V2 = 4/3 * π * (r/7)^3
V2 = 4/3 * π * (r^3)/343
Thus we can conclude that the value of the volume will be decreased by a factor of 343
Meaning the ratio of the old volume to the new volume will be 1 to 343
Think of the 13-ft length of the ladder as the hypotenuse of a right triangle. Represent the horiz. distance from foot of ladder to base of tree by x, or 5 ft.
Represent the vert. dist. from base of tree to top of ladder by y, which is unknown.
Then (13 ft)^2 = (5 ft)^2 + y^2, or
169 ft^2 = 25 ft^2 + y^2. This simplifies to y^2 = 144. Thus y = + 12 feeet.
Note: Please pay attention to your spelling: "lader i up agenst a tree" should be "the top of a 13-ft ladder is placed against a tree."
