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A flower vase, in the form of a hexagonal prism, is to be filled with 512 cubic inches of water. Find the height of the water if the wet portion of the flower vase and its volume are numerically equal.
a container trough is in the form of a triangular prism whose opposite sides are equilateral triangles with side 2 feet and are 4 feet apart.
a. find the height of the triangle
b. find the volume of the trough
if 2 cubic feet of water is placed inside the trough,
c. what is the level of the water
d. find the area of the wet portion.
a. find the height of the triangle
b. find the volume of the trough
if 2 cubic feet of water is placed inside the trough,
c. what is the level of the water
d. find the area of the wet portion.
The population of a colony of bacteria doubles every "a" days, where "a" is a positive integer. If the population is 4,000n on day 8a, on which of the days is the population 500n?
Adriana earns 5% commission on her sales up to $25 000 , 5.5% on any sales between $25 000 and $35 000 , 6% on any sales between $35 00 and $45 000 , and 7% for any sales over $45 000. Draw a graph to represent how Adriana's earning depend on her sales. what sales value does she need to ear $2000?
A university invests $600,000 at simple interest, part at 6%, half that amount at 4.5%, and the rest at 3.5%. What is the most the university can invest at 3.5% and be guaranteed at least $24,600 in interest per year?
A teacher has 21 red pens. If the ratio of red pens to blue pens is 3:1 how many pens did she have total?
A city council fire brigade officer claims that it takes, on average 10.9 minutes to reach its destination in emergency calls. To check on this claim, the agency which licenses fire brigade service providers had them timed on 50 emergency calls, getting a mean of 10.3 minutes with a standard deviation of 0.8 minutes. At the level of significance of 0.05, does this constitute evidence that the figure claimed is too high?
The price-earnings ratio of a stock that sells for $46.75 per share and earns $4.25 per share is..?
In the context of admission to IGOU, give examples of the following:
i) an implication;
ii) the converse of (i) above;
iii) a two-way implication which is true;
iv) a statement involving both ∀and ∃.
v) the contrapositive of (i) above. (10)
b) Prove that if A and B are any two sets such that A ⊆B, then A ∪B = B
i) by direct method;
ii) by proving its contrapositive;
iii) by contradiction. (10)
i) an implication;
ii) the converse of (i) above;
iii) a two-way implication which is true;
iv) a statement involving both ∀and ∃.
v) the contrapositive of (i) above. (10)
b) Prove that if A and B are any two sets such that A ⊆B, then A ∪B = B
i) by direct method;
ii) by proving its contrapositive;
iii) by contradiction. (10)
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