Answer:
120 cubic inches
Step-by-step explanation:
12*4*5=240
240/2=120
3,751x2=7,502 or 5,689+1,831=7,502 or <span>8,965-1,463=7,502</span>
Answer:
1/160
Step-by-step explanation:
Assuming that you want to roll a 5 and then select the ace of hearts that would make this a sequence of events. In order to find the probability of this happening, you would need to multiply the probability of each of these events happening separately with one another.
Since there are a total of 6 possible outcomes when rolling a die (1,2,3,4,5,6) which rolling a 5 is only one of the options. Meaning that the probability of rolling a 5 is 1/5.
In a deck of cards, there are a total of 32 cards in the deck and only 1 of those cards is an ace of hearts. Meaning that the probability of getting the ace of hearts is 1/32. Now we simply multiply these two probabilities together to get the probability of the sequence.
1/5 * 1/32 = 1/160
Answer:
<1 : 36 degrees
<2 : 90 degrees
<3 : 36 degrees
<4 : 54 degrees
Step-by-step explanation:
First off, rhombus's have right angles formed at the middle, meaning that <2 is 90 degrees. Then, it's given that angle is 54 degrees, and its alternate interior angle is the one that is adjacent to <3. To find <1, add 90 and 54, and subtract that from 180. So <1 is 36 degrees. So that automatically makes < 3, 36 degrees and < 4, 54 degrees.
<h3>
Answer: AC = sqrt(21)/2</h3>
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Explanation:
Triangle CDA is congruent to triangle CDB. We can use the HL (hypotenuse leg) congruence theorem to prove this. This only works because we have two right triangles.
Since CDA and CDB are congruent, this means their corresponding pieces are the same length. Specifically AD = DB, so
AD+DB = AB
AD+AD = 3
2*AD = 3
AD = 3/2 = 1.5
For triangle CDA, we have AD = 3/2 = 1.5 and CD = sqrt(3). We can use the pythagorean theorem to find the missing side AC
a^2 + b^2 = c^2
(AD)^2 + (CD)^2 = (AC)^2
(3/2)^2 + (sqrt(3))^2 = (AC)^2
9/4 + 3 = (AC)^2
(AC)^2 = 9/4 + 3
(AC)^2 = 9/4 + 12/4
(AC)^2 = 21/4
AC = sqrt(21/4)
AC = sqrt(21)/sqrt(4)
AC = sqrt(21)/2
This is the same as writing (1/2)*sqrt(21) or 0.5*sqrt(21)
