Answer:
Step-by-step explanation:
<h3>Given</h3>
<h3>To find</h3>
- A. m∠MIH
- B. m∠AVM
- C. Obtuse angle at the intersection of AV and HI
<h3>Solution</h3>
A...................................
∠MIH and ∠IHS are same side interior angles and sum up to 180° as per property, therefore
- m∠MIH = 180° - 34° = 146°
B...................................
∠AVM and ∠VAS are same side interior angles
and ∠VAS and ∠LAH are vertical angles, which are equal as per property of vertical angles, so:
- m∠AVM = 180° - m∠VAS = 180° - 110° = 70°
C...................................
Obtuse angle at the intersection of AV and HI, if name the intersection point O:
- ∠AOI = ∠HOV
- ∠AOI = 180° - ∠AOH = 180° - (180° - 34° - 70°) = 104°
They have, in total, 96 inches, 8 feet, or 32 yards
Answer:
10.) If you buy all larger cans (aka the 7-gallon cans), you would have saved approx. $30.21
9.) Seth would need a score of 95% in order to average an 80%
Step-by-step explanation:
10.) It costs $15.50 per 5-gal. If you want to buy 45 gallons, it would cost you <u>$139.50</u> if you bought 5-gallon cans.
It costs $17.00 per 7-gallon. If you want to buy 45 gallons, it would cost you <u>$109.29</u> if you bought 7-gallon cans.
Now, let's compare prices. Buying 45 gallons worth of 7-gallon cans is less expensive by.... (139.50 - 109.29 = 30.21)
Therefore, you saved $30.21.
9.) An average is done by adding up all the numbers and dividing it by how many numbers you added it by. Let's write an equation to make things easier. So far, we don't know the score he needs to get on his fourth test so let's make it a variable x.
(82 + 68 + 75 + x) / 4 = 80
Let's solve for x.
(82 + 68 + 75 + x) / 4 = 80 *Multiply both sides by 4
82 + 68 + 75 + x = 320 *Add like terms
225 + x = 320 *Subtract 225 from boths to get x on one side
x = 95
Answer:
With replacing
Assuming replacing for the first selection we have a total of 52 cards and 4 possible options and for the second selection since we put again the card again in the deck we have the same probability of selection for a jack. We can assume independence between the events and we got:
![p = \frac{4}{52} *\frac{4}{52}= 0.0059](https://tex.z-dn.net/?f=%20p%20%3D%20%5Cfrac%7B4%7D%7B52%7D%20%2A%5Cfrac%7B4%7D%7B52%7D%3D%200.0059)
Without replacing
Assuming replacing for the first selection we have a total of 52 cards and 4 possible options and for the second selection since we don't put again the card again in the deck so we will have 3 possible options and 51 total cards. We can assume independence between the events and we got:
![p = \frac{4}{52} *\frac{3}{51}= 0.0045](https://tex.z-dn.net/?f=%20p%20%3D%20%5Cfrac%7B4%7D%7B52%7D%20%2A%5Cfrac%7B3%7D%7B51%7D%3D%200.0045)
Step-by-step explanation:
For this case we assume that we have a standard deck of 52 cards
And we have 4 Jacks on the deck
With replacing
Assuming replacing for the first selection we have a total of 52 cards and 4 possible options and for the second selection since we put again the card again in the deck we have the same probability of selection for a jack. We can assume independence between the events and we got:
![p = \frac{4}{52} *\frac{4}{52}= 0.0059](https://tex.z-dn.net/?f=%20p%20%3D%20%5Cfrac%7B4%7D%7B52%7D%20%2A%5Cfrac%7B4%7D%7B52%7D%3D%200.0059)
Without replacing
Assuming replacing for the first selection we have a total of 52 cards and 4 possible options and for the second selection since we don't put again the card again in the deck so we will have 3 possible options and 51 total cards. We can assume independence between the events and we got:
![p = \frac{4}{52} *\frac{3}{51}= 0.0045](https://tex.z-dn.net/?f=%20p%20%3D%20%5Cfrac%7B4%7D%7B52%7D%20%2A%5Cfrac%7B3%7D%7B51%7D%3D%200.0045)