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Naya [18.7K]
1 year ago
6

Lisa played soccer for 234 hours on Saturday and for 135 hours on Sunday. How many hours did she play soccer during the weekend?

Mathematics
2 answers:
Aleks04 [339]1 year ago
4 0

Answer:

Lisa played 4.35 hours over the weekend :)

Step-by-step explanation:

KengaRu [80]1 year ago
4 0
She played 369 hours of soccer during the weekend.
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A die is rolled. If you roll a 1, 2 or 3, you will toss 10 coins. If you roll a 4, 5 or 6, you will toss 20 coins. Let X denote
trasher [3.6K]

Answer:

a) The support of X is {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

b) The mean of X is 7.5

c) The variance of X is 10

Step-by-step explanation:

a) Since you can toss up to 20 coins, and from that you can obtain any number of heads from 0 to 20, then the support of X {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

b) To compute the mean of X, we need to see how is the <em>behavior</em> of X. Since 3 dices will gives 10 coins to toss and the other 3 will give us 20, then there is a probability of 1/2 that we tossed 10 coins and a probability of 1/2 that we tossed 20.

The random variable X, conditioned to the event 'The dice is 1,2 or 3' (or equivalently, 10 coins are tossed), will have a binomial distribution with paramenters n = 10, p = 1/2. The mean of X in this case is np = 5. If X is conditioned to the event 'The dice is 4,5 or 6', then X will have also binomial distribution, but this time with paramenters n = 20, p = 1/2. The mean of X in this case is 20*1/2 = 10.

Since each event we conditioned in had probability 1/2 to occur, then E(X) = 1/2 * 5 + 1/2 * 10 = 7.5.

c) Remember that V(X) = E(X²)- E(X)². Since we alredy know the mean of X, we just need to compute the mean of X squared.

The variance of a binomial distribution Z with paramenters n and p is

V(Z) = np(1-p)

since V(Z) = E(Z²)- E(Z)² = E(Z²)- n²p², then

E(Z²) = V(Z) + E(Z)² = np(1-p) + n²p² = p²(n²-n) + np

Therefore

E(X²) = E(X² | 10 coins are tossed) * 1/2 + E(X² | 20 coins are tossed) * 1/2 =

1/2*(0.5²(10²-10) + 5) + 1/2*(0.5²(20²-20) + 10) = 13.75 + 52.5 = 66.25

As a consecuence

V(X) = 66.25 - 7.5² = 10

The variance of X is 10.

5 0
2 years ago
Triangle ABC has &lt; A ≅ &lt; B and BC ≅ AC. Find m
lapo4ka [179]

there is no drawing how should I do

4 0
2 years ago
1 inch = 2.54cm 1 mile = 1.6km a map has a scale of 1 inch represents 1 mile use the given conversions to show that 1cm on the m
lara31 [8.8K]
Note: 1 inch = 2.54 cm is an exact converion, while 1 mile=1.6km is only approximate.

Using conversion
1 inch=2.54 cm
1 mile = 1760*3*12 = 63360 in = 160934.4 cm 
If 1 inch = 1 mile, then 
2.54 cm : 1 mile = 1.609344 km
1 cm : 0.6336 km   (exactly), or
1 cm : 0.6 km (approximately)

Using both conversions:
1 inch = 2.54 cm : 1 mile = 1.6 km
=>
2.54 cm : 1.6 km
1 cm : 1.6/2.54=0.6299 km (approximately), or
1 cm : 0.6 km (approximately)
8 0
3 years ago
WILL GIVE A BRAINLEST
Gnoma [55]

Answer: "No, the triangles are not necessarily congruent." is the correct statement .


Step-by-step explanation:

In ΔCDE, m∠C = 30° and m∠E = 50°

Therefore by angle sum property of triangles

m∠C+m∠D+m∠E=180°

⇒m∠D=180°-m∠E-m∠C=180°-30°-50°=100°

⇒m∠D=100°

In ΔFGH, m∠G = 100° and m∠H = 50°

Similarly m∠F +∠G+m∠H=180°

⇒m∠F=180°-∠G-m∠H=180°-100°-50=30°

⇒m∠F=30°

Now ΔCDE and ΔFGH

m∠C=m∠F=30°,m∠D=m∠G=100°,m∠E=m∠H=50°

by AAA similarity criteria  ΔCDE ≈ ΔFGH but can't say congruent.

Congruent triangles are the pair of triangles in which corresponding sides and angles are equal . A congruent triangle is a similar triangle but a similar triangle may not be a congruent triangle.


8 0
3 years ago
Read 2 more answers
Base 100 inches, height 75 inches ​
ladessa [460]

Answer:

what's the question?

Step-by-step explanation:

8 0
3 years ago
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