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3 years ago

A 10-foot ladder leans against a wall with its foot braced 3 feet from wallÍs base. How far up the wall does the ladder reach?

1 answer:

5 0

The answer is √91 feet (which is the same as 9.54 feet).

Imagine this as a right triangle. A length of the foot is actually a hypotenuse (c). The distance from wall's base to the ladder foot is one of the sides of the triangle (let it be a).
So, using the Pythagorean theorem:
c² = a² + b²
It is given:
c = 10 feet
a = 3 feet
b = ?
c² = a² + b²
⇒ 10² = 3² + b²
100 = 9 + b²
b² = 100 - 9 = 91
⇒ b = √b² = √91 ≈ 9.54 feet

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The number of boots that 25 students had in their homes in Florida were recorded

wolverine [178]

Answer:

Min = 0; Q₁ = 0; Median = 2; Q₃ = 2; Max = 8

Step-by-step explanation:

Assume that your sorted data are

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 8

1. Minimum

Min = 0

2. Median

The median is the middle value in a sorted data set. There are 25 items, so the median is the 13th item.

Median = 2

3. First quartile

Q₁ is the median of the lower half of the data set.

The median of 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2 is 0.

Q₁ = 0

4. Third quartile

Q₃ is the median of the upper half of the data set.

The median of 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 8 is 3.

Q₃ = 3

5. Maximum

Max = 8

7 0

2 years ago

Find the domain of the function:<br><br> V(X)= the square root of 9+X

stellarik [79]

Answer:

[-9,∞)

Step-by-step explanation:

3 0

3 years ago

Make d the subject of the formula h=<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B3%7D" id="TexFormula1" title="\frac{d}{3}

lakkis [162]

First you would subtract 2 to get d/3 by itself. On the left side you would have h-2 and one the right d/3 (h-2=d/3). Then you divide by 3 to get d by itself. So the answer is h/3-2/3=d

4 0

3 years ago

Couple has got 5 children , what is the probability of have 3girls and 2 boys ?

Delicious77 [7]

5 children so you have 2^5=32 possibilities to "assign" genders
P(3 girls):
how many possibilities are there to "assign" the 3 girl-genders to the 5 children? the first girl has 5 possibilities then the next 4, 3 -> 5*4*3=60
but these possibilities include orders of assigned genders, while children 1-5 might differ the gender "girl" is always the same so we have the remove the orderings of the 3 girl-gender assignments which is 3*2*1=6
if we divide 60/6 we get 10 possibilities to have 3 girls, so what is the resulting chance? the 10 possibilities divided by the total 32 possibilities: 10/32=5/16=P(3 girls)=P(2 boys)

this is a bit of lengthy way of saying "use the binomial coefficient" equation/explaining it a bit which is (n!)/(k!(n-k)!) with n=5, k=3:
5*4*3*2*1/((3*2*1)*(2*1))=
5*4*3*2/(3*2*2)=
5*4*3*2/(3*4)=
5*2=
10 possibilities again

P(girls>=4)=P(boys<=1)=P(boys=1)+P(boys=0)
(or P(girls=4)+P(girls=5))

P(boys=0) is the easy case: simply multiply the chance of getting a girl 5 times: (1/2)^5=1/32
P(boys=1)= again the binomial coefficient with n=5 and k=1:
5*4*3*2*1/((1)*(4*3*2*1))=
5*4*3*2/(4*3*2)=
5 possibilities
so the P(boys=0)=1 possibility + P(boys=1)=5 possibilities totals to 6 possibilities
again the chance is the 6 possibilities divided by all 32 possibilities: 6/32=3/16

P(alternate gender starting with boy): when thinking about the possibilities then there is only a single way to build that order: bgbgb, so one possibility
knowing there is only one way we already know P(alternate...)=1/32 by again dividing by the total amount of possibilities
the alternative way would be to multiply P(boy)*P(girl)*P(boy)*P(girl)*P(boy)=(1/2)^5= 1/32 again

5 0

3 years ago

Using the digits 1, 3, 5, 7 at most once, you can make many three-digit numbers. What is the maximum possible sum of two such di

lyudmila [28]

Answer:

1504

Step-by-step explanation:

Given the digits :

1, 3, 5, 7

The maximum possible sum of two distinct three digit numbers formed from the digits above will be the sum of the the two hight possible three digit numbers that can be formed.

Highest three digit number = 753

Next highest = 751

The sum of these two. Values gives :

753 + 751 = 1504

3 0

2 years ago