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4 years ago

So i need help (picture included)

Mathematics

1 answer:

alisha [4.7K]4 years ago

5 0

We have that
y=-2x+3
y=(1/3)x-4

using a graph tool
see the attached figure

the solution of the system is the point (3,-3)

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Calculating conditional probabilities - random permutations. About The letters (a, b, c, d, e, f, g) are put in a random order.

Evgesh-ka [11]

A="b is in the middle"

B="c is to the right of b"

C="The letter def occur together in that order"

a) b can be in 7 places, but only one is the middle. So, P(A)=1/7

b) X=i, "b is in the i-th position"

Y=j, "c is in the j-th position"

$P(B)=\displaystyle\sum_{i=1}^{6}(P(X=i)\displaystyle\sum_{j=i+1}^{7}P(Y=j))=\displaystyle\sum_{i=1}^{6}\frac{1}{7}(\displaystyle\sum_{j=i+1}^{7}\frac{1}{6})=\frac{1}{42}\displaystyle\sum_{i=1}^{6}(\displaystyle\sum_{j=i+1}^{7}1)=\frac{6+5+4+3+2+1}{42}=\frac{1}{2}$

P(B)=1/2

c) X=i, "d is in the i-th position"

Y=j, "e is in the j-th position"

Z=k, "f is in the i-th position"

$P(C)=\displaystyle\sum_{i=1}^{5}( P(X=i)P(Y=i+1)P(Z=i+2))=\displaystyle\sum_{i=1}^{5}(\frac{1}{7}\times\frac{1}{6}\times\frac{1}{5})=\frac{1}{210}\displaystyle\sum_{i=1}^{5}(1)=\frac{1}{42}$

P(C)=1/42

P(A∩C)=2*(1/7*1/6*1/5*1/4)=1/420

$P(B\cap C)=\displaystyle\sum_{i=1}^{3} P(X=i)P(Y=i+1)P(Z=i+2)\displaystyle\sum_{j=i+3}^{6}P(V=j)P(W=j+1)=\displaystyle\sum_{i=1}^{3}\frac{1}{6}\frac{1}{7}\frac{1}{5}(\displaystyle\sum_{j=1+3}^{6}\frac{1}{4}\frac{1}{3})=1/420$

P(B∩A)=3*(1/7*1/6)=1/14

P(A|C)=P(A∩C)/P(C)=(1/420)/(1/42)=1/10

P(B|C)=P(B∩C)/P(C)=(1/420)/(1/42)=1/10

P(A|B)=P(B∩A)/P(B)=(1/14)/(1/2)=1/7

P(A∩B)=1/14

P(A)P(B)=(1/7)*(1/2)=1/14

A and B are independent

P(A∩C)=1/420

P(A)P(C)=(1/7)*(1/42)=1/294

A and C aren't independent

P(B∩C)=1/420

P(B)P(C)=(1/2)*(1/42)=1/84

B and C aren't independent

8 0

3 years ago

A summer biathalon-style race requires running a certain distance, and then biking a distance 2 miles more than the length of th

Vesnalui [34]

Answer:

The run is 4.875 miles long, while, the bike is 6.875 miles long.

Step-by-step explanation:

Let d = running distance and d' = biking distance.

Given that d' = d + 2 and v = running speed = 6 mph and v' = biking speed = 10 mph.

Since time, t = distance/speed, running time, t = running distance/running speed = d/6 and biking time, t' = biking distance/biking time = d'/10 = (d + 2)/10.

Since the total time, t" = 90 minutes = 1.5 hours,

t + t' = t"

So, d/6 + (d + 2)/10 = 1.5

multiplying through by the L.C.M, 30, we have

30 × d/6 + 30 ×(d + 2)/10 = 30 × 1.5

5d + 3(d + 2) = 45

expanding the brackets, we have

5d + 3d + 6 = 45

collecting like terms, we have

8d = 45 - 6

8d = 39

d = 39/8

d = 4.875 miles

d' = d + 2 = 4.875 + 2 = 6.875 miles

So, the run is 4.875 miles long, while, the bike is 6.875 miles long.

4 0

3 years ago

What is the equation for (-7,0) and (8,0)

vichka [17]

$\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}$

Actually Welcome to the concept of straight lines.

==> y-y1 = m(x-x1)

==> y = mx+c

these two are the straight line equation, so we get as,

=> 0-0 = m(8-(-7)

==> 0 = m(15)

==> hence, 15m = 0

4 0

3 years ago

Combine like terms.<br><br> -2x4+16+2x4+9-3x5

Mademuasel [1]

Answer:

25 - 3x^5

Step-by-step explanation:

-2x^4+16+2x^4+9-3x^5

Combine like terms

-2x^4+2x^4+9+16-3x^5

0 + 25 -3x^5

6 0

4 years ago

Read 2 more answers

Find the surface area of the polyhedron below. The area of each base is 65 cm^2<br>

yarga [219]

Answer:

D. 290 square cm

Step-by-step explanation:

Surface area of polyhedron

$= 2 \times 65 + 7 \times 8 + 4 \times 8 + 3 \times 8 + 3(2 \times 8) \\ = 130 + 56 + 32 + 24 + 48 \\ = 290 \: {cm}^{2}$

8 0

3 years ago