MATHEMATICS COLLEGE

Celia bought a bag of 121212 goldfish for \$3$3dollar sign, 3.What is the cost of 111 goldfish?

Answers

Answer 1

Answer:

Answer: $0.25

Step-by-step explanation:

We are given that the cost of 12 goldfish = $3

To find the cost of one goldfish we use division operator and divide the cost of 12 gold fishes by 12.

Then , the cost of one gold fish = $\$3/ 12$

⇒ Cost of 1 gold fish $=(\$3)/(12)$

⇒ Cost of 1 gold fish $=(\$1)/(4)$ [Divide numerator and denominator by 3.]

⇒ Cost of 1 gold fish $=\$0.25$ [Simplify by dividing 1 by 4]

Therefore , the cost of 1 goldfish = $0.25

Answer 2

Answer:

Answer:

0.25

Step-by-step explanation:

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A swimming pool whose volume is 10 comma 000 gal contains water that is 0.03% chlorine. Starting at tequals0, city water containing 0.001% chlorine is pumped into the pool at a rate of 6 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 hour? When will the pool water be 0.002% chlorine?

Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 4 right angle0,−4 in the directions parallel to and normal to the plane that makes an angle of StartFraction pi Over 3 EndFraction π 3 with the positive x-axis. Show that the total force is the sum of the two component forces.

Answers

Answer:

$F_p = < - √(3) , -3 >\n\nF_o = < √(3) , -1 >$

Step-by-step explanation:

- A plane is oriented in a Cartesian coordinate system such that it makes an angle of ( π / 3 ) with the positive x - axis.

- A force ( F ) is directed along the y-axis as a vector < 0 , - 4 >

- We are to determine the the components of force ( F ) parallel and normal to the defined plane.

- We will denote two unit vectors: ( $u_p$ ) parallel to plane and ( $u_o$ ) orthogonal to the defined plane. We will define the two unit vectors in ( x - y ) plane as follows:

- The unit vector ( $u_p$ ) parallel to the defined plane makes an angle of ( 30° ) with the positive y-axis and an angle of ( π / 3 = 60° ) with the x-axis. We will find the projection of the vector onto the x and y axes as follows:

$u_o$ = < cos ( 60° ) , cos ( 30° ) >

$u_o = < (1)/(2) , (√(3) )/(2) >$

- Similarly, the unit vector ( $u_o$ ) orthogonal to plane makes an angle of ( π / 3 ) with the positive x - axis and angle of ( π / 6 ) with the y-axis in negative direction. We will find the projection of the vector onto the x and y axes as follows:

$u_p = < cos ( (\pi )/(6) ) , - cos ( (\pi )/(3) ) >\n\nu_p = < (√(3) )/(2) , -(1)/(2) >\n$

- To find the projection of force ( F ) along and normal to the plane we will apply the dot product formulation:

- The Force vector parallel to the plane ( $F_p$ ) would be:

$F_p = u_p(F . u_p)\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ < 0 , - 4 > . < (1)/(2) , (√(3) )/(2) > ]\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ -2√(3) ]\n\nF_p = < -√(3) , -3 >\n$

- Similarly, to find the projection of force ( $F_o$ ) normal to the plane we again employ the dot product formulation with normal unit vector ( $u_o$ ) as follows:

$F_o = u_o ( F . u_o )\n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ < 0 , - 4 > . < (√(3) )/(2) , - (1)/(2) > ] \n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ 2 ] \n\nF_o = < √(3) , - 1 >$

- To prove that the projected forces ( $F_o$ ) and ( $F_p$ ) are correct we will apply the vector summation of the two orthogonal vector which must equal to the original vector < 0 , - 4 >

$F = F_o + F_p\n\n< 0 , - 4 > = < √(3), -1 > + < -√(3), -3 > \n\n< 0 , - 4 > = < √(3) - √(3) , -1 - 3 > \n\n< 0 , - 4 > = < 0 , - 4 >$ .. proven

At the "cloth for you" shop, you can buy a top for £10.00 and a Bermuda trouser for £12.00. Due to a sensational sell, there is a 20% discount on all tops. If you buy one top and two Bermuda trousers, how much money do you spend in total?

Answers

Answer:

£32 in total for the top and two trousers

Step-by-step explanation:

The price for a top In the "cloth for you" shop= £10

The price for a bermuda trouser In the "cloth for you" shop= £12

There is a 20% discount on tops

The price If I bought one top and would trouser will be

(10-(0.2*10)) for the top

2(12) for the trouser

Total= (10-(0.2*10))+ 2(12)

Total = 10-2+24

Total = £32

So I spent £32 in total for the top and two trousers

A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let Xrepresent the number of occupants in a randomly chosen car.a. Find the probability mass function of X.

b. Find P(X ≤ 2).

c. Find P(X > 3).

d. Find μX.

e. Find σX

Answers

Answer:

a) X 1 2 3 4 5

P(X) 0.7 0.15 0.10 0.03 0.02

b) $P(X \leq 2) = P(X=1) +P(X=2) = 0.7+0.15=0.85$

c) $P(X >3) = 1-P(X \leq 3) = 1-[P(X=1) +P(X=2)+P(X=3)]=1-[0.7+0.15+0.1]= 0.05$

d) $E(X) = \sum_(i=1)^n X_i P(X_i) = 1*0.7 +2*0.15+ 3*0.1+4*0.03+ 5*0.02= 1.52$

e) $E(X^2) = \sum_(i=1)^n X^2_i P(X_i) = 1*0.7 +4*0.15+ 9*0.1+16*0.03+ 25*0.02=3.18$

$Var(X) = E(X^2) -[E(X)]^2= 3.18- (1.52)^2 = 0.8996$

$\sigma= √(Var(X))= √(0.8996)= 0.933$

Step-by-step explanation:

Part a

From the information given we define the probability distribution like this:

X 1 2 3 4 5

P(X) 0.7 0.15 0.10 0.03 0.02

And we see that the sum of the probabilities is 1 so then we have a probability distribution

Part b

We want to find this probability:

$P(X \leq 2) = P(X=1) +P(X=2) = 0.7+0.15=0.85$

Part c

We want to find this probability $P(X>3)$

And for this case we can use the complement rule and we got:

$P(X >3) = 1-P(X \leq 3) = 1-[P(X=1) +P(X=2)+P(X=3)]=1-[0.7+0.15+0.1]= 0.05$

Part d

We can find the expected value with this formula:

$E(X) = \sum_(i=1)^n X_i P(X_i) = 1*0.7 +2*0.15+ 3*0.1+4*0.03+ 5*0.02= 1.52$

Part e

For this case we need to find first the second moment given by:

$E(X^2) = \sum_(i=1)^n X^2_i P(X_i) = 1*0.7 +4*0.15+ 9*0.1+16*0.03+ 25*0.02=3.18$

And we can find the variance with the following formula:

$Var(X) = E(X^2) -[E(X)]^2= 3.18- (1.52)^2 = 0.8996$

And we can find the deviation taking the square root of the variance:

$\sigma= √(Var(X))= √(0.8996)= 0.933$

Find the measure of angle b

Answers

Answer:

40 degrees

Step-by-step explanation:

180-140=40

Answer:

40° that's the answer hope I helped

N<2^2. mathematical induction

Answers

Answer:

Inequality Form:
n < 4

Interval Notation:
(-, 4)

God bless you have a beautiful blessed day and I hope this makes it!

The ratio between the number of red and green marbles in a box is 3:7. How many marbles are in the box if there are 20 fewer red marbles than green marbles?PLS HELP QUICK LIKE IN 1 SECOND!!

Answers

there are 50 marbles

Answer:

Step-by-step explanation:

difference of ratio=7-3=4

sum of ratio=3+7=10

if difference 4 total=10

if difference 20 total=10/4×20=50

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