All Answers 356462 Answers

A fox, a coyote, and a wolf weigh a total of 120 pounds. The ratio of the weight of the fox to the weight of the coyote is 3:8. The weight of the coyote is 32 pounds. What is the weight of the wolf?

Hello Guest!

\(f+c+w=120\\ f:c=3:8\\ c=32\\f:32=3:8\\ f=3\cdot32/8=12\\ 12+32+w=120\\ w=120-12-32=76\)

The wolf weighs 76 pounds.

  !

There are only three possible values of a: 0, 32, and 36.

The coefficient of x^3 is -3.

There are 14 quarters and 8 dimes left over, which add up to $4.30.

note that \(\lfloor r \rfloor + \lfloor \frac{r}{2} \rfloor\) will be an integer, so r must be \(x+0.5\), where x is some positive integer.

Therefore,

\(\lfloor x+0.5 \rfloor + x + 0.5 + \lfloor \frac{x+0.5}{2} \rfloor = 15.5\\ x+ x + 0.5 + \lfloor \frac{x}{2} \rfloor = 15.5\\ 2x+\lfloor \frac{x}{2} \rfloor=15\)

If x is even, it reduces to \(\frac{5}{2}x=15\), which has one solution x=6, meaning that \(r=6\) is a solution.

If x is odd, we can write it as 2y+1, where y is some positive integer. The equation turns out to be: 

\(2(2y+1)+y=15\\ 4y+2+y=15\\ 5y=13\)

since 13 is not a multiple of 5, no integer solutions exist for y, meaning that no odd solutions exist.

That means that 6 is the only solution, meaning that there is \(\boxed{1}\) value of r satisfying that condition.

A mathematician works for t hours per day and solves p problems per hour, where t and p are positive integers and 1

*** error ***

My answer is incorrect..... 

  see   Guest answer  !

25 %  is the same as   25/100 = 1/4 th

1/4 x  + 45   = 1/3 x

1/12 x = 45

x =   45 * 12 = ________ syringes

If the number of remaining syringes used at night was 1/3 of the number that Dr. Malcolm started with, then the total of the number used during the morning and afternoon was 2/3 of the total.

Let s be the total number of syringes that Dr. Malcolm started with.

Then:

number of syringes used in the morning = 0.25s = s/4

number of syringes used ion the afternoon = 45

And:

s/4 + 45 = 2s/3

Multiply both sides by 12:

3s + 540 = 8s

5s = 540

s = 108

Dr. Malcolm started with 108 syringes.

angle BMC + angle A = 201°

angle BMC = 201° - angle A  (eq. 1)

angle BMC + angle AMC = 180° (straight line at point M)

angle AMC = 180° - angle BMC

angle AMC = 180° - (201° - angle A) (by substituting from eq. 1 above for angle BMC)

angle AMC = angle A - 21° (eq. 2)

If AM = CM, then angle A = angle ACM (eq. 3)

The three angles for triangle ACM add to 180°:

180° = angle A + angle ACM + angle AMC

180° = angle A + angle A + angle A - 21° (by substituting from eq. 2 and eq. 3 from above for angle AMC and angle ACM respectively)

180° = 3 angle A - 21°

201° = 3 angle A

angle A = 67°

If BM = CM, then angle B = angle BCM (eq. 4)

The three angles for triangle ABC add to 180°:

180° = angle A + angle ACM + angle BCM + angle B (where we have used the fact that angle C = angle ACM + angle BCM)

180° = angle A + angle A + angle B + angle B (by substituting from eq. 3 and eq. 4 for angle ACM and angle BCM respectively)

180° = 2 angle A + 2 angle B

90° = angle A + angle B

angle B = 90° - angle A

angle B = 90° - 67°

angle B = 23°

assume girls are x, boys are (15+x)

  1/4x - 1/5 (15+x) = 2

      1/4x - 1/5x = 5

                1/20x = 5

                       x = 100

15 + x = 115

sum = 115 + 100 = 215

Triangle side rule says that any two sides summed must be GREATER than the third side

25 + x > 80

x > 55

x = 56 minimum

Goats are 2 out of (3 + 2) = 2/ 5

Cows are 3/5

2/5 x    = number of goats        ( x = total animals)

2/5 x   + 210 = 3/5 x

1/5 x = 210

x = 1050 animals

You are so close. 

As n increases, a_n should also increase, however in the choice you selected, a_n decreases. 

a_1 = 1200, a_2 = 420. 

When it says increase by, you add a 1 to it. 1 + .35 = 1.35. 

If the starting value is x, and you want to increase it by 35%, you are looking for x + .35x = (1+.35)x. 

=^._.^=

Yah...it is the last one !

First I extracted easy info by looking at the formula.

It is a concave up parabola.  The axis of symmetry is the y axis (x=0) 

The closest point to the origin would have to be in the part under the x axis.

I decided to use calculus to get the answer.  If you have not done any calculus then there must be a different way to do it.

You will need to tell us if you have not done any calc yet.

I took the 2 points

\((0,0) \qquad and \qquad \left(x,\frac{1}{\sqrt2}(x^2-3)\right)\)

I used the distance formula to get an expression for the distance between them. I called it D

Then I differentiated that with respect to x   to get    dD/dx

I then put that =0 to get the stationary (stat) points.  I knew from the graph that any stat point would give a minumum value.

The stat points I got were x= +/- sqrt2.

Find the y value that goes with that and from that find D.

I drew this to help you see what is happening.  It is interactive, you can move the P point to see that these two answer points give the minimum distance from (0,0)

https://web2.0calc.com/questions/i-need-help-fast-please

For f (-3)        -3 <=1      sooo   f(-3) =  2 - (-3) = 5

for  f(0)                                                  2-(0)    = 2

for f(3)            3 > 1     soooo   f(3) = 2(3)- (3)^2 = -3                  5 +2 + (-3) = __________

Here's a hint, a has to be 1, and b has to be a prime number. :)

Find the probability that a chosen is 1, and b chosen is a prime number, and multiply them together. 

=^._.^=

I think it might be latex that is messing up. 

Try rewriting the entire problem, without latex from a copy/paste. 

=^._.^=

What instructions were you given

Were you supposed to use a particular method to find these?

You have asked this question appropriately, thanks for that,  but you have not said why do you think the original answers are incorrect?  

I have not looked at it but if Heueka, Dragan and Jugoslav all have the same answer I would say it is most likely correct.

They are all respected members.