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Tub capacity = 100 L           Hot water = H          Cold water = C

H => 6 min = 40 L

H + C => 3 min = 20 L + 25 L

At this point, the tub is 85% filled with water.

In one minute:     H = 6²/₃ L,       C = 8¹/₃ L,          D = 10 L        (D - drain)

Hence, it will take 3 minutes for the tub to be filled.

BC = 33/4.

ABCD is a kite.

$\sin x - \cos x = \frac{1}{\sqrt{2}}$

$1 - \sin 2x = \frac{1}{2}$

$\sin 2x = \frac{1}{2}$

$2x = \frac{\pi}{6}$ or $2x = \frac{5 \pi}{6}$

$x = \frac{\pi}{12}$ or $x = \frac{5 \pi}{12}$

See my answer in your original post.

In this question, concept of solution of simultaneous equation is applied.

Let, x  be number of markers and y 

be number of crayons.

According to question,

  x + y = 132 (1)

She have equal number of markers and crayons left, when she gave away 4/5 of markers and 18 crayons.

x - 4/5x = y - 18

x/5 = y - 18

x = 5y - 90

5y - x = 90 (2)

Solving (1) and (2)

x + y + 5y - x = 132 + 90

6y = 222

y = 222 ÷ 6 = 37

Put y = 37 in (1)

x = 132 - 37 = 95

a)

Firstly she had 95 markers.After giving 4/5 of markers, she had

95 - 4/5 × 95 = 19 markers.

b)

She had 37 crayons at first.

Hi Melody! Thanks for the compliment! :D Also thanks for the point! :D

Find the range of the function h(x).

Hello Guest!

The range in real numbers of the function h(x) is 
\(\{\mathbb R\ |\ -43 \leq R< 5 \}\)

  !

Thanks 

How about responding to Gino's answer to your last question first?   

He asked you to interact with him.

y(0) is the y value when x is 0.    So is this the y intercept?    What do you think?

Hi Solveit  

o you mean:

There are 10 billiard balls

One is taken and not returned.

Then a second one is taken.

How many ways can the two be taken?

there are 10 ways that the first one can be taken and then 9 ways the second one can be taken so that is 

10*9 = 90 ways

Note: If order does not matter then you will have to divide this by 2 and get  45 ways.

Here is the original question.

Hello Guest,

The sum of two numbers is 235, and the difference of the same two numbers is 41. Find these numbers.

\(a+b=235\)

\(a-b=41\)

\(\mbox {You can change the variables by the first equation.}\)

\(b+a=235\)

\(a-b=41\)

\(b+a=235\)

\(-b+a=41\)

\(\mbox {Subtract a from the first equation.}\)

\(b=-a+235\)

\(-b+a=41\)

\(\mbox {Substitute } b=-a+235 \mbox { in the second equation.}\)

\(b=-a+235\)

\(2a-235=41\)

\(\mbox {Add } 235 \mbox { by } 41\)

\(b=-a+235\)

\(2a=276\)

\(\mbox {Solve for a}\)

\(b=-a+235\)

\(a=138\)

\(\mbox {Substitute } a \mbox { into the first equation. }\)

\(b=97\)

\(a=138\)

\(\mbox {This equation was solved with the variables a and b having the values } (a,b)=(138,97) \mbox { . }\)

Straight

So is y(0) the y intercept?

sum_(n=1)^202 (-1)^(n + 1) (2022 - 10 n) = 1010

I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 30 miles per hour instead, then I would have arrived 28 minutes later. How many miles did I drive?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Time => t    (in minutes)

40t = 30(t + 28)           

t = 84 minutes     (min)

40 miles / 60 min = x miles / 24 min

x = 16

You drove 56 miles

This is NOT the correct solution for the question asked.

We are told two rolled-dice sum to a prime.  How the dice roll to produce this prime sum is irrelevant.

Equivalent restatement of question:

Given that the sum of two numbers on fairly-rolled dice is a prime number, what is the probability that the sum is three (3)?

Solution:

Calculate the Relative Probabilities of its occurrence by weighting the occurrence of each possible prime by its Absolute Probability.

\(\begin{array}{|rccc|} \hline & Sum &\text {Absolute Probability} &\text{Relative Probability }\\ &2 &2.78\% &6.67\% \\ &3 &5.56\% &13.34\% \\ &5 &11.11\% &26.67\% \\ &7 &16.67\% &40.00\% \\ &11 &5.56\% &13.34\% \\ \hline \end{array}\\ \text{ }\\ \hspace{16em}\; \;\text {The probability is } \mathrm {13.34\%}\\ \)

GA

--. .-

another unrelated question has been deleted.   (Melody)

Refer here:

A fractional coefficient is one that is a fraction:  ¾ x     --->     The 'x' term has the fractional coefficient ¾

To solve part (a):  replace d with the value 18 and finish:  L(d)  =  196 - 7 · 18     [finish this]

To solve part (b):  replace L(d) with 0 and solve for d:  0  =  196 - 7d    [finish this]

This is a line whose value for y is always 8 and can have any value for x.

When graphed, this is a horizontal line.

Its equation is:  y = 8.