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nlexa [21]
3 years ago
6

There are two water tanks, Tank #1 fills into Tank #2.

Mathematics
1 answer:
cricket20 [7]3 years ago
5 0

Answer:

  35 minutes

Step-by-step explanation:

The total amount of water is 200 +60 = 260 gallons. The two tanks will have equal amounts when each has half that, or 130 gallons.

If the volume in tank 2 is increasing at 2 gallons per minute, it will increase by 70 gallons from 60 gallons to 130 gallons in 70/2 = 35 minutes.

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Which real-world story is represented by the addition problem (–2 1/2) + (–3 1/4) = –5 3/4?
allochka39001 [22]

Answer:

A

Step-by-step explanation:

A is the correct answer because the equation matches option A.

(-2 1/2) + (-3 1/4)

The minus sign in -2 1/2 shows that the submarine descended and then descended again with the addition sign. Though the addition sign can mean that it ascended its incorrect.

With the equation in hand, we can prove that option A is correct.

If the submarine descended 2 1/2 miles then here must be a minus sign next to the 2 1/2. But if it ascended then there would've been an addition sign to show that it ascended. The other value - 3 1/4 also shows that it ascended with the help of the addition sign.

Ascends - values increase from smallest to highest.

Descends - values decrease from highest to smallest.

4 0
3 years ago
F(x) = x2 − x − ln(x) (a) find the interval on which f is increasing. (enter your answer using interval notation.) find the inte
Mekhanik [1.2K]

Answer:

(a) Decreasing on (0, 1) and increasing on (1, ∞)

(b) Local minimum at (1, 0)

(c) No inflection point; concave up on (0, ∞)

Step-by-step explanation:

ƒ(x) = x² - x – lnx

(a) Intervals in which ƒ(x) is increasing and decreasing.

Step 1. Find the zeros of the first derivative of the function

ƒ'(x) = 2x – 1 - 1/x = 0

           2x² - x  -1 = 0

     ( x - 1) (2x + 1) = 0

         x = 1 or x = -½

We reject the negative root, because the argument of lnx cannot be negative.

There is one zero at (1, 0). This is your critical point.

Step 2. Apply the first derivative test.

Test all intervals to the left and to the right of the critical value to determine if the derivative is positive or negative.

(1) x = ½

ƒ'(½) = 2(½) - 1 - 1/(½) = 1 - 1 - 2 = -1

ƒ'(x) < 0 so the function is decreasing on (0, 1).

(2) x = 2

ƒ'(0) = 2(2) -1 – 1/2 = 4 - 1 – ½  = ⁵/₂

ƒ'(x) > 0 so the function is increasing on (1, ∞).

(b) Local extremum

ƒ(x) is decreasing when x < 1 and increasing when x >1.

Thus, (1, 0) is a local minimum, and ƒ(x) = 0 when x = 1.

(c) Inflection point

(1) Set the second derivative equal to zero

ƒ''(x) = 2 + 2/x² = 0

             x² + 2 = 0

                   x² = -2

There is no inflection point.

(2). Concavity

Apply the second derivative test on either side of the extremum.

\begin{array}{lccc}\text{Test} & x < 1 & x = 1 & x > 1\\\text{Sign of f''} & + & 0 & +\\\text{Concavity} & \text{up} & &\text{up}\\\end{array}

The function is concave up on (0, ∞).

6 0
3 years ago
How do you simplify 8+(9t+4)
IrinaVladis [17]
8+(9t+4)
remove (  )
since there's a + in front of the (  ) the value will not change

8+9t+4
combine like terms

9t+12
Hope this helps
3 0
3 years ago
Pls can someone help me. I m giving 10 pts . I may mark you as the braniliest
worty [1.4K]

100 notes were altogether

<em><u>Solution:</u></em>

Given that ratio of the number of $2 notes to the number of $5 notes was 4 : 1

number of $2 notes : number of $5 notes = 4 : 1

Let 4x be the number of $ 2 notes

Let 1x be the number of $ 5 notes

Given that total value of notes is $ 260

Therefore,

$ 2 (number of $ 2 notes ) + $ 5(number of $ 5 notes ) = $ 260

$ 2(4x) + $ 5(1x) = $ 260

8x + 5x = 260

13x = 260

x = 20

<em><u>Thus number of notes altogether is given as:</u></em>

4x + 1x = 4(20) + 1(20) = 80 + 20 = 100

Thus 100 notes were altogether

4 0
3 years ago
If a single card is drawn from a standard 52-card deck, what is the probability that it is an ace or a spade?
klasskru [66]

A 52-card deck is made up of an equal number of diamonds, hearts, spades, and clubs. Because there are 4 suits, there is a 1/4 chance to draw one of them, in our case, spades.

There are 4 aces in a 52-card deck, so the chance of drawing one is 4/52, or 1/13.

The question asks for the probability of drawing an ace or a spade. Because it uses the word "or," we add the probabilities together. This is because there is a chance of drawing either of the cards; it doesn't have to meet both requirements to satisfy the statement.

However, if the question were to say "and," we would multiply the two probabilities.

Let's add 1/4 and 1/13. First, we can find a common denominator. We can use 52 because both fractions can multiply into it (since the ratio came from a deck of 52 cards as well).

\frac{1}{4} -- > \frac{13}{52}

\frac{1}{13} -- > \frac{4}{52}

Now we can add them together.

\frac{13}{52} + \frac{4}{52} = \frac{13+4}{52} = \frac{17}{52}

This cannot be simplified further, so the probability is 17 in 52, or 33%.

hope this helps!

7 0
1 year ago
Read 2 more answers
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