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Steven runs a pizza shop. Since he added breakfast pizza to the menu, 54 out of 78 customers have ordered the new pizza. If Stev

murzikaleks [220]

Answer:

26 people are more and likely to order pizza in the morning.

Step-by-step explanation:

5 0

3 years ago

A tank initially contains 50 gallons of brine, with 30 pounds of salt in solution. Water runs into the tank at 6 gallons per min

balandron [24]

Answer:

1.857 minutes

Step-by-step explanation:

From the given information:

Consider the amount of salt present in the tank as x(t) at a given time (t); &

The volume of the solution = V(t)

At t = 0 i.e. (at initial conditions) x(0) = 30; and V(0) = 50

However, the overall increase taken place for 1 gallon per minute is:

V(t) = 50 + t

The amount of salt x(t) at any given point for time (t) is;

$\dfrac{x(t)}{V(t)}= \dfrac{x(t)}{50+t}$

After 5 gallons of solution exit per minute; the concentration of the salt solution changes at:

$\dfrac{dx(t)}{dt}= -\dfrac{5x(t)}{50+t}$

Taking the integral of what we have above, we get:

In x(t) = - 5 In(t + 50) + In (C)

In x(t) = In (t+ 50)⁻⁵ + In (C)

In x(t) = In C ( t + 50)⁻⁵

x(t) = C(t + 50)⁻⁵ (General solution)

To estimate the required solution; we apply the initial conditions x(0) = 30;

Thus;

x(0) = C(50)⁻⁵ = 30

⇒ C = 30 × 50⁵

Hence; x(t) = 30 × 50⁵ × (t + 50)⁻⁵

The above expression can be re-written as:

$x(t) = 25 \implies 30 \times \bigg ( \dfrac{50}{t+50} \bigg ) ^5= 25$

i.e.

$\bigg ( \dfrac{50}{t+50} \bigg ) ^5= \dfrac{25}{30}$

$\dfrac{50}{t+50}= \bigg ( \dfrac{25}{30}\bigg) ^{\dfrac{1}{5}}$

$\dfrac{50}{t+50}= 0.964192504$

${50}= 0.964192504(t+50)$

50 = 0.964192504t + 48.2096252

50 - 48.2096252 = 0.964192504t

1.7903748 = 0.964192504t

t = 1.7903748 / 0.964192504

t ≅ 1.857 minutes

We can thereby conclude that the estimated time it will require until there are 25 pounds of salt in the tank is 1.857 minutes.

7 0

2 years ago

What is the value of y? PLEASE EXPLAIN<br> 8.5 = y/3 <------ Fraction

NISA [10]

Answer:

y=25.5

Step-by-step explanation:

To find y, you need to get it by itself. Ask yourself, what is being done to y, then to undo that, do the opposite. For example, if 3 was added to y, you would need to subtract 3 to cancel out the 3. In this case, what is being done to y? It's being divided by 3. So, you multiply by 3 to cancel that out. Whatever you do to one side of an equation, you also have to do to the other. So,

8.5= $\frac{y}{3}$ Multiply both sides by 3

3(8.5) = 3( $\frac{y}{3}$ ) multiply on the left side, and on the right side the 3s cancel out

25.5=y

5 0

2 years ago

Work out the nth of this sequence:

Gekata [30.6K]

Answer:

$a_n = -11 +3(n -1)$

Explanation:

The $n$ th term of an arithmetic sequence is explicitly defined as $a_n = a_1 +d(n -1)$ where $a_1$ is the first term of the sequence and $d$ is the the common difference.