Please answer this correctly

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Leto [7]

Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday

= Sum of ( Adult + Children's ) tickets = 1,678 + 976 = 2,654 .... (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold = 2 times the number of adult tickets sold on Friday

= 1,678 x 2 = 3,356

Children's Tickets sold = 3 times the number of children's tickets sold on Friday.

= 976 x 3 = 2, 928

So, the total number of tickets sold on Saturday

= Sum of ( Adult + Children's ) tickets = 3,356 + 2,928 = 6, 284 .... (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 + 6, 284 = 8,938

Hence, total number of tickets sold over these two days is 8,938.

6 0

2 years ago

Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

Let $a$ and $b$ represent two positive numbers (that is: $a > 0$ and $b > 0$ .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for $x$ :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then $(x - 4)$ , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

7 0

2 years ago

Find the perimeter of a square that is 3 3/4 inches on a side.

Dahasolnce [82]

perimeter would be s x 4

so 3 3/4 x 4 = 15

B is the correct answer

6 0

3 years ago

Farmer George is painting 3 chicken coops. He started painting this morning. Now he only has 3/4 of a chicken coop left to paint

mariarad [96]

If Farmer George starts painting in the morning, and only has 3/4 of a chicken coop left to paint:
3-3/4=
12/4-3/4=9/4 painting in the morning
To put it in a mixed number, 2 1/4 (aka 2.25)

3 0

2 years ago

Read 2 more answers

A company sells two versions of an antivirus software. The home edition costs $23.50, and the business edition costs $58.75. Las

Kamila [148]

Answer:

x + y = 745

23.50x + 58.75y = 29,668.75

Step-by-step explanation:

Since 745 copies were sold and x represents the number of copies of the home edition sold and y represents the number of copies of the business edition sold:

x + y = 745

Since the home edition costs $23.50, and the business edition costs $58.75:

The money earned from home edition is = 23.50x

The money earned from business edition is = 58.75y

Since the company earned $29,668.75:

23.50x + 58.75y = 29,668.75

6 0

3 years ago