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2 years ago

A book store is hosting a special night in which families can enjoy a story and craft time. Tickets to the

Mathematics

2 answers:

Arturiano [62]2 years ago

7 0

Answer:

75 total tickets

Step-by-step explanation:

METHOD 1:

We know that 45 children's tickets have been sold, being 60% of the total tickets having been sold.

So, basically, we solve for x:

We have, 60% × x = 45

or, 60/100 × x = 45

Multiplying both sides by 100 and dividing both sides by 60,

we have x = 45 × 100/60

x = 75

If using calculator, enter 45x100/60, which will give you the answer.

------------------------

METHOD 2:

Division is the opposite of multiplication

Start with the formula to calculate the percentage of total

y=value÷ percentage/100

Substitute values in the equation

y=45÷60/100

Simplify and solve

y=45÷0.6

y=75

Both methods give you 75, therefore 75 tickets have been sold

nataly862011 [7]2 years ago

4 0

So your supposed to do 1.50/1 x 60% which is 90

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Employees in 2012 paid 4.2% of their gross wages toward social security (FICA tax), while employers paid another 6.2%. How much

Dafna1 [17]

Answer:

$3066

Step-by-step explanation:

We have been given that employees in 2012 paid 4.2% of their gross wages toward social security (FICA tax), while employers paid another 6.2%. We are asked to find the amount paid by an employee earning $73,000 per year toward social security.

To find the amount paid by an employee with annual gross earnings of $73,000, we need to find 4.2% of $73,000.

$\text{Amount paid by the employee}=\$73,000\times \frac{4.2}{100}$

$\text{Amount paid by the employee}=\$730\times \frac{4.2}{1}$

$\text{Amount paid by the employee}=\$3066$

Therefore, the employee will pay $3066 toward social security out of their gross wages.

6 0

3 years ago

Let C be the boundary of the region in the first quadrant bounded by the x-axis, a quarter-circle with radius 9, and the y-axis,

rewona [7]

Solution :

Along the edge $C_1$

The parametric equation for $C_1$ is given :

$x_1(t) = 9t , y_2(t) = 0 \ \ for \ \ 0 \leq t \leq 1$

Along edge $C_2$

The curve here is a quarter circle with the radius 9. Therefore, the parametric equation with the domain $0 \leq t \leq 1$ is then given by :

$x_2(t) = 9 \cos \left(\frac{\pi }{2}t\right)$

$y_2(t) = 9 \sin \left(\frac{\pi }{2}t\right)$

Along edge $C_3$

The parametric equation for $C_3$ is :

$x_1(t) = 0, \ \ \ y_2(t) = 9t \ \ \ for \ 0 \leq t \leq 1$

Now,

x = 9t, ⇒ dx = 9 dt

y = 0, ⇒ dy = 0

$\int_{C_{1}}y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$

And

$x(t) = 9 \cos \left(\frac{\pi}{2}t\right) \Rightarrow dx = -\frac{7 \pi}{2} \sin \left(\frac{\pi}{2}t\right)$

$y(t) = 9 \sin \left(\frac{\pi}{2}t\right) \Rightarrow dy = -\frac{7 \pi}{2} \cos \left(\frac{\pi}{2}t\right)$

Then :

$\int_{C_1} y^2 x dx + x^2 y dy$

$=\int_0^1 \left[\left( 9 \sin \frac{\pi}{2}t\right)^2\left(9 \cos \frac{\pi}{2}t\right)\left(-\frac{7 \pi}{2} \sin \frac{\pi}{2}t dt\right) + \left( 9 \cos \frac{\pi}{2}t\right)^2\left(9 \sin \frac{\pi}{2}t\right)\left(\frac{7 \pi}{2} \cos \frac{\pi}{2}t dt\right) \right]$