Math Extended Problems Sequences

You just graduated college (age 23) and now have your dream job of a computer animator. Your gross salary is 43,000 a year. Answ

Kipish [7]

Answer:

$93.72

Step-by-step explanation:

To be able to find how much is deducted from our paycheck monthly, we have to compute for the total amount left to pay for the health insurance.

Insurance = $4500

Company % = 75% or 0.75

Total amount left = $4500- $4500x0.75

Total amount left = $1125

Now that we know the total amount left, we simply divide the total by 12 to find the monthly payments.

Monthly Payment = $1125/12

Monthly Payment = $93.72

So a total of $93.72 will be deducted from our monthly paycheck for the health insurance.

5 0

3 years ago

Read 2 more answers

James bought 5 baseball cards at a garage sale for $0.65

forsale [732]

Answer:

c 11.25 I think is correct

6 0

3 years ago

Can someone please answer this for me.

Levart [38]

Answer:

See picture

Step-by-step explanation:

The rule is ...

$x^{m/n}=\sqrt[n]{x^m}$

The index of the surd becomes the denominator of the exponents inside.

4 0

3 years ago

Read 2 more answers

If A = 41 degree, <br> Angle BDC = 58 degree, <br> and y = 8, Find x.

love history [14]

Check the pictures below.

make sure your calculator is in Degree mode, since the angles are in degrees.

4 0

4 years ago

Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

4 0

3 years ago