What decimal number does point A on the number line below represent? −0.75 0.75 −1.25 1.25

Mathematics

1 answer:

MatroZZZ [7]3 years ago

8 0

Answer:

-1.75

Step-by-step explanation:

Point A is in between - 1 and -2

This interval is split in 4 equal parts and has 3 marker points.

Point A is on the bottom marker point, which indicates:

-1 * 3/4 = - 3/4 = - 0.75

Since it is below -1, we add up - 1 and - 0.75:

- 1 + (-0.75) = - 1.75

Point A represents: -1.75 on the number line

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Barbara's gross earnings for the week ending on December 21 amount to \$1,100 . Her cumulative gross earnings for the year up th

zlopas [31]

Answer:

b) $44

Step-by-step explanation:

Barbara's cumulative gross earnings for the year up through her last pay date amount to 55000.

As per attached table this amount falls in 4% region ($50001 - $70000).

Her tax per current pay period is:

$1100*0.04 = $44

Correct choice is b)

6 0

3 years ago

Leno4ka [110]

Answer:

$\frac{s^2-25}{(s^2+25)^2}$

Step-by-step explanation:

Let's use the definition of the Laplace transform and the identity given: $\mathcal{L}[t \cos 5t]=(-1)F'(s)$ with $F(s)=\mathcal{L}[\cos 5t]$ .

Now, $F(s)=\int_0 ^{+ \infty}e^{-st}\cos(5t) dt$ . Using integration by parts with u=e^(-st) and dv=cos(5t), we obtain that $F(s)=\frac{1}{5}\sin(5t)e^{-st} |_{0}^{+\infty}+\frac{s}{5}\int_0 ^{+ \infty}e^{-st}\sin(5t) dt=\int_0 ^{+ \infty}e^{-st}\sin(5t) dt$ .

Using integration by parts again with u=e^(-st) and dv=sin(5t), we obtain that

$F(s)=\frac{s}{5}(\frac{-1}{5}\cos(5t)e^{-st} |_{0}^{+\infty}-\frac{s}{5}\int_0 ^{+ \infty}e^{-st}\sin(5t) dt)=\frac{s}{5}(\frac{1}{5}-\frac{s}{5}\int_0^{+ \infty}e^{-st}\sin(5t) dt)=\frac{s}{5}-\frac{s^2}{25}F(s)$ .