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3 years ago

Mental Math A typical tip in a restaurant is 15% of the total bill. If the bill is $60, what would the

Mathematics

1 answer:

xenn [34]3 years ago

6 0

Answer:

It would be $9.

Because 60 * 0.15 = 9

Step-by-step explanation:

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PLZ help solve !!!!!!!

Ivahew [28]

37 I think I’m not sure just saying a random number don’t trust me I just needed the points

4 0

3 years ago

An isosceles triangle with legs of 8 cm and a base of 10 cm in length has a median drawn

bazaltina [42]

Answer:

89 cm and vertex 8cm length of the seng.ent 10 cm

7 0

1 year ago

If a,b,c and d are positive real numbers such that logab=8/9, logbc=-3/4, logcd=2, find the value of logd(abc)

Eva8 [605]

We can expand the logarithm of a product as a sum of logarithms:

$\log_dabc=\log_da+\log_db+\log_dc$

Then using the change of base formula, we can derive the relationship

$\log_xy=\dfrac{\ln y}{\ln x}=\dfrac1{\frac{\ln x}{\ln y}}=\dfrac1{\log_yx}$

This immediately tells us that

$\log_dc=\dfrac1{\log_cd}=\dfrac12$

Notice that none of $a,b,c,d$ can be equal to 1. This is because

$\log_1x=y\implies1^{\log_1x}=1^y\implies x=1$

for any choice of $y$ . This means we can safely do the following without worrying about division by 0.

$\log_db=\dfrac{\ln b}{\ln d}=\dfrac{\frac{\ln b}{\ln c}}{\frac{\ln d}{\ln c}}=\dfrac{\log_cb}{\log_cd}=\dfrac1{\log_bc\log_cd}$

so that

$\log_db=\dfrac1{-\frac34\cdot2}=-\dfrac23$

Similarly,

$\log_da=\dfrac{\ln a}{\ln d}=\dfrac{\frac{\ln a}{\ln b}}{\frac{\ln d}{\ln b}}=\dfrac{\log_ba}{\log_bd}=\dfrac{\log_db}{\log_ab}$

so that

$\log_da=\dfrac{-\frac23}{\frac89}=-\dfrac34$

So we end up with

$\log_dabc=-\dfrac34-\dfrac23+\dfrac12=-\dfrac{11}{12}$

###

Another way to do this:

$\log_ab=\dfrac89\implies a^{8/9}=b\implies a=b^{9/8}$

$\log_bc=-\dfrac34\implies b^{-3/4}=c\implies b=c^{-4/3}$

$\log_cd=2\implies c^2=d\implies\log_dc^2=1\implies\log_dc=\dfrac12$

Then

$abc=(c^{-4/3})^{9/8}c^{-4/3}c=c^{-11/6}$

So we have

$\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}$

4 0

2 years ago

Is this the correct answer, yall?

ehidna [41]

Yes, yes it is; well done.

4 0

2 years ago

Identify the 34th term of the arithmetic sequence 2, 7, 12

torisob [31]

The equation is AN=A1+D(N-1) A1 being the first number (2) D being the difference (in this case 5) and N being the nth term to find (34) so here you have AN=2+5(34-1) then AN=2+5(33). the answer here is 167.

5 0

3 years ago