17. Carole Winer deposits the following in her checking account: 7 five-

Monica paid sales tax of $1.50 when she bought a new bike helmet. The sales tax rate was 5%, how much did the store charge?

grin007 [14]

Answer

1.50 cents for 5% sales tax on 30 dollars

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Jojo likes to paint. She estimates the number of paintings she completes using the function P of w equals two thirds times w min

pantera1 [17]

Answer:

$P = \frac{2}{3} [J(y)] - 2$

Step-by-step explanation:

If Jojo completes P number of paintings working w weeks then the relation between P and w is given by $P = \frac{2}{3} w - 2$ . ........ (1)

Again, the function J(y) represents how many weeks per year she spends painting.

So, w = J(y). ...... (2)

Therefore, the composite function which represent how many paintings Jojo completes in a year, is given by

$P = \frac{2}{3} [J(y)] - 2$ (Answer)

3 0

3 years ago

Read 2 more answers

Danny walks at an average speed of 5 m/s foe 1 minute. Work out the distance that Danny has travelled in metres.

Dahasolnce [82]

Answer:

D = 300 m

Step-by-step explanation:

Given :

Speed = 5 m/s

Time = 1 min = 60 secs

Required:

Distance = ?

Formula :

Speed = Distance/Time

Solution:

Distance = Speed × Time

D = 5 × 60

D = 300 m

4 0

3 years ago

Read 2 more answers

PC-CSIL

pav-90 [236]

The equality used is Subtraction property of equality

Option A is correct

Step-by-step explanation:

We need to identify which option best explains or justifies Step 1.

Step 1 is: $-c = ax^2 + bx$

The given equation is: $0 = ax^2 + bx + c$

To get the equation for step 1 we need to subtract c on both sides of equation i.e using subtraction property of equality

$0-c = ax^2 + bx + c-c$

$-c = ax^2 + bx$

So, The equality used is Subtraction property of equality

Option A is correct.

Keywords: Solving Quadratic Equations

Learn more about Solving Quadratic Equations at:

#learnwithBrainly

5 0

3 years 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

3 years ago