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Gennadij [26K]
3 years ago
6

Caleb bought groceries and paid $1.60 in sales tax. The sales tax rate is 2.5%. What was the price of Caleb’s groceries, before

before tax?
Mathematics
1 answer:
-Dominant- [34]3 years ago
8 0

Answer:

$ 64

Step-by-step explanation:

Given:

Caleb paid in sales tax = $1.60

Rate of sales tax = 2.5%

Question asked:

What was the price of Caleb’s groceries, before tax = ?

Solution :

Let  price of Caleb’s groceries, before before tax =

2.5% of price of groceries = $1.60

\frac{2.5}{100} \times x = 1.60\\

Multiplying both side by 100

2.5x = 1.60 \times 100\\2.5x = 160

Dividing both side by 2.5

x = \frac{160}{2.5}

x = 64

Therefore, the price of Caleb’s groceries, before tax = $ 64

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For what values of x is f(x) = |x + 1| differentiable? I'm struggling my butt off for this course
pav-90 [236]

By definition of absolute value, you have

f(x) = |x+1| = \begin{cases}x+1&\text{if }x+1\ge0 \\ -(x+1)&\text{if }x+1

or more simply,

f(x) = \begin{cases}x+1&\text{if }x\ge-1\\-x-1&\text{if }x

On their own, each piece is differentiable over their respective domains, except at the point where they split off.

For <em>x</em> > -1, we have

(<em>x</em> + 1)<em>'</em> = 1

while for <em>x</em> < -1,

(-<em>x</em> - 1)<em>'</em> = -1

More concisely,

f'(x) = \begin{cases}1&\text{if }x>-1\\-1&\text{if }x

Note the strict inequalities in the definition of <em>f '(x)</em>.

In order for <em>f(x)</em> to be differentiable at <em>x</em> = -1, the derivative <em>f '(x)</em> must be continuous at <em>x</em> = -1. But this is not the case, because the limits from either side of <em>x</em> = -1 for the derivative do not match:

\displaystyle \lim_{x\to-1^-}f'(x) = \lim_{x\to-1}(-1) = -1

\displaystyle \lim_{x\to-1^+}f'(x) = \lim_{x\to-1}1 = 1

All this to say that <em>f(x)</em> is differentiable everywhere on its domain, <em>except</em> at the point <em>x</em> = -1.

4 0
3 years ago
Charlie cannot remember how much he financed to buy his car. He does remember that his monthly payment is $200. His add-on inter
Mazyrski [523]
First find the total payments
Total paid
200×30=6,000 (this is the future value)

Second use the formula of the future value of annuity ordinary to find the monthly payment.
The formula is
Fv=pmt [(1+r/k)^(n)-1)÷(r/k)]
We need to solve for pmt
PMT=Fv÷[(1+r/k)^(n)-1)÷(r/k)]
PMT monthly payment?
Fv future value 6000
R interest rate 0.09
K compounded monthly 12
N=kt=12×(30months/12months)=30
PMT=6000÷(((1+0.09÷12)^(30)
−1)÷(0.09÷12))
=179.09 (this is the monthly payment)

Now use the formula of the present value of annuity ordinary to find the amount of his loan.
The formula is
Pv=pmt [(1-(1+r/k)^(-n))÷(r/k)]
Pv present value or the amount of his loan?
PMT monthly payment 179.09
R interest rate 0.09
N 30
K compounded monthly 12
Pv=179.09×((1−(1+0.09÷12)^(
−30))÷(0.09÷12))
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The answer is 4795.15
5 0
3 years ago
What's the solution to<br> 1/5+1/3x&gt;1/2-1/4?
Serjik [45]

Answer:

x> 3/20

Step-by-step explanation:

Let's solve your inequality step-by-step.

1 /5  +  1 /3  x>  1 /2  −  1 /4

Step 1: Simplify both sides of the inequality.

1 /3 x+  1 /5  >  1 /4

Step 2: Subtract 1/5 from both sides.

1 /3 x+  1/ 5  −  1 /5  >  1 /4  −  1 /5  1 /3  x>  1 /20

Step 3: Multiply both sides by 3.

3*( 1 /3 x)>3*( 1 /20 ) x> 3 /20

Answer:

x>  3/ 20

Hope this helps!!

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Sure What do u need help with I am always here
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ch4aika [34]

Answer:

16

Step-by-step explanation:

8 times 2 equals 16

7 0
2 years ago
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