Henry bought a basketball that was on sale for $12. It was 40% off. What was the original price of the basketball? Please Help.

A man deposits $ 14,850 into a bank, which pays 4% interest that is compounded

Ganezh [65]

Given:

Principal = $14850

Rate of interest = 4% compounded semiannually.

Time = 3 years

To find:

The amount after 3 years.

Solution:

Formula for amount is:

$A=P\left(1+\dfrac{r}{n}\right)^{nt}$

Where, P is principal, r is the rate of interest in decimal, n is the number of times interest compounded and t is the number of years.

The interest is compounded semiannually, so n=2.

Putting $P=14850, r=4, n=2, t=3$ in the above formula, we get

$A=14850\left(1+\dfrac{0.04}{2}\right)^{2(3)}$

$A=14850\left(1+0.02\right)^{6}$

$A=14850\left(1.02\right)^{6}$

On further simplification, we get

$A=14850(1.12616242)$

$A=16723.511937$

$A\approx 16723.51$

Therefore, the amount in the account after three years is $16723.51.

6 0

3 years ago

If : f(x)=x^2, g(x)=x-1. Find (f×g)(x).<br>

kramer

Answer:

$\boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}$

Step by step explanation:

Given that,

$f(x) = {x}^{2}$

$g(x) = x - 1$

Solution:

Solving for (f•g)(x):

$= f(x) \cdot g(x)$

Now substitute the given values.

$= x {}^{2} \cdot(x - 1)$

$= x {}^{2} (x - 1)$

Apply distributive property:

$= (x ^{2} \cdot x) - x {}^{2} \cdot 1$

$\boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}$

Hence,f•g(x) will be $x {}^{3} - x {}^{2}$ .

8 0

2 years ago

Please help! what is an equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32)?

grandymaker [24]

Answer:

$f(x)=-4(x-2)(x+7)$

Or, in standard form:

$f(x)=-4x^2-20x+56$

Step-by-step explanation:

We can use the factored form of a quadratic equation:

$f(x)=a(x-p)(x-q)$

Where a is the leading coefficient and p and q are the zeros of the quadratic.

We know that the x-intercepts are at (2, 0) and (-7, 0).

So, let's substitute 2 for p and -7 for q. This yields:

$f(x)=a(x-2)(x+7)$

Now, we need to determine a.

We know that it passes through the point (1, 32). In other words, if we substitute 1 for x, we should get 32 for f(x). Therefore:

$32=a(1-2)(1+7)$

We can now solve for a. First, compute:

$32=a(-1)(8)$

Multiply:

$32=-8a$

Divide both sides by -8:

$a=-4$

So, the value of a is -4.

Therefore, our entire equation is:

$f(x)=-4(x-2)(x+7)$

Notes:

We can expand this into standard form:

$f(x)=-4(x-2)(x+7) \\ f(x)=-4(x^2+5x-14) \\ f(x)=-4x^2-20x+56$

5 0

3 years ago

1.Hannah walked the same number of miles each day for 5 days. Let m represent the total number of miles Hannah walked. Write a l

mamaluj [8]

1) Given m represent the total number of miles Hannah walked.

Let us assume Hannah walked x miles each day.

So total number of miles Hannah walked in 5 days is m=5x.

2)Given Jimmy brought 2 books per day and Peter brought 4 books per day.

If d is the number of days the book drive, total number of books they brought

=total number books brought by Jimmy+ total number of books brought by Peter

= 2d+4d = 6d

3) Given that c represent cost of the clothes.

Then 30% discount = 0.3c

Hence cost of the clothes = c-0.3c = 0.7c

4) Given c represent the cost of their meal before tipping.

And tip is 15% of the cost.

Hence tip = 0.15c

Hence total bill = c+0.15c=1.15c

5) Given that Tommy had 40$ in his pocket.

And pair of pants cost 37$ with 10% sales tax.

Hence cost of pants including sales tax = 37+37*0.1 = 40.1$ >40$

Hence Tommy cannot afford the pants with 40$ in his pocket.

For following problems, we should group the like terms together and then simplify.

6) (x+8)+(3x-12) = (x+3x)+8-12 = 4x-4

7) 5x+7-(3x-4) = 5x+7-3x+4 = (5x-3x)+7+4 = 2x+11

8) (x-2)-(-4x+1)=x-2+4x-1 = (x+4x)-2-1 = 5x-3

8 0

3 years ago

What is the solution for the inequality shown below W+4>0

myrzilka [38]

The answer is: W>-4
I hope this helps

4 0

3 years ago

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