Answer:
2 problems per minute
Step-by-step explanation:
Because 48 problems divided by 24 minutes is 2 so the final answer is 2 problems per minute
Mean if data 40/5 = 8 she is corrrect
In <span>equilateral triangle all sides are equal =x,
from right triangle that is formed by </span>apothem , height 7*3= 21
hypotenuse /opposite leg = sin angle,
hypotenuse is a side of triangle =x, opposite leg is apotheme =21,
angle in equilateral triangle =60⁰
21/x= sin 60, x*sin60=21, x=21/sin60, x=21/(√3/2), x=42/√3
Area of triangle =1/2 x*x*sin angle
Area of triangle =1/2 *42/√3*42/√3*sin 60=1/2*(42²/3)*(√3/2) ≈ 255 cm²
this is just second way to do this problem, that I did at first (either way is correct)
<span> apothem divides one side by half,
so we get small right triangle with sides x hypotenuse, x/2 is one leg , and 21 is another leg
</span>by Pythagorean theorem
x²=(x/2)² +21²
x²-x²/4=441
3x²/4=441
3x²=441*4=1764
x²=1764/3
x=42/√3
Area of triangle =1/2*base *height =1/2*42/√3 *21≈255 cm²
Each horse and person has 1 head
we know that people+horses=74
p+h=74
1 person has 2 legs
1 house has 4 legs
p=number of people
h=number of hourses
number of legs=196
4 times h=number of legs if h hourses
2p=number of legs if p people so
196=2p+4h
divide by 2
98=p+2h
multiply first equation by -1
-p-h=-74
add to current equation
p-p+2h-h=98-74
0p+h=24
there were 24 hourses
subsitute
24+p=74
ssubtract 24
50=p
there were 524 horses and 50 people
the answer is B
Using compound interest, it is found that:
- The equation is:
![A(t) = 3520(1.065)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%203520%281.065%29%5Et)
- After 3 years, he has $4,252 in the account.
- After 10 years, he has $6,608 in the account.
<h3>What is compound interest?</h3>
The amount of money earned, in compound interest, after t years, is given by:
![A(t) = P\left(1 + \frac{r}{n}\right)^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%5Cleft%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D)
In which:
- A(t) is the amount of money after t years.
- P is the principal(the initial sum of money).
- r is the interest rate(as a decimal value).
- n is the number of times that interest is compounded per year.
- t is the time in years for which the money is invested or borrowed.
In this problem:
- Jack was given $3520 from his grandma, hence P = 3520.
- The account pays 6.5% interest rate that is compounded annually, hence n = 1, r = 0.065.
Hence, the equation is:
![A(t) = P\left(1 + \frac{r}{n}\right)^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%5Cleft%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D)
![A(t) = 3520\left(1 + \frac{0.065}{1}\right)^{t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%203520%5Cleft%281%20%2B%20%5Cfrac%7B0.065%7D%7B1%7D%5Cright%29%5E%7Bt%7D)
![A(t) = 3520(1.065)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%203520%281.065%29%5Et)
After 3 and 10 years, respectively, the amount in dollars in the account are given by:
![A(3) = 3520(1.065)^3 = 4252](https://tex.z-dn.net/?f=A%283%29%20%3D%203520%281.065%29%5E3%20%3D%204252)
![A(10) = 3520(1.065)^{10} = 6608](https://tex.z-dn.net/?f=A%2810%29%20%3D%203520%281.065%29%5E%7B10%7D%20%3D%206608)
More can be learned about compound interest at brainly.com/question/25781328