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Leviafan [203]
3 years ago
14

(40 POINTS)

Mathematics
1 answer:
34kurt3 years ago
3 0

Answer:

1.   y= 25400(1 + 0.11)^x

2.  2019

Step-by-step explanation:

1. y = a(1 + r)^x       <em> </em>

<em>(exponential growth formula :</em>

<em>a = initial value (the amount before measuring growth or decay) </em>

<em>r = growth or decay rate (usually represented as a percentage and expressed as a decimal) </em>

<em> x = number of time units that have passed)</em>

y= 25400(1 + 0.11)^x

so in 1 year, in 1996, we would say

y=25400(1+0.11)^1

y=25400(1.11)

y=28194

2. I found the answer by plugging in numbers into x

with x = 24

y= 25400(1+0.11)^24

y= 310874

so in 24 years, the population will surpass 302438 which would be 1995+24= 2019

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A store receives tomatoes in boxes of 40 tomatoes each. About 4 tomatoes per box cannot be sold due to damage. Write an algebrai
monitta

Answer:

40b - 4b    or 36 b

Step-by-step explanation:

No. of tomatoes in each box = 40

No. of box shipped = b

No. of tomatoes in those b box = b*No. of tomatoes in each box = 40b

No. of tomatoes damaged in each box = 4

No. of box shipped = b

No. of tomatoes damaged in those b box = b*No. of tomatoes damaged in each box = 4b

Thus, total no. of tomatoes that can be sold by store = No. of tomatoes in those b box - No. of tomatoes damaged in those b box  = 40b - 4b

Algebraic expression to express the no. of tomatoes that can be sold from those b box is

40b - 4b = 4b(10-1) = 4b(9) = 36b (Answer)

3 0
4 years ago
Find the simple interest paid to the nearest cent for each loan amount, interest rate, and time.
myrzilka [38]

Answer:

I = $ 1,937.50

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

Step-by-step explanation:

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4 0
3 years ago
Evaluate the given integral by changing to polar coordinates. sin(x2 + y2) dA R , where R is the region in the first quadrant be
koban [17]

Set

\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dA=r\,\mathrm dr\,\mathrm d\theta

The region R is given in polar coordinates by the set

R=\left\{(r,\theta)\mid2\le r\le3,0\le\theta\le\dfrac\pi2\right\}

So we have

\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_2^3r\sin(r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac\pi4(\cos4-\cos9)}

8 0
4 years ago
Which statement best describes a method that can be used to sketch the graph. y = |x - 2| a. Translate the graph of y = |x| two
ser-zykov [4K]

f(x) + n - translate the graph of f(x) n units up

f(x) - n - translate the graph of f(x) n units down

f(x + n) - translate the graph of f(x) n units left

f(x - n) - translate the graph of f(x) n units right

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We have

y = |x - 2|

f(x) = |x| → f(x - 2) = |x - 2|

<h3>Answer: c. Translate the graph of y = |x| two units right.</h3>
6 0
3 years ago
Solve sec2theta + tantheta - 3 =0 for 0
Serhud [2]

Answer:

Ф = \frac{\pi }{4} ,\frac{5\pi}{4}

Step-by-step explanation:

It is a bit difficult to input the work here, so I uploaded an image

  • First we can use the trig identities to change sec²(Ф) to tan²(Ф) + 1
  • Then we can combine like terms
  • Then we can factor this as a polynomial function
  • Then we can set each term equal to zero and solve for Ф
  • The first term tan(Ф) - 2 = 0 has no solution because tan(Ф) ≠ -2 anywhere
  • The second term tan(Ф) - 1 = 0 has two solutions of \frac{\pi}{4} and \frac{5\pi}{4} so these are the solutions to the problem

7 0
3 years ago
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