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Fantom [35]
3 years ago
13

A farm grew 19.8 tons of wheat in 2013. The farm's wheat output increased by 9.8% from 2013 to 2014 and by 5.1% from 2014 to 201

5. Which expression represents a for estimating the total output of wheat, in tons, in 2015?
A. 20 + 10 + 5
B. 20(10)(5)
C. 20 + 1.1 + 1.05
D. 20(1.1)(1.05)

Mathematics
1 answer:
7nadin3 [17]3 years ago
3 0

Answer: Choice D

Explanation:

The increase of 9.8% rounds to 10% when rounding to the nearest ten

An increase of 10% would use the multiplier 1.1

Think of it like saying 1 + 0.10 = 100% + 10%

Similarly, the 5.1% rounds to 5% and an increase of this amount will use the multiplier 1.05

So if we started with 20 items, then 20(1.1)(1.05) is the expression that estimates an increase of 10% followed by an increase of 5%. The order doesn't matter (so you could increase by 5% first, then 10% later).

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PLEASE HELP I REALLY DONT UNDERSTAND HOW TO DO THESE QUESTIONS!!!!! THANK YOU I APPRECIATE YOU!!!!
liraira [26]

Answer:

a) $42,580

b) $43,900

Step-by-step explanation:

Recall, "mode" refers to the value which occurs most frequently.

In this case, the question says that there are 2 modes,

this means $34,000 and $50,500 both share the spot for the most frequently appearing salary.

because there are only 5 employees (and hence 5 salaries), the only possible way that there are two modes is if there are two of each mode, leaving only the last salary unknown.

i.e  if we list the 5 salaries (in no particular order)

$34,000   $34,000  $50,500   $50,500   $ x

where x is the 5th unknown salary.

Given that the mean is $42,100

Then (34,000 + 34,000 + 50,500 + 50,500 + x) / 5 = 42,100

solving for x gives x = $41,500

Now we know all the values, we can rearrange them in increasing value:

$34,000   $34,000  $41,500   $50,500   $50,500  

from this, we can see that the median salary is $41,500

Given that the median salary gets a $2400 raise,

the new median salary = $41,500 + $2400 = $43,900 (Ans for part b)

new mean salary,

= ($34,000  + $34,000 + $43,900 +  $50,500  + $50,500  ) / 5

= $42,580 (answer for part a)

4 0
3 years ago
In rectangular form, 6(cos120°, isin120°)
anastassius [24]

Answer:

  (-3, 3√3)

Step-by-step explanation:

Evaluate each of the coordinates. Keep or drop the "i" as your convention requires.

  6(cos(120°), i·sin(120°)) = (6·cos(120°), i·6·sin(120°)) = (6(-0.5), i·6·√3/2)

  = (-3, 3√3 i)

You may want the (x, y) coordinates written as (-3, 3√3).

___

In the complex plane, this is -3+i·3√3.

7 0
3 years ago
Derive the equation of the parabola with a focus at (3,1) and a directrix of y = 5
serg [7]
So hmmm  check the picture below

so... the vertex is "p" distance from the focus and the directrix, thus, the vertex is really half-way between both

in this case, 2 units up from the focus or 2 units down from the directrix, and thus it lands at 3,3

now, the "p" distance is 2, however, the directrix is up, the focus point is below it, the parabola opens towards the focus point, thus, the parabola is opening downwards, and the squared variable is the "x"

because the parabola opens downwards, "p" is negative, and thus, -2

now, let's plug all those fellows in then

\bf \begin{array}{llll}
(x-{{ h}})^2=4{{ p}}(y-{{ k}})\\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-----------------------------\\\\

\begin{cases}
h=3\\
k=3\\
p=-2
\end{cases}\implies (x-3)^2=4(-2)(y-3)\implies (x-3)^2=-8(y-3)
\\\\\\
-\cfrac{(x-3)^2}{8}=y-3\implies \boxed{-\cfrac{1}{8}(x-3)^2+3=y}

5 0
3 years ago
The area of this rectangle is 4x2
meriva

Answer:

8 units squared.

Step-by-step explanation:

Assuming the numbers are the length and width, we can use the formula for finding the area of the rectangle.

The area should be eight units squared.

a = l * w\\a = 4 * 2\\a= 8

3 0
3 years ago
Solve the equation 4(2+3c)=56
AfilCa [17]
C=4 this is as long as you distribute the terms
8 0
3 years ago
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