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Step2247 [10]
3 years ago
6

Find the prod (4x+5)(5x +9) OA. 0.2

Mathematics
1 answer:
Sedaia [141]3 years ago
7 0

It's simple.

25x²+61x+45

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Let C(x) be the cost to produce x batches of​ widgets, and let R(x) be the revenue in thousands of dollars. R(x) = − x² + 6x​, C
Musya8 [376]

Answer:

Step-by-step explanation:

Let C(x) be the cost to produce x batches of​ widgets, and let R(x) be the revenue in thousands of dollars.

R(x) = -x^2 + 6x,\\ C(x) = x + 4.

Profit function = Revenue  - cost

So we get profit function by subtracting C(x) from R(x) using algebraic method of subtraction.

Profit function of x

= Pr(x) = R(x) -C(x)\\= -x^2+6x-x-4\\=-x^2+5x-4

7 0
3 years ago
HIiiiiiiiiiiiiiiiiiiiiiiiii
professor190 [17]

Answer:

hi the answer is 7.3

Step-by-step explanation:

hope it helps you have a good day

8 0
3 years ago
Divide 270 in the ratio 3:2:1​
Contact [7]

3 + 2 + 1 = 6

270 ÷ 6 = 45

45 × 3 = 135

45 × 2 = 90

45 × 1 = 45

3 : 2 : 1

135 : 90 : 45

6 0
3 years ago
What is the nth term rule of the quadratic sequence below?
Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

<u>Given sequence</u>:

6, 20, 40, 66, 98, 136, ...

Calculate the <u>first differences</u> between the terms:

6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136

As the first differences are not the same, calculate the <u>second differences:</u>

14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38

As the <u>second differences are the same</u>, the sequence is quadratic and will contain an n² term.

The <u>coefficient</u> of the n² term is <u>half of the second difference</u>.

Therefore, the n² term is:  3n²

Compare 3n² with the given sequence:

\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}

The second operations are different, therefore calculate the differences <em>between</em> the second operations:

3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18

As the differences are the same, we need to add 5n as the second operation:

\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2  +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2  &-2  & -2  \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0
1 year ago
Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while fighting forest fi
Marysya12 [62]

Answer:

Step-by-step explanation:

Hello!

Data

Year/Firefighters

2000: 20

2001: 18

2002: 23

2003: 30

2004: 20

2005: 12

2006: 24

2007: 9

2008: 25

2009: 15

2010: 8

2011: 11

2012: 15

2013: 34

<u>Common measures of variation</u>

<u>Variance</u>

S²= \frac{1}{n-1}[sumX^2-\frac{(sumX)^2}{n} ]

∑X= 20 + 18 + 23 + 30 + 20 + 12 + 24 + 9 + 25 + 15 + 8 + 11 + 15 + 34

∑X= 264

∑X²= 20² + 18² + 23² + 30² + 20² + 12² + 24² + 9² + 25² + 15² + 8² + 11² + 15² + 34²

∑X²= 5770

n= 14

S²= \frac{1}{13}[5770-\frac{(264)^2}{14} ]

S²= 60.90

<u>Standard deviation</u>

The standard deviation is the square root of the variance

S= √S²= √60.90= 7.80

<u>Coefficient of variation</u>

Is a relative standard deviation, it is defined as the division of the standard deviation (S) by the mean (X[bar)]. It has not units and is usually expressed in percentage. It shows the variability in relation to the mean.

C.V.= \frac{S}{X[bar]}*100 = \frac{7.80}{18.86}*100= 41.36%

The mean or average is a measurement of position and gives you an idea of the central value of the distribution of the data.

X[bar]= ∑X/n= 264/14= 18.86

<u>Range</u>

In the interval between the max and min values. It allows you to have an idea of the dispersion of the values.

R= Xmax - Xmin= 34 - 8= 26

Xmax= 34

Xmin= 8

<u>Inter Quartile Range</u>

Is the difference between Quantile 1 (C₁) and Quantile 3 (C₃). It shows the 50% mid values of the sample.

IQR= C₃ - C₁= 23.5 - 11.5 = 12

Quantile 1 (C₁) is the value that leaves 25% of the sample below and 75% of the sample above.

Pos1: n/4= 14/4= 3.5

The first quantile is the number between position 3 and position 4

8, 9, 11, 12, 15, 15, 18, 20, 20, 23, 24, 25, 30, 34

C₁= (11+12)/2= 11.5

Quantile 3 (C₃) is the value that leaves 75% of the sample below and 25% of the sample above.

Pos3: n*3/4= 14*3/4= 10.5

The third Quantile is between position 10 and 11

8, 9, 11, 12, 15, 15, 18, 20, 20, 23, 24, 25, 30, 34

C₃= (23+24)/2= 23.5

The measurements of variation don't allow you to know the origin of the data, that it is from consecutive years.

I hope it helps!

6 0
3 years ago
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