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2 years ago

Factorise completely

1 answer:

4 0

1. Number that adds up to -12 and multiplied by the same # that gives u -13. Set it up like this because both are negative so, u need 1 negative and 1 positive.
(x-13)(x+1)

2. Same rule applies. GCF
8y(4y+1)

3. (x+3)(x-3)

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A rectangle has a perimeter of 35 1 half feet. If the length is 12 feet, what is the area of the rectangle?

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Answer:

The area of the rectangle is 69 feet squared.

Step-by-step explanation:

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2 years ago

Inessa [10]

Answer:

Approximately 920.324 p/m

Step-by-step explanation:

so to figure this out, we need to simply divide 6,688 people by 7.267 square miles. 6,688/7.267=920.324.... So we have approximately 920.324 people per square mile

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3 years ago

Which matrices can be added together?

MaRussiya [10]

The ones that have the same number of rows and columns

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3 years ago

Assume you have noted the following prices for books and the number of pages that each book contains. Book Pages (x) Price (y) A

belka [17]

Answer:

a) $y=0.00991 x +1.042$

b) $r^2 = 0.7503^2 = 0.563$

c) $r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

Step-by-step explanation:

Data given

x: 500, 700, 750, 590 , 540, 650, 480

y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50

Part a

We want to create a linear model like this :

$y = mx +b$

Wehre

$m=\frac{S_{xy}}{S_{xx}}$

And:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=2595100-\frac{4210^2}{7}=63085.714$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=30095-\frac{4210*49}{7}=625$

And the slope would be:

$m=\frac{625}{63085.714}=0.00991$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{4210}{7}=601.429$

$\bar y= \frac{\sum y_i}{n}=\frac{49}{7}=7$

And we can find the intercept using this:

$b=\bar y -m \bar x=7-(0.00991*601.429)=1.042$

And the line would be:

$y=0.00991 x +1.042$

Part b

The correlation coefficient is given by:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=7 $\sum x = 4210, \sum y = 49, \sum xy = 30095, \sum x^2 =2595100, \sum y^2 =354$

$r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

The determination coefficient is given by:

$r^2 = 0.7503^2 = 0.563$

Part c

$r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

4 0

3 years ago

The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% p

andrew11 [14]

Answer: There are 32 pints of first type and 128 pints of second type in mixture.

Step-by-step explanation:

Since we have given that

Percentage of pure fruit juice in first type = 60%

Percentage of pure fruit juice in second type = 85%

Percentage of pure fruit juice in mixture = 80%

We will use "Mixture and Allegation" to find the ratio of first and second type in mixture:

First type Second type

60% 85%

80%

------------------------------------------------------------------------

85-80 : 80-60

5% : 20%

1 : 4

so, the ratio of first and second type is 1:4.

Total number of pints of mixture = 160

Number of pints of mixture of first type in mixture is given by

$\dfrac{1}{5}\times 160\\\\=32\ pints$

Number of pints of mixture of second type in mixture is given by

$\dfrac{4}{5}\times 160\\\\=4\times 32\\\\=128\ pints$

Hence, there are 32 pints of first type and 128 pints of second type in mixture.

6 0

3 years ago