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3 years ago

Can someone plz help me on mixed numbers plz

Mathematics

2 answers:

IRINA_888 [86]3 years ago

3 0

Answer:

The answer 3/4

Step-by-step explanation:

olga2289 [7]3 years ago

3 0

Answer:

\frac{3}{4}

[tex]convert \: the \: mixed \: numbers \: into \: a \: fraction frac{9}{4} - \frac{3}{2}

applying the fractions formula for subtraction

(9 \times 2) - (3 \times 4) \\ 4 \times 2 \\ = 18 - 12 \\ 8 \\ = \frac{6}{8} \\ then \: diide \: each \: number \: by \: 2 \: and \: get \\ \: \frac{3}{4}

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Find area of the isosceles triangle formed by the vertex and the x-intercepts of parabola y=x2+4x−12.

xz_007 [3.2K]

The area of the isosceles triangle is 64 sq units.

<u>Solution:</u>

Part 1: x-intercepts

The x-intercepts occur at the points on the function where y=0

So, we need to solve

$x^2-4x-12=0$

The left side factors fairly easily into:

$(x-6)(x+2)=0$

So solution occur when

$x-6=0\rightarrow x=6$

and

$x+2=0\rightarrow x=(-2)$

So the x-intercepts are at (0,6) and (0,−2)

Part 2: vertex of the parabola

The vertex of a simple quadratic parabola occurs when the derivative of the quadratic is equal to 0.

The derivative of the given quadratic is

$\frac{dy}{dx}=2x-4$

By observation, this is equal to 0 when x=2

When x=2 the original equation becomes

$y=(2)^2-4(2)-12$

$y=-16$

Therefore the vertex of this parabola is at (2,−16)

The endpoints of the base of the isosceles triangle are (-6, 0) and (2, 0)

$\Rightarrow$ so its base is 8

The height of the triangle reaches from the midpoint of the base (-2, 0) and the vertex (2, -16)

$\Rightarrow$ so its height is 16

The area is $\frac{1}{2}\times \text { base }\times \text { height }=\frac{1}{2}\times8\times16=64 \text{ sq units }$

6 0

3 years ago

A paint box contains 12 bottles of different colors. If we choose equal quantities of 3 different colors at random, how many col

Debora [2.8K]

Answer:

220 color combinations are possible.

Step-by-step explanation:

A combination is a way of selecting members from a grouping, such that the order of selection does not matter.

in our case we have 3-combinations of a set of 12 elements:

C(12, 3) = 12!/(3! (12-3)!)

C(12, 3) = 12!/(3! 9!)

C(12, 3) = (10*11*12)/(2*3)

C(12, 3) = 220 color combinations are possible.

3 0

3 years ago

Read 2 more answers

I don’t understand it

aliya0001 [1]

Answer:

474

Step-by-step explanation:

4 0

3 years ago

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How do you solve this?

Firdavs [7]

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7 0

4 years ago

Read 2 more answers

A coach is assessing the correlation between the number of hours spent practicing and the average number of points scored in a g

cricket20 [7]

Answer:

a) $r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

b) $m=\frac{90}{15}=6$

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

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

c) For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

Step-by-step explanation:

We have the following data:

Number of hours spent practicing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score in the game (y) 5 8 11 14 17 20 23 26 29

Part a

The correlation coefficient is given:

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

For our case we have this:

n=9 $\sum x = 18, \sum y = 153, \sum xy = 396, \sum x^2 =51, \sum y^2 =3141$

$r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

Part b

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

Where:

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

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

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=51-\frac{18^2}{9}=15$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=396-\frac{18*153}{9}=90$

And the slope would be:

$m=\frac{90}{15}=6$

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

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

Part c

For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

5 0

3 years ago