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Rzqust [24]
2 years ago
8

Write in Standard Form: 9a^2 + 5 = 0

Mathematics
1 answer:
Levart [38]2 years ago
4 0

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

It is in standard form!!!

:)

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

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Allison bought some shirts for he clothing store for $15 each. She received $50 off her entire purchase and spent a total of $40
k0ka [10]

The $50 off was like a coupon after you brought all your merchandise to the counter, so we have to add it back in to determine the number of shirts.

$400+$50=$450 original price of shirts

Original price ÷ price per shirt= quantity purchased

$450 ÷ $15/shirt= 30 shirts purchased

Allison bought 30 shirts.

Hope this helps! :)


6 0
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
Find inequalities with solutions that have this graph.
Oduvanchick [21]
Moooooooosssssssssseeeeeeeeseseses
8 0
3 years ago
A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th
Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let S(t) be the amount of sugar in the tank at time t. Then S(0)=25.

Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of

\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}

Separate variables, integrate, and solve for <em>S</em>.

\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt

\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt

-100\ln\left|P-\dfrac S{100}\right|=t+C

\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t

P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}

\dfrac S{100}=P-Ce^{-100t}

S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}

Use the initial value to solve for <em>C</em> :

S(0)=25\implies 25=100P-C\implies C=100P-25

\implies S(t)=100P-(100P-25)e^{-100t}

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick <em>P</em> such that

S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}

5 0
2 years ago
How can we get to peace?​
-BARSIC- [3]

Answer: Charmaine Diyoza: "Come on, Kane. Without graveyard McCreary, my internal problem is solved. Without the Red Queen, our problem external is. This is how we get to peace."

Step-by-step explanation: The 100

7 0
2 years ago
Read 2 more answers
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