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Shkiper50 [21]
3 years ago
5

You buy a sweater for $32, which is 30% off the original price. what was the original price?

Mathematics
1 answer:
Nataliya [291]3 years ago
8 0

Answer:

45.71 = original price

Step-by-step explanation:

The sale price is equal to the original price minus the discount

sale price = original price - discount

The discount is equal to the original price  times the percent off

discount = original price * percent off

Substitute into the first equation

sale price = original price - original price * percent off

Factor out the original price

sale price = original price (1-percent off)

We know the sale price=32 and the discount = 30% = .3

32 = original price (1-.3)

32 = original price (.7)

Divide each side by .7

32/.7 = original price (.7)/.7

45.71 = original price

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A population of amoebas in a petri dish will triple in size every 20 minutes. at the start of experiment the population is 800.
sp2606 [1]
If we are to derive the equation that models the growth of the amoeba, we make use of the general form:
p = po k^t
where po is the initial population
k is the multiplicative rate of change

From the problem
3po = po k^(20)
k = 1.06

The equation is
p = 800 (1.06)^t
4 0
4 years ago
What value of y satisfies the system of equations:<br><br> y=-6x+2<br><br> y=x^2+11
Nataly [62]

Answer:

The value of y that satisfies the system of equations is 20

Step-by-step explanation:

we have

y=-6x+2

y=x^{2}+11

we know that

The solution of the system of equations is the intersection point both graphs

using a graphing tool

the intersection point is (-3,20)

see the attached figure

therefore

The value of y that satisfies the system of equations is 20

8 0
3 years ago
Use the given data to find a regression line that best fits the price-demand data for price p in dollars as a function of the de
Rufina [12.5K]

Answer:

m=-\frac{7600}{8250}=-0.921

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

\bar x= \frac{\sum x_i}{n}=\frac{550}{10}=55

\bar y= \frac{\sum y_i}{n}=\frac{1042}{10}=104.2

And we can find the intercept using this:

b=\bar y -m \bar x=104.2-(-0.921*55)=104.707

So the line would be given by:

y=-0.921 x +104.707

Step-by-step explanation:

For this case we have the following data given:

Demand (x): 10,20,30,40,50,60,70,80,90,100

Price (y): 141 , 133,126, 128,113,97, 90, 82,79,53

We want to construct a linear model like this:

y = mx +b

For this case we need to calculate the slope with the following formula:

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}

So we can find the sums like this:

\sum_{i=1}^n x_i =550

\sum_{i=1}^n y_i =1042

\sum_{i=1}^n x^2_i =38500

\sum_{i=1}^n y^2_i =115882

\sum_{i=1}^n x_i y_i =49710

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}=38500-\frac{550^2}{10}=8250

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=49710-\frac{550*1042}{10}=-7600

And the slope would be:

m=-\frac{7600}{8250}=-0.921

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

\bar x= \frac{\sum x_i}{n}=\frac{550}{10}=55

\bar y= \frac{\sum y_i}{n}=\frac{1042}{10}=104.2

And we can find the intercept using this:

b=\bar y -m \bar x=104.2-(-0.921*55)=104.707

So the line would be given by:

p(x)=-0.921 x +104.707

4 0
3 years ago
Can someone please explain the math on this one to me? Thanks!
kodGreya [7K]

Answer:

18 men = 36 tons in 6 hours

Step-by-step explanation:

3 men = 1 ton in 1 hour

6 men = 2 ton in 1 hour

9 men = 3 tons in 1 hour

with this you find a pattern

3 men = 2 tons in 2 hours

3 men = 3 tons in 3 hours

3 men = 6 tons in 6 hours

6 men = 12 tons in 6 hours

9 men = 18 tons in 6 hours

12 men = 24 tons in 6 hours

15 men = 30 tons in 6 hours

18 men = 36 tons in 6 hours

(This is how i worked it out)

8 0
3 years ago
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How might you solve a problem that has both a fraction and a decimal in it
Anni [7]
Well, one way is to convert one of the numbers to the other. For example, if I have 3/5 and 0.5, I could convert 3/5 to a decimal. So, I would have 0.6 (3/5 converted to a decimal), and 0.5. Next, I would just add the two together to get my answer of 1.1
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4 years ago
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