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4 years ago

If 6 is {2\over 5} of a number N,then N=

Mathematics

1 answer:

Alex4 years ago

8 0

Answer:

Step-by-step explanation:

set up the equation 2/5n=6 and solve for N by dividing each side by 2/5, which is also multiplying each side by 5/2. n=15

check by substituting 15 in for N.

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There are two possible offers that could be applied to orange juice that would each explain this reduction in the total bill. 4:

svlad2 [7]

Incomplete question. The full question read;

My local store sometimes runs offers on some of its products. There are three different types of offers that could be in place:

Buy a certain number of a particular product and get an extra one for half price.
A percentage discount (always a multiple of 5%) on one particular product.
A percentage discount (always a multiple of 5%) on purchases worth a total of more than $10.

The store only ever has one of these offers in place at any time.

Last week I bought

3 cartons of orange juice for $4 each
1 loaf of bread for $3
5 packets of snacks for $1 each

This week I bought the same set of items, but only paid $18 even though the individual items still had the same price.

(4) There are two possible offers that could be applied to orange juice that would each explain this reduction in the total bill.

What are these two offers?

(5) What are the other two offers that could explain the reduction in the total bill?

Answer:

<u>1. Buy a certain number of a particular product and get an extra one for half price</u>

Step-by-step explanation:

By buying 2 and getting one at half the price matches the offer:

Buy a certain number of a particular product and get an extra one for half price.

This means two (2) cartons of orange juice cost $8 (4*2) + $2 cost the extra one at half price.

6 0

3 years ago

Which of the following is a solution to sin(x/2) = radical 3/2

Vinvika [58]

Answer:

sin ( x/ 2 ) = - √ 3 /2

Take the inverse sine of both sides of the equation to extract x

from inside the sine.

x/ 2 = arcsin ( − √ 3/ 2 )

The exact value of arcsin ( − √ 3 /2 ) is − π /3 .

/x 2 = − π /3

Multiply both sides of the equation by 2 .

2 ⋅ x /2 = 2 ⋅ ( − π /3 )

Simplify both sides of the equation.

x = − 2 π /3

The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from 2 π , to find a reference angle. Next, add this reference angle to π to find the solution in the third quadrant.

x /2 = 2 π + π/ 3 + π

Simplify the expression to find the second solution.

x = 2 π /3

4 π

Add 4 π to every negative angle to get positive angles.

x = 10 π /3

The period of the sin ( x /2 ) function is 4 π so values will repeat every 4 π radians in both directions.

x =2 π /3 + 4 π n , 10 π/ 3 + 4 π n , for any integer n

Exclude the solutions that do not make sin ( x /2 ) = − √ 3/ 2 true.

x = 10 π /3 + 4 π n , for any integer n

4 0

3 years ago

An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce p

ludmilkaskok [199]

Answer:

a) $y=-0.317 x +46.02$

b) Figure attached

c) $S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

Step-by-step explanation:

We assume that th data is this one:

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

a) Find the least-squares line appropriate for this data.

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:

$\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720$

$\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324$

$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

$\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540$

$\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900$

And the slope would be:

$m=-\frac{1900}{6000}=-0.317$

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

$\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60$

$\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27$

And we can find the intercept using this:

$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

So the line would be given by:

$y=-0.317 x +46.02$

b) Plot the points and graph the line as a check on your calculations.

For this case we can use excel and we got the figure attached as the result.

c) Calculate S^2

In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:

$MSE=\frac{SSE}{df_{E}}$

The degred of freedom for the error are given by:

$df_{E}=n-2=12-2=10$

We can calculate:

$S_{y}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=9540-\frac{324^2}{12}=792$

And now we can calculate the sum of squares for the regression given by:

$SSR=\frac{S^2_{xy}}{S_{xx}}=\frac{(-1900)^2}{6000}=601.67$

We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]

So then :

$S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

5 0

3 years ago

What is the ratio of surface area to volume for a sphere with the following

Aneli [31]

The answer would be A Im Sure If not I apologize

5 0

4 years ago

Read 2 more answers

total of 420 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tic

Gnoma [55]

<span>2x + x = 420
3x = 420
x = 140 Adult tickets </span>

4 0

4 years ago