MATHEMATICS COLLEGE

Decorating your house for Christmas takes 106ft of lights. You use two lengths of lights,the short length of lights is 5 ft and the long length of lights is 11 ft. The total number of
strings of lights you use is 14. How many of each type of light do you have?

Answers

Answer 1
Answer:

Answer:

  • 8 short and 6 long strings

Step-by-step explanation:

Let the number of lights are short = s and long = l.

According to question we have:

  • s + l = 14
  • 5s + 11l = 106

Subtract 5 times the first equation from the second one to solve for l:

  • 5s + 11l - 5s - 5l = 106 - 5*14
  • 6l = 36
  • l = 36/6
  • l = 6

Find s:

  • s = 14 - 6 = 8
Answer 2
Answer:

Answer:

A good rule of thumb is 100 lights for every 1.5 feet of tree. However, if you love lights, you may want to double, or even triple, that amount.

Step-by-step explanation:

Just a guess because  you gave no answer choices

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A preliminary sample of holiday shoppers revealed that the standard deviation of the amount of money they are planning to spend on gifts during the coming holiday season is $80. How many holiday shoppers should be sampled in order to estimate the average amount of money spent on gifts by all holiday shoppers with a margin of error of $7 and with a 99% confidence

Answers

Answer:

n=((2.58(80))/(7))^2 =869.407 \approx 870

So the answer for this case would be n=870 rounded up to the nearest integer

Step-by-step explanation:

Information given

\sigma = 80 represent the deviation

ME = 7 represent the margin of error

Solution

The margin of error is given by this formula:

ME=z_(\alpha/2)(\sigma)/(√(n))    (a)

And on this case we have that ME =7 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=((z_(\alpha/2) \sigma)/(ME))^2   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance level would be \alpha=0.01 and \alpha/2 =0.05. The critical value would be z_(\alpha/2)=2.58, replacing into formula (b) we got:

n=((2.58(80))/(7))^2 =869.407 \approx 870

So the answer for this case would be n=870 rounded up to the nearest integer

Each student in a class of 25 students wrote down a random digit. what is the predicted number of students who will win a digit that is greater than 7?

Answers

Comment
I'm going to assume that 0 is below 1 and not above 9. Furthermore that there are 10 digits altogether.

Argument
I may not understand the problem, but I think it means that how many students will randomly choose an 8 or 9.

Since both can come up (randomly) 1/10 of the time, it would seem to me that the answer should be

1/10 * 25 + 1/10 * 25 = 5 

so 5/25 students will come up with an 8 or 9.
so P(8 or 9) = 0.2 <<<< answer

Note
Any two digits should give you the same result.

Answer:

5

Step-by-step explanation:

At Food Lion, an 8-ounce container of Daisy sour cream is $1.52. Kraft sour cream sells for $2.92 for 12 ounces. Which is the better buy and by how much?

Answers

Answer:

The 8-ounce container of daisy sour cream

Step-by-step explanation:

It's the 8-ounce container of Daisy sour cream because if you buy two of those, it would cost $3.04 for 16 ounces. If you bought one Kraft sour cream for 12 ounces, it would be $2.92. So you can get two 8-ounce containers of Daisy sour cream near the price of the price for the Kraft sour cream for $2.92. You would have to pay an extra 12 cents if you want 16 ounces of sour cream.

Help to solve   y'''-y''-4y'+4y=5-e^x+e^2x

Answers

By solving the equation "y'''-y''-4y'+4y=5-e^x+e^2x" we get "y = Ae^x+Be^(2e)+Ce^(-2x)+(5)/(4)+(xe^x)/(3) +(xe^(2x))/(4)".

As we know the auxiliary equations,

  • m^3-m^2-4m+4=0
  • (m-1)(m-2)(m+2) =0

here,

m = 1, 2, -2

Thus,

The general equation will be:

→ y = Ae^x+Be^(2x)+Ce^(-2x)

Particularly,

  • 5 = (5)/(4)
  • e^x= x((1)/(1-4)e^x ) = -(xe^x)/(3)
  • e^(2x) = x((e^(2x))/((2+2)(2-1)) )= (xe^(2x))/(4)

hence,

The complete equation will be:

→ y = Ae^x+Be^(2e)+Ce^(-2x)+(5)/(4)+(xe^x)/(3) +(xe^(2x))/(4)

Thus the above answer is right.

Learn more:

brainly.com/question/22449567

Answer:

Step-by-step explanation:

First of all write the auxialary equation as

m^3-m^2-4m+4 =0\n(m-1)(m-2)(m+2)=0

m=1,2,-2

Hence general solution is

y=Ae^x+Be^(2x) +Ce^(-2x)

Particular solution of 5 is

(5)/(4)

Particular solution of e^x is

x((1)/(1-4) e^x =(-xe^x)/(3)

Particular solution of e^2x is

x(e^(2x) )/((2+2)(2-1)) =(xe^(2x) )/(4)

Together full solution is

y=Ae^x+Be^(2x) +Ce^(-2x)+(5)/(4) +(xe^x)/(3) +(xe^(2x) )/(4)

Find the slope of the line that asses through the pair of oints (17,11) and (21,19)

Answers

Answer:

The slope of the two points is 2. (8/4)

Answer:

The slope of the two points is 2. (8/4)

Step-by-step explanation:

thats it

The nth term of a sequence is -3-3n what is the 6th term

Answers

Answer:

-21

Step-by-step explanation:

if for s(n) = -3-3n

then s(6) = -3-3*6 = -3-18 = -21
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