MATHEMATICS COLLEGE

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal. (a) Determine the sample mean in cents (Round to 3 decimal places)

Answers

Answer 1

Answer:

Answer:

53¢

Step-by-step explanation:

First, I'll put these in order.

20¢;30¢; 30¢;75¢;40¢;40¢;40¢;40¢;50¢;55¢55¢65¢;65¢; $1.50;

Then, I'll combine like terms.

30+30=60

40+40+40+40(or 40 x 4)=160

55+55=110

65+65=130

60+160+110+130+20+75+50+$1.50=$7.55/14=53¢

PLZ correct me if i'm wrong :-D

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Which system of equations has infinitely many solutions? 4 x + 2 y = 5. Negative 4 x minus 2 y = 1. Negative 10 x + y = 4. 10 x minus y = negative 4. Negative 8 x + y = 2. 8 x minus y = 0. Negative x + 2 y = 6. 7 x minus 2 y = 12.

Answers

Answer:

$\left \{ {{-10x+y=4} \atop {10x-y=-4}} \right.$

Step-by-step explanation:

Which system of equations has infinitely many solutions?

4 x + 2 y = 5 // -4x - 2y = 1

-10x + y = 4 // 10x - y = -4.

-8x + y = 2 // 8x-y = 0.

-x + 2 y = 6 // 7x-2y = 12.

It's important to know that a linear system of equations has infinitely many solutions when both equations represents the same line, that means one line is on top of the other one, that's why the shared infinite points.

In this case, notice that if we compare the second system, you would find that both equations are the same,

$\left \{ {{-10x+y=4} \atop {10x-y=-4}} \right.$

If we multiply the first equation by -1

$\left \{ {{10x-y=-4} \atop {10x-y=-4}} \right.$

Which means the system has infinitely many solutions, because both equations represent the same line, so the shared all possibles points.

Therefore, the right answer is the second choice.

Answer:

Step-by-step explanation:

Promise

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The number of bacteria at the beginning of an experiment was 30 and the bacteria grow at an hourly rate of 1.4 percent. Using the model given by () = 0e, estimate the number of bacteria, rounded to the nearest whole number after 20 hours.

Answers

Answer:

The estimated number of bacteria after 20 hours is 40.

Step-by-step explanation:

This is a case where a geometrical progression is reported, which is a particular case of exponential growth and is defined by the following formula:

$n(t) = n_(o)\cdot \left(1+(r)/(100) \right)^(t)$ (1)

Where:

$n_(o)$ - Initial number of bacteria, dimensionless.

$r$ - Increase growth of the experiment, expressed in percentage.

$t$ - Time, measured in hours.

$n(t)$ - Current number of bacteria, dimensionless.

If we know that $n_(o) = 30$ , $r = 1.4$ and $t = 20\,h$ , then the number of bacteria after 20 hours is:

$n(t) = 30\cdot \left(1+(1.4)/(100) \right)^(20)$

$n(t) \approx 39.616$

$n(t) = 40$

The estimated number of bacteria after 20 hours is 40.

Evaluate the expression 2x2 - yl yl + 3xº for x = 4 and y = 7

Answers

Answer:

replace the given values of x and y

Step-by-step explanation:

hope it helped!!!

Please help!!! The purple shape is a dilation of the black shape. What is the scale factor or the dial action?

Answers

Answer:

I belive it would be 1/5. ;;;

203.530 divided by 0.7=

Answers

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Use Gauss's approach to find the following sum (do not use formulas):5+11+17+23...+83

Answers

Denote the sum by S. So

S = 5 + 11 + 17 + 23 + ... + 83

There's a constant difference of 6 between consecutive terms in S, so the 3 terms before 83 are 77, 71, and 65. So

S = 5 + 11 + 17 + 23 + ... + 65 + 71 + 77 + 83

Gauss's approach involves inverting the sum:

S = 83 + 77 + 71 + 65 + ... + 23 + 17 + 11 + 5

If we add terms in the same position in the sums, we get

2S = (5 + 83) + (11 + 77) + ... + (77 + 11) + (83 + 5)

and we notice that each grouped term on the right gives a total of 88. So the right side consists of several copies n of 88, which means

2S = 88n

and dividing both sides by 2 gives

S = 44n

Now it's a matter of determining how many copies get added. The terms in the sum form an arithmetic progression that follows the pattern

11 = 5 + 6

17 = 5 + 2*6

23 = 5 + 3*6

and so on, up to

83 = 5 + 13*6

so n = 13, which means the sum is S = 44*13 = 572.

Final answer:

To find the sum of the given arithmetic series, we can use Gauss's approach by finding the number of terms and then calculating the sum using the formula for the sum of an arithmetic series.

Explanation:

To find the sum of the given series, we can use Gauss's approach. The series is an arithmetic progression with a common difference of 6. We can find the number of terms in the series using the formula for the nth term of an arithmetic sequence and then use the formula for the sum of an arithmetic series to find the sum.

Find the number of terms (n):
1. The first term (a) is 5, and the common difference (d) is 6.
2. Find the last term (l) using the formula: l = a + (n - 1)d
3. Substitute the values and solve for n: 83 = 5 + (n - 1)6
4. Simplify and solve for n: n = 15
Find the sum (S):
1. The formula for the sum of an arithmetic series is: S = (n/2)(a + l)
2. Substitute the values and solve for S: S = (15/2)(5 + 83)
3. Calculate the sum: S = 15(44)
4. Simplify the sum: S = 660

Learn more about Gauss's here:

brainly.com/question/31322009

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