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Nikitich [7]
2 years ago
12

I am thinking of six different odd numbers, the mean of the numbers is 16, the median is 15, the range is 26, the greatest numbe

r is 31, what is the greatest number value for the 2nd number?
Mathematics
1 answer:
Sedaia [141]2 years ago
4 0

Answer:

Step-by-step explanation:

information from the range

If the range is 26 and the largest number is 31 then the smallest number is 31 - 26  = 5

Information from the median

The median must consist of 2 numbers because we have 6 integers for the data and median must consist of the middle 2. Since we are told that the median is 15 and we need 2 integers the other integer must  be 15 as well..

So what do we know so far.

5      15 15         31

Information from the mean

There are six integers making up the series of numbers. The mean is 16. Therefore all 6 integers added together must be 6 * 16 = 96

What do we have so for?

5 + 15 + 15 + 31 = 66

What do the other two numbers sum to?

96 -66 = 30

Getting the answer.

The first number to try must be 13. It has to be below 15 (the median and odd. That's 13).

So now we have

5 13 15 15 ___ 31

But from the mean we need 30

30 - 13 = 17

And we have a winner because 17 is above 15.

Answer

5 13 15 15 17 31

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Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi
miss Akunina [59]

Answer:

\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.

Step-by-step explanation:

1st boat:

Parabola equation:

y=ax^2 +bx+c

The x-coordinate of the vertex:

x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a

Equation:

y=ax^2 -2ax+c

The y-coordinate of the vertex:

y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10

Parabola passes through the point (-8,1), so

1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1

Solve:

c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}

Parabola equation:

y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}

2nd boat:

Parabola equation:

y=ax^2 +bx+c

The x-coordinate of the vertex:

x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0

Equation:

y=ax^2+c

The y-coordinate of the vertex:

y_v=a\cdot 0^2+c\Rightarrow c=-7

Parabola passes through the point (-8,1), so

1=a\cdot (-8)^2-7\\ \\64a-7=1

Solve:

a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7

Parabola equation:

y=\dfrac{1}{8}x^2 -7

System of two equations:

\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.

7 0
3 years ago
Read 2 more answers
40y^14/10y^8 simplify radicals and use properties of rational exponents
Vadim26 [7]

Answer:

4y^6

Step-by-step explanation:

Take out the constants:

40y^14/10y^8

= 40/10 * y^14 / y^8

= 4 * y^(14-8)

= 4 * y^6

= 4y^6

Hope this helped you :3

7 0
3 years ago
A researcher is going to estimate the average typing speed of students of a college. He selects a random sample of 20 students a
Stella [2.4K]

Answer:

The margin of error of the 90% confidence interval of a student's average typing speed is of 1.933 wpm.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 20 - 1 = 19

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.9}{2} = 0.95. So we have T = 1.7291

The margin of error is:

M = T\frac{s}{\sqrt{n}}

In which s is the standard deviation of the sample and n is the size of the sample. For this question, we have s = 5, n = 20. So

M = T\frac{s}{\sqrt{n}}

M = 1.7291\frac{5}{\sqrt{20}}

M = 1.933

The margin of error of the 90% confidence interval of a student's average typing speed is of 1.933 wpm.

8 0
3 years ago
I need the answer ASAP please
Nastasia [14]

Answer:

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Step-by-step explanation:

7 0
2 years ago
Please answer the attached question by selecting of the the given answers.
Alchen [17]

Answer:

The correct answer is option A. Base = 11 cm and height = 13 cm

Step-by-step explanation:

It is given that, height of a triangle is 2 cm more than its base.Then height is increased by 2 cm.Then the area of triangle becomes 82.5 cm²

<u>To find the base an d height of original triangle</u>

Let x be the original base 'b' then the height  h = x + 2

New height h = x + 2 + 2 = x + 4

Area = bh/2

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Take positive value x = 11

Therefore base = 11 and height = x + 2 = 13 cm

The correct answer is option A. Base = 11 cm and height = 13 cm

5 0
3 years ago
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