What is the median of the set 5,6,9,11,12,14,20,23,24,24,30?

A class has 4 boys and 10 girls. What is the ratio in the simplest form that compares a number of boys to a total number of stud

sergejj [24]

Answer:

4 to 14 should be the right answer

6 0

2 years ago

The Nuthouse offers a mixture of soy nuts and almonds, Almonds

elena55 [62]

Answer:

14 pounds

Step-by-step explanation:

The given equations can be solved for y by substituting for x. The first equation is convenient for writing x in terms of y.

<h3>Solution</h3>

x = 20 -y . . . . . . . subtract y from the first equation

7(20 -y) +5.5y = 119 . . . . . substitute for x in the second equation

140 -1.5y = 119 . . . . . . . . simplify

21 = 1.5y . . . . . . . . . . . add 1.5y -119 to both sides

14 = y . . . . . . . . . . . .divide by 1.5

14 pounds of soy nuts should be used in the mixture.

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<em>Additional comment</em>

There are many ways to solve a system of two linear equations. The attachments shows a matrix solution using a suitable calculator. It tells us that x=6 and y=14, as we found above.

6 0

2 years ago

What two rational expressions sum to 2x+3/x^2-5x+4

Anni [7]

Answer:

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

Step-by-step explanation:

Given the rational expression: $\frac{2x + 3}{x^2 - 5x + 4}$ , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

$x^2 - 5x + 4$

$x^2 - 4x - x + 4$

$(x^2 - 4x) - (x + 4)$

$x(x - 4) - 1(x - 4)$

$(x- 1)(x - 4)$

Thus, we now have: $\frac{2x + 3}{(x- 1)(x - 4)}$

Step 2: Apply the concept of Partial Fraction

Let,

$\frac{2x + 3}{(x- 1)(x - 4)}$ = $\frac{A}{x- 1} + \frac{B}{x - 4}$

Multiply both sides by (x - 1)(x - 4)

$\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4)$ = $(\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)$

$2x + 3 = A(x - 4) + B(x - 1)$

Step 3:

Substituting x = 4 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(4) + 3 = A(4 - 4) + B(4 - 1)$

$8 + 3 = A(0) + B(3)$

$11 = 3B$

$\frac{11}{3} = B$

$B = \frac{11}{3}$

Substituting x = 1 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(1) + 3 = A(1 - 4) + B(1 - 1)$

$2 + 3 = A(-3) + B(0)$

$5 = -3A$

$\frac{5}{-3} = \frac{-3A}{-3}$

$A = -\frac{5}{3}$

Step 4: Plug in the values of A and B into the original equation in step 2

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}$

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

7 0

3 years ago

The table lists the speeds of the fastest roller coasters in North America and Asia.

kotykmax [81]

The difference of the means of the two data sets is = 4.57

The mean absolute deviation of the roller coaster speeds in North America is 13.3

The mean absolute deviation of the roller coaster speeds in Asia is 16.8

<h3>How to solve for the means</h3>

First we have to start with the data for North America

128, 120, 100, 93, 92, 80.8, 85, 82, 80, 77

To get the mean you have to sum up the values and divide through by the total number 10

937.8/10

Mean = 93.78

Mean Absolute Deviation = (128 - 93.78) + ( 120 - 93.78) + ( 100 - 93.78) + ( 93 - 93.78) + ( 92 - 93.78) + ( 80.8 - 93.78) + ( 85 - 93.78) + ( 82 - 93.78) + ( 80 - 93.78) + ( 77 - 93.78) / 10

133.32/10 = 13.3

For Asia, we have the data as

149.1, 106.9, 95, 83, 90, 80.3, 78.3, 71.5, 69.6, 68.4

Mean for Asia = 892.1/10

= 89.21

Mean Absolute Deviation = (149.1 - 89.21) + ( 106.9 - 89.21) + ( 95 - 89.21) + ( 83 - 89.21) + ( 90 - 89.21) + ( 80.3 - 89.21) + ( 78.3 - 89.21) + ( 71.5 - 89.21) + ( 69.6 - 89.21) + ( 68.4 - 89.21) / 10

= 168.32/10

16.8

The difference in the means = 93.78 -89.21

= 4.57