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3 years ago

Correctly order the proceed for solving for x using the algebraic properties of equality.

Mathematics

1 answer:

Snezhnost [94]3 years ago

6 0

Answer:

Step-by-step explanation:

Step 1: Subtract 9

50.24 = 3.14x²

Step 2: Divide by 3.14

x² = 16

Step 3: Square root both sides

x = ±4

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The perimeter of an isosceles triangle is 32 inches. If the base is longer than half of the two other equal sides by 2 inches, f

Leona [35]

Answer:

Step-by-step explanation:

Let equal sides of an isosceles triangle = a inches

Base = $\frac{1}{2}a+2$ inches

Perimeter = 32 inches

a + a + $\frac{1}{2}a+2$ = 32

$2a + \frac{1}{2}a+2 = 32\\\\\frac{2a*2}{1*2}+\frac{1}{2}a+2=32\\\\\frac{4a}{2}+\frac{1}{2}a+2=32\\\\\frac{5}{2}a+2 = 32\\\\$

Subtract 2 from both sides

$\frac{5}{2}a=32-2\\\\\frac{5}{2}a=30\\\\a=30*\frac{2}{5}\\\\a=6*2$

a = 12 inches

base = $\frac{1}{2}*12+2$

= 6 + 2

Base = 8 inches

6 0

2 years ago

MATH PLEASE HELP!! HELP BADLY NEEDED....

Molodets [167]

Corresponding angles- a, d, h, l and s
Alternate interior- c, f, i, o, and t
Same side interior- e, g, k, m, and p
Alternate exterior- n, q, r
• for j and b I’m not sure

3 0

3 years ago

Two thirds of 12 minus d

fenix001 [56]

Step-by-step explanation:

2 /3 of 12 - d

2/3 * 12 - d

8 - d

7 0

2 years ago

Read 2 more answers

Which equations will the number 2 make true?

butalik [34]

Answer:

none of them

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviati

Ket [755]

Answer:

$\sigma = 11.28$ --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Explain how the standard deviation is calculated.

<u>Start by calculating the mean</u>

To do this, we divide the sum of the products of grade and number of students by the total number of students;

i.e.

$\bar x = \frac{\sum fx}{\sum f}$

So, we have:

$\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}$

$\bar x = \frac{7531}{91}$

$\bar x = 82.76$

Next, calculate the variance using the following formula:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}$

i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset

So, we have:

$\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}$

$\sigma^2 = \frac{11580.6816}{91}$

$\sigma^2 = 127.26$

Lastly, take the square root of the variance to get the standard deviation

$\sigma = \sqrt{\sigma^2}$

$\sigma = \sqrt{127.26}$

$\sigma = 11.28$ --- approximated

<em>Hence, the standard deviation is approximately 11.28</em>

Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.

8 0

2 years ago