MATHEMATICS HIGH SCHOOL

Help plz show workWrite the inequality alberacally
graph the inequality on the real number line
Write the inequality in interval notation.
7.x is not equal to 3.
8. x is not equal to 3.
9. x is not equal to 2 and x is not equal to 7.
10.x is not equal to -4 and x is not equal to 0.

Answers

Answer 1
Answer:

Answer:  see below

Step-by-step explanation:

7) Algebraic Inequality: x ≠ 3  

   -->    -∞ < x < 3 and 3 < x < ∞

   Graph:  ←-----------o-----------→

                               3

  Interval Notation: (-∞,3) ∪ (3, ∞)

8) This is a duplicate question of #7

9) Algebraic Inequality: x ≠ 2 and x ≠ 7

    -->  -∞ < x < 2 and 2 < x < 7 and 7 < x < ∞

   Graph:  ←-------o-------o-------→

                           2        7

  Interval Notation: (-∞, 2) ∪ (2, 7) ∪ (7, ∞)

10) Algebraic Inequality: x ≠ -4 and x ≠ 0

    -->  -∞ < x < -4 and -4 < x < 0 and 0 < x < ∞

   Graph:  ←-------o-------o-------→

                          -4        0

  Interval Notation: (-∞, -4) ∪ (-4, 0) ∪ (0, ∞)

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Suppose y = 48 + 3(2n - 1) is an explicit representation of an arithmetic sequence for integer values n ≥ 1. Find the xth partial sum of the series, as a quadratic function, where x represents the term number.
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Find two consecutive numbers whose sum is 117

Adam builds model rockets. Where he lives , his backyard is 12 feet below sea level. When he ignites his rocket, it flies a maximum of 350 feet straight up into the air before releasing its parachute. What is the altitude of adams rocket at its highest point, as measured from sea level?

Answers

Answer:

The answer is 338 feet.

Step-by-step explanation:

Adam builds model rockets. Where he lives , his backyard is 12 feet below sea level.

The rocket flies a maximum of 350 feet straight up into the air before releasing its parachute.

So, the altitude of Adams rocket at its highest point, as measured from sea level = 350-12=338 feet
350 _ 12= 338 ft above sea level.

What would be the probability that randomly choosing 3 states from the top 6 murder states would actually be the top 3 states for murders in the United States in the exact correct descending order?
Each state and # of murders
1.California 1790
2.Texas 1089
3.New York 774
4.Pennsylvania 636
5.Michigan 613
6.Georgia 522

Answers

The chances would be (if you cant get duplicates)

1/6

1/5

1/4

If you want the states in order

You multiply them together

6 x 5 x 4 = 1/120 chance to get them in that order

The Greek alphabet contains 24 letters. How many fraternity names with Greek letters can be formed if each fraternity name contains 3 letters and repetition of letters is not permitted?a)69
B)12144
c)13824

Answers

For the first letter we have 24 choices. Since letters can't repeat the second letter has 23 choices (24 minus 1 that was used for the first slot) and the third has 22 (24 minus one for the first slot and one for the second slot).

The total number of combinations is thus: 24 x 23 x 22= 12,144
slot method

1st slot=24 options
2nd slot=23 options (1 went to 1st slot)
3rd slot=22 options (another to previous slot)

multiply them
24*23*22=12144 ways

B

Grandma’s Bakery sells single-crust apple pies for $6.99 and double crust cherry pies for $10.99. The total number of pies sold on a busy Friday was 36. If the amount collected for all the pies that day was $331.64, how many of each type were sold?

Answers

Answer:

15 single-crust apple pies were sold and 21 double-crust cherry pies were sold.

Step-by-step explanation:

Let a be the number of single-crust apple pies sold

Let c be the number of double-crust cherry pies sold

In how many different ways can 5 books be arranged on a shelf?

Answers

Permutation:

5! = 5 * 4 * 3 * 2 * 1 = 120

A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.

Answers

The answer is f(x) = 500 + 3.8x

The number of weeks is x. So, weekly, the tree grows 3.8x. 
If the measurements of the growth begin when the tree started to grow, the equation would be: f(x) = 3.8x.
But, the measurements begin when the tree is 5 m tall. Since 1 m is 100 cm, this means that 5 m is 500 cm. Thus, the equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall is:
f(x) = 500 + 3.8x

Answer:

n=500+8(n-1)

DO NOT FORGET that the tree is already 5 meters tall on the FIRST WEEK, not the 0th week. So, f(x)=500+3.8x is incorrect.

(For example, on the second week the tree should be 503.8 meters tall. But if you plug 2 in f(x)=500+3.8x, you would get 507.6, which is the height of the tree on the third week.)
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