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4 years ago

Are all vertical lines parallel?

Mathematics

1 answer:

BartSMP [9]4 years ago

4 0

Answer: Yes

Step-by-step explanation: All vertical lines have the same slope and because of that they are always parallel.

You might be interested in

What is the answer for all these numbers

Leya [2.2K]

3=12
4=13
5=14
6=15
7=16

6 0

3 years ago

2. Mark has scored 12, 14, 10, 8, and 5 points in the past 5 basketball games. Write and solve the inequality that

marusya05 [52]

Answer:

Mark must score at least 11 points to have an average of 10 points per game.

Step-by-step explanation:

The average of a set of data is its sum, divided by the number of data points in the set. If p is the number of points Mark scores in his next game, and he wants his average at least 10, then the relation is ...

(12 +14 +10 +8 +5 +p)/6 ≥ 10

49 +p ≥ 60 . . . . . . . . . multiply by 6 and simplify

p ≥ 11 . . . . . . . . . . . subtract 49

Mark must score at least 11 points in the next game to average at least 10 points per game.

_____

Additional comment

Sometimes, it is convenient to work with the average directly. Relative to the average Mark wants (10), his scores so far are +2, +4, 0, -2, -5, for a total of -1. In order to bring the average to the value Mark wants, he must bring this total to 0 or higher. That is, he must score at least 10+1 = 11 points in his next game.

5 0

3 years ago

A university surveyed recent graduates of the English department for their starting salaries. Four hundred graduates returned th

NeX [460]

Answer:

Step-by-step explanation:

We want to determine a 95% confidence interval for the mean salary of all graduates from the English department.

Number of sample, n = 400

Mean, u = $25,000

Standard deviation, s = $2,500

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z × standard deviation/√n

It becomes

25000 ± 1.96 × 2500/√400

= 25000 ± 1.96 × 125

= 25000 ± 245

The lower end of the confidence interval is 25000 - 245 =24755

The upper end of the confidence interval is 25000 + 245 = 25245

Therefore, with 95% confidence interval, the mean salary of all graduates from the English department is between $24755 and $25245

3 0

4 years ago

Find the value of x. Round to the nearest tenth.

denpristay [2]

Answer:

$\displaystyle x \approx 38.2 ^{\circ}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Pre-Calculus

Law of Sines: $\displaystyle \frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}$

A, B, C are angle measures
a, b, c are leg lengths

Step-by-step explanation:

Step 1: Identify

A = 27°, a = 11

B = x°, b = 15

Step 2: Solve for x

Substitute [LOS]: $\displaystyle \frac{sin(27^{\circ})}{11} =\frac{sin(x^{\circ})}{15}$
Cross-multiply: $\displaystyle 11sin(x^{\circ}) = 15sin(27^{\circ})$
Isolate x term: $\displaystyle sin(x^{\circ}) = \frac{15sin(27^{\circ})}{11}$
Isolate x: $\displaystyle x = sin^{-1}(\frac{15sin(27)}{11})$
Evaluate: $\displaystyle x = 38.2488 ^{\circ}$
Round: $\displaystyle x \approx 38.2 ^{\circ}$