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3 years ago

Suppose we want to choose 2 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair

Mathematics

1 answer:

Paraphin [41]3 years ago

7 0

Answer: First off. Question or statement? Secondly. What?

Step-by-step explanation: Third. What?

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Ilmage: 1 apple. 3 oranges for each of 5 steps on the slider]

Nady [450]

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4 0

2 years ago

What interest rate, to the nearest tenth of a percent, that is required for an investment subject to continuous compounding to i

Sunny_sXe [5.5K]

Answer:

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

Step-by-step explanation:

Use the formula for continuous compounding

$X(t) = Pe^{rt}$

where r stands for the (annual) interest rate, t for time in years, P for the initial principal (investment) and X is the amount after t years.

(this formula can be beautifully derived from just basic considerations, btw)

We are given t=5, and percent increase on the initial P, so we can solve for r

$X(5) = 1.5P=Pe^{r\cdot5}\\1.5=e^{r\cdot5}\\\ln 1.5=\ln e ^{5r}\\\ln 1.5=5r\\r = \frac{\ln 1.5}{5}=0.081\rightarrow 8.1\%$

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

5 0

3 years ago

Consider the statement | x − 4 | < 0.5 |x-4|<0.5. What is the meaning of this statement? Select all that apply. a. All val

stich3 [128]

Answer:

Option D.

Step-by-step explanation:

The given statement is

$|x-4|$

x-4 is difference between x and 4.

|x-4| distance from x because distance can not be negative.

Inequality sign "<" means less than.

$|x-4|$ represent all values of x whose distance from 4 is less than 0.5.

Therefore, the correct option is D.

8 0

3 years ago

Solve the right angle trig problem.

iris [78.8K]

Answer:

x = 53.6588°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Trigonometry

[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] cos∅ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use trig to find the missing angle.

Step 2: Identify Variables

POV from angle x

Angle = x

Adjacent = 16

Hypotenuse = 27

Step 3: Solve for x

Substitute: cosx° = 16/27
Inverse: x° = cos⁻¹(16/27)
Evaluate: x = 53.6588°

7 0

2 years ago

Teacher's salaries in Georgia are normally distributed with an average salary of $52,000 with a standard deviation of $12,000. W

suter [353]

Answer:

81.85%

Step-by-step explanation:

We have the following information:

mean = m = 52000

standard deviation = sd = 12000

a = 40000

b = 76000

we need to find the probability between a and b, that is:

P (a <x <b) = P (40,000 <x <76000)

P [(40000 - m) / sd <(x - m) / sd <(76000 - m) / sd]

replacing

P [(40000 - 52000) / 12000 <z <(76000 - 52000) / 12000]

P (-1 <z <2)

P (z <= -1) - P (z <= 2)

We look for this value of z, in the attached table:

0.9772 - 0.1587

P = 0.8185

In other words, the probability is 81.85%

8 0

3 years ago