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3 years ago

Identify three solutions of the inequality x < 1

Mathematics

2 answers:

Simora [160]3 years ago

8 0

Answer:

-3, -4,-5

Step-by-step explanation:

< means less than. In this situation, you want x to be less than 1, so basically, any number under 1 is correct.

oksano4ka [1.4K]3 years ago

5 0

Answer:

-1, -2, -3

Step-by-step explanation:

any number less than 1 will work

You might be interested in

A rectangle has a perimeter of 30 ft. Find a function that models its area A in terms of the length x of one of its sides. What

Vedmedyk [2.9K]

Answer:

Step-by-step explanation:

Let the other side of the rectangle be y. The perimeter of the rectangle is expressed as P = 2(x+y)

Given P = 30ft, on substituting P = 30 into the expression;

30 = 2(x+y)

x+y = 15

y = 15-x

Also since the area of the rectangle is xy;

A = xy

Substitute y = 15-x into the area;

A = x(15-x)

A = 15x-x²

The function that models its area A in terms of the length x of one of its sides is A = 15x-x²

The side of length x yields the greatest area when dA/dx = 0

dA/dx = 15-2x

15-2x = 0

-2x = -15

x = -15/-2

x = 7.5 ft

Hence the side length, x that yields the greatest area is 7.5ft.

Since y = 15-x

y = 15-7.5

y = 7.5

Area of the rectangle = 7.5*7.5

Area of the rectangle = 56.25ft²

6 0

3 years ago

2. The quality assurance department inspects its production line. The product either fails or passes the inspection. Past experi

Oksana_A [137]

Answer:

(a) $E(X) = 950$

(b) $COV = 0.007255$

Step-by-step explanation:

The given problem can be solved using binomial distribution since the product either fails or passes, the probability of failure or success is fixed and there are n repeated trials.

probability of failure = q = 0.05

probability of success = p = 1 - 0.05 = 0.95

number of trials = n = 1000

(a) What is the expected number of non-defective units?

The expected number of non-defective units is given by

$E(X) = n \times p \\\\E(X) = 1000 \times 0.95 \\\\E(X) = 950$

(b) what is the COV of the number of non-defective units?

The coefficient of variance is given by

$COV = \frac{\sigma}{E(X)}$

Where the standard deviation is given by

$\sigma = \sqrt{n \times p\times q} \\\\\sigma = \sqrt{1000 \times 0.95\times 0.05} \\\\\sigma = 6.892$

So the coefficient of variance is

$COV = \frac{6.892}{950}$

$COV = 0.007255$

(c) What is the probability of having more than 980 non-defective units?

We can use the Normal distribution as an approximation to the Binomial distribution since n is quite large and so is p.

$P(X > 980) = 1 - P(X < 980)\\\\P(X > 980) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\$

We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution) to approximate discrete probability distribution (Binomial distribution).

$P(X > 980) = 1 - P(Z < \frac{979.5 - 950}{6.892} )\\\\P(X > 980) = 1 - P(Z < \frac{29.5}{6.892} )\\\\P(X > 980) = 1 - P(Z < 4.28)\\\\$

The z-score corresponding to 4.28 is 0.99999

$P(X > 980) = 1 - 0.99999\\\\P(X > 980) = 0.00001\\\\$

So it means that it is very unlikely that there will be more than 980 non-defective units.

8 0

4 years ago

My Dream is I become a Mathematician what is your dream career, please don't delete it

In-s [12.5K]

Answer:

I wanna become a doctor..

3 0

2 years ago

Read 2 more answers

Which number sentence correctly solves this problem? There were 52,165 people at the soccer game on Friday. There were 49,872 pe

Romashka [77]

Answer: D.

Step-by-step explanation:

52,165 + 49,872 = 102,037

8 0

3 years ago

One lap around a parking lot is 3/10 mile.this represents 15% of the total distance Gregory ran.what is the total distance in mi

sattari [20]

Given:

One lap around a parking lot = 3/10 mile
3/10 mile is 15% of the total distance Gregory ran.

To determine the total distance (in mile) that Gregory ran, we refer to the given percentage:

3/10 mile / 0.15 = 2 miles

The total distance that Gregory ran is 2 miles. <span />

4 0

3 years ago