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3 years ago

Choose the inequality that represents the following graph.

Mathematics

1 answer:

zmey [24]3 years ago

4 0

Answer:

(b) x ≤ -4

Step-by-step explanation:

There are a few things to note when reading an inequality on a number line.

The number line would contain the following:

i. circles: These can be closed or open. Closed circles are denoted by a shaded small circle showing that the point or number shown on the number line is included in the inequality. Open circles are denoted by an unshaded small circle showing that the point or number shown on the number line is not included in the range of inequality.

ii. arrows: An arrow can point to the right or left. When it points to the right, that means the values greater than the number specified on the number line are included in the range. When it points to the left, the values less than the number are included.

From the given number line,

The type of circle is a closed circle since it is shaded. This means that the number pointed at on the number line (-4 in this case) is included in the range.

Also, the arrow is pointing leftwards. This means that values less than the number pointed at (-4 in this case) are included in the range.

Therefore, the inequality should read,

x ≤ -4

This shows that all values of x less than or equal to -4 are included in the range.

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An internet start-up predicts its revenue by a straight-line method with a slope of $7000 per month. In its 6 th month it had re

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Given that the method of revenue calculation is straight line method, the equation modeling this will be given by:
y=mx+c
where:
m=slope
x=time
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3 years ago

Naval intelligence reports that 4 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 9 vessels are randomly targete

icang [17]

Answer:

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Fleet of 17 means that $N = 17$

4 are carrying nucleas weapons, which means that $k = 4$

9 are destroyed, which means that $n = 9$

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

$P(X > 1) = 1 - P(X \leq 1)$

In which

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294$

$P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412$

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588$

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

8 0

3 years ago

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Sati [7]

Yes you can i think........

4 0

3 years ago

Read 2 more answers

Remi invests ?600 for 5 years in a saving account. By the end of the 5 years he has received a total of ?75 simple interest. Wor

Allushta [10]

Answer:

2.5 %

Step-by-step explanation:

The simple interest formula is

I = Prt

Data:

I = $75

P = $600

t = 5 yr

Calculation:

75 = 600 × r × 5

75 = 3000 r

Divide each side by 3000

r = 75/3000 = 0.025 = 2.5 % APR

The annual percentage rate is 2.5 %.

4 0

3 years ago

If X²⁰¹³ + 1/X²⁰¹³ = 2, then find the value of X²⁰²² + 1/X²⁰²² = ?

enyata [817]

Step-by-step explanation:

$\bf➤ \underline{Given-} \\$

$\sf{x^{2013} + \frac{1}{x^{2013}} = 2}\\$

$\bf➤ \underline{To\: find-} \\$

$\sf {the\: value \: of \: x^{2022} + \frac{1}{x^{2022}}= ?}\\$

$\bf ➤\underline{Solution-} \\$

Let us assume that:

$\rm: \longmapsto u = {x}^{2013}$

Therefore, the equation becomes:

$\rm: \longmapsto u + \dfrac{1}{u} = 2$

$\rm: \longmapsto \dfrac{ {u}^{2} + 1}{u} = 2$

$\rm: \longmapsto{u}^{2} + 1 = 2u$

$\rm: \longmapsto{u}^{2} - 2u + 1 =0$

$\rm: \longmapsto {(u - 1)}^{2} =0$

$\rm: \longmapsto u = 1$

Now substitute the value of u. We get:

$\rm: \longmapsto {x}^{2013} = 1$

$\rm: \longmapsto x = 1$

Therefore:

$\rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 1 + 1$

$\rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 2$

★ Which is our required answer.

$\textsf{\large{\underline{More To Know}:}}$

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)³ = a³ + 3ab(a + b) + b³

(a - b)³ = a³ - 3ab(a - b) - b³

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

(x + a)(x + b) = x² + (a + b)x + ab

(x + a)(x - b) = x² + (a - b)x - ab

(x - a)(x + b) = x² - (a - b)x - ab

(x - a)(x - b) = x² - (a + b)x + ab

6 0

3 years ago