prove that n2 − 7n 12 is nonnegative whenever n is an integer with n ≥ 3

The solution of the inequality, |x + 6| ≥ 5 is given as follows,

(A) x > -1

(B) It follows that x either belongs to the interval (-∞, -11) or to the interval (-1,∞) for the given absolute inequality.

(A) Solving the Given Inequality:

|x + 6| ≥ 5

x+6 ≥ 5 or x+6 ≤ (-5)

x+6-6 ≥ 5-6 or x+6-6 ≤ (-5)-6

x ≥ -1 or x ≤ -11

Hence the solution of the given inequality is given as,

x ∈ (-∞, -11] or x ∈ [-1, ∞)

(B) Description of the Solution

From the given absolute inequality, it can be concluded that x either belongs to the interval (-∞, -11] or to the interval [-1, ∞). Hence, on the number line, the solution of the inequality will be shown as a shaded region from -∞ to -11 and from -1 to ∞. The area between -1 and -11 will remain unshaded.

In the deduced solution, the interval is either open or closed on both sides. Open interval means the extreme value is not includes. On the other hand, closed interval indicates inclusion of the extreme point in the solution of the inequality.

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The difference between the tallest and shortest heights is 0.787 × 10

From tallest to shortest:

Difference between tallest and shortest heights =

3.212 x 10⁴ - 2,425

= 3.212 x 10⁴ - 2.425 × 10³

= (3.212 - 2.425) × 10^4 - 3

= 0.787 × 10

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Using excel, we can determine that the likelihood that a randomly picked steel plate measuring 1 foot by 1 foot contains two or fewer faults is 0.862.

This is further explained below.

Generally, the characteristic or condition of being probable; the degree to which something is likely to occur or be the case. the likelihood of anything happening or something is the case.

In conclusion, In this section, we will make the assumption that the number of defects found in a steel plate measuring 1 foot by 1 foot has a Poisson distribution with a mean of 1.28.

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Answer:

obtuse angle triangle

Step-by-step explanation:

please make me Brilliant for this correct answer

Answer:

C.

Step-by-step explanation:

For any of the given functions, all of the first input values (x-values) in the relation are considered the domain values. On the other hand, the output values (y-values) are called the range values of the given equation.

The mapped relation is the domain (1, 2, 3). Since this is domain values (x-values), the correct answer will be the mapped with 1, 2, and 3 on the left side.

The correct answer is C.

Hope this helps!

Answer:

y = - [tex]\frac{7}{4}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{7}{4}[/tex] x - 2 ← is in slope- intercept form

with slope m = - [tex]\frac{7}{4}[/tex]

• Parallel lines have equal slopes , then

y = - [tex]\frac{7}{4}[/tex] x + c ← is the partial equation

to find c substitute (4, - 2 ) into the partial equation

- 2 = - 7 + c ⇒ c = - 2 + 7 = 5

y = - [tex]\frac{7}{4}[/tex] x + 5 ← equation of line

The value of 8√6 as a square root is √384

Surd are written as the square root of prime numbers. Given the expression below;

8√6

This is can be written as;

8√6 = √(8 * 8 * 6)

8√6 = √64 * 6

8√6 = √384

Therefore the value of 8√6 as a square root is √384

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Answer:

A, C, E, F

Step-by-step explanation:

since nothing else was said, it is a general triangle. nothing special about it.

so, the only rules are that the sum of any pair of sides must be longer than the 3rd side (otherwise, if the 3rd side is longer, the sides could not connect).

A. 10.

so, we have

6 + 9 > 10 true

6 + 10 > 9 true

9 + 10 > 6 true

therefore this is a possible 3rd side.

B. 2.

so, we have

6 + 9 > 2 true

6 + 2 > 9 false

9 + 2 > 6 true

therefore this is NOT a possible 3rd side.

C. 4.

so, we have

6 + 9 > 4 true

6 + 4 > 9 true

9 + 4 > 6 true

therefore this is a possible 3rd side.

D. 15.

so, we have

6 + 9 > 15 false

6 + 15 > 9 true

9 + 15 > 6 true

therefore this is NOT a possible 3rd side (this triangle is a special case as 6+9 = 15 : it can only exist as a completely flat line and is therefore not a triangle).

E. 12.

so, we have

6 + 9 > 12 true

6 + 12 > 9 true

9 + 12 > 6 true

therefore this is a possible 3rd side.

F. 7.

so, we have

6 + 9 > 7 true

6 + 7 > 9 true

9 + 7 > 6 true

therefore this is a possible 3rd side.

Using the properties of logarithms, it is found that the earthquake in Japan in 2011 was 12.92 times more severe.

As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are [tex]R_1, R_2 > 0, R_1 > R_2[/tex], the ratio of the intensities is given by:

[tex]10^{\frac{R_1}{R_2}}[/tex]

The intensities for this problem are [tex]R_1 = 9, R_2 = 8.1[/tex], hence the ratio is:

[tex]10^{\frac{9}{8.1}} = 12.92[/tex]

The earthquake in Japan in 2011 was 12.92 times more severe.

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Hello,

[tex]( \frac{1}{3} ) {}^{3} = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1 {}^{3} }{3 {}^{3} } = \frac{1}{27} [/tex]

Hi! ⋇

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\sf\color{darkblue}{( \frac{1}{3}) ^{3} = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1} {27} }[/tex]

Players no longer need commitment strategies to reach a mutually-beneficial cooperative equilibrium when games are repeated.

This is an exercise related to Game Theory.

The extended form is typically used to depict repeated games, commonly referred to as supergames, in game theory since they occur repeatedly across time.

The potential of collaborating means that we may choose to compromise in order to continue earning a payout over time, knowing that if we do not fulfill our part of the bargain, our adversary may decide not to either.

As contrast to one-shot games, recurring games provide a new set of incentives.

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "area and graphs." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer:

Step-by-step explanation:

Answer

False but close.

The intercept arc and the central angle are equal.

Answer:

Step-by-step explanation:

Mabye later

Answer: 100

Step-by-step explanation:

The angles with measure 100° and x° are vertical angles, which are two opposite angles made from two intersecting lines. These vertical angles are always the same measure.

Hence, both x and 100 have the same measure.

Multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.

Pythagoras's principle follows the rule:

c² = a² + b²

where

Therefore, Pythagorean triples are a² + b² = c² where a, b and c are the three positive integers. The most known and smallest triplets are (3,4,5).

If we reduced the length of the side of the triangle with the greatest common factor, it should give us 3, 4, 5.

Hence,

21, 28 and 35 has greatest common factor as 7

21 / 7 , 28 / 7 and 35 / 7

3, 4, 5

Hence, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.

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Use the rules of exponents to simplify the expression.

[tex]\large\displaystyle\text{$\begin{gathered}\sf (C^{4})^{3} \end{gathered}$}[/tex]

To raise a power to another power, multiply the exponents.

[tex]\large\displaystyle\text{$\begin{gathered}\sf C^{4\times3} \ \to \ Multiply \end{gathered}$}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf C^{12} \end{gathered}$}}[/tex]

Therefore, the correct option is "C".

Step-by-step explanation:

You already know that we use tn=an²+bn+c for these kinds of sequences:

4, 7, 14, 25, ...

now

7–3=4

So 2a=4===> a=2

[tex] a_{1} = 4 = = > n = 1 \\ 4 = 2 \times {1}^{2} + b + c = = = = > \\ b + c = 2[/tex]

[tex] a_{2} = 7 = = > n = 2 = = = > \\ 7 = 2 \times {2}^{2} + 2 \times b + c = = = > \\ - 1 = 2b + c[/tex]

b=–3, c=5

So the final result is:

[tex] t_{n} = 2 {n}^{2} - 3n + 5[/tex]

The area of the triangle LMN is 4 units squared.

The area of a triangle can be described as follows:

The area of the triangle by using the base and height of the triangle.

area of a triangle = 1 / 2 bh

where

Therefore,

base = NL = 4 units

height = PM = 2 units

Therefore,

area of the triangle = 1 / 2 × 4 × 2

area of the triangle = 8 / 2

area of the triangle = 4 units²

Therefore, the area of the triangle LMN is 4 unit squared.

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Answer: B. 4 Square Units

Step-by-step explanation:

Answer: [tex]5\sqrt{2}[/tex] m

Step-by-step explanation:

Using the pythagorean theorem, we get that the shortest distance it can travel is [tex]\sqrt{3^2+4^2+5^2}[/tex] = [tex]5\sqrt{2}[/tex] m

The time that a member hold his/her position at the agency is approximately 0.1 year.

Given that twenty members are elected to an agency every two years and there are 100 members on a average overall.

We have to find the time that a member hold his position at the agency.

To calculate the time we have to use multiplication which means product of two numbers.

In 2 years agency elected 20 members. It shows like under:

2 years=20 members

We require 100 members at one end so we will multiply by 5 both sides.

10 years=100 members

Now take 100 to left side of equal to sign.

10/100=1 member

1 member=1/10

=0.1

Hence a member holds 0.1 year at the agency.

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Answer:

24

Step-by-step explanation:

3x4x2=24

When finding the answer to this problem, you times all of the options by each other.

The value of X is 100 degree.

According to the statement

we have to find the value of x degree which represent the angle.

In this figure

we see that there are two angles which are vertically opposite angles and there is rule that the values of vertically opposite angles are always same.

So, due this reason Here the value of x is 100 degree

because in this figure the given angle which is 100 degree are vertical to the angle which we have to find and that angle which x, so, the value of x is same as the value of vertical angle.

so these angles are vertical angles. that's why x is 100 degree.

So, The value of X is 100 degree.

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It is true that the U.S. economic system would be seriously strained if we completely eliminated poverty level wages."

The poverty level wages stipulates the lowest or minimum possible wages that a person can be paid in a functional economy. The maintenance of the poverty level wages helps the economy to remain functional and afloat.

Thus, it is a true statement that; From a functionalist view point, the U.S. economic system would be seriously strained if we completely eliminated poverty level wages."

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For two bathroom remodel estimate budget is $[tex]20000[/tex] for both remodels. when the project is finished all the supplies came in at the estimated budget except for two vanities which were each $[tex]100[/tex] less than the budgeted .So the actual cost of two bathroom remodel is $ [tex]19800[/tex] and the different of actual and expected budgets is $[tex]200[/tex]

How can we find the actual costing of the bathroom remodel ?

Expected estimate budget of two bathroom's remodel is $[tex]20000[/tex]

So budget of one bathroom remodel is

[tex]20000/2\\=10000[/tex]

All supplies are come except for two vanities which were each $[tex]100[/tex]

So for two bathroom remodels

[tex]=2*100\\=200[/tex]

So the actual cost of remodel of both bathroom is

[tex]=20000-200\\=19800[/tex]

And difference between actual and estimated cost is

[tex]=20000-19800\\=200[/tex]

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The rate of change is also known as the slope. The formula to find the slope of a line is (y2 - y1) / (x2 - x1).

You can use any two points, as long as both are on the line.

Point 1 = (2, 55)

Point 2 = (8, 220)

slope = (220 - 55) / (8 - 2)

slope = 165 / 6

slope = 55 / 2 = 27.5 / 1

Lavaughn earns $27.50 for working one hour.

Hope this helps!

The new location is in Quadrant IV and The new location has a positive x-coordinate and a negative y-coordinate. Hence, option b and c are correct.

Solution:

If the point were to reflect across the y-axis, it would fall into the fourth quadrant.

Additionally, the coordinates will be positive for the x-axis and negative for the y-axis.

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I hope you are trying to ask the question below:

Question

A point in Quadrant III is reflected across the y-axis. What is true about the new location? Check all that apply.

a. The new location is in Quadrant II.

b. The new location is in Quadrant IV.

c. The new location has a positive x-coordinate and a negative y-coordinate.

d. The new location has a negative x-coordinate and a positive y-coordinate.

e. The new location has negative x- and y-coordinates.

The true mean expenditure per student is different from $10,337.

What is hypothesis in math?

Sample size is greater than 30 and the population standard deviation is given. Thus, in order to test

H0: µ =$10,337

H1: µ≠$10,337

The appropriate test is one sample z test.

The formula for one sample z test:

Z=   x−μ / σ √ n

x−μ

​x=10798

μ=10337

σ=1560

n=150

[tex]Z = \frac{10798 - 10337}{1560 / \sqrt{150} } = 3.62[/tex]

Computation of p-value:

The EXCEL formula to find the p-value for a two-tailed z-test is

“=2*(1-NORM.S.DIST(3.62, TRUE))”

Thus, the p-value obtained is 0.00029

Conclusion using α = 0.05:

Rejection rule using p-value:

If p-value ≤ α, then reject the null hypothesis.

Since, 0.00029 < 0.05, there is sufficient evidence to reject the null hypothesis.

Therefore, the true mean expenditure per student is different from $10,337.

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Yes we can prove that in the group of more than two people that there are at least two people that have the same number friends given the condition here.

Let us create a variable P. P is an individual called Joe. Now Joes seems to know all at this party. This tells us that all at this party should at least know him.

We have the set  {1,2,...n-1} , given that the minimum number of persons that one person knows is 1.

Let us assume we have Harry. Harry is a party crasher who came to the party. Hence it is possible that someone like Joe that knows all at the party may not even know him. Hence the maximum persons that a person would know is given to be n. The set would then be {0, 1,...,n-2}.

There are n elements in the 2 sets that we have above. Given that n people are at this function, and there are n possibilities for the number that one person can know of the participants, then we can say that at least two people can then know equal number of persons at the party.

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Use a³+b³ +c³ - 3abc

Here a = 2a²

b= -a

And c = 1

Answer:

Step-by-step explanation: