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3 years ago

What is the solution to the inequality 2n+5 > 1

Mathematics

2 answers:

melomori [17]3 years ago

6 0

Solve this like a regular equation:

2n + 5 > 1
2n > -4
n > -2

Hope this helped!

Darina [25.2K]3 years ago

4 0

Answer:

The solution to the inequality $2n+5>1$ is; the set of solutions of the inequality is the interval i.e, $(-2 , \infty)$

Step-by-step explanation:

To find the solution of the inequality: $2n+5>1$

Subtraction property of equality states that you subtract the same number to both sides of an equation.

Subtract 5 to both sides of an equation, we get;

$2n+5-5>1-5$

Simplify:

$2n>-4$

Division property of equality states that you divide the same number to both sides of an equation.

Divide by 4 to both sides of an equation;

$\frac{2n}{2}>\frac{-4}{2}$

Simplify:

$n > -2$

All real numbers greater than -2 satisfy the inequality.

therefore, the set of solutions of the inequality is the interval $(-2 , \infty)$

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work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company deci

NISA [10]

Answer:

Step-by-step explanation:

Here is the complete question.

Dominique, Marco, Roberto , and John work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company decides that the two individuals who get to attend will have their names drawn from a hat. This is like obtaining a simple random sample of size 2. (a) Determine the sample space of the experiment. That is, list all possible simple random samples of size n = 2. (b) What is the probability that Dominique and Marco attend the conference? (c) What is the probability that John attends the conference? (d) What is the probability that John stays home?

Since there are four employees to select the two to send from. then for us to get the sample space for the experiment we need to merge all possible two employees and represent them as set.

Let D = Dominique, M = Marco, R = Roberto and J = John

a) The sample space for the experiment is the total number of possible outcomes that we can have. It is as given below

S = 4C2 = 4!/(4-2)!2! (Selecting 2 out of 4 employees)

Total sample space = 4!/2!2!

Total sample space = 4*3*2!/2!2

Total sample space = 12/2 = 6

The sample space are S = {DM, DR, DJ, MR, MJ, RJ}

b) Probability is the ratio of number of event to the sample space.

P = n(E)/n(S)

Given n(S) = 6

n(E) is the event of Dominique and Marco attending the conference.

E = {DM}

n(E) = 1

P(D and M) = 1/6

Hence the probability that Dominique and Marco attend the conference is 1/6

c) For John to attend the conference, the event outcome will be given as;

E = {DJ, MJ, RJ}

n(E) = 3

n(S) = 6

Probability for John to attend the conference is 3/6 = 1/2

d) Probability that John stays at home = 1 - Prob (John attends the conference)

Probability that John stays at home = 1 - 1/2

Probability that John stays at home = 1/2

7 0

3 years ago

find the area of the trapezium whose parallel sides are 25 cm and 13 cm The Other sides of a Trapezium are 15 cm and 15 CM

Snezhnost [94]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - A trapezium ABCD with non parallel sides of measure 15 cm each ! along , the parallel sides are of measure 13 cm and 25 cm

To find - Area of trapezium

Refer the figure attached ~

In the given figure ,

AB = 25 cm

BC = AD = 15 cm

CD = 13 cm

Construction -

$draw \: CE \: \parallel \: AD \: \\ and \: CD \: \perp \: AE$

Now , we can clearly see that AECD is a parallelogram !

$\therefore$ AE = CD = 13 cm

Now ,

$AB = AE + BE \\\implies \: BE =AB - AE \\ \implies \: BE = 25 - 13 \\ \implies \: BE = 12 \: cm$

Now , In ∆ BCE ,

$semi \: perimeter \: (s) = \frac{15 + 15 + 12}{2} \\ \\ \implies \: s = \frac{42}{2} = 21 \: cm$

Now , by Heron's formula

$area \: of \: \triangle \: BCE = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \sqrt{21(21 - 15)(21 - 15)(21 - 12)} \\ \implies \: 21 \times 6 \times 6 \times 9 \\ \implies \: 12 \sqrt{21} \: cm {}^{2}$

Also ,

$area \: of \: \triangle \: = \frac{1}{2} \times base \times height \\ \\\implies 18 \sqrt{21} = \: \frac{1}{\cancel2} \times \cancel12 \times height \\ \\ \implies \: 18 \sqrt{21} = 6 \times height \\ \\ \implies \: height = \frac{\cancel{18} \sqrt{21} }{ \cancel 6} \\ \\ \implies \: height = 3 \sqrt{21} \: cm {}^{2}$

Since we've obtained the height now , we can easily find out the area of trapezium !

$Area \: of \: trapezium = \frac{1}{2} \times(sum \: of \:parallel \: sides) \times height \\ \\ \implies \: \frac{1}{2} \times (25 + 13) \times 3 \sqrt{21} \\ \\ \implies \: \frac{1}{\cancel2} \times \cancel{38 }\times 3 \sqrt{21} \\ \\ \implies \: 19 \times 3 \sqrt{21} \: cm {}^{2} \\ \\ \implies \: 57 \sqrt{21} \: cm {}^{2}$

hope helpful :D

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2 years ago

The World Equity Index function shown contains two valuation metrics for the S&P 500. The Verizon description page contains

Nikitich [7]

Answer: Verizon is less expensive than the S&P 500 on both a P/E and dividend yield basis.

Step-by-step explanation:

When a Price to Earnings ratio is relatively high this means that the Price of the security is high because investors believe the company has good prospects.

When a Dividend Yield is relatively low, this means that the dividends being declared are quite lower than the price because Dividend yield is dividends as a percentage of security price. Lower Dividend Yields therefore mean high security prices.

Looking at the Verizon Chart and the S&P 500 you see that Verizon P/E ratio is 11.71 while S&P is 19.01.

This means that the price of Verizon's is less than S&P 500.

Also notice that Verizon's Dividend yield is 4.09% while S&P 500's is 1.91% again signifying that Verizon is cheaper.

I have attached the full question.