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2 years ago

Kerel is creating a rectangular dog run in his backyard. The length of the dog run is

Mathematics

2 answers:

Rama09 [41]2 years ago

8 0

The range of values for the width of the dog run is 73.5 ≥ w ≤ 237

<h3>Compound inequality</h3>

Perimeter of a rectangle = 2(length + width)

Length = 67 feet
Width = w

The inequality:

281 ≥ 2(67 + w) ≤ 608

281 ≥ 134 + 2w ≤ 608

solve independently

281 ≥ 134 + 2w

281 - 134 ≥ 2w

147 ≥ 2w

w ≥ 147/2

w ≥ 73.5

2(67 + w) ≤ 608

134 + 2w ≤ 608

2w ≤ 608 - 134

2w ≤ 474

w ≤ 474 / 2

w ≤ 237

Learn more about inequality:

brainly.com/question/25275758

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Hunter-Best [27]2 years ago

3 0

The width of the dug run is 73.5 ≤ w ≤ 237

<h3>What is a compound inequality?</h3>

A compound inequality is an inequality formed by combining two simple inequalities.

Analysis:

Let the width of dug run be w

perimeter = 2(67 + w) = 134 + 2w

281 ≤ 134 + 2w

147 ≤ 2w

73.5 ≤ w

Also, 134 + 2w ≤ 608

2w ≤ 474, w ≤237

In conclusion, the range of values of the width of the dug run is 73.5≤w≤237

Learn more about compound inequality: brainly.com/question/1604153

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Step-by-step explanation:

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Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,...

katovenus [111]

Answer:

$a_{12}=-244140625$

Step-by-step explanation:

Considering the geometric sequence

$5,-25,\:125,\:...$

$a_1=5$

As the common ratio ' $r$ ' between consecutive terms is constant.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$r=\frac{-25}{5}=-5$

$r=\frac{125}{-25}=-5$

The general term of a geometric sequence is given by the formula:

$a_n=a_1\cdot \:r^{n-1}$

where $a_1$ is the initial term and $r$ the common ratio.

Putting $n = 12$ , $r = -5$ and $a_1=5$ in the general term of a geometric sequence to determine the 12th term of the sequence.

$a_n=a_1\cdot \:r^{n-1}$

$a_n=5\left(-5\right)^{n-1}$

$a_{12}=5\left(-5\right)^{12-1}$

$=5\left(-5^{11}\right)$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$=-5\cdot \:5^{11}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$=-5^{1+11}$ ∵ $5\cdot \:5^{11}=\:5^{1+11}$

$=-244140625$

Therefore,

$a_{12}=-244140625$

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3 years ago

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Answer:

$P(X \geq 1)=1-P(X$

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And replacing we got:

$P(X \geq 1) = 1-0.9801 = 0.0199$

Step-by-step explanation:

Let X the random variable of interest "number of craked eggs", on this case we now that:

$X \sim Binom(n=2, p=0.01)$

The probability mass function for the Binomial distribution is given as:

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Where (nCx) means combinatory and it's given by this formula:

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

And we want to find this probability:

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And we can find the probability:

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And replacing we got:

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Answer:

The answer in the procedure

Step-by-step explanation:

The question does not present the graph, however it can be answered to help the student solve similar problems.

we know that

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$f(x)=a(x-h)^{2}+k$

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case A) we have

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case B) we have

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therefore

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