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3 years ago

How many square corners does a pentagon have

1 answer:

3 0

I assume that by square corners you mean 90 degree angles. if this is the case then there are 2 in a pentagon. Hope I helped :)

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List all the possible order you can have

astra-53 [7]

wala ako pake sau

Step-by-step explanation:

wala ako pake sau

7 0

2 years ago

The height of a triangle is 5 cm shorter than its base. If the area of the triangle is 25 cm2, find the height of the triangle.

Olin [163]

Answer:

$h = 5\ cm$

Step-by-step explanation:

Let's call B at the base of the triangle and call h at the height of the triangle. Then we know that:

The height of a triangle is 5 cm shorter than its base. This means that:

$h = B-5$ .

The area of the triangle is 25 cm²

By definition the area of a triangle is:

$A = 0.5Bh$

For this triangle we know that $A = 25\ cm^2$ and $h = B-5$ . We substitute these values in the equation and solve for B.

$25 = 0.5B (B-5)$

$0.5B ^ 2-\frac{5}{2}B-25 = 0$

Now we use the quadratic formula to solve the equation.

For an equation of the form $ax ^ 2 + bx + c = 0$ the quadratic formula is:

$B=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

In this case note that: $a=0.5,\ \ b=-\frac{5}{2}\ \ c=-25$

Then:

$B=\frac{-(-\frac{5}{2})\±\sqrt{(-\frac{5}{2})^2-4(0.5)(-25)}}{2(0.5)}$

$B=\frac{\frac{5}{2}\±\sqrt{\frac{25}{4}+50}}{1}$

$B=\frac{5}{2}\±\frac{15}{2}$

The solutions are:

$B_1=\frac{5}{2}+\frac{15}{2}=10$

$B_2=\frac{5}{2}-\frac{15}{2}=-5$

For this problem we take the positive solution.

$B=10\ cm$

Now we substitute the value of B in the equation to find the height h

$h = 10-5$

$h = 5\ cm$

6 0

3 years ago

According to the National Oceanic and Atmospheric Administration, the blue whale is the largest animal on Earth. Blue whales wei

never [62]

Answer: The blue whale's weight is 150 times heavier than the narwhal's weight.

Step-by-step explanation:

Given: Weight of Blue whale = $3\times10^5\text{ pounds}$

Weight of Narwhal = $2\times10^3\text{ pounds}$

Number of times blue whale's weight is heavier than the narwhal's weight = $=\dfrac{\text{Weight of Blue whale}}{\text{Weight of Narwhal }}$

$=\dfrac{3\times10^5}{2\times10^3}\\\\=1.5\times10^{5-3}\ \ \ [\dfrac{a^m}{a^n}=a^{m-n}]\\\\=1.5\times10^2\\\\=1.5\times100=150$

Hence, the blue whale's weight is 150 times heavier than the narwhal's weight.

5 0

2 years ago

Do you know parallelogram WXYZ Parkway 270° around point W what will be the length of the image WZ

Lerok [7]

Answer:

5 units

Step-by-step explanation:

Even if there is a transformation, it is asking for the length.

Therefore the length of WZ is 5 units

7 0

2 years ago

Memory module consists of 9 chips. The device is designed with redundancy so that it works even if one of its chips is defective

soldier1979 [14.2K]

Answer:

a) $P[C]=p^n$

b) $P[M]=p^{8n}(9-8p^n)$

c) n=62

d) n=138

Step-by-step explanation:

Note: "Each chip contains n transistors"

a) A chip needs all n transistor working to function correctly. If p is the probability that a transistor is working ok, then:

$P[C]=p^n$

b) The memory module works with when even one of the chips is defective. It means it works either if 8 chips or 9 chips are ok. The probability of the chips failing is independent of each other.

We can calculate this as a binomial distribution problem, with n=9 and k≥8:

$P[M]=P[C_9]+P[C_8]\\\\P[M]=\binom{9}{9}P[C]^9(1-P[C])^0+\binom{9}{8}P[C]^8(1-P[C])^1\\\\P[M]=P[C]^9+9P[C]^8(1-P[C])\\\\P[M]=p^{9n}+9p^{8n}(1-p^n)\\\\P[M]=p^{8n}(p^{n}+9(1-p^n))\\\\P[M]=p^{8n}(9-8p^n)$

$P[M]=(0.999)^{8n}(9-8(0.999)^n)=0.9$

This equation was solved graphically and the result is that the maximum number of chips to have a reliability of the memory module equal or bigger than 0.9 is 62 transistors per chip. See picture attached.

d) If the memoty module tolerates 2 defective chips:

$P[M]=P[C_9]+P[C_8]+P[C_7]\\\\P[M]=\binom{9}{9}P[C]^9(1-P[C])^0+\binom{9}{8}P[C]^8(1-P[C])^1+\binom{9}{7}P[C]^7(1-P[C])^2\\\\P[M]=P[C]^9+9P[C]^8(1-P[C])+36P[C]^7(1-P[C])^2\\\\P[M]=p^{9n}+9p^{8n}(1-p^n)+36p^{7n}(1-p^n)^2$

We again calculate numerically and graphically and determine that the maximum number of transistor per chip in this conditions is n=138. See graph attached.

6 0

3 years ago