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krok68 [10]
3 years ago
14

According to a recent study, the carapace length for adult males of a certain species of tarantula are normally distributed with

mean of u = 18.55 mm
and a standard deviation of o = 1.51 mm. Complete parts (a) through (d) below.
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
a. Find the percentage of the tarantulas that have a carapace length between 17 mm and 18 mm.
Mathematics
1 answer:
seraphim [82]3 years ago
3 0
Idk tbh sorry bye ok hbye
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Use lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point (0, 2, 5).
horsena [70]
Lagrangian:

L(x,y,z,\lambda)=x^2+(y-2)^2+(z-5)^2+\lambda(x-2y+3z-6)

where the function we want to minimize is actually \sqrt{x^2+(y-2)^2+(z-5)^2}, but it's easy to see that \sqrt{f(\mathbf x)} and f(\mathbf x) have critical points at the same vector \mathbf x.

Derivatives of the Lagrangian set equal to zero:

L_x=2x+\lambda=0\implies x=-\dfrac\lambda2
L_y=2(y-2)-2\lambda=0\implies y=2+\lambda
L_z=2(z-5)+3\lambda=0\implies z=5-\dfrac{3\lambda}2
L_\lambda=x-2y+3z-6=0

Substituting the first three equations into the fourth gives

-\dfrac\lambda2-2(2+\lambda)+3\left(5-\dfrac{3\lambda}2\right)=6
11-7\lambda=6\implies \lambda=\dfrac57

Solving for x,y,z, we get a single critical point at \left(-\dfrac5{14},\dfrac{19}7,\dfrac{55}{14}\right), which in turn gives the least distance between the plane and (0, 2, 5) of \dfrac5{\sqrt{14}}.
7 0
3 years ago
The cost of one pound of peanuts is 60% of the cost of one pound of cashews. If one pound of cashews costs $2, what is the cost
Sophie [7]
Based on the given problem above, this would appear that,
one pound of peanuts = 0.60*2 = $1.2
one pound of cashews = $2
Therefore, the cost of one pound of peanuts is $1.2.
The total cost of two pounds of peanuts and one pound of cashews would be this: 1.2 + 1.2 + 2 = $4.4
Hope this answers your question. 
8 0
3 years ago
What is the HCF of two consecutive numbers?
Luba_88 [7]

Answer:  The HCF o two consecutive numbers is always one.

Step-by-step explanation: The reason behind this is that the two consecutive numbers do not have any common factor other than 1. Hence 1 becomes the highest common factor between two consecutive numbers

please mark brainliest

6 0
2 years ago
What are the roots of f(x) = x2 – 48? –48 and 48 –24 and 24 Negative 8 StartRoot 3 EndRoot and 8 StartRoot 3 EndRoot Negative 4
Ivanshal [37]

Answer:

x=4\sqrt{3},\:x=-4\sqrt{3} are the roots.

Step-by-step explanation:

x=4\sqrt{3},\:x=-4\sqrt{3}

Considering the expression

x^2\:-\:48

Solving

x^2-48=0

x^2-48+48=0+48

x^2=48

\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

x=\sqrt{48},\:x=-\sqrt{48}

Solving

x=\sqrt{48}

  = \sqrt{2^4\cdot \:3}

  \mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}

  = \sqrt{3}\sqrt{2^4}

  \mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^m}=a^{\frac{m}{n}}

  \sqrt{2^4}=2^{\frac{4}{2}}=2^2

  =2^2\sqrt{3}

  =4\sqrt{3}

So,

x=4\sqrt{3}

Similarly,

x=-\sqrt{48}=-4\sqrt{3}

Therefore, x=4\sqrt{3},\:x=-4\sqrt{3} are the roots.

Keywords: roots, expression

Learn more about roots from brainly.com/question/3731376

#learnwithBrainly

9 0
3 years ago
Read 2 more answers
Please can someone help me with this question?
zhannawk [14.2K]

Answer:

a = 16 π cm²      Exact answer

a = 50.24 cm²       Decimal approximation

Step-by-step explanation:

Radius of the circle

16/2 = 8

Area of the circle

a = πr²

a = π4²

a = 16 π cm²      Exact answer

a = 16 * 3.14

a = 50.24 cm²       Decimal approximation

7 0
2 years ago
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