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4 years ago

PLEASE HELP!!!!!! the sum of a number times 10 and 15 is at most -17

Mathematics

1 answer:

Brilliant_brown [7]4 years ago

3 0

Let the number = x

Writing the equation you have:

10x + 15 <= -17

Solve for x

Subtract 15 from both sides:

10x <= -32

Divide both sides by 10:

X <= -32/10

Simplify:

X <= -16/5 as a fraction or -3.2 as a decimal

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Answer:

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2 years ago

6) Supplementary Exercise 5.51

tresset_1 [31]

Answer:

$P(X \le 4) = 0.7373$

$P(x \le 15) = 0.0173$

$P(x > 20) = 0.4207$

$P(20\ge x \le 24)= 0.6129$

$P(x = 24) = 0.0236$

$P(x = 15) = 1.18\%$

Step-by-step explanation:

Given

$p = 80\% = 0.8$

The question illustrates binomial distribution and will be solved using:

$P(X = x) = ^nC_xp^x(1 - p)^{n-x}$

Solving (a):

Given

$n =5$

Required

$P(X\ge 4)$

This is calculated using

$P(X \le 4) = P(x = 4) +P(x=5)$

This gives:

$P(X \le 4) = ^5C_4 * (0.8)^4*(1 - 0.8)^{5-4} + ^5C_5*0.8^5*(1 - 0.8)^{5-5}$

$P(X \le 4) = 5 * (0.8)^4*(0.2)^1 + 1*0.8^5*(0.2)^0$

$P(X \le 4) = 0.4096 + 0.32768$

$P(X \le 4) = 0.73728$

$P(X \le 4) = 0.7373$ --- approximated

Solving (b):

Given

$n =25$

Required

$P(X\le 15)$

This is calculated as:

$P(X\le 15) = 1 - P(x>15)$ --- Complement rule

$P(x>15) = P(x=16) + P(x=17) + P(x =18) + P(x = 19) + P(x = 20) + P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)$

$P(x > 15) = {25}^C_{16} * p^{16}*(1-p)^{25-16} +{25}^C_{17} * p^{17}*(1-p)^{25-17} +{25}^C_{18} * p^{18}*(1-p)^{25-18} +{25}^C_{19} * p^{19}*(1-p)^{25-19} +{25}^C_{20} * p^{20}*(1-p)^{25-20} +{25}^C_{21} * p^{21}*(1-p)^{25-21} +{25}^C_{22} * p^{22}*(1-p)^{25-22} +{25}^C_{23} * p^{23}*(1-p)^{25-23} +{25}^C_{24} * p^{24}*(1-p)^{25-24} +{25}^C_{25} * p^{25}*(1-p)^{25-25}$

$P(x > 15) = 2042975 * 0.8^{16}*0.2^9 +1081575* 0.8^{17}*0.2^8 +480700 * 0.8^{18}*0.2^7 +177100 * 0.8^{19}*0.2^6 +53130 * 0.8^{20}*0.2^5 +12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1 +1 * 0.8^{25}*0.2^0$

$P(x > 15) = 0.98266813045$

So:

$P(X\le 15) = 1 - P(x>15)$

$P(x \le 15) = 1 - 0.98266813045$

$P(x \le 15) = 0.01733186955$

$P(x \le 15) = 0.0173$

ii)

$P(x>20)$

This is calculated as:

$P(x>20) = P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)$

$P(x > 20) = 12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1 +1 * 0.8^{25}*0.2^0$

$P(x > 20) = 0.42067430925$

$P(x > 20) = 0.4207$

iii)

$P(20\ge x \le 24)$

This is calculated as:

$P(20\ge x \le 24) = P(x = 20) + P(x = 21) + P(x = 22) + P(x =23) + P(x = 24)$

$P(20\ge x \le 24)= 53130 * 0.8^{20}*0.2^5 +12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1$

$P(20\ge x \le 24)= 0.61291151859$

$P(20\ge x \le 24)= 0.6129$

iv)

$P(x = 24)$

This is calculated as:

$P(x = 24) = 25* 0.8^{24}*0.2^1$

$P(x = 24) = 0.0236$

Solving (c):

$P(x = 15)$

This is calculated as:

$P(x = 15) = {25}^C_{15} * 0.8^{15} * 0.2^{10}$

$P(x = 15) = 3268760 * 0.8^{15} * 0.2^{10}$

$P(x = 15) = 0.01177694905$

$P(x = 15) = 0.0118$

Express as percentage

$P(x = 15) = 1.18\%$

The calculated probability (1.18%) is way less than the advocate's claim.

Hence, we do not believe the claim.

5 0

3 years ago

Find the surface area of a square pyramid whose base edge is 6cm and whose slant edge is 5cm

dmitriy555 [2]

Check the picture below.

so let's notice, the base is a 6x6 square, and triangular faces have a base of 6 and an altitude/height of 5. So we can just get the area of the square and the triangles and sum them up and that's the area of the pyramid.

$\bf \stackrel{\textit{triangles' area}}{4\left[ \cfrac{1}{2}(6)(5) \right]}+\stackrel{\textit{square's area}}{(6\cdot 6)}\implies 60+36\implies 96$

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svlad2 [7]

Answer:

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Step-by-step explanation:

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