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Salsk061 [2.6K]

3 years ago

10

What Is The scale factor of the dilation? A)-1/2 B)1/2 C)-2 D)2

1 answer:

Vadim26 [7]3 years ago

5 0

Answer:

B) 1/2

Step-by-step explanation:

You might be interested in

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

$n =25$

i)

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

Factor completely.<br> (X^2+ x – 6)(2x^2 + 4x) =<br> What’s the answer

lyudmila [28]

Answer:

(X^2+x−6)⋅2x(x+2

Step-by-step explanation:

7 0

3 years ago

Lina has 12 coins in her purse. D of them are dimes and the rest are quarters.

tester [92]

Answer:

we need more info but 11 q and 1 dime or 12 q and 0 dime

Step-by-step explanation:

Sorry need more info

7 0

4 years ago

Evaluate w (-9).<br> w (n) = n2 +5

Artyom0805 [142]

Answer:

w(-9) = 86

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Algebra I</u>

Function Notation

Step-by-step explanation:

<u>Step 1: Define</u>

w(n) = n² + 6

w(-9) is n = -9

<u>Step 2: Evaluate</u>

Substitute: w(-9) = (-9)² + 5
Exponents: w(-9) = 81 + 5
Add: w(-9) = 86

5 0

3 years ago

Which stress rating describes the greatest number of students? How many students responded with this rating?

vlada-n [284]

Answer:

24

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers