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il63 [147K]
3 years ago
7

Find the values of the unknown constants for the identities

Mathematics
1 answer:
ankoles [38]3 years ago
5 0

Answer:

a = 1 and b = - 10

Step-by-step explanation:

Expand the right side of the identity

x(ax² - 3x + b) - 3(ax² - 3x + b)

= ax³ - 3x² + bx - 3ax² + 9x - 3b

= ax³ - x²(3 + 3a) + x(b + 9) - 3b

Equate the coefficients of like terms on both sides of the identity

x³ terms → ax³ with x³ ⇒ a = 1

x terms → - x with (b + 9)x ⇒ b + 9 = - 1 ⇒ b = - 10


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What is the value of t?
frutty [35]

Answer:

-39 2/3

Step-by-step explanation:

t - 122= 2t - 3

subtract 't' from each side to get:

-122 = 3t - 3

add 3 to each side to get:

-119 = 3t

divide each side by 3 to get:

t = -39 2/3

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2 years ago
Is 18/54 equivalent to 3/9?
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A pair of shoes costs $30.99 and the state sales tax is 5%. Use the formula C = p + rp to find the total cost of the shoes, wher
liberstina [14]
First, write the rate as a decimal by moving the decimal point two places to the left from the percent.

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Answer: The total cost is $32.54
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6 0
2 years ago
A given population proportion is .25. What is the probability of getting each of the following sample proportions
anyanavicka [17]

This question is incomplete, the complete question is;

A given population proportion is .25. What is the probability of getting each of the following sample proportions

a) n = 110 and = p^ ≤ 0.21, prob = ?

b) n = 33 and p^ > 0.24, prob = ?

Round all z values to 2 decimal places. Round all intermediate calculation and answers to 4 decimal places.)

Answer:

a) the probability of getting the sample proportion is 0.1660

b) the probability of getting the sample proportion is 0.5517

Step-by-step explanation:

Given the data in the questions

a)

population proportion = 0.25

q = 1 - p = 1 - 0.25 = 0.75

sample size n = 110

mean = μ = 0.25

S.D = √( p( 1 - p) / n ) = √(0.25( 1 - 0.25) / 110 ) √( 0.1875 / 110 ) = 0.0413

Now, P( p^ ≤ 0.21 )

= P[ (( p^ - μ ) /S.D) < (( 0.21 - μ ) / S.D)

= P[ Z < ( 0.21 - 0.25 ) / 0.0413)

= P[ Z < -0.04 / 0.0413]

= P[ Z < -0.97 ]

from z-score table

P( X ≤ 0.21 ) = 0.1660

Therefore, the probability of getting the sample proportion is 0.1660

b)

population proportion = 0.25

q = 1 - p = 1 - 0.25 = 0.75

sample size n = 33

mean = μ = 0.25

S.D = √( p( 1 - p) / n ) = √(0.25( 1 - 0.25) / 33 ) = √( 0.1875 / 33 ) = 0.0754

Now, P( p^ > 0.24 )  

= P[ (( p^ - μ ) /S.D) > (( 0.24 - μ ) / S.D)

= P[ Z > ( 0.24 - 0.25 ) / 0.0754 )

= P[ Z > -0.01 / 0.0754  ]

= P[ Z > -0.13 ]

= 1 - P[ Z < -0.13 ]

from z-score table

{P[ Z < -0.13 ] = 0.4483}

1 - 0.4483

P( p^ > 0.24 )  = 0.5517

Therefore, the probability of getting the sample proportion is 0.5517

6 0
2 years ago
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