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xxTIMURxx [149]
2 years ago
11

(90 POINTS) Explain how to solve 3ˣ⁻⁴ = 6 using the change of base formula. Include the solution for x in your answer. Round you

r answer to the nearest thousandth.
Mathematics
1 answer:
IceJOKER [234]2 years ago
7 0

Given: 3^(x − 4) = 6

To find: Solution to the given expression using change of base formula

Answer: The given expression is 3^(x − 4) = 6 Taking log on both sides, we get - log(3^(x − 4)) = log6

(x - 4) log3 = log6

x - 4 = log6/ log3

x - 4 =   (∵ change of base formula)

x - 4 = 1.631

x = 5.631

Thus x = 5.631 is the answer in the nearest thousandth.

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A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If
Alinara [238K]

Answer:

Test statistic  z= 1.708

Step-by-step explanation:

given that a  television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot.

Sample size n = 827

Sample proportion p = \frac{438}{827} \\=0.5297

H_0: p =0.5\\H_a: p >0.5

(right tailed test)

This is because they would be interested if more than half viewers are ready for the change

Test statistic = Z = p difference/std error

p difference = 0.0297

Std error =\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.5*0.5}{827} } \\=0.0174

Z =1.708

p valu e= 0.9562

Since p >0.05 we fail to reject H0

Test statistic  z= 1.708

8 0
3 years ago
What is the area of a rectangle with vertices at (−3, −1), (1, 3), (3, 1), and (−1, −3)?
Jobisdone [24]

Using the distance formula, the area of the rectangle is: 16 units².

<h3>What is the Area of a Rectangle?</h3>

Area of a rectangle = (length)(width).

Given the vertices:

  • A(−3, −1)
  • B(1, 3)
  • C(3, 1)
  • D(−1, −3)

Area = (AB)(BC)

Apply the distance formula, d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, to find AB and BC:

AB = √[(1−(−3))² + (3−(−1))²]

AB = √[(4)² + (4)²]

AB = √32

BC = √[(1−3)² + (3−1)²]

BC = √[(−2)² + (2)²]

BC = √8

Area = (√32)(√8) = √256

Area = 16 units²

Learn more about area of rectangle on:

brainly.com/question/25292087

#SPJ1

6 0
3 years ago
What is the area<br> of this no<br> rectangle?
LUCKY_DIMON [66]

Answer:

60

Step-by-step explanation:

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3 years ago
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Jun swims 18 laps and Mara swims 25 laps. How many fewer laps did Jun swim than Mara ?
marysya [2.9K]

Answer:

7

Step-by-step explanation:

All you have to do to solve this is subtract 18 from 25

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3 years ago
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