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4 years ago

10 POINTS ARE AWARDED! :(

Mathematics

1 answer:

alex41 [277]4 years ago

8 0

Answer:

Step-by-step explanation:

To solve indices problems you need to know the laws of indices.

The laws will guide you in answering any problem related to indices, these laws are for a ≠ 0

law 1

aᵇ * aⁿ = aᵇ⁺ⁿ

example 5³ * 5⁵ = 5³⁺⁵= 5⁸

law 2

aᵇ / aⁿ = aᵇ⁻ⁿ

example 7⁵/ 7³ = 7⁵⁻³ = 7²

law 3

(aᵇ)ⁿ = aᵇⁿ

example (5³)⁴ = 5³ * 5⁴ = 5¹²

law 4

a⁰ = 1

example 8⁰ = 1

law 5

a⁻ⁿ = 1/aⁿ

example 7⁻² = 1/7² = 1/49

law 6

a^¹/ₙ = ⁿ√a

example 27^¹/₃ = ∛27 = 3

law 7

a^ᵇ/ₙ = (ⁿ√a)ᵇ = ⁿ√aᵇ

example 8^²/₃ = (∛8)² = (2)² = 4

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Find the median of following test grades: 100 80 70 90 100

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Answer:

Step-by-step explanation:

The Median can be found by finding the number in the middle of the set after ordering the numbers from least to greatest.

Order the numbers from least to greatest:

70, 80, 90, 100, 100

90 is the number in the middle of the set, therefore, 90 is your answer.

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A snail is 20 inches above the ground. It slips down 6 inches and then creeps up 12 inches. What is the snail's height now?

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Step-by-step explanation:

20 inches minus 6 inches plus 12

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It’s been found that 85% of American adults suffer from triskaidekaphobia (fear of the number 13). Researchers think this is too

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Answer:

Null Hypothesis, $H_0$ : p $\leq$ 85%

Alternate Hypothesis, $H_A$ : p > 85%

Step-by-step explanation:

We are given that it's been found that 85% of American adults suffer from triskaidekaphobia (fear of the number 13).

A USA Today/Gallup poll asked 1,006 randomly selected people 18 years old and older in telephone interviews "Suppose you checked into a hotel and were given a room on the thirteenth floor. Would this bother you or not?" 87% of the survey respondents answered they would be bothered.

Let p = proportion of respondents who would be bothered about given a room on the thirteenth floor

SO, Null Hypothesis, $H_0$ : p $\leq$ 85%

Alternate Hypothesis, $H_A$ : p > 85%

Here, null hypothesis states that the proportion of respondents who would be bothered about given a room on the thirteenth floor is less than or equal to 85%.

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In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled a

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Answer:

T = - 7.5 Cos π/12( t - 4 ) + 10.5

Step-by-step explanation:

Given that the

Maximum temp. = 18 degree Celsius

Minimum temp. = 3 degree Celsius

The half way between 10 am and 10 pm is 4 am

The sine and cosine functions can be used to model fluctuations in temperature data through out the year. An equation that can be used to model these data is of the form:

T = A cos B(t - C) + D, where A,B,C,D, are constants, T is the temperature in °C and t is the hour (1–24)

A = amplitude = (Tmax - Tmin)/2

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C = units translated to the right

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D = ymin + amplitude = units translated up

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