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Rama09 [41]
3 years ago
15

Which pair of expressions is equivalent using the Associative Property of Multiplication?

Mathematics
2 answers:
ehidna [41]3 years ago
8 0

Answer: 6(4a\cdot2)=(6\cdot4a)\cdot2

Step-by-step explanation:

The associative property of multiplication says that when we multiply three or more than three real numbers, the product is always the same nevertheless of their regrouping by using parenthesis.

i.e. a\cdot(b\cdot c)=(a\cdot b)\cdot c

Hence, the right option is 6(4a\cdot2)=(6\cdot4a)\cdot2

ki77a [65]3 years ago
6 0
<span>6(4a ⋅ 2) = (6 ⋅ 4a) ⋅ 2</span>
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Reliance on solid biomass fuel for cooking and heating exposes many children from developing countries to high levels of indoor
kherson [118]

Answer:

A) 95% confidence interval for the population mean PEF for children in biomass households = (3.314, 3.486)

95% confidence interval for the population mean PEF for children in LPG households

= (4.195, 4.365)

Simultaneous confidence interval for both = (3.314, 4.365)

B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.

C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.365)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Step-by-step explanation:

A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.

Finding the critical value from the z-tables,

z-critical value for 95% confidence level = 1.960 (from the z-tables)

For the children in the biomass households

Sample mean = 3.40

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.20

N = sample size = 756

σₓ = (1.20/√756) = 0.04364

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 3.40 ± (1.960 × 0.04364)

CI = 3.40 ± 0.08554

95% CI = (3.31446, 3.48554)

95% Confidence interval = (3.314, 3.486)

For the children in the LPG households

Sample mean = 4.28

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.19

N = sample size = 752

σₓ = (1.19/√752) = 0.043395

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 4.28 ± (1.960 × 0.043395)

CI = 4.28 ± 0.085054

95% CI = (4.1949, 4.3651)

95% Confidence interval = (4.195, 4.365)

Simultaneous confidence interval for both = (3.214, 4.375)

B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.

The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.

Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂

The null hypothesis is

H₀: μ ≥ 0 or μ₁ ≥ μ₂

The alternative hypothesis is

Hₐ: μ < 0 or μ₁ < μ₂

Test statistic for 2 sample mean data is given as

Test statistic = (μ₂ - μ₁)/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = 3.40

n₁ = 756

s₁ = 1.20

μ₂ = 4.28

n₂ = 752

s₂ = 1.19

σ = √[(1.20²/756) + (1.19²/752)] = 0.061546

z = (3.40 - 4.28) ÷ 0.061546 = -14.30

checking the tables for the p-value of this z-statistic

Significance level = 0.01

The hypothesis test uses a one-tailed condition because we're testing in only one direction.

p-value (for z = -14.30, at 0.01 significance level, with a one tailed condition) = 0.000000001

The interpretation of p-values is that

When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.

Significance level = 0.01

p-value = 0.000000001

0.000000001 < 0.01

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.

C) For FEY for biomass households,

Sample mean = 2.3 L/s

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation = 0.5

N = sample size = 756

σₓ = (0.5/√756) = 0.018185

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 2.30 ± (1.960 × 0.018185)

CI = 2.30 ± 0.03564

95% CI = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.365)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Hope this Helps!!!

3 0
3 years ago
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Serjik [45]
37 degrees Ill explain in a second but thats it!

6 0
3 years ago
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kakasveta [241]
He goes 1.5k/h. To get that you divide the km by the hour. Then multiply the hour by 1.5 to get the km. (Ex. 2hrs x 1.5km = 3km)
6 0
2 years ago
Please resolve this is for today
Fynjy0 [20]

Answer:

A Square plus B square equals

Step-by-step explanation:

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5 0
3 years ago
Is the following statement a good definition? Why? An integer is divisible by 100 if and only if its last two digits are zeros.
kifflom [539]
The given statement is:
An integer is divisible by 100 if and only if its last two digits are zeros

The two conditional statements that can be made are:

1) If an integer is divisible by 100 its last two digits are zeros.

This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have last two digits zeros. 

2) If the last two digits of an integer are zeros, it is divisible by 100.

This is also true. If last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.

Therefore, the two conditional statements that are formed are both true.

So, the option A is the correct answer.
Yes, it is. When the definition is separated into two conditional statements, both of the statements are true
6 0
3 years ago
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