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3 years ago

What is Index Law 3? please give explanation

2 answers:

8 0

The third and last law tells us that when we have to multiply a power in a bracket, by another power outside the bracket, we have to multiply the two powers together to get the answer.

rodikova [14]3 years ago

6 0

Answer:

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Step-by-step explanation:

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A pole that is 2.5 m tall casts a shadow that is 1.07 m long. At the same time, a nearby tower casts a shadow that is

valkas [14]

Answer:

The tower is 61.65 meters tall.

Step-by-step explanation:

7 0

3 years ago

the product of two integers is positive.is the quotient of those same integers positive, negative,or impossible to predict? expl

KiRa [710]

Answer:

Step-by-step explanation:

pi is irrational. That was proven long ago. Unfortunately the proof is harder to understand than the proof that the square root of 2 is irrational, which is accessible to most high school students.

To prove that p is irrational you need to understand calculus, up through integration. Even then, the proof is rather intense and takes careful attention.

8 0

2 years ago

which of the following group of numbers are all prime numbers a.2,5,15,19 b.7,17,29,49 c.3,11,23,31 d.2,3,5,9,

antoniya [11.8K]

Prime numbers are those that cannot be divided by another number (other than themselves and 1). In other words, prime numbers have factors of themselves and 1.

For example, 3 is a prime number because its only factors are 3 and 1.

6 is not a prime number because it can be factored to 3*2.

Therefore, the correct answer is c. 3,11,23,31

6 0

3 years ago

Read 2 more answers

Complete these ordered pairs for this equation. (0, ), (-2, ), (4, ) y=2x

quester [9]

Answer:

Part 1) The ordered pair is (0,0)

Part 2) The ordered pair is (-2,-4)

Part 3) The ordered pair is (4,8)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a direct variation

$y=2x$

Complete the ordered pairs

Part 1) we have (0,?)

For x=0

Substitute in the equation and solve for y

$y=2(0)=0$

therefore

The ordered pair is (0,0)

Part 2) we have (-2,?)

For x=-2

Substitute in the equation and solve for y

$y=2(-2)=-4$

therefore

The ordered pair is (-2,-4)

Part 3) we have (4,?)

For x=4

Substitute in the equation and solve for y

$y=2(4)=8$

therefore

The ordered pair is (4,8)

3 0

3 years ago

Two machines are used for filling plastic bottles to a net volume of 16.0 ounces. A member of the quality engineering staff susp

aleksandrvk [35]

Answer:

Step-by-step explanation:

Hello!

The objective is to test if the two machines are filling the bottles with a net volume of 16.0 ounces or if at least one of them is different.

The parameter of interest is μ₁ - μ₂, if both machines are filling the same net volume this difference will be zero, if not it will be different.

You have one sample of ten bottles filled by each machine and the net volume of the bottles are measured, determining two variables of interest:

Sample 1 - Machine 1

X₁: Net volume of a plastic bottle filled by the machine 1.

n₁= 10

X[bar]₁= 16.02

S₁= 0.03

Sample 2 - Machine 2

X₂: Net volume of a plastic bottle filled by the machine 2

n₂= 10

X[bar]₂= 16.01

S₂= 0.03

With p-values 0.4209 (for X₁) and 0.6174 (for X₂) for the normality test and using α: 0.05, we can say that both variables of interest have a normal distribution:

X₁~N(μ₁;δ₁²)

X₂~N(μ₂;δ₂²)

Both population variances are unknown you have to conduct a homogeneity of variances test to see if they are equal (if they are you can conduct a pooled t-test) or different (if the variances are different you have to use the Welche's t-test)

H₀: δ₁²/δ₂²=1

H₁: δ₁²/δ₂²≠1

α: 0.05

$F= \frac{S^2_1}{S^2_2} * \frac{Sigma^2_1}{Sigma^2_2} ~~F_{n_1-1;n_2-1}$

Using a statistic software I've calculated the test

$F_{H_0}= 1.41$

p-value 0.6168

The p-value is greater than the significance level, so the decision is to not reject the null hypothesis then you can conclude that both population variances for the net volume filled in the plastic bottles by machines 1 and 2 are equal.

To study the difference between the population means you can use

$t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2}{Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}$

The hypotheses of interest are:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

α: 0.05

$Sa= \sqrt{\frac{(n_1-1)S^2_1+(N_2-1)S^2_2}{n_1+n_2-2}} = \sqrt{\frac{9*9.2*10^{-4}+9*6.5*10^{-4}}{10+10-2} } = 0.028= 0.03$

$t_{H_0}= \frac{(16.02-16.01)-0}{0.03*\sqrt{\frac{1}{10} +\frac{1}{10} } } = 0.149= 0.15$

The p-value for this test is: 0.882433

The p-value is greater than the significance level, the decision is to not reject the null hypothesis.

Using a significance level of 5%, there is no significant evidence to reject the null hypothesis. You can conclude that the population average of the net volume of the plastic bottles filled by machine one and by machine 2 are equal.

I hope this helps!

8 0

3 years ago