(5+6b^3)^2 expand and combine like terms

Emmet rolls a number cube. In 5 out of 24 trials, he rolls a six. What is the

V125BC [204]

Answer:

A.

Step-by-step explanation:

3 0

2 years ago

harry invests £6000 in a savings account. the account pays 3.4% compound interest per year. work out the value of his investment

Nataly_w [17]

Invested amount (P0 = £6000.

Rate of interest (r) = 3.4% = 0.034.

We know compound interest formula

A = P(1+r)^t

We need work out the value of his investment per year.

So, we need to plug t=1 and plugging values of P and r in the formula above, we get

A = 6000(1+0.034)^1

A = 6000(1.034)

A = 6204.

<h3>Therefore, the value of his investment per year is £ 6204.</h3>

Now, we need to work out the value of his investment after 3 years.

So, we need to plug t=3.

A = 6000(1+0.034)^3

A = 6000(1.034)^3

1.034^3=1.105507304

A = 6000 × 1.105507304

A = 6633.04

<h3>Therefore, the value of his investment after 3 year is £ 6633.04.</h3>

6 0

2 years ago

An ant weigh 0.000003 kg. How much would 2 ants weigh, expressed in scientific notation?

Alik [6]

The correct answer is 6*10^-6 ..........................

5 0

3 years ago

In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from

Maksim231197 [3]

Answer:

$z=\frac{0.0003214 -0.00034}{\sqrt{\frac{0.00034(1-0.00034)}{420095}}}=-0.654$

$p_v =2*P(Z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.005$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.

Step-by-step explanation:

1) Data given and notation

n=420095 represent the random sample taken

X=135 represent the subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)

$\hat p=\frac{135}{420095}=0.0003214$ estimated proportion of subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)

$p_o=0.00034$ is the value that we want to test

$\alpha=0.005$ represent the significance level

Confidence=99.5% or 0.995

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the brain or nervous system at a rate that is different from the rate of 0.0340% :

Null hypothesis: $p=0.00034$

Alternative hypothesis: $p \neq 0.00034$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.0003214 -0.00034}{\sqrt{\frac{0.00034(1-0.00034)}{420095}}}=-0.654$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.005$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.005$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.

4 0

3 years ago

A Square was altered so that one side is increased by 9 inches in the other side is decreased by 2 inches.The area of the result

LekaFEV [45]

Let s represent the length of any one side of the original square. The longer side of the resulting rectangle is s + 9 and the shorter side s - 2.

The area of this rectangle is (s+9)(s-2) = 60 in^2.

This is a quadratic equation and can be solved using various methods. Let's rewrite this equation in standard form: s^2 + 7s - 18 = 60, or:

s^2 + 7s - 78 = 0. This factors as follows: (s+13)(s-6)=0, so that s = -13 and s= 6. Discard s = -13, since the side length cannot be negative. Then s = 6, and the area of the original square was 36 in^2.

4 0

2 years ago