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2 years ago

Write 4.7 as a mixed number with a fraction in simplest form.

Mathematics

2 answers:

julia-pushkina [17]2 years ago

8 0

4.7 = 4 + 0.7
7/10
4 7/10

Answer: D)

lozanna [386]2 years ago

3 0

Answer:

D) 4 7/10

Step-by-step explanation:

Any fraction may be written as a mixed number. This type of number is formed by one or more whole parts plus a fractional part.

4.7 = 4 + 0.7

4 + 7/10

4 7/10

Following this same reasoning we can turn a mixed number into improper fraction and improper fraction into mixed number.

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Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The filling processes can be assumed to be n

CaHeK987 [17]

Answer:

a) Null hypothesis: $\mu_{1}-\mu_{2}=0$

Alternative hypothesis: $\mu_{1} - \mu_{2}\neq 0$

b) $z=\frac{(16.015-16.005)-0}{\sqrt{\frac{0.015^2}{10}+\frac{0.018^2}{10}}}=1.350$

c) Since is a bilateral test the p value would be:

$p_v =2*P(z>1.350)=0.177$

Comparing the p value with the significance level $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and the difference between the two groups is NOT significantly different.

d) $0.01-1.96\sqrt{\frac{0.015^2}{10}+\frac{0.018^2}{10}}=-0.0045$

$0.01+1.96\sqrt{\frac{0.015^2}{10}+\frac{0.018^2}{10}}=0.025$

So on this case the 95% confidence interval would be given by $-0.0045 \leq \mu_1 -\mu_2 \leq 0.025[/tex] Step-by-step explanation:For this case we have the following info:Machine 1: 16.03 16.01 16.04 15.96 16.05 15.98 16.05 16.02 16.02 15.99Machine 2: 16.02 16.03 15.97 16.04 15.96 16.02 16.01 16.01 15.99 16.00We can calculate the sample mean with the following formula:[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}$

$\bar X_{1}=16.015$ represent the mean for sample 1

$\bar X_{2}=16.005$ represent the mean for sample 2

$\sigma_{1}=0.015$ represent the population standard deviation for 1

$\sigma_{2}=0.018$ represent the sample standard deviation for 2

$n_{1}=10$ sample size for the group 2

$n_{2}=10$ sample size for the group 2

Significance level provided

z would represent the statistic (variable of interest)

Concepts and formulas to use

Part a

We need to conduct a hypothesis in order to check if the difference in the population means, the system of hypothesis would be:

Null hypothesis: $\mu_{1}-\mu_{2}=0$

Alternative hypothesis: $\mu_{1} - \mu_{2}\neq 0$

We have the population standard deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

Part b

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

With the info given we can replace in formula (1) like this:

$z=\frac{(16.015-16.005)-0}{\sqrt{\frac{0.015^2}{10}+\frac{0.018^2}{10}}}=1.350$

Part c

P value

Since is a bilateral test the p value would be:

$p_v =2*P(z>1.350)=0.177$

Part d

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =16.015-16.005=0.01$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Confidence interval

Now we have everything in order to replace into formula (1):

$0.01-1.96\sqrt{\frac{0.015^2}{10}+\frac{0.018^2}{10}}=-0.0045$

$0.01+1.96\sqrt{\frac{0.015^2}{10}+\frac{0.018^2}{10}}=0.025$

So on this case the 95% confidence interval would be given by $-0.0045 \leq \mu_1 -\mu_2 \leq 0.025$

5 0

2 years ago

Please I'm in urgent need of help. what must be added to make (1/4)x^2-(2/3)xy a perfect square?.

Ipatiy [6.2K]

Answer:

$\bigg(\frac{2}{3} {y} \bigg)^{2}$

STEP BY STEP EXPLANATION

$\frac{1}{4} {x}^{2} - \bigg( \frac{2}{3} \bigg)xy \\ \\ = \bigg(\frac{1}{2} {x} \bigg)^{2} - 2. \bigg(\frac{1}{2} {x} \bigg)\bigg( \frac{2}{3} y \bigg ) + \bigg(\frac{2}{3} {y} \bigg)^{2} \\ \\ = \bigg(\frac{1}{2} {x} - \frac{2}{3} y\bigg)^{2} \\$

To make $\red{\bold{\frac{1}{4} {x}^{2} - \bigg( \frac{2}{3} \bigg)xy}}$ a perfect square we should add $\purple{\bold{\bigg(\frac{2}{3} {y} \bigg)^{2}}}$

8 0

1 year ago

Read 2 more answers

PLEASE HELP ME!!!!!!!!!

Genrish500 [490]

Develop a passion for learning. If you do, you will never cease to grow.

7 0

2 years ago

Pls help me on this!

Ira Lisetskai [31]

Answer:

5 2/3

Step-by-step explanation:

So because it is a mixed number that means you want to have a whole plus a fraction. You keep the 5 as the whole and because 2/3=.666666. You add them together making 5 2/3.

3 0

2 years ago

Point x is located at (-2,-6) and point z is located at (0,5). Find the y value for the point y that is located 1/5 the disteanc

Sedaia [141]

Answer:

-3 1/2

Step-by-step explanation:

We have to find the distance between x and z along the y-axis.

This will be: 5 - -6 = 11 units

1/5 of 11 = 1/5 × 11

= 11/5

= 2 1/5

Now add 2.5 to -6

2 1/2 + -6 = -3 1/2

The value of y = -3 1/2

8 0

3 years ago