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4 years ago

Svetlana's hair is 3 cm long. Her hair

1 answer:

3 0

Required inequality is 1.5x + 3 < 18 and solution is x < 10, that is number of months svetlana can allow her hair to grow must be less than 10 so that her hair length will be less that 18 cm

Solution:

Given that

Svetlana's hair is 3 cm long.

Her hair grows 1.5 cm per month

Need to write an inequality to determine the number of months Svetlana can allow her hair to grow.

Let assume number of months Svetlana can allow her hair to grow be represented by variable "x"

Length of hair grows in one month = 1.5 cm

So Length of hair grows in "x" months = $\text { Length of hair grows in one month } \times x=1.5 \times x=1.5 x$

As Svetlana wanted her hair to be less than 18 cm long

So Length of hair grows in "x" months plus current length of hair must be less than 18 cm

=> 1.5x + 3 < 18

On solving the above inequality for "x" we get ,

1.5x < 18 – 3

=> 1.5x < 15

=> $x < \frac{15}{1.5}$

=> x < 10

Thus required inequality is 1.5x + 3 < 18

Number of months sultana can allow her hair to grow must be less than 10 so that her hair length will be less that 18 cm.

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A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of

kolezko [41]

Answer:

a) Parameter of interest $p$ representing the true proportion of the plates have blistered.

b) Null hypothesis: $p\leq 0.1$

Alternative hypothesis: $p > 0.1$

c) $z=\frac{0.14 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=1.33$

d) For this case we need to find a value in the normal standard distribution that accumulates 0.1 of the area in the right tail and for this case is:

$z_{critc}= 1.28$

e) For this case since our calculated value is higher than the critical value 1.33>1.28 we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly higher than 0.1

f) $p_v =P(z>1.33)=0.0917$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the true proportion is higher than 0.1 or 10%

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

Part a

Parameter of interest $p$ representing the true proportion of the plates have blistered.

X=14 represent the number of the plates have blistered.

$\hat p=\frac{14}{100}=0.14$ estimated proportion of the plates have blistered.

$p_o=0.1$ is the value that we want to test

$\alpha=0.1$ represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

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

Part b: Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that more than 10% of all plates blister under such circumstances.:

Null hypothesis: $p\leq 0.1$

Alternative hypothesis: $p > 0.1$

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 $p_o$ .

Part c: Calculate the statistic

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

$z=\frac{0.14 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=1.33$

Part d: Rejection region

For this case we need to find a value in the normal standard distribution that accumulates 0.1 of the area in the right tail and for this case is:

$z_{critc}= 1.28$

Part e

For this case since our calculated value is higher than the critical value 1.33>1.28 we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly higher than 0.1

Part f

Since is a right taild test the p value would be:

$p_v =P(z>1.33)=0.0917$

7 0

3 years ago

Please explain for me I’m clueless 3t + 3/5 =6 T=__

Igoryamba

Answer:

$\frac{3t + 3}{5} = 6 \\ 3 (\frac{t + 1}{5}) = 6 \\ \frac{t + 1}{5} = 2 \\ t + 1 = 10 \\ t = 9 \: or \\ 3t + 3 = 30 \\ 3t = 27 \\ t = 9$