Given:

Suppose you are asked to find the area of a rectangle that is 2.1-cm wide by 5.6-cm long. Your calculator answer would be 11.76

Vladimir79 [104]

Answer:

The area of the rectangle is 12 cm² ⇒ in 2 significant figures

Step-by-step explanation:

* Lets talk about the significant figures

- All non-zero digits are significant

# 73 has two significant figures

- Zeroes between non-zeros digits are significant

# 105.203 has six significant figures

- Leading zeros are never significant

# 0.00234 has three significant figures

- In a number with a decimal point, zeros to the right of the last

non-zero digit are significant

# 19.00 has four significant figures

- Lets make a number and then approximate it to different significant

∵ 12.7360 has 6 significant figures

∴ 12.736 ⇒ approximated to 5 significant figures

∴ 12.74 ⇒ approximated to 4 significant figures

∴ 12.7 ⇒ approximated to 3 significant figures

∴ 13 ⇒ approximated to 2 significant figures

∴ 10 ⇒ approximated to 1 significant figure

- Another number with decimal point

∵ 0.0546700 has 6 significant figures

∴ 0.054670 ⇒ approximated to 5 significant figures

∴ 0.05467 ⇒ approximated to 4 significant figures

∴ 0.0547 ⇒ approximated to 3 significant figures

∴ 0.055 ⇒ approximated to 2 significant figures

∴ 0.05 ⇒ approximated to 1 significant figures

* Lets solve the problem

∵ The width of the rectangle is 2.1 cm

∵ The length of the rectangle is 5.6 cm

- Area of the rectangle = length × width

∴ Area of the rectangle = 2.1 × 5.6 = 11.76 cm²

- Approximate it to two significant figures

∴ Area of the rectangle = 12 ⇒ to the nearest 2 significant figures

* The area of the rectangle is 12 cm² ⇒ in 2 significant figures

3 0

4 years ago

A large manufacturer that sells consumer products on-line wishes to publicize its customer satisfaction in an advertisement. Spe

sergejj [24]

Answer:

$z=\frac{0.93 -0.9}{\sqrt{\frac{0.9(1-0.9)}{400}}}=2$

$p_v =P(z>2)=0.0228$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who say yes is significantly higher than 0.9 or 90%.

Step-by-step explanation:

Data given and notation

n=400 represent the random sample taken

X=372 represent the number of people who say yes

$\hat p=\frac{372}{400}=0.93$ estimated proportion of people who say yes

$p_o=0.9$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that that more than 90% of its costumers would tell their friend to buy a product from the manufacturer.:

Null hypothesis: $p\leq 0.9$

Alternative hypothesis: $p > 0.9$

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 $p_o$ .

Calculate the statistic

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

$z=\frac{0.93 -0.9}{\sqrt{\frac{0.9(1-0.9)}{400}}}=2$

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 assumed for this case is $\alpha=0.05$ . The next step would be calculate the p value for this test.

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

$p_v =P(z>2)=0.0228$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who say yes is significantly higher than 0.9 or 90%.

8 0

3 years ago

nine fewer than half a number is five more than four times the number define a variable,write an equation and solve to find the

Svetllana [295]

1/2x - 9 = 4x + 5

-3 1/2x = 14

x=4

8 0

3 years ago

Read 2 more answers

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

artcher [175]

In the right triangle, one of the angles has measure 60 deg, so the remaining angle has measure 30 deg. In such a 30-60-90 triangle, the sides occur in a ratio of 1 to $\sqrt3$ to 2 (shorter leg to longer leg to hypotenuse). This means

$2n=4\implies n=2$

$n\sqrt3=m\implies m=2\sqrt3$

making the answer C.

6 0

4 years ago

A student has some $1 and $5 bills in his wallet. He has a total of 16 bills that are worth $40. How many of each type of bil

zvonat [6]

86////////////////////////////////////

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4 years ago