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Scrat [10]
3 years ago
5

Put 983 in scientific notation.

Mathematics
2 answers:
Inessa [10]3 years ago
8 0
9.83• ten to the negotiation two
sladkih [1.3K]3 years ago
3 0
To the left of the decimal point needs to be somewhere between 1 and 9 (one place). 983 in scientific notation would be 9.83 x 10^2. Do you understand how i got that? I got the 10^2 because i am moving the decimal point over two places to the left. If i move the decimal point to the right, then the exponent would be negative. Example:
0.00983 in scientific notation would be 9.83 x 10^-3 because i moved the decimal point three places to the right.
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Answer:

How to Graph x=5

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Step-by-step explanation:

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8 0
3 years ago
Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to
attashe74 [19]

Answer:

a) Null hypothesis:\mu \leq 30.2  

Alternative hypothesis:\mu > 30.2  

b) X \sim N(\mu=32.12, \sigma=4.83)

And the distribution for the random sample is given by:

\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)

c) t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81    

p_v =P(t_{(49)}>2.81)=0.0035  

d) If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.  

e) The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation  

\bar X=32.12 represent the sample mean  

s=4.83 represent the sample standard deviation

n=50 sample size  

\mu_o =30.2 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

a. Define the parameter and state the hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 30.2 mpg, the system of hypothesis would be:  

Null hypothesis:\mu \leq 30.2  

Alternative hypothesis:\mu > 30.2  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

b. Define the sampling distribution (mean and standard deviation).

Let X the random variable who represent the variable of interest. And we know that the distribution for X is:

X \sim N(\mu=32.12, \sigma=4.83)

And the distribution for the random sample is given by:

\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)

c. Perform the test and calculate P-value

Calculate the statistic

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

t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=50-1=49  

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

p_v =P(t_{(49)}>2.81)=0.0035  

d. State your conclusion.

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.  

e. Explain what the p-value means in this context.

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

6 0
3 years ago
A home repair service company earned $990 performing annual inspections. They charged $55 for each inspection. How many inspecti
OlgaM077 [116]
They performed 18 home inspections
8 0
3 years ago
Read 2 more answers
Really need help on this! Thanks so much for whoever answers this.
Rufina [12.5K]

can you comment the question?

3 0
2 years ago
A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean
djyliett [7]

Answer:

The probability is 0.0069

Step-by-step explanation:

First thing to do here is to calculate the z-score

Mathematically;

z-score = (x-mean)/SD/√(n)

where x = 9.1 , mean = 8.4 , SD = 1.8 and n = 40

Plugging these values into the z-score equation, we have;

z-score = (9.1-8.4)/1.8/√(40) = 0.7/1.8/6.325 = 0.0615

Now, we check the standard normal table for P(z > 2.46) = 0.0069

8 0
3 years ago
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