1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alex777 [14]
3 years ago
14

The last Ice age ended about 10,000 years ago write this length of time in scientific notation

Mathematics
1 answer:
MAVERICK [17]3 years ago
4 0
10*10^3
also =
1*10^4
because the number has to be in between the numbers 10 and 1 so it could go either way really
You might be interested in
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
How much do you think a 12lb cat would weight on the moon? How did you decide that mathematically (bases on the information from
tekilochka [14]

Answer:

1.98

Step-by-step explanation:

Weight on earth/ 9.81 m/s^2 * 1.622m/s^2

5 0
2 years ago
Read 2 more answers
I will mark you brainly Answer the following questions. Questions What is an amount between $2 and $10? (A) __________ What is a
Ganezh [65]

Answer:

  • f8tt8t7tifiigfifitfyhuihhhhyhufghuiioffiggigiuoupoyfufudueurufufiogghuuyofifotogiflvkgkfhbjjsheheh28828282882828u3uu3uu4664678388283i3ushsbsbbsb

Step-by-step explanation:

hahhehhe

7 0
2 years ago
Someone help me out please
uysha [10]

1 step (B): raise both sides of the equation to the power of 2.

(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2,\\   (x+3)-2\sqrt{x+3}\cdot \sqrt{2x-1}+(2x-1)=4,\\ 3x+2-2\sqrt{x+3}\cdot \sqrt{2x-1}=4.

2 step (A): simplify to obtain the final radical term on one side of the equation.

-2\sqrt{x+3}\cdot \sqrt{2x-1}=4-3x-2,\\ -2\sqrt{x+3}\cdot \sqrt{2x-1}=2-3x,\\ 2\sqrt{x+3}\cdot \sqrt{2x-1}=3x-2.

3 step (F): raise both sides of the equation to the power of 2 again.

(2\sqrt{x+3}\cdot \sqrt{2x-1})^2=(3x-2)^2,\\ 4(x+3)(2x-1)=(3x-2)^2.

4 step (E): simplify to get a quadratic equation.

4(2x^2-x+6x-3)=(3x)^2-2\cdot 3x\cdot 2+2^2,\\ 8x^2+20x-12=9x^2-12x+4,\\ x^2-32x+16=0.

5 step (D): use the quadratic formula to find the values of x.

D=(-32)^2-4\cdot 16=1024-64=960, \\ \sqrt{D} =8\sqrt{5} ,\\ x_{1,2}=\dfrac{32\pm 8\sqrt{5}}{2} =16\pm 4\sqrt{5}.

6 step (C): apply the zero product rule.

x^2-32x+16=(x-16-4\sqrt{5}) (x-16+4\sqrt{5}) ,\\ (x-16-4\sqrt{5}) (x-16+4\sqrt{5}) =0,\\ x_1=16+4\sqrt{5} ,x_2=16-4\sqrt{5}.

Additional 7 step: check these solutions, substituting into the initial equation.

3 0
3 years ago
Why does math even exist?
natita [175]
I know I dislike it as well! Sorry you are having trouble with it! :)
4 0
3 years ago
Read 2 more answers
Other questions:
  • What is the completely factored form of the expression 16x^2+8x+32
    6·2 answers
  • If 3 times a certain number is increased by 4 the result is 28. What is the number?
    13·1 answer
  • Suppose you add two linear equations that form a system, and you get the result −5 = −5. How many solutions does the system have
    10·1 answer
  • at dinner jeremy and his friend spent $24. They left a 20% tip and then split the cost. How much did each person pay?
    12·2 answers
  • What is the approximate volume of a cone with a height of 12 in and radius of 9 in ? Use 3 14 to approximate pi, and express you
    9·1 answer
  • There are 472 stuffed beats in stock at a factory. The factory has 35 cartons of bears. There are 16 in a carton. How many more
    12·2 answers
  • What type of transformation is shown on this graph?
    9·1 answer
  • 127°<br> 37°<br> Х<br> Calculate the size of angle x.<br> angle x =
    11·1 answer
  • Set of integers x such that x - 5 ​
    6·1 answer
  • 10 more than 10 times a number is -10. Group of answer choices
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!