Step-by-step explanation: To round a decimal, you first need to know the indicated place value position you want to round to. This means that you want to first find the digit in the rounding place which will usually be underlined.
Once you locate the digit in the rounding place, look to the left of that digit. Now, the rules of rounding tell us that if a number is less than 4, we round down but if a number is greater than or equal to 5, we round up.
I'll show an example.
<em>Round the following decimal to the indicated place value.</em>
<em>0.80</em><u><em>0</em></u><em>5</em>
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<em>To round 0.80</em><u><em>0</em></u><em>5 to the indicated place value position, first find the digit in the rounding place which in this case is the 0 in the thousandths place.</em>
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<em>Next, find the digit to the right of the rounding place which in this case is 5. Since 5 is greater than or equal to 5, we round up.</em>
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<em>This means we add 1 to the digit in the rounding place so 0 becomes 1. So we have 0.801. Now, we change all digits to the right of the rounding place to 0 so 5 changes to 0.</em>
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<em>Finally, we can drop of any zeroes to the right of our decimal as long as they're also to the right of the rounding position.</em>
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<em>So we can write 0.8010 as 0.801.</em>
Image provided.
Answer:
The dimensions of the pool are:
Width: 8.944 feet
Length: 17.888 feet
Step-by-step explanation:
From Geometry, the area of a rectangle (), measured in square feet, is determined by the following equations:
(1)
Where:
- Width, measured in feet.
- Length, measured in feet.
If we know that ,
and
, then we get the following second order polynomial:
(1)
And we solve the expression for :
Then, the dimensions of the pool are, respectively:
and
Answer: The correct congruence statement is .
Explanation:
It is given that A triangle Q D J. The base D J is horizontal and side Q D is vertical. Another triangle M C W is made. The base C W and side M C are neither horizontal nor vertical. Triangle M C W is to the right of triangle Q D J.
The sides Q D and M C are labeled with a single tick mark. The sides D J and C W are labeled with a double tick mark. The sides Q J and M W are labeled with a triple tick mark.
Draw two triangles according to the given information.
From the figure it is noticed that
So by SSS rule of congruence we can say that .
Answer:
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).
The null and alternative hypothesis are:
Step-by-step explanation:
<em>The question is incomplete: To test this claim a sample or population standard deviation is needed.</em>
<em>We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.</em>
<em> NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.</em>
This is a hypothesis test for the population mean.
The claim is that the batteries power the laptops for significantly less than 4 hours.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=500.
The sample mean is M=3.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.