A ramp leading into a building makes a 15o angle with the ground. the end of the ramp is 10 feet from the base of the building.
1 answer:
You might be interested in
system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is and
.
<u>Step-by-step explanation:</u>
Here we have , A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. We need to find Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y . Let's find out:
Let the price in dollars of each large candle, x, and each small candle, y .So
A customer at a store paid $64 for 3 large candles and 4 small candles
Equation is :
⇒ .....(1)
At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles.
Equation is :
⇒ .......(2)
3(2)-(1) i.e.
⇒
⇒
⇒
So ,
⇒
⇒
Therefore , system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is and
.
Answer:
II. This finding is significant for a two-tailed test at .01.
III. This finding is significant for a one-tailed test at .01.
d. II and III only
Step-by-step explanation:
1) Data given and notation
represent the battery life sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
2) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean battery life is equal to 18 or not for parta I and II:
Null hypothesis:
Alternative hypothesis:
And for part III we have a one tailed test with the following hypothesis:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-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".
3) Calculate the statistic
We can replace in formula (1) the info given like this:
4) P-value
First we need to calculate the degrees of freedom given by:
Since is a two tailed test for parts I and II, the p value would be:
And for part III since we have a one right tailed test the p value is:
5) Conclusion
I. This finding is significant for a two-tailed test at .05.
Since the . We reject the null hypothesis so we don't have a significant result. FALSE
II. This finding is significant for a two-tailed test at .01.
Since the . We FAIL to reject the null hypothesis so we have a significant result. TRUE.
III. This finding is significant for a one-tailed test at .01.
Since the . We FAIL to reject the null hypothesis so we have a significant result. TRUE.
So then the correct options is:
d. II and III only
Answer:
First Case:
Second Case:
Step-by-step explanation:
We know that the first three terms of an arithmetic series are:
Since this is an arithmetic sequence, each subsequent term is <em>d</em> more than the previous term, where <em>d</em> is our common difference.
Therefore, we can write the second term as;
And, likewise, for the third term:
Let's solve for <em>d</em> for each of the equations.
Subtracting in the first equation yields:
And for the second equation:
To avoid fractions, let's multiply the first equation by 2. Hence:
Therefore:
Simplifying yields:
Solve for <em>p</em>. We can factor:
Factor:
Grouping:
Zero Product Property:
Then, we can use the second equation to solve for <em>d</em>. So:
Substituting:
So, for the first case, <em>p</em> is 5/2 and <em>d</em> is -2.
Likewise, for the second case:
So, for the second case, <em>p </em>is -5/4, and <em>d</em> is 7/4.
By using the values, we can determine our series.
For Case 1, we will have:
17, 15, 13.
For Case 2, we will have:
-11/2, -15/4, -2.
<h2>Hello!</h2>
The answer is:
The slant height is 13.43 m.
To solve the problem, we need to use the following equations to calculate the total surface area and the lateral surface area of right cone:
Where,
r, is the radius of the cone.
l, is the slant height of the cone.
We are given the following information:
So, calculating the area of the base(circle) in order to find the lateral surface area, we have:
Then, substituting the area of the base into the total surface area to calculate the surface area of the cone, we have:
Now, calculating the slant height, we have:
Substituting, we have:
Hence, we have that the slant height is 13.43 m.
Have a nice day!