Are the triangles congruent?a-yesb-noc-not enough information
1 answer:
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Answer: The hook would be 2.2 inches (approximately) above the top of the frame
Step-by-step explanation: Please refer to the picture attached for further details.
The top of the picture frame has been given as 9 inches and a 10 inch ribbon has been attached in order to hang it on a wall. The ribbon at the point of being hung up would be divided into 5 inches on either side (as shown in the picture). The line from the tip/hook down to the frame would divide the length of the frame into two equal lengths, that is 4.5 inches on either side of the hook. This would effectively give us two similar right angled triangles with sides 5 inches, 4.5 inches and a third side yet unknown. That third side is the distance from the hook to the top of the frame. The distance is calculated by using the Pythagoras theorem which states as follows;
AC^2 = AB^2 + BC^2
Where AC is the hypotenuse (longest side) and AB and BC are the other two sides
5^2 = 4.5^2 + BC^2
25 = 20.25 + BC^2
Subtract 20.25 from both sides of the equation
4.75 = BC^2
Add the square root sign to both sides of the equation
2.1794 = BC
Rounded up to the nearest tenth, the distance from the hook to the top of the frame will be 2.2 inches
Answer:
Pvalue of 0.0446 < 0.05, which means that we reject the null hypothesis and accept the alternative hypothesis, that the true mean is larger than the specification.
Step-by-step explanation:
The average weight of a package of rolled oats is supposed to be at most 18 ounces.
This means that the null hypothesis is:
Is the true mean larger than the specification?
Due to the question asked, the alternate hypothesis is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
18 is tested at the null hypothesis:
This means that
A sample of 18 packages shows a mean of 18.20 ounces with a sample standard deviation of 0.50 ounces.
This means that
Value of the test statistic:
Pvalue of the test:
Probability of finding a sample mean above 18.2, which is 1 subtracted by the pvalue of z = 1.7.
Looking at the z-table, z = 1.7 has a pvalue of 0.9554.
1 - 0.9554 = 0.0446
0.0446 < 0.05, which means that we reject the null hypothesis and accept the alternative hypothesis, that the true mean is larger than the specification.