4th grade math! Please help.
2 answers:
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Answer:
Null Hypothesis, :
250 W
Alternate Hypothesis, :
> 250 W
Step-by-step explanation:
We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.
They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
<u><em>Let </em></u><u><em> = mean power consumption of microwave ovens.</em></u>
So, Null Hypothesis, :
250 W
Alternate Hypothesis, :
> 250 W
Here, <u>null hypothesis states tha</u>t the mean power consumption of microwave ovens is no more than 250 W.
On the other hand, <u>alternate hypothesis sates that</u> the mean power consumption of microwave ovens is more than 250 W.
The test statistics that would be used here is <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
Hence, this would be the appropriate hypotheses to determine if the manufacturer's claim appears reasonable.
Answer:
4.
5.
Step-by-step explanation:
The sides of a (30 - 60 - 90) triangle follow the following proportion,
Where (a) is the side opposite the (30) degree angle, () is the side opposite the (60) degree angle, and (2a) is the side opposite the (90) degree angle. Apply this property for the sides to solve the two given problems,
4.
It is given that the side opposite the (30) degree angle has a measure of (8) units. One is asked to find the measure of the other two sides.
The measure of the side opposite the (60) degree side is equal to the measure of the side opposite the (30) degree angle times (). Thus the following statement can be made,
The measure of the side opposite the (90) degree angle is equal to twice the measure of the side opposite the (30) degree angle. Therefore, one can say the following,
5.
In this situation, the side opposite the (90) degree angle has a measure of (6) units. The problem asks one to find the measure of the other two sides,
The measure of the side opposite the (60) degree angle in a (30-60-90) triangle is half the hypotenuse times the square root of (3). Therefore one can state the following,
The measure of the side opposite the (30) degree angle is half the hypotenuse (the side opposite the (90) degree angle). Hence, the following conclusion can be made,