(6x + 14) - (9x + 5)
1 answer:
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Based on the calculations, the depth of tent is equal to 12 feet.
<h3>How to calculate the depth of the tent?</h3>Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):
- Triangle ABC is an isosceles triangle (AB = AC).
- The front and back of the triangle are identical triangles.
- Side AD is perpendicular side BC.
- CD is the midpoint of BC i.e CD = BC/2 = 6/2 = 3 feet.
Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:
AC² = AD² + DC²
AD² = AC² - DC²
AD² = 5² - 3²
AD² = 25 - 9
AD² = 16
AD = √16
AD = 4 feet.
Also, we would determine the area of the triangle (ABC):
Area = 1/2 × b × h
<u>Where:</u>
- b is the base area.
- h is the height.
Substituting the given parameters into the formula, we have;
Area = 1/2 × 6 × 4
Area = 12 feet².
Depth of tent = 3 × height of ADC
Depth of tent = 3 × 4
Depth of tent = 12 feet.
Read more on area of triangle here: brainly.com/question/21917592
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Because this is a positive parabola, it opens upwards, like a cup, and the vertex dictates what the minimum value of the function is. In order to determine the vertex, I recommend completing the square. Do that by first setting the function equal to 0 and then moving the 9 to the other side by subtraction. So far: 
. Now, to complete the square, take half the linear term, square it, and add that number to both sides. Our linear term is 6. Half of 6 is 3 and 3 squared is 9. So add 9 to both sides. 
. The right side reduces to 0, and the left side simplifies to the perfect square binomial we created while completing this process. 
. Move the 0 back over and the vertex is clear now. It is (-3, 0). Therefore, 0 is the minimum point on your graph. The first choice above is the one you want.
Answer:
The conclusion for this hypothesis test would be that the average American consumes less than or equal to 17 ounces of ice cream per month.
Step-by-step explanation:
We are given that Breyers is a major producer of ice cream and would like to test if the average American consumes more than 17 ounces of ice cream per month.
A random sample of 25 Americans was found to consume an average of 19 ounces of ice cream last month. The standard deviation for this sample was 5 ounces.
<u><em>Let </em></u><u><em> = average ounces of ice cream consumed by American per month</em></u>
So, Null Hypothesis, :
17 ounces {means that the average American consumes less than or equal to 17 ounces of ice cream per month}
Alternate Hypothesis, :
> 17 ounces {means that the average American consumes more than 17 ounces of ice cream per month}
The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about population standard deviation;
T.S. = ~
where, = sample average = 19 ounces
s = sample standard deviation = 5 ounces
n = sample of Americans = 25
So, <u><em>test statistics</em></u> = ~
= 2
The value of the test statistics is 2.
<em>Now at 0.025 significance level, the </em><u><em>t table gives critical value of 2.06 at 24 degree of freedom for right-tailed test</em></u><em>. Since our test statistics is less than the critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to </em><u><em>which we fail to reject our null hypothesis</em></u><em>.</em>
Therefore, we conclude that the the average American consumes less than or equal to 17 ounces of ice cream per month.