Round this number to the given place values:
1 answer:
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Answer:
Lateral Area = 624 square units
Surface area = 1,200 square units
Volume = 960 cubic units
Step-by-step Explanation:
==>Given:
Dimensions of the square pyramid as shown in the figure are:
length of 1 side of the square base (s) = 24
Slant height (l) = 13
Perpendicular height (h) = ?
==>Required:
a. Lateral area (L.A) = 4 × ½sl
b. Surface Area (S.A) = Base area (s²) × Lateral area (4 × ½sl)
c.Volume of the pyramid = ⅓ × Base area (s²) × perpendicular height (h)
==>SOLUTION:
a. Lateral area (L.A) = the area of the 4 lateral faces of the pyramid, which are triangular faces.
L.A = 4 × ½sl
From the figure given, s = 24; l = 13,
Therefore, L.A = 4 × ½ × 24 × 13
= 4 × 1 × 12 × 13
Lateral Area = 624 square units
b. Surface Area (S.A) = Base area (s²) × Lateral area (4 × ½sl)
Base area (s²) = 24² = 576 square units
Lateral area (4 × ½sl) = 624 square units
Therefore, total surface area = 576 + 624
= 1,200 square units
c. c.Volume of the pyramid using the formula ⅓ × Base area (s²) × perpendicular height (h)
Base area (s²) = 576 square units
Perpendicular height (h) is not given in the figure = h
Since already know the slant height (s), let's use Pythagorean theorem to find the perpendicular height (h) bearing in mind that a right triangle is formed in the middle of the pyramid as illustrated in the figure attached below.
The base of the right triangle = ½ of side length of the base (s) = ½ × 24 = 12
The hypotenuse (l) = 13
Therefore using the Pythagorean Theorem formula a² + b² = c², let's find the perpendicular height (h).
Where,
a² = h²
b² = (½s)² = 12²
c² = l² = 13²
Thus, h² + 12² = 13²
h² = 13² - 12²
h² = 169 - 144
h² = 25
h = √25
h = 5
==>Volume of pyramid (V) = ⅓ × Base area (s²) × perpendicular height (h)
V = ⅓ × 576 × 5
V = ⅓ × 2,880
V = 960 cubic units
Answer:
a)
If we compare the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of rejected items is less than 0.03.
b) We can use a 95 percent upper confidence interval.
On this case we want a interval on this form :
So the critical value would be on this case and we can use the following excel code to find it: "=NORM.INV(1-0.05,0,1)"
We found the upper limit like this:
And the interval would be:
And since our value (0.02) is contained in the interval We fail to reject the hypothesis that p=0.03
Step-by-step explanation:
Part a
Data given and notation
n=500 represent the random sample taken
X=10 represent the number of objects rejected
estimated proportion of objects rejected
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that 70% of adults say that it is morally wrong to not report all income on tax returns.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a one tailed left test the p value would be:
If we compare the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of rejected items is less than 0.03.
Part b
We can use a 95 percent upper confidence interval.
On this case we want a interval on this form :
So the critical value would be on this case and we can use the following excel code to find it: "=NORM.INV(1-0.05,0,1)"
We found the upper limit like this:
And the interval would be:
And since our value (0.02) is contained in the interval We fail to reject the hypothesis that p=0.03
Answer:
The true statements are;
Point D represents a number less than the number Point C represents
Point E represents the smallest number of all the numbers represented by points
Step-by-step explanation:
The given information are;
The number line with points are
In decimal format, with Microsoft Excel and Word, we have;
-1.375, -1.25, -1.125, -1, -0.875, -0.75, -0.625, -0.5, -0.375, -0.25, -0.125, 0, 0.125, 0.25, 0.375
We have, E = -1.25, B = -1, D = -0.875, C = -0.25, A = 0, F = 0.25
The correct options are;
Point D = -0.875 < Point C = -0.25
Point E = -1.25 which is the second number on the number line and the smallest number of the numbers represented by points