Answer:
24 foot
Step-by-step explanation:
We are given that
Length of ladder=26 foot
Height of building=10 foot
We have to find the distance between the bottom of ladder and the bottom of building.
Pythagorus theorem:
We have hypotenuse =AC=26 foot
Perpendicular side =AB=10 foot
Base=BC
Substitute the values in the given formula
(Take positive because length is always positive)
BC=24 foot
Hence, the bottom of the ladder will be 24 foot from the bottom of the building.
Answer:
f(x) = -19/9(x + 3)² + 5
Step-by-step explanation:
Given the vertex, (-3, 5) and the point, (0, 14):
Use the following quadratic equation formula in vertex form:
f(x) = a(x - h)² + k
where:
(h, k) = vertex
a = determines whether the graph opens up or down, and makes the graph wide or narrow.
<em>h</em><em> </em>= determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Plug in the values of the vertex, (-3, 5) and the given point, (0, 14) to solve for <em>a</em>:
f(x) = a(x - h)² + k
14 = a(0 + 3)² + 5
14 = a(3)² + 5
14 = a(9) + 5
Subtract 5 from both sides:
-14 - 5 = 9a
-19 = 9a
Divide both sides by 9 to solve for a:
-19/9 = 9a/9
-19/9 = a
Therefore, the quadratic function in vertex form is:
f(x) = -19/9(x + 3)² + 5
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We reject our null hypothesis, H₀, at a level of significance of =0.01 since the P-value is less than that threshold. There is compelling statistical data to indicate that since 1991, the proportion of drivers who love driving has decreased.
Given,
The Pew Research Center recently polled n=1048 U.S. drivers and found that 69% enjoyed driving their automobiles.
In 1991, a Gallup poll reported this percentage to be 79%. using the data from this poll, test the claim that the percentage of drivers who enjoy driving their cars has declined since 1991.
To report the large-sample z statistic and its p-value,
Null hypothesis,
H₀ : p = 0.79
Alternative hypothesis,
Ha : p < 0.79
Level of significance, α = 0.01
Under H₀
Test statistic,
Z₀ = -7.948
The alternative hypothesis(Ha) is left-tailed, so the P-value of the test is given by
P-value = P(z <-7.945)
= 0.000 (from z-table)
Since the P-value is smaller than given level of significance, α=0.01 we reject our null hypothesis, H₀, at α=0.0.1 level Strong statistical evidence to conclude that the percentage of drivers who enjoy driving their cars has declined since 1991.
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