Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation

Triangle with sides 27, x and y. Here y is the hypotenuse so we get

Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get

. That is,

We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:

and replace

and

using expressions that contain an expression in terms of x from the first two equations we came up with.
That gives us:

which we solve for x as follows:

Now that we know x we can substitute 36 for x into the equation

and solve for z as follows:

This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.
Answer:
75% confidence interval is 91.8±16.66. That is between 75.1 and 108.5 pounds.
Step-by-step explanation:
The question is missing. It is as follows:
Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains had the following weights (pounds): 69 104 125 129 60 64
Assume that the population of x values has an approximately normal distribution.
Find a 75% confidence interval for the population average weight μ of all adult mountain lions in the specified region. (Round your answers to one decimal place.)
75% Confidence Interval can be calculated using M±ME where
- M is the sample mean weight of the wild mountain lions (
)
- ME is the margin of error of the mean
And margin of error (ME) of the mean can be calculated using the formula
ME=
where
- t is the corresponding statistic in the 75% confidence level and 5 degrees of freedom (1.30)
- s is the standard deviation of the sample(31.4)
Thus, ME=
≈16.66
Then 75% confidence interval is 91.8±16.66. That is between 75.1 and 108.5
Answer:
-17y + 16x
Step-by-step explanation:
-3(3y - 2x) + 2(5x - 4y) = -9y + 6x + 10x - 8y = -17Y + 16X.
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Answer:
Step-by-step explanation:
4x - 12 ≤ 16 + 8x
4x - 8x ≤ 16 + 12
- 4x ≤ 28
<em>x ≥ - 7 or [ - 7, ∞ )</em>
Lauryn has more marbles because 128 is greater than 118