Answer: the flagpole is 16 feet tall.
Step-by-step explanation:
A right angle triangle is formed.
The distance of the point on the ground from the base of the flagpole represents the adjacent side of the right angle. The height of the flagpole from the ground represents the opposite side of the right angle.
To determine the height, h of the flagpole, we would apply the Tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 53 = h/12
h = 12Tan53 = 12 × 1.327
h = 16 feet to the nearest whole number
Answer:
Step-by-step explanation:
Let the number of apples picked by Kate be x
So the number of apples picked by Michaela is 7x
Plz mark it as brainliest:)
Answer:
$32.30
Step-by-step explanation:
19x.30 (to find the 30%)
5.7 needs to be take off of the second shirt.
19 (the first shirt) + (19-5.7) = $32.3
The formula for a z-score is
![z=\frac{X- \mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7BX-%20%5Cmu%7D%7B%5Csigma%7D)
We don't have μ, the mean, or σ, the standard deviation. We can, however, set up a system of two equations with the information we do have. We know:
![-3=\frac{60- \mu}{\sigma} \text{ and } 2=\frac{85- \mu}{\sigma}](https://tex.z-dn.net/?f=-3%3D%5Cfrac%7B60-%20%5Cmu%7D%7B%5Csigma%7D%20%5Ctext%7B%20and%20%7D%202%3D%5Cfrac%7B85-%20%5Cmu%7D%7B%5Csigma%7D)
We can make this look more like a "typical" system of equations by cancelling the fractional part of each equation. We do this by multiplying the bottom of each equation by σ:
![-3*\sigma=\frac{60- \mu}{\sigma}*\sigma \text{ and } 2*\sigma=\frac{85- \mu}{\sigma}*\sigma \\ \\-3\sigma=60- \mu \text{ and } 2\sigma=85- \mu](https://tex.z-dn.net/?f=-3%2A%5Csigma%3D%5Cfrac%7B60-%20%5Cmu%7D%7B%5Csigma%7D%2A%5Csigma%20%5Ctext%7B%20and%20%7D%202%2A%5Csigma%3D%5Cfrac%7B85-%20%5Cmu%7D%7B%5Csigma%7D%2A%5Csigma%0A%5C%5C%0A%5C%5C-3%5Csigma%3D60-%20%5Cmu%20%5Ctext%7B%20and%20%7D%202%5Csigma%3D85-%20%5Cmu)
Now we'll get the variables on the same side of the equation. We'll do this by adding μ to both sides:
![-3\sigma + \mu=60- \mu + \mu \text{ and } 2\sigma+ \mu =85- \mu + \mu \\ \\-3\sigma+\mu=60 \text{ and } 2\sigma+\mu=85](https://tex.z-dn.net/?f=-3%5Csigma%20%2B%20%5Cmu%3D60-%20%5Cmu%20%2B%20%5Cmu%20%5Ctext%7B%20and%20%7D%202%5Csigma%2B%20%5Cmu%20%3D85-%20%5Cmu%20%2B%20%5Cmu%0A%5C%5C%0A%5C%5C-3%5Csigma%2B%5Cmu%3D60%20%5Ctext%7B%20and%20%7D%202%5Csigma%2B%5Cmu%3D85)
Now we'll write this vertically:
![\left \{ {{-3\sigma+\mu=60} \atop {2\sigma+\mu=85}} \right.](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7B-3%5Csigma%2B%5Cmu%3D60%7D%20%5Catop%20%7B2%5Csigma%2B%5Cmu%3D85%7D%7D%20%5Cright.%20)
We will "eliminate" μ by subtracting the bottom equation:
![\left \{ {{-3\sigma+\mu=60} \atop {-(2\sigma+\mu=85)}} \right. \\ \\-5\sigma=-25](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7B-3%5Csigma%2B%5Cmu%3D60%7D%20%5Catop%20%7B-%282%5Csigma%2B%5Cmu%3D85%29%7D%7D%20%5Cright.%20%0A%5C%5C%0A%5C%5C-5%5Csigma%3D-25)
Divide both sides by -5:
![\frac{-5\sigma}{-5}=\frac{-25}{-5} \\ \\\sigma=5](https://tex.z-dn.net/?f=%5Cfrac%7B-5%5Csigma%7D%7B-5%7D%3D%5Cfrac%7B-25%7D%7B-5%7D%0A%5C%5C%0A%5C%5C%5Csigma%3D5)
Our standard deviation is 5. Substituting this into our top equation we have:
-3(5)+μ=60
-15+μ=60
Cancel the -15 by adding it to both sides:
-15+μ+15=60+15
μ=75
Our mean is 75.