Answer:
9
Step-by-step explanation:
In a equilateral triangle all angles are equal and 60° each so
7x - 3 = 60° ➡ 7x = 63° ➡ x = 9
Answer:
Test statistic = 1.818
Reject H0
Step-by-step explanation:
H0 : μ = 90
H1 : μ > 90
xbar = 94 ; s = 22 ; n = 100
The test statistic : (xbar - μ) ÷ (s/√(n))
Test statistic = (94 - 90) ÷ (22/√100)
Test statistic = 4 ÷ 2.2
T = 1.818
The critical value :
At α = 0.10
Degree of freedom = n - 1 = 100 - 1 = 99
Tcritical(0.10, 99) = 1.290
Decison region :
Reject H0 if Test statistic > |Tcritical |
1.818 > 1.290
We reject H0
Answer:
slope = 0
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 7, - 8) and (x₂, y₂ ) = (5, - 8)
m =
=
= 0
Answer:
The company needs to sell either 30 or 40 items.
Step-by-step explanation:
We are given that the cost for selling <em>x</em> items given by the function:

And the revenue for selling <em>x</em> items is given by:

The profit function is the cost function subtracted from the revenue function:

Substitute and simplify:

To find how many items must be sold in order to obtain a weekly profit of $300, we can let <em>P</em> equal 300 and solve for <em>x</em>. So:

Solve for <em>x</em>. Subtract 300 from both sides:

We can divide both sides by -0.4:

Factor:

Zero Product Property:

Solve for each case:

So, in order to obtain a weekly profit of $300, the company need to sell either 30 <em>or</em> 40 items.
since the point (4,13) is on the circle, then the distance from the center to it, is the radius of the circle.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{13})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-2)]^2+[13-5]^2}\implies r=\sqrt{(4+2)^2+(13-5)^2} \\\\\\ r=\sqrt{36+64}\implies r=\sqrt{100}\implies r=10 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20%28%5Cstackrel%7Bx_1%7D%7B-2%7D~%2C~%5Cstackrel%7By_1%7D%7B5%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B4%7D~%2C~%5Cstackrel%7By_2%7D%7B13%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Bradius%7D%7Br%7D%3D%5Csqrt%7B%5B4-%28-2%29%5D%5E2%2B%5B13-5%5D%5E2%7D%5Cimplies%20r%3D%5Csqrt%7B%284%2B2%29%5E2%2B%2813-5%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20r%3D%5Csqrt%7B36%2B64%7D%5Cimplies%20r%3D%5Csqrt%7B100%7D%5Cimplies%20r%3D10%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-2}{ h},\stackrel{5}{ k})\qquad \qquad radius=\stackrel{10}{ r}\\[2em] [x-(-2)]^2+[y-5]^2=10^2\implies (x+2)^2+(y-5)^2=100](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bequation%20of%20a%20circle%7D%5C%5C%5C%5C%20%28x-%20h%29%5E2%2B%28y-%20k%29%5E2%3D%20r%5E2%20%5Cqquad%20center~~%28%5Cstackrel%7B-2%7D%7B%20h%7D%2C%5Cstackrel%7B5%7D%7B%20k%7D%29%5Cqquad%20%5Cqquad%20radius%3D%5Cstackrel%7B10%7D%7B%20r%7D%5C%5C%5B2em%5D%20%5Bx-%28-2%29%5D%5E2%2B%5By-5%5D%5E2%3D10%5E2%5Cimplies%20%28x%2B2%29%5E2%2B%28y-5%29%5E2%3D100)