Answer:
![\small \sf \frac{2}{3} = x \\](https://tex.z-dn.net/?f=%5Csmall%20%5Csf%20%5Cfrac%7B2%7D%7B3%7D%20%20%20%3D%20x%20%5C%5C%20)
Step-by-step explanation:
Solve for x;
2x - ( x - 2 ) = 4x
distribute minus sign through parantheses
combine like terms
subtract x from both side
- x - x + 2 = 4x - x
- 2 = 3 x
Divide each side by 3
![\small \sf \frac{2}{3} = \frac{3x}{3} \\](https://tex.z-dn.net/?f=%20%5Csmall%20%5Csf%20%5Cfrac%7B2%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3x%7D%7B3%7D%20%5C%5C%20)
![\small \sf \frac{2}{3} = x\: \\](https://tex.z-dn.net/?f=%5Csmall%20%5Csf%20%5Cfrac%7B2%7D%7B3%7D%20%20%3D%20x%5C%3A%20%5C%5C%20)
If we use our trusty ti's this will be a breeze
domain is the numbers we can use
obviously we can't have negative time so therefor the domain is all positive integers (0,1,2,2.3, 3/2,3,pi...)
zeroes is when you set absolute max using ti is
remember vertex form which is
max height of something in
ax^2+bx+c form is -b/2a
-16t^2+60t+0
a=-16
b=60
-60/(2 times -16)
-60/-32=30/16=15/8=1 and 7/8 so subsitute for t
g(15/8)=-16(15/8)^2+60(15/8)=225/4=56.25=max height
zeroes is when the equation equals 0
so set it to zero
0=-16t^2+60t
factor
0=(-4t)(4x-15)
set each to zero
-4x=0
x=0
4x-15=0
add 15
4x=15
divid 4
x=15/4
so the zeros are t=0 and t=15/4
domain is all the nuumbers that can be used logically for time
logically, we cannot have negative time, so all real positive
[0,∞)
(that means from 0 to infinity includng 0 so 0<span><</span>t<∞))
range is the output
output=height
we find the min height and max height
min=0
max=56.25
so range=0 to 56.25 or
[0,56.25]
max height=56.25 ft (15/8 seconds)
zeroes=0 sec and 15/4 sec
domain=all real positive numbers including zero or [0, ∞)
range=[0,56.25]
Answer:
The diameter of the circle would be: 6.4 cm. rounded or 6.36619772 cm.
The radius of the circle would be: 3.2 cm. rounded or 3.18309886 cm.
Step-by-step explanation:
<h3>The diameter can be solved using: D =
![\frac{C}{\pi }](https://tex.z-dn.net/?f=%5Cfrac%7BC%7D%7B%5Cpi%20%7D)
</h3>
So, the first step would be : D = ![\frac{20}{\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7B%5Cpi%20%7D)
Then : D = 20 ÷ ![\pi](https://tex.z-dn.net/?f=%5Cpi)
Finally, the answer will be : 6.36619772 cm. or 6.4 cm.
<h3>The Radius can be Solved using: r =
![\frac{c}{2\pi }](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B2%5Cpi%20%7D)
</h3>
The first step would be : r = ![\frac{20}{2\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7B2%5Cpi%20%7D)
Then : 20 ÷ 6.2831853071796 (2
)
Finally, the answer will be : 3.18309886 cm. or 3.2 cm.
Answer:
The correct answer is
.
Step-by-step explanation:
We want to solve for y in the given equation. We can do this by rearranging the equation and using operational techniques to simplify.
![6y + x = 8 \ $\tex Subtract x from both sides of the equation.](https://tex.z-dn.net/?f=6y%20%2B%20x%20%3D%208%20%5C%20%24%5Ctex%20Subtract%20x%20from%20both%20sides%20of%20the%20equation.)
![6y + x - x = 8 - x \ $\tex Carry out the operation.](https://tex.z-dn.net/?f=6y%20%2B%20x%20-%20x%20%3D%208%20-%20x%20%5C%20%24%5Ctex%20Carry%20out%20the%20operation.)
![6y = 8 - x \ $\tex Rearrange so the equation lists the variables first and the constants second.](https://tex.z-dn.net/?f=6y%20%3D%208%20-%20x%20%5C%20%24%5Ctex%20Rearrange%20so%20the%20equation%20lists%20the%20variables%20first%20and%20the%20constants%20second.)
![6y = -x + 8 \ $\tex Create a coefficient for the x-variable (this is -1).](https://tex.z-dn.net/?f=6y%20%3D%20-x%20%2B%208%20%5C%20%24%5Ctex%20Create%20a%20coefficient%20for%20the%20x-variable%20%28this%20is%20-1%29.)
![6y = -1x + 8 \ $\tex Divide by 6 on both sides of the equation in order to isolate the y-variable.](https://tex.z-dn.net/?f=6y%20%3D%20-1x%20%2B%208%20%5C%20%24%5Ctex%20Divide%20by%206%20on%20both%20sides%20of%20the%20equation%20in%20order%20to%20isolate%20the%20y-variable.)
![\frac{6y}{6}=\frac{-1x}{6} + \frac{8}{6} \ $\tex Carry out this operation by simplifying the fractions and dividing out the operations accordingly.](https://tex.z-dn.net/?f=%5Cfrac%7B6y%7D%7B6%7D%3D%5Cfrac%7B-1x%7D%7B6%7D%20%2B%20%5Cfrac%7B8%7D%7B6%7D%20%5C%20%24%5Ctex%20Carry%20out%20this%20operation%20by%20simplifying%20the%20fractions%20and%20dividing%20out%20the%20operations%20accordingly.)
![y = -\frac{1}{6}x+\frac{4}{3} \ $\tex Be sure to verify that all fractions and terms are simplified as far as they can be and that the equation is written in proper syntax.](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B6%7Dx%2B%5Cfrac%7B4%7D%7B3%7D%20%5C%20%24%5Ctex%20Be%20sure%20to%20verify%20that%20all%20fractions%20and%20terms%20are%20simplified%20as%20far%20as%20they%20can%20be%20and%20that%20the%20equation%20is%20written%20in%20proper%20syntax.)
Because we have the <em>y</em>-variable isolated from the rest of the equation, we are done!
Answer:
The statement that cushion A is twice as popular as cushion B cannot be verified
Step-by-step explanation:
From the question we are told that:
Sample size n=38
Type a size A ![X_a=28](https://tex.z-dn.net/?f=X_a%3D28)
Type a size B
Generally the probability of choosing cushion A P(a) is mathematically given by
![P(a)=\frac{28}{38}](https://tex.z-dn.net/?f=P%28a%29%3D%5Cfrac%7B28%7D%7B38%7D)
![P(a)=0.73](https://tex.z-dn.net/?f=P%28a%29%3D0.73)
Generally the equation for A to be twice as popular as B is mathematically given by
![P(b)+2P(b)=3P](https://tex.z-dn.net/?f=P%28b%29%2B2P%28b%29%3D3P)
Therefore Hypothesis
![Null H_0: p \leq \frac{2P}{3P} \\Altenative H_A:p>\frac{2P}{3P}](https://tex.z-dn.net/?f=Null%20H_0%3A%20p%20%5Cleq%20%5Cfrac%7B2P%7D%7B3P%7D%20%5C%5CAltenative%20H_A%3Ap%3E%5Cfrac%7B2P%7D%7B3P%7D)
Generally the equation normal approx of p value is mathematically given by
![z=\frac{x-np_0-0.5}{\sqrt{np_0(1-p_0)} }](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-np_0-0.5%7D%7B%5Csqrt%7Bnp_0%281-p_0%29%7D%20%7D)
![z=\frac{28-(38*2/3)_0-0.5}{\sqrt{38*2/3*1/3} }](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B28-%2838%2A2%2F3%29_0-0.5%7D%7B%5Csqrt%7B38%2A2%2F3%2A1%2F3%7D%20%7D)
![z=0.75](https://tex.z-dn.net/?f=z%3D0.75)
Therefore from distribution table
![Pvalue=1-\theta (0.75)](https://tex.z-dn.net/?f=Pvalue%3D1-%5Ctheta%20%280.75%29)
![Pvalue=0.227](https://tex.z-dn.net/?f=Pvalue%3D0.227)
Therefore there is no sufficient evidence to disagree with the Null hypothesis ![H_0](https://tex.z-dn.net/?f=H_0)
Therefore the statement that cushion A is twice as popular as cushion B cannot be verified