Answer:
18
Step-by-step explanation:
The test statistic for the hypothesis would be 1.413.
Given that the participants in its new diet program lose, on average, more than 13 pounds and the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds.
The objective is to text the advertisement's claim that participants in new diet program lose weight, on average, more than 13 pounds.
Hypothesis:
Null hypothesis:H₀:μ=13
Alternative hypothesis:Hₐ:μ>13
Here, μ be the mean weight loss of all participants.
n=30,
Degree of freedom n-1=30-1=29
=13.8 and s=3.1
To test the null hypothesis H₀, the value of test static would be calculated as follows:
![\begin{aligned}t&=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\\ t_{29}&=\frac{13.8- 13}{\frac{3.1}{\sqrt{30}}}\\ &=\frac{0.8}{0.566}\\ &=1.413\end](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dt%26%3D%5Cfrac%7B%5Cbar%7Bx%7D-%5Cmu%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D%5C%5C%20t_%7B29%7D%26%3D%5Cfrac%7B13.8-%2013%7D%7B%5Cfrac%7B3.1%7D%7B%5Csqrt%7B30%7D%7D%7D%5C%5C%20%26%3D%5Cfrac%7B0.8%7D%7B0.566%7D%5C%5C%20%26%3D1.413%5Cend)
Hence, the value of the test static for the hypothesis with the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds is 1.413.
Learn more about hypothesis from here brainly.com/question/14783359
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Answer:
V1 = 60 km/h
V2 = 40 Km/h
Step-by-step explanation:
The speed of an object is defined as
Speed = distance / time
Let
V1 be the speed of the faster car
V2 be the speed of the other car
t1 the time it took for the first car to arrive
t2 the time it took for the second car to arrive
d1 the distance traveled by first car
d2 the distance traveled by second car
We know thanks to the problem that
V1 = V2 + 20 Km/h
t1 = t2 - 1 hour
d1 = d2 = 120 Km
d1 = V1 * t1
d2 = V2* t2
V1 * t1 = V2* t2
V1* t1 = (V1 -20)*(t1 +1)
The system of equations
(V1 -20)*(t1 +1) = 120
V1 * t1 = 120
120 + (120/t1) -20*t1 = 140
(120/t1) -20*t1 = 20
Which gives,
t1 = 2
This means
V1 = 60 km/h
V2 = V1 - 20 Km/h = 40 Km/h
![\left \{ {{S=14+L} (I) \atop {S+L=124}(II)} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7BS%3D14%2BL%7D%20%28I%29%20%5Catop%20%7BS%2BL%3D124%7D%28II%29%7D%20%5Cright.)
<span>Substitute (I) into (II), we have:
</span>
![S+L=124](https://tex.z-dn.net/?f=S%2BL%3D124)
![(14+L)+L=124](https://tex.z-dn.net/?f=%2814%2BL%29%2BL%3D124)
![14 + 2L = 124](https://tex.z-dn.net/?f=14%20%2B%202L%20%3D%20124)
![2L = 124 - 14](https://tex.z-dn.net/?f=2L%20%3D%20124%20-%2014)
![2L = 110](https://tex.z-dn.net/?f=2L%20%3D%20110)
![L = \frac{110}{2}](https://tex.z-dn.net/?f=L%20%3D%20%20%5Cfrac%7B110%7D%7B2%7D%20)
![\boxed{L = 55}](https://tex.z-dn.net/?f=%5Cboxed%7BL%20%3D%2055%7D)
<span>Replace (II) in (I), we have:
</span>
![S=14+L](https://tex.z-dn.net/?f=S%3D14%2BL)
![S = 14+ 55](https://tex.z-dn.net/?f=S%20%3D%2014%2B%2055)
![\boxed{S = 69}](https://tex.z-dn.net/?f=%5Cboxed%7BS%20%3D%2069%7D)
Answer:
each student sell:
Lori = 55 pizzasSteve = 69 pizzas<span>
</span>
Answer:
-9
Step-by-step explanation:
The triangle has two sides that are the same, so it is an isosceles triangle. Therefore, the base angles are the same.
Angles of a triangle add up to 180°, so:
70 + (x + 64) + (x + 64) = 180
70 + 2x + 128 = 180
2x = -18
x = -9