Answer:
A, y = {x²+ 6 x < 3
{-x + 6 x ≥ 3
Step-by-step explanation:
the parabola (the u shaped graph or the graph that is on top) is expressed by the function x² + 6, as it is 6 units up from the origin (0,0)
the line is expressed by the function -x + 6, as its first reflected across the x axis from the origin (0,0) and is then shifted 6 units up
these functions on this graph represent a piecewise function
looking at x² + 6, we see that it has an open circle on (3, 15). this means that the x coordinate 3 is not included in the solution to the function, and any x values that would be included are less than 3. in an inequality, this is expressed as x < 3
looking at our answer choices, this matches answer A. but let me continue with the explanation in case you run into a question that doesnt have it that easy
when we look at -x + 6, we see that it has a closed circle on (3,4) (approx (3,4), not sure about y-coordinate but its still the same). a closed circle means that the x coordinate 3 is included in the solution, and any numbers <em>greater than 3</em> are included in the solution. as an inequality, this is expressed as x ≥ 3
again we look at our answer choices and see that A is the only choice that supports both of these functions, so A is our answer
Answer:
Do not reject H0. The mean days surfed for longboarders is significantly larger than the mean days surfed for all shortboarders
Step-by-step explanation:
The null hypothesis is that the mean days surfed for all long boarders is larger than the mean days surfed for all short boarders
H0: μL > μs against the claim Ha: μL≤ μs
the alternate hypothesis is the mean days surfed for all long boarders isless or equal to the mean days surfed for all short boarders (because long boards can go out in many different surfing conditions)
The test statistic is
t= x1- x2/ √s1/n1+ s2/n2
1) Calculations
Longboards
Mean
ˉx=∑x/n=4+8+9+4+9+7+9+6+6+11+15+13+16+12+10+12+18+20+15+10+15+19+21+9+22+19+23+13+12+10/30
=377/30
=12.5667
Longboard Variance S2=[∑dx²-(∑dx)²/n]/n-1
=[831-(-13)²/30]/29
=831-5.6333/29
=825.3667/29
=28.4609
Shortboard Mean
ˉx=∑x/n=6+4+6+6+7+7+7+10+4+6+7+5+8+9+4+15+13+9+12+11+12+13+9+11+13+15+9+19+20+11/30
=288/30
=9.6
Shortboard Variance S2=[∑x²-(∑x)²/n]/n-1
=[ 3270-(288)2/30]/29
=3270-2764.8/29
=505.2/29
=17.4207
2) Putting values in the test statistic
t=|x1-x2|/√S²1/n1+S²2/n2
t =|12.5667-9.6|/√28.4609/30+17.4207/30
t =|2.9667|/√0.9487+0.5807
t=|2.9667|/√1.5294
t=|2.9667|/1.2367
t=2.3989
3) Degree of freedom =n1+n2-2=30+30-2=58
4) The critical region is t ≤ t(0.05) (58) =1.6716
5) Since the calculated t= 2.4 does not fall in the critical region t(0.05) (58) ≤ 1.6716 we do not reject H0.
The p-value is 0.008969. The result is significant at p <0 .05.
Answer:
y = 1/2x+4
Step-by-step explanation:
First we find the slope
m = (y2-y1)/(x2-x1)
= (3-6)/(-2-4)
= -3/-6
=1/2
The equation of a line in slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y =1/2x+b
Substitute one of the point into the equation
6 = 1/2(4) +b
6 = 2+b
b=4
y = 1/2x+4
9514 1404 393
Answer:
- 4 3-point baskets
- 7 2-point baskets
Step-by-step explanation:
Let x represent the number of 2-point baskets Nicoli made. Then (x -3) is the number of 3-point baskets. The total number of points is ...
2x +3(x -3) = 5x -9 = 26
5x = 35 . . . . . . add 9
x = 7 . . . . . . . divide by 5
(x -3) = 4 . . . find the number of 3-point baskets
Jokic made 7 2-point baskets and 4 3-point baskets.
Answer:
(x+2)(3x+1) are the factors
