Answer: (A) The image of JKL after a 90° counterclockwise about the origin is shown in figure 1. (B) The image of JKL after a reflection across the y-axis is shown in figure 2.
Explanation:
(A)
From the given figure it is noticed that the coordinate points are J(-4,1), K(-4,-2) and L(-3,-1).
If a shape rotate 90 degree counterclockwise about the origin, then,
![(x,y)\rightarrow (-y,x)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28-y%2Cx%29)
![J(-4,1)\rightarrow J'(-1,-4)](https://tex.z-dn.net/?f=J%28-4%2C1%29%5Crightarrow%20J%27%28-1%2C-4%29)
![K(-4,-2)\rightarrow K'(2,-4)](https://tex.z-dn.net/?f=K%28-4%2C-2%29%5Crightarrow%20K%27%282%2C-4%29)
![L(-3,-1)\rightarrow L'(1,-3)](https://tex.z-dn.net/?f=L%28-3%2C-1%29%5Crightarrow%20L%27%281%2C-3%29)
Therefore, the vertex of imare are J'(-1,-4), K'(2,-4) and L'(1,-3). The graph is shown in figure (1).
(B)
If a figure reflect across the y-axis then,
![(x,y)\rightarrow (-x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28-x%2Cy%29)
![J(-4,1)\rightarrow J''(4,1)](https://tex.z-dn.net/?f=J%28-4%2C1%29%5Crightarrow%20J%27%27%284%2C1%29)
![K(-4,-2)\rightarrow K''(2,-4)](https://tex.z-dn.net/?f=K%28-4%2C-2%29%5Crightarrow%20K%27%27%282%2C-4%29)
![L(-3,-1)\rightarrow L''(3,-1)](https://tex.z-dn.net/?f=L%28-3%2C-1%29%5Crightarrow%20L%27%27%283%2C-1%29)
Therefore, the vertex of imare are J''(4,1), K''(2,-4) and L''(3,-1). The graph is shown in figure (2).
Answer:
Step-by-step explanation:
Hello!
The variable of interest is:
X: number of daily text messages a high school girl sends.
This variable has a population standard deviation of 20 text messages.
A sample of 50 high school girls is taken.
The is no information about the variable distribution, but since the sample is large enough, n ≥ 30, you can apply the Central Limit Theorem and approximate the distribution of the sample mean to normal:
X[bar]≈N(μ;δ²/n)
This way you can use an approximation of the standard normal to calculate the asked probabilities of the sample mean of daily text messages of high school girls:
Z=(X[bar]-μ)/(δ/√n)≈ N(0;1)
a.
P(X[bar]<95) = P(Z<(95-100)/(20/√50))= P(Z<-1.77)= 0.03836
b.
P(95≤X[bar]≤105)= P(X[bar]≤105)-P(X[bar]≤95)
P(Z≤(105-100)/(20/√50))-P(Z≤(95-100)/(20/√50))= P(Z≤1.77)-P(Z≤-1.77)= 0.96164-0.03836= 0.92328
I hope you have a SUPER day!
Let h=height. then h/36 = 8/12
12h=288
h=24 feet
Answer:
The total cost depends on the weight of the package
Step-by-step explanation:
When looking at a graph, know that the x-axis is the independent variable. It can change, but is independent of other factors.
The y-axis is the dependent variable, which changes based on the independent variable.