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zalisa [80]
3 years ago
5

What is the ordered pair of C′ after point C (1, 2) is rotated 90° clockwise?

Mathematics
2 answers:
Ahat [919]3 years ago
7 0

Answer: (2,-1)

Step-by-step explanation:

The rule for rotation of a shape about 90° clockwise is given by :-

(x,y)\rightarrow(y,-x)  [i.e. interchange x by y and y by negative of x  ]

Given point : C (1, 2)

When point C is rotated 90° clockwise , then the  ordered pair for its image C' will be :-

C(1,2)\rightarrow (2,-1)

Hence, the  ordered pair of C′ after point C (1, 2) is rotated 90° clockwise = (2,-1).

ivolga24 [154]3 years ago
4 0

Answer:

C'(2,-1)

Step-by-step explanation:

1) Transform point C(1,2) to polar coordinates.

C(1,2)=C(x,y)=C(r,tetha)=C(squareroot(5),63.44Degrees)

2) Substract 90 degress to get C'

C'=(squareroot(5),-26.56)

3) Transform point C' to cartesian coordinates.

C'=(x,y)=(squarerott(5)cos(-26.56),squareroot(5)sin(-26.56)

=C'(2,-1)

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Answer:

(a) The proportion of tenth graders reading at or below the eighth grade level is 0.1673.

(b) The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.198, 0.260).

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Let <em>X</em> = number of students who read above the eighth grade level.

(a)

A sample of <em>n</em> = 269 students are selected. Of these 269 students, <em>X</em> = 224 students who can read above the eighth grade level.

Compute the proportion of students who can read above the eighth grade level as follows:

\hat p=\frac{X}{n}=\frac{224}{269}=0.8327

The proportion of students who can read above the eighth grade level is 0.8327.

Compute the proportion of tenth graders reading at or below the eighth grade level as follows:

1-\hat p=1-0.8327

        =0.1673

Thus, the proportion of tenth graders reading at or below the eighth grade level is 0.1673.

(b)

the information provided is:

<em>n</em> = 709

<em>X</em> = 546

Compute the sample proportion of tenth graders reading at or below the eighth grade level as follows:

\hat q=1-\hat p

  =1-\frac{X}{n}

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The critical value of <em>z</em> for 95% confidence interval is:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

Compute the 95% confidence interval for the population proportion as follows:

CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

     =0.229\pm 1.96\times \sqrt{\frac{0.229(1-0.229)}{709}}\\=0.229\pm 0.03136\\=(0.19764, 0.26036)\\\approx (0.198, 0.260)

Thus, the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.198, 0.260).

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70.49 divided by 19 pls help
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