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musickatia [10]
3 years ago
6

What is the image of point (4, 5) after a counterclockwise rotation of 270º about the origin?

Mathematics
1 answer:
andriy [413]3 years ago
3 0
A <span>counterclockwise rotation of 270º about the origin is equivalent to a </span><span>clockwise rotation of 90º about the origin.

Given a point (4, 5), the x-value, i.e. 4 and the y-value, i.e. 5 are positive, hence the point is in the 1st quadrant of the xy-plane.

A clockwise rotation of </span><span>90º about the origin of a point in the first quadrant of the xy-plane will have its image in the fourth quadrant of the xy-plane. Thus the x-value of the image remains positive but the y-value of the image changes to negative.
Also the x-value and the y-value of the original figure is interchanged.
For example, given a point (a, b) in the first quadrant of the xy-plane, </span><span>a counterclockwise rotation of 270º about the origin which is equivalent to a <span>clockwise rotation of 90º about the origin will result in an image with the coordinate of (b, -a)</span>

Therefore, a </span><span>counterclockwise rotation of 270º about the origin </span><span>of the point (4, 5) will result in an image with the coordinate of (5, -4)</span> (option C)
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Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 85
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Answer:

The p value for this test is given p_v = 0.1071

Since the p value is higher than the significance level given of \alpha=0.05 we have enough evidence to FAIL to reject the null hypothesis. And we can say that the true proportion of firms in the manufacturing sector still do not offer any child-care benefits to their workersis is not significantly higher than 0.85 or 85% at 5% of significance.

Step-by-step explanation:

We define the proportion of interest as p who represent the true proportion of firms in the manufacturing sector still do not offer any child-care benefits to their workers

And we want to anaylze the following system of hypothesis:

Null hypothesis: p \leq 0.85

Alternative hypothesis: p >0.85

And the statistic for this test is given by:

z =\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}

The p value can be calculated with this formula:

p_v = P(z>z_{calc})

And the p value for this test is given p_v = 0.1071

Since the p value is higher than the significance level given of \alpha=0.05 we have enough evidence to FAIL to reject the null hypothesis. And we can say that the true proportion of firms in the manufacturing sector still do not offer any child-care benefits to their workersis is not significantly higher than 0.85 or 85% at 5% of significance.

4 0
3 years ago
If a varies directly as the cube root of B and if a equals to 3 when B equals to 64 find the formula connecting the variables he
Brrunno [24]

Answer:

a=k1\sqrt[3]{B}

B=125

Step-by-step explanation:

Given :

a=3

B=64

According to question

a ∝ \sqrt[3]{B}

therefore

a=k1 \sqrt[3]{B}........Eq(1)

K1=\frac{a}{\sqrt[3]{B} }......Eq(2)

Putting the value of a and B we get in Eq(2) we get

K1=\frac{3}{4}

Putting the value of k1 in Eq(1)

a=\frac{3}{4}\sqrt{B} .......................Eq(3)

putting the value of a=15/4 IN Eq(3) we get

\frac{15}{4}\ =\frac{3}{4} \sqrt[3]{B}  \\\\\sqrt[3]{B}\ =\ 5\\Cubing\  both\  side\  we\  get\\B=125

5 0
3 years ago
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