If f(x) is a third degree polynomial function, how many distinct imaginary roots are possible

The point (5, -2) is rotated 90° about the origin. Its image is

tigry1 [53]

rotated 90° about the origin
(x,y) = (-y, x)

so (5, -2) is rotated 90° about the origin = (2, 5)

answer
b.(2, 5)

7 0

3 years ago

In 1925, Zbigniew Morón published a rectangle that could be dissected into nine different sized squares as shown in the diagram.

Vlada [557]

Answer:

Area of the rectangle = 1056 square units

Step-by-step explanation:

Rectangle published could be dissected into nine different squares with different sizes.

Area of the squares with different measure of sides will be,

For side length = 1 unit

Area of the square = (Side)²

= 1²

= 1 square units

For side length = 4 units

Area of the square = 4² = 16 units²

For side length = 7 units

Area of the square = 7² = 49 units²

For side length = 8 units

Area of the square = 8² = 64 units²

For side length = 9 units

Area of the square = 9² = 81 square units

For side length = 10 units

Area of the square = 10² = 100 square units

For side length = 14 units

Area of the square = 14² = 196 square units

For side length = 15 units

Area of the square = 15² = 225 square units

For side length = 18 units

Area of the square = 18² = 324 square units

Total area of the rectangle by adding these 9 squares

= 1 + 16 + 49 + 64 + 81 + 100 + 196 + 225 + 324

= 1056 square units

8 0

4 years ago

A birthday cake is shaped like a square. The area of the square is 64

anastassius [24]

Answer:

8 square inches. You find area by length x height. A square's sides are all of equal length. So what number x itself is 64? The answer is 8 because 8 x 8 equals 64.

3 0

3 years ago

Help Please! Find The Circumference Of A Circle With D=22.1.

Pavlova-9 [17]

Answer:

72.25663

Step-by-step explanation:

C=2πr=2·π·11.5≈72.25663

8 0

3 years ago

In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from

Maksim231197 [3]

Answer:

$z=\frac{0.0003214 -0.00034}{\sqrt{\frac{0.00034(1-0.00034)}{420095}}}=-0.654$

$p_v =2*P(Z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.005$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.

Step-by-step explanation:

1) Data given and notation

n=420095 represent the random sample taken

X=135 represent the subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)

$\hat p=\frac{135}{420095}=0.0003214$ estimated proportion of subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)

$p_o=0.00034$ is the value that we want to test

$\alpha=0.005$ represent the significance level

Confidence=99.5% or 0.995

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the brain or nervous system at a rate that is different from the rate of 0.0340% :

Null hypothesis: $p=0.00034$

Alternative hypothesis: $p \neq 0.00034$

When we conduct a proportion test we need to use the z statistic, and the is given by:

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.0003214 -0.00034}{\sqrt{\frac{0.00034(1-0.00034)}{420095}}}=-0.654$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.005$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.005$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.

4 0

3 years ago