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4 years ago

Simply Each Expression

Mathematics

2 answers:

vitfil [10]4 years ago

3 0

Answer:

$\frac{4}{9x^2}$

Step-by-step explanation:

$(\frac{2x^3}{3x^4} )^2$

$= (\frac{2}{3x} )^2$

$= \frac{4}{9x^2}$

Vsevolod [243]4 years ago

3 0

$\left( \dfrac{2x^2}{3x^4} \right)^2 = \dfrac{4x^6}{9x^8} = \dfrac{4}{9x^2}$

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In the diagram, AD=CD=CB and measure of angle A=40°. How many degrees are in angle DCB?

Ad libitum [116K]

Answer:

$20^{\circ}$

Step-by-step explanation:

Consider triangle ACD. This triangle is isosceles triangle, because AD = DC. Angles adjacent to the base AC are congruent abgles, so

$m\angle DAC=m\angle DCA=40^{\circ}$

The sum of the measures of all interiror angles in the triangle is always $180^{\circ},$ then

$m\angle DAC+m\angle DCA+m\angle ADC=180^{\circ}\\ \\40^{\circ}+40^{\circ}+m\angle ADC=180^{\circ}\\ \\m\angle ADC=180^{\circ}-40^{\circ}-40^{\circ}=100^{\circ}$

Angles ADC and BDC are supplementary angles (add up to $180^{\circ}$ ), then

$m\angle BDC=180^{\circ}-100^{\circ}=80^{\circ}$

Consider triangle BCD. This triangle is isosceles triangle because BC = DC. Angles adjacent to the base BD are congruent abgles, so

$m\angle BDC=m\angle DBC=80^{\circ}$

The sum of the measures of all interiror angles in the triangle is always $180^{\circ},$ then

$m\angle DBC+m\angle BDC+m\angle BCD=180^{\circ}\\ \\80^{\circ}+80^{\circ}+m\angle BCD=180^{\circ}\\ \\m\angle BCD=180^{\circ}-80^{\circ}-80^{\circ}=20^{\circ}$

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3 years ago

For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a f

sashaice [31]

Answer: First of all, we will add the options.

A. Yes, because 3 inches falls above the maximum value of lengths in the sample.

B. Yes, because the regression equation is based on a random sample.

C. Yes, because the association between length and weight is positive.

D. No, because 3 inches falls above the maximum value of lengths in the sample.

E. No, because there may not be any 3-inch fish of this species in the pond.

The correct option is D.

Step-by-step explanation: It would not be appropriate to use the model to predict the weight of species that is 3 inches long because 3 inches falls above the maximum value of lengths in the sample.

As we can see from the question, the model only accounts for species that are within the range of 0.75 to 1.35 inches in length, and species smaller or larger than that length have not been taken into consideration. Therefore the model can not be used to predict the weights of fishes not with the range accounted for.

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3 years ago

The population of a town with a 20162016 population of 87 comma 00087,000 grows at a rate of 1.91.9% per year. a. Find the rate

SCORPION-xisa [38]

Answer:

Given,

The initial population, P = 87,000,

Annual rate of increasing, r = 1.9 %,

a) Thus, the population after t years,

$A=P(1+\frac{r}{100})^t$