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2 years ago

Please give answer to this problem

Mathematics

1 answer:

andrey2020 [161]2 years ago

5 0

The two roots $a +\sqrt{b}$ and $a -\sqrt{b}$ are called conjugate radicals

<h3>Conjugate of a radical </h3>

The conjugate of a radical is the value which when multiplied with the radical expression clears the radical. Conjugates have the same numbers but the opposite sign in the middle.

The given roots are

$a +\sqrt{b}$ and $a -\sqrt{b}$

They have the same numbers but opposite signs in the middle.

Hence, the two roots $a +\sqrt{b}$ and $a -\sqrt{b}$ are called conjugate radicals

Learn more on Conjugate radicals here: brainly.com/question/20523059

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Choose the equation of the horizontal line that passes through the point (2,4)

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Answer:

y = 4

Step-by-step explanation:

The point (2, 4) has the x intercept = 2 and y intercept = 4.

A horizontal line has a slope of 0, therefore every point on a horizontal line has the same value and a slope of 0.

So to find the equation of the horizontal line, we use the value of y intercept which can be written in the form y = b where point is (a, b).

Since the point given here is (2, 4), therefore the equation of the horizontal line which passes through it will be y = 4.

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How to calculate a circumference of a circle?

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Answer:

πd or 2πr

Step-by-step explanation:

To calculate the circumference of a circle, multiply the diameter of the circle by pi or multiply 2 times the radius times pi.

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Which expression best represents the product of two consecutive integers?

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Answer:

(B) x(x+1)

Step-by-step explanation:

If we take x as one of the integers,

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3 years ago

When the sample size and the sample proportion remain the same, a 90 percent confidence interval for a population proportion p w

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Answer:

A 90% confidence interval for p will be narrower than the 99% confidence interval.

Step-by-step explanation:

The formula to compute the (1 - α) % confidence interval for a population proportion is:

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

Here $\hat p$ is the sample proportion.

The margin of error of the confidence interval is:

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

The MOE is dependent on:

Confidence level
Standard deviation
Sample size

The MOE is directly related to the confidence level and standard deviation.

So if any of the two increases then the MOE also increases, thus widening the confidence interval.

And the MOE is inversely related to the sample size.

So if the sample increases the MOE decreases and vice versa.

It is provided that the sample size and the sample proportion are not altered.

The critical value of z for 90% confidence level is:

$z_{\alpha/2}= z_{0.10/2}=z_{0.05}=1.645$

And the critical value of z for 99% confidence level is:

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

So as the confidence level increases the critical value increases.

Thus, a 90% confidence interval for p will be narrower than the 99% confidence interval.

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3 years ago

Country A has a growth rate of 2.2% per year. The population is currently 5,667,000, and the land area of Country A is 31,000,00

Akimi4 [234]

Answer:

It will be 290 years until there be one person for every square yard of land.

Step-by-step explanation:

We are looking for when the country's population is equivalent to its area in square yards: 31,000,000,000.

Write an equation for the situation: (Trickiest part)

p(x) = (5,667,000)(1 + 0.022)ˣ <= Can modify compound interest equation

31,000,000,000 = (5,667,000)(1 .022ˣ)

Started rounding off numbers

547.056 = 1 .022ˣ <= $x = \frac{log(ans)}{log(base)}$

Solve using log.

x = 2.738 / 0.00945 <= log(547.056) / log(1.022)

x = 289.7 <= Round up because rate is annual. Before the 290th year, the population is less than the number of square yards.

x = 290

Total amount with annual compound interest equation applied to this problem:

$A = P(1 + r)^{t}$ (Principle is starting investment)

Population = (Starting population)(1 + growth rate)^(time)

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4 years ago