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3 years ago

Which of the following is correctly written in Standard Form?

Mathematics

1 answer:

Marta_Voda [28]3 years ago

8 0

9514 1404 393

Answer:

(b) 4x- 3y = 6

Step-by-step explanation:

Standard form is ...

ax +by = c

where a, b, c are mutually prime integers and a > 0. (If a=0, then b>0.)

A: slope-intercept form with variables on both sides of the equal sign.

B: standard form

C: coefficients aren't integers

D: coefficients aren't integers; leading coefficient is negative.

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The population of bacteria in a certain culture can be modeled by the function P(t)=10000(1.03)^t. Is the population of bacteria

ch4aika [34]

Answer:

The population of bacteria is increasing.

Step-by-step explanation:

The function modelling the population of bacteria in the given culture is an exponential function; We have a base 1.03 and an exponent t. An exponential function is said to be increasing if the base is strictly greater than 1, this implies that the population of the bacteria is increasing as t increases from 0 to infinity.

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3 years ago

Read 2 more answers

Which of the choices below is not a possible correlation coefficient?

fiasKO [112]

Answer:

The condition for r is the following:

$-1 \leq r \leq 1$

And for this case if we analyze the options the only impossible value is given by:

1.0528

Because this value is higher than 1 and not satisfy the general limits for r

Step-by-step explanation:

The correlation coefficient is a measure of dispersion and is a value between -1 and 1, and is defined as:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

The condition for r is the following:

$-1 \leq r \leq 1$

And for this case if we analyze the options the only impossible value is given by:

1.0528

Because this value is higher than 1 and not satisfy the general limits for r

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3 years ago

Find all constants a such that the vectors (a, 4) and (2, 5) are parallel.

Nezavi [6.7K]

Answer:

$\displaystyle a = \frac{8}{5}$ .

Step-by-step explanation:

Two vectors $(x_1,\, y_1)$ and $(x_2,\, y_2)$ are parallel to one another if and only if the ratio between their corresponding components are equal:

$\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}$ .

Equivalently:

$\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ .

For the two vectors in this equation to be parallel to one another:

$\displaystyle \frac{a}{4} = \frac{2}{5}$ .

Solve for $a$ :

$\displaystyle a = \frac{8}{5}$ .

$\displaystyle \frac{8}{5}$ would be the only valid value of $a$ ; no other value would satisfy the $\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ equation.