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3 years ago

Which statement is true about the value of (6^-n)(6^n)

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

5 0

They are a not equal because one variable is positive and the other is not

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A veterinarian will prescribe an antibiotic to a dog based on its weight. The effective dosage of the antibiotic is given by d ≥

gregori [183]

Answer:

B) (35, 260)

Step-by-step explanation:

A veterinarian will prescribe an antibiotic to a dog based on its weight. The effective dosage of the antibiotic is given by d ≥ 1∕5w2, where d is dosage in milligrams and w is the dog's weight in pounds. Which of the following ordered pairs gives an effective dosage of antibiotics for a 35-pound dog?

A) (35, 240)

B) (35, 260)

C) (260, 35)

D) (240, 35)

Ordered pairs is composed of pairs, usually an x coordinate and a y coordinate. It refers to a location of a point on the coordinate. It matches numbers to functions or relations.

Given the relation between d is dosage in milligrams and w is the dog's weight in pounds as d ≥ 1∕5w²

For a 35 pound dog (i.e w = 35 pound). The dosage is given as:

d ≥ 1∕5(35)² ≥ 245 milligrams.

For an ordered pair (x, y), x is the independent variable (input) and y is the dependent variable (output).

The dog weight is the independent variable and the dosage is the dependent variable.

From the ordered pairs, the best option is (35, 260) because 260 ≥ 240

6 0

3 years ago

There are 442 boy students in class

poizon [28]

Answer:

520

Step-by-step explanation:

This problem is

boys + girls = total

Boys = 442

Girls = 15% of the total

Therefore, substituting in, gives us:

442 + .15t = t, where t is total

Then 442 = .85t and

t = 520

5 0

3 years ago

PLZ HELP!!! Use limits to evaluate the integral.

Marrrta [24]

Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:

$\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]$

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

$r_i=\dfrac{2i}n$

where $1\le i\le n$ . Each interval has length $\Delta x_i=\frac{2-0}n=\frac2n$ .

At these sampling points, the function takes on values of

$f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}$

We approximate the integral with the Riemann sum:

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3$

Recall that

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

so that the sum reduces to

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}$

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

$\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}$

Just to check:

$\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28$

4 0

3 years ago

Write the expanded form for 34.75

S_A_V [24]

Answer:

30+4+0.7+0.05

Step-by-step explanation:

Because the expanded form is added the number.

3=30

4=4.

7=0.7

and 5=0.05 so all together is 30+4+0.7+0.05

7 0

2 years ago

Graph the six terms of a finite series where a1 = −3 and r = 1.5.

s344n2d4d5 [400]

We are given the first term and the common ratio, this means they belong to a geometric series.

For the given series:

$a_{1}=-3 \\ 
r=1.5$

Each term of the geometric series is obtained by multiplying the previous term by common ratio.

So the next terms will be:

-4.5, -6.75, -10.125, -15.1875, -22.78125

The general formula for the G.P would be:

$a_{n}=-3(1.5)^{n-1}$

On plotting the series, the result will be like this:

6 0

4 years ago

Read 2 more answers