Which statement describes the value of the expression 15*(8+45)?

NISA [10]

1 km=1093.61yards

6 km= 6*1093.61yards
6 km= 6561.66yards

Answer= 6561.66 yards

7 0

3 years ago

Which definite integral approximation formula is this: the integral from a to b of f(x)dx ≈ (b-a)/n * [<img src="https://tex.z-d

Stella [2.4K]

The answer is most likely A.

The integration interval [a, b] is split up into n subintervals of equal length (so each subinterval has width (b - a)/n, same as the coefficient of the sum of y terms) and approximated by the area of n rectangles with base (b - a)/n and height y.

n subintervals require n + 1 points, with

x₀ = a

x₁ = a + (b - a)/n

x₂ = a + 2(b - a)/n

and so on up to the last point x = b. The right endpoints are x₁, x₂, … etc. and the height of each rectangle are the corresponding y 's at these endpoints. Then you get the formula as given in the photo.

• "Average rate of change" isn't really relevant here. The AROC of a function G(x) continuous* over an interval [a, b] is equal to the slope of the secant line through x = a and x = b, i.e. the value of the difference quotient

(G(b) - G(a) ) / (b - a)

If G(x) happens to be the antiderivative of a function g(x), then this is the same as the average value of g(x) on the same interval,

$g_{\rm ave}=\dfrac{G(b)-G(a)}{b-a}=\dfrac1{b-a}\displaystyle\int_a^b g(x)\,\mathrm dx$

(* I'm actually not totally sure that continuity is necessary for the AROC to exist; I've asked this question before without getting a particularly satisfying answer.)

• "Trapezoidal rule" doesn't apply here. Split up [a, b] into n subintervals of equal width (b - a)/n. Over the first subinterval, the area of a trapezoid with "bases" y₀ and y₁ and "height" (b - a)/n is

(y₀ + y₁) (b - a)/n

but y₀ is clearly missing in the sum, and also the next term in the sum would be

(y₁ + y₂) (b - a)/n

the sum of these two areas would reduce to

(b - a)/n = (y₀ + 2 y₁ + y₂)

which would mean all the terms in-between would need to be doubled as well to get

$\displaystyle\int_a^b f(x)\,\mathrm dx\approx\frac{b-a}n\left(y_0+2y_1+2y_2+\cdots+2y_{n-1}+y_n\right)$

7 0

3 years ago

Which description is correct for the x-intercept(s) of Function A and Function B?

ArbitrLikvidat [17]

Answer:

Step-by-step explanation:

Generally,

A straight line equation is given as

y = mx + c

Where,

m is the slope or gradient of the line

c is the intercept of y axis, when x = 0

Now,

Given the function A

g(x) = 0 7 0 2 -2

x = -2 3. 5 -1 0

So, we said the intercept c is when x = 0,

Therefore, in this case when x=0, g(x) = -2

Then, the intercept is -2 on y axis

Then, it has only one intercept, which is -2 on y-axis

To get the intercept on x axis, we will set y to zero,

In this case,

g(x) = 0, then, we have the intercept on x-axis to be -2 and 5

So it has 2-intercept on x axis, one positive and one negative

Given the function B

F(x) = |x| - 3

Comparing this to equation of a line, y= mx + c,

Then we notice that, the intercept is -3

Then, it has only one intercept which is -3 on y axis.

Now, to get the intercept on x axis, we will set f(x) = 0

F(x) = |x| - 3

0 = |x| - 3

Then, |x| = 3

Then, x = 3 or -x =3

Note that, |x| means x and -x

Then, x = 3 or x = -3

So it has also two intercept on the x axis, one positive and one negative.

Then, the third option is the correct option

Both functions have one negative and one positive x-intercept.

5 0

3 years ago

9 friends are lining up. Joe, Susan, John, and Meredith must be beside each other. How many ways can they line up?

ZanzabumX [31]

<h3>Answer: 17,280</h3>

This is one single number slightly over 17 thousand.

You may need to erase the comma when typing the answer in.

=========================================================

Explanation:

Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).

The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.

There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.

Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.

So overall the answer is 4!*6! = 24*720 = 17,280

You may need to erase the comma when typing the answer in.

-------------

Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.

6 0

3 years ago

??????????????????????????

djyliett [7]

Step-by-step explanation:

1 )48

2 )11

answer is this

5 0

2 years ago

Read 2 more answers