What graph shows a rate of $7.50 per hour

What is h(x)=4x+1 if the value of h is (-3)

Reil [10]

Step-by-step explanation:

Salna, it is a question about simple function

Substitute x= -3 into function,

h(-3) = 4 x (-3) + 1

= -11

5 0

3 years ago

In a normally distributed data set a mean of 55 where 99.7% of the data fall between 47.5 and 62.5, what would be the standard d

NeX [460]

Given that normally distributed data set has a mean of 55 and 99.7% of data fall between 47.5 and 62.5.

Let s be the standard deviation of data set.

Since 99.7% data fall within 3 standard deviations of mean, z-value for 47.5 and 62.5 has an absolute value of 3.

That is |z|=3

But z= $\frac{x-mean}{standard deviation}$

Let us plugin x=47.5 and mean =55 and equate it to 3.

That is $|\frac{47.5-55}{s}| = 3$

$|\frac{-7.5}{s} | =3$

Since x is always positive ( being standard deviation), $|\frac{-7.5}{s} | = \frac{|-7.5|}{s} = \frac{7.5}{s}$

Hence $\frac{7.5}{s}= 3$

$s=\frac{7.5}{3} = 2.5$

We will get same value with 62.5 as well.

Hence standard deviation of data set is 2.5.

3 0

4 years ago

Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative. f"(x) = 2x + 9e

ad-work [718]

Answer:

$f(x)=\frac{x^3}{3}+9e^x+Cx+D$

Step-by-step explanation:

The function F(x) is an antiderivative of the function f(x) on an interval I if

F′(x) = f(x) for all x in I.

The function F(x) + C is the General Antiderivative of the function f(x) on an interval I if F′(x) = f(x) for all x in I and C is an arbitrary constant.

The Indefinite Integral of f(x) is the General Antiderivative of f(x).

$\int {f(x)} \, dx =F(x)+C$

To find the first antiderivative you must integrate the function $f''(x) = 2x + 9e^x$

$f'(x)=\int { 2x + 9e^x} \, dx \\\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int \:2xdx+\int \:9e^xdx = x^2+9e^x\\\\\mathrm{Add\:a\:constant\:to\:the\:solution}\\\\x^2+9e^x+C$

To find the second antiderivative you must integrate the function $f'(x) =x^2+9e^x+C$

$f(x)=\int {x^2+9e^x+C} \, dx\\\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int \:x^2dx+\int \:9e^xdx+\int \:Cdx= \frac{x^3}{3}+9e^x+Cx\\\\\mathrm{Add\:a\:constant\:to\:the\:solution}\\\\\frac{x^3}{3}+9e^x+Cx+D$

Therefore,

$f(x)=\frac{x^3}{3}+9e^x+Cx+D$

8 0

3 years ago

Help please, it is easy but not for me.

Grace [21]

Answer:

60.28.

Step-by-step explanation:

We need the sine function because we are given the opposite side and we need the hypotenuse.

sin 71 = 57 / x

Cross multiply

x * sin 71 = 57

x = 57 / sin 71

= 60.28.

6 0

3 years ago

A sum of compounded annually, amount to Rs

wolverine [178]

Answer:

Step-by-step explanation:

ollowing is the formula for calculating compound interest when time period is specified in years and interest rate in % per annum.

A = P(1+r/n)nt

CI = A-P

Where,

CI = Compounded interest

A = Final amount

P = Principal

t = Time period in years

n = Number of compounding periods per year

r = Interest rate

Calculation Examples

You can solve for any variable by rearranging the compound interest formula as illustrated in the following examples:-

1. What is the compound interest of 75000 at 7.9% per annum compounded semi-annually in 3 years?

Ans. A = P(1+r/n)nt = 75000(1 + (7.9 / 100) / 2)6 = 94625.51

Interest = 94625.51 - 75000 = 19625.51

8 0

3 years ago