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Gennadij [26K]
3 years ago
14

If f(x)= x-3/x and g(x)= 5x-3, what is the domain of (f•g)(x)

Mathematics
1 answer:
ad-work [718]3 years ago
4 0

f(x)=\dfrac{x-3}{x},\ D_f:x\neq0\\\\g(x)=5x-3,\ D_g=\mathbb{R}\\\\(f\cdot g)(x)=f(x)\cdot g(x)\\\\(f\cdot g)(x)=\dfrac{x-3}{x}\cdot(5x-3)=\dfrac{(x-3)(5x-3)}{x}\\\\D_{(f\cdot g)}=D_f

Answer: The domain of (f•g)(x) is all real numbers except for 0

D=\mathbb{R}-\{0\}

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Find the radius of the sphere with the given volume<br><br>volume= 9/16 (pie symbol)ft cubed
xz_007 [3.2K]
Remember, the volume formula of a sphere is \frac{4}{3}  \pi  r^{3}.

Set that equation equal to whatever volume they give you and solve for r.

\frac{4}{3} \pi r^{3} = \frac{9}{16} \pi

Now solve for r! I know you can do this. If you need help, just comment.


5 0
3 years ago
The thicknesses of 81 randomly selected aluminum sheets were found to have a variance of 3.23. Construct the 98% confidence inte
Yuliya22 [10]

Answer:

The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.

Step-by-step explanation:

The confidence interval for population variance is given as below:

[(n - 1)\times S^{2}  /  X^{2}  \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2}  / X^{2} 1- \alpha/2, n- 1 ]

We are given

Confidence level = 98%

Sample size = n = 81

Degrees of freedom = n – 1 = 80

Sample Variance = S^2 = 3.23

X^{2}_{[\alpha/2, n - 1]}   = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401

(By using chi-square table)

[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]

[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]

2.3004 < σ^2 < 4.8263

Lower limit = 2.30

Upper limit = 4.83.

8 0
2 years ago
Can someone help me figure out the answer?
love history [14]

Answer:

8763

Step-by-step explanation:

Let x represent the number of students the college had last year. Then this year's enrollment is ...

... x - 3%·x = 8500

... x(1 - 0.03) = 8500 . . . . . collect terms

... x = 8500/0.97 ≈ 8762.89 . . . . divide by the coefficient of x

Enrollment last year was about 8763.

_____

Of course, you know 3% = 3/100 = 0.03.

5 0
3 years ago
What is y+0.4=2? help please
sveticcg [70]
Y + 0.4 = 2 .....subtract 0.4 from both sides
y = 2 - 0.4
y = 1.6 <==
8 0
3 years ago
Read 2 more answers
What is 106 divided by 5
Bas_tet [7]

Answer:

21.2

Step-by-step explanation:

5 0
2 years ago
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