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miskamm [114]
2 years ago
13

If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?

Mathematics
1 answer:
Vladimir79 [104]2 years ago
5 0

Answer:

  x ≥ 1

Step-by-step explanation:

There are no domain restrictions on a(x), so we can find the domain of the composite function by looking at that composition:

  (b \circ a)(x)=b(a(x)) = b(3x+1)=\sqrt{(3x+1)-4}\\\\(b \circ a)(x)=\sqrt{3x-3}=\sqrt{3(x-1)}

The argument of the square root function must be non-negative, so we must have ...

  3(x -1) ≥ 0

  x -1 ≥ 0 . . . . . divide by 3

  x ≥ 1 . . . . . . . add 1

The domain of b(a(x)) is x ≥ 1.

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Write a decimal that represents the value of one 1 bill and 5 quarters
andrey2020 [161]

Answer:

$2.25

Step-by-step explanation:

Note that 4 quarters = one dollar, which means that one quarter = 1.00/4 = 0.25

Multiply the value of 1 quarter (0.25) with the amount of quarters there are:

0.25 x 9 = 2.25

$2.25 is your answer

~

5 0
3 years ago
Read 2 more answers
Two trains leave stations 456 miles apart at the same time and travel toward each other. One train travels at 105 miles per hour
love history [14]

Answer:

let x=distance 105 mph train traveled

(456-x)=distance 85 mph train traveled

Travel time = distance/speed (equal in both directions)

 

x/105=(456-x)/85

85x=105*456-105x

190x=105*456

x=105*456/190=252 miles

travel time=252/105=2.4 hrs

ans:

The two trains will meet in 2.4 hrs

Step-by-step explanation:

there brainliest pls

6 0
3 years ago
How many solutions can be found for the equation 2 + x = 6?
White raven [17]
I think it's "B"?(6-2=x)

6 0
4 years ago
Refer to the Trowbridge Manufacturing example in Problem 2-35. The quality control inspection proce- dure is to select 6 items,
Ivanshal [37]

Answer:

77.64% probability that there will be 0 or 1 defects in a sample of 6.

Step-by-step explanation:

For each item, there are only two possible outcomes. Either it is defective, or it is not. The probability of an item being defective is independent of other items. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The true proportion of defects is 0.15

This means that p = 0.15

Sample of 6:

This means that n = 6

What is the probability that there will be 0 or 1 defects in a sample of 6?

P(X \leq 1) = P(X = 0) + P(X = 1)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{6,0}.(0.15)^{0}.(0.85)^{6} = 0.3771

P(X = 1) = C_{6,1}.(0.15)^{1}.(0.85)^{5} = 0.3993

P(X \leq 1) = P(X = 0) + P(X = 1) = 0.3771 + 0.3993 = 0.7764

77.64% probability that there will be 0 or 1 defects in a sample of 6.

5 0
3 years ago
Please help!!
crimeas [40]
1)~3x+12=3(x+4)\\\\ 2)~7y-7=7(y-1)\\\\ 3)~5x+30y=5(x+6y)\\\\ 4)~8m+36n=4(2m+9n)\\\\ 5)~6a^2+27=3(2a^2+9)\\\\ 6)~4y^2-24y=4y(y-6)\\\\ 7)~21cd-3d=3d(7d-1)\\\\ 8)~14gh-18h=2h(7g-9)\\\\ 9)~15a^2b-30ab=15ab(a-2)\\\\ 10)~16bc^2+24bc=8bc(2c+3)
3 0
3 years ago
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