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4 years ago

Help Please, anyone good at domain values of composite functions.

Mathematics

1 answer:

spayn [35]4 years ago

7 0

Answer:

second choice

Step-by-step explanation:

First, do the composition of the functions.

$(f \circ g)(x) = f(g(x))$

$= f(\sqrt{x + 3})$

$(f \circ g)(x) = -8\sqrt{x + 3} - 4$

Now we find (fog)(9).

$(f \circ g)(9) = -8\sqrt{9 + 3} - 4$

$(f \circ g)(9) = -8\sqrt{12} - 4$

$(f \circ g)(9) = -16\sqrt{3} - 4$

(fog)(9) evaluates to a real number, so 9 is in the domain of the composition of functions f and g.

Answer: second choice

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Can someone help with my homework?

Len [333]

Answer:

1a) $-\frac{15}{4}$

1b) $\frac{95}{33}$

2a) $-84$

2b) 1

3a) $\frac{171}{550}$

3b) $4\frac{2}{7}$

Step-by-step explanation:

For the first equation, let's use $\frac{-a}{b} =\frac{a}{-b} =-\frac{a}{b}$ to right a new fraction.

Step 1- Reduce the fraction with 4.

$-\frac{\frac{12/4}{4/4} }{\frac{4}{5} } = -\frac{3}{\frac{4}{5} }$

Step 2- Simplify the complex fraction(LCD or Least Common Denominator).

$-\frac{3}{\frac{4}{5} } = -\frac{15}{4}$

An alternative form for this fraction is $-3\frac{3}{4} or -3.75$ .

For the second equation..

Step 1- Convert the mixed number to an improper fraction.

$\frac{6\frac{3}{9} }{\frac{11}{5} } = \frac{\frac{57}{9} }{\frac{11}{5} }$

Step 2- Simplify the complex fraction.

$\frac{\frac{57}{9} }{\frac{11}{5} } = \frac{95}{33}$

An alternative form for this fraction is $2\frac{29}{33} or 2.87$ .

For the third equation use $\frac{-a}{b} =\frac{a}{-b} =-\frac{a}{b}$ ...

Step 1- Simplify the complex fraction(LCD).

$-\frac{7}{\frac{1}{12} } = -84$

For the fourth equation...

Write the fraction as a division.

$\frac{12}{8}$ ÷ $\frac{3}{2}$

To divide a fraction, multiply by the reciprocal of that fraction.

$\frac{12}{8} *\frac{2}{3} = \frac{12*2}{8*3}$

Reduce the fraction with 3.

$\frac{4*2}{8}= \frac{4}{4} = 1$

For the fifth equation...

Convert the mixed number to an improper fraction.

$\frac{-1\frac{8}{11} }{-5\frac{5}{9} } = \frac{-\frac{19}{11} }{-\frac{50}{9} }$

Reduce the fraction with -1, this eliminates the negative sign.

Simplify the complex fraction.

$\frac{\frac{19}{11} }{\frac{50}{9} } = \frac{171}{550}$

An alternative form for this fraction is 0.3109.

For the sixth equation..

Write the fraction as a division.

$\frac{3}{7}$ ÷ $\frac{1}{10}$

To divide by a fraction, multiply by the reciprocal of that fraction.

$\frac{3}{7}$ ×10= $\frac{3*10}{7}$

Multiply the numbers.

$\frac{3*10}{7} = \frac{30}{7}$

Alternative form of this fraction is $4\frac{2}{7}$ or 4.285714.

Hope this helps! :)

8 0

3 years ago

23 is 12% of what number

Anon25 [30]

$\frac { 12 }{ 100 } \cdot x=23\\ \\ \Rightarrow \quad \frac { 3 }{ 25 } \cdot x=23\\ \\ \Rightarrow \quad \frac { 25 }{ 3 } \cdot \frac { 3 }{ 25 } \cdot x=23\cdot \frac { 25 }{ 3 } \\ \\ \Rightarrow \quad x=\frac { \left( 20+3 \right) \left( 25 \right) }{ 3 } \\ \\ \Rightarrow \quad x=\frac { 500+75 }{ 3 } \\ \\ \Rightarrow \quad x=\frac { 575 }{ 3 }$

8 0

4 years ago

Consumer Reports uses a 100-point customer satisfaction score to rate the nations major chain stores. Assume that from the past

zzz [600]

Answer:

(A) Mean = 84

(B) Variance = 118.714

Step-by-step explanation:

Data provided:

number of observations, n = 15

sample of 15 costco customer satisfaction scores follow

X $X-\bar{X}$ $(X-\bar{X})^2$

95 11 121

90 6 36

83 -1 1

64 -20 400

95 11 121

98 14 196

80 -4 16

83 -1 1

82 -2 4

93 9 81

86 2 4

80 -4 16

94 10 100

75 -9 81

62 -22 484

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

∑X = 1260 ∑= 1662

Now,

(A) Mean = $\frac{\textup{Sum of all observations}}{\textup{Total number of observations}}$

Mean = $\frac{\textup{1260}}{\textup{15}}$ = 84

(B) Variance = $\frac{\sum(X-\bar{X})^2}{n-1}$

Variance = $\frac{1662}{15-1}$

Variance = 118.714

7 0

3 years ago

$70 interested at 12% compunded continuously after a period of 4 years

MariettaO [177]

Our principal is $70. The rate is 12%
It can only be assumed that it's compounded once a year and it is invested for 4 years.
Therefore, using the equation:
P(1+r/n)^nt
We have 70(1 + .12/1)^(1)4
simplify for your answer:
70(1.12)^4
110.1464

4 0

4 years ago

Mr. Huyck needs 8 gallons of punch for the school dance. How many<br> quarts of punch would he need?

koban [17]

32 bc eight times four equals 32

8 0

3 years ago

Read 2 more answers