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yuradex [85]
3 years ago
9

If f(x) = x2 – 3 and g(x) = 4x +3, then f(g(2)) =

Mathematics
1 answer:
WARRIOR [948]3 years ago
8 0

Answer:

4*+1

Step-by-step explanation:

To find

g

(

f

(

x

)

)

you must substitute

f

(

x

)

or

4

x

+

3

for each occurrence of

x

in

g

(

x

)

.

g

(

x

)

=

x

−

2

becomes:

g

(

f

(

x

)

)

=

(

4

x

+

3

)

−

2

g

(

f

(

x

)

)

=

4

x

+

3

−

2

g

(

f

(

x

)

)

=

4

x

+

1

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The figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
Mila [183]

We know angle x=y(vertically opposite angles)

Since 3 angles lie on a straight line,

y+60+70=180 (linear pair)

y+130=180

y=180-130

y=50 degrees

7 0
3 years ago
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.The ma
Lana71 [14]

Answer:

The advertisement should use 16 minutes.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \mu e^{-\mu x}

In which \mu = \frac{1}{m} is the decay parameter.

The probability that x is lower or equal to a is given by:

P(X \leq x) = \int\limits^a_0 {f(x)} \, dx

Which has the following solution:

P(X \leq x) = 1 - e^{-\mu x}

The probability of finding a value higher than x is:

P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.

This means that m = 3.5, \mu = \frac{1}{3.5} = 0.2857

What number of minutes should the advertisement use?

The values of x for which:

P(X > x) = 0.01

So

e^{-\mu x} = 0.01

e^{-0.2857x} = 0.01

\ln{e^{-0.2857x}} = \ln{0.01}

-0.2857x = \ln{0.01}

x = -\frac{\ln{0.01}}{0.2857}

x = 16.12

Rounding to the nearest number, the advertisement should use 16 minutes.

5 0
3 years ago
Samuel makes a dozen of mini cupcakes using 5/8 ​ cups of sugar, 3 cups of chocolate chips and 1/2 cup of butter. If each cupcak
baherus [9]

I don't what form of measurement to use (like grams, cusp, etc.) but I'm pretty sure it'd be cups

I think it's 5/96 or .05208333

So, 5/8 is .625. Dividing that up in throwing it into 12 cupcakes.

8 0
2 years ago
The expression √93 is in between two whole numbers. Write the two numbers with a comma and a space in between (for example: 1, 2
Ann [662]

Answer:

9, 10

Step-by-step explanation:

9² = 81

10² = 100

3 0
3 years ago
Calculate the gradient of the line using rise/run method.
Lapatulllka [165]

Given:

The graph of line.

To find:

The gradient of the line using rise/run method.

Solution:

We know that the gradient of a line is also known as slope.

Slope=\dfrac{Rise}{Run}

Consider the two intercepts, then rise is distance between origin and y-intercept and run is the distance between origin and the x-intercept. But rise must be negative because the value of y decreased from 3 to 0.

Rise=-3

Run=2

Now,

Slope=\dfrac{Rise}{Run}

Slope=\dfrac{-3}{2}

The gradient of the line is -\dfrac{3}{2}.

Therefore, the correct option is C.

8 0
3 years ago
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