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Marizza181 [45]
4 years ago
8

Let f(x)=6x+7 and g(x)=8x+2, and find the following (Fog)(-3) Answer please

Mathematics
1 answer:
andrezito [222]4 years ago
8 0
G( - 3 ) = 8 * ( - 3 ) + 2 = -24 + 3 = - 21 ;
( fog )(-3) = f( g(-3) ) = f( - 21 ) = 6 * ( -21 ) + 7 = - 126 + 7 = - 119
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3 years ago
A theater group surveyed 146 audience members after a show and found that 132 of them wanted to see the show again. Find the sta
Sophie [7]

Answer:

0.024

Step-by-step explanation:

Sample size (n) = 146 people

The proportion (p) of people who answered that they would be interested in seeing the show again is:

p=\frac{132}{146}\\ p=0.9041

The standard error for a sample of size 'n' and proportion 'p' is:

SE = \sqrt{\frac{p*(1-p)}{n}}\\SE = \sqrt{\frac{0.9041*(1-0.9041)}{146}}\\ SE=0.024

The standard error for the sample proportion of audience members who want to see the show again is 0.024.

4 0
3 years ago
A line passes through point A(10,15). A second point on the line has an x-value that is 125% of the x-value of point A and a y-v
melisa1 [442]

The equation of the line in the point-slope form is y - 15 = -\frac{3}{2} (x - 10)

Step-by-step explanation:

The point-slope form of a linear equation is y-y_{1}=m(x-x_{1}) , where

  • m is the slope of the line, where m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} , (x_{1},y_{1}) and (x_{2},y_{2}) are two points on the line
  • (x_{1},y_{1}) is a point on the line

∵ Point A = (10 , 15)

∵ The x-coordinate of the second point is 125% of x-coordinate

  of point A

∴ x-coordinate of second point = \frac{125}{100} × 10

∴ x-coordinate of second point = 12.5

∵ The y-coordinate of the second point is 75% of y-coordinate

  of point A

∴ y-coordinate of second point = \frac{75}{100} × 15

∴ y-coordinate of second point = 11.25

∴ The coordinates of the second point are (12.5 , 11.25)

Let us find the slope of the line by using the rule of it above

∵ (x_{1},y_{1}) = (10 , 15)

∵ (x_{2},y_{2}) = (12.5 , 11.25)

∴ m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}

Now we can write the equation

∵ The point-slope form is y-y_{1}=m(x-x_{1})

∵ m=-\frac{3}{2}

∵ (x_{1},y_{1}) = (10 , 15)

- Substitute these values in the form of the equation

∴ y - 15 = -\frac{3}{2} (x - 10)

The equation of the line in the point-slope form is y - 15 = -\frac{3}{2} (x - 10)

Learn more:

You can learn more about the linear equation in brainly.com/question/4152194

#LearnwithBrainly

5 0
3 years ago
What is something that could be true about the value of x
crimeas [40]
Any value you choose for x will make the equation a TRUE statement. This type of equation is called an identity, and the solution set is all real numbers.
8 0
3 years ago
A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the flo
Arada [10]

Answer:

The parabolic shape of the door is represented by y - 32 = -\frac{2}{49}\cdot x^{2}. (See attachment included below). Head must 15.652 inches away from the edge of the door.

Step-by-step explanation:

A parabola is represented by the following mathematical expression:

y - k = C \cdot (x-h)^{2}

Where:

h - Horizontal component of the vertix, measured in inches.

k - Vertical component of the vertix, measured in inches.

C - Parabola constant, dimensionless. (Where vertix is an absolute maximum when C < 0 or an absolute minimum when C > 0)

For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:

V (x,y) = (0, 32) (Vertix)

A (x, y) = (-28, 0) (x-Intercept)

B (x,y) = (28. 0) (x-Intercept)

The following equation are constructed from the definition of a parabola:

0-32 = C \cdot (28 - 0)^{2}

-32 = 784\cdot C

C = -\frac{2}{49}

The parabolic shape of the door is represented by y - 32 = -\frac{2}{49}\cdot x^{2}. Now, the representation of the equation is included below as attachment.

At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:

y -32 = -\frac{2}{49} \cdot x^{2}

x^{2} = -\frac{49}{2}\cdot (y-32)

x = \sqrt{-\frac{49}{2}\cdot (y-32) }

If y = 22 inches, then x is:

x = \sqrt{-\frac{49}{2}\cdot (22-32)}

x = \pm 7\sqrt{5}\,in

x \approx \pm 15.652\,in

Head must 15.652 inches away from the edge of the door.

8 0
3 years ago
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