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Nataliya [291]
3 years ago
14

Find the domain of the function. Write your answer in interval notation. f(x)=-4x² + 5x +1

Mathematics
1 answer:
nirvana33 [79]3 years ago
6 0

Answer:

All real numbers

(-∞, ∞)

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

We see here that our function is a parabola. We also see that we can plug in any number <em>x </em>and we would get an output <em>y</em>. Therefore, our domain is all real numbers:

(-∞, ∞)

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Rewrite the equation x = 65 - 60p by factoring the side that contains the variable p.
grigory [225]

Answer: x=5(13-12p)


Step-by-step explanation:

Given equation: x=65-60p

\\\Rightarrowx=(5\times13)-(5\times12)p

Since 5 is the greatest common factor of 65 and 60 in the given expression.

Therefore, the above expression can be written as

x=5(13-12p)

Hence, by factoring the side that contains the variable p we have the expression x=5(13-12p).




7 0
3 years ago
Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace
joja [24]

Answer:

The answer is "".

Step-by-step explanation:

Please find the complete question in the attached file.

We select a sample size n from the confidence interval with the mean \muand default \sigma, then the mean take seriously given as the straight line with a z score given by the confidence interval

\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\

Using formula:

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}  

The probability that perhaps the mean shells length of the sample is over 4.03 pounds is

P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)

Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution

=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z

the required probability: P(z>0.8349)=1-P(z

4 0
2 years ago
I need to find the surface area and volume of all three figures. If you could provide what equations you used to I will be grate
Margarita [4]

Answer:

Part 1) <em>Sphere</em> The surface area is equal to SA=196\pi\ m^{2} and the volume is equal to V=\frac{1,372}{3}\pi\ m^{3}

Part 2) <em>Cone</em> The surface area is equal to SA=(16+4\sqrt{65})\pi\ units^{2} and the volume is equal to V=\frac{112}{3}\pi\ units^{3}

Part 3) <em>Triangular Prism</em> The surface area is equal to SA=51.57\ mm^{2} and the volume is equal to V=17.388\ mm^{3}

Step-by-step explanation:

Part 1) The figure is a sphere

a) Find the surface area

The surface area of the sphere is equal to

SA=4\pi r^{2}

we have

r=14/2=7\ m ----> the radius is half the diameter

substitute

SA=4\pi (7)^{2}

SA=196\pi\ m^{2}

b) Find the volume

The volume of the sphere is equal to

V=\frac{4}{3}\pi r^{3}

we have

r=14/2=7\ m ----> the radius is half the diameter

substitute

V=\frac{4}{3}\pi (7)^{3}

V=\frac{1,372}{3}\pi\ m^{3}

Part 2) The figure is a cone

a) Find the surface area

The surface area of a cone is equal to

SA=\pi r^{2} +\pi rl

we have

r=4\ units

h=7\ units

Applying Pythagoras Theorem find the value of l (slant height)

l^{2}=r^{2} +h^{2}

substitute the values

l^{2}=4^{2} +7^{2}

l^{2}=65

l=\sqrt{65}\ units

so

SA=\pi (4)^{2} +\pi (4)(\sqrt{65})

SA=16\pi +4\sqrt{65}\pi

SA=(16+4\sqrt{65})\pi\ units^{2}

b) Find the volume

The volume of a cone is equal to

V=\frac{1}{3}\pi r^{2}h

we have

r=4\ units

h=7\ units

substitute

V=\frac{1}{3}\pi (4)^{2}(7)

V=\frac{112}{3}\pi\ units^{3}

Part 3) The figure is a triangular prism

a) The surface area of the triangular prism is equal to

SA=2B+PL

where

B is the area of the triangular base

P is the perimeter of the triangular base

L is the length of the prism

<em>Find the area of the base B</em>

B=\frac{1}{2} (2.7)(2.3)=3.105\ mm^{2}

<em>Find the perimeter of the base P</em>

P=2.7*3=8.1\ mm

we have

L=5.6\ mm

substitute the values

SA=2(3.105)+(8.1)(5.6)=51.57\ mm^{2}

b) Find the volume

The volume of the triangular prism is equal to

V=BL

where

B is the area of the triangular base

L is the length of the prism

we have

B=3.105\ mm^{2}

L=5.6\ mm

substitute

V=(3.105)(5.6)=17.388\ mm^{3}

5 0
3 years ago
Find the inverse function of f informally. f(x) = 6x
yaroslaw [1]
f^-^1(x) =  \frac{x}{6}
8 0
3 years ago
(ANSWER FOR POINTS AND BRAINLEST!!!) Identify the scale factor in the image below.
igor_vitrenko [27]

Answer:

it should be 3/2  !

4 0
3 years ago
Read 2 more answers
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