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Nataly [62]
3 years ago
10

Which of the following equations represents a linear function?

Mathematics
1 answer:
Sphinxa [80]3 years ago
4 0

Answer:

Following equations represents a linear function:

y = 6x

y = 4x - √2

x – 4y = 6

Step-by-step explanation:

We know that a linear function is of the form

where m is the rate of change or slope and b is the y-intercept.

Please note that y = mx+b represents a straight line because the degree of a linear function is always 1.

Now, let us check whether the given functions represent the linear functions or not.

Checking y = 6x

y = 6x

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The binomial probability is determined by the formula

\begin{gathered} P_x=\binom{n}{x}p^xq^{n-x} \\ \text{where} \\ P\text{ is the binomial probability} \\ x\text{ is the number of times for a specific outcome within }n\text{ trials} \\ p\text{ is the probability of success on a single trial} \\ q\text{ is the probability of failure on a single trial} \\ n\text{ is the number of trials} \end{gathered}

Here, we will assume that finding the flaw is the "success" of the trial hence the following given

\begin{gathered} p=0.05 \\ q=0.95 \\ n=30 \end{gathered}

Finding the probability of one flawed scarf

\begin{gathered} P(X=1)=\binom{30}{1}(0.05)^1(0.95)^{30-1} \\ P(X=1)=0.3389 \end{gathered}

Finding the probability of no flawed scarves

\begin{gathered} P(X=0)=\binom{30}{0}(0.05)^0(0.95)^{30-0} \\ P(X=0)=0.2146 \end{gathered}

Finding the probability of more then three flawed scarves

\begin{gathered} P(X>3)=1-P(X\le3) \\ P(X>3)=1-0.93922843869 \\ P(X>3)=0.0608 \end{gathered}

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50 boxes of ice cream bars with 12 bars in each box if 520 people had ice cream bars how many are left
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if 10 800 cm2 of material is available to make a box with a square base and an open top find the largest possible volume of the
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Let

x--------> the length side of the square base of the box

y-------> the height of the box

we know that

The surface area of the box is equal to

SA=4xy+x^{2}

SA=10,800\ cm^{2}

so

10,800=4xy+x^{2}

y=(10,800-x^{2})/(4x)

y=(2,700-0.25x^{2})/(x) --------> equation A

the volume of the box is equal to

V=x^{2}y --------> equation B

Substitute the equation A in the equation B

V=x^{2}*(2,700-0.25x^{2})/(x)

V=x*(2,700-0.25x^{2})

V=(2,700x-0.25x^{3})

using a graphing tool

see the attached figure

For x=60\ cm

Volume=108,000\ cm^{3}

the point (60,108,000) is a maximum of the function

<u>Find the dimensions of the box </u>

x=60\ cm

Find the value of y

V=x^{2}y

y=V/x^{2}

y=108,000/60^{2}

y=30\ cm

<u>The dimensions of the box are</u>

60\ cm*60\ cm*30\ cm

<u>The largest possible volume of the box is</u>

108,000\ cm^{3}

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