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3 years ago

What is the equation of the line in slope-intercept form?

Mathematics

1 answer:

cricket20 [7]3 years ago

6 0

Answer:y = 3x/4 + 4

Step-by-step explanation:

The equation of a line in the slope-intercept form is represented by

y = mx + c

Where c = y-intercept

Slope, m = change in the value of y on the vertical axis / change in the value of x in the horizontal axis.

change in the value if y is y2 -y1 and change in the value of x is x2 - x1

Where

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the graph,

y2 = 4

y1=0

x2=0

x1 = -3

we can determine the slope.

Slope, m = (4-0) / (0- -3)

= 4/3

Let us pick points (0,4) to determine the intercept

Substituting x = 0 , y = 4 and m = 4/3 into the slope-intercept equation,

y = mx + c

4 = 3/4×0 + c

c = 4

Equation of the line in slope-intercept form is

y = 3x/4 + 4

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Step-by-step explanation:

The compound interest formula can help with that.

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2 years ago

Prove A-(BnC) = (A-B)U(A-C), explain with an example

NikAS [45]

Answer:

Prove set equality by showing that for any element $x$ , $x \in (A \backslash (B \cap C))$ if and only if $x \in ((A \backslash B) \cup (A \backslash C))$ .

Example:

$A = \lbrace 0,\, 1,\, 2,\, 3 \rbrace$ .

$B = \lbrace0,\, 1 \rbrace$ .

$C = \lbrace0,\, 2 \rbrace$ .

$\begin{aligned} & A \backslash (B \cap C) \\ =\; & \lbrace 0,\, 1,\, 2,\, 3 \rbrace \backslash \lbrace 0 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace \end{aligned}$ .

$\begin{aligned}& (A \backslash B) \cup (A \backslash C) \\ =\; & \lbrace 2,\, 3\rbrace \cup \lbrace 1,\, 3 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace\end{aligned}$ .

Step-by-step explanation:

Proof for $[x \in (A \backslash (B \cap C))] \implies [x \in ((A \backslash B) \cup (A \backslash C))]$ for any element $x$ :

Assume that $x \in (A \backslash (B \cap C))$ . Thus, $x \in A$ and $x \not \in (B \cap C)$ .

Since $x \not \in (B \cap C)$ , either $x \not \in B$ or $x \not \in C$ (or both.)

If $x \not \in B$ , then combined with $x \in A$ , $x \in (A \backslash B)$ .
Similarly, if $x \not \in C$ , then combined with $x \in A$ , $x \in (A \backslash C)$ .

Thus, either $x \in (A \backslash B)$ or $x \in (A \backslash C)$ (or both.)

Therefore, $x \in ((A \backslash B) \cup (A \backslash C))$ as required.

Proof for $[x \in ((A \backslash B) \cup (A \backslash C))] \implies [x \in (A \backslash (B \cap C))]$ :

Assume that $x \in ((A \backslash B) \cup (A \backslash C))$ . Thus, either $x \in (A \backslash B)$ or $x \in (A \backslash C)$ (or both.)

If $x \in (A \backslash B)$ , then $x \in A$ and $x \not \in B$ . Notice that $(x \not \in B) \implies (x \not \in (B \cap C))$ since the contrapositive of that statement, $(x \in (B \cap C)) \implies (x \in B)$ , is true. Therefore, $x \not \in (B \cap C)$ and thus $x \in A \backslash (B \cap C)$ .
Otherwise, if $x \in A \backslash C$ , then $x \in A$ and $x \not \in C$ . Similarly, $x \not \in C \!$ implies $x \not \in (B \cap C)$ . Therefore, $x \in A \backslash (B \cap C)$ .

Either way, $x \in A \backslash (B \cap C)$ .

Therefore, $x \in ((A \backslash B) \cup (A \backslash C))$ implies $x \in A \backslash (B \cap C)$ , as required.

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3 years ago

Suppose that the length of a phone call in minutes is an exponential random variable with parameter λ = 1/ 8. If someone arrives

Elis [28]

Answer:

a) P=0.535

b) P=0.204

c) P=0.286

Step-by-step explanation:

The exponential distribution is expressed as

$F(x>t)=e^{-\lambda t}$

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a) The probability of having to wait more than 5 minutes

$F(x>5)=e^{-0.125*5}=e^{-0.625}=0.535$

b) The probability of having to wait between 10 and 20 minutes

$F(1020)=e^{-0.125*10}-e^{-0.125*20}\\\\F(10$

c) The exponential distribution is memory-less, so it is independent of past events.

If you have waited 5 minutes, the probability of waiting more than 15 minutes in total is the same as the probability of waiting 15-5=10 minutes.

$F(x>15|t^*=5)=F(x>15)/F(x>5)=\frac{e^{-0.125*15}}{e^{-0.125*5}}=e^{-0.125*(15-5)}\\\\ F(x>15|t^*=5)=e^{-0.125*(10)}=F(x>10)=0.286$

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3 years ago

Describe the transformation using words

nata0808 [166]

Answer:

The type of transformation that is used here is translation. Translation is when one shape slides to another location. According to the picutre, the shape is the same size and not rotated. Therefore, it is a translation.

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3 years ago