Select the correct answer. Martin runs 100 meters in 15 seconds. What is the equation for d, the distance in meters that Martin covers per second? O A. 15+ d = 100 B. 100 + d = 15 O c. dx 15 = 100 D. d x 100 = 15​


Answer 1


C) d*15=100

Step-by-step explanation:

The word problem already gives us the product or the end result “Martin runs 100 meters in 15 seconds. So the 100 has to be equal to the expression.


Per second” this suggests that we should multiply

the most logical answer is d*15=100 or dx15=100

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Find the slope (m) and the y-intercept (b) of the given line on the graph. pls show work/explanation!



m= 1/2

b= (0,6)

Step-by-step explanation:

Slope is rise over run

The y intercept is when x=o or just look at the vertical line

What is the rule for the reflection?A) r y=x (y,x) -> (-y,-x)
B) r y=-x (x,y) -> (-y,-x)
C) r y=x (x,y) -> (y,x)
D) r y=-x (x,y) -> (y,x)


the rule for the reflection is (B)

Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from the left, or neither. f(x) = x + 4 if x < 0 ex if 0 ≤ x ≤ 1 8 − x if x > 1 x = (smaller value) continuous from the right continuous from the left neither


Using continuity concepts, it is found that the function is left-continuous at x = 1.


A function f(x) is said to be continuous at x = a if:

\lim_(x \rightarrow a^(-)) f(x) = \lim_(x \rightarrow a^(+)) f(x) = f(a)

  • If only \lim_(x \rightarrow a^(-)) f(x) = f(a), the function is left-continuous.
  • If only \lim_(x \rightarrow a^(+)) f(x) = f(a), the function is right-continuous.


The piece-wise definition of the function f(x) is:

x + 4, x < 0

x, 0 \leq x \leq 1

8 - x, x > 1

We have to check the continuity at the points in which the definitions change, that is, x = 0 and x = 1.


At x = 0:

  • The definition at 0 is f(0) = 0
  • Approaching x = 0 from the left, we have values less than 0, thus:

\lim_(x \rightarrow 0^(-)) f(x) = \lim_(x \rightarrow 0) x + 4 = 0 + 4 = 0

  • Approaching x = 0 from the right, we have values greater than 0, thus:

\lim_(x \rightarrow 0^(+)) f(x) = \lim_(x \rightarrow 0) x = 0

Since the limits are equal, and also equal to the definition at the point, the function is continuous at x = 0.


At x = 1:

  • The definition at 1 is f(1) = 1
  • Approaching x = 1 from the left, we have values less than 1, thus:

\lim_(x \rightarrow 1^(-)) f(x) = \lim_(x \rightarrow 1) x = 1

  • Approaching x = 1 from the right, we have values greater than 1, thus:

\lim_(x \rightarrow 1^(+)) f(x) = \lim_(x \rightarrow 1) 8 - x = 8 - 1 = 7

To the right, the limit is different, thus, the function is only left continuous at x = 1.

A similar problem is given at


the function is continuous from the left at x=1 and continuous from the right at x=0

Step-by-step explanation:

a function is continuous from the right , when

when x→a⁺ lim f(x)=f(a)

and from the left when

when x→a⁻ lim f(x)=f(a)

then since the functions presented are continuous , we have to look for discontinuities only when the functions change

for x=0

when x→0⁺ lim f(x)=lim  e^x = e^0 = 1

when x→0⁻ lim f(x)=lim  (x+4) = (0+4) = 4

then since f(0) = e^0=1 , the function is continuous from the right at x=0

for x=1

when x→1⁺ lim f(x)=lim  (8-x) = (8-0) = 8

when x→1⁻ lim f(x)=lim e^x = e^1 = e

then since f(1) = e^1=e , the function is continuous from the left at x=1

The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.Requried:
a. What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?
b. Suppose the manager agrees to pay each employee a​ $50 bonus if they meet a certain goal. On a typical​ Saturday, the​ oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample, there
would be a​ 10% chance of the mean​ oil-change time being at or below what​ value? This will be the goal established by the manager.



(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 ​minutes i=0.0001.

(b) The mean oil-change time is 15.55 minutes.

Step-by-step explanation:

Let us denote the sample mean time as x

From the Then x = mean time = 16.2 minutes

  The given standard deviation = 3.4 minutes

The value of  n sample size = 45


Which is NOT a multiple of 15?



2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16 and anything else after 16

Step-by-step explanation:

I can’t see any answer choices so the multiples of 15 are: 15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,270,285,300,315,330,345,360,375,390,405,420,435,450,465,480,495,510,525,540,555,570,585,600,615,630,645,660,675,690,705,720,735
So I guess anything but those numbers, hope this helps

Suppose that X is a random variable with probability function x 0 1 2 3 4 5 P(x) 0.00032 0.0064 0.0512 0.2048 0.4096 0.32768 and that the random variable Y = 9X2 − 36X + 4. (a) What is the range of Y ? (b) Calculate P{Y = 4}. (c) Calculate P{Y = 0}.


(a) For each value of X we have:

X=0\quad\Rightarrow\quad Y=4\n\nX=1\quad\Rightarrow\quad Y=-23\n\nX=2\quad\Rightarrow\quad Y=-32\n\nX=3\quad\Rightarrow\quad Y=-23\n\nX=4\quad\Rightarrow\quad Y=4\n\nX=5\quad\Rightarrow\quad Y=49

so the range of Y = {-32, -23, 4, 49}




Y cannot equal 0, so