Which graphs represent functions?
Answers
Final answer:
Graphs that represent functions have one input corresponding to one output. Examples include straight lines, parabolas, and sine waves.
Explanation:
Graphs that represent functions are those in which every input has exactly one output. In other words, there can only be one value of y for each value of x. For example, a straight line, a parabola, or a sine wave are graphs that represent functions.
On the other hand, graphs that do not represent functions may have one input value mapping to multiple output values or no output values at all. Examples of such graphs include circles, ellipses, or a graph with one vertical line intersecting it at multiple points.
It's important to note that in a function, the vertical line test can be used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, then the graph does not represent a function.
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The lifetime of a certain type of battery is normally distributed with a mean value of 10 hours and standard deviation of 2 hours. Find the probability that a randomly selected battery has a lifetime greater than 12 hou g
Answers
Final answer:
To reduce the average cost per item to less than $500, it is necessary to produce more than 20 items according to the function C(x)=300x+6000.
Explanation:
The function C(x)=300x+6,000 represents the cost to produce x items. The average cost per item is given by C(x)/x. We need to find when this average cost is less than $500.
Setting up the inequality, we get C(x)/x < 500. Substituting the value of C(x) into the inequality, we get (300x + 6000)/x < 500. Simplifying this inequality, we end up with: x > 20.
Therefore, more than 20 items need to be produced for the average cost to be less than $500.
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Answer:
More than 30 items
Step-by-step explanation:
C(x)=300x+6,000
First, find c(x), the average cost function.
c(x)c(x)=C(x)x=300x+6,000x
The average cost function is shown below.
c(x)=300x+6,000x
We want the function c(x) to be less than 500.
c(x)<500
Substitute the rational expression for c(x).
300x+6,000x<500x≠0
Subtract 500 to get 0 on the right.
300x+,6000x−500<0
Find the LCD, and rewrite the left side as one quotient.
300x+6,000x−500xx−200x+6,000x<0<0
Factor the numerator to show all factors.
−200(x−30)x<0
Find the critical points when the numerator or denominator are equal to 0.
−200(x−30)−200≠0x−30x=0x=0=0=30
More than 30 items must be produced to keep the average cost below $500 per item.
Answers
20/9 = $2.22 per sheet
$2.22*15 = $33.33
Answers
Answer: Yes, Yukio is correct.
Step-by-step explanation:
Assuming that Triangle DEF and ABC have the same angles (they do because they are right-angled), we can take the length from the larger triangle (DEF) and divide it by the length of the smaller triangle (ABC).
Length of DEF = 6cm
Length of ABC = 2cm
= 6/2
= 3
Proves that scale of DEF to ABC is 3:1
Answers
Final answer:
To find the value of 4x + 3y, the given equation can be solved by clearing the fractions and simplifying the expression. The value of 4x + 3y is 30.
Explanation:
To find the value of 4x + 3y, we need to first solve the given equation for either x or y. Let's solve the equation for x:
2/3x + 1/2y = 5
Multiplying both sides of the equation by 6 to clear the fractions gives us:
4x + 3y = 30
Therefore, the value of 4x + 3y is 30.
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2.000
2.667
=1.333
x−intercept=
4
30
=
2
15
=7.50000
y−intercept=
−3
30
=
−1
10
=−10.00000
Answers
Answer:
x=1, x=-6
Step-by-step explanation:
x^2+5x-6=0 can be reduced to (x+6)(x-1)=0
we now have x+6=0 and x-1=0
solve by subtracting 6 from each side in the first equation and adding 1 to each side in the second.
x=1, x=-6
the radius as 7cm and height 10cm.
Answers
Answer:
1539.38cm³
Step-by-step explanation:
V=πr2h=π·72·10≈1539.3804cm³