NO LINKS!! NOT MULTIPLE CHOICE!!
For each of the functions below, find the following information. Then sketch a graph.
a. x- int and y-int.
b. vertical asymptote(s) or any holes
c. end behavior asymptotes
d. domain and range
33. g(x) = (x - 2)/(x^2 - 2x - 3)
34. k(x)= (x^2 - x - 2)/(x - 3)
35. f(x)= -x/(x^3 - 4x)
Answers
Answer:
Question 33
a) x-int (2, 0). y-int (0, 2/3)
b) Vertical asymptotes: x = -1 and x = 3
Horizontal asymptote: y = 0
c) f(x) → -∞, as x → -1⁻
f(x) → +∞, as x → -1⁺
f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
d) Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)
Range: (-∞, ∞)
Question 34
a) x-int (-1, 0) and (2,0). y-int (0, 2/3)
b) Vertical asymptote: x = 3
c) f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
d) Domain: (-∞, 3) ∪ (3, ∞)
Range: (-∞, 1] ∪ [9, ∞)
Question 35
a) No axis intercepts
b) Vertical asymptotes: x = -2 and x = 2. Hole at (0, ¹/₄).
c) f(x) → -∞, as x → -2⁻
f(x) → +∞, as x → -2⁺
f(x) → +∞, as x → 2⁻
f(x) → -∞, as x → 2⁺
d) Domain: (-∞, -2) ∪ (-2, 0) ∪ (0, 2) ∪ (2, ∞)
Range: (-∞, 0) ∪ (¹/₄, ∞)
Step-by-step explanation:
Definitions
The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0.The y-intercept is the points at which the curve crosses the y-axis, so when x = 0.The domain of a function is the set of all possible input values (x-values).The range of a function is the set of all possible output values (y-values).A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.A horizontal asymptote occurs at y = 0 if the degree of the numerator is less than the degree of the denominator.A hole occurs when a rational function has a factor with an x that is in both the numerator and the denominator.Question 33Given rational function:
[tex]g(x) =\dfrac{x - 2}{x^2 - 2x - 3}[/tex]
x-intercept
[tex]\begin{aligned}y=0 \implies \dfrac{x - 2}{x^2 - 2x - 3}&=0\\x - 2&=0\\x&=2\end{aligned}[/tex]
y-intercept
[tex]x=0 \implies \dfrac{0 - 2}{0^2 - 2(0) - 3}=\dfrac{2}{3}[/tex]
Vertical asymptotes
Set the denominator to zero and solve for x:
[tex]\implies x^2-2x-3=0[/tex]
[tex]\implies x^2-3x+x-3=0[/tex]
[tex]\implies x(x-3)+1(x-3)=0[/tex]
[tex]\implies (x+1)(x-3)=0[/tex]
[tex]\implies x+1=0 \implies x=-1[/tex]
[tex]\implies x-3=0 \implies x=3[/tex]
Horizontal asymptote
As the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at y = 0.
Holes
Factor the denominator:
[tex]g(x) =\dfrac{x - 2}{(x+1)(x-3)}[/tex]
There are no holes as there is no common factor in the numerator and the denominator.
End behaviour near the vertical asymptotes
f(x) → -∞, as x → -1⁻
f(x) → +∞, as x → -1⁺
f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
Domain
As there are vertical asymptotes at x = -1 and x = 3, the domain is restricted:
Interval notation: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)Range
The range is unrestricted:
Interval notation: (-∞, ∞)Question 34Given rational function:
[tex]k(x)= \dfrac{x^2 - x - 2}{x - 3}[/tex]
x-intercepts
[tex]\begin{aligned}y=0 \implies \dfrac{x^2 - x - 2}{x - 3}&=0\\x^2 - x - 2&=0\\x^2-2x+x-2&=0\\x(x-2)+1(x-2)&=0\\(x+1)(x-2)&=0\\\\x+1&=0 \implies x=-1\\x-2&=0 \implies x=2\end{aligned}[/tex]
y-intercept
[tex]x=0 \implies \dfrac{(0)^2 - 0 - 2}{0 - 3}=\dfrac{2}{3}[/tex]
Vertical asymptotes
Set the denominator to zero and solve for x:
[tex]\implies x-3=0[/tex]
[tex]\implies x=3[/tex]
Holes
Factor the numerator:
[tex]k(x)= \dfrac{(x+1)(x-2)}{x - 3}[/tex]
There are no holes as there is no common factor in the numerator and the denominator.
End behaviour near the vertical asymptote
f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
Domain
As there is vertical asymptote at x = 3, the domain is rest:
Interval notation: (-∞, 3) ∪ (3, ∞)Range
The extreme points are (1, 1) and (5, 9). Therefore, the range is restricted:
Interval notation: (-∞, 1] ∪ [9, ∞)Question 35Given rational function:
[tex]f(x)= -\dfrac{x}{x^3 - 4x}[/tex]
x-intercepts
As the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at y = 0. Therefore, there are no x-intercepts.
y-intercept
Substitute x = 0 and solve for y:
[tex]x=0 \implies -\dfrac{0}{0(x+2)(x-2)}=\dfrac{0}{0}=\textsf{unde\:\!fined}[/tex]
Therefore, there is no y-intercept.
Factor the denominator:
[tex]f(x)= -\dfrac{x}{x(x+2)(x-2)}[/tex]
Cancel the common factor x:
[tex]f(x)= -\dfrac{1}{(x+2)(x-2)}[/tex]
Vertical asymptotes
Set the denominator to zero and solve for x:
[tex]\implies (x+2)(x-2)=0[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Holes
Factor the denominator:
[tex]f(x)= -\dfrac{x}{x(x+2)(x-2)}[/tex]
As the numerator and denominator have a common factor of x, the function is not defined when x = 0. Therefore, there is a hole when x = 0.
To find the y-value of the hole, cancel the common factor x and input x = 0 into the resulting function:
[tex]x=0 \implies -\dfrac{1}{(0+2)(0-2)}=\dfrac{1}{4}[/tex]
Therefore, there is a hole at (0, ¹/₄).
End behaviour near the vertical asymptotes
f(x) → -∞, as x → -2⁻
f(x) → +∞, as x → -2⁺
f(x) → +∞, as x → 2⁻
f(x) → -∞, as x → 2⁺
Domain
As there are vertical asymptotes at x = -2 and x = 2, and a hole at (0, ¹/₄), the domain is restricted:
Interval notation: (-∞, -2) ∪ (-2, 0) ∪ (0, 2) ∪ (2, ∞)Range
As there is a hole at (0, ¹/₄) and a horizontal asymptote at y = 0, the range is restricted:
Interval notation: (-∞, 0) ∪ (¹/₄, ∞)
Related Questions
(v) (5-6i)+(3+4i) - (5-7)
Answers
Answer:
Step-by-step explanation
Multiply mentally 70 • 100 • 400 = (Type a whole number)
Answers
In order to set premiums at profitable levels, insurance companies must estimate how much they will to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of a randomly selected car of one model to the insurance company. The probability distribution of C is given below C $0 $1000 $4000 $10,000 P(C) 0.60 0.05 0.13 0.22 The probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is: a.0.05 b.0.13. c.0.22. d.0.35. e.0.406. The expected value of C is a.$0 b.$554 c.$2770 d.$3750 e.$40577. Which of the following is the best interpretation of expected value? (In the choices below,"Exp(C)" represents expected value you found in question 5). a.If the company insures 10 cars of this model, they know they will incur 10×Exp(C) in costs. b.The maximum cost to the company for insuring this car model is Exp(C) per car. c.The company must insure at least Exp(C) of these cars to make a profit. d.If the company insures a large number of these cars, they canexpect the cost per car to average approximately Exp(C). e.If the company insures a large number of these cars, they can expect the variability in cost per car to average approximately Exp(C).
Answers
The probability of a claim of at least $4000 is 0.35, option(d), the expected value of C is $2770 option (c), and the best interpretation is If the company insures a large number of these cars, they can expect the cost per car to average approximately Exp(C), option(d).
Given probability distribution
C $0 $1000 $4000 $10000
P(C) 0.60 0.05 0.13 0.22
The probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is
= (1-0.60-0.05) = 0.35
so the expected value of C
= 0x0.60 + 1000x0.05 + 4000x0.13 + 10000x0.22
= 50+520+2200 = $2770
Now, the best interpretation of expected value:
If the company insures a large number of these cars, they can expect the cost per car to average approximately Exp(C).
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The perimeter of a certain rectangle is 26 m. Also, the difference between the length of the rectangle and the breath is 3 m. Find the length and the breadth of the rectangle.
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A rectangle having perimeter 26 m has a length of 8m and breadth of 5m.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
The value for perimeter of a rectangle is - 26 m
Let x be the length of the rectangle and y be the breadth.
The formula for perimeter of rectangle is 2(l + b)
From the given information, it is known that -
Perimeter = 2(x + y) = 26 m...(1)
Difference between the length and breadth = x - y = 3 m....(2)
Use the first equation to solve for one of the variables in terms of the other -
2x + 2y = 26
x + y = 13....(3)
Add equation (2) and (3) -
x + y + x - y = 13 + 3
2x = 16
x = 16/2
x = 8 m
Now substitute the value of x in equation (2) -
x - y = 3
8 - y = 3
y = 8 - 3
y = 5 m
Therefore, the length is 8 m and the breadth is 5 m.
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A sample was taken of the salaries of four employees from a large company. The following are their salaries (in thousands of dollars) for this year. 33 31 24 36 The variance of their salaries is A. 5.1. B. 31. C. 26.
Answers
The variance of the four employees' salaries is 5.1, meaning that the difference in their salaries is 5.1 thousand dollars.
Step 1: Find the mean of the four salaries
33 + 31 + 24 + 36 = 124
124 ÷ 4 = 31
Mean = 31
Step 2: Find the difference between each salary and the mean
33 - 31 = 2
31 - 31 = 0
24 - 31 = -7
36 - 31 = 5
Step 3: Square each of the differences
2² = 4
0² = 0
(-7)² = 49
5² = 25
Step 4: Add up the squared differences
4 + 0 + 49 + 25 = 78
Step 5: Divide the sum by the number of salaries (minus 1)
78 ÷ (4 - 1) = 78 ÷ 3 = 26
Step 6: Take the square root of the variance
√26 = 5.1
Variance = 5.1
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(-1.2) (-3.5) (-2.7) (-0.4) a positive product?
Answers
We have the product of 4 negative numbers, by the rule of signs, we can see that the product is positive.
Is the product positive?Here we need to reember the rule of signs for the product, it is:
(-)*(-) = +
(+)*(+) = +
(+)*(-) = -
(-)*(+) = -
So the product between two negative numbers is positive, now let's look to our product.
(-1.2)*(-3.5)*(-2.7)*(-0.4)
We can rewrite this as:
(-1.2*-3.5)*(-2.7*-0.4)
The negative sings cancell, then we get:
(-1.2*-3.5)*(-2.7*-0.4)
(4.2)*(1.08)
Now we have the product of two positive numbers, this will be positive.
(4.2)*(1.08) = 4.536
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dillon places a ladder against the wall the base of the ladder is 5 feet from the wall the ladder is 12 feet long how will shorting the distance between the base of the ladder and the wall affect the dimentions of the triangle they form explain in terms of the pyhagoren therom
Answers
The base distance will be 10.9 feet .
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
The Pythagorean theorem states that, in a right triangle, the length of the hypotenuse squared equals the sum of the squares of the other two sides or legs of the triangle. Algebraically, a2+b2=c2. In your example, the length of the ladder would be the hypotenuse and the distance from the wall would be one of the legs. So substitute these values into the equation to get: 25+b2=144 or 25+b2=144 and then subtract 25 from both sides to get b2=119. Therefore b=√119≈10.908. If your problem requires an exact answer in its most simplified form, please note that √119=10.9
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Which figures have rotational symmetry?
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In the supermarket, 7/12 of Marco’s bill is for fruit and vegetables. If 1/8 is for fruit, what fraction is for vegetables?
Answers
In other words, 3/4 fraction of the bill are for vegetables, while 1 part is for fruit.
How is this determined?Using the data provided in the issue, we can determine what percentage of Marco's bill is made up of veggies. We are aware that fruit and vegetables account for 7/12 of the total bill and make up 1/8 of the total. By deducting the portion of the bill that is for fruit from the portion that is for fruit and vegetables, we can determine the portion of the cost that is for vegetables.
We must identify a common denominator for the two fractions in order to accomplish this. Since 12 and 8 have a denominator of 24, we convert both fractions to have a denominator of 24.
1/8 turns becomes 3/24
7/12 changes to 21/24.
We deduct 3/24 from 21/24 in order to derive the percentage of fruit from the percentage of fruit and vegetables.
21/24 - 3/24 = 18/24
Vegetables make up 18/24, or 3/4, of Marco's bill.
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The following inequalities form a system. y is greater than or equal to two-thirds times x plus 1 y is less than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (−6, 3.5) (−6, −3) (−4, 3) (−4, 4)
Answers
Answer: The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.
What exactly is inequality?
A variation between two values indicates whether one is smaller, larger, or otherwise unrelated to the other.
In other words, inequality is the inverse of equality. For example, if 2 = 2, it is equal; however, if I say 3 = 6, it is incorrect; the correct expression is 3 6.
Step-by-step explanation:As per the given phrase,
y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1
y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2
Substitute, point (−6, −3)
-3 ≥ (2/3)(-6) + 1
-3 ≥ -3
Substitute in second inequality,
-3 < (-1/4)(-6) + 2
-3 < 7/2
Triangle AA'B'C" is the result of dilating AABC about point P by a scale factor of 2.
Answers
Answer:
FalseFalse==============================================
Explanation for problem 1
The center of dilation is point P, which is not located on line AB. This means line A'B' will move further away from P after applying the scale factor. It means segments AB and A'B' are not on the same line.
Side note: Side BC is through line P, so segment B'C' shares the same line with BC.
---------------------------
Explanation for problem 2
The scale factor enlarges the side lengths. In this case, the scale factor 2 will double each side. This in turn doubles the perimeter.
perimeter of A'B'C' = 2*(perimeter of ABC)
new perimeter = 2*(old perimeter)
Therefore, the perimeters are not the same.
PLEASE HELP!!!!! Complete the two-column proof.
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The equation will be 5x + 7x = 180. Then the value of the variable 'x' will be 15.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
∠TSR = 5x and ∠UVW = 7x
Angle ∠TSR and angle ∠UVW are the supplementary angles. Then the equation is given as,
5x + 7x = 180
12x = 180
x = 180 / 12
x = 15
The equation will be 5x + 7x = 180. Then the value of the variable 'x' will be 15.
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In order to produce my movie, I need to shoot a scene for a high-speed chase and I need to shoot a scene for a bank robbery. The film production crew will be putting the movie together. I have the stunt crew for the chase scene from 10 am to 11 am and I have the stunt crew for the robbery from 6pm to 7 pm. Will the order I shoot the scenes in matter? What mathematical property did you use to answer this question?
Answers
The order in which you shoot the scenes will not matter in terms of the final outcome of the movie.
The mathematical property that one can use to answer this question is scheduling.
How to illustrate the information?From the information, in order to produce the movie, one needs to shoot a scene for a high-speed chase and need to shoot a scene for a bank robbery.
Here, the film production crew will be putting the movie together. However, it may impact the logistics of the production process and the scheduling of the crews. It is not a mathematical property that I used to answer this question. It is simply a matter of logistics and scheduling.
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In this diagram, circle A has radius = 11.5 and BC = 13.1. BC is a tangent line, calculate the distance of CD.
Answers
The distance of CD is 5.93.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Given a circle.
Radius of circle = 11.5
AB = AD = 11.5
Since the tangent line is perpendicular to the radius of the circle at the point of tangency, ABC is a right angled triangle.
AC² = AB² + BC²
= 11.5² + 13.1²
= 303.86
AC = 17.432
CD = AC - AD
= 17.432 - 11.5
= 5.93
Hence the distance of CD is 5.93.
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Use the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals.
Answers
The slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.
1) Biconditional statement: If two lines are parallel, then the alternate interior angles formed by a transversal are equal.
Formula: m∠1 = m∠3 and m∠2 = m∠4
Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the alternate interior angles formed by the transversal must have the same measure (m∠1 = m∠3 and m∠2 = m∠4).
2) Biconditional statement: If two lines are parallel, then the corresponding angles formed by a transversal are equal.
Formula: m∠1 = m∠4 and m∠2 = m∠3
Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the corresponding angles formed by the transversal must have the same measure (m∠1 = m∠4 and m∠2 = m∠3).
3) Biconditional statement: If two angles are equal, then the lines that form them are parallel.
Formula: m1 = m2
Calculation: If two angles have the same measure, then the slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.
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The average pencil has 5,425 pencil shavings. How many pencils are found in 76,450 pencil shavings?
Answers
Answer:
14
Step-by-step explanation:
We can divide 76,450 shavings by the average shavings per pencil, 5,425 to get an answer of 14.09... This can be rounded to 14.
EACH COPAYMENT IS 20% OF THE COST FIND THE COPAYMENT AND BENIFIT AMOUNT 4,200,00+0=3,072.00
Answers
The copayment amount, given that it is 20 % of the amount is $ 840
The benefit amount is $ 3, 360
How to find the copayment amount ?A copayment for health insurance is a defined dollar amount that is determined by the insurance plan and used to divide the cost of covered treatments between the plan and the consumer.
The copayment amount is 20 % of the cost which is $ 4, 200 so the copayment is:
= 20 % x 4, 200
= $ 840
This then means that the benefit amount would be;
= Cost - copayment
= 4, 200 - 840
= $ 3, 360
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Round 11,900 to the nearest thousand.
Answers
Answer:
12,000
Step-by-step explanation:
How can we do this?
We can do this by taking the number 11,900,
11,900
looking at the hundredths place,
11,900
and figuring out if it is closer to 10, or 0. 9 is closer to 10, so we round up.
12,000
Therefore, 11,900 rounded to the nearest thousand is 12,000.
item 18 time remaining 4 hours 13 minutes 48 seconds 04:13:48 ebook item 18 time remaining 4 hours 13 minutes 48 seconds04:13:48 if bob can produce more donuts in one day, if
Answers
If Bob is able to produce more donuts than Sue in one day, that means that Bob has an absolute advantage in the production pf donuts.
Absolute advantage is when a particular person is able to produce more amount of product than the other with the same amount of input of resources, for example, time. Comparative advantage on the other hand is based on the opportunity cost.
Comparative advantage is basically the ability to produce a good or a service for an opportunity cost which is lower than that of a competitor. Since, Bob is able to produce more donuts than Sue, Bob has an absolute advantage over Sue.
--The given question is incomplete, the complete question is
If Bob can produce more donuts in one day than Sue can produce in one day, then:
a. Bob has a comparative advantage in the production of donuts.
b. Sue has a comparative advantage in the production of donuts.
c. Bob has an absolute advantage in the production of donuts.
d. Sue has an absolute advantage in the production of donuts."--
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Is x = 6 a solution to the equation 5(x – 3) = x + 13? Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true.
2. Simplify both sides. Show your work.
3. Is x = 6 a solution to the equation? Why or why not?
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
Answers
Answer:
see below
Step-by-step explanation:
Step 1
5(x – 3) = x + 13
Step 2
See if x is a solution
5 (6-3) ?= 6+13
5 (3) ?= 19
15 ?= 19
Step 3
This is not true so it is not a solution
Step 4
5(x – 3) = x + 13
Distribute
5x-15 = x+3
Subtract x from each side
5x-x -15 = x+13-x
4x-15 = 13
Add 15 to each side
4x-13+13 = 15+13
4x =28
Divide each side by 4
4x/4 = 28/4
x = 7
7 is a solution
Answer:
First you substitute 6 for x!
5(6 - 3) = 6 + 13
6 - 3 = 3
The equation is now:
5 * 3 = 6 + 13
5 * 3 = 15
6 + 13 = 19
The result is:
15 = 19 which is not a true statement.
x is not equal to 6.
Now lets try 7.
5(7 - 3) = 7 + 13
7 - 3 = 4
7 + 13 = 20
5 * 4 = 20
Thus: x = 7
Step-by-step explanation:
Hope it helps! =D
a student sets up the following equation to convert a measurement. (the ? stands for a number the student is going to calculate.) fill in the missing part of this equation. (39 . N/cm) . ____ = ? N/mm
Answers
The resulting answer is 39000 N/mm, this equation can be used to convert a given measurement from N/cm to N/mm.
39000/1 = ? N/mm
Multiply 39 by 1000 to convert centimeters to millimeters.
39000/1 = ? N/mm
Divide the measurement 39000 N/cm by 1 to convert it to N/mm.
The answer is 39000 N/mm.
To convert a measurement from N/cm to N/mm, the equation that needs to be set up is 39000/1 = ? N/mm. This equation can be broken down into two steps. First, the measurement needs to be multiplied by 1000 to convert centimeters to millimeters. Then, 39000/1 needs to be divided to convert the measurement from N/cm to N/mm. The resulting answer is 39000 N/mm. Therefore, this equation can be used to convert a given measurement from N/cm to N/mm.
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Any one help me please the question is in the screenshot.
Answers
The answers include the following below:
The sale price is 85% of the regular price.The equation which can be used to find the sale price, s, of an oil change is s = 0.85(30).What is Sale price?This is referred to as the discounted price at which goods or services are being sold.
Since we were told that the discount is 15%, then the sale price will be (100-85)% of $30 which is 85% of $30.
This therefore means that the equation to find the sale price will be 85/100 × 30 = 0.85(30).
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B = 1 4 1 2
0 1 3 -4
0 2 6 7
2 9 5 -1
Can every vector in R^4 be written as a linear combination of the columns of the matrix B above? Do the columns of B span R^3
Answers
Yes, every vector in R^4 can be written as a linear combination of the columns of the matrix B.
This can be proven using the definition of linear combinations, which is as follows: a vector v in R^n can be written as a linear combination of vectors v1, v2, ..., vk if and only if there exist scalars c1, c2, ..., ck such that v = c1*v1 + c2*v2 + ... + ck*vk. With this definition, we can prove that the columns of B span R^4 by showing that for any vector v in R^4, there exist scalars c1, c2, c3, c4 such that v = c1*B1 + c2*B2 + c3*B3 + c4*B4, where B1, B2, B3, B4 are the columns of the matrix B above. To prove this, we can simply solve the system of equations given by c1*B1 + c2*B2 + c3*B3 + c4*B4 = v for c1, c2, c3, c4. This can be done by using Gaussian elimination, which will yield a set of scalars c1, c2, c3, c4 that can be used to express any vector in R^4 as a linear combination of the columns of the matrix B, thus proving that the columns of B span R^4.
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I don't understand how to calculate IQR here. Is 2 the median?
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A statement which is false about the distribution of Kobe’s streak lengths from the 2009 NBA finals include the following: E. The shortest streak is of length 1.
How to determine the false statement?In this scenario, the distribution of Kobe’s streak lengths from the 2009 NBA finals is plotted on a histogram with the length represented by the x-coordinate (x-axis) while the count is represented by the y-coordinate (y-axis).
By critically observing the histogram, we can reasonably infer and logically deduce the following true statements:
The distribution of Kobe’s streak lengths is right skewed and unimodal because it has only one clear peak (most frequent value).Since the median of the distribution of Kobe’s streak lengths is at 0, the typical length of a streak is equal to 0.The interquartile range (IQR) of the distribution is 1 i.e IQR = Q₃ - Q₁.In conclusion, the shortest streak lengths is 0 while the longest streak of baskets is of length 4.
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Complete Question:
Which of the following is false about the distribution of Kobe’s streak lengths from the 2009 NBA finals.
A. The distribution of Kobe’s streaks is unimodal and right skewed.
B. The typical length of a streak is 0 since the median of the distribution is at 0.
C. The IQR of the distribution is 1.
D. The longest streak of baskets is of length 4.
E. The shortest streak is of length 1
Penny created a circle graph to show what percentage of students in her class walk to school, ride the bus, or ride in a car.
What percent of students in Penny’s class ride the bus to school?
HELPPPP ASAPPPPP
Answers
Answer:
45
Step-by-step explanation:
100-25-30=45
Exercise 2:
Identify the missing terms:
4a (-2a³+4__+3)+ 2a(__a³- 2a+_)= -2a*+12a²+26a
JE
Answers
The complete expression of the algebra is;
4a(-2a³ + 4a + 3) + 2a(3a³ - 2a + 7) = -2a⁴ + 12a² + 26a
How to expand algebraic expressions?We are given the expression as;
4a(-2a³ + 4__ + 3) + 2a(__a³ - 2a + _) = -2a* + 12a² + 26a
Expanding the left hand side gives;
-8a⁴ + __(16a) + 12a + __(2a⁴) - 4a² + __(2a)
Grouping like terms gives;
-8a⁴ + __(2a⁴) + 12a + __(2a) + __(16a) - 4a²
Factorizing out exponents gives;
a⁴(-8 + __(2)) + a(12 + __(2)) + a²((16/a) - 4)
Comparing this with the right hand side gives;
a⁴(-8 + __(2)) = -2a* -----(1)
((16/a) - 4)a² = 12a² -----(2)
(12 + __(2))a = 26a ----(3)
From eq 1, we can see that;
* = 4
From eq 2;
((16/a) - 4) = 12
16/a = 12 + 4
a = 16/16
a = 1
From eq 3;
(12 + __(2)) = 26
___ * 2 = 26 - 12
___ = 14/2
___ = 7
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What is the total area, in square inches, of the shaded sections of the trapezoid below? 5 in 6.3 in 8 in 5.4 in
Answers
The total area of the shaded sections of the trapezoid in square inches is 32.76 square inches.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely fill the entire surface of an enclosed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
The shaded sections in the trapezoid are triangles.
The area of the triangle is given by the following formula:
A = 1/2 (b)(h)
For the first triangle, b = 5 and h = 6.3. Substituting the value in the formula we have:
A1 = 1/2 (5)(6.3)
A1 = 15.75
For the second triangle, b = 5.4 and h = 6.3. Substituting the value in the formula we have:
A2 = 1/2 (5.4)(6.3)
A2 = 17.01
The total area of the shaded region of the trapezoid is calculated by adding the area of the individual shaded portion:
A = A1 + A2
A = 15.75 + 17.01
A = 32.76
Hence, the total area of the shaded sections of the trapezoid in square inches is 32.76 square inches.
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The weight of an organ in adult males has a bell-shaped distribution with a mean of 330 grams and a
standard deviation of 50 grams. Use the empirical rule to determine the following.
(a) About 95% of organs will be between what weights?
(b) What percentage of organs weighs between 280 grams and 380 grams?
(c) What percentage of organs weighs less than 280 grams or more than 380 grams?
(d) What percentage of organs weighs between 180 grams and 430 grams?
Answers
According to the empirical rule -
a) About 95% of organs will be in range of weights of organs 230 grams and 430 grams.
b) 68% percentage of organs weighs between 280 grams and 380 grams.
c) 32% percentage of organs weighs less than 280 grams or more than 380 grams.
d) 97.35% percentage of organs weighs between 180 grams and 430 grams.
What is empirical rule?
The empirical rule 68-95-99.7 tells us that:
68% of the data is expected to be within 1 standard deviation from the mean.
95% of the data is expected to be within 2 standard deviation from the mean.
99.7% of the data is expected to be within 3 standard deviation from the mean.
There is a bell shaped distribution ( assume as approximately normal) with mean of 330 g and standard deviation of 50 g.
a) This happens for an interval with ±2 standard deviations from the mean.
That is:
X1 = μ + z1 × σ X2 = μ + z2 × σ
X1 = 330 - 2 × 50 X2 = 330 + 2 × 50
X1 = 330 - 100 X2 = 330 + 100
X1 = 230 X2 = 430
Therefore, the range of weights of organs is 230 grams and 430 grams.
b) Calculate the z-scores for each value to know how many standard deviations are from the mean.
z1 = (x1 - μ)/σ z2 = (x2 - μ)/σ
z1 = (280 - 330)/50 z2 = (380 - 330)/50
z1 = -50/50 z2 = 50/50
z1 = -1 z2 = 1
The values are 1 standard deviations from the mean each.
Therefore, the expected percentage is 68%.
c) This is the complementary of the point b.
Then, it is expected that (100 - 68)% = 32% of the organs weigh less than 280 grams or more than 380 grams.
d) Calculate the z-scores for each value to know how many standard deviations are from the mean.
z1 = (x1 - μ)/σ z2 = (x2 - μ)/σ
z1 = (180 - 330)/50 z2 = (430 - 330)/50
z1 = -150/50 z2 = 100/50
z1 = -3 z2 = 2
The values are 1 standard deviations from the mean each.
Therefore, the expected percentage is 68%.
The values are 3 standard deviations from the mean each. Between 180 and 330 there is 99.7%/2 = 49.85% of the data.
The values are 2 standard deviations from the mean each. Between 330 and 430 there is 95%/2 = 47.5% of the data.
Then, between 180 grams and 430 grams there is (49.85% + 47.5)% = 97.35% of the data.
Therefore, the expected percentage is 97.35%.
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mation.
2) (x-3)(x-8)= 0
Answers
Answer:
x-3 =0 or x-8 =0
x= +3 or x = +8
(x - 3)(x - 8) = 0
We will solve for x, this problem will have two solutions.
First, we will make both equations equal to 0:
x - 3 = 0
x - 8 = 0
Next, solve for x, add 3 and 8 to both sides:
x = 3
x = 8
There are your two solutions. Hope this step by step explanation helped!
consider the following argument, premise 1: if the sum of the digits in (student id) is divisible by 3 then (student id) is divisible by 3. premise 2: the sum of the digits in (student id) is divisible by 3. conclusion: (student id) is divisible by 3. substitute your eight-digit numeric student id for (student id) in the above argument and determine whether the argument, filled-in with your student id, is sound or unsound. justify your answer and include your student id in your explanation.
Answers
The argument, filled-in with the student ID 12345678, is sound because the two premises are true and the conclusion follows logically from them. The sum of the digits in 12345678 is 36, which is divisible by 3, so the first premise is true.
My student ID is 12345678.
The argument, filled-in with my student ID, is sound. This is because the two premises are true and the conclusion follows logically from them. The sum of the digits in 12345678 is 36, which is divisible by 3, so the first premise is true. The second premise is also true since it states that the sum of the digits in 12345678 is divisible by 3, which is the case. Therefore, the conclusion that 12345678 is divisible by 3 is logically valid from the two premises.
Student ID: 12345678
The argument, filled-in with the student ID 12345678, is sound because the two premises are true and the conclusion follows logically from them.
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