(50 Points Please help)
Drag the expression that is the most reasonable measurement for each object.
Answers
Answer:
A. Length of a Tour Bus ↔ #2. 1.1 × 10¹ meters
B. Width of an apple ↔ #3. 4 × 10⁰ centimeters
C. Distance from Earth to a Satellite ↔ #6. 8 × 10² kilometers
D. Thickness of a human hair ↔ #5. 9 × 10¹ micrometers
Step-by-step explanation:
The length of a tour bus should be measured in meters. It sure is way less than 1 kilometer and way more than a few centimeters. It could be about some meters, more than 5 meters, may be between 10 meters and 15 meters.
The measurement in the box # 2. is 1.1 × 10¹ meters, which is equivalent to 1.1 × 10 meters = 11 meters. Thus, this is a reasonable length.
B. Width of an apple.
The most appropriate unit to measure the width of an apple should be centimeter. It certainly is shorter than 1 meter and bigger than 1 mm.
The width of an apple could be, more or less, around 8 centimeters. The only measurement in the boxes that is in that order is that in the box #3., 4 × 10⁰ centimeters, because 10⁰ = 1, so 4 × 10⁰ = 4 × 1 = 4 centimeters.
C. Distance from Earth to a Satellite
The distance from Earth to a satellite should be measured in kilometers.
You can find in the internet that the distances of the satellites are between 700 kilometers and 36,000 kilometers.
The number in the box #1 is too big, in the order of ten trillions of kilometers, because one trillion is 10¹²; thus that is nonseasonal (too big).
The number in the box #6 is 8 × 10² kilometers, which is equal to 8 × 100 = 800 kilometers.
Thus, 8 × 10² kilometers (box #6) is the most reasonable measurement for the distance from Earth to a Satellite
D. Thickness of a human hair
Of course, kilometers, meters, centimeters and even millimeters are units too big to measure the thickness of a human hair.
One micrometer is 10⁻⁶ meters or 10⁻³ millimeters.
In the internet you can find that diameter of the human hair is in the range from 17 micrometers to 181 micrometers.
The measurement in the box #5. is 9 × 10¹ micrometers, which is equivalent to 9 × 10 = 90 micrometers.
Thus, 9 × 10¹ micrometers is the most reasonable measurement for the thickness of a human hair.
A. Length of a Tour Bus ↔ 2. 1.1 × 10¹ meters
B. Width of an apple ↔ 3. 4 × 10⁰ centimeters
C. Distance from Earth to a Satellite ↔ 6. 8 × 10² kilometers
D. Thickness of a human hair ↔ 5. 9 × 10¹ micrometers
What is Satellite?
A satellite is a moon, planet or machine that orbits a planet or star. For example, Earth is a satellite because it orbits the sun. Likewise, the moon is a satellite because it orbits Earth.
What is expression?
An act, process, or instance of representing in a medium (such as words) : utterance freedom of expression. Something that manifests, embodies, or symbolizes something else this gift is an expression of my admiration for you.
According to question, we have to drag the expression that is the most reasonable measurement for each object.
Length of Tour Bus is generally between 1 meter to 2 meters.
So, Reasonable measurement for Length of a Tour Bus is [tex]1.1[/tex]× [tex]10^{1}[/tex] meters
Width of an apple is generally between [tex]2[/tex] centimeters to [tex]6[/tex] centimeters
So, Reasonable measurement for Width of an apple is [tex]4[/tex]×[tex]10^{0}[/tex] centimeters .
Distance from Earth to a Satellite is generally between [tex]700[/tex] kilometers to [tex]3600[/tex] kilometers.
So, Reasonable measurement for Distance from Earth to a Satellite is
[tex]8[/tex]×[tex]10^{2}[/tex] kilometers.
Thickness of a human hair is generally between 17 micrometers to 181 micrometers.
So, Reasonable measurement for Thickness of a human hair is [tex]9[/tex]×[tex]10^{1}[/tex] micrometers.
Hence, we can conclude that the following expression is the most reasonable measurement for each object.
A. Length of a Tour Bus ↔ 2. 1.1 × 10¹ meters
B. Width of an apple ↔ 3. 4 × 10⁰ centimeters
C. Distance from Earth to a Satellite ↔ 6. 8 × 10² kilometers
D. Thickness of a human hair ↔ 5. 9 × 10¹ micrometers
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Related Questions
A fire hydrant that is 1.5 feet high casts a shadow that is 2.5 feet long. At the same time of day, a lamppost casts a shadow 15 feet long. What is the height of the lamppost?
Answers
Answer:
9 feet
Step-by-step explanation:
GRADE 12 DATA MANAGEMENT!!! HELP PLEASE
The Leafs’ coach stated that “the likelihood of us winning the next game are 2/9, the likelihood of tying the next game are 1/2, and likelihood of us loosing the next game are 2/5”. Can the coach’s predictions be entirely correct? Justify your response
Answers
2/5+1/2+2/9
(36+45+20)/90
101/90
So he obviously has serious issues with mathematics :P
By these numbers there is about 112% chance that they will either win, lose, or tie. However there can be at most a 100% chance of anything :)
The coach's predictions cannot be entirely correct because the sum of the probabilities given by the coach does not equal 1. Therefore, the coach's predictions are not consistent with the rules of probability.
Explanation:The coach's predictions cannot be entirely correct because the sum of the probabilities of all possible outcomes must equal 1. In this case, the sum of the probabilities given by the coach is 2/9 + 1/2 + 2/5 = 49/90, which is not equal to 1. Therefore, the coach's predictions are not consistent with the rules of probability.
To justify this, we can add up the probabilities of winning, tying, and losing the next game. The correct probabilities should add up to 1 since these are the only possible outcomes.
If we add these probabilities together: 2/9 + 1/2 + 2/5 = 49/90, which is not equal to 1. Therefore, the coach's predictions cannot be entirely correct.
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Tan (25pi/2) = ___
A). 1
B). 0
C). -1
D). Undefined
Answers
Type it in your calc. to find
Aida is attending a trekking camp. She walks from her tent to a hilltop in 2 hours. She has a picnic with her friends on the hilltop for 6 hours. Aida walks back to her tent in 1 hour. Which graph best represents the distance, y, in miles, traveled by Aida for a certain amount of time, x, in hours? A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 2, 4. The second straight line joins ordered pairs 2, 4 and 8, 4. The third straight line joins ordered pairs 8, 4 and 9, 0. A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 1, 4. The second straight line joins ordered pairs 1, 4 and 8, 4. The third straight line joins ordered pairs 8, 4 and 9, 0. A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 2, 4. The second straight line joins ordered pairs 2, 4 and 7, 4. The third straight line joins ordered pairs 7, 4 and 9, 0. A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 1, 4. The second straight line joins ordered pairs 1, 4 and 7, 4. The third straight line joins ordered pairs 7, 4 and 9, 0.
Answers
The correct answer among the given choices is the first one:
“A graph shows Time in hours on the x-axis and Aida’s Distance from Tent in miles on y-axis. The graph shows three straight lines. The first straight line joins ordered pairs 0, 0 and 2, 4. The second straight line joins ordered pairs 2, 4 and 8, 4. The third straight line joins ordered pairs 8, 4 and 9, 0.”
The given ordered pairs is in the format of (t, d) where t is time and distance is d. Time will always be on the x-axis since it is always an independent variable.
The first ordered pair should be (2, 4) since it took her 2 hours to trek to the hilltop. From the given choices, only the 1st and 3rd choice has this first ordered pairs so we are down to two choices.
Now the second ordered pair should be (8, 4) since she spent 6 hours at the top but no change in distance. And only the 1st choice has this value therefore it is the answer.
The probability of a randomly selected car crashing during a year in a certain country is 0.04770.0477. if a family has threethree cars, find the probability that at least one of them has a car crash during a year. is there any reason why the probability might be wrong?
Answers
P(having NO crash) = 1- 0.0477 = 0.9523
ⁿCₓ(p)ˣ. (1-p)ⁿ⁻ˣ
n= number of cars
x = number of crashes
p = 0.0477 (1 crash)
1-p = 0.9523 (NO crash:
Probability of NO crashes at all:
³C₀(0.0477)⁰(0.9523)⁽³⁻⁰⁾
³C₀(1)(0.9523)³ = 0.9523³ = 0.8636 Then P(NO CRASH) = 0.8636
P(at LEAST one crash) = 1 - 0.8636
P(at LEAST one crash) = 0.136
So we are going to find P(none of the cars crashes), then we will subtract it from 1, since:
P(at least one car crashes)+P(no car crashes)=1, as they are 2 disjoint complement events, either one or the other will happen, so the probability that either one or the other happens is 1.
P(a car not crashing)=1-0.0477=0.9523
P(car 1 not crash, car 2 not crash, car 3 not crash)=[tex]0.9523^{3}= 0.864[/tex]
P(at least 1 of the cars crashes)=1-P(none of the 3 cars crash)=[tex]1-0.9523^{3}=1-0.864=0.136[/tex]
Choose the equation that represents the line passing through the point (-2,-3) with a slope of -6
Awnsers are
A) y=-6x-15
B) y=-6x-20
C) y=-6x+15
D) y=-6x+20
Answers
The slope : m = - 6
The line passes through the point ( x, y ) = ( - 2, - 3 )
- 3 = ( - 6 ) * (- 2 ) + b
- 3 = 12 + b
b = - 3 - 12
b = - 15
Answer:
A ) y = - 6 x - 15
Answer:A
Step-by-step explanation:
In the formula that gives the circumference of a circle, which quantity is multiplied by 2 ?
Answers
Answer (APEX):
- Radius
Name three common measurements that are expressed as a ratio of two units.
Answers
Density , Speed and Mileage(Fuel Economy) are the three common measurements which can be expressed as a ratio of two units.
What are Fundamental Units?
A fundamental unit is a tool for measuring a base quantity. Any physical quantity that cannot be expressed in terms of another physical quantity is referred to as a basic quantity. They are
Length - meter (m)Time - second (s)Amount of substance - mole (mole)Electric current - ampere (A)Temperature - kelvin (K)Luminous intensity - candela (cd)Mass - kilogram (kg)Three Common Measurements be Density , Speed and Mileage where
Density = [tex]\frac{kg}{m^{3} }[/tex]
Speed = [tex]\frac{m}{s}[/tex]
Mileage = [tex]\frac{km}{L}[/tex]
Hence , the three common measurements which can be expressed as a ratio of two units are Density , Speed and Mileage
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The mean diastolic blood pressure for a random sample of 70 people was 94 millimeters of mercury. if the standard deviation of individual blood pressure readings is known to be 12 millimeters of mercury, find a 90% confidence interval for the true mean diastolic blood pressure of all people.
Answers
To solve this problem, we make use of the formula for Confidence Interval:
Confidence Interval = X ± z * σ / sqrt (n)
where X is the mean value, z is the z score which is taken from the standard tables, σ is the standard deviation, and n is the number of samples
z = 1.645 (at 90% Confidence Level)
Substituting the values into the equation:
Confidence Interval = 94 ± 1.645 * 12 / sqrt (70)
Confidence Interval = 94 ± 2.36
Confidence Interval = 91.64, 96.36
Therefore at 90% confidence level, the blood pressure reading ranges from 91.64 mmHg to 96.36 mmHg.
PLEASE HELP!!!! IMAGE ATTACHED find the value of x
Answers
If the triangles are congruent then x = 7.
A family has ninenine children. if this family has exactly threethree boysboysâ, how many different birth and gender orders areâ possible
Answers
You can calculate it as:
[tex]\binom{9}{3} = \frac{9!}{3! \cdot 6!} = \frac{362880}{6\cdot720} = 84[/tex]
Billy Goats invested some money in stocks and bonds. The total amount he invested was $\$165,\!000$. If he invested 4.5 times as much in stocks as he did in bonds, what was his total investment in stocks?
Answers
s + b = 165,000
s = 4.5b
4.5b + b = 165,000
5.5b = 165,000
b = 165,000/5.5
b = 30,000...his investment in bonds
s + b = 165,000
s + 30,000 = 165,000
s = 165,000 - 30,000
s = 135,000 <=== his investment in stocks
An equation is formed when two equal expressions. The total investment that Billy made in stocks is $135,000.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the amount that is invested in stocks be represented by x, while the amount that is been invested in bonds is represented by y.
Given that Bily invested 4.5 times as much in stocks as he did in bonds. Therefore, the equation to represent the given situation can be written as,
x = 4.5y
Also, given that the total amount that Billy invested is $165,000. Therefore, the total invested amount can be written as,
$165,000 = x + y
Substitute the value of x in the equation,
$165,000 = 4.5y + y
$165,000 = 5.5y
y = $165,000 / 5.5
y = $30,000
Now substitute the value of y in the first equation to know Billy's investment in stocks.
x = 4.5y
x = 4.5($30,000)
x = $135,000
Hence, the total investment that Billy made in stocks is $135,000.
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A triangle has squares on its three sides as shown below. What is the value of x? Three squares having side lengths 6 cm, x cm, and 8 cm joining to form right triangle at the centre 2 centimeters 6 centimeters 8 centimeters 10 centimeters
Answers
The third side of the triangle is AC = 10 centimeters
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measures of the sides of the triangle are
The measure of side AB = 6 cm
The measure of side BC = 8 cm
Now , For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
On simplifying , we get
The measure of side AC = √ ( AB )² + ( BC )²
The measure of side AC = √ ( 6 )² + ( 8 )²
The measure of side AC = √ ( 36 + 64 )
The measure of side AC = √ ( 100 )
The measure of side AC = 10 cm
Therefore , the value of AC is 10 cm
Hence , the right triangle is solved and the side AC = 10 cm
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Simplify the following expression: (Multiple Choice)
a + 2c − 5b − c + a − b
1. 2a − 6b + 2c
2. 2a − 6b + c
3. a − 6b + c
4. a − 5b + 2c
Answers
Answer:
a + a - 5b - b + 2c - c
2a - 6b + c
the answer is 2
The length of a rectangle is three inches more than the width. the area of the rectangle is 460 inches. if the width is x, what is the length in terms of x?
Answers
l=3+x if x is the width
The length and width of the given rectangle are 23 and 20 inches respectively.
Suppose the width of the given rectangle=x inch
So, the length of the given rectangle = x+3 inch
What is the area of a rectangle?The area of a rectangle with length l and width b is lb.
So, the area of the given rectangle = x(x+3)
Given that area of the rectangle = 460 squared inches
So, x(x+3)=460
[tex]x^{2} +3x=460[/tex]
[tex]x^{2} +x-460=0[/tex]
[tex]x^{2} +23x-20x-460=0[/tex]
[tex]x(x+23)-20(x+23) =0[/tex]
[tex](x+23) (x-20)=0[/tex]
[tex]x=-23[/tex]...Not possible
[tex]x=20[/tex]
The width of the rectangle =20 inches
So, the length of the rectangle =20+3 = 23 inches
Therefore, the length and width of the given rectangle are 23 and 20 inches respectively.
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Find the perimeter and area of a square with side lengths of 16
Answers
perimeter = 4S = 16*4 = 64 units
area = S^2 = 16^2 = 256 square units
Answer:
The perimeter of a square with side lengths of 16 units is 64 units.
The area of a square with side lengths of 16 units is [tex]256 unit^2[/tex].
Step-by-step explanation:
Length of the square = a = 16 units
Perimeter of the square = P = [tex\]4\times a[/tex]
[tex]P=4\times 16 units = 64 units[/tex]
Area of the square = A = [tex]a^2[/tex]
[tex]A=a^2=(16 unit)^2=256 unit^2[/tex]
The perimeter of a square with side lengths of 16 units is 64 units.
The area of a square with side lengths of 16 units is [tex]256 unit^2[/tex].
Find (r-s) (t-s) + (s-r) (s-t) for all numbers r, s, and t. (a) 0 (b) 2 (c) 2rt (d) 2(s-r) (t-s) (e) 2(r-s) (t-s)
Answers
(r-s) is just (s-r) times (-1)
similarly
(t-s) is just (s-t) times (-1)
this means that :
(r-s) (t-s) + (s-r) (s-t)=-(s-r)[-(s-t)]+(s-r) (s-t)
the 2 minuses in the first multiplication cancel each other so we have:
-(s-r)[-(s-t)]+(s-r) (s-t)=(s-r) (s-t)+(s-r) (s-t)=2(s-r) (s-t)
Answer:
d)2(s-r) (t-s)
Answer:
d
Step-by-step explanation:
Solve (2/3)-(1/x)=5/6
Answers
[tex]2 - \frac{1(3)}{x} = \frac{5(3)}{6} [/tex] Simplify the numerators
[tex]2 - \frac{3}{x} = \frac{15}{6} [/tex] Multiply both sides by 6
[tex]12 - \frac{3(6)}{x} = 15[/tex] Simplify the numerator
[tex]12 - \frac{18}{x} = 15[/tex] Multiply both sides by x
12x - 18 = 15x Subtract 12x from both sides
-18 = 3x Divide both sides by 3
-6 = x Switch the sides to make it easier to read
x = -6
Check your answer by plugging -6 in for the x in the original problem:
[tex] \frac{2}{3} - \frac{1}{x} = \frac{5}{6} [/tex] Plug in -6 for x
[tex] \frac{2}{3} - \frac{1}{-6} = \frac{5}{6} [/tex] Change [tex] \frac{2}{3} [/tex] to [tex] \frac{4}{6} [/tex] so all denominators are the same
[tex] \frac{4}{6} - \frac{1}{-6} = \frac{5}{6} [/tex] Change [tex] \frac{1}{-6} [/tex] to [tex] \frac{-1}{6} [/tex] for easier work
[tex] \frac{4}{6} - \frac{-1}{6} = \frac{5}{6} [/tex] Subtract the numerators (4 - (-1) )
[tex] \frac{5}{6} [/tex] = [tex] \frac{5}{6} [/tex]
So, x = -6 .
Negative numbers are less than positive numbers. Does this mean that the absolute value of a negative number must be less than the absolute value of a positive number? Explain.
Answers
Example: |-6| > |4|
If a convex polyhedron has 18 edges and 12 vertices, then how many faces does it have?
Answers
V + F - E = 2
12 + F - 18 = 2
F - 6 = 2
add 6 to both sides
F = 8
CHECK:12 + 8 - 18 ??=?? 2
20 - 18 = 2 checks
Determine the width of the garden. Nina must put 60 feet of fencing around her rectangular garden. The length of the garden is three feet longer than twice the width. What is the solution set for 2w + 2(2w + 3) = 60 given the replacement set {6, 7, 8, 9}?
Answers
2w+2(2w+3)=60
2w+4w+6=60
6w+6=60
6w=54
w=54/6 =9
the width is 9 feet
Answer:
9 is a solution.
Step-by-step explanation:
The replacement set is the set of values that can be substituted in the equation (for the variables).
Given a replacement set, we need to substitute every value of the set in our equation and see if the equation holds for that value. If it does, then the value is a solution of the equation.
In this problem we have the equation 2w + 2(2w + 3) = 60 and the replacement set is {6,7,8,9}
We are going to start replacing the different values of the set.
w = 6[tex]2w + 2(2w + 3) = 60\\2(6) + 2(2(6)+3) = 60\\12 + 2(12+3) = 60\\12 + 2(15) = 60\\12 + 30 \neq 60[/tex]
Thus, 6 is not a solution.
w = 7[tex]2w + 2(2w + 3) = 60\\2(7) + 2(2(7) +3) = 60\\14 + 2 (14+3) =60\\14 + 2(17)=60\\14+34=60\\48 \neq 60[/tex]
Thus, 7 is not a solution.
w = 8[tex]2w + 2(2w + 3) = 60\\2(8) + 2(2(8)+3) = 60\\16 + 2(16+3)=60\\16 +2 (19) =60\\16 + 38 \neq 54[/tex]
Thus, 8 is not solution.
w = 9[tex]2w + 2(2w + 3) = 60\\2(9) + 2(2(9) + 3) =60\\18 + 2 (18+3) =60\\18 +2(21)=60\\60=60[/tex]
Thus, 9 is a solution.
whitch of the following is (are) the solution(s) to 11x+3=6
Answers
can someone explain how to do this plzz
Answers
1 of the shapes will be a small square. The dimensions for it would be 4 by 3 (12)
The second shape, the bigger rectangle has the dimensions, 12 by 6 (72)
Now add these two values 12+72 and you get, 84
you answer is A 84 square inches
What is 0.0333333333333333 as a fraction?
Answers
A bag contains 10 marbles: 4 are green, 2 are red, and 4 are blue. Christine chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue? Write your answer as a fraction in simplest form.
Answers
2nd marble is blue is 3/9
Multiple together and the probability is 12/90 or 2/15
Answer:
The probability that both marbles she chooses are blue is [tex]\frac{2}{15}[/tex]
Step-by-step explanation:
Given : A bag contains 10 marbles: 4 are green, 2 are red, and 4 are blue. Christine chooses a marble at random, and without putting it back, chooses another one at random.
To find : What is the probability that both marbles she chooses are blue?
Solution :
Total number of marbles = 10
Green marbles = 4
Red marbles = 2
Blue marbles = 4
Probability is favorable outcome upon total number of outcomes.
Probability of getting first marble is blue
[tex]\text{P(first blue marble)}=\frac{4}{10}=\frac{2}{5}[/tex].
Without replacement,
i.e. Blue marble left = 3
Total marble left = 9
Probability of getting second marble is blue
[tex]\text{P(second blue marble)}=\frac{3}{9}=\frac{1}{3}[/tex]
The probability that both marbles she chooses are blue is
[tex]\text{P(both blue marble)}=\frac{2}{5}\times\frac{1}{3}[/tex]
[tex]\text{P(both blue marble)}=\frac{2}{15}[/tex]
Therefore, The probability that both marbles she chooses are blue is [tex]\frac{2}{15}[/tex]
A construction worker needs to put a rectangular window in the side of a building. He knows from measuring that the top and bottom of the window have a width of 9 feet and the sides have a length of 12 feet. He also measured one diagonal to be 15 feet. What is the length of the other diagonal?
Answers
Answer: 15 feet
Step-by-step explanation:
The length of other diagonal is 15 feet.
What are properties of diagonal of rectangle?Both diagonals bisect opposite angles of the quadrilateral. Both diagonals form symmetry lines for the quadrilateral. The diagonals divide the quadrilateral into four congruent right triangles. The intersection point of the diagonals is the incenter of the quadrilateral
Given:
width= 9 feet
length= 12 feet
Diagonal length = 15 feet
We know the diagonals of a rectangle are equal and bisect each other.
So,
The length of other diagonal is 15 feet.
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what is the quotient? x-3 divided into 4x2+3x+2
Answers
The quotient of x-3 divided into 4x^2+3x+2 is 4x+9.
Explanation:To find the quotient of x-3 divided into 4x^2+3x+2, we need to perform polynomial long division.
Divide the first term of the numerator (4x^2) by the first term of the denominator (x) to get 4x. Write this as the first term of the quotient.Multiply the entire denominator (x-3) by the quotient term (4x) and subtract it from the numerator (4x^2+3x+2).Bring down the next term from the numerator (-3x).Repeat steps 1 and 2 with the new numerator (-3x) and the denominator (x-3).Continue this process until there are no more terms to bring down and divide.After performing polynomial long division, the quotient is 4x+9.
Final answer:
To find the quotient of x-3 divided into 4x^2+3x+2, you can use long division. The quotient is 4+15 with a remainder of 47.
Explanation:
To find the quotient of x-3 divided into 4x2+3x+2, we can use long division.
First, divide the 4x2 term by the x term, which gives us 4x.Multiply 4x by x-3 to get 4x2-12x.Subtract 4x2-12x from 4x2+3x+2 to get 15x+2.Now, divide 15x by x to get 15.Multiply 15 by x-3 to get 15x-45.Subtract 15x-45 from 15x+2 to get 47.Since there are no more terms to divide, the quotient is 4+15 and the remainder is 47.Therefore, the quotient of x-3 divided into 4x2+3x+2 is 4+15 with a remainder of 47.
Use the graph below to answer the question that follows:
What is the average rate of change between the interval of x = 0 and x = pi/2?
A) 2/pi
B) pi/2
C) pi/4
D) 4/pi
Answers
Answer:
the correct answer is option D.
Step-by-step explanation:
average rate of change in the graph in interval x = 0 and x = pi/2
when we look into the graph between interval x = 0 and x = pi/2
we can see that on y - axis
at x = 0 value of y = 3 and
at x = π/2 value of y = 5
rate of change = [tex]\frac{change\ in y-axis}{change\ in\ x-axis}[/tex]
= [tex]\dfrac{y_2-y_1}{x_2- x_1}[/tex]
=[tex]\dfrac{5-3}{\frac{\pi}{4} - 0}[/tex]
= 4/π
hence, the correct answer comes out to be 4/π
hence, the correct answer is option D.
A six-sided die is rolled three times. what is the probability that all three rolls will be 6?
Answers
you have a 1/6 probability of rolling a 6
so for 3 6's it would be
1/6 x 1/6 x 1/6 = 1/216
think of a number. add two. multiply by three. add your original number. multiply by 2. add 2. subtract your original number. divide by 7. add three. subtract your original number. add five. Why is the answer always ten?
Answers
adding 2 we get x+2
multiply by 3 we get 3x+6
add original number we get 4x+6
multiply by 2 we get 8x+12
add 2 we get 8x+14
minus original number we get 7x+14
divide by 7 we get x+2
add 3 we get x+5
minus original number we get 5
add 5 we get 10
because the numer you pick cancels out in the end
we can write it out fully into one big equation
if x is the number
then the resulting expression is looking like this
[tex]\frac{2(3(x+2)+x)+2-x}{7}+3-x+5[/tex]