The prime factorization of 200 using exponential notation is [tex]2^3 *5^2[/tex] that is correct option is (b)
First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.
1) [tex]200\div2=100[/tex] (Even number)
2) [tex]100\div2=50[/tex](Even number)
3) [tex]50\div2=25[/tex](Even number)
4) [tex]25\div5=5[/tex](Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
5) [tex]5\div5=1[/tex](Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
Now, we construct the prime factorization using exponential notation:
[tex]200=2^3\cdot5^2[/tex]
The prime factorization of 200 using exponential notation is [tex]2^3\cdot5^2[/tex] that is option (b)
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The prime factorization of 200 using exponential notation is 2^3*5^2 that is correct option is (b)
First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.
1) 200/2=100 (Even number)
2) 100/2=50 (Even number)
3)50/2=25 (Even number)
4) 25/5=5 (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
5) 5/5=1 (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
Now, we construct the prime factorization using exponential notation:
200=2^3*5^2
The prime factorization of 200 using exponential notation is 2^3*5^2 that is option (b)
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The diagram below shows a section of the steel support structure of a roller coaster. Use the diagram for the problem below. Given segment JK is parallel to segment PL, m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)°, what is the measure, in degrees, of ∠JKL and ∠PLK? (HINT: m∠JKL and m∠PLK is not 90 degrees)
The measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.
What are parallel segments?Parallel segments are defined as lines on a plane that never meets.
The properties of parallel segments include:
The vertically opposite angles are equalThe corresponding angles are equalThe alternate exterior angles are equalThe alternate interior angles are equalGiven the angles;
m∠JKL = (10x + 5)° m∠PLK = (12x - 1)°We can see that the two angles are vertically opposite angles and thus equal.
Then,
m∠JKL = m∠PLK
substitute the values
10x + 5 = 12x - 1
collect like terms
10x - 12x = -1 - 5
-2x = - 6
Make 'x' the subject of formula
x = 3
But:
m∠JKL = (10x + 5)° = 10(2) + 5 = 25°
m∠PLK = (12x - 1)° = 12(2) - 1 = 23°
Thus, the measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.
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Evaluate each logarithm.
log₂1/4
The answer of the logarithmic form is -2 .
In mathematics, the logarithmic function is the inverse of power. Then the function is given as f(x) = log xThe logarithm base is a. This can be read as the logarithmic base a of x. The two most common bases used in logarithmic functions are base 10 and base e.The logarithm function has several properties that allow the logarithm to be simplified when the input is in the form of products, quotients, or values raised to powers.We have given an equation [tex]log_2\frac{1}{4}[/tex] ..... (1)
Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{loh_ax}[/tex] in equation (1) ,we get
[tex]log_2\frac{1}{4}=\frac{log\frac{1}{4} }{log2}[/tex] ..(2)
[tex]log\frac{1}{4}[/tex] can be written as [tex]log1-log4[/tex] using property [tex]log\frac{a}{b} =loga-logb[/tex] whereas [tex]log1=0[/tex]
Then , the equation (2) becomes
[tex]log_2\frac{1}{4}=\frac{log1-log4 }{log2}\\\\log_2\frac{1}{4}=\frac{0-log4 }{log2}\\\\log_2\frac{1}{4}=\frac{-log4 }{log2}[/tex]
[tex]log4[/tex] can be written as [tex]log2^2[/tex]
The equation (2) becomes
[tex]log_2\frac{1}{4}=\frac{-log2^2 }{log2}[/tex]
using property [tex]loga^b=bloga[/tex]
[tex]log_2\frac{1}{4}=\frac{-2log2 }{log2}\\log_2\frac{1}{4}=-2[/tex]
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–7.64 + 8d = 14.21 + 17.5d
Is it no solution, one solution, or infinite solution? Please Help
Answer:
This equation has one solution I believe if you substitute the variable 68.3375
Step-by-step explanation:
Find any points of discontinuity for each rational function. y= x²-x-2 / 3 x²-7 x+2
The point of discontinuity for y= x²-x-2 / 3 x²-7 x+2 is x= 1/3 and x= 2.
What is discontinuous function?
Mathematics, functions, and applications all place a premium on continuous functions. But not every function is continuous. A function is said to have a discontinuity there if it is not continuous at that point in its domain.
Given,
y = x²-x-2 / 3 x²-7 x+2
It can be expressed in the form of -
⇒ y = (x-2) (x+1) / (3x-1) (x-2)
The function will be undefined if the denominator will be 0
⇒ 3x-1 = 0
⇒ x = 1/3
⇒ x-2 = 0
⇒x = 2
So, we can conclude that the given function will be having points of discontinuity as x = 2, 1/3
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What is the rate of change seen in the graph below?
Answer: There is none
Step-by-step explanation:
Victoria drew a diagram of her laptop that she uses at school. It is in the shape of a rectangle. The dimensions are as follows:
Length: 13x - 9 units
Width: 4.5x + 8 units
If the length is greater than the width, which inequality represents this situation?
The inequality that represents the given situation is 13x - 9 > 4.5x + 8
Writing an InequalityFrom the question, we are to determine the inequality that represents the given situation
From the given information, we have that
The length of the laptop is given by 13x - 9 units
and
The width of the laptop is given by 4.5x + 8 units
If the length is greater than the width, then we can write that
13x -9 > 4.5x + 8
Hence, the inequality is 13x - 9 > 4.5x + 8
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The prize money on a game show about collecting tokens is found using the
formula below.
Keelan won £8695. How many tokens did he collect?
p=20x+75
Using given algebraic equation, Keelan collected 431 tokens.
What is an algebraic equation?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
At least one variable and one operation must be present in an algebraic expression (addition, subtraction, multiplication, division). One such algebraic statement is 2(x + 8y).
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic statement. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we may substitute those values for the original variables before evaluating the expression.
Given,
p=20x+75
p = 8695
8695 = 20x + 75
x = 8695 - 75 / 20
x = 431
Therefore Keelan collected 431 tokens.
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HLEP NUMBER 3 HELPPOO
Answer:
8.3333333 square & root of 25
Step-by-step explanation:
Find the perimeter of the polygon with the given vertices:
U (-1,4)
V (3, 4)
W (3, 1)
The perimeter of the polygon = ?
I need help with this
The perimeter of the polygon is 12.
The perimeter of a closed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides. All sides add up to the perimeter.
The distance between the two points A(x, y) and B(x₁, y₁ ).
AB = √ [ (x₁ - x)² + (y₁ - y)² ]
Consider the vertices U ( -1, 4), V (3, 4), W (3, 1).
Then,
UV = √ [ ( 3 +1)² + (4 - 4)² ] = √4² = 4
VW = √ [ ( 3 - 3)² + ( 1 - 4)² ] = √(- 3)² = 3
UW = √ [ ( 3 + 1)² + ( 1 - 4)² ] = √ [ ( 4)² + (-3)² ] = √ [ 16 + 9 ] = √25 = 5
Then the perimeter of the polygon will be:
perimeter = UV + VW + UW
perimeter = 4 + 3 + 5 = 12
Hence, the perimeter of the polygon is 12.
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Space Use the formula for maximum velocity v=-0.0098 t+c ln R . Find the mass ratio of a rocket with an exhaust velocity of 3.1km/s, a firing time of 50s, and a maximum shuttle velocity of 6.9km/s .
The mass ratio of the rocket is 10.8468 kg/C.
What is mass ratio of a rocket?An indicator of a rocket's effectiveness is its mass ratio. It describes the ratio of the rocket's wet mass to its dry mass, or how much more massive the vehicle is with propellant than without.Given:
v = - 0.0098(t) + c (ln (R) ), where:v = maximum shuttle velocityt = firing timec = velocity of exhaustR = mass ratioHere, c = 3.1 km/s, t = 50s, v = 6.9km/sTo find: Mass ratio (R) = ?
Finding:
On substituting the values of 'c', 't', 'v', we get:
6.9 = - 0.0098 (50) + 3.1 (ln (R) )
=> 6.9 + 0.49 = 3.1 (ln (R) )
=> 7.39 = 3.1 (ln (R) )
=> ln (R) = [tex]\frac{7.39}{3.1}[/tex]
=> R = [tex]e^{\frac{739}{310}}[/tex] ≈ 10.8468
Hence, the mass ratio of the rocket is 10.8468 kg/C.
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Your grandmother gives your little brother 42 coins. Some are dimes and some are
nickels, but they total to $3.00. How many dimes does your little brother have?
Taking into account the definition of a system of linear equations, you little brother has 6 dimes.
System of linear equationsA system of linear equations is a set of equations that have more than one unknown, appearing in several of the equations but necessarily in all of them. The equations relate the unknowns to each other.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. In other words, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Amount of dimesIn this case, a system of linear equations must be proposed taking into account that:
"d" is the amount of dimes."n" is the amount of nickels.You know that:
Your grandmother gives your little brother 42 coins. Some are dimes and some are nickels, but they total to $3.00.The system of equations to be solved is
[tex]\left \{ {{d+n=42} \atop {0.1d + 0.05n=3}} \right.[/tex]
It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "n" from the first equation:
n= 42 -d
Replacing this expression in the second equation obtained:
0.1d + 0.05×(42 - d)= 3
Solving:
0.1d + 0.05×42 - 0.05d= 3
0.1d + 2.1 - 0.05d= 3
0.15d + 2.1=3
0.15d= 3 -2.1
0.15d= 0.9
d= 0.9÷0.15
d= 6
Finally, you little brother has 6 dimes.
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17. The time it takes Sonia to mow 1 acre of land
is shown in the table. If Sonia has to mow
2.5 acres of land with a push mower, how
long does it take her to mow?
Push Mower
1.25 hours per acre
35 minutes per acre
Gas Mower
The time taken by Sonia to mow 2.5 acres of land with push mower is 3.125 hours .
According to the question we have been given that
Time taken by push mower to mow 1 acre land = 1.25 hours
Time taken by Gas mower to mow 1 acre land = 35 minutes
We need to find how many hours Sonia take to mow 2.5 acre of land with push mower.
To find this we will use unitary method. That is
1 acre = 1.25 hours
2.5 acre = 1.25*2.5 hours
= 3.125 hours.
Hence the time taken by Sonia to mow 2.5 acres of land with push mower is 3.125 hours .
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What is 1/20 as a percentage
Answer:
1/20 = 5%
Hope this helps with your question :)
Step-by-step explanation:
1. Multiply numerator and denominator by 5 to get 100 in the denominator.
1/20 = 5/100
2. A number over 100 means it is that number on top of 100.
5/100 = 5% out of 100%
3. So final answer is 5%
Name the sides of angle 4
The sides of angle 4 will be side CD and side DG.
We are given a ray diagram.
We need to tell the sides or the rays of the angle 4.
an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.
Here, angle 4 has the sides as CD and DG.
Therefore, the sides of angle 4 will be side CD and side DG.
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3 - 1/2d = 3/2d + 4 - d.
I don't get the fractions, they confuse me and I don't know what to do with them to be able to finish the problem.
The solution to the equation 3 - 1/2d = 3/2d + 4 - d is d = -7
How to evaluate the expression?The expression is given as
3 - 1/2d = 3/2d + 4 - d.
Multiply through the expression by 2
So, we have
6 - d = 3d + 8 - 2d
Evaluate the like terms
6 - d = d + 8
Evaluate the like terms
2d = -14
Divide by 2
d = -7
Hence, the solution to the equation 3 - 1/2d = 3/2d + 4 - d is d = -7
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A hot air balloon rises from the ground to 150 feet elevation. But the wind is too strong, so the pilot ascends another 75 feet
Answer: 225
Step-by-step explanation:
I may not be right but I’m taking that ascends is basically adding up the height so 150+75=225
Evaluate
5.7 x 0.049 / 0.681
Give your answer rounded to 2 DP.
Answer:
0.41
Step-by-step explanation:
let h(x) = 3x+2 if h(x) = 11 find x
Answer:
3
Step-by-step explanation:
11 = 3x+2
9 = 3x
x = 3
five balls are randomly chosen, without replacement, from an urn that contains 5 red, 6 white, and 7 blue balls. find the probability that at least one ball of each color is chosen.
The probability that at least one ball of each color is chosen is 105/8568.
Given that:-
Number of red balls in the urn = 5
Number of white balls in the urn = 6
Number of blue balls in the urn = 7
We have to find the probability that at least one ball of each color is chosen.
Let us consider the that 1 ball of each color has been chosen.
Hence, we are left with 4 red balls, 5 white balls and 6 blue balls.
Now we have to choose 2 balls from them.
Hence,
Number of ways in which we can choose 2 balls from (4+5+6) that is 15 balls = [tex]^{15}C_2=105[/tex]
Total number of ways in which we can choose 5 balls from 18 balls =
[tex]^{18}C_5=8568[/tex]
Hence,
Probability that at least one ball of each color is chosen = 105/8568
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A family plans to have 3 children. For each birth, assume that the probability of a boy is the same as the probability of a girl. What is the probability that they will have at least one boy and at least one girl?.
Probability of at least one boy and one girl = [tex]\frac{3}{4}[/tex]
The probability of no of boys = 1/2 ×1/2×1/2= 1/8
The probability of no of girls = 1/2×1/2×1/2= 1/8
Now we have to find the probability of at least one girls
Probability of one boy and one girl = 1 - (1/8 + 1/8)
= 1 - 1/4
= 3/4
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Please helppppp no wowo
Answer:
d-(8,15)
Step-by-step explanation:
69497694646946464646463434644
In Exercises 4 and 5, find the area of the polygon with the given vertices.
4. P(1,1) Q(-2,1), R(-1,-4)
5. A(3,7), B(5,7), C(3,-7), D(5,-7)
Answer:
#4: 7.5
#5: 28
Step-by-step explanation:
Polygon in #4
is a triangle
base = 1 - (-2) = 1+2 = 3
height = 1-(-4) = 1 + 4 = 5
Area of a triangle with base b and height h = (1/2)b.h
So area of this triangle = (1/2) (3) (5) = 15/2 = 7.5
Polygon in #5
is a rectangle with length = 7 - (-7) = 7 +7 = 14
and width = 5-3 = 2
Area of a rectangle with length l and width w = lw
Area of this rectangle = 14 x 2 = 28
Hope that helps
The area of the polygon for exercise 4 is 7.5 square units and for exercise 5 the area is 28 square units.
What is an area?The space occupied by the object in two-dimensional space is called as the area.
For a triangle, the area will be calculated as,
base = 1 - (-2) = 1+2 = 3
height = 1-(-4) = 1 + 4 = 5
Area of a triangle with base b and height,
h = (1/2)b.h
Area of this triangle,
A = (1/2) (3) (5) = 15/2 = 7.5
Rectangle with length = 7 - (-7) = 7 +7 = 14
Rectangle width = 5-3 = 2
Area of a rectangle with length l and width w = lw
Area of this rectangle = 14 x 2 = 28 square units
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SOMEONE HELP PLEASE ME
1) The converse of the function is; If not q, then p
2) The Inverse of the function is; If not p, then q.
3) The contrapositive of the function is; If q, then not p
How to Interpret Conditional Statements?
Suppose we have a conditional statement, If it is raining, we will not play. Let, A: It is raining and B: we will not play. Then; If A is true, that is, it is raining and B is false, that is, we played, then the statement A implies B is false.
The conditional statement is given as;
If p, then not q.
1) The converse of the function is; If not q, then p
2) The Inverse of the function is; If not p, then q.
3) The contrapositive of the function is; If q, then not p
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A car travels at a rate of 45 m iles per hour for 5 hours. Let y be the distance in miles that a car travels for a
given amount of time, x, in hours. The situtation can be modeleAndd by a function. Which of these describes how their
domain of the function?
Answer:477.47 revolutions
Step-by-step explanation:
2. If an airplane's speed is 625 miles per hour, what is its speed in feet per second? Round
your answer to the nearest whole number. There are 5,280 feet in a mile.
A.
B.
C.
D.
426 feet per second
917 feet per second
55,000 feet per second
1,188,000 feet per second
Answer: The answer is B
Three positive integers are (x - 1), x and (x + 1). If their sum is 105, find the numbers.
The three positive integers are 34, 35, 36
Three positive integers are given as (x-1),x and (x+1)
Sum of these three integers are 105,
As we know the total sum of the three positive integers, we can get the value by adding the three integers to the sum value.
Thus,
(x-1) + x + (x+1) = 105
x - 1 + x + x + 1 = 105
3x + 0 = 105
3x = 105
x = 105/3
x = 35
Then, the integers are (35 - 1) , 35 , (35 + 1)
Therefore, the three positive integers are 34, 35, 36
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In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
magnitude 7.7 in San Francisco, California, in 1906
1) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.
2) The earthquake at New Madrid was of lesser intensity than earthquake at Valdivia.
3) The earthquake at New Madrid was of greater intensity than earthquake at Charlottesville.
4) The earthquake at New Madrid was of greater intensity than earthquake at Kobe.
In mathematics, the greater than sign is a basic mathematical notation used to represent an inequality between two values. The symbol used to denote greater inequality is “>”. It is the commonly accepted mathematical notation of two strokes of equal length that meet at an acute right angle. A typical use of the greater than sign is to compare two values, where the first is greater than the second, or one is greater than the other. The greater than sign is an approximation of a closing square bracket.Learn more about greater sign here
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The question is incomplete. The complete question is
In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
1. magnitude 7.7 in San Francisco, California, in 1906
2. magnitude 9.5 in Valdivia, Chile, in 1960
3. magnitude 3.2 in Charlottesville, in 2001
4. magnitude 6.9 in Kobe, Japan, in 1995
In the image above angle 3 is 79 degrees, what is angle 11?
Since in the image above angle 3 is 79 degrees, angle 11 is also equal to 79 degrees based on the vertical angles theorem.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is the vertical angles theorem?The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are generally formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
In Geometry, when two (2) parallel lines are cut by a transversal, the interior angles that are formed on the same side of the transversal are supplementary angles, which makes:
Angle 3 = Angle 14
Angle 14 = Angle 9
Angle 3 ≅ Angle 9 (Congruent angles or supplements of the same angle)
By applying the vertical angles theorem, we have:
Angle 9 ≅ Angle 11 = 79 degrees.
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What are the solutions of each equation? Check your answers.
(a) ln x=2
According to the question, the solution for the equation [tex]ln(x)=2[/tex] is [tex]e^{2}[/tex]. And the procedure for the given equation is as follows:
Expression: [tex]ln(x)=2[/tex]
Removing logarithmic function from the equation, equate it to exponential. Therefore, the expression can be re-written as:
[tex]ln(x)=2\\(x)=e^{2}[/tex]
Therefore, the solution for the equation is :[tex]x=e^{2}[/tex].
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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Work out (7 x 10°) (2 × 10²) 4 Give your answer in standard form.
Answer:
[tex] {1.4 \times 10}^{3} | [/tex]
Step-by-step explanation:
*winks and runs off ;)*