11th term of the given geometric sequence is [tex]a_{n} = 7(5^{n-1})[/tex]
What is Geometric sequence?In a Geometric Sequence each term is found by multiplying the previous term by a constant.
Given geometric sequence = 7,35,175
Nth term of the geometric sequence [tex]a_{n}=a_{1} .r^{n-1}[/tex]
[tex]a_{1}=7[/tex]
[tex]r= \frac{35}{7} =5[/tex]
Nth term of the geometric sequence
[tex]a_{n} = 7(5^{n-1})[/tex]
Hence, the Nth term of the given geometric sequence is [tex]a_{n} = 7(5^{n-1})[/tex]
Alexa earns 5% commission as a salesperson. She sold a gold necklace that cost $78. How much commission did Alexa earn?
Answer:
Step-by-step explanation:
= 5 /100 * 78 = 39 /10 = 3.9
$3.90
25. The circle has a radius of 7. Angle C
intercepts the arc with a length of 28.
What is the measure of angle C in radians?
The measure of angle C in radians is 3.6 radians.
What is arc length of circle formula?The arc length of a circle is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.
Given that, the circle has a radius of 7 and angle C intercepts the arc with a length of 28π.
We know that, formula to find the arc length of circle is Arc length= θ/360 ×2πr
28π= θ/360×2π×7
4= θ/360×7
θ=1440/7
θ=205.7
θ=3.6 radians
Therefore, the measure of angle C in radians is 3.6 radians.
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Find the asymptotes, domain and range.
For the given function,
Vertical asymptote = -5/4
Horizontal asymptote = -5/4
Domain = (-∞,-5/4) ∪ (-5/4,∞)
Range = (-∞,-5/4) ∪ (-5/4,∞)
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The given function is
[tex]f(x) = \frac{-5x+2}{4x+5}[/tex]
The given function has a vertical asymptote at x = -5/4. This is because the function tends to ∞ as x tends to -5/4.
The horizontal asymptote of the function is when x tends to ∞ .
[tex]\lim_{x \to \infty} \frac{-5x+2}{4x+5} = \frac{-5+2/x}{4+5/x} = \frac{-5}{4}[/tex]
The horizontal asymptote of function is at y = -5/4.
Since at x = -5/4, the function becomes undefined.
The domain is all real numbers except x = -5/4
Domain = (-∞,-5/4) ∪ (-5/4,∞)
Since the function is not defined at y = -5/4 as well, the range is also
(-∞,-5/4) ∪ (-5/4,∞) .
Therefore for the given function,
Vertical asymptote = -5/4
Horizontal asymptote = -5/4
Domain = (-∞,-5/4) ∪ (-5/4,∞)
Range = (-∞,-5/4) ∪ (-5/4,∞)
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10. Sixteen teams play in a one-game elimination
match. The winners of the first round go on to
play a second round until only one team remains
undefeated and is declared the champion.
4
a. Make a table of values for the number of
rounds and the number of teams participating.
b. What is the reasonable domain and the range
of this function? Explain.
c. Find the rate of decay.
d. Find the decay factor.
a. Here's a table of values for the number of rounds and the number of teams participating:
Round Number of Teams
1 16
2 8
3 4
4 2
5 1 (Champion)
.b. domain: [1 5]
Range: {1 16]
C. Rate of decay = 8
D. Decay factor = 0.5
How to solve for the rate of decayb. The reasonable domain of this function would be the number of rounds, and the range would be the number of teams participating in each round.
The domain would be all positive integers from 1 to the maximum number of rounds,
The range would be all positive integers from 1 to the starting number of teams (16 in this case).
c. To find the rate of decay, we can calculate the ratio of the change in the number of teams to the change in the number of rounds.
Using Round 1 to Round 2,
= (16 - 8) / (2 - 1)
= 8.
d. The decay factor is the ratio of the number of teams in a given round to the number of teams in the previous round.
Using Round 1 to Round 2, the decay factor is
= 8 / 16
= 0.5
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30% of 750 using a table
Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Evaluate each algebraic expression for the given values.
1. 9.8t^2 + 20t + 8 for t = -2, 0, 3.5
2. -3(2.1x - 7.9) for x = -18.1, -0.3, 14.4
The numeric values for each of the expressions are given as follows:
1. 9.8t² + 20t + 8:
t = -2: 7.2.t = 0: 8.t = 3.5: 198.05.2. -3(2.1x - 7.9):
x = -18.1: 137.73. x = -0.3: 25.59x = 14.4: -67.02.How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
Then the numeric values are given as follows:
1. 9.8t² + 20t + 8:
t = -2: 9.8(-2)² + 20(-2) + 8 = 7.2.t = 0: 8. 9.8(0)² + 20(0) + 8 = 8.t = 3.5: 9.8(3.5)² + 20(3.5) + 8 = 198.05.2. -3(2.1x - 7.9):
x = -18.1: -3 x (2.1(-18.1) - 7.9) = 137.73.x = -0.3: -3 x (2.1(-0.3) - 7.9) = 25.59.x = 14.4: -3 x (2.1(14.4) - 7.9) = -67.02.Learn more about the numeric values of a function at brainly.com/question/28367050
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5x+1=2x+10 (Please include the steps)
Answer:
x = 3
Step-by-step explanation:
5x + 1 = 2x + 10
1.) Subtract 2x from both sides to get 2x on the other side
5x - 2x + 1 = 10
2.) Subtract 1 from both sides to get 1 to the other side
5x - 2x = 10 - 1
3.) Combine like terms
3x = 9
4.) Divide 3 on each side to get x by itself
x = 3
What is terminal value formula ?
The terminal value formula helps estimate the value of a business beyond the explicit forecast period,
the terminal value formula = FCFF 6 / (WACC – Growth Rate)
We can say that in a DCF model with a five-year free cash flow projection, the terminal value formula = FCFF 6 / (WACC – Growth Rate)
It could be accountable that in finance, the terminal value (also known as “continuing value” or “horizon value” or "TV") of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. It is most likely often used in multi-stage discounted cash flow analysis and also allows for the limitation of cash flow projections to a several-year period; see Forecast period (finance). Forecasting results beyond such a period is impractical and exposes such projections to a variety of risks limiting their validity, primarily the great uncertainty involved in predicting industry and macroeconomic conditions beyond a few years.
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When a number is increased by 5%, the result is 25. What is the original number to the nearest tenth?
Anwser : 23.8
Step 1: Subtract 5% from 25.
25 - (5% of 25) = 25 - (0.05 x 25)
Step 2: Simplify the equation.
25 - (0.05 x 25) = 25 - 1.25
Step 3: Subtract 1.25 from 25.
25 - 1.25 = 23.75
3/4 x ( z^3 x 4) equivalent expressions
The required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4). which is the correct answer .
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
her, we have,
We have been given expression as:
3/4 x ( z^3 x 4)
To determine the equivalent expression to the given expression
3/4 x ( z^3 x 4)
⇒ 3* z^3
Here the variable z has an exponent is 3 which is positive,
Rearrange the terms of variables z in the above expression
⇒3 · z³
Therefore, the required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4).
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A Ferris wheel has a radius of 218 feet. What is the
total distance covered if the Ferris wheel makes 6
rotations? Write an exact answer in terms of Pi.
The total distance covered by the Ferris wheel after 6 rotations is 2616π feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The Ferris wheel has a radius of 218 feet. The total distance covered if the Ferris wheel makes one rotation is the perimeter of the wheel.
Perimeter = 2π * radius = 2π * 218 feet = 436π
For 6 rotations:
Total distance covered = 6 * 436π = 2616π
The total distance is 2616π feet
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8. Fill in the missing statements and reasons to complete the following proof
The completed two-column table used to prove that the quadrilateral WXYZ is a parallelogram is presented as follows;
Statement [tex]{}[/tex] Reason
1. m∠y = 49, m∠z = 131°, m∠w = 49 [tex]{}[/tex] Given
2. m∠y + m∠z + m∠w + m∠x = 360 [tex]{}[/tex] 1. ∠ sum property of a quadrilateral
3. 49 + 131 + 49 + m∠x = 360[tex]{}[/tex] Substitution Property of Equality
4. 229 + m∠x = 360 [tex]{}[/tex] 2. Summation of values
5. m∠x = 131 3. Subtraction Property of Equality
6. ∠x ≅ ∠z and ∠w ≅ ∠y [tex]{}[/tex] Angles with equal measures are ≅
7. WXYZ is a parallelogram 4. The opposite ∠s of a ║ are ≅
What is a parallelogram?A parallelogram is a quadrilateral that has two pairs of parallel facing sides.
The details of the reasons used in the two-column table method to prove that the quadrilateral WXYZ is parallelogram are illustrated as follows;
∠ sum property of a quadrilateral
The angle (∠) sum property of a quadrilateral, indicates that the addition of the four interior angles of a quadrilateral has a result of 360°
Summation of a set of values
The sum of the values 49 + 131 + 49 is 229
Subtraction Property of Equality
The subtraction property of equality states that the subtraction of the same amount from both sides of an equation produces two new quantities or expressions on both sides of the equation that remain equivalent.
Angles with the same measures are ≅
Angles that are congruent, ≅, are angles that have the same measure
The opposite angles of a ║ are ≅
The angles located in the facing corners of a parallelogram, ║, are congruent.
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How do i get desmos to show both square roots?
To get Desmos to show both square roots, you can use the formula y = √x + √(-x). Desmos can then graph this equation, showing both the positive and negative square roots.
To get Desmos to show both square roots, you can use the formula y = √x + √(-x).This formula can be used to graph two square roots. The first square root is √x, which is the positive square root of x. The second square root is √(-x), which is the negative square root of x. To calculate the roots, you would take the square root of both x and -x. For example, if x is 4, the two roots would be √4 = 2 and √(-4) = 2i, where i is the imaginary unit. Desmos can then graph this equation, showing both the positive and negative square roots.
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I NEED HELP ON THE FIRST QUESTION ASAP!!!!!!!!
Answer to question 1 is [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex]
=========================================================
Explanation:
The first task is to find the equation of the line through the given points in the table.
Pick any two points you want. I'll pick (0,100) and (50,80)
Determine the slope:
[tex](x_1,y_1) = (0,100) \text{ and } (x_2,y_2) = (50,80)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{80 - 100}{50 - 0}\\\\m = \frac{-20}{50}\\\\m = -\frac{2}{5}\\\\[/tex]
The slope is -2/5.
The y intercept is b = 100 because of the point (0,100)
We go from [tex]\text{y} = m\text{x}+b[/tex] to [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]
Each point from the table is found on this line. For instance, let's check the point (140,44)
[tex]\text{y} = -\frac{2}{5}\text{x}+100\\\\44 = -\frac{2}{5}*140+100\\\\44 = -56+100\\\\44 = 44\\\\[/tex]
This confirms (140,44)
I'll let you check the other points.
------------------
Any point on the line mentioned represents a scenario where César spends all of the $50.
If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.
This means we want to shade the region below the boundary line [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]
We'll replace the equal sign with a "less than or equal" sign
We arrive at [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex] as the final answer to question 1.
Answer: Answer to question 1 is =========================================================Explanation:The first task is to find the equation of the line through the given points in the table. Pick any two points you want. I'll pick (0,100) and (50,80) Determine the slope:The slope is -2/5.The y intercept is b = 100 because of the point (0,100)We go from to Each point from the table is found on this line. For instance, let's check the point (140,44)This confirms (140,44)I'll let you check the other points.------------------Any point on the line mentioned represents a scenario where César spends all of the $50.If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.This means we want to shade the region below the boundary line We'll replace the equal sign with a "less than or equal" signWe arrive at as the final answer to question 1.
Step-by-step explanation:
a man travels from Nigeria to Ghana by air and from Ghana to Liberia by ship .he returns by the same means he has 6 airlines and 4 shipping lines to choose from .in how many ways can he make his journey without using the same airline or shipping line
There will be 360 different ways without using the same airline or shipping line.
What is a combination?A combination in mathematics is a selection of items from a set with distinct members, where the order of selection is irrelevant.
Let's first consider the number of ways the man can choose his outbound journey. He has 6 airlines to choose from, and once he has made his choice of airline, he has 4 shipping lines to choose from.
Therefore, there are 6 × 4 = 24 ways he can choose his outbound journey.
For his return journey, he cannot use the same airline or shipping line that he used for his outbound journey.
This means he now has 5 airlines and 3 shipping lines to choose from. Therefore, there are 5 × 3 = 15 ways he can choose his return journey.
The total number of ways he can make his journey is:
24 × 15 = 360
Therefore, he can make his journey in 360 different ways without using the same airline or shipping line.
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{10x + 7y= - 12
9x+ 5y = -16
Answer: x=-4, y=4
Step-by-step explanation:
We can use elimination method to solve this problem.
Let's eliminate y.
In equation 2, use the coefficient of y (i.e 5) to multiply equation 1. DO the same for other equation. Thus,
5(10x+7y=-12)
7(9x+5y=-16)
=> 50x+35y=-60
63x+35y= -112
clearly, y can be eliminated by subtraction.
Therefore,
-13x = 52 [-63+50 and 112-60)]
x = -4.
When x = -4,
9x+5y =-16
9(-4) +5y =-16
5y = 36-16
y=4.
What is the distance d between the student and the mirror?
Using the fact that the two triangles must be similar, we will see that d = 7.5 ft
What is the distance between the student and the mirror?To find the distance d we will use the fact that the two triangles must be similar triangles.
That means that the quotients between the legs must be equal.
For the triangle on the left side, the quotient is:
50ft/30ft
For the triangle on the right side, the quotient is:
d/height of the student.
We know that the height of the student is 4.5ft, so that quotient is:
d/4.5ft
Now we can write the equation:
d/4.5ft = 50ft/30ft
Solving this for d, we will get:
d = 4.5ft*(50ft/30ft) = 7.5 ft
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Is 1/3(36m+12) and 12m+4 equivalent expressions
The expressions 1/3(36m+12) and 12m+4 are equivalent
What are equivalent expressions?
Equivalent expressions are defined as algebraic expressions that have the same solution but differ in the mode of the arrangement of values.
These expressions are known to have variables, constants, terms, coefficients, and factors.
They are also made up of mathematical operations.
We have the expression;
1/3(36m+12)
Now, expand the bracket
36m/3 + 12/3
Divide the values
12m + 4
Hence, the expression is 12m + 4
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Three numbers are given below. Use prime factorisation to determine the HCF and LCM 1848, 132 and 462
Answer:
The HCF is the highest common factor of 1848, 132 and 462, which is 14.Step-by-step explanation:
Prime factorisation is a mathematical method that breaks a number down into its prime factors, the smallest positive integers that are multiples of that number.The highest common factor of 1848, 132 and 462 is the smallest number that divides all three.The lowest common multiple is the smallest number that multiples all three numbers!What is 76 degree F in C?
76 degrees Fahrenheit was found to be equal to approximately 24.4 degrees Celsius using the formula of conversion.
To convert Fahrenheit to Celsius, you can use the following formula:
Celsius = (Fahrenheit - 32) x 5/9
Plugging in 76 degrees Fahrenheit, we get:
Celsius = (76 - 32) x 5/9
Celsius = 44 x 5/9
Celsius = 220/9
Celsius ≈ 24.4
Therefore, 76 degrees Fahrenheit is approximately 24.4 degrees Celsius.
On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.
On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.
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To catch up to Group B, Group Aw
4) Group A: y = 3x
Group B: y = 2x + 1
Graph the equation y = 3x.
The graph of the equation is added as an attachment
How to determine the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
y = 3x
The above expression is a linear equation
A linear equation is represented as
y = mx + c
Where
Slope = m and y-intercept = c
This means that
y = 3x has a slope of 3 and a y-intercept of 0
Next, we plot the graph
See attachment for the graph of the equation
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help help help help help help
What is the equation of this graph
In this equation, the value of x is fixed at 2, which means that every point on the graph will have the same x-coordinate value of 2. This creates a vertical line that passes through the point (2, y), where y can be any real number.
Therefore, the proper equation for the graph presented is:
[tex]x=2[/tex]
If you flip a coin 8 times, what is the best prediction possible for the number of times it will land on tails?
What are the zeros of the function f(x) = x² - 4x² - 5?
+√5 ti
±2, ti
±5, ti
O +√2 ti
You must check the box below prior to submitting your exam!
The zeros of the function f(x) = x² - 4x - 5 are given as follows:
x = -1 and x = 5.
How to solve the quadratic function?The quadratic function for this problem is defined as follows:
f(x) = x² - 4x - 5
The coefficients are given as follows:
a = 1, b = -4, c = -5.
Then the discriminant is given as follows:
D = b² - 4ac
D = (-4)² - 4(1)(-5)
D = 36
Hence the zeros are given as follows:
x = (4 + sqrt(36))/2 = 5.x = (4 - sqrt(36))/2 = -1.More can be learned about quadratic functions at https://brainly.com/question/1214333
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Need help!
Use the Savings plan to find the amount A=? if monthly payments are $250 with APR=4% for 10 years.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
The required formula is :
[tex] \qquad \dashrightarrow \sf \: A = P \times \dfrac{{\bigg(1 + \dfrac{APR}{n} \bigg) }^{ny} - 1}{\dfrac{APR}{n}}[/tex]
[tex] \textsf{A = Total accumulated savings } [/tex][tex] \textsf{P = regular deposit } [/tex][tex] \textsf{APR = annual percentage rate } [/tex][tex] \textsf{n = number of payment period per year} [/tex][tex] \textsf{y = number of years } [/tex]Now, plug in the values ~
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + \dfrac{0.04}{12} \bigg) }^{(12 \times 10)} - 1}{\dfrac{0.04}{12}}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + 0.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{1.4908- 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{0.4908}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.249[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]
[tex] \qquad \dashrightarrow \sf \: A =\$ 36812.45[/tex]
That's the required value ~
based on each set of triangles or parallel lines crest a proportion and solve it to find the missing value
pls help
The value of the x in the given triangle is 7.5 units.
What is proportion?Proportion definition, comparative relation between things or magnitudes as to size, quantity, number.
Given is a triangle having sides, 12, 4 and 10 there is a missing side x we need to find is value,
Using the concept of parallel lines crest a proportion,
x / 10 = 12 / 16
x = 120 / 16
x = 7.5
Hence, the value of the x in the given triangle is 7.5 units.
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Which of the following values is a rational number?
A. O √²
B. O √49+√7
C. O √225+ √169
D. O √2x √121
E. O √11x16
The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called a rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
Let's check all the options, then we have
A. √(4)² = 4, is a rational number.
B. √49 + √7 = 7 + √7, is an irrational number.
C. √225+ √169 = 25 + 13, is a rational number.
D. √2 x √121 = 11√2, is an irrational number.
E. √11 x 16 = 4√11, is an irrational number.
The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.
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Ms. Liu has a cylinder container measuring 12 cm tall and 6 cm across. The height of Jeff's container is twice Ms. Liu's but the width is 1/3 of Miss Liu's container. Julie's cylinder container has the same width as Miss Liu but it has twice the height of Miss Lui's container. Who has the largest container and who has the smallest container?
The person with the largest container is Julie and the person with the smallest container is Jeff.
Who has the largest container and the smallest container?The volume of each container has to be determined.
Volume of a cylinder = πr²h
Where:
π = 3.14r = radius = diameter / 2 h = heightVolume of Ms. Liu's container:
r = 6/2 = 3h = 123.14 x 3² x 12 = 339.12 in³
Volume of Ms. Julie's container:
h = 12 x 2 = 24 r = 6/2 = 3Volume = 3.14 x 3² x 24 = 678.24 in³
Volume of Jeff's container:
h = 2 x 12 = 24 d = 1/3 x 6 = 2 r = 2/2 = 1Volume = 3.14 x 1² x 24 = 75.36 in³
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What is the sum of the distinct prime factors of the number 560?
A. 20
B. 14
C. 18
D. 16
E. 1488
The sum of the distinct prime factors is (b) 14
How to determine the sum of the distinct prime factorsFrom the question, we have the following parameters that can be used in our computation:
distinct prime factors of the number 560
The distinct prime factors of the number 560 are
Factors = 2, 5, 7.
When these numbers are added, we have
Sum = 2 + 5 + 7
Evaluate
Sum = 14
Hence , the sum is (b) 14
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