Answer:
D)
Step-by-step explanation:
Percentage word problems:Let the original length be 'x'.
Percentage error = 5 %
So, (100 -5)% = 95% of the original measurement is 3.99 m
95% of x = 3.99
[tex]\sf \dfrac{95}{100}*x = 3.99[/tex]
[tex]\sf x = \dfrac{3.99*100}{95}\\\\x = \dfrac{399}{95}\\\\\\x = 4.2 m[/tex]
Original length = 4.2 m
What is the sum of: 1 + x + x2 + x3 + x4 + x5 + ⋯ + x100?
The Sum is 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)
What is Series?A finite series is one that has a finite number of terms.
If the series [tex]a_1[/tex]+ [tex]a_2[/tex] + [tex]a_3[/tex] +... + a has n terms and is a finite series with n terms.
As a result, [tex]S_n[/tex] is used to represent the series' sum as follows:
[tex]S_n[/tex]=∑ [tex]a_n[/tex]
Given:
1 + x + x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex]
let P= 1/ 1-x
P - Px= 1
P= 1+ Px
= 1 + (P)x
= 1 + (1+ Px) x
= 1+ x + Px²
= 1+ x + (1+ Px)x²
= 1+ x + x² + Px³ and so on
So, 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)
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Katrina buys a 66-ft roll of fencing to make a rectangular play area for her dogs. Use 2(l+w) = 66 to write a function. for the length, given the width. Graph the function. What is a reasonable domain for the situation? Explain. The function f(w) = gives the length as a function of the width. (Simplify your answer.)
The function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted
The total length of the roll = 66 feet
The perimeter of the rectangular paly area = 66
The perimeter of the rectangle = 2(l + w)
Then the equation will be
2(l + w) = 66
l + w = 66/2
l + w = 33
The function for length when the width is given
l = 33 - w
Therefore the domain of the function is 0 < w < 33
When w = 1
l = 33 - 1
l = 32
The first point is (1, 32)
When w = 32
l = 33 - 32
l = 1
The second point is (32, 1)
Draw the graph of the function
Hence, the function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted
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Consider the polynomial
below.
p(x) = - 3x³ - 18x²-9x + 30 and the completed synthetic division exercise below.
Answer:
5
Step-by-step explanation:
NO LINKS!! Use the diagram below to answer the following questions Part 4
Answer:
Parallel LinesCoplanar lines that do not intersect.Arrows are used to indicate the lines are parallel.[tex]\textbf{Symbolic Notation:} \quad \overleftrightarrow{AB} \parallel \overleftrightarrow{CD}[/tex]Parallel PlanesPlanes that do not intersect.[tex]\textbf{Symbolic Notation:} \quad \mathcal{J} \parallel \mathcal{K}[/tex]Skew LinesNon-coplanar lines that do not intersect.[tex]\textbf{Examples:} \quad \overline{PS} \; \& \; \overline{QU}[/tex][tex]\overline{TW} \; \& \; \overline{RV}\\\\ \overline{PV} \; \& \; \overline{TU}[/tex]
Step-by-step explanation:
Coplanar: In the same plane.
Parallel LinesCoplanar lines that do not intersect.Arrows are used to indicate the lines are parallel.[tex]\textbf{Symbolic Notation:} \quad \overleftrightarrow{AB} \parallel \overleftrightarrow{CD}[/tex]The notation for a line is a double-ended arrow placed above two points contained on the line.
The symbol denotating two objects are parallel is a vertical double line.
Parallel PlanesPlanes that do not intersect.[tex]\textbf{Symbolic Notation:} \quad \mathcal{J} \parallel \mathcal{K}[/tex]A plane can be named by a capital letter (often written in script), or by the letters naming three non-collinear points in the plane.
The symbol denotating two objects are parallel is a vertical double line.
Skew LinesNon-coplanar lines that do not intersect.[tex]\textbf{Examples:} \quad \overline{PS} \; \& \; \overline{QU}[/tex][tex]\overline{TW} \; \& \; \overline{RV}\\\\ \overline{PV} \; \& \; \overline{TU}[/tex]
The notation for a line segment is a bar placed above the endpoints of the line segment.
There are a Total of 11 bicycles and tricycles altogether in the shop window. They have a total of 29 wheels. How many bicycles are there ?
Please answer very correctly
The number of bicycles that are there is 4.
How to find the number of bicycles?There are a Total of 11 bicycles and tricycles altogether in the shop window.
They have a total of 29 wheels.
Therefore, the number of bicycles that are there can be calculated as follows;
Bicycles has 2 wheels and tricycles has 3 wheels.
Therefore,
let
x = number of bicycle
y = number of tricycle
2x + 3y = 29
x + y = 11
Multiply equation(ii) by 2
2x + 3y = 29
2x + 2y = 22
y = 7
x = 11 - 7
x = 4
Therefore the number of bicycle is 4.
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PLEASE ANSWER I CANT FAIL!
Answer:
D ,
Step-by-step explanation:
4cd(6-9c)
5(x+5)
Please see photo of multiple questions
The features from the graph of the function are given as follows:
a) The domain is {x | x ≠ -2}.
b) The range is {y | y ≠ 1}.
c) The x-intercept is: x = 0.
d) The y-intercept is: y = 0.
What are the domain and range?The domain of the function is the set of input values of the function, hence the values of x from the graph.
From the graph, the function is not defined at x = -2, hence the domain is:
{x | x ≠ -2}.
The range of the function is the set of input values of the function, hence the values of y from the graph.
From the graph, the function has an asymptote at y = 1, hence the range is:
{y | y ≠ 1}.
What are the intercepts?The x-intercept is the value of x at which the function crosses the x-axis, hence:
x = 0.
The y-intercept is the value of y at which the function crosses the y-axis, hence:
y = 0.
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$4.25,$6.71,$3.24,$5.06,$4.94 what is the average ?
The average of the number given is $4.84.
The average can be calculated as follows:
Sum up all the numbersGiven X
X =$4.25+$6.71+$3.24+$5.06+$4.94
X =$24.2
To find the average, you need to divide the X by n or the amount of numbers, where n=5= X ÷ n
= $24.2 ÷ 5
= $4.84
Hence, the average is $4.84
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7=3 + h over 6
solving 2 step equations
Answer:
h=24
Step-by-step explanation:
7=3+h/6
-3 -3
4=h/6
x6. x6
24=h
hopes this helps please mark brainliest
x- (3/2)y=-2 find five solutions and plot
Five solutions of the given equation x- (3/2)y = -2 is given by as follow:
( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).
Plotted graph of the given function is attached.
As given in the question,
Given equation is equal to :
x- (3/2)y = -2
Simplify the given equation we get,
2x - 3y = -4
⇒ y = ( 1 / 3) ( 2x + 4 )
Now , five solutions of the given function to be plotted on the graph.
When x = 0
⇒ y = 4/3
When x = 1
⇒ y = (1/3)(2 +4)
⇒ y = 2
When x = 4
⇒ y = (1/3)( 8 + 4)
⇒y = 4
When x = -2
⇒y = (1/3)(-4 +4)
⇒y=0
When x = -5
⇒y = (1/3)(-10 +4)
⇒y= -2
Five solutions are ( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).
Plotted graph of the given function is attached.
Therefore, five solutions of the given equation x- (3/2)y = -2 is given by as follow:
( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).
Plotted graph of the given function is attached
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If (n factorial) is equal to 720, what is n? n! Select the correct response:
A216
B 343
C125
D 64
Answer: B
Step-by-step explanation:
An investor bought 500 shares of stock, some at $6.00 per share and some at $4.00 per share. If the total cost was $2550.00, how many shares of each stock did the
investor buy?
Answer: An investor bought 500 shares of stock , some at $ 3.50 per share and some at $6.00 per share. If the total cost was $ 2187.50, how many shares of each stock did the investor buy?
(a) How will you set up the problem?
Let # of 3.50 shares be "x" ; value is 3.5x dollars
# of 6.00 shares is "500-x" ; value is 6(500-x)=3000-6x dollars
EQUATION:
value = value = 2187.50
3.5x + 3000-6x = 2187.5
-2.5x = -812.5
x = 325 (# of 3.50 shares)
500-x = 175 (# of 6.00 shares)
Step-by-step explanation:
Anya has a change jar that contains $1.06 in pennies and dimes. The number of pennies is 10 more than two times the number of dimes. How many of each type of coin does she have?
The number of pennies that Anya has is equal to 15.6 pennies.
The number of dimes that Anya has is equal to 2.8 dimes.
How to determine the number of coins?In order to solve this word problem, we would assign variables to the number of pennies and dimes, the total number of coins, and then translate the word problem into algebraic equation as follows:
Let d represent the number of dimes.Let p represent the number of pennies.Let T represent the total number of coins.Note: 1 penny is equal to 0.05 dollar and 1 dime is equal to 0.10 dollar.
Therefore, translating the word problem into an algebraic equation, we have the following;
p = 10 + 2d ......equation 1.
0.05p + 0.1d = 1.06 .......equation 2.
Substituting equation 1 into equation 2, we have:
0.05(10 + 2d) + 0.1d = 1.06
0.5 + 0.1d + 0.1d = 1.06
0.5 + 0.2d = 1.06
0.2d = 1.06 - 0.5
0.2d = 0.56
Dimes, d = 0.56/0.2
Dimes, d = 2.8 dimes.
For the number of pennies, we have:
p = 10 + 2d
p = 10 + 2(2.8)
p = 10 + 5.6
p = 15.6 pennies.
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if you finish all of the work right u willget 100 points
The value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.
First, let us know some laws of exponent:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹We are given;
[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] and [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex].
Now, we will solve one by one;
[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex]
[tex]= \sqrt[5]{\frac{2^{10}(x^{-10})}{(2^5x^{-15})}}[/tex]
[tex]=[({2^{10}. 2^{-5}) (x^{-10}.x^{15})}]^\frac{1}{5}[/tex]
[tex]=[({2^{10-5}) (x^{-10+15})]^\frac{1}{5}[/tex]
[tex]=[({2^{5}) (x^{5})]^\frac{1}{5}[/tex]
= 2x
So, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x.
Now,
[tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex]
[tex]=\frac{(2^3x^6y^{-3})^\frac{1}{3} }{(2^3x^3y^3)}[/tex]
[tex]=\frac{(2x^26y^{-1})}{(2^3x^3y^3)}[/tex]
[tex]=\frac{1}{(2^{3-1}x^{3-2}y^{3+1})}[/tex]
[tex]=\frac{1}{(2^{2}x^{1}y^{4})}[/tex]
= 1 / 4xy^4
So, the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.
Thus, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.
Please find the figure for the questions below.
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An intravenous (IV) solution of 8% D/W (Dextrose in water) is infusing at a rate of 2.15 milliliters (mL) per minute. How many mL would infuse in 5.25 hours?
By evaluating a linear equation, we can see that 677.25 mL will be infused in 5.25 hours.
How many mL would infuse in 5.25 hours?We know that the solution is being infused at a rate of 2.15 mL per minute.
So, t minutes after the infusion starts, the volume infused is given by the linear equation:
V(t) = 2.15mL*t
Here we want to see how many mL would infuse in 5.25 hours, to do that, we need to write that time in hours:
We know that one hour = 60 min, then:
5.25 h = 5.25*60 min = 315 min
Then the volume infused is:
V(315) = 2.15mL*315 = 677.25 mL
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10. Your family decides to construct a below ground swimming pool in the backyard. The
pool will be:
.8 feet deep,
20 feet long, and
• 14 feet wide.
The local fire department will fill the pool with water for a $50 fee plus $12.60 for the
first 1,000 gallons and then $27.20 for each 1,000 gallons after that.
The amount of water will be rounded up to the nearest 1,000 gallons. In other words,
7,280 gallons is rounded up to 8,000 gallons.
How much will the water cost to fill the swimming pool?
Answer:
$497.8
Step-by-step explanation:
1. get the pool volume
volume = 8 x 20 x 14 = 2240 ft3
2. convert ft3 to gallons
2240 x 7.481 = 16757.44
3. You need 17000 gallons
4. Fee you have to pay fee + first 1000 gallon + the rest of the gallon
50 + 12.60 + 16 x 27.20 = 497.8
Please help me !!!!!
Answer: [tex]2\frac{19}{36}[/tex]
Step-by-step explanation:
You subtract the woman's height from her son:
Woman's height: [tex]60\frac{5}{18} =\frac{(60*18)+5}{18} =\frac{1085}{18}[/tex]Son's height: [tex]57\frac{3}{4} =\frac{(57*4)+3}{4} =\frac{231}{4}[/tex][tex]60\frac{5}{18} -57\frac{3}{4} =\frac{1085}{18} -\frac{231}{4} =\frac{1085*2}{18*2} -\frac{231*9}{4*9} =\frac{2170-2079}{36} =\frac{91}{36} =2\frac{19}{36}[/tex]
Study the graph and the parent function, and then identify the transformations. p(x) = 7 log2 (x) – 2: r(x) = –2 log2 (x) + 3:
The transformations to the graphs of each function are presented as follows:
p(x): Vertical stretch by a factor of 7, shift down by 2 units.r(x): Vertical stretch by a factor of 2, reflection over the x-axis, shift up 3 units.What are the transformations to each function?The parent function is defined as follows:
f(x) = log2(x).
Function p(x) is defined as follows:
p(x) = 7log2(x) - 2.
The transformations are listed as follows:
Multiplication by 7: vertical stretch by a factor of 7.Subtraction by 2: shift down by 2 units.Function r(x) is defined as follows:
r(x) = -2log2(x) + 3.
The transformations are listed as follows:
Multiplication by -2: vertical stretch by a factor of 2, and a reflection over the x-axis, due to the multiplication by the negative number.Addition by 3: shift up by 3 units.More can be learned about transformations at https://brainly.com/question/28792248
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Answer:
its c b a
Step-by-step explanation:
other person was wrong
What expression represents the verbal phrase?
one-half times a number m plus twenty-five
The expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.
According to the question,
We have the following information,
The given verbal phrase is one-half times a number m plus twenty-five.
Now, we will solve it step by step.
Now, we will first find one-half times a number m. We know that we will replace the word times with multiplication. So, we have the following expression:
m/2
Now, adding 25 to this term, we have the following final expression:
m/2+25
Hence, the expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.
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Clayton's mortgage payment was originally $2,460 per month. Now, after refinancing his home loan, Clayton's mortgage payment is $1,968. What is the percent of decrease in Clayton's mortgage payment?
please
Answer:
20%
Step-by-step explanation:
2460-1968=492
492/2460=0.20
Check answer2460 x 0.20 = 492
Two trains going opposite directions leave at the same time. Train B travels 5 mph faster than train A. In 6 hours the trains are 810 miles apart. Find the speed of each.
The speed of train A is ___ mph
The spend of train B is ___ mph
Answer:
Step-by-step explanation:
The train A speed is 45 mph. The train B speed is 70 mph.
Chandler buys a mattress priced at $975.90.If the sales tax is are 10%, how much tax will Chandler pay?
Answer:
97.59
Step-by-step explanation:
975.90*0.10
97.59
Hope this Helps!!!
Circle Centered at (5,-3)
Radius=9
Standard form:
general form:
The standard form of the equation of the circle is (x-5)² + (y+3)² = 9² and the general form is x² + y² + 10x + 6y - 47 = 0 .
We know that the general form of the equation of a circle is given by the following equation:
(x-h)² + (y-k)² = r² . Where r is the radius of the circle and (h, k) is the center of the circle.
So the general equation of the circle is (x-5)² + (y+3)² = 9² .
Let's first define a circle in order to determine its equation. A circle is formed by every point in a plane that is uniformly spaced from another point.
The constant point is located at the center of the circle. The radius of a circle is the separation between its center and any point along its circumference.
(x-5)² + (y+3)² = 9²
or, x² + 10x + 25 + y² + 6y + 9 = 81
or, x² + y² + 10x + 6y - 47 = 0
Hence the general form of the circle is x² + y² + 10x + 6y - 47 = 0.
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The graph of y = f(x) is graphed below. What is the end behavior of f(x)?
Answer:
(a) as x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞
Step-by-step explanation:
You want to know the end behavior of the 4th-degree function shown in the graph.
Arrows on the graphThe graph has an arrow on each end of the curve shown in the figure. The left arrow points upward, indicating a tendency to +∞ as x gets more negative.
The right arrow also points upward, indicating a tendency to +∞ as x gets more positive.
As x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞.
What is the coefficient of the first term in this expression
8c³+3+b³
Answer:
8c³
Step-by-step explanation:
What is a coefficient?
A coefficient is a number that does not stand alone. For example, 3w means 3 times w, and "w" is a variable, so 3 is a coefficient.
How do we find the first term?
We can find the first term by putting the numbers from greatest to least. For example, if we had the numbers: 3x+7p+2 we would rearrange the series to this: 7p+3x+2. The number that comes first in the series would be the first term.
Could you guys please help?
The real roots of the function is {0,-2} and there are no repeated roots.
Given function:
f(x) = [tex]x^{2} +2x[/tex]
[tex]x^{2} +2x=0[/tex]
take x as common
x(x+2) = 0
x = 0 and x + 2 = 0
x+2 = 0
x = -2,0.
Therefore the real roots of the function is {0,-2} and there are no repeated roots.
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In a water park, there is a swimming pool of dimensions 40 m × 20 m × 2 m. The management wants to repaint it, if the cost of painting an area of 1 m 2 is ₹13, then how much amount of money is required to paint the swimming pool?
The cost of repainting the swimming pool is 15,600 pounds
The swimming pool forms a three-dimensional object. Three-dimensional space is a geometric setting in which three values are required to determine the position of an element or its area.
The area of the object is the space the swimming pool occupies
How to find the area of the swimming pool?
Mathematically represented as: A =lbh metres square
A=areal =lengthb=breadthA=40x20x2
A=1200m²
The cost of im² is 13 pounds
Therefore, multiplying the area by cost of 1m per square
Cost=1200x13
Cost=15,600 pounds
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what are the two estimates of 1,624 divided by 3
A number is divisible by 3 it the sum of its digits is divisible by 3. In this case, we have
which is not divisible by 3. The nearest multiples of 3 are 1623 and 1626. If you divide these numbers by 3, you have
So, the result of our division is between 541 and 542.
If these numbers are too complex to divide, we have to choose easier numbers, but we will lose some accuracy. For example, we can see that 1624 is between 1500 and 1650, which are very easily divisible by 3. We have
So, the result of our division is between 500 and 550. This is still true, but as you can see it is a much looser approximation than the one before.
Can you have with some vocabulary answers
Answer:
Down Here ↓↓↓↓↓↓↓
Step-by-step explanation:
Hello!
Supplementary angles are angles that add up to 180°Vertical angles are opposite and equal angles, formed by the intersection of 2 linesA linear pair of angles sum up to 180°, and forms adjacent anglesAdjacent angles share a common vertex and sideThis is all the information we need to fill up the blank spots:
Two angles whose sum is 180° are supplementary angles.
Vertical angles are formed by the opposite angles when two lines intersect.
Vertical angles are congruent/equal/equal in measure.
A linear pair of angles form adjacent angles, and the sum of their measures is 180°.
Adjacent angles share a common vertex and side.
Please explain how you get your answer so i get a better understanding of this...
Using the image below, if I is parallel to M, find the value of y.
(im really struggling with this question so please do explain your answering.)
Answer:
16.11 (appx.)
Step-by-step explanation:
since l and m are parallel and a line intersects them, so we can say that the line is the transversal. from the figure we see that
7x + 12 = 12x - 28 [they are internal alternate angles and alternate angles are always equal to one another]
now, we can find the value of x from the equation
12x - 7x = 28 + 12
⇒ 5x = 40
⇒ x = 8
so the angle (7x+12)° is ((7*8)+12) = 68°
so (12x-28)° is also equal to 68° [cause of being alternate angles]
now, look at the figure,
angle (9y-77)° & (12x-28)° add upto a straight line as in 180°
and we know (12x-28)° = 68°
so now,
9y-77 = 68
⇒9y = 68+77
⇒9y = 145
⇒y = 16.11 (appx.)