2.9% of the people in Antonie's middle school have an extra rib
How to calculate the number of people with an extra rib ?Ribs are curved bones that are located in the chest, they help to protect the delicate organs in that part of the body.
About 2 in every 400 people have an extra rib
There are 580 people in Antoine's middle school
The number of people with an extra rib cage can be calculated as follows
= 580 × 2/400
= 1160/400
= 2.9
Hence 2.9% people have an extra rib cage.
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A serviceman charges ₱450 per hour for doing mechanical jobs. How much does he get for 6.75 hours of doing the job?
Pa help po
Answer:
450×6.75 = 2 956.5
So the serviceman will get 2 956.5 after 6.75 hours of doing the job
Select the expression that has a quotient greater than 1. Explain your reasoning PLEASE ANSWER THIS
1. 4 2/3 ÷ 5 1/4
2. 3 1/8 ÷ 2 2/5
3. 1 6/7 ÷ 2 1/3
4. 5 3/4 ÷ 7 3/8
The expression involving fractions that have a quotient less than 1 is: 2. 3 ⅛ ÷ 2 ⅖
How to Solve Fractions?To solve each of the expressions involving fractions, convert mixed fractions into improper fractions before finding the quotient of each.
1. 4 ⅔ ÷ 5 ¼
Convert to improper fractions
14/3 ÷ 21/4
14/3 × 4/21
= 56/63 (less than 1)
2. 3 ⅛ ÷ 2 ⅖
Convert to improper fractions
25/8 ÷ 12/5
25/8 × 5/12
125/96 (greater than 1)
3. 1 6/7 ÷ 2 1/3
13/7 ÷ 7/3
13/7 × 3/7
= 39/49 (less than 1)
4. 5 3/4 ÷ 7 ⅜
23/4 ÷ 59/8
23/4 × 8/59
= 184/236 (less than 1)
Therefore, the expression involving fractions that have a quotient less than 1 is: 2. 3 ⅛ ÷ 2 ⅖
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What is the third common multiple of two numbers is 72
Answer:
x-2-10123
y0.1 0.3 0.9 2.7 8.1 24.3
I have an equation that I have an answer but no idea how it's solution works. This is an example for using the squeeze theorem, and the answer is 0:
[tex]f(x)=\frac{e\frac{-1}{13+\frac{1}{x^2}}\sin(1+cos\frac{\pi }{x^3})\sqrt{3x^4+5x^6}}{(x+x^\frac{1}{3})(3+arctan\sqrt{7+\frac{1}{x^8}})}[/tex]
The way the answer is arrived at is supremely confusing. Also the textbook used absolute values alongside inequalities when performing the algebraic manipulations (direct sub. doesn't work), which I also don't understand why. Please explain how this equations limit is zero in simple terms.
Step-by-step explanation:
You want to know how the squeeze theorem applies to help you find the limit of f(x) is zero as x approaches zero.
SummaryThe short of it is that you have ...
f(x) = [messy finite function] × [function that cleanly approaches 0 at x=0]
The zero product rule tells you that the product of any finite value and 0 is zero, so the limit of this product is 0 at x=0.
The graph in the attachment shows the "function that cleanly approaches 0" in red. When multiplied by the "messy finite function", the result is the blue curve. You can see that the result is a function that has a limit of 0 at x=0.
How to get thereHere, we'll decompose f(x) into two parts:
messy finite function (g(x))function that cleanly approaches zero at x=0 (h(x))Messy finite function
The numerator sine function factor of f(x) gets increasingly messy as x approaches zero, due to the cosine term it contains. We can define ...
[tex]g(x)=\sin(1+\cos(\pi x^{-3}))[/tex]
Because this is a sine function, its value is always in the range |g(x)| ≤ 1.
Function cleanly approaching zero
The remaining factors of f(x) need to be rearranged a bit to make a function that obviously approaches zero at x=0. We do that by factoring ∛x from the denominator and rearranging the leading fraction.
[tex]h(x)=\dfrac{e\dfrac{-1}{13+x^{-2}}\sqrt{3x^4+5x^6}}{(x+x^{1/3})(3+\arctan\sqrt{7+x^{-8}})}\\\\=-e\dfrac{x^2}{13x^2+1}\cdot\dfrac{x^2\sqrt{3+5x^2}}{x^{1/3}(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}\\\\h(x)=-e\dfrac{x^{11/3}\sqrt{3+5x^2}}{(13x^2+1)(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}[/tex]
Recognizing that the arctangent term will approach π/2 as x→0, this can be (more or less) directly evaluated at x=0 to give ...
[tex]h(0)=-e\dfrac{0\cdot\sqrt{3}}{1\cdot1\cdot(3+\dfrac{\pi}{2})}=0[/tex]
The sign of h(x) will be opposite the sign of x. The graph of h(x) is shown in red in the attachment.
The squeezeAs h(x) approaches zero, the product ...
f(x) = g(x)·h(x)
approaches zero. This is the essence of the squeeze.
Starting from our description of g(x) above, we can multiply both sides of the inequality by the positive value |h(x)| to get ...
|g(x)| ≤ 1 . . . . . . . . . . the range of the sine function
|h(x)|·|g(x)| ≤ |h(x)|·1 . . . . . . multiply by |h(x)|
Simplifying, this is ...
|f(x)| ≤ |h(x)| . . . . true for all x
So, the limit is ...
[tex]\displaystyle \lim_{x\to0}|f(x)|\le\lim_{x\to 0}|h(x)|\\\\\lim_{x\to0}|f(x)|=0[/tex]
The attachment illustrates this nicely, showing that the oscillating f(x) has its amplitude limited by h(x), which approaches zero.
__
Additional comments
The limit of x^-8 is positive infinity as x approaches zero. This means the arctangent function argument is positive infinity as x approaches zero, so the function value is π/2. The sign of x is irrelevant.
We cannot tell if the fraction following "e" in this function is supposed to be an exponent. The two typeset versions of f(x) seem to show "e" as a multiplier, not the base of an exponential term. Even if an exponential term is what is intended, that term would approach 1 at x=0, so the conclusion here remains unchanged.
The cost of producing 390 calculators is $3100. Producing 490 calculators would cost $3700. Assuming the total cost is a linear function, write an equation for the cost of producing x calculators?
Answer:
y = 6x + 760
Step-by-step explanation:
In the problem you are given two pairs of numbers. These are both a pair of inputs and outputs, (x, y):
(390, 3100) also,
(490, 3700)
Write an equation by finding and filling in m and b in the following equation:
y = mx + b
To find m, which is the slope of the line, subtract y-y and put that on top. Then subtract x-x and put that on the bottom. See image.
Next, find b by use EITHER pair of numbers to find b.
I used (390, 3100).
see image.
m = 6 and b = 760
Fill these into
y= mx + b
y = 6x + 760
In case they ask, this means each calculator takes $6 to make and it costs $760 to set up your operation even before you have made any calculators.
whats the meaning of literature
Answer:
literature most commonly refers to works of the creative imagination, including poetry, drama, fiction, nonfiction, and in some instances, journalism, and song.
Help fast please pamdas
12x + 36 -14 -8x +5 =
Answer:
4x + 27
Step-by-step explanation:
12x + 36 - 14 - 8x + 5 Combine like terms (36, -14, 5)
12x + 27 - 8x Combine like terms (12x, -8x)
Calculate the area of a rhombus with vertices A(0,-5), B(9,2), C(12,13), and D(2,7) to the nearest tenth of a unit.
Answer:
93 square units (the figure is not a rhombus)
Step-by-step explanation:
You want the area of the figure whose vertex coordinates are A(0,-5), B(9,2), C(12,13), and D(2,7).
Area from coordinatesThe formula for the area of a polygon based on its coordinates might be written ...
[tex]\displaystyle A=\frac{1}{2}\left|\sum_{k=1}^n{x_k(y_{k+1}-y_{k-1})}\right|[/tex]
where coordinate indices wrap around from the end to the beginning.
Using this formula, we find the area to be ...
A = 1/2|0(2-7) +9(13-(-5)) +12(7-2) +2(-5-13)|
A = (1/2)|0 +162 +60 -36| = 1/2(186) = 93
The area of the figure is 93 square units.
DiagonalsThe area of a rhombus could be calculated as half the product of the lengths of the diagonals. This is only true because the diagonals of a rhombus cross at right angles.
Here, the differences between diagonally opposite coordinates are ...
AC = (12, 18) . . . . slope = 18/12 = 3/2
BD = (-7, 5) . . . . slope = 5/-7 = -5/7
If the diagonals are perpendicular, their slopes have a product of -1. Here, the product is ...
(3/2)(-5/7) = (-15/14) ≠ -1
The given figure is not a rhombus.
If we assume the diagonals are perpendicular, then the area would be ...
A = 1/2√(12²+18²)√((-5)²+7²) = 1/2√34632 ≈ 93.048
Rounded to the nearest tenth, this area would be 93.0 square units.
The diagonals actually cross at an angle of about 88.152°, so the area is actually ...
93.048·sin(88.152°) = 93 square units (exactly)
(Development of this formula is beyond the scope of this answer.)
Name all the line segments that are skew to line segment BF
The line segment that is skew line to line segment BF is CD.
Skew line:
Skewed lines are two lines that are not parallel to one another, and neither do they intersect. Only dimensions greater than two-dimensional space can have skew lines. They must be non-coplanar, which means that they must exist on several planes. Two lines in two-dimensional space can either intersect or run parallel to one another. Therefore, skew lines are impossible in 2D space.
The line segment AB is perpendicular to the line segment BF which means it is not the skew line to line segment BF
The line segment CD is not parallel and not perpendicular to the given line segment BF which means it is a skew line to the given line segment BF.
Therefore, The line segment that is skew line to line segment BF is CD.
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Mike took a loan of $20,000 from a bank on 4 February 2009 at the rate of 8% p.a and paid back the same on 6th July 2009. Find the total amount paid by Mike
A. N20,666.30
B. N21,777.40
C. N22,888.50
D. N24,999.60
The equation
3x-15
= 4x models temperature change, where x represents the difference in degrees in the last 24 hours. Solve for x.
Answer:
15
Step-by-step explanation:
[tex]3x-15=4x \\ \\ x-15=0 \\ \\ x=15[/tex]
A soccer coach purchased one goal and some soccer balls for the team. The expression 180 + 15x represents the cost before tax. What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. cost of goal total cost of soccer balls
The meaning of the terms and factors in the expression are
180 ⇒ cost of goal15x ⇒ total cost of soccer ballsx ⇒ Number of soccer balls180 + 15x ⇒ total cost of soccer balls and goalHow to determine what the different parts of the expression model represents?The expression is given as
180 + 15x
The above expression can be split as follows:
180 15xx180 + 15xThe meaning of the above terms and factors are
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Kubin Company’s relevant range of production is 12,000 to 16,000 units. When it produces and sells 14,000 units, its average costs per unit are as follows:
Average Cost per Unit
Direct materials $ 7.30
Direct labor $ 4.30
Variable manufacturing overhead $ 1.80
Fixed manufacturing overhead $ 5.30
Fixed selling expense $ 3.80
Fixed administrative expense $ 2.80
Sales commissions $ 1.30
Variable administrative expense $ 0.80
Required:
1. Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 14,000 units?
b. What is the total indirect manufacturing cost incurred to make 14,000 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 14,000 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the Manufacturing Department?
3. Assume the cost object is the company’s various sales representatives. Furthermore, assume that the company spent $39,200 of its total fixed selling expense on advertising and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives’ compensation.
a. When the company sells 14,000 units, what is the total direct selling expense that can be readily traced to individual sales representatives?
b. When the company sells 14,000 units, what is the total indirect selling expense that cannot be readily traced to individual sales representatives?
Show less
3. Assume the cost object is the company’s various sales representatives. Furthermore, assume that the company spent $39,200 of its total fixed selling expense on advertising and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives’ compensation.
a. When the company sells 14,000 units, what is the total direct selling expense that can be readily traced to individual sales representatives? (Round per unit value to 2 decimal places.)
b. When the company sells 14,000 units, what is the total indirect selling expense that cannot be readily traced to individual sales representatives?
3a. Sales commissions per unit
3a. Number of units sold
3a. Total sales commission $0
3a. Fixed portion of sales representatives’ compensation
3a. Total direct selling expense $0
3b. The total indirect selling expense
1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600.
1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200.
2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600.
2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200.
3a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.
3b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.
4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.
4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.
3a. Sales commissions per unit is $1.30.
3a. The number of units sold is 14,000 units.
3a. Total sales commission is $18,200.
3a. Fixed portion of sales representatives’ compensation is $14,000.
3a. Total direct selling expense is $18,200.
3b. The total indirect selling expense is $14,000.
Data and Calculations:Relevant production range = 12,000 to 16,000 units
Production and sales units = 14,000 units
Average Cost
per Unit
Direct materials $ 7.30
Direct labor $ 4.30
Variable manufacturing overhead $ 1.80
Direct cost per unit $13.40
Fixed manufacturing overhead $ 5.30
Total manufacturing cost per unit $18.70
Fixed selling expense $ 3.80 $53,200 ($3.80 x 14,000)
Fixed administrative expense $ 2.80 $39,200 ($2.80 x 14,000)
Total fixed costs per unit $6.60 $92,400 ($6.60 x 14,000)
Variable selling and admin:
Sales commissions $ 1.30
Variable administrative expense $ 0.80
Total variable selling and admin per unit = $2.10
1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600 ($13.40 x 14,000).
1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200 ($5.30 x 14,000).
2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600 ($13.40 x 14,000).
2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200 ($5.30 x 14,000).
3) Fixed selling expenses = $53,200 ($3.80 x 14,000)
Advertising expenses = $39,200
Sales Compensation = $14,000 ($53,200 - $39,200)
Sales Commission = $18,200 ($1.30 x 14,000)
Total Salespersons' compensation = $32,200
a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.
b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.
4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.
4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.
3a. Sales commissions per unit is $1.30.
3a. The number of units sold is 14,000 units.
3a. Total sales commission is $18,200 (14,000 x $1.30)
3a. Fixed portion of sales representatives’ compensation is $14,000.
3a. Total direct selling expense is $18,200.
3b. The total indirect selling expense is $14,000.
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HELP ASAP!!!
Determine the direction in which the graph of the function f(x)=x^2+x-2 opens.
A.upward
B.downward
C.to the left
D.to the right
Answer:
A
Step-by-step explanation:
Since the leading coefficient of the function is greater than 0, then it opens upward.
Which data set has the same standard deviation as the data set {1, 1, 3, 5, 8} ?
{9, 8, 9, 8, 9}
{2, 2, 4, 6, 9}
{1, 2, 6, 6, 9}
{1, 1, 1, 2, 2}
The data set that has the same standard deviation with the given data set is: B. {2, 2, 4, 6, 9}.
How to Find the Standard Deviation of a Data Set?Given the data set, {1, 1, 3, 5, 8}, the standard deviation (σ) is calculated as shown below:
Standard deviation (σ) = √(SS/n)
Count (n) = 5
Mean (μ) = 3.6
Sum of Squares (SS) = 35.2
Standard deviation (σ) = (√35.2/5)
Standard deviation (σ) = √7.04
Standard deviation (σ) ≈ 2.7
Also, the standard deviation of {2, 2, 4, 6, 9} is calculated as shown below:
Count (n) = 5
Mean (μ) = 4.6
Sum of Squares (SS) = 35.2
Standard deviation (σ) = (√35.2/5)
Standard deviation (σ) = √7.04
Standard deviation (σ) ≈ 2.7
Therefore, the data set that has the same standard deviation with the given data set is: B. {2, 2, 4, 6, 9}.
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What is the area of FGH? (Please help it’s due tmrw !! I’ll mark you brainliest)
Answer:
102.0625 square units
Step-by-step explanation:
First determine the length of each side using the distance formula for two points. Then use Heron's formula to determine the area of a triangle given three sides
Distance Formula
The distance between two points is the length of the path connecting them
The distance between points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean theorem:
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
Let's compute the lengths of the sides FH, FG and HG
The three vertices are F(-2, 5) G(7, -10) and H(-9, -6) as indicated on the graph
So length FG between (-2,5) and (7,-10)
[tex]FG= \sqrt {(7 - (-2))^2 + (-10 - 5)^2}[/tex]
[tex]= \sqrt {(9)^2 + (-15)^2}[/tex]
[tex]= \sqrt {{81} + {225}}[/tex]
[tex]= \sqrt {306}[/tex]
FG [tex]= 17.492856[/tex] (round to 17.5)
Length FH between(-2,5) and (-9, -6) is
[tex]FH = \sqrt {(-9 - (-2))^2 + (-6 - 5)^2}[/tex]
[tex]= \sqrt {(-7)^2 + (-11)^2}[/tex]
[tex]= \sqrt {{49} + {121}}[/tex]
[tex]= \sqrt {170}[/tex]
FH [tex]= 13.038405[/tex] (can be rounded to 13.04
Length GH between (7, -10) and (-9, -6) is
[tex]GH = \sqrt {(-9 - 7)^2 + (-6 - (-10))^2}[/tex]
[tex]= \sqrt {(-16)^2 + (4)^2}[/tex]
[tex]= \sqrt {{256} + {16}}[/tex]
[tex]= \sqrt {272}[/tex]
GH [tex]= 16.492423[/tex] (can be rounded to 16.5)
Determining the area of a triangle given 3 sides
Heron's formula allows us to find the area of a triangle given 3 sides If the sides are a, b and c the general form of Heron's formula is
[tex]Area = \sqrt {s(s-a)(s-b)(s-c)}[/tex]
where s is the semi-perimeter = [tex]\frac{a+b+c}{2}[/tex]
Substituting values we get
s = [tex]\frac{17.5+13.04+16.5}{2} = 23.52[/tex]
[tex]Area = \sqrt {23.52(23.52-17.5)(23.52-13.04)(23.52-16.5)}[/tex]
[tex]= \sqrt{23.52\cdot6.02\cdot10.48\cdot7.02}[/tex]
[tex]102.0625[/tex] square units
(2thousands 7 tens) multiple by 10
Answer:
207 2 hundreds seven ones
Step-by-step explanation:
how does the vertical line test work?
Answer:
To see if something is a function, just draw lines down the graph, if it touches the line twice, then that means it does not pass the vertical line test, meaning it is not a function
(By the line, I mean what you wrote on the paper,)
For example, a parabola is a function, because when you do the vertical line test, it only touches the line at one point, and not two,
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
(I included a picture that should help explain better)
7
Yuki works at an aquarium. To clean a tank, she calculates of the tank's total volume, and
900
she adds that much cleaning solution to the tank. For a certain tank, this works out to be 2 L
of cleaning solution.
02/1
3
What is the total volume of the tank?
The total volume of the tank is 300L.
The volume of a 3D figure is the space that it occupies.
Here, we are given that Yuki adds cleaning solution that is 7/900 of the tank's total volume.
Let the total volume of the tank be V
We know that the cleaning solution required to clean this tank is 2 1/3 L
Firstly, we need to convert this mixed fraction into an improper fraction, Thus, 2 1/3 = (2*3 + 1)/ 3
= 7/3 L
Thus, we can make the following equation,
(7/900)* V = 7/3
V = 7/3 (900/7)
V = 900/ 3
V = 300
Thus, the volume of the tank is 300L.
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Your question was incomplete. Check for full content here-
Yuki works at an aquarium. To clean a tank, she calculates 7/ 900 of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be 2 1/3 L of cleaning solution. What is the total volume of the tank?
Answer:
300L
Step-by-step explanation:
Just did it on Khan academy.
The sales tax in Jorge's state is 7%. Jorge bought a Ford Mustang having a sales tax of $1,928.22. What was the cost of the car?
The cost of the car is $27,546
How to calculate the cost of the car ?The sales tax is 7%
Jorge bought a ford mustang having a sales tax of $1,928.22
Therefore the cost of the car can be calculated as follows
1928.22÷ 7/100
= 1928.22/0.07
= 27,546
Hence the cost of the car is $27,546
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reflection across the y-axis please I need help
Graph the linear equation.
x - 2y = - 2
The graph of the linear equation can be seen in the image below.
How to graph the linear equation?Here we have the linear equation:
x - 2y = -2
To graph it, we need to find two points that belong to the line, and then we can graph these and connect them with a line.
If x = 0, we have:
0 - 2y = -2
y = -2/-2 = 1
if x = 1 then:
1 - 2y = -2
1 + 2 = 2y
3 = 2y
3/2 = y
Then we have the points (0, 1) and (1, 3/2), now just graph these points on a coordinate axis and then connect them with a line, we will get:
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Which graph represents the function h(x)=−x√+2?
Of like f(x)= - √x+2
A b c d
Answer:
use air math
Step-by-step explanation:
hope that helps
I need help with 4B please. Thank you!
The equation to the tangent line to [tex]y = e^{(x^2)}[/tex] at point (1,0) is given by:
y = 2e(x - 1).
What is the equation to the tangent line of a function of a point?Supposing that we have a function f(x) at a point [tex](x_0, y_0)[/tex], the equation of the tangent line to this function is given by:
[tex]y - y_0 = f^{\prime}(x_0, y_0)(x - x_0)[/tex]
In which f' is the derivative.
In this problem, the function is:
[tex]f(x) = e^{(x^2)}[/tex]
Applying the chain rule, the derivative is:
[tex]f^{\prime}(x) = 2xe^{(x^2)}[/tex]
At x = 1, the derivative is:
[tex]f^{\prime}(1) = 2(1)e^{((1)^2)} = 2e[/tex]
Hence the tangent line at point (1,0) is given by:
y = 2e(x - 1).
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find the sum of the sequence 33 + 34 + 35 + 36 + . . . + 100
Answer:
230
Step-by-step explanation:
Paula refills the flour bin after it has been empty for a while. She pours in the flour at a constant rate. She stops pouring flour when the bin is full.
Which graph could represent this scenario?
Answer:
a
Step-by-step explanation:
because the chart matches the scenario
What is the distance of this line segment?
Answer:
5 studs (3^3)
(3^3) = 5
Step-by-step explanation:
M is the midpoint of AB. Q is the midpoint of AM. and T is the midpoint of QM. If the coordinates of A and B are a and b. find the coordinates of Q and T in terms of a and b.
The the coordinates of Q and T in terms of a and b is -
Q [(3a + b)/4] and T [(5a + 3b)/4].
What is Mid-point of a Line segment?
The mid-point of a line segment is a point on the line segment which divides it into two equal parts.
Given is a line segment AB whose mid-point is M with a and b being the coordinates of A and B respectively. Further, Q is the midpoint of AM and T is the midpoint of QM.
[Refer to the image attached for clear explanation]
Since M is the mid-point of AB, therefore the coordinates of point M will be = M [(a + b)/2]
Now, Q is the mid-point of AM. Therefore, the coordinates of Q will be =
[(a + b)/2 + a]/2 = Q [(3a + b)/4]
and
T is the mid-point of QM. Therefore, its coordinates will be =
(a + b)/2 + (3a + b)/4 = T [(5a + 3b)/4]
Hence, the the coordinates of Q and T in terms of a and b is -
Q [(3a + b)/4] and T [(5a + 3b)/4]
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Aisha wants to ride her bicycle 18.2 miles this week. She has already ridden 5 miles. If she rides for 4 more days, write and solve an equation which can be used to determine mm, the average number of miles she would have to ride each day to meet her goal.
The equation that could be used to determine, m, is 4m = 18.2 - 5
The average number of miles (m) is 3.3 miles to ride each day to meet her goal.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Total distance of ride Alisha wants by her bicycle (d) = 18.2 miles.
And, She has already ridden 5 miles.
She rides for 4 more days.
Now, Let the average number of miles = m
She has already ridden 5 miles.
And, She rides for 4 more days.
The number of miles she needs to ride more is
18.2 miles - 5 miles
= 13.2 miles
If m is the average number of miles she must cycle in 4 days to reach her objective,
Hence, we can formulate;
4m = 13.2
Divide both side by 4,
m = 3.3 miles
So, The equation that could be used to determine, m, is 4m = 18.2 - 5
The average number of miles is 3.3 to ride each day to meet her goal.
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