[tex]\bf \begin{array}{ccll} gallons&minutes\\ \cline{1-2} 4.39&1\\ 280&x \end{array}\implies \cfrac{4.39}{280}=\cfrac{1}{x}\implies 4.39x=280\implies x=\cfrac{280}{4.39} \\\\\\ x\approx \stackrel{\textit{minutes}}{63.78}~\hspace{7em}63.78 ~~\begin{matrix} min \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \cdot \cfrac{hr}{60 ~~\begin{matrix} min \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ } \implies \boxed{1.063~hr}[/tex]
A class used cars and vans to go on a field trip because of the buses were already in use the use 12 vehicles to go on the trip each car holds for students in each van holds 11 students if 83 students went on the trip and how many of each type of vehicle did the class use
Please answer
Answer:5 vans 7 cars
Step-by-step explanation:
c=cars v=vans
c+v= 12
c =( 12-v)
11v + 4(12-v) = 83
11v + 48-4v = 83
7v = 35
v= 5
c = 12-5 c = 7
7 cars x 4 students = 28 students
5 vans x 11 students = 55 students
55+28 = 83 students
Y=-3x+4. What is the y intercept?
Answer:
4
Step-by-step explanation:
The equation is in the form
y= mx+b
where m is the slope and b is the y intercept
y = -3x +4
-3 is the slope and 4 is the y intercept
Answer:
y intercept is 4
Step-by-step explanation:
When you are finding the Y intercept, you need to pretend that x=0. Cover up the x and you would find the y-intercept which is 4
if it is wrong, let me know and I will fix it
hope this helps!
Find the value of m<3-m<1.
A. 20°
B. 50°
C. 90
D. 120°
Answer:
B. 50°
Step-by-step explanation:
70° and m<1 are Complementary Angles, meaning they add up to 90°, so, m<1 is 20°. Now, m<3 is also 70° because they are Alternative Angles, meaning that they are reflexive. Now you can perform your deduction:
70 - 20 = 50
I am joyous to assist you anytime.
What is the value of x in the equation 3/4(1/4x+8)-(1/2x+2)=3/8(4-x)-1/4x ?
Answer: x = 24
Step-by-step explanation:
3/4 (x/4 + 8) - x/2 +2 = 3/8 (4-x) - x/4
3x/16 + 6 - x = 3/2 - 3x/8 - x/4
collect like term
3x/16 - x+ 3x/8 +x/4 = 3/2 -6
3x-16x+6x +4x / 16 = 3-12 / 2
-3x/16 = -9/2
cross multiply
-6x = -144
Divide bothside by -6
-6x/-6 = -144/6
x = 24
Sure, let's solve the equation:
\[ \frac{3}{4}\left(\frac{1}{4}x + 8\right) - \left(\frac{1}{2}x + 2\right) = \frac{3}{8}(4 - x) - \frac{1}{4}x \]
First, distribute the fractions across the terms inside the parentheses:
\[ \frac{3}{4} \cdot \frac{1}{4}x + \frac{3}{4} \cdot 8 - \frac{1}{2}x - 2 = \frac{3}{8} \cdot 4 - \frac{3}{8} \cdot x - \frac{1}{4}x \]
[Simplify the terms]:
\[ \frac{3}{16}x + 6 - \frac{1}{2}x - 2 = \frac{3}{2} - \left(\frac{3}{8} + \frac{1}{4}\right)x \]
Now, combine like terms:
\[ \frac{3}{16}x - \frac{8}{16}x + 4 = \frac{3}{2} - \frac{3}{8}x - \frac{2}{8}x \]
\[ -\frac{5}{16}x + 4 = \frac{3}{2} - \frac{5}{8}x \]
Next, we want to solve for \( x \), so we'll move all the \( x \)-terms to one side and the constants to the other side:
\[ -\frac{5}{16}x + \frac{5}{8}x = \frac{3}{2} - 4 \]
Convert \( \frac{5}{8} \) to a fraction with a denominator of 16:
\[ -\frac{5}{16}x + \frac{10}{16}x = \frac{6}{4} - \frac{16}{4} \]
Combine like terms again:
\[ \frac{5}{16}x = -\frac{10}{4} \]
\[ \frac{5}{16}x = -2.5 \]
Finally, solve for \( x \):
\[ x = \frac{-2.5}{\frac{5}{16}} \]
\[ x = -2.5 \cdot \frac{16}{5} \]
\[ x = -2.5 \cdot 3.2 \]
\[ x = -8 \]
So the solution for \( x \) in the given equation is \( x = -8 \).
Which situation represents a proportional relationship? A) The cost of a taxi cab ride of $2.00 per mile with an initial fee of $3.00. B) The height of a tree that grows 1 foot a month with a starting height of 4 feet. C) The number of pounds of dirt in a wheelbarrow with each 5 pound shoveled scoop of dirt. D) The cost of a gym membership with a cost of $22.00 per month and a one time sign-up fee of $50.00.
Answer:
I think the answer is (c)
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The only one that doesn't require the initial part, since the initial part should be 0, in order, for a relationship to be proportional is answer C.
A) Initial fee of $3 (we need the initial to be 0).
B) Initial height of 4 ft (we need the initial to be 0).
C) I see nothing about a starting or initial so far this is it!
D) Initial fee is 50 dollars (we need the initial to be 0).
Which inequality statement best represents the graph?
Answer:
Step-by-step explanation:
If you have choices, you really should list them.
Here is the graph for y = (x + 0.25)(x - 1.75) which will look like yours. There are all sorts of variations that are possible, but at least I could reproduce a similar looking graph.
Any line with a slope of zero is parallel to the
O y-axis
O x-axis
O line y = x
Answer:
x-axis
Step-by-step explanation:
A line with a slope of zero has the same y-value everywhere, so is parallel to the line y=0, the x-axis.
Answer:
x- axis
Step-by-step explanation:
We are given that any line whose slope is zero.
We have to find the line with a slope of zero is parallel to which axis.
We know that when any line is parallel to x- axis
It means y does not change with
Therefore, [tex]\frac{dy}{dx}=0[/tex]
Slope of a line which is parallel to x- axis is zero because y does not vary with x.
But when a line parallel to y - axis then slope of that line is undefined.
When line y=x
Then , [tex]\frac{dy}{dx}=1\neq 0[/tex]
Hence, any line with slope of zero is parallel to the x- axis.
Answer:x- axis.
Twenty one-slips of paper are each marked with a different letter of the alphabet and placed in a basket. A slip is pulled out, it’s letter recorded and the slip is replaced. This is done 6 times. Find the probability that the word riddle is formed. Assume that each letter in the word is also in the basket
Answer:
0.095
Step-by-step explanation:
the probability of getting the word riddle is 0.095.
I'm sorry if the answer is wrong.... I'm not that good at maths either but I wanted to help :)
Choose the inverse of y=X2-2
Answer:
26
Step-by-step explanation:
For this case we must find the inverse of the following function:
[tex]y = x ^ 2-2[/tex]
We exchange the variables:
[tex]x = y ^ 2-2[/tex]
We clear the variable "y":
Adding 2 to both sides we have:
[tex]x + 2 = y ^ 2[/tex]
Applying square root on both sides of the equation:
[tex]y = \pm \sqrt {x + 2}[/tex]
We change y by [tex]f ^ {- 1} (x)[/tex]:[tex]f ^ {- 1} (x) =\pm \sqrt {x + 2}[/tex]
Answer:
[tex]f ^ {- 1} (x) = \pm\sqrt {x + 2}[/tex]
Find the value of x rounded to the nearest degree
Answer:
b 44 degrees
Step-by-step explanation:
cos x = adjacent side / hypotenuse
cos x = 15/21
cos x = 5/7
Take the inverse cos of each side
cos ^-1 (cos (x) )= cos ^-1 (5/7)
x =44.4153086
To the nearest degree
x = 44 degrees
Answer:
The correct answer is option(b). 44°
Step-by-step explanation:
From the figure we can see a right angled triangle with one angle is x° and two sides are given.
To find the value of x
From the given figure we get the adjacent side of angle is given
Therefore we can write,
Cos x = Adjacent side/Hypotenuse
= 15/21
= 0.7142
x = Cos ⁻¹ (0.7142)
= 44°
Therefore the value of x = 44°
The correct answer is option(b). 44°
Point K is the midpoint of QZ. Point K is located at (-1,-11), and point Z is located at (7,-3). Where is point Q located?
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad Z(\stackrel{x_2}{7}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{7+x}{2}~~,~~\cfrac{-3+y}{2} \right)~~=~~\stackrel{\stackrel{midpoint}{K}}{(-1,-11)}\implies \begin{cases} \cfrac{7+x}{2}=-1\\[1em] 7+x=-2\\ \boxed{x=-9}\\ \cline{1-1} \cfrac{-3+y}{2}=-11\\[1em] -3+y=-22\\ \boxed{y=-19} \end{cases}[/tex]
Answer:
[tex](-9,-19)[/tex]
Step-by-step explanation:
Givens
[tex]K(-1,-11)\\Z(7,-3)\\Q(x_{1},y_{1})[/tex]
Now, the definition of midpoint is
[tex]K(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2}}{2} )[/tex]
But, we know that [tex]K(-1,-11)[/tex], so we replace each vale, where [tex]x_{2} =7[/tex] and [tex]y_{1}=-3[/tex]
[tex]-1=\frac{x_{1}+7 }{2} \\-2=x_{1}+7\\-2-7=x_{1}\\x_{1}=-9\\[/tex]
[tex]\frac{y_{1}+y_{2}}{2}=-11\\y_{1}-3=-22\\y_{1}=-22+3\\y_{1}=-19[/tex]
Therefore, Q is located at [tex](-9,-19)[/tex]
A customer is tiling a shower, the main, back wall of which is 6' by 4'.
The tile they want to use is 3" x 6", which comes 20 pieces to a box.
How many pieces of this tile do they need for this project? (No Waste)
Answer:
a lot
Step-by-step explanation:
Answer:
192 pieces of tiles will be required.
Step-by-step explanation:
A customer is tiling a shower's back wall which is in the dimensions of 6' by 4'
This area of the wall is = 6 × 4 square feet = 24 feet²
Customer wants to cover this wall with the tiles measuring 3" by 6" or 3 inches by 6 inches.
Now we will convert these dimensions of the tiles in foot.
Since 12 inches = 1 foot
Therefore, 1 inch = [tex]\frac{1}{12}[/tex] foot
Dimensions of one tile in foot will be [tex]\frac{3}{12}[/tex] foot by [tex]\frac{6}{12}[/tex] foot.
In simplified form, dimensions of the tile is [tex]\frac{1}{4}[/tex] foot by [tex]\frac{1}{2}[/tex] foot.
Area of one tile = [tex]\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}[/tex] square feet
Number of tiles = [tex]\frac{\text{Area of the wall}}{\text{Area of one tile}}[/tex]
= [tex]\frac{24}{\frac{1}{8}}[/tex]
= 24×8
= 192 tiles
Therefore, 192 pieces of tiles will be required.
What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm?
Answer:
the area of a sector is 151.976 cm²....
Step-by-step explanation:
Area of sector(A)is given by:
A=πr².θ/360°
where,
r is the radius and θ is the angle in degree.
As per the statement:
A central angle of 4π/5 radians and a radius of 11 cm.
r=11cm
Use conversion:
1 radian=180/π
then:
4π/5 radians=180/π * 4π/5
=144°
θ=144°
Substitute these given values and use 3.14 for π we have;
A=3.14*(11)²*144/360
A=3.14(121)*144/360
A=379.94*0.4
A=151.976 cm²
Therefore the area of a sector is 151.976 cm²....
The area of a sector with a central angle of 4π/5 radians and a radius of 11 cm is approximately 96.8 cm², calculated using the formula A = (θ/2π) * πr² and rounded to two significant figures.
To find the area of a sector of a circle with a given central angle in radians and a specific radius, you can use the formula:
A = (θ/2π) * πr²
where A is the area of the sector, θ is the central angle in radians, and r is the radius of the circle.
In this case, the central angle is 4π/5 radians and the radius is 11 cm. Substituting the given values into the formula:
A = (4π/5/2π) * π * (11 cm)²
= (2/5) * π * 121 cm²
= (2/5) * 3.1415927 * 121 cm²
= 96.76 cm² to two significant figures, since the radius is given to two significant figures.
Hence, the area of the sector is approximately 96.8 cm².
Can someone please explain how this answer was produced?
Answer:
Step-by-step explanation:
First, we know that the sin function is odd which means:
sin(-x) = -sin(x).
Secondly evaluating an inverse trigonometric function with a normal trigonometric function as the argument can be rewritten as an algebraic expression.
Let [tex]t = \sin(-\frac{11\pi}{4}) = - \sin(\frac{11\pi}{4})[/tex]
We know the certain identity.
[tex]\sin(\theta) = \sin(2\pi + \theta)[/tex]
We use it to evaluate sin(11 pi / 4).
[tex]\sin(\frac{11 \pi}{4}) = \sin({\frac{8\pi}{4} + \frac{3 \pi}{4}}) = \sin(2\pi + \frac{3 \pi}{4}) = \sin(\frac{3\pi}{4})[/tex]
Another helping identity is the following:
[tex]\sin(\theta) = \sin(\pi - \theta)[/tex]
[tex]\sin(\frac{3\pi}{4}) = \sin(\pi - \frac{3\pi}{4}) = \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}[/tex]
But let's not forget that t = -sin(11 pi/4) = - sqrt(2) / 2
Now we end up with the following equation.
[tex]\cos^{-1}(-\frac{\sqrt{2}}{2}) = x\\\cos(x) = -\frac{\sqrt{2}}{2} => x = \frac{3\pi}{4}[/tex]
what is the point-slope form of the equation for the line with a slope of -2 that passes through the point (4,-6)
Answer: y+6=-2(x-4)
Step-by-step explanation:
Point slope form: Y-y1=m(x-x1)
Answer:
[tex]y+6=-2(x-4)[/tex]
Step-by-step explanation:
Point-slope form of a line is [tex]y-y_1=m(x-x_1)[/tex] where the slope is [tex]m[/tex] and [tex](x_1,y_1)[/tex] is a point on the line.
We know both of those things so we have enough information without doing any math to do this problem. You just got to plug in.
So replace [tex]m[/tex] with -2, [tex]x_1[/tex] with 4, and [tex]y_1[/tex] with -6.
Like so:
[tex]y-(-6)=-2(x-4)[/tex].
You can simplify a little:
[tex]y+6=-2(x-4)[/tex].
In a museum, Nick is looking at a famous painting through a mirror at an angle of 58 degrees Find the angle the painting makes with the mirror. Also, find m
here's your answer
The angle of incidence of the painting is 58°, one property of mirrors is angle of incidence = angle of reflection. Therefore angle of reflection the painting makes with the mirror is 58°.
HOPE IT HELPS....
Answer:
58 degree
Step-by-step explanation:
We know that in mirror angle of incident equal to the angle of reflection.Here angle between reflected ray and mirror is 58 degree (let angle of reflection ). Therefore the angle of incident (angle between painting and mirror) must be 58 degree.
Hence the angle of the painting with the mirror =58 degree.
Ms. Ramos buys a rare painting for m dollars. She sells it for 5 times the amount she paid for it, or 5m. Her profit is
5m-m
She purchases another painting using half of the profit from the sale. Which expression represents how much MS
Ramos paid for the second painting?
•4m+2. •5m+2. •5m/2. •4m/2
Answer:
(D) 4m/2
Step-by-step explanation:
took test
using the distributive property write numerical expression that is equivalent to 25+10
Answer:
5(5 + 2).
Step-by-step explanation:
5 is a factor of 25 and 10 so :
15 + 10 = 5(5 + 2).
For this case we have that by definition, the distributive property establishes:
[tex]a (b + c) = ab + ac[/tex]
Then, using the above definition, we must write an expression equivalent to:
[tex]25 + 10[/tex]:
The largest integer that divides both numbers without leaving residue is 5, then:
[tex]5 (5 + 2) = 5 * 5 + 5 * 2 = 25 + 10[/tex]
Answer:
[tex]5 (5 + 2)[/tex]
Need Help Answer Plz!!
Answer:
[tex]\large\boxed{\overline{AC}\ and\ \overline{DF}}[/tex]
Step-by-step explanation:
[tex]\triangle ABC\cong\triangle DE F\\\\\text{Corresponding angles:}\\\\\angle A\to\angle D\\\angle B\to\angle E\\\angle C\to\angle F\\\\\text{Corresponding sides:}\\\\AB\to DA\\AC\to}DF\\BC\to EF[/tex]
Sin(x) = 1/7
A.3.2
B.8.2
C.12.4
D.14.3
Answer: B
Step-by-step explanation: If you use inverse sin, then you can take sin^-1(1/7) and get 8.2. To check this, do sin(8.2) and it comes out to 1/7
NEED HELP QUICK
What is the mean of this set: {2, 6, 7, 9, 9, 9}?
6
7
8
9
The mean of a dataset if given by the sum of the elements divided by the number of elements:
[tex]M = \dfrac{2+6+7+9+9+9}{6} = \dfrac{42}{6}=7[/tex]
B. 7
Explanation:The mean (also known as the average) is found by adding all of the numbers in the set together, then dividing the result by how many numbers are in the set.
First, add the numbers together. [tex]2+6+7+9+9+9=42[/tex]
Finally, divide that by the amount of numbers in the set. [tex]\frac{42}{6}=7[/tex]
Determine, to the nearest tenth, the perimeter of the triangle shown in the accompanying diagram.
A. 29.7
B. 23.3
C. 24.9
D. 28.5
Answer: c) 24.9
Step-by-step explanation:
Use the distance formula then add and round to nearest tenth
The perimeter of the triangle ABC will be 24.9. Then the correct option is C.
What is the distance between two points?Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x – h)² + (y – k)²
The vertices of the triangle are A(1, 3), B(11, 4), and C(7, 9).
The distance between AB will be
AB² = (11 – 1)² + (4 – 3)²
AB² = 101
AB = 10.05
The distance between BC will be
BC² = (11 – 7)² + (4 – 9)²
BC² = 41
BC = 6.40
The distance between AC will be
AC² = (7 – 1)² + (9 – 3)²
AC² = 72
AC = 8.50
Then the perimeter of the triangle ABC will be
Perimeter = AB + BC + CA
Perimeter = 10.05 + 6.40 + 8.50
Perimeter = 24.95 ≈ 24.9
The perimeter of the triangle ABC will be 24.9.
Then the correct option is C.
Learn more about the distance between two points here:
https://brainly.com/question/18296211
#SPJ2
A pizza restaurant recently advertised two specials. The first special was a 14-inch pizza for $12. The second special was two 4-inch pizzas for $8. Determine the
better buy. (Hint: First compare the areas of the two specials and then find a price per square inch for both specials.)
Choose the correct answer below.
14-inch diameter pizza
two 4-inch diameter pizzas
Answer:
14-inch pizza
Step-by-step explanation:
The area of a circle (or a pizza) is πr^2, if r is the radius.
For a 14-inch pizza, the radius is 14/2=7 and therefore the area is π*7^2 which is approximately 154 square inches. Therefore, the price per square inch is 12/154, or approximately 0.078 dollars per inch.
Similarly, the area of a 4-inch pizza is π*2^2 which is approximately 12.5 square inches, two 4-inch pizzas are 25, and so the price per square inch is 8/25 which is approximately 0.32 dollars per inch.
So the 14-inch pizza is the better deal.
Subtract the sum of _36/11 and 49/22 from the sum of 33/8 and _19/4.
Answer:37/88
Step-by-step explanation:
Sum of -36/11&49/22=- 1,1/22
Sum of 33/8&-19/4=- 5/8
-5/8-(-1,1/22)=37/88
solve the equation below x
cx -4=7
A x=11/C
B x=3/C
C x= c/3
D x= c/11
Answer:
A
Step-by-step explanation:
Given
cx - 4 = 7 ( isolate the term in x by adding 4 to both sides )
cx = 11 ( divide both sides by c )
x = [tex]\frac{11}{c}[/tex] → A
REALLY EASY NEED ANSWER BY 10:00 P. M. AND WILL GIVE BRAINLEIST. PLS HURRY IF YOU HAVE TIME PLEASE ANSWER OTHER QUESTIONS PLS THANK YOU.
Answer:
no
Step-by-step explanation:
it asks if the given value is a solution of the inequality, but I'm pretty sure it's not
Explain why the two sets are equivalent.
A={The letters in the word SEAT}
B={The letters in the word TASTE}
A. The two sets are not equivalent because set A has 4 letters and set B has 5.
B. Both sets contain the same elements.
C. Both sets contain objects.
D. Both sets contain letters.
Answer:
B. Both sets contain the same elements.
Step-by-step explanation:
Given:
A={The letters in the word SEAT}
B={The letters in the word TASTE}
Writing the sets in elements form
A = {S,E,A,T}
B={A,S,T,E} => the letter T appears two times but the repeating elements are written only once.
Hence, both sets contain the same letters.
Therefore, the correct answer is:
B. Both sets contain the same elements ..
If f(x) = [tex]x^{2} -2^x,[/tex] what is the value of f(3) ?
PLEASE HELP! WILL PUT BRAINLIESTT!
Answer:
f(3) = 1
Step-by-step explanation:
f(x) = x² - 2ˣ
You are solving for f(3). Plug in 3 for x in the equation:
f(3) = (3)² - (2)³
Simplify. First, simplify each number by solving the powers, then subtract:
f(3) = (3 * 3) - (2 * 2 * 2)
f(3) = (9) - (8)
f(3) = 9 - 8
f(3) = 1
f(3) = 1 is your answer.
~
Approximate area under the curve f(x) =-x^2+2x+4 from x=0 to x=3 by using summation notation with six rectangles and use the the right endpoint value for x to calculate the height
Answer:
Summation notation:
[tex]\frac{1}{2}\sum_{k=1}^6f((.5k))[/tex]
or after using your function part:
[tex]\frac{1}{2}\sum_{k=1}^6(-(.5k)^2+2(.5k)+4)[/tex]
After evaluating you get 11.125 square units.
Step-by-step explanation:
The width of each rectangle is the same so we want to take the distance from x=0 to x=3 and divide by 6 since we want 6 equal base lengths for our rectangles.
The distance between x=0 and x=3 is (3-0)=3.
We want to divide that length of 3 units by 6 which gives a length of a half per each base length.
We are doing right endpoint value so I'm going to stat at x=3. The first rectangle will be drawn to the height of f(3).
The next right endpoint is x=3-1/2=5/2=2.5, and the second rectangle will have a height of f(2.5).
The next will be at x=2.5-.5=2, and the third rectangle will have a height of f(2).
The fourth rectangle will have a height of f(2-.5)=f(1.5).
The fifth one will have a height of f(1.5-.5)=f(1).
The last one because it is the sixth one will have a height of f(1-.5)=f(.5).
So to find the area of a rectangle you do base*time.
So we just need to evaluate:
[tex]\frac{1}{2}f(3)+\frac{1}{2}f(2.5)+\frac{1}{2}f(2)+\frac{1}{2}f(1.5)+\frac{1}{2}f(1)+\frac{1}{2}f(.5)[/tex]
or by factoring out the 1/2 part:
[tex]\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))[/tex]
To find f(3) replace x in -x^2+2x+4 with 3:
-3^2+2(3)+4
-9+6+4
1
To find f(2.5) replace x in -x^2+2x+4 with 2.5:
-2.5^2+2(2.5)+4
-6.25+5+4
2.75
To find f(2) replace x in -x^2+2x+4 with 2:
-2^2+2(2)+4
-4+4+4
4
To find (1.5) replace x in -x^2+2x+4 with 1.5:
-1.5^2+2(1.5)+4
-2.25+3+4
4.75
To find f(1) replace x in -x^2+2x+4 with 1:
-1^2+2(1)+4
-1+2+4
5
To find f(.5) replace x in -x^2+2x+4 with .5:
-.5^2+2(.5)+4
-.25+1+4
4.75
Now let's add those heights. After we obtain this sum we multiply by 1/2 and we have our approximate area:
[tex]\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))[/tex]
[tex]\frac{1}{2}(1+2.75+4+4.75+5+4.75)[/tex]
[tex]\frac{1}{2}(22.25)[/tex]
[tex]11.125[/tex]
Okay now if you wanted the summation notation for:
[tex]\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))[/tex]
is it
[tex]\frac{1}{2}\sum_{k=1}^{6}(f(.5+.5(k-1)))[/tex]
or after simplifying a bit:
[tex]\frac{1}{2}\sum_{k=1}^6 f((.5+.5k-.5))[/tex]
[tex]\frac{1}{2}\sum_{k=1}^6f((.5k))[/tex]
If you are wondering how I obtain the .5+.5(k-1):
I realize that 3,2.5,2,1.5,1,.5 is an arithmetic sequence with first term .5 if you the sequence from right to left (instead of left to right) and it is going up by .5 (reading from right to left.)
Assume red and green are equally likely occurrences. Using Pascal’s triangle, what is the probability that you will get one green light in a row of five lights? a. 3/16 b. 1/32 c. 5/16 d. 5/32
Answer:
5/32.
Step-by-step explanation:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
As there are 5 lights we need the last row in the above Pascals triangle.
And there is 1 red and 4 green ( = 5) and it can happen in 5 ways, so that gives us the second term in the last row . The total in that last row = 1+5+10+10+5+1 = 32.
so the probability is 5/32.