Let S be the sum,
S = 2 + 4 + 6 + ... + 2 (n - 2) + 2 (n - 1) + 2n
Reverse the order of terms:
S = 2n + 2 (n - 1) + 2 (n - 2) + ... + 6 + 4 + 2
Add up terms in the same positions, so that twice the sum is
2S = (2n + 2) + (2n + 2) + (2n + 2) + ... + (2n + 2)
or
2S = n (2n + 2)
Divide both sides by 2 to solve for S :
S = n (n + 1)
The probability of sandy flipping a coin twice and getting heads both times is 0.25 the probability of john's spinner stopping on the color red is
The true statement is (c) Neither. Both events are equally likely.
Complete questionThe probability of Sandy flipping a coin twice and getting heads both times is 0.25. The probability of John's spinner stopping on the color red is 1/4.
Which of these events is more likely?
-Sandy flips a coin twice and gets heads both times.
-John's spinner stops on the color red.
-Neither. Both events are equally likely.
How to determine the likely event?The given parameters are:
P(Head twice) = 0.25
P(Red) = 1/4
Rewrite P(Red) as:
P(Red) = 0.25
By comparison, we have:
P(Red) = P(Head twice) = 0.25
This means that both events are equally likely
Hence, the true statement is (c)
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which is the greatest 30000 millimeters 1 kilometer 5000 meters or 6000 centimeters?
what is the midpoint of (-2, -1) and (0, 9)
Answer:
(-1,4)
Step-by-step explanation:
For x the midpoint between -2 and 0 is -1
for y the midpoint between -1 and 9 is 4
Answer:
(-1,4)
Step-by-step explanation:
Midpoint can be found by:
(x1+x2)/2 ; (y1+y2)/2
So, if we substitute, we can find:
(-2+0)/2 ; (-1+9)/2
This gives us -2/2 and 8/2, which is:
(-1, 4)
Hope this helps!
Complete the table for y=1/2x-3
Tables are created by substitute a set of input values into the function to create outputs. The required table is as shown below
x | y
0 -3
1 -2.5
2 -2
Tables and valuesTables are created by substitute a set of input values into the function to create outputs
Using x = 0, 1 and 2 as the input values
Given the function
y = 1/2x - 3
If x = 0
y = 1/2(0) - 3
y = -3
If x = 1
y = 1/2(1) - 3
y = -2.5
If x = 2
y = 1/2(2) - 3
y = -2
Hence the required table is as shown below
x | y
0 -3
1 -2.5
2 -2
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Jessie invests $33 in the stock market. Over the 3 years she has this invested she gets an average return of 7,8%. How much will her investment be worth after the 3 years?
Answer:
it would end up being about $40.73
Step-by-step explanation:
multiply 0.078 by 3 then multiply that by 33
Answer:
hope you can understand
I don’t know how to do this please help
Answer:
84 cm²
Step-by-step explanation:
The figure has a uniform horizontal cross section, so its area is the product of that cross section length and its vertical dimension.
__
A = bh
A = (6 cm)(14 cm) = 84 cm²
The area of the shape is 84 square centimeters.
_____
Additional comment
You could decompose the figure into a rectangle with base 6 and height 8, and a parallelogram with base 6 and height 14-8=6. The area formula is the same for each: A = bh, so the area of the composite figure is ...
A = 6×8 +6×(14 -8)
= 6×(8 +(14 -8))
= 6×14 . . . . same as above.
Using the cards 3,2,4,7 show a valua closest to 5000
4,7,3,2
Step-by-step explanation:
THESE ARE THE THE ARRANGEMENT OF NUMBERS IN ORDER TO GET THE CLOSEST TO 5000
What is the distance between points (5, 1) and (2, -3)?
Answer:
5
Step-by-step explanation:
The distance between two points [tex]P[/tex] and [tex]Q[/tex] is [tex]d = \sqrt{\sum_{i=1}^{n} \left(q_{i} - p_{i}\right)^{2}}[/tex] ([tex]n[/tex] s the number of coordinates of each of the two points, [tex]p_i[/tex] , [tex]i=1..n[/tex] and [tex]q_i,i=1..n[/tex]
are the coordinates of the first and the second points respectively).
Thus, [tex]d = \sqrt{\left(2 - 5\right)^{2} + \left(-3 - 1\right)^{2}}=5.[/tex]
Hi, so I was wondering if anyone knows the surface area of a cylinder if the diameter is 7.5? Thank you so much! :)
Answer:
206.17
Key(s):
[tex]A = 2\pi \frac{d}{2} h + 2\pi \left(\frac{d}{2}\right)^2[/tex]
Substitute d for the actual diameter, 7.5, and h for the height, which is 5.
Step-by-step explanation:
[tex]A = 2\cdot\pi \cdot\frac{7.5}{2} \cdot5 + 2\cdot\pi \cdot\left(\frac{7.5}{2}\right)^2[/tex] ≈ 206.17(2 DP)
Kevin evaluated the expression below. 75 - 6 (8 - 6) + 3 Step 1: 75 - 6 x 2 + 3 Step 2: 75 - 6 x 5 Step 3: 75 - 30 Step 4: 45 Kevin made an error in solving the expression. What error did Kevin make? Which step contains the error? What error did Kevin make? Explain how you would correct Kevin's error. Be sure to include the correct answer in your explanation.
The error Kevin made was in step 2 when he added before he multiplied.
What error did Kevin make?
This question would be solved using the BODMAS rule. The BODMAS rule provides the order in which mathematical problems should be solved. The order is:
bracket of division multiplication addition subtractionStep 1 : 75 - 6 x 2 + 3Step 2: 75 - 12 + 3 Step 3 : 75 - 9 Step 4: 66To learn more about addition, please check: https://brainly.com/question/349488
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Please help me
Find the value of x
Answer:
x = 5 and y = 22
Step-by-step explanation:
See attached image.
0. on a saturday evening in chicago, 34% of the people go out to dinner, 18% go out to
see a movie, 13% go out to a party, and 35% stay home. if five people are randomly
selected on monday morning, what is the probability that all but one went out saturday
night?
a) 0.048
b) 0.116
c) 0.181
d) 0.312
(Refer to the attached image)
Explanation:
Provided 2 length sides and one angle also need to find one missing side.
So, use cosine rule:
a² = b² + c² - 2bc cos(A)
Part 1c² = 9² + 11² - 2(11)(9) cos(57)
c² = 94.16147
c = √94.16147 = 9.70 cm
Part 2d² = 5² + 7² - 2(5)(7) cos(48)
d² = 27.16
d = √27.16 = 5.21
Part 35² = 7² + 9² - 2(7)(9) cos(H)
-126cos(H) = 25 - 49 - 81
cos(H) = -105/-126
cos(H) = 5/6
H = cos⁻¹(5/6) = 33.56°
Part 48² = 4² + 7² - 2(4)(7) cos(J)
-56cos(J) = 64 - 16 - 49
cos(J) = -1/-56
J = cos⁻¹(1/56) = 88.98°
Passcode: 3142
Solve 4 x 5/6 Change to a mixed number and reduce.
Answer:
10/3 or 3.333333
Step-by-step explanation:
- 4 x 5/6 is 3 1/3
- 3 1/3 is a mixed number
- 3 1/3 reduced is 10/3
Write the equation of the trigonometric graph.
Answer:
[tex]f(x)= \sin(6x)+3[/tex]
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
[tex]f(x) = \sf A \sin (B(x + C)) + D[/tex]
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftThe parent function y = sin(x) has the following:
Amplitude (A) = 1Period = 2πPhase shift (C) = 0Vertical shift (D) = 0Mid-line: y = 0From inspection of the given graph:
Amplitude (A) = 1[tex]\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}[/tex]Phase shift (C) = 0Vertical shift (D) = +3 (as mid-line is y = 3)[tex]\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6[/tex]
Substituting the values into the standard form:
[tex]\implies f(x) =1 \sin (6(x + 0)) + 3[/tex]
[tex]\implies f(x) = \sin (6x) + 3[/tex]
Therefore, the equation of the given trigonometric graph is:
[tex]f(x)= \sin(6x)+3[/tex]
Answer(s):
[tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3 \\ y = -sin\:(6x \pm \pi) + 3 \\ y = sin\:6x + 3[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{12}} \hookrightarrow \frac{\frac{\pi}{2}}{6} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\pi \\ Amplitude \hookrightarrow 1[/tex]
OR
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\pi \\ Amplitude \hookrightarrow 1[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = cos\:6x + 3,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{12}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{12}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{12}} = \frac{\frac{\pi}{2}}{6}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-\frac{5}{12}\pi, 2],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{12}, 2],[/tex]they are obviously [tex]\displaystyle \frac{\pi}{3}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{3}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 3,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Can the sides of a triangle have lengths 2, 8, and 19?
Answer:
No
Step-by-step explanation:
NO...... any two sides added together must be GREATER THAN the third side .... 2 + 8 is NOT greater than 19
The circumference of a circle is 37.68 meters. What is the circle's diameter?
C = 37.68 m
Use 3.14 for л.
Answer:
The diameter is 12.
Explain: i used this formula C= Dπ or C= 2rπ
(37.68) = Dπ Divide by 3.14, as the instructions in this question specify to do so.
37.68/3.14 = D π/ 3.14
D = 12 The diameter equals twelve.
Hope This Helped
find the coordinate plane that represents the solution of this system y > -x - 1 y + 4 ≤ x
Answer:
The graph will open to the right and will be mostly in quadrant 1
Step-by-step explanation:
00B0J0DD:
TIME REMAINING
57:39
The head of the math department compared the scores of students in two classes on the Chapter 2 test. He found that
the mean score of both classes was the same. He also found that there was greater variability in the scores of Ms.
Biren's students than in the scores of Mr. Hayes's students. Which quality of the data sets would lead the department*
head to that conclusion?
The median score i Ms. Biren's class is greater than the median score in Mr. Hayes's class.
The
median score in Ms. Biren's class is less than the median score in Mr. Hayes's class.
The range of scores in Ms. Biren's class is greater than the range of scores in Mr. Hayes's class.
The range of scores in Ms. Biren's class is
less than the range of scores in Mr. Hayes's class. The median score
Answer: B.
Explanation and reasoning:
help me please :)
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Answer:
what ya need man I can help but give me a question
Which graph can be used to find the solution(s) to x2 – 4x + 4 = 2x + 1 + x2?
The solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have an equation:
x² – 4x + 4 = 2x + 1 + x²
After solving:
-4x + 4 = 2x + 1
6x = 3
x = 1/2 = 0.5
Thus, the solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
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what contribution to geometry is attributed to the work of rene descartes
Answer: Analytic geometry
what is 2x-45y=22 when y=21
answer:
483.5
step by step explanation:
2x-45y=22
2x-45(21)=22
2x-945=22
2x =22+945
2x=967
x=483.5
Volume of pyramids cones and spheres
Answer:
48 cm³Step-by-step explanation:
Volume = (1/3) * base_area * height
1/3 * 4 * 4 * 9 =
48 cm³
simplify (x^3+2x-3)-(x^2-2x+4)
Answer:
x³ - ((x+1)(x+1))
Step-by-step explanation:
x³ + 2x -3 - x² - 2x + 4
x³ - x² + 1
x³ - ((x+1)(x+1))
Answer:
x^3−x^2+4x−7
Step-by-step explanation:
Hope this helps! Have a great day!!
Use the Distributive Property to write each expression as an equivalent expression. Then evaluate it. 3(5+1)
Answer:
18
Step-by-step explanation:
[tex]3(5 + 1) \\ 3(5) + 3(1) \\ 15 + 3 \\ 18[/tex]
The distributive property means you distribute the multiple to all terms in the parenthesis, in this case the terms are 5 and 1.
An exponential function contains the points (1, 0.9) and
(2, 1.62). What is an exponential function that contains
these points?
Answer:
Hi,
Step-by-step explanation:
Let's say y=a*b^x the equation of the exponential function.
0.9=a*b^1 (1)
1.62=a*b² (2)
(2)/(1) ==> b=1.62/0.9=1.8
and
0.9=a*1.8 ==> a=0.5
y=0.5*1.8^x
right triangles to find the exact length of:
T
30°
14 in
a) TI = in
60°
R
a) TI = 7√3 in
b) IR = 7 in
Explanation:Using cosine rule:
[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]
[tex]\hookrightarrow \sf cos(30) = \dfrac{TI}{14}[/tex]
[tex]\hookrightarrow \sf TI = 14cos(30)[/tex]
[tex]\hookrightarrow \sf TI = 7\sqrt{3}[/tex]
Using sine rule:
[tex]\sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\hookrightarrow \sf sin(30) = \dfrac{IR}{14}[/tex]
[tex]\hookrightarrow \sf IR = 14sin(30)[/tex]
[tex]\hookrightarrow \sf IR = 7[/tex]
Which intervals show f(x) decreasing?
Solve this please-
Thanks!!!
Answer:
130 m²
Step-by-step explanation:
Area of a parallelogram is given by the formula :
A = bh (b is the base length and h is the perpendicular height)
Now we simply substitute values given in diagram to find our answer:
A = bh
A = (13)(10)
A = 130
Units will be m² as this is area
Hope this helped and have a good day