It seems like you want to find the sum of 38 to 115:
[tex] \displaystyle \large{38 + 39 + 40 + 41 + ... + 114 + 115}[/tex]
If we notice, this is arithmetic series or the sum of arithmetic sequences.
To find the sum of the sequences, there are three types of formulas but I will demonstrate only one and the best for this problem.
[tex] \displaystyle \large{S_n = \frac{n(a_1+a_n) }{2} }[/tex]
This formula only applies to the sequences that have the common difference = 1.
Given that a1 = first term of sequence/series, n = number of terms and a_n = last term
We know the first term which is 38 and the last term is 115. The problem here is the number of sequences.
To find the n, you can use the following formula.
[tex] \displaystyle \large{n = (a_n - a_1) + 1}[/tex]
Substitute an = 115 and a1 = 38 in the formula of finding n.
[tex] \displaystyle \large{n = (115 - 38) + 1} \\ \displaystyle \large{n = (77) + 1} \\ \displaystyle \large{n = 78}[/tex]
Therefore the number of sequences is 78.
Then we substitute an = 115, a1 = 38 and n = 78 in the sum formula.
[tex] \displaystyle \large{S_{78} = \frac{78(38+115) }{2} } \\ \displaystyle \large{S_{78} = \frac{39(38+115) }{1} } \\ \displaystyle \large{S_{78} = 39(153) } \\ \displaystyle \large \boxed{S_{78} = 5967}[/tex]
Hence, the sum is 5967.
FInd the volume of the figure
Answer:
785.4
I think it is right
Answer:
Solution: Here, Radius of cylindrical tank (r)=2ml Height of cylindrical tank (h)=8ml volume of that cylindrical tank (v)=?
Now,
we know that,
Volume of cylindrical(v)=V=πr2h=3.14×2×2×8=100.48ans.
Arborist 96% positive tree has a disease, 97% trees do not have disease. Probability of a false positive?
Answer:
Step-by-step explanation:
the probability that the test result is positive (suggesting the person has the disease), given that the person does not have the disease, is only 2 percent; the probability that the test result is negative (suggesting the person does not have the disease), given that the person has the disease, is only 1 percent.
-4x – 3 = -X – 30
how do i do this ?
Answer:
x=9
Step-by-step explanation:
-4x-3=-x-30
-4x+x=-30+3
-3x=-27
x=9
After leaving an airport, a plane flies for 2 hours on a course of 60 degrees at a speed of 200 kilometers per hour. The plane then flies for 3 hours on a course of 210 degrees at a speed of 100 kilometers per hour What is the distance of the airport from the plane in kilometers? Round to the nearest tenth
Answer: 205.3
I suppose all measures of angles are done from the same axis (for example x-axis)
Step-by-step explanation:
You just have to use the theorem of Al'Kashi:
[tex]d^2=400^2+300^2-2*300*400*cos(30^o)\\\\d\approx{205.3(km)}[/tex]
According to this diagram, what is tan 62°?
62°
17
18
280
90°
15
O A.
8
17
OB.끝
O c. 1
8
15
D.
15
8
O
E.
17
15
F.
15
17
Answer:
15/8
Step-by-step explanation:
tan(62)=P/B
tan(62)=15/8
HLP HLP 20 PTS 20 PTS PTS PTSPTS
Answer:
9^4 * 2^4
Step-by-step explanation:
We know (a*b) ^c = a^c * b^c
(9*2) ^4
9^4 * 2^4
Answer:
[tex]9^{4} * 2^{4}[/tex]
Step-by-step explanation:
rule:
[tex](a*b)^{c} = a^{c} * b^{c}[/tex]
distribute the exponent to both bases:
[tex]9^{4} * 2^{4}\\\\[/tex]
look at the image below
Answer:
16
Step-by-step explanation:
volume= Length x width x height
Answer:
Volume: [tex]1/3\times Area\; of\; base\;\times height[/tex]
[tex]= 1/3\times2\times 2\times 4[/tex]
[tex]=16/3\; ft^{3}[/tex]
[tex]=5.3\; ft^{3}[/tex]
OAmalOHopeO
Which equation would represent 30 kittens divided into groups of 4
Answer:
30÷4
Step-by-step explanation:
Solve for x.
−4x + 60 < 72 OR 14x + 11 < −31
Choose 1 answer:
A) x < -3 or x > -3
B) x > -3
C) x <- 3
D) There are no solutions
E) All values of x are solutions
Answer:
A. x < -3 or x > -3
Step-by-step explanation:
Let's start with the equation -4x + 60 < 72.
-4x + 60 < 72
First using the order of operations, subtract 60 from both sides.
-4x + 60 - 60 < 72 - 60
- 4x < 12
Next we want to divide -4 from both sides to isolate the variable.
-4x/-4 < 12/-4
x > -3
When you divide a negative number, always make sure the change the sign.
Solve the next equation, 14x + 11 < -31, the same way we solved the last.
14x + 11 < -31
Subtract 11 from both sides.
14x + 11 - 11 < -31 -11
14x < -42
Divide 14 from both sides.
14x/14 < -42/14
x < -3
The equations have different signs.
A. x < -3 or x > -3
Convert 1.6 L to cubic centimeters
Answer:
1600
Step-by-step explanation:
multiply the volume value by 1000
simplify√50-3√2(2√2-5) -5√32
Answer:
-12
Step-by-step explanation:
√50-3√2(2√2-5) -5√32
= 5√2 -12+15√2-5(4)√2
= 5√2 -12+15√2-20√2
= -12
round 32.68 to the nearest hundredth
Answer:
32.70
Step-by-step explanation:
round up
help please i need this now step by step
Answer:
40 mi ^2
Step-by-step explanation:
SA = 2(lw+wh+lh) where l is the length, w is the width, h is the height
SA = 2( 2*2 + 2*4 * 2*4)
= 2( 4+8+8)
= 2(20)
= 40 mi ^2
What is the solution to each system
3) y=3x+1
3x+y=1
4) y=2x+1
y=2x+4
5) y= -5x+1
y=2x+4
Answer:
3)x=0 y=1
Step-by-step explanation:
3) y=3x+1
3x+y=1
y=1-3x
1-3x=3x+1
1-1=3x+3x
0=6x
x=0
by substitute in 1
y=3x+1
y=3*0+1
y=1
5) -5x+1=2x+4
-5x-2x=4-1
-7x=3
x=-3/7
by substitute in (y=2x+4)
y=2*-3/7+4
=25/7
Use the points to describe the data and determine the line of best fit.
What type of correlation do the data points represent?
What is the equation that best represents the data?
Answer:
Answer: negative
Y= -500x + 4,500
Step-by-step explanation:
Answer:
C. negative
B. Y= -500x + 4,500
I just did it
A man earns RS.95 in a day how much does we earn in 18 days
Answer:
RS 17.10
Step-by-step explanation:
If they earn 0.95 a day, you can multiply that income by the number of days, which is 18.
RS 17.10
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!! Chapt 15 part 2a
Explain the process of matrix multiplication. What are the dimensions 9f of the resulting matrix? Use the following matrices for your explanation of the process. AB. Show your work.
We are given the matrices A and B
[tex]A = \left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right][/tex]
[tex]B = \left[\begin{array}{ccc}2\\1\\2\end{array}\right][/tex]
Multiplying these matrices:
We multiply matrices by taking the first column of the first matrix and the first row of the second matrix
we will multiply all the terms of the first column of the first matrix and multiply them by the terms of the first row of the second matrix, one by one
[tex]AB = \left[\begin{array}{ccc}2(2) + 3(1) + -1(2)\\0(2) + 2(1) + 5(2)\\2(2) + 4(1) + 0(2)\end{array}\right][/tex]
[tex]AB = \left[\begin{array}{ccc}5\\12\\8\end{array}\right][/tex]
9514 1404 393
Explanation:
Two matrices with dimensions (numbers of (rows, columns)) of (a, b) and (c, d) can only be multiplied if the number of columns in the left matrix is equal to the number of rows in the right matrix. That is, b=c. The dimensions of the product matrix will be (a, d).
For row i of the left matrix and column j of the right matrix, element a(i,j) of the product matrix is the dot-product of row i with column j. (The dot-product of two vectors is the sum of the products of corresponding elements.)
__
The example matrices have (row, column) dimensions (3, 3) and (3, 1), so can be multiplied with a result having dimensions (3, 1).
It is useful to refer to an element of a matrix by specifying the row and column in which it resides. An element of matrix 'A' in row 2 and column 3 can be referred to as A(2,3). Often, subscripts are used, as in ...
[tex]A_{i,j}[/tex]
For matrix C = A·B, the element C(1,1) will be the sum ...
A(1,1)B(1,1) +A(1,2)B(2,1) +A(1,3)B(3,1)
Calculators, apps, spreadsheets, and web sites are available that will perform this arithmetic for you. It can be a bit tedious to do by hand.
Here the product is ...
[tex]A\cdot B=\left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right] \cdot\left[\begin{array}{c}2&1&2\end{array}\right] =\left[\begin{array}{c}2(2)+3(1)+(-1)(2)&0(2)+2(1)+5(2)&2(2)+4(1)+0(2)\end{array}\right] \\\\=\left[\begin{array}{c}5&12&8\end{array}\right][/tex]
What is the slope of a roof on a house that has a vertical height of 2.4 feet from the ceiling of the top floor to the top of the pitch and a length of 8.2 feet from the center of the edge of the house?
Answer:
Step-by-step explanation:
It is unclear from the phrasing what dimension 8.2 ft represents.
If 8.2 ft is the direct distance from the edge of the roof to the top of the pitch, then the horizontal distance from the edge to the top is √(8.2²-2.4²) ≅ 7.84 ft, and the slope is 2.4/7.84 ≅ 0.31
If 8.2 ft is the horizontal distance from the edge of the root to the top of the pitch, then the slope is 2.4/8.2 ≅ 0.29
The slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The diagram below shows the house with the roof.
The vertical height of roof on a house, rise = 2.4 feet
The horizontal length of a roof on a house, run = 8.2 feet
The slope of a roof can be found as
[tex]Slope = \frac{rise}{run}[/tex]
⇒ [tex]slope = (\frac{2.4}{8.2} )[/tex]
⇒ [tex]slope = 0.2926[/tex]
The angle of the slope of a roof can be found as
[tex]tan \alpha =\frac{vertical height}{horizontal length}[/tex]
⇒ [tex]\alpha =tan^{-1} (\frac{2.4}{8.2} )[/tex]
⇒ [tex]\alpha =tan^{-1} (0.2926)[/tex]
⇒ [tex]\alpha =16.31[/tex]
Hence we can conclude that the slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
Learn more about slope of a line here
https://brainly.com/question/6204743
#SPJ2
How do we find the second and the third derivative of this equation? Please help!
Answer:
[tex]\frac{7}{2\sqrt{2} }[/tex]
Step-by-step explanation:
substitute 2 in for x. the square root of 2 is already in radical form
PLEASE SOLVE AL QUESTIONS, PLEASEEE!!
9514 1404 393
Answer:
a) 2
b) left: 3; lower right: 5
c) upper right: 53°; bottom: 82°
Step-by-step explanation:
3.a) The top side of polygon B is 5 units; the corresponding top side of polygon A is 2.5 units, so the dimensions of polygon A are multiplied by the scale factor 5/2.5 = 2 to give the dimensions of polygon B.
the scale factor is 2
__
b) Sides of polygon B are 2 times the length of the corresponding side of polygon A.
left side: 2×1.5 = 3
lower right side: 2×2.5 = 5
__
c) Corresponding angles of similar figures are congruent.
upper right angle: 53°
bottom angle: 82°
___
4.
The arithmetic of problem 4 is correct as shown.
(0.5, -1)
(-1, 0.5)
(2, -4)
(1, -2)
Answer:
so your answer is (0.5,-1)
thank you for the help every one
Answer:
1. 1.66in
2. 6.66in
3. 3.33in
4. 1inch
Step-by-step explanation:
the area of a rectangle is found by multiplying the length times width or the two sides.
5 x 1/3 is about 1.66 inches
5 x 4/3 is about 6.66 inches
5/2 x 4/3 is about 3.33 inches
and 7/6 x 6/7 is 1 inch
Solve the equation for y. Identify the slope and y- intercept. Then graph the equation. 2y-3x=10
Answer:
y=3/2x+5
The slope is 3/2 and the y-intercept is 5
Step-by-step explanation:
Solving for y will give us the slope and y-intercept
Isolate y
2y/2=10+3x/2
y=5+3/2x
The slope is 3/2 and the y-intercept is 5
Graph it by graphing (0,5) and using the slope (up 3 over 2) to put other points
find the volume of the following figure round your answer to the nearest tenth if necessary and make sure to use pi
Answer:
524cm^2
Step-by-step explanation:
Formula for Volume of sphere= 4/3 πr^2
We have,
r=5cm
Now,
Volume(v)=4/3 πr^2 = 4/3π 5^3= 4/3π 125 = 166.666666667π = 523.598775599
Rounding to the nearest tenth,
Volume=524cm^2
If you have 2 distinct black playing cards and 2 distinct red playing cards, how many ways can you arrange the four cards given that the red cards can never be next to each other
Answer:
I'm not 100% on the interoperation of this question...
are the two red cars out of a 52 card deck and you can try all the combinations of two red and black cards ????
for this answer i will assume that you have 4 coins two nickels and 2 quarters
and the question is " how many ways can you arrange the four coins given that the nickels can not be next to the quarters"
in that case I think the answer is 8
Step-by-step explanation:
1- N1 Q1 N2 Q2
2- N1 Q2 N2 Q1
3- N2 Q1 N1 Q2
4- N2 Q2 N1 Q1
5- Q1 N2 Q2 N1
6- Q2 N2 Q1 N1
7- Q1 N1 Q2 N2
8- Q2 N1 Q1 N2
[tex]2\cdot \left(\left(2\:choose\:1\right)\:\cdot \:\left(2\:choose\:1\right)\right)[/tex]
To make sky blue Sam uses two drops of blue paint for every eight drops of white paint. He wants to
make a large amount of sky blue paint. If he uses sixteen drops of blue, how many drops of white will he
need?
Answer:
64
Step-by-step explanation:
The Ratio of Blue to White drops is 2:8
16*4=64,... 16:64 Have a nice day!
Need help plz + will give brainlest
Thanks in advance
Answer:
it is D.
Step-by-step explanation:
Simplify this radical.
90
3/10
6/10
9/10
103
Need help please on this
Answer:
3[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Assuming you mean [tex]\sqrt{90}[/tex]
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{90}[/tex]
= [tex]\sqrt{9(10)}[/tex]
= [tex]\sqrt{9[/tex] × [tex]\sqrt{10}[/tex]
= 3[tex]\sqrt{10}[/tex]
Which equation describes this graph?
Step-by-step explanation:
The graph clearly has a positive slope. So Answer D couldn't be correct. Next: the y-intercept of this line is (0, -2), so b in the formula y = mx÷ b must be -2.
Therefore the correct equation of this line is
y = x - 2 (choice a)
Venn Diagram HELP
What numbers am I missing in the slots:
A.) B.) C.) ?
Answer:
A = 123
B = 39
C = 379
Step-by-step explanation:
If 569 freshmen like at least one of these 3 types os music, it means that the sum of the numbers inside the 3 circles have to be 569, and it also means that the difference between these freshmen (those inside the 3 circles) and the total freshmen surveyed don't like any of these type of music, so:
692 – 569 = 123 freshmen that don't like these 3 types of music, and this is the slot A
Now, for the slot B, we have to sum all the numbers inside the circles and see how much left to be equal to 569 (the total of freshmen that like at least one of the 3 type of music):
87 + 106 + 63 + 163 + 87 + 24 + B = 569
530 + B = 569
B = 569 – 530
B = 39
And now, the slot C is the number of freshman that don't like rock, so we have to sum all the numbers outside the circle purple:
87 + 106 + 63 + A = C
We know that A = 123, so:
C = 87 + 106 + 63 + 123
C = 379
