The sum of finite arithmetic series 10+20+30+ . . . . . +110+120 is 780
Suppose we are given an arithmetic series:
a(1) + a(2) + a(3) + ... + a(n)
The sum of the first nth terms is given by:
S(n) = n/2 [a(1) + a(n)]
Where:
a(1) is the first term and a(n) is the nth term.
The given series is:
10+20+30+ . . . . . +110+120
We get, then,
a(1) = 10
a(n) = 120
To find n, recall the formula of the nth term of an arithmetic sequence:
a(n) = a(1) + (n-1) . d
where d is the common difference.
From the given series, we get:
d = 20 - 10 = 10
Substitute a(1) =10, d = 10, and a(n) = 120 into the formula:
120 = 10 + (n-1) . 10
120 = 10 n
n = 12
Substitute n = 12 into the sum formula:
S(n) = n/2 [a(1) + a(n)]
S(12) = 12/2 (10 + 120)
= 6. 130 = 780
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Three divers kept track of the number of crabs they've seen this year.
Diver Crabs observed Dives
Scuba Sam 33 11
Wet Suit Willy 81 18
Deep Diving Dan 104 26
Which diver saw the most crabs per dive?
Choose 1 answer:
The diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.
What is an average?An average is a mean or the central value obtained by dividing the sum of all data values by the number of data values.
Data and Calculations:Diver Crabs observed Dives Average Crab per dive
Scuba Sam 33 11 3
Wet Suit Willy 81 18 4.5
Deep Diving Dan 104 26 4
Thus, the diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.
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Eileen is 3y years old now. Her mother is 4 times as old as her. Find their total age in 7 years' time. Give your answer in terms of y.
Answer:
15y+14
Step-by-step explanation
Answer: 14 + 15y
Step-by-step explanation:
E = Eileen’s age = 3y
M = Mum’s age
Total Age = 14 + 3y + 4(3y)
= 14 + 15y
Total age in 7 years time is their current ages plus 7 years for each (14 years)
Eileen is 3y, and her mum is 4 times that, which is 12y, meaning that their total ages are 3y + 12y, or, 15y.
Total age is then 15y + 14. Since we don’t know what y equals, we cannot add these two terms, and we can just leave them like that!
So, the answer is 14 + 15y.
Given two functions
F(x) = 2x+1 and G(X) = x^2-40
Find f(-4) + g(-7)
Answer:
f(-4) = -7
g(-7) = 9
Step-by-step explanation:
f(x) = 2x + 1
f(-4) = 2(-4) + 1 = -8 + 1 = -7
g(x) = x^2 - 40
g(-7) = (-7)^2 - 40 = 49 - 40 = 9
Please help with this answer! Thank you so much guys really thanks
How do you solve 9=x+3/5 when the x and 3 are together above the five?
Answer:
x = 42
Step-by-step explanation:
9*5 = x+3/5*5
45 - 3= x+3 - 3
42 = x
UR WELCOME
A chemist is heating water so it can dissolve a larger amount of sodium chloride. The water's temperature increases 7°C each minute from an initial temperature of 21°C. How long will it take for the water to reach 49°C? Write and solve an equation to find the answer.
The time taken by the water to reach 49 degree Celsius is 4 minutes.
According to the question, larger amount of sodium chloride is dissolved in the heating water. And the given data states that the water temperature increases 7 degree Celsius every minute.
Initial temperature of water is 21 degree Celsius.
Let us assume, water reaches at 49° C after 'm' minutes.
As per question, every minute temperature increases as 7°C. So, the expression can be written as: (21 + 7m)°C
⇒ 21 + 7m = 49
⇒m = 4 minutes.
Hence, the time taken to reach 49° C is 4 minutes.
What is temperature?
Temperature defines the atmosphere hotness. And it is expressed in different scales as well as in different parameters like Celsius etc. It is measured through the device known as thermometer.
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What is f(-3) for the function f(x)=-3 x+6 ?
The value of f(-3) is 15.
The given function is f(x) = -3x+6. Now, f(-3) = x = -3
Substituting and Evaluating the value of x in the equation f(x) = -3x+6, we get
f(-3) = -3(-3)+6f(−3)=−3(−3)+6
f(-3) = 9+6f(−3)=9+6
f(-3) = 15f(−3)=15
∴ The value of f(-3) for the function f(x) = -3x+6 is equal to 15.
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PLs solveg g g g g g g g g g g g
Answer:
4°=1
g g g g g g g g g g
Step-by-step explanation:
5. A city has a population of 350,000.
The
population has decreased by 30% in the past
ten years. What was the population of the city
ten years ago?
The population of city 10 years ago before 30% decrease in population was 500,000
In the given statement is :
A city has a population of 350,000.The population has decreased by 30% in the past ten years.
The formula for calculating the percent change between two values over the time is given by:
[tex]p=\frac{A-B}{B}[/tex]×[tex]100[/tex]
where,
'p' represents the percent change
'A' represents the New value
'B' represents the Old value
Since, p is the percent (decreased) = -30
Substitute the given values and solve for B;
then;
[tex]-30=\frac{350,000-B}{B}[/tex] × 100
Divide both sides by 100 we get;
[tex]-0.3=[/tex] [tex]\frac{350,000-B}{B}[/tex]
By cross multiply we get;
-0.3B = 350,000 - B
Add both sides B, we get
-0.3B + B = 350,000
0.7B = 350,000
Divide both sides by 0.7 we get;
B = 500,000
Therefore, The population of city 10 years ago before 30% decrease in population was 500,000
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Coordinates of the y- intercept
Answer:
(0, - 9 )
Step-by-step explanation:
the y- intercept is where the line crosses the y- axis
the line crosses the y- axis at (0, - 9 ) and is the y- intercept
If the measure of angle 1 = (7x-19), and the measure of angle 2 = (x+5) find the measure of angle 2
We can say that if the measure of angle 1 = (7x-19), and the measure of angle 2 = (x+5), then the measure of angle 2 is 18°.
Define supplementary angle.
Supplementary angles are those two angles whose sum is always equal to 180 degrees.
Mathematically, a supplementary angle is calculated as follows:
Q + R = 180
Since the angles on this line segment are supplementary angles, we have:
Angle (1) + Angle (2) = 180° - Angle 3
Substituting the given values into the formula, we get;
7x - 19 + x + 5 = 180 - 90
8x - 14 = 90
8x = 90 + 14
8x = 104
x = 104/8
x = 13
Now, we can calculate the length of angle 2 by putting the 'x' value:
Angle 2 = x + 5
Angle 2 = 13 + 5
Angle 2 = 18°
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20 POINTS
If f(x) = x - 5, what is the value of x when f(x) = 15?
10
20
5
0
Answer: The value of x is 20.
Algebraic function :
Given function is,
We have to find the value of x when
The value of x is 20.
Step-by-step explanation: hope this helps
Peter bought three items at a store. Here are their prices (in dollars):
18.23, 6.39, and 15
What is the total amount Peter paid at the store? Do not round your answer.
$____
Type your numerical answer below.
-
Answer: $39.62
Step-by-step explanation: To get the answer to the cost of Peter's three items, I took the prices of the three and added them together. This amount would be the amount he paid WITHOUT TAX.
Please help (show steps too)
Answer:
5
Step-by-step explanation:
[tex]d=\frac{|-3(5)-4(5)+10|}{\sqrt{(-3)^2+(-4)^2}}=5[/tex]
Find 1, 305 x 81. Then estimate to check your answer.
A. 1, 305 x 81 = 85, 705 Check: 1,000 × 8 = 80,000
B. 1, 305 x 81 = 105, 705. Check: 1,400 x 90 = 12, 600 :
C. 1,305 x 81 = 105, 705 Check: 1, 200 × 80 = 96,000
D. 1, 305 x 81 105, 705 Check: 1,300 x 80 = 104, 000
the estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104,000 and Actual 1,305 × 81 = 105,706
The correct option is D.
In the given statement is:
Find 1, 305 x 81. Then estimate to check your answer.
The estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104000 and Actual 1,305 × 81 = 105706
How to estimate and then compute the product check that your answer is reasonable?
The product expression is given as
1,305 × 81
As an estimate, we have
1305 = 1300
81 = 80
So, we have:
1,305 × 81 ≈ 1300 * 80
Evaluate the product
1,305 × 81 ≈ 104000
For the actual product, we have
The estimate and the actual product both approximate to 100000
Hence, the estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104,000 and Actual 1,305 × 81 = 105,706
The correct option is D.
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If f + j = 115 and j+k= 103 what is the value of j
The value of j is j = 103 - k = 115 - f.
A collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.
Consider the two equations,
f + j = 115 ----------------------(1)
j + k = 103 ----------------------(2)
Consider equation (2),
j + k = 103
Subtracting k from each side of the equation.
j + k - k = 103 - k
j = 103 - k
Consider equation (1),
f + j = 115
Subtraction f from each side of the equation,
f + j - f = 115 - f
j = 115 - f
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Identify the property illustrated by the equation.
5+(-5)=0
Identify the property illustrated by the equation.5+(-5)=0 Additive Inverse
What is an additive Inverse ?
The number that produces zero when added by -a is known as the additive inverse of a number, or a, in mathematics. The opposite, a shift in the sign, and negation are other names for this number.The definition of the additive inverse, which permits a wide application to mathematical objects other than numbers, is its inverse element under the binary operation of addition.Double additive inverse has no net effect, as with any inverse operation: −(−x) = x.To learn more about additive inverse, refer:
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What is the equation of the line that passes through the point (-2,-1)(−2,−1) and has a slope of 5/2
The equation of line having slope of 5/2 is given as 2y -5x = 8.
What is termed as the equation of line in point-slope form?A line's equation written in point slope form is (y - y₁) = m(x – x₁).When the line passing through the origin the equation of a line with slope m is: y - 0 = m(x = 0), i.e. y = mx.where m is the slope and (x₁, y₁) are the coordinates passing point on the line .As, per the given question;
The slope of the line is given as; m = 5/2
The coordinates of the passing points (-2, -1).
Thus, (x₁, y₂) = (-2, -1).
The equation of the becomes.
(y - y₁) = m (x – x₁)
Put the values;
y - (-1) = (5/2)(x - (-2))
Simplifying
y + 1 = (5/2)(x + 2)
2y + 2 = 5x + 10
2y -5x = 8
The equation of line is calculated as 2y - 5x = 8.
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i need help please
Y=CD-8 for C
Answer:
c = (y+8)/d
Step-by-step explanation:
I WILL MARK BRAINLIST!!! PLEASE HELP ITS MATH QUESTION Determine the approximate value of x using basic trigonometry.
Thank you so much for helping !
Step-by-step explanation:
I'm not sure but this is the solution hehe
The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
r = x/8,d= ___, C=?
A circle is a curve sketched out by a point moving in a plane. The diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that radius of the circle is x/8 units. Therefore, the diameter and the circumference of the circle can be written as,
Diameter of circle = 2 × (Radius of the circle)
= 2 × (x/8) units
= x/4 units
Circumference of circle = 2 × π × (Radius of the circle)
= 2 × π × (x/8) units
= (x/4)π units
Hence, the diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
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(PLEASE HELP!!)
Solve the following system of equations using either Gaussian elimination or a matrix. Write your answer as a point and explain how you would check your work:
2xy + 4z = 33
x + 2y - 3z = -26
-5x - 3y + 5z = 23
Using Gaussian elimination, the solution to the given system of equations is given as follows:
x = 5, y = -11, z = 3.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the equations are given as follows:
2x - y + 4z = 33.x + 2y - 3z = -26.-5x - 3y + 5z = 23.(I suppose there was a typing mistake on the first equation, as Gaussian elimination can only be applied to solve linear systems).
For Gaussian elimination, the first step is building the matrix of the system, in which:
The first three columns contain the coefficients of x, y and z, respectively.The last column contains the results of the operations.Hence, the matrix of the system is given as follows:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]
Then, we need to make the coefficient of x zero in the second and third rows, hence:
R2 -> 2R2 - R1.R3 -> 5R1 + 2R3.Then the matrix will be given by:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]
Now we need to make the coefficient of y on the third row zero, hence:
R3 -> 11R2 + 5R3.
Then:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]
From the third row, we have that:
40z = 120
z = 120/40
z = 3.
From the second row, we have that:
5y - 10z = -85
5y - 30 = -85
5y = -55
y = -11.
From the first row, we have that:
2x - y + 4z = 33
2x + 11 + 12 = 33
2x = 10
x = 5.
Hence the solution of the system is given by:
x = 5, y = -11, z = 3.
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Which is the first step in simplifying the expression 2(x 3) 5? 2x 2(3) 5 2x 3 5 2 x 3 5 2(5) x 3
The first step in simplifying the expression 2(x+3)+5 = 2x+2(3)+5.
Given expression in 'x' is 2(x+3)+5.
In order to simplify this expression, we need to expand it by opening the parenthesis. That is, we need to distribute 2 over (x+3) first. For this we multiply 2 into (x+3) and then only we can add 5 to it.
So, 2(x+3) +5 = 2x + 2(3) +5
= 2x +6 +5
= 2x+11
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Find the sum of each finite series. Σ¹° n = 5 (20-n)
The sum of the given finite series is 75
The given series is:
[tex]\sum\limits^{10}_{n=5} {(20-n)}}[/tex]
To find the sum of this series,
Expand the summation notation by using the properties of sum operator:
Σ(a+b) = Σa + Σb
Hence,
[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]
If a is a constant, then Σa = k. a, where k is the number of terms = upper limit - lower limit + 1
Using this property:
[tex]\sum\limits^{10}_{n=5} {20} = (10 - 5+1)\times20=6\times20=120[/tex]
Expand
[tex]\sum\limits^{10}_{n=5} {n}=5+6+7+8+9+10=45[/tex]
Hence,
[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]
= 120 - 45 = 75
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find the value of x
2x+5=6x-3
Answer:
Step-by-step explanation:
2x+5=6x-3
subtract 6x
2x-6x+5=6x-6x-3
-4x+5=-3
subrtract-5
-4x+5-5= -3-5
-4x=-8
divide-4
-4x÷-4=-8÷-4
x=2
Lee is laying out a design for the tiles of a section of his bathroom floor. he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design. how many of each type of tile will lee use?
If Lee is laying out a design for the tiles of a section of his bathroom floor and he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design then the number of white and black tiles Lee will use is equal to 4 and 24 respectively.
The number of white and black tiles Lee will use can be determined by using an algebraic expression.
As 1 white tile is used for every 6 black tiles, an algebraic expression can be represented as,
x + 6x = 28
By solving the value of x, the number of each type of tile that Lee will use can be calculated,
x + 6x = 28
7x = 28
x = 28 ÷ 7
x = 4
As there is one white tile for every six black tiles,
White tiles = 1(x) = 1(4) = 4
Black tiles = 6(x) = 6(4) = 24
Hence the number of white tiles Lee will use is equal to 4 and the number of black tiles Lee will use is equal to 24.
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Find the value of x.
Answer:
43
Step-by-step explanation:
the plane is 180 degrees
subtract 2x4
172
divide by 4
43
BOOM
Amy is paddling her canoe across a lake at a speed of 10 feet per second headed due north. The wind is blowing 40°C east of north with a velocity of 2.8 feet, per second. What is Amy's resultant velocity? Express your answer as a vector. Show your work.
The resultant velocity is about 12.3 feet per second at a heading of 8.4°east of north, <1.8, 12.14>
In this question,
Amy is paddling her canoe across a lake at a speed of 10 feet per second headed due north.
The wind is blowing 40°C east of north with a velocity of 2.8 feet, per second.
We need to find Amy's resultant velocity.
We write the direction vector for Amy in component form.
Due north is equivalent to 90° from the horizontal.
x-component:
x = 10 cos(90°)
x = 0
And y-component:
y = 10 sin(90°)
y = 10
The component form for Amy’s vector is <0, 10>.
Now we write the direction vector for wind in component form.
40 east of north is equivalent to 50° from the horizontal.
x-component:
x = 2.8 cos(50°)
x = 1.8
And y-component:
y = 2.8 sin(50°)
y = 2.14
The component form for the wind’s vector is <1.8, 2.14>
Add the vectors for Amy and the wind.
<0, 10> + <1.8, 2.14> = <1.8, 12.14>
Now, we determine the vector's magnitude by using Pythagoras theorem.
Let v be the velocity of Amy.
Let θ be the angle made by Amy with the horizontal
⇒ tan(θ) = |y/x|
⇒ tan(θ) = |12.14 / 1.8|
⇒ θ = 81.6°
81.6° with the horizontal is equivalent to 8.4° east of north.
Therefore, the resultant velocity is about 12.3 feet per second at a heading of 8.4°east of north, <1.8, 12.14>
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Find the coordinates of the midpoint of the segment with the endpoints (5, 24) and
(-1, 10).
5x-48=-3x+8 solve for x
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
[tex]5x + 3x = 8 +48[/tex]
⬇️
8x = 8 + 48
⬇️
8x = 56
Divide both sides of the equation by the coefficient of the variable;
[tex]x = \frac{56}{8}[/tex]
Cross out common factors;
[tex]x=7[/tex]
