The sum of the given series is 50
The summation notation or sigma notation is used to simplify the writing of long summation into a single formula.
The given series in sum notation is:
[tex]\sum\limits^5_{n=1} {(3n+1)}[/tex]
Substitute n = 1 ...5 into the nth term formula inside the sum notation:
a(1) = 3 . (1) + 1 = 4
a(2) = 3. (2) +1 = 7
a(3) = 3. (3) +1 = 10
a(4) = 3. (4) +1 = 13
a(5) = 3. (5) +1 = 16
Hence, the series:
4 + 7 + 10 + 13 + 16
We can evaluate the sum directly by adding all the terms:
S(5) = 4 + 7 + 10 + 13 + 16 = 50
Or we can also use the sum formula of an arithmetic series:
S(n) = n/2 [a(1) + a(n)]
For n = 5
S(5) = 5/2 (4 + 16)
S(5) = 5/2 . 20 = 50
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The sum of k and 8 __ k + 8 ___
The algebraic expression of the mathematical statement is given as "The sum of k and 8" is k + 8
How to represent the mathematical statement as an algebraic expression?The mathematical statement is given as:
The sum of k and 8
In algebraic expression, "Sum" means +
This means that, the interpretation of the question is that we add k and 8
So, we have the following algebraic representation:
The sum of k and 8 ⇒ k + 8
Remove the mathematical statement in the above algebraic representation
i.e. k + 8
Hence, the algebraic expression of the mathematical statement is given as "The sum of k and 8" is k + 8
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I will mark BRAINLIEST AND GIVE EXTRA POINTS TO WHOEVER ANSWERS
I really don't understand this please help meh thanks :)
Write down the Equation
Answer:
[tex]2 \sqrt{45} [/tex]
Answer: (1) y= 2*4-1
(2) y= 2*0-1
Step-by-step explanation:(1) y=8-1
y=7
(2) y=0-1
y= -1
This is for physical science
You call your parents to explain your issue with having a smashed phone and your parents travel at 0 meters in 2.5 hours. How fast did your parents rush to get here?
After calling the parents, and explaining them the issue of smashed phone, they travelled at a speed of 2.223 m/s = 8.0028 km/hr
As per the question statement, we are given that we call our parents to explain our issue with having a smashed phone and your parents travel at 20000 meters in 2.5 hours. We are supposed to find out that how fast did the parents rush to get here. Basically we have to find their speed of travelling.
Before solving the question, we must be aware that what is speed.
[tex]speed = \frac{distance}{time}[/tex]
and distance and time should be in SI units.
Given distance = 20,000 meters
Given time = 2.5 hours
[tex]1 hour = 60 min\\2.5 hour = 2.5*60\\2.5 hour = 150 min[/tex]
[tex]1 min = 60 sec\\150 min = 150*60 sec\\150 min= 9000 sec[/tex]
Therefore given time = 9000 sec
Therefore speed = [tex]\frac{distance}{time} = \frac{20000}{9000}[/tex]
Speed= 2.223 m/sec
Hence they travelled at a speed of 2.223 meters per second
2.223 m/s = 8.0028 km/hr
Speed: The speed it the distance covered by an object or body or person per unit time or time taken by him/her to cover the given distance. SI Unit: [tex]m/sec[/tex]To learn more about speed, distance and time, click on the link given below:
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Please help. im in need
3*3=9
4*3=12
9*12=108 sq feet
In+terms+of+resale+value,+is+remodeling+a+kitchen+worth+the+cost?+at+the+5%+significance+level,+what+can+you+conclude?
The resale value is not significantly higher than the cost of remodeling a kitchen based on the computed p-value of 0.42 and 0.21.
What is the null hypothesis?Any variation between the selected attributes that you observe in a collection of data is thought to be the result of chance, according to the null hypothesis.For instance, any discrepancy between the average profits in the data and zero is caused by chance if the expected earnings for the gambling game are actually equal to zero.An assertion that there is no correlation between two population measures is referred to as a null hypothesis.To prepare the ground for additional experimentation or study that explains the position of interest, researchers reject or refute the null hypothesis.Both the p-values of 0.42 and 0.21 are greater than the level of significance of 0.05. Hence, we fail to reject the null hypothesis. So, the resale value is not significantly higher than the cost of remodeling a kitchen based on the computed p-value of 0.42 and 0.21.
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2. Find the midpoint of AB
given A(-3, 8) and B(-7, -6).
Answer:
the midpoint is (-5,1)
Step-by-step explanation:
How is -89 represented using 8-bit two's compliment? (the answer should be 8 binary digits)
-89 can be represented by using 8-bit two's compliment as 10100111.
What is binary encoding?Binary encoding can be defined as a standard technique that is designed and developed to convert data in plain text (source alphabets) to a form that is easily used by different operating systems (OS), especially through the use of a binary digit (bit) or two-symbol system.
In Computer programming, two's complement of base-10 is generally easier to implement because it has a single representation of 0 only.
How to convert a binary (base-10) to decimal (base-2)?First of all, we would determine the positive version of -89, which is 89:
2 | 89
2 | 44 R 1
2 | 22 R 0
2 | 11 R 0
2 | 5 R 1
2 | 2 R 1
2 | 1 R 0
2 | 0 R 1
Next, you would read the decimal number (base-2) upward and this gives:
89₂ = 01011001.
For the negative integer number representation on 8-bits, we would replace all the 0s with 1s and the 1s with 0s as follows:
01011001 = 10100110
For the 8-bit two's complement, we would add 1 to the above number:
-89 = 10100110 + 1
-89 = 10100111.
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Bronson is creating a right triangular flower bed. If two of the sides of the flower bed are 7 feet long each, what is the length of the third side to the nearest foot?
The length of the third side of the right triangular flower bed is 10 feet.
A right-angled triangle is a triangle with one of its interior angles equal to 90°. The side opposite to the right angle is the largest side and is referred to as the hypotenuse. Hypotenuse is always greater than any of the other two sides.
If two of the sides of the flower bed are 7 feet long each, then these are the sides adjacent to the right angle. We are to find the length of the third side, which is the hypotenuse, using the Pythagorean theorem.
Pythagorean Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two other sides.
c^2 = a^2 + b^2
where a and b are the adjacent sides to the right angle
c is the hypotenuse
c^2 = 7^2 + 7^2
c^2 = 49 + 49
c^2 = 94
c = 9.899
Hence, he length of the third side of the right-angled triangular flower bed is 10 feet.
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A 36-inch diameter pie is cut into 6 slices. What is the area of one of the slices?
A. 54pi inches
B. 216pi inches
C. 6pi inches
D. 24pi inches
E. None of the above
The area of one of the slices is 54π square inches
What is the area of one of the slices?The given parameters are
Diameter = 36 inches
Number of slices = 6
The pie represents take the shape of a circle
And the area (A) of a circle using the diameter (d) is
A= π(d/2)^2
Multiply the above area by 1/6 to get the area of a slice of the pie
So, we have
Area = 1/6 * π(d/2)^2
This means that the area of one of the slices is calculated by
Area = 1/6 * π(d/2)^2
Where
d represents the diameter of the pie i.e. d = 36 inches
So, we have
Area = 1/6 * π * (36/2)^2
Evaluate
Area = 54π
Hence, the area of one of the slices is 54π square inches
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The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
A basketball player plays 2, 181 minutes the first year of his career, 2, 583 minutes the second year of his career, and 2, 716
minutes the third year of his career. How many minutes has he played in three years?
He played 7480 minutes across three years.
The information provided, expressed in minutes per year, is as follows:
The first year is 2181 minutes, the second is 2583 minutes, and the third is 2716 minutes.
Add that now to determine the total amount of time:
The sum of the three years is 7480 minutes (2181 + 2583 + 2716).
The gamer used 7480 minutes throughout the course of three years.
How much time in total?The measurement of continuously occurring events is done in terms of time. In hours, seconds, and minutes, it is measured. The well accepted established formulae can be used to compute it.
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14 < -2a + 6-2a
What is the inequality
Answer:
a < -2.
Step-by-step explanation:
14 < -2a + 6-2a
14 < -4a + 6
14 - 6 < -4a
-4a > 8
Divide both sides by -4:
a < -2.
Note that the inequality flips because we are dividing by a negative number.
find the exact length of the line segments whose endpoints are (10, 1) and (9, -4)
The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37
How to find the exact length of the line segments whose endpoints are (10, 1) and (9, -4)?The points are given as (10, 1) and (9, -4)
The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is calculated as
d = √[(x2 - x1)^2 + (y2 - y1)^2]
So, we have
d = √[(10 - 9)^2 + (1 + 5)^2]
Evaluate
d = √37
Hence, the exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37
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Evaluate each expression 2^6
Answer:
64
Step-by-step explanation:
2^6=2x2x2x2x2x2 which then equals to 64
Write the equation of the line in slope-intercept form.
3y+9=-6x
The equation of the line in slope-intercept form is y = (-2)x + (-3) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is 3y + 9 = -6x .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
3y + 9 = -6x
3y = -6x - 9
On dividing both sides of above equation by 3, we will get
y = (-2)x + (-3) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = -2
Intercept = c = -3
The equation of the line in slope-intercept form is y = (-2)x + (-3) .
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Solve the quadratic equation by compeleting the square. x^2 + 8x = 10
The value of x for the quadratic equation is 1.099 or -9.099 .
What is completing the square?
Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .
To solve ax²+bx+c=0 by completing the square:
1. Transform the equation so that the constant term, c , is alone on the right side.
2. If a , the leading coefficient (the coefficient of the x² term), is not equal to 1 , divide both sides by a .
3. Add the square of half the coefficient of the x -term, to both sides of the equation.
4. Factor the left side as the square of a binomial.
5. Take the square root of both sides. (Remember: (x+q)²=r is equivalent to x+q= ±√ r.)
6. Solve for x .
According to the question
Quadratic equation by completing the square
x² + 8x = 10
As we will try to make complete square of left side
for that
we have to add to both sides of the equation
As
a = 1
2ab = 8
b = 4
x² + 8x + 4² = 10 + 4²
By using the identity ( )
(x + 4)² = 10 + 16
(x + 4)² = 26
x + 4 = ±
x + 4 = ± 5.099
x = 5.099 - 4
x = 1.099
or
x = -5.099 - 4
x = -9.099
Hence, The value of x for the quadratic equation is 1.099 or -9.099 .
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The equation for the change of position of a train starting at x = 0 m is given by . the dimensions of b are what?
It involves determining the fundamental quantities and units of measurement and tracking these dimensions while computations or comparisons are made.
What is meant by Dimensional Analysis?Dimensional analysis is the study of the relationships between various physical quantities in engineering and science. It involves determining the fundamental quantities and units of measurement and tracking these dimensions while computations or comparisons are made. Dimensional Analysis is a problem-solving technique that makes use of the fact that any number or statement may be multiplied by one without changing its value. It is also known as the Factor-Label Method or the Unit Factor Method.Now, in that equation above, b represents the velocity of the motion. Now, the formula for velocity is;
Velocity = Distance/Time
Now, distance is also named Length and represented by L in basic parameters units while Time is represented by T.
Thus, the dimensions of b are; L/T or expressed as LT⁻¹.
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331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? Create equation here.
The required equation is 6x+7=331 and the no. of students traveling on each bus is 54.
What is an equation?A mathematical equation can be defined in a variety of ways. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. One or more variables are used in the most basic and simple algebraic equations in mathematics.
Given data:
Total no. of students: 331
Number of students on bus = 7
No. of buses = 6
Let the no. of the students on each bus be x.
So according to the given condition,
6x+7=331
6x=331-7
6x=324
x=324/6
x=54
Therefore, the required equation is 6x+7=331 and the no. of students travelling on each bus is 54.
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Priya has some money to spend at a fair. It costs $6 to get in and $0.50 per ride ticket. Write an expression to represent how much Priya spends at the fair, in dollars. Let `x` represent the number of ride tickets Priya buys.
Answer
.50x + 6
If you need a step-by-step explanation or just the explanation tell me
WILL MARK BRAINLIEST + 50 POINTS!
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion. 16/x = 0
the equation has
a. no solutions
b. infinite solutions
c. one solution
A value of a that makes the equation false is ____, which when substituted into the equation and simplified makes the equation turn into ____=_____ Another value of x that makes the equation false is _____, which when substituted and simplified makes the equation turn into ____=____
Answer:
Part 1: The equation has no solution
Part 2: A value of a that makes the equation false is 2, which when substituted into the equation and simplified makes the equation turn into 2=4.
Another value of a that makes the equation false is -1, which when substituted and simplified makes the equation turn into -1=1.
There are honestly a lot of possible values for x for the second part here, but let me know if this is right
Step-by-step explanation:
Give me brainliest if that helped :)
Instructions for roasting meat: Cook for 30 minutes at 230°C. Turn down the heat to 180 °C. Allow 30 minutes cooking time for every 450g. A piece of meat takes 2 hours altogether to cook. How heavy is it?
The piece of meat has a weight of 1,800g.
What is the definition of a mathematical operation?The principle of superposition denotes a mathematical operation (e.g., differentiation, multiplication by a constant) in which the action on the sum of two functions is the sum of the action on each function.So, as the question says allow 30 minutes of cooking to each 450g.
Total time is taken = 2 hours.30 × 4 = 120 minutes is, 2 hours.Similarly,
450 × 4 = 1,800Therefore, the piece of meat has a weight of 1,800g.
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Answer:
1800
Step-by-step-explanation:
Find the measure of the missing angle
Answer: 55 degrees
Step-by-step explanation:
a+90+35=180 ==> a straight line measures 180 degrees and the angles a, a right angle, and 35 lie on that line. A 180 degree angle is called a straight angle. Also, if there is a tiny box in between an angle, that means that the angle is a right angle.
a+125=180
a+125-125=180-125
a=180-125
a=55 degrees
Write an explicit and a recursive formula for each arithmetic sequence. 17,8,-1, . . . . .
For sequence: 17,8,-1, ., the explicit formula is a(n) = 26 - 9n, the recursive formula is a(n) = a(n-1) - 9
To find the recursive and explicit formula, we need to find the common difference (d) first.
In an arithmetic sequence, the common difference is the difference between two consecutive terms.
So, in the given sequence: 17,8,-1, ..
d = a(2) - a(1) = a(3) - a(2)
d = 8 - 17 = -1 - 8 = -9
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(0,7) (1,5) (-1,13)
How to find the quadratic equation given only these points (standard form)
Answer:
(x - 1)^2 =1/2 ( y - 5) or 2x^2 - 4x - y + 7 = 0
Step-by-step explanation:
(x - 1)^2 =1/2 ( y - 5)
or
x^2 - 2x + 1 = y/2 - 5/2
2x^2 - 4x + 2 - y + 5 = 0
2x^2 - 4x - y + 7 = 0
Summit (1,5) = (h,k)
4p = 2
p = 1/2
(x - h)^2 = 1/2(y - k)
First person to answer gets brainliest!
Please give me a step-by-step explanation for question m).
No links are allowed, and will be blocked. ❌
Answer:
Step-by-step explanation:
10² + 2(6 - 3)²
100 + 2 (3)²
100 + 2(9)
100 + 18
118
Given f(x)= 4 x 2 + 3, find the value of f(−1)
[tex]f(x) = 4x^2+3\\f(-1)=4(-1)^2+3\\f(-1)=\boxed{7}[/tex]
Draw a rectangle that has a diagonal twice as long as its width. Then write an equation to find the length of the rectangle.
The drawing of rectangle that has diagonal twice as long as its width is attached with this.
The equation for the length of the rectangle is l = [tex]\sqrt{3} x[/tex]
Given,
Width of rectangle, w= x
Diagonal of rectangle, d = 2x
We have to find the equation for length of rectangle.
We know that d² = l² + w²
Here,
(2x)² = l² + x²
4x² = l² + x²
l² = 4x² – x²
l² = 3x²
l = [tex]\sqrt{3}[/tex]x
That is the equation for length of rectangle is l = [tex]\sqrt{3}[/tex]x
Lets take width of rectangle, x = 3
Diagonal of rectangle, d = 2 × 3 = 6
L = [tex]\sqrt{3}[/tex] × 3 = 5.20
Here we proved that the equation is correct.
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Simplify these ratios: a 24:36 b 12:2
c 16:4 d 18:3
Answer: 2:3, 6:1, 4:1, 6:1
Step-by-step explanation:
The first step is by finding the GCF. For 24:36 the GCF is 12. Once you divide you get 2:3. For 12:2 the GFC is 2. For 16:4 it is 4 and you get 4:1 and finally 18:3 the GCF is 3 and you get 6:1.
x-y=4 et xy=21 calculer x^3-y^3
Answer:
316 or -316.
Step-by-step explanation:
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
= 4(x^2 + y^2 + 21)
x - y = 4
xy = 21
Substitute x = 4 + y in the last equation
(4 + y) y = 21
y^2 + 4y - 21 = 0
(y + 7)(y - 3) = 0
y = 3, -7.
So, x = 7, - 3.
So, x and y are 7 and 3 or -7 and -3.
But x^2 + y^2 = 9 + 49 = 58 whichever is true,
So, x^3 - y^3
= 4(x^2 + y^2 + 21)
= 4 (58 + 21)
= 316,
If x = -3 and y = -7 , then the answer is
-316.
Aisha is working two summer jobs, making $7 per hour babysitting and $8 per hour
landscaping. Last week Aisha worked 2 more hours babysitting than hours
landscaping and earned a total of $134. Write a system of equations that could be used to determine the number of hours Aisha worked babysitting last week and the number of hours she worked landscaping last week.
The number of hours Aisha worked babysitting and landscaping last week is 7.9 hours and 9.9 hours respectively.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given that Aisha is working two summer jobs, making $7 per hour babysitting and $8 per hour landscaping
Let the number of hours babysitting would be x
And the number of hours landscaping would be y
Last week Aisha worked 2 more hours babysitting than hours landscaping and earned a total of $134.
y = x + 2
7x + 8y = 134
Substitute the value of y = x + 2 in the equation,
7x + 8(x + 2) = 134
7x + 8x + 16 = 134
15x = 134 - 16
15x = 118
x = 118/15
x = 7.9
Substitute the value of x = 7.9 in the equation y = x + 2 ,
y = 7.9 + 2
y = 9.9
Therefore, the number of hours Aisha worked babysitting and landscaping last week is 7.9 hours and 9.9 hours respectively
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Answer:
(x,y)=(10,8)
Step-by-step explanation:
Let x be hours worked babysitting and y be hours worked landscaping.
We would have our first equation, 7x+8y=134.
Knowing that she worked 2 more hours babysitting than landscaping, we can determine and replace the x variable as: x=y+2
7(y+2)+8y=134
Use the distributive property to multiply 7 by y+2.
7y+14+8y=134
Combine 7y and 8y to get 15y.
15y+14=134
Subtract 14 from both sides.
15y=134−14
Subtract 14 from 134 to get 120.
15y=120
Divide both sides by 15.
y=120/15
Divide 120 by 15 to get 8.
y=8
and since she worked 2 more hours babysitting, x=10.
Let's replace our values in the original equation:
7x+8y=134
7(10)+8(8)=134.
70+64=134.
Therefore, we can conclude that Aisha worked 10 hours babysitting and 8 hours landscaping last week.
Hope this helped!
