If an infinite geometric series is a convergent series then it must have a sum.
What is a convergent series?
If a series' partial sum sequence tends to a limit, it is said to be convergent (or to be convergent)This indicates that as partial sums are added in the order indicated by the indices, they approach closer and closer to a certain number. When a series becomes closer to a particular value as it gets closer to infinity, it is said to be convergent. A series in mathematics is the total of all the terms in an infinite series of numbers.Two forces must be moving in concert for there to be convergence. If a finite real number L serves as the limit of a sequence of real numbers, the sequence is said to be convergent.To learn more about convergent series, refer:
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The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Work out the cost of a) 1 kg of turnips. b) 1 kg of mushrooms. check image
If the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.
Given that the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.
We are required to find the cost of 1 kg of mushrooms and the cost of 1 kg of turnips.
Cost is basically the expenditure that we do in order to buy or produce a product.
Suppose the cost of 1 kg of mushrooms be x and the cost of 1 kg of turnips be y. The equations will be as under:
2x+2.5y=8.55------1
3x+4y=13.10-------2
Equation1 *3 and Equation2 *2.
6x+7.5y=25.65-----3
6x+8y=26.20-------4
Subtract 4 from 3.
6x+7.5y-6x-8y=25.65-26.20
-0.5y=-0.55
y=1.1
Put the value of y in 1.
2x+2.5*1.1=8.55
2x+2.75=8.55
2x=8.55-2.75
2x=5.80
x=2.9
Hence if the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(3, 1) and (5,-2)
8.06 is the distance between the two points .
What is distance in math?
The length or width between two objects, points, lines, etc. the quality or condition of being remote from something else in space; remoteness. a straight line in space It would take too long to walk seven miles in one hour. a big area.A wide body of water encircled the ship.Using their coordinates, an algebraic expression provides the distances between two places (see coordinate system). The distance formulas for points in rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.distance d = [tex]\sqrt{( 5 + 3)^{2} + ( -2 + 1)^{2} }[/tex]
d = [tex]\sqrt{8^{2} + (-1)^{2} }[/tex]
d = [tex]\sqrt{64 + 1}[/tex]
d = √ 65
d = 8.06225 ≈ 8.06
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Help! 25 points! 5h=60. what does h equal to
Answer:
the answer is 12.
Step-by-step explanation:
to find the answer divide 60 by 5 and you'll get the answer (aka 12)
Answer:
12
Step-by-step explanation:
5h=60
h= 60÷5
=12
ans: h=12
Find the geometric mean between each pair of numbers.
8 and 36
A group of products are averaged to determine central tendency using the geometric mean. The geometric mean of 8 and 36 is 6√8.
What is meant by geometric mean?
The geometric mean in mathematics is a mean or average that, by using the product of the values of the numbers, shows the center tendency or usual value of a set of numbers.
The geometric mean, sometimes known as the compounded annual growth rate, is a tool used in finance to determine average growth rates.
The Geometric Mean (GM) is the average value or mean that reveals the central tendency of a group of numbers by adding up the values of those numbers.
Formula to calculate G.M is
x = √(a × b)
Where, a = 8 and b = 36
x = √(8 × 36)
x = 6√8
Therefore, the value of x = 6√8.
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solve for x with explanatory proccess
Answer:
x = -6.8
Step-by-step explanation:
2.4x - 9.1x + 12.5x = -39.44
combine all like terms
5.8x = -39.44
÷5.8 ÷5.8
x = -6.8
I hope this helps!
Four quarter circles are cut out from a 16cm square. Work out the shaded area. Convert your answer to mm^2
the required area of shaded part is 549.3807mm^2
Four quarter circles are cut out from a 16 cm square
that is we have given that square has each side 16 cm
we know that
area of square = (side) ^2
= 16*16 cm^2
= 256 cm^2
four quarter circles are cut out from a 16 cm square
we know that
area of sector = N/360 ( pi *r^2)
= 90/360( pi* 8^2) it makes angle 90 degree and r=8cm
= 1/4( pi* 64)
therefore area of four quarter circles is given by
=4*(1/4)*(64*pi)
=64pi
now the required area of the shaded part is equal to
=area of square - area of four quarter circles
= 256 - 64pi
= 256 - 201.06193
= 54.93807 cm^2
we know that 1cm is equal to 10mm
54.93807*10 =549.3807mm^2
Hence the required area of shaded part is 549.3807mm^2
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While taking a personal finance course, Lakshmi decided to create and follow a personal financial plan. To estimate her annual expenses, she kept track of everything that she spent for one month. She was surprised to discover that she spent $150 on clothing and accessories. If Lakshmi decided to cut her monthly clothing and accessories expenditure in half, how much could she save in a year?
Using proportions, it is found that she would save $900 in a year.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
She spends $150 a month on clothing and accessories, hence, if she saves half of that, the amount saved in a month is:
0.5 x 150 = $75.
In a year, this amount will add up to:
75 x 12 = $900.
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There are different methods to solving this problem. Which do you think is the best? Why? Enter your answer.
The best method to solve a problem is Brainstorming.
According to the statement
We have to find that the which method is the best for solving the problem.
So, For this purpose, we know that the
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem.
From the given information:
There are different methods to solving this problem.
Then
we know that the to solve a problem there are lot of the method, but the some method are the best to solve the problem.
The method is called a brainstorming session.
It is the Brainstorming is a problem-solving activity where students build on or develop higher order thinking skills. Encourages creative thought. Brainstorming encourages students to think creatively.
And due to their special capability it is the best method.
So, The best method to solve a problem is Brainstorming.
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Evaluate the sum of the finite geometric series. 3+6+12+24+48+ . . . +768
The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term. The sum of the finite geometric series 3 + 6 + 12 + 24 + 48 + . . . + 768 is 1533.
What is geometric series?The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term.
The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.
Let the finite geometric series be
3 + 6 + 12 + 24 + 48 +. . . + 768
Where, the first term, a = 3
common difference, r = 6/3 = 2
n = 9
The equation be Sn = a(1 - [tex]$$r^{n}[/tex])/(1 - r)
substitute the values in the above equation, we get
S9 = 3(1 - [tex]$$2^{9}[/tex]))/(1 - 2)
simplifying the above equation, we get
= 3(1- 512)/(-1)
= 3(-511))/(-1)
= 3(511) = 1533
Therefore, the sum of the finite geometric series 3 + 6 + 12 + 24 + 48 + . . . + 768 is 1533.
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Use the given information to determine whether LM is a perpendicular bisector, median, and/or an altitude of ΔJ K L .
JM ≅KM
If JM ≅KM then M is the midpoint of ΔJKL then LM is the median of
JM ≅ KM.
What is the difference between perpendicular bisectors, medians, and altitudes of a triangle?
A perpendicular bisector is a 90° angle line that intersects and passes through the midpoint of a given segment.
The median of a triangle is a line segment that connects a vertex to the midpoint of the opposing side. Each triangle has three medians, one from each vertex, which all intersect at the triangle's centroid.
The altitude of a triangle is a line segment that runs through a vertex and is perpendicular to the baseline.
We know that JM ≅ KM then M is the midpoint of ΔJKL. Therefore, LM is the median of JM ≅ KM.
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Find the value of x for the given values of a and b .
a+8=-4(x-b) , for a=8 and b=3
The value of x so that the equation based on a and b has a solution is x = -4/3
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
As we can see, we have the following equation:
a + 8 = -4(xb)
and we have the values of the coefficients a and b, and these are:
a = 8b = 3We substitute these values in the equation:
(8) + 8 = -4 [x(3)] We solve the equation
16 = -4(3x)
16 = -12x
x = 16-/12
x = 8/-6
x = 4/-3
x = -4/3
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Use the number line below to show 10 + (–6). What is the sum of 10 + (–6)?
Answer:
4
Step-by-step explanation:
when you add a positive number to a negative number you subtract the two instead!
so, rephrase your math problem to
10-6=?
well 4
using the image you go back 6 places and you get 4
Ty plays football at his neighborhood park with his friends. He can make field goals and touchdowns. Field goals are worth 1 point each and touchdowns are worth 6 points each. Ty can no more than 18 points before his neighborhood buddies kick him out of the game for dominating too much.
Write an inequality to describe the constraints.
Use "f" for field goal and "t" for touchdown.
***THE PICTURE IS PART 2***
The inequality that describes the constraints is f + 6t ≤ 18
If Ty has 4 field goals and 3 touchdowns, he cannot remain on the team.
What is the inequality that describes the constraints?Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is ≤ because Ty's score has to be at most 18 points.
The from of the inequality that describes the constraints is:
(point of a touchdown x number of touchdowns) + (point of field goals x number of field goals) ≤ maximum points
(1 x f) + (6 x t) ≤ 18
f + 6t ≤ 18
Ty's total score when he has 3 touch downs and 4 field goals
(1 x 4) + (6 x 3) ≤ 18
4 + 18 ≤ 18
22 ≤ 18
Ty cannot remain on the team because his score exceeds 18. (i.e. 22 > 18).
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HELP ASP SHOW WORK YOULL GET BRAINILEST
Answer:Ill try my best.
The answer is
3rd one
Step-by-step explanation:
subtract 70 from both sides of the equation
.........................................................................................................
Answer:
256
Step-by-step explanation:
20-8=12
12+4=16
16x16=256
Answer:
256
Step-by-step explanation:
Evaluate: 54.25÷6.2−3.8
Answer: 4.95
Step-by-step explanation:
54.25÷6.2−3.8=
54.25/6.2−3.8=
8.75-3.8=
8.75-3.80=
8-3+0.75-0.80=
5-0.05=4.95
You swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder?
IfIf you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.
How much faster or slower is the third lengthFirst step is to calculate the different in speed between first and fourth length
Using this formula
Speed =-First length time in seconds +(- Fourth length time in seconds)
Let plug in the formula
Speed=-0.23+(-0.42)
Speed=-0.65
Second step is to calculate the third length
Speed=-0.65+0.11
Speed=-0.54 seconds
Therefore If you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.
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Ten times the sum of half a number and 6 is 8 in number form
The required no . is ( - 10. 4 ) .
According to ques .
10 * [ ( 1 / 2 ) x + 6 ] = 8
Solving linear equation in one variable above ,
( 1 / 2 ) x = ( 8 / 10 ) - 6
( 1 / 2 ) x = - 52 / 10
x = ( - 52 / 10 ) * 2
x = - 10 . 4
Hence , the no . is ( - 10 . 4 ) .
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Evaluate each logarithm.
log₂ 1/2
Answer:
well done ......hope it's helpful
Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624. Find the amount of his tax.
Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624 the amount paid as tax is $ 3,765.
Given details in the question are as follows:
Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624,
By using the given tax table on the screenshot we are calculating the tax paid by Jim.
if your taxable income is greater than the $23,600 but lesser than the $23,624 and you fill separate tax return, the amount will be paid as tax is
$ 3,765.
what is a separate tax return?Married filing separately is a tax status for married couples who choose to record their respective incomes, exemptions, and deductions on separate tax returns.
The alternative to married filing separately is married filing jointly. Usually, it makes sense financially for married couples to file jointly. However, when one spouse has significant medical expenses or miscellaneous itemized deductions, or when both spouses have about the same amount of income, it might be wiser to file separately.
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A shopkeeper packed two bags of sugar each 120 Kg into 3 Kg and 2 Kg packets respectively. There were half as many 2 Kg packets as 3 Kg packets. How many 3 Kg packets did he obtain?
Answer:
60
Step-by-step explanation:
Since both bags of sugar were 120 kg, there is a total of 240 kg of sugar to be distributed into the packs. Let x represent the number of 2 kg packets and y represent the number of 3 kg packets. We know that all the sugar was packed into these two kinds of packets, so:
[tex]2x+3y=240[/tex]
And we know that there were half as many 2 kg packets as 3 kg packets, so:
[tex]x=\frac{1}{2} y[/tex]
Now, we have a system of equations!
[tex]\left \{ {{2x+3y=240} \atop {x=\frac{1}{2}y }} \right.[/tex]
Let's put the second equation equal to y, since that removes the fraction:
[tex]x=\frac{1}{2}y\\ 2x=y[/tex]
Now substitute y into the first equation:
[tex]2x+3y=240\\2x+3(2x)=240[/tex]
Now simplify to find x:
[tex]2x+3(2x)=240\\2x+6x=240\\8x=240\\x=30\\[/tex]
There are 30 of the 2 kg packets! Now, we can use x to find y, the number of 3 kg packets!
[tex]2x=y\\2(30)=y\\60=y[/tex]
There are 60 of the 3 kg packets!
Which choice could you use to find the distance (d) between the points shown on the number line?
Answer:
d = 380 units
Step-by-step explanation:
Find the absolute value of the difference of the 2 numbers, that is
d = | - 235 - 145 | = | - 380 | = | 380 | = 380
or
d = | 145 - (- 235) | = | 145 + 235 | = | 380 | = 380
How many different 4-digit PIN codes are there that only include the digits 2, 3, 4, 6, 7, 8 and 9
if each of those digits is only allowed to be used once?
The number of different 4-digit PIN codes if each of those digits is only allowed to be used once is 840
How to determine the number of different 4-digit PIN codes if each of those digits is only allowed to be used once?The digits are given as:
2, 3, 4, 6, 7, 8 and 9
There are 7 digits represented in the above list
If each of those digits is only allowed to be used once, then we have the following possibilities
First character: Any of the 7 digits
Second character: Any of the remaining 6 digits
Third character: Any of the remaining 5 digits
Fourth character: Any of the remaining 4 digits
The number of 4-digit PIN codes is
Number = 7 * 6 * 5 * 4
Evaluate
Number = 840
Hence, the number of different 4-digit PIN codes if each of those digits is only allowed to be used once is 840
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Summerfield's zoo has two elephants. The male elephant weighs 7 1/12 tons and the female elephant weighs 1 1/3 tons. How much more does the male weigh than the female?
4.313
Step-by-step explanation:
A grocer is going to sort 13.5 pounds of candy into bags weighing 0.75 pounds each. How much candy will be left over?
Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth. (Lesson 10-1) C=23cm
Answer:
radius: 3.66 Diameter: 7.32
Step-by-step explanation:
Radius = C/2π 3.6605636911136
Diameter = C/2π7.3211273822272
If In triangleABC, (AB)^2 + (BC)^2 = (AC)^2, then triangleABC is a right triangle.
Determine whether this conjecture is true or false and find a counter example if it is false.
The triangle of ABC is a right-angle triangle is true.
In Triangle of ABC
⇒(AC)^2=(BC)^2+(AB)^2 ----equation (1)
given by
Pythagoras theorem,
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
The hypotenuse is the longest side in this situation because it makes an angle of 90°
⇒(hypotenuse)^2=(one side)^2+(other side)^2 ---equation (2)
comparing one (1) and (2)
we get, AC is a hypotenuse of a triangle.
⇒ hypotenuse is the longest side of a right-angled, opposite the right angle.
⇒ opposite angle of AC is ⇒∠ B.
Hence, ∠ B is a right angle of triangle ABC. so, the triangle of ABC is a right angle triangle is true.
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Evaluate the following algebraic expressions when
x = -2, y = -3, z =4
Write the value of the expressions in the boxes
a) 2x+3y
b) 2(y - z)
c) 6x over 2y
This question means you need to divide the top by the value of 2y
Answer:
Solutions below
Step-by-step explanation:
This question requires the concept of substitution and order of operations (Bracket > Multiplication / Division > Addition / Subtraction).
Given x = - 2, y = - 3 and z = 4,
a) 2 x + 3 y = 2 (- 2) + 3 (- 3) = - 4 + (- 9) = - 4 - 9
= - 13
b) 2(y - z) = 2 (- 3 - 4) = 2 (- 7) = - 14
c)
[tex] \frac{6x}{2y} \\ = \frac{6( - 2)}{2( - 3)} \\ = \frac{ - 12}{ - 6} \\ = 2[/tex]
How to factor this? Please help. Question attached
Answer:
(y+4)²
Step-by-step explanation:
[tex](a+b)^2=a^2 + 2ab+b^2[/tex]
Here, a=y and b=4.
Need answers ASAP!!!!
solve the pairs of simultaneous equation x+ 2y =7 and 4x +2y =10
Answer:
Step-by-step explanation:
Okay
x+2y=7
x+2y-2y=7-2y
x=7-2y
4x+2y=10
4x+2y-2y=10-2y
4x=10-2y
divide both sides by 4
4x/4=(10/4)-(2y/4)
x=(5-y)/2
Hope this helps! ^^
