The [tex]n[/tex]-th term [tex](n\ge1)[/tex] in the series is evidently
[tex]\dfrac{2n-1}{(2n-1)!} = \dfrac{2n-1}{(2n-1)(2n-2)!} = \dfrac1{(2n-2)!}[/tex]
By the ratio test, the infinite series converges, since
[tex]\displaystyle \lim_{n\to\infty} \left| \frac{\frac1{(2(n+1)-2)!}}{\frac1{(2n-2)!}}\right| = \lim_{n\to\infty} \frac{(2n-2)!}{(2n)!} = \lim_{n\to\infty} \frac1{2n(2n-1)} = 0 < 1[/tex]
What is the solution (a, b) to this system of linear equations? 3a 6b=45 2a-2b=-12 (-27, 6) (-1, 7) (1, 7) (27, -6)
The solution of the system of linear equation are (1, 7)
How to solve system of equation?3a + 6b = 45
2a - 2b = -12
multiply equation(ii) by 3
Therefore,
3a + 6b = 45
6a - 6b = -36
9a = 9
a = 1
Hence,
2(1) - 2b = -12
2 - 2b = -12
-2b = -12 - 2
- 2b = - 14
b = -14 / -2
b = 7
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The price of a car is £2750.
In a sale, the price is reduced by 20%
Work out the price of the car in the sale
Answer: $2200
Step-by-step explanation:
20% = 0.2
2750 x 0.2 = 550
2750 - 550 = 2200
OR
2750 x (1-0.2) =
2750 x (0.8) = 2200
Answer:
£2200
Step-by-step explanation:
Formula:
20% off
so:
2750x0.20= x Price of car with 80% off
2750-x= Price of car with 20% off
Find answer:
(look in image to see my work on 2750x0.20, I used Microsoft Whiteboard)
2750x0.20=550.00
2750-550=2200
The price of the car 20% off is £2200
Five little girls taken in couples weigh 129 pounds, 125 pounds, 124 pounds, 123 pounds, 122 pounds, 121 pounds, 120 pound, 118 pounds, 116 pounds and 114 pounds on a weighing machine. What was the weight of each one of the five little girls if taken separately
The weight of each one of the five little girls if taken separately is 242.4 lb.
Weight of each girl when taken separatelyThe weight of each girl can be determined from the average weight of the girls.
Weight of each girl = (Total weight) / number of girls
W = (129 + 125 + 124 + 123 + 122 + 121 + 120 + 118 + 116 + 114)/5
W = 1,212/5
W = 242.4 lb
Thus, the weight of each one of the five little girls if taken separately is 242.4.
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Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.)
A grocery store chain has been tracking data on the number of shoppers that use coupons. the data shows that 71% of all shoppers use coupons. 36 times out of 40 these results were considered accurate to within 2.5%. what is the confidence interval?
The confidence interval comes out to be (0.685,0.735).
Calculating the Confidence Level and Other Terms
The confidence level can be calculated as follows,
z = [tex]\frac{36}{40} * 100%[/tex]%
z = 90 %
The margin error is given as, E= 0.025
The p value in this case is 0.71
Calculating the Confidence Interval
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
Confidence interval can be obtained by using the following formula,
(p-E, p+E) = (0.71-0.025, 0.71+0.025).
Therefore, the confidence interval is (0.685, 0.735).
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AB ≅ BC and AD ≅ CD
Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.
What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?
What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
The additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.
How to illustrate the information?From the information, Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.
In this case, the additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.
Also, the additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem is that AX and CX are congruent.
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Answer:
What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?
✔ AC and BD are perpendicular.
What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
✔ AX and CX are congruent.
Step-by-step explanation:
right on edge
I need help to find the justification for this problem!
The tangents that exists between the two given circles are not common tangents because they are not of the same size or circumference.
What is a tangent?A tangent can be defined as the plane line that touches a curved surface such as a circle but doesn't pass through the circle.
From the diagram given, the two circles are not of the same size, that is, they have different circumstances. This means that the point where the line meets the both circles are not the same.
Therefore, the tangents that exists between the two given circles are not common tangents.
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help me please!!!! 15 points
Answer:
17 sq. cm
Step-by-step explanation:
1st you split into 2 smaller shapes
Smaller shape:
A = lw
= 1(2)
= 2
Bigger Shape:
A = lw
= 3(5)
= 15
Add them together
15 + 2 = 17
-8√147x simplify do you know how to answer this?
Answer:
-56√3x
Step-by-step explanation:
√147 = 7√3
-8(7√3x)
-56√3x
Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010 ? The population of Town C in 2000 was of the population in 2005. The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Statement 1: The population of Town C in 2000 was 2/3 of the population in 2005
This tells us the population change from 2000 to 2005 since we need to know the population change from 2000 to 2010, this statement is not sufficient.
Statement 2: The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Since statement 2 provides no information about the population change from 2000 to 2005, there is no to answer this question with certainty. thus, statement 2 is not sufficient
Statement 1 and Statement 2 combined:
Let X= the population in 2000
Let Y= the population in 2005
Let Z= the population in 2010
From statement 1, we can write: X=[tex]\frac{2}{3}[/tex]Y
Multiply both sides by 3 to get [tex]3X=2Y[/tex]
Divide both sides by 2 to get [tex]\frac{3}{2}X=Y[/tex]
=>[tex]Y=1.5X[/tex]
As per statement 2, let's first determine the increase in the number of people from 2000 to 2005
If [tex]Y=1.5X[/tex], we know
X= the population in 2000
1.5X= the population in 2005
[tex]1.5X-X=0.5X[/tex]
So, the population increased [tex]0.5X[/tex] from 2000 to 2005
So, from 2005 to 2010, the population increased at least 0.5X
1.5X= the population in 2005
[tex]1.5X+0.5X=2.0X[/tex]
So, the population in 2010 was at least 2.0X
In other words, the population at least doubled from 2000 to 2010
So, the answer to the target question is yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010?
(1) The population of Town C in 2000 was 2/3 of the population in 2005.
(2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
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A student can pitch a fast ball at 65 miles per hour. Convert this
speed to yards per second.
O 95.33 yd/sec
O 132.95 yd/sec
O 31.77 yd/sec
O 21.67 yd/sec
Answer:
31.77 yd/sec
Step-by-step explanation:
Conversions:
1 mile = 1760 yards1 hour = 3600 secondsGiven:
[tex]\sf 65\:miles\:per\:hour=65\:miles/hour=\dfrac{65\:miles}{hour}[/tex]
Therefore, to convert 65 mph to yards per second:
[tex]\implies \sf \dfrac{65\:miles}{hour}=\dfrac{65 \times 1760\:yards}{3600\:seconds}=31.777...\:yd/s[/tex]
Answer:
c.) 31.77... yd/sec
Explanation:
Given: 1 hours → 65 miles
Conversions:
(i) 1 hour = 60 minutes = 3600 seconds
(ii) 1 miles = 1760 yards
Then,
1 hour = 3600 seconds65 miles = (1760 × 65) = 114400 yards Speed:⇒ distance/speed
⇒ 114400/3600
⇒ 31.77777...
⇒ 31.77 yd/sec
A recipe calls for 11 tablespoons of sugar and 22 teaspoons of salt. How many
teaspoons of salt are needed for just one tablespoon of sugar?
On the double number line below, fill in the given values, then use multiplication or
division to find the missing value:
It will require 2 tablespoons of salt for just 1 tablespoon of sugar for the combination.
What are word problems?Word problems are a systematic approach used in mathematics for solving real-life cases by determining unknown values.
From the given information:
If it takes 11 tablespoon + 22 teaspoon to make 1 recipe.i.e.
11 tablespoon of sugar + 22 teaspoon of salt = 1 recipe
Then it will require 2 tablespoons of salt for just 1 tablespoon of sugar.
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linear slope help pls
A slope is also known as the gradient of a line. The slope of the given linear table is $250 per car.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the linear table is,
m = ($4,000 - $2,500)/(12-6) = $250 per cars
Hence, the slope of the given linear table is $250 per car.
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Bill's Roast Beef sells 8 times as many sandwiches as Pete's Deli. The difference between their sales is 434 sandwiches. How many sandwiches did each sell?
Okay, so let's call B = the number of sandwiches Bill sells
and P = the number of sandwiches Pete sells
Since Bill sells 7 times as many sandwiches as Pete, then
B = 7P
And the difference between their sales is 414 sandwiches. Since we know that Bill sells more than Pete, then
B - P = 434
So, now we can substitute for B from the equation above B = 7P
x = bill's
y = pete's
x = 8y
B - P = 434
7P - P = 434
6P = 434
P = 72.33
Therefore, Pete sells 72.33 sandwiches
Bill sells 7 x 72.33 = 506 sandwiches.
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Carissa pays $2.10 each day for lunch. her money is in an account that is deducted each time she buys a lunch. there are 6 days until the end of the school year and her account has $12.75 in it. how much money will she get back at the end of the year?
Answer:
15¢
Step-by-step explanation:
$12.75 - 6 × $2.10 = $12.75 - $12.60 = $0.15
Answer: 15 cents
Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.
2-5x=2x - 3
=
OA. X 0.75
OB. x= -0.75
OC. x 1.25
OD. x= -1.25
2
The solution to the equation below to the nearest fourth of a unit is 0.75
Solving linear equationGiven the linear equation below expressed as:
2-5x=2x - 3
Collect the like terms
-5x - 2x = -3- 2
-7x = -5
Divide both sides by -7 to have:
-7x/-7 = -5/-7
x = 5/7
x = 0.75
Hence the solution to the equation below to the nearest fourth of a unit is 0.75
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1/8 of passengers of a train were children. if there were 40 children travelling in the train on a certain day, how many adults were there in the train?
280 adults were there in the train.
What is linear equation definition and example?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of linear equation is y=mx + b. noun. 20. A polynomial equation of the first degree (such as x = 2y - 7)Given,
Total children are in the train = 40
1/8 are children in train and no of children in train ,
∴ 1/8 × x = 40
x = 40 × 8 ⇒ 320
The no of passenger in train = 320
in total passenger, 40 are children .
So, rest adults passengers are = 320 - 40 ⇒ 280
There fore, 280 adults were there in the train.
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Suppose that the relation H is defined as follows.
H= = {(2, 7), (2, -1), (-8, -2)}
Give the domain and range of H.
Write your answers using set notation.
domain = = 0
range = 0
X
Answer:
Domain = {-8, 2}Range = {-2, -1, 7}Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
What is the down payment for this vehicle: $37,850.00 at 7% down
Answer:
$2,649.50
Step-by-step explanation:
s
The train will take 1h, then the bus will take and a half hours. i need to allow half an hour to change between them. how long will the whole journey take?
Total time for whole journey would be 3 hours.
The total trip is divided into three intervals :-
Travelling by trainTravelling by busTime taken to change between themHence to find the total time of the trip we need time taken in each interval and just add them up.
The final expression would be :-
Total time taken = Time taken by bus + Time taken by train +
Time taken to change between them
Given:-
Time taken by bus = 1.5 hrsTime taken by train = 1 hrsTime taken to change between them = 0.5 hrsThus Total time for whole journey would be 3 hours.
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Given: 4x + 5 = −6x + 5
Prove: x = 0 using two column proof
1) [tex]4x+5=-6x+5[/tex] (given)
2) [tex]4x=-6x[/tex] (subtraction property of equality)
3) [tex]10x=0[/tex] (addition property of equality)
4) [tex]x=0[/tex] (division property of equality)
Tiger Biscuits factory planing to produce 10,000 units in Month Standard time per 200 units is 8 hours! the Company pays. Rs. 40 per her.
The total cost or amount that Tiger Biscuits will pay will be Rs 16000.
How to calculate the cost?From the information given, the factory is planing to produce 10,000 units and the standard time per 200 units is 8 hours.
The time taken to produce 10000 units will be:
= (10000/200) × 8
= 400 hours.
The amount that the company will pay will be:
= 400 × Rs 40
= Rs 16000
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Prove that the triangles formed due to the diagonal of rectangle are congruent to one another
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.The triangles formed due to the diagonal of the rectangle are congruent to one another.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
For the given rectangle ABCD, the length of the diagonals AC and BD can be written as,
AC = √(x² + y²)
BD = √(x² + y²)
Now, the triangles formed due to the diagonals AC and BD are ΔABC and ΔBCD. Also, for ΔABC and ΔBCD we can write,
∠ABC = ∠BCD = 90°
AB = CD = x {Oppsite sides of the rectangle are equal}
BC = AD = y {Oppsite sides of the rectangle are equal}
Hence, the two triangles are equal. Therefore, the triangles formed due to the diagonal of the rectangle are congruent to one another.
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Hassan wants to ride his bicycle 26.8 miles this week. He has already ridden 6 miles.
If he rides for 4 more days, what is the average number of miles he would have to ride
each day to meet his goal?
AnsTHE OTHER GUY GOT IT RIGHT SORRY I DID THE MATH WRONG :( Step-by-step explanation:
Answer:
5.2 miles
Step-by-step explanation:
Distance left to ride = 26.8miles - 6 miles = 20.8 miles
There are 4 days left, so on average,
Hassan has to ride:
[tex] \frac{20.8}{4} \\ = 5.2mi[/tex]
5. Try It #5
If f(x) is a linear function, with f(2)=-11, and f(4)=-25, find an equation for the function in slope-intercept form.
The function in slope-intercept form is mathematically given as
f(x)=14x+154
What is an equation for the function in slope-intercept form.?
Parameters
f(2)=-11,
f(4)=-25
Generally, the equation for the slope is mathematically given as
[tex]m=\frac{-25+11}{2-}[/tex]
m=7
In conclusion, the line equation
y-2=7(x-+11)
y as subject
y=14x+154
f(x)=14x+154
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−5(−5x+3)−5x+5= -50
Solve for X
Answer:
x = -2
Step-by-step explanation:
you can fist distribute -5 into the parenthesis
25x - 15 - 5x + 5 = -50
then combine like terms
20x - 10 = -50
add 10 to both sides
20x = -40
lastly divide both sides by 20
x = -2
that is your answer
The marks price of an article is 4500.after allowing some percent of and levying 10% VAT it is sold at 4400, find the discount percent
The discount percent for the given transaction is calculated as; 6.11%
What is the percentage Discount?We are given;
Mark Price; M.P = 4500
Now, formula for discount amount is;
Discount amount = %Discount * M.P
Discount amount = x% * 4500 = 45x
Also;
Selling price is;
S.P = M.P - Discount Amount
S.P = 4500 - 45x
VAT = Vat% * S.P
VAT = (10%*4500) - 45x
VAT = 450 - 45x
S.P with VAT = S.P + VAT Amount = 4500 - 45x + 450 - 45x = 4950 - 90x
Thus;
4950 - 90x = 4400
Solving for x gives;
x = 6.11%
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HELP ASAP!!!
REASONS ONLY
Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus
The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.
What is a Rhombus?A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.
What is the above proof?∠DEC ≅ ∠BFC Reason = All Right Angles with Equal dimensions are congruent.∠C ≅ ∠C Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.Δ DEC ≅ Δ BFC Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.[tex]\overline {DC}[/tex] ≅ [tex]\overline {BC}[/tex] Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.ABCD is a Rhombus Reason = Its sides are all congruent.Learn more about Rhombus at;
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In a class test containing 20 questions, 5 marks are given for every correct answers, ( -2 ) marks given for every incorrect answers and zero mark for question not attempted. Anju gets 9 correct answer and 11 incorrect answers. What is her total score?
Answer:
she has 23 points
Step-by-step explanation:
hope this helps and mark brainliest please
Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?
The triangle is acute because 22 + 52 > 42.
The triangle is acute because 2 + 4 > 5.
The triangle is not acute because 22 + 42 < 52.
The triangle is not acute because 22 < 42 + 52.
Answer:
The triangle is not acute because 2² + 4² < 5².
Step-by-step explanation:
Answer:
The triangle is not acute because 2² + 4² < 5²
Step-by-step explanation:
got it correct on my quiz