The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
According to the statement
We have a given that the maximum sum of the positive integers is 400.
And we have to find the value of n which is a maximum number of integers by which the value of sum become 400.
So, to find the value of the n we use the
A.P. Series'Summation formula
According to this,
S = n (n+1)/2
Here the value of s is 401
Then
S = n (n+1)/2
401 = n (n+1)/2
401*2 = n (n+1)
802 =n (n+1)
n (n+1) = 802
n^2 + n -802 =0
By the use of the Discriminant formula the
value of n becomes n = -28 and n = 27.
The negative value of n is neglected.
Therefore the value of n is 27.
So, The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
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Please help me, random answers will be reported
Answer:
the side length of hypotenuse is 16.28
Step-by-step explanation:
[tex]a^{2}+b^{2}=c^{2}[/tex]
= [tex]11^{2}+12^{2}= C^{2}[/tex]
= [tex]121+144=c^{2}[/tex]
= [tex]265= c^{2}[/tex]
= [tex]\sqrt{265} = c[/tex]
= [tex]c = 16.28\\[/tex]
Answer:
A = 42.5° (nearest tenth)
B = 47.5° (nearest tenth)
C = 90°
a = 11
b = 12
c = √(265) = 16.3 (nearest tenth)
Step-by-step explanation:
Information:
Side a is opposite angle A.
Side b is opposite angle B.
Side c is opposite angle C.
From inspection of the triangle:
a = 11b = 12C = 90°To find the missing side length, use Pythagoras Theorem:
Pythagoras Theorem
a² + b² = c²
(where a and b are the legs and c is the hypotenuse of a right triangle).
Substitute the given values of a and b into the formula and solve for c:
⇒ 11² + 12² = c²
⇒ 121 + 144 = c²
⇒ c² = 265
⇒ c = √(265)
To find one of the missing angles, use the Sine Rule.
Sine Rule
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Substitute the given values into the formula:
[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin B}{12}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]
Solve for angle A:
[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]
[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{1}{\sqrt{265}}[/tex]
[tex]\implies \sf \sin A=\dfrac{11}{\sqrt{265}}[/tex]
[tex]\implies \sf A=\sin^{-1} \left(\dfrac{11}{\sqrt{265}}\right)[/tex]
[tex]\implies \sf A=42.51044708...^{\circ}[/tex]
Therefore, A = 42.5° (nearest tenth)
Interior angles of a triangle sum to 180°:
⇒ A + B + C = 180°
⇒ 42.5° + B + 90° = 180°
⇒ B + 132.5° = 180°
⇒ B = 47.5°
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In his first month of training,Landon biked 3.1 miles and ran 0.75 miles each workout. He completed 18 workouts that month. What is the total distance that he biked in his first month of training?
Taking into account the change of units, the total distance that he biked in his first month of training is 55.8 miles.
Rule of threeIn first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
Total distance that he biked in his first month of trainingIn his first month of training,Landon biked 3.1 miles and ran 0.75 miles each workout. He completed 18 workouts that month.
So you can apply the following rule of three: if for each workout Landon biked 3.1 miles, in 18 workouts he biked how far?
1 workout ⇒ 3.1 miles
18 workouts ⇒ total distance
So: [tex]total distance=\frac{18 workoutsx3.1 miles}{1 workout}[/tex]
Solving:
total distance= 55.8 miles
In summary, the total distance that he biked in his first month of training is 55.8 miles.
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Order the number from least to greatest square root of 1, 1/3,2.5,square root of 2
The required order of the number from least to greatest square root is
1/√3 < √1 < √2 < √2.5
Which number is greatest in value:
In the above numbers 1, 1/3 and 2.5 do not have square roots.
So, we will write 1, 1/3 and 2.5 inside the square root as shown below.
√1 = 1
√(1/3) = 1/√3 = 0.577350269
√2.5 = 1.58113883
√2 = 1.414
Arranging these numbers according to their value, we get the order as-
0.577350269 < 1 < 1.414 < 1.581138831
Hence, the required order of the number from least to greatest square root is 1/√3 < √1 < √2 < √2.5.
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Dina's mother is four times older than Dina. Dina is 35 years younger than her father. Dina's father was 5 years older than Dina's mother when Dina was born. How old is Dina now?
Answer:
10 years old
Step-by-step explanation:
Let m = mother's age
Let f = father's age
Let d = Dina's age
m = 4d d = f-35 f = m+5
Substitute the middle equation in to the first equation
m = 4(f - 35) Use the distributive property
m = 4f - 140 subtract 4f from both sides
*m -4f = -140
In equation 3 above, subtract m from both sides to get
f = m+5
f - m = 5 rearrange so that the m term is first
*-m + f = 5
Now add the equations together that have *
m -4f = -140
-m + f = 5
-3f = -135 Divide both sides by -3
f = 45 This is the father's age. To find Dina's age, plug 45 into the second equation above:
d = f -35
d = 45 -35
d = 10.
To find the mom's age, use the third equation:
f = m+5
45 = m + 5
40 = m
You can check this by plugging the answers you found and you can see that all three equations are solved.
m = 4d d = f - 35 f = m + 5
40 = 4(10) 10 = 45 - 35 45 = 40 + 5
40 = 40 10 = 10 45 = 45
Five chess players take part in a tournament. Every player plays once with each of his/her opponents. How many games are play?
There is a total of 10 games played.
How many games are played?
There are 5 players, If we select a given player, then that player will play one game with each of the other 4 players.
So we have 4 games at the moment.
Now we select one of the other 4 players, (we don't count the one we choose before). The one that we choose now will play one game wich each one of the remaining 3, so we add 3 more games.
Now we do the same with the remaining 3, this time we add 2 more games.
Now we do that with the remaining 2, now we add 1 more game.
Adding all the games we have:
4 + 3 + 2 + 1 = 10
There is a total of 10 games played.
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10 points please help me I've been struggling with these
Answer:
57pi
Step-by-step explanation:
First, let's get the area of the entire circle, including the shaded region:
pi*(8+3)^2 = 121pi
Next, let's get the area of the unshaded circle
pi*8^2 = 64pi
If we subtract the inner circle from the full circle, we get the shaded region:
121pi-64pi =
57pi
Answer: 57π
Step-by-step explanation:
You have to calculate the area of the whole circle created by the sum of the inner circle and the ring, so 8+2=11=r, now use the formua for getting area of a circle, π*r², which is "121π"
After that, subtract the area of the inner circle (its area is π*8²)
So 121π-64π = 57π
A dog takes 3 steps to walk the same distance for which a cat takes 4 steps. Suppose 1 step of the dog covers 1 foot. How many feet would the car cover in taking 12 steps
Answer:
the cat would take 13 steps
Can someone help me out on this problem and show work please !!
Given the area of the rectangular community garden, the length and width of the garden are 30ft and 10ft respectively.
What is the length and width of the garden?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
Area of a rectangle is expressed as;
A = length × Width
Given the data in the question;
Area of the rectangular community garden A = 300ft²Let width w = xLength = three times width = 3xWe substitute the values into the equation
A = length × breadth
300 = 3x × x
300 = 3x²
Divide both sides by 3
x² = 100
Take the square root of both sides
x = ±√100
x = 10, -10
Since, dimension of a rectangle cannot be Negative.
x = 10
Hence;
Width w = x = 10ft
Length = 3Width = 3x = 3( 10 ) = 30ft
Given the area of the rectangular community garden, the length and width of the garden are 30ft and 10ft respectively.
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Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?
If segment DC bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
If segment DC bisects segment AB, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
If segment AD bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
If segment AD bisects segment AB, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
Option A is correct. If segment DC bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. This can be obtained using perpendicular bisector theorem.
What is perpendicular bisector theorem ?Perpendicular bisector theorem : In a plane, if we choose a point, say D, on the perpendicular bisector,say PQ, drawn from segment, say AB, then the point D is equidistant from the endpoints, that is A and B, of the segment.
That is, perpendicular bisector PQ of line segment AB is the line with Q = 90° and Q is the midpoint of AB ⇒ AQ = BQ. A point on PQ say D is equidistant from A and B ⇒AD and BD.
Thus in the given question we can use perpendicular bisector theorem.
Here DC is the perpendicular bisector of the line segment AB and therefore AD and BD are equal.
Hence it is clear that Option A is correct.
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ProblemSolving One leg of an isosceles
right triangle has endpoints (1, 1) and (6, 1). The other
leg passes through the point (6, 2). Draw the triangle
5 on the coordinate plane below. Then show how you
can use the Distance Formula to find the length of the
hypotenuse. Round your answer to the nearest tenth.
The length of the hypotenuse of the isosceles triangle is 7.1 units.
We can use the distance formula to find the length of ST (base) and TU(perpendicular). Further, using these lengths, we can find the hypotenuse of the isosceles triangle.
The distance formula is given as follows,
d = √(x₂ - x₁)² + (y₂ - y₁)²
Here, d is the distance between the two points (x₁, y₁) and (x₂, y₂)
As shown in the drawn isosceles triangle STU,
The length of the base ST is given as,
ST = √(x₂ - x₁)² + (y₂ - y₁)²
Here,
x₁ = 1 and y₁ = 1
x₂ = 6 and y₂ = 1
∴ ST = √(6-1)² + (1-1)²
ST = √5²
ST = 5 units
Similarly, for TU as the other leg passes through the point(6,2) and is of length 5 units ( STU being isosceles triangle), we have,
x₁ = 6 and y₁ = 1
x₂ = 6 and y₂ = 6
Also, TU = 5 units
Now, using Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
(SU)² = (ST)² + (TU)²
(SU)² = (5)² + (5)²
(SU)² = 50
SU = √50
SU = 7.071 units
SU ≈ 7.1 units (after rounding of to the nearest tenth)
hence, the hypotenuse of the isosceles triangle is of 7.1 units.
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Determine the period.
Answer:
[tex]5 \cos( \frac{2\pi x}{7} ) [/tex]
The period of the given graph is 2π.
A period is the amount of time between two waves, whereas a periodic function is one whose values recur at regular intervals or periods. In other terms, a periodic function is one whose values recur after a specific interval.
This specific time span indicated above is the function's period.
The length of one function wave is referred to as the period.
The sine and cosine functions have a period of 2π radians, or 360 degrees. The period of the tangent function is π radians, or 180 degrees.
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(6x - 4)(3 - 2x)/4x - 6
[tex] \frac{(6x - 4)(3 - 2x)}{(4x - 6)} = \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} [/tex]
[tex] \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} = \frac{(3x - 2)(3 - 2x)}{(2x - 3)} [/tex]
[tex] \frac{(3x - 2)(3 - 2x)}{(2x - 3)} = \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} [/tex]
[tex] \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} = - (3x - 2)[/tex]
[tex] - (3x - 2) = 2 - 3x[/tex]
Calculate the first difference between 7, and where 7,-688. 2
The difference between the numbers given is 6.882.
How to illustrate the information?Based on the information given, it should be noted that difference means subtraction.
The difference between the numbers given will be:
= 7 - (7 - 6.882)
= 7 - 0.118
= 6.882
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During a very cold winter, water pipes sometimes burst because:
The water pipe sometimes bursts in winter because of the flowing water getting transformed into freezing water due to drop in temperature and the volume increases creating more pressure on the wall pipes.
Bursting of Water Pipes During a Very Cold Winter
The straightforward explanation is that during very cold winters, as water freezes into ice, it expands, causing solid ice to fill a larger volume than the liquid that was previously flowing through the pipes.
As we know that, the pressure P increases with increase in volume, V, the increased volume of frozen water leads to increase in the pressure inside the pipe.
The pressure that the ice builds up inside the pipes could rupture the pipe walls.
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University Data
Receiving
Not Receiving
Total
Financial Aid
Financial Aid
Undergraduates
4222
3898
8120
Graduates
1879
731
2610
Total
6101
4629
10730
If a student is selected at random, what is the
probability that the student is a graduate
(rounded to the nearest percent)? [ ? ]%
Answer:
24 % (to the nearest percent)
Step-by-step explanation:
the probability that the student is a graduate is equal to :
[tex]=\frac{\text{the total number of graduates} }{\text{the total number of students} }[/tex]
[tex]=\frac{2610}{10730} \\=0.243243243243[/tex]
Converting to percentage:
0.243243243243×100
= 24.3243243243 %
im not he brighest with math and i need help
Answer:
113.04 ft^2
Step-by-step explanation:
area of the circle= 3.14*(6)^2
A medication order states, normal saline (ns) iv to infuse at 125 ml/hr. How many ml will infuse in 8 hours? (record answer as a whole number. Do not use a trailing zero. )
The amount of medicine infused in 8 hours is 1000ml.
According to the statement
we have given that the medicine normal saline (ns) iv to infuse at 125 ml/hr.
and we have to find the total amount of medicine infuse in the 8 hours in the whole number value.
So,
An infusion is the creation of a new substance by steeping another substance in a liquid, usually water
we have given a rate of infusion of medicine per hour which is 125 ml/hr.
And
Amount of medicine infuse in 1 hour is 125 ml
And the Amount of medicine infuse in 8 hours = 125*8
Amount of medicine infuse in 8 hours = 1000 ml.
So, The amount of medicine infused in 8 hours is 1000ml.
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you can afford to invest $150 per month in an annuity that earns 4% per year, compounded monthly. How long will it take before your investment is worth $6000?
The time it will take before your investment is worth $6000 = 7 years
Calculation of simple interestThe amount of money invested per month = $150
Therefore the amount principally invested yearly;
= 12 × 150 = $1,800
Simple interest = $6000
Rate = 4%
Time = ?
Using the formula for Simple interest (SI)= P×T×R/100
Make T the subject of formula,
T = SI × 100/P×R
T = $6000×100/1800×4
T = 600000/7200
T= 83 months/ 12 = 7 years
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if m = 2 and n = 5 then find the value of 6m+5n
Answer:
37
Step-by-step explanation:
6m+5n
plug in your given values
6(2) + 5(5)
12+25
=37
Answer:
37
Step-by-step explanation:
6m + 5n
6*2 + 5*5 = 12 + 25
= 37
BRAINLIEST TO PERSON WHO HELPS
Mrs. Lindy is purchasing notebooks for her students. She spends $52 on n notebooks. Each notebook costs $3.25
Select the equation that matches this situation.
Answer:
B. 52= 3.25n
Step-by-step explanation:
Unit price multiplied by quantity equals total. So, each notebook cost $3.25 and she buys 'n' notebooks.
She totally spends $52.
In conclusion, 3.25 (unit price × n [quantity]) = 52.
And that is.. 52 = 3.25n.
<3
Answer:
B
Step-by-step explanation:
Let's think about what does the given info mean.
Because of n notebooks, she spent $52
One notebook is $3.25.
So 3.25n = 52
Take it this way if you don't understand
Let's say I spent 4$ on two (2) pens
What's the value of one pen?
We want to find the value of one pen and then multiply it by 2, to get 4$
So we normally would do 4/2
However, to set up an equation, we would create
v (value of one pen) x 2 (pens) = 4$ (cost)
v = 4$/2 = 2$
Answer:
9
——- =
-2.1
Answer:
-9/2
In alternate forms -4•5,-4 1/2
can someone help me!!
I am a 3 digit positive number. The sum of my digits is 18. My middle digit is the product of -2 and -4. My first digit is 3^2.
Hi! ⋇
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The first digit of this number is 3², which is 9.
The Number is : 9xx
________
The second digit is: -2·(-4)=8.
The Number is : 98x.
________
The sum of all the digits is 18. This gives us an equation that we can solve in terms of x!
[tex]\multimap\sf{9+8+x=18}[/tex] (x is the digit we are looking for)
Now it takes a little arithmetic to find x :)
[tex]\multimap\sf{17+x=18}[/tex]. Just subtract 17 from both sides to find x!
[tex]\multimap\sf{x=1}[/tex]. And Now, can you see the number!
It's 981, of course :)
Hope this made sense to you!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\large\it{\overbrace{Calligrxphy}}[/tex]
Which of the following are factor pairs for 12?
1. 1 and 12
2. 2 and 4
3. 2 and 6
3. 3 and 4
4. 3 and 5
NEED ANSWER QUICK PLEASE!!
Answer:
FACTOR pairs are a set of two integers that when multiplied together gives a particular product.FACTOR pairs of 12 are :1 and 12 because 1 x 12 = 122 and 6 because 2 x 6 =123 and 4 because 3 x 4 = 12Hope you understandHope this helps.Good luck ✅.Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answer:
A. f(-x) = f(x)
Step-by-step explanation:
When plugged into a graph, we can see that the y value of -x is equal to x.
This means, that if we compare the y value of x=3 and x=-3, they will be the same on the graph.
Point W is located at (-5, -3).
Select all of the following that are 5 units from point W.
Choose all answers that apply:
A. (-5, 2)
B. (−8,−5)
C. (-5, 0)
The point that is 5 units from W is (A) (-5, 2)
How to determine the points?The point is given as:
W= (-5, -3)
A point 5 unit from W can be any of the following
W' = (-5 ± 5, -3)
W' = (-5, -3 ± 5)
When the above expressions are evaluated, we have:
W' = (0, -3), (-10, -3), (-5, 2) and (-5, -8)
Hence, the point that is 5 units from W is (A) (-5, 2)
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Select one or more expressions that together represent all solutions to the equation.
Your answer should be in radians.
Assume n is any integer.
30 cos (30x) + 14 = -16
Choose all answers that apply:
Answer:
D. π/30 + n(π/15)
Step-by-step explanation:
The given equation can be solved by isolating the cosine function and using the inverse function to find the angles.
Solution30cos(30x) +14 = -16
30cos(30x) = -30 . . . . . . subtract 14
cos(30x) = -1
This is an extreme value of the cosine function that first occurs where the argument is π, and repeats every 2π after that:
30x = π +2nπ
x = π/30 +n(π/15) . . . . . odd multiples of π/30
__
Additional comment
The answer choices other than D include all multiples of π/30, or only even multiples of π/30. Either way, they are not part of the correct answer.
Help please!!! Write an equation that represents the line.
Use exact numbers.
30 A club of 12 people would like to choose people for the offices of president, a vice president, and a secretary. How many different ways are there to select the officers so that only one person holds each office?
1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary. This can be obtained by using the formula of permutation.
How many different ways are there to select the officers so that only one person holds each office?Total number of people in the club = 12
total number of positions = (president, vice president, secretary) = 3
From 12 people 3 people are taken at a time.
That is, using the formula for permutation we get,
ⁿPₓ = [tex]\frac{n!}{(n-x)!}[/tex]
Here n = 12 and x = 3
P(12,3)= 12!/(12-3)! =12!/9! = 10×11×12 = 1320
Hence 1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary.
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A four-person committee is chosen from a group of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
•
1001
•
15
1001
10
143
O
133
143
Answer:
The chance of the committee being all boys is 28.57% or 29%