limₐ→∞xₙₐ= limₙ→∞xₙ= L;
Let xₙ be a monotonically increasing sequence. Thus:
xₙ₊₁≥xₙ
Consider a subsequence of xₙ namely xₙₐ. Then:
xₙₐ≥xₙ, ∀nₐ≥n
We are also given that:
limₐ→∞xₙₐ=L
Given that fact we know that xₙₐ is bounded above. Therefore:
xₙ≤xₙₐ≤L
Now by monotone convergence theorem a monotone bounded sequence must be convergent. Also by uniqueness of a limit for a convergent sequence and the fact that all its subsequences are also convergent to the same limit:
limₐ→∞xₙₐ= limₙ→∞xₙ= L
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What expressions are equal to -5
Find the compound interest on ₹ 31,250 at 12% pa for 2 1/2 years
pls give step by step explanation
Answer:
42,183
Step-by-step explanation:
We will use the Continuous Compounding Interest since a regular interval was not stated.
P(t) = Pe^(rt)
We will plug in the variables to the formula
P(t) = 31250 * e^(.12 * 2.5)
We can simplify and evaluate the compound interest.
P(t) = 42183.08
Which expression is equivalent to (3x-2)(x+3) ?
A. 4x^2 + 4x + 1
B. 3x^2 + 11x + 6
C. 3x^2 + 7x - 6
D. 4x + 1
Answer: C. 3x^2 + 7x - 6
Step-by-step explanation:
3x^2 + 9x -2x -6
3x^2 + 7 - 6
Hope you got it.
Mark me as Brainliest Please.
julian needs to spend at least seven hours each week practicing the drums. he has already practiced five and one third hours this week. he wants to sp
The minimum number of hours is 5/6 and the inequality is x ≥ 5/6 hours.
What exactly is an inequality?An inequality is a relationship that compares two numbers and perhaps other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.
According to the given data:Let x = the number of hours practicing the drums
we know that Julian needs to spend at least seven hours each week practicing
the drums x ≥ 7 hours
He has already practiced 5*(1/3) hours this week.
Convert mixed number to an improper fraction 5*(1/3) = 16/3hours.
Subtract 16/3 from 7,
7 - (16/3)
= 5/3
Divide 5/3 by 2,
(5/3)/2
=5/6
Hence,
The inequality that represent the minimum number of hours he needs to practice on each of the two days is x ≥ 5/6 hours.
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The given question is not complete.
Julian needs to spend at least seven hours each week practicing the drums. He has already practiced 5 1/3 hours this week. He wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours he needs to practice on each of the two days.
MAKING AN ARGUMENT In an aerial ski competition, you perform two acrobatic ski jumps. The scores on the two jumps are then added together.
An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).In this exercise, you're required to describe the score which this ski jumper must earn on the second jump to beat his or her competitor. Therefore, let x represent the score of his or her second acrobatic ski jump.
Based on the competitor's score of 119.8 in the second jump, this ski jumper must earn the following score represented by this inequality:
x > 119.8
Who is correct?From the table (see attachment), we can logically deduce that the competitor's score in the first ski jump is equal to 117.1. This ultimately implies that, the ski jumper's score can be modeled by this inequality:
x > 117.1
In this context, we can reasonably infer and logically deduce that both the coach and the teammate are correct because a score of "118.4" and "117.5" are greater than a score of "117.1."
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Complete Question:
MAKING AN ARGUMENT
In an aerial ski competition, you perform two acrobatic ski jumps. The scores on the two jumps are then added together.
a. Describe the score that you must earn on your second jump to beat your competitor.
b. Your coach says that you will beat your competitor if you score 118.4 points. A teammate says that you only need 117.5 points. Who is correct? Explain.
Describe and correct the error in using the diagram to find the value of x.
Hi there!
The error in using the diagram to find x in the solving is that they only picked two angles and equated to 180° which is wrong. You'll find out that their final value for x contains a decimal point which should never be in angles.
The above diagram is a revolution (360°) or angle at a point, so all the angles have to be considered and equated to 360° and NOT 180°
Below is the corrected solving.
[tex]13x + 45 + 12x - 40 + 19x + 3 + 6x + 2 = 360[/tex]
(reason: angles at a point = 360°)
Collect like terms, and make x the subject of formula.
[tex]⟹50x + 10 = 360[/tex]
[tex]⟹50x = 360 - 10[/tex]
[tex]⟹50x = 350[/tex]
Now, divide both sides by 50 to find the value of x.
[tex] \frac{50x}{50} = \frac{350}{50} [/tex]
Therefore:
[tex]x = 7[/tex]
use the substituation method to solve 6=-4x+y -5x-y=21
Answer:
x=-3 y=-6
Step-by-step explanation:
solve for y on the first equation then plug the answer into the second
A school has 109 students signed up for a science workshop. The school will buy every student attending the workshop a pencil, a folder, and an eraser. A package of 12 erasers is $0.75. Only whole packages of erasers can be bought. Folders are $0.10 each. A package of 8 pencils is $0.50. Only whole packages of pencils can be bought. How much will the school spend?
Answer:
The amount is $25.4
Step-by-step explanation:
There are 109 students to attend the science workshop.
Number of erasers needed is 109, but whole packages of erases can be bought which consist 12 erasers. The total packages of erasers needed would be 10.
The cost of 10 packages of erasers = $0.75 x 10
= $7.5
The cost of 109 folders = 109 x $0.10
= $10.9
Number of pencils needed is 109, but whole packages of pencils can be bought which consist 8 pencils. The total packages of pencils needed would be 14.
The cost of 14 packages of pencils = $0.50 x 14
= $7.0
Total cost = $7.5 + $10.9 + $7.0
= $25.4
The amount that would be spent by the school is $25.4
Answer:
25.4
Step-by-step explanation:
\left|\left|x-5\right|+2\right|\le 3
Answer:= x +27 Solve for x x = 326 = 8 32 ≈ 8.666666667
Write the augmented matrix for the following system of equations.
-2z=-4y-9x
0=4x+6z+2
2z=2+3y
The augmented matrix for the system of equations is given as follows:
[tex]\left[\begin{array}{cccc}9&4&-2&0\\4&0&6&-2\\0&-3&2&2\end{array}\right][/tex]
What is a system of equations?A system of equations is when multiple variables are related, and equations are constructed to find the values of each variable. There are multiple ways to solve a system, and one of the most usual is in a matricial way, as the augmented matrix of the system is constructed.
In standard notation, the system is given by:
9x + 4y - 2z = 0.4x + 0y + 6z = -2.0x - 3y + 2z = 2.The augmented matrix for a system with variables x, y and z is constructed as follows:
The first column contains the coefficients of x.The second column contains the coefficients of y.The third column contains the coefficients of z.The fourth column contains the results of the operations.Hence for this system, the matrix is given by:
[tex]\left[\begin{array}{cccc}9&4&-2&0\\4&0&6&-2\\0&-3&2&2\end{array}\right][/tex]
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A cyclist travels 21 miles in 45 minutes.
What is his average speed in mph?
Answer:
28 mph
Step-by-step explanation:
1h = 60m
45m --- 21 miles
60m --- [tex]\frac{60}{45}[/tex] × 21 miles = 28 miles
Thus, his average speed is 28 mph.
Which graph represents the solutions to the inequality |2x - 6 < 4? (5 points)
-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
9
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-9-8-7 -6 -5 -4 -3 -2 -1
0 1 2 3 4 5 6 7 8 9
Answer:
[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Therefore, the 3rd graph represents the solutions to inequality.
Please also check the graph below.
Step-by-step explanation:
Given the expression
[tex]|2x\:-\:6|\:<\:4[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex]
[tex]-4<2x-6<4[/tex]
[tex]2x-6>-4\quad \mathrm{and}\quad \:2x-6<4[/tex]
condition 1
[tex]2x-6>-4[/tex]
Add 6 to both sides
[tex]2x-6+6>-4+6[/tex]
[tex]2x>2[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}>\frac{2}{2}[/tex]
[tex]x>1[/tex]
condition 2
[tex]2x-6<4[/tex]
Add 6 to both sides
[tex]2x-6+6<4+6[/tex]
[tex]2x<10[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}<\frac{10}{2}[/tex]
[tex]x<5[/tex]
combine the intervals
[tex]x>1\quad \mathrm{and}\quad \:x<5[/tex]
Merging overlapping intervals
[tex]1<x<5[/tex]
Thus,
[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Therefore, the 3rd graph represents the solutions to inequality.
Please also check the graph below.
Tyler has a ramp for his skateboard that measures 17 feet long. The vertical height is 8
feet from the ground to the top of the ramp. What is the horizontal distance from the base
of the ramp to the support? (Hint: draw a picture)
Answer:
15
Step-by-step explanation:
Hypotenuse: 17ft long
Height: 8ft long
17^2 = 8^2 + b^2
b^2 = 17^2 - 8^2
b = √225
b = 15
There are 270 calories in 5 ounces of a certain ice cream how many calories are there in 2 pounds
1 pound = 16 ounces (general knowledge)
270 calories divided 5 ounces
1 ounce= 54 calories
2 pounds = 32 ounces
32 ounces × 54 calories = 1728
2 pounds = 1728 calories
i will give brainliest to best answer
That's a Congruent Triangle question.
The first thing that we should to analize is it: What figure is EFGH? The question say for us that [tex]\overline{EF} \cong \overline{GH}[/tex] and [tex]\overline{EH} \cong \overline{GF}[/tex], therefore, EFGH is a parallelogram because its parallel sides are congruents (equals).
Now, we should to proof that [tex]\triangle EFH \cong \triangle GHF[/tex]. The simbol "≅" means congruence, that is, [tex]\triangle EFH \cong \triangle GHF[/tex] means that the triangles EFH and GHF are equals.
Let's proof:
[tex]\overline{HF}[/tex] is a diagonal of the parallelogram EFGH. When we have a diagonal in a parallelogram, the opposite angles are congruents (look at the picture: the blue angles are congruent and the red angles are congruents too). Therefore, [tex]E\hat{F}H \cong F\hat{H}G[/tex] and [tex]E\hat{H}F \cong H\hat{F}G[/tex].
Both triangle has a comum side: the diagonal [tex]\overline{HF}[/tex]. The diagonal [tex]\overline{HF}[/tex] is between two angles that we know that are congruents, Therefore, by the case ASA (Angle, Side, Angle), we proof that [tex]\triangle EFH \cong \triangle GHF[/tex].
Darien could swim 30 laps an
hour last year. This year he can
swim 36 laps an hour. Determine the
percent change
Answer:
D
Step-by-step explanation:
If the percent change is 30 to 36 you can already see that it is an increase
here is the work
36 - 30
30
x 100% = 20%
Answer:
20% increase, which corresponds to the light
Step-by-step explanation:
(y - x)/x * 100
(36 - 30)/30 * 100
(6 * 100)/30
600/30
20% increase
In an equation, y varies directly as x varies. If y = 72 when x = 12 what is the value of x when y = 48?
Answer:
8
Step-by-step explanation:
y=kx where k is a constant.
72=12k
k=72/12=6
y=6x
48=6x
x=48/6=8
Which function of x has the least value for the y-intercept?
A
y=-4x+ 15
Х
B
Х
4
3
2
1
-4-3-2-1
-1
-3
-
С
y=2x-3
D
x
Answer:a
Step-by-step explanation:
pls help i need the answer
Answer:
(3,22.50)
(6, 33)
Rise/Run using two points
33-22.50/ 6-3
10.5/3
Rate = 3.5
30% of all Skittles are supposed to be purple.
a) If there are 84 skittles in a pack, how many should be purple? (Response area)
b) What percentage or skittles are not purple? (Response area)
c). Assuming that there are 18 purple Skittles in a pack, then how many total Skittles are there? (response area)
Answer:
a) 25
b) 59
c) Too lazy
Step-by-step explanation:
If 30% were to be a decimal, it would be 0.3 because 30% of 1 is 0.3. We will use this to figure out how many purple skittles there are.
A) To find the amount of purple skittles we must multiply the total number of skittles by the percent (in this case 0.3). Equation = (84*0.3=25.2) You can't really have 0.2 of a skittle so we would round down to the whole number (25).
B) Knowing the number of purple skittles, finding the number of non-purple skittles is straightforward. All you have to do is subtract the # of purple skittles from the total amount of skittles (84-25=59).
C) Kinda forgot how to do this but good luck
Yesterday 3. Hali was making a bouquet of flowers. 60% of her bouquet was made up of roses. Show much of her bouquet was made up of roses on the model below. Write the fraction and decimal equivalent to 60%. h 441
Answer:
0.6, 3/5
Step-by-step explanation:
60%=
100% * 60/100=
1*60/100=
60/100=6/10=0.6
6/10=3/5
help what does 2 1⁄3 ÷ 1 1⁄2 =
Answer:
[tex]1\frac{5}{9}[/tex]
Step-by-step explanation:
This is the answer because:
1) Reduce the expression, if possible, by cancelling the common factors.
2) You can also find the reciprocal of 1 1/2 = 3/2 while dividing the expression:
1. Convert both fractions into improper fractions:
[tex]2\frac{1}{3} = \frac{7}{3}[/tex]
[tex]1\frac{1}{2} = \frac{3}{2}[/tex]
2. Divide both fractions:
[tex]\frac{7}{3}[/tex] ÷ [tex]\frac{3}{2}[/tex] = [tex]\frac{7}{3}[/tex] x [tex]\frac{2}{3}[/tex] = [tex]\frac{14}{9}[/tex] = [tex]1\frac{5}{9}[/tex]
Therefore, the answer is [tex]1\frac{5}{9}[/tex]
Hope this helps! :D
Which function is linear?
A)
f(x) = 8x² + 2
B)
8
f(x) -
X
+ 2
f(x) - 8x? - 2
D)
f(x) = -2
Answer:
4
Step-by-step explanation:
5-1=4
Answer:
B)
Step-by-step explanation:
Assuming the numbers following the variables are exponents, (ex: 8x2, x8), the only function that is linear would be option B. This is because linear functions do not have exponents following their variables. If graphed, t are a straight line.
Which equation represents the linear function that is shown on the graph below ?
A. Y=1/2 x+4
B. Y=1/2 x-2
C. Y=4 x-2
D. Y= -2 x +4
Answer:
First one
Step-by-step explanation:
Y=1/2x+4
state if the triangle is a right triangle.
a²+b²=c²
4²+ 8\sqrt 2²=12²
16+11.3=144
27.3=144
this answer in the back says that this triangle is supposed to be a right triangle so could you help me if you see an errors that I made. I'm pretty sure I did in regards to the square root section.
Yes, it is a right-angled triangle.
A right triangle, sometimes known as a right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle or two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.Use the Pythagorean theorem.The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.a² + b² = c²(4)² + (8√2)² = (12)²16 + (64*2) = 14416 + 128 = 144144 = 144The left hand side is equal to the right hand side.Hence, it is a right angled triangle.To learn more about the Pythagorean theorem, visit :
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if a bag has 22 orange 18 red and 8 blue marbles what is the probability, that I draw blue marble, keep it, then draw another blue marble?
Answer:
The probability is 8/48
Step-by-step explanation:
There is a total of 48 marbles and 8 of them are blue.
A car traveled 180 miles at a constant rate.
Part 1. Complete the table to show the rate at which the car was traveling if it completed the same distance in each number of hours.
travel time (hours) rate of travel (miles per hour)
(5:
1040)
(4.5:
520)
(3:
360)
(2.25:
180)
Answer 1:
1040
Answer 2:
520
Answer 3:
360
Answer 4:
180
Which point lies on the circle x^2+y^2=100
A (0,-100)
B (10,-10)
C (25,75)
Answer:
NOT a single ordered pair satisfies the equation.
Step-by-step explanation:
Given the equation
[tex]x^2+y^2=100[/tex]
Let us substitute all the given ordered pairs to find which ordered pair satisfies the equation.
For (0, -100)
[tex]x^2+y^2=100[/tex]
substitute x=0 and y=-100
[tex]0^2+\left(-100\right)^2=100[/tex]
[tex]10000=100[/tex]
FALSE
Thus, the ordered pair (0, -100) does NOT satisfy the equation.
For (10, -10)
[tex]x^2+y^2=100[/tex]
substitute x=10 and y=-10
[tex]10^2+\left(-10\right)^2=100[/tex]
[tex]200=100[/tex]
FALSE
Thus, the ordered pair (10, -10) does NOT satisfy the equation.
For (25, 75)
[tex]x^2+y^2=100[/tex]
substitute x=25 and y=75
[tex]25^2+\left(75\right)^2=100[/tex]
[tex]6250=100[/tex]
FALSE
Thus, the ordered pair (25, 75) does NOT satisfy the equation.
Therefore, NOT a single ordered pair satisfies the equation.
Which of the following is a factor of 32x + 4? (1 point)
O 2x -1
O 4x-4x + 1
O 4x²- 2x + 1
O Nonc of thc abovc
Answer:
2x-1
Step-by-step explanation:
hope you get help from me
Step 2 of the Coefficient Method involves blank x-term and y-term coefficients.
Answer:
Dividing
Step-by-step explanation: