This is a geometric progression
Common ratio=1/16÷1/4 =1/4first term =a=1/4So
The general formUla is
[tex]\\ \rm\Rrightarrow a(n)=ar^{n-1}[/tex]
[tex]\\ \rm\Rrightarrow a(n)=\dfrac{1}{4}\left(\dfrac{1}{4}\right)^{n-1}[/tex]
Answer:
[tex]\displaystyle \lim_{n \to \infty} \dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)[/tex]
Step-by-step explanation:
Series: the sum of the elements of a sequence.
Therefore, as the numbers have been defined as a series and we need to find [tex]S_n[/tex]:
[tex]\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}+...[/tex]
First determine if the sequence is arithmetic or geometric.
If it is an arithmetic sequence, there will be a common difference between consecutive terms.
if it is a geometric sequence, there will be a common ratio between consecutive terms.
From inspection of the terms, we can see that there is a common ratio of 1/4, as each term is the previous term multiplied by 1/4, so it is a geometric series.
Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Given:
[tex]a=\dfrac{1}{4}[/tex]
[tex]r=\dfrac{1}{4}[/tex]
Substitute the values of a and r into the formula:
[tex]\implies S_n=\dfrac{\frac{1}{4}\left(1-\left(\frac{1}{4}\right)^n\right)}{1-\frac{1}{4}}[/tex]
[tex]\implies S_n=\dfrac{\frac{1}{4}\left(1-\left(\frac{1}{4}\right)^n\right)}{\frac{3}{4}}[/tex]
[tex]\implies S_n=\dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)[/tex]
Therefore:
[tex]\displaystyle \lim_{n \to \infty} \dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)[/tex]
Write the sentence as an equation.
253 equals the product of 232 and k
Type a slash ( / ) if you want to use a division sign.
The solution to a given word problem by writing it as an equation is k = 253/232
Expressing word problems in mathematical forms:The process of expressing word problems in mathematical forms takes a logical and chronological approach while taking the variables and arithmetic operations given into consideration.
From the given information, to express the word problem in mathematical form, we have:
253 = 232 × k253 = 232kMaking k the subject of the equation, we have:
k = 253/232
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Which linear function has the steepest slope?
Answer:
[tex]y=-8x+5[/tex]
Slope-intercept form:
[tex]\implies y=mx+b[/tex] [tex](\text{m=slope};\text{b=y-intercept})[/tex]
Using the slope-intercept form, let's identify the other slopes:
Option A:
[tex]y=-8x+5[/tex]
[tex]\text{slope}=-8[/tex]
Option B:
[tex]y-9=-2(x+1)[/tex] (This equation is in point-slope form, the slope it too the left, making it -9)
[tex]\text{slope}=-9[/tex]
Option C:
[tex]y=7x-3[/tex]
[tex]\text{slope}=7[/tex]
Option D:
[tex]y+2=6(x+10)[/tex]
[tex]\text{slope}=2[/tex] (Using point-slope terms, we can find the slope.)
⇒ A 'steep'est slope is closest to almost having a vertical slope or pitch, or relatively high gradient, as a hill, an ascent, stairs, etc.
[tex]\text{This could be a line }[/tex] ⇒ ([tex]\text{positive or negative}[/tex])
Hence, the linear function with the steepest slope is Option A: [tex]y=-8x+5[/tex].
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Sahil chooses a number, divides it by 8 , adds 8 to the answer. Then multiples the answer with 8 . He obtains the result as 952 . The number he chooses in the beginning was
I'M IN LOVE WITH A FAIRYTALE
EVEN THOUGH IT HURTS
CAUSE I DON'T CARE IF I LOOSE MY MIND
I'M ALREADY CURSED
Answer:
888
Step-by-step explanation:
let the number be n then divide by 8 , that is [tex]\frac{n}{8}[/tex]
now add 8 to this
[tex]\frac{n}{8}[/tex] + 8 and finally multiply this by 8 and equate to 952
8([tex]\frac{n}{8}[/tex] + 8) = 952 ( divide both sides by 8 )
[tex]\frac{n}{8}[/tex] + 8 = 119 ( subtract 8 from both sides )
[tex]\frac{n}{8}[/tex] = 111 ( multiply both sides by 8 to clear the fraction )
n = 888
the number chosen was 888
Determine the measure of the indicated angle!
The measure of the angle PUT is 13 degrees and the measure of the angle PQR = 21 degrees
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have triangles shown in the picture.
In the first triangle SUT:
PU is bisecting the angle SUT:
The measure of angle PUT:
Angle PUT = Half of Angle SUT
= 26/2
= 13 degrees
In the triangle SQR:
Angle SQP = Angle PQR
Angle SQP = 21 degrees
Angle PQR = 21 degrees
Thus, the measure of the angle PUT is 13 degrees and the measure of the angle PQR = 21 degrees
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One lucky day, you meet a leprechaun who promises to give you fantastic wealth, but hands you only a penny before disappearing. You head home and place the
penny under your pillow. The next morning, to your surprise, you find two pennies under your pillow. The following morning, you find four pennies, and the morning after
that, eight pennies.
Suppose that you could keep making a single stack of the pennies. After how many days would the stack be long enough to reach a star that is about 3x10¹3 km
away? (Assume that 1 penny = 1.5 mm)
The number of days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days
How to find the number of days the penny would stack?Since from the question, we see that the number of pennies double with each day. It forms a geoemetric progression with
first term a = L and common ratio , r = 2.Since the number of pennies after n days equals N = 2ⁿ
Let
L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ mSo, after n days, the length of the stack of pennies is the geoemetric progression D = 2ⁿ × L
Number of days pennies would stack to reach starMaking n subject of the formula, we have
n = ㏒(D/L)/㏒2
Since D = the distance of the star = 3 × 10¹³ km = 3 × 10¹⁶ m, and L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ mSubstituting the values of the variables into the equation, we have
n = ㏒(D/L)/㏒2
n = ㏒(3 × 10¹⁶ m/1.5 × 10⁻³ m)/㏒2
n = ㏒(3/1.5 × 10¹⁹)/㏒2
n = ㏒(2 × 10¹⁹)/㏒2
n = ㏒2 + ㏒10¹⁹/㏒2
n = (19㏒10 + ㏒2)/㏒2
n = (19 + 0.3010)/0.3010
n = 19.3010/0.3010
n = 64.1
n ≅ 64 days
So, the number of days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days
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the roots of x+1/x=3 are: (x not equal to 0)
Answer:
x^2-2x-3
Step-by-step explanation:
(x+1)(x-3)
x(x-3)+1(x-3)
Explain what happens when you have an exponent to the power of another exponent.
Answer:
The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 52 raised to the 3rd power is equal to 56.
Step-by-step explanation:
I give you 12 points if you help me ;) it’s math
Answer:
y=23.6
Step-by-step explanation:
20+0.45×8
20+3.6
23.6
Select all numbers that are a solution of the inequality.
Every month a salesperson adds 7 new accounts. The algebraic expression that represents the number of new accounts that he will add in m months is _____.
The algebraic expression that represents the number of new accounts that he will add in m months is x ≥ 7m.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Every month, a salesperson adds 7 new accounts.
Let m be the number of the month and x be the number of the accounts.
Then the inequality equation will be
x ≥ 7m
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b) The height of the control tower. a) The shortest distance between the pilot and the base of the control tower. From a horizontal distance of 10.5km, a pilot observes that the angles of depression of the top and base of a control tower are 36° and 41 degrees respectively. Calculate he following:
From the calculations, the height of the tower is 26.4 Km
What is the angle of depression?If we know that the base of the tower is B and he top of the tower is T then to find the shortest distance between the pilot and the base of the control tower;
Sin 41 = 10.5//BP/
/BP/ = 10.5/Sin 41
/BP/ = 15.9 Km
Now, the height of the control tower is obtained from;
First /AB/ = √(15.9)^2 - (10.5)^2
/AB/ = 11.9 Km
Given that;
Tan 36 = 10.5//BT/
/BT/= 10.5/Tan 36
/BT/= 14.5 Km
Hence the height of the tower is 11.9 Km + 14.5 Km = 26.4 Km
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como faltar a la escuela
Answer:
Como faltar a la escuela. Por favor, ¿cuál es el significado?
4 apples and 3 pears=£2.70 2 apples and 5 pears =£2.40 how much does 1 apple cost and 1 pear
Answer:
The answer is 0.45 pounds for an apple and 0.3 pounds for a pear
Step-by-step explanation:
Answer:
Cost of each apple: [tex]0.45[/tex].
Cost of each pear: [tex]0.30[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the cost of each apple. Let [tex]y[/tex] denote the cost of each pear.
The question states that the cost of [tex]4[/tex] apples and [tex]3[/tex] pears is [tex]2.70[/tex]. Thus:
[tex]4\, x + 3\, y = 2.70[/tex].
Likewise, since the cost of [tex]2[/tex] apples and [tex]5[/tex] pears is [tex]2.40[/tex]:
[tex]2\, x + 5\, y = 2.40[/tex].
Solve this system of equations for [tex]x[/tex] and [tex]y[/tex] to find the price of each fruit.
[tex]\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & 2\, x + 5\, y = 2.40\end{aligned}\right.[/tex].
Multiply both sides of the equation [tex]2\, x + 5\, y = 2.40[/tex] by [tex]2[/tex] to match the coefficient of [tex]x[/tex] in the first equation:
[tex]\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & (2\times 2)\, x + (2 \times 5)\, y = (2 \times 2.40)\end{aligned}\right.[/tex].
[tex]\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & 4\, x + 10\, y = 4.80 \end{aligned}\right.[/tex].
Substitute the first equation from the new equation to eliminate [tex]x[/tex] and solve for [tex]y[/tex]:
[tex]\begin{aligned}& 4\, x + 10\, y - (4\, x +3\, y) = 4.80 - 2.70\end{aligned}[/tex].
[tex]10\, y - 3\, y = 2.10[/tex].
[tex]7\, y = 2.10[/tex].
[tex]y = 0.30[/tex].
Substitute [tex]y = 0.30[/tex] into an equation from the original system to eliminate [tex]y[/tex] and solve for [tex]x[/tex].
[tex]2\, x + 5\, y = 2.40[/tex].
[tex]2\, x + 5 \times 0.30 = 2.40[/tex].
[tex]2\, x = 0.90[/tex].
[tex]x = 0.45[/tex].
Thus, [tex]x = 0.45[/tex] and [tex]y = 0.30[/tex].
In other words, the price of each apple would be [tex]0.45[/tex]. The price of each pear would be [tex]0.30[/tex].
A store selling school supplies advertises a bundle deal. The consumer can
pick a backpack, a binder, a pack of pencils, and notebook paper for a set
price. There are 6 types of backpacks, 4 types of binders, 5 types of pencils,
and 2 types of notebook paper. How many outcomes are possible in this
bundle?
Using the Fundamental Counting Theorem, it is found that the number of outcomes possible in this scenario is given by:
D. 240.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The number of options for each selection are given as follows:
[tex]n_1 = 6, n_2 = 4, n_3 = 5, n_4 = 2[/tex]
Hence the number of outcomes is given by:
N = 6 x 4 x 5 x 2 = 240.
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A quadrilateral has three congruent sides. Each of the congruent sides is 5 cm shorter than the forth side. If the quadrilateral has a perimeter of 33 cm, find the length of the longest side
The length of the three congruent sides is 7 cm and the fourth side length is 12cm.
Given quadrilateral has three congruent sides and perimeter of quadrilateral is 33 cm.
A quadrilateral can be expressed as ABCD and three congruent sides are AB, BC, CD and the fourth side is AD.
Let AD=x
then AB=BC=CD=x-5
This means if all the sides of a quadrilateral are known, we can get its perimeter by adding all its sides.
So, Perimeter = AB + BC + CD + DA.
Substitute values
(x-5)+(x-5)+(x-5)+x=33
4x-15=33
4x= 48
x=12
Hence the fourth side length is 12cm and the other sides are 7 cm longer.
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The midpoint of AB is M(-2, -1) If the coordinates of AA are (-7, 2) what are the coordinates of B?
Answer:
(3,-4)
Step-by-step explanation:
If b = 5, then the exact value of a is?
Answer:
5sqrt3
Step-by-step explanation:
You can use trigonometry to figure out the answer
TOA is tan(any angle) = opposite/adjacent
Tan(30) = 5/x
tan(30) = sqrt3/3
x = tan inverse (30) multiplied by 5
x = 5sqrt3
there are 2 quarters 1 nickle and 2 dimes in a pocket what is the probility of choosing a coin not returning it too the pocket and then choosing another of greater value
6. Find the distance between points A = (2, 0) and B = (0, 9). Round your answer to the nearest
tenth.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:\approx 9.2 \:\: units [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Using distance formula : - } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{(2 - 0) {}^{2} + (0 - 9) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{(2) {}^{2} + (- 9) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{ 4 + 81} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{85} \: \: units[/tex]
[tex]\qquad \tt \rightarrow \: \approx 9.2 \: \: units[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The distance between points A and B is 9.2 units.
We have,
To find the distance between two points (a, b) and (c, d) in a coordinate plane, you can use the distance formula:
Distance = √[(c - a)² + (d - b)²]
In this case, point A is (2, 0) and point B is (0, 9).
Now, plug the values into the distance formula:
Distance = √[(0 - 2)² + (9 - 0)²]
Distance = √[(-2)² + 9²]
Distance = √[4 + 81]
Distance = √85
Now, round the answer to the nearest tenth:
Distance ≈ √85 ≈ 9.2 (rounded to the nearest tenth)
Thus,
The distance between points A and B is 9.2 units.
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Find the solution to the system
of equations.
4
y = 2x + 2
3
2
([?], [ ])
-4-3-2/1
1 2 3 4
y=-x-3
-1
-2
3
-4
Answer:
(- 2, - 2 )
Step-by-step explanation:
the solution to the system is at the point of intersection of the 2 lines.
the 2 lines intersect at (- 2, - 2) , then
solution to the system is (2, - 2 )
what does a equal if 2÷a=(5/2)÷(5/4)
Question:
2÷a=(5/2)÷(5/4)
Answer:
a = 1
In the given figure, lines AC and BD intersect each other at point E.
If ∠AEB:∠BEC = 9 : 11, find all the angles.
The value of the angle AED = 99 degree , Angle BEC is 99 degree , angle DEC = 81 degree , angle AEB is 81 degree
What is angle of a Straight Line ?The straight line has an angle of 180 degree.
The two lines AC and BD intersects such that
∠AEB:∠BEC = 9 : 11
Let angle BEC be x
Then
Angle AEB is 9x/11
and angle AEC + BEC = 180 degree
(9x/11) + x = 180
9x +11x = 11 * 180
20x = 11 * 180
x = 99 degree
Angle BEC is 99 degree
and angle AEB is 81 degree
As Angle AED is vertically opposite to angle BEC
Therefore angle AED = 99 degree
As Angle DEC is vertically opposite to angle AEB
Therefore angle DEC = 81 degree.
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Please solve it. It will help me for my exam preparation.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} }{(p - y) {}^{y} } + \cfrac{ - 2p}{(p - y) {}^{y - 1} } + \cfrac{1}{(p - y) {}^{y - 2} } [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + ( - 2p)(p - y) + 1(p - y) { }^{2} }{(p - y) {}^{y} } [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2}- 2p {}^{2} + 2py + p {}^{2} + y{ }^{2} - 2py}{(p - y) {}^{y} } [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + {p}^{2} - 2p {}^{2} + 2py - 2py + y{ }^{2} }{(p - y) {}^{y} }[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]
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help i am struggling
Answer: it's D
Step-by-step explanation:
A trader bought 30 baskets of pawpaw and 100 baskets of mangoes for 2450. she sold the pawpaw at a profit of 40% and the mangoes at a profit of 30%. if her profit on the entire transaction was 855, find the cost price of a basket of pawpaw and the selling price of 100 baskets of mangoes.
The cost price of pawpaw is 40 and the cost if the basket of mangoes is 1250.
How to calculate the price?Based on the information given, the equations to solve the question will be:
30p + 100m = 2450 .... i
1.3 × 40p - 30 p + 1.3 × 100m = 855 ..... ii
30p + 100m = 2450
12p + 30m = 855
Solving simultaneously, the price of pawpaw is 40 and the price of mango is 12.5.
Therefore, the cost of 100 basket of mangoes will be:
= 12.5 × 100
= 1250
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Which classification describes the following system of equations?
12x+5y-3z= 36
x-2y+4z=3
9x-10y+5z = 27
A consistent and independent system of equations describes the given system of equations.
The consistent and independent system of equations are given below.
12x+5y-3z= 36x-2y+4z=39x-10y+5z = 27What is a consistent independent equation?A consistent equation is a system of linear equations that is consistently unbiased when it has precisely one solution. While this is the case, the graphs of the lines within the system move at exactly one point. In inconsistent, a system of linear equations is inconsistent if it has no solutions.
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Which graph represents the function r(x) = |x-2| -1
It's whichever graph is an absolute function and is shifted to the right by 2 and is shifted down by 1.
Since I don't have a picture of the graph this is the best I can do to help.
Answer:
see attached
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Given function:
[tex]r(x) = |x - 2| - 1[/tex]
The parent function of the given function is: [tex]f(x) = |x|[/tex]
Translated 2 units to the right: [tex]f(x-2)=|x-2|[/tex]
Translated 1 unit down: [tex]f(x-2)-1=|x-2|-1[/tex]
Graph of Modulus function
Line y = x where x ≥ 0
Line y = -x where x ≤ 0
Vertex at (0, 0)
Therefore, the graph of the given function is the graph of the modulus function translated 2 units to the right and 1 unit down. So, its vertex is at (2, -1).
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How much weight does the women in the video lose in a year? 80 pounds 90 pounds 50 pounds 20 pounds
Medical practitioners recommend losing around 365 pounds or 730 pounds per year.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Medical practitioners recommend losing around 1–2 pounds (0.5–0.9 kg) per week.
Hence for a year:
Amount of weight loss = (1 * 365) or (2 * 365)
Medical practitioners recommend losing around 365 pounds or 730 pounds per year.
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question below, NEED ASAP!! THANK YOU!!!
Answer:
1
Step-by-step explanation:
[tex] log_{3}(5) \times log_{25}(9) = \frac{ log(5) }{ log(3) } \times \frac{ log(9) }{ log(25) } = \frac{ log(5) }{ log(3) } \times \frac{2 log(3) }{ 2log(5) } = \frac{2}{2} = 1[/tex]
which greek mathematician wrote the most definitive text on geometry, one that is still referred torday.
Answer:
Pythagoras
Step-by-step explanation:
please mark me as brainlest
Find the value of y.
Answer:
its 0
Step-by-step explanation:
you just gotta do the math correctly to get the answer. x & y are both values with different meanings. but in this case it's 0
