Answers
Answer:
Geometric
an=an-1₋(.25);a₁=192
an=192(.25)^n-1
7.32421875*10^−4
Step-by-step explanation:
Answer:
The sequence shown is geometric
Recursive function:
[tex]a_{n} = a_{n-1}\times r[/tex]
with [tex]a_1 = 192[/tex]
Explicit function: [tex]a_n = 192 \times 0.25^{n-1} [/tex]
10th term: 0.000732421876
Step-by-step explanation:
In a geometric sequence the n+1 term divide by the n term is constant
48/192 = 0.25
12/48 = 0.25
3/12 = 0.25
From this result we can deduce the recursive function:
[tex]a_{n} = a_{n-1}\times r[/tex]
with [tex]a_1 = 192[/tex]
Explicit function:
[tex]a_n = a \times r^{n-1} [/tex]
where a is the first term in the sequence (= 192) and r is the common ratio (= 0.25). Replacing:
[tex]a_n = 192 \times 0.25^{n-1} [/tex]
The 10th term is:
[tex]a_{10} = 192 \times 0.25^9 = 0.000732421876 [/tex]
Related Questions
In Exercises 13 - 18 , find the value of x so that the function has the given value. (See Example 3.)
Answers
Answer:
-9
The problem:
If h(x)=-7x and h(x)=63, the what is the value of x?
Step-by-step explanation:
h(x)=-7x
You are asked to find x such that h(x)=63.
So you are solving:
h(x)=63 for x:
-7x=63
Divide both sides by -7:
x=63/-7
Simplify:
x=-9
Let's check:
h(x)=-7x
h(-9)=-7(-9)
h(-9)=63
So -9 is the answer.
The value of x in the equation y = 9 + 3x for a given y value can be found by rearranging the equation to x = (y - 9) / 3, and substituting the desired y value.
Explanation:The subject of this question is determining the value of x in the equation y = 9 + 3x. In this equation, the b term is 9 and the m term is 3, representing the y-intercept and the slope respectively. To find the value of 'x' that gives a specific 'y' value, one must rearrange the equation to solve for 'x': x = (y - 9) / 3. For example, if we wanted the y value to be 15, we would substitute into the equation and find that x = (15 - 9) / 3 = 2
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Rectangle HIJK has vertices H(-3, 2), I(4, 2), J(4, -3), and K(-3, -3). What are the coordinates of the image of I after a dilation by a factor of 1.5 centered at the origin?
A. I’(3, 6)
B. I’(6, 3)
C. I’(6, 2)
D. I’(8, 4)
Answers
Answer:
B. I’(6, 3)
Step-by-step explanation:
Multiply I(4, 2) by 1½:
2 × 1½ = 3
4 × 1½ = 6
So, your new coordinate is I'(6, 3).
I am joyous to assist you anytime.
Answer: B. I’(6, 3)
Step-by-step explanation:
The coordinates (x,y) of a shape after dilation by a factor of k centered at the origin is given by :-
[tex](x,y)\rightarrow(kx,ky)[/tex]
Given : Rectangle HIJK has vertices H(-3, 2), I(4, 2), J(4, -3), and K(-3, -3).
The coordinates of the image of I after a dilation by a factor of 1.5 centered at the origin will be :_
[tex]I(4,2)\rightarrow I' (1.5\times4, 1.5\times2)=I'(6,3)[/tex]
Hence, the coordinates of the image of I after a dilation by a factor of 1.5 centered at the origin =I’(6, 3)
-9x-6y=15,9x-10y=145
Answers
-9x-6y=15
9x-10y=145
Find y first by eliminating the x.
Add the two equations together.
-9x+9x-6y+-10y=15+145
-6y+-10y=15+145
-6y-10y=160
-16y=160
divide both sides by -16 to get +y
-16y/-16=160/-16
y=-10
Use the substitution method to find x
-9x-6y=15
-9x-6(-10)=15
Do the bracket first
-9x+60=15
Move +60 to the other side. Sign changes from +60 to -60.
-9x+60-60=15-60
-9x=-45
Divide both sides by -9
-9x/-9=-45/-9
x=5
Answer:
( 5,-10)
Thom earns $12.40 per hour at the
Yankee Bowling Alley. He regularly
works 40 hours per week. He is paid
time and a half for each our of overtime
work. Last week he worked 42 hours.
What was his gross pay for the week?
Answers
Answer:
$3,645.6
Step-by-step explanation:
1hr=$12.4
42hrs=x
x=$520.8×7 =$3,645.6
AN ice cream factory makes 230 quarts of ie cream in 2 hours. how many quarts could be made in 12 hours?what was the rate per day
Answers
it makes 2760 per 12 hours
how do you solve 2i and 2ii
Answers
Answer:
15 and 21
Step-by-step explanation:
Given the n th term formula
T = 2n + 5
To find the 5 th and 8 th terms substitute n = 5 and n = 8 into the formula
[tex]T_{5}[/tex] = (2 × 5) + 5 = 10 + 5 = 15
[tex]T_{8}[/tex] = (2 × 8) + 5 = 16 + 5 = 21
Given:
Tn = 2n+5
`The fifth term, i.e., n=5Substituting the value inside the formula we get,
2(5) + 5 => 10 + 5 => 15
2. The Eighth term, i.e., n=8
Substituting the value inside the formula we get,
2(8) + 5 => 16 + 5 => 21
1.6w - 1.2w + 3.5 + 4.7w
Answers
Answer:
8.6
Step-by-step explanation:
basically just do the order of operations
Which number has the lowest value ?
a) 1/2 +0.30 b) 0.10 + 3/4 c) 1/3 + 0.50 d) 1/3 +0.40
Answers
Hey!
-------------------------------
Let's Solve A:
1/2 = 0.5
0.5 + 0.30 = 0.80
a = 0.80
-------------------------------
Let's Solve B:
3/4 = 0.75
0.10 + 0.75 = 0.85
b = 0.85
-------------------------------
Let's Solve C:
1/3 ≈ 0.33
0.33 + 0.50 = 0.83
c = 0.83
-------------------------------
Let's Solve D:
1/3 ≈ 0.33
0.33 + 0.40 = 0.73
d = 0.73
-------------------------------
Answer:
By solving each equation we can see that option A has the lowest value!
-------------------------------
Hope This Helped! Good Luck!
Among these options, option (d) with a value of 0.73 has the lowest value.
How did we determine the lowest value?
To determine which number has the lowest value among the given options, let's calculate the values of each option:
a) 1/2 + 0.30 = 0.5 + 0.30 = 0.80
b) 0.10 + 3/4 = 0.10 + 0.75 = 0.85
c) 1/3 + 0.50 = 0.33 + 0.50 = 0.83
d) 1/3 + 0.40 = 0.33 + 0.40 = 0.73
Among these options, option (d) with a value of 0.73 has the lowest value.
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There is a spinner with 13 equal areas, numbered 1 through 13. If the spinner is spun one time, what is the probability that the result is a multiple of 6 or a multiple of 4?
Answers
Answer:
5 out of 13
Step-by-step explanation:
you will see all the multiples of six and 4 between 1 and 13.Which are
6=6 and 12
4=4,8,12
which are five numbers so 5 out of 13
If a point, Ray, line segment, or plane intersects a segment at its midpoint, then it______ the segment
Answers:
Bisects
Multiplies
Parallels
Subtends
Answers
Answer: If A Point, Ray, Line Segment, or Plane intersects a segment at its midpoint, then it Bisects the segment.
Step-by-step explanation: A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Point is equidistant from two points if its distance from each point is the same.
The wrong choice can be defined as follows
Multiplies is wrong because it is used as a mathematical sign.In maths, the parallel is also known as the lines that are not a plane and don't meet.The subtends are used as the contrary and stretch a straight angle from one side to the other, that's why it's wrong.Therefore, the "Bisects" is the correct choice.
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A baker has 5 1/4 pies in her shop. She cut the pies in prices that are each 1/8 of a whole pie. How many slices of pie does she have
Answers
5_1/4 = 21/4.
21/4 - 1/8
LCD = 8
(42 - 1)/8
41/8 remains.
2, 8, 7, 8, 6, 15, 6, 3, 8
What is the range of the data?
ОА. 2
Ов. 6
Ос. 8
Op. 13
OE. 15
Answers
Answer: 13
Step-by-step explanation: To find the range of the data set shown here, let’s first go over what range is. The range of a data set is the difference between the greatest number and the least number.
To find the range of the data set shown here, we will need to subtract the least number from the greatest number.
Least number = 2
Greatest number = 15
Greatest number - least number = range
15 - 2 = range
13 = range
Therefore, the range of the data set shown here is 13.
Kyle practices 2.5 times as many hours as Grant does. Write an expression to
show how many hours Kyle practices. Let t equal the number of hours Grant
practices.
Answers
The expression to show how many hours Kyle practices is 2.5t, where t equals the number of hours Grant practices.
Explanation:If Kyle practices 2.5 times as many hours as Grant does, and we let t represent the number of hours Grant practices, then the expression to show how many hours Kyle practices would simply be 2.5t. This is because we are given the ratio of Kyle's practice time to Grant's practice time, which we can use to express Kyle's practice time in terms of Grant's.
0.003 is 1/10 of which decimal?
Ⓐ0.3
Ⓑ0.03
Ⓒ0.33
Ⓓ 0.333
Answers
The total cost after tax to repair Deborah’s computer is represented by 0.07(4 0h) + 4 0h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of tax Deborah has to pay? Explain
Answers
Answer:
depending on the national/ regional legal provisions in favour of the tax contributor where either the work is provided/ the computer was aquired/ placed, repaired/ the repair company has declared fiscal residency the cost ( in hours) could be determined by 0.07 ( 40h)
Final answer:
The expression 0.07(40h) in the equation represents the amount of tax Deborah has to pay. 0.07 stands for the 7% tax rate applied to the cost of repair, which is denoted by 40h.
Explanation:
The student has asked to identify the part of the expression in 0.07(4 0h) + 4 0h, which represents the tax Deborah has to pay for her computer repairs, where h represents the number of hours it takes to repair the computer. In this expression, the tax component is given by 0.07(40h).
The 0.07 represents the 7% tax rate on the cost of repair. The cost of repair, before tax, is represented by the term 40h. When you multiply 40h by 0.07, you are calculating 7% of the repair cost which equates to the tax amount.
John and his three brothers share a cell phone plan. The cell phone company charges a flat rate of $90 per month, which the four brothers share equally. In addition, the cell phone company charges 25 cents per megabyte of data downloaded. Each brother pays for his own downloaded data.
John's share of the current cell phone bill is $147.50.
Which equation determines how many megabytes of data John downloaded?
Answers
Answer:
(147.50 - 22.5)/.25
Step-by-step explanation:
First subtract his portion of the $90. Which is $22.5, when subtracted from 147.5 you get $125. Now divide $125 by .25 cents and you get the amount of megabytes he downloaded.
Answer: 22.5+0.25x=147.50
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
Flat rate: $90, (share equally among the four brothers means 90/4 =$$22.5 each) Cost per megabyte: $0.25 John's share: $147.50So, the equation is
22.5+0.25x=147.50
Where "x" is the number of megabytes of data that john downloaded
Feel free to ask for more if needed or if you did not understand something.
SUBTRACT
(−2x4−2x3+8x2+2)−(x4−5x3+2x+7)
Enter your answer, in standard form, in the box.
Answers
Answer:
[tex] -3x^{4} + 3{x}^{3} + 8{x}^{2}- 2x - 5[/tex]
Step-by-step explanation:
To avoid confusion, distribute the negative amongst all terms in the second set of parentheses.
I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
Based on the calculations, the solution to the expression is [tex]-3x^4+3x^3+8x^2-2x-5[/tex]
What is the distribution property of multiplication?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.
Based on the information provided above, we have this expression:
[tex](-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)[/tex]
By applying the distributive property of multiplication to the given expression, we would open the parentheses by distributing the negative sign as follows:
[tex]-2x^4-2x^3+8x^2+2-x^4+5x^3-2x-7\\\\-3x^4+3x^3+8x^2-2x-5[/tex]
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Complete Question:
SUBTRACT
[tex](-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)[/tex]
Enter your answer, in standard form, in the box.
which of the following is the equation of a line parallel to the line y = -x + 1, passing through the point (4,1)?
Answers
Answer:
○ A. x + y = 5
Step-by-step explanation:
Parallel lines have SIMILAR RATE OF CHANGES [SLOPES], so -1 remains the same:
1 = -[4] + b
↑
-4
5 = b
You have the equation, but all answer choices are in Standard Form, so we need to convert from Slope-Intercept to Standard:
y = -x + 5 >> Parallel Equation
+x + x
_________
x + y = 5 >> Standard Equation
I am joyous to assist you anytime.
Is 63÷17= 37?I don't know
Answers
Answer:
No.
Step-by-step explanation:
The answer needs to be rounded, but it's approximately 3.706
Answer:
No it is 3.70588235294
You can also round it up to 3.705 or 3.706
Which of the following statements best summarizes nationalism in the Middle East during the 1920s?
Answers
The most accurate summary of nationalism in the Middle East during the 1920s is option c: Broken Western promises and conflicting nationalist goals set the nations of the former Ottoman Empire on the path to conflict.
After World War I, the Middle East experienced a surge in nationalist aspirations as the Ottoman Empire collapsed. However, the promises of self-determination made by Western powers, particularly through the Sykes-Picot Agreement and the Balfour Declaration, were largely unfulfilled.
This led to widespread discontent and conflicting nationalist goals, creating tensions and setting the stage for regional conflicts. Additionally, the imposition of artificial borders and the interference of Western powers further fueled nationalist sentiments, contributing to a turbulent period of political, social, and economic unrest in the Middle East during the 1920s.
The failure of Western promises and the clash of nationalist ambitions indeed played a pivotal role in shaping the trajectory of the region.
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The probable question may be:
Which of the following statements best summarizes nationalism in the Middle East during the 1920s?
a. Self-determination allowed the peaceful creation of new, modern nation states in the former Ottoman Empire.
b. The discovery of resources encouraged regional cooperation and introduced an era of prosperity for all people.
c. Broken Western promises and conflicting nationalist goals set the nations of the former Ottoman Empire on the path to conflict.
d. Turkey re-established the Ottoman Empire with a policy of tolerance towards the diverse groups of the region.
What is 72 ÷ 8 + 4y3 when y = 3?
Answers
Answer:
117
Step-by-step explanation:
Given
72 ÷ 8 + 4y³ with y = 3, substitute y = 3 into the expression
= 72 ÷ 8 + 4 × 3³ ← evaluate exponent
= 72 ÷ 8 + 4 × 27 ← evaluate division and multiplication
= 9 + 108 ← calculate addition
= 117
It’s simple I swear!!! what is the square root of 25 times the square root of 9
Answers
Answer:
15
Step-by-step explanation:
1st multiply the numbers: 25 × 9 = 225
2nd factor the number: 225 = √15^2
3rd apply radical rule: √15^2 = 15
Hope I helped :)
Answer:25 square root of 9
=25^9
Step-by-step explanation: if its a graph go to wolfram to see it because i cant draw it .
I hope I helps you.
Sam makes enough muffins to give 8 of her
friends 3 muffins each. Each tray holds 6
muffins. How many trays does she need?
Answers
Sam needs [tex]4[/tex] trays.
Given:
The number of friends is [tex]8[/tex].
Muffins required for each friend are [tex]3[/tex].
The capacity of each tray is [tex]6[/tex] muffins.
To find:
The required number of trays.
Explanation:
Let [tex]x[/tex] be the required number of trays.
Total quantity of muffins in [tex]x[/tex] trays is [tex]6x[/tex].
Total quantity of required muffins is:
[tex]8\times 3=24[/tex]
Now,
[tex]6x=24[/tex]
[tex]x=\dfrac{24}{6}[/tex]
[tex]x=4[/tex]
Therefore, Sam needs [tex]4[/tex] trays.
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You are playing basketball with your friends. The height (in feet) of the ball above the ground t seconds after a shot is released from your hand is modeled by the function f(x)=-16^2 + 32t + 5.2
Answers
Answer:the ball is released when t = 0
The ball is 5.2 feet above the ground when it is released
The ball is 5.2 feet in height from the ground and it will hit the ground after 2 seconds.
What is a function?
A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
Given the function has height with time t
f(x)=-16t² + 32t + 5.2
At the time of release, the value of time t will be 0
So, t = 0
f(x) = 0 + 0 + 5.2 ⇒ f(x) = 5.2 feet
So height is 5.2 feet
Now,
The time taken to cover this height will be
5.2 = 16t² + 32t + 5.2
16t² + 32t = 0
16t(t + 2) = 0
t = 0 and -2
Since if some height exists then time can never be 0 and time also does not exist in negative so consider 2.
Hence "The ball is 5.2 feet in height from the ground and it will hit the ground after 2 seconds.
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PLEEASSSSEEEE HHEEEEELLLLPPPPPPPP !!!!!!!!!!!!!!!!!!!!!!!!!!! Circle R is shown. Line segments Q R and S R are radii. The length of Q R is 18. Sector Q R S is shaded. The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared
Answers
Answer:
[tex]144\pi\ un^2.[/tex]
Step-by-step explanation:
In the attached diagram, circle R is shown. Line segments QR and SR are radii and QR = SR = 18 units.
The measure of the central angle QRS is [tex]\dfrac{8\pi}{9}[/tex]
1. Find the area of the whole circle:
[tex]A_{circle}=\pi r^2=\pi \cdot 18^2=324\pi \ un^2.[/tex]
2. Note that the whole circle is determined by the full rotation angle with measure [tex]2\pi[/tex] radians. So,
[tex]\begin{array}{cc}\text{Angle}&\text{Area}\\ \\2\pi &324\pi \\ \\\dfrac{8\pi }{9}&A_{sector}\end{array}[/tex]
So, write a proportion:
[tex]\dfrac{2\pi}{\frac{8\pi}{9}}=\dfrac{324\pi}{A_{sector}}[/tex]
Cross multiply
[tex]2\pi \cdot A_{sector}=324\pi \cdot \dfrac{8\pi }{9}\\ \\A_{sector}=162\pi \cdot \dfrac{8}{9}=144\pi\ un^2.[/tex]
Answer:
144
Step-by-step explanation:
What is the equation for the line that passes through the points (-5, 2) and (5,-6)?
Answers
Answer:
4x + 5y = -10 or y = -⅘x - 2
Step-by-step explanation:
First, find the rate of change [slope]:
-y₁ + y₂\-x₁ + x₂ = m
[tex] \frac{ -2 - 6}{5 + 5} = - \frac{8}{10} = - \frac{4}{5} [/tex]
Then use the Point-Slope Formula since we are given points. Now, according to this formula, all negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting the coordinates into the formula with their CORRECT signs. It does not matter which one you choose:
y - y₁ = m(x - x₁)
y + 6 = -⅘(x - 5)
y + 6 = -⅘x + 4
- 6 - 6
_______________
y = -⅘x - 2
If you want it in Standard Form:
y = -⅘x - 2
+⅘x +⅘x
___________
⅘x + y = -2 [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]
5[⅘x + y = -2]
4x + 5y = -10 >> Line in Standard Form
__________________________________________________________
y - 2 = -⅘(x + 5)
y - 2 = -⅘x - 4
+ 2 + 2
______________
y = -⅘x - 2
y = -⅘x - 2
+⅘x +⅘x
___________
⅘x + y = -2 [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]
5[⅘x + y = -2]
4x + 5y = -10 >> Line in Standard Form
** You see? I told you that it would not matter which ordered pair you choose because you will always get the exact same result!!!
I am joyous to assist you anytime.
the factors of 6x-30 are ?
Answers
Answer:
6 and x - 5
Step-by-step explanation:
Given expression,
[tex]6x-30[/tex]
Since, factor of a number or an expression is obtained after breaking up the number or expression,
Or we can say a number is always divisible by its factor.
[tex]\because 6x - 30 = 6x - 6\times 5 = 6(x-5)[/tex] ( By the converse of distributive property )
Thus, 6 and x - 5 are the factors of 6x - 30.
what is the answer to Simplify: √3/√15
Answers
Answer:
[tex]\frac{1}{\sqrt5}[/tex]
Step-by-step explanation:
[tex]\large{\frac{\sqrt{3}}{\sqrt{15}}=\frac{\sqrt{3}}{\sqrt{3.5}}=\frac{\sqrt{3}}{\sqrt{3}.\sqrt{5}}=\frac{1}{\sqrt{5}}}[/tex]
What happened on September 11, 2001?
Answers
Answer:
On 11 September 2001 (known as 9/11 in America), Islamist extremists hijacked four planes that were flying above the US. Two of them were flown into the twin towers of the World Trade Center in New York. Another was crashed into the Pentagon, the top military building in the capital city, Washington DC.
Step-by-step explanation:
Answer:
On the morning of September 11, 2001, 19 al-Qaeda terrorists hijacked four commercial passenger jet airliners, intentionally crashing two into the World Trade Center in New York City. The hijackers crashed a third airliner into the Pentagon. The fourth plane crashed in a field near Shanksville, Pennsylvania.
Hope this helps :)
The product of twice a number and six is the same as the difference of eleven times the number and 6/5 . Find the number
Answers
Answer:
-6/5
Step-by-step explanation:
solution;
let,the number be x,
product of twice of x and six = the difference
difference of eleven times x and 6/5
or, (2x×6)=(11×x)-(6/5)
or, 12x = 11x - 6/5
or, 12x - 11x = -6/5
therefore,x =-6/5
Therefore, the number required is (-6/5) whose product of twice a number and six is the same as the difference of eleven times the number and 6/5 .