The Recursive formula for the given explicit formula is u(1) = 1 and u(n+1) = u(n) + 4 , for n = 1 , 2 , 3 .... , the correct option is (b) .
In the question ,
it is given that ,
the explicit formula is u(n) = 4n - 1 .
and u(n) = 1 ,
we need to find the recursive formula ,
We substitute n + 1 in place of n , in the equation u(n) = 4n - 1
after substitution , we get
u(n+1) = 4(n + 1) - 1
u(n+1) = 4n + 4 - 1
u(n+1) = 4n + 3
Subtracting u(n) = 4n - 1 from u(n+1) = 4n + 3 ,
we get
u(n+1) - u(n) = 4n + 3 - (4n - 1)
u(n+1) - u(n) = 4n + 3 - 4n + 1
u(n+1) - u(n) = 3 + 1
u(n+1) - u(n) = 4
u(n+1) = u(n) + 4
Therefore , The Recursive formula for the given explicit formula is u(1) = 1 and u(n+1) = u(n) + 4 , for n = 1 , 2 , 3 ....
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Jessica cuts a ribbon with a length of 12 inches into three pieces such that the length of one piece is 312 inches and the lengths of the other two are the same. What is the length of each of the other two pieces?.
The length of each of the other two pieces = 0.
Jessica cuts a ribbon with a length of 12 inches into three pieces.
The length of one piece is [tex]3\frac{1}{2}[/tex]
The lengths of the other two are the same
To find out the length of each of the other two pieces:
Based on the given conditions, we write formula as
(3-3)÷2
The sum of two opposites equals O: [tex]\frac{3-3}{2}[/tex]
Apply Zero property of Multiplication: 0
So we get the result = 0
Hence the answer if the length of each of the other two pieces = 0.
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Jace works as a salesperson at an electronics store and sells phones and phone accessories. Jace earns a $11 commission for every phone he sells and a $3 commission for every accessory he sells. On a given day, jace made a total of $102 in commission from all accessory and phone sales and he sold twice as many accessories as phones. Determine the number of phones sold and the number of accessories sold.
The sales of phones and accessories should be 6 and 12 each, correspondingly.
Explain the term commission?A simple definition of commission accounting is an income or expense incurred by the business throughout the course of a transaction. Usually, commission-based real estate companies or other sales organizations employ this style of bookkeeping.The data stated in question-
For each phone he sells, Jace receives a $11 commission, and for each accessory, he receives a $3 commission. Jace sold twice quite so many components as phones on any given day, generating a commission of $102 from both types of transactions.Let 'P' be the number of the phones sold.
Then, the accessory sold be '2P'.
The equation will form for the total cost will be;
11P + 3(2P) = 102
11P + 6P = 102
17P = 102
P = 102 / 17 =
P = 6 (number of sold phones)
Accessories sold = 2P = 2 x 6 = 12
Thus, the sales of phones and accessories should be 6 and 12 each, correspondingly.
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Sierra Left a 4.50$ tip for a waiter what was 18% of the bill before the tip
Answer:
$25.00
Step-by-step explanation:
Total amount of bill is $25.
Given information:
The amount of tip = $4.50
The percentage given = 18%
4.50 of 18% is $25
Chris is decorating a bulletin board with boarders. She will put them along each side of the bulletin board (on the
Perimeter of rectangle) with Length 2.6 meters and width 1.2 meters. How much would she use?
Write numerical answer only (no sentences, no units)
Pls do it step by step on how to do it
Answer: 7.6 meters.
Step-by-step explanation:
1.2(2) + 2.6(2)
2.4 + 5.2
7.6
Remember, perimeter is L(2) + W(2).
last answer is 3 btw
Answer:
the rd one
Step-by-step explanation:
its the -21/2
if u need help tell me
From a balloon 849 feet high, the angle of depression to the ranger headquarters is 55°11'. How far is the
headquarters from a point on the ground directly below the balloon (to the nearest foot)?
The distance from the headquarters to a point on the ground directly below the balloon (to the nearest foot) is 1221 feet
How to find the distance requiredThe distance is calculated using tangent of the angle using the formula
tan x = opposite / adjacent
From the question it can be deduced that
x = 55°11'
opposite = the required distance
adjacent = 849 feet
solving for the opposite
tan x = opposite / adjacent
tan 55°11' = opposite / 849
opposite = 849 * tan 55°11'
opposite = 1220.793
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Arrange the following measurements in order from smallest to largest.
5 grams 0.35 kilograms 9.4 grams
Answer:
5 grams, 9.4 grams, 0.35 kilograms
Step-by-step explanation:
9.4 g and 5g are already converted so don't worry about those.
0.35 kilograms translates to 350 grams.
from smallest to largest thatd be
5, 9.4, 350
Find the y- intercept -1/6,(12,-2
The y intercept of the line passing through the points (12,-2) and slope -1/6 is 0 .
In the question ,
it is given that ,
the slope of the line is -1/6 ,
the line passes through the points (12 , -2)
we know that the equation of the line is written as
y = mx + c
where, "m" is the slope
and c is the y intercept .
Since the line passes through point (12,-2) , it should satisfy the equation of the line , that is
-2 = (-1/6)*12 + c
-2 = -2 + c
c = -2 + 2
c = 0
So , y intercept is 0 .
Therefore , The y intercept of the line passing through the points (12,-2) and slope -1/6 is 0 .
The given question is incomplete , the complete question is
Find the y intercept of the line passing through (12,-2) and slope = -1/6 ?
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hi guys the question and numbers are in the image. could someone explain this in detail pls? I need to be able to do this by myself to.
help I WILL GIVE BRAINLIEST
What’s the answer for this equation: x<-x+7(x-2)
Answer:
x > 2.8
Step-by-step explanation:
x < -x + 7(x - 2)
Expand using the Distributive Property
x < -x + 7x - 14
x < 6x - 14
Subtract x from both sides
0 < 6x - 14 - x
0 < 5x - 14
Add 14 for both sides
5x > 14
x > 14/5
x > 2.8
Square root of 15.625
Square root of 15.625 is 3.906
What in mathematics is a square root?
A number can be generated by multiplying the square root of that number by itself. The word" square root" is represented by the symbol" sqrt" square root of, end square root. The reverse of squaring a number is chancing the square root.
How is the square root calculated?
The result of multiplying a number by itself yields its square value, while the square root of a number can be set up by looking for a number that, when squared, yields the original value. It follows that a a = b if" a" is the square root of"b."
Find the nearest perfect square, in this case 16 .
Subtract 4 from the number (15.625) (the square root of 16). The outcome is around 3.906
Calculate 3.953 by averaging 4 and 3.906. This approximate value represents the square root of 15.625.
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U GET BRAINLIST IF U HELP ME AND GIVE ME THE RIGHT ANSWER
The area of the given shape is 78.5 unit²
Given,
The shape is 1/4th part of circle.
The radius is given as 10 units
We have to find the area of the shape.
Here,
The area of a circle is pi times the radius squared (A = π r²).
Area of circle = π × r²
Then
Area of 1/4th part of circle = π × r² / 4
That is,
Area of 1/4th part of circle = 3.14 × 10² / 4
Area of 1/4th part of circle = 314 / 4
Area of 1/4th part of circle = 78.5 unit²
That is,
The area of the given shape is 78.5 unit²
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the time (in hours) required to repair a machine follows an exponential distribution, and the mean repair time is 2.5 hours. (a) what is the probability that a repair will take less than 2 hours?
0. 63212 is the probability that a repair will take less than 2 hours.
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.
P( X > 2 ) = 1 - P ( X/ leq2 )
= 1 - F( 2)
= 1 - [tex]e^{0.5 * 2}[/tex]
= 0. 63212.
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pew research center reported that among months, familt size is shrinking. suppose we are to randomly select one mother and record the number of children
It is a valid probability model when pew research center reported that among months, family size is shrinking.
Given that,
pew research center reported that among months, family size is shrinking. suppose we are to randomly select one mother (age 40 to 44) and record the number of children she has. Here is a probability model.
We have to find explain why this is a valid probability model.
We know that,
In the picture we can see,
Probability is 0.22+0.41+0.24+0.13 = 1
Since all probability are less than 1 and sum of all probability is equal to 1.
Therefore, It is a valid probability model when pew research center reported that among months, family size is shrinking.
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helium is pumped into a spherical balloon at a rate of 5 cubic feet per second. how fast is the radius increasing after 2 minutes?
The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³
Given,
The constant rate at which helium is pumped into the spherical balloon, r = 5 ft.³/s
We have to find the rate at which the radius of the balloon is increasing after 2 minutes.
Here,
dV/dt = (dV/dr) × (dr/dt)
Then,
dr/dt = (dV/dt) / (dV/dr)
The volume of balloon after 2 minutes (120 seconds) V₁₂₀ ;
V₁₂₀ = 120 s × 5 ft.³/s = 600 ft.³
The radius of balloon after 2 minutes ;
V = 4/3 π r³
dV/dr = 4 π r²
r = [tex]\sqrt[2]{\frac{2}{4.\pi } V}[/tex]
Then,
r₁₂₀ = [tex]\sqrt[2]{\frac{2}{4.\pi } 600}[/tex] ≈ 9.77
dr/dt = (dV/dt) / (dV/dr) = 5 / 4π r²
At t = 2 minutes (120 seconds), r ≈ 9.77 feet
dr/dt ≈ 5 / 4π 9.77² ≈ 4.16 × 10⁻³
That is,
The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³
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Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below: A. The thickness of the slices will be dx for both methods. B. When using the shell method, we cut the region into small slices perpendicular to the x-axis. C. When using the disk method, we cut the region into small slices perpendicular to the x-axis. D. The volume of the solid of revolution can be interpreted as the limit of Riemann sums. E. When using the shell method, we cut the region into small slices parallel to the x-axis. F. The shell method will always result in a less complicated integral. G. When using the disk method, we cut the region into small slices parallel to the z-axis.
The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.
(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.
(e) When using shell method, we cut region into small slices parallel to x-axis.
In the question ,
seven statements are given about a solid of revolution obtained by rotating a region R around the x-axis.
we have to find statement which are true .
Option (a)
Thickness of the slide is dx for disk method and
dy for the shell method while rotating about x - axis ,
So , statement of option(a) is false .
Option(b)
In shell method , elementary cylinders are drawn with axis of symmetry same as axis of rotation ,
thus the cylinder elements will be parallel to x axis rather than being perpendicular to the x axis ,
So , statement of option (b) is false .
Option(c)
In disk method , the slices are cut perpendicular to the axis of rotation , since we are rotating the region about x axis ,
Thus , slices are cut perpendicular to the x axis .
statement of option (c) is True .
Option (d)
As in 2D , the bounded area can be interpreted as a limit of Riemann sums , Similarly in 3D , the volume formed by rotating the bounded region about the x axis can be interpreted as a limit of Riemann sums .
So , statement of option(d) is True .
Option(e)
When using shell method, we cut region into small slices perpendicular to the x-axis .
So , statement of option(e) is False .
Option(f)
There can be both the kinds of cases , like in some cases disk method is easier than shell method and
in other cases shell method can be easier than disk method .
So , statement of option(f) is False .
Option(g)
When using disk method, we cut region into small slices perpendicular to x-axis .
So , statement of option (g) is False .
Therefore , The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.
(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.
(e) When using shell method, we cut region into small slices parallel to x-axis.
The given question is incomplete , the complete question is
Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below:
(a) The thickness of the slices will be dx for both methods.
(b) When using the shell method, we cut the region into small slices perpendicular to the x-axis.
(c) When using the disk method, we cut the region into small slices perpendicular to the x-axis.
(d) The volume of the solid of revolution can be interpreted as the limit of Riemann sums.
(e) When using the shell method, we cut the region into small slices parallel to the x-axis.
(f) The shell method will always result in a less complicated integral.
(g) When using the disk method, we cut the region into small slices parallel to the z-axis.
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what is the answer for 63 divided by (5-48 equal
Answer:
-35.4
Step-by-step explanation:
Using PEMDAS divide 63 first by 5 and u will get:
63÷5=12.6Now we have 12.6-48. If we subtract them together we will get:
12.6-48= -35.4Hence, the answer is -35.4
use the picture to determine x and y
The unknown value of x and y from the attached picture of a square is 8 and 11 respectively.
What is the variable in the square?A square is a four sided polygon with 4 equal angles and length.
The angle at each corner of a square = 90°The fourth corner = 90° - 36°
= 54°
Recall,
Alternate angles are equal
So,
(4x + 4)° = 36°
substract 4 from both sides
4x = 36 - 4
4x = 32
divide both sides by 4
x = 32/4
x = 8
(4y + 10)° = 54°
substract 10 from both sides
4y = 54 - 10
4y = 44
divide both sides by 4
y = 44/4
y = 11
In conclusion, the value of the following given equations are:
(4x + 4)° = 36°
4(8) + 4 = 36
32 + 4 = 36
36° = 36°
(4y + 10)° = 54°
4(11) + 10 = 54
44 + 10 = 54
54 ^= 54°
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Heya hiya party people just need sum help!
If the equation for the this graph is f(x)= 2x - 3 and g(x) comes from translating f(x) down 2 units, what is the equation for g(x)?
g(x) = 2x - 3
g(x) = x + 1
g(x) = 2x - 5
g(x) = -x -5
Answer: a is the correct answer
Step-by-step explanation:
A 2-digit odd number is a factor of 60 and a multiple of 3, What is the number?
Answer:
15
Step-by-step explanation:
Let's try to list the factors of 60 first.
60 { 1,2,3,4,5,6,10,12,15,20,30,60}
Now, it says it's a double digit number, so these are the remaining answers.
{10,12,15,20,30,60}
Since it is a multiple of 3, these are the possibilities.
12,15,20,30,60
After that, since it says that it's odd, we only have one possible solution left.
15
how to find the number of solutions to a system of equations
If a triangle is equiangular, then the triangle is a(n) _ triangle
Equilateral
O Isosceles
Scalene
O Right
If the triangle is equiangular, then the triangle is an equilateral triangle.
What is equiangular triangle?
A triangle with three equal interior angles is called an equiangular triangle. In an equiangular triangle, the measure of each of its interior angles is 60
What is equilateral triangle?
an equilateral triangle is a triangle that has all its sides equal in length. Also, the three angles of the equilateral triangle are congruent and equal to 60 degrees. The sum of all three angles of an equilateral triangle is equal to 180 degrees. 60° + 60° + 60° = 180°.
As we can see, that in equilateral triangle, all the angles are of 60, as same as of equiangular triangle.
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Write a linear function rule for the data in the table. x 0 1 2 3 4 y 3 1 –1 –3 –5 A. f(x) = 2x + 3 B. f(x) = –2x + 3 C. f(x) = 2x – 6 D. f(x) = –2x – 6
Answer:
f(x) = –2x + 3
Step-by-step explanation:
The population of bacteria in an experiment
increases by 90% each day. If there were 100
bacteria at the beginning, how many would
there be after 5 days?
Hel
Skip
Answer:
450 bacteria
Step-by-step explanation:
90 percent of 100 is 90 90x5 is 450
drew thinks the answer to the question 3/7 ÷ -2/3 is -6/21. Is drew correct.
No drew is incorrect and the right answer to this question is - 9/14 which can be calculated by using BODMAS rule.
What is BODMAS rule?
It stands for Bracket Of Division Multiplication Addition Subtraction which is a simple rule for solving calculation. It means first we solve brackets of a statement and so on.
Main Body:
Given :
⇒3/7÷ 2/3
This can be solved by changing the division to multiplication and taking reciprocal of the term behind it.
⇒3/7×-3/2
⇒-9/14
Hence the correct answer to the statement is -9/14.
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Which points are on the graph of k(x)=(1/4)^x ?
Select each correct answer.
Responses
(−1, 4)
begin ordered pair negative 1 comma 4 end ordered pair
(0, 14)
begin ordered pair 0 comma 1 fourth end ordered pair
(3, 164)
begin ordered pair 3 comma 1 over 64 end ordered pair
(1, 4)
Answer:
(3, 1/64)
(−1, 4)
Step-by-step explanation:
took the test
Answer:
(3, 1/64)
(−1, 4)
Step-by-step explanation: toom the test :)
For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as.
For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic are as follows:
p-value = 0.09 is the probability of obtaining a value for the test statistic.
We are going step by step
Step 1) the p-value is the probability of obtaining a value for the test statistic at least as extreme as that provided by the sample
Step 2) Here the Confidence level is equal to 0.95
So the level of significance is equal to 0.05
p-value = 0.09
Since the p-value is higher than the level of significance that we do not reject the null hypothesis.
Hence the answer, the p-value = 0.09 is the probability of obtaining a value for the test statistic.
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It’s due today! I need help asap!!
a) Using PEMDAS, the value of expression 5² - 9 ÷ 3 is 22.
b) Using PEMDAS, the value of expression 8 + 6 - 2× 2 -3² is 1.
Define PEMDAS.According to the PEMDAS rule, the computation wrapped in brackets or the parenthesis comes first in the order of operation. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and finally addition and subtraction.
Given,
Expressions:
a) 5² - 9 ÷ 3
Using PEMDAS,
Squaring,
25 - 9 ÷ 3
Dividing,
25 - 3
Subtracting,
22
Using PEMDAS, the value of expression 5² - 9 ÷ 3 is 22.
b) 8 + 6 - 2× 2 -3²
Using PEMDAS,
Squaring,
8 + 6 - 2 × 2 - 9
Multiplying,
8 + 6 - 4 - 9
Adding,
14 - 4 -9
Subtracting,
1
Using PEMDAS, the value of expression 8 + 6 - 2× 2 -3² is 1.
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1) Which three lengths could be the lengths of the sides of a triangle?
A. 11 cm, 11cm, 24 cm
B. 18 cm, 12cm, 9 cm
C. 9 cm, 19 cm, 10 cm
D. 4 cm, 7 cm, 23 cm
2) The length of two sides of a triangle are 9 and 15. What can be said about the length of the third side?
A. it must be greater than or equal to 6 and less than 24
B. it must be greater than or equal to 6 and at most 24
C. it must be greater than 6 and less than 24
D. it must be greater than 6 and at most 24
1. The three lengths are B. 18cm, 12cm, and 9cm which cοuld be the lengths οf the sides οf a triangle.
2. The third side D. It must be greater than οr equal tο 6 and at mοst 24.
What is length?A physical measure οf distance between twο places in space is length. It is a fundamental quantity that is emplοyed in bοth engineering and physics. The Internatiοnal System οf Units (SI) uses metres as the unit οf length (m). In geοmetry, length plays a crucial rοle in describing the size and lοcatiοn οf geοmetrical shapes in space.
Accοrding tο the Triangle Inequality Theοrem,
The tοtal οf twο sides οf a triangle must be greater than the sum οf the third side, accοrding tο this theοrem. If all three cοmbinatiοns are true, yοu will have a true triangle.
1) Yοu must gο thrοugh each οf these οptiοns οne by οne tο ensure that the triangle is feasible. Cοnsider the triangle tο have the side lengths a, b, and c, and the theοrem tο be an inequality, which states:
a+b > c, a+c > b, and b+c > a.
As per οptiοn (B),
a = 18, b = 12, and c = 9
Here, Triangle Inequality Theοrem satisfies.
Thus, the three lengths are 18cm, 12cm, and 9cm which cοuld be the lengths οf the sides οf a triangle.
2. By the prοperties οf the triangle, the sum οf the square οf twο lengths is equal tο the third side length οf the triangle.
Always remember that when yοu add twο sides tο a triangle, the sum will cοme οut tο be higher than the third side’s length.
Hence, D. It must be greater than οr equal tο 6 and at mοst 24.
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