The formula for obtaining the value of a term of a sequence is given as a
as a recursive formula.
Responses:
The information as a sequence is; R1, 2·R1, 4·R1, 8·R1, 16·R1, ...The sequence of the information is a geometric sequenceHow is the given information expressed as a sequence?The amount of pocket money Smith gets = 2 × The amount he gets in the previous day
The amount Smith gets on the first day = R1
Required:
The given information expressed as a sequence.
Solution:
The amount of money smith gets can be expressed as follows;
Amount he gets on day 1 = R1
On day 2, R2 = 2·R1
On day 3, R3 = 2·R2 = 2·2·R1 = 4·R1
On day 4, R4 = 2·R3 = 2·2·2·R1 = 8·R1
On day 5, R5 = 2·R4 = 2·2·2·2··R1 = 16·R1
The information written as a sequence is therefore;
R1, 2·R1, 4·R1, 8·R1, 16·R1, ...The type of sequence is a geometric sequence, or progression where the first term is R1, and the common ratio, r = 2Learn more about geometric sequence here:
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The table below shows the median weekly earnings of a certain population of workers. If this trend continues, predict the median weekly earnings in 2016. For this
exercise, find a linear and a quadratic regression equation and use both to predict the earnings in 2016. Let x be the number years since the year 2000 and y be
the weekly earnings in dollars
2002 2004
2006
2008 2010
Year
Weekly Earnings
Kin dollars)
567
580
616
625
618
A linear regression equation is y=[]
(Use integers or decimals for any numbers in the equation Round to three decimal places as needed)
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A regression can take several forms such as linear models and quadratic models
The linear regression equation is: [tex]y = 7.35x + 557.1[/tex] and the quadratic regression equation is [tex]y = -1.196x^2 +21.707 x+523.6[/tex]
How to determine the regression equationsThe data set is given as:
x 2 4 6 8 10
y 567 580 616 625 618
Next, we make use of a graphing calculator to determine the regression equations
From the graphing calculator, we have the following calculation summary
Sum of X = 30Sum of Y = 3006Mean X = 6Mean Y = 601.2Sum of squares (SSX) = 40Sum of products (SP) = 294So, the linear regression equation is:
[tex]y = 7.35x + 557.1[/tex]
And the quadratic regression equation is:
[tex]y = -1.196x^2 +21.707 x+523.6[/tex]
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how many is
x + 54 = 987? Pls step by step
Answer:
X=933
Step-by-step explanation:
987-54=933
Please help, I am so confused. If anyone understands this please help
Answer:
12 ft
Step-by-step explanation:
It is sometimes helpful to start from what you are given and see what develops.
Here, angle B is 30°. That means angle CAB is 60° (the acute angles of a right triangle are complements). AL bisects that 60° angle, meaning two things:
ΔALC is a 30°-60°-90° triangle, so you know its side ratios∠LAB = 30°, so ΔALB is isosceles and AL = LBThe side ratios of a 30°-60°-90° triangle are 1 : √3 : 2, so AL is 2 times the length of CL.
AL = 2 × (6 ft) = 12 ft
We know that AL = LB, so LB = 12 ft.
The Flash runs 100 km in 25 seconds. What is the Flash's velocity
Answer:
yo moma smell like stank
Step-by-step explanation:take showers
PLEASE HELP ME QUICKKK, FIRST CORRECT PERSON GETS BRAINLIEST
Answer:
c and d
Step-by-step explanation:
they both have a percent increase >50
Jennifer mixes 600ml of orange juice with 900ml of apple juice to m
ake a fruit drink. Write the ratio of apple juice to orange juice in its simplest form.
Answer:
2:3
Step-by-step explanation:
So OJ is 600ml and AJ is 900ml
we can divide both by 100 so
600÷100= 6
900÷100= 9
Ratio is now 6:9 but we can simplify it more by 3
so 6÷3=2 and 9÷3=3
So therefor ratio is 2:3
4. (1pt each) Solve for the missing angle, x.
Answer:
a) 112º
b) 62.5º
Step-by-step explanation:
a) x=180–34*2=112º
b) x=(180–55)/2=62.5º
What’s the correct answer for this?
Answer:
201 minutes
Step-by-step explanation:
60 x 3 = 180
180 +21 = 201
You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do
you have in each subject?
You have math problems.
You have science problems
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The cost of 4 dozen bananas is rupee 60. How many bananas can be purchased for rupee 12.50?
Answer:
10 bananas
Step-by-step explanation:
Compare same things in the same order to write a proportion
(fraction = fraction)
bananas/rupees
=4dozen/R60
=4(12)/R60
=48/60
=4/5
The question says
bananas/rupees
=unknown/R12.5
4/5 = x/12.5
crossmultiply
4(12.5) = 5x
50 = 5x
divide by 5
10 = x
You can buy 10 bananas for R12.5
10 bananas
Step-by-step explanation:
In ₹60, we can purchase 4 dozen bananas
=> 4×12
=> 48 bananas
In ₹1, we can purchase:-
[tex] \frac{48}{60} [/tex]bananas
In ₹12.50, we can purchase:-
[tex] \frac{48}{60} \times 12.50[/tex]
[tex] = > \frac{48 \times 1250}{60 \times 100}[/tex]
[tex] = > \frac{8 \times 125}{100}[/tex]
By reducing to lowest terms, we get,
[tex]10[/tex]
Hence, 10 bananas can be purchased for ₹12.50
A library shelf contains seven books. Three books are math books and four books are science books. In how many ways may the books be arranged on the shelf so that all the math books will be together
There are 720 different ways to arrange the books.
In how many ways we can order the books?
Here we know that there are a total of 7 books, 3 of math and 4 of sciences.
We know that the 3 math books must be together, so first let's analyze this element.
The number of permutations of these 3 books is 3! = 3*2*1 = 6
Now we have 5 elements, 4 books of science and a "group of math books."
So there are 5 positions in which the group of math books can be, and for the four science books we have 4! = 4*3*2*1 = 24 permutations.
The total number of different combinations is given by the product of the numbers we found above:
combinations = (permutations of math)*(possible positions of math)*(permutations of science).
Combinations = 6*5*24 = 720
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circumfrence of a circle r=4 iready
a. 50.24
b. 12.56
c. 200.96
d. 6.28
e. 25.12
Answer:
E. 25.12
Step-by-step explanation:
C=2πr = 2π(4) = 25.1
what is the domain of the given relation {(2,2),(3,2),(2,3),(1,4}
Check the picture below.
HELPPP
Use the information shown on the auger shell. What is the value of x?
Simplify the expression.
2/5y−4+7−9/10y =
PLEASE WHOEVER TELLS ME THIS (CORRECT) ANSWER ILL MAKE ANOTHER QUESTION WITH 30 POINTS
Answer:
6y - 1/2y
Step-by-step explanation:
So...
We need to multiply by 5y/5y to write -4 as a fraction with a common denom.
2/5y - 4 * 5y/5y + 7 - 9/10y
Simplify...
Combine the -4 and 5y/5y
2/5y + -4(5y)/5y + 7 - 9/10y
Combine the numer over the common denom
2 - 4(5y)/5y + 7 - 9/10y
Simplify the numerator by factoring 2 out of then 2 out of -4 * 5y and then 2 out of 2(1) + 2 (-2 * 5y)
2(1) - 4 * 5y/5y + 7 - 9/10y
2(1) + 2(-2 * 5y)/5y + 7 - 9/10y
2(1 - 2 * 5y)/5y + 7 - 9/10y
Now multiply -2 by 5
2(1 - 10y)/5y + 7 - 9/10y
Now we do the same 5y/5y with 7
Combine...
2(1 - 10y)/5y + 7(5y)/5y - 9/10y
Combine more.
2(1 - 10y) + 7(5y)/5y - 9/10y
Now we need to simplify more
Distributive property application
2 * 1 + 2 (-10y) + 7 * 5y/5y - 9/10y
Multiply 2 by 1
2 + 2(-10y) + 7 * 5y/5y - 9/10y
-10 by 2
2 - 20y + 7 * 5y/5y - 9/10y
Then 7 by 5
2 - 20y + 35y/5y - 9/10y
Then -20y by 35y
2 + 15y/5y - 9/10y
Now we have to multiply 2 + 15y/5y by 2/2
2+ 15y/5y * 2/2 - 9/10y
Now we write with a common denom of 10y and multiply with a factor of 1
(2 + 15y) * 2/5y * 2 - 9/10y
Multiply 2 by 5
(2 + 15y) * 2/10y - 9/10y
Combine again
(2 + 15y) * 2 - 9/10y
Simplify again with the distrib property
2 * 2 + 15y * 2 - 9/10y
Multiply 2 by 2
4 + 15y * 2 - 9/10y
Then 2 by 15
4 + 30y - 9/10y
Then subtract 9 from 4
30y - 5/10y
Factor out 5 from 30y - 5...
5(6y) -5/10y
5(6y) - 5/10y
Factor 5 out of -5
5(6y) + 5(-1)/10y
Then 5 out of 5(6y) + 5(-1)
5(6y - 1)/10y
Now we cancel more common factors which is 5 here
6y - 1/2y
A house on the market was valued at $461,000. After several years, the value decreased by 9%. By how much did the houses volume decrease in dollars? What is the current value of the hous
Answer:
$41,490
Step-by-step explanation:
9% = 0.09
Do 9% of 461,000
which is 0.09 times 461000.
Answer:
The house decreased by $41490. The current value of the house is $419510
Step-by-step explanation:
The house starts at 100% value and goes down by 9%.
100-9 is 91
you move the decimal over 2 places to the left and get .91
you multiply 461000(.91) and you get 419510
that's the current value on the house
to find the amount, lost subtract
416000-419510
and you get $41490.
Riley makes a necklace for his sister. Twelve beads take up 5 inches of string.
How many beads fit on 1 foot of string?
Hey how was your day? What did you do today?
Answer:
28.8
If rounded 28
Step-by-step explanation:
If every 12 beads takes up 5 inches that means that 1 foot (12 inches) would be divided by 5 (12/5) (A. 2.4) and then multiplied by 12. which would give you 12.8 or since you cant have 28.8 beads, you can only put on 28 when rounded.
Polygon ABCD is a rectangle. What is its area? Round your answer to the
nearest tenth.
A. 12.2 square units
B. 24.4 square units
C. 6.1 square units
D. 37.0 square units
Find the quotient 820,00^3
Answer:
Correct me if I'm wrong......
if y=2x^2-5x-3 find the value of y if x= -1
Answer:
y = 4
Step-by-step explanation:
First we want to raise -1 to the power of 2
y = 2 * 1 - 5 * -1 - 3
Multiply
2 - 5 * -1 - 3
Multiply
y = 2 + 5 - 3
y = 7 - 3
y = 4
A rectangle has a length of 26 yards less than 8 times it’s width. If the area of the rectangle is 682 square yards, find the length of the rectangle.
Answer:
Length is 62 yards
Step-by-step explanation:
A = wL
L = 8w-26
682 = w(8w-26)
682 = 8w^2 -26w
0 = 8w^2 - 26w - 682
Use the quadratic formula (it's really hard to type it but just look it up if you want to see the explanation)
w = 11
L = 8(11) - 26 = 62 yards
Check: 62(11) = 682
Alan has 13 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating N to F. Then graph your equation using the axes below.
Answer:
13-f=n
Step-by-step explanation:
he starts with 13 folds some number "f" of them and has some number "n" still to do
The linear equation that links N and F in the previously stated condition is N + F = 13.
What is a linear equation?
Because a straight line emerges when we attempt to display the graph of the provided linear function, a linear equation is known as linear.
Given Alan has 13 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them.
The linear equation that satisfies the above statement is
N + F = 13
therefore, N + F = 13 is the linear equation that relates N and F in the above-given condition.
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Dominic and Candice are both selling cookie dough for a fundraiser. Although Dominic has already sold 5 tubs, Candice hasn't sold any yet. If Dominic starts selling 6 tubs per day and Candice begins selling 7 tubs per day, they will eventually sell the same amount of cookie dough. How many tubs will each sell? How many days will that take?
Answer:
5 days, 35 tubs
Step-by-step explanation:
We can create an equation.
Let d be the number of days it will take.
Note that in all Dominic will have sold 6d + 5 tubs, and Candice 7d.
So, if 6d - 5 = 7d then d = 5.
So, it will take 5 days, and each will have sold 6 * 5 + 5 = 7 * 5 = 35 tubs of cookie dough.
Help math math math ASAP
Answer:
B
Step-by-step explanation:
parallel lines have the same gradient,
and for y = 3x-2; m= 3
The answer is B. Hope this helps :)
What value of x is in the solution set of 4x - 12 = 16 + 8x?
-10
-9
-8
ОО
-7
Step-by-step explanation:
Question: 4x - 12 = 16 +8x
Answer: 4x-8x =16+12
-4x=28
x=-28/4
x=-7
D) -7 is your answer
hope this helps you
have a great day :)
The thiciness of a fingernail is about 1
The thickness of a fingernail is about 10^-5 inch
From the complete question, we have the following parameter
Thickness = 1/100000 inch
To represent the thickness in standard form, we do the following:
Express the thickness as a decimal
Thickness = 0.00001 inch
So, the standard form would be:
Thickness = 1 * 10^-5 inch
This gives
Thickness = 10^-5 inch
Hence, the complete statement is:
The thickness of a fingernail is about 10^-5 inch
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Use the diagram to find the angle measures
of the triangle. Recall that the sum of the
angle measures of a triangle is 180º.
9x
(x+4)
.
x =
(x+4)° = °
9x =
Answer:
x=16
(x+4)=20
9x=144
Step-by-step explanation:
9x+x+4+x=180
11x+4=180
11x=180-4
11x=176
[tex]x = \frac{176}{11} [/tex]
x=16
Question 3 of 44 What is the circumference of a circular swimming pool with a radius of 8 feet? (Round your answer to the nearest tenth.) O A. 25.1 ft O B. 100.5 ft C. 201.1 ft OD D. 50.3 ft SUBMIT
Answer:
D. 50.3 ft
Step-by-step explanation:
C = 2 x pi x r
C = 2 x 3.14 x 8
C = 50.3 ft
Which expression is equivalent to 2^4 x 2^-7
Answer:
[tex]2 ^ { 4 } \times 2 ^ { - 7 }\\= 2^{4 + (-7)} \\= 2^{-3} \\= \frac{1}{2^{3} } \\=\boxed{ \frac{1}{8} }[/tex]
Hope it helps ⚜
please help with slope
Answer:
-2/3
Step-by-step explanation:
down 2, right 3
Slope:-
[tex]\\ \rm\hookrightarrow m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\\ \rm\hookrightarrow m=\dfrac{-4+1}{-5+9}[/tex]
[tex]\\ \rm\hookrightarrow m=\dfrac{-3}{4}[/tex]