Answer:
24 correct questions
Step-by-step explanation:
Find the first five terms of the sequence given by a 1 = 2, a n = 3 a n -1 - 1.
Answer:
2, 5, 14, 41, 122
Step-by-step explanation:
Using the recursive rule with a₁ = 2
a₂ = 3a₁ - 1 = 3(2) - 1 = 6 - 1 = 5
a₃ = 3a₂ - 1 = 3(5) - 1 = 15 - 1 = 14
a₄ = 3a₃ - 1 = 3(14) - 1 = 42 - 1 = 41
a₅ = 3a₄ - 1 = 3(41) - 1 = 123 - 1 = 122
The first 5 terms are 2, 5, 14, 41, 122
Answer:
[tex]a_{1}\\\\[/tex] = 2
[tex]a_{2\\}\\\\[/tex] = 5
[tex]a_{3\\}\\\\[/tex] = 14
[tex]a_{4\\}\\\\[/tex] = 41
[tex]a_{5\\}\\\\[/tex] = 122
Step-by-step explanation:
If I've properly understood:
[tex]a_{1}\\\\[/tex] = 2
[tex]a_{n} = 3 a_{n-1}\\[/tex] - 1
so, the first 5 terms are:
[tex]a_{1}\\\\[/tex] = 2
[tex]a_{2\\}\\\\[/tex] = 3. 2 - 1 = 5
[tex]a_{3\\}\\\\[/tex] = 3. 5 - 1 = 14
[tex]a_{4\\}\\\\[/tex] = 3. 14 - 1 = 41
[tex]a_{5\\}\\\\[/tex] = 3. 41 - 1 = 122
What’s the answer, if you don’t know please do not answer.
Answer:
Yes, the bathroom has enough water and shampoo for all of them.
Step-by-step explanation:
70L+ 60S < 5600 70(8) + 60(7) = 560 + 420 = 980 There is enough water.0.02L + 0.01S 0.02(8) + 0.01(7) = 0.16 + 0.07 = 0.23 There is enough shampoo.Answer:It takes 250 g of pasta and 240 ml of sauce to make one batch of spaghetti and it takes 600g of pasta and 700ml of sauce to make one batch of lasagna.
Case 1: Pasta
The chef wants to make spaghetti and lasagna using more than 4000 g of pasta.
S denote the number of batches of spaghetti he makes and L the number of batches of lasagna he makes.
So the equation becomes :
Case 2: Sauce
chef wants to make spaghetti and lasagna using more than 5000 ml of sauce.
S denote the number of batches of spaghetti he makes and L the number of batches of lasagna he makes.
So the equation becomes:
Answer :
The two equations are :
For pasta:
For sauce:
Step-by-step explanation:
6 points
11) Use synthetic division to divide the two polynomials.
(2x3 – 12x — 2) = (x – 5)
A. (x - 5)(2x2 - 10x + 38) - 190
B. (x - 5)(2x2 + 10x + 38) + 188
C. (x + 5)(x2 + 50x + 190) + 188
D. (x + 5)(2x2 - 5x - 90) - 190
Answer:
the is a
Step-by-step explanation:
9x + 3y - 7x - 8y =
Answer:
2x-5y
Step-by-step explanation:
9x-7x= 2x
3y-8y= -5y
Answer:
....................
Step-by-step explanation:
how many solutions does the equation 2(9x-6)=18x+2 have??? Please help
Answer:
x=5.889
Step-by-step explanation:
2(9x6)=18x+2
108=18x+2
106=18x
x=106÷18
x=5.888888889
This is the last question from my questions before
Answer:
Just right the numbers they put
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the line y = - x
a point (x, y ) → (- y, - x ) , thus
M(- 7, 1 ) → M'(- 1, 7 )
N(- 4, 1 ) → N'(- 1, 4 )
O(- 4, - 4 ) → O'(4, 4 )
P(- 7, - 4 ) → P'(4, 7 )
Consider the rates 4/5 miles in 8 minutes and 4 minutes to travel 2/5 mile
Answer:
960
Step-by-step explanation:
I'm not sure exactly what's the question, but here's what I found. Lets first put it in our own words.
Consider the speed 4/5 miles in 12 minutes to travel 2/8.
8 + 4 = 12, so you can replace that with 12 minutes.
Now, you can absolutely guess your question.
Time = 12 minutes.
Distance = x (Let x be distance)
Speed = 4/5.
Now, you find distance.
Distance Formula: You can use the equivalent formula d = st which means distance equals rate times time.
So 4/5 × 12, is 9.6.
In fraction, if you have 1 numbers after the decimal point, multiply both numerator and denominator by 10. So 9.6 = (9.6 × 10) × 10 = 960.
Here is a pattern I found
2/5 divided by 4 is 1/10
4/5 divided by 8 is 1/10
If , we consider the given rates , we find that both rates are equivalent.
Two rates are given which are 4/5 miles in 8 minutes and 2/5 miles in 4 minutes.
We have to find out what they actually indicate.
What is the unitary method?
The unitary method is a method in which we find the value of a unit and then the value of the required number of units.
As per the question ;
Two rates are given which are ; 4/5 miles in 8 minutes and 2/5 miles in 4 minutes.
Let's find out what they are actually indicating.
So ;
If , distance travelled in 8 minutes = 4/5 miles
Then ;
In 1 minute , distance travelled will be ;
= [tex]\frac{4}{5*8}[/tex]
= [tex]\frac{4}{40}[/tex]
= 1 / 10 miles
and
If , distance travelled in 4 minutes = 2/5 miles
Then ;
In 1 minute , distance travelled will be ;
= [tex]\frac{2}{5*4}[/tex]
= [tex]\frac{2}{20}[/tex]
= 1 / 10 miles
So , we can conclude that both rates are equivalent.
Thus , if we , consider the given rates , we find that both rates are equivalent.
To learn more about unitary method click here ;
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#SPJ2
You go to Wal-Mart to buy some holiday candy. You decide to buy snickers because they have a special deal on snickers. A bag
of snickers costs $3.45, but if you buy 4 or more bags, they only cost $3.00 per bag.
Create a piecewise function to represent the cost of the bags of snickers.
6
SNICKERS
Let "n" be the number of bags of snickers
and "C(n)" be the cost of all bags of snickers purchased.
The piecewise function is
C(n) - {(first option)
{ (second option)
Answer:
The piecewise function is given as follows;
[tex]\begin{cases}C(n) = \$ 3.45 \times n & \text{ if } x< 4 \\ C(n) = \$ 3.00 \times n & \text{ if } x\geq 4 \end{cases}[/tex]
Step-by-step explanation:
The given parameters are;
The cost of each bag of snickers = $3.45
The cost of each bag of sneakers when buying 4 or more bags = $3.00
Let "n" be the number of bags of snickers and "C(n)" be the cost of all the snickers purchased
The piecewise function is C(n) = {($3.45 × n) for n < 3
{($3.00 × n) for n ≥ 4
At a furniture store, the employees earn a 2.5% commission on every sale they make.
If Robert made $8,850 in sales one week, how much money in commission did he earn?
Francisca made $279 in commission that same week. How much money in sales did she make?
Step-by-step explanation:
Let x be the money made in sales. Let y be the money made in commissions.
First, convert 2.5% to a decimal.
2.5% = 0.025
Equation:
0.025x = y
Robert:
0.025(8850) = y
y = $221.25
Francisca:
0.025x = 279
x = 279/0.025
x = $11,160
A constant volume of pizza dough is formed into a cylinder with a relatively small height and large radius. The dough is spun and tossed into the air in such a way that the height of the dough decreases as the radius increases, but it retains its cylindrical shape. At time t=k, the height of the dough is 13 inch, the radius of the dough is 12 inches, and the radius of the dough is increasing at a rate of 2 inches per minute.
(a) At time t=k, at what rate is the area of the circular surface of the dough increasing with respect to time? Show the computations that lead to your answer. Indicate units of measure.
(b) At time t=k, at what rate is the height of the dough decreasing with respect to time? Show the computations that lead to your answer. Indicate units of measure. (The volume V of a cylinder with radius r and height h is given by V=πr2h.)
(c) Write an expression for the rate of change of the height of the dough with respect to the radius of the dough in terms of height h and radius r.
Answer:
a) [tex]\frac{dA}{dt} = 48 \pi\frac{in^{2}}{min}[/tex]
b) [tex] \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}[/tex]
c) [tex]\frac{dh}{dt} = - 2\frac{h}{r} \frac {dr}{dt}[/tex]
Step-by-step explanation:
In order to solve this problem, we must first picture a cylinder of height h and radius r (see attached picture).
a) So, in order to find the rate at which the area of the circular surface of the dough is increasing with respect to time, we need to start by using the are formula for a circle:
[tex]A=\pi r^{2}[/tex]
So, to find the rate of change of the area, we can now take the derivative of this formula with respect to the radius r:
[tex]dA = \pi(2) r dr[/tex]
and divide both sides into dt so we get:
[tex]\frac{dA}{dr} = 2\pi r \frac{dr}{dt}[/tex]
and now we can substitute:
[tex]\frac{dA}{dr} = 2\pi(12in)(2\frac{in}{min})[/tex]
[tex]\frac{dA}{dt} = 48\pi\frac{in^{2}}{min}[/tex]
b) In order to solve part b, we can start with the formula for the volume:
[tex]V=\pi r^{2} h[/tex]
and solve the equation for h, so we get:
[tex]h=\frac{V}{\pi r^{2}}[/tex]
So now we can rewrite the equation so we get:
[tex]h=\frac{V}{\pi}r^{-2}[/tex]
and now we can take its derivative so we get:
[tex]dh=\frac{V}{\pi} (-2) r^{-3} dr[/tex]
we can rewrite the derivative so we get:
[tex]\frac{dh}{dt}=-2\frac{V}{\pi r^{3}}\frac{dr}{dt}[/tex]
we can take the original volume formula and substitute it into our current derivative, so we get:
[tex]\frac{dh}{dt}= -2\frac{\pi r^{2} h}{\pi r^{3}} \frac{dr}{dt}[/tex]
and simplify:
[tex]\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}[/tex]
so now we can go ahead and substitute the values provided by the problem:
[tex]\frac{dh}{dt} =-2\frac{13in}{12in} (2\frac{in}{min})[/tex]
Which simplifies to:
[tex] \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}[/tex]
c)
Part c was explained as part of part b where we got the expression for the rate of change of the height of the dough with respect to the radius of the dough in terms of the height h and the radius r:
[tex]\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}[/tex]
The rate of change of the height of the pizza with respect to (w.r.t.) time
can be found given that the volume of the pizza is constant.
(a) The rate of increase of the surface area with time is 4·π in.²/min(b) The rate at which the height of the dough is decreasing is [tex]\underline{4.\overline 3 \ in./min}[/tex](c) Rate of change the height of the dough with respect to the radius [tex]\dfrac{dh}{dr}[/tex], is [tex]\underline{-2 \cdot \dfrac{h}{r}}[/tex]Reasons:
The height of the dough when t = k is 13 inches
Radius of the dough = 12 inches
Rate at which the radius of the dough is increasing, [tex]\dfrac{dr}{dt}[/tex] = 2 in.²/min
(a) Required: The rate of increase of the surface area with time
Solution:
The circular surface area, A = π·r²
By chain rule of differentiation, we have;
[tex]\dfrac{dA}{dt} = \mathbf{\dfrac{dA}{dr} \times \dfrac{dr}{dt}}[/tex]
[tex]\dfrac{dA}{dt} = \dfrac{d ( \pi \cdot r^2)}{dr} \times \dfrac{dr}{dt} = 2 \cdot \pi \times 2 = 4 \cdot \pi[/tex]
The rate of increase of the surface area with time, [tex]\mathbf{\dfrac{dA}{dt}}[/tex] = 4·π in.²/min.
(b) Required: The rate of decrease of the height with respect to time
The volume of the pizza is constant, given by; V = π·r² ·h
Therefore;
[tex]h = \mathbf{ \dfrac{V}{\pi \cdot r^2}}[/tex]
[tex]\dfrac{dh}{dt} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} \times \dfrac{dr}{dt} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} \times \dfrac{dr}{dt} = \mathbf{-2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt}}[/tex]
[tex]\dfrac{dh}{dt} = -2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt} = -2 \times \dfrac{13}{12} \times 2 = \dfrac{13}{3} = 4. \overline 3[/tex]
The rate at which the height of the dough is decreasing, [tex]\mathbf{\dfrac{dh}{dt}}[/tex]= [tex]\underline{4.\overline 3 \ in./min}[/tex]
(c) Required:]The expression for the rate of change the height of the dough with respect to the radius of the cone.
Solution:
[tex]\dfrac{dh}{dr} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} = -2 \cdot \dfrac{h}{r}[/tex]
[tex]\dfrac{dh}{dr} = \mathbf{ -2 \cdot \dfrac{h}{r}}[/tex]
The rate of change the height of the dough w.r.t. the radius is [tex]\underline{\dfrac{dh}{dr} = -2 \cdot \dfrac{h}{r}}[/tex]
Learn more here:
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Atrain travels at a speed of 58.6 km'hi Express this speed
a.ms
b. m/min
Answer:
16.27
Step-by-step explanation:
if 1000m rep 1km
therefore :
58.6km/h in ms = 58.6km×1000/3600
=16.277 ms
The temperature at 10 A.M. was -4 °F. By noon the temperature had risen 8 °F. At 8 P.M., the temperature had dropped 10° F. What was the temperature at 8 P.M.? *
Answer:
-6
Step-by-step explanation:
-4+8=4
4-10= -6
Find the minimum coordinate due in 5 min
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Answer:
(4, -6)
Step-by-step explanation:
The minimum is the vertex of the parabolic section in the 4th quadrant. The coordinates appear to be (4, -6).
*show all work for full credit
1. 6x=25
Answer and Step-by-step explanation:
All we have to do is solve for x.
Divide both sides by 6.
x = [tex]\frac{25}{6}[/tex]
This is your answer.
If you want to have the decimal version, then it would be 4.166 repeating.
#teamtrees #WAP (Water And Plant) #SPEW (Society for the Promotion of Elfish Welfare)
You have at most $28 to spend at a market. Apples cost $0.45 each, and pears cost $0.60 each. Let a be numbers of apples and p be numbers of pears. Write an inequality that represents the numbers of apples and pears you can afford
Answer:
$0.45a+$0.60p ≤$28
Step-by-step explanation:
Answer:
0.45a + 0.60p <= 28
Step-by-step explanation:
Given that triangle RST is isosceles, find the value of x.
Answer:
x = 10
Step-by-step explanation:
RST is an isosceles triangle.
[tex]m\angle T = m \angle R\\\\
8x\degree = (3x + 50)\degree \\\\
8x = 3x + 50\\\\
8x - 3x = 50\\\|
5x = 50\\\\
x = \frac{50}{5} \\ \\ x = 10[/tex]
Eeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
The lowest point is 9 ft below see level and the highest point is 108 ft above sea level
Step-by-step explanation:
Here, we want to select the correct option
From the question, we have the following;
The lowest point is -9 while the highest point is +108
-9 indicates that it is 9 units below zero
+108 indicates that it is 108 units above zero
So, the correct option here is that;
The lowest point is 9 ft below see level and the highest point is 108 ft above sea level
Answer:
A. The lowest point is 9 feet below sea level and the highest point is 108 above sea level
Step-by-step explanation:
have a nice day
Joe, Luis, Albert and Lupe want to share 3 oranges so that everyone gets an equal amount. How much orange will each child get? ~PLEASE ANSWER QUICK~
Answer:
Half an orange
Step-by-step explanation:
It would be half an orange because it says 4 other people. Joe, Luis, Albert, and Lupe. And it says 3 oranges so that everyone would get an equal amount. So if you think about it, theirs no other way to let everyone have an equal piece. So you would have to split them in half and through the left overs away that cant be shared.
please mark as brainly
BRAINLIEST TO RIGHT ANSWER! ASAP!
Answer:
y=-1/2x+1
Step-by-step explanation:
What is the answer to -9 = 2/7x + 5
Answer: x = -49
Step-by-step explanation:
hope this helped
PLEASE HELP ME!! THIS IS A MATH TEST!! PLEASE HELP!!
Person A buys 6 granola bars and 4 cups of yogurt for $10.50. Person B buys 4 granola bars and 8 cups of yogurt for $11. Find the cost of each item.
Granola Bar costs:
a cup of yogurt costs:
PLEASE AND THANK YOUUU!!!!!!
the granola bar costs $1.50
the yogurt costs 50 cents = $0.50
could someone please help me with my math? i really need help and i am struggling
https://brainly.com/question/20134003
Answer:
yes
Step-by-step explanation:
equation with variables on both sides: decimals & fractions 4x + 8 = 7.2 + 5x
Answer:
4x + 8 = 7.2 + 5x
1. 4x - 4x + 8 = 7.2 + 5x - 4x
2. 8 = 7.2 + x
3. 8 - 7.2 = 7.2 - 7.2 + x
4. 0.8 = x
Step-by-step explanation:
Final Answer: [tex]x = 0.8[/tex]
Steps/Reasons/Explanation:
Question: Equation with variables on both sides: decimals & fractions [tex]4x + 8 = 7.2 + 5x[/tex].
Step 1: Subtract [tex]4x[/tex] from both sides.
[tex]8 = 7.2 + 5x - 4x[/tex]
Step 2: Simplify [tex]7.2 + 5x - 4x[/tex] to [tex]7.2 + x[/tex].
[tex]8 = 7.2 + x[/tex]
Step 3: Subtract [tex]7.2[/tex] from both sides.
[tex]8 - 7.2 = x[/tex]
Step 4: Simplify [tex]8 - 7.2[/tex] to [tex]0.8[/tex].
[tex]0.8 = x[/tex]
Step 5: Switch sides.
[tex]x = 0.8[/tex]
~I hope I helped you :)~
b -2 = 9/b-2
Answer ?
Step-by-step explanation:
I don't know if it's correct
Which statement is true for the following graph:
4
3
O
3
-2
3
4
-51
F
The domain is all real numbers
G
The domain is all real numbers between -3 and 4
H
The range is all real numbers
J
The range is all real numbers between -3 and 4
9514 1404 393
Answer:
H the range is all real numbers
Step-by-step explanation:
The arrows on the ends of the curve mean the curve extends to infinity. Then the domain (x-extent) is -3 to infinity.
The range (y-extent) is -infinity to infinity, all real numbers.
The appropriate description is ...
H The range is all real numbers
The length of a dog on a scale drawing is 6 cm. If the scale is 1 cm : 7 cm, what is the actual length of the dog? (A) 15 cm (B) 30 cm (C) 42 cm (D) 108 cm
Answer: (C) 42 cm
Work Shown:
(length on paper)/(real length) = (length on paper)/(real length)
(1 cm)/(7 cm) = (6 cm)/(x cm)
1/7 = 6/x
1*x = 7*6
x = 42
The actual length of the dog is 42 cm.
Tyler bought two tickets to a basketball game on the website Game Finder. Each ticket cost $65, and the website charged a convenience fee that was a small percent of the ticket cost.
If Tyler’s total bill came to $132.60, what percent was the convenience fee?
First you write down the formula. How do you get 132.60 in the first place? I included a pic, please try to understand it. As it'd be v useful in daily life too.
Answer:
the answer is 2%
Step-by-step explanation:
I got 2.0 but you round it so it would be 2% the other girl worked it out just right
What is 11% of 600?
80
45
60
66
Answer:
66 is the answer to your question
Answer:
66
Step-by-step explanation:
11 % = 0.11
600 × 0.11 = 66
If 10% of x is 20, what is 23% of x?
A.
33
B.
46
C.
200
D.
230
Answer:
46
Step-by-step explanation:
Answer:
46
Step-by-step explanation:
First get x
x= (20/10) * 100
x=200
23% of 200 = (23*200)/100 = 46
Jo is a diabetic who uses three doses of insulin each day. Each dose is 0.06 ml. A bottle contains 1 cl of insulin. How many complete days will a bottle last her?
Answer:
55 complete days
Step-by-step explanation:
It is given that Jo is diabetic and she uses three doses of insulin in one day. One dose of insulin is 0.06 ml and one bottle has 1 cl of insulin.
We know, 1 cl = 10 ml
So the insulin bottle contains 10 ml of insulin.
1 dose = 0.06 ml
3 doses = 0.06 x 3
= 0.18 ml
So Jo takes 0.18 ml of insulin in one day.
Dividing 10 ml by 0.18 ml, we get
[tex]$=\frac{10}{0.18}$[/tex]
[tex]$=\frac{1000}{18}$[/tex]
= 55.55
So, the bottle will last for 55 complete days.