The explicit function is f(n) = 3f(n - 1)
Solution:Given, sequence is 16, 48, 144, 432 ….
We have to find the explicit function.
Now, if we observe the given sequence, every term is three times its previous term.
That is, the next term in sequence is obtained by multiplying the previous term by 3
48 = 16 x 3
144 = 48 x 3
432 = 144 x 3
So, explicit function f(n) will be
nth term = 3 x (n – 1)th term
F(n) = 3 x f(n – 1) [ since nth term is f(n) ]
We derived the above function just by generalizing the sequence and making it into the function.
The nth term is obtained by multiplying the n - 1 term with 3
Hence explicit function is f(n) = 3f(n - 1)
five friends will pay $9 per ticket, $3 per drink, and $6 per popcorn at the movies. write an expression that could be used to determine the cost for them to go to the movies
Final answer:
To calculate the total movie-going cost for five friends, multiply the cost of each item by five and sum them up. The total cost is represented by the expression [tex](5 \times\$9) + (5 \times\$3) + (5 \times\$6)[/tex], which simplifies to $90.
Explanation:
The question involves writing an expression to determine the cost for five friends to attend a movie considering the cost of tickets, drinks, and popcorn. To calculate the total cost for the group, we need to know the price per individual item and the quantity consumed. We know that each ticket costs $9, each drink costs $3, and each popcorn costs $6. Since there are five friends, we will multiply each of these costs by five to get the total cost per item for the group.
The expression for the total cost for the movie tickets is [tex]5\ tickets \ \times \$9/ticket[/tex], for drinks it's [tex]5\ drinks\ \times\$3/drink[/tex], and for popcorn, it's [tex]5\ popcorns \times\$6/popcorn[/tex]. To find the overall total, we add these expressions together:
Total Cost = [tex](5 \times\$9) + (5 \times\$3) + (5 \times\$6)[/tex]
The expression simplifies to:
Total Cost = ($45) + ($15) + ($30)
Therefore, the simplified expression for the total cost is:
Total Cost = $90
a 13 ounce package of pistachios costs $5.99 find the unit rate
Answer:
about 0.46 cents per ounce
Step-by-step explanation:
5.99 divided by 13 gives you a long decimal and you round to 0.46
Which of the following shapes is the cross-section for a cone
A.triangle
B.square
C.circle
D.pentagon
Final answer:
The correct shape for the cross-section of a cone, when cut perpendicularly to its axis, is a circle. This is known as a conic section. The correct option is C.
Explanation:
The student asked which shape represents the cross-section for a cone. The cross-sectional shape of a cone depends on the angle at which it is cut. If a cone is cut by a plane perpendicular to its axis (the center line from the tip to the base), the cross-section is a circle. Therefore, the correct shape for the cross-section of a cone, when cut perpendicularly to its axis, is a circle.
Graph the solution of the inequality.
Answer:
[tex]\displaystyle -16 < x[/tex]
Step-by-step explanation:
[tex]\displaystyle -4[\frac{x}{-4}] < 4[-4] → x > -16[/tex]
Whenever you divide\multiply by a negative, you reverse the inequality symbol.
** The above answer is written in reverse, which is the exact same result.
≥, ≤ → Solid Circle [●]
>, < → Blank Circle [○]
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A cylindrical well has a radius of 10 feet and a height of 15 feet. What volume of water will it take to fill in the well?
Answer:
4712.39(2 decimal place)
Step-by-step explanation:
Volume of cylinder is πr^2(h)
π10^2(15):
is 4712.39(2dp)
Answer:
1500π
Step-by-step explanation:
The volume of water is just the normal volume so,
the volume of a cylinder is πr²h
where π is pi, as in 3.14 ..., r is the radius, and h is the height.
Using what was given to us, we can plug this into the formula
so, π ×10² ×15 = 100π×15 = 1500π
Mrs. Battle is designing a brick walkway to install in her front yard.
How many square feet of bricks will be needed for the walkway?
A 130
B 122
C 94
D 80
Answer:
B 122
Step-by-step explanation:
just thinking ur her
Answer this please, thank you !
Answer:
m∠ADC=55°
Step-by-step explanation:
step 1
Find the value of x
we know that
m∠CDE+m∠EDF=180° ----> by supplementary angles (form a linear pair)
substitute the given values
[tex](2x+1)\°+(x-7)\°=180\°[/tex]
solve for x
[tex]2x+x=180+6[/tex]
[tex]3x=186[/tex]
[tex]x=62[/tex]
step 2
Find the measure of angle ∠ADC
we know that
m∠ADC=m∠EDF ----> by vertical angles
m∠EDF=(x-7)°
substitute the value of x
m∠EDF=(62-7)°=55°
therefore
m∠ADC=55°
Which statements are true about the graph of
y< 2x + 1? Check all that apply.
Graph: y < }x+1
The slope of the line is 1.
The line is solid.
The area below the line is shaded.
A solution to the inequality is (2.3).
The x-intercept of the boundary line is (-3.0).
Draw
Click or tap the graph to plot a point
Answer:
The area below the line is shaded.
Step-by-step explanation:
Using the zero-interval test [test point (0, 0)], we plug in 0 for both y and x to determine whether we shade below the line [the portion that DOES contain the origin] or above the line [the portion that does not contain the origin]. This is where me must verify the inequality as false or true:
[tex]\displaystyle 0 < 2[0] + 1 → 0 < 1[/tex]
This is a genuine statement, therefore we shade below the line.
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Ronny read for 2.75 hours yesterday. His older brother read for 1.18 hours and his younger brother read for 0.43 hours.
How much longer did Ronny read than his two brothers combined?
1.14 hours
1.57 hours
1.61 hours
2.32 hours
Please help ‼️‼️
The student council is selling Candy bars to earn money towards their budget for the school dance explain why the number of candy bars is the independent variable
Answer:
the number of candy bars they have is not affected by the other factors like the budget or the student council
Final answer:
The number of candy bars is the independent variable because it can be manipulated or changed by the student council to affect the amount of money they earn.
Explanation:
The number of candy bars is considered the independent variable in this scenario. The independent variable is the one that is manipulated or changed in an experiment, and its value does not depend on any other variable.
In this case, the student council is selling candy bars to earn money for their budget, and the number of candy bars they sell is the variable that they have control over.
By increasing or decreasing the number of candy bars sold, they can affect the amount of money they earn for their budget.
Definition: This is the process of cell reproduction where cell splits into two daughter cells. Example: Mitosis
Answer:
Cell division
Step-by-step explanation:
During the process where the cell splits, it’s going through a process of cell division where the cell divides into two
Biff is 25 years older than Hannah today. Four years from now,Biff will be 6 times as old as Hannah will be. How old is Hannah today? Use algebra to solve.
Hannah is 1 year old, and Biff is 26 years old today.
Let's denote Hannah's current age as H and Biff's current age as B.
According to the given information, we can set up two equations based on the provided conditions.
Biff is 25 years older than Hannah today:
B=H+25
Four years from now, Biff will be 6 times as old as Hannah will be:
B+4=6(H+4)
Now, we have a system of two equations with two variables.
We can substitute the expression for B from the first equation into the second equation:
(H+25)+4=6(H+4)
Combine like terms:
H+29=6H+24
Subtract H from both sides:
29=5H+24
Subtract 24 from both sides:
5H=5
Divide by 5:
H=1
So, Hannah is currently 1 year old. To find Biff's age, we can use the first equation:
B=H+25
B=1+25
B=26
Therefore, Hannah is 1 year old, and Biff is 26 years old today.
what is the total cost of a sweatshirt if the regular price is $42 and the sales tax is 5 1/2
Answer:
$44.31
Step-by-step explanation:
Regular Price = $42
Sales Tax Rate = 5 1/2% or 5.5%
The total cost would be the regular price PLUS the sales tax. We find the sales tax by finding 42's 5.5%.
First, converting percentage to decimal (dividing by 100):
5.5% = 5.5/100 = 0.055
Now finding 5.5% of $42:
42 * 0.055 = $2.31
Now, the total price is the SUM of regular and this sales tax:
Total Price = 42 + 2.31 = $44.31
Y=-3 write in the general form of equation
Answer:
y + 3 = 0Step-by-step explanation:
The general form of an equation of a line:
Ax + By + C = 0
We have
y = -3 add 3 to both sides
y + 3 = -3 + 3
y + 3 = 0
where A = 0, B = 1, C = 3
15 points!! will mark brainliest
Using the Pythagorean theorem:
L = √(15^2 - 9^2)
L = √(225 - 81)
L = √144
L = 12
The answer is 12'
Which similarity postulate or theorem can be used to verify that the two triangles shown below are similar?
Answer:
SAS Theorem
Step-by-step explanation:
It would be the SAS theorem because you know 2 sides that have an angle in common on both triangles.
Which of the following is something that will not affect your homeowners insurance premium?
a. the age of the home
b. the size of the home
c. the color of the home
d. the location of the home
Please select the best answer from the choices provided
Answer:
c. the color of the homeStep-by-step explanation:
Option C is the most reasonable answer, because there's no way that the color of the house affects the homeowners insurance premium.
A homeowners insurance premium refers to a monthly or annual payment to an insurance company which maintain the house and stuff insured. This amount can be variate depending on the size, location and age of the home, but not depends on the color of it.
Given the equation f(x) = 2x² + 4x - 1, what is axis of symmetry? a. 1 c. -1 b. 2 d. 0
Answer: x=-1
Step-by-step explanation:
the x value of the vertex = -b/2a if the equation is in "ax^2+bx+c" for
you are in luck
x value of the vertex = -4/4 = -1
the line of symmetry is a vertical line, and since it must pass through the vertex
line of symmetry: x=-1
8. Which equation has no solution?
A.
-5+8x - 9=3(x+3)
B.
-216-3x) = -12 +6x
C. 6-213-2x) = -413-x)
D.
-(4x +9) = 2x - 3(2x+3)
Answer:
Step-by-step explanation:
-5+8x-9=3(x+3)
8x-14=3x+9
8x-3x-14=9
5x-14=9
5x=9+14
5x=23
x=23/5
----------------------
-216-3x=-12+6x
-216-3x-6x=-12
-216-9x=-12
9x=-216-(-12)
9x=-216+12
9x=-204
x=-204/9
x=-68/3
------------------
6-213-2x=-413-x
-207-2x=-413-x
-207-2x-(-x)=-413
-207-2x+x=-413
-207-x=-413
x=-207-(-413)
x=-207+413
x=206
------------------------
-(4x+9)=2x-3(2x+3)
-4x-9=2x-6x-9
-4x-9=-4x-9
Infinitely many solutions.
−4 1/3÷−2 3/5 please help need a 100
Answer:
1 2/3
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Exact Form:
5/3
Decimal Form:
1.6
Mixed Number Form:
1 2/3
Answer:
-4 1/3 divided by -2 3/5 equals 5/3
NFL quarterback Patrick mahomes threw a pass that clocked 62mph. How fast is this in yards per second?
Answer:
The speed of the pass that clocked is 30.31 yards per seconds
Step-by-step explanation:
Given as :
The speed of the pass = 62 miles per hour
Let The speed in yards per second = x yps
So, ∵ The speed = 62 miles per hour
Or, The speed = [tex]\dfrac{\textrm 62 miles}{\textrm 1 hour}[/tex]
or, The speed = [tex]\dfrac{\textrm 62 miles}{\textrm 3600 secons}[/tex]
∵ In 1 hour = 3600 seconds
So, The speed = 0.0172 miles per second
Now, Again
Since 1 mile = 1760 yards
So, 62 miles = 1760 × 62 = 109,120 yards
∴ The speed in yard per second = [tex]\dfrac{\textrm 109,120 yard}{\textrm 3600 seconds}[/tex]
I.e The speed in yards per second = 30.31 yards per seconds
Hence The speed of the pass that clocked is 30.31 yards per seconds Answer
solve the equation y=11.3x + 13.8 estimates the amount that businesses will spend, in billion of dollars on a certain business technology where x is the number of years after 2000 for what years will the spending be more than $59 billion where spending will be more than $59 billion more than blank years after 2000
Answer:
Spending will be more than $59 billion more than 4 years after 2000.
Step-by-step explanation:
Given:
[tex]y=11.3x + 13.8[/tex]
x is the number of years.
Business spending is $59 billion.
Hence we can say that y = $59.
Now Substituting the value of y in above equation we will find the value of x in number of years.
[tex]11.3x+13.8=59\\11.3x=59-13.8\\ 11.3x= 45.2\\\\x=\frac{45.2}{11.3} = 4 years.[/tex]
Hence we can say that,
After 4 years after 2000 the spending will be more than $59 billion.
or
Spending will be more than $59 billion more than 4 years after 2000.
The equation demonstrates that the spending will exceed $59 billion more than 4 years after 2000.
Explanation:To solve the problem, we first need to set the equation y = 11.3x + 13.8 to greater than 59, as we are trying to find out when the spending will be more than $59 billion. The equation will therefore be, 11.3x + 13.8 > 59.
Then, we subtract 13.8 from both sides of the equation to isolate the term with x, resulting in 11.3x > 45.2.
Finally, we divide each side by 11.3 to solve for x, which will give us x > 4. Consequently, the spending will be more than $59 billion more than 4 years after 2000.
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The amount y in cups of flour is proportional to the number x of eggs in a recipe. The recipe calls for 7 cups of flour for every 5 eggs
A: write and equation that represents the situation
B: interpret the slope
C: how many eggs are included when the recipe uses 14 cups of flour
Answer:
A. y=3/2x
B. y=3/2x
C. 18
Step-by-step explanation:
-5s=21.5 how do solve it
Answer:
s=-4.1
Step-by-step explanation:
you just need to divide by -5 of each item
so we have -5s/-5=21.5/-5
s=-4.1
the total heigh of bill mary and rob is 180 cm bob is twice as tall as bill and mary is 28 cm taller than bill how tall is rob
Answer:
Rob is 76 cm tall.
Step-by-step explanation:
Let b = height of bill.
Let m = height of Mary.
Let r = height of Rob.
"the total heigh of bill mary and rob is 180 cm"
b + m + r = 180 Equation 1
"bob* is twice as tall as bill"
*I think you meant Rob is twice as tall as Bill.
r = 2b
"mary is 28 cm taller than bill"
m = b + 28
Substitue r = 2b and m = b + 28 into Equation 1.
b + b + 28 + 2b = 180
4b + 28 = 180
4b = 152
b = 38
r = 2b
r = 2(38) = 76
Rob is 76 cm tall.
Rob height is 76cm.
Given that,
Total height of Bill, Mary and Rob is 180cm.Rob is twice tall as Bill.Mary is 28cm taller than Bill.We need to find the height of Rob.According to the given data, computation of the data are as follows,
Let Bill height be X, then Rob height is 2X and Mary height is X + 28.
So, X + 2X + X + 28 = 180cm
4X = 180 - 28
X = 152 [tex]\div[/tex] 4
X = 38
Hence, Bill height = X = 38cm
Rob height = 2X = 76cm
Mary height = X + 28 = 66cm
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Need help plz very difficult
Answer:
D - 9x^(2)+2x-5
Step-by-step explanation:
Solve for x. Round your answer to the nearest hundredth.
13.48x − 200 < 256.12
Answer:
x<33.84
Step-by-step explanation:
13.48x - 200 < 256.12
13.48x - 200 + 200 < 256.12 + 200
13.48x < 456.12
13.48x / 13.48 < 456.12 / 13.48
x < 33.84
Answer:
b
Step-by-step explanation:
A bean plant grows at a constant rate for a month. After 10 days, the plant is
35 centimeters tall. After 20 days, the plant is 55 centimeters tall.
Which equation models the height of the plant, y, after x days?
A. y+35 = 2(x+10)
B. y - 35 = 2(x - 10)
C. y - 10 = 2(x - 35)
D. y - 35 = 1/2 (x - 10)
Answer:
B. y - 35 = 2(x - 10)
Step-by-step explanation:
The height of the plant, y, after x days could be modeled by the equation
y-y0=k(x-xo) (1),where y0 was the initial height at 'x0'th. day, and k is the constant of proportionality.From equation (1), k could be evaluated as follows:k=(y-y0)/(x-x0) From the problem statement, we may determine k by plugging in the given values, e.g. y0= 35, x0=10, y=55, x=20.Thus,k=(55-35)/(20-10)=2Therefore, the model equation becomesy-35=2(x-10)Answer:
the answer is B
Step-by-step explanation:
A business has two loans totaling $85,000. One loan has a rate of 4.5% and the other has a rate of 6%. This year, the business expects to pay $4,650 in interest on the two loans. How much is each loan?
Answer:
$30,000 and $55,000
Step-by-step explanation:
If 4.5% loan is x, and the 6% loan is y, then:
x + y = 85000
0.045x + 0.06y = 4650
Solve the system of equations with substitution or elimination. Using substitution:
0.045x + 0.06(85000 − x) = 4650
0.045x + 5100 − 0.06x = 4650
450 = 0.015x
x = 30000
y = 55000
Loan I = $ 30,000
Loan II = $ 55,000
Further Explanation
Total loan of $ 85,000
Loan I rate at 4.5%
Loan II rate at 6%
This year's loan repayments are $ 4,650
0.045 + 0.06 = 4,650
Loan II = $ 85,000 - Loan I
0.045 ($85,000-b)+0.06 b= 4,650
Loan II = $55,000
Loan I = $ 85,000 - Loan II
Loan I = $85,000 - $55,000
Loan I = $30,000
Loan I rate = $ 1,350
Loan II rate = $ 3,300
Total Loans rate (I + II) - Payments = ($ 1,350 + $ 3,300) - $ 4,650 = $ 0 (Remaining balance)
Loans are a type of debt that can involve all types of tangible objects, although usually more often are identified with monetary loans. Like other debt instruments, a loan requires a redistribution of financial assets over time between the borrower (indebted) and the debtor (the creditor).
The borrower initially receives an amount of money from the lender to be paid back, often in the form of periodic installments, to the lender. This service is usually provided with certain costs which are referred to as interest on the debt. Borrowers can also get restrictions in the form of loan conditions.
Before applying for a loan you should know how to calculate the percent interest on a loan to check the correctness of the interest calculation specified on your credit.
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Details
Grade: High School
Subject: Mathematics
Keyword: loan, payment, borrowers
The forestry service personnel at a national forest are estimating the average height of the trees in the forest. They measure the heights of 31 trees and prepare the histogram above. What percentage of the trees are less than 75 feet tall?
A. 45.2
B. 80.6
C. 19.4
D. 77.4
Answer:
The correct answer is A. 45.2
Step-by-step explanation:
1. Let's review all the information provided for solving this question:
Number of trees of the sample = 31
Number of trees of the sample with a height between 60 and 65 feet tall height = 3
Number of trees of the sample with a height between 65 and 70 feet tall height = 3
Number of trees of the sample with a height between 70 and 75 feet tall height = 8
Number of trees of the sample with a height between 75 and 80 feet tall height = 10
Number of trees of the sample with a height between 80 and 85 feet tall height = 5
Number of trees of the sample with a height between 85 and 90 feet tall height = 2
2. Let's calculate the percentage of the trees that are less than 75 feet tall:
Percentage of the trees less than 75 feet tall = [(Number of trees of the sample with a height between 60 and 65 feet tall + Number of trees of the sample with a height between 65 and 70 feet tall + Number of trees of the sample with a height between 70 and 75 feet tall)/Number of the trees of the sample] * 100
Replacing with the real values, we have:
Percentage of the trees less than 75 feet tall = [(3 + 3 + 8)/31] * 100
Percentage of the trees less than 75 feet tall = [(14)/31] * 100
Percentage of the trees less than 75 feet tall = 0.451613 * 100
Percentage of the trees less than 75 feet tall = 45.1613% = 45.2% (Rounding to one decimal place)
The correct answer is A. 45.2