Given:
f(x) is an exponential function.
[tex]f(2.5)=26[/tex]
[tex]f(6.5)=81[/tex]
To find:
The value of f(12), to the nearest hundredth.
Solution:
The general exponential function is
[tex]f(x)=ab^x[/tex]
For, x=2.5,
[tex]f(2.5)=ab^{2.5}[/tex]
[tex]26=ab^{2.5}[/tex] ...(i)
For, x=6.5,
[tex]f(6.5)=ab^{6.5}[/tex]
[tex]81=ab^{6.5}[/tex] ...(ii)
Divide (ii) by (i).
[tex]\dfrac{81}{26}=\dfrac{ab^{6.5}}{ab^{2.5}}[/tex]
[tex]\dfrac{81}{26}=b^4[/tex]
Taking 4th root on both sides, we get
[tex]\sqrt[4]{\dfrac{81}{26}}=b[/tex]
[tex]b\approx 1.32855[/tex]
Putting b=1.32855 in (i), we get
[tex]26=a(1.32855)^{2.5}[/tex]
[tex]26=a(2.03444)[/tex]
[tex]\dfrac{26}{2.03444}=a[/tex]
[tex]a\approx 12.7799[/tex]
Now, the required function is
[tex]f(x)=12.7799(1.32855)^x[/tex]
Putting x=12, we get
[tex]f(12)=12.7799(1.32855)^{12}[/tex]
[tex]f(12)=386.4224[/tex]
[tex]f(12)\approx 386.422[/tex]
Therefore, the value of f(12) is 386.422.
3-6i
hi can you guys help me solve this, i’m not understanding it. construct a polynomial?
Answer:
3i
Step-by-step explanation:
You subtract it and add the I
Which power does NOT have a value of 64?
A. 2 ˄6
B. 8 ˄2
C. 4 ˄3
D. 32 ˄2
At a university, 73% of the students are undergraduates. .
If there are 6,700 students, how many of them
are undergraduates?
Answer:4,891 are undergraduate students .
Step-by-step explanation:
Total Number of students = 6700
Percentage of Undergraduate students = 73%
Number of Undergraduatre students = Percentage of Undergraduate students x Total Number of students
= 73% x 6700
73/100 x6700
=4,891 are undergraduate students .
Johnny drove 300 miles using 20 gallons of gas. How many miles can he drive on 1
gallon of gas?
just divide 300/20 to get 15
answer is 15
hope this helps
:)
yoko made $231 for 11 hours of work. At the same rate, how much would she make for 8 hours of work.
Answer:
Step-by-step explanation:
If Yoko made 231 dollars in 11 hours, it means that she makes
231/11=21 dollars per hour
in 8 hours
8*21=168 dollars in 8 hours
Answer:
168
Step-by-step explanation:
We need to find how much money she makes in one hour. Then multiply that by 8.
231 ÷ 11 = 21
21 × 8 = 168
What is 60.861 rounded to the nearest hundredth?
Answer:
60.900
Step-by-step explanation:
All of the zero's are optional, i feel safer putting them.
530 is what percent of 212
Answer:
250 is the answer to your question
A farmer raises only ducks and pigs. There are 55 animals in all on his farm, and 146 legs.
Find the number of ducks and pigs on his farm by setting up and solving a system of equations.
Define the variables
Equations
Show all work
Answer:
Number of ducks = 37
Number of pigs = 18
Step-by-step explanation:
Let,
x be the number of ducks
y be the number of pigs
According to given statement;
x+y=55 Eqn 1
2x+4y=146 Eqn 2 (As ducks will have 2 legs and pigs will have 4)
Multiplying Eqn 1 by 2
2(x+y=55)
2x+2y=110 Eqn 3
Subtracting Eqn 3 from Eqn 2
(2x+4y)-(2x+2y)=146-110
2x+4y-2x-2y=36
2y=36
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{36}{2}\\y=18[/tex]
Putting y=18 in Eqn 1
x+18=55
x = 55-18
x = 37
Hence,
Number of ducks = 37
Number of pigs = 18
10^7+9+1^3
Found it on khan
i giveeeee brainlilsttt pls helppppppp
Answer:
man have a good day
Step-by-step explanation:
hope your days going good
Answer:
I am pretty sure that u and t are gonna stay where they are and v is gonna be (-5,9)
Step-by-step explanation:
flyaj210 sent me
A surf charges $6 to rent a wetsuit and $12 per hour to rent a surfboard write the function to model the cost for wetsuit and hours for the surfboard
Answer:
6h+12h=m
h m
1 18
2 36
3 54
4 72
5 90
6 108
7 126
8 144
9 162
10 180
Step-by-step explanation:
A crate has 272 red and green apples. How many green apples are there?
Answer:
149
Step-by-step explanation:
An analyst wants to determine the relationship between speed, in miles per hour, and the time, in hours, it takes to drive 5 miles. Twenty trials are completed and the correlation coefficient between speed and time is determined to be -0.276. Therefore, slower speed was related to greater time. How is the correlation affected if the units for time are changed from hours to minutes?
Answer:
Answer below:
Step-by-step explanation:
SPEED (in miles/hour), TIME (in hours)
This analyst determined the relationship between the 2 measures above, using 20 trials.
The correlation coefficient between both factors was -0.276
Now, correlation coefficient is a figure that shows the strength and direction of two quantities. The quantities here are speed and time.
The minus sign in this correlation coefficient shows a negative movement of one quantity against the other. In other words, as one quantity moves up, the other goes down, and vice versa. An increase in magnitude of speed will result in a decrease in magnitude of time spent driving. Vice versa.
If you plot speed against time, the graph (that joins each point of intersection of speed and time together) will slope downwards showing the opposing movements of time and speed.
How is the correlation affected if the units for time (time only, not speed) are changed from hours to minutes?
If the units for each time measured are changed to minutes while that of speed is left in hours, the magnitude of each time measured will increase by 60.
For example, if three of the twenty trials have the following values for time - 1.5 hours, 2.3 hours, 3.6 hours
then they will be multiplied by 60, in order to change to minutes. The new values are shown below:
90 minutes, 138 minutes, 216 minutes
THIS CHANGE ON THE VARIABLE TIME ALONE, WILL CAUSE IT TO CARRY MORE MAGNITUDE WHILE THE TIME IN THE MEASUREMENT OF SPEED REMAINS THE SAME.
WHAT THIS WILL DO TO THE CORRELATION COEFFICIENT IS: to lower the value of the figure from 0.276 to a value like 0.043
The minus sign will still remain, as speed and time are still moving in opposite directions.
The value of the correlation coefficient will drop!
Internetlivestats.com reported in December 2017 around 41% of the world population has an Internet connection today. If there are
3,062,263,517 users, what is the world population? (Round your answer to the nearest whole number.)
Answer:
World population = 7,468,935,407
Step-by-step explanation:
Given that:
Percent of people who have internet connection = 41%
Number of people who have internet connection = 3,062,263,517
Let,
x be the world population.
41% of x = 3062263517
[tex]\frac{41}{100}x=3062263517\\[/tex]
0.41x = 3062263517
Dividing both sides by 0.41
[tex]\frac{0.41x}{0.41}=\frac{3062263517}{0.41}\\x=7468935407[/tex]
Hence,
World population = 7,468,935,407
O will give te brainliest plz help
Answer:
B
Hope it helps uwu
What is the surface area of the right cone below?
Answer:
The TOTAL surface Area is
Side Surface Area (15*8) * PI = 120 PI PLUS
Bottom Surface Area = (8*8) * PI = 64 PI equals
184 PI units
Answer is D
Step-by-step explanation:
Answer:
Step-by-step explanation:
184 my man right
solve for o 9=5+o i need this for math like asap
Answer: its 4
Step-by-step explanation:
Answer:
o = 4
Step-by-step explanation:
So we have to do the whole inverse operation thingy so our equation is:
9 - 5 = 4
So o = 4
hope this helps:)
Please answer this correctly without making mistakes
Answer:
1 pound 3.4 ounces
Step-by-step explanation:
Factor the expression completely. 5x + 4.0
Answer: I think it should stay as is
Step-by-step explanation:
It is already simplified
Select the correct answer. A basketball team played 15 games and won 80% of them. If the team expects to play 30 games in all, how many more games must it win to finish the season with a 90% winning percentage? O A 12 B. 14 Ос. D. US
Answer:
12 more games
Step-by-step explanation:
15 + 12 = 27
27 is 90% of 30 , so they need to win 12 more games but 27 overall out of the 30
30 = 100%
27 = x
x = 27×100%/30
x = 2700%/30
x = 90%
How can you use the distributive property to rewrite 15p+10q as a product?
Answer:
Both of those terms are divisible by 5, so you could express it also as
5(3p + 2q)
The equivalent expression is [tex]5(3p+2q)[/tex].
Important information:
The given expression is [tex]15p+10q[/tex].We need to find the equivalent expression by using the distributive property.
Distributive property:According to the distributive property:
[tex]a(b+c)=ab+ac[/tex]
The given expression can be written as:
[tex]=5\times 3p+5\times 2q[/tex]
[tex]=5(3p+2q)[/tex]
Therefore, the equivalent expression is [tex]5(3p+2q)[/tex].
Find out more about 'Distributive property' here:
https://brainly.com/question/13130806
Rewrite the decimal as a simple fraction in lowest terms. 0.005
Answer:
1/200
Step-by-step explanation:
the answer is that 0.005 is 1/200
Answer:
1/200
Step-by-step explanation:
If you calculate it out into a regular fraction, it will equal 5/1000.
Divide 5 and 1000 by 5 and you get 1/200.
Pam is a wedding planner She is setting up a room to seat at least 100 guests. She has some tables that seat 10 people and some tables that seat 5 people. She only has 10 of the tables that seat 5.
1. Let x = the number of 10-person tables, and y = the number of 5-person tables. Write an inequality to describe the number of tables Pam could set up for the wedding.
2. Write a second inequality based on the fact that there are only 10 tables that seat 5.
Answer:
1. 10x + 5y ≥ 100
2. y ≤ 10
The length and width of a garden are in a ratio of 10:8. The perimeter of the garden is 324 feet. What is the length and width?
Answer:
length= 90feet
width =72 feet
Step-by-step explanation:
perimeter=2(L+W)
324=2(L+W)
324/2=L+W
162=L+W( at a ratio of 10:8)
length=10/18 * 162=90
width=8/18*162=72
2(90+72)=324
I need help with this question, in the picture.
Answer:
34 degrees
Step-by-step explanation:
34 degrees
the angle is 90 degrees
90-56=34
======================================================
Explanation:
Refer to the diagram below. I've added the variable y as the base angles to the isosceles triangle on the left.
Recall that the angles opposite the congruent sides are the base angles. The base angles of any isosceles triangle are the same measure.
Let's solve for y
y+y+56 = 180 .... all angles in a triangle add to 180
2y+56 = 180
2y = 180-56
2y = 124
y = 124/2
y = 62
I've also added the variable z, which is adjacent to one of the y angles.
Since y and z combine to form a straight angle, this means the two angles add to 180
y+z = 180
z = 180-y
z = 180-62
z = 118
Now focus on the isosceles triangle on the right. It has angles x, x, and z = 118.
x+x+z = 180
x+x+118 = 180
2x+118 = 180
2x = 180-118
2x = 62
x = 62/2
x = 31
Ashley’s school took a field trip. A total of 32 vehicles were needed for the trip. Some students took the bus, and some students car-pooled. There were 27 people on each bus and 3 people in each car. 408 people altogether attended the trip. How many buses and cars were needed for the trip?
Answer:
19 cars
13 buses
Step-by-step explanation:
We have a system of equations as follows
X + y = 32 -----1
3x + 27y = 408 ----2
x = car
y = bus
From equation 1
x + y = 32
x = 32 - y ---- 3
We put equation 3 into equation 2
3(32-y) + 27y = 408
96y -3y + 27y = 408
96 + 24y = 408
24y = 408 - 96
24y = 312
Divide through by 24 to get the value of y
Y = 312/24
Y = 13
We put the value of y in equation 3
x = 32 - 13
x = 19
So 19 cars would be needed for the trip and also 13 buses would also be needed
Eloise ran 2 3/12 miles yesterday and 1 8/12 miles today how far does Eloise run in all
Answer:
3 11/12
Step-by-step explanation:
Answer:
Different ways to answer
Step-by-step explanation:
mixed number: 3 11/12
decimal: 3.916 repeating
imporper fraction: 47/12
PLEASE MARK ME BRAINLIEST
The radius of a circle is 3.8 feet. Find the diameter.
Answer:
7.6ft
Step-by-step explanation:
Answer:
7.6
Step-by-step explanation:
3.8 + 3.8 = 7.6
The radius of a circle is half of the diameter
The radius is half of the circle length and the diameter is the whole length
remember that :)
how do you solve this as a solution 9(2 + 3x) < 72
Answer:
x <2
Step-by-step explanation:
9(2 + 3x) < 72
Divide each side by 9
9/9 *(2 + 3x) < 72/9
2+3x < 8
Subtract 2 from each side
2+3x-2 < 8-2
3x<6
Divide each side by 3
3x/3 <6/3
x <2
m=p/n+4 make n the subject
Answer:
[tex] n = \frac {p - 4m}{m} [/tex]
Step-by-step explanation:
Given the algebraic expression;
[tex] m = \frac {p}{n + 4} [/tex]
To make n the subject of formula.
Cross-multiplying, we have;
[tex] m*(n+4) = p [/tex]
[tex] mn + 4m = p[/tex]
Rearranging the equation, we have;
[tex] mn = p - 4m [/tex]
[tex] n = \frac {p - 4m}{m} [/tex]
Answer:
[tex]m = \frac{p}{(n + 4)} \\ (n + 4)m = p \\ nm + 4m = p \\ nm = p - 4m \\ n = \frac{p - 4m}{m} \\ n =( \frac{p}{m} - 4)[/tex]
n=p/m-4 is the right answer.