Given:
Initial value = $800 per acre
Growth rate = 3% per year
To find:
How long will it be before the land is worth $1000 per acre.
Solution:
The exponential growth model is:
[tex]y=a(1+r)^t[/tex]
Where, y is the new value, a is the initial value, r is the growth rate in decimal and t is the number of years.
Putting [tex]y=1000, a=800, r=0.03[/tex], we get
[tex]1000=800(1+0.03)^t[/tex]
[tex]\dfrac{1000}{800}=(1.03)^t[/tex]
[tex]1.25=(1.03)^t[/tex]
Taking log both sides, we get
[tex]\log 1.25=\log (1.03)^t[/tex]
[tex]0.09691=t\log (1.03)[/tex]
[tex]0.09691=0.012837t[/tex]
Isolating the variable t, we get
[tex]\dfrac{0.09691}{0.012837}=t[/tex]
[tex]7.54927=t[/tex]
[tex]t\approx 7.55[/tex]
Therefore, the land is worth $1000 per acre after 7.55 years.
Derek reads at a rate of 25 words per minute. If he reads constantly until he is finished how long would it take him to read a 225 word article?
Answer:
9
Step-by-step explanation:
if you divide 225 by 25 u get 9
Answer:
225/25 = 9
Step-by-step explanation:
took the test
1/2 x ( 6 x 4 ) divided by (3 + 2)
Answer:
Step-by-step explanation:
[tex]\frac{\frac{1}{2} *(6*4)}{3+2}\\\\\frac{12}{5} \\\\2.4 = 2\frac{2}{5}[/tex]
Lines m and n are parallel.
what is m<2
options are:
39°
57°
67°
74°
Answer:
67°
Step-by-step explanation:
9x+2=74
9x=72
x=8
m<2 = 180-(5(8)-1+74)
= 180-(39+74)
=180+113
= 67°
pls help with 6 a pls
Answer:
a=2054cm2
b=822cm2
Step-by-step explanation:
a=(26×47) + [(25×16)×2]=2054cm2
b=(26×47)-(25×16)=822cm2
What is the mean absolute deviation of the data set?
{20, 10, 30, 20, 50, 30, 40, 20} 08 O 10 o 12 O 20
Answer:
The answer is 10
Step-by-step explanation:
-add all numbers in a sum
-divide by total of numbers
-use 1.5 strategy
-you get ten
Answer:
10
Step-by-step explanation:
took quiz
Question 8
Find the surface area of the equilateral triangular pryamid.
15 cm
10 cm
Answer:
268.3 cm³
Step-by-step explanation:
Surface area of triangular pyramid = Base Area + ½*(perimeter of base)(height of pyramid)
Base area = 43.3 cm²
Perimeter of base = 10 + 10 + 10 = 30 cm
Height of pyramid = 15 cm
Plug in the values
Surface area = 43.3 + ½(30)(15)
Surface area = 43.3 + 225
= 268.3 cm³
solve for n:
4n-40=7(-2n+2)
Step-by-step explanation:
hope this helped you :)) !!
Determine the value of the variable that makes the equation true.
`1=-10c`
Answer:
please the answer is-10
Want two numbers multiply to get -30 and add to get -13
Answer:
-15 and 2
Step-by-step explanation:
-15 x 2 = -30
-15 + 2 = -13
what number completes the square x^2+18x+_____
(a).81
(b) .324
(c) .-9
(d).9
Step-by-step explanation:
a) 81 is the answer of your question
hope it is helpful to you
Complete the factored form.
7x² +37x + 10 = (7x + 2)()
Find the degree of the polynomial below.
9x2 – 25
Answer:
[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]
[tex] {9x}^{2} - 25[/tex]
✏ Degree is the highest value of the exponent in the polynomial. In this polynomial 2 is the degree of the polynomial.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
Answer:
9x² - 25
2 is the degree of the polynomial.
a line that passes through the point (3,-1) and has a slope of -2/3
Answer:
y = -2/3x + 1
Step-by-step explanation:
y = -2/3x + b
-1 = -2/3(3) + b
-1 = -2 + b
1 = b
y = -2/3x + 1
What is 615.75 rounded to the nearest hundredth?
Answer:
615.75
Step-by-step explanation:
can someone please please please answer this :(
i really need this right now so please :(
yesterday was the deadline I'm late :(
A right rectangular prism is shown below.
What is the volume of the prism in cubic inches?
Answer:
Hello! answer: 264
Step-by-step explanation:
Volume is super simple you just do multiply all of these together for it so...
5 1 /2 × 12 × 4 = 264 HOPE THAT HELPS!
A plane intersects both nappes of a double-napped cone, and it does not contain the vertex of the cone.
Which conic section is formed?
ellipse
parabola
circle
hyperbola
Answer:
ellipse i think
Step-by-step explanation:
Answer:
ellipse
Step-by-step explanation:
In the formula for volume of a right cone, solve for the variable k: V = 1/3 * pi * r ^ 2 * h Note: In this formula, V is volume, h is height, and r is radius of the base of the cone
A. h = (3r ^ 2 * V)/pi
B. h = (3V)/(pi * r ^ 2)
C. h = (3pi * V)/(r ^ 2)
D. h = v/(3pi * r ^ 2)
The height of the cone can be written as h = 3V/(π × r²).
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The formula for the volume of cone is given as V = 1/3 × π × r² × h.
It can be written in terms of h by the method of solving a linear equation as follows,
V = 1/3 × π × r² × h
=> 3V = π × r² × h
=> h = 3V/(π × r²)
Hence, the expression for height from the given formula can be written as h = 3V/(π × r²).
To know more about linear equation click on,
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The number of bacteria in a Petri dish increases by 18% every hour. If there were initially 200 bacteria placed in the Petri dish, which function can be used to determine the number of bacteria in the Petri dish in exactly x hours?
Answer:
y=36x, I think would be the correct answer
PLS HELP!! WILL GIVE BRAINLIST!!
SP and Enrich are water pump manufacturers. SP claims that its water pumps have a higher maximum discharge flow rate than Enrich water pumps with the same specifications. To test the claim, a consumer bureau selected 10 water pumps from each manufacturer by visiting the distribution sites of both SP and Enrich and blindly selecting one water pump from 10 different lots at their sites. The consumer bureau found that, on average, SP water pumps had a 4% higher maximum discharge flow rate than Enrich water pumps. Given the bureau’s data collection method and report, what conclusion can be made?
A. The collection method was unfair because SP's claim may have influenced the bureau's report.
B. The collection method was random because the selection process ensured a random representation of each manufacturer's water pumps.
C. The collection method was fair because SP water pumps had the higher maximum discharge flow rate.
D. the collection method was nonrandom because only 10 water pumps from each manufacturer were selected.
Answer:
The collection method was random because the selection process ensured a random representation of each manufacturer’s water pumps.
Step-by-step explanation:
Given the Bureau’s data collection method and report, the conclusion that can be made is "The collection method was random because the selection process ensured a random representation of each manufacturer's water pumps.". Option B. This is further explained below.
What is data collection?Generally, data collection is simply defined as the process of acquiring and measuring information on variables of interest in a systematic manner
In conclusion, with the Bureau's data collecting technique and report, one might draw the following conclusion; The collection method was random since the selection procedure assured a random representation of each manufacturer's water pumps.
Read more about Data Collection
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Carson's wheelbarrow can hold 345 pounds. He has p pounds of rocks in his wheelbarrow. Write the inequality to represent this situation:__
plsssssss help!!!!!!!!!!!!!!!!!!1
Answer:
umm
Step-by-step explanation:
The maximum number of pounds p is 224
Step-by-step explanation:
Let
p ----> the maximum number of pounds he can pull without going over the weight limit
we know that
121 pound of rock in the wheelbarrow plus p pounds must be at most 345 pounds
In this problem the word "at most" means "less than or equal to"
so
The inequality that represent this situation is
solve for p
subtract 121 both sides
therefore
The maximum number of pounds is 224
Two functions are given below. How do they compare?
f(x) = -3x + 1
g(x) = -3x + 4
a) f(x) is less steep than g(x)
b) f(x) has the same y-intercept as g(x)
c) f(x) is translated 3 units down from g(x)
d) f(x) is translated 3 units up from g(x)
Answer:
I'm pretty sure the answer is D
Someone help me with proving identities? and please show the work if you can!
Answer:
See Below.
Step-by-step explanation:
11)
We have:
[tex]\displaystyle \cos\theta\cdot \cot\theta+\sin^2\theta\cdot \csc\theta=\csc\theta[/tex]
Rewrite:
[tex]\displaystyle \cos\theta\left(\frac{\cos\theta}{\sin\theta}\right)+\sin^2\theta\left(\frac{1}{\sin\theta}}\right)=\csc\theta[/tex]
Multiply:
[tex]\displaystyle \frac{\cos^2\theta}{\sin\theta}+\frac{\sin^2\theta}{\sin\theta}=\csc\theta[/tex]
Combine:
[tex]\displaystyle \frac{\cos^2\theta+\sin^2\theta}{\sin\theta}=\csc\theta[/tex]
According to the Pythagorean Identity, sin²θ + cos²θ = 1. Hence:
[tex]\displaystyle \frac{1}{\sin\theta}=\csc\theta[/tex]
Simplify:
[tex]\csc\theta=\csc\theta[/tex]
12)
We have:
[tex]\displaystyle \frac{\cos^2\theta +\sin^2\theta}{1+\tan^2\theta}=\cos^2\theta[/tex]
Pythagorean Identity:
[tex]\displaystyle \frac{1}{1+\tan^2\theta}=\cos^2\theta[/tex]
From the Pythagorean Identity, if we divide both sides by cos²θ, we acquire that tan²θ + 1 = sec²θ. Hence:
[tex]\displaystyle \frac{1}{\sec^2\theta}=\cos^2\theta[/tex]
Simplify:
[tex]\cos^2\theta =\cos^2\theta[/tex]
13)
We have:
[tex]\displaystyle \frac{\csc\theta\cdot \cos\theta}{\tan\theta +\cot\theta}=\cos^2\theta[/tex]
Rewrite:
[tex]\displaystyle \frac{1/\sin\theta\cdot \cos\theta}{\sin\theta/\cos\theta+\cos\theta/\sin\theta}=\cos^2\theta[/tex]
Multiply both top and bottom by cosθsinθ. Hence:
[tex]\displaystyle \frac{\cos^2\theta}{\sin^2\theta +\cos^2\theta}=\cos^2\theta[/tex]
By the Pythagorean Identity:
[tex]\displaystyle \frac{\cos^2\theta}{1}=\cos^2\theta[/tex]
Simplify:
[tex]\cos^2\theta=\cos^2\theta[/tex]
4b^2+10 if b=5 please help and I need to use distributive property
Answer:
fonite is amzing
Step-by-step explanation:
question is in the snapshot
Answer:
I believe it would be C.
Step-by-step explanation:
First, you have to subtract 2 from both sides and that gives you 2t>4. Divide by 2 to get t>2 and you have the solution of the number line, which also shows the same thing.
Please answer 5 (I GIVE BRAINLIEST)
Answer:
Graph D
Step-by-step explanation:
The slope of the data is 2.5 because 2.5 cups of flour are used for every ounce of butter. Some points on the graph we can use is (0,0) and (10,4).
(0,0): When there are 0 cups of flour, there are 0 ounces of butter.
(10,4): When there are 10 cups of flour, there are 4 ounces of butter.
Slope=m
[tex]m=\frac{Change(y)}{Change(x)}[/tex]
[tex]m=\frac{10-0}{4-0}[/tex]
[tex]m=\frac{10}{4}[/tex]
[tex]m=2.5[/tex]
Graph D is the only graph containing the point (10,4) and (0,0). So, Graoh D is the correct graph.
the glass gauge on a cylindrical coffee maker shows there are 45 cups left when the coffee maker is 36% full. How many cups of coffee does it hold when its full?
Answer:
125 cups
Step-by-step explanation:
45 is 36% of what number?
45 = 0.36n
n = 45 / 0.36
n = 125
Find the slope of the line
Answer:
2 or 2/1
Step-by-step explanation:
First we put -"3y" to the other side of the equation to get
3y=6x+6
Now divide everything by 3 to get "y" by itself.
y=2x+2
The slope is 2 or 2/1
Answer:
b.2
Step-by-step explanation:
6x-3y+6=0
-3y=-6x-6 divide both sides by -3
y=2x+2
On Monday, Courtney spent 14 minutes solving 1 math problem and 2 biology problems. On Tuesday, Courtney spent 16 minutes solving 2 math problems and 1 biology problem. Write and solve a system of equations to find how long it takes Courtney to solve each math problem and each biology problem
Answer:
the timing taken to solve each math problem and each biology problem is 4 minutes each respectively
Step-by-step explanation:
Let us assume the timing taken for math problem be x
And, the time taken for biology problem be y
Now as per the question
The following equations should be considered
x + 2y = 14 .............(1)
2x + y = 16. ...................(2)
Multiply by 2 in equation 1
So,
2x + 4y = 28
2x + y = 16
3y = 12
y = 4 minutes
So, x = 14 - 2(4)
= 12 - 8
= 4 minutes
hence, the timing taken to solve each math problem and each biology problem is 4 minutes each respectively