Answer:
1. a = 5400
2. r = 0.96
3. Percentage decrement = 65.4%
Step-by-step explanation:
Given
N = ar^t
Solving (a): Write down the value of a
a implies the first term
And from the question, we understand that the initial number of trees is 5400.
Hence,
a = 5400
Solving (b): Show that r = 0.96
Using
N = ar^t
When a = 5400, t = 1 i.e. the first year and N = 5184
Substitute these values in the above expression
5184 = 5400 * r¹
5184 = 5400 * r
5184 = 5400r
Solve for r
r = 5184/5400
r = 0.96
Solving (c): Show that the trees has decreased by over 65% in 2040
First, we need to calculate number of years (t) in 2040
t = 2040 - 2014
t = 26
Substitute 26 for t, 5400 for a and 0.96 for r in N = ar^t to get the number of trees left
N = 5400 * 0.96^26
N = 1868.29658019
N = 1868 (approximated)
Next, we calculate the percentage change as thus:
%Change = (Final - Initial)/Initial * 100%
Where the initial number of trees =5400 and final = 1868
%Change = (1868 - 5400)/5400 * 100%
%Change = -3532/5400 * 100%
%Change = -3532%/54
%Change = -65.4%
The negative sign indicates a decrements or reduction.
Hence, percentage decrement = 65.4% and this is over 65%
Patrick is 5.432 feet tall, Ivan is 5.503 feet tall, Laura is 5.413 feet tall, and Daisy is 5.510 feet tall. Which of the following lists them in order from tallest to shortest?
Answer:
Daisy, Ivan, Patrick, Laura
Step-by-step explanation:
That's just the numbers biggest to smallest.
Which is a valid proportion?
Answer:
A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio.
Snow Dome Ski Resort has 65 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resort has 74 inches of snow. Currently it is snowing there at a rate of ½ inch per hour.
a) Write equations that show the amount of snow at each resort as a function of the number of hours of snow.
b) If the snow continues at this rate, when will Snow Dome have more snow than Mt. Winterpark? Show your solution process clearly.
Answer:
a) Equation for Snow Dome Ski Resort:
[tex]I_s = 65+t[/tex]
Equation for Mt. Winterpark Ski Resort:
[tex]I_m = 74+\frac{t}{2}[/tex]
b) After 19 hours, Snow dome will have more snow.
Step-by-step explanation:
Given that:
Initial snow at Snow Dome Ski Resort = 65 inches
Snowing rate at Snow Dome Ski Resort = 1 inch per hour
Initial snow at Mt. Winterpark Ski Resort = 74 inches
Initial snow at Mt. Winterpark Ski Resort = [tex]\frac{1}{2}[/tex] inch per hour
a) To write equations that show amount of snow at each resort.
Let the time in hours be represented by [tex]t[/tex].
Snow increased in [tex]t[/tex] hours by snowing at Snow Dome Ski Resort = [tex]1\times t = t[/tex] inches per hour
Snow increased in [tex]t[/tex] hours by snowing at Mt. Winterpark Ski Resort = [tex]\frac{1}{2}\times t = \frac{t}{2}[/tex] inches per hour
Equation for Snow Dome Ski Resort:
[tex]I_s = 65+t[/tex]
Equation for Mt. Winterpark Ski Resort:
[tex]I_m = 74+\frac{t}{2}[/tex]
b) Time at which Snow Dome has more snow.
Using the above equations, we can write the following inequality:
[tex]65+t>74+\dfrac{t}{2}\\\Rightarrow t-\dfrac{t}{2}>74-65\\\Rightarrow \dfrac{t}{2}>9\\\Rightarrow t>18\ hours[/tex]
After 18 hours have passed, they will have equal amount of snow.
After 19 hours, Snow dome will have more snow.
A company has 3835 employees. Each employee is to be given an ID number that consists of one capital letter followed by 1 digits.
How many different ID numbers are possible?
Answer:
7670
Step-by-step explanation:
During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of 390. The next month, 400 units of electricity and 250 units of gas were used for a total cost of $326. Find the cost per unit of gas.
Answer:
cost per unit of gas i.e y= 0.36
Step-by-step explanation:
Let cost per unit of electricity = x
and cost per unit of gas = y
The equations required will be:
[tex]600x+100y=390 ---- eq(1)\\400x+250y=326----eq(2)[/tex]
We need to find value of y i.e cost per unit of gas
Solving equations to find value of y
We will use elimination method
Multiply equation 1 by 4 and 2 by 6
[tex]2400x+400y=1560 ---- eq(1)\\2400x+1500y=1956----eq(2)[/tex]
Subtracting eq 1 from eq 2
[tex]2400x+1500y=1956----eq(2)\\2400x+400y=1560 ---- eq(1)\\- \ \ \ \ \ - \ \ \ \ \ \ \ \ \ \ -\\----------------\\1100y=396\\y=\frac{396}{1100}\\y=0.36[/tex]
Solving we get y=0.36
Putting value of y in eq(1) to find value of x
[tex]600x+100y=390\\600x+100(0.36)=390\\600x+36=390\\600x=390-36\\600x=354\\x=\frac{354}{600}\\x=0.59[/tex]
Value of x = 0.59
But we need to find only cost of unit of gas i.e y
So, cost per unit of gas i,e y= 0.36
Which one? 1, 2 , 3 , 4 , or 5 ? Select all
Answer:
1, 2, and 4
Step-by-step explanation:
jakakla j. sjsjsj
Answer:
5 ok how much is the same as the rest of volunteers and you can just leave
What is the value of [(3/5)^0]^-12
Answer:
The value is 1
Step-by-step explanation:
3/5 = 0.6
0.6^0 = 1
1^-12 = 1
Ruth got to the library at 1030 am.
She stayed at the library for 50 minutes.
Then she walked home.
Ruth took 1 1/4 hours to walk home.
(b) At what time did Ruth get home?
Answer:
She got home at 12:35 P.M.
Step-by-step explanation:
She got to the library at 10:30 am.
She spent 50 minutes there
10:30 + 50 mins can be seperated to 30 mins and 20 mins
So, 30 mins goes to 11 and 20 mins more equals 11:20.
She took 1 1/4 hours to get home
1 hour more means 12:20, and since 1/4 of an hour is 15 mins,
12:20 + 15 = 12:35 P.M
hope this helped!
PLEASE PPL ARE GETTING IT WRONG!!!
Answer:
0.59
Step-by-step explanation:
the process is of unitary method
Sam bought a video game console for $150. He later sold the video game console for 13/12 of price he originally paid. Which statement about the price sam sold the video game consol for is true?
Answer:
1/45
Step-by-step explanation:
40 subtracted from five times a number is 8 more than the number write the equation
Answer (let x be the number):
5x - 40 = x + 8
I hope this helps!
The number in the equation 5n - 40 + 8 = n is 8.
What is a numerical expression ?A numerical expression is formed by numbers and their operation.A numerical expression can also be constructed from given statements.
We can also construct numerical expression form real life scenarios.
According to to the question statement 40 subtracted from five times a number is 8 more than the number and we have to form an numerical expression.
Let the number be 'n'.
∴ 5n - 40 + 8 = n
5n - n = 40 - 8.
4n = 32.
n = 32/4.
n = 8.
learn more about numerical expression here :
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Find each value
1. ∛x³
2. 6³
3. 10³
Answer:
1.no answer x
Step-by-step explanation:
2. 216
3. 1000
Which of the following numbers is not a prime number?
A) 13
B) 17
C) 18
D) 19
E) 23
Guys I need y’all help ! ASAP . Pleaseeeee !!!!!
Use the function Y=2x^2+3x+7 to answer the following questions
Answer:
What are the questions?
Please answer this thanks
Answer:
c
Step-by-step explanation:
Harriet used the work below to determine the percent equivalent to One-eighth.
Step 1: One-eighth = StartFraction question mark Over 100 EndFraction
Step 2: 8 divided by 100 = 0.08
Step 3: 0.08 times 1 = 0.08
Step 4: 0.08 percent
What was Harriet’s error?
In Step 1, she set up the proportions incorrectly.
In Step 2, she divided 8 by 100 instead of 100 by 8, so she cannot multiply the numerator by the factor.
In Step 3, she multiplied the numerator instead of the denominator by the factor.
In Step 4, she forgot to move the decimal.
Answer:
B
Step-by-step explanation:
Answer: B
Step-by-step explanation: It's B
PLEASE HELPP ILL MARK BRAINLIEST According to a personal study, the equation ý= 8.6067x +116.6567 models the average number of calories burned by
a 160 lb individual, where x is amount of time spent weight lifting, in minutes, given the individual started the workout with a 10-minute
jog.
According to this regression equation, what is the approximate calories burned for an individual who spent 30 minutes weight lifting?
about 258 calories
o about 375 calories
about 406 calories
about 452 calories
Answer:
if x: 10 y: 202 then...
x: 30 y: 374.858 burned calories.
therefore, 375 calories.
About 375 calories burned for an individual who spent 30 minutes weight lifting
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given,
ý= 8.6067x +116.6567 the average number of calories burned by
a 160 lb individual.
In the given equation x is amount of time spent weight lifting, in minutes, given the individual started the workout with a 10-minute jog.
We need to find the approximate calories burned for an individual who spent 30 minutes weight lifting
To find this we just need to put x value as 30
ý= 8.6067(30)+116.6567
y=258.201+116.6567
y=374.85
y=375
Hence, about 375 calories burned for an individual who spent 30 minutes weight lifting
To learn more on slope intercept form click:
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Please help me with question number 2
Answer:
this is easy u need just to put values in the formula
Step-by-step explanation:
putting values in the formula
T =
[tex]2\pi \sqrt{l \div g} [/tex]
T =2×3.14√0.65÷9.8
T= 6.28√0.066
T=6.28×0.25
T=1.617s answer
FOR BRAINLIEST! which expression is the simplest form of - (4x^3+x^2) + 2(x^3-3x^2)?
JUAN VIAJO DE SALAMANCA A CELAYA Y RECORRIO 25 CM. ¿CUÁNTOS METROS
RECORRIO?
Answer:
0.025
Step-by-step explanation:
Answer:
0.25 metros.
Step-by-step explanation:
cada centimetro es 0.01 metro.
Hiii this due today can you draw a digram for 5 times 20 please THIS IS DUE TODAY THANK You
Answer:
draw the diagram and multiply 5x20
someone pleaseee answer
Answer:
B
Step-by-step explanation:
B-aby you got the stuff
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
105 is on the graph
Answer:
Probability =0.8854 (Approx)
Step-by-step explanation:
Given:
Mean μ = 100
Standard deviation σ = 15
Computation:
Z at 70
Z = (70-100)/15
Z at 70 = -2
Z at 120
Z = (120-100)/15
Z at 100 = 1.33
Probability = φ(1.33) - φ(-2.0)
Probability = 0.9082-0.0228
Probability = 0.8854 (Approx)
Unit 3 lesson 16 homework
Answer:
huh what is your question ????
The perimeter of a triangle is 40 inches. The middle length side is twice as long as the short
side. The longest side is 10 inches longer than the sum of the other two sides. Set up an
equation to model this situation. Then find the length of each side
Answer:
67
Step-by-step explanation:
Problem
What is the constant of proportionality in the equation y=3xy
Answer:
-3
Step-by-step explanation:
y=3xy and subtract y on both sides that gives u -1 and then you have -1=3x and then divide 3 on both sides you are left with -3 =x
Factor the algebraic expression 18a + 14 18a + 14 = (Factor completely.)
Answer:
You cannot factor that any more.
Step-by-step explanation:
The equation is as simple as it can be.
Let f(x) = 3x + 2 and g(x) = - 2x + 1 Find g(f(- 2))
is it
a: -7
b: 17
c: 0
d:9
Answer:
(d) 9
Step-by-step explanation:
f(x) = 3x + 2
g(x) = - 2x + 1
g(f(x)) = - 2(3x + 2) + 1 = - 6x - 4 + 1 = - 6x - 3
g(f(-2)) = - 6(- 2) - 3 = 9
1) What is the unit rate for a train that travels 10.5 kilometers in 8 minutes?
O A. 1.75
O B.0.762
C. 84
D. 840
Step-by-step explanation:
Given that,
Distance, d = 10.5 km = 10500 m
Time, t = 8 minutes = 480 s
We need to find the unit rate of a train motion. The distance divided by time is equal to the speed of the object.
[tex]\text{Rate}=\dfrac{\text{Distance}}{\text{time}}\\\\=\dfrac{10500\ m}{480\ s}\\\\=21.87\ m/s[/tex]
So, the unit rate is 21.87 m/s.