Step-by-step explanation:
b > 1 is growth. decay would be less than 1
The exponential growth the term b>1
What is exponential growth?But sometimes things can grow (or the opposite: decay) exponentially, at least for a while.
So we have a generally useful formula:
y(t) = a × ekt
Where y(t) = value at time "t"
a = value at the start
k = rate of growth (when >0) or decay (when <0)
t = time
for example,
Example: 2 months ago you had 3 mice, you now have 18. What is the "k" value? How many mice 2 Months from now? How many mice 1 Year from now?
Start with the formula:
y(t) = a × ekt
We know a=3 mice, t=2 months, and right now y(2)=18 mice:
18 = 3 × e2k
Now some algebra to solve for k:
Divide both sides by 3: 6 = e2k
Take the natural logarithm of both sides: ln(6) = ln(e2k)
ln(ex)=x, so: ln(6) = 2k
Swap sides: 2k = ln(6)
Divide by 2: k = ln(6)/2
Notes:
The step where we used ln(ex)=x is explained at Exponents and Logarithms.
we could calculate k ≈ 0.896, but it is best to keep it as k = ln(6)/2 until we do our final calculations.
We can now put k = ln(6)/2 into our formula from before:
y(t) = 3 e(ln(6)/2)t
Now let's calculate the population in 2 more months (at t=4 months):
y(4) = 3 e(ln(6)/2)×4 = 108
And in 1 year from now (t=14 months):
y(14) = 3 e(ln(6)/2)×14 = 839,808
As, per the formula for exponential growth the factor b will tells whether there is exponential growth or decay.
so, when b>1 then it is exponential growth and b<1 shows decays.
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3X^7 +12X^6-36X^5 GCF how to solve
What is the correct time 56 minutes after 10:56 AM?
Answer:
11:52 am
Step-by-step explanation:
Raymond used 36 cubes to build the first layer of a rectangular prism. The edge length of each cube was 1 inch. The finished prism had a total of 8 layers. What is the volume of Raymond’s prism in cubic inches?
Answer:
[tex]Volume=288in^{3}[/tex]
Step-by-step explanation:
Given
Base Cubes =36
Layers = 8
The number of base cubes represents the base area and the number of layers represents the height of the prism.
So, the volume is calculated as:
Volume = Base Cubes * Layers, i.e Base Area * Heights
Volume = [tex]36*8[/tex]
Volume = [tex]36in^{2} * 8 in[/tex]
Volume = [tex]288in^{2}[/tex]
guys please help me with this question, I’d appreciate it a lot
Answer:
B. 84. cubic cm.
Step-by-step explanation:
Remember volume = l*w*h or b*h
Have an awesome day. Let me know if you need any other questions to be answered.
As part of statistics project, math class weighed all the children who were willing to participate as shown below.
How many children weighed less than 50 pounds?
Answer:
18
Step-by-step explanation:
The key of this leaf stem-leaf plot is:
4 | 5 = 45
Therefore, the data points that represents children with weight that is less than 50 pounds would be as follows:
First row => 12, 13, 15, 15 15, 16, 16, 19
Second row => 23, 25
Third row => 33, 35, 37, 38, 39
Fourth row => 44, 45, 45
Therefore, the number of children that weigh less than 50 pounds = 18
what is this answer???
Answer:
<AEB = 51.2
Step-by-step explanation:
Remark
A straight line has a degree value of 180. There are 3 angles. One of them is 90. The other two must add to 90
Equation
2.7x + 8 + 3.8x - 22 = 90 combine like terms on the left.
6.5x - 14 = 90 add 14 to both sides
6.5x = 90 + 14
6.5x = 104 Divide by 6.5
x = 104/6.5
x = 16
<AEB = 2.7*16 + 8
<AEB = 51.2
Two angles are supplementary. One angle is 155º. What is the measure of the other
angle?
Answer:
b
Step-by-step explanation:
Answer:
supplementary means angles that add up to 180°
one angle = 155°
other angle = 180° - 155° = 25°
A) 25°
hope this answer helps you......
Oliver is building a box kite. The frame of the kite has the dimensions shown. He covered the sides of the kite (but not the top and bottom) with 720072007200 cm^2 squared of lightweight fabric. What is the volume inside the kite?
Answer:
54000 cm²
Step-by-step explanation:
Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!
Answer:
[tex]5:3[/tex]
Step-by-step explanation:
To find the simplest ratio, you need to divide by the greatest common factor. In this case, the GCF is 2. So we need to divide both sides by 2. Doing so will get us 5 and 3
Will mark brainly
ASAP
Answer:
58
Step-by-step explanation:
you you have to get the 32 and subtract that by 90 you go by the right angle and subtract 32
Answer:
C) 58
Step-by-step explanation:
CD = 90°
BXC = 32°
Since AXB and these two angles form a straight line, add the first two angles and subtract from 180 (a straight line)
90 +32 = 122
180-122 = 58
The weight of oranges growing in an orchard is normally distributed with a mean
weight of 7 oz. and a standard deviation of 0.5 oz. Using the empirical rule, what
percentage of the oranges from the orchard weigh between 6.5 oz. and 7.5 oz.?
Answer:
The correct anser for delta math is 68%
Step-by-step explanation:
I gave up on delta math
Two rectangular prisms are shown. The prisms have the same dimensions. What is the total volume of both prisms?
Answer:
V= 2* L*B*H
Step-by-step explanation:
Although we are not given the dimension of the rectangular prisms in this question
The volume of a rectangular prism is
V= L*B*H
Since the number of the prism is two
Hence the volume of the two prisms
V= 2* L*B*H
Therefore, when the plugin the dimensions of the prism into the expression above, you will get the volume of the two prisms combined
Select the correct answer.
Brandon is analyzing the profits from two of his restaurant locations. The first location showed a profit of $3,000 in the first week of the year but
has a showed a steady decrease in profits of 1.5% each week since then.
His second location showed a profit of $1,500 in the first week of the year and has showed a steady increase in profits of 1.2% each week since
then.
Which system of equations can Brandon use to determine the number of weeks, x, until the profits, y, from the two locations are the same?
ОВ.
OA y = -3,000(0.985)
y = 1,500(1.012)
y = 3,000(1.015)"
y = 1,500(1.012)"
OC.
y = -3,000(1.015)"
y = 1,500(1.012)
y = 3,000(0.985)
y = 1,500(1.012)"
OD.
Answer:
y=3,000(0.985)^x
y=1,500(1.012)^x
Step-by-step explanation:
System of equations Brandon can use for two location are y= 3000[tex](0.985)^{x}[/tex] and y =[tex]1500(1.012)^{x}[/tex]
What is profit and loss percentage?Profit and loss percentage are used to refer to the amount of profit or loss that has been incurred in terms of percentage.
According to question
Brandon is analyzing the profits from two of his restaurant locations.
where
x = number of week
y = the profit
1st restaurant : showed a profit of $3,000 in the first week of the year but
has a showed a steady decrease in profits of 1.5% each week since then
So in equation we can write it as
y= [tex]3000(1 - 0.015)^{x\\}[/tex]
y= 3000[tex](0.985)^{x}[/tex]
2nd restaurant : showed a profit of $1,500 in the first week of the year and has showed a steady increase in profits of 1.2% each week since then.
So in equation we can write it as
y = [tex]1500(1+0.012)^{x}[/tex]
y =[tex]1500(1.012)^{x}[/tex]
Hence, system of equations can Brandon use to determine the x and y form the two location are y= 3000[tex](0.985)^{x}[/tex] and y =[tex]1500(1.012)^{x}[/tex]
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20 POINTS‼️Jeremy can row 3/8 of a mile in 1/4 of an hour. What is the unit rate that describes the miles per hour?
A. 1 1/2 miles per hour
B. 3/4 miles per hour
C. 1 1/2 hours per mile
D. 3/4 hours per mile
PLEASE HELP THIS IS FOR A TEST!!!! DO YOUR BEST TO SHOW WORK FOR BRAINLIEST!!!!
Answer:
A 1 1/2 miles per hour
Step-by-step explanation:
Take the amount of miles he can row in 1/4 of an hour (3/8) and multiply it by 4, since it will tell you how many miles he can row in one hour. You get 12/8 miles per hour, which simplifies to 1 1/2 miles per hour
Hopefully this helps - let me know if you have any questions!
Which statement is true???
9514 1404 393
Answer:
B, C, E
Step-by-step explanation:
When the central angles are congruent, the corresponding triangles are congruent:
ΔJHK ≅ ΔLHM . . . . selection E
and the base chords are congruent:
ML ≅ JK . . . . selection B
The subtended arcs are also congruent, so adding arc LK to each will result in congruent arc measures:
arc MLK ≅ arc LKJ . . . . selection C
Zye takes out a loan for $6,000 to but a sno conne cart. The bank charges him 8% on the loan. After 5 years, how much interest will be add to the loan?
Answer:
3, 750
Step-by-step explanation:
The interest added to the loan would be $3, 750
Guys pls help me the question and answere choices are in the image pls help
Answer:
Zoe is wrong because she added all the dimensions instead of multiplying all the dimensions
Step-by-step explanation:
to find the volume of a rectangular prism the formula is: Multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Please help i dont understand
Answer:
672
Step-by-step explanation:
• There are 20 pounds of the mixture.
• Peanuts cost $2.95 per pound.
• Almonds cost $5.95 per pound.
• The mixture costs $4.00 per pound.
How many pounds of peanuts will there be?
Answer:
6.63 pounds
Step-by-step explanation:
Total pounds of mixture = 20
The contents of the mixture are; peanuts and almonds. Of which;
Peanuts cost = $2.95 per pound
Almonds cost = $5.95 per pound
The mixture cost = $4.00 per pound
Total cost of contents of the mixture = $8.90
The pounds of peanuts = [tex]\frac{2.95}{8.90}[/tex] x 20
= 6.63
Therefore, 6.63 pounds of peanuts was used in producing 20 pounds of the mixture.
The function of fx and gx are shown on the graph Fx=x2
What is gx
Answer:
Step-by-step explanation:
g(x) =(1/4 x)²
g(x) = 4x² will be the equation of the parabola.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given, two parabolas f(x) and g(x),
From the general equation of the parabola,
y = a(x – h)² + k or x = a(y – k)² +h.
Here (h, k) denotes the vertex.
As we can see in our case, the vertex is (0, 0)
Thus, the equation of the parabola will be
y = ax²
Since the given parabola passes through the point (1, 4)
Substitute the values,
4 = a(1)²
a = 4
therefore, the equation of the parabola g(x) will be,
g(x) = 4x²
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Ryan has 7 black pairs of socks, 3 pair of brown socks, and 8 white pairs of socks in his wardrobe. He randomly picks one pair. Find P(NOT Black) in fraction form
Answer:
Black socks pairs = 7
Brown socks pairs = 3
White socks pairs = 8
P(not black) = ?
First, you need to add the brown & white socks pairs,
[tex]3 + 8 = 11[/tex]
Then you need to add the total number of socks pairs,
[tex]7 + 3 + 8 \\ = 7 + 11 \\ = 18[/tex]
P(not black)
[tex] = \frac{11}{18} [/tex]
Step-by-step explanation:
solution given:
total pair of socks[S]=(7+3+8)=18
total pair of black socks[B]=7
total pair of brown socks [C]=3
total pair of white socks[W]=8
total no of orange marbles[O]=2
now
the P( not black) =?
we have
P( not black) =1-[tex] \frac{n[B]}{n[S]} [/tex]
P( not black) =1-[tex] \frac{7}{18} [/tex]
P( not black) =[tex] \frac{18-7}{18} [/tex]
P( not black) =[tex] \frac{11}{18} [/tex]
so 11/18 is a required probabilty.
Tarush is a landscape architect. For his first public project he is asked to create a small scale drawing of a garden to be placed in the corner of a city park. The garden is a right triangle with base 25, and height 30.
Draw the garden such that 1 unit on the grid below represents 5
Answer:
Given that the garden is a right triangle with base 25m start and height 30 m The length of the hypothenus can be achieved by using pythagorean theorem. Please find the attached file for the diagram. I made a large unit for the sake of clarity.
Answer:
6.0 on the left side 5.0 at the bottom 7.8 on the right side
Step-by-step explanation:
Evaluate: 4h+j, where h=−4 and j=−2
Answer:
Substitute the value of the variable into the expression and simplify.
− 18
Step-by-step explanation:
I'm sorry if it's not what you are looking for.
All the answers to the SLO spring test 6th grade
Answer:
Don't have them
lol
The population P, of Caribou in the Yukon is modeled by P=6x^2-120x+1250 where X is the number of years from today. After how many years with the Caribou population route 21,000 round to one decimal place
Answer:
It will take approximately 68.2 years for the Caribou population to reach 21,000.
Step-by-step explanation:
The population P of Caribou in the Yukon is modeled by P=6x²-120x+1250 where x is the number of years from today.
If the population P of Caribou in the Yukon is 21000, then, replacing you get:
21000= 6x²-120x+1250
So:
0= 6x²-120x+1250 -21000
0= 6x²-120x - 19750
This is a quadratic function of the form: 0= ax²+ bx +c, where: a=6, b= -120 and c=-19750
To solve a quadratic function and determine the value of x you can use the expression:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]
Replacing the values of a, b and c and solving you get:
[tex]x1,x2=\frac{-(-120)+-\sqrt{(-120)^{2}-4*6*(-19750) } }{2*6}[/tex]
[tex]x1,x2=\frac{120+-\sqrt{14400+474000 } }{12}[/tex]
[tex]x1,x2=\frac{120+-\sqrt{488400 } }{12}[/tex]
[tex]x1,x2=\frac{120+-698.86 }{12}[/tex]
So:
[tex]x1=\frac{120+698.86 }{12}[/tex]
x1= 68.24 ≅ 68.2
and
[tex]x2=\frac{120-698.86 }{12}[/tex]
x2= -48. 24 ≅ -48.2
As time cannot be negative, it will take approximately 68.2 years for the Caribou population to reach 21,000.
Write a system of linear inequalities represented by the graph. 20 pts!
Given:
The graph of the system of inequalities.
To find:
The system of inequalities.
Solution:
From the given graph it is clear that the first line passes through the points (0,2) and (1,-1). So, the equation of the boundary line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-2=\dfrac{-1-2}{1-0}(x-0)[/tex]
[tex]y-2=-3x[/tex]
[tex]y=-3x+2[/tex]
The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.
[tex]y\geq -3x+2[/tex]
The second line passes through the points (0,-2) and (3,0). So, the equation of the boundary line is:
[tex]y-(-2)=\dfrac{0-(-2)}{3-0}(x-0)[/tex]
[tex]y+2=\dfrac{2}{3}x[/tex]
[tex]y=\dfrac{2}{3}x-2[/tex]
The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.
[tex]y\geq \dfrac{2}{3}x-2[/tex]
Therefore, the system of inequalities contains two linear inequalities [tex]y\geq -3x+2[/tex] and [tex]y\geq \dfrac{2}{3}x-2[/tex].
OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS- PLSS TELL ME I ALREADY DID THE TOP AND THE F. BTW SO NO NEED JUST PLS HELP IN THE OTHER QUESTIONS IN BOTTOM :(.. /C. D. AND E. PLS HELP :( /
Answer: for C it is that 1/2 is half of an whole therefore 1/2 is half is less than the rest
for D you will have to add more 1/2 for it to be greater than but for now, it is less than.
for E you will have to add more 1/2 for it to be greater than
What is 2/3 – (-2/3)?
A. -4/3
B. 4/3
C. 0
D. 2/3
Answer is B
Answer:
answer b
Step-by-step explanation:
lol points ig
Triangle ABC pictured above has a right angle at C. If a=4.3 and c=9, find the measure of angle B. Round to the nearest tenth of a degree.
I ONLY NEED THE ANSWER HELP MEEEEEE
Help ASAP! Find the measure of Arc AP.
Answer:
57
Step-by-step explanation:
<=1/2(AP-BN)
12=1/2(x-33)
(2) 12=1/2(x-33) (2)
24=x-33 24+33
57=x
57=AP