Answer:
The exponential model n(t) is [tex]n(t) = 46(1.1487)^t[/tex]
Step-by-step explanation:
Exponential model of population growth:
An exponential model for population growth has the following model:
[tex]n(t) = n(0)(1+r)^t[/tex]
In which n(0) is the initial value and r is the growth rate, as a decimal.
Observed to double every 5 hours.
This means that [tex]n(5) = 2n(0)[/tex]
We use this to find 1 + r. So
[tex]n(t) = n(0)(1+r)^t[/tex]
[tex]2n(0) = n(0)(1+r)^5[/tex]
[tex](1+r)^5 = 2[/tex]
[tex]\sqrt[5]{(1+r)^5} = \sqrt[5]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{5}}[/tex]
[tex]1 + r = 1.1487[/tex]
So
[tex]n(t) = n(0)(1+r)^t[/tex]
[tex]n(t) = n(0)(1.1487)^t[/tex]
Initially has 45 bacteria
This means that [tex]n(0) = 45[/tex]. So
[tex]n(t) = n(0)(1.1487)^t[/tex]
[tex]n(t) = 46(1.1487)^t[/tex]
The exponential model n(t) is [tex]n(t) = 46(1.1487)^t[/tex]
what's the answer I have 30 something more questions to go
Answer:
9 cm
Step-by-step explanation:
y = 12 - 3
y = 9
if the vertex of triangle abc is A(2, 3) B(4, 5) C(6, 2) . find the reflection of it through y axis
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
A (2, 3 ) → A' (- 2, 3 )
B (4, 5 ) → B' (- 4, 5 )
C (6, 2 ) → C' (- 6, 2 )
Question 2 of 20
Which of the following are roots of the polynomial function below?
Check all that apply.
F(x) = x3 - 3x2 + 2
O A. 2+ v12
B.
2-12
3 + 17
D. 1
E. 3-17
SUBMIT
The rational root of the function f(x) = x³ - 3x² + 2 is - 1.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, A polynomial function of degree three f(x) = x³ - 3x² + 2.
Now, The roots of the function is when f(a) = 0.
The last term is, 2, Hence the roots must be,
± 1, ± 2, The factors of 2.
f(-1) = - 2.
f(1) = 0.
f(-2) = - 18.
f(2) = - 2.
So, The only rational root is x = - 1 and the other roots are irrational and can be obtained by the obtained quadratic equation after factoring or by long division.
learn more about polynomials here :
https://brainly.com/question/11536910
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Which step is incorrect? Look at picture
Answer: step 4 is incorrect
Step-by-step explanation:
Answer:
step 4 is incorrect.
there must be;
cos(π/2-x)cos(y)-sin(π/2-x)siny
Can someone help me with this fast?
Answer:
Angle B 66
Step-by-step explanation:
Complementary angles means their sum is 90
if angle 2 is 24, angle 3 is 90-24
How many terms are there in this expression? 3a + b - 4c
——-
3
6
5
There's 3 terms
3a-----1
+b -----2
-4c------3
llll answer this an i will mark u brainliest
Answer: yeah the other person is right
Step-by-step explanation:
Solve 2x^2
+ x - 4= 0.
x2 +
= 0
DONE
[tex]\\ \sf\longmapsto 2x^2+x-4=0[/tex]
[tex]\\ \sf\longmapsto 2x^2+x=4[/tex]
[tex]\\ \sf\longmapsto 8(2x^2+x=4)[/tex]
[tex]\\ \sf\longmapsto 16x^2+8x=32[/tex]
[tex]\\ \sf\longmapsto (4x)^2+2(4x)(1)=32[/tex]
[tex]\\ \sf\longmapsto 4x^2+2(4x)(1)+1^2=32+1^2[/tex]
[tex]\\ \sf\longmapsto (4x+1)^2=33[/tex]
[tex]\\ \sf\longmapsto 4x+1=\pm\sqrt{33}[/tex]
[tex]\\ \sf\longmapsto 4x=-1\pm\sqrt{33}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-1\pm\sqrt{33}}{4}[/tex]
An airplane flying into a headwind travels the -mile flying distance between Indianapolis, Indiana, and Phoenix, Arizona, in hours. On the return flight, the airplane travels this distance in hours and minutes. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
Answer:
the airspeed of the plane = 660 miles/hr
the speed of the wind = 60 miles/hr
Step-by-step explanation:
The values are missing in the given information in the question.
To able to solve this question, we will make some assumptions.
Let's assume that:
The airplane heading into the wind travels 1800 miles in 3 hours.
While returning via the same distance, it travels 2 hours 30 minutes.
We are to determine the plane's airspeed as well as the wind speed.
First, let us say that the speed of the plane is p and the wind speed is q
during the time the plane is traveling for 1800 miles in 3 hrs.
Then, we can say
3p -3q = 1800 ----- (1)
However, in 2hours 30 minutes, we have 2.5 hours
So, when the plane is returning, we have the following equation:
2.5p + 2.5q = 1800 ---- (2)
So, to find p and q, we can use the elimination method.
Simply by multiplying equation (1) with 5 and equation (2) with 6
(5)3p - (5)3q = (5) 1800
(6)2.5p + (6)2.5q = (6) 1800
15p - 15q = 9000
+
15p + 15q = 10800
30p - 0 = 19800
30p = 19800
p = 19800/30
p = 660
Since p = 660, then from equation (1) we can obtain the value of q:
So; Using equation (1):
3p -3q = 1800
3(660) - 3q = 1800
1980 - 3q = 1800
-3q = 1800 - 1980
-3q = -180
q = 180/3
q = 60
Therefore, the airspeed of the plane = 660 miles/hr
the speed of the wind = 60 miles/hr
What would be the length of AB I need urgent help?
Answer:
8 units
Step-by-step explanation:
AB = √(4×(4+12))
= √(4×16)
= 2×4
= 8 units
f(x)=3√x²-1 and f(x)=2 find x
Answer:
5
Step-by-step explanation:
See the image below:)
Jasmine's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 1 senior citizen ticket and 2
child tickets for a total of $33. The school took in $46 on the second day by selling 1 senior citizen tickets and 3 child tickets What is the
cost of buying 5 senior citizen tickets and 7 child tickets?
Answer:
$126
Step-by-step explanation:
HELPP AND. D IS 10 it got cut out
Answer: 2
Step-by-step explanation:
2
Answer:
A
Step-by-step explanation:
The graft go's by twos
A coach collected data for his runners for 2 weeks. Week 1: Mean = 14.5 miles/ MAD = 1.15 Week 2: Mean = 16 miles/ MAD = 1.5. Which statement correctly compares the variability from Week 1 to Week 2? *
What is the radius in the eqution below? (x - 5) ^ 2 + (y + 3) ^ 2 = 49
Answer:
7.
Step-by-step explanation:
The equation of a circle is
(x - h)² + (y - k)² = r²
Where
(h, k) is the center and r is the radius, so we only need to work with r.
The expression states that
r² = 49 or the radius squared is equal to 49. So solve for r to find the radius.
r² = 49
Take the square root.
r = 7
The radius of the equation is 7.
I NEED HELP WITH THIS !! PLS HELP!!
Answer:
Step-by-step explanation:
2/14 * 1/23 = 1/91
Peter and Mary take turns throwing one dart at the dartboard. Peterhits the bulls eye with probabilitypand Mary hits the bullseye with probabilityr.Whoever hits the bullseye first wins. Suppose Peter throws the first dart.(a) What is the probability that Mary wins
Answer:
[tex]P(Mary) = (1 - p) * r[/tex]
Step-by-step explanation:
Given
[tex]p \to[/tex] Peter hits
[tex]r \to[/tex] Mary hits
Required
The probability that Mary wins
From the question, we understand that Peter throws the first.
If Mary is to win, then Peter has to lose his throw
Using the complement rule, the probability that Peter misses is:
[tex]p' = 1 - p[/tex]
So, the probability that Mary wins is:
[tex]P(Mary) = p' * r[/tex]
This gives:
[tex]P(Mary) = (1 - p) * r[/tex]
49-3m=4m+4 bbbbbbbbbbbbbbbbbbbbbbbb
Answer:
m = 6.43 (approx. )Step-by-step explanation:
49 - 3m = 4m + 4
=> 49 - 4 = 4m + 3m
=> 45 = 7m
[tex] = > \frac{45}{7} = m[/tex]
=> 6.428571... = m
=> m = 6.43 (approx. ) (Ans)
Answer:
m = - 6 . 43
Step-by-step explanation:
49 - 3m = 4m + 4
= 49 - 4 = 4m + 3m
=45 = 7m
= 6.428571... = m
= m = 6.43
A sample of 1600 computer chips revealed that 43% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 44% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is below the stated percentage. Is there enough evidence at the 0.05 level to support the manager's claim
Answer:
The p-value of the test is 0.209 > 0.05, which means that there is not enough evidence at the 0.05 level to support the manager's claim.
Step-by-step explanation:
The company's promotional literature states that 44% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is below the stated percentage.
At the null hypothesis, we test if the proportion is of 44%, the stated value. So
[tex]H_0: p = 0.44[/tex]
At the alternate hypothesis, we test if the proportion is below the stated value, that is, it is less than 0.44. So
[tex]H_1: p < 0.44[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.44 is tested at the null hypothesis:
This means that [tex]\mu = 0.44, \sigma = \sqrt{0.44*0.56}[/tex]
A sample of 1600 computer chips revealed that 43% of the chips fail in the first 1000 hours of their use.
This means that [tex]n = 1600, X = 0.43[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.43 - 0.44}{\frac{\sqrt{0.44*0.56}}{\sqrt{1600}}}[/tex]
[tex]z = -0.81[/tex]
P-value of the test:
The p-value of the test is the probability of finding a sample proportion below 0.43, which is the p-value of z = -0.81.
Looking at the z-table, z = -0.81 has a p-value of 0.209.
The p-value of the test is 0.209 > 0.05, which means that there is not enough evidence at the 0.05 level to support the manager's claim.
Please help! It’s too hard
Answer: for sure c.
Step-by-step explanation: Let me know if im right!
The area of a rectangle is 259 cm sq and its length is 18.5cm find its breadth and perimeter
Answer:
Step-by-step explanation:
let it's breadth be x
area of rectabgle=l*b
259=18.5*b
259/18.5=b
14=b
perimeter of rectangle=2(l+b)
=2(18.5+14)
=2*32.5
=65 cm
Answer:
Breadth = 14 cm
Perimeter = 65 cm
Step-by-step explanation:
Length = [tex]18.5cm[/tex]Area = [tex]259cm^{2}[/tex] = l * b
Therefore, breadth = area / length
Breath = 259 / 185 = 1.4 * 10 = 14 cm
Perimeter = 2 * (l + b)Perimeter = 2 (18.5 + 14)
Perimeter = 2 (32.5)
Therefore, perimeter = 65 cm
I hope this helps :)
-4 (3+8h) =30 round to nearest hundredth
Answer
-1.31 if its getting rounded to nearest number.
The fraction will be -21/16
A baker used 5 7/10 bags of flour one week. The same baker used 7 3?10 bags the next week. How many more bags of flour did the baker use the second week than the first week?
Answer: 1 6/10
Step-by-step explanation:
Subtract 7 3/10 with 5 7/10 !!!btw subscribe to Aphmua and unspeakable!
substract 8 times the sum of a and b from 9y
Answer:
Step-by-step explanation:
according to the question ur equation is
9y-8(a+b)
9y-8a-8b
a tourist drove his car for the total of 17.5 hours while on a 3-day vacation on the first day he drove 4.5 hours in the second day he drove for 2.5 times as many hours as he drove on the first day how many hours did the tourist drive on the third day of his vacation (HELP PLEASE)
Answer:
1.75 hours
Step-by-step explanation:
Time for day 1 : 4.5 hrs
Time for day 2: (4.5 ×2.5)
Time for day 3: let it be denoted by a variable ,say T.
Total Time= 17.5
(Time for day 1 ) + (Time for day 2) +(Time for day 3) =17.5
4.5 + (4.5×2.5) + T = 17.5
4.5+11.25+T =17.5
15.75+T=17.5
T=17.5-15.75
T= 1.75
What is the quotation -3/8 divided by -1/4
Answer:
3/2
Step-by-step explanation:
Answer:
3/2
Step-by-step explanation:
-3/8 / -1/4
Negative divided by negative is positive.
To divide by a fraction, change the division to a multiplication and flip the fraction.
-3/8 / -1/4 =
= 3/8 * 4/1
= 12/8
= 3/2
help MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
Step-by-step explanation:
using pythagoras theorem formula
a^2+b^2=c^2
19^2+52^2=c^2
361+2704=c^2
[tex]\sqrt{3065}[/tex]=c
55.36=c
55=c
Determine the cubic function that is obtained from the parent function y = x^3
after each sequence of transformations
Vertical stretch by a factor of 3; vertical translation up 4 units; horizontal translation left 2 units
Answer:
The answer here depends on whether you want to do them individually or collectively. If we go individually, then:
The vertical scaling gives us y = 3x³
The vertical translation gives us y = x³ + 4
The horizontal translation gives us y = (x + 2)³
On the other hand, if we want to apply all three at the same time, we get:
starting with a vertical scaling of 3, we get:
start with scaling: y = 3x³
add vertical translation: y = 3x³ + 4
and finally add horizontal translation: y = 3(x + 2)³ + 4
What is the constant of proportionality for the table below?
х
10
8
4
2
y
25
20
10
5
Ο Α. 5
B. 215
O C. 2.5
O D. 25
Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are listed below. 16, 14, 14, 21, 15
Answer:
1st
Step-by-step explanation:
You need to add the numbers and then dicuvde by how many numbers are there.
Answer:
16
Step-by-step explanation:
"Mean" is another way of asking for the average. Add all numbers together, then divide by how many numbers you started with.
16 + 14 + 14 + 21 + 15 = 80
80 ÷ 5 = 16