To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, both to find the needed time and to find the inverse function. From this, we get that:
It will take 7.6 years for 21 of the trees to become infected.The logarithmic model is: [tex]g(x) = \frac{\ln{x}}{0.4}[/tex]Number of trees infected after t years:
The number of trees infected after t years is given by:
[tex]f(t) = e^{0.4t}[/tex]
Question 1:
We have to find the number of years it takes to have 21 trees infected, that is, t for which:
[tex]f(t) = 21[/tex]
Thus:
[tex]e^{0.4t} = 21[/tex]
To isolate t, we apply the natural logarithm to both sides of the equation, and thus:
[tex]\ln{e^{0.4t}} = \ln{21}[/tex]
[tex]0.4t = \ln{21}[/tex]
[tex]t = \frac{\ln{21}}{0.4}[/tex]
[tex]t = 7.6[/tex]
Thus, it will take 7.6 years for 21 of the trees to become infected.
Question 2:
We have to find the inverse function, that is, first we exchange y and x, then isolate x. So
[tex]f(x) = y = e^{0.4x}[/tex]
[tex]e^{0.4y} = x[/tex]
Again, we apply the natural logarithm to both sides of the equation, so:
[tex]\ln{e^{0.4y}} = \ln{x}[/tex]
[tex]0.4y = \ln{x}[/tex]
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
Thus, the logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
For an example of a problem that uses exponential functions and logarithms, you can take a look at https://brainly.com/question/13812761
What are the amplitude, period, phase shift, and midline of f(x) = 7 cos(2x + π) − 3? (6 points) Amplitude = −3; period: π; phase shift: x = negative pi over 2 ; midline: y = 3 Amplitude: 7; period: π; phase shift: x = negative pi over 2 ; midline: y = −3 Amplitude: 7; period: 2π; phase shift: x = pi over 2 ; midline: y = 3 Amplitude: −3; period: 2π; phase shift: x = pi over 2 ; midline: y = −3
Answer:
So the amplitude is 7
The period is pi
The phase shift is negative pi/2
The midline is -3
Step-by-step explanation:
A trigonometric function is the same as
[tex]f(x) = a \cos(b(x + c)) - d[/tex]
Where a is the amplitude, 2 pi/ absolute value of b is the period, c is the phase shift, and d is the vertical shift or midline.
Given the function
[tex]7 \cos(2x + \pi) - 3[/tex]
The amplitude is 7, and the midline is -3. The period is
[tex] \frac{2\pi}{2} = \pi[/tex]
The phase shift is
[tex]2x + \pi = 0[/tex]
[tex]2x = - \pi[/tex]
[tex]x = - \frac{\pi}{2} [/tex]
So the amplitude is 7
The period is pi
The phase shift is negative pi/2
The midline is -3.
Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. Suppose that we select random samples from this population of American adults ages 25 and older. For each sample we then calculate the proportion that had never been married.
For which of the following sample sizes will the sampling distribution be approximately normal?
Wang, W., and Parker, K. (2014). Record Share of Americans Have Never Been Married. Pew Research Center. http://www.pewsocialtrends.org/2014/09/24/record-share-of-americans-have-never-married/
A) 25
B) 50
C) 75
Answer:
B. 50
Step-by-step explanation:
Central limit theorem is used to calculate the sampling distribution of the given case. The number of adults who are 25 years of age or above and not married is 20% of the samples selected. The standard deviation is 0.06 while the sample size should be 50 to conclude the results.
An item is regularly priced at $95. It is on sale for 85% off the regular price.
Answer:
14.25
Step-by-step explanation:
95*0.85=80.75
95-80.75=14.25
Answer:
The sale took $14.25 off the original price, so the item is currently $80.75 with the sale.
Find the cross product (7,9, 6)x 44, 1, 5). Is the resulting vector perpendicular to the given vectors?
a. (-57, 43, 33); yes
c. (33. – 59, - 57); no
b. (39, – 59,43), yes
d. (33, - 57, 49); no
Answer:
Option B, (39, -59, 43)
Answered by GAUTHMATH
HELPPPPPPPP!!!!!!!!!!!!!!!!!
find the lenght of the missing side:
Answer:
x=15.73292
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos 70 = x / 46
46 cos 70 =x
x=15.73292
Answer:
15.73
Step-by-step explanation:
cos(x) = adjacent leg / hypotenuse
cos(70) = x / 46
0.342 = x / 46
0.342 x 46 = x
x = 15.73
name the property that the following statement illustrates 84+8=8+84
Answer:
the commutative property of addition :)
helpppp: write the rule that describes the composition of transformations
Which graph represents the function? f(x)=5√x
Step-by-step explanation:
Since the x is inside of the square root, the x value must be positive. This makes x {0,infinity). Yet, when square rooting x, you should have both a negative and a positive value for y. So, this should be your graph.
0.4 x 10 =....
1.25 x 10 =
97.465 x10 =
Answer:
0.4 × 10 = 4
1.25 × 10 = 12.5
97.465 × 10 = 974.65
You flip a coin and roll a six-sided die. What is the
probability of flipping heads and rolling a number greater
than or equal to 5?
Answer:
The probability of flipping heads is 1/2
The probability of rolling 5 or more is 1/3.
So the total probability is 1/2 x 1/3 , which is 1/6.
Let me know if this helps!
Answer:
1/6
Step-by-step explanation:
The probability of flipping heads is 1/2
The probability of rolling 5 or more is 1/3.
So the total probability is 1/2 x 1/3 , which is 1/6.
The difference of a number and 11
Answer:
x - 11
Step-by-step explanation:
"A number" is the same thing as a variable.
Answer:
x-11
Step-by-step explanation:
PLEASEE HELP ASAP........
Answer:
(C). 126
Step-by-step explanation:
[tex]\frac{45}{x}[/tex] = [tex]\frac{65}{182}[/tex]
x = 126
Answer:
Hello,
Answer C\\
Step-by-step explanation:
Triangle EUT is similar to triangle EGF
[tex]\dfrac{EU}{EG} =\dfrac{ET}{EF} \\\\\dfrac{140-90}{140} =\dfrac{45}{EF} \\\\\\EF=\dfrac{45*140}{50} \\\\\\RF=126\\\\Answer\ C\\[/tex]
Which expression is equivalent to….
Answer:
the answer is {2^5}
hope it helps :)
(2^1/2×2^3/4)^2
(2^(2/4+3/4))^2
(2^5/4)^2
2^(5/4×2)
2^(5/2)
√2^5
Answered by Gauthmath must click thanks and mark brainliest
Given the function g(x) = x2 + 10x + 18, determine the average rate of change of
the function over the interval -11 < x < -1.
Answer:
-2.
Step-by-step explanation:
Average rate of change of the function = [ f(-1) - f(-11)] / [(-1 - (-11)]
= [(-1)^2 + 10*-1 + 18 - ((-11)^2 + 10*-11 + 18)] / 10
= (1 - 10 + 18 - (121 - 110 + 18) / 10
= (9 - (29) /10
= -20/10
= -2.
Answer:
Step-by-step explanation:
The answer is +2 or 2.
You would like to know how effective a diet program is at helping people lose weight. 18 over-weight people are randomly selected to participate in the program. They are weighed before and after the program and the results are listed below. Do these results give evidence that the diet program is effective at the 1% significance level?
Answer:
There is not enough evidence to support the claim that drug is effective at 1%
Step-by-step explanation:
For this we use the pored test as we have dependent test;
Difference :
10,5,-5,3,-3,4,2,-3,0,10,8,-2,3,-2,5,5,4,0
Hypothesis :
H0 : μd = 0
H0 : μd ≠ 0
The mean of d, dbar = Σd / n = 44 / 18 = 2.44
The standard deviation, Sd = 4.45 (using calculator)
The test statistic, T : dbar / (Sd/√n)
T = 2.44 / (4.45/√18)
T = 2.44 / 1.0488750
T = 2.326
Degree of freedom, df = n - 1 ; 18 - 1 = 17
The Pvalue = 0.0326
α = 0.01
Since Pvalue < α ; we fail to reject H0
42 deliveries in 3 hours = deliveries per hour
Answer:
14 deliveries per hour
Step-by-step explanation:
42/3
14
The person makes 14 deliveries per hour
Answer:
14
Step-by-step explanation:
42 / 3 = 14
Is 6272 a perfect square? If not find the smallest number by which it must be divided so that the product becomes a perfect square.
Answer:
(2^7)*(7^2)
Step-by-step explanation:
2*2*2*2*2*2*2*7*7=6272where2 is the smallest number by which it becomes a perfect square
Samuel takes 5 hours to make a table and a chair. He takes 9 hours to make 3 chairs
and a table. How much time does he take to make a table?
Answer:
3 hours
Step-by-step explanation:
t = time to make a table
c = time to make a chair
t + c = 5
t+3c = 9
Subtract the second equation from the first
t+3c = 9
-(t + c = 5)
-----------------------
2c = 4
Divide by 2
2c/2 = 4/2
c =2
2 hours for the chair
t+c = 5
t+2 = 5
t = 5-2
t = 3hours
Answer:
It takes 3 hours to make a table.
Step-by-step explanation:
Table and chair : 5 hours
Table and 3 chairs : 9 hours
(Table and 3 chairs) - (Table and chair) = (2 chairs)
9 hours - 5 hours = 4 hours
2 chairs : 4 hours / 1 chair : 2 hours
Table and chair : 5 hours
Chair : 2 hours
Table: x hours
5 - 2 = 3
Table : 3 hours
If 1 angle is four time of another angle in linear pair find the angles. Please do it fast as you can
Answer:
let the angle be x then other angle is 4x
so,
x + 4x = 180
5x = 180
x = 36
so other angle I.e 4x = 4 × 36 = 144
Let one angle be x
Other angle=4xBoth are linear pair hence their sum will be 180
[tex]\\ \sf \longmapsto x+4x=180[/tex]
[tex]\\ \sf \longmapsto 5x=180[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{180}{5}[/tex]
[tex]\\ \sf \longmapsto x=30[/tex]
[tex]\\ \sf \longmapsto 5x=5(30)=150[/tex]
A retailer bought 1000 glass tumblers at rs 80 each.50 glass tumblers were broken and he sold the rest at Rs 96 each .find his profit or loss percent
Step-by-step explanation:
Soln
Given
Cp of 1 glass tumbler=80.1000
=Rs 80000
Number of broken glass tumbler=50
Number of remaining glass tumbler=1000-50
=950
Sp of one glass tumbler=96
Sp of 950 glass tumbler=96.950
=91200
Now
Sp > Cp so it is profit
Profit%=sp-cp/cp.100
=91200-80000/80000.100
=11200/80000.100
=14%
Answer:
14%profit
Step-by-step explanation:
Cost of 1000 tumblers=1000×80=80,000
50 of them were broken: 1000-50=950
: He sells 950 tumblers of rs.96 each= ( 950×96)
S.P=91200
We can clearly see he gains for rs.11200.
P%=gain/C.P×100
11200×80000×100
=14%
any 5
algebraic formulas
Answer:
a2 – b2 = (a – b)(a + b)
(a + b)2 = a2 + 2ab + b2
a2 + b2 = (a + b)2 – 2ab
(a – b)2 = a2 – 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
a4 – b4 = (a – b)(a + b)(a2 + b2)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4
Answer:
a2 – b2 = (a – b)(a + b)
(a + b)2 = a2 + 2ab + b2
a2 + b2 = (a + b)2 – 2ab
(a – b)2 = a2 – 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
a4 – b4 = (a – b)(a + b)(a2 + b2)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
factorize = n!+(n-1)!
Answer:
Hello,
Step-by-step explanation:
n! + (n-1)!
=(n-1)! * n+ (n-1)!
=(n-1)! * (n+1)
ayudenme pls aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
aslo bien jjjjjjj
Step-by-step explanation:
Four times an angle is equal to half of its supplement. Find the measures of both angles.
Answer:
The bigger angle is 144 degrees and the smaller one is 36 degrees
Find the place value of 8 in 2456.1387.
Tenths
Hundredths
Thousandths
Thousands
Answer: Third Choice. Thousandths
Step-by-step explanation:
Concept:
Here, we need to know the order and name of each place value.
Please refer to the attachment below for the specified names.
Solve:
STEP ONE: Orde and name each place
2 ⇒ One Thousands
4 ⇒ Hundreds
5 ⇒ Tens
6 ⇒ Ones
.
1 ⇒ Tenths
3 ⇒ Hundredths
8 ⇒ One Thousandths
7 ⇒ Ten Thousandths
STEP TWO: Find the number [8] in the number
As we can see from the list above, 8 is at the right of the decimal point, thus, the place value is Thousandths.
Hope this helps!! :)
Please let me know if you have any questions
1. The product of two consecutive numbers is 42. What are the numbers?
Answer:
6, 7
Step-by-step explanation:
6 x 7 = 42
What is the constant of proportionality in the equation x 2
—- = ——
Y 9
Answer:
The Constant is 9/2
cho tứ giác ABCD. Gọi M,N,P,Q là trung điểm của các cạnh AB, CD, AD, BC. Chứng minh rằng vecto MP = vecto QN, vecto MQ = vecto PN
Answer:
Step-by-step explanation:
Xét tam giác DAB có: P là trung điểm AD, M là trung điểm AB
=> MP là đường trung bình của tam giác DAB => MP//BD và MP=[tex]\frac{1}{2}[/tex]BD (1)
Xét tam giác DBC có: N là trung điểm DC, Q là trung điểm BC
=> QN là đường trung bình của tam giác DBC => QN//BD và QN=[tex]\frac{1}{2}[/tex]BD (2)
Từ (1) và (2) => vecto MP song song cùng chiều với vecto QN
và độ dài MP = độ dài QN = [tex]\frac{1}{2}[/tex]BD
=> vecto MP = vecto QN
Tương tự xét các tam giác DAC và tam giác ABC => vecto MQ = vecto PN
(Picture) Could someone help me solve this I need to use Inverse Operations but I don't fully understand? I'll mark brainliest, 10 Points.
Answer:
[tex]x = - 8[/tex]
Step-by-step explanation:
First,Step write the given equation.
[tex] \frac{x}{2} + 7 = 3[/tex]
In Algebra, we learn how to solve for a missing term called a variable. We must use inverse operations to undo terms to isolate our variable. Inverse operations means that we do the opposite of the given.
Opposite of Addition is Subtraction, vice versa.Opposite of Multipication is Division, vice versa.For example, say we have a equation
[tex]x + 2 = 3[/tex]
We would subtract 2 from both sides. E.g( remember the golden rule of algebra). What we do to one side, we do the other. This applies when we solving for a variable.
This means that
[tex]x = 1[/tex]
And if we substitute 1 in for x, it is indeed true.
[tex]1 + 2 = 3 = 3[/tex]
Now, back to the question.
[tex] \frac{x}{2} + 7 = 3[/tex]
First, we subtract 7 from both sides to get rid of the 7 on the left side. Also remeber to undo terms that aren't included in the variable when solving these problems.
So now we got
[tex] \frac{x}{2} = - 4[/tex]
Then we multiply 2 by both sides since that the opposite of division.
[tex] \frac{x}{2} \times 2 = x = -4 \times 2 = - 8[/tex]
So this means that
[tex]x = - 8[/tex]
If we plug this in, this is true.
[tex] \frac{ - 8}{2} + 7 = 3[/tex]
