The biomass a year later is [tex]& \ y \approx 3.23 \times 10^7 \mathrm{~kg}[/tex] and t=1.58 years to reach 4 times 107 kg of biomass.
The following differential equation: [tex]& \Rightarrow \frac{d y}{d t}=k y\left(1-\frac{y}{M}\right) \\[/tex]
[tex]& \Rightarrow \frac{d y}{d t}=k y\left(\frac{M-y}{M}\right)[/tex]
Using variable separable method:
[tex]$$\Rightarrow \frac{d y}{y(M-y)}=\left(\frac{k}{M}\right) d t$$[/tex]
Integrate both sides:
[tex]$$\begin{gathered}\Rightarrow-\int \frac{d y}{y(y-M)}=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{M}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{y-(y-M)}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int\left(\frac{1}{y-M}-\frac{1}{y}\right) d y=\int\left(\frac{k}{M}\right) d t\end{gathered}$$[/tex]
[tex]\Rightarrow-\frac{1}{M}(\ln (y-M)-\ln y)=\frac{k t}{M}+C \\[/tex]
Let C1 be a constant such that C1 = MC, therefore,
[tex]$$\begin{gathered}\Rightarrow-\ln (y-M)+\ln y=k t+C_1 \\\Rightarrow \ln \frac{y}{y-M}=k t+C_1 \\\Rightarrow \frac{y}{y-M}=e^{k t+C_1} \\\\\Rightarrow y=y e^{k t+C_1}-M e^{k t+C_1} \\\\\Rightarrow y e^{k t+C_1}-y=M e^{k t+C_1} \\\\\Rightarrow y=\frac{M e^{k t+C_1}}{e^{k t+C_1}-1} \\\\\Rightarrow y=\frac{M}{1-e^{-k t-C_1}} \\\Rightarrow y=\frac{M}{1-e^{-k t} e^{C_1}}\end{gathered}$$[/tex]
Let A be a new constant such that:
[tex]\Rightarrow y=\frac{M}{1-A e^{-k t}}[/tex]
Substitute the values of M and k, we'll get:
[tex]\Rightarrow y=\frac{7 \times 10^7}{1-A e^{-0.76 t}}[/tex]
Substituting the given initial condition:[tex]\Rightarrow y(0)=2 \times 10^7[/tex]
[tex]\Rightarrow 2 \times 10^7=\frac{7 \times 10^7}{1-A e^{-0.76(0)}} \\\\\\Rightarrow 2=\frac{7}{1-A} \\[/tex]
=2-2A=7
=A=-2.5
Therefore, [tex]\Rightarrow y=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}}[/tex]
On simplification, we'll get:
[tex]$$\begin{aligned}& \Rightarrow y \approx 32270466.08 \mathrm{~kg} \\& \Rightarrow y \approx 3.23 \times 10^7 \mathrm{~kg}\end{aligned}$$[/tex]
(b). Substitute the given value in the equation
[tex]$$\begin{gathered}\Rightarrow 4 \times 10^7=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4=\frac{7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4+10 e^{-0.76 t}=7\end{gathered}$$[/tex]
On simplification, we'll get t=1.58 years
Therefore, it will take for the biomass to reach 4 times 107 kg is 1.58 years.
For such more questions about biomass
https://brainly.com/question/21525417
#SPJ4
10
8
f(x)=x-2x-6 6
4
10 -8 -6 -4
20
-2
6
-8
0 3
-10
24 6 8 10
Function h is two times the square
of the difference of x and 1.
Select the correct answer from each drop-down.
-2
-1
0
1
2
3
k(z) = ¹ k
89
f
h
The function that has the least minimum value is function
The function that has the greatest minimum value is function
G
76
11
-4
-5
-4
11
Bz - 4
The function that has the least minimum value is the following function.
Function k(x).
What are the minimum values of each function?From the graph given, looking at it's vertex, the minimum value of function f(x) is given as follows:
-7.
From the table given, the minimum value of function g(x) is given as follows:
-5, due to the symmetry from x = 0 to x = 2.
Function h(x) is defined as follows:
h(x) = 2(x - 1)².
Which has a minimum value of zero, as the y-coordinate of the vertex is not changed with the transformation.
Using a graphing calculator, as shown by the image at the end of the answer, the minimum value of function k(x) is given as follows:
-9.
Which is the least minimum value of all these functions.
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
Sketch a graph of the polynomial function f(x) = x³ + 4x² + 3x. Use it to complete each statement.
• f(x) is
·
D
.
f(x) is
f(x) is
Choose...
Choose...
Choose...
f(x) is Choose...
on the intervals (-∞, -3) and (-1,0).
on the intervals (-∞, -2) and (-0.5, 00).
on the intervals (-3,-1) and (0, 00).
on the interval (-2,-0.5).
The graph of the polynomial is given below.
The interval of the polynomial is
(-∞, 3) U (-3, -1) U (-1, ∞).
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
f(x) = x³ + 4x² + 3x
The graph of this polynomial is given below.
The interval of the graph are:
(-∞, 3) U (-3, -1) U (-1, ∞)
Thus,
The graph is given below.
The interval of the graph is (-∞, 3) U (-3, -1) U (-1, ∞).
Learn more about polynomials here:
https://brainly.com/question/2284746
#SPJ1
There are 8 ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon.
1 L≈ 0.26 gallons
7 KL= cups
Work out the difference in minutes between 2 hour 35 minutes and 1 3/4 hours
Answer: The difference in minutes between 2 hours 35 minutes and 1 3/4 hours is 30 minutes.
Step-by-step explanation:
To find the difference in minutes between 2 hours 35 minutes and 1 3/4 hours, we can first convert 1 3/4 hours to minutes.
There are 60 minutes in 1 hour, so 1 3/4 hours is equal to 1 + 3/4 = 1 3/4 hours = 1.75 hours.
Since there are 60 minutes in 1 hour, 1.75 hours is equal to 1.75 * 60 = 105 minutes.
Then, we can subtract 105 minutes from 2 hours 35 minutes to find the difference in minutes:
2 hours 35 minutes - 105 minutes = 135 minutes - 105 minutes = 30 minutes
So, the difference in minutes between 2 hours 35 minutes and 1 3/4 hours is 30 minutes.
YOUR ANSWER IS IN THE ATTACHMENT
HOPE IT HELPS!!!!!!
MARK AS BRAINLIEST
Thankyou
You mailed 20 identical Christmas cards weighing more than 1 ounce each. Mailing
each card costs $.44 for the first ounce, plus .17 for each additional ounce. The
postage for all cards totalled $15.60.
Postage of the total cards is 20(.17w + .44) = 15.60 (word problem)
given, total no of cards = 20
cost of each card = .44
additional cost for each ounce = .17
total cards = 20(.17w + .44) = $15.60
Word Problems:
Because they require students to apply their knowledge of many areas to "real-life" situations, word problems are a crucial part of the basic curriculum. They help children learn mathematics terms like "more," "fewer," "subtract," "difference," "totally," "equal," "sharing," "multiplied," and "reduced," among others.A word problem is a description of a situation in real life when a computation is necessary to solve a problem. Learning to answer word problems will help students apply mathematical ideas to a variety of real-world situations. Students must therefore be conversant with the vocabulary associated with the mathematical symbols they are used to in order to comprehend the word problem.Word problems often show mathematics happening more naturally in the real world. Word problems can vary from simple to complexTo know more about Word Problems:
https://brainly.com/question/2610134
#SPJ1
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2).
x1 0 1 2 µ = 1.2, s2 = 0.56
p(x1) 0.2 0.4 0.4
(a) Determine the pmf of To = X1 + X2. to 0 1 2 3 4 p(to)
(b) Calculate µTo. µTo = How does it relate to µ, the population mean? µTo = · µ
(c) Calculate sTo2. sTo2 How does it relate to s2, the population variance?
sTo2 = · s2
(d) Let X3 and X4 be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With To = the sum of all four Xi's, what now are the values of E(To) and V(To)?
E(To) =
V(To) =
(e) Referring back to (d), what are the values of
P(To = 8) and P(To = 7)
[Hint: Don't even think of listing all possible outcomes!] (Enter your answers to four decimal places.)
P(To = 8) =
P(To = 7) =
A commuter passes through two traffic lights on their way to and from work. Let X1 represent the number of lights the commuter must stop at while traveling to work, and X2 represent the number of lights he must stop at. stop when returning from work. It is connected to the population mean.
a) P(To=0) = 0.2*0.2 = 0.04
P(To=1) = 0.2*0.4 + 0.4*0.2 = 0.24
P(To=2) = 0.4*0.4 + 0.2*0.2 + 0.4*0.2 = 0.36
P(To=3) = 0.2*0.4 + 0.4*0.4 = 0.24
P(To=4) = 0.2*0.2 = 0.04
b) µTo = 0*0.04 + 1*0.24 + 2*0.36 + 3*0.24 + 4*0.04 = 2
It is equal to the population mean µ.
c) sTo2 = (0-2)2*0.04 + (1-2)2*0.24 + (2-2)2*0.36 + (3-2)2*0.24 + (4-2)2*0.04 = 0.56
It is equal to the population variance s2.
d) E(To) = 0*0.04 + 1*0.24 + 2*0.36 + 3*0.24 + 4*0.04 + 5*0 + 6*0 + 7*0 + 8*0 = 2
V(To) = (0-2)2*0.04 + (1-2)2*0.24 + (2-2)2*0.36 + (3-2)2*0.24 + (4-2)2*0.04 + (5-2)2*0 + (6-2)2*0 + (7-2)2*0 + (8-2)2*0 = 0.56
e) P(To = 8) = 0
P(To = 7) = 0.2*0.2*0.2*0.2 = 0.0016
Learn more about population mean here
https://brainly.com/question/19538277
#SPJ4
Name: Sally Jonas, single, 1 exemption.
Pay Rate: $5.95 per hour
Hours Worked: M-8, T-7, W-8, T-9, F-8
Total Hours Worked :
Wage for Week :
FICA Tax (7.65 %) :
Federal Tax :
State Income Tax (at 3%) :
City Income Tax (1.5%) :
Total Tax :
Paycheck after Taxes :
The total hours worked is 40 hours, the total wage for the week is $238, the Total tax is 12.15%, and the paycheck after taxes is $209.44
What is tax?Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses.
Given:
Pay Rate: $5.95 per hour,
Hours Worked: M-8, T-7, W-8, T-9, F-8,
FICA Tax (7.65 %),
State Income Tax (at 3%),
City Income Tax (1.5%),
Calculate the total working hours as shown below,
Total working hours = 8 + 7 + 8 + 9 + 8 = 40 hours
Calculate the total tax,
Total tax = 7.65 + 3 + 1.5 = 12.15%
Calculate total wage,
Total wage = no of hours × 5.95
Total wage = 40 × 5.95 = $238
Paycheck after-tax deduction = Total wage - 12.15 % of $238
Paycheck after-tax deduction = 238 - 28.56
Paycheck after-tax deduction = $209.44
To know more about Tax:
https://brainly.com/question/19032638
#SPJ1
8−
n
m
+p
2
8, minus, start fraction, m, divided by, n, end fraction, plus, p, squared when m=8m=8m, equals, 8, n=2n=2n, equals, 2, p=7p=7p, equals, 7.
The answer is 53
What is the method of substitution for solving equations?It is the process of substituting values of individual respective variables and solving using elementary arithmetic operations.
Given here, the expression as 8 - (m/n) + p² & substituting the values as m=8 , n=2 , p=7 we get
8- 8/2 + 7² = 8-4+53
= 53
Hence, the final answer is equal to 53
Learn more about method of substitution here:
https://brainly.com/question/19356264
#SPJ1
The graph below shows the average cost of renting a studio apartment in one city in each of the years 2002 through 2006. By what percentage does the average price increase from 2002 to 2003? Obtain a second version of the graph by sliding a piece of paper over the bottom of the graph so that the bars start at 300. In this new graph, by what percentage does the price appear to increase from 2002 to 2003?
In the new graph, the price appears that is increase from 2002 to 2003 is 25% and 100%. Hence, option A is correct.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from.
Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the data mentioned in the question,
Average cost to rent studio in 2002 = 400 and,
Average cost to rent studio in 2003 = 500
Then percent increase from year 2002 to 2003 will be,
% increase = (500 - 400)/400 × 100
% increase = 25%
Then, % increase from 2002 to 2003 is 25%,
(200 - 100)/100 × 100 = 100%.
To know more about Percentage:
https://brainly.com/question/29306119
#SPJ1
The percentage of total variation in the dependent variable that is described by the independent variable is expressed by_________.
a. coefficient of determination
b. correlation coefficient
c. coefficient of covariation
d. regression coefficient
a. coefficient of determination
The percentage of total variation in the dependent variable that is described by the independent variable is expressed by coefficient of determination . So, correct answer is option (a).
The coefficient of determination R² is equal to the square of the correlation coefficient, r² expressed as a percentage, represents the percentage of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression line. Coefficient of determination is a statistical measure that examines how differences in one variable can be explained by differences in her second variable. In other words, this coefficient, commonly known as R-squared (or R²), measures how strong the linear relationship between two variables is. This coefficient is commonly known as the R-square (or R²) and is sometimes called the "goodness of fit". This measurement is expressed as a value between 0.0 and 1.0..
To learn more about Cofficient of determination, refer:
https://brainly.com/question/17237825
#SPJ4
A university polls 200 students. 80 students drink tea, 140 drink
coffee, and 30 drink neither. What is the probability that you choose a
random student that they drink both
The probability of selecting a student that drink both coffee and tea is
1/10.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
From the algebra of sets, we know n(A∪B) = n(A) + n(B) - n(A∩B).
A university polls 200 students. 80 students drink tea, 140 drink coffee, and 30 drink neither.
Therefore,
200 = 140 = 80 - N(A∩B).
200 = 220 - N(A∩B).
N(A∩B) = 20.
So, out 0f 200 students 20 drink both.
Therefore the probability of students drink both is,
= 20/200.
= 1/10.
learn more about probability here :
https://brainly.com/question/743546
#SPJ1
suppose there is a game where you throw a marble and if it lands in a circle on the ground it is counted as a success. suppose that the probability of you throwing a marble and landing in the circle on the ground is 25%. using the normal distribution, approximate the probability of landing in the circle on the ground 10 times or less if you play the game for 30 rounds a. 56%
b. 65%
c. 71%
d. None of these
e. 47%
Using the Normal Distribution , the probability of landing in the circle on ground 10 times or less is 85.32 % , the correct option is (d) None of these .
The term Normal Distribution is defined as a continuous probability distribution where the values lie in a symmetrical fashion mostly situated around mean .
it is given that ,probability(p) of landing marble on ground is 25% = 0.25
game is played for 30 rounds (n) = 30 ; q = 1 - 0.25 = 0.75 .
we know the mean (μ) = n×p = 30 × 0.25 = 7.5 ;
the standard deviation is (σ) = √n×p×q = √30×0.25×0.75
= √5.625 = 2.38
By using Normal Distribution , X follows N(μ,σ²)
that is X follows N(7.5 , 2.38²) ;
we have to find P[X<10] = P[ (x-μ)/σ < (10 - 7.5)/2.38]
= P[ z < 2.5/2.38] = P[ z < 1.05 ] = 0.85314094 = 85.32 %
Therefore , the required probability is 85.32 % .
Learn more about Probability here
https://brainly.com/question/12532428
#SPJ4
Solve this question
Answer:
the degree is 6
Step-by-step explanation:
would you expect the proportion of stay-at-home residents to be higher in virginia than in arkansas? support your conclusion with the results obtained in parts (b) and (c). from the results obtained in parts (b) and (c), we would expect the number of stay-at-home residents to be higher correct: your answer is correct. in arkansas than virginia. the sample results show that, rounded to two decimal places, the estimated percentage of arkansas residents who were born there is %. the sample results also show that, rounded to two decimal places, the estimated percentage of virginia residents who were born there is %.
As per the estimated percentage, the test statistic is 0.6167 or 61.67%
What is the percentage?
The term percentage is defined as the number or ratio that can be expressed as a fraction of 100.
Here we have given that in Arkansas than Virginia. the sample results show that rounded to two decimal places, the estimated percentage of Arkansas residents who were born there is %. the sample results also show that rounded to two decimal places, the estimated percentage of Virginia residents who were born there is %.
And we need to find the test statistics.
While we looking into the given situation we have identified the following values,
=> H0 : p = 0.577
=> Ha : p ≠ 0.577
Now, we have estimated the proportion of stay-at-home residents in Arkansas is calculated as,
Here the Proportion of stay-at-home residents in Arkansas is written as,
=> p = 74/120 = 0.6167
Therefore, the test statistic is 0.6167.
To know more about Percentage visit.
brainly.com/question/13729841
#SPJ4
A child asks his parents for some money. The parents make the following offers.Father’s offer: The child flips a coin. If the coin lands heads up, the father will give the child $20. If the coin lands tails up, the father will give the child nothing.Mother’s offer: The child rolls a 6-sided die. The mother will give the child $3 for each dot on the upside of the die.Which offer has the greater expected value?answer choices:Mother's OfferFather's Offer
The mother will give the child $3 for each dot on the upside of the die. the greater expected value is Mother's Offer
The expected value of father's offer is $10, since the probability of getting heads is 50% and the reward for getting heads is $20.
The expected value of mother's offer is $3, since the probability of getting any number is 1/6 and the reward for getting any number is $3.
Therefore, the mother's offer has a greater expected value than the father's offer.
Learn more about expected value here
https://brainly.com/question/18523098
#SPJ4
Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s).b=5 c=6 B=20 degreesA) single triangle is produced, where C degrees=___. A degrees=___ a=____B) Two triangles are produced, where the triangle with the smaller angle C has C1= ___ A1=____ and a1=____ / Triangle with the larger angles has C2=___ A2=___ and a2=____C) No triangles are produced
Using the Law of Sines, we get an angle of 2.41 degrees and no triangles are produced.
Option (C) is the correct one.
Given, Two sides and an angle are given below.
we have to determine whether the given information results in one triangle, two triangles, or no triangle at all.
If b = 5, c = 6 and B = 20 degrees in the triangle.
On using the concept of Laws of Sines, we get
sinA/a = sinB/b = sinC/c
sin 20°/5 = sin C/6
0.34/5 = sin C/6
0.007 = sin C/6
sin C = 0.042
C = 2.41
So, the angle C be 2.41 degrees.
which implies that no triangle can be formed or produced with the given data of the triangle.
Hence, No triangles are produced.
Learn more about Law of Sines here https://brainly.com/question/27613782
#SPJ4
a vertex of a rooted tree is called a leaf if it has no children. vertices that have children are called internal vertices. if d is a vertex in a tree, the with d as its root is the subgraph of the tree containing d and its descendants and all edges incident to these descendants.
The root of a tree is the vertex from which all other vertices can be reached by following edges. The root of a tree is the only vertex that does not have an incoming edge.
In a rooted tree, a vertex is called a leaf if it has no children (i.e., it does not have any edges going out from it). Internal vertices are those that have children and are connected by edges to other vertices in the tree. If a vertex d is the root of a tree, the subgraph with d as its root is defined as the set of vertices that can be reached from d by traversing its edges, as well as the edges connecting them. The root is the only vertex that does not have an incoming edge, and all other vertices can be reached from the root.
Learn more about vertex here
https://brainly.com/question/29030495
#SPJ4
Find dy/dx for the indicated function y
The derivative of y = 5ˣ + e⁷ is 5ˣ ln 5.
What is derivative?
A derivative is a two-party contract whose price or value is based on an underlying asset. Futures, options, forward contracts, and swaps are the four most popular types of derivatives. It is a financial instrument whose price and value are determined by the underlying assets.The instantaneous pace at which a function changes with regard to one of its variables is known as the derivative. Finding the slope of the tangent line to the function at a certain location is equal to doing this.dy/dx = d(5ˣ + e⁷) / dx
= 5ˣ ln 5 + 0
= 5ˣ ln 5
e⁷ is constant with respect to x , the derivative of e⁷ with respect to x is 0.
Hence, the derivative of y = 5ˣ + e⁷ is 5ˣ ln 5.
To know more about derivative check the below link:
https://brainly.com/question/23819325
#SPJ1
Choose the graph that corresponds to the given system.
3x + y ≥-3
x + 2y ≤ 4
Answer:
See Attached Images
Step-by-step explanation:
First, draw the lines without < or > signs, just use equals signs:
3x + y = -3
y = -3x - 3 (slope of -3, y-intercept at (0,-3) )
x + 2y = 4
2y = -x + 4
y = -(1/2)x + 4
Now shade the region above and including line (1) and below and including line (2).
Note for similair problems: If you have to multiply or divide by a negative number when solving for y, remember to flip the < or > sign to the other one when determining where to shade on the graph.
Find the indefinite integral by using appropriate substitutions. (Use C for the constant of integration.) ∫In(cos(x)) tan(x) dx
Refer to the photo taken. Please rate :)
david and amy start at the same point and begin biking in different directions. david is biking west at a speed of 17 miles per hour. amy is biking south at a speed of 15 miles per hour. after how many hours will they be exactly 23 miles apart? round your answer to two decimal places.
The Time taken for David and Amy to be exactly 23 miles apart is 1.014 Hours.
Let [tex]t[/tex] be the time taken to reach 23 miles apart from a single point.
David and Amy start at same point and move towards different directions, making them move at perpendicular to each other.
According to Pythagoras theorem, and distance = Speed x time.
[tex](17t)^2 + (15t)^2 = 23^2[/tex]
[tex]289t^2 + 225t^2 = 529[/tex]
[tex]\therefore 514t^2 = 529[/tex]
[tex]t^2 = \frac{529}{514}[/tex]
[tex]t^2 = 1.029[/tex]
[tex]\therefore t = \sqrt{1.029} = 1.014 \text{ hours}[/tex]
To know more about Algebra, visit: https://brainly.com/question/24875240
#SPJ4
Evaluate the expression and enter your answer.
2 • |6 + 2|
Answer:
16
Step-by-step explanation:
2 × | 6 + 2 |
= 2 × | 8 |
= 2 × 8
= 16
mark dropped an object from a bridge 400400 feet above ground level with an initial velocity of 0.0. he knows that the gravitational pull of the earth is about 1616 feet per second squared. he wants to find how many seconds, t,t, it will take the object to hit the ground. match each expression with the correct equation that models this situation or solution
The correct equation is t = 5 seconds.
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Let me mention first that there is an error in the statement that the gravitational pull of the Earth is 16 ft/s^2. It is in fact 32 ft/s^2, and the actual equation uses half of the acceleration multiplied by the square of the variable time, so it gives as final expression :
y(t) = -16t² + 0t + 400
and we want to find the value/s for "t" that make this equation equal zero (when it reaches the ground and the object just touches the ground. This makes the equation we want to solve:
0 = -16t² + 0t + 400
16t² + 0t - 400 = 0
which solving for "t" becomes:
16t² - 400 = 0
16t² = 400
t² = 25
t = √25
t = ± 5
So we adopt the positive answer (positive time) since the negative value has no physical meaning for this problem.
That is: t = 5 seconds
To learn more about equation from the given link
https://brainly.com/question/17145398
#SPJ1
7 the area of the rhombus
The area of a rhombus is --336[tex]in^{2}[/tex]
A rhombus is a type of parallelogram where all the sides are equal in length. opposite sides of a rhombus are parallel to each other and opposite angles are equal.
The diagonals of a rhombus bisect each other at the right angle.
side of a rhombus (x) is - 25inone diagonal of a rhombus(a) is - 14inlet, another diagonal of a rhombus is -b in
another diagonal of a rhombus, b = [tex]\sqrt{4x^{2} -a^{2} }[/tex]
= [tex]\sqrt{4*25^{2} - 14^{2} }[/tex]
=[tex]\sqrt{4*625 - 196}[/tex]
=[tex]\sqrt{2500 - 196}[/tex]
= [tex]\sqrt{2304}[/tex]
= 48 in
Area of the rhombus (A) = [tex]\frac{a * b }{2}[/tex]
= [tex]\frac{14 * 48 }{2}[/tex] [tex]in^{2}[/tex]
= 7 * 48 [tex]in^{2}[/tex]
= 336 [tex]in^{2}[/tex]
The area of a rhombus is --336[tex]in^{2}[/tex]
Read more about rhombus:
https://brainly.com/question/29629002
https://brainly.com/question/20627264
making the assumption of no compounding interest, suppose you purchase a perpetuity bond from sense/net corporation for $3,000 with an annual coupon rate of 3% . specify all answers to the nearest dollar, and assume a discount rate equal to that of the current interest rate.
Therefore for computing the annual return we simply fund with coupon rate in percentage is 90 dollar
What is a percent simple definition?
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
The additional sum of money over the principal sum of deposit or loan is called compound interest.
The yearly return on $ 3 ,000 investment will be $90.
This can be estimated as:
Investment = $3,000
Coupon rate in percentage = 3%
The computation of yearly return can be estimated as:
= $3,000 × 3%
= $90
Therefore for computing the annual return we simply fund with coupon rate in percentage.
To learn more about coupon rate and interest follow the link:
brainly.com/question/6959763
#SPJ4
compose 560 tenths + 48 thousandths
Answer:
.5648
Step-by-step explanation:
i am good at math :)
Answer:
= 56 + 0.048
= 56.048
Step-by-step explanation:
560 tenths + 48 thousandths
= 560 × 0.1 + 48 × 0.001
= 56 + 0.048
= 56.048
pls rate as brainliest
g use the formula for the sum of a geometric series to find the sum or state that the series diverges 100/81 10/9 1 9/10 81/100 729/1000
On solving the provided question we can sat that, the geometric series' total is 12.34, and they care convergent.
What is geometric series?An infinite series in mathematics known as a geometric series has the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. One straightforward illustration is the geometric series with a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, totaling 2 (or 1 if the first term is locked out).
The answer to the query is
The geometric series is made up of the numbers 100/81, 10/9, 1, 9/10, 81/100, 729/1000, and so on.
The provided series appears to be moving forward geometrically with a fixed ratio r.
r = second term, first term, or a2, a1.
[tex]= (10/9) / (100/81)[/tex]
[tex]= > 9/10[/tex]
We are aware that convergence occurs when 'r' is smaller than 1.
In this case, 9/10 1 is convergent.
This sums up an endless geometric sequence, without a doubt.
Infinite series' sum in GP equals a. (1 - r)
The usual ratio is 9/10, where an is the first word.
The geometric series' sum is equal to (100/81) / (1 - 9/10).
[tex]= > (100 / 81) / ( 1 / 10)\\ = > 100 / 8.1\\ = > 12.34[/tex]
The given series is therefore convergent, and its total is 12.34.
To know more about geometric series visit:
https://brainly.com/question/4617980
#SPJ4
fit a multiple regression model to describe the relationship between weight and the predictors length and age. (use x1 for length and x2 for age. round your numerical values to two decimal places.)
The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
What is multiple regression?
A probit model is a type of regression in statistics where the dependant variable can only take two values.
We have:
Regress smoker on cubic polynomials of age
If we use linear probability model.
Here the data are missing, but we can say about the estimate that:
Only the estimate intercept is statistically significant at the 5% level is wrong,
Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
Learn more about regression here:
brainly.com/question/23389011
#SPJ4
Calculate curl(F and then apply Stokes' Theorem to compute the flux of curI(F) through the surface in the figure using line integral. The surface is a wedge-shaped box (bottom included, top excluded) with an outward-pointing normal. Assume that parameter a = 2. F= (x+yz - 16,x√(y^2 + 1)
(Express numbers in exact form: Use symbolic notation and fractions where needed ) curI(F) = ______ flux of curl(F) = _____
the flux of curI(F) through the surface area in the figure as with integral:
flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z
First, we calculate the curl of F: curI(F) = (2z, -2x, 2y).
Next, we apply Stokes' Theorem to calculate the flux of curI(F) through the surface in the figure. We start by computing the line integral of F around the boundary of the surface. This is given by:
flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz
We can now evaluate this line integral by splitting it into a sum of integrals:
flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz
= 2∫x dx + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32∫dz + 4∫yz dz
= 2x^2/2 + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32z + 4yz^2/2
= x^2 + 4yz∫dx + 2∫x√(y^2 + 1) dy - 32z + 2y^2z
Finally, we can evaluate the flux of curI(F) through the surface in the figure as:
flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z
Learn more about integral here
https://brainly.com/question/18125359
#SPJ4
College question need help shark attack probability, in the next year, what is the probability there will be:
The probabilities, using the Poisson distribution, are given as follows:
11. A shark attack next year: 0.038.
12. More than one shark attack next year: 0.001.
13. At least one shark attack in the next 100 years: 0.982.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.Considering that there have been 8 attacks in 200 years, the mean for n years is given as follows:
[tex]\mu = \frac{8n}{200}[/tex]
Hence the probability of one shark attack in the next year(n = 1, mean = 0.04) is given as follows:
[tex]P(X = 1) = \frac{e^{-0.04}(0.04)^{1}}{(1)!} = 0.038[/tex]
The probability of more than one shark attack is obtained as follows:
P(X > 1) = 1 - P(X ≤ 1)
In which:
P(X ≤ 1) = P(X = 0) + P(X = 1).
Then:
P(X = 0) = e^(-0.04) = 0.961.P(X = 1) = 0.038.Thus:
P(X > 1) = 1 - (0.961 + 0.038) = 0.001.
For 100 years, the mean is of:
100 x 8/200 = 4.
Thus the probability of at least one attack is of:
P(X > 0) = 1 - e^(-4) = 0.982.
More can be learned about the Poisson distribution at https://brainly.com/question/7879375
#SPJ1