Answer:
Step-by-step explanation:
Consider the function of the rate of flow of money in dollar per year is
[tex]f(t)= 400e^{0.03t}[/tex]
The objective is to find the present value of this income over 10 years period an assume an annual interest rate of 8% compounded continuously.
Given that,
[tex]f(t)= 400e^{0.03t}[/tex]
r = 0.08, t = 10
if f(t) is the rate of continuously money flow at an interest rate r to T year,
the present value is,
[tex]P= \int\limits^T_0 {f}(t)e^{-rt} \, dt[/tex]
Now input the values to get
[tex]p=\int\limits^{10}_0 400e^{0.03t}*e^{-0.08t} dt[/tex]
[tex]=400\int\limits^{10}_0 e^{0.03t}*^{-0.08t} dt[/tex]
[tex]= 400\int\limits^{10}_0 e^{-0.05t} dt[/tex]
[tex]=400(-\frac{e^{-0.05t}}{0.05} )|_0^1^0[/tex]
[tex]=-\frac{400}{0.05} (e^{-0.05*10}-e^{-0.05*0})\\\\=-\frac{400}{0.05} (e^{-0.5}-e^{*0})\\\\=3147.75[/tex]
Therefore, the present value is $3147.75What is the value of x in the equation 3X minus 4Y equals 65, when Y equals four
Answer:
Step-by-step explanation:
3x-4y=65
3x=65+4y
x=(65+4y)/3, when y=4
x=(65+4*4)/3
x=(65+16)/3
x=81/3
x=27
Consider the polynomials p1(t) = 1 + t , p2(t) = 1 -t , and p3(t) = 2 (for all t). By inspection, write a linear dependence relation among p1, p2, and p3. Then find a basis for Span{ p1 , p2 , p3 }.
Answer:
[tex]\{p_1,p_2\}$ is a basis of Span\{p_1,p_2,p_3\}[/tex]
Step-by-step explanation:
Given the polynomials:
[tex]p_1(t) = 1 + t\\ p_2(t) = 1 -t\\p_3(t) = 2\\[/tex]
On Inspection
[tex](1+t)+(1-t)=1+1+t-t=2\\$Therefore:\\p_1(t)+p_2(t)=p_3(t)[/tex]
By the Spanning Theorem
If one vector in S is a linear combination of the others, we can delete it and get a subset (one vector smaller) [tex]S' \subseteq S[/tex] that has the same span.
Therefore, since [tex]p_3(t)=p_1(t)+p_2(t)[/tex]
[tex]Span\{p_1,p_2,p_3\}=Span\{p_1,p_2\}[/tex]
[tex]p_1$ and p_2[/tex] are linearly independent because [tex]p_1[/tex] cannot be written in terms of [tex]p_2[/tex].
Therefore, [tex]\{p_1,p_2\}$ is a basis of Span\{p_1,p_2,p_3\}$ as required.[/tex]
A linear dependence relation among the polynomials p₁, p₂, and p₃ is given as p₁ + p₂ = p₃
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
Consider the polynomials are
[tex]\rm p_1(t) = 1 + t\\\\ p_2(t) = 1 -t \\\\ p_3(t) = 2[/tex]
a linear dependence relation among p₁, p₂, and p₃ will be
Let add the p₁ and p₂, we have
1 + t + 1 -t = 2
We get the polynomial p₃.
Thus the linear relation is p₁ + p₂ = p₃
More about the polynomial link is given below.
https://brainly.com/question/17822016
Barry Beach was convicted of murder in 1983 and sentenced to life in prison without parole. In 2015, Governor Bullock commuted Beach's sentence after years of controversy surrounding Beach's confession, trial and subsequent conviction. A news program in Bozeman wanted to find out more about how people in Montana feel about Beach's release. The local program invited viewers to go their website and indicate their opinions. At the end of the show, 72% of people who voted in the poll indicated they agreed with Bullock's decision.
What is the population of interest?
1- All Montana residents
2- Viewers of this TV show
3- Residents of Bozeman, MT
4- Residents of Poplar, MT
Answer:
The correct answer to the following question will be Option 1 (All Montana residents).
Step-by-step explanation:
Barry Beach told journalists managed to gather next to the front main entrance of Montana federal penitentiary across lunchtime that perhaps the point in time seemed to be 'surreal.'A news broadcast in Bozeman was desperately trying to find out how and why individuals in Montana perceive and say about the official launch of Beach. It certainly indicates 'All Montana Residents' seems to be the group of people of benefit after that.Other choices aren't linked to just the scenario in question. Option 1 seems to be the perfect solution.
2. If I paid $1.45 for an apple and an orange, and the apple cost 15 cents more than the orange, how much did the orange cost?
Answer:
0.80 + 0.65 = 1.45
Step-by-step explanation:
apple: 0.80
orange: 0.65
What is the system of equations in this problem
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
7 nickels, 12 dimes
Step-by-step explanation:
n+d= 19
5n+10d= 155 ⇒ n+2d= 31
comparing the 2 equations we get
d=12, then n= 7
What is the definition of an obtuse angle?
Answer:
an obtuse angle is an angle more than 90 degrees but less than 180 degrees
Step-by-step explanation:
:)
what are possible rational roots of f(x)= 3x^4-x^3+x^2_x+5
Answer:
x=0
so the roots are (0,0)
The population of a small town in central Florida has shown a linear decline in the years 1992-2000. In 1992 the population was 48000 people. In 2000 it was 44880 people.
A) Write a linear equation expressing the population of the town P
P
in terms of t
t
, the number of years since 1992.
Answer: c
B) If the town is still experiencing a linear decline, what will the population be in 2003?
Answer:
P = -390t +48,000P = 43,710 in 2003Step-by-step explanation:
A) We are given two pairs of (t, P): (0, 48000), (8, 44880). We can use these with the 2-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
P = (44880 -48000)/(8 -0)(t -0) +48000
P = -3120/8t +48000
P = -390t +48000
__
B) In 2003, t = 11, so we have ...
P = -390(11) +48000 = 43710
The population in 2003 is predicted to be 43,710.
9(x-4) = 9x-33
how many solutions does this have?
Answer:
No solution
Step-by-step explanation:
Because x = 0
kojo had 1800 bags of rice in stock for sale. in January, he sold 2/3 of it. In February, he sold 3/4 of what was left.
a. what fraction of the stock of rice did he sell
(a) in February?
(b) in January and February ?
b. How many bags of rice were left unsold, by the end of February?
Answer:
Kojo had 1800 bags of rice in stock for sale.
In January, he sold 2/3 of it.
=> Number of bag he sold in January: 1800 x 2/3 = 1200
=> The number of bags of rice left: 1800 - 1200 = 600
In February, he sold 3/4 of what was left.
=> Number of bag he sold in February: 600 x 3/4 =450
=> Total number of bags he sold in January and February:
1200 + 450 = 1650
=> The number of bags of rice left at the end of February: 600 - 450 = 150
Hope this helps!
:)
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. f(x)= -(x-3)^(2)-2
Step-by-step explanation:
graphing the parabola, using the direction, vertex, focus, an axis of symmetry, we see that the direction it opens is down, like the picture shows. The vertex is at (3, -2), focus is (3,-9/4), axis of symmetry is x=3, and the directrix is y = -7/4 just as the picture shows. Therefore, A is the correct answer.
Hope this helps!!
Answer:
A. [tex]F(x)=-(x-3)^2-2[/tex]
Step-by-step explanation:
For the function F(x) to flip upside-down, there needs to be a negative sign in front. This eliminates answers "B," and "D." The function F(x) shifted 3 units to the right, meaning there needs to be a -3 being subtracted. The function also shifted downwards 2 units, meaning there's a -2 being subtracted.
This makes the correct answer be "A."
00:00
Which of the following is a statistical question?
O
A.
00:00
How tall is Mr. Leung?
B.
00:00
What are the ages of all your cousins?
00:00
What is the formula for the volume of a cube?
D.
00:00
What is the school's address?
The correct answer is B. What are the ages of all your cousins?
Explanation:
Statistics focus on using numbers to analyze variables in a population or in a specific sample taken from this population. This means statistical questions can be answered by analyzing different features in a population. For example, you can wonder what is the time students on a class spend doing homework?.
According to this, the one that is a statistical question is "What are the ages of all your cousins?" because this question focuses on analyzing one variable or factor in a population; in this case, the ages of your cousins, which requires gathering information and then using numbers to represent and analyze this, which is the objective of statistics.
What is the midpoint of the segment?
Answer:
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. hope that helps love!
Chef Gordie uses 250 ml of broccoli in his Vitafibermin loaf. How many liters is that?
Answer:
.250 L
Step-by-step explanation:
We know that 1 L = 1000 mL
250 mL * 1L /1000 mL = .250 L
Answer:
Step-by-step explanation:
its 1/25 or .25 liters. A milliliter (ml) is one thousandth of a liter, so 1000 ml would be 1 liter. Btw, why is he measuring broccoli in ml?
There are 10 clean individual socks in your sock drawer. There is only one matching pair among them. In the dark, you reach into the drawer and randomly pick 2 socks. What is the probability that you choose the matching pair
The required probability of choosing the matching pair of socks is approximately 0.0222 or 2.22%.
To find the probability of choosing the matching pair of socks, we need to consider the total number of possible outcomes and the number of favorable outcomes.
In this case, there are 10 individual socks in the drawer, and only one matching pair. When you randomly pick 2 socks, there are C(10, 2) = 45 possible outcomes, as you are choosing 2 socks out of 10.
The favorable outcome is when you choose the matching pair, which can occur in only one way.
Therefore, the probability of choosing the matching pair of socks is:
P(matching pair) = favorable outcomes / total outcomes
= 1 / 45 ≈ 0.0222
So, the probability of choosing the matching pair of socks is approximately 0.0222 or 2.22%.
Learn more about probability here:
https://brainly.com/question/31090980
#SPJ4
The difference between those graphs
Answer:
B
Step-by-step explanation:
the negative on the outside makes it a reflection over the x-axis
Answer:
b
Step-by-step explanation:
because if you say make up points the plot them then youll see there across from each other
Multiply. Write your answer in simplest form. 4/9 x 2/3
Answer:
8/27
Step-by-step explanation:
4/9 * 2/3
Multiply the numerators
4*2 = 8
Multiply the denominators
9*3 = 27
Put the numerator over the denominator
8/27
This is in simplest form
What is the vertex of the graph of y=-x^2
Answer:
(0,0)
Step-by-step explanation:
The Graph shows that 0,0 is the first x-y value which is vertex
Answer:c
Step-by-step explanation:
The same Honey is sold in two different size jars. Large jar= 540g for £4.10 Small jar= 360g for £2.81. By considering the amount of honey per penny, work out which jar is the best value for money. Working must be shown.
Answer:
From our calculations the large jar is the best value for money because a penny buys more honey
Step-by-step explanation:
In this problem we are expected to determine which purchase of honey is the cheapest ? large jar or small jar ?.We will determine which has the best value for money using the quantity a pound can purchase.
firstly for the large jar.
if £4.10 will purchase 540g of honey then,
£1.00 will purchase xg
cross multiplying to find x will have
[tex]x=[/tex] [tex]\frac{1.00*540g}{4.10}[/tex]
[tex]x= 131.7grams[/tex]
Hence for the large jar a penny would buy 131.7g of honey
secondly for the small jar
if £2.81 will purchase 360g of honey then,
£1.00 will purchase xg
cross multiplying to find x will have
[tex]x=\frac{1.00*360g}{2.81}\\x= 128.1gram[/tex]
Hence for the small jar a penny would buy 128.1g of honey
20
Select the correct answer.
What is the purpose of a FICA tax?
A. It provides health insurance for people who are retired or disabled.
B. It helps the state government finance education projects.
C. It helps local councils finance development projects.
Reset
Next
Answer:
A. It provides health insurance for people who are retired or disabled.
Step-by-step explanation:
FICA stands for Federal Insurance Contributions Act, which is a law. It is a compulsory tax from the payroll of all employees in the United State to provide health insurance for retired as well as disabled people. It has a definite percentage with no conditional or exemption deductions to assist the government to fund social security and medicare.
This make it possible for the government to cater for the two sects of people in the society that are registered easily.
What’s the correct answer for this question?
Answer:
THE ANSWER OF THIS QUESTION IS CONE
Answer:
B. Cone
Step-by-step explanation:
The flashlight beam is of the shape of a cone
How do you do this question
Step-by-step explanation:
use the formula in picture
Line p is parallel to line q. Parallel lines p and q are crossed by lines a and b to form 2 triangles. At parallel line p, angle 4 is formed by line b and angle 5 is formed by line a. Angle 6 is the third angle. At parallel line q, angle 3 is formed by line 3 and angle 2 is formed by line b. Angle 1 is the third angle. Which set of statements about the angles is true? Angle 1 is congruent to angle 6, angle 5 is congruent to angle 4, angle 3 is congruent to angle 2 Angle 2 is congruent to angle 4, angle 3 is congruent to angle 6, angle 1 is congruent to angle 5 Angle 3 is congruent to angle 6, angle 1 is congruent to angle 2, angle 5 is congruent to angle 4 Angle 6 is congruent to angle 1, angle 5 is congruent to angle 3, angle 4 is congruent to angle 2
Answer:
add all angles
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
What is the value of 4p − 2, when p = 8? 16 24 30 34
Answer:
4p - 2
4(8) - 2
32 - 2 = 30
The answer is 30.This is because you have to substitute the value of the number they give into the equation. This will give you the number of 4 to be multiplied by 8. This is because the x is the number 8.
Hope this helped!
Answer:
What is the value of 4p − 2 when P 8?
the answer is 30.
Step-by-step explanation:
The inverse of G(X) is a function.
A. True
B. False
Answer:
true its just a filp with the y and x and resolved
Step-by-step explanation:
can the value of y be the same for all X values in a function
Answer:
yes
Step-by-step explanation:
One such function is ...
f(x) = 0
No matter what the value of x is, the value of y is 0. The graph of it is a horizontal line.
Find f(-3) if f(x) = x•x
Answer:
9
Step-by-step explanation:
f(x) = x•x
f(-3) = -3*-3
f(-3)= 9
What is the equation of a line that has a slope of 2 and passes through the point (4,6) ?
Answer:
[tex]y-6=2\,(x-4)[/tex]
or in slope y-intercept form :
[tex]y=2x-2[/tex]
Step-by-step explanation:
The easiest way of find the answer for this is to use what is called the "point-slope" form of a line, because you are in fact given the value of the slope (m) and also a point [tex](x_0,y_0)[/tex] it goes through:
[tex]y-y_0=m\,(x-x_0)[/tex]
In our case the equation becomes:
[tex]y-y_0=m\,(x-x_0)\\y-6=2\,(x-4)\\[/tex]
This can also be written in the slope-intercept form by solving for "y" and operating to remove the parenthesis:
[tex]y-6=2\,(x-4)\\y=2x-8+6\\y=2x-2[/tex]
What number is 144% of 5.19
Answer:
7.4736
Step-by-step explanation:
A = 144% of 5.19 means: A = (144/100) x 5.19 = 7.4736
Hope this helps!