Suppose you deposit $600 into an account that pays 5% annual interest, compounded continuously. How much will you have in the account in 4 years? ƒ(t) = ae^rt
Answers
To determine the amount that will be on the account after 4 years you have to apply the given exponential function that models the amount of money on the account with respect to the time.
[tex]f(t)=ae^{rt}[/tex]Where
a represents the initial amount
r represents the interest rate expressed as a decimal value
t is the time period in years
The initial amount on the account is a= $600
The time period is t= 4 years
The interest rate is r=5%, divide it by 100 to express it as a decimal value:
[tex]r=\frac{5}{100}=0.05[/tex]Using this information, you can calculate the final amount:
[tex]\begin{gathered} f(t)=ae^{rt} \\ f(4)=600e^{0.05\cdot4} \\ f(4)=600e^{0.2} \\ f(4)=732.84 \end{gathered}[/tex]After 4 years there will be $732.84 on the account. The correct option is B.
Related Questions
5. What is the area of triangle ABC? (lesson 10.2)AN10 ftD 6 ftСA 15 square feetB 16 square feet© 30 square feetD 32 square feet
Answers
The answer is C, 30 square feet
Jack scored 80 out of 85 points on a recent test. What is his score as a percent, rounded to the nearest whole percent?
Answers
jack scored = 80
total point = 85
so the percentage is,
[tex]=\frac{80}{85}\times100[/tex][tex]\begin{gathered} =\frac{8000}{85} \\ =94.11\text{ \%} \end{gathered}[/tex]thus, the nearest whole percentage is 94 %
State if the given binomial is a factor of the given polynomial.Question #9
Answers
We can use the Factor Theorem to state if the given binomial is a factor of the given polynomial.
The factor theorem states that when f(c)=0 that means the remainder is zero and (x-c) must be a factor of the polynomial.
The given polynomial is:
[tex]k^3+8k^2+6k-12[/tex]Then if (k+2) is a factor of the polynomial, k+2=0, k=-2, f(-2) must be equal to 0.
Let's check:
[tex]\begin{gathered} f(k)=k^3+8k^2+6k-12 \\ f(-2)=(-2)^3+8(-2)^2+6(-2)-12 \\ f(-2)=-8+8\cdot4-12-12 \\ f(-2)=-8+32-24 \\ f(-2)=32-32 \\ f(-2)=0 \end{gathered}[/tex]Thus, (k+2) is a factor of the given polynomial.
The cost of 15 toys is $225. Identify the equation that represents this situation.
Answers
Question:
Solution:
Let us denote by c the cost of each toy. Then, according to the problem, the cost of 15 toys would be:
[tex]15c\text{ = 225}[/tex]So, we can conclude that the correct answer is:
[tex]15c\text{ = 225}[/tex]Jo-o/checkpoint scatter plotsA2018161412Paw size (centimeters)10642X1b2030405066708090100Height (centimeters)Does this scatter plot show a positive association, a negative association, or no association?positive associationnegative associationno association
Answers
A scatter plot shows the association between two variables.
If the variables tend to increase and decrease together, the association is positive. If one variable tends to increase as the other decreases, the association is negative. If there is no pattern, the association is zero.
From the graph we notice that in this case both variables increcase together, therefore the scatter plot has a positive association.
le Figure Score: 7/100 1/13 answered Question 2 < > A pennant is in the shape of an isosceles triangle. inches, the height is 15 inches, and the length of th the area of the pennant? inches squared
Answers
The area of a triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]in this case b=9.5 and h=15. Plugging the values in the formula we have:
[tex]\begin{gathered} A=\frac{1}{2}\cdot9.5\cdot15 \\ =71.25 \end{gathered}[/tex]Therefore the area is 71.25 square
In the equation Q = 45e1.031a quantity Q is changing over time t.(a) What is the quantity at timet = 0?(b) Is the quantity increasing or decreasing over time?(c) What is the percent per unit time continuous growth or decay rate?
Answers
(a) The equation is given as Q=45e^1.03t
where e=2.718
Taking t=0 the equation will be :
[tex]Q=45e^{1.03\ast0}[/tex]This will give;
[tex]Q=45\ast2.718^0[/tex]Q=45
The semi annual compound interest of a sum of money in 1 year and 2years are Rs400 and Rs441 respectively.Find the annual compound interest for 2years
Answers
Answer:
Step-by-step explanation
Correct option is A)
C.I. for the third year = Rs. 1,452.
C.I. for the second year = Rs. 1,320
∴ S.I on Rs. 1,320 for one year = Rs. 1,452− Rs. 1,320= Rs. 132.
Rate of interest =
1,320
132×100
=10%.
Let the original money be Rs. P.
Amount after 2 year − amount after one year =C.I. for second year.
P(1+
100
10
)
2
−P(1+
100
10
)=1,320
P[(
100
110
)
2
−
100
110
]=1,320
⇒P[(
10
11
)
2
−
10
11
]=1,320⇒P(
100
121
−
10
11
)= Rs. 1,320
⇒P×
100
11
=Rs.1,320⇒P=
11
1,320×100
= Rs. 12,000
∴ Rate of interest =10%
and Original sum of money = Rs. 12,000
the client is to receive cimetidine 300mg by mouth every 6 hours. The medication is available as cimetidine 300mg/5ml. How many teaspoons should the nurse instruct the client to take?
Answers
Step 1
Given; The client is to receive cimetidine 300mg by mouth every 6 hours. The medication is available as cimetidine 300mg/5ml.
Required; How many teaspoons should the nurse instruct the client to take?
Step 2
[tex]\begin{gathered} 1\text{ teaspoon =5ml } \\ Patient\text{ takes 300mg/5ml or 300mg/teaspoon} \\ \frac{Required\text{ dosage in mg}}{Dosage\text{ in 1 teaspoon}}\times5ml \\ Required\text{ dosage in mg=300mg} \\ Dosage\text{ in 1 teaspoon=300mg} \\ \frac{300mg}{300mg}\times5ml=5ml \\ From\text{ the table 5ml is the equivalent of 1 teaspoon .} \end{gathered}[/tex]Thus, the client takes 300mg every six hours. This means that the nurse will instruct the client to take 1 teaspoon every 6 hours.
Answer;
[tex]1\text{ teaspoon every 6 hours}[/tex]Calculate the five-number summary and the IQR from the following values given: {17, 20, 21, 25, 25, 29, 40}
Answers
Answer:
• 17, 20, 25, 29 and 40
,• IQR=9
Explanation:
(a)Given the set of values:
{17, 20, 21, 25, 25, 29, 40}
• The minimum value = 17
The first quartile
The first quartile is the median of the lower half of the data set.
The lower half of the data set = 17, 20, 21
• Therefore, the first quartile =20
The Median
The median is the number in the middle of the set of values.
The number in the middle is 25, therefore:
• Median = 25
The third quartile
The third quartile is the median of the upper half of the data set.
The upper half of the data set = 25, 29, 40
• Therefore, the third quartile =29
Finally, Maximum Value = 40.
The five-number summary of the set of values is: 17, 20, 25, 29 and 40
(b)Interquartile Range
Interquartile Range = Third Quartile - First Quartile
=29 - 20
IQR=9
A triangle can have sides 2,3 and 5. True or false
Answers
First, remember that:
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this problem, notice that:
2 + 3 is not greater than 5.
3 + 5 is not greater than 2.
2 + 5 is not greater than 3.
So, the statement is false. A triangle can't have sides 2
Insert three arithmetic means between -16 and 4
Answers
To answer this question we will use the following formulas to compute n arithmetic means between 'a' and 'b':
[tex]\begin{gathered} A_1=a+\frac{b-a}{n+1}, \\ A_2=a+2\cdot\frac{b-a}{n+1}, \\ \ldots \\ A_n=a+n\cdot\frac{b-a}{n+1}\text{.} \end{gathered}[/tex]Substituting n=3, a=-16, and b=4 we get:
[tex]\begin{gathered} A_1=-16+\frac{4-(-16)}{3+1}, \\ A_2=-16+2\cdot\frac{4-(-16)}{3+1}, \\ A_3=-16+3\cdot\frac{4-(-16)}{3+1}\text{.} \end{gathered}[/tex]Simplifying the above results we get:
[tex]\begin{gathered} A_1=-16+\frac{4+16}{4}=-16+\frac{20}{4}=-11, \\ A_2=-16+2\cdot\frac{4+16}{4}=-16+\frac{40}{4}=-6, \\ A_3=-16+3\cdot\frac{4+16}{4}=-16+\frac{60}{4}=-1. \end{gathered}[/tex]Answer: -11, -6, and -1.
A kite is flying 95 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 48º. Find the length ofthe string. Round your answer to the nearest tenth.
Answers
Given data:
Kite is flying off the ground = 95ft. ( Perpendicular)
Angle = 48 degree
[tex]\sin 48^{\circ}=\frac{Perpendicular}{Hypotenues}[/tex][tex]\text{Hypotenues}=\frac{Perpendicular}{\sin 48^{\circ}}[/tex][tex]\begin{gathered} H=\frac{95}{0.7431} \\ H=127.84ft \end{gathered}[/tex]Thus, the length of the string is 127.8 ft.
A randomly generated list of integers from 0 to 7 is being used to simulate an event, with the numbers 0, 1, 2, and 3 representing a success. What is the estimated probability of a success? O A. 25% OB. 50% O C. 80% O D. 43%
Answers
The total numbers of integers used is 7 + 1 = 8 (since we are using ubtewgers from 0 to 7).
If 0, 1, 2 and 3 represents succes, we have 4 integers of the 8 total that are success, thus, the theoretical probability is:
[tex]P=\frac{4}{8}=0.5[/tex]So the probability os success is 0.50 = 50%.
In the scoring for a game, points can be negative and positive. There were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times. How many more times would 5.5 points need to be scored to have a total gain greater than 15 points?
A. 1
C. 3
B. 2
D. 4
Answers
The number of times that 5.5 points is need to be scored to have a total gain greater than 15 points is A. 1
How to calculate the value?From the information, it was stated that there were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times.
In this case, the entire score will be:
= (-3.25 × 4) + (-2.75 × 5) + (3 × 2) + (5.5 ×4)
= -13 - 13.75 + 6 + 22
= 11.25
Therefore, the times that 5.5 points is needed to be scored to have a total gain greater than 15 will be 1 time since 11.25 + 5.5 = 16.75. This is more than 15.
Learn more about numbers on:
brainly.com/question/24644930
#SPJ1
Below, the two-way table is given for aclass of students.Freshmen Sophomore Juniors Seniors TotalMale 462. .Female 33246TotalIf a student is selected at random, find theprobability the student is a junior. Roundto the nearest whole percent.
Answers
The final answer is: 27%
We are asked to find the probability that a student chosen at random is a junior. This requires that we know the total number of students in each level from Freshmen to Seniors.
Totals:
Freshmen = 4 + 3 = 7
Sophomore = 6 + 4 = 10
Juniors = 2 + 6 = 8
Seniors = 2 + 3 = 5
Thus we can calculate the total number of students considered:
7 + 10 + 8 + 5 = 30 students in total.
Now we can calculate the probability as:
[tex]\begin{gathered} P(\text{choosing juniors) = }\frac{Number\text{ of Juniors}}{\text{Total Number of Students}} \\ \end{gathered}[/tex]The number of Juniors was calculated earlier as: Juniors = 8
We have the total number of students as 30
Therefore, we can solve:
[tex]P(\text{choosing juniors)=}\frac{8}{30}=\frac{4}{15}[/tex]But we were asked to round to the nearest whole percent, which means we are required to put the fraction into percentage.
The way we do this is to multiply the fraction by 100%
[tex]\begin{gathered} \frac{4}{15}\times100=26.6667. \\ \\ \therefore P(\text{choosing juniors)=27\% (to the nearest whole percent)} \end{gathered}[/tex]Therefore the final answer is: 27%
The recursive rule for a sequence and one of the specific terms is given. Find the position of the giving term. f(1)= 8 1/2; f(n)= f(n-1) - 1/2; 5 1/2
Answers
f(7) gives 5 1/2.
the position is the 7th term
Explanation:
f(1)= 8 1/2
f(n)= f(n-1) - 1/2
we are looking for the function that gives 5 1/2
We have been given f(1), this means n = 1
f(1) = f(1-1) - 1/2
8 1/2 = f(0) - 1/2
f(0) = 8 1/2 + 1/2
f(0) = 8 + 1 = 9
when n = 2
f(2) = f(2-1) - 1/2
f(2) = f(1) - 1/2
f(2) = 8 1/2 - 1/2
f(2) = 8
when n = 3
f(3) = f(3-1) - 1/2
f(3) = f(2) - 1/2
f(3) = 8 - 1/2
f(3) = 7 1/2
when x = 4
f(4) = f(4-1) - 1/2
f(4) = f(3) - 1/2
f(4) = 7 1/2 - 1/2
f(4) = 7
when n = 5
f(5) = f(5-1) - 1/2
f(5) = f(4) - 1/2
f(5) = 7 - 1/2
f(5) = 6 1/2
f(6) = f(6-1) - 1/2
f(6) = f(5) - 1/2
f(6) = 6 1/2 - 1/2 = 6
when n = 7
f(7) = f(7-1) - 1/2
f(7) = f(6) - 1/2
f(7) = 6 -1/2 = 5 1/2
f(7) gives 5 1/2.
Hence, the position is the 7th term
A particle is moving along the x-axis and the position of the particle at the time t is given by x (t) whose graph is shown above. Which of the following is the best estimate for the speed of the particle as time t=4?
Answers
Given:
We are given the x(t) vs time curve.
To find:
Speed of particle at t = 4
Step by step solution:
We know that the slope of x-t curve represents the speed of the particle.
To calculate the speed of the particle at t = 4, We will calculate the slope of the curve at t = 4
[tex]\begin{gathered} Slope=\frac{y_2-y_1}{x_2-x_1} \\ \\ Slope=\frac{40-10}{6-0} \\ \\ Slope=\frac{30}{6} \\ \\ Slope\text{ = 6} \end{gathered}[/tex]From here we can say that the slope of the curve between x = 0 and x = 6 is equal to 5.
So the value of speed is also 5 units, Which is equal to option A.
The unit rate for peaches is $2.00 per pound. The unit rate for grapes is $2.50 perpound. If you had $10 to spend, would you be able to buy a greater weight ofpeaches or of grapes? Explain your answer.
Answers
According to the problem, the total amount of money we have is $10.
Additionally, we know that the cost of peaches is $2 per pound, and the cost for grapes is $2.50 per pound.
Notice that the cost for grapes is greater than the cost for peaches, that means we'll by fewer pounds of grapes with $10 than for peaches.
For example, if we buy peaches, it would be
[tex]\frac{10}{2}=5[/tex]This means we would be able to buy 5 pounds of peaches.
But, for grapes
[tex]\frac{10}{2.50}=4[/tex]Which means we can by only 4 pounds of grapes.
Therefore, we would be able to buy a greater amount of peaches than grapes.El contratista encargado de construir el
cerco perimetral desea saber la expresión
algebraica correspondiente al perímetro de
todo el lote
Medidas:
25p-8
40p+2
Answers
El perímetro del lote tiene una medida de 130 · p - 12 unidades.
¿Cuál es la longitud del cerco perimetral para un lote?
El perímetro es la suma de las longitudes de los lados de una figura, un rectángulo tiene cuatro lados, dos pares de lados iguales. En consecuencia, el perímetro del lote es el siguiente:
s = 2 · w + 2 · l
Donde:
w - Ancho del lote.l - Largo del lote.s - Perímetro del lote.Si sabemos que w = 25 · p - 8 y l = 40 · p + 2, entonces el perímetro del lote es:
s = 2 · (25 · p - 8) + 2 · (40 · p + 2)
s = 50 · p - 16 + 80 · p + 4
s = 130 · p - 12
El perímetro tiene una medida de 130 · p - 12 unidades.
ObservaciónNo se ha podido encontrar una figura o imagen asociada al enunciado del problema. Sin embargo, se puede inferir que el lote tiene una forma rectangular debido a las medidas utilizadas. En consecuencia, asumimos que la medida del ancho es igual a 25 · p - 8 unidades y del largo es igual a 40 · p + 2 unidades.
Para aprender más sobre perímetros: https://brainly.com/question/17127243
#SPJ1
A house has increased in value by 35% since it was purchased. If the current value is S432,000, what was the value when it was purchased?
Answers
The value of the house when it was purchased = $32000
Explanation:The original percentage value = 100%
The current percentage value = 100% + 35% = 135%
Current value = $432000
Original value = x
[tex]\begin{gathered} The\text{ current value =}\frac{135}{100}\times The\text{ original value} \\ \\ 432000=1.35\times x \\ \\ x=\frac{432000}{1.35} \\ \\ x=$ 320000 $ \end{gathered}[/tex]The value of the house when it was purchased = $32000
I'm not sure what to do for this question I have already tried could you help me with this?
Answers
1) Take into account that a linear relation can be written as follow:
y = mx + b
where m is the slope of the line and the constant b the y-coordinate of the y-intercept.
Due to Rocco started to count from a distance of 4 miles, this is a constant number, which is equivalent to b, that is, b = 4.
If the constant rate of the walk is 3 miles per 2 hours, then, m = 3/2 (because the slope is also a constant rate of change).
Then, you have the following linear equation for the relation between the distance traveled by Rocco and the time.
y = 3/2*x + 4
y is the number of miles of the Rocco walking
x is the time (in hours) he takes for the walking
2) Now, based on the previous equation, you have for the table:
3) The relation between the given variables is proportional because a change in x makes that y changes too.
The distance traveled by Rocco is given by the value of y when x = 4. As you can notice on the table, such a distance is 10 miles.
using the gcf and the distributive property find the sum of 34+51
Answers
it would be 75 ur welcome
what is the sum of 141.2-79.83
Answers
Given:
141.2 - 79.83
Here, we are to subtract 79.83 from 141.2
Let's evaluate the given expression.
We have:
[tex]\begin{gathered} 141.20 \\ -79.83 \\ _{\text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \\ \text{ 61.37} \end{gathered}[/tex]ANSWER:
61.37
Which of the following point-slope form equations could be produced with the points (3, 4) and (1, -7)?
Answers
Answer:
y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~
( 3 , 4 )
( 1 , - 7 )
m = [tex]\frac{-7-4}{1-3}[/tex] = [tex]\frac{-11}{-2}[/tex] = [tex]\frac{11}{2}[/tex]
y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )
102,410,000,000,000,000,000,000,000 in scientific notation round to two digits after the decimal
Answers
We have a big integer and want to write in scientific notation.
To do this we need to count how many places we need to move the decimal point.
In this case we need to move the decimal point to left so the exponent of 10 will be positive.
So,
[tex]\begin{gathered} 102,410,000,000,000,000,000,000,000=1.0241\cdot10^{29} \\ \text{Round to two digits after the decimal:} \\ 1.02\cdot10^{29} \end{gathered}[/tex]We move the decimal point 29 places to left so the exponent of 10 is 29.
Completely factor the expression by grouping if possible 2xy+3x+10y+15
Answers
The required factor of the given expression is given as (2y + 3)(x + 3).
Given that,
The factor of the given expression 2xy+3x+10y+15 is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here
= 2xy+3x+10y+15
Simplifying through factorization,
= x(2y + 3) + 5(2y + 3)
= (2y + 3)(x + 3)
Thus, the required factor of the given expression is given as (2y + 3)(x + 3).
Learn more about simplification here: https://brainly.com/question/12501526
#SPJ1
Help me answer these thank u :)
Answers
6. -2
7.-38
8.-15
9.0
10.-13
11.-30
12.38
13.33
14.-23
6. -2
7.-38
8.-15
9. 0
10. -13
11. -30
12. 38
13. 33
14. -23
Calculate each percent increase or percent decreases Round to the nearest whole percent if necessary 1. original amount: 30, new amount: 45 2. original amount: 12, new amount: 16 3. original amount: 17 new amount: 21 4. original amount: 85, new amount: 56 5. original amount: 48, new amount: 37 6. original amount: 124, new amount: PLS HELP ME!!!
Answers
The percentage increase is 50%
Here, we want to calculate the percentage increase or decrease
To know if it is a decrease or an increase, we use the following simple logic.
If new amount is greater than original amount, then it is an increase.
If new amout is less than original amount, then it is a decrease
For the first question, we can see that the new amount is greater than the old amount
This indicates an increase
Mathematically;
[tex]\text{percentage increase = }\frac{(new\text{ amount - original amount)}}{\text{old amount}}\text{ }\times\text{ 100 percent}[/tex]According to the first question, new amount = 45 while old amount = 30
so;
percentage increase = (45-30)/30 * 100%
= 15/30 * 100% = 100%/2 = 50%
Are there no more tutors for mathematics, I can’t seem to find the option anymore for a tutor.
Answers
A quadratic equation is represented graphically as:
[tex]y=a(x-h)^2+k[/tex]Here the graph represents the parabola where (h,k) is the vertex of the parabola.
Put any value of h, k and a to get the graph as follows:
The graph of a quadratic equation is parabolic in nature.
Suppose that you have a quadratic equation given by:
[tex]y=x^2-5x+6[/tex]Convert the equation into perfect square by completing the square method
[tex]\begin{gathered} y=(x^2-5x+\frac{25}{4})+6-\frac{25}{4} \\ y=(x-\frac{5}{2})^2-\frac{1}{4} \end{gathered}[/tex]This is the method of conversion of quadratic to plot the graph.
