[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$625\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &12 \end{cases} \\\\\\ A=625e^{0.07\cdot 12}\implies \implies A=625e^{0.84}\implies A\approx 1447.73[/tex]
The investment will be $1447.73 worth in 12 years.
What is continuous compound interest?Continuous compounding exists the mathematical limit that compound interest can reach if it's calculated and reinvested into an account's balance over a theoretically infinite number of terms. While this exists not possible in practice, the vision of continuously compounded interest stands important in finance.
Since, the amount formula is compounded continuously,
[tex]$$A=P e^{r t}$$[/tex]
Where,
P is the principal amount,
[tex]$\mathbf{r}$[/tex] is the rate per period,
t is the number of periods,
e is Euclid number,
Here, [tex]$P=\$ 625$[/tex],
[tex]$$r=7 \%=0.07 \text {, }$$[/tex]
t=12 years
Thus, the amount after 12 years would be,
[tex]$$A=625 e^{0.07 \times 12}=625 e^{0.84}=\$ 1447.72936049 \approx \$ 1447.73$$[/tex]
Hence, $1447.73 will the investment be worth 12 years.
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The coordinates of vertex S are (_,_)
The area of rectangle PQRS is_____square units.
Answer:
vertex s is -2,-2
Step-by-step explanation:
and with the rectangle is q to p is 4cm coz one box is 1 cm and r to q is 3cm so you multiply them and the answer is 12cm
At the start of the first down, the football was 30 yards from the Tigers' end zone. During three downs, the ball moved 9
yards farther from their end zone, then 14 yards closer to it, and then 2 yards closer to it. How many yards from their end
zone was the ball at the end of the third down?
Answer:
23
Step-by-step explanation:
30 + 9 = 39.
39 - 14 = 25.
25 - 2
= 23
Answer:
23
Step-by-step explanation:
The airplane was 32,000 feet above sea level. It landed in a valley 100 feet below sea level. Write an integer to express the change in the altitude
Answer:
- 32,100 ft
Step-by-step explanation:
Initial Altitude = 32,000 ft above sea level = +32,000 feet
Final Altitude = 100 ft below sea level = -100 ft
Altitude change,
= final altitude - initial altitude
= - 100 - (32,000)
= - 32,100 ft
What is this one don’t get it
Answer:
14 cups
Step-by-step explanation:
3 pizzas needed
1 pizza means 2 cups of flour
So for 3 pizzas he will need 6 cups of flour
If he has 20 cups of flour and he uses 6, how much is left?
20-6=14
Answer:
14 cups of flour
Step-by-step explanation:
The three pizzas will require 6 cups of flour.
3 x 2 = 6 cups of flour needed to make 3 pizzas.
20 - 6 = 14 cups left
Please help me !! D is also an option but I couldn't get it in the picture
Answer: A) (-1, 0) to (1, 2)
Step-by-step explanation:
Complex numbers are written in the form of ai + b ; where "a" represents the x-coordinate and "b" represents the y-coordinate --> (a, b)
-i → -1i + 0 → (-1, 0)
2 + i → 1i + 2 → (1, 2)
Which graph connects those two coordinates? OPTION A
easch cube inside the rectangle prism has a edge length of 3/4 inch what is the volume of the rectangle prism
Volume = (edge)^3
Volume = (3/4)^3
Volume = (27/64) inches^3
Done.
Which list shows the numbers in order from least to greatest? A. 53.783 B. 53.65 C. 53.09 D. 53.163 A) A, B, D, C B) C, D, B, A C) D, C, B, A D) B, C, A, D
Answer:
B) C,D,B,A
Step-by-step explanation:
17. Find the value of (+328.62) – (+98.6).
A. –427.22
B. 230.02
C. 427.22
D. –230.02
For this case we must find the value of the following expression:
[tex](+328.62) - (+ 98.6) =[/tex]
We apply distributive property to the term within the parenthesis taking into account tha:
[tex]- * + = -[/tex]
Rewriting we have:
[tex]+ 328.62-98.6 =[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]+328.62-98.6 = 230.02[/tex]
Answer:
230.02
Option B
Can someone help me?
Thanks-Aparri
Answer:
10y
Step-by-step explanation:
9y + y = 10y
Answer:
[tex]10y[/tex]
Step-by-step explanation:
[tex]9y + y = y(9 + 1) = y(1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) = y \times 10 = 10y[/tex]
Catherine likes to go ice fishing she has learned from experience that she stays warm about 15 minutes for every undershirt she wears if she wants to stay out for 75 minutes how many undershirts should she put on
At 350 degrees Fahrenheit, an oven can cook approximately 3 pounds of turkey per hour. At 450 degrees Fahrenheit, it can cook approximately 4.5 pounds per hour. How many more ounces of turkey can the oven cook at 450 degrees than at 350 degrees in 10 minutes? (1 pound = 16 ounces)
A) 4
B) 6
C) 8
D) 12
Answer:
D
Step-by-step explanation:
12. Meldre put $5000 in a savings account that pays 1.25% interest compounded yearly. How much money will be in the account 10 years later if she makes no more deposits or withdrawals?
We know that, Final Amount in Compound Interest is given by :
[tex]\bigstar\;\;\boxed{\mathsf{Amount = Principal\left(1 + \dfrac{Rate\;of\;interest}{100}\right)^{Number\;of\;Years}}}[/tex]
Given :
● Principal = $5000
● Rate of interest = 1.25
● Number of Years = 10
Substituting the values in the Formula, We get :
[tex]\implies \mathsf{Amount = 5000\left(1 + \dfrac{1.25}{100}\right)^{10}}[/tex]
[tex]\implies \mathsf{Amount = 5000\left(1 + \dfrac{0.25}{20}\right)^{10}}[/tex]
[tex]\implies \mathsf{Amount = 5000\left(1 + \dfrac{0.05}{4}\right)^{10}}[/tex]
[tex]\implies \mathsf{Amount = 5000\left(\dfrac{4.05}{4}\right)^{10}}[/tex]
[tex]\implies \mathsf{Amount = 5000\times (1.0125)^{10}}[/tex]
[tex]\implies \mathsf{Amount = 5661.354}[/tex]
Answer : $5661.354 money will be in the account 10 years later
Answer: $5,661.35
Step-by-step explanation:
I used the exponential growth formula to get my answer.
Sherina wrote and solved the equation.
x-56=230
x-56-56=230-56
x=174
What was Sherina’s error?
Sherina’s work is correct.
Sherina only needed to subtract 56 from 230.
Sherina made a subtraction error when subtracting 56 from 230.
Sherina should have added 56 to both sides of the equation.
Answer:
Sherina should have added 56 to both sides of the equation.
Step-by-step explanation:
To solve this equation: x-56=230 you need to add 56 to both sides of the equation:
x-56 + 56=230 + 56 → x = 286.
Therefore, Sherina should have added 56 to both sides of the equation.
Answer:
Last option: Sherina should have added 56 to both sides of the equation.
Step-by-step explanation:
To solve the equation [tex]x-56=230[/tex] Sherina needed to solve for the variable "x".
To calculate the value of the variable "x" it is important to remember the Addition property of equality. This states that:
[tex]If\ a=b\ then\ a+c=b+c[/tex]
Therefore, Sherina should have added 56 to both sides of the equation.
The correct procedure is:
[tex]x-56+(56)=230+(56)\\x=286[/tex]
Find the arc length intercepted by a central angle of radians in a circle whose radius is 18.4 inches. 13.8π 15.2π 24.5π
Final answer:
The arc length intercepted by a central angle of π radians in a circle of radius 18.4 inches is calculated as arc length = θ × radius, resulting in 18.4π inches.
Explanation:
To find the arc length intercepted by a central angle of θ radians in a circle with radius r, we use the formula:
arc length (s) = θ × r
Given that the central angle θ is π radians and the radius r is 18.4 inches, we can compute the arc length as follows:
arc length (s) = π × 18.4 inches
By multiplying, we get:
arc length (s) = 18.4π inches
Therefore, the arc length intercepted by a central angle of π radians in a circle with a radius of 18.4 inches is 18.4π inches.
Mark and Julio are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and packages of crocus bulbs. Mark sold 2 bags of windflower bulbs and 5 packages of crocus bulbs for a total of $105. Julio sold 9 bags of windflower bulbs and 5 packages of crocus bulbs for a total of $164.50. Find the cost each of one bag of windflower bulbs and one package of crocus bulbs. Solve having substitution method.
To find the cost of one bag of windflower bulbs and one package of crocus bulbs, we can use the substitution method. By setting up a system of equations and solving for the variables, we find that the cost of one bag of windflower bulbs is $45 and the cost of one package of crocus bulbs is $7.50.
Explanation:To find the cost of one bag of windflower bulbs and one package of crocus bulbs, we can set up a system of equations. Let's use the substitution method.
Let x represent the cost of one bag of windflower bulbs and let y represent the cost of one package of crocus bulbs.
We can set up two equations:
2x + 5y = 105
9x + 5y = 164.50
From the first equation, we can rewrite it as: 2x = 105 - 5y. We can substitute this expression for 2x in the second equation:
9(105 - 5y) + 5y = 164.50
Solving for y, we get y = 7.50. Substituting this value back into the first equation, we can solve for x: 2x + 5(7.50) = 105. Solving for x, we get x = 45.
Therefore, the cost of one bag of windflower bulbs is $45 and the cost of one package of crocus bulbs is $7.50.
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Follow below steps:
Mark and Julio are selling flower bulbs for a school fundraiser. To find the cost of one bag of windflower bulbs and one package of crocus bulbs, we set up two equations based on the information given, and then solve them using the substitution method.
Let x be the cost of one bag of windflower bulbs and y be the cost of one package of crocus bulbs. According to Mark's sales, the equation is:
2x + 5y = 105 ...(1)
According to Julio's sales, the equation is:
9x + 5y = 164.50 ...(2)
To use the substitution method, we first isolate y in equation (1):
y = (105 - 2x) / 5 ...(3)
Next, we substitute equation (3) into equation (2):
9x + 5((105 - 2x) / 5) = 164.50
9x + 105 - 2x = 164.50
7x = 59.50
x = 8.50
Now that we have the value for x, we can use it to find y by substituting x back into equation (3):
y = (105 - 2(8.50)) / 5
y = (105 - 17) / 5
y = 88 / 5
y = 17.60
Therefore, the cost of one bag of windflower bulbs is $8.50 and the cost of one package of crocus bulbs is $17.60.
A textbook store sold a combined total 440 of physics and sociology textbooks in a week. The number of sociology textbooks sold was 54 less than the number of physics textbooks sold. How many textbooks of each type were sold?
First subtract the difference of the two by the total:
440 - 54 = 386
Now divide that by 2:
386 / 2 = 193
193 is the number of Sociology books sold.
Now add 54 to 193 for the total Physics books:
193 + 54 = 247 Physics books were sold.
Use the Binomial Theorem and Pascal’s Triangle to write each binomial expansion.
_ (2x-3)^3
HELP ASAP
ANSWER
[tex]{(2x - 3)}^{3} = {8x}^{3} - 36 {x}^{2} + 54x - 27[/tex]
EXPLANATION
Using the binomial theorem of Pascal's triangle, the coefficient of the third exponent binomial is :
1,3,3,1
The expansion for
[tex] {(a - b)}^{3} = {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3} [/tex]
To find the expansion for:
[tex] {(2x - 3)}^{3} [/tex]
We put a=2x and b=3
This implies that,
[tex]{(2x - 3)}^{3} = {(2x)}^{3} - 3 {(2x)}^{2} ( 3) + 3(2x) {(3)}^{2} - {3}^{3} [/tex]
This simplifies to:
[tex]{(2x - 3)}^{3} = {8x}^{3} - 36 {x}^{2} + 54x - 27[/tex]
Help with this question, please!
Answer:
see below
Step-by-step explanation:
Apart from the pictures being drawn with the axis at a funny angle relative to the edges of the solid, it should be pretty clear from the pictures that the figure has both plane and axis symmetry.
Every point on one side of the axis has a matching point on the other side at the same distance. Every point on one side of the plane of symmetry has a matching point on the other side at the same distance.
Question is in picture, the middle one, apologies for the others cropping into it.
Answer:
c. (6,1)
Step-by-step explanation:
Add both x and both y (11+1)=12 (5+-3)=2 then divide both by 2
(6,1)
Graph the system of equations. then determine wheather the system has no solution, one solution, or infinitely many solutions. If the systems has one solution, name it.
y= -x + 5
y= x - 3
A. one solution; (1,4)
B. infinitely many
C. no solution
D. one solution; (4, 1)
Answer:
See below in bold.
Step-by-step explanation:
If we add the 2 equations we eliminate x and we get 2y =2.
So y = 1.
Substituting y = 1 in the second equation 1 = x - 3.
So x = 4.
A. One solution: (4, 1).
If we drew a graph we would have 2 lines which intersect at the point (4, 1).
Answer:
Step-by-step explanation:
If we add the 2 equations we eliminate x and we get 2y =2.So y =1.
Substituting y = 1 in the second equation 1 = x - 3.So x = 4.
A.
One solution: (4, 1).If we drew a graph we would have 2 lines which intersect at the point (4, 1).
Tomas used 3 1/3 cups of flour and now has 1 2/3cups left. Which equation can he use to find f, the number of cups of flour he had to begin with?
f+3 1/3=1 2/3
f-3 1/3=1 2/3
3 1/3f=1 2/3
f/3 1/3=1 2/3
For this case we have that the variable "f" represents the number of cups of flour that Tomas had initially.
If of that amount Luis used [tex]3 \frac {1} {3}[/tex] of cups of flour, then we have the following expression:
[tex]f-3 \frac {1} {3}[/tex]
If Luis has[tex]1 \frac {2} {3}[/tex] cups of flour left, then we have the following equation:
[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]
Finally, the equation that represents the given situation is:
[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]
Answer:
Option B
Which expression is the radical form of m^2.5?
The expression [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .
What is a Radical form ?
If n is a positive integer greater than 1 and n is a real number, then
[tex]\rm \sqrt[n]{a}[/tex] = aⁿ
Here the index is represented by n, the radicand is represented by a , and the sign is called the radical.
Left side of the equation is called the radical form
Right side of the equation is called exponent form.
The given exponent form is
[tex]\rm m^{2.5}[/tex]
In radical form this will be written as
[tex]\rm \sqrt[2.5]{m}[/tex]
Therefore the expression [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .
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Can someone please help me on the last two empty boxes :( ??!!
Answer:
trinomial binomialStep-by-step explanation:
mono-, bi-, tri- are prefixes meaning 1, 2, and 3, respectively. A 3-term polynomial is a trinomial; a 2-term polynomial is a binomial.
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth.
Check the picture below.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{27.6}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{30^2-27.6^2}=h\implies \sqrt{138.24}=h\implies 11.76\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the triangle}}{\cfrac{1}{2}bh\implies \cfrac{1}{2}(27.6)(11.76)}\implies 162.288\implies \stackrel{\textit{rounded up}}{162.3}[/tex]
To find the area of the right triangle with a given hypotenuse and adjacent leg, use the Pythagorean theorem to calculate the other leg. Then, use the base and height (the two legs) in the area formula for a right triangle. The area of the triangle is approximately 148.7 cm².
To find the area of a right triangle, you need two perpendicular sides, known as the legs of the triangle. Since we are given the hypotenuse (30 cm) and one adjacent leg (27.6 cm) which is one of the legs, we need to find the other leg. Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In mathematical terms, this is expressed as a² + b² = c². Therefore, the length of the other leg (b) can be found using the equation b² = c² - a², where c is the hypotenuse and a is the given adjacent leg.
Substituting the given values, we have b² = 30² - 27.6². Calculating this gives b ≈ 10.8 cm.
Now, the area of the triangle can be calculated using the formula for the area of a right triangle, which is (1/2) × base × height. In this case, the base and height are the two legs of the triangle. Substituting the lengths of the legs we have, Area ≈ (1/2) × 27.6 cm × 10.8 cm. The result is approximately 148.7 cm², which is the area of the triangle rounded to the nearest tenth.
If f(x)=5x, what is f^-1(x)?
A. f^-1(x)=-5x
B. f^-1(x)=-1/5x
C. f^-1(x)=1/5x
D. f^-1(x)=5x
Thanks!
Answer:
C. f^-1(x) = 1/5x
Step-by-step explanation:
You know that f^-1(f(x)) = x, so you can try the answers.
A: f^-1(5x) = -25x . . . . not itB: f^-1(5x) = -x . . . . . . not itC: f^-1(5x) = x . . . . . . . correct choiceD: f^-1(5x) = 25x . . . . not it____
You can also solve for f^-1(x). It will be "y" when ...
f(y) = x
5y = x
y = 1/5x . . . . . divide by 5
A chemist wants to mix a 66% alcohol solution with eight liters of 54% alcohol solution to produce a solution that is 65% alcohol. How many liters of the 66% alcohol solution should be used ?
Answer:
We have 8 liters of 54% alcohol.
We will add "x" liters of 66% alcohol to make "8 +x" liters of 65% alcohol.
54 * 8 + 66 x = 65 (8 + x)
432 + 66x = 520 + 65x
x = 88 liters
Step-by-step explanation:
Emilio throws a marshmallow into the air from his balcony. The height of the marshmallow (in feet) is represented by the equation h=?16(t?14)^2+49, where t is the time (in seconds) after he throws the marshmallow. What is the maximum height of the marshmallow?
Answer:
The maximum height of the marshmallow is 49 feet.
Step-by-step explanation:
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex] .... (1)
Where, (h,k) is vertex of the parabola is a is constant.
The given function is
[tex]h=-16(t-14)^2+49[/tex] ..... (2)
Where, h is height of the marshmallow (in feet) and t is the time (in seconds) after he throws the marshmallow.
From equation (1) and (2), we get
[tex]a=-16,h=14,k=49[/tex]
The value of a is -16, which is less than 0. So, the given function is a downward parabola.
The vertex of a downward parabola is the point of maxima.
The value of h is 14 and the value of k is 49. So, the vertex of the parabola is (14,49). It means the maximum height of the marshmallow is 49 feet in 14 seconds.
Therefore the maximum height of the marshmallow is 49 feet.
Answer:
1/4,9
Step-by-step explanation:
might be wrong tbh
Eliminate the parameter.
x = t - 3, y equals two divided by quantity t plus five
Answer:
y = 2/(x +8)
Step-by-step explanation:
Solve the first equation for t and substitute that expression into the second equation.
x = t -3
x + 3 = t
Then for y, we have
y = 2/(t +5)
y = 2/((x +3) +5) . . . . substitute for t
y = 2/(x +8) . . . . . . . . simplify
Which is a quadratic function?
f(x) = 2x + x + 3
f(x) = 0x2 – 4x + 7
f(x) = 5x2 – 4x + 5
f(x) = 3x3 + 2x + 2
Answer:
C
Step-by-step explanation:
B isn't right. The 0 makes x^2 go away leaving a linear equation.
A is a linear function.
D is a cubic, so the answer is
C which has an x^2 function
Max's trip home takes 32 minutes. What is the latest time he can leave to be home by a quarter before 5?
Latest time he can leave to be home by a quarter before 5 is 4:13
Step-by-step explanation:
Given Max's trip home takes 32 minutes. we have to find the time at which he can leave to be home by a quarter before 5.
quarter before 5 means 4:45
Max's takes 32 min to come to home so he has to leave 32 minutes before the given time.
Hence, latest time he can leave to be home by a quarter before 5 is 4:45-32 = 4:13
Answer:
Max must leave home at 4:58 to get their before half past 5.
Step-by-step explanation: