The focus here is the use of "Compounding interest rate" and these entails addition of interest to the principal sum of the deposit.
Tyra will definitely prefer the Account 2 over the Account 1 Tyra balance from account 2 over 3.7 years is $6,261.37
The below calculation is to derive maturity value when annual rate of 3.1% is applied.
Principal = $5,400
Annual rate = 3.1% semi-annually for 1 years
A = P(1+r/m)^n*t where n=1, t=2
A = 5,400*(1 + 0.031/2)^1*2
A = 5,400*(1.0155)^2
A = 5,400*1.03124025
A = 5568.69735
A = $5,568.70.
In conclusion, the accrued value she will get after one years for this account is $5,568.70,
- The below calculation is to derive maturity value when the amount compounds continuously at an annual rate of 4%
Principal = $5,400
Annual rate = 4% continuously
A = P.e^rt where n=1
A = 5,400 * e^(0.04*1)
A = 5,400 * 1.04081077419
A = 5620.378180626
A = 5620.378180626
A = $5,620.39.
In conclusion, the accrued value she will get after one years for this account is $5,620.39.
Referring to how much would Tyra's balance be from Account 2 over 3.7 years. It is calculated as follows:
Annual rate = 4% continuously
A = P.e^rt where n=3.7
A = 5,400 * e^(0.04*3.7)
A = 5,400 * e^0.148
A = 5,400 * 1.15951289636
A = 6261.369640344
A = $6,261.37
Therefore, the accrued value she will get after 3.7 years for this account is $6,261.37
Learn more about Annual rate here
brainly.com/question/14170671
twice the difference of a number and 8 is 6. use the variable x for the unknown number.
Answer:
11
Step-by-step explanation:
Unknown number = x
If twice the difference of x and 8 is 6:
2(x-8) = 6
2x-16 = 6
2x = 6 + 16
2x = 22
x = 22/2
x = 11
Answer from Gauthmath
How much bigger is the Sum of first 50 even numbers than the sum of first 50 odd numbers?
Answer:
50
Step-by-step explanation:
Sum Even numbers
n = 50
d = 2
a1 = 2
The last number is
an = a1 + (n-1)d
an = 2 + (50 - 1)*2
an = 2 + 49 * 2
an = 2 + 98
an = 100
Sum of the even numbers
Sum = (a1 + a50)*n/ 2
Sum = (2 + 100)*50/2
sum = 102 * 25
sum = 2550
Sum of the first 50 odd numbers
a1 = 1
n = 50
d = 2
l = ?
Find l
l = a1 + (n - 1)*2
l = 1 + 49*2
l = 99
Sum
Sum = (1 + 99)*50/2
Sum = 2500
The difference and answer is 2550 - 2500 = 50
Help me plz help me plz
Answer: 4 13/30 cups
Step-by-step explanation:
Since Lila used 1 2/5 times as much lemonade as Naomi did (3 1/6 cups), we have to multiply 1 2/5 by 3 1/6:
1 2/5 ⋅ 3 1/6 = ?
19/6 ⋅ 7/5 = 133/30
133/30 = 4 13/30
4 13/30 cups
The maximum and minimum Values of a quadratic function are called as______of the function.
Answer:
the answer is B ...Extreme Values
I need your help once again, Brian
Answer:
3b^2+2b-8
Step-by-step explanation:
(3b-4)(b+2)
FOIL
first:3b*b = 3b^2
outer:2*3b = 6b
inner: -4b
Last: -4*2 = -8
Add together
3b^2 +6b-4b-8
Combine like terms
3b^2+2b-8
Answer:
[tex]3b^2+2b-8[/tex]
Step-by-step explanation:
Again, we can use FOIL to expand this equation:
First: [tex]3b(b)=3b^2[/tex]
Outer: [tex]3b(2)=6b[/tex]
Inner: [tex]-4(b)=-4b[/tex]
Last: [tex]-4(2)=-8[/tex]
We can combine the b terms to get [tex]2b[/tex], and we have our answer as [tex]3b^2+2b-8[/tex]
Does anyone know the answer??
Answer:
I think the answer is 39x, 13y
Step-by-step explanation:
point : extra points
1 : 3
y : 39
y= 39÷3
y= 13
What are the coordinates of the point on the directed line segment from (-2,6) to (3,-9) that partitions the segment into a ratio of 3 to 2?
9514 1404 393
Answer:
(1, -3)
Step-by-step explanation:
The point P that partitions AB into the ratio m:n is ...
P = (mB +nA)/(m+n)
The point you're looking for is ...
P = (3(3, -9) +2(-2, 6))/(3+2) = (9-4, -27+12)/5 = (5, -15)/5
P = (1, -3)
What is an explicit formula for the geometric sequence -64,16,-4,1,... where the first term should be f(1).
Answer:
[tex]a_{n} = -64(-\frac{1}{4})^{n-1}[/tex]
it seems like the first term is -64, so lets write the formula accordingly:
a_n = a1(r)^(n-1)
where 'n' is the number of terms
a1 is the first term of the sequence
'r' is the ratio
the ratio is [tex]-\frac{1}{4}[/tex] because -64 * [tex]-\frac{1}{4}[/tex] = 16 and so on...
the explicit formula is :
[tex]a_{n}[/tex] = [tex]-64(-\frac{1}{4} )^{n-1}[/tex]
On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set.
X1=-2 and x2=1
You would just need to plug the first y equation value into the 2nd equation to get what I got in the photo. Then solve for the x’s to get the coordinates.
A concave polygon can never be classified as a regular polygon true or false??? Need answer ASAP please
Answer:
Regular Polygons are never concave by definition.
Step-by-step explanation:
Help me plz help me plz plz
Im sorry I don't know the answer to the question
AABC is reflected across the x-axis and then translated 4 units up to create AA'BC. What are the coordinates of the vertices of AABC?
Can you please help me with this question
Answer:
Where is the question?
Step-by-step explanation:
Python is an interpreted high-level general-purpose programming language. Python's design philosophy emphasizes code readability with its notable use of significant indentation.
The correlation coefficient, r, between the ages of employees, x, and the number of sick days taken per year, y, equals 0.81.
Complete the statement based on the information provided.
The value of r is
✔ positive
and is relatively close to
✔ 1
, so the variables are
✔ closely
associated. It appears that, as the age of an employee increases, the number of sick days taken
✔ increases
.
Answer:
✔ positive
✔ 1
✔ closely
✔ increases
ED2021
in a survey of 90 students, the ratio of those who work outside the home to those who don't is 6:4. How many students work outside the home according to this survey? SHOW ALL WORK! AND ONLY ANSWER IF YOU KNOW THE ANSWER!
9514 1404 393
Answer:
54
Step-by-step explanation:
The fraction of the total that work outside the home is ...
outside/(outside +inside) = 6/(6+4) = 6/10
Then the number of those surveyed who work outside the home is ...
(6/10)(90) = 54 . . . work outside the home
A one lane highway runs through a tunnel in the shape of one half a sine curve cycle
The sine curve equation, y = 10·sin(x·π/24), that models the entrance of the
tunnel with a cross section that is the shape of half of a sine curve and the
height of the tunnel at the edge of the road, (approximately 7.07 ft.) are
found by applying the following steps
(a) The equation for the sine curve is y = 10·sin(x·π/24)
(b) The height of the tunnel at the edge of the road is approximately 7.07 feet
The reason for the above answers are presented as follows;
(a) From a similar question posted online, the missing part of the question
is, what is the height of the tunnel at the edge of the road
The known parameters;
The shape of the tunnel = One-half sine curve cycle
The height of the road at its highest point = 10 ft.
The opening of the tunnel at road level = 24 ft.
The unknown parameter;
The equation of the sine curve that fits the opening
Method;
Model the sine curve equation of the tunnel using the general equation of a sine curve;
The general equation of a sine curve is y = A·sin(B·(x - C) + D
Where;
y = The height at point x
A = The amplitude = The distance from the centerline of the sine wave to the top of a crest
Therefore;
The amplitude, A = The height of half the sine wave = The height of the tunnel = 10 ft.
D = 0, C = 0 (The origin, (0, 0) is on the left end, which is the central line)
The period is the distance between successive points where the curve passes through the center line while rising to a crest
Therefore
The period, T = 2·π/B = 2 × Opening at the road level = 2 × 24 ft. = 48 ft.
T = 48 ft.
We get;
48 = 2·π/B
B = 2·π/48 = π/24
By plugging in the values for A, B, C, and D, we get;
y = 10·sin((π/24)·(x - 0) + 0 = 10·sin(x·π/24)
The equation of the sine curve that fits the opening is y = 10·sin(x·π/24)
(b) The height of the tunnel at the edge of the road is given by substituting
the value of x at the edge of the road into the equation for the sine curve
as follows;
The width of the shoulders = 6 feet
∴ At the edge of the road, x = 0 + 6ft = 6 ft., and 6 ft. + 12 ft. = 18 ft.
Therefore, we get;
y = 10 × sin(6·π/24) = 10 × sin(π/4) = 5×√2
y = 10 × sin(18·π/24) = 10 × sin(3·π/4) = 5×√2
The height of the, y, tunnel at the edge of the road where, x = 6, and 18 is y = 5·√2 feet ≈ 7.07 ft.
Learn more about the sine curve here;
https://brainly.com/question/3827606
The answer pl shhaoksngausinxbbs pls
Answer:
D. 3
Step-by-step explanation:
A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
Simply stated, any polygon with three (3) lengths of sides is a triangle.
In Geometry, a triangle is considered to be the most important shape.
Generally, there are three (3) main types of triangle based on the length of their sides and these include;
I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.
II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.
III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.
In Geometry, an acute angle can be defined as any angle that has its size less than ninety (90) degrees.
Hence, we can deduce that the greatest number of acute angles that a triangle can contain is three (3) because the sum of all the interior angles of a triangle is 180 degrees.
The product of two positive integer numbers is 30 and the sum of the same two numbers is 11. Find the
numbers.
Answer:
5 and 6
Step-by-step explanation:
call them a and b, respectively
we have a*b=30 -> a=30/b
a+b=11 -> b+ 30/b=11
b=6 and a=5
surface area of cylinders
2in radius 4in height use 3.14 for pi. need help
Answer:
Step-by-step explanation:
A = (2)(3.14)(2)(4) + (2)(3.14)(2^2)
A = 75.36 in
PLS HELP! What is the mistake made below in solving x2 – 12x + 10 = 0 using the completing the square method?
x2 – 12x + 10 = 0
x2 – 12x + (- 6)2 = - 10 + (- 6)2
x2 – 12x + 36 = 26
(x – 6)(x – 6) = 26
x – 6 = √26
x = 6 + √26
Answer:
Step-by-step explanation:
Everything is correct. But you forgot to add
x = 6 - square root of 26. The answer is
x = 6 + square root of 26 or
x = 6 - square root of 26
THIS IS NOT A TEST OR ASSESSMENT!! NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE EXPLAIN!! Chapter 13
1. What is a conic ? How would you be able to model different conic sections at home(how would you slice a 3D shape to create the conic sections)?
2. How does the equation for the ellipse compare to the equation for a hyperbola? How can you determine the difference?
3. What is the difference between a vertex, a focus, and a directrix?
9514 1404 393
Explanation:
1.A cone is a 3-dimensional object created by revolving a line about an axis that intersects that line. This figure is a "double-napped" cone. The point where the revolved line and the axis meet is the a.pex, or vertex, of the cone. Typically, we're concerned with a finite portion of the cone, from the vertex to a base that is a circle in a plane perpendicular to the axis.
A "conic" is a 2-dimensional figure that results from the intersection of a plane and a cone. There are four general categories, named according to the angle the plane makes with the axis and/or the side of the cone. These are illustrated in the attachment.
a circle - the plane of intersection is perpendicular to the axisan ellipse - the plane of intersection is at an angle between 90° and the angle of the side relative to the axis. Both an ellipse and a circle are closed figures.a parabola - the plane of intersection is at the same angle as the side of the cone. A parabola is a one-sided open figure.a hyperbola - The plane of intersection is at an angle between that of the side of the cone and the axis of the cone. The plane will intersect both parts of a double-napped cone producing a double-sided open figure.Producing these at home can be an interesting project. A circle can be made using a compass.
An ellipse can be drawn using a pair of pins and a loop of string. The pins would be placed at the foci of the ellipse, and the string would constrain the drawing instrument (pen or pencil) to have a constant total distance to the two foci.
A parabola can be drawn on graph paper using coordinates derived from an equation for it. It can also be drawn using a compass and a set square by plotting points that are equidistant from the focus and a line that is called the directrix. If you have a physical cone-shaped object, you can cut it at an angle that will produce a parabola.
A hyperbola can be drawn on graph paper from an equation. It can also be drawn using a compass by plotting points that have a constant difference in their distance to the two foci, or by plotting points whose ratio of distance to focus and directrix is a constant. A physical cone-shaped object can be cut to produce a hyperbola.
__
2.The general form equation for a conic is ...
Ax² +Bxy +Cy² +Dx +Ey +F = 0
Usually, we're concerned with conics that have axes parallel to the coordinate axes, so B=0. The equation of an ellipse has A and C with the same sign. The equation of a hyperbola has A and C with opposite signs,
In standard form, the equations for figures centered at the origin are ...
ellipse: x²/a +y²/b = 1hyperbola: x²/a -y²/b = 1 (opens horizontally)hyperbola: y²/a -x²/b = 1 (opens vertically)__
3.The vertex of a conic is an extreme point on the (major) axis of the conic. The focus is a point used in the definition of the conic. The focus is "inside" the curve, on the axis of symmetry. The directrix is a line used in the definition of the conic. The directrix is "outside" the curve, perpendicular to the axis. The second attachment shows these for a parabola.
Show that the equation 2x + 3 cos x + e ^ x = 0 has a root on the interval [- 1, 0]
If x = -1, you have
2(-1) + 3 cos(-1) + e ⁻¹ ≈ -0.0112136 < 0
and if x = 0, you have
2(0) + 3 cos(0) + e ⁰ = 4 > 0
The function f(x) = 2x + 3 cos(x) + eˣ is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < c < 0 such that f(c) = 0.
Find the area of the circle round your answer to the nearest 10th
Answer:
The area is 19.63.
Step-by-step explanation:
Step-by-step explanation:
Area of a circle is
[tex]area = \pi \: r ^{2} [/tex]
area=3.14(2.5)²
19.63in²
g Two different factories named A and B both produce an automobile part. If a part came from A, the probability that the part is defective is .04. If the part came from B, the probability that it is defective is .05. In a sample of 180 parts, 100 came from A and 80 came from B. (a) What is the probability that a part chosen at random (from the sample) was defective
Answer:
0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.
Step-by-step explanation:
Probability of a defective part:
0.04 of [tex]\frac{100}{180}[/tex], that is, coming from A.
0.05 of [tex]\frac{80}{180}[/tex], that is, coming from B. So
[tex]p = 0.04\frac{100}{180} + 0.05\frac{80}{180} = \frac{0.04*100 + 0.05*80}{180} = 0.0444[/tex]
0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.
A dinner mint costs 85¢ and a toffee costs 73¢. What is the cost of both sweets rounded to the nearest dollar?
Answer:
85 rounded to the nearest dollar would be $1. 73 rounded to the nearest dollar would also be $1
Step-by-step explanation:
C 89. What is the power of 5, so that 1 its value become ? (५ को घाताङ्क 25 कति हुदा त्यसको मान 25 हुन्छ ?) .7
C 89. What is the power of 5, so that 1 its value become ?
The power is 0. because if 0 is tge powwe of any variable or letters the value becomes 1.
let a function F:A➡️B be defined by f(x)=x+1÷2x-1 with A={-1,0,1,2,3,4} and B= {-1,0,4/5,5/7,1,2,3,}.Find the range of f. plzzzz help
Answer:
Range: {-1, 0, 5/7, 4/5, 1, 2}
Step-by-step explanation:
We know that:
f(x) = (x + 1)/(2x - 1)
And:
f: A ⇒ B
where:
A={-1,0,1,2,3,4}
B= {-1,0,4/5,5/7,1,2,3,}
We want to find the range of f(x).
The range of f(x) will be the set of the outputs of f(x) (and because f goes from A to B, we will only take the outputs that belong to B).
Then we only need to evaluate all the values of A in f(x), and see if the output belongs to B.
we have:
f(x) = (x + 1)/(2x - 1)
f(-1) = (-1 + 1)/(2*-1 - 1) = 0 (this does belong to B)
f(0) = (0 + 1)/(2*0 - 1) = -1 (this does belong to B)
f(1) = (1 + 1)/(2*1 - 1) = 2 (this does belong to B)
f(2) = (2 + 1)/(2*2 - 1) = 1 (this does belong to B)
f(3) = (3 + 1)/(2*3 - 1) = 4/5 (this does belong to B)
f(4) = (4 + 1)/(2*4 - 1) = 5/7 (this does belong to B)
So the range of f(x) is the set with all these outputs, which is:
Range: {-1, 0, 5/7, 4/5, 1, 2}
Please help I’m really stuck!!
Step 1: Solve for one variable
---I will be using the first equation and solving for a.
a + c = 405
a = 405 - c
Step 2: Substitute into the other equation
---Now that we have a value for a, we can substitute that value into the second equation. Then, we can solve for c.
12a + 5c = 3950
12(405 - c) + 5c = 3950
4860 - 12c + 5c = 3950
-12c + 5c = -910
-7c = -910
c = 130
Step 3: Plug back into the first equation
---We now know one variable, which means we can plug back into our first equation and solve for the other.
a = 405 - c
a = 405 - 130
a = 275
Answer: 275 adults, 130 children
Hope this helps!
Muka saved 476.60. He gave Kelvin 429.10 and bought T-Shirt for 432.05, how much money he has left over
A toy rocket is shot vertically into the air from a launching pad 9 feet above the ground with an initial velocity of 88 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function
h(t) - 16^2 + 88ft +9. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ____ second(s) after launch.
(Simplify your answer.)
Answer:
Step-by-step explanation:
The position function for this is:
[tex]s(t)=-16t^2+88t+9[/tex]. We can use this equation to find the position (or height) of the rocket at ANY TIME during its flight. I could find out the height of the rocket at 3 seconds by plugging in a 3 for t and solving for s(t); I could find the height of the rocket at 12 seconds by plugging in a 12 for t and solving for s(t), etc.
The first derivative of position is velocity:
v(t) = -32t + 88.
If we are looking for the time the rocket reaches it max height, we need to remember from physics class that this happens when the velocity of the object is at 0. We set the velocity equation equal to 0 then and solve for t:
0 = -32t + 88 and
-88 = -32t so
t = 2.75 seconds. This means that 2.75 seconds after the rocket is launched, it reaches its max height. In order to find what that max height is we plug 2.75 into the position equation for t and solve:
[tex]s(2.75)=-16(2.75)^2+88(2.75)+9[/tex] to get that
s(2.75) = 130
The max height is 130 feet and it reaches this point at 2.75 seconds into its motion.
