Given:
Initial value = 400
Interest rate = 5% compounded quarterly.
To find:
The function that gives you the amount of money in dollars, J(t) in t years after the initial deposit.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is principal, r is the rate of interest in decimals, n is the number of times interest compounded in an year and t is the number of years.
The interest rate is 5% compounded quarterly. So, r=0.05 and n=4.
Substituting [tex]P=400,\ r=0.05,\ n=4[/tex] in the above formula, we get
[tex]A=400\left(1+\dfrac{0.05}{4}\right)^{4t}[/tex]
[tex]A=400\left(1+0.0125\right)^{4t}[/tex]
[tex]A=400\left(1.0125\right)^{4t}[/tex]
The required function notation is:
[tex]J(t)=400\left(1.0125\right)^{4t}[/tex]
Therefore, the amount of money in dollars, J(t) in t years after the initial deposit is [tex]J(t)=400\left(1.0125\right)^{4t}[/tex].
2. Find the base of a triangle which has an area of 2 1/4 square inches, and a height of 1/8 in.
Answer:
36 inches
Step-by-step explanation:
Given data
Area of triangle =2 1/4 square inches
Area =9/4 square inches
Height of triangle =1/8 inches
We know that the expression for the area of triangle is
Area = 1/2Base *Height
9/4=1/2*Base *1/8
9/4=Base/16
Cross multiply
16*9=Base*4
144=Base*4
Base =144/4
Base=36 inches
Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the next degree, the smallest angle of the triangle. (A)35° (B)36° (C)37° (D)38° (E)53°
[tex]\boxed{Given:}[/tex]
Length of the perpendicular ( opposite ) = 6 cm.
Length of the base ( adjacent ) = 8 cm.
[tex]\boxed{To\:find:}[/tex]
The smallest angle of the triangle.
[tex]\boxed{Solution:}[/tex]
[tex]\sf\purple{C.\:37°}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
In a right-angled triangle, if two sides are given, the measure of the unknown angle can be known.
Since the value of opposite and adjacent sides are given, we use the tangent formula.
tan θ = [tex]\frac{opposite}{adjacent}[/tex]
✒ tan θ = [tex]\frac{6 \: cm}{8 \: cm}[/tex]
✒ θ = [tex]{tan}^{ - 1}[/tex] (0.75)
✒ θ = 36.9°
✒ θ = 37°
Now let us find the other unknown angle 'x'.
We know that,
Sum of angles of a triangle = 180°
✒ 37° + x + 90° = 180° (90° since it is a right-angled triangle)
✒ x + 127° = 180°
✒ x = 180° - 127°
✒ x = 53°
Therefore, the three angles of the triangle are 37°, 53° and 90°.
Hence, the smallest angle is 37°.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
Please help me! That would be great if you can.
Does this app actually work for ya'll????
Answer:
Yessssss!
Step-by-step explanation:
Answer:
yess!! look up your question before you ask it :))))
thx for the points too hehe
Pleasee help with this question asap I’m begging y’all
==================================================
Work Shown:
[tex]y = \frac{4x+30}{x+5}\\\\y = \frac{4x+20+10}{x+5}\\\\y = \frac{(4x+20)+10}{x+5}\\\\y = \frac{4(x+5)+10}{x+5}\\\\y = \frac{4(x+5)}{x+5}+\frac{10}{x+5}\\\\y = 4+\frac{10}{x+5}\\\\[/tex]
Therefore, a = 10
--------------
As an alternative approach, we could work in reverse like this:
[tex]y = 4+\frac{a}{x+5}\\\\y = 4*\frac{x+5}{x+5}+\frac{a}{x+5}\\\\y = \frac{4(x+5)}{x+5}+\frac{a}{x+5}\\\\y = \frac{4(x+5)+a}{x+5}\\\\y = \frac{4x+20+a}{x+5}\\\\[/tex]
Then notice that the 20+a must be 30, so solving 20+a = 30 leads to a = 10
--------------
As yet another alternative approach (well I suppose it's actually 2 extra approaches) we could use either polynomial long division or synthetic division. Either way, you should end up with a remainder of 10, which corresponds directly to a = 10
Which of the following is equivalent to the expression below?
log 4-log 24
Answer:
log (1/6)
Step-by-step explanation:
Using the property that log a - log b = log(a/b), we get that log 4 - log 24 = log(4/24) = log (1/6)
I hope this helps! :)
Mr. Cox filled up his car with gas yesterday. He paid $24 for 6 gallons of gas.
How much would 10 gallons of gas cost?
Answer:
40 gallons of gas
Step-by-step explanation:
HELPP PLEASEEE thanks!
Answer:
about 1587
that is the answer to the question
Step-by-step explanation:
I just typed it in a calculator
Answer: D
Step-by-step explanation:
Area is pi x r^2
Diameter is 2r
46.7/2 = 23.35
3 x 23.35^2 = 1635.67 or closest to D
Factor the expression x^2+6x+8
84784+24849+748429+123456
Answer:
981,518
Step-by-step explanation:
Have a nice day :)
the function f is given by f(x) = (x - 6)(x - 2). Multiply out the factors using the area model or distributive property. What expression do you get
Get–Around Cab Company charges $2.50 upon entry and $2 per mile. Write the function that represents the cost C of a ride of m miles. C(m) = m +
Answer:
C(m) = 2.50 + 2m
Step-by-step explanation:
The fixed charge = charge per entry = $2.50
Charge per mile = $2
Function which represents the cost of a ride of m miles ;
Cost for m miles, C(m)
C(m) = charge per entry + cost per mile * number of miles
Where, number of miles = m
C(m) = 2.50 + 2m
Answer:
C(m) =2 m + 2.5
Step-by-step explanation:
I DID IN ED
whats the anserw plz (8x+10y)+(-4x-3y) i need help!!!
Answer:
me :- mighty assassin-,-
xd
If p and q vary inversely and p is 9 when q is 16, determine q when pis equal to 18.
Answer:
[tex]p \: \alpha \: \frac{1}{q} \\ p = \frac{k}{q} \\ k \: is \: a \: constant \: of \: proportionality \\ when \: p \: is \: 9.. \: \: q = 16 \\ 9 = \frac{k}{16} \\ k = 144 \\ when \: p \: is \: 18 : \\ 18 = \frac{144}{q} \\ q = \frac{144}{18} \\ q = 8[/tex]
Which is the correct answer!!!
Answer:
the answer is the alphabet a
identify the precision unit for the measuring tool below
What is the total Jeff has a painted
A. 180 square inches
B.40 square inches
C.100 square inches
D.90 square inches
Answer:
180 square inches
Step-by-step explanation:
let separate the figure and form two rectangles
first rectangle
length = 10 in
breadth = 9 in
let's find its area
area =l*b
=10*9
=90 in.^2
second rectangle
length = 15 in.
breadth = 6 in.
area =l*b
=15 *6
=90 in.^2
area of a whole he painted =area of first rectangle + area of second rectangle
=90 + 90 in.^2
=180 in .^2
Solve for xxx in the diagram below.
PLS HELP ASAPPPPPPPPPPPPPP
Answer:
G
Step-by-step explanation:
36+36=72
180-72=108
360-(108×2)
144
144÷2
72
Let a=2 and b=1, find the value of 2a + 3b
Answer:
7 is a answer
Step-by-step explanation:
2a+3b
2×2+3×1
4+3
7
hope it helps....
[tex] \sf a = 2,\: b = 1[/tex]
[tex] \sf Q) \:2a + 3b = {?}[/tex]
[tex] \sf \implies 2a + 3b[/tex]
[tex] \sf \implies 2(2) + 3(1)[/tex]
[tex] \sf \implies 4 + 3[/tex]
[tex] \sf \implies 7[/tex] is the required answer.
Which transformation is a translation?
Answer:
i don't know but o o o o right e o right e auto park
Answer:
4234324tgfgdfgdgd
Step-by-step explanation:
The graph of f(x) = |x – h| + k contains the points (–6, –2) and (0, –2). The graph has a vertex at (h, –5). Describe how to find the value of h. Then, explain how this value translates the graph of the parent function.
Answer:
ty
Step-by-step explanation:
mtj
Which is a true statement?
A. m^2– n^2 = (m-n)(m-n)
B. m^2 + n² = (m + n) (m + n)
c. m^3 - n^3= (m - n) (m^2+ mn + n^2)
D. m^3+ n^3 = (m+n)(m^2 + mn +n^2)
Answer:
C-true
Step-by-step explanation:
A-false
B-false
C-true
D-false
used substitution
The product of the two expressions (m - n)(m + n) gives x² - 4
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the expression (m - n)(m + n):
Multiplying the two expressions gives:
m² + mn - mn - n²
This gives:
m² - n²
The product of the two expressions (m - n)(m + n) gives x² - 4
Find out more on equation at: https://brainly.com/question/2972832
#SPJ2
Which step in the construction of copying a line segment ensures that the new line segment has the same length as the original lie segment?
Answer:
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
Step-by-step explanation:
Here are the steps I think you probably will go through.
1. Draw a line that is longer than the segment but shorter than the width of the page.
1a. Make sure this line is at least 1/2 inch from the left hand side.
2. Use a compass to measure the length of the original segment. Never use a ruler. Rulers do not exist in pure geometry.
3. Measure out the distance on the line you just drew with the compass. One end is on the left hand edge and the other end (the pencil end) is marking the segment so it is the same length as the compass. You are done.
The key step either two or three.The steps to copy a line segment are given below:
1. Lets start with a line segment AB that we have to copy.
2. Now mark a point C. below or above AB, that will be one endpoint of the new line segment.
3. Now, put the compass tip on point A of the line segment AB.
4. Spread the compass up to point B, so as the compass width is equal to length of AB.
5. Without changing the compass width, now place the compass tip on the point C that you made in step 2.
6. Now, draw an arc roughly without changing the compass settings. Mark that point D. This will form the new line segment.
7. Draw a line from C to D.
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
Use the tree diagram below to answer the question how many outcomes are there that contain blue shirts
Answer:
3
Step-by-step explanation:
i got it right on my test
Which of the following is the value of 2x3 + 5x + 9 wher
x= 10?
Answer:
Ans = 65
Step-by-step explanation:
2x3 + 5x + 9
2x3 + 5x10 + 9
6 + 50 + 9
56 + 9
= 65
7.865 rounded to the nearest whole number
Answer:
8
Step-by-step explanation:
Since the first decimal place is greater than 5, it rounds to 8, because 8 is the next whole number to 7.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Is -33.1 a whole number
Answer:
No
Step-by-step explanation:
This is because it's part of a whole. It has to be an integer to be whole.
Answer:
no because Whole numbers include positive integers along with 0 and also Whole numbers include natural numbers that begin from 1 onwards and also this a negative are not considered as a whole number so its a no
Step-by-step explanation:
(NEED HELP ASAP) The map is similar to the map from the previous unit. The x-axis runs from -110 to +110. For the y-axis, the values run from -80 to +80. Each tick mark on the axes has the value of 5 m (so each square on the grid represents 10 m). The additional path, Archimedes Alley has been added to the map.
The standard form for one of the three equations is 9x - 20y - 900 = 0.
i) Determine the x- and y-intercepts for the line.
ii) Identify its equivalent equation in slope y-intercept form.
iii) Explain how you chose the equation in slope y-intercept form.
Answer the question.
Answer:
[tex] \frac{8 {x}^{2} y}{6 {x}^{2} {y}^{2} } \\ = \frac{8×3}{6 {y}^{2} } \\ = \frac{24}{6 \times {3}^{2} } \\ = \frac{4}{9} [/tex]
