For finding the compound Interest first we need to get the amount and then subtract the value of principal from amount
Calculation Begins
Principal = 5000, Rate of Interest = 5%, Time = 2 yrs
[tex] \looparrowright \sf{A = P(1 + \frac{r}{100} )^{n} } \\ \\ \looparrowright \frak{ {\sf A} = 5000(1 + \frac{5}{100} )^{2} } \\ \\ \looparrowright \frak{ {\sf A} = 5000(1 + \frac{1}{20} )^{2} } \\ \\ \looparrowright \frak{ {\sf A} = 5000( \frac{21}{20})^{2} } \\ \\ \looparrowright \frak{ {\sf A} =5000 \times \frac{441}{400}} \\ \\ \looparrowright \frak{ {\sf A} = 12.5 \times 441} \\ \\\looparrowright \frak{ {\sf A} = 5152.5} [/tex]
Hence the amount is 5152.5
Compound Interest = Amount - Principal
= 5152.5 - 5000 = 152.5
152.5 is the Compound InterestDenali
, North America's highest peak, is 20,310 feet above sea level. Death Valley is
282 feet below sea level. What is the difference between their two positions?
Answer:
above the sea level means height than the sea and below sea level means lower than sea height
This is Quadratics.
(5n−5)(2+2n)
Answer: 10n^2 - 10
Step-by-step explanation:
(5n - 5)(2+2n) becomes (5n-5)(2n+2)
= (5n)(2n) + (5n)(2) + (-5)(2n) + (-5)(2)
= 10n^2 - 10
One of the legs of a right triangle measures 16cm and its hypotenuse measures 13 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
9.3
Step-by-step explanation:
Four friends want to share two large
pizzas equally. Each pizza is cut into
ten slices. How many slices will each
person get?
Answer: 5
Step-by-step explanation:
2 pizzas ten slices eatch, so 20 slices. 20 slices devided by 4 is five. :)
Solve x + 5= -7
I need this ASAP
plese help me fast I will mark you brainlist
[tex]\\ \sf\longmapsto 5x+5+4x-5=180[/tex]
[tex]\\ \sf\longmapsto 5x+4x+5-5=180[/tex]
[tex]\\ \sf\longmapsto 9x=180[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{180}{9}[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
y=x=20z=5x+5=5(20)+5=100+5=105Step-by-step explanation:
hope this helps u ✌️✌️
Make mister as brainliest
Someone please help me.
This pool has a deep end and a shallow end.The pools perimeter is 70 ft.Hiw wide is the deep end,d?
Work Shown:
L = d+9 = length along the horizontal
W = 10 feet = width along the vertical
P = 2(L+W) = perimeter of rectangle = 70 feet
70 = 2(d+9+10)
70/2 = d+19
35 = d+19
d+19 = 35
d = 35-19
d = 16
The deep end is 16 feet wide
Solve the following system of equations, using any method. Express your answers in one decimal place.
Answers:
x = 0y = 6.9The value of x is exact. The y value is approximate.
==================================================
Explanation:
Let's subtract the equations straight down.
The x terms subtract to -22x since 9x-31x = 22xThe y terms go away because 7y-7y = 0The terms on the right hand side subtract to 0After doing those three sets of subtractions, we have the new equation -22x = 0. This solves to x = 0 after dividing both sides by -22.
Plug this x value into any of the two original equations to solve for y
9x + 7y = 48
9(0) + 7y = 48
7y = 48
y = 48/7
y = 6.857 approximately
y = 6.9
5 less than 3 times a number is 7. How would I write this as an equation
Answer:
The equation would be 5-3x=7
Step-by-step explanation:
5 less than indicates subtraction, and 3 times a number indicates both values being multiplied with each other, so it's 3x. Hope that helped.
6 + [-25 = (-3 + 2. 1)]
Answer:
6+[25=(-0.9)]
6+[-22.5]
-16.5
Step-by-step explanation:
the answe of this question will be -16.5
is 2π greater than √44
9514 1404 393
Answer:
no
Step-by-step explanation:
2π ≈ 6.28
√44 ≈ 6.63
2π < √44
i need help with this pls
Ana sold $234,654 in sales. She earns a 14.5% commission on all sales. Find her commission.
Step-by-step explanation:
$334,654 ×14,5% = $34,024.83
therefore that is your answer
2. An investment firm purchases a $65,000 CD from a bank at 2%. How much is the investment worth
(rounded to the nearest cent) at the end of 4 years if interest is compounded quarterly?
Answer:
$70.399.62
Step-by-step explanation:
To find the final amount, we have to use the compound interest formula
A = P(1 + r/n)ⁿˣ
A = Final amount
P = Starting amount (65,000)
r = rate (0.02)
n = time applied (4 since it's quarterly, meaning 4 times every year)
x = years (4)
Our equation will look like this
A = 65,000(1 + 0.02/4)¹⁶
You should use a calculator to plug to solve 65,000(1 + 0.02/4)¹⁶
A = 70,399.62483294155
Please someone help
[tex]\begin{array}{l}\begin{cases} \begin{array}{l}\sin \alpha =\frac{x}{12} \Leftrightarrow x=12\sin \alpha \end{array}\\\cos \alpha =\frac{y}{12} \Leftrightarrow y=12\cos \alpha \end{cases}\\\\\text{Thus,\ the\ area\ is}\\\\A=\frac{xy}{2} =\frac{12\sin \alpha \cdotp 12\cos \alpha }{2}\\\\\Longrightarrow A=72\sin \alpha \cos \alpha \end{array}[/tex]
D
At the 2010 Olympics in Vancouver, Yu-Na Kim scored 226.56 points in woman's figure skating. Akiko Suzuki scored 181.44 points in the event. About how many more points did Yu-Na Kim score than Akiko Suzuki?
Answer:
5 more matches was won by yu-na kim
Hero and his coworkers had lunch at a restaurant near their work and 18% tip on the bill was $10.08 how much was the bill not including the tip!
Answer:
$8.27
Hope this is right <3
What is the next term in the geometric sequence? 1,4,-16,64
Answer:
256
Step-by-step explanation:
1,4,16,64,256
As 4 is being multiplied in each case.
step by step explaining
how to multiply 2 digit number to 2 digit number..
-31+(-42)=
38+(-43)=
Answer:
-31+(-42)= -31-42 = -73
38+(-43)= 38-43 = -5
(-) - (-) = +
(-)+(-) = +
(-)+(+) = -
What is the 8th number in the arithmetic sequence 26, 31, 36, 41, 46...
Answer 61
Step-by-step explanation:
The answer is 61 bc the pattern is +5
Answer:
26, 31, 36, 41, 46, 51, 56, 61
the eighth number is 61.
Step-by-step expanation:
How do you get 2.5 out of 20/8
9514 1404 393
Explanation:
If you can't operate a calculator, perhaps you can do long division. The attachment shows the work for that.
__
[tex]\dfrac{20}{8}=\dfrac{5\cdot4}{2\cdot4}=\dfrac{5}{2}\\\\=\dfrac{5\cdot5}{2\cdot5}=\dfrac{25}{10}=2.5[/tex]
We assume that you know dividing by 10 moves the decimal point one place left.
express 8% as a decimal fraction
Hello :D
The answer is 0.08
I hope this helps :)
someone plz help radius is 1.5 ft
Answer:
Area =
[tex]\pi {r}^{2} [/tex]
=3.14×1.5^2
=3.14×2.25
=7.065
Hence the area of circle is 7.065.
what is 174 dived by 6 and how u solved it
Answer:
Step-by-step explanation:
187 divided by 7 is 6.5
Answer: 29
Step-by-step explanation:
174 = dividend
6 = divisor
The divisor (6) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top Multiply the divisor by the result in the previous step (6 x 0 = 0) and write that answer below the dividend. Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.
Move down the 2nd digit of the dividend (7) like this:
0
6 ⟌ 1 7 4
- 0
1 7
Multiply the divisor by the result in the previous step (6 x 2 = 12) and write that answer at the bottom:
0 2
6 ⟌ 1 7 4
- 0
1 7
1 2
Subtract the result in the previous step from the number written above it. (17 - 12 = 5) and write the answer at the bottom.
0 2
6 ⟌ 1 7 4
- 0
1 7
- 1 2
5
Move down the last digit of the dividend (4) like this:
0 2
6 ⟌ 1 7 4
- 0
1 7
- 1 2
5 4
Multiply the divisor by the result in the previous step (6 x 9 = 54) and write the answer at the bottom:
0 2 9
6 ⟌ 1 7 4
- 0
1 7
- 1 2
5 4
5 4
Subtract the result in the previous step from the number written above it. (54 - 54 = 0) and write the answer at the bottom.
0 2 9
6 ⟌ 1 7 4
- 0
1 7
- 1 2
5 4
- 5 4
0
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 174 divided by 6 calculated using Long Division is:
29
0 Remainder
Its long but your welcome :)
a community center is trying to raise $1680 to purchase exercise equipment. the center is hoping to receive equal contributions from members of the community. write and algebraic expression to determine how much will be needed from each person if n people contribute. Then evaluate the expression for 10, 12, 14, or 16 people.
Lets find f(n) formula
[tex]\boxed{\sf f(n)=\dfrac{1680}{n}}[/tex]
Now
[tex]\\ \sf\longmapsto f(10)=\dfrac{1680}{10}=168[/tex]
[tex]\\ \sf\longmapsto f(12)=\dfrac{1680}{12}=140[/tex]
[tex]\\ \sf\longmapsto f(16)=\dfrac{1680}{16}=105[/tex]
[tex]\\ \sf\longmapsto f(14)=\dfrac{1680}{14}=120[/tex]
Geometry. Need help on how to solve G and H
Answer:
G) tan 60 = opp / adj = 30 / x
which equals
1.7321 = 30 / x
x = 30 / 1.7321
x = 17.3200161653
H) secant = hyp / adj
secant 30 = 16 / x
1.1547 = 16 / x
x = 16 / 1.1547
x = 13.8564
Here's a good site for trig functions : http://www.1728.org/trigcalc.htm
Step-by-step explanation:
The climactic moment in the film "The Eggplant That Ate New Jersey" comes when the brilliant young scientist announces his discovery of the equation for the volume of the eggplant: V(fe) = 3.53 X 10-2 exp(2?) where t is the time in hours from the moment the vampire injected the eggplant with a solution prepared from the blood of the beautiful dental hygienist.
(a) What are the units of 3.53 X 10-2 and 2?
(b) The scientist obtained the formula by measuring V versus t and determining the coefficients by linear regression. What would he have plotted versus what on what kind of coordinates? What would he have obtained as the slope and intercept of his plot?
(c) The European distributor of the film insists that the formula be given for the volume in m3 as a function of t(s). Derive the formula.
(a) Concerning the coefficients of the equation for the volume of the eggplant ( [tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex]), the units of the coefficients with values [tex]3.53 \times 10^{-2}[/tex] and 2 are cubic feet and [tex]\frac{1}{h^{2}}[/tex], respectively.
(b) Regarding the determination of the coefficients by linear regression, the scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.
(c) After the solicitation of the European distributor of the film, the new formula is [tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex], where volume is in cubic meters and time is in seconds.
Note - The statement reports typing mistakes. We present the correct statement below:
The climatic moment in the film "The Eggplant that Ate New Jersey" comes when the brilliant young scientist announces his discovery of the equation for the volume of the eggplant: [tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex], where [tex]t[/tex] is the time in hours from the moment the vampire injected the eggplant with a solution prepared from the blood of the beautiful dental hygienist.
(a) What are the units of [tex]3.53\times 10^{-2}[/tex] and [tex]2[/tex]?
(b) The scientist obtained the formula by measuring [tex]V[/tex] and [tex]t[/tex] and determining the coefficients by linear regression. What would he have plotted versus what on what kind of coordinates? What would he have obtained as the slope and intercept of his plot?
(c) The European distributor of the film insists that the formula must be given for the volume in cubic meters ([tex]m^{3}[/tex]) as a function of time, in seconds. Derive the formula.
(a) In this exercise, we must make use of principles for dimensional analysis. We know that the equation for the volume of the eggplant is represented by:
[tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex] (1)
Dimensionally speaking, we have the following case:
[tex][L]^{3} = [A]\cdot e^{[B]\cdot [t]^{2}}[/tex] (2)
By direct inspection and some algebraic handling, we conclude that:
[tex][A] = [L]^{3}[/tex]
[tex][B] = [t]^{-2}[/tex]
Therefore, the units of [tex]3.53 \times 10^{-2}[/tex] and 2 are cubic feet and [tex]\frac{1}{h^{2}}[/tex], respectively.
(b) The curve fit for the exponential expression used by the scientist is of the form:
[tex]V = A\cdot e^{B\cdot t^{2}}[/tex] (3)
If we apply logarithms on both sides of the expression above, then we have the following form:
[tex]\ln V = \ln A\cdot e^{B\cdot t^{2}}[/tex]
[tex]\ln V = \ln A + B\cdot t^{2}[/tex] (4)
The scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.
(c) An hour equals 3600 seconds and a cubic feet equals 0.028 cubic meters. Hence, we can adapt (1) to fulfill the requirements of the European film distributor by using the following conversions:
[tex]t' = 3600\cdot t[/tex] (5)
[tex]V' = 0.028\cdot V[/tex] (6)
Where:
[tex]t[/tex] - Time, in hours.[tex]t'[/tex] - Time, in seconds. [tex]V[/tex] - Volume, in cubic feet.[tex]V'[/tex] - Volume, in cubic meters.By applying (5) and (6) in (1), we have the resulting formula:
[tex]V' = 0.028\cdot [3.53\times 10^{-2}\cdot e^{2\cdot \left(\frac{t'}{3600} \right)^{2}}][/tex]
[tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex]
The new formula is [tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex], where volume is in cubic meters and time is in seconds.
We kindly invite to check this question on exponential functions: https://brainly.com/question/2456547
After a small online search, I've found that the volume equation is:
[tex]V[ft^3] = 3.53 \cdot10^{-2} \cdot exp(2 \cdot t^2)[/tex]
a) We want to see what are the units of the first factor:
[tex]3.53 \cdot10^{-2}[/tex]
You can see that the volume is in cube feet, and the only part in the equation that can have units is this one, so the units of this factor should be cube feet.
b) On the vertical coordinate he would see the volume and on the horizontal coordinate he would see the time.
The graph of this function is an increasing exponential function, that grows slow at the beginning and then grows faster.
c) Remember that the term with the units is:
[tex]3.53 \cdot10^{-2}[/tex]
So we should write this as:
[tex]3.53 \cdot10^{-2} ft^3[/tex]
Now we know that:
[tex]1m^3 = 35.3 ft^3\\\\1 = \frac{1 m^3}{35.3 ft^3}[/tex]
Now we can multiply our measure by this to get:
[tex]3.53 \cdot10^{-2} ft^3 = ( \frac{1 m^3}{35.3 ft^3})*(3.53 \cdot10^{-2} ft^3) = 0.1 m^3[/tex]
Then the equation is:
[tex]V = 0.1m^3\cdot exp(2 \cdot t^2)[/tex]
If you want to learn more you can read:
https://brainly.com/question/172096
YALL HELP OMG FOR ALL OF THEM MUST SHOW WORK ! 35POINTS MUST SHOW WORK FOR ALL.
Answer:
1) answer 3)88 students for 4 classes
10)answer=285parts
2. The equation of a circle is x2 + y2 – 4x + 6y – 77 = 0.
a) Find the x-coordinates of the points A and B where the circle intersects the x-axis.
b) Find point of intersection of the tangents to the circle at A and B.
a) The x-coordinates of the points A and B are [tex]x_{A} = 11[/tex] and [tex]x_{B} = -7[/tex].
b) The point of intersection of the tangents to the circle at A and B is [tex](x,y) = (2, 27)[/tex].
a) In this part we simplify the equation of the circle and solve for [tex]x[/tex] to determine the coordinates associated to the required points:
The coordinates of the two points so that circle intersects the x-axis, occurs when the following condition is met:
[tex]f(x, 0) = 0[/tex] (1)
Where [tex]f(x,y)[/tex] is in implicit form.
If we know that the equation of the circle is [tex]x^{2} + y^{2} - 4\cdot x + 6\cdot y - 77 = 0[/tex] and [tex]y = 0[/tex], then the reduced equation is:
[tex]x^{2} - 4\cdot x - 77 = 0[/tex] (2)
And we obtain the x-coordinates of the points by factoring (2):
[tex](x-11) \cdot (x + 7) = 0[/tex]
The x-coordinates of the points A and B are [tex]x_{A} = 11[/tex] and [tex]x_{B} = -7[/tex].
b) Lines are defined by both slope and intercept. Slope is defined by implicit differentiation and intercept is found by equation of the line.
Given that [tex]A(x,y) = (11, 0)[/tex] and [tex]B(x,y) = (-7, 0)[/tex], we determine line equations corresponding to each tangent line:
Slope
[tex]2\cdot x + 2\cdot y \cdot \dot y - 4 + 6\cdot \dot y = 0[/tex]
[tex](2\cdot y + 6)\cdot \dot y = 4 - 2\cdot x[/tex]
[tex]\dot y = \frac{2 - x}{y + 3}[/tex]
Point A
[tex]\dot y = \frac{2-11}{0 + 3}[/tex]
[tex]\dot y = -3[/tex]
Point B
[tex]\dot y = \frac{2-(-7)}{0 + 3}[/tex]
[tex]\dot y = 3[/tex]
Intercept
Point A ([tex]A(x,y) = (11, 0)[/tex], [tex]\dot y = -3[/tex])
[tex]b = y - m\cdot x[/tex]
[tex]b = 0 - (-3)\cdot (11)[/tex]
[tex]b = 33[/tex]
Point B ([tex]B(x,y) = (-7, 0)[/tex], [tex]\dot y = 3[/tex])
[tex]b = y - m\cdot x[/tex]
[tex]b = 0 - 3\cdot (-7)[/tex]
[tex]b = 21[/tex]
The equations of the lines tangent to the circle are:
[tex]y = -3\cdot x +33[/tex] (3)
[tex]y = 3\cdot x +21[/tex] (4)
The point of intersection is the solution of this system of linear equations:
[tex](x,y) = (2, 27)[/tex]
The point of intersection of the tangents to the circle at A and B is [tex](x,y) = (2, 27)[/tex].
We kindly invite you to see this question on circles: https://brainly.com/question/23988015