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
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
Need help please and thanks :)
Answer:
4 digits keep repeating
7569
[tex] \boxed{ \boxed{explanation}}[/tex]
By observing the given number with it's decimal expansion, we can say that there are four numbers which are repeating after the decimal.
i.e 7569.
So, 4 is the correct answer
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.
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.
The relative frequency table below displays the proportion of 40 residents in an apartment complex who prefer certain social media sites.
Upstart, 0.10; Aster, 0.25; Babble, 0.35; Techy, 0.30.
Which of the following is the corresponding frequency table?
Upstart, 10; Aster, 25; Babble, 35; Techy, 30.
Upstart, 8; Aster, 12; Babble, 10; Techy, 10.
Upstart, 4; Aster, 14; Babble, 10; Techy, 12.
Upstart, 4; Aster, 10; Babble, 14; Techy, 12.
Answer:
D
Step-by-step explanation:
multiply each number by 40
ex:
.10x40=40
Answer:d
Step-by-step explanation:
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
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:
express 8% as a decimal fraction
Hello :D
The answer is 0.08
I hope this helps :)
A farmer sold 53.2 pounds of carrots and 29.4 pounds of aspargus to a restaurant. How many pounds of these two vegetables did the restaurant buy?
Answer:
82.6
Step-by-step explanation:
First you add 53 and 29 which equals 82 then you do 4 plus 2 which equals 6 and so the answer is 82.6
Choose the best answer. If necessary, use the paper you were given.
Question
Joanna wants to tile a square floor that measures 8 feet on one side. If each tile is a 6-inch square, how
many tiles will she need for the floor?
O 64 tiles
O 192 tiles
O 256 tiles
O 324 tiles
The number of tiles needed to cover the floor is 256 tiles.
The given parameter:
the length of a side of the floor = 8 feet
the length of a side of the tile, = 6-inches
To find:
how many tiles she will need for the floorConvert the unit of the floor to inches
1 ft = 12 inches
8 ft = (8 x 12) = 96 inches
The area of the floor = 96 in x 96 in
The area of the floor = 9216 in²
The area of a tile = 6 in x 6 in
The area of a tile = 36 in²
The number of tiles needed to cover the floor:
[tex]number \ of \ tiles = \frac{Area \ of \ floor}{Area \ of \ a\ tile} = \frac{9216}{36} = 256 \ tiles[/tex]
Thus, the number of tiles needed to cover the floor is 256 tiles.
Learn more here: https://brainly.com/question/17182640
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.
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. :)
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
Denali
, 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
evaluate 7m + 3mn when m=8 and n=14
Answer:
392
Step-by-step explanation:
7(8) + 3(8)(14)
56 + 336
=392
*Brackets mean to multiply.
Simplify the expression. 10 (n^2+ n) - 6 (n^2 - 2)
please mark this answer as brainlist
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
-31+(-42)=
38+(-43)=
Answer:
-31+(-42)= -31-42 = -73
38+(-43)= 38-43 = -5
(-) - (-) = +
(-)+(-) = +
(-)+(+) = -
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
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.
A baby elephant that is 4 ft tall casts a
shadow that is 6 ft long. Find the length
of the shadow that a 6 ft lawn ornament
casts.
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:
i need help with this pls
Evaluate the expression for u = –8. Simplify your answer. –8 u
9514 1404 393
Answer:
64
Step-by-step explanation:
Put the value where the variable is and do the arithmetic.
-8u = -8(-8) = 64
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
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
Jessica, an experienced bungee jumper, leaps from a tall bridge and falls toward the river below. The bridge is 200 feet above the water and Jessica's bungee cord is 130
feet long unstretched. When will Jessica's cord begin to stretch? Round your answer to two decimal places
Answer:
70 feet above the water will it begin to stretch.
Step-by-step explanation:
200 - 130 = 70
20 points help quick
Answer:
6s-36 is the answer . Hope this helps you.
Answer:
6(x-6) = 6x-36
Step-by-step explanation:
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]