Answer:
y=-2/5x+21/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-5)/(3-(-2))
m=-2/(3+2)
m=-2/5
y-y1=m(x-x1)
y-5=-2/5(x-(-2))
y-5=-2/5(x+2)
y=-2/5x-4/5+5
y=-2/5x-4/5+25/5
y=-2/5x+21/5
How much must you deposit in an account that pays 6.25% interest, compounded annually, to have a balance of $700 after two years?
= $
The compound interest is applied to the remaining balance in the account
each subsequent year.
The amount that must be deposited is approximately $620.07Reasons:
The given compound interest rate, r = 6.25% = 0.0625
The balance in the account after 2 years, A = $700
Required:
The required deposit, P, that gives the given account balance after 2 years.
Solution:
The following is the compound interest formula to use;
[tex]A = \mathbf{P \times \left(1+r \right)^{ t}}[/tex]Where;
t = 2 years
We get;
[tex]\displaystyle P = \mathbf{ \frac{A}{(1 + r)^t}}[/tex]
Which gives;
[tex]\displaystyle P = \frac{700}{(1 + 0.0625)^2} \approx \mathbf{620.07}[/tex]
The amount that must be deposited to give $700 after 2 years is P ≈ $620.07Learn more about compound interest here:
https://brainly.com/question/10028292
givien the function 6x+6y=5 rearrange the equation so that x is the independant varible
Answer:
so 6x = -6y + 5
divide by 6
x = 5
Step-by-step explanation:
What is the largest integer whose cube is less than 10,000?
Answer:
8 512 =8 X 8 X 8
Step-by-step explanation:
find the divergence and curl of the vector
F=(3x²y² +2z)i + (3x² + y +yz )j - (3x²z² +2yx + xyz)k
Divergence:
div(F) = ∂(3x²y² + 2z)/∂x + ∂(3x² + y + yz)/∂y - ∂(3x²z² + 2yx + xyz)/∂z
div(F) = 6xy² + 1 + z - 6x²z - xy
Curl:
curl(F) = [∂(3x² + y + yz)/∂z + ∂(3x²z² + 2yx + xyz)/∂y] i
… … … … … - [∂(3x²y² + 2z)/∂z + ∂(3x²z² + 2yx + xyz)/∂x] j
… … … … … + [∂(3x²y² + 2z)/∂y - ∂(3x² + y + yz)/∂x] k
curl(F) = (-xz - 2x - y) i + (6xz² + yz + 2y + 2) j + (6x - 6x²y) k
Mr. Schnee is refinancing his home. His loan officer has presented him with the following two offers; it is worth noting that Mr. Schnee is expecting to move back home to Michigan in five years. Using a system of linear equations, help Mr. Schnee decide which offer to take in order to maximize his benefit. Mr. Schnee has already determined that he definitely wants to refinance as he is currently paying $1,744.67.
4.5% Interest Rate for 30 years with a monthly payment of $1,266.71 with $256 Closing Costs
4.0% Interest Rate for 30 years with a monthly payment of $1,193.54 with $10,362 in Closing Costs
The option that best suits him is 4.0% Interest Rate for 30 years with a monthly payment of $ 1,193.54 with $ 10,362 in Closing Costs.
Given that Mr. Schnee is refinancing his home, and his loan officer has presented him with two offers, to determine which offer should he take in order to maximize his benefit, the following calculation must be performed:
A) 4.5% Interest Rate for 30 years with a monthly payment of $ 1,266.71 with $ 256 Closing Costs
1,266.71 x 30 x 12 + 256 = X
1,266.71 x 360 + 256 = X
456,015.60 + 256 = X
456,271.60 = X
B)4.0% Interest Rate for 30 years with a monthly payment of $ 1,193.54 with $ 10,362 in Closing Costs
1,193.54 x 30 x 12 + 10,362 = X
1,193.54 x 360 + 10,362 = X
429,674.40 + 10,362 = X
440,036.40 = X
Therefore, the option that best suits him is 4.0% Interest Rate for 30 years with a monthly payment of $ 1,193.54 with $ 10,362 in Closing Costs.
Learn more about maths in https://brainly.com/question/25866144
Question 10 of 10
To model some data, Pat ran an exponential regression and found the
regression equation to be y = 0.496.1.3%,
The scatterplot and residual plot are shown.
Scatterplot
Residual plot
y
4
2
Select the true statements.
O A. The model is a good fit because the patterns in the plots are both
curves.
B. The points in the scatterplot follow a line, so a linear model would
fit the data better.
O C. The residual plot changes direction, so a quadratic model would
fit the data better.
D. The model is not a good fit because there is a pattern in the
residual plot.
Answer:
B.)The points in the scatterplot follow a line, so a linear model would fit the data better
A.)The model is not a good fit because there is a pattern in the residual plot.
Step-by-step explanation:
The linear model would best fit the scatter plot while the quadratic model would fit the residual plot. The true statements are: B and C.
What is a Linear Model and a Quadratic Model?A linear model is appropriate for data points that lie along a straight line on graph. If the line is not straight but curved and changes direction, a quadratic model is a better model for such data.
Thus, since the data points on the scatter plot are on a straight line, a linear model would fit the data.
For the residual plot that changes direction, a quadratic model would better fit the data.
The true statements are therefore: B and C.
Learn more about linear and quadratic model on:
https://brainly.com/question/13496810
#SPJ2
identify which of the following in NOT equivalent to
[tex]2 \frac{2}{3} [/tex]
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\boxed{A}\qquad \sqrt[4]{8}\implies \sqrt[4]{2^3}\implies 2^{\frac{3}{4}} \\\\\\ \boxed{B}\qquad \sqrt[4]{2^3}\implies 2^{\frac{3}{4}} \\\\\\ \boxed{C}\qquad 2^{\frac{1}{4}}\times 2^{\frac{1}{2}}\implies 2^{\frac{1}{4}+\frac{1}{2}}\implies 2^{\frac{1+2}{4}}\implies 2^{\frac{3}{4}} \\\\\\ \boxed{D}\qquad \left( 2^{\frac{1}{4}} \right)^{\frac{1}{2}}\implies 2^{\frac{1}{4}\cdot \frac{1}{2}}\implies 2^{\frac{1}{8}}\qquad \textit{\large \checkmark}[/tex]
Need help with Pre college
Answer:
check online for more information
Find the volume of the following figure. Use 3.14 for pi. best answer gets brainliest also 100 points
Answer: 301.44 cubic inches.
Step-by-step explanation:
The formula for the volume of a cone is [tex]V = \pi r^2 \frac{h}{3}[/tex], so by plugging in the radius (6) and height (8), and using 3.14 as pi, you can get 301.44 as the total volume.
Since it is volume, it is in inches cubed, Therefore, the final answer is 301.44 cubic inches.
I hope this helps! :)
how many units is -3 2/3 from zero on the number line
Answer:
It is 3 2/3 away from zero or 3.7 (3.66666666667) away from zero.
Step-by-step explanation:
It is 3 2/3 away from zero or 3.7 (3.66666666667) away from zero.
Part D: Your parents put in fencing around the walkway for safety. If 110 feet of
fencing is used, what are the dimensions of the pool? Show your work.
Answer:
Step-by-step explanation:
Not near enough information to know.
I ASSUME that the pool is surrounded by a walkway of constant width (w = 2 ft, from comments)
The pool shape is important as well. No mention of the shape
If the pool is circular and the walkway is 3 ft wide
the fence encloses a diameter of 110/π = 35 ft
so the diameter of the pool would be 35 - 2(3) = 29 ft.
POOL IS RECTANGULAR from comments
If the pool is square and the walkway is 2 ft wide, each side of the fence is
110 / 4 = 27.5 ft and the pool would be 27.5 - 2(2) = 23.5 ft on a side.
There are an infinite number of rectangular width and length dimensions and walkway dimensions which would result in a fence length of 110 ft.
Edit from comments
Still an infinite number of rectangular length an width dimensions for a pool with a 2 ft wide walkway around it.
Let's say that we are told the pool is 12 ft wide with 2 ft walkway.
Let L be the pool length
110 = 2(12 + 2(2)) + 2(L + 2(2))
110 = 32 + 2L + 8
70 = 2L
L = 35 ft
find the 99th term of the arithimic sequence 2, 5/2, 3, 7/2, ...
Answer:
99th term is 51
Step-by-step explanation:
Arithmetic sequence equation
a1= first term = 2
d= common difference = 0.5 or 1/2
2, 5/2 = 5/2 - 2 = 0.5 or 1/2
3 - 5/2 = 1/2
7/2 - 3 = 1/2
an = a1 + (n - 1)d
a99 = 2 + (99-1) 1/2
a99= 2 + 98 (1/2)
a99 = 2 + 49
a99 = 51
what is the value of y so that the equation is true y^2 = -81
Step-by-step explanation:
to make the equation true the value of y must be.
-1×9²-1×81-81hope it helps.
stay safe healthy and happy.
Answer:
y=-/+9
Step-by-step explanation:
y^2=81
find the square root
y=positive/negative 9
13. What is the equation of the line through the two points (5,2) and (5.-3)
Answer:
yes i love this app , this app so good
Question
Round to the nearest ten: 1,078
Answer:
7 = 7 * 10 = 70
Step-by-step explanation:
Answer:
• 1080
Step-by-step explanation:
How to Calculate Rounding to the Nearest Tens Whole Number?
If the ones digit (first number after decimal point) of the number is greater than or equal to 5 we add 1 to tens of number, If the ones digit of the number is less than 5 we change ones digit to 0.
Example:
1026The ones number is 66 is greater than 5, so we add 1 to tens.Result = 1030[tex] \: [/tex]
Liam cuts a 48-inch piece of string into two pieces. One piece is 12 inches longer than the other. If s represents the length of the shorter string, which diagram best represents this scenario?
The length of the shorter string is 18 inch while that of the longer string is 30 inch.
An equation is an expression used to show the relationship between two or more variables and numbers.
Let s represent the length of the shorter string.
One piece is 12 inches longer than the other
Length of longer string = s + 12
Since a 48-inch piece of string is cut into two pieces. Hence:
s + (s + 12) = 48
2s + 12 = 48
2s = 36
s = 18
Length of longer string = 18 + 12 = 30
The length of the shorter string is 18 inch while that of the longer string is 30 inch.
Find out more on equation at: https://brainly.com/question/2972832
You invested $5,000 in a 10 year CD at the age of 12. The account pays 2.5% interest compounded continuously. How much money will you have after 10 years? (Round to the nearest cent.)
Answer:
Do PRT: 5009.31
Step-by-step explanation:
Princable: 5000
Rate: 2.5
Time: 10
Answer:
.. Write the number word of 0.036???
Answer:
zero point zero three six
rewrite equation in slope - intercept form: (Solve for y)
2x-y=7
Answer:
y = 2x-7
Step-by-step explanation:
I'm not really sure this is the slope-intercept form, as I've never called it like that before, but if it is, there you go.
Answer:
[tex]\huge\boxed{\sf y = 2x - 7}[/tex]
Step-by-step explanation:
Given equation is:
2x - y = 7
Add y to both sides
2x = 7 + y
Invert the equation
7 + y = 2x
Subtract 7 to both sides
y = 2x - 7
This is the required equation in slope-intercept form y = mx + b where m is slope and b is y-intercept.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Write a number using the following clues:
a multiple of 6
greater than 40, but less than 90
Answer:
48
Step-by-step explanation:
There are various multiples of 6 that are greater than 40, but less than 90. Including 42, 48, 54, 60, 66, 72, 78, and 84. :)
HELP ME OUT PLEASE
Which symbol makes the sentence true?
Answer:
A
Step-by-step explanation:
The square root of 50 is less than the square root of 78.
Find all the perfect cubes between 1000 and 2000.
Pls help I’ll brainlest ASAP
Which of the following is the decimal counterpart of the binary number 10012? a. 9 b. 10 c. 11 d. 12
Answer:
maybe it's 12 but i don't know...
i need help i don’t understand this i’m a freshman in highschool doing a mi
You have a Right Triangle with side lengths of 9ft and 12ft; solve for its perimeter and area.
Step-by-step explanation:
of course, we have to use Pythagoras.
c² = a² + b²
c is the Hypotenuse = the side opposite of the 90° angle.
and here is the problem : are 9 and 12 the legs. or is one of them the Hypotenuse ?
I don't know from the description.
let's see what we get one way or the other :
assumption : the known sides are the "legs".
c² = 9² + 12² = 81 + 144 = 225
c = 15 ft
that is a nice number. so, it looks like that was the intention.
just to be sure, here also the other options :
9² = 12² + side²
81 = 144 + side² that makes side² negative, so, not valid.
12² = 9² + side²
144 = 81 + side²
63 = side²
side = sqrt(63) this is not a nice round number, so, we go with the first option.
therefore, the 3 sides are
9 ft, 12 ft, 15 ft
perimeter = 9+12+15 = 36 ft
area = baseline×height/2
since this is a right-angled triangle, the "legs" with the enclosed 90° angle serve as baseline and height.
area = 9×12/2 = 9×6 = 54 ft²
please help i only have a few minutes!!
what are the measures of 1 and 2?
Answer:
3;87
Step-by-step explanation:
Since they are complementary, they add up to 90°. This allows you to write the equation
[tex]x+(16x+39) = 90 \rightarrow 17x=90-39 \rightarrow 17x=51 x=\frac{51}{17}=3[/tex]
The second angle measures then [tex]90-3 = 87[/tex]
Mrs. Goldstein pours 3 juice boxes into a bowl to make punch each juice box hold 236 ml how much juice it does Mrs.Goldstein pour into the bowl
708 ml
When each box contains 236 ml of juice and she pours three boxes into the bowl, you need to multiply 236 by 3. After completing the calculation, you would get 708.
find the maclaurin series of the given function f(x)=ln(1-x)
Answer:
[tex]-a-\frac{a^2}{2}-\frac{a^3}{3}-\frac{a^4}{4}-...-\frac{a^n}{n}-...[/tex]
Step-by-step explanation:
1) the rule is:
[tex]ln(1+a)=a-\frac{a^2}{2}+\frac{a^3}{3}-\frac{a^4}{4}+...+(-1)^{n-1}\frac{a^n}{n}+...[/tex]
2) according to the rule above:
[tex]ln(1+(-a))=(-a)-\frac{(-a)^2}{2}+\frac{(-a)^3}{3}-\frac{(-a)^4}{4}+...+(-1)^{n-1}\frac{(-a)^n}{n}+...[/tex]
finally,
[tex]ln(1-a)=-a-\frac{a^2}{2}-\frac{a^3}{3}-\frac{a^4}{4}-...-\frac{a^n}{n}-...[/tex]
Evaluate the following expression [(15+1)/2-4]*6
Answer:
24
Step-by-step explanation:
By BODMAS rule,
[ ( 15 + 1 ) / 2 - 4 ] * 6
= [ 16 / 2 - 4 ] * 6
= [ 8 - 4 ] * 6
= 4 * 6
= 24
Based on the information given, the value of the equation will be -48.
From the information given, the expression is given as:
= (15+1)/2-4]*6
We'll solve the bracket first.
= (15+1)/2-4]*6
= (16 / 2 - 4) × 6
= (16/-2) × 6
= -8 × 6
= -48
In conclusion, the value of the equation will be -48.
Learn more about equations on:
https://brainly.com/question/13802812