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:
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10.) - 3x - y = - 36
4x + 4y = 72
!PLS HELP ASAP 30 POINTS !Determine the seating of an auditorium with 35 row of seats if there are 10 seats in the first row, 13 seats in the second row, 16 seats in the third row, 19 seats in the forth, and so on. What is the total number of seats?
Answer: 2135
step by step explanation:
I don't really think this is necessary
Quadratic functions 30pt
Answer:
y= -x -3
Step-by-step explanation:
A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).
Let's find the slope of the line segment.
\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }slope=x1−x2y1−y2
Slope of line segment
= \frac{4 - ( - 8)}{5 - ( - 7)}=5−(−7)4−(−8)
= \frac{4 + 8}{5 + 7}=5+74+8
= \frac{12}{12}=1212
= 1
The product of the slopes of 2 perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
m(1)= -1
m= -1
y= -x +c
To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.
Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.
\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}midpoint=(2x1+x2,2y1+y2)
Midpoint of line segment
= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )=(25−7,24−8)
= ( \frac{ - 2}{2} , \frac{ - 4}{2} )=(2−2,2−4)
= (-1, -2)
y= -x +c
When x= -1, y= -2,
-2= -(-1) +c
-2= 1 +c
c= -2 -1
c= -3
Thus, the equation of the perpendicular bisector is y= -x -3.
Tell whether tripling the dimensions of a square pyramid would triple the
surface area.
No. Tripling the dimensions (the side of the square base and the height) would increase the surface area of the pyramid by a factor of [tex]3^2[/tex] or [tex]9[/tex]
Let
[tex]h=\text{the height of the pyramid}\\s=\text{length of one side of the square base}\\t=\text{total surface area of the pyramid}[/tex]
The total surface area of the square-based pyramid is given by
[tex]t=b(b+\sqrt{4h^2+b^2})[/tex]
Let the tripled dimensions be given by [tex]B=3b[/tex] and [tex]H=3h[/tex], then the new surface area will be
[tex]T=B(B+\sqrt{4H^2+B^2})\\=3b(3b+\sqrt{4(3h)^2+(3b)^2})\\=3b(3b+\sqrt{9(4h^2+b^2)})\\=3b(3b+3 \sqrt{4h^2+b^2})\\=9b(b+\sqrt{4h^2+b^2})\\=9t[/tex]
The new surface area will be greater than the original by a factor of [tex]9[/tex]
Learn more about scale factors here: https://brainly.com/question/1440011
Answer: It will be more than triple the area because you square the side to find the area of the base.
Step-by-step explanation:
It will be more than triple the area because you triple the side to find the area of the base. To calculate the surface area of a square pyramid, you need to first calculate the area of the base. To do this, you will need to multiply the length of one side of the square by itself (or square it). Since you are tripling the dimensions of the square pyramid, you will need to triple the side of the base, which will result in an area that is more than three times larger.
What is the y-intercept of the line?
1
-2
1/2
0
Answer:
The y-intercept is 1.
Step-by-step explanation:
The y-intercept is where a line crosses the y-axis, so from looking at the graph, we can see that it crosses at (0,1), giving you a y-intercept of 1.
What is the volume of the following cylinder?
150.72 in. 3
301.44 in. 3
75.36 in. 3
602.88 in. 3
Answer:
150.72 in³
Step-by-step explanation:
We know that
Radius = Diameter/2
Radius = 8/2
Radius = 4 in
Now,
Volume of cylinder = πr²h
=> 3.14 × (4)² × 3
=> 3.14 × 16 × 3
=> 150.72 in³
Answer:
The correct answer is option 150.72 in³.
Step-by-step explanation:
Given :
✧ Diameter of cylinder = 8 in.✧ Height of cylinder = 3 in.To Find :
✧ Volume of cylinderUsing Formula :
[tex]\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}[/tex]
[tex]\star{\small{\underline{\boxed{\sf{\pink{V = \pi{r}^{2}h}}}}}}[/tex]
»» r = Radius »» D = Diameter »» V = Volume »» h = heightSolution :
Firstly, finding the radius of cylinder by substituting the values in the formula :
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \dfrac{D}{2}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \dfrac{8}{2}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \cancel{\dfrac{8}{2}}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = 4 \: in}}}[/tex]
[tex]{\star{\underline{\boxed{\sf{\red{Radius_{(Cylinder)} = 4 \: in}}}}}}[/tex]
Hence, the radius of cylinder is 4 in.
[tex]\rule{300}{1.5}[/tex]
Now, finding the volume of cylinder by substituting the values in the formula :
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \pi{r}^{2}h}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(4)}^{2} \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(4 \times 4)} \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(16)} \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times 16 \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314}{100} \times 16 \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314 \times 16 \times 3}{100}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314 \times 48}{100}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{15072}{100}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = Rs.150.72 \: {cm}^{3}}}}[/tex]
[tex]\star{\small{\underline{\boxed{\sf{\red{Volume_{(Cylinder)} = Rs.150.72 \: {cm}^{3}}}}}}}[/tex]
Hence, the volume of cylinder is 150.72 in³.
[tex]\rule{300}{1.5}[/tex]
the local store where tim shops charges a 7% sale tax for clothing complete the table by figuring the cost of jeans after tax is applied the first row is done
Answer:
$51.36
$77.04 i think
Step-by-step explanation:
Multiply the cost of the number of pairs of jeans by the sales tax amount, 7%.
cost of 2 pairs: 48 + 7/100 x 48 = $51.36
cost of 3 pairs: 72 + 7/100 x 72 = $77.04
Find an equation in slope-intercept form of the line satisfying the specified conditions.
Through (8,-3), perpendicular to -6x + 7y=-62.
Answer:
[tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex]
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
-6x +7y= -62
Rewriting this equation into the slope-intercept form:
7y= 6x -62
[tex]y = \frac{6}{7} x - \frac{62}{7} [/tex]
The product of the slope of 2 perpendicular lines is -1.
Let the slope of the unknown line be m.
[tex]m( \frac{6}{7} ) = - 1[/tex]
[tex]m = - 1 \div \frac{6}{7} [/tex]
[tex]m = - \frac{7}{6} [/tex]
Substitute the value of m into the equation:
[tex]y = - \frac{7}{6} x + c[/tex]
To find the value of c, substitute a pair of coordinates into the equation.
When x= 8, y= -3,
[tex] - 3 = - \frac{ 7}{6} (8) + c[/tex]
[tex] - 3 = - \frac{28}{3} + c[/tex]
[tex]c = \frac{28}{3} - 3[/tex]
[tex]c = \frac{19}{3} [/tex]
[tex]c = 6 \frac{1}{3} [/tex]
Thus, the equation of the line is [tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex].
what is the answer? SIMPLE
Answer:
true i think
Step-by-step explanation:
A train travels from point A to B at a speed of 100km/h. how long it will take to travel 25 km
Answer:
Step-by-step explanation:
25 km / 100 km/hr = 0.25 hr or 15 minutes
It will take 0.25 hours to travel 25 km.
Given
A train travels from point A to B at a speed of 100km/h.
Distance;
Distance is defined as the product of speed and time.
The following formula is used to calculate the time;
[tex]\rm Time =\dfrac{Distance}{Speed}\\\\[/tex]
Substitute all the values in the formula;
[tex]\rm Time =\dfrac{Distance}{Speed}\\\\\rm Time =\dfrac{25}{100}\\\\Time = 0.25 \ hours[/tex]
Hence, it will take 0.25 hours to travel 25 km.
To know more about distance click the link given below.
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Rewrite in standard form.
4y = 3 - 4/5x
Answer:
−17x+10y=3
Step-by-step explanation:
Extended Problems, Extraneous Solutions
I need help asap please, this is due in 1 day!
100 POINTS
Answer:
1a. 2 is the solution
1b. -3 is because square root of 1 doesn't equal -1.
1c.-3
Step-by-step explanation:
1.
[tex](x + 2 = \sqrt{3x + 10} [/tex]
Square both sides
[tex](x + 2) {}^{2} = 3x + 10[/tex]
Remeber perfect square Rule
[tex](x + y) {}^{2} = {x}^{2} + 2xy + {y}^{2} [/tex]
So now we got
[tex]x {}^{2} + 4x + 4 = 3x + 10[/tex]
[tex] {x}^{2} + x + 4 = 10[/tex]
[tex] {x}^{2} + x - 6 = 0[/tex]
Factor into binomial.
[tex](x + 3)(x - 2) = 0[/tex]
So our solution is 3 or 2. However, let's check our work.
[tex] - 3 + 2 = \sqrt{3( - 3) + 10} [/tex]
[tex] - 1 = \sqrt{1} [/tex]
However square root of 1 is 1. It could be 1 but in Math, We only take the principal square root which is positive always. So -3 isn't a solution.
So let try 2.
[tex]2 + 2 = \sqrt{3(2) + 10} = 4 = \sqrt{16} = 4 = 4[/tex]
So this is indeed the solution.
Make up equation for 2 and 3. Ask me if you need help.
If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is what?
we can change cos to sin by saying cosx=sin(90-x)
now we drop sin and make the angles equal (nothing needs to be added or subtracted since its in the first quadrant)
90-x=20+x+k.360.......kEZ (k is an element of set of integers) (we say k.360 if it's cos and sin and k.180 if it's tan)
-x-x=20-90+k.360........kEZ
-2x=-70+k.360.........kEZ
divide all terms by -2
x=35-k.180.......kEZ
Answer:
x=35°
Step-by-step explanation:
If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is 35°.
Please someone help me i dont want fail
Answer:
D
Step-by-step explanation:
(point D)
Answer:
Point D
Step-by-step explanation:
5 units right on the x axis, 3 units down on the y-axis.
What is the solution to this system?
8
Answer:
(2,2)
Step-by-step explanation:
The solution to a system is the point on the graph where both lines intersect.
Multiply: x^1/6(x^1/6+x^3/4)
[tex]x^{\tfrac 16} \left(x^{\tfrac 16} + x^{\tfrac 34} \right)\\\\\\=x^{\tfrac 16} \cdot x^{\tfrac 16} + x^{\tfrac 16} \cdot x^{\tfrac 34}\\\\\\=x^{\left(\tfrac 16 + \tfrac 16\right)} + x^{\left(\tfrac 16 +\tfrac 34\right)}\\\\\\=x^{\tfrac 26} + x^{\tfrac {11}{12}}\\\\\\=x^{\tfrac 13} +x^{\tfrac{11}{12}}[/tex]
7. at + b = ar – c
Solve for a
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Which ordered pair is a solution of the inequality
y < 3x + 1?
(-3,-2) (1,-3) (3,14) (1,6)
Answer:
the answer is the 4 option
A market increased the price of cheese selling for $4.98 per pound by 3%. What is the new
price for two pounds of cheese?
QUICK
Answer:
$10.26
Step-by-step explanation:
$4.98x0.03= 0.1494,
4.98+0.1494= 5.13
2; 5.13+5.13= 10.26
Answer:
$10.26
Step-by-step explanation:
$4.98*103/100=x
x=5.1294
2 pounds=2x=$10.2588=$10.26
Plz help me NOW I will mark you brainliest
Answer:
[tex] \frac{mn}{p} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
3. Write an equation in slope-intercept form for the line with a slope of 5/4 and a
y-intercept of 2.
Answer:
y = [tex]\frac{5}{4}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{5}{4}[/tex] and c = 2 , then
y = [tex]\frac{5}{4}[/tex] x + 2 ← equation of line
What is 27.6 / 8???????????
Answer:
seriously??
have you heard of calculators lol
the answer is 3.45
Dean ran 5 miles this week and wants to know how many kilometers he ran. His work is below.
Answer:
Dean ran 8.0467 kilometers
Step-by-step explanation:
First, you need to know how much kilometers are in a mile. 1 mile is 1.60934 kilometers, so once you found that out, then you would do 1.60934x5 which gets you 8.0467. Hope it helps!
HELP PLSSS
Use the commutative
property to make an
equivalent
expression.
4+m=?
A. 4-m
B. m+4
Answer:
B. m+4
Step-by-step explanation:
You are just writing the same equation but backwards so that the numbers still stay the same as well as the answer.
Answer: A
Step-by-step explanation:
Which of the following equations represents the graph shown?
Answer:
F(x)=-x+2
Step-by-step explanation:
equation
mx+b
m= slope
x
b = y-intercept
The formula p=F/A can be used to relate pressure force and area. Solve the formula for A.
[tex]P=\dfrac{F}{A}\\\\\implies PA = F\\\\\implies A = \dfrac{F}{P}[/tex]
Help help math please I’m stuck help help help
Answer:
12x
Step-by-step explanation:
I am not really sure how to explain it I just looked it up
A farmer has 220 bushels of apples to sell at roadside stand. She sells an average of 14 3/5 each day. Represent the total change in the number of bushels has for sale after 6 days.The total change in the number of bushels has for sale is ???, please answer as a fraction
Answer:
Step-by-step explanation:
He has sold (16+1/4) bushels/day x 5 days = (16 x 5) + (1/4 x 5) = 80 + 5/4 = 81 + 1/4 = 81.25
The change in the number of bushels is 140 - 81.25 = 58.75 or 58 and 3/4 bushels
In other words, he has 58.75 (or 18 and 3/4) bushels remaining and has sold 81.25 (or 81 and 1/4) bushels
HELP, pANYONE PLEASE !!!!
Answer:
A
Step-by-step explanation:
The line starts at -35, meaning that she starts the ascent 35 meters below the surface and goes upwards over time.
Answer:
a
Step-by-step explanation:
the starting point of the graph or also known as the y axis starts at -35
Translate and simplify: the product of –12 and the difference of p and q.
Hey there!
“Product” is multiplication so let’s say it means “multiply” & “difference” is subtraction so let’s say it means “subtract”
p & q is/are the variables, whereas -12 is a coefficient
“The [PRODUCT of -12] and the [DIFFERENCE of p & q]”
Product = multiply/multiplication
“-12 ×”
DIFFERENCE
“p - q”
So, based on that information we have your answer: “-12 × p - q”
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)