Answer:
It takes 22.52 years for the balance to triple in value.
Step-by-step explanation:
Continuous compounding:
The amount of money earned using continuous compounding is given by the following equation:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial amount of money and r is the interest rate, as a decimal.
Interest rate of 5%.
This means that [tex]r = 0.05[/tex], and thus:
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = A(0)(1+0.05)^t[/tex]
[tex]A(t) = A(0)(1.05)^t[/tex]
Time for the balance to triple?
This is t for which [tex]A(t) = 3A(0)[/tex]. So
[tex]A(t) = A(0)(1.05)^t[/tex]
[tex]3A(0) = A(0)(1.05)^t[/tex]
[tex](1.05)^t = 3[/tex]
[tex]\log{(1.05)^t} = \log{3}[/tex]
[tex]t\log{1.05} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{\log{1.05}}[/tex]
[tex]t = 22.52[/tex]
It takes 22.52 years for the balance to triple in value.
What is an equation of the line that passes through the points (-5,6) and (7,6)?
Find the mean, median, and mode of the following set of data:
54, 48, 37, 55, 51, 54, 42, 52, 53
Answer:
Step-by-step explanation:
mode is means the data which is repeated maximum number of times.
here 54 is repeated maximum number of times so the mode of the given data is 54.
to calculate median u must arrange the data from ascending to descending order.
37 , 42 , 48 , 51 , 52 , 53 , 54 , 54 , 55 ,
median = (N + 1) /2 (N means number of data)
=9 + 1/2
=10/2
=5 th term
=52
Find the radius y of circle C, given that x = 12 and z = y + 8.
PLEASEEE HELP ME
The radius of the given circle is 5, option C is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In the given figure, y is the radius.
By pythagoras theorem we find the radius
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
AC²+AB²=BC²
y²+12²=(y+8)²
y²+12²=y²+64+16y
144=16y+64
Subtract 64 from both sides
144-64 = 16y
80=16y
Divide both sides by 16
y=5
Hence, the radius of the given circle is 5, option C is correct.
To learn more on trigonometry click:
https://brainly.com/question/25122835
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Ranking correct answer brainliest! If you need more points check unanswered questions
Answer:
8.66
Step-by-step explanation:
b = a sqrt(3)
Bird A has the genotype ll for bill length, and Bird B is LL. The bills of their offspring would be
Answer:
false
Step-by-step explanation:
it is false bird a has the genotype ll for bill length and bird b is LL. A short bill describes bird a's genotype
Applying L'Hospital's rule is not allowed
Answer:
-1/2
Step-by-step explanation:
lim x-> π/2 cos x /(2x-π) =
lim (x-π/2)->0 sin (π/2 - x) /2(x-π/2) =
lim (x-π/2)->0 - sin (x - π/2)/2(x-π/2) = -1/2
Need help on number 3 please!!
Answer:
f(x) - g(x) = x - 3
Step-by-step explanation:
f(x) - g(x) starting with the basic equation
2x - (x + 3) implementing the values into equation
x - 3 subtracting x and 3 from 2x making 2x into 1x (or just x) and making a negative 3
PLEASE SOMEONE HELP ME WITH THESE QUESTIONS I'VE BEEN STUCK ON HERE FOR SO LONG
Answer:
# means number
Step-by-step explanation:
Distance = Y-axis or output
Cost= X-axis or input
you do not need to add the brackets for the formula(BEDMAS), but it makes things clearer
For A -
the Y-intercept is where the first coordinate, or the # or the X-axis, is 0 (on the graph the y-intercept 0,4)
For B -
y = mx + b
m = slope
x = input or # on the X-axis
b = y-intercept
or
formula = (input x increase in the slope) + output for 0 or (distance x increase in cost) + output for 0
input(x axis) output(y axis)
0 5 ← output for 0
1 9
2 13
there is a +4 increase in the slope, the increase in the slope is an output #(in this case 9) - the previous output number (in this case 5)
formula = (input x increase in the slope) + output for 0 = distance
formula in use = (3 x 4) + 5 = 17
For C:
The dependent variable is the output or the cost because the input or the distance will determine the cost travelled. Eg. if I travel 9 miles it will cost $41. If the dependent variable is the cost then the independent variable is the distance
For D: (input x increase in the slope) + output for 0
(4.2 miles x $4) + 5
16.8 + 5 = $21.8; It will cost $21.8 to travel 4.2miles
For E: (distance x increase in cost) + output for 0
(? x 4) + 5 = 14
(14 - 5) = 9
9 ÷ 4 = 2.25miles; with 14 dollars I could travel 2.25 miles
(It is a bit confusing lol, but this is the way I understand it, if you can't understand it this way then use y = mx + b)
Line A has a slope of 3/2 and passes through the point (3, 3). Line B has a slope of – 1/3 and passes through the point (-4, -2). At what point does line A intersect line B? Line Aintersects line B at the point ( , ).
Answer:
The lines meet at (-1, -3)
Step-by-step explanation:
Line A :
[tex](x_1, y_1) = (3, 3) \ ; \ slope, \ m_A = \frac{3}{2}\\\\Equation \ of \ line \ A : (y - 3) = \frac{3}{2}(x - 3)[/tex]
[tex]2(y - 3) = 3(x-3)\\2y - 6 = 3x - 9\\2y = 3x - 9 + 6\\2y = 3x -3[/tex]
Line B :
[tex](x_2,y_2) = (-4, -2) \ ; \ slope , m_B = -\frac{1}{3}\\\\Equation \ of\ line \ B: (y -(-2)) = -\frac{1}{3}(x -(-4))[/tex]
[tex]3(y + 2) = -1(x+4)\\3y + 6 = -x -4\\3y = -x - 4 - 6 \\3y = -x - 10[/tex]
Solve for x and y from the linear equation to find where line A and line B meets :
2y = 3x - 3 => 3x - 2y = 3 ------- (1)
3y = -x - 10 => -x = 3y + 10
=> x = - 3y - 10 --------(2)
Substitute (2) in (1) : => 3(- 3y - 10) - 2y = 3
-9y - 30 -2y = 3
-11y = 3 + 30
-11y = 33
y = -3
Substitute y in (2) : => x = -3 (-3) - 10 = 9 - 10 = -1
Write each absolute value in a box to show the order from least to greatest.
Answer:
From least to greatest: -12 -8 -2 5 11
Step-by-step explanation:
Please mark brainliest have a good day and i hope i helped :)
Answer:
(11)=(3)-(1)+(6)=6
Step-by-step explanation:
Jen's test grades for this term are 85,92, and 95. She wants to have a test average of at least 90 for this term, and she will have one more test. What is the lowest score that she can get to have a test average of at least 90?
Answer:
Step-by-step explanation:
(85+92+95+x)/4
=90
(272+x)/4
=90
90×4=360
272+x=360
x=360-272=88
so it's the lowest score
Lily weighs 57.7 kg while her sister weighs 59.02 kg, how much more does Lily's sister weigh then her? Please provide the calculation!
2w - 5 = 8
W =
Plllssssss helppoo
Answer:
w = 13/2 or 6.5
Step-by-step explanation:
2w - 5 = 8
Add 5 to each side
2w - 5+5 = 8+5
2w = 13
Divide by 2
2w/2 = 13/2
w = 13/2 or 6.5
Answer:
13/2
Step-by-step explanation:
the steps are in the screenshot attached.
Raj is travelling to another country.
He flies for 5 hours at an average speed of 950 km/h on one plane.
He then flies for 6 hours 30 minutes at an average speed of 830 km/h on a second plane.
What is the total distance, in km, he travelled by plane?
Answer:
9,315 km
Step-by-step explanation:
Recall that distance = rate times time.
The distance flown at 950 km/h is (950)(5) km = 4,740 km
and:
The distance flown at 830 km/h is (830)(5.5) km = 4,565 km
Then the total distane Raj traveled is (4,740 km + 4,565 km) = 9,315 km
Which pair of angles is complementary?
V
31°
56°
699
340
o
What type of graph uses intervals to show the frequency of data?
+
A. Bar graph
B. Line graph
C. Histogram
O D. Circle graph
SUB
John gets paid $76 a day at his new job printing t-shirts. He also earns $2.50 for every t-shirt sold. Create
and equation to describe how much money John makes in a day. Write the equation for this problem in
function notation. Then interpret how much money John would makes in one day after selling 32 t-shirts.
Make sure to define your variables and show all of your work.I swear who ever answers this I will Give them brainlist please help
Answer:
y=76+2.5x where y is the amount he earns in a day and x is the number of tshirts sold
y=76+2.5(32)
y=76+80
y=156
he earns 156 dollars if he sold 32 tshirts
Step-by-step explanation:
1.en cada unos de los siguientes monomios identificó el coeficiente y la parte literal , halló el grado y el valor numérico para los valores . ×=3,Z =5. (a) 3ײ (b) 4ײ y (c) - 5ײy²z².
porfa me ayudan
Which graph shows the solution to the system of linear inequalities?
x+5y>5
Y<2x+4
PLEASE HELP!!!
Answer:
x+5y >5 => red
y< 2x+4 => blue
Step-by-step explanation:
you can substitute x and y in each inequality to determine
Date
Page
Out
of
100 students who appeared in
grade.VIII annual examination
of
Ram
Janaki Secondary School.60 passed in
mothematics, 50 in science and 20 students
passed in both subject find how
many
failed in both subject ? Aso show above information
student
in Venn-
bright
Venn-diagram
huan anatoa )
Sonnant Babase
eigshoos te
oloh
Answer:
10 student failed in both subjects.
Step-by-step explanation:
Since out of 100 students who appeared in grade VIII annual examination of Ram Janaki Secondary School, 60 passed in mathematics, 50 in science and 20 students passed in both subjects, to determine how many failed in both subjects the following calculation must be performed:
(100 - 20) - (60 - 20) - (50 - 20) = X
80 - 40 - 30 = X
40 - 30 = X
10 = X
Therefore, 10 student failed in both subjects.
What is the area of the right triangle shown below?
Answer:
60 units²
Step-by-step explanation:
Find the other side length:
8² + x² = 17²
64 + x² = 289
x² = 225
x = 15
Find the Area:
1/2(8 x 15) = Area
1/2(120) = Area
Area = 60
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Triangle PQR is similar to triangle XYZ. The length of PQ is one-half the length of XY. THe length of RP is 2 cm. Which proportion can be used to find the length of ZX?
Answer:
[tex]ZX = 4cm[/tex]
Step-by-step explanation:
Given
[tex]\triangle PQR[/tex] similar to [tex]\triangle XYZ[/tex]
[tex]PQ = \frac{1}{2}XY[/tex]
[tex]RP = 2cm[/tex]
Required
Find ZX
[tex]\triangle PQR[/tex] similar to [tex]\triangle XYZ[/tex] implies that, the following sides are similar
[tex]PQ \to XY[/tex]
[tex]QR \to YZ[/tex]
[tex]RP \to ZX[/tex]
To find ZX, we make use of the following equivalent ratio
[tex]PQ : XY = RP : ZX[/tex]
Where
[tex]PQ = \frac{1}{2}XY[/tex]
[tex]RP = 2cm[/tex]
So, we have:
[tex]\frac{1}{2}XY : XY = 2cm : ZX[/tex]
Express as fraction
[tex]\frac{\frac{1}{2}XY }{ XY }= \frac{2cm }{ ZX}[/tex]
[tex]\frac{1}{2}= \frac{2cm }{ ZX}[/tex]
Make ZX the subject
[tex]ZX = 2 * 2cm[/tex]
[tex]ZX = 4cm[/tex]
The surface area of Canada is 9,984,671 square kilometers. Which number, written in scientific notation, is the best approximation of the surface area?
Answer:
9.99 *10 ^ 6 km
Step-by-step explanation:
Given that the surface area of Canada is 9,984,671 square kilometers.
The standard form of scientific notation is expressed as;
A * 10^n
A is any values between 1 to 9
n is an integer
Given
9,984,671 square kilometers.
9,984,671 = 9.99 *10 ^ 6
Hence the required scientific notation is 9.99 *10 ^ 6
Mrs. Smith is creating a rectangular flower bed such that the width is half of the
length. The area of the flower bed is 34 square feet. Write and solve an equation
to determine the width of the flower bed, to the nearest tenth of a foot.
Answer:
As for this problem, we will first establish that the length of the flower bed be represented as x, the width of the flower bed be represented as x/2 ,and the area of the flower bed be taken as it is since it is given. We then follow the formula for area which is length multiplied to width which is:
A = LW
we then substitute them
34 square feet = x (x/2)
now all we need to do is find x first.
34 square feet = x squared / 2
now do a cross multiplication
68 square feet = x squared
then get the square root of both sides
8.246 feet = x
Since x is equal to the length of the flower bed, all we have to do to get the width of it is to divide it by 2. So...
W = x/2
W = 8.246 feet / 2
W = 4.123 feet
And since the problem asked it to find the width of the flower bed to the nearest tenth of a foot, the answer would be 4.1 ft.
NUM ALDITORIO HA 224 CADEIRAS ORGANIZADAS EM 8 FILEIRAS COM A MESMA QUANTIDADE DE CADEIRAS QUANTAS CADEIRAS HA EM CADA FILEIRA
Answer:
The number of chains in each fileiras = 28.
Step-by-step explanation:
Total number of chains = 224
Number of fileiras = 8
Number of chains in each fileiras is given by the divison of total number of chains to the number filerias.
[tex]\frac{224}{8}\\\\=28[/tex]
Help, need index form
Refer to the attachment for complete calculation.
3²× 11^-9
Question 2
Find the equation of the line parallel to y = x - 2 that passes through the point (-3,2).
Answer:
The equation of the required line is y = x + 5
Step-by-step explanation:
The equation of the given line is y = x - 2
The required line = A line parallel to the given line
The point through which the required line passes = (-3, 2)
The general form of the equation of a straight line, is y = m·x + c
Where;
m = The slope of the line
By comparison, the slope of the given line, m = 1
When two lines are parallel, their slope are equal
Therefore, the slope of the required line = m = 1
The equation of the required line in point and slope form is therefore;
y - 2 = x - (-3) = x + 3
∴y = x + 3 + 2 = x + 5
The equation of the required line is therefore;
y = x + 5.
Silas has 5 1/4 cups of flour. He uses 3 1/2 cups to bake bread, then he borrows another 2 cups from his neighbor. He wants to bake cookies, which take 2 3/4 cups of flour. Does he have enough? How much will he have left over, or how much more does he need?
Answer:
He has enough to bake the cookies with 1 cup of flour left over.
Step-by-step explanation:
5.25 cups to start - 3.5 for the bread = 1.75 remaining
1.75 cups + 2 cups from neighbors = 3.75 cups
3.75 - 2.75 for cookies = 1 cup left over.
Sunny and Rashika collect stamps. Sunny has collected 3 times as many stamps as Rashika. Together, they have 304 stamps. How many stamps does each person have? Show your work.
Answer:
Sunny = 228 stampsRashika = 76 stampsStep-by-step explanation:
Sunny has collected 3 times the stamps that Rashika has collected but in total they have both collected 304 stamps.
Assume that Rashika has x stamps. This would mean that Sunny has (3 * x) or 3x stamps.
In an equation this would be:
x + 3x = 304
4x = 304
x = 304/4
x = 76 stamps
Rashika has 76 stamps.
Sunny has 3 times that number:
= 76 * 3
= 228 stamps
slope = 4, point (3,-2) is on the line
Answer:
y = 4x + b
Step-by-step explanation:
We know that (3, -2) is on this line. So 3 = m(-2)+b.
This leaves us with two variables the slope (m) and the y intercept (b).
But wait a minute, the slope is given to us since it says slope = 4.
Our equation is now, 3 = 4(-2)+b
3 = -8 + b
b = 11.
Our final equation is now y = 4x + b.
(y,x) is a point on this line.
Hope this helped!
JoeLouis2