The future value with continuous compounding is $127,420.39.
What is the future value?The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate15,000 x (e^0.06) x 8 = $127,420.39
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PLS HELP ME Solve the following equation: five eighths plus two eighths equals
three eighths,
seven sixteenths,
seven eighths,
or eight sevenths.
Least common multiple of 35 and 70
Answer:
70
Step-by-step explanation:
【Answer】The least common multiple of 35 and 70 is 70.
[tex]\orange{ {\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedure}}{\hspace{50pt}\above 1.2pt}}[/tex]
To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.
This method consists of extracting the common and uncommon prime factors, then
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{35 \ \ \ 70}\\ 35 \ \ \ 35\\ 7 \ \ \ \ 7\\ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 5\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]
[tex]\sf{L.c.m.(35,70)=2\times5\times7}[/tex]
[tex]\boxed{\boxed{\sf{L.c.m.(35,70)=70}}}[/tex]
{ Pisces04 }4. Identify a transformation of the function f(x) = x by observing the equation of the function g(x)
= x - 90.
The base graph has been shifted left 90 units.
The base graph has been shifted up 90 units.
The base graph has been shifted down 90 units.
The base graph has been shifted right 90 units.
Answer: The base graph has been shifted down 90 units.
Step-by-step explanation:
See attached image.
The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ? Use the distance formula to help you decide: .
A.
B.
C.
D.
The slope is m=6 and length of line is 3.5√37.
What is slope?The slope of a line is a measure of its steepness.
Given:
endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5
slope= 8-2/3-2= 6
Now, using distance formula,
d= √(3-2)² + (8-2)²
d= √1+ 36
d= √37
As, Line AB is dilated by a scale factor of 3.5.
So, new d= √37*3.5
new d= 3.5√37
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Find an equation of the line. Write the equation using function notation.
Through (8,8); perpendicular to 5y = x - 10
Answer:
f(x) = -5x +48
Step-by-step explanation:
A fairly easy way to write the equation of the perpendicular line is to swap the x- and y-coefficients, negating one of them. Then choose the constant in the equation to make it true at the given point.
Swapped coefficientsIn this instance, we find it convenient to leave the coefficient of y as positive.
5y = x -10 . . . . . . original equation
y = -5x +c . . . . . . with coefficients swapped, x-coefficient negated
New constantAt the given point, the equation becomes ...
8 = -5(8) +c
48 = c . . . . . . . add 40
Equation of the perpendicular lineThe equation of the line is then ...
y = -5x +48
f(x) = -5x +48 . . . . . . in functional notation
How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters
(a) is allowed?
Your answer is :
Correct
(b) is not allowed?
Your answer is :
The number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
How to determine the waysFormula for permutation with repetition
[tex]^nPr = n^r[/tex]
Formula for permutation without repetition
[tex]^nPr = \frac{n!}{n-r!}[/tex]
We have = 5
r = 3
a. If repetition is allowed,
Permutation = [tex]5^3[/tex] = 125 ways
b. If repetition is not allowed,
Permutation = [tex]\frac{5!}{5-3!}[/tex]
Permutation = [tex]\frac{5*4*3*2*1}{2*1}[/tex]
Permutation = [tex]\frac{120}{2}[/tex]
Permutation = 60 ways
Thus, the number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
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QUESTION 1 -
If f(x)=3x²-5x+4, then f(-2)=
a.) - 18
b.) 26
c.) 2
d.) 6
Question 2 -
For an ordered pair (x, y) in a relation, the y element represents the _____
a.) input
b.) range
c.) domain
d.) function
Need help urgently! Will give brainliest.
Given: f(x) = 3x² -5x + 4
To find f(-2), simply substitute x = -2 in function f(x).
f(-2) = 3(-2)² -5(-2) + 4
f(-2) = 12 + 10 + 4
f(-2) = 26
Answer: 26
#2For an ordered pair (x, y) in a relation, the y element represents the range.
Answer: range
Deepak stacked 14 copies of the
same book. Each book is 13 inches
thick. How high is the stack of books?
8
inches
Answer:
182 inches
Step-by-step explanation:
1 book is 13 inches thick.
So when 14 of those books are stacked together (lets take the book cover has non-existent thickness since the question did not mention),
Height of stack of 14 books = 14 x Thickness of 1 book = 14 x 13inches
= 182 inches
0,2,14,36,68,?
Find the next number in the sequence
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
Geometric sequenceGeometric sequence are sequence that increase in an exponential manner.
Given the recursive sequence 0, 2, 14, 36, 68
From the sequence
0 + 2 = 2
2 + 12 = 14
14 + 22 = 36
36 + 32 = 68
68 + 42 = 110
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
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A bird can fly 5 miles in 15 minutes how many miles can it fly in 60 minutes?
Please show the process
The number of miles the bird can fly for 60 minutes is 20 miles.
How to find rate and distance?A bird can fly 5 miles in 15 minutes.
Let's find the rate before we can find the number of miles the bird can fly in 60 minutes.
Therefore,
rate = distance / time
rate = 5 / 15 = 1 / 3 miles per minutes
Therefore,
1 / 3 = d / 60
cross multiply
60 = 3d
d = 60 / 3
d = 20 miles
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MATH: GRAPHING PIECE-WISE...HELP! 15 PTS
Answer:
Step-by-step explanation:
The area of one triangle is 270 square centimeters when its height is 30 centimeters and its base length is 18 centimeters. What
is the area of a triangle having a height of 25 centimeters and a base length of 16 centimeters?
Answer:
[tex]200 cm^2[/tex]
Step-by-step explanation:
A = (1/2)bh
A = (1/2)(18)(30)
A = 270 square cm
A = (1/2)(16)(25)
A = 200 square cm
Answer:
200 square centimeters
Step-by-step explanation:
The area of a triangle can be calculated using the formula: [tex]A = \frac{1}{2}bh[/tex] where b is the base and h is the height. So if the base is 16 cm and the height if 25 cm you simply plug the values into the equation to find the area
Plug Values In:
[tex]A = \frac{1}{2}(16 cm)(25 cm)[/tex]
Multiply 16 cm and 25 cm:
[tex]A = \frac{1}{2}(400 cm^2)[/tex]
Multiply by 0.5 (or technically divide by 2)
[tex]A = 200 cm^2[/tex]
Whats the correct answer answer asap for brainlist
Answer:
option A: West Europe, East Europe, and Asia
Explanation: Europe and Asia as a whole are called Eurasia.
hope that helps...
Simplify √3. √21
√24
√63
O 3√7
09√7
Answer:
•3✓7
✓3.✓21
=✓3×✓3✓7
=3✓7
Answer:
3rd answer is correct
Step-by-step explanation:
√3 × √21
√3 × √(7 × 3)
√( 3 × 3 × 7 )
√ ( 3 × 3 ) × √7
3√7
simplify the expression 1-cos^2(t) / cos^2(t)
Answer: [tex]\tan^2 t[/tex]
Step-by-step explanation:
[tex]\sin^{2} t+\cos^2 t=1 \implies 1-\cos^2 t=\sin^2 t\\\\\implies \frac{1-\cos^{2}t}{\cos ^2 t}=\frac{\sin ^2 t}{\cos^2 t}=\tan^2 t[/tex]
Determine whether the triangle is a scalene, isosceles of equilateral
Answer:
Equilateral triangle: All three sides are equal.
Isosceles triangle: All two sides are equal.
Scalene triangle: No sides are equal.
Step-by-step explanation: Step 1: Label the given points as A, B, and C, and plot them as vertices of a triangle with connecting lines to draw the triangle we are working to identify.
Step 2: Calculate the side length AB using the distance formula.
Step 3: Calculate the side length BC using the distance formula.
Step 4: Calculate the side length AC using the distance formula.
Step 5: Compare the side lengths AB, BC, and AC from the previous steps to define the triangle type.
e.Water has a density of about 0.0361 pounds/cubic inch. You might know that wood floats on water. What can you conclude about the densities of objects that float and the densities of objects that do not?
Answer:
Step-by-step explanation:
the objects which have less density than water will float
and the objects which have more density than the density of liquid will sink in liquid or will not float.
What is the equation for the line of reflection
X=6
Y=6
Y=x
Y=2
Answer: x = 6
Step-by-step explanation:
B(7,3) maps onto B'(5,3).
The perpendicular bisector of [tex]\overline{BB'}[/tex] is x=6, so that is also the line of reflection.
Answer:
x = 6
Step-by-step explanation:
Taking test as we speak
Which figure shows a line of reflectional symmetry for the letter T?
A letter T is folded at the horizontal line.
A letter T is folded diagonally.
A letter T is folded vertically through the middle.
A letter T is folded diagonally through its center.
Mark this and return
The figure that will depict a line of reflectional symmetry of letter T is: Option C: A letter T folded vertically through the middle.
What is a Line of Reflectional Symmetry?A line of reflectional symmetry is defined as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.
When a line divides letter T vertically, it means that two mirror images will be created.
Therefore, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
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What is the determinant of K =
[6 8
0 3]
find the lowest common multiple ( L.C.M. ) of the (a² - 4), (a³ - 8), ( a + 2 ) ²
Answer: according to my work i got
LCM - Lowest Common Factor
HCF - Highest common factor
Step-by-step explanation:
please mark brainlest!!
yw! =^.^=
A collection of coins has a value of 64 cents. There are two more nickels than dimes and three times as many pennies as dimes. How many of each kind of coin are there?
There are 5 nickels, 3 dimes, and 9 pennies.
Let d = The number of dimes
Let n = number of nickels
Let p = The number of pennies
As given, there are two more nickels than dimes and three times as many pennies as dimes:
d+2=n
3d=p
0.10d+0.05n+0.01p=0.64
Plug in the value to find d
[tex]0.10d+0.05(d+2)+0.01(3d)=0.64[/tex]
[tex]0.10d+0.05d+0.1+0.03d=0.64[/tex]
[tex]0.18d=0.64[/tex]
[tex]d=3[/tex]
What is the value of p?The value of p is equal to 3d
p=3(3)=9
n=d+2
n=3+2
n=5
Hence, there are 5 nickels, 3 dimes, and 9 pennies.
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A line that includes the points (-8, f) and (-6, 4) has a slope of 6. What is the value of f?
f =?
Answer:
-8
Step-by-step explanation:
Slope = (y1-y2) / ( x1-x2)
= ( f-4) / (-8 - -6) = 6
(f-4) / -2 = 6
f-4 = -12
f = - 8
Answer:
f = -8
Explanation:
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here given:
points: (-8, f), (-6, 4)slope : 6Inserting into slope formula:
[tex]\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6[/tex]
[tex]\sf \rightarrow \dfrac{4-f}{2 } = 6[/tex]
[tex]\sf \rightarrow 4-f = 12[/tex]
[tex]\sf \rightarrow -f = 12-4[/tex]
[tex]\sf \rightarrow -f =8[/tex]
[tex]\sf \rightarrow f =-8[/tex]
Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.
Enter the correct answer in the box by replacing the values of m and b.
Answer:
[tex]y = -2x + 5[/tex]
m = -1
b = 5
Step-by-step explanation:
Hello!
Slope - Intercept Form: [tex]y = mx+b[/tex]
m = slopeb = y-interceptSlopeThe slope of the line is the rate of change, or how the graph changes in y as it changes in x.
Slope can be calculated by the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
We need two points on the line to get the x and y-values. I'm going to choose points (0,5) and (4,-3).
Calculate Slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]m = \frac{5 - (-3)}{0 - 4}[/tex][tex]m = -\frac{8}{4}[/tex][tex]m = -2[/tex]The slope is -2.
Y-interceptThe y-intercept of the line is where the graph touches the y-axis (x = 0). It can be found by looking at the intersection of the graph and the axis.
The intersection happens at point (0,5), so the y-intercept is 5.
EquationWe found m, the slope, to be -2 and b, the y-intercept, to be 5. We can just plug it into the equation format.
Equation: [tex]y = -2x + 5[/tex]
Please help!! Find the solution for t in the equation:
Answer:
t = 1.322
Step-by-step explanation:
4×(2^t) = 10
2^t = 10/4 = 2.5
t = log2(2.5)
now, the logarithm to the base 2 of 2.5 must be larger than 1, as 2.5 is larger than 2.
so, it can be only the 4th answer option.
now, to actually calculate it :
log2(2.5) = log10(2.5) / log10(2) = 1.321928095... ≈
≈ 1.322
we were correct.
Answer:
t = 1.322
Step-by-step explanation:
Given equation:
[tex]4(2^t)=10[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4(2^t)}{4}=\dfrac{10}{4}[/tex]
[tex]\implies 2^t=2.5[/tex]
Method 1Take natural logs of both sides:
[tex]\implies \ln 2^t = \ln 2.5[/tex]
[tex]\textsf{Apply the natural log power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies t \ln 2 = \ln 2.5[/tex]
Divide both sides by ln 2:
[tex]\implies \dfrac{t \ln 2}{\ln 2} = \dfrac{\ln 2.5}{\ln 2}[/tex]
[tex]\implies t= \dfrac{\ln 2.5}{\ln 2}[/tex]
[tex]\implies t=1.321928095...[/tex]
Method 2[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]
[tex]\implies \log 2 (2.5)=t[/tex]
[tex]\implies t=1.321928095...[/tex]
SolutionTherefore, the solution that is nearest to the exact solution is t = 1.322
find x and y
pls help
Step-by-step explanation:
(3x+6)= 48(Alternate angles)
3x=48-6
3x=42
x=14
2y+48=5y-9 (Sum of two opposite interior angles= exterior angle)
48+9=5y-2y
57=3y
y=19
Which equation is equivalent to 162 - 32+³?
=
=
O 84 - 84+3
O 84-84+12
O 28 - 25p+15
=
O 28P = 25p+3
[tex]{ \red{ \bold{option \: (d)}}} \: { \green{ \tt{ {2}^{8p} = {2}^{5p + 3}}}} [/tex]
Step-by-step explanation:
I said option (d) is correct. Because, the answer of 2^8 is 256 i.e.,
[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}}}[/tex]
[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{256}}}[/tex]
The value of 16^2 = 256.
Also, the answer of 2^5 is 32. i.e.,
[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2}}}[/tex]
[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{32}}}[/tex]
Solve for x. Round to the nearest tenth, if necessary.
X
H
In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.
Trigonometric Functions: SOH-CAH-TOA
Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.
tan(23) = x / 2
x = tan(23) * 2
x = 0.8489
x = 0.8
Hope this helps!
Step-by-step explanation:
ATTACHED IS THE SOLUTION!Complete the equation of this circle:
(x − [?])²+(y - [ ])²=[ ]
Answer:
(x+2)²+(y-4)²=36
Step-by-step explanation:
1) to determine the coordinates of the centre of the given circle. It is point A (-2;4);
2) to determine the length of the radius: to calculate the distance between the point A(-2;4) and any point on the circle, it is 6 [units];
3) to make up the required equation according to the scheme:
(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the coordinates of the centre, r - the length of the radius.
4) finally, (x+2)²+(y-4)²=6².
PS. for more details see the attachment.
median mark of 3,2,0,1,9,12,3,5
Answer: 3
Step-by-step explanation:
Median is a statistical measure that determines the middle value of a dataset listed in ascending order.
arranged data is 0,1,2,3,3,5,9,12
number of data terms=8
if data is even then
median=(3+3)/2=3