Answer:
Dot number 2. Makayla invests her money 2 years longer.
Step-by-step explanation:
Calvin 400$ with 5% interest compounded monthly will get you to 666.0294029241$ after 13 months or 1 year and 1 month
Makayla 300$ with 6% interest quarterly
1st year 378.743088$(4 quarters)
2nd year 478.1544223592$(+4 quarters)
3rd year 603.6589415506$(+4 quarters)
3rd year and 1 quarter 639.8784780436$
Answer:
So the second option is the answer: Makayla invests her money 2 years longer.
Step-by-step explanation:
Formula for compound interest: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Calvin:
[tex]A=658.80[/tex]
[tex]P=400[/tex]
[tex]r=0.05[/tex]
[tex]n=12[/tex]
[tex]t=?[/tex]
Makayla:
[tex]A=613.04[/tex]
[tex]P=300[/tex]
[tex]r=0.06[/tex]
[tex]n=4[/tex]
[tex]t=?[/tex]
Lets solve for [tex]t[/tex].
1) Divide both sides of the equation by [tex]P[/tex].
[tex]\frac{A}{P} =(1+\frac{r}{n})^{nt}[/tex]
2) Take the natural log of both sides.
[tex]ln(\frac{A}{P}) =ln((1+\frac{r}{n})^{nt})[/tex]
3) Rewrite the right side of the equation using properties of exponents.
[tex]ln(\frac{A}{P}) =nt*ln(1+\frac{r}{n})[/tex]
4) Divide each side of the equation by [tex]n*ln(1+\frac{r}{n})[/tex]
[tex]\frac{nt*ln(1+\frac{r}n)}{n*ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}[/tex]
5) Cancel the common factor [tex]n[/tex] on the left side of the equation.
[tex]\frac{t*ln(1+\frac{r}n)}{ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}[/tex]
6) Cancel the common factor of [tex]ln(1+\frac{r}{n})[/tex].
[tex]t=\frac{ln(\frac{A}{P)}}{n*ln(1+\frac{r}{n})}[/tex]
Now we have an equation for [tex]t[/tex] that we can use to answer your question.
For Calvin:
[tex]t=\frac{ln(\frac{658.80}{400)}}{12*ln(1+\frac{0.05}{12})}[/tex]
[tex]t=10[/tex]
For Makayla:
[tex]t=\frac{ln(\frac{613.04}{300)}}{3*ln(1+\frac{0.06}{3})}[/tex]
[tex]t=12[/tex]
So the second option is the answer: Makayla invests her money 2 years longer.
Note: This question took me 2 minutes to answer but typing it took 30. lol
Triangle abc is represented. points d and f are marked on side ab and points e and g are marked on side ac. segments de and fg are drawn.
if , then line segment
is parallel to line segment
.
If points d and f are on side ab and points e ang g are on side ac then line segment de and fg are parallel.
Given There is a triangle abc.
Parallel lines are those lines that do not meet at any point. If we draw a triangle abc and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle.
Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.
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Answer:D-E is parallel to FG which is parallel to B-C meaning all three are parallel
Step-by-step explanation:
Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?
The resulting polynomial when 5x -6 is subtracted from 3x² -6x +2 is; 3x² -11x +8.
What is the result of the polynomial subtraction?It follows from the task content that the polynomial 5x -6 is to be subtracted from 3x² -6x +2.
Hence, the subtraction goes thus; 3x² -6x +2 -(5x-6).
Hence, 3x² -6x +2 -5x+6
= 3x² -11x +8.
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Mrs. Cooper hosts an annual art contest for kids. She has records of the number of entries for the last 9 years. She received 30 entries in the first year. Over the next 3 years, the number of entries increased by 10 kids per year. In the next 2 years after that, there were 60 entries each year, and in the last 3 years, the number of entries increased by 15 kids per year. Which graph models the piecewise function for the given situation, where x represents time after the first year and y represents the number of entries in that year?
To graph this situation we must take into account the data and the organization of each of them on the X axis and Y axis.
How to graph this situation?To graph this situation we must take into account the data we have:
YearsTicketsBased on these data, we assign the horizontal axis to count years and the vertical axis to count tickets per year. We must continue the pattern of increased attendance over the years.
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what does a equal if 2÷a=(5/2)÷(5/4)
Question:
2÷a=(5/2)÷(5/4)
Answer:
a = 1
Find the reflection of the point (25, 25) across the y-axis.
Answer:
(-25, 25)
Step-by-step explanation:
let me know if you want an explanation!
PLEASE HELP FAST!!!
By trigonometric functions and law of cosines, the value of x associated with a missing angle in the geometric system is between 7.701 and 7.856.
How to find a missing variable associated to an angle by trigonometry
In this question we have a geometric system that includes a right triangle, whose missing angle is determined by the following trigonometric function:
sin (7 · x + 4) = 12/14
7 · x + 4 = sin⁻¹ (12/14)
7 · x + 4 ≈ 58.997°
7 · x = 54.997°
x ≈ 7.856
In addition, the geometric system also includes a obtuse-angle triangle and that angle can be also found by the law of the cosine:
7² = 8² + 6² - 2 · (8) · (6) · cos (7 · x + 4)
17/32 = cos (7 · x + 4)
7 · x + 4 = cos⁻¹ (17/32)
7 · x + 4 ≈ 57.910°
7 · x ≈ 53.910°
x ≈ 7.701
Hence, we conclude that the value of x associated with a missing angle in the geometric system is between 7.701 and 7.856.
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Help please
A.-3
B.-1/3
C.1/3
D.3
The slope of a line perpendicular to the line containing (0,3)and (-2,0) is: The slope of a line perpendicular to the line containing ( 0,3 ) and ( -2,0 ) is :
Answer:
Step-by-step explanation:
Which of the lines below is a line of symmetry?
O A. Red
•
B. Yellow
C. Neither
• D. Both
Both the Red and Yellow lines are lines of symmetry, Option D is correct.
What is Coordinate system?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Lines of symmetry in a figure are lines that divide the figure into equal parts.
The given figure is a square as we observe the four sides are equal in the given shape.
In a square, there are four lines of symmetry, each of which divides it into two identical parts.
The symmetry lines of a square are both its diagonals and the lines joining the midpoints of its opposite sides (bisectors).
In the given Figure, the Red lines cuts the shape into 2 equal halves vertically and the Yellow line cuts the shape into 2 equal halves diagonally.
Hence, both the Red and Yellow lines are lines of symmetry, Option D is correct.
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The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, where y is the height above water and x is the horizontal distance in feet. If a beam of light is shone upward at an angle modeled by the equation x + y = 10, at what height from the water's surface will the beam of light hit the dolphin?
Answer:
5 feet
The graphs intersect at x = 5.
Sunil draws a regular hexagon and a convex quadrilateral on a sheet of paper, so that no side of the quadrilateral lies on the same line as a side of the hexagon. what is the maximum total number of points in which the sides of the quadrilateral can intersect the sides of the hexagon?
Maximum total 8 points in which the sides of the quadrilateral can intersect the sides of the hexagon.
A regular hexagon is a closed shape polygon which has six equal sides and six equal angles. In case of any regular polygon, all its sides and angles are equal.
A convex quadrilateral is a four-sided polygon that has interior angles that measure less than 180 degrees each. The diagonals are contained entirely inside of these quadrilaterals
Take a look at just one side of the quadrilateral—a straight line. Since we are told that no side of the quadrilateral lies on the same line as a side of the hexagon, the maximum number of times a side of the quadrilateral could intersect the hexagon is 2. We can use a ruler to test this on the image of the hexagon. There is no way to pass a straight line through the hexagon and have it intersect the shape more than 2 times. Therefore, the maximum number of points at which the quadrilateral could intersect the hexagon would be
at 2 points per side, at 2 × 4 = 8 points.
Hence, Maximum total 8 points in which the sides of the quadrilateral can intersect the sides of the hexagon.
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Given √b6.
What is the rational exponent form of this expression?
O b1/3
0 b3
O b6
O b3/2
The rational exponent form of the given expression is b³. The correct option is the second option b³
Evaluating an expressionFrom the question, we are to determine the rational exponent form of the given expression
The given expression is
[tex]\sqrt{b^{6} }[/tex]
From one of the laws of indices, we have that
[tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]
Thus,
[tex]\sqrt{b^{6} } = b^{\frac{6}{2} }[/tex]
= [tex]b^{3}[/tex]
∴√b⁶ = b³
Hence, the rational exponent form of the given expression is b³. The correct option is the second option b³
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The side length of a square is 3x^2 . Find The area of the square
Answer: A=9x^4
Step-by-step explanation:
Hii, do you need to find the area of a square with a side length of 3x^2? Let me help you out! (:
AreaTo find the area of a square, you need to square its side length.
Sounds strange, right?
The formula is shown below.
[tex]\LARGE\boldsymbol{A=a^2}[/tex]
Here "A' (capital A) denotes the area
"a" (lower-case a) denotes the side length
The 2 above the a tells us that we need to multiply the side length times itself.
Alright, now it's just a matter of sticking in the known values...
[tex]\sf A=(3x^2)^2[/tex]
Simplify
[tex]\sf A=9x^4[/tex]
Voila! There's our answer, cheers! (;
_________Hope I helped! Best wishes! (:
Reach far. Aim high. Dream big.
________[tex]\underbrace[/tex]
7 times 36 = 21 times ?
help needed asap :)
Answer:
7*36=21*x
252=21x
x=12
Hope it helps!
Answer:
12
Step-by-step explanation:
Let x be the unknown number.
Method 1
[tex]\implies \sf 7 \times 36 = 21 \times x[/tex]
[tex]\implies \sf 252 = 21x[/tex]
[tex]\implies \sf \dfrac{252}{21} = \dfrac{21x}{21}[/tex]
[tex]\implies \sf 12=x[/tex]
[tex]\implies \sf x=12[/tex]
Method 2 (using mental arithmetic)
[tex]\implies \sf 7 \times 36 = 21 \times x[/tex]
As 7 and 21 are both multiples of 7, divide both sides by 7:
[tex]\implies \sf 36=3x[/tex]
Divide both sides by 3:
[tex]\implies \sf 12=x[/tex]
[tex]\implies \sf x=12[/tex]
Pretest: Manipulating and Interpreting Expressions
Drag each expression to the correct location on the table.
Place each algebraic expressions next to its corresponding verbal description.
5³-²-1 (5-4)³
the difference of 5 times the cube of x cubed and
the quotient of 4 times x and 3
5 times the cube of x divided by 4 times x
the quotient of the difference of 5 times x cubed and 4 and x
the cube of the difference of 5 times x and 4
Submit
Answer:
9
Step-by-step explanation:
0
Please help me smart peeps
Determine if the two triangles below are similar and state how you know.
The first and foremost rule for determining if 2 triangles are similar is checking if their angles are the same. Obviously, in this example, the angles are completely different, so the triangles are not similar.
Have a nice day!
And good luck on the assignment!
Find the original price of a pair of shoes if the sale price is 9$ after a 75% discount
Answer:
Original price=$12
Step-by-step explanation:
First set that up as an equation
9/a=75/100
Now cross multiply
75a=900
Then divide 75 from both sides for original price
75a/75=900/75
a=12
There's your answer
Hope this helped :)
Write the equation of the line that is parallel to the line y = -x - 2 through the
point (4,-2)
Answer:
y = -x +2
Step-by-step explanation:
Equation of a line in slope-intercept form :
y = mx + b where m = slope and 'b' is the y-axis intercept
y = -x-2 is in this form..... slope m = -1 b = -2
the parallel line will have the same slope = -1 and will look like
y = -x + b
to calculate the value of 'b' for this line, substitute in the point given:
-2 = - (4) + b shows b = 2
so your line becomes y = -x + 2
Answer:
y =-x + 2
Step-by-step explanation:
Equation of line:Parallel lines have same slope.
y = -x - 2
Compare with the equation of the line in slope y-intercept form: y =mx + b
Slope = m = -1
So, equation of line: y = -x + b
Point(4 ,-2) is going through this line. so, substitute x = 4 & y = -2 in the above equation.
-2 = -4 + b
-2 + 4 = b
[tex]\sf \boxed{b = 2}[/tex]
Equation of the required line:
[tex]\sf \boxed{\bf y = -x + 2}[/tex]
OVER DUED HOMEWORK pls help!! T-T
Answer:
see explanation
Step-by-step explanation:
(9m + 4)² - (9m - 4)² ← expand both factors using FOIL
= 81m² + 72m + 16 - (81m² - 72m + 16) ← distribute parenthesis by - 1
= 81m² + 72m + 16 - 81m² + 72m - 16 ← collect like terms
= 144m
= 72(2m)
which is divisible by 72 for all m
The composite figure is made up of a parallelogram and a rectangle. Find the
area. (choices in picture)
Answer:
88 sq. units
Step-by-step explanation:
1st. BxH
12-4 = 8 is our Base
8x8=64 that is out 1st area
and 2nd area is LxW which is 12x2 = 24
64+24= 88 sq. units
What is necessary to determine the z-score for a raw score in a particular set of scores?.
Answer:
See below
Step-by-step explanation:
The mean score and the standard deviation are needed
The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. Which statement is correct?
The complete question is
"The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. Which statement is correct?
a. The domain of this function represents the total cost for a job
b. H is a function of C
c. The painter charges a $35 service fee in addition to an hourly rate
d. The painters hourly rate is $35.00"
The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. So, the correct option is D. The painters hourly rate is $35.00
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours.
The fixed fee, or service fee, is $60.
$35 is the hourly fee since in the function, it is 35 that is multiplied by the number of hours.
So, the correct option is D. The painters hourly rate is $35.00
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What shift will occur to the graph given the following equation?
y≤ |x + 2|
Graph will shift 2 units to the left.
Graph will shift 2 units to the right.
Graph will shift 2 units down.
Graph will shift 2 units up
Answer:
Graph will shift 2 units to the left
Question Progress
Find the following, giving your answers
to 1 decimal place.
10 cm/
Homework Progress
17/21 Marks
6 cm
8 cm
a) The volume of the cone.
b) The curved surface area of the cone.
Vol = ²
Curved
surface area
Answer:
[tex]\pi \times radius \times hieght[/tex]
Find the mean of the following group of numbers: 6. 1, 5. 9, 4. 2, 5. 9, and 10. 7. Round your answer to the nearest tenth
Answer:
6.6
Step-by-step explanation:
the "mean" of a data set is what we commonly refer to as the average. We find this estimate of values by adding up all of the values of the data set, and then dividing by the number of values we added together.
{for example: the mean [average] of 1, 5, 6:
1 + 5 + 6 = 12
12 ÷ 3 [we have 3 numbers] = 4}
our values:
6.1 ; 5.9 ; 4.2 ; 5.9 ; 10.7
> 6.1 + 5.9 + 4.2 + 5.9 + 10.7 = 32.8
[we have 5 numbers]
32.8 / 5 = 6.56
when rounding a number, we look to the digit one place to the right. If it is greater than or equal to 5, we "round up" our digit [we move it up to the next digit]
if it is less than 5, we keep our digit the same
(the tenths place = _ . _ _ _ ones. tenths)
so if we round 6.56 to the nearest tenth:
6.56
[6 > 5]
6.6
So, the mean of this data set rounded to the nearest tenth is 6.6
hope this helps!!
1
2
3
Click on each graph to enlarge it.
4
Suppose f(x) = x. Find the graph of f(x) + 4.
Click on the correct answer.
graph 1
graph 3
↓
graph 2
graph 4
Answer:
its most likley graph 4
Step-by-step explanation:
hope this helps and if its wrong im very sorry
What is the square root of 48 simplified?
x= help me please thank u :)
Step-by-step explanation:
the product of segments theorem :
products of segments of intersecting chords are equal.
the 2 chords helping us are
the "4 + 25" chord.
the "x + x" chord (that connects then outwards to the 20 segment).
so, based on that theorem
4 × 25 = x × x
100 = x²
x = sqrt(100) = 10
Answer two questions about system a and b
Answer:
Question 1: A. Replace one equation with a multiple of the other equation
Question 2: B. No
Step-by-step explanation:
1) How can we get System B from System A?
Choose 1 answer:
A. Replace one equation with a multiple of the other equation
B. Replace one equation with a multiple of itself
C. Swap the left-hand sides of both equations
D. Swap the order of the equations
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
Choose 1 answer:
A. Yes
B. No
The answer to both questions is in bold and in the "Answer" section.
Hope this helps!
If not, I am sorry.
A rectangular tank measures 1.2m by 0.8m by 0.5m.
(a) Water flows from the full tank into a cylinder at a rate of 0.3m3
/min.
Calculate the time it takes for the full tank to empty.
Give your answer in minutes and seconds.
By knowing that water outflow is stable and the known geometry, the draining time of the rectangular tank is equal to a time of a minute and 36 seconds.
How to determine the draining time of a rectangular tank
In this question we must determine the draining time of a tank whose dimensions are known and whose water outflow is stable. The draining time is equal to the volume of the rectangular tank divided by outflow rate:
V = (1.2 m) · (0.8 m) · (0.5 m)/(0.3 m³/min)
V = 1.6 min
By knowing that water outflow is stable and the known geometry, the draining time of the rectangular tank is equal to a time of a minute and 36 seconds.
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