The interest rate needed to make $3,472.32 from simple interest on a principal of $1,200.00 over 9 years is 21.04% per year.
How to determine simple interest rate?Simple interest is expressed mathematically as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is rate and t is the time period.
Given the data in the question;
Principal P = $1200 Accrued amount A = $3472.3Time period t = 9 yearsInterest rate r = ?Plug the given values into the simple interest formula and solve for r
A = P( 1 + rt )
r = (1/t)(A/P - 1)
r = ( 1/9 )( $3472.3/$1200 - 1)
r = ( 1/9 )( 2.8936 - 1)
r = ( 1/9 )( 1.8936)
r = 0.2104
Convert to percentage
r = 0.2104 × 100%
Rate r = 21.04%
Therefore, the interest rate of the loan is 21.04%.
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MANUFACTURING At a factory, molten glass is poured into molds to make
paperweights. Each mold is a rectangular prism with a height 4 inches
greater than the length of each side of its square base. Each mold holds
63 cubic inches of molten glass. What are the dimensions of the mold?
The dimensions of the mold are a length and width of 3 inches and a height of 7 inches.
What is the volume of a rectangular prism?The volume of a rectangular prism is the space that it contains. We know that the volume of any prism is calculated by multiplying its base area by its height.
Given :
Let's assume that the length and the width of the "box" is x.
It is said that the height is 4 inches greater, so the height is x+4.
The volume of the mold is:
V = (x)(x)(x +4)
V = x²(x +4 ) using the Distributive Property.
V = x³ + 4x²
Since from the question we have Volume = 63 cubic inches
The equation we have is,
63 = x³ + 4x²
Subtracting 63 from both sides of the equation,
x³ + 4x²- 63 = 0
The cubic equation can be written as,
(x−3)(x²+7x+21) = 0
The solution of the quadratic equation (x²+7x+21) is,
x = -b ±√(b² - 4ac) / 2a
a = 1 , b =7 and c = 21
Substituting the values in the formula,
x = -7 ±√(7² - 4(1(21)) / 2(1)
x = -7 ±√-35 / 2
Hence,there are no real solutions to the quadratic equation.
There is only one real solution to the equation x = 3.
Therefore, the length and width of the rectangular prism are 3 inches and the height is x+4 = 3+4 = 7 inches.
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The relationship between the number of $4 lunches you buy with a $105 school lunch card and the money remaining on the card
The relationship will be a solid line.
How many $4 meals you may purchase with a $100 school lunch card and how much money is still on the card.
Given that the slope is common and linear, the connection will be a solid line. The balance on the card will drop by $5 each time you purchase lunch.
Let x be the amount of lunches you purchase.
Let the balance on the card be = y.
Equation then becomes:
y= 105-4x
when x=1
y = 105 - 4(1) = 101
when x= 2
y= 105 - 4(2) = 97
when x=3
y= 105 - 4(3) = 93
We can see that the decline is gradual and same.
On the graph that is provided, you can also observe that a straight line is created.
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Question content area top Part 1 The temperature in a town is 31.6 during the day and -17.2 at night. Find the difference in the temperatures.
Answer: The difference in temperature is 45.9F.
For Items 12–14, use the figure shown.
Two vertical parallel lines are intersected by two diagonal transversals, one slanting up and one slanting down. They intersect the left line at the same point, creating 6 angles, starting at the bottom left of the right line and moving clockwise, they are: 3, 2, 1, left parenthesis 4 y times 3 right parenthesis, left parenthesis 3 x times 9 right parenthesis, and left parenthesis 5 x right parenthesis. The line slanting up intersects the right vertical line creating 4 angles, starting at the bottom left and moving clockwise, they are: 6, 4, 5, and left parenthesis 9 x times 3 right parenthesis. The line slanting down intersects the right vertical line creating 4 angles, starting at the bottom left and moving clockwise, they are: 8, 7, left parenthesis 7 y times 6 right parenthesis, and 9.
What is m∠2?
A. 12
B. 18
C. 45
D. 120
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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if 2 x 2 whats the divided by -3 to 4
Answer:its 2
Step-by-step explanation:
How to draw two equilateral triangles that are not congruent
No, it is not feasible to produce any two structuring elements that is not always congruent with one another. This is because equilateral triangles have no internal angles.
This is further explained below.
What is an equilateral triangle?Generally, In the field of geometry, a triangle is said to be equilateral if all three of its sides have the same length.
In the well-known geometry of Euclidean, an equilateral triangle is also an equiangular triangle. This means that all three of the triangle's interior angles are equivalent to each other and are each 60 degrees.
No, it is not possible to create any two equilateral triangles that are not always congruent with one another.
In conclusion, The logic for this is that while each angle in an equilateral triangle is 60 degrees, the sides of the triangle cannot always be identical.
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-3x+14-11+11x I tried getting help with this question and it didn’t give me enough information to fully understand.
Answer:
0.375
Step-by-step explanation:
-3x+14-11+11x
-3x+11x = 8x
14-11 = 3
8x=3
÷8 on both sides
What is the equation of the line?
Answer:
Thr equation is y=x-1
Step-by-step explanation:
The y intercept is negative 1 so that eliminates options 1 and 3 and the slope goes up which leaves only option 2 left
Solve {2c+8}={10c} . Answer in simplest fraction form.
Answer: c=1
Step-by-step explanation:
Move the variable to the left side
2c+8−10c=0
Subtract the terms
−8c+8=0
Move the constant to the right side
−8c=0−8
Subtract the terms
−8c=−8
Divide both sides
−8c = −8
−8 -8
Simplify
what set of numbers dose -17 belong to?
A. integers, rational numbers, real numbers
B. rational numbers, real numbers
C. whole numbers, integers, real numbers
D. whole numbers, integers, rational numbers, real numbers
A
-------------------------------------------------------
bc it is an integer but not whole numbers
What is the slope of the line that passes through the points (7,-6) and (6, -6)
Write your answer in simplest form
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (7, - 6 ) and (x₂, y₂ ) = (6, - 6 )
m = [tex]\frac{-6-(-6)}{6-7}[/tex] = [tex]\frac{-6+6}{-1}[/tex] = [tex]\frac{0}{-1}[/tex] = 0
HELPHELPHELPHELP plssssssssssssssssssssssss
The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer in simplest form. ( wouldn't allow me to insert full picture. will message it to you.)
To find the scale factor, we just have to divide
[tex]\frac{8}{20}=\frac{2}{5}[/tex]Hence, the scale factor is 2/5.
Sandra Keegan worked 38 hours at $12.95 per hour and 6 hours of overtime at time and a half what was her pay for the week?
Answer:
$569.80
Step-by-step explanation:
She worked $12.95 per hour for 6 hours of overtime, meaning we would multiply $12.95 by 6 which is equal to $77.70, since she worked for 38 hours that week, we would multiply $12.95 by 38 which is $492.10, so now we add how much she earned for the total. Her overtime pay was $77.70 + her regular pay was $492.10 which adds up to $569.80
Determine whether the given function is even, odd or neither. *(1 Point)f(x) = x3 - 2x
Given:
The function is,
[tex]f(x)=x^3-2x[/tex]Replace x by -x in the given function,
[tex]\begin{gathered} f(x)=x^3-2x \\ f(-x)=(-x)^3-2(-x) \\ =-x^3+2x \\ =-(x^3-2x) \\ =-f(x) \end{gathered}[/tex]It is observed that, when the x is replace by -x the function end up with exactly opposite of the given function.
Thus, the given function is odd.
Andrew would like to put six different Rubik's cubes onto 3 shelves. The order of the cubes does not matter.
In how many ways can Andrew do this if a shelf can have zero cubes?
What if each shelf must have at least one cube?
Answer:
540
Step-by-step explanation:
how does x equal y in three dimesional math
Step-by-step explanation:
in 3-dimensional math we have 3 dimensions, and not just 2.
we have
forwards - backwards
left- right
up- down
so, we have there x, y and z.
and the equations typically are
z = ax + by
or even more general
cz = ax + by
or more complex functions of x and y.
z = f(x, y).
I am not sure what else you could mean with that question.
What is equivalent to 0.325 in as a fraction
Answer:
0.325 as a fraction is expressed as 13/40
Step-by-step explanation:
What is a fraction ?
A fraction is a portion of any quantity out of a whole. It consists of a numerator and a denominator.
To convert a decimal number into a fraction, we write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly. Then, this fraction can be simplified.
In this case, 0.325 has three numbers after the decimal, so, we place 1000 in the denominator and remove the decimal point.
⇒ 325/1000
After reducing this fraction we get,
⇒ (325 ÷ 25) / (1000 ÷ 25) = 13/40
So, 0.325 as a fraction is 13/40.
(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)
Stay positive and Take care,
A fellow mate,
Cheers !
Please help me with this question, if it’s wrong I will report you, thank you for your help!
IN THE ATTACHED PICTURE YOU CAN SEE THE YELLOW VERTICAL LINE TOUCHED THE GRAPH ONCE IT MEANS THE GRAPH ABOVE IS A FUNCTION.
THEREFORE THE LAST OPTION IS THE SOLUTION. THE GRAPH IS A FUNCTION BECAUSE IT PASSES THE VERTICAL LINE TEST .
HOPE THIS HELPS
The directions on a seed packet say to plant the seeds 1 7/8 inches apart. What is the decimal equivalent of this mixed number?
Enter your answer in the box.
Answer:
1 7/8 inches is 1.875 in decimal form.
help please
What is the correct way to break 12 into parts and multiply each part by 6?
Answer:
2nd one
Step-by-step explanation:
Hope I helped!
What is the probability of
spinning an A?
B B
A
B
A
[?]%
Answer:
I believe you have a 25% of spinning an A
Step-by-step explanation:
If there are two possible A's to land on and there are 8 different choices,
2/8 = 1/4 and 1/4 is equal to 25%
So the probability would be "not likely"
Hope this helps! Please have an amazing day! :)
line has an x-intercept of -5 and a y-intercept of 3. Use this information for questions
8 through 10.
8.
Find the slope of the line.
9. Write the equation of the line in slope-intercept form.
10. Write the equation of the line in standard form.
Answer:
[tex](1)\;\;\;\text{Slope }= \dfrac{3}{5}\\[/tex]
(2) Equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]
(3) Equation of line in standard form is:
[tex]5y - 3x = 15[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept
Slope = [tex]\dfrac{y2 - y1}{x2-x1}[/tex]
where (x1, y1) and (x2, y2) are two points on the line.
y2 - y1 is known as the rise
x2 - x1 is known as the run
Slope is also defined as rise/run
We are given x-intercept = -5.
The ex-intercept is the point at which the line crosses the x-axis. At this point the y-value = 0.
So we get one of the points (-5, 0)
We are given y-intercept = 3
The y-intercept is the point at which the line crosses the y-axis. At this point the x-value is 0
So another point on the line is (0, 3)
Knowing this we can compute rise and run
rise = y2 - y1 = 3 - 0 = 3
run = x2 - x1 = 0 - (-5) = 0+5 = 5
[tex](1)\;\;\;\text{Slope = $\dfrac{3}{5}$}[/tex]
(2) Equation is
y = mx + b where m = slope and b = y-intercept
Slope = 3/5 from (1) and y-intercept = 3
So equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]
(3) Equation in standard form
In (2) subtract (3/5)x from both sides.
[tex]y - \dfrac{3}{5}x = 3[/tex]
We can multiply both sides by 5 to get
[tex]5(y - \dfrac{3}{5}x )= 5 \times 3\\\\= 5y - 3x = 15[/tex]
soyala went to the college traveling 25 mph and returned home traveling 15 mph. if the total trip took 8 hours, how long did soyala travel at each speed?
Soyala travelled for 3 hours with a speed of 25 mph and 5 hours with a speed of 15 mph
We know that Distance = Rate x Time. The distance traveled to the library is assumed to be same as the distance traveled on the way to home from the library. Let t be the time it took to travel to the library after which (8 - t) = the time it took to travel back home. We can write following two equations using the formula for distance:
d = 25t ---------> (1)
d = 15(8 - t) = 120 - 15t -----------> (2)
Since the distance d is equal for both trips, let's set the two expressions of time t equal to each other.
25t = 120 - 15t
40t = 120
t = 3 hours
Therefore, Soyala travelled for 3 hours at 25 mph and for 8 - 3 = 5 hours at 15 mph. Each rate will yield a distance traveled of 125 miles.
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3/4 + 1/3 as a fraction
Answer:
Step-by-step explanation:
Answer:1 1/12
Step-by-step explanation: 3/4+1/3=13/12=1 1/12
Which postulate could we use to prove that the angles
The postulate that could be used is the: linear pair postulate.
What is the Linear pair Postulate?If two angles share a common side and also a common vertex lie on a straight line, they both form a special angle relationship that is called the linear pair.
Based on the linear pair postulate, it is proven that angles that form a linear pair add up to 180 degrees and are therefore regarded as supplementary.
Angle CAD and angle CAB have a common side, side CA, and a common vertex, angle A. They are also on the straight line, line AB.
Thus, it can be proved that the angles CAB and CAD are supplementary based on the linear pair postulate.
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The slope of MN¯¯¯¯¯¯¯ is −6. what segments are parallel to MN¯¯¯¯¯¯¯?
The slope of the parallel line to line MN -6
How to determine the slope of the line?From the question, the line is given as
Line MN
Also, we have the slope of line MN to be
Slope of MN = -6
As a general rule in linear functions and parallel lines
The slopes of parallel lines are equal
This means that any line that is parallel to the line MN and the line MN would have the same slope of -6
Hence, the slope of the line segments that are parallel to line MN is -6
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What is the slope of the line that passes through the points (10, 8) and
(7, 14)? Write your answer in simplest form.
Answer:
Formula for slope is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).
Slope of line = (14-8)÷(7-10)
= 6÷(-3)
= -2
we know that on average the time it takes to complete a homework assignment is 2.3 hours with a standard deviation of .5 hours. with 13 students in the class, the average to complete the homework was 1.5 hours. what is the percentile of this class
In standard deviation, 120 is the percentile of this class.
Why is there a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.Test statistic (z) = (weekly study time - average study time)/standard deviation
weekly study time = 2.3 hours
average study time = .5 hours
standard deviation = 1.5 hours
z = (2.3 - 0.5)/1.5
= 1.8/1.5 = 1.2 (to 2 decimal places)
Cumulative area of the test statistic is 1.2
Percentile = 1.2×100 = 120
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In a class of 25 students, 13 are female and 15 have an A in the class. There are 10 students who are female and have an A in the class. What is the probability that a student has an A given that the student is female?
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
25 students in total.
13 are female. therefore, 25-13 = 12 students are male.
15 students have an A.
10 students are female and have an A.
therefore, 15-10 = 5 male students have an A.
"given that a student is female".
this reduces our totally possible cases to 13.
so, the probability that a female student has an A is
10/13 = 0.769230769...