At a glassware factory, molten cobalt glass is poured into molds to make paperweights. Each mold is a rectangular prism whose height is 3 inches greater than the length of each side of the square base. A machine pours 20 cubic inches of liquid glass into each mold. What are the dimensions of the mold?
Answers
Therefore, the dimensions of the mould are 7 inches by 7 inches by 10 inches.
Let x be the length of each side of the square base of the mould. Then the height of the mould is x + 3.
The volume of the mould is given by:
V = length x width x height
Since the base is a square, the length and width are both equal to x. Thus, we have:
V = x * x * (x + 3)
We know that 20 cubic inches of glass are poured into each mould, so we can set this equal to V:
20 = x * x * (x + 3)
Simplifying this equation, we get:
\(x^3 + 3x^2 - 20 = 0\)
We can solve for x using the cubic formula or by using trial and error to find a value of x that satisfies the equation. One possible method is to try values of x starting from 2 and increasing by 1 until we find a value that works:
For x = 2, we get:
\(2^3 + 3(2^2) - 20 = 0\)
This is not true, so we try x = 3:
\(3^3 + 3(3^2) - 20 = 38\)
This is too large, so we try x = 4:
\(4^3 + 3(4^2) - 20 = 68\)
This is too large as well, so we try x = 5:
\(5^3 + 3(5^2) - 20 = 105\)
This is too large, so we try x = 6:
\(6^3 + 3(6^2) - 20 = 152\)
This is too large, so we try x = 7:
\(7^3 + 3(7^2) - 20 = 203\)
This works, so the dimensions of the mould are:
Length = Width = x = 7 inches
Height = x + 3 = 10 inches
Therefore, the dimensions of the mould are 7 inches by 7 inches by 10 inches. We can verify that the volume of the mould is indeed 20 cubic inches:
V = length x width x height
= 7 inches x 7 inches x 10 inches
= 490 cubic inches
The volume of the mould is 490 cubic inches, which is 24.5 times the amount of glass poured into it. This is because the mould has extra space to allow for the expansion of the molten glass as it cools and solidifies.
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Related Questions
n a history class there are 88 history majors and 88 non-history majors. 44 students are randomly selected to present a topic. What is the probability that at least 22 of the 44 students selected are non-history majors
Answers
Answer:
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
Step-by-step explanation:
The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Approximation:
We have to use the mean and the standard deviation of the hypergeometric distribution, that is:
\(\mu = \frac{nk}{N}\)
\(\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}\)
In this question:
88 + 88 = 176 students, which means that \(N = 176\)
88 non-history majors, which means that \(k = 88\)
44 students are selected, which means that \(n = 44\)
Mean and standard deviation:
\(\mu = \frac{44*88}{176} = 22\)
\(\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88\)
What is the probability that at least 22 of the 44 students selected are non-history majors?
Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, this is \(P(X \geq 22 - 0.5) = P(X \geq 21.5)\), which is 1 subtracted by the p-value of Z when X = 21.5. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{21.5 - 22}{2.88}\)
\(Z = -0.17\)
\(Z = -0.17\) has a p-value of 0.4325
1 - 0.4325 = 0.5675
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
I need help with this practice sheet
I'm confused with this
Answers
End behavior is when the graph goes left or right, does it go up or down.
In this graph, when it goes left it goes up, and when the graph goes right it goes down
as x => - infinity, f(x) => Infinity
as x => Infinity, f(x) => - infinity
The leading coefficient is negative.
The degree is even.
Is 10.6 x 10^14 scientific notation
Is 2.019 x 10^12 scientific notation
is 9.5 x 10^-7 scientific notation
0.526 x 10^-2 scientific notation
Answers
Answer:
The top and the bottom numbers are not in scientific notation; the other two are in scientific notation.
For the two numbers listed, find two factors of the first number such that their product is the first number and their sum is the second number - 36,5
Answers
Answer:
The two factors of the first number are -4 and 9.
Step-by-step explanation:
We're given:
Two numbers have a product of -36The same two numbers have a sum of 5Let the two numbers be a and b:
\(ab=-36\)\(a+b=5\)Solving for bIsolate a in the second equation and solve for b:
\(a+b=5\\a=5-b\)
\((5-b)b=-36\\5b-b^2=-36\)
Arrange in \(ax^2+bx+c=0\) format:
\(-b^2+5b+36=0\)
Divide both sides by -1:
\(b^2-5b-36=0\)
Factor:
\(b^2+4b-9b-36=0\\b(b+4)-9(b-4)=0\\(b-9)(b+4)=0\)
Solve for b using the zero product property:
\(b=-4,9\)
Solve for aSubstitute b back into the second equation to solve for a:
\(a+b=5\)
First, let b = -4:
\(a-4=5\\a=9\)
Let b = 9:
\(a+9=5\\a=-4\)
Simplify
−
4
x
+
2
y
+
z
−
3
x
+
2
y
−
2
z
Answers
Answer: -7x+4y-z would be the answer
Step-by-step explanation:
Find the weight of one square in hanger a and the weight of a pentagon in hanger b
Answers
Answer:
the first and second M is undefined because we have no information to make an equation
The graph of this line shows the total amount Katrina earns for working a corresponding number of hours. How much did Katrina earn for working 7 hours?
Answers
The correct statement is that for each hour, the earnings go up by $7. Option A
What is straight line graph?If we have the equation of the line, we can substitute the value of 7 for the number of hours into the equation and solve for the earnings. The equation would typically be in the form of "earnings = slope * hours + y-intercept," where the slope represents the rate of earnings per hour and the y-intercept represents the earnings when no hours are worked.
We can find the slope of the graph to know as said above;
m = y2 - y1/x2 - x1
m = 14 - 0/2 - 0
m = 7
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Which of the realtions are total orderings?
Answers
The relations are total orderings will be {(a, c), (b, a), (b, c), (d, d)},{(a, a), (a, b), (b, b), (c, c), (d, d)} and {(a, a), (a, b), (a, c)}.
What are total orderings?A complete order is a set plus a relation on the set (also known as a total order), which meets the prerequisites for a partial order as well as an extra criterion known as the comparability condition.
Total orders are sometimes referred to as simple orders, connex orders or whole orders.
A set that has entire order is referred to as a totally ordered set; other words like a linearly ordered set, lost, and simply ordered set are also used. Although the word "chain" is occasionally used as a synonym for "completely ordered set, it more commonly refers to a particular type of fully ordered subsets of a given partially ordered set.
A linear extension of a partial order occurs when it is extended from the partial order to the entire order.
Thus, the relations are total orderings will be {(a, c), (b, a), (b, c), (d, d)},{(a, a), (a, b), (b, b), (c, c), (d, d)} and {(a, a), (a, b), (a, c)}.
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How to show work for 339.3÷13
Answers
Step-by-step explanation:
Refer to the notes on long division
7 whole number 1 over 2 percent to it's lowest term
Answers
The fraction in its lowest terms for 7 1/2 percent is 3/40.
To express the mixed number 7 1/2 percent as a fraction in its lowest terms, we need to convert it to a fraction and simplify.
First, we convert the mixed number to an improper fraction:
7 1/2 percent = 7 1/2 / 100
To simplify this fraction, we find the least common multiple (LCM) of the denominator (2) and the percent denominator (100), which is 200.
Now, we can rewrite the fraction with the common denominator:
7 1/2 / 100 = (7 * 2 + 1) / 200 = 15/200
To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 200 is 5.
15/200 = (15 ÷ 5) / (200 ÷ 5) = 3/40
Therefore, the fraction in its lowest terms for 7 1/2 percent is 3/40.
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calculate the difference quotient and use your results to find the slope of the tangent line
Answers
Approximate Slope of a Function
We are given the function:
\(H(x)=8\ln x+3\)We will find the approximate value of the slope at (e,11).
It's required to use 3 possible values of the approximation differential h.
Let's use h=0.1 and evaluate the function at x = e + 0.1 = 2.8182818
Compute:
\(H(e+0.1)=8\ln 2.8182818+3=11.2890193\)Compute the difference quotient:
\(H^{\prime}=\frac{11.2890193-11}{0.1}=2.890193\)Now we use h=0.01:
\(H(e+0.01)=8\ln 2.728281828+3=11.02937635\)The difference quotient is:
\(H^{\prime}=\frac{11.02937635-11}{0.01}=2.9376353\)Finally, use h=0.001:
\(H(e+0.001)=8\ln 2.719281828+3=11.00294249\)\(H^{\prime}=\frac{11.00294249-11}{0.001}=2.9424943\)The last result is the most accurate, thus the slope of the tangent line is 2.94
voting rates in presidential elections from 1996-2012 are modeled below
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The statement that does not model the situation:
(1) For citizens 18-29 years of age, the rate of change in voting rate was greatest between the years 2000-2004.
What is a confidence interval?A confidence interval is a range of values that are constrained by the statistic's mean and that is likely to include an unidentified population parameter. The proportion of likelihood, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn several times is referred to as the confidence level.
Given:
Voting rates in presidential elections from 1996-2012 are modeled below.
Voting Rates in Presidential Elections, by Age, for the Voting-Age Citizen Population: 1996-2012
The interpretation of the statements is given below;
(1) For citizens 18-29 years of age, the rate of change in voting rate was greatest between the years 2000-2004.
No, the greatest was in the year 2008.
(2) From 1996-2012, the average rate of change was positive for only two age groups.
True, the age groups are 39.6 to 45.0 and 69.1 to 72.0.
(3) About 70% of people 45 and older voted in the 2004 election.
Yes.
(4) The voting rates of eligible age groups lie between 35 and 75 percent during presidential elections every 4 years.
Yes, the interval difference is 4.
Therefore, option (1) is incorrect.
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Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
NO LINKS!!! URGENT HELP PLEASE!!!!
Manny bought a brand new car in 2012 for $28,750. If the car depreciaites by 12% each year, write an exponential function to model the situation, then find how many years until the car is only worth $10,000
Answers
It will take approximately 8.53 years for the car to be worth $10,000, assuming a constant annual depreciation rate of 12%.
To model the depreciation of Manny's car, we can use the method for exponential decay:
\(y = a(1 - r)^t\)
Wherein:
y = the cost of the car at time ta = the initial value of the car (in 2012)r = the annual depreciation price (as a decimal)t = the time in yearsIn this situation, we've:
a = $28,750r = 12% = 0.12 (as a decimal)y = $10,000Substituting those values into the method, we get:
\($10,000 = $28,750(1 - 0.12)^t\)
Dividing each aspects by $28,750, we get:
\(0.3478 = (0.88)^t\)
Taking the logarithm of both facets (base 10), we get:
\(log(0.3478) = t*log(0.88)\)
Solving for t, we get:
\(t = log(0.3478)/log(0.88)\)
= 8.53 (rounded to two decimal locations)
Consequently, it'll take approximately 8.53 years for the car to be worth $10,000.
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Answer:
8.26 years
Step-by-step explanation:
To model the depreciation of the car over time, we can use an exponential decay function in the form:
\(\large{\boxed{V(t) = V_0(1 - r)^t}\)
where:
V₀ is the initial value of the car.r is the depreciation rate per year (as a decimal).t is the time elapsed (in years)V(t) is the value of the car after t years.Given values:
V₀ = $28,750r = 12% = 0.12V(t) = $10,000Substitute these values into the formula and solve for t:
\(V(t) = V_0(1 - r)^t\)
\(10000=28750(1-0.12)^t\)
\(10000=28750(0.88)^t\)
\(\dfrac{10000}{28750}=(0.88)^t\)
\(\dfrac{8}{23}=(0.88)^t\)
\(\ln \left(\dfrac{8}{23}\right)=\ln (0.88)^t\)
\(\ln \left(\dfrac{8}{23}\right)=t\ln (0.88)\)
\(t=\dfrac{\ln \left(\dfrac{8}{23}\right)}{\ln (0.88)}\)
\(t=8.2611657...\)
Therefore, the car will be worth $10,000 after approximately 8.26 years, or about 8 years and 3 months.
Note: After 8 years, the car will be worth $10,339.49. After 9 years, the car will be worth $9,098.75. So the value of the car will reach $10,000 during the 9th year. Therefore, rounding up to 9 years may be more appropriate if the answer should be in whole years.
HELP I NEED THIS WITHIN 2 MINUTES AB if AC = 13.2 And BC = 6.8
Answers
Answer:
AB = 6.4
Step-by-step explanation:
Assuming that AB + BC is AC, then we can say the following:
AB + BC = AC
AB + 6.8 = 13.2
AB + 6.8 + -6.8 = 13.2 + -6.8
AB = 6.4
Cheers.
Explanation:
AB + BC = AC
AB + 6.8 = 13.2
AB = 13.2 - 6.8
AB = 6.4
Therefore, AB = 6.4
Simplify the expression: 4(2x - 4)
Answers
Answer: 8x-16
Step-by-step explanation:
Answer: 8x-16
Step-by-step explanation:
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
Latoya's softball team won 75%, or 18, of its game. Define a variable. Write and solve an equations to determine the number of games the team played.
Will give brainliest
Answers
100%=?
If you divide 18 by 3=6
So 6 =25%
So 25%+75%=100%
Therefore
6+18=24=100%
So an equation would look like.
(18dividedby3)4=n
Good luck!
Answer:
18 / 3 * 4 = a
a = 24
Step-by-step explanation:
so we know that 18 is = to %75 but we need to know what %100 is, to figure this out lets find a common denominator
so we know that %75 of something is 3/4, and to double check, we can take the fraction 3/4 and divide it the way its written, bc thats what a fraction is, a small division problem
3 / 4 = 0.75 or 75/100 or %75
so now we know we have 3 out of 4 parts of something, to find out how big each part is, we divide the number (18) by how many pieces we have...
18 / 3 = 6
so each 1/4 is = to 6, now to figure out the whole, we multiply by how many pieces are in said whole, in this case by 4
6 * 4 = 24
so since we know that 6 is = to %25 and we multiplied 6 by 4, we can do the same to %25...
25 * 4 = 100
and have the whole
this is basically a detailed explanation of the other answer
hope this helps :)
cuanto es 1 mas 1? dende ecuaciones y detalles es para mi examen virtual please
Answers
Answer:
2
Step-by-step explanation:
1+1=2
IM NOT GOOD AT MATH PLEASE HELP WITH THESE FEW QUESTIONS ASAP
Answers
Answer:
for the first question
solve for t:t= square root of 2da/a (2da over a)
Solve for a : a= 2d/t squared
Solver for d: d=t squared /2(over 2)
Step-by-step explanation:
the ratio measures of two complementary angles is 5:4. what is the measure of the lager angle
Answers
Answer:
5=50
4=40
Step-by-step explanation:
the angles are 5x and 4x because 5x:4x is 5:4
And it is equal to 90
5x + 4x = 90
9x=90
x=10
Which of these contexts describes a situation that is impossible?
Rolling a number less than 1 on a standard six-sided die, numbered
from 1 to 6,
Spinning a spinner divided into four equal-sized sections colored
red/green/yellow/blue and landing on some color,
Winning a raffle that sold a total of 100 tickets if you bought 50 tickets,
Reaching into a bag full of 15 strawberry chews and 5 cherry chews
without looking and pulling out a strawberry or a cherry chew.
Answers
Rolling a number less than 1 on a standard six-sided die, numbered
from 1 to 6 is an impossible situation.
What is a sure event?Suppose we have a coin with sides heads and tails then the occurrence of a head or a tail is a sure event.
If we observe the given options we can conclude that Rolling a number less than 1 on a standard six-sided die, numbered from 1 to 6 is an impossible situation as we couldn't get a number less than 1 on the die not possible right?
All the other options seem possible in some different ways but the first option is an impossible situation.
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f(x) =x(x-1) on R to R
find A and B such that g: A to B defined by g(x)=f(x) is bijective
this is an algebra question, help.
details are needed
Answers
Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.
To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.
So, let's assume that g(x1) = g(x2). Then, we have:
f(x1) = f(x2)
x1(x1-1) = x2(x2-1)
x1^2 - x1 = x2^2 - x2
x1^2 - x2^2 - x1 + x2 = 0
(x1 - x2)(x1 + x2 - 1) = 0
Since x1 and x2 are distinct, we must have x1 + x2 = 1.
But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.
To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.
So, let's solve the equation f(x) = y for x:
x(x-1) = y
x^2 - x - y = 0
Using the quadratic formula, we get:
x = (1 ± √(1 + 4y))/2
Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.
Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.
Please help!
Find the value of x for which ABCD must be a parallelogram.
Answers
Answer:
x=5
Step-by-step explanation:
5x-8=2x+7
5x-2x=7+8
3x=15
X=15/3
x=5
Answer:
5
Step-by-step explanation:
cause
angle c and angle a are alternate angle and alternate angle are always equal so 5X-8=2x+7
5x-2x=7+8
3x=15
or x=5
Integration of [(x+1)/(x-1)]dx
Answers
Hello!
∫[(x+1)/(x-1)dx
∫t+2/t dt
∫t/t + 2/t dt
∫1 + 2/t dt
∫1dt + ∫2/t dt
∫t + 2In (|t|)
x - 1 + 2In (|x-1|)
x + 2In (|x-1|) + C, C ∈ R
Good luck! :)
simplify the expression -19c-4c+9+16
Answers
The algebraic expression -19c - 4c + 9 + 16 when simplified is -23c + 25
Simplifying the algebraic expressionFrom the question, we have the following parameters that can be used in our computation:
-19c-4c+9+16
Express properly
So, we have
-19c - 4c + 9 + 16
Evaluate the like terms
This gives
-19c - 4c + 9 + 16 = -23c + 25
Hence, the algebraic expression when simplified is -23c + 25
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Pls Help! the question is down below
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Please mark brainliest!
What is the volume of the right rectangular prism, in cubic centimeters?
Vx
9 cm
3 cm
4 cm
cubic centimeters
©
Answers
Answer:
108 cm³
Step-by-step explanation:
Formula: V = w×h×l
Solution: V = whl = 4·3·9 = 108
Hence, the answer is 108 cm³
\(6 \times 2\)
please I need ur help
Answers
Answer:
12
Step-by-step explanation:
You do 6+6, or 2+2+2+2+2+2=12
Just add 6, 2 times so 6, 12
Or add 2, 6 times so 2,4,6,8,10,12
A bank charges 12% Simple interest p.a on cash loans to its clients.tito has asked for R10000loan amount and has promised to repay the the loan over 4years
Calculate the interest which Tito has to pay on loan ?
Determine the total amount to be paid back
Determine the monthly repayment amount
Answers
If Tito took a loan of $10000 from a bank to be repaid within 4 years, at 12% Simple interest per annum, then, he will have to pay overall $4800 as interest to the bank over 4 years and a total payment of $14800 at the end of the 4th year to repay and close off the loan.
As per the question statement, a bank charges 12% Simple interest per annum on cash loans to its clients and Tito took a loan of $10000 from the same bank to be repaid within 4 years.
We are required to calculate the overall interest Tito has to pay to bank if he repays and closes the loan at the end of 4th year, and also to calculate the total payment required to repay and close off the loan at the end of the 4th year.
To solve this question, we need to know the formula to calculate the interest amount in case of simple interest which goes as
Interest (I) \(=(\frac{P*R*T}{100} )\)
where, "P" = Principle amount of Loan,
"R" = Rate of simple interest charged on the principle per annum, and
"T" = Time period within which, the loan is to be repaid.
Here, (P = 10000), (R = 12%) and (T = 4). Then, the overall interest Tito will have to pay at the end of 4th year = \((\frac{10000*12*4}{100}) = (100*12*4)=(48*100)=4800\)
And total amount to be paid to repay and close of the loan at the end of 4th year will be = $[4800 + 10000] = $14800.
Simple interest: As the name itself suggests, "Simple" interest refers to the straightforward crediting of cash flows associated with some investment or deposit.To learn more about Simple Interest, click on the link below.
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