Using the formula of simple interest, the total interest paid on a $20000 loan at rate of 2% over 4 years is $1600
Simple InterestSimple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
Principal: The principal is the amount that initially borrowed from the bank or invested. The principal is denoted by P.Rate: Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 10%, or 13%, etc. The rate of interest is denoted by R.Time: Time is the duration for which the principal amount is given to someone. Time is denoted by T.Amount: When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called Amount.The formula is given S.I = P(1 + RT)
Data;
P = 20000r = 2%t = 4 yearsS.I = 20000(1 + 0.02 * 4)
S.I = 21600
The total interest paid is 21600 - 20000 = 1600
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One year, the population of a city was 209,000. Several years later it was 217,360. Find the percent increase.
The percentage of the increase in population is 4%
How to determine the percentage of the increase?From the question, we have the following parameters that can be used in our computation:
Initial population = 209000
New population = 2017360
The percentage of the increase is then calculated using the following percentage equation
Percentage increase = (New population - Initial population )/Initial population * 100%
Substitute the known values in the above equation, so, we have the following representation
Percentage increase = (217360 - 209000)/209000 * 100%
Evaluate
Percentage increase = 4%
Hence, the increase percentage is 4%
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explain what an exponential function is. please do not palgraize
As below it is described what is exponential function with some examples.
What is Function ?A function is simply a “mapping” between 2 sets of objects (usually numbers but they could really be anything) such that, every object in the first set (the domain) is mapped to a single object in the second set. What you usually see as examples of functions (e.g. f(x)=x²) actually define the relationship between the sets. This is what I mean by “mapping”. Often, we don’t explicitly state what the sets are, because it’s understood from the context, but technically, it’s not a function unless we state the sets. E.g., instead of saying f(x)=x², we should say f:x↦x²|x∈ℂ (pronounced “f maps x to x² such that x is a complex number”), meaning that we map the complex numbers to themselves using the rule that we square each input. You can define it differently, so that, for example, we map complex to reals. However, and this is important, that would be a different function, even though the “rule” for turning inputs into outputs is the same.
Exponential Function:
Exponential functions are functions of the form f(x) = b^x where b is a constant.
The real mathematical importance of exponential functions is in their being proportional to their derivatives meaning the bigger x is, the steeper the slope of the function. This means they grow extremely fast: exponentially fast.
A common example of exponential growth is a bacterial population. Since bacteria reproduce rapidly by mitosis, for every bacterium in a culture, there will, before long be two bacteria. Thus, if I have 10 bacteria to start, one minute later I will have 20, and in another minute, each of those twenty will have reproduced and I will have 40; one minute later the same will have happened again and before long, the culture will be overrun with bacteria. The more bacteria there are, the more bacteria there are to make even more bacteria the next minute.
All exponential functions are proportional to their derivatives, but the function f(x) = e^x (where e = 2.718281828459…) is actually equal to its derivative meaning the y value of the function at a particular x value is equal to the slope of the curve at that same x value. Thus when dealing with exponential functions in calculus, e becomes a very natural number to use as a base. This is why e is such a big deal and why teachers try to introduce the number early on in Algebra 2, even though it doesn’t have much use at that point in one’s mathematical education.
When plotting an exponential curve by hand, one ought to simply pick whole number x values and multiply the base by itself an x number of times to calculate the corresponding y value. This will give a rough plot of the graph of the curve, although a calculator is requires to plot the points not on whole number x values. The curve of simple exponential functions is always increasing and concave up, or vice versa for b^-x. For a positive exponential function like f(x) = e^x, as x approaches ∞, f(x) approaches ∞, and as x approaches -∞, f(x) approaches 0. The curve has no absolute maximum or minimum value and has a horizontal asymptote at y = 0.
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The length of a rectangle is three times its width. If the perimeter of the rectangle is 72 yd, find its length and width.
solve asap pls. i need this done right now.
Answer:
-5/12
Step-by-step explanation:
Answer: 3 1/12
Step-by-step explanation: First We Would Do 2 1/2 + -7/6 First. We Would Get 1 1/3 Because We Change The Mixed Fractions Into Improper Fractions. So We Would Do 5/2 + - 7/6. We Would Then Find A Common Denominator Which Would Be 12. So 7/6 Would Be 14/12 & 5/2 Would Be 30/12. If You Did The Math Correctly You Would Get 1 1/3. Now 1 1/3 - 1 3/4 Would Be 3 1/12. You Would Change The Fractions To Improper Fractions And Then Subtract. You Would Also Need To Find The Common Denominator Which Is 12.
Hoped This Helped!
please help it’s due tomorrow
[x + y = -4
[x - y = 2
Answer:
which one substitution or elimination
Step-by-step explanation:
Substitution: (-1,-3 )
Elimination: (-1,-3)
i hope this helps you :)
Please mark me brainlest
If I work from 4:30pm to 9:00pm how many hours did I work?
Answer:
4 hours and 30 minutes.
Step-by-step explanation:
You count, 4, 5, 6, 7, 8, then you take the 30 from 4:30 and add another 30 to it to make it five. 5+4=9 or 4.5 + 4.5=9. (In this case, 30 is half of an hour, hence the 4.5 instead of 4.3).
Answer:
5 hours and 10 minutes.
Step-by-step explanation:
9:00 minus 4:30 = 4:70.
4:70 = 5 hours and 10 minutes.
A movie theater sells popcorn in a reusable bucket for $3.50. They offer refills for $2.50 each.
Write an equation in slope-intercept form to model the cost in dollars, y, for x refills.
The equation in slope-intercept form to model the cost in dollars, y, for x refills is 3.50 = 2.50x + b.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
We have been given that movie theater sells popcorn in a reusable bucket for $3.50. They offer refills for $2.50 each.
The value of y is popcorn cost = $3.50
The slope will be $2.50
Therefore, the equation is y = mx + b
Plug the values; y = 3.50 and m = 2.50
3.50= 2.50x + b
Hence, the equation in slope-intercept form to model the cost in dollars, y, for x refills is 3.50= 2.50x + b.
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am i shadowbanned why aren't people answering my questions
Answer:
no
Step-by-step explanation:
your questions are so tricky to pass
One coral reef is located 19 feet below sea level. Another is located 26 feet below sea level. What is the difference in the depths of the two reefs?
help asap 45 points
Coach Rogers listed the number of the different types of balls in the storage room. What is the ratio of baseballs to all of the balls?
Group of answer choices
1 : 5
1 : 4
1 : 10
1 : 50
Answer:
1:4
Step-by-step explanation:
Ratio of 40 to 10 = 40:10 = 4:1 (after reducing 40:10 to lowest form). Hence, ratio of 40 to 10 is 4:1.
9x - 4 - 5x + 7
evaluate the above for x = 2
Answer: 11
Step-by-step explanation:
9(2) - 4 - 5(2) + 7
18 - 4 - 10 + 7
14 - 10 + 7
4 + 7
11
Calvin drew a rectangle with one side greater than 10 but
less than 20. He multiplies to find its area.
Calvin's work: 8x3+8 x 10 = 104
Find the dimensions of Calvin's rectangle.
Explain how you know that your answer is correct.
Please help!!!!
Step-by-step explanation:
LET WIDTH= X
LENGTH= X+5
PERIMETER= 2(L+B)= 170
2(X+X+5)= 170
2X+5= 85
2X= 80
X= 40
WIDTH= 40
LENGTH= 45
The length of a rectangle is five more than the width. The perimeter is 170. What is the length and width? Write the equation and solve.
100 points
Find the maximum value of the objective function and the values of x and y for which it occurs.
f=5x+2y
x+2y[tex]\leq[/tex]=6 x[tex]\geq[/tex]=0 and y[tex]\geq[/tex]=0
2x+y[tex]\leq[/tex]=6
Answer:
Maximum value of the objective function is 15
This occurs at x = 3, y = 0
Step-by-step explanation:
Attached is a plot of the two inequalities. The feasible region is the dark shaded area bounded by the points O, A, B and C
The maximum value of the objective function will occur at one of the corner points
The four corner points are
O (0,0)
A(0,3)
B(2,2)
C(3,0)
Plug in each of these values into the objective function, see which of the corner points will yield the maximum value and those will be the optimal values of x and y
Corner point (x, y) O.F Value (5x + 2y)
(0, 3) 5(0) + 2(3) = 6
(2, 2) 5(2) + 2(2) = 14
(3, 0) 5(3) + 2(0) = 15 (Maximum value)
What is the measure of angle b?
A. 36 degrees
B. 63 degrees
C. 144 degrees
D. 180 degrees
Answer:
A - 36 degrees
Step-by-step explanation:
117 - 81, to find another angle when given the outside of the triangle and another part of the triangle, all you have to do is subtract
HELP ASAP PLSS!!
I think it’s b I’m not so sure
Answer:
Step-by-step explanation: I think it is 'b' too (sorry if wrong)
If using the method of completing the square to solve the quadratic equation x 2 + 14 x − 1 = 0 which number would have to be added to "complete the square"?
The values of x after solving the quadratic equation x²+14x-1 , using completing the square method is -√50-7 or +√50-7.
What is a quadratic equation?
A Quadratic equations is second-degree algebraic expressions and is of the form ax² + bx + c = 0.
Uisng the method of completing the square to solve the equation below, we following the steps.
Equation ⇒ x²+14x-1 = 0
Step 1:
Take the constant to the other side of the equation
x²+14x = 1Step 2:
Find half the coefficient of x, square, and add it to both side of the equation.
Coefficient of x = 14Half coefficient of x = 14/2 = 7square of half the coefficient of x = 7²There,
x²+14x+7² = 1+7²x²+14x+7² = 50Step 3:
Express the trinomial on the left side as a square of binomial
(x+7)² = 50Step 4:
Take the square root of both side.
√(x+7)² = √50x+7 = ±√50Step 5:
Make x the subject of the equation by moving 7 to the other side of the equation
x = ±√50-7Step 6:
Seperate the expression for each value of x
Either x = -√50-7or x = +√50-7Hence, the value of x is -√50-7 or +√50-7.
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what is the answer for
y=x−4y=−x+6
Answer: Your answers are Y = 1 and X = 5
Step-by-step explanation:
y=x-4 y=-x+6 Substitute x - 4 for y in y=-x+6 x-4=-x+6Add X on each side x-4+x =-x+6+x 2x - 4 = 6Add 4 on each side 2x-4+4 = 6+4 2x = 10Divide by 2 on each side 2x ÷ 2 = 10 ÷ 2 x = 5 Now we have X To find Y we substitute 5 for x in y= x-4 y = 5 - 4 y = 1 so you answers would be Y= 1 and x = 5 i hoped this helped:)
You have an ace, king, queen, and jack from a deck of cards. After shuffling the cards, you draw one card. Then you replace the card, shuffle again, and again draw a card. What is the probability that you will draw a king and a queen in either order? An ace, king, queen, and jack playing card. CLEARCHECK The total number of possible outcomes is x . The probability of drawing a king and a queen in either order is x
Answer:
[tex]\dfrac{2}{169}[/tex]
Step-by-step explanation:
A standard 52-card deck comprises 4 suits (Spades, Hearts, Diamonds, and Clubs).
Each suit comprises 10 numerical cards (numbered 2 through 10, plus an "ace") and 3 "court" cards (jack, queen and king).
Therefore:
The total number of possible outcomes is 52.There are 4 kings and 4 queens in a standard deck of cards.[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
[tex]\implies \sf P(Queen)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]
[tex]\implies \sf P(King)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]
Therefore, the probability of drawing a king, replacing the card, and drawing a queen is:
[tex]\implies \sf P(King)\;and\;P(Queen)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]
Similarly, the probability of drawing a queen, replacing the card, and drawing a king is:
[tex]\implies \sf P(Queen)\;and\;P(King)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]
Therefore, the probability of drawing a king then a queen, or a queen then a king is:
[tex]\implies \sf P(King\;and\;Queen)\;or\;P(Queen\;and\;King)=\dfrac{1}{169}+\dfrac{1}{169}=\dfrac{2}{169}[/tex]
Write a linear function for the graph, and state and interpret the slope and y-intercept for the given scenario:
Bamboo grows very quickly. Use the information in the graph to write an equation that models the height (y) at time (x).
The linear function for the given graph is y = x + 20.
What is a linear function?
A straight line on the coordinate plane is represented by a linear function. It has one independent variable and one dependent variable. For slope (m) and y-intercept (b) form, the equation is given by:
y = mx + b
From the graph,
The coordinates of the given graph are (0,20) and (20,40)
Then, slope (m) = (40-20)/(20-0) = 20/20 = 1
and y-intercept (b) = 20
So, the equation will be y = 1x + 20
Hence, the linear function for the given graph is y = x + 20.
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$1450 is invested at 6.5 % compounded continuously. How long will it take for the balance to reach $2900?
Answer:
Step-by-step explanation:
94.25 days
Katherine is younger than Alexandra. Their ages are consecutive integers.
square of Katherine's age and 5 times
Find Katherine's age if the sum of the
if the sum of the
Alexandra's age is 109.
Using equations to solve the word problem, Katherine's age is 8 years
Word ProblemWord problem are often mathematical problem that are represented in words and sometimes can be solved using an equation.
To solve this problem, we have to represent the problem using mathematical equations;
Let;
Katherine's age = x²
Alexandra = 5(x + 1)
Sum of their age = 109
5(x + 1) + x² = 109
5x + 5 + x² = 109
x² + 5x - 104 = 0
Solving for the equation; x = 8
Katherine's age is 8
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What is the common ratio and the general term equation, a, of the geometric sequence?
The common ratio and the general term equation, a, of the geometric sequence is A. r = 1/2 , an = 16(1/2)^(n - 1).
What is a geometric sequence?A geometric sequence simply means the sequence of non zero numbers whereby the term after the first is simony found by multiplying the previous number by a common ratio
Based on the information, the common ratio will be:
= Second term / First term
= -8 / -16
= 1/2
The nth term will then be 16(1/2)^(n - 1).
The correct option is A.
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A 0.8-liter bottle of Mexican wine costs 99 pesos. At thatprice, how much would a half-gallon jug of the same wine cost indollars?
A gallon of Mexican wine have a price of 433.13 Mexican pesos.
How much does a half-gallon jug of Mexican wine cost?
Herein we know that 0.8 liters of Mexican wine have a cost of 99 pesos and we need to determine the price for a gallon of the same beverage, that is, 3.5 liters. The price for a gallon can be determined by cross multiplication:
x = 99 MXN × (3.5 L / 0.8 L)
x = 433.13 MXN
A price of 433.13 Mexican pesos must be paid for a gallon of Mexican wine.
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Tell wether the data in the table can be modeled by a linear equation. Explain.
If possible, write a linear equation that represents y as a function of x. If not possible, leave blank.
Answer:
yes
By dividing the difference between each two corresponding data values, we get a constant rate of change.
y = 0.2x + 1.2
Step-by-step explanation:
1. Find the rate of change between each pair of data values in the table and compare to see if they are equal:
(1.4-1.2)/(1-0) = 0.2/1 = 0.2
(1.6-1.4)/(2-1) = 0.2/1 = 0.2
(2-1.6)/(4-2) = 0.4/2 = 0.2
2. Substitute the numbers found in step 1 for m, and the y-value in the data pair (0,1.2) as b in the equation y = mx + b: y = 0.2x + 1.2
SOLVE FOR T
t+3/2 = -2
T =
Answer:[tex]t= -\frac{7}{2}[/tex]
Step-by-step explanation:
[tex]=t+\frac{3}{2}=-2\\=t=-2-\frac{3}{2} \\=t=-\frac{7}{2}[/tex]
Kyle ran the width of a field, a distance of 35 meters. Then he ran the length of the field, a distance of 84 meters. Finally, he ran diagonally across it to get back to his starting point. How far did Kyle run?
The total distance travelled by Kyle is 210 m.
What is Pythagoras theorem?Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².
The given length of the field is 84 m.
And, the width is 35 m.
Now, the diagonal of the field can be calculated using Pythagoras theorem as below,
Diagonal = √((84)² +(35)²)
= 91
Then, the total length is found by summing the length, width and the diagonal as below,
= 84 + 35 + 91
= 210
Hence, Kyle run for the distance of 210 m.
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How many days are in 42 weeks?
294 days
504 days
1,008 days
2,520 days
Answer:
294 days
Step-by-step explanation:
Multiply 42 x 7 and you've got 294 days, which will be your answer.
brad says that if a second number is 125% of the first number, then the first number must be 75% of the second number. is he correct? justify your anwser.
The first number is 80% of the second number, not 75%, hence, Brad is wrong.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, a second number is 125% of the first number.
Let the first number be 100, then the second number will be:
125% of 100
= (125/100) × 100
= 125
Now, divide the first number, 100, by the second number, 125, and then multiply with 100 to know how much % the first number is of the second number:
(100/125) ×100%
=80%
Therefore, the first number is 80% of the second number, not 75%.
Hence, Brad is wrong.
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Solve the equation (1+3)³-(2)2 + 4 =
Answer:
64
Step-by-step explanation:
We can solve this using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). We do parentheses first, then exponents, all the way down to subtraction:
1. Parentheses
(1 + 3)³ -(2)2 + 4
4³ - (2)2 + 4
(By the way, (2)2 is considered multiplication not parentheses).
2. Exponents
4³ - (2)2 + 4
64 - (2)2 + 4
3. Multiplication
64 - (2)2 + 4
64 - 4 + 4
4. Division
None.
5. Subtraction
(Even though PEMDAS is labeled as addition before subtraction, in the MD | AS part, whichever one comes first in either section of the equation goes first):
64 - 4 + 4
60 + 4
6. Addition
60 + 4
64
Solution:
64
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Write a system of equations to describe the situation below, solve using substitution, and fill
in the blanks.
Nina is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $12,
and her grandmother has pledged $1 per mile. If Nina walks a certain distance, the two
donors will end up owing the same amount. How much will each donor owe? What is that
distance?
Nina's mother and grandmother will each owe $
if she walks
miles.
Nina's mother and grandmother will each owe $12 if she walks 12 miles
What is an equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.
According to the question we get to know
mother = 12
Grandmother = x
12 = x
x = 12
$ 12 , she walks 12 miles
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