lex has $1,780.80 in his savings in his saving account that he opened 6 years ago his account has an annual interest rate of 6.8% compounded annually how much money did lex use to open his savings
Answer:
To find the principal, P we can use the same formula, A=P(1+rn)nt. We have the balance of the account, A, after 6 years, $1,780.80. The interest rate, r, is 6.8% (or 0.68 as a decimal) and is compounded annually, so n=1. The time, t, is 6, since we know he opened his account 6 years ago. Plug in the known values into the formula and solve for the missing variable, P.
Step-by-step explanation:
1,780.80 = P (1+0.0681 divided 1^(6)
1,780.80= 1.484P
1,200=P the principal amount Lex used to open his account 6 years ago
You can perform 6 push-ups in 16 seconds. Write and
graph an equation that represents the relationship between
time and the number of push-ups. At this rate, how many
pushups can you perform in 2 minutes?
Answer:
320 pushups
Step-by-step explanation:
16/6= 8/3
8/3*120=32
the fraction 3/5 fits into 2 1/5 less than more than 1 time
Answer:
Q = 3.667
Step-by-step explanation:
Perry borrows $150 from his brother to fix his car. His brother doesn't like lending Perry money and so charges him 7% interest per month. a. Write a rule in the "y=..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments.
Answer: Let's say,
y = the amount of money Perry will owe his brother after n months.
x = the principal (the initial amount borrowed) = 150
r = the interest rate per month = 7/100 = 0.07
n = number of months.
We know that Interest on a loan is calculated by multiplying the principal by the interest rate.
Therefore, the interest for n months is (0.07*x)*n
So to find the total amount Perry will owe his brother after n months, we need to add the interest to the principal amount.
y = x + interest
y = x + (r*x)n
y = x(1 + rn)
Therefore, the rule in the "y =..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments is:
y = 150(1 + 0.07*n)
It's worth noting that this formula can be used to calculate the amount he will owe after any number of months by changing the value of n, and It's assuming he doesn't make any payments, meaning if he makes any payments, the total amount he will owe will change.
Step-by-step explanation:
Solve each equation if [tex]f (x) = 2x^{2} - 2[/tex] and [tex]g(x) = 6x + 3[/tex]
) If x, x+10 makes a right angle, find them.
Answer:
x+x+10=90 being Right angle triangle.
2x=90-10
2x=80
x =40
then x+10= 40 + 10
= 50
A house 20 meters long and 15 meters wide is surrounded by a verandah of uniform width of 3 meters. Find the cost of the flooring the verandah at RS 200 per square meter
Answer:
49200 rs. so the cost of flooring =246*200=49200 rs
Step-by-step explanation:
we measure the area of veranda by taking width in addition of length and breadth- house area
it means
area of veranda =outer rectangle-inner rectangle
⇒area= (20+3+3)*(15+3+3)-20*15
⇒area=26*21-300
⇒area= 546-300
⇒area=246 m²
Hence , the cost of flooring =246*200=49200 rs.
Question 5, Please Answer and Explain
The trigonometric ratios for the angle x in the triangle are given as follows:
tan(x) = f/e.cos(x) = e/d.sin(x) = f/d.What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.In the right triangle in this problem, we have that d represents the hypotenuse, while the sides relative to angle x are given as follows:
Adjacent side: length of e.Opposite side: length of f.These sides are used along with the definitions of each ratio to give the three trigonometric ratios of angle x.
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What is the domain of this function?
F(x)=3 square root x-2
x-2>0= x>2
The domain of the function F(x) = 3 [tex]\sqrt{x-2}[/tex] is {x : x ≥ 2 and x is a real number}.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given function is,
F(x) = 3 [tex]\sqrt{x-2}[/tex]
Domain of this function is all the values of x for which the function is defined.
The expression [tex]\sqrt{x-2}[/tex] is defined only when the value of x - 2 is positive.
x - 2 > 0 ⇒ x > 2
So the function will be defined for all x > 2.
Hence the domain of the function is the set of all x such that x > 2.
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Solve Using substitution 3x+5y=-28 Y=x+4
Answer:
(-6, -2) x=-6, y=-2
Step-by-step explanation:
3x + 5(x+4) = -28
3x + 5x+20=-28
8x+20=-28
8x=-48
x=-6
Y=-6+4
y=-2
Lenore rounds each factor to the nearest ten to estimate the product of 51 times 37 as 1,500.is Lenore’s estimate reasonable?Explain.
Answer:
yes
Step-by-step explanation:
51 to nearest ten is 50
37 to nearest ten is 40
50 * 40 = 2000
and it's an estimate so yes
f(x)=x/x-9 g(x)= -8/x What's 1. f(g) 2. g(f) 3. f(f) 4. g(g)
The function f(g) is 8/(8+9x) and the function g(f) is -8x/(x-9).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are f(x)=x/(x-9) and g(x)= -8/x.
1) f(g)
Here, f(-8/x)= -8/x ÷ (-8/x -9)
= -8/x ÷ (-8-9x)/x
= -8/x × x/(-8-9x)
= 8/(8+9x)
2) g(f)
Now, -8/x/(x-9)
-8x/(x-9)
3) f(f)
Here, f(f) = x/(x-9) ÷ (x/(x-9) -9)
= x/(x-9) ÷ ((x-9x+81)/(x-9))
= x/(x-9) × (x-9)/(-8x+81)
= x/(-8x+81)
4) g(g)
Now, -8/(-8/x)
= 64/x
Therefore, the function f(g) is 8/(8+9x).
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Nataliah can read 160 words per minute. Let w represent the total number of words
Nataliah reads, and let m represent the number of minutes she spends reading. Create a
table and a graph to show how many words Nataliah will read from 1 to 5 minutes. Don't
forget to label your axes.
Please review the analysis for the dependent and independent variables. Equation: The total probability for the number w=160 m on the chart is 160 m.
What is the probability ?Equation w=160 m.w (words) equals 160 words in the first minute and 320 words in the next two minutes. 800 words in five minutes, 480 words in three minutes, and 640 words in four minutes. The probability of A or B is equal to p(A or B) = p(A) + p(B) if occurrences A and B are mutually exclusive (B).
The steps listed below can be used to determine an event's likelihood: Step 1: Identify an event that has only one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favourable outcomes from the total number of outcomes that are feasible. A probability is a number that expresses the possibility or likelihood that a specific event will take place.
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Which table represents a function
Answer:
The table with (-3, 2), (0, 2), etc.
Every input has exactly one output.
Hope this helps :)
Solve for the roots in the following equation. Hint: Factor both quadratic expressions.
(4+5x²-36)(2x²+9x-5) = 0
Using the provided quadratic expression and factorizing it, The answer is x = ± √6.4 or x = ± 2.51 and x = 1 or x = -2.5 .
What is a equation?An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.
What are roots of the equation?Roots of an equation are the values of the variable that make the equation true. For example, the roots of the equation x^2 + 2x - 3 = 0 are -1 and 3, because (-1)^2 + 2(-1) - 3 = 0 and 3^2 + 2(3) - 3 = 0. In general, finding the roots of an equation can be a difficult task and may require the use of mathematical techniques such as factoring, graphing, or numerical methods. Roots are also known as solutions or zeroes of an equation. They can be found by setting the equation equal to zero and solving for the variable.
(4+5x²-36) = 0 or (2x²+9x-5) = 0
Solving the first factor:
4+5x²-36 = 0
5x²-32 = 0
5x² = 32
x² = 6.4
x = ± √6.4
x = ± 2.51 or -2.51
Solving the second factor:
2x²+9x-5 = 0
x²+4.5x-2.5 = 0
(x-1)(x+2.5) = 0
x = 1 or x = -2.5
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
D.
Step-by-step explanation:
4/5 ÷ 3 = 4/5 * 1/3
This is 1/3 of 4/5.
Lin solved the equation incorrectly. Find the errors in her solution.
x = 3/4 is the correct solution of the given expression.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
The expression Lin tried to solve
8(x-3)+7=2x(4-17)
Simplifying the expression,
8x - 24 = 2x(-13)
8x - 24 = -26x
8x+26x = 24
32x = 24
x = 24/32
x = 3/4
Thus, x = 3/4 is the correct solution of the given expression.
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WILL GIVE BRAINLIEST
There are 6.02 × 10^23 atoms in 1 gram of hydrogen. How many atoms are there in 400 grams of hydrogen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.
If possible PLEASE write the answer in the form of 54x10^3
The number of atoms that are there in 400 grams of hydrogen will be 2.408 × 10^26.
How to illustrate the scientific notation?Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.
In this case, there are 6.02 × 10^23 atoms in 1 gram of hydrogen.
The number of atoms that are there in 400 grams of hydrogen will be:
= 6.02 × 10^23 × 400
= 2408 × 10^23
= 2.408 × 10^3 × 10^23
= 2.408 × 10^26
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they are yes and no choices except the one that’s one the pic
helpppp
Therefore , the solution of he given problem of linear equation comes out to be x = 5.
A linear equation is defined.A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Given : 2x-4=6
To prove x =5
Thus,
We have to find the value of x
[tex]= > 2x =10\\= > x =10/2\\= > x =5[/tex]
Therefore , the solution of he given problem of linear equation comes out to be x = 5.
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The length of a rectangle is 4 feet more than twice the width. The perimeter is 116. Find the dimensions of the rectangle
The dimensions of the rectangle are 40 and 18 units respectively
What is the area and perimeter of the rectangle?The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.
Given here: The length of a rectangle is 4 feet more than twice the width.
Then let the width be x then length is equal to 2x+4 and therefore the perimeter is 2(2x+4+x)=116
3x+4 = 58
3x = 54
x = 18
Hence, the dimensions of the rectangle are 40 and 18 units respectively.
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The triangle flap of an envelope has two sides that are 6 centimeters long and meet at a right angle. How long is the envelope? Round to the 10ths if needed.
Answer:
Step-by-step explanation:
This is a right triangle that has two equal sides - so it is also isosceles.
It can be solved using Pythagoren Theorem.
a² + b² = c²
In this case a = b
so:
6² + 6² = c²
36 + 36 = c²
72 = c²
[tex]\sqrt{72[/tex] = [tex]\sqrt{c^{2} }[/tex]
8.49 = c
round to 8.5
This is the length of the flap.
The proportional relationship between the
number of inches a candle has burned away, b, at
any time in hours, t, can be represented by the
equation b = 0.75t. At what rate does the
candle burn, in inches per hour?
Candles should burn one hour for every 1 inch in diameter of the actual candle size. For example, a candle that is 2 inches across should burn for 2 hours.
At what rate does then candle burn, in inches per hour?
Smaller candles with smaller wicks will burn at a rate of 7 to 9 hours per 28 g of wax used. Larger candles with larger wicks consume wax at a faster rate. The larger wicks can be expected to yield 5 to 7 hours per 28 g of wax used.
Estimate the total number of burns by dividing the total wax weight used in the candle (not the weight of the candle with container) by the amount of wax used from burning the candle. Finally, multiply the estimated total burns by the burn time hours. This will provide an estimate of the candle's burn time.
The two main factors for burning candles is wick size and type of wax. Wider or thicker wicks will burn much faster than thin ones, and the material the wick is made with can also make an impact. Different types of candle wax burn at different temperatures.
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Ben has 50 toys. 15 of them are new and 9 are his favorites; 2 are new and favorites.
Ben is giving away all the toys that are neither new nor favorites. How many toys
does Ben give away?
Answer:
28 toys
Step-by-step explanation:
Ben has 50 toys, of which 15 are new, 9 are favorites, and 2 are new and favorites. You want to know the number that are neither new nor favorite.
GroupingsThe number of new toys includes (new and favorite) and (new and not favorite). That is ...
15 = 2 + new and not favorite
So ...
new and not favorite = 15 -2 = 13
Likewise, the number of favorite toys includes (new and favorite) and (not new and favorite). That is ...
9 = 2 + not new and favorite
not new and favorite = 9 -2 = 7
Donated
The total of 50 toys includes ...
total = (new and favorite) + (new and not favorite) + (not new and favorite) + (not new and not favorite)
50 = 2 + 13 + 7 + (not new and not favorite)
Then the number of (not new and not favorite) is ...
not new and not favorite = 50 -2 -13 -7 = 28
These are the toys that Ben gives away.
Ben gives away 28 toys.
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A system of linear equations with an infinite number of solutions is a(n).
_____system.
Answer:
It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.
which of the expressions below has a 6 in the tenths place if the difference a) 17.45 - 8,81 b) 12.35 - 1.76 c) 5.78 - 2.16 d) 19.34 - 1.69
Find the product.
(6a² + 4b) (a²- b)
On solving the provide question, we can say that - the quadratic equation [tex](6a^2 + 4b)(a^2 - b)[/tex] = -4
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
here, we have
[tex](6a^2 + 4b)(a^2 - b)[/tex]
a = 0 and b = 1
-4
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It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed, estimate how much longer I will be driving for. this is my questions its muliple choice, the answer ive come to is 1h 25m but thats not one of the answers to chose from what do i do?
If the total length of the journey is 146 km and he maintain the same speed, the longer time he will be using for driving will be 65m.
How can the time be calculated?The total length of my journey is 146 km.
Then the remain of the journry to reach 146 km = 146- 48 = 98
Then the if the same speed is maintained the estimate of longer time he will be using for driving will be calculated as :
(32 * 98)/48
Then get the productor quotient = 196/3 = 65 minutes
Therefore, option E is correct.
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MISSING OPTIONS:
A. 32
B.40
C. 52
D. 60
E.65
Mark bought five packs of markers for $12.25. What is the cost of a pack of markers, in dollars, if all the packs cost the same?
Answer:
The cost of a single pack would be $2.45.
Step-by-step explanation:
If a 5 pack costs 12.25 then to find the cost of 1 packet we need to divide.
We would divide by 5.
$12.25/5=$2.45
Show your work please!!!
Answer:
Error is in line 3
Error description: Root of 4 is 2 not 4
Correct answer should be 9*√5 (12*√5 - 3*√5)
I REALLY NEED HELP WITH PLINK A PLUNK
Therefore ,We can see that in equation 1 plunk yields the most lorgs at 30. So the plunk coin is the most valuable.
Describe equation.A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 5x - 5 = 25 is an equation. We can find that the variable x has a value of 6 by resolving this equation.
Here,
we need to convert everything to the same unit in order to establish a legitimate comparison when comparing units like inches, feet, and yards. Therefore, we would have to convert everything, for example, to inches. For these five coins, the same concept holds true. Either lorgs, sinds, plunks, harps, or dalts must be used for everything (pick one of those five).
It's equivalent to attempting to change a dollar amount into cents (for example, $1.37 becomes 137 cents). The alternative is to think about it as 1 dollar = 100 cents, 1 quarter = 25 cents, 1 dime = 10 cents, and so on.
The procedures in the various parts below are designed to convert all coinage to lorgs, which will serve as our base unit. Trial and error led me to the conclusion that the lorg coin had the lowest worth, thus I'm striving to obtain everything in lorgs.
The four equations provided are
4 lorgs to a sind
5 dalts x 2 plunks
2 harps from 5 sinds.
3 harps equal 1 plunk.
In that order, I'll refer to them as equations (1) through (4).
One sind equals four logs (1)
5 sinds = 20 lorgs; add 5 to both sides.
2 harps = 20 lorgs; in the equation, swap out "5 sinds" with "2 harps" (3)
1 harp = 10 lorgs; multiply both sides by 2, then write this as an equation (5)
Equation: 1 plunk = 30 lorgs (6)
Each of those equations enables us to determine the lorg value of the coins sind, dalt, harp, and plunk.
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The complete question is : " A nation has five types of coins: sinds, dalts, lorgs, harps, and plunks.1 sind = 4 lorgs ,2 plunks = 5 dalts ,5 sinds = 2 harps , 1 plunk = 3 harps Which coin is the most valuable? a) sindb) daltc) harpd) plunk"