The simple interest earned on a 2,000 principal at 8% interest for 5 years is I = $1,937.50.
What is meant by simple interest formula?Simple interest is calculated by multiplying the daily interest rate by the principal and the number of days between payments. Customers who pay their loans on time or early each month save money on interest.Interest-only loans are prevalent for short-term personal loans and car loans. Simply multiply the principal amount by the interest rate and the time to determine simple interest.The written formula is "Simple Interest = Principal x Interest Rate x Time." Simple interest is calculated on the loan principal or the first deposit into a savings account.Due to the fact that simple interest does not compound, a creditor will only pay interest on the principal amount, and a borrower will never be required to pay interest on previously accumulated interest.Therefore,
I = Prt
First, converting R percent to r a decimal
r = R/100 = 3.875%/100 = 0.03875 per year,
then, solving our equation
I = 10000 × 0.03875 × 5 = 1937.5
I = $ 1,937.50
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 3.875% per year
for 5 years is $ 1,937.50.
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[tex]\sf -31 - 4x = -5 - 5(1 + 5x)[/tex]
Answer:
x = 1
Step-by-step explanation:
Given equation,
→ -31 - 4x = -5 - 5(1 + 5x)
Now the value of x will be,
→ -31 - 4x = -5 - 5(1 + 5x)
→ -31 - 4x = -5 - 5 - 25x
→ -4x + 25x = -10 + 31
→ 21x = 21
→ x = 21/21
→ [ x = 1 ]
Hence, the value of x is 1.
The value of the variable x in the equation -31 -4x = -5- 5(1+ 5x) will be 1.
The given algebraic expression with the variable x is,
-31 - 4x = -5 -5(1+ 5x)
By further solving it, we get,
- 31 - 4x = -5 -5 -25x
To simplify the equation, we have to first separate the constants and variables,
=> 25x - 4x = -5 -5 + 31
=> 21x = 31 - 5 -5
=> 21x = 31- 10
=> 21x = 21
=> x = 21/21
=> x= 1.
Hence, the value of the variable x in the algebraic expression, -31 - 4x = -5 -5(1+ 5x), is found to be 1.
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a square matrix is nilpotent if for some positive integer . let be the vector space of all matrices with real entries. let be the set of all nilpotent matrices with real entries. is a subspace of the vector space ?
An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
What is nilpotent matrix?A nilpotent matrix in linear algebra is a square matrix N such thatfor some positive integer kk. The index of occasionally the degree of the smallest such k A nilpotent transformation, more generally speaking, It is a linear transformation of a vector space such that Lk=0 for some positive integer. Both of these ideas are specific examples of the more basic idea of nilpotence, which is applicable to rings' constituent parts.acc to our question-
When n=1, the only 1×1 nilpotent matrix is (0). Thus U={(0)} and it is a subspace of VIn this case, we prove that the set U of all 2×2 nilpotent matrices is not a subspace of V.The set U is not a subspace because it is not closed under addition as the following example shows.Hence,An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
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3. Consider the right triangle below in which a = 5 and b = 5.
A. Use the Pythagorean Theorem to solve for c.
Show your work!
B. What is the value of c rounded to the nearest hundredth?
C. What is the value of c in simplified radical form?
Answer:
Consider the right triangle below: State the Pythagorean Theorem as it relates to the above triangle. List the trig identities as they relate to the triangle above. Now suppose hypotenuse C represents a vector R, while sides B and A represent vector components Rx and Ry respectively. Redraw the triangle with the new labels below. Using Pythagorean Theorem, derive the equation for R.
help meeeeeeeeeeeeeeeeee please
Answer:
Step-by-step explanation:
x² + (x + 2)² = (x + 3)²
x² + x² + 4x + 4 = x² + 6x + 9
x² - 2x - 5 = 0
[tex]x_{1}[/tex] = [tex]\frac{-(-2)+\sqrt{4+20} }{2}[/tex] = 1 + √6 ≈ 1 + 2.45 = 3.45 units
[tex]x_{2}[/tex] = [tex]\frac{-(-2)-\sqrt{4+20} }{2}[/tex] = 1 - √6 < 0 can not be solution of the given problem.
x ≈ 3.4 units
x + 2 ≈ 5.4 units
x + 3 ≈ 6.4 units
Karen buys a pack of 8 bottles of water.
The pack costs £1.25
Karen sells all 8 bottles of water for 50p each
Work out Karen's percentage profit.
The percentage of the profit gain by karen on a pack of 8 bottles is 220%.
Karen buys a pack of bottles of water. = 8
Karen sells all 8 bottles of water for rupees = 50p each
= 50p/100 each
= 0.5 rupees
Total rupees for 8 bottles = 8 x 0.5 = 4
The pack costs = 1.25
Profit % = (Profit / C.P.) × 100
Profit = SP - CP
= 4 - 1.25
= 2.75
then using these values in equation we get :
profit = [tex]\frac{4 - 1.25}{1.25} * 100[/tex]
profit = (2.75/1.25 )x 100
profit = 2.2 x 100 = 220
profit = 220%
The percentage of the profit gain by karen on a pack of 8 bottles is 220%.
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Evaluate f(x) = log₂ (x) for f(8).
The value of f(8) is 3.
What is logarithm?
The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b. For instance, since 1000 = 103, log10 of 1000 is 3, or [tex]log_1_0=3[/tex].
Let, [tex]f(x) = log_2(x)[/tex]
We have to find the value of f(8).
Plug x = 8 in the above equation.
[tex]f(8) =log_2(8)[/tex]
Here 8 = 2 x 2 x 2 = 2^3
So, replace 8 with 2^3 in the above equation.
[tex]f(8) = log_2(2^3)[/tex]
Using the log rule: [tex]log_a(a^b) = b[/tex]
Here a = 2, b = 3
So, [tex]log_2(2^3) = 3[/tex]
Hence, f(8) = 3.
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Identify the kind of sequence shown: 2, 7, 14, 23, 34 ... *
O Arithmetic
O Geometric
ONeither
Answer:
(c) Neither
Step-by-step explanation:
You want to know the kind of sequence that as terms 2, 7, 14, 23, 34, ....
DifferencesThe first differences of terms of this sequence are ...
7 -2 = 5
14 -7 = 7
23 -14 = 9
34 -23 = 11
These difference are not constant, so the sequence is not arithmetic.
These differences do not have a common ratio, so the sequence is not geometric.
Second differencesHowever, these differences do have a common difference:
7 -5 = 2
9 -7 = 2
11 -9 = 2
The fact that second differences are constant means this is a polynomial sequence of second degree. It is a quadratic sequence, neither arithmetic nor geometric.
__
Additional comment
The sequence is described by the quadratic equation ...
a(n) = n² +2n -1
3x-y=6 2x+3y=4 elimination method
Answer:
Step-by-step explanation:
my answer is attached in the photo below
Divide.
8 3/4÷(−3 1/2)
Enter your answer as a mixed number, in simplified form, in the box.
Sara solved the inequality -4x + > 9 and graphed the solution set. She made a mistake but cannot determine where. Her work is shown
Answer:
step 2 is where she made her mistake
Step-by-step explanation:
- 4x + 1 > 9 ( subtract 1 from both sides )
- 4x > 8
divide both sides by - 4 , reversing the symbol as a result of dividing by a negative quantity.
x < - 2
Is 4x + 7y divisible by 2?
⇒ Is 4x + 7y divisible by 2?⇔ This question simply is asking you if there is a possibility that you can take out the highest common factor of 2 in the expression 4x+7y.
⇒ We cannot take out the highest common factor of 2 in this expression since there is the term 7y that has the coefficient 7 which is NOT divisible by 2. the expression 4x+7y
cannot be written in the form a(b+c)
⇒∴ 4x + 7y is not divisible by 2
If you want me to clarify more in this question please say so as soon possible so that I can make time for you.
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k
The given function is f(x)=7x^2.
The given vertex = (3,5)
The equation of the parabola with the vertex of (h,k) is
y=a(x-h)^2+k
On comparing we get; a=7, h=3, k=5
Now putting the value
f(x)=7(x-3)^2+5
Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
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Find X in all three problems below
The lengths for the missing side of each case, determined by the use of trigonometric functions, are listed below:
Case D: 50.513
Case E: 46.165
Case F: 2.052
How to determine missing lengths of right triangles by trigonometric functions
In this problem we have three cases of right triangles, each of which has an unknown side length. Each length can be found by using trigonometric functions. Now we proceed to determine it for each case:
Case D
tan 29° = 28 / x
x = 28 / tan 29°
x ≈ 50.513
The missing side length is approximately 50.513 units.
Case E
tan 18° = 15 / x
x = 15 / tan 18°
x ≈ 46.165
The missing side length is approximately 46.165 units.
Case F
cos 70° = x / 46
x = 46 · cos 70°
x ≈ 2.052
The missing side length is approximately 2.052 units.
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a square has a side length that is increasing at a rate of 14 inches per hour. what is the rate of change of the area of the square when the side length is 8 inches
The rate of change of the area of the square when the side length is 8 inches is 224 inches per hour.
Let s be the side of the given square.
A = s²
dA/dt = d (s²)/dt
dA/dt = 2s × ds/dt
Given ds/dt= 14 inches per hour, s = 8 inches
dA/dt = 2×14×8
dA/dt = 224 inches per hour
The area of the square is s². Since we need to find the rate of change we need to differentiate the area with respect to time which will give us 2s × ds/dt. Once we replace the given values with their respective positions we will get the desired answer. Hence the rate of change in the area of the square is 224 inches per hour.
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A group of friends wants to go to the amusement park. They have no
more than $465 to spend on parking and admission. Parking is $12.50,
and tickets cost $33 per person, including tax. Which inequality can be
used to determine p, the maximum number of people who can go to
the amusement park?
14 people can go to the amusement park. Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.
How to calculate No. of people?Inequality: 33p + $12.50 ≤ $465
14 people can go to the amusement park
Inequality:
$465= Amount of money they have
$12.50= Parking Cost
$33= Cost of tickets per person
Because they only have $465, they can't spend more than that amount.
Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (aka x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:
33p+ $12.50 ≤ $465
$465- $12.50 = $452.5 (452.5 is how much is left for tickets after subtracting the parking cost)
$33 x1 4 = $462 (14 tickets can be bought for the price of $33)
$462 - $452.5 = $9.5 (9.5 isn't enough for another person)
So, the solution to the inequality is 14 people can go to the amusement park.
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Answer: 45.5p is less than or equal to 465
Miguel took his son to college in boulder, colorado, 300mi from their hometown. on his way home, he was slowed by a snowstorm so that his speed was 10mph less than when he was driving to boulder. his total driving time was 11hr. how fast did miguel drive on each leg of the trip?
Miguel drove at a speed of 60 mph in the first part of the trip and at a speed of 50 mph in the second part of the trip.
Let the speed while dropping his son to college be x mph
Therefore speed while returning is (x - 10) mph
The distance is 300 mi
Speed = Distance/Tie
or, Time = Distance/Speed
Hence the time taken during the first part of the journey = 300/x hrs
and,
Time taken for the next part of the journey
= 300/(x - 10) hrs
It is given that the total time taken was 11 hrs
Hence we get
300/x + 300/(x - 10) = 11
or, (300x - 3000 + 300x) / x(x - 10) = 11
or, (600x - 3000) / (x² - 10x) = 11
or, 600x - 3000 = 11x² - 110x
or, 11x² -710x + 3000 = 0
Applying the shreedharacharya rule gives us
x = (710 ± √(710² -132000)/22)
x = 50/11 or x = 60
If x = 50/11 then x - 10 will be negative.
hence x = 60
Therefore Miguel drove at a speed of 60 mph in first half and 50 mph in second half.
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DIMENSIONAL ANALYSIS (MATH) GIVING BRAINILIEST!
Q1: What is the speed of a horsefly in feet per second? Round to the nearest hundredth.
Q2: How many times does a dragonfly's wing beat per minute?
Q3: About how many times can a bumble bee travel in one minute?
1) The speed of a horsefly in feet per second is; 0.63 beats per minute
2) The number of times that the dragonfly's wing beats per minute is; 3 ft/s
3) The number of times that a bumble bee travels in one minute is; 0.11 miles per minute
How to carry out dimensional Analysis?Dimensional analysis is defined as the study of the relationship that exists between physical quantities with the help of dimensions and units of measurement.
Dimensional Analysis is also defined as a method of problem solving that takes into consideration the identity property of multiplication whereby the product of a number and 1 will always give the same number, that is 1 × n = n whereby the value "n" remains the same after the multiplication.
1) We are given from the table that the speed of a horsefly in miles per hour = 4.4 miles per hour. We want to know the speed expressed in feet per second.
From conversions, we know that;
1 mile per hour = 1/1.467 ft/s
Thus; 4.4 miles per hour = 4.4 * 1/1.467 = 3 ft/s
2) We are given from the table that the dragonfly's wing beat per second = 38 beats per second. We want to know the dragonfly's in wing beat per minute
From conversions, we know that;
1 beat per second = 1/60 beat per minute
Thus; 38 beats per second = 38 * 1/60 = 0.63 beats per minute
3) We are given from the table that the speed of a bumble bee in miles per hour = 6.4 miles per hour. We want to know the speed expressed in miles per minute
From conversions, we know that;
1 mile per hour = 1/60 miles per minute
Thus;
6.4 miles per hour = 6.4 * 1/60 = 0.11 miles per minute
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The graph states f(x) is at(4,3) and g(x) is at (4,3) what input value produces the same output value for the two functions on the graph?
The ordered pair of the values of f(x) and g(x) of (4, 3) and (4, 3) indicates that the input value that produces the same output value for f(x) and g(x) functions is x = 3
What are the input and output values of a function?The input values of a function are the values that serve as the argument of the function. They are also known as the independent variable. The operations of a function are performed on the input values such that each input produces only one output, which is known as the dependent variable. The set of the input values is known as the domain of the function.
The output value of a function are the values of the function that gives the image of the input values, and they are known as the dependent variable. The set of the output values is the range of the function.
The points on the graph are;
f(x) = (4, 3), and g(x) = (4, 3)Therefore, from the graph, at the point x = 3, f(x) = g(x) = 4
The input value that produces the same output value for the two functions on the graph is the x-value of 3
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What is the area of the parallelogram shown?
A= In^2
The area of the parallelogram shown is 6.6 square inches.
According to the question,
We have the following information:
We have a parallelogram with base 2.2 inches and height 3 inches.
We know that the following formula is used to find the area of parallelogram:
Area of parallelogram = Base*height
Area of parallelogram = 2.2*3
Area of parallelogram = 6.6 square inches
(Please note that area of any object or figure is always given in square units. For example, it may be square meters, square inches, square feet, etc.)
Hence, the area of the parallelogram shown is 6.6 square inches.
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What is the equation of the line that passes through the point (8, 6) and has a slope
of o?
The equation of the line that passes through the point (8, 6) and has a slope of 0 is y = 8.
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through the point (8, 6) and has a slope of 0.
Therefore,
m = 0
Hence, let's find the y-intercept using the (8, 6)
y = mx + b
6 = 0(8) + b
b = 8
Therefore, the equation is y = 8
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TWO trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train
travels at 95 miles per hour. How long will It take for the two trains to be 396 miles apart?
Do not do any rounding.
consider the polynomial function p given by p(x)=5x^3+6x^2+4x
evaluate the function at x=-5 and x=15
Answer:
p(-5) = -495p(15) = 18285Step-by-step explanation:
You want the value of p(x)=5x^3+6x^2+4x for x=-5 and x=15.
Horner formWriting a polynomial in Horner form can simplify evaluation.
p(x) = ((5x +6)x +4)x
p(-5)p(-5) = ((5(-5) +6)(-5) +4)(-5) = (-19(-5) +4)(-5) = 99(-5) = -495
p(15)p(15) = ((5(15) +6)(15) +4)(15) = (81(15) +4)(15) = 1219(15) = 18285
5(4 − 9 · 2) − 2( 3 · 2 + 4) + 7?
Answer: i think its -18
Step-by-step explanation:
5*(4-9*2)-2*(3*2+4)+7
= 5*(4-18)-2*(3*2+4)+7
= 5*(-14)-2*(3*2+4)+7
= 5*-14-2*(3*2+4)+7
= 5*-14-2*(6+4)+7
= 5*-14-2*(10)+7
= 5*-14-2*10+7
= -70-2*10+7
= -70-20+7
= -90+7
= -83
What is the equation of the line that passes through the points (-2, -6) and (1, 2)?
The equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.
According to the question,
We have the following information:
Points through which line is passing = (-2,-6) and (1,2)
Now, we have the following values:
x1 = -2, y1 = -6
x2 = 1 and y2 = 2
We know that the following formula is used to find the slope of the line:
m = (y2-y1)/(x2-x1)
m = (2+6)/(1+2)
m = 8/3
Now, the following formula is used to find the equation of the line:
y-y1 = m(x-x1)
y+6 = 8/3(x+2)
y+6 = 8x/3+16/3
Subtracting 6 from both sides:
y = 8x/3+16/3-6
y = 8x/3-2/3
Hence, the equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.
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PLEASE HELP ASAP I WILL GIVE BRAINLIEST
Find x and y
The values of the variables x and y in the triangle are 1.25 and 1.75
How to determine the values of the variables x and y?The tringle represents the given parameter
On the triangle, we have the following equivalent ratio
5 : 8 = 5 + x : 10
7 : 8 = 7 + y : 10
These are true because the horizontal lines of the triangles are parallel
So, we have
5 : 8 = 5 + x : 10
Express as fraction
5/8 = 5 + x/10
This gives
5 + x = 6.25
Solve for x
x = 1.25
Similarly, we have
7 : 8 = 7 + y : 10
So, we have
7/8 = 7 + y/10
This gives
7 + y = 10*7/8
Evaluate
7 + y = 8.75
So, we have
y = 1.75
Hence, the values of x and y are 1.25 and 1.75
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What is the interquartile range of the data set???
Answer:
14.
Step-by-step explanation:
The interquartile range (IQR) contains the second and third quartiles or the middle half of your data set.
Please give brainliest, will be appreciated.
Answer:
The interquartile range (IQR) measures the spread of the middle half of your data.
the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. what is the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes?
The probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .
What is probability?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.
A highway construction site's cycle time for trucks transporting concrete is evenly spread over the range of 50 to 70 minutes, thus a = 50 and
b = 70
f(x) = 1/[b - a] = 1/[70 - 50] = 1/20 = 0.05, thus a uniform distribution.
Let P(cycle time is less than 65 minutes if it is known that the cycle time exceeds 55 minutes) be:
P(60 < X < 65) = ₆₀∫⁶⁵ f(x) dx = ₆₀∫⁶⁵ (0.05) dx = 0.05*[65 - 60] = 0.05*5
= 0.25
Thus, the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .
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Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-intercept form.
X
15
20
25
30
35
y
175
210
245
280
315
A population of values has an unknown distribution with
ll
= 83.3 and o
= 10.4. You intend to draw a random
sample of size n
= 212.
What is the mean of the distribution of sample means?
flie
(Please enter an exact answer.)
What is the standard deviation of the distribution of
sample means?
Ox
(Please report your answer accurate
to 2 decimal places.)
By using the concept of mean and standard deviation, it can be obtained that
The mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3
Standard deviation of distribution ([tex]\sigma_x[/tex]) = 0.714
What is mean and standard deviation?
Suppose there is a data set and an average value of the data set needs to be calculated. To find the average value of the data set, mean is used
For Standard deviation, at first, it is important to know about variance
Variance is the sum of the square of deviation from mean.
Square root of variance is the standard deviation
A population of values has an unknown distribution with
[tex]\mu = 83.3[/tex] and [tex]\sigma = 10.4[/tex], n = 212
So the mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3
Standard deviation of distribution ([tex]\sigma_x[/tex]) = [tex]\frac{10.4}{\sqrt{212}}[/tex] = 0.714
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Please help ASAP!! Screenshot below. 10 points
Answer:
The answer to this equation is (-1,1)
