Step-by-step explanation:
FV = PV ( 1 + i)^n FV = future value ....what you are looking for
PV = present value = $ 6000
i = decimal periodic interest = .07/12
n = periods = 5 yr * 12 monts/yr = 60 periods
FV = $ 6000 ( 1 + .07/12)^60 = $ 8505.75
Kyle wrote a matrix to represent a system of equations. The matrix is shown below.
[1 -3 1 4 | 4]
[3 2 1 | 3]
[-6 -4 -2 | 1]
Which of the following describes the solution to the system of equations?
- consistent
- dependent
- inconsistent
- independent
The system is inconsistent and has no solution. Therefore, the answer is "inconsistent".Since the last row is of the form [0 0 0 | b], where b is nonzero (b=7
To determine whether the system of equations represented by the given matrix has a solution, we can use row operations to put the matrix into reduced row echelon form. If the resulting matrix has a row of the form [0 0 ... 0 | b], where b is nonzero, then the system is inconsistent and has no solution. If there are any free variables in the reduced row echelon form, then the system has infinitely many solutions and is dependent. If there are no free variables and no rows of the form [0 0 ... 0 | b], then the system has a unique solution and is independent.
Using row operations, we can put the given matrix into reduced row echelon form as follows:
[tex][1 -3 1 4 | 4] (R1)[3 2 1 | 3] (R2)[-6 -4 -2 | 1] (R3)[/tex]
([tex]R2 - 3*R1) - > R2:[/tex]
[tex][1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[-6 -4 -2 | 1] (R3)(R3 + 6*R1) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 -22 4 | 25] (R3)(R3 + 2*R2) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 0 0 | 7] (R3)[/tex]
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A fruitier had 300 oranges and apples at first.20%of apples were sold in the morning.the fruitier then stocked up another 35 oranges.the total numbers of oranges and apple became 298.how many apples were there at first?
Answer:
185 apples
Step-by-step explanation:
We have to work in reverse to find the original number of apples.
298-35= 263 apples and oranges after 20% apples sold
300-263 = 37 apples
37 apples = 20%
For total apples:
37 apples x 5 = 20% x 5
185 apples = 100% of apples
There were 185 apples at first
Hope that helps :)
Find the amount and C.I on a sum of Rs. 62500 for 1 year at 5% per annum compounded yearly.
The amount and the compound interest on a sum of Rs. 62500 are Rs. 65625 and Rs. 3125, respectively.
Calculating the amount and the compound interestGiven:
Principal amount (P) = Rs. 62500
Rate of interest (R) = 5%
Time period (t) = 1 year
Interest is compounded yearly.
Formula for calculating compound interest is given as:
A = P(1 + R/100)ᵗ
where A is the amount.
Using this formula, we can find the amount (A) after one year:
A = 62500(1 + 5/100)¹
A = 65625
Therefore, the amount after one year is Rs. 65625.
To find the compound interest, we can subtract the principal from the amount:
Compound Interest = A - P
= 65625 - 62500
= 3125
Therefore, the compound interest is Rs. 3125.
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Jolen has a bag with 25 popsicles sticks, each numbered 1-25. How many sticks are labeled with a prime number?
A. 8
B. 9
C. 10
D. 11
Show your work.
Answer:
B: 9
Step-by-step explanation:
The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23.
why does this series [tex]tan(2^{-n} )[/tex] converge?
*its a series from 2 to infinity, but there is no symbol for that.
The series [tex]\tan(2^{-n})[/tex] is convergent.
What is convergence of series?In mathematics, the cοnvergence οf a series refers tο the behaviοr οf the series' partial sums as mοre terms are added. A series cοnverges if its sequence οf partial sums apprοaches a finite limit, which is called the sum οf the series. If the sequence οf partial sums dοes nοt apprοach a finite limit, the series diverges.
The series [tex]\tan(2^{-n})[/tex] converges because of the following reasons:
As n increases, [tex]2^{-n}[/tex] becomes very small, which makes [tex]\tan(2^{-n})[/tex] close to its linear approximation. Therefore, we can use the linear approximation of [tex]\tan(2^{-n})[/tex] to estimate its value.
The linear approximation of [tex]\tan(2^{-n})[/tex] is [tex]2^{-n}[/tex], which means that [tex]\tan(2^{-n})[/tex] ≈ [tex]2^{-n}[/tex] when [tex]2^{-n}[/tex] is small.
Since the series [tex]2^{-n}[/tex] is convergent, by comparison test, the series [tex]\tan(2^{-n})[/tex] is also convergent.
Alternatively, we can also use the fact that the series tan(x) is convergent for x ∈ (0, π/2), and since [tex]2^{-n}[/tex] → 0 as n → ∞, we have [tex]\tan(2^{-n})[/tex] → tan(0) = 0, which implies that the series [tex]\tan(2^{-n})[/tex] is convergent.
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I need help with my homework
The average rate of change representing the state whose temperature is decreasing slower is given as follows:
-1.5ºF/day.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
For Maine, in 9 days, the temperature fell by 13.5ºF, hence the rate is given as follows:
-13.5/9 = -1.5ºF/day.
For Connecticut, in 2.5 days, the temperature fell by 6.25ºF, hence the rate is given as follows:
-6.25/2.5 = -2.25 ºF/day.
A slower decline is in Maine, as it has a lower rate of change.
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Determine the rage of the following graph
The range of function is values on the y-axis: R=[-7,2].
What is function?A function is a mathematical concept that describes the relationship between two sets of numbers. It is a rule that assigns to each input (or element in the domain) exactly one output (or element in the range). In simpler terms, a function is like a machine that takes in a number and produces another number as output, according to some specific rules. The input is usually denoted by x, and the output by f(x), which is read as "f of x". Functions can take many forms, such as linear, quadratic, trigonometric, exponential, logarithmic, and more. They are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.
Here,
To find the range of a function, you need to determine all possible output values of the function. Start by identifying the function's domain, which is the set of all possible input values of the function. Once you know the domain, apply the function to each input value in the domain and record the corresponding output values. Once you have a list of output values, identify the smallest and largest values in the list. These values represent the range of the function. For example, consider the function f(x) = 2x + 1. The domain of this function is all real numbers.
To find the range, apply the function to several input values in the domain:
f(-3) = -5
f(-2) = -3
f(-1) = -1
f(0) = 1
f(1) = 3
f(2) = 5
f(3) = 7
These output values give us a set of possible output values, which are {-5, -3, -1, 1, 3, 5, 7}. The smallest value in the set is -5 and the largest value is 7, so the range of the function is [-5, 7].
Note that for some functions, it may be difficult or impossible to find the exact range. In such cases, you can use techniques such as graphing or calculus to estimate the range.
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2. The ratio of boys to girls in the school
choir is 3:4. If there are 12 girls in the
choir, how many boys are in the choir?
Answer:
9 Boys
Step-by-step explanation:
As we Know, 12 ÷ 4 is 3
3 x 3 is 9
therefore, it's 9
What is the lowest common multiple of 8 and 12?
Answer:
2 hope that helps
Step-by-step explanation:
1. How many telephones per 100 inhabitants did Bermuda have?
2. In 2005, the population of Luxembourg was 470,000. How many telephones were in use in Luxembourg?
Please help with two questions!!!
In Bermuda, there are a total of 90 telephones for each 100 people. Also there are a total of 3,76,000 telephones in use in Luxembourg according to simple calculations.
Here, they given that a telephone symbol is equal to 5 telephones.
Then according to the given diagram,
1. There are:
= (5 + 5 + 5 + 3) 5 telephones
= ( 18 ) 5 telephones
= 90 telephones.
Therefore, there are a total of 90 telephones for each 100 people.
2. In 2005, the population of Luxembourg was 470,000.
According to the given diagram, there are 80 telephones available for every 100 people.
For 4,70,000:
100 -------------- 80
4,70,000 ------ (x)
After cross multiplication,
x * 100 = 80 * 470000
x = 8 * 47000
x = 3,76,000
Therefore, there are total of 3,76,000 telephones in use in Luxembourg.
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if 1 kg is equal to 1,000 G how many grams are in 7.28 kg explain how you found your answer
Answer:
here is your answer attached
Step-by-step explanation:
Evaluate the following limit. Enter the exact answer in fraction form, if necessary.
Answer:
To evaluate this limit, we can factor out the highest power of x from the numerator and denominator, which is x^14. Then, we can divide both the numerator and denominator by x^14. This gives:
lim x→∞ (6x^14 + 8x^11 + 37x^14) / x^14
= lim x→∞ (6x^14 / x^14 + 8x^11 / x^14 + 37x^14 / x^14)
= lim x→∞ (6 + 8 / x^3 + 37)
= 6 + 0 + 37 (since as x approaches infinity, 8/x^3 approaches zero)
= 43
Therefore, the value of the limit is 43.
A square wrestling mat has a perimeter of (12x−32)
feet. Write an expression in simplest form that represents the side length (in feet) of the mat.
Answer:
The perimeter of a square is given by the formula P = 4s, where s is the side length. In this case, we are given that the perimeter is (12x - 32) feet, so we can set up an equation:
P = 4s
(12x - 32) = 4s
To solve for s, we can divide both sides by 4:
(12x - 32)/4 = s
Simplifying the expression on the left:
3x - 8 = s
Therefore, the expression in simplest form that represents the side length of the square wrestling mat is 3x - 8 feet.
Answer:
Step-by-step explanation:
the answer would be 3 x − 8 3x-8 3x−8 ft
HELPPPPPP PLEASE PLEASEEEEEE
Determine a function type that
could represent the values in the
table.
x f(x)
0 −18
1 −15
2 −12
3 −9
4 −6
◻ linear
◻ quadratic
◻ exponential
Answer: Linear
Step-by-step explanation:
Since the difference between consecutive values of f(x) is constant, this suggests that the function could be linear. To confirm this, we can calculate the differences between consecutive values:f(1) - f(0) = -15 - (-18) = 3
f(2) - f(1) = -12 - (-15) = 3
f(3) - f(2) = -9 - (-12) = 3
f(4) - f(3) = -6 - (-9) = 3
Since the differences are constant and equal to 3, this confirms that the function is linear.
To find the equation of the linear function, we can use the slope-intercept form of a linear equation:
y = mx + bwhere m is the slope and b is the y-intercept.
We can use the first two points (0, -18) and (1, -15) to find the slope:
m = (change in y) / (change in x) = (-15 - (-18)) / (1 - 0) = 3
Now we can use the slope and one of the points to find the y-intercept:
y = mx + b
-18 = 3(0) + b
b = -18
Therefore, the equation of the linear function is:
f(x) = 3x - 18
So the function type that could represent the values in the table is linear.
Gina started making sugar cookies for her friends at 12:15 P.M. It took her 1 hour and 15 minutes to make
Gina finished making sugar cookies at 1:30 P.M.
What is the basic arithmetic operations?The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find out what time Gina finished making sugar cookies, we need to add the time it took her to make them to the starting time.
Starting time: 12:15 P.M.
Time it took to make cookies: 1 hour and 15 minutes
To add the time, we first convert 1 hour and 15 minutes to hours by dividing the minutes by 60:
1 hour and 15 minutes = 1 + 15/60 hours = 1.25 hours
Now we can add 1.25 hours to 12:15 P.M.:
12:15 P.M. + 1.25 hours = 1:30 P.M.
Hence, Gina finished making sugar cookies at 1:30 P.M.
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Complete question:
Gina started making sugar cookies for her friends at 12:15 P.M. It took her 1 hour and 15 minutes to make. By what time Gina finished making sugar cookies?
Show working out please need to understand
The prοbability that mοre than twο machines need cοrrecting is apprοximately 0.0826 οr 8.26%.
What is binοmial distributiοn?Binοmial distributiοn is a prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, where each trial can οnly have twο οutcοmes: success οr failure.
Accοrding tο questiοn:
Let X be the number οf machines that need cοrrecting adjustments during a day's prοductiοn run, and let p = 0.2 be the prοbability that any οne machine needs cοrrecting.
Then, X fοllοws a binοmial distributiοn with parameters n = 6 (the number οf machines) and p = 0.2 (the prοbability οf a machine needing cοrrecting).
The prοbability οf X is:
P(X > 2) = 1 - P(X <= 2)
Tο calculate P(X <= 2), we can sum the prοbabilities οf X taking οn the values 0, 1, and 2:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)
P(X = 0) = (6 chοοse 0) * 0.2⁰ * 0.8⁶ = 0.2621
P(X = 1) = (6 chοοse 1) * 0.2¹ * 0.8⁵ = 0.3932
P(X = 2) = (6 chοοse 2) * 0.2²* 0.8⁴ = 0.2621
Therefοre,
P(X <= 2)
= 0.9174
And
P(X > 2)
= 1 - P(X <= 2)
= 1 - 0.9174
= 0.0826
Sο the prοbability that mοre than twο machines need cοrrecting is apprοximately 0.0826 οr 8.26%.
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What is the image of the point (-3 , 14) after a counterclockwise rotation about the origin through an angle of 90 degrees?
ms walker has 15 kilograms of clay she wants to give 3 students an equal amount of clay what is the mass of the clay that each student will get
Answer: 5kg
Step-by-step explanation:
If Ms. Walker has 15 kilograms of clay that she wants to distribute evenly among 3 students, all you need to do is divide 15 by 3. Doing so, we get:
15 kg / 3 = 5 kg
Therefore, each student will receive 5 kilograms of clay.
The mass of clay that each student will get is 5kg.
Here, the given questions ask for a solution that deals with the concept of the basic principle of division. hence implementing the principle we can see that,
The given total amount of clay by Ms. walker is 15 kilograms(kg).
Furthermore, this total amount of clay needs to be divided equally between the 3 students.
Then, let the mass of clay given to each student equally be denoted by M in the equation to find out the solution can be written as
M = Total amount of clay ÷ Total number of students
Then,
M = 15 ÷ 3
M = 5 kg
Therefore, The mass of clay that each student will get is 5kg.
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how do i get it to stop making me watch a ad.
Answer:
Brainly Plus.
Step-by-step explanation:
You have to pay money. Otherwise, I don't think you can.
Maybe you could try just installing a bunch of ad-blockers.
But pretty much the only way is Brainly Plus.
Janelys has a points card for a movie theater.
She receives 20 rewards points just for signing up.
• She earns 12.5 points for each visit to the movie theater.
She needs at least 165 points for a free movie ticket.
Write and solve an inequality which can be used to determine x, the number of visits
Janelys can make to earn her first free movie ticket.
Answer: 12 times
Step-by-step explanation:
165-20=145
12.5x11=137.5
12.5x12=150
Answer: 12.5x+20≥165
x≥11.6
Step-by-step explanation:
The answer please cause I don’t know if somebody could help m
Answer:
bottom two
Step-by-step explanation:
if "=", equation
if no "=", expression
Answer:
The ones without an equal sign.
Hope this helps!
Step-by-step explanation:
4x - 7 = 5
4x - 7 is the expression
4x, 7, and 5 are terms
4x - 7 = 5 is the equation
Find the probability of winning second prize in a 5/45 lottery. That is, picking 4 of the 5 winning numbers
Answer:
The probability of winning second prize in a 5/45 lottery is 1 in 8,145. This is calculated by taking the total number of possible combinations (8,145) and dividing it by the total number of possible outcomes (1).
Rapunzel was sitting in her tower and waiting for the prince to come for tea. “He’s coming in 15 1/2 minutes, so I had better hurry and tidy up. Rapunzel started cleaning and finished with 55 seconds to spare. How long did it take to clean her room
It took Rapunzel approximately 14.58 minutes to clean her room.
What is cleaning ?
Cleaning refers to the process of removing dirt, dust, and other unwanted substances from a surface or an object.
Let's start by converting the time to minutes.
15 1/2 minutes = 15.5 minutes
Let's now subtract the time she finished cleaning from the time she started cleaning:
15.5 - 0.92 = 14.58 minutes
Therefore, it took Rapunzel approximately 14.58 minutes to clean her room.
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Please help asap, will give brainliest if correct. What is the constant of proportionality of this table?
Show your work.
The constant of proportionality of this table is: k = 1/7.
Explain about the constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional.Proportional relationships appear as straight lines that go through the origin on a graph. The slope of a graph is equal to the constant of proportionality in the equation, and it refers to how steep a line is relative to other lines.When y and x are two values that are direct proportion to one another, the proportionality constant k is defined as k=y/x.
Thus, using the x and its respective y values.
As the values are in direct proportion.
The constant of proportionality is:
k = 1/7
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5 times 100 times 105
Answer:
52500
Step-by-step explanation:
first do 5*105 to get 525 then mutiply by 100 to get 52500
Your sister has R375 000 and wants to retire. She expects to live for another 25 years, and she also expects to earn 8% on her invested funds. How much could she withdraw at the beginning of each of the next 25 years, and end up with zero in the account?
Answer:
Step-by-step explanation:
Your sister can use the formula for calculating the present value of an annuity to determine how much she can withdraw each year.
The formula for the present value of an annuity is:
PV = Payment x (1 - (1 + r)^-n) / r
Where:
- PV is the present value of the annuity
- Payment is the amount of each withdrawal
- r is the annual interest rate
- n is the number of periods (in this case, 25 years)
We can rearrange this formula to solve for Payment:
Payment = PV x r / (1 - (1 + r)^-n)
We know that your sister has R375 000 to start with, and she wants to end up with zero in 25 years. So, her present value (PV) is R375 000, and we can assume her future value (FV) is zero.
Using the future value formula, we can calculate the interest rate she needs to earn in order to end up with zero in 25 years:
FV = PV x (1 + r)^n
0 = 375000 x (1 + r)^25
(1 + r)^25 = 1
1 + r = (1)^1/25
r = 0
This means that your sister needs to withdraw all of her money over the 25 years in order to end up with zero at the end.
Her withdrawal each year would be:
Payment = PV x r / (1 - (1 + r)^-n)
Payment = 375000 x 0.08 / (1 - (1 + 0.08)^-25)
Payment = R34,028.82 per year
Your sister can withdraw R34,028.82 at the beginning of each year for the next 25 years, and she will end up with zero at the end, assuming she earns an 8% return on her invested funds.
Cybersecurity is a field limited to only government agencies and defense contractors. true or false
Explanation:
Any company that has an online presence (eg: website) needs to take cybersecurity seriously. This is safeguard their customers against online criminals, and also keep their employees safe. Cybersecurity isn't limited to government roles or defense contractor roles only.
1. You purchase a car using a $12,500 loan with a 5.6% simple interest rate.
(a) Suppose you pay the loan off after 6 years. How much interest do you pay on your loan? Show your work.
(a) Suppose you pay the loan off after 3 years. How much interest do you save by paying the loan off sooner? Show your work.
The interest that is paid on the loan in 6 years will be $4,200.
The amount of interest that is saved is $2,100.
What is the interest on the loan?The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.
Simple interest = loan x time x interest rate
Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200
Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100
Interest saved = $4200 - $2100 = 2100
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What is the least amount of wrapping paper needed to wrap a gift box that measures 8 inches by 8 inches by 10 inches.
The first thing we must do for this case is to find the surface area of the rectangular prism.
We have then:
[tex]A = 2 \times (l \times h) + 2 \times (h \times w) + 2 \times (w \times l)[/tex]
Where,
w: width
l: long
h: height
Substituting values we have:
[tex]A = 2 \times (10 \times 8) + 2 \times (8 \times 8) + 2 \times (8 \times 10)[/tex]
[tex]A = 448 \ in ^ 2[/tex]
Answer:
the least amount of wrapping paper needed to wrap the gift box answer is:
A = 448 in²
Which expression is equivalent to -63k-56?