Answer:
Equation is A = 5000(1.015)^(4t)
Her investment will be worth $10,000 in about 11.63888 years
Rounding up to the nearest whole number gets to 12 years
==========================================================
Explanation:
Part 1) Finding the equation
The compound interest formula is
A = P(1+r/n)^(n*t)
Here are the variables
A = final amountP = starting amount, or deposit, or principalr = interest rate in decimal formn = number of times money is compounded per yeart = number of yearsIn this case,
P = 5000r = 0.06 from the 6% annual interestn = 4 times a year is the compounding frequencyt = unknown amount of timeTherefore, the equation is
A = P(1+r/n)^(n*t)
A = 5000(1+0.06/4)^(4t)
A = 5000(1.015)^(4t)
The decimal value is exact.
--------------------------
Part 2) Let's plug in A = 10,000 and solve for t.
You'll need to use logarithms to isolate the exponent.
A = 5000(1.015)^(4t)
10,000 = 5000(1.015)^(4t)
10,000/5000 = (1.015)^(4t)
2 = (1.015)^(4t)
Log[ 2 ] = Log[ (1.015)^(4t) ]
Log(2) = 4t*Log( 1.015 )
4t = Log(2)/Log(1.015)
4t = 46.5555256308062
t = 46.5555256308062/4
t = 11.6388814077015
t = 11.63888
It takes about 11.63888 years for the investment to reach $10,000.
Therefore, at the 12 year mark is when the investment is more than $10,000.
Answer:
11 years and 9 months
Step-by-step explanation:
Compound Interest Formula
\(\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}\)
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
A = $10000P = $5000r = 6% = 0.06n = 4 (as compounded quarterly)t = yearsSubstitute the given values into the equation and solve for t:
\(\implies 10000=5000\left(1+\dfrac{0.06}{4}\right)^{4t}\)
\(\implies \dfrac{10000}{5000}=\left(1+0.015\right)^{4t}\)
\(\implies 2=\left(1.015\right)^{4t}\)
Take natural logs of both sides:
\(\implies \ln 2=\ln \left(1.015\right)^{4t}\)
Apply the power log law:
\(\implies \ln 2=4t\ln \left(1.015\right)\)
Simplify:
\(\implies t=\dfrac{\ln 2}{4 \ln 1.015}\)
\(\implies t=11.63888141\)
11.6388141... years ≈ 11 years and 7.7 months
As the interest is earned quarterly, round this to the nearest quarter
⇒ 11 years and 9 months.
Therefore, Kim's investment will be worth more than $10,000 at 11 years and 9 months.
Need help with math homework
e^x=10^(x-1)
Answer:
Step-by-step explanation:
This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:
ln(e^x) = x-1
In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:
ln(10^(x-1)) = x-1
e^(x-1) = 10^x
The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.
Debra runs 4 miles in 30 minutes. At the same rate, how many miles would she run in 48 minutes?
========================================================
Work Shown:
(4 miles)/(30 minutes) = (x miles)/(48 minutes)
4/30 = x/48
4*48 = 30x
30x = 4*48
x = 4*48/30
x = 6.4
“Draw the graph of the line with equation y=3/4x-2”
Can someone please tell me how to draw this graph
Step-by-step explanation:
You have multiple ways, all revolving around finding 2 points.
The easiest point to use is the y intercept (the value of y when x=0), and is the constant term, giving you \((0; -2)\)
The second point can be found in a number of ways:
Look for the x intercept (when y=0), and you will get some point by solving for x;put any value of x you haven't used so far (ie, 0), compute it, and you will find a second point.plug a "smarter" value of x that will make computation easy: in this case you have a fraction, so I would pick the denominator to simplify: (you got \(\frac34\), so \(x=4 \rightarrow y=\frac34(4)-2 = 3-2=1\) giving a second point \((4;1)\))since the equation is in slope-intercept form, Just remember the slope tells you how many vertical units you move (numerator) when you move right the number of units in the denominator, with the sign telling you up or down: in our case you move 3 up (since it's positive) every 4 "steps" right.In any case, the graph will look something like the one in the image
A faucet leaks at a rate of 2 milliliters per second. What is the rate in liters per minute?
A
12 -
B
0.12 L/min
12LT
D
120 L/min
Answer: 0.12 per minute
Step-by-step explanation: I actually had to reread this one a couple times, as the setup is a bit confusing. Here's how I would solve it personally:
1. Since it's leaking 2ml per second, and there are 60 seconds in a minute, multiply 2ml times 60 seconds to get 120ml every minute.
2. 1ml equals 0.001 liters, so multiply 120ml by 0.001 to find out how many liters that is. 120(0.001)=0.12.
Hope this helps,
Lacia
Please help me with this math question! Thank you!
The expression that illustrate the diagram below is f(x) = 47-2x
What are linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
In the diagram, the total no of box is 45 and 2 boxes are missing on the second box. Therefore the constant in the the expression is 45+2 = 47. Let x be the variable.
Therefore f(x) = 47-2x
when it is pattern 1
x= 1
f(1) = 47-2 = 45
when it's pattern 2
f(x) = 47-2×2 = 43
when it's pattern 3
f(x) = 47- 2×3 = 41
therefore the expression that can illustrate the diagrams is f(x) = 47-2x
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-3*10^2t=-28 Solve the equation for
t
Express the solution as a logarithm in base-
10
The solution for t is t = log(28/3) / 2, the Logarithm in base-10.
The equation -3 * 10^(2t) = -28 for t, the exponential term and then take the logarithm of both sides. Let's go through the steps:
Step 1: Divide both sides of the equation by -3:
(10^(2t)) = -28 / -3
Step 2: Simplify the right-hand side:
(10^(2t)) = 28/3
Step 3: Take the logarithm of both sides using base-10 logarithm (log):
log(10^(2t)) = log(28/3)
Step 4: Apply the power rule of logarithms to bring down the exponent:
2t * log(10) = log(28/3)
Step 5: Since log(10) = 1, we have:
2t = log(28/3)
Step 6: Divide both sides of the equation by 2:
t = log(28/3) / 2
Therefore, the solution for t is t = log(28/3) / 2, where log represents the logarithm in base-10.
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calculate the force acting on a man of mass 600g running to a tree through a distance of 20m
120N
f= mgh
=o. 6x10x20
= 120N
Step-by-step explanation:
given,
mass ( m)=0.6kg
gravity=9.8 m/s^2
by the formula of force,
f= ma
=0.6×9.8
therefore force is 5.88 n.
When Solving Quadratics, What questions should I ask myself?
Answer:
Step-by-step explanation:
In as much as I might give a warning on not to doubt oneself, I also need to put out what one should take note of when solving quadratic problems.
Using the general formula, it's of utmost importance to not mix the variables together. Remember, making "a", "b" and "b", "a" will lead to an entirely different answer, which is most likely wrong anyway.
It's important to take note of the signs too. Remember, the formula say,
-b ± √(b² - 4ac) / 2a
The first b is negative, and that means a negative value will turn positive there. These are very trivial steps, but they can also make or mar our efforts in getting the correct answer
Jack leaves home for school on his bike every day at 6 a.m., travelling at 32 km/h.
One day he forgot his homework, which his mother discovered in the car 15 minutes after he had left.
She immediately left home and chased after Jack, travelling at 52 km/h.
At what time did she catch up to him?
Find the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity.
Step-by-step explanation:
To calculate the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity, we can use the formula for the present value of an annuity due:
PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)
where:
- PV is the present value of the annuity due ($32,000)
- PMT is the monthly payment we want to find
- r is the annual interest rate (7.9%)
- n is the number of times interest is compounded per year (12 for monthly compounding)
- t is the number of years (10)
PMT = PV / ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n) = **$292.07**
Therefore, the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity is **$292.07**.
2.
Elena has a
pet parakeet that weighs 6 when measured in one unit and
170 when measured in a different unit. Which measurement is in ounces,
and which is in grams?
170
Measurement of weight 6 is in ounces and the measurement of weight 170 is in grams.
What is measurement?
An object or event's attributes are quantified through measurement so that they can be compared to those of other things or events. Measurement, then, is the process of establishing how big or small a physical quantity is in relation to a fundamental reference quantity of the same kind.
Given:
Elena has a pet parakeet that weighs 6 when measured in one unit and
170 when measured in a different unit.
We have to find the correct units from grams and ounces for these.
We know that, 1 ounce is greater than 1 gram.
1 ounce = 28.3495 grams
Multiply both sides by 6.
6 ounces = 170.097 grams
Approximate the values to the nearest whole number.
6 ounces = 170 grams
Therefore, 6 ounces = 170 grams.
Hence, measurement of weight 6 is in ounces and the measurement of weight 170 is in grams.
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Let f(x) = 2x – 1 and g(x) = 3x
Find g(f(x))
which function will have the greatest value at
\(x = 16 \)
\( y = {10}^{16} \)
\(y = {x}^{2} - 17x + 182\)
\(y = {1.17}^{x} \)
The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.
How to determine the corresponding output value for the given function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;
\(y = 10^{16}\)
y = 10,000,000,000,000,000.
y = x² - 17x + 182
y = 16² - 17(16) + 182
y = 256 - 272 + 182
y = 166.
\(y = 1.17^x\\\\y = 1.17^{16}\)
y = 12.330304108137675851908392069373.
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Makeeya only has $25 to spend on a custom T-shirt. It costs $10 for a plain T-shirt, and there is a charge of $$1.50 for each square inch of design added to the T-shirt. Which solution represents the number of square inches of design,x , Makeeya can put on her T-shirt?
Answer:
10 square inches
Step-by-step explanation:
cost of a plain t-shirt = $10
cost of 1 square inch of design addition = $1.50
let there be x square inches of design
then cost of x square inches of design = x*cost of 1 square inch of design
= 1.50*x = 1.5x
Total cost for t-shirt with x square inches of design = cost of a plain t-shirt + cost of x square inches of design = 10 + 1.5 x
It is given that Makeeya has only $25, then total cost which can be afforded by him will be $25 only
Thus,
10 + 1.5 x = 25
=> 1.5x = 25-10 = 15
=> x = 15/1.5 = 10
Thus, Makeeya can put 10 square inches of design on her T-shirt.
Suppose that you want to know how tall a building is. You are standing 60 meters from a flagpole that you know is 35 meters tall. Along the same straight line, you are standing 170 meters from the front of the building.
Notice that the triangle formed by you and the flagpole and the triangle formed by you and the building are similar (you can form the smaller triangle from the larger one by dilation). Using this fact, determine the height of the building.
1. Determine the height of the building using the scale factor r.
2. Determine the height of the building using ratios within the two triangles.
3. Determine the height of the building using ratios between the two triangles.
4. If the angle indicated at the flagpole in the figure measures 60 degrees, what does the unknown angle at the top of the building measure?
The height of the building, h, found using ratios between similar figures and within similar figures is as follows;
1. The scale factor, r = 17/6
The height of the building is 99 1/6 meters
2. The within figure ratio is 35/60 = h/170
Heiught of the building is 99 1/6 meters
3. The between figure ratio is 35/h = 60/170
Height of the building is 99 1/6 meters
4. The measure of the angle at the top of the building is 60°
What are similar triangles?Similar triangles are triangles that have corresponding sides that are proportional, such that the sides of each triangle are a constant multiple of the sides of the other.
The distance from the flagpole = 60 meters
Height of the flagpole = 35 meters
The distance from the building = 170 meters
1. The height of the building found using a scale factor is as follows;
The scale factor, s.f. is the know ratio of the distance from the building to the distance from the flagpole
Therefore; s.f. 170/60 = 17/6
The height of the flagpole is 35 meters
Height of the building = Height of the flagpole × Scale factor
Height of the building = 35 m × 17/6 = 99 1/6
The height of the building found using scale factors is 99 1/6 meters
3. The height of the building found using ratios within the two triangles is found as follows;
The triangles are similar, therefore, their interior angles are congruent, and the trigonometric ratios of the angles are the same.
Within the two triangles, we get;
\(\frac{Height \ of \ flagpole}{Distance \ from \ flagpole} = \frac{Height \ of \ building}{Disrtance \ from \ building}\)
35/60 = h/170
h = 170 × (35/60) = 99 1/6
Height of the building = 99 1/6 meters
3. The triangles formed with the flagpole and the triangle formed with the building are similar triangles, therefore;
Between the two triangles, we get
\(\frac{Height \ of \ the \ flag[pole}{Height \ of \ the \ building } =\frac{Distance \ from \ the \ flagpole}{Distance \ from \ the \ building}\)
Plugging in the known values, we get;
\(\frac{35}{Height \ of \ the \ building} = \frac{60}{170}\)
Height of the building = 35 × 170/60 = 99 1/6
The height of the building is about 99 1/6 meters
4, The triangle formed by the flagpole and the building are similar, therefore, the corresponding angles in the triangles are congruent
The angle at the top of the flagpole corresponds with the angle at the top of the building, therefore;
The angle formed at the top of the flagpole is congruent to the angle formed at the top of the building
The measure of corresponding angles are the same, therefore, the anglle at the top of the building is equal to the angle at the flagpole, which is 60°
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heeeeeeeeeeeeeeeeeeeelllllppp
Answer:
120 degrees.
Step-by-step explanation:
All the angles in a triangle add up to 180. You have two of the angles given:
50 degrees and 70 degrees
To find the third angle of the triangle (BAC), use the expression:
180 - (50 + 70)
180 - 120
60
So, the third angle in the triangle is 60 degrees. Looking at angle DAB, you can see that it forms a straight line with angle BAC. A straight line is 180 degrees. Since we know BAC is 60, and BAC + DAB = 180, by doing 180 - 60, you can see that angle DAB is 120 degrees.
Below are monthly rents paid by 30 students who live off campus.
640 640 640 840 610 500
600 940 650 530 630 595
470 650 560 570 760 830
510 530 670 600 620 410
640 710 730 750 630 655
What is the value of the expression? Do not use a calculator.
tan
Tan2pie/3
The value of tan 2π/3 without calculator is -√3.
What is the value of tan 2π / 3 without calculator?The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;
the value of π = 180 degrees
So we can replace the value of π in the function with 180 degrees as follows;
tan ( 2π / 3) = tan (2 x 180 / 3)
tan (2 x 180 / 3) = tan (2 x 60)
tan (2 x 60) = tan (120)
tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.
tan (120) = - tan (180 - 120)
= - tan (60)
= -√3
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Which one of the following statements is correct when the homoskedasticity assumption is violated while the rest of the OLS assumptions are correct.?
a.The beta parameter estimates can be calculated but they are wrong.
b.The beta parameter estimates are biased
c.The beta parameter estimates are unbiased because homoskedasticity assumption is not required for unbiasedness.
d.The beta parameter estimates cannot be calculated
The correct answer is option b. When the homoskedasticity assumption is violated, The beta parameter estimates are biased while the rest of the OLS assumptions are correct.
When the homoskedasticity assumption is violated, the ordinary least squares (OLS) estimator is still consistent but no longer efficient. This means that the estimates of the regression coefficients (beta parameters) are still unbiased, but they have higher variances and covariances.
In other words, the OLS estimator is no longer the best linear unbiased estimator (BLUE) and it may be biased when the errors are heteroscedastic. Therefore, option b is correct.
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Factorise fully 6x+8
Answer: To factorize the expression 6x + 8 fully, we can first look for the greatest common factor (GCF) of the two terms. In this case, the GCF is 2.
Step 1: Factor out the GCF:
2(3x + 4)
Now, we have the expression 3x + 4 inside parentheses. This expression cannot be further factorized since there are no common factors other than 1.
Therefore, the fully factorized form of 6x + 8 is:
2(3x + 4)
Step-by-step explanation:)
The factored expression is:
↬ 2(3x + 4)Step-by-step explanation:
To factor the expression, look at its GCF (greatest common factor).
Clearly the GCF of both terms is 2. So what we do next is we divide both terms by 2 :
6x ÷ 2 + 8 ÷ 2The result is :
3x + 4And now the 2 goes outside the parenthesis:
2(3x + 4)Hence, the answer is 2(3x + 4).
n the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches, and standard deviation of 5.8 inches. A) What is the probability that a randomly chosen child has a height of less than 46.3 inches
Answer:
The probability is 0.0643 to 4 decimal places
Step-by-step explanation:
To calculate this probability, we find the z-score
Mathematically;
z-score = (x-mean)/SD
where in the question;
x = 46.3
mean = 55.1
SD = 5.8
Plugging these values, we have;
z-score = (46.3-55.1)/5.8 = -8.8/5.8 = -1.52
The probability we want to calculate is;
P(z < -1.52)
We can get this answer by using the standard normal distribution table;
Thus from the table, we have;
P(z < -1.52) = 0.064255 which is 0.0643 to 4 decimal places
How do write 400% as a fraction , mixed number, or whole number
Answer:
400/10
Step-by-step explanation:
yeet
Answer:
4
Step-by-step explanation:
400% = 400/100 = 4
solve the equation and justify each step using the algebraic properties of equality
Answer:
-5
Step-by-step explanation:
3x=-13-2
3x=-15
x=-5
Which of the following is equal to the ratio 5cm:5m:0.02km?
A. 10: 400 C. 1: 100: 400
B. 300:2000 D. 10: 500
Answer:
Its C. When you are getting ratios, we need to convert the units too...
The correct ratio which is equal to the ratio 5cm:5m:0.02km is,
⇒ 1 : 100 : 400
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
We have to given that;
The ratio is,
⇒ 5cm:5m:0.02km
Now, We can simplify the ratio as;
⇒ 5 cm : 5 m : 0.02 km
⇒ 5 cm : 5 x 100 cm : 0.02 x 100000
⇒ 5 cm : 500 cm : 2000 cm
⇒ 1 : 100 : 400
Thus, The correct ratio which is equal to the ratio 5cm:5m:0.02km is,
⇒ 1 : 100 : 400
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Using log evaluate 3^x=10
Answer:
x ≈ 2.09590327429
Step-by-step explanation:
You want the solution to 3^x = 10 using logarithms.
LogsTaking logarithms of both sides of the given equation, we have ...
x·log(3) = log(10)
Dividing by the coefficient of x gives ...
x = log(10)/log(3)
x ≈ 2.09590327429
__
Additional comment
If the logarithm to the base 10 is used, then this becomes ...
x = 1/log₁₀(3)
The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.
For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.
<95141404393>
The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).
Taking the log of both sides, we get:
log(3^x) = log(10)
Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:
x * log(3) = log(10)
Next, we can divide both sides of the equation by log(3) to isolate the variable x:
x = log(10) / log(3)
Using a calculator, we can evaluate the right side of the equation:
x ≈ 1.46497
Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
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Use the procedures developed to find the general solution of the differential equation. (Let x be the independent variable.)
2y''' + 15y'' + 24y' + 11y= 0
Solution :
Given :
2y''' + 15y'' + 24y' + 11y= 0
Let x = independent variable
\((a_0D^n + a_1D^{n-1}+a_2D^{n-2} + ....+ a_n) y) = Q(x)\) is a differential equation.
If \(Q(x) \neq 0\)
It is non homogeneous then,
The general solution = complementary solution + particular integral
If Q(x) = 0
It is called the homogeneous then the general solution = complementary solution.
2y''' + 15y'' + 24y' + 11y= 0
\($(2D^3+15D^2+24D+11)y=0$\)
Auxiliary equation,
\($2m^3+15m^2+24m +11 = 0$\)
-1 | 2 15 24 11
| 0 -2 - 13 -11
2 13 11 0
∴ \(2m^2+13m+11=0\)
The roots are
\($=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$\)
\($=\frac{-13\pm \sqrt{13^2-4(11)(2)}}{2(2)}$\)
\($=\frac{-13\pm9}{4}$\)
\($=-5.5, -1$\)
So, \(m_1, m_2, m_3 = -1, -1, -5.5\)
Then the general solution is :
\($= (c_1+c_2 x)e^{-x} + c_3 \ e^{-5.5x}$\)
What is the range of the function? f(x)=3^x−1−2
The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is y > -2
Calculating the range of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 3ˣ ⁻ ¹ - 2
The above equation is an exponential function
The rule of an exponential function is that
The domain is the set of all real numbersHowever, the range is always greater than the constant termIn this case, it is -2
So, the range is y > -2
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which is the estimate quotient for 530÷9
Answer:
55
Step-by-step explanation:530 would be rounded to 550 and 9 would be rounded to 10
550 divided by 10 is 55
Pls give me brainliest if this helps
Jamie receives 20 emails total on Monday morning she responds to eight of the emails what is the ratio emails that Jamie received to the mail that she answered
Answer:
5:2
Step-by-step explanation:
A ratio is basically a fraction but horizontally for eg. this: 5:8! This question is asking us to find the ratio of the emails that Jamie received to the emails that she answered.
According to the question, Jamie got 20 emails and responds to 8 of them. The ratio would look like this: 20:8 (because a ratio is just a fraction but horizontal, doesn't mean that there will be mixed numbers!) but not this 8:20. Ratios have a specific order that they have to be in and that will vary depending on the question. If the question says to find the ratio of emails that Jamie responded to to the emails that she received, then in this case 8:20 would be correct.
For now, the answer is 20:8. However, we still need to simplify it by finding its lowest common factor (unless the question asks you to not simplify it, it's better to simplify the answer like a fraction). The lowest common factor would be 4 for 20 and 8. 4 goes in 20 5 times sand 4 goes into 8 2 times.
Your final answer should be: 5:2
If you have any further questions please ask!
Can someone plz help? I will mark brainliest
Answer:
Step-by-step explanation:
easy, f(-4) means what is the range (output of -4)
well in graph case, usually the domain in the x-axis and the range in the y-axis
so we're going to go to -4 in the x-axis then go up until we reach the point that is the range,
so the range is "4"
hope you happy with this answer!