you put $20,000 into an account that pays 7.25% compounded continuously. How much money will you have in there after 10 years?
Answers
To calculate the compound continuosly in a certain ammount of time we need to use the formula
\(A=Pe^{rt}\)where P is the principal invesment, r is the interest rate in decimal form, and t is the time.
In our case P is $20,000, r is 0.075, and t is 10. Then
\(\begin{gathered} A=20000e^{0.075\cdot10} \\ =42340 \end{gathered}\)Therefore she will have $42,340 after ten years.
Related Questions
Lin uses an app to graph the charge on her phone.
When did she start using her phone?
When did she start charging her phone?
While she was using her phone, at what rate was Lin’s phone battery dying?
Answers
Answer:
See belowStep-by-step explanation:
Use the graph to answer the following questions:
When did she start using her phone?
At 2 afternoonWhen did she start charging her phone?
At 8 afternoonWhile she was using her phone, at what rate was Lin’s phone battery dying?
From 100% to 40% between 2PM and 4 PM:
(100 - 40)/(4 - 2) = 60/2 = 30% per hourAnswer:
she start using her phone at 2 hours after noonshe start charging her phone at 8 hours after noon.rate when Lin’s phone battery dying: \(\frac{40-100}{4-2}\) : \(\frac{-60}{2}\) : \(-30\)%/hr{ observation from the graph given }
I’ll give brainliest! Please help
Answers
Answer:
65
Step-by-step explanation:
The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65
Explain how the shapes shown have been sorted. Two groups of shapes. In group A, one shape has four equal side lengths of three, and no right angles. The opposite sides are parallel. Two shapes have two pairs of opposite equal side lengths. One shape has side lengths of four and eight. The other side lengths are three and two. Opposite sides are parallel, and there are no right angles. In group B there are three four sided shapes. One has opposite equal side lengths of seven and four and four right angles. One shape has four equal side lengths of three and four right angles. One shape has one set of opposite parallel sides and one right angle. None of the side lengths in the last shape are equal.
Answers
There are different kinds of shapes. The shapes have been sorted below:
The shape that has one shape has four equal side lengths of three, and no right angles is rhombus.The opposite sides are parallel is parallelogram .Two shapes have two pairs of opposite equal side lengths is a parallelogram.A shape that has side lengths of four and eight is quadrilateral and octagon.Opposite sides are parallel, and there are no right angles is a parallelogramHeptagon has opposite equal side lengths of seven Quadrilaterals and triangle shape has shape has four equal side lengths of three and four right angles.Trapezoids has one set of opposite parallel sides and the shape that has one right angle is right-angled triangles.None of the side lengths in the last shape are equal is scalene triangle. What do you understand by the term shapes?The term shape is a word that connote the form or dimensions of an object and also their outline.
It is made up of outer boundary and also outer surface. Most of everything in the world today do have shape.
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Answer:
rectangle
Step-by-step explanation:
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Add polynomials (intro) Add. Your answer should be an expanded polynomial in standard form. (3x^3 + 4x²) + (3x^3 – 4x^2 – 9x) =
Answers
(3x^3 + 4x²) + (3x^3 – 4x^2 – 9x) =
We have to combine like terms, terms that have x raised to the same power:
First, eliminate the parenthesis:
3x^3 + 4x² + 3x^3 – 4x^2 – 9x =
We have 2 terms raised to the second power (4x^2 and -4 x^2) simply add and subtract.
3x^3+3x^3+4x^2-4x^2-9x
6x^3-9x
In a cumulative relative frequency curve, the interval with the highest proportion of measurements is the interval with the:_______
a. flattest slope.
b. steepest slope
c. backward slope.
d. negative slope.
Answers
Answer:
b. steepest slope
Step-by-step explanation:
The cumulative relative frequency curve also known as Ogive is used for reading the median, upper quartile, lower quartile from the curve and calculating the semi-interquartile range when needed.
From the cumulative relative frequency curve, the interval with the highest proportion of measurements is the interval with the steepest slope. This is because the cumulative relative frequency curve always have a positive slope, and given that the interval has the highest proportion, then the slope will be steepest.
Growth or decay? And percentage rate
Determine if the exponential function shows exponential growth or decay and find the rate at which is growing/decaying as a percent.
Answers
The exponential functions are interpreted below
exponential function growth / decay rate
y =3,500(1,12)^t growth 12%
y = 10000(0.9)^t decay 10%
y = 5(1.025)^t growth 2.5%
y = 160(0.79)^t decay 21%
y = 1,950(0.875)^t decay 12.5%
for the function plotted in graph
f(x) = 2(1.5)^x growth 50%
f(x) = 2(0.8)^x decay 20%
How to interpret the given exponential functionsExponential functions are functions of the form
f(x) = a(b)ˣ
the initial = a
the base = b
the exponents = x
The base is used as described
0 < b < 1 decay function b > 1 growth functionrate
for growth function rate, r = b - 1
for decay function rate, r = 1 - b
y =3,500(1,12)^ t
b = 1.12 (growth)
r = 1.12 - 1 = 12%
y = 10000(0.9)^t
b = 0.9 (decay)
r = 1 - 0.9 = 0.1 = 10%
y = 5(1.025)^t
b = 1.025
r = 1.025 - 1 = 0.025 = 2.5%
y = 160(0.79)^t
b = 0.79
r = 1 - 0.79 = 0.21 = 21%
y = 1950(0.875)^ t
b = 0.875
r = 1 - 0.875 = 12.5%
The plotted functions
f(x) = 2(1.5)ˣ
b = 1.5 (growth)
r = 1.5 - 1 = 0.5 = 50%
f(x) = 2(0.8)^x
b = 0.8 (decay)
r = 1 - 0.8 = 0.2 = 20%
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Ryan buys lunch for $16.83. If sales tax is 8.4%, How much money does Ryan need total for lunch
Answers
\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.4\% of 16.83}}{\left( \cfrac{8.4}{100} \right)16.83} ~~ \approx ~~ 1.41~\hfill \underset{ Total~for~lunch }{\stackrel{ 16.83~~ + ~~1.41 }{\approx\text{\LARGE 18.24}}}\)
A 12-sided solid has faces numbered 1 to 12. The table shows the results of rolling the solid 200 times. Find the experimental probability of rolling a number greater than 10.
Answers
The experimental probability of rolling a number greater than 10 is approximately 0.035 or 3.5%.
What is probability?Probability is a metric for determining the possibility or chance that a specific event will take place. It is stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the event.
By dividing the number of favorable outcomes by the total number of possible outcomes, one can calculate the chance of an occurring. For example, if you toss a fair coin, the probability of getting heads is 0.5, because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).
The ratio of the number of instances an event occurs to all trials or experiments is known as the experimental probability of the occurrence.
In this case, we are rolling a 12-sided solid with faces numbered 1 to 12, and we want to find the experimental probability of rolling a number greater than 10. According to the table, the number of times the solid was rolled is 200.
Looking at the table, we can see that the number of times a number greater than 10 was rolled is 7. Therefore, the experimental probability of rolling a number greater than 10 can be calculated as:
Experimental probability = Number of times the event occurred / Total number of trials
Experimental probability = 7 / 200
Experimental probability = 0.035
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The solutions to the given equation can be written in the form m+-squre root K/2, where m and k are integers. What is the value of m + k ?
x^2-4x-9=0
Answers
m=2 and k=13, and the value of m+k is 2+13=15.
What is solutions to equation?
Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is considered a solution to the problem.
To solve x²-4x-9=0, we can use the quadratic formula:
\(x = (-b ± \sqrt(b^2-4ac))/2a\)
In this case, a=1, b=-4, and c=-9. Substituting these values into the quadratic formula, we get:
\(x = (-(-4) ± \sqrt{((-4)^2-4(1)(-9)))/2(1)}\\\\x = (4 ± \sqrt{(16+36))/2}\\\\x = (4 ± \sqrt{(52))/2}\\\\x = 2 ± \sqrt{(13)}\)
Therefore, m=2 and k=13, and the value of m+k is 2+13=15.
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ABCD is a rectangle. Its diagonals are AC and BD. If AC = 12cm, then BD = _______cm
Answers
Answer:
\(BD = 12\ cm\)
Step-by-step explanation:
Given
Shape: Rectangle
Diagonals: AC and BD
\(AC = 12\ cm\)
Required
Determine BD
From the question, we understand that the shape is a rectangle and its diagonals are AC and BD
Every rectangle has 2 diagonals, both of which are equal.
This implies that:
\(BD = AC\)
Recall that:
\(AC = 12\ cm\)
Hence,
\(BD = 12\ cm\)
The diameter of a circle measures 12 cm. What is the circumference of the circle?
Answers
Answer
The circumference is 37.699
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Step-by-step explanation:
the circumference of the circle with diameter 12cm=2π(d/2)=2×π×12/2=12πcm
There are 1100 students at school.
540 students are girls, the rest are boys.
1/10 of girls are left handed.
1/8 of the boys are left handed.
Work out the number of left handed students in the school.
Answers
Answer:
54 girls are left handed.
70 boys are left handed.
70+54 = 124 left handed students in the school
Step-by-step explanation:
A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0 - 3000
2%
3001 - 5000
3%
5001 - 17,000
5%
17,001 and up
5.75%
Calculate the state income tax
owed on an $80,000
per year salary.
tax = $[? ]
Round your answer to the nearest whole dollar amount.
Answers
Based on the progressive tax rates, the state income tax owed on an $80,000 per year salary is $4,342.50.
What is the progressive tax system?With the progressive tax system, the tax rates increase as the taxable income of the eligible tax payer increases.
Thus, the progressive tax system does not impose a flat rate or amount on the tax payer. Individuals with lower incomes pay less taxes.
Income Progressive Range ($) Tax Rate
0 - 3000 2%
3001 - 5000 3%
5001 - 17,000 5%
17,001 and up 5.75%
Annual salary = $80,000
State Income Tax:
Income Tax
$3,000 x 2% = $60
$2,000 x 3% = $60
$12,000 x 5% = $600
$63,000 x 5.75% = $3,622.50
$80,000 = $4,342.50
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Data representing the price and quantity demanded for hand-held electronic organizers were analyzed every day for 15 days. The logarithmic function of best fit to the data was found to be y= 398-73 lnx. Use this to predict the number of hand-held electronic organizers that would be demanded if the price were $275. Round to the nearest whole number.
a. 6 electronic organizers
b. 5 electronic organizers
c. 4 electronic organizers
d. 7 electronic organizers
Answers
Answer:
\(x=5\)
Step-by-step explanation:
From the question we are told that
The logarithmic function \(y= 398-73 lnx\)
Price p= $275
Generally we solve mathematically for the equation \(y= 398-73 lnx\)
\(y= 398-73 lnx\)
\(275= 398-73 lnx\)
\(73 lnx=123\)
\(lnx=\frac{123}{73}\)
Therefore
\(x=e^(^\frac{123}{73}^)\)
\(x=5.4\)
Nearest whole number
\(x=5\)
The number of required hand-held electric organizers would be 5, option b. Understand the step-by-step calculations below.
Logarithm:The logarithm is an exponent or power to which a base must be raised to obtain a given number.
Mathematically, logarithms are expressed as, m is the logarithm of n to the base b if \(bm = n\), which can also be written as \(m = log_nb\).
Given function is,
\(y=398-73 lnx\)
Also, the cost is $275 then from the given equation,
\(398-73 lnx=275\)
Now, solving the above equation we get,
\(398-73 lnx=275\\73ln=398-275\\lnx=\frac{123}{73}\)
Now, shifting the algorithm into another side we get the exponential equation as,
\(\\x=e^{\frac{123}{73} }\\x=5.39\\x\approx5\)
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Two methods, A and B, are available for teaching a certain industrial skill. The failure rate is 30% for method A and 10% for method B. Method B is more expensive, however, and hence is used only 20% of the time. (Method A is used the other 80% of the time.) A worker is taught the skill by one of the two methods, but he fails to learn it correctly. What is the probability that he was taught by using method A
Answers
Answer:
Probability that he was taught by using method A is 14/17
Step-by-step explanation:
Following probabilities are given -
P (F|A) = 0.2
P (F|B) = 0.1
P (A) = 0.7
P (B) = 0.3
Now, P(A|F) = { P (F|A)* P(A)}/{{ P (F|A)* P(A)} + P (F|B)* P(B)}}
P(A|F) = (0.2*0.7)/( (0.2*0.7)+(0.1*0.3)) = 14/17
State the restrictions and then simplify:(16x^2+ 8x + 1)/(4x+ 1)²
Answers
We are given the following expression:
\(\frac{16x^2+8x+1}{(4x+1)^2}\)We are asked to find the restrictions for this expression. The restrictions for a fractional expression is that the denominator must be different to zero, that is mathematically like this:
\((4x+1)^2\ne0\)Now we solve for "x", first by taking square root on both sides:
\((4x+1)\ne0\)Now we subtract 1 on both sides:
\(\begin{gathered} 4x+1-1\ne-1 \\ 4x\ne-1 \end{gathered}\)Now we divide both sides by 4:
\(\begin{gathered} \frac{4x}{4}\ne-\frac{1}{4} \\ x\ne-\frac{1}{4} \end{gathered}\)This means that the domain of the expression is restricted to values of "x" different from -1/4. Now we will simplify the expression by factoring the numerator
We factor the numerator using the perfect square trinomial method. We take the square root to the first and third terms of the denominator, and rewrite it like this:
\(16x^2+8x+1=(4x+1)^2\)Replacing this in the expression we get:
\(\frac{16x^2+8x+1}{(4x+1)^2}=\frac{(4x+1)^2}{(4x+1)^2}=1\)Therefore the expression is equivalent to 1.
which measure of center would you use to describe a data set with no extreme values and no big gaps? explain your reasoning.
Answers
Answer:
The median always exists. The median does not have to be one of the data values. The median does not use all of the data values, only the one(s) in the middle. The median is resistant to change, it is not affected by extreme values.
Step-by-step explanation:
A rectangular prism has a width of x2 inches and a length of xy2 inches and a height of xy inches.
Which expression represents the volume of the rectangular prism in cubic inches?
2x^2y^2
2xy^3 + 2x^2y
2x^4y^3
x^3y^2
Answers
In this case, the width is x^2 inches, the length is xy^2 inches, and the height is xy inches.
Substituting these values into the formula, we get:
V = (xy^2)(x^2)(xy)
Simplifying, we get:
V = x^4y^3
Therefore, the expression that represents the volume of the rectangular prism in cubic inches is x^4y^3.
Tickets for a reserved seat, r, for the basketball game cost $4 each and student tickets, s, cost $3 each. There were 1,787 people who attended the basketball game and a total of $5,792 was earned in ticket sales. Select the two equations that represent the situation.
A) r+s=5,792
B) r+s=1,787
C) 3r+4s=5,792
D) 4r+s=5,792
E) 4r+3s=5,792
Answers
The two equations which can be used to represent the situation are;
r + s = 1787
4r + 3s = 5,792
The correct answer choice is option B and E
Write two equations that represent the situation?Reserved seat for basketball game = r
Students seat for basketball game = s
Cost of reserved seat tickets = $4
Cost of students tickets = $3
Total number of people who attended the basketball game= 1,787 people
Total amount earned for tickets sales= $5,792
r + s = 1787
4r + 3s = 5,792
Therefore, the basketball game situation can be represented by the equation r + s = 1787; 4r + 3s = 5,792
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Brainlyest FOR BEST ANSWER thank u
Answers
Answer: B
Step-by-step explanation:
To calculate the mean (average) of a list of numbers, simply add up the numbers and divide by the number of numbers
How would you solve
"if f(x) / (x - 2) = x ^ 3 + 2x - 4 + 13/(x - 2) what is f(2)"
and
"if f(x) / (x + 3) = 3x ^ 2 - 4x + 2 what is f(-3)"
Answers
The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.
To solve the given equations, we need to find the value of the function f(x) for specific values of x.
"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"
To find f(2), we can substitute x = 2 into the equation and solve for f(2).
Plugging in x = 2, we get:
f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)
Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.
"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"
To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).
Plugging in x = -3, we get:
f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2
Simplifying, we have:
f(-3) / 0 = 3(9) + 12 + 2
f(-3) / 0 = 27 + 12 + 2
f(-3) / 0 = 41
Additional information or context is needed to solve for f(-3).
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In a right-angled triangle the ratio of the two smaller angles is 3:2. Find the sizes of each of the angles.
Answers
Answer:
36° , 54° , 90°
Step-by-step explanation:
since the triangle is right then one angle is 90°
the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )
the sum of the 3 angles in the triangle is 180° , that is
3x + 2x + 90 = 180
5x + 90 = 180 ( subtract 90 from both sides )
5x = 90 ( divide both sides by 5 )
x = 18
Then
3x = 3 × 18 = 54°
2x = 2 × 18 = 36°
the 3 angles measure 36° , 54° , 90°
The mug is 5/8 full, the mug contains 3/4 of water find the capacity of the mug
Answers
The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).
What is capacity?It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.
In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.
Let the capacity of the mug be x.
Given,
Mug is 5/8 full and contains 3/4 of water
So, 5/8 of the mug is filled with water
Therefore,
5/8 of x = 3/4
(5/8 )x = (3/4)
x = (3/4) × (8/5)
x = (24/20)
x = 1.2
Therefore, the capacity of the mug is 1.2.
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Which number line shows how to find 3 - 5?
A.
HH
H
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
O B.
H
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
OC. HHH
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
D
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Answers
Answer:
(d)shows how to find 3 - 5
Step-by-step explanation:
in the image above
The correct answer is option D.
Number lineA pictorial representation of the numbers both, negative and positive is named as number line.
How to represent 3-5 on number line?To carry out the solution for 3-5, first go to 3 from the 0 and then, go back up to 5 units in the reverse direction i.e, towards the negative axis.
Hence, the number line representation is shown.
As a result, Option D is the correct answer.
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This figure represents a garden box that is to be filled with soil.
How much soil will it take to fill the garden box?
Enter your answer in the box.
ft³
Three-dimensional figure that could be formed by placing a smaller rectangular prism on top of a larger rectangular prism such that the widths of the prisms are the same. The larger bottom prism has a length of 19 feet, a width of 12 feet, and a height of 6 feet. The smaller top prism has a length of 10 feet and a height of 3 feet.
Answers
Answer:
1134 ft^3
Step-by-step explanation:
The third term of the sequence is 165. Find the first term
Term to term rule is subtract 2 and then multiply by 3
Answers
The value of the first term in the sequence is 21.
How to calculate the first term?Let the second term teen be x.
Since the term to term rule is subtract 2 and then multiply by 3. This will be:
(x - 2) × 3 = 165
3(x - 2) = 165
3x - 6 = 165
Collect like terms
3x = 165 + 6
3x = 171
Divide
x = 171 / 3.
x = 57
Second term = 57
We will do same thing again to get first term. Let first term be a.
(a - 2) × 3 = 57
3a - 6 = 57
Collect like terms
3a = 57 + 6
3a = 63
Divide
a = 63/3
a = 21
The first term is 21.
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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 270 engines and the mean pressure was 5.6 pounds/square inch (psi). Assume the population standard deviation is 0.8. The engineer designed the valve such that it would produce a mean pressure of 5.5 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answers
Answer:
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the valve pressure is significantly different from 5.5 psi.
P-value = 0.04
Test statistic z=2.05
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the valve pressure is significantly different from 5.5 psi.
Then, the null and alternative hypothesis are:
\(H_0: \mu=5.5\\\\H_a:\mu\neq 5.5\)
The significance level is 0.02.
The sample has a size n=270.
The sample mean is M=5.6.
The standard deviation of the population is known and has a value of σ=0.8.
We can calculate the standard error as:
\(\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.8}{\sqrt{270}}=0.049\)
Then, we can calculate the z-statistic as:
\(z=\dfrac{M-\mu}{\sigma_M}=\dfrac{5.6-5.5}{0.049}=\dfrac{0.1}{0.049}=2.054\)
This test is a two-tailed test, so the P-value for this test is calculated as:
\(\text{P-value}=2\cdot P(z>2.054)=0.04\)
As the P-value (0.04) is bigger than the significance level (0.02), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the valve pressure is significantly different from 5.5 psi.
Find an equation of the line
Through (-3,-7); parallel to 2x + 3y = 5
Answers
Answer:
2x +3y = -27
Step-by-step explanation:
You want an equation for a line parallel to 2x +3y = 5 and through the point (-3, -7).
Parallel lineA parallel line will have the same slope as the given line, but will have different intercepts. In the standard-form equation given, that means the coefficients of the variables will be the same, but the constant will be different.
To make the constant appropriate for the given point, we use the (x, y) values of the given point to find it:
2x +3y = c
2(-3) +3(-7) = c = -6 -21 = -27
The desired equation is ...
2x +3y = -27
4.2 The Court lines are 50 mm wide. Court paint covers 7 m² per litre of paint. 4.2.1 Calculate the total length of the centre circle and the two goal semi circles to be repainted. You may use the formula: Total length Circumference of a centre circle + 2 x Circumference of a semicircle =
Answers
The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.
How to calculate the Calculate the total length of the centre circle and the two goal semi circles to be repaintedGiven:
Court lines are 50 mm wide.
Court paint covers 7 m² per litre of paint.
The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr
Radius of the entire circle = 9 m / 2 = 4.5 m
Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m
Circumference of the centre circle = 2π(4.45 m) = 27.94 m
Next, let's calculate the circumference of the semicircles:
The semicircles are half circles, so the circumference is given by the formula: Circumference = πr
The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.
Circumference of a semicircle = π(4.5 m) = 14.14 m
Total length = Circumference of the centre circle + 2 x Circumference of a semicircle
Total length = 27.94 m + 2(14.14 m)
Total length = 56.22 m
Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.
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Is 3/4 greater than 3/5
Answers
Answer:
Yes.
Explanation:
3/4 is 75% of a whole, 3/5 is 60%.