It will take at least 12 years for Sarah's $600 deposit at a 2.5% annual interest rate to grow to more than $800, assuming the interest is compounded annually.
To determine how long it will take for Sarah's $600 deposit at a 2.5% annual interest rate to grow to over $800, we can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for in years.Since the problem doesn't specify the compounding frequency, let's assume it's compounded annually for simplicity:
[tex]A = 600(1 + 0.025)^t[/tex]. We need A to be greater than $800.
To find the minimum number of years (t), we solve for t:
[tex]800 < 600(1 + 0.025)^t[/tex]
Solving for t gives us: t > ln(800/600) / ln(1.025).
Using a calculator, we find that t > 11.89.
Therefore, it will take at least 12 years for the amount in Sarah's account to exceed $800.
A cup of coffee contains 130 mg of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how much caffeine will remain in the body after 3 hours?
Write the exponential function and solve.
a.
4072-06-01-04-00_files/i0260000.jpg; 184 mg
b.
4072-06-01-04-00_files/i0260001.jpg; about 346 mg
c.
4072-06-01-04-00_files/i0260002.jpg; less than 1 mg
d.
4072-06-01-04-00_files/i0260003.jpg; about 92 mg
35 points!
What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Help please! Math Nation Section 6 Test Yourself Practice Tool.
Answer: D) [tex]y=-5(x-5)^2+1125[/tex]
Step-by-step explanation:
Let x be the number of $2 increases in price and y be the revenue.
By using the given table , lets check all the options
A) [tex]y=(x+5)^2-1125[/tex]
For x=1, y=1045
[tex]y=(1+5)^2-1125=36-1125=-1089\\\\But\ 1045\neq-1089[/tex]
B) [tex]y=(x-5)^2+1125[/tex]
For x=1, y=1045
[tex]y=(1-5)^2+1125=14+1125=1139\\\But\ 1045\neq1139[/tex]
C) [tex]y=-5(x+5)^2-1125[/tex]
[tex]y=-5(1+5)^2-1125=-5(36)-1125=-1305\\\\But\ 1045\neq-1305[/tex]
D) [tex]y=-5(x-5)^2+1125[/tex]
[tex]y=-5(1-5)^2+1125=-5(16)+1125=1045[/tex]
Hence, this is the quadratic equation that models the data.
Based on the table of values, an equation of the quadratic that models the data is: D. [tex]y = -5(x-5 ) ^2+ 1125[/tex]
In Mathematics and Euclidean Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:
[tex]y = a(x - h)^2 + k[/tex]
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.In order to determine an equation for the line of best fit or quadratic regression line that models the data points contained in the table of values, we would have to use a graphing calculator (Microsoft Excel).
Based on the scatter plot (see attachment) which models the relationship between the number of $2 increase in price (in dollars), x and revenue, y, the quadratic regression is given by:
[tex]y =-5x^2 + 50x + 1000\\\\y = -5(x^2 - 10x) + 1000\\\\y = -5(x^2 - 10x + (\frac{10}{2})^2 ) + 1000+ (\frac{10}{2})^2\\\\y = -5(x^2 - 10x + 25 ) + 1000+25\\\\y = -5(x-5 ) ^2+ 1125[/tex]
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation. 3x + 2y = −21 x − 3y = 4
If two 6-sided number cubes are rolled, what is the probability that you will roll a 1 first and then roll a 5 with the second cube?
Final answer:
The probability of rolling a 1 first and then rolling a 5 with two 6-sided number cubes is 1/36.
Explanation:
To find the probability of rolling a 1 first and then rolling a 5 with the second cube, we need to consider the probabilities of each event separately. The probability of rolling a 1 on the first cube is 1/6, since there is only one face with a 1 out of six possible outcomes.
The probability of rolling a 5 on the second cube is also 1/6. Since these events are independent, we can multiply their probabilities to find the overall probability:
Probability of rolling a 1 first and then rolling a 5 = (1/6) * (1/6) = 1/36
Determine the 10th term 0.1,0.5,2.5
If the train that Megan is riding covers 60 miles in 2 hours, how fast is the train traveling?
Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4. (2 points)
A f(x) = –16x2
B f(x) = – x2
C f(x) = x2
D f(x) = 16x2
Equation of parabola with focus at (0,-4) and directrix is y=4 .
As we know parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is (x,y).
Distance from focus(0,-4) to (x,y) = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]
Distance from (x,y) to directrix, y=4 is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |\\{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]
→x²+y²+8 y +16 = y² - 8 y+16
→ x² = -8 y - 8 y= -16 y [ Cancelling y² and 16 from L.H.S and R.H.S ]
So , equation of parabola is , x²= - 16 y or f(x)= -x²/16
The Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
Equation of parabola with focus at [tex](0,-4)[/tex] and directrix is [tex]y=4[/tex] .
Parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is [tex](x,y)[/tex].
Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^2+(y+4)^2[/tex]
[tex]d=\sqrt{x^2+(y+4)^2[/tex]
Distance from [tex](x,y)[/tex] to directrix, [tex]y=4[/tex] is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^2+(y+4)^2}=\left | y-4 \right |[/tex]
[tex]d={x^2+(y+4)^2=(y-4)^2[/tex]
[tex]x^2+y^2+8y+16=y^2-8y+16[/tex]
[tex]x^2=-8y-8y[/tex]
[tex]x^2=-16y[/tex]
[tex]y=\dfrac{-x^2}{16}[/tex]
So, the Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
Learn more about parabola here:
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Val rented a bicycle while she was on vacation. A paid a flat rental fee of $55 plus $8.50 each day the total cost was 123 dollars write an equation you can use to find the number of days when she rented to bicycle
will give brainlist
what is the approximate area of the figure
Answer:
the answer is 137.1
Step-by-step explanation:
Divide the figure into recognizable shapes. Find the area of each shape and add them together.
Two f-18s are catapulted off an aircraft carrier and fly on courses that diverge at a 60° angle. if each flies at a constant rate of 500 mph, after how many hrs will the fighters be 1200 mi apart?
A parallelogram has vertices E(−8, 3), F(2, −2), G(−1, 3), and H(−5, −2). What are the coordinates of the midpoint of each diagonal?
(3, −0.5)
(−4.5, 3)
(−3, 0.5)
(0.5, −1.5)
The cake store is having a 25\%25%25, percent off sale on all of its cakes. If the cake you want regularly costs \$9$9dollar sign, 9, how much would you save with the discount?
Answer:
$2.25.
Step by step explanation:
We have been given that the cake store is having a 25% off sale on all of its cakes.
To find our savings with the discount we will find 25% of $9 (regular cost of cake).
[tex]\text{Savings with the discount}=9\times\frac{25}{100}[/tex]
[tex]\text{Savings with the discount}=9\times\frac{1}{4}[/tex]
[tex]\text{Savings with the discount}=\frac{9}{4}=2.25[/tex]
Therefore, we will save $2.25 with the given discount.
What is the relative minimum of the function?
Answer:
The required relative minimum is -5
Step-by-step explanation:
Relative minimum is the point where the graph shows its minimum point or the lowest point of the graph.
Like here, we have been given a parabolic shape so, the minimum of this parabola is the coordinate of y in its vertex point.
So, its relative minimum is -5.
Solve the single variable equation for n.
4(-n + 4) + 2n = 2n
a. n = 4
b. no solution
c. infinitely many solutions
Consider the two functions shown here. What is the rate of change of each function?
Function 2: y = ½ x + 7
1400 principal earning 7% compounded monthly after 22 years
The future value of a $1,400 investment at a 7% interest rate compounded monthly over 22 years using the compound interest formula is $44,923.
The question regards a principal amount of $1,400 earning a 7% interest rate compounded monthly over 22 years. To calculate the future value of this investment, one would typically use the compound interest formula:
[tex]A = P(1 +rn)^n[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount ($1,400 in this case).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.
To calculate the future value using our example, you can substitute the given values into the formula:
A = [tex]1400(1+(0.07){12})^{12*22}[/tex] = 44923
After 22 years, the balance in the account with a $1,400 principal earning 7% interest compounded monthly would be approximately $3,808.39. This is calculated using the compound interest formula with the given parameters: principal, interest rate, compounding frequency, and time.
To find the balance in the account after 22 years with a $1,400 principal earning 7% interest compounded monthly, we use the compound interest formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
[tex]- \( A \) is the amount of money accumulated after \( t \) years,- \( P \) is the principal amount (the initial amount of money),- \( r \) is the annual interest rate (in decimal),- \( n \) is the number of times interest is compounded per year, and- \( t \) is the time the money is invested for in years.[/tex]
Given:
[tex]- \( P = $1,400 \),- \( r = 0.07 \) (7% interest rate converted to decimal),- \( n = 12 \) (compounded monthly),- \( t = 22 \) years.[/tex]
Plugging in the values:
[tex]\[ A = 1400 \left(1 + \frac{0.07}{12}\right)^{(12)(22)} \]\[ A = 1400 \left(1 + \frac{0.07}{12}\right)^{264} \]\[ A = 1400 \left(1 + \frac{0.005833}{1}\right)^{264} \]\[ A = 1400 \left(1.005833\right)^{264} \][/tex]
Now, we calculate:
[tex]\[ A \approx 1400 \times 2.72028 \]\[ A \approx $3,808.39 \][/tex]
So, the balance in the account after 22 years would be approximately $3,808.39.
Translate shapes , pls help me with this
Answer:
A: (-4,-2)
B: (-3,-4)
C: (0,2)
D: (-2,-1)
Hope this helps! I'm not the best at math though, so it could be incorrect.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Name the Property of Equality that justifies the statement: If m<A + M<B = M<C. Then, M<A = M<C - M<B
Transitive Property
Symmetric Property
Reflexive Property
Subtraction Property
Answer:
subtraction property
Step-by-step explanation:
Javier is 175% heavier than his brother. If Javier’s brother weighs 80 pounds, how much does Javier weigh?
Let us say weight of Javier is x pounds.
Weight of his bother = 80 pounds
Javier is 175 % or 1.75 times heavier than his brother.
So Javier's weight = x pounds= 1.75 *80 = 140 pounds.
Answer: Javier's weight is 140 pounds.
6. Angle ABC is congruent to which angle?
1. Angle CAB
2. Angle XYZ
3. Angle XZY
4. Angle YZX
~
7.
Side CA is congruent to which side?
1. ZX
2.YX
3.XY
4.YZ
Answer:
[tex]\angle ABC \cong \angle XYZ[/tex]
[tex]CA \cong ZX[/tex]
Step-by-step explanation:
According to the given figures:
[tex]\angle ABC \cong \angle XYZ[/tex]
Also,
[tex]CA \cong ZX[/tex]
Therefore, the answer to the first question is Angle XYZ, and the answer to the second question is ZX.
You can deduct these answers by observing the number of line that match each pair of congruent elements.
10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE. DO BOTH PARTS OF 1 AND ALL OF 2.
Which are the solutions of this equation 4x2-7x=3x+24
Answer: x = -3/2 x =4
Answer:
3rd and last choice on ed
Step-by-step explanation:
Line segment AC has endpoints A (-1,-3.5) and C (5,-1). Point B is on line segment AC and is located at (0.2,-3). What is the ratio of AB/BC
Answer:
AB/BC = (1.3) / (5.2). Hope this helps :)
Step-by-step explanation:
2. The triangles are similar. write a similarity statement for the triangles.
A. Triangle JKL ~ Triangle NPM
B. Triangle JKL~ Triagle PNM
C. Triangle JKL~ Triangle MNP
D. Triangle JKL~ Triangle PMN
Answer:
The correct option is C.
Step-by-step explanation:
In triangle JKL and MNP,
[tex]\angle J=\angle M[/tex] (Given)
[tex]\angle L=\angle P=90^{\circ}[/tex] (Given)
According to AA property of similar triangle, two triangles are similar if their two corresponding angles are same.
Here, J is corresponding angle of M, K is corresponding angle of N and L is corresponding angle of P.
Using AA property of similar triangles,
[tex]\triangle JKL\sim \triangle MNP[/tex]
Therefore the correct option is C.
Suppose that 1% of the students in a school have head lice and the test for head lice is accurate 75% of the time. What is the probability that a student in the school has head lice, given that the test came back positive?,
If the test is positive, there is a 2.9% chance that the subject has head lice.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Assume that the school has 100 students. If 1 student has lice and 99 others don't, that means one student has lice.
Suppose that all students took the test. Only 0.75 of 1 people with lice would have a positive test result because it is only 75% accurate.
Because the test is only 75% accurate, out of the 99 students who do not have lice, 25% would test positive. 24.75 false positive tests are involved here!
So far, 25.50 of our students have had positive tests, although only 0.75 of them truly have lice. 2.9% is 0.75 out of 25.5.
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Which is the best estimate for (6.3x10^-2)(9.9x10^-3) written in scientific notation?
Answer:
[tex]6 \times 10^{-4}.[/tex]Step-by-step explanation:
We are given expression [tex](6.3 \times 10^{-2})(9.9\times 10^{-3})[/tex].
In order to multiply above given expression, we need to multiply 6.3 by 9.9 first.
On multiplying 6.3 by 9.9 , we get 62.37.
Now we would multiply [tex]10^{-2} \ by \ 10^{-3}.[/tex]
Therefore,
[tex]10^{-2} \times 10^{-3}= 10^{-2-3}= 10^{-2-3} = 10^{-5}.[/tex]
Therefore,
[tex](6.3 \times 10^{-2})(9.9\times 10^{-3}) =62.37 \times 10^{-5}[/tex]
Again [tex]62.37 \times 10^{-5}[/tex] could be written as [tex]6.237 \times 10^{-4}[/tex].
Now, [tex]6.237 \times 10^{-4}[/tex] could be round to [tex]6 \times 10^{-4}.[/tex]
Therefore, correct answer is [tex]6 \times 10^{-4}.[/tex]
A segment has endpoints at (3,−4) and (3,−17). How many units long is the segment?
[tex]\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{We have the points}\ (3,\ -4)\ \text{and}\ (3,\ -17).\ \text{Substitute:}\\\\d=\sqrt{(3-3)^2+(-17-(-4))^2}=\sqrt{0^2+(-13)^2}=\sqrt{(-13)^2}=13\\\\Answer:\ \boxed{13\ units}[/tex]
Which answer describes the transformation of f (x) = x^2 −1 to g(x)=(x+2)^2−1 ?
a horizontal compression by a factor 2
a vertical stretch by a factor of 2
a horizontal translation 2 units to the left
a vertical translation 2 units down