Answers
Answer:
The correct equation is
[tex]y = - \frac{7}{5} x + 4[/tex]
Related Questions
5. Use the equation E =- my?my where E is kinetic energy, m is the mass of an object, and v is the object'svelocityLet E = 100, 000 J and v = 24 m/s. Find the object's mass.Show your work here:Choose the correct answer:173.6 kg86.8 kg8333.3 kg347.2 kg
Answers
In general, the kinetic energy is given by the formula below
[tex]E=\frac{1}{2}mv^2[/tex]Where m is the mass and v is the speed of the object.
Therefore, in our case,
[tex]\begin{gathered} E=100000,v=24 \\ \Rightarrow100000=\frac{1}{2}m(24)^2 \end{gathered}[/tex]Solve for m as shown below
[tex]\Rightarrow m=\frac{200000}{576}=347.2222\ldots[/tex]Thus, the answer is 347.2 kg, approximately.
Zach puts $1000 into a savings account earning 5% compound interest for 5 years. How much
interest has Zach earned at the end of the the 5 years?
$_______
Do not enter the dollar sign as part of your answer
Answers
The amount of interest Zach earn in 5 years given the principal and interest rate compounded for 5 years is 276.3
What is the amount of interest Zach earned?A = P(1 + r/n)^nt
Where,
A = principal + interestPrincipal, P = $1000Interest rate, r = 5% = 0.05Time, t = 5 yearsNumber of periods, n = 1A = P(1 + r/n)^nt
= 1000(1 + 0.05/1) ^(1×5)
= 1000(1 + 0.05) ^5
= 1000(1.05)^5
= 1000(1.2762815625)
= 1,276.2815625
Approximately,
1,276.3
Hence,
A = principal + interest
1, 276.3 = 1000 + interest
1276.3 - 1000 = interest
Interest = 276.3
Therefore, the amount of interest earned in 5 years is 276.3
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The following data for a random sample of banks in two cities represent the ATM fees for using another bank's ATM. Compute the sample variance for ATM fees for each city.City A1.25 1.00 1.50 1.25 1.50City B2.50 1.25 1.00 0.00 2.00The variance for city Ais $(Round to the nearest cent as needed.)
Answers
City A (n = 5)
1.25 1.00 1.50 1.25 1.50
City B
2.50 1.25 1.00 0.00 2.00
The variance formula is:
So, the mean A is:
(1.25 + 1.00 + 1.50 + 1.25 + 1.50)/5 = 1.30
The variance for city A is:
s²_A = 0.04
For city B:
Mean B = 1.35
The variance for city B is:
s²_B = 0.92
find the range of the data set show in the table below
Answers
Remember that
the range is the spread of your data from the lowest to the highest
so
range=Maximum value-Minimum value
we have
Maximum value=170
Minimum value=27
Range=170-27=143
therefore
answer is
Range 143Given that sin A= -4 over 5 and angle A is in quadrant 3, what is the value of cos(2A)?
Answers
Solution:
Given;
[tex]\sin(A)=-\frac{4}{5}[/tex]Then, the value of cosine x is;
[tex]\cos(A)=-\frac{3}{5}[/tex]Because cosine and sine are negative on the third quadrant.
Then;
[tex]\begin{gathered} \cos(2A)=\cos^2(A)-\sin^2(A) \\ \\ \cos(2A)=(-\frac{3}{5})^2-(-\frac{4}{5})^2 \\ \\ \cos(2A)=\frac{9}{25}-\frac{16}{25} \\ \\ \cos(2A)=-\frac{7}{25} \end{gathered}[/tex]Challenge The vertices of ABC are , , and . ABC is reflected across the y-axis and then reflected across the x-axis to produce the image A''B''C''. Graph and .
Answers
The graph shows triangle ABC with vertices as follows;
[tex]\begin{gathered} A=(-5,5) \\ B=(-2,4) \\ C=(-2,3) \end{gathered}[/tex]When translated 6 units to the right, and 7 units down, its becomes,
[tex]\begin{gathered} A^{\prime}=(1,-2) \\ B^{\prime}=(4,-3) \\ C^{\prime}=(4,-4) \end{gathered}[/tex]That means its reflected across the y-axis and the x-axis as follows;
[tex](x,y)\rightarrow(x+6,y-7)[/tex]After this the translation is complete.
A book store sells used books. Paperback books cost $1.00. Hardback books sell for $5.00. The store sold 100 books and made $260 from the sale, How many paperback books did the store sell?
Answers
ANSWER
60 paperback books
EXPLANATION
We have that:
Paperback books sell for $1.00
Hardback books sell for $5.00
The store sold 100 books and made $260.
Let the number of paperback books be x
Let the number of hardback books be y.
This means that:
x + y = 100 _____(1)
and
1 * x + 5 * y = 260
=> x + 5y = 260 ____(2)
We have two simultaneous equations:
x + y = 100 ____(1)
x + 5y = 260 ___(2)
From (1):
x = 100 - y
Put that in (2):
100 - y + 5y = 260
=> 100 + 4y = 260
Collect like terms:
4y = 260 - 100
4y = 160
y = 160 / 4
y = 40 books
This means that:
x = 100 - 40
x = 60 books
Therefore, 60 paperback books were sold.
Choose the expression that is equal to 28.3A. 3³+27.2-6.8+2⁴-3.1B. 3³+27.2-(6.8+2⁴-3.1)C. [3³+(27.2-6.8)]+2⁴-3.1D. 3³+27.2-(6.8+2⁴)-3.1
Answers
solution
For this case we can solve each case and we have:
A) 27 +27.2 -6.8 +16 -3.1= 60.3
B) 27 +27.2 -(6.8 +16 -3.1)= 54.2- 19.7= 34.5
C) 27 + 20.4 +16 -3.1= 30.1
D) 27 +27.2 - 22-8 -3.1= 28.3
then the correct solution for this case would be:
D)
Is (4,-3) a solution to the following system of equations?X - y = 42x + y = 5
Answers
No, (4, -3) is not a solution to the system of equations
Explanation:If (4, -3) is a solution to the given system of equations, then
for x = 4, and y = -3, both of the equations are satisfied.
x - y = 4 - (-3)
= 4 + 3
= 7
This is not 4, so the first equation is not satisfied
2x + y = 2(4) + (-3)
= 8 - 3
= 5
This equation is satisfied
It is sufficient to conclude that (4, -3) is not a solution to the system of equations since it doesn't satisfy the first equation
Given the diagram shown, which of the following statements are true.
Answers
I,II
1) Since in this diagram we have two triangles, whose sides AI and LH are parallel to each other we can state the following:
2) And since similar triangles have congruent angles and proportional sides, we can state as true the following:
I.∠JHL ≅ ∠JIK Similar triangles have congruent angles
As they are similar triangles we can write out the following ratios:
[tex]\frac{JI}{JH}=\frac{JK}{JL}[/tex]These are true
And the third is not correct.
3) Hence, the answer is I,II
Find the domain of the rational function.f(x)=(x−7)/(x+8)
Answers
Answer:
[tex](-\infty,-8)\cup(-8,\infty)[/tex]Explanation:
Given the rational function:
[tex]f(x)=\frac{x-7}{x+8}[/tex]The domain of f(x) is the set of the values of x for which the function is defined.
A rational function is undefined when the denominator is 0.
Set the denominator of f(x) equal to 0 in order to find the value(s) of x at which f(x) is undefined.
[tex]\begin{gathered} x+8=0 \\ \implies x=-8 \end{gathered}[/tex]-8 is the excluded value of the domain.
Therefore, the domain of f(x) is:
[tex](-\infty,-8)\cup(-8,\infty)[/tex]
Which inequality is represented by the graph
Answers
The inequality 4x - 2y < 12 is represented by the attached graph. which is the answer would be an option (B).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per option (B),
4x - 2y < 12
We can see that the x-intercept is (0, -6), and the y-intercept is (2.5, 0) in the given graph which is determined by substituting the value of x and y is equal to 0 in the equation 4x - 2y = 12.
The inequality 4x - 2y < 12 is represented by the attached graph.
Hence, the answer would be option (B).
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Jessica borrowed $1,450 for three months at an annual rate of 8.75%under a single-payment plan. How much interest must she pay?a. $0.30b. $31.72c. $4,893.75d. $108.75
Answers
Given:
Principal amount (P)= $1450
Rate (R) = 8.75%
Time (T)= 3 months
The interest is given by the formula,
[tex]\begin{gathered} I=\frac{P\times R\times T}{100\times12} \\ =\frac{1450\times8.75\times3}{100\times12} \\ =31.71875 \end{gathered}[/tex]The graph shows the number of cups of coffee Sherwin consumed in one day and the number of hours he slept that same night:A scatter plot is shown. Data points are located at 1 and 9, 3 and 5, 5 and 6, 4 and 4, 2 and 7, and 6 and 4. A line of best fit crosses the y-axis at 10 and passes through the point 6 and 4.How many hours will Sherwin most likely sleep if he consumes 9 cups of coffee? (4 points)1, because y = −x + 102, because y = −x + 109, because y = −x + 1010, because y = −x + 10
Answers
Given:
The two endpoints (1, 9) and (6, 4).
To find the number of hours will Sherwin most likely sleep if he consumes 9 cups of coffee:
Using the two-point formula,
[tex]\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-9}{4-9}=\frac{x-1}{6-1} \\ \frac{y-9}{-5}=\frac{x-1}{5} \\ y-9=-x+1 \\ y=-x+10 \end{gathered}[/tex]Substitute x=9 we get,
[tex]\begin{gathered} y=-9+10 \\ y=1 \end{gathered}[/tex]Hence, the answer is,
[tex]1,because\text{ y=-x+10}[/tex]From a window 100ft above the ground in building A, the top and bottom of building B are sighted so that the angles are 70 degrees and 30 degrees respectively. Find the height of building B?
Answers
Given:-
From a window 100ft above the ground in building A, the top and bottom of building B are sighted so that the angles are 70 degrees and 30 degrees respectively.
To find:-
The height of building B.
So now, the image of the given data is,
So now we find the value of PS. so we get,
[tex]\begin{gathered} \tan \text{ 30=}\frac{100}{PS} \\ \frac{1}{\sqrt[]{3}}=\frac{100}{PS} \\ PS=100\sqrt[]{3} \end{gathered}[/tex]So now we find the height of QS,
[tex]\begin{gathered} \tan \text{ 70=}\frac{QS}{PS} \\ 2.7474=\frac{QS}{100\sqrt[]{3}} \\ QS=100\sqrt[]{3}\times2.7474 \\ QS=475.84 \end{gathered}[/tex]So the total height is,
[tex]100+475.84=575.84[/tex]So the height of building B is 575.84
Solve 3x-9 = 6.A. x = 2B. x=-1C. x = 1D. x = 5
Answers
Step 1. The expression that we have is:
[tex]3x-9=6[/tex]And we need to solve for x.
If we are going to solve for x, we need to have the 'x' alone on one side of the equation.
For that, the first step is to add 9 to both sides:
[tex]3x-9+9=6+9[/tex]Step 2. On the left side, -9+9 cancel each other, and on the right side 6+9 is 15:
[tex]3x=15[/tex]Step 3. The next step is to divide both sides by 3:
[tex]\frac{3x}{3}=\frac{15}{3}[/tex]In this way, 3/3 on the left side cancel each other and we are left only with x:
[tex]x=\frac{15}{3}[/tex]And on the right side, 15/3 is equal to 5:
[tex]\boxed{x=5}[/tex]This is shown in option D.
Answer:
D. x=5
I need to solve each system by graphing. so pls help! This is Algebra 1
Answers
Given the system of inequalities:
2x + 3y < -6
-2x + 3y < 6
Let's solve the system by graphing.
To graph, rewrite the inequalities in slope-intercept form:
y = mx + b
Inequality 1:'
Subtract 2x from both sides:
2x - 2x + 3y < -2x - 6
3y < -2x - 6
Divide all terms by 3:
[tex]\begin{gathered} \frac{3y}{3}<-\frac{2x}{3}-\frac{6}{3} \\ \\ y<-\frac{2}{3}x-2 \end{gathered}[/tex]Inequality 2:
Add 2x to both sides:
-2x + 2x + 3y < 2x + 6
3y < 2x + 6
Divde all terms by 3:
[tex]\begin{gathered} \frac{3y}{3}<\frac{2x}{3}+\frac{6}{2} \\ \\ y<\frac{2}{3}x+2 \end{gathered}[/tex]Now, let's plot 3 points from each inequlality and connect using a straight edge.
Inequality 1:
When x = -3
Substitute -3 for x and solve for y:
[tex]\begin{gathered} y<-\frac{2}{3}(-3)-2 \\ \\ y<2-2 \\ \\ y<0 \end{gathered}[/tex]When x = 0:
[tex]\begin{gathered} y<-\frac{2}{3}(0)-2 \\ \\ y<-2 \end{gathered}[/tex]When x = 3:
[tex]\begin{gathered} y<-\frac{2}{3}(3)-2 \\ \\ y<-2-2 \\ \\ y<-4 \end{gathered}[/tex]From inequality 1, we have the points:
(x, y) ==> (-3, 0), (0, -2), (3, -4)
For inequlity 2:
When x = -3:
[tex]\begin{gathered} y<\frac{2}{3}(-3)+2 \\ \\ y<-2+2 \\ \\ y<0 \end{gathered}[/tex]When x = 0:
[tex]undefined[/tex]How much work is done when a book weighting 2.0 new newtons is carried at a constant velocity from one classroom to another classroom 26 meters away.
Answers
find the mean the median the mode range and standard invitation of each data set that is obtained after adding the given content to each value (number 1)
Answers
Answers:
Mean = 43.7
Median = 44.5
Mode = doesn't exist
Standard deviation = 4.78
Explanation:
First, we need to add the constant to each value, so the new data is:
33 + 11 = 44
38 + 11 = 49
29 + 11 = 40
35 + 11 = 46
27 + 11 = 38
34 + 11 = 45
36 + 11 = 47
28 + 11 = 39
41 + 11 = 52
26 + 11 = 37
Now, we can organize the data from least to greatest as:
37 38 39 40 44 45 46 47 49 52
Then, the mean is the sum of all the numbers divided by 10, because there are 10 values in the data. So, the mean is:
[tex]\begin{gathered} \operatorname{mean}=\frac{37+38+39+40+44+45+46+47+49+52}{10} \\ \operatorname{mean}=43.7 \end{gathered}[/tex]The median is the value that is located in the middle position of the organized data. Since there are 10 values, the values in the middle are the numbers 44 and 45, so the median can be calculated as:
[tex]\operatorname{median}=\frac{44+45}{2}=44.5[/tex]The mode is the value that appears more times in the data. Since all the values appear just one time, the mode doesn't exist.
To calculate the standard deviation, we will calculate first the variance.
The variance is the sum of the squared difference between each value and the mean, and then we divided by the number of values. So, the variance is equal to:
[tex]\begin{gathered} (37-43.7)^2+(38-43.7)^2+(39-43.7)^2+(40-43.7)^2+ \\ (44-43.7)^2+(45-43.7)^2+(46-43.7)^2+(47-43.7)^2+ \\ (49-43.7)^2+(52-43.7)^2=228.1 \end{gathered}[/tex][tex]\text{Variance}=\frac{228.1}{10}=22.81[/tex]Finally, the standard deviation is the square root of the variance, so the standard deviation is:
[tex]\text{standard deviation =}\sqrt[]{22.81}=4.78[/tex]What does the constant 1.6 reveal about the rate of change of the quantity?
Answers
The form of the exponential growth/decay function is
[tex]f(x)=a(1\pm r)^x[/tex]a is the initial amount
r is the rate of growth/decay per x years
We use + with growth and - with decay
Since the given function is
[tex]f(t)=2700(1.6)^{7t}[/tex]Where t is time per week
Compare the two functions
[tex]\begin{gathered} a=2700 \\ (1+r)=1.6 \\ x=7t \end{gathered}[/tex]Since 1.6 is greater than 1, then
The function is growth
Equate 1.6 by (1 + r) to find r
[tex]\begin{gathered} 1+r=1.6 \\ \\ 1-1+r=1.6-1 \\ \\ r=0.6 \end{gathered}[/tex]Change it to percent by multiplying it by 100%
[tex]\begin{gathered} r=0.6\times100\text{ \%} \\ \\ r=60\text{ \%} \end{gathered}[/tex]Since x = 7t then the time is every 7 weeks
The answer is
The function is growing exponentially at a rate of 60% every 7 weeks
Write using an exponent: 1×7×7×7×7×7a. 1×7×5b.[tex]1 \times {7}^{5} [/tex]c. [tex]1 \times {5}^{7} [/tex]
Answers
In the expression, the number 7 is multiplied to itself 5 times or five 7's are multiplied with each other. So exponential expression for the equation is,
[tex]1\cdot7\cdot7\cdot7\cdot7\cdot7=1\cdot7^5[/tex]Option B is correct.
For the function f(x) = x^2 + 3x,a) Find f(-2).b) Is this function linear or quadratic? Justify your answer.c) Will the graph of this function appear as a line or a parabola?
Answers
a) Evaluating the function at x= -2 we get:
[tex]f(-2)=(-2)^2+3(-2)=4-6=-2[/tex]b) Notice that the given function has the form:
[tex]y=ax^2+bx+c[/tex]Therefore f(x) is a quadratic function.
c) Since f(x) is a quadratic function its graph is a parabola.
Find the value of x and y.
Answers
These 3 angles are equal value
5x + 1 = 6x - 10 = y
Then
5x + -6x = -10 - 1
-x = 11
x= 11
NOW find y value
y = 5x + 1
y= 6x - 10
y = 5•( 11) + 1= 56
y= 6•( 11) -10= 56
Answer is y= 56
Question 7. Y=(5/2)^xSketch the graph of each of the exponential functions and label three points on each graph.
Answers
Given:
[tex]y=\mleft(\frac{5}{2}\mright)^x[/tex]To sketch the graph:
First find the three points.
Put x=-1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^{-1} \\ =\frac{2}{5} \\ =0.4 \end{gathered}[/tex]Put x=0 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^0 \\ =1 \end{gathered}[/tex]Put x=1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^1 \\ =2.5 \end{gathered}[/tex]Therefore, the three points are, (-1, 0.4), (0, 1), and (1, 2.5).
The graph is,
4 The number of cars in 5 different parkinglots are listed below.35, 42, 63, 51, 74What is the mean absolute deviation ofthese listed numbers?
Answers
The number of cars in 5 different parking lots are given as data points as follows:
[tex]35\text{ , 42 , 63 , 51 , 74}[/tex]We are to determine the Mean Absolute Deviation ( MAD ). It is a statistical indicator which is used to quantify the variability of data points. We will apply the procedure of determining the ( MAD ) for the given set of data points.
Step 1: Determine the Mean of the data set
We will first determine the mean value of the data points given to us i.e the mean number of cars in a parking lot. The mean is determined by the following formula:
[tex]\mu\text{ = }\sum ^5_{i\mathop=1}\frac{x_i}{N}[/tex]Where,
[tex]\begin{gathered} \mu\colon\text{ Mean} \\ x_i\colon\text{ Number of cars in ith parking lot} \\ N\colon\text{ Total number of parking lots} \end{gathered}[/tex]We will use the above formulation to determine the mean value of the data set:
[tex]\begin{gathered} \mu\text{ = }\frac{35\text{ + 42 + 63 + 51 + 74}}{5} \\ \mu\text{ = }\frac{265}{5} \\ \textcolor{#FF7968}{\mu=}\text{\textcolor{#FF7968}{ 53}} \end{gathered}[/tex]Step 2: Determine the absolute deviation
The term absolute deviation is the difference of each point in the data set from the central tendency ( mean of the data ). We determined the mean in Step 1 for this purpose.
To determine the absolute deviation we will subtract each data point from the mean value calculated above.
[tex]AbsoluteDeviation=|x_i-\mu|[/tex]We will apply the above formulation for each data point as follows:
[tex]\begin{gathered} |\text{ 35 - 53 | , | 42 - 53 | , | 63 - 53 | , | 51 - 53 | , | 74 - 53 |} \\ |\text{ -18 | , | -11 | , | 10 | , | -2 | , | }21\text{ |} \\ \textcolor{#FF7968}{18}\text{\textcolor{#FF7968}{ , 11 , 10 , 2 , 21}} \end{gathered}[/tex]Step 3: Determine the mean of absolute deviation
The final step is determine the mean of absolute deviation of each data point calculated in step 2. Using the same formulation in Step 1 to determine mean we will determine the " Mean Absolute Deviation ( MAD ) " as follows:
[tex]\begin{gathered} \mu_{AD}\text{ = }\frac{18\text{ + 11 + 10 + 2 + 21}}{5} \\ \mu_{AD}\text{ = }\frac{62}{5} \\ \textcolor{#FF7968}{\mu_{AD}}\text{\textcolor{#FF7968}{ = 12.4}} \end{gathered}[/tex]Answer:
[tex]\textcolor{#FF7968}{MAD=12.4}\text{\textcolor{#FF7968}{ }}[/tex]Yoko, Austin, and Bob have a total of $57 in their wallets. Austin has $7 less than Yoko. Bob has 2 times what Yoko has. How much does each have?
Answers
Yoko has $16 money, Austin has $9 and Bob has $32.
According to the question,
We have the following information:
Yoko, Austin, and Bob have a total of $57 in their wallets. Austin has $7 less than Yoko. Bob has 2 times what Yoko has.
Now, let's take the money Yoko has to be $x.
So, we have the following expressions for the money Austin and Bob have:
Austin = $(x-7)
Bob = $(2x)
Now, we have the following expression by adding them:
x+x-7+2x = 57
4x-7 = 57
4x = 57+7
4x = 64
x = 64/4
x = $16
Now, the money Austin has:
16-7
$9
Money Bob has:
2*16
$32
Hence, Yoko has $16 money, Austin has $9 and Bob has $32.
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Find the value of the test statistic z using z =P-Ppan37) A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics includen = 1158 subjects with 30% saying that they play a sport.Answer: - 13.6138) The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, andthe sample statistics include n = 647 drowning deaths of children with 30% of them attributable to beaches.Answer: 2.94
Answers
37. The given p-value is 0.5
Also the observed proportion is:
[tex]\hat{p}=30\%=0.3[/tex]And q is (1-p), so:
[tex]q=1-0.5=0.5[/tex]And the n-value is given 1158.
By replacing these values into the test statistic formula we obtain:
[tex]z=\frac{\hat{p}-p}{\sqrt[]{\frac{p\cdot q}{n}}}=\frac{0.3-0.5}{\sqrt[]{\frac{0.5\cdot0.5}{1158}}}=\frac{-0.2}{\sqrt[]{0.0002}}=\frac{-0.2}{0.015}=-13.61[/tex]The answer is -13.61
Draw the dilation of PQRS using center Q and scale factor 1/2. Label the dilation TUWX. 2. Draw the dilation of PQRS with center R and scale factor 2. Label the dilation ABCD. 3. Show that TUWX and ABCD are similar.
Answers
Based on the given image, you obtain the following figures:
Draw the dilation of PQRS using center Q and scale factor 1/2
Draw the dilation of PQRS with center R and scale factor 2. Label the dilation ABCD
You can notice that both figure TUWX and ABCD are similar because the quotient between sides TU and PQ, XW and RS, UW and BC, TX and AD are the same.
which choice is equivalent to the quotient below? sqrt 7/8* sqrt7/187/16/121/23/47/12
Answers
We can apply the following properties of radicals:
[tex]\begin{gathered} \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\Rightarrow\text{ Product property} \\ \sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\Rightarrow\text{ Quotient property} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} \text{ Apply the product property} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{7}{8}\cdot\frac{7}{18}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{7\cdot7}{8\cdot18}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{49}{144}} \\ \text{ Apply the quotient property} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\frac{\sqrt[]{49}}{\sqrt[]{144}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\frac{7}{12} \end{gathered}[/tex]Therefore, the choice that is equivalent to the given product is:
[tex]\frac{7}{12}[/tex]Suppose someone wants to accumulate $120,000 for retirement in 30 years. The person has two choices. Plan A is a single deposit into an account with annual compounding and an APR of 6%. Plan B is a single deposit into an account with continuous compounding and an APR of 5.8%. How much does the person need to deposit in each account in order to reach the goal?The person must deposit $______ into the account for Plan A to reach the goal of $.The person must deposit $______ into the account for Plan B to reach the goal of $.(Round to the nearest cent as needed.)
Answers
We want to calculate the amount needed as an initial investment to have 120000 after 30 years.
Recall that the formula of annual compounding is given by the formula
[tex]S\text{ =}P\text{ \lparen1+r\rparen}^t[/tex]where P is the principal, r is the interest rate and t is the time in years. When compounded continously the formula is
[tex]S=Pe^{rt}[/tex]where the variables have the same meaning. In both cases we want to find P sucht that
[tex]S=120000[/tex]when t=30 and r is the interest rate that we are given.
So we have the following equation in the first case
[tex]120000=P\text{ \lparen1+}\frac{6}{100})^{30}[/tex]so if we divide both sides by (1+6/100)^30 we get
[tex]P=\frac{120000}{(1+\frac{6}{100})^{30}}\approx20893.22[/tex]so for Plan A 20893.22 is needed to have 120000 after 30 years.
now, we want to do the same with the second plan. We have
[tex]120000=Pe^{\frac{5.8}{100}30}[/tex]so we divide both sides by exp(5.8*30/100). So we get
[tex]P=\frac{120000}{e^{\frac{5.8}{100}\cdot30}}\approx21062.45[/tex]so for Plan B 21062.45 is needed to have 120000 after 30 years