Using the compound amount formula, account B will yield the greater balance at the end of 15 years and Noah earn $4 more money by choosing this more profitable account.
In the given question,
Noah may choose between two accounts in which to invest $4000.
Principal Amount(P) = $4000
Account A offers 2.2% annual interest compounded monthly.
Rate(r) = 2.2% = 0.022
In a year have twelve month so n=12
Account B offers continuous compound interest.
Noah plans to leave his investment untouched for 15 years.
Time(t) = 15
Formula for amount after t years = P(1+ r/n)^nt
Amount after 15 years = 4000(1+ 0.022/12)^12*15
Simplifying
Amount after 15 years = 4000(1+0.00183)^180
Amount after 15 years = 4000(1.00183)^180
Amount after 15 years = 4000*1.39
Amount after 15 years = $5560
Account B offers compounded continuously.
So formula used = Pe^(rt)
Amount after 15 years = 4000*e^(0.022*15)
Amount after 15 years = 4000*e^(0.33)
Amount after 15 years = 4000*1.391
Amount after 15 years = $5564
(a) We have to find which account will yield the greater balance at the end of 15 years.
As we can see in Account A amount after 15 years is $5550 and in Account B amount after 15 years is $5564.
So account B will yield the greater balance at the end of 15 years.
(b) We have to find how much more money does Noah earn by choosing this more profitable account.
Noah earn money more by profitable account=Account B amount-Account A amount
Noah earn money more by profitable account=$5564-$5560
Noah earn money more by profitable account=$4
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HELPP PLEASEEEEEEEeeee
Answer:
60°
Step-by-step explanation:
basically if you rotate the figure by a specified amount it will return to the original orientation, in this case is is asking you to do this with the least angle rotation
answer (2 + 2) - 4 + 2
start by solving whats inside the parentheses
[tex]4-4+2[/tex]solve the addition
[tex]\begin{gathered} 0+2 \\ 2 \end{gathered}[/tex]a bakery typically sells its cupcakes for $24 per box for the first week of school they have a sale of $10 off of each box of cupcakes how much will a box of cupcakes cost during the first week of school
cupcakes = $24/box
If they sold each box $10 off, the sold each box for only 24 - 10 = $14
Each box was sold for $14.00
Simplify this expression x^-12 x x^2. Assume that x is nonzero.
Answer:
x^-9
x^-12+x+x^3=x^-9
Hello, I'm unsure about the process of this equation, please help me.
Answer:
144 employees
Explanation:
• The ratio of men to women = 3:5
,• The number of men in the company = 54.
Let the total number of employees = x.
The proportion of men in the company will be:
[tex]\frac{3}{3+5}=\frac{3}{8}[/tex]Since there are 54 men in the company, we can then say that:
[tex]\begin{gathered} \frac{3}{8}\text{ of x}=54 \\ \implies\frac{3}{8}x=54 \end{gathered}[/tex]Multiply both sides by 8/3 to solve for x.
[tex]\begin{gathered} \frac{8}{3}\times\frac{3}{8}x=\frac{8}{3}\times54 \\ x=144 \end{gathered}[/tex]The total number of employees is 144.
In 1994, an outbreak of illness due to ice cream contaminated with the bacteria salmonella occurred in the United States. The outbreak affected an estimated 224,000 people.If the total population in the U.S. at that time was 260,000,000, which is the best estimate for the percentage of people who were affected?About 0.1%About 1%About 5%About 10%About 25%Complete the following statement: Approximately 86 out of every people in the United States were affected by the 1994 salmonella outbreak.
Given:
Population affected = 224,000
Total population = 260,000,000
To find the percentage, we use the formula:
[tex]\%=\frac{portion}{total}\times100[/tex]Replacing information given, on the formula:
[tex]\%=\frac{224000}{260000000}\times100=0.086\%[/tex]ANSWER: About 0.1%
Santa bought a jacket that was marked 55% off the original price of $48. The sales tax was 6%. What did he pay altogether for the jacket? Find the discount price first and then find the tax. Round your answer to the nearest cent.
First we need to find the discount
48 * 55%
48 *.55
26.40
Subtract this from the price of the jacket
48-26.40
21.60
The sale price is 21.60
Now we need to find the sales tax
21.60 * 6%
21.60 * .06
1.296
Rounding to the nearest cent
1.30
Add the sales tax to the price of the jacket
21.60 +1.30
22.90
Santa will have to pay 22.90 for the jacket.
Search topics and ska Learning DIQQOUTE Analytics Recommendations Sodal studies Language arts Scance Y 2 Find the shop om uwa points 20 Find the slope of the line that passes through (8,6) and (3, 15). Simplify your answer and write it as a proper fraction, improper fraction, or integer. Submit Work it out
Given the points:
(x1, y1) ==> (8, 6)
(x2, y2) ==> (3, 15)
To find the slope of the line that passes through the points, use the slope formula below:
[tex]slope,m\text{ = }\frac{y2-y1}{x2-x1}[/tex]Input the values into the formula:
[tex]\begin{gathered} m=\frac{15-6}{3-8} \\ \\ m\text{ = }\frac{9}{-5} \\ \\ m=-\frac{9}{5} \end{gathered}[/tex]The slope is an improper fraction
[tex]-\frac{9}{5}[/tex]ANSWER:
[tex]-\frac{9}{5}[/tex]Identify the range of the function shown in the graph?
Answer:
C
Step-by-step explanation:
The range is the lowest and highest y point on the graph, -1 and 1
Simplify the expression below (w^0*x^{-3})^{-2} The base is AnswerThe exponent is Answer
given expression,
[tex](w^0\ast x^{-3})^{-2}[/tex]let us simplify,
[tex]\begin{gathered} (w^0\ast x^{-3})^{-2} \\ =\frac{1}{(w^0\ast x^{-3})^2} \\ =\frac{1}{w^0}\ast\frac{1}{(x^{-3})^2} \\ =1\ast\frac{1}{x^{-6}} \\ =\frac{1}{\frac{1}{x^6}} \\ =x^6 \end{gathered}[/tex]the base is x.
the exponent is 6.
match each system with its solution setoptions:A. (8, 2)B. no solutionC. infinite solutionsD. (2, 8)
• 1.
x+y=3
2x+2y= 6
Multiply the first equation by 2, and then subtract both equations.
2x+2y=6
-
2x+2y=6
_______
0x+0y=0
0
Since both variables are eliminated, there are INIFINITE SOLUTIONS
• 2.
y= 2x-3
-2x+y=6
Put the first equation into the second equation, (replace y )
-2x+(2x-3) = 6
Solve for x
-2x+2x-3=6
-3= 6
Since -3 is not equal to 6, there is NO SOLUTION.
• 3.
X+3y = 14
-5x+6y=-28
Multiply the first equation by 2, then subtract the equations:
2x+6y=28
-
-5x+6y=-28
_________
7x= 56
x= 56/7
x= 8
Replace x=8 on any equation and solve for y:
8+3y= 14
3y=14-8
3y= 6
y=6/3
y=2
Solution = (8,2)
• 4.
-1/2x+3y=23
y=5x-2
Put the second equation into the first equation ( replace y) and solve for x
-1/2x + 3 (5x-2)= 23
-1/2x+ 15x - 6 = 23
-1/2x +15x = 23+ 6
29/2 x = 29
x = 29/ (29/2)
x = 2
Replace x on any equation and solve for y
y= 5x-2
y=5(2)-2
y= 10-2
y=8
Solution: (2,8)
I dont understand the thing with the parallel lines and the perpendicular
Given;
[tex]\begin{gathered} \bar{AD}\perp\bar{DB} \\ \bar{DB}\perp\bar{BC} \\ \bar{AB}\cong\bar{CD} \end{gathered}[/tex]Line AD is perpendicular to line DB, line DB is perpendicular to line BC and line AB is congruent to line CD.
To prove that line AB is perpendicular to line DC, we have to establish that the alternate angles ABD and BDC are congruent.
[tex]\angle ABD\cong\angle BDC[/tex]From congruent triangles, we know that when two triangles have two congruent sides (Hypothenuse and a side) and both have a right angle then they are congruent (RHS - Right angle Hypothenuse Side).
For Triangle ADB and triangle CBD,
The sides AD and CB are congruent, and also side DB is congruent to BD.
[tex]\begin{gathered} \bar{AB}\cong\bar{CD}\text{ ----Hypothenuse} \\ \bar{DB}\cong\bar{BD}\text{ -----side} \\ \angle ADB\cong\angle CBD\cong90^{0\text{ }}-----Right\text{ angle} \end{gathered}[/tex]Therefore, triangle ADB and triangle CBD are congruent.
So, corresponding sides and angles of the two congruent triangles are also congruent.
[tex]\begin{gathered} \bar{AD}\cong\bar{BC} \\ \angle ABD\cong\angle BDC \end{gathered}[/tex]Therefore, since the alternate angles ABD and BDC then line AB is parallel to DC.
[tex]\bar{AB}\parallel\bar{DC}[/tex]Reason: Alternate interior angles.
If two lines are cut by a transversal and the alternate interior angles are equal (or congruent), then the two lines are parallel.
Find the exact length of the third side. 6 2
We can draw the triangle for clarification:
We can use the pythagoras theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ b^2=c^2-a^2 \\ b=\sqrt[]{c^2-a^2}=\sqrt[]{6^2-2^2}=\sqrt[]{36-4} \\ b=\sqrt[]{32}=\sqrt[]{16\cdot2}=\sqrt[]{16}\cdot\sqrt[]{2} \\ b=4\cdot\sqrt[]{2} \end{gathered}[/tex]The exact length of the third side is:
[tex]4\cdot\sqrt[]{2}[/tex]Un paquete de queso de 12 oz cuesta $1.38 ¿ Cuanto cuesta 1 Lb del mismo queso ?
Given:
A 12 oz package of cheese costs $ 1.38 How much does 1 Lb of the same cheese cost?
First, we will convert from Lb to an ounce
so,
1 Lb = 16 ounces
Using the ratio and proportions
Weight : Price
12 oz : $1.38
16 oz : x
So, we will find x as follows using the cross product
[tex]x=\frac{16}{12}\times1.38=1.84[/tex]So, the answer will be:
The cost of 1Lb of cheese = $1.84
8 students were in the cafeteriaThey increased to 12 students. What is percent of change?
Percentage of change = 50%
Explanation:Old number of students in the cafeteria= 8
New number of students in the cafeteria= 12
percentage of change = (New - old)/old × 100
percentage of change = (12 - 8)/8 × 100
= 4/8 × 100
= 1/2 × 100
Percentage of change = 50%
Please help me on this problem (below the last line is this ( =____ ) couldn’t fit it into the photo)
The slope of a line is calculated with the following formula
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]From our exercise we have the following 2 points
[tex]\begin{gathered} (1,6)\to(x_1,y_1_{}_{}) \\ (2,3)\to(x_2,y_2) \end{gathered}[/tex][tex]slope=\frac{3_{}-6_{}}{2-1_{}}[/tex][tex]\begin{gathered} slope=\frac{-3_{}}{1_{}} \\ slope=-3_{} \end{gathered}[/tex]Find the value of each variable in the parallelogram.lg + 4) 7.16- h65°g=h=
h = 9
g = 61°
Explanation:The opposite sides of a parallelogram are parallel and congruent.
This means the opposite sides are equal
equating the sides:
7 = 16 - h
subtract 16 from both sides:
7 - 16 = - h
-9 = -h
divide both sides by -1
-9/-1 = -h/-1
h = 9
The opposite angles of a parallelogram are equal
equating the angles:
(g + 4)° = 65°
g + 4 = 65
subtract 4 from both sides:
g + 4 -4 = 65 -4
g = 61°
For a given set of rectangles, the length varies inversely with the width. In one ofthese rectangles, the length is 77 and the width is 2. For this set of rectangles,calculate the width of a rectangle whose length is 14.
Ok, so
Let L represent length of rectangle and W represent width of the rectangle.
We have been given that for a given set of rectangles, the length varies inversely with the width.
We know that the equation:
y = k/x
represents the relation where y is inversely proportional to x and k is the constant of proportionality.
So our required equation would be:
L = k/W.
In this case, we know that L = 77 and W = 2, so we're going to find k:
77 = k / 2
And k = 77*2, which is equal to 154.
Now, we know that k = 154, so our general equation would be:
L = 154/W
Finally, we replace the value of our lenght, which is 14.
14 = 154 / W
And W = 154/14
W=11
Therefore, the width of a rectangle whose length is 14, will be 11
Give the domain of the function represents in the table x: 3,-2,1 y:2,-8,-2
We have the following table:
The domain of a function is the set into which all of the input of the function is constrained to fall. In other words, its the set of departure:
where f is the function.
Therefore, the domain is the set {3,-2,1}.
Muhammed has money to invest in one of two accounts.Account 1 requires a $2,000 investment for 4 years. It earns 3% interest compounded monthly.Account 2 requires a $2,200 investment for 2 years. It earns 5% interest compounded daily.Which account will earn more interest for Muhammed, and how much?Select the answer that is completely correct.Account 2 earns $232.39 more than Account 1.Account 1 earns $23.30 more than Account 2.Account 1 earns $18.87 more than Account 2.Account 2 earns $176.70 more than Account 1
Given:
Account 1:
Principal, P = $2000
Time, t = 4 years
Rate, r = 3% = 0.03
number of times compounded, n = monthly = 12 months/year
Account 2:
Principal, P = $2200
Time, t = 2 years
Rate, r = 5% = 0.05
number of times compounded, n = daily = 365 days/year
Let's determine the account which will earn more interest.
Apply the compound interest formula:
[tex]I=(P(1+\frac{r}{n})^{nt})-P[/tex]Where:
P is the Principal
r is the interest rate
n is the number of times the ineterest is compounded per unit time'
t is the time in years
Now, let's find the interest earned in each account.
• ACCOUNT 1:
[tex]\begin{gathered} I=(2000(1+\frac{0.03}{12})^{12\times4})-2000 \\ \\ I=(2000(1+0.0025)^{48})-2000 \\ \\ I=(2000(1.0025)^{48})-2000 \\ \\ I=2254.66-2000 \\ \\ I=254.66 \end{gathered}[/tex]
The interest earned in account 1 is $254.66
• ACCOUNT 2:
[tex]\begin{gathered} I=(2200(1+\frac{0.05}{365})^{730})-2200 \\ \\ I=(2200(1+0.00013698)^{730})-2200 \\ \\ I=2431.36-2200 \\ \\ I=231.36 \end{gathered}[/tex]
The interest earned in account 2 is $231.36
We can see the interest earned in account 1 is greater than the interest earned in account 2.
To find the difference, we have:
$254.66 - $231.36 = $23.30
Therefore, Account 1 earns $23.30 more than Account 2.
ANSWER:
Account 1 earns $23.30 more than Account 2.
wants to buy some boxes of candy that cost $1.50 each.If Billy has $7.50 remaining, which of the following equations will give you the number of boxes, X, thatBilly could buy?a.) 1.5x = 7.5Ob.) x= 7.51.5c.) 7.5x = 1.5d.) X= 1.575 =
Equation for the given statement is, 1.50[tex]x[/tex] = 7.50
option (a) is correct
Linear equation in one variable:
Equation having one variable and and degree is one, called linear equation in one variable.
given,
Cost of each box of candy is $1.50
Billy has $7.50 remaining
Billy bought x number of boxes,
so,
1.50[tex]x[/tex] = 7.50
[tex]x = \frac{7.50}{1.50} \\x = 5[/tex]
Thus we can say the equation for above statement will be,
1.50[tex]x[/tex] = 7.50
while value of x will be 5
Hence, Option (a) is correct
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The Barnett triplets went to the school carnival. Henry rode on 5 rides, bought 2 drinks , 1 bag of popcorn and spent $20.50. Mary spent $16.50 on 3 rides, 3 drinks and 1 bag of popcorn. While Tim rode rode on 6 rides only purchased 1 drink and spent $20.00. How much did each ride cost?a: $12b: $3c: $2d: $4
Let:
x = Cost of each ride
y = Cost of each drink
z = Cost of each bag of pocorn
so:
Henry rode on 5 rides, bought 2 drinks , 1 bag of popcorn and spent $20.50:
[tex]5x+2y+z=20.50_{\text{ }}(1)[/tex]Mary spent $16.50 on 3 rides, 3 drinks and 1 bag of popcorn:
[tex]3x+3y+z=16.5_{\text{ }}(2)[/tex]Tim rode rode on 6 rides only purchased 1 drink and spent $20.00:
[tex]6x+y=20_{\text{ }}(3)[/tex]Solve the system:
[tex]\begin{gathered} (1)-(2) \\ 5x-3x+2x-3y+z-z=20.5-16.5 \\ 2x-y=4_{\text{ }}(4) \end{gathered}[/tex][tex]\begin{gathered} (3)+(4) \\ 6x+2x+y-y=20+4 \\ 8x=24 \\ x=\frac{24}{8} \\ x=3 \end{gathered}[/tex]Answer:
Each ride cost $3
Identify the domain and range to the following relations and state whether or not the relations are functions. State why or why not the relation is a function.
Here, we want to get the range and the domain of the function
The domain refers to the x-values
Looking at the plot, we can see the x-values from 2 to 6
In an interval form, we have this as;
[tex]2\leq x\leq6\text{ or \lbrack{}2,6\rbrack}[/tex]For the range values, we have these as the possible y-values
We can see that the lowest y value is at -4 and the highest y-value is at the point y = 5
So the range is;
[tex]-4\leq y\leq5[/tex]Now, we want to answer if the relation is a function
For a relation to be a function, no domain value will have 2 range values
But, we can have a single range value having two domain values
As we can see, this rule is correctly followed on the plot and thus, we can confirm that the relation is a function
It is a function because each of the x-values have a single y-value. This means that for every domain value, there is only a range value attached
#6-7 identify angles name a pair of complementary angles and a pair of supplementary angles?
6. ∠STR and ∠UWV are complementary (their addition makes 90°)
∠QTS and ∠UWV are supplementary (their addition makes 180°)
7. ∠GLH and ∠HLJ are complementary (their addition makes 90°)
∠GLJ and ∠JLK are supplementary (their addition makes 180°)
Calculate the speed at the edge of a disc of radius 8.5 cm that rotates at the rate of 2.5 rev/s.
Answer in units of m/s.
this is physics
Answer:
11 m/s
Step-by-step explanation:
cause 8.5 add 2.5 then 11 then m/s
I've tried similar questions to this I still don't understand it also I'm not entirely sure if the top piece is correct
One way to make sure that the regression you made is by replacing one of the values of c, from your table and see if the predicted value that your regression gives you is close to the actual value from your table.
In this case, when we replace the first value of c (11.5) into the equation that you got from the regression, we can see that the value of p equals 13.73, which is actually close to the value reported in the table (13.8), since it is a regression it is not expected to obtain the exact value but the closest one.
If we want to find how many murders per 100000 residents we could have when c equals 8400, we just have to use the formula that you found (the regression) and calculate p, the result would be:
[tex]p=0.829\times8400+4.199=6967.799[/tex]If we want to know the number of weapons, we just have to solve for c from the equation of the regression and replace the number of murders per 100000 residents, like this:
[tex]\begin{gathered} p=0.829\times c+4.199 \\ p-4.199=0.829\times c \\ \frac{p-4.199}{0.829}=c \\ c=\frac{p-4.199}{0.829} \end{gathered}[/tex]Now, we can calculate the value of c, by replacing 9.5 into p
[tex]c=\frac{9.5-4.199}{0.829}=6.39[/tex]then c=6, since we have to round it to the nearest whole number
A diagram of a basketball court uses the scale of 1 inch: 4 feet. If the length of the diagram is 16 inches, what’s the length of the actual basketball court? Show your work
Since the scale factor is 1in:4ft, we get that 1 inch in the diagram represents 4 feet in the actual basketball court.
Therefore:
[tex]16in=16\cdot1in\rightarrow16\cdot4ft=64ft.[/tex]Then, the fulfilled table is:
Therefore, the length of the actual basketball court is 64ft.
Answer:
Therefore, the length of the actual basketball court is 64ft.
Two sprinters, Nick and Ryan, want to find out who has the faster time when compared to each of their teams. Nick has a time of 10.8 seconds, and his team has a mean time of 11.4 seconds and a standard deviation of 0.4 seconds. Ryan has a time of 11.2 seconds, and his team has a mean of 11.5 seconds and a standard deviation of 0.1 seconds. Who has the faster time when compared to each of their teams?a) Nick b) Ryan c) The times are equal when compared to each of their teams.d) There is not enough information
Given data:
The time taken by Nick is 10.8 seconds.
The mean time taken by Nick is 11.4 seconds.
The given standard deviation of Nick is 0.4 seconds.
The time taken by Ryan is 11.2 seconds.
The mean time taken by Ryan is 11.5 seconds.
The given standard deviation of Ryan is 0.1 seconds.
The z-score of Nick is,
[tex]\begin{gathered} z=\frac{10.8-11.4}{0.4} \\ =\text{ -1.5} \end{gathered}[/tex]The z-score of Ryan is,
[tex]\begin{gathered} z=\frac{11.2-11.5}{0.1} \\ =\text{ -3} \end{gathered}[/tex]Thus, Ryan z-score is lower, so Ryan has the faster time when compared to each of their teams, option (b) is correct.
Which angle forms a linear pair with
A linear pair angle must add up to 180 degrees. The angle that form a linear pair with angle MON is expressed below
[tex]\begin{gathered} \angle MON+\angle QOM=180\text{ degre}es \\ \text{therefore} \\ \angle MON\text{ and }\angle QOM\text{ are linear pair} \end{gathered}[/tex]In distributive property; 6(30+4)