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Related Questions
Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.
Alexander thought the equivalent quarterly interest rate would be 2%. Is Alexander correct? If he is, explain
why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your
answer. i need to show my work and everything
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For the annually rate we have that:
[tex] V_{0} =(1+ i_{a} ) ^{1} [/tex]
Where
[tex] V_{0}[/tex] = initial investment.
[tex] i_{a} [/tex] = annually interest rate in decimal form.
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
[tex] V_{0} =(1+ i_{q} ) ^{4} [/tex]
Where
[tex] V_{0}[/tex] = initial investment.
[tex] i_{q}[/tex] = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
[tex](1+ i_{a} )=(1+ i_{q} ) ^{4} [/tex]
Notice that we are not using the initial investment [tex] V_{0} [/tex] since they are the same.
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
[tex](1+0.07)=(1+ i_{q} ) ^{4} [/tex]
[tex]1.07=(1+ i_{q} ) ^{4} [/tex]
[tex] \sqrt[4]{1.07} =1+ i_{q} [/tex]
[tex] i_{q} = \sqrt[4]{1.07} -1[/tex]
[tex] i_{q} =0.017[/tex]
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
Martha took 48 pictures of flowers and 36 pictures of beautiful scenery.she wants to display the pictures so there are the same number of each kind of picture in each display.what is the greatest number of displays she can make?
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Simplify the expression. (4 − 4i)(−2 + 5i)
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is your answer
4(-2+5i) + -4i(-2+5i)
Simplify - -8+20i +8i -20i²
-20i² + 28i - 8
Hope this helps- Please mark brainliest :)
Write the polynomial in factored form. 4x3 + 8x2 – 96x
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Explanation:
4x^3, 8x^2 and 96x have 4x as a common factor. Hence
4x^3+8x^2-96x = 4x*(x^2+2x-24)
Furthermore, (x^2+2x-24)= (x-4)(x+6)
because 6-4=2 and 6*(-4) = -24.
So 4x^3+8x^2-96x = 4x*(x^2+2x-24) = 4x(x-4)(x+6).
i think its D but who knows HEEEEELELELLELEELEP
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you plus 4 friends = 5 people
them multiply 5 by m sp you get 5m
D is the correct answer
20 POINTS PLEASE HELP Write an equation for a trend line and predict the value when x is 15
X 0 3 6 9 12
Y 17.5 35.4 50.5 60.6 66.3
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Add the values as presented on the image. Select the values and then go t the menu "Insert" and look for "Charts" and then "Insert scatter chart". After this, select one of the dots from the graph and then press the right button of the mouse and select "add trendline". Now you have a trend line. Format the trendline selecting the option "Display Equation on chart" (and also if you want "Display R-squared value on chart"). Now you have the equation and you can easily predict the value when X is 15, you just need to substitute on the equation the X by the 15:
y = 4.0933Χ + 21.5 <=> y = 82.8995
What is the LCM of 5 and 6?
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Answer: 30
Explanation: To find the least common multiple of lcm of 5 and 6, we begin by listing the first few multiples of each number.
Multiples of 5
1 x 5 = 5
2 x 5 = 10
3 x 5 = 15
4 x 5 = 20
5 x 5 = 25
6 x 5 = 30
Notice that we skipped 0 x 6 in our list of multiples. That's because 0 x 6 is 0 and our least common multiple can't be 0.
Next we list the multiples of 6. When we list the multiples of 6, it's a good idea to keep an eye on the list of multiples for 6 so that we know when we have found a least common multiple.
Multiples of 6
1 x 6 = 6
2 x 6 = 12
3 x 6 = 18
4 x 6 = 24
5 x 6 = 30
Notice that 30 appears in both lists so we can stop here.
This means that the least common multiple of 5 and 6 is 30.
Answer:
30
Step-by-step explanation:
both 6 and 5 go into 30 :)
A web store offers two versions of a popular song. The size of the standard version is 2.5 MB. The size of the high quality is 4.3 MB. Yesterday, there was 1180 downloads of the song, for a total size of 3850 MB. How many downloads of the high quality version were there?
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Answer:
250
Step-by-step explanation:
If c(x)= [tex] \frac{5}{x-2} [/tex] and d(x) = x + 3, what is the domain of (cd)(x)?
all real values of x
all real values of x except x = 2
all real values of x except x = –3
all real values of x except x = 2 and x = –3
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now, for a fraction, if its denominator ever becomes 0, the fraction becomes undefined, because it'd be a division by 0.
when does that happen? let's zero out the denominator to check,
x - 2 = 0, thus x = 2
so, if "x" ever becomes 2, the fractions goes kaput.
so, that domain is all real values except that one, that makes the fraction undefined.
The domain of the composite function (cd)(x), where c(x) = 5/(x-2) and d(x) = x + 3, includes all real values except x = 2 due to a division by zero condition in the function c(x).
Explanation:In this problem, we need to figure out the domain of the combined function (cd)(x). The domain constitutes the set of all real values of x that make the function defined. The first function, c(x) = rac{5}{x-2}, isn't defined for x = 2 because it would lead to a division by zero. The second function, d(x) = x + 3, is defined for all real values since it's a linear function.
When these functions are multiplied to form (cd)(x), the domain will be the intersection of the individual function domains. This means, with c(x) having a restriction with x != 2, the composite function (cd)(x) will maintain this restriction despite d(x) being defined for all real values. So the domain for (cd)(x) is all real values except for x = 2.
Learn more about Domain of Composite Function here:https://brainly.com/question/31810210
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One number is four times another. the greater number is xx. write an expression for the lesser number.
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What’s the ratio of 42¢ to $1.25? (Change dollars to cents)
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Answer:
42 125 becuase i got um right bozzzzzzzz
Step-by-step explanation:
A vending machine needs to be programmed to accept any combination of coins totaling 0.75, excluding pennies, and half dollars. How many combinations are possible?
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Combination 2: 2 quarters and 5 nickels.
Combination 3: 2 quarters, 2 dimes, 1 nickel.
Combination 4: 15 nickels
Combination 5: 7 dimes and 1 nickel.
Combination 6: 1 quarter, 5 dimes
Combination 7: 1 quarter, 1 dime, 7 nickels.
Combination 8: 1 quarter, 2 dimes, 6 nickels.
Combination 9: 1 quarter, 3 dimes, 4 nickels.
Combination 10: 1 quarter, 4 dimes, 2 nickels.
I believe those are all the possible combinations.
I hope that helped you! :)
Ana wants to paint her dogs doghouse. She has 4 colors: Green, Maroon, Blue and Wheat. One color will cover the walls, and another color will be used for the trim. (For example, green walls with wheat trim = GW.) Which one of these answers show all of the possible color combinations?
A. BW, BM, BG, BB, MW, MB, MG, MM, GW, GB, GM, GG
B. GM, GB, GW, MG, MB, MW, BG, BM, BW, WG, WM, WB
C. MM, MG, WB, WM, WG, BB, BG, BM, WB, GB, GM, GW
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Let us take this one by one. One color can pair with three colors.
Green = Maroon, Blue, Wheat = GM, GB, GW
Maroon = Green, Blue, Wheat = MG, MB, MW
Blue = Green, Maroon, Wheat = BG, BM, BW
Wheat = Green, Maroon, Blue = WG, WM, WB
So the combinations are:
GM, GB, GW, MG, MB, MW, BG, BM, BW, WG, WM, WB
Which is letter B.
The awnser is b trust I got it right thank you for your time nd day
Find the greatest common factor of 16, 27 and 20
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The factors for 16 are 1,2,4,8,16.
The factors for 27 are 1,3,9,27.
The factors for 20 are 1,2,4,5,10,20.
If 6 1/2is the lesser number in an inequality, which statement is true about the other number in the inequality?
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I KNOW ITS NOT A. But i think it is B. HOPE THIS HELPS!
Is is true that the coefficient of the expression 18z-7(-3+2z) of z is 13
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= 18z + 21 - 14z
= 4z + 21
answer is False
coefficient of z is 4, not 13
Can somebody plz help me
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A store sells small notebooks for $8 and large notebooks for $10. if a student buys 6 notebooks and spends $56, how many of each size did he buy?
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Answer: 2 small, 4 large
15. How much less would a 25 year old male pay for a $50,000 policy of 20 y life insurance @ $5.84 per $1000, than a straight life policy @ $15.66 per $1000? (Points : 1)
$783
$491
$292
$415
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Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
Amount for policy = $50,000
If he opt for life insurance @$5.84 per $1000,
then, his amount of premium will be
[tex]50000\times \frac{5.84}{1000}=\$292[/tex]
If he opt for straight policy @ $15.66 per $1000,
then, his amount of premium will be
[tex]50000\times \frac{15.66}{1000}=\$783[/tex]
Difference in both the cases will be
[tex]783-292=\$491[/tex]
Hence, Second option is correct.
Solve for x: the quantity of x plus 4 / 3 = 2.
A.x = −2 B.x = 2 C.x = 2/ 3 D. x = negative 10/ 3
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Macs farm has a total of 18 horses and 27 cows. what is the ratio of horses to cows in simplest form?
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Ratio = 18/27
When expressing it to its simplest form, make sure it is reduced. 18 and 27 are both factors of 9. So,
Ratio = 9*2/9*3
Cancelling out 9, the ratio at its simplest form is: 2/3
Answer:
2/3
Step-by-step explanation:
What is the measure of x?
A.36
B.72
C.144
D.360
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Is 9.103 greater than 9.13
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Answer:
false 9.13 is greater
Step-by-step explanation:
103 thousanths are smaller then 13 hundreths
with decimals the farther you go the lower you get bc its half a number
1/2 to 1/4 to 1/8 it gets smaller
find the root of 6x-48=0
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(6)(-48)=0
set to zero
x-8=0
add 8 to both sides
x=8
the root is at x-8
X=8
A garden table and a bench cost $573 combined. The garden table costs $77 less than the bench. What is the cost of the bench?
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• 573 - 77 = 496
So, the bench costs $496.00.
Hope this helps! :D
~PutarPotato
64.125 - 20.37 i need the answer
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Answer:
43.755 what the other person said but I know that is the answer
Step-by-step explanation:
Mark had $19.00 to spend on stamp packets. They sell for $1.78 each. How many packets can he buy?
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That equals 10.67
so you can by 10 stamps.
Answer:
[tex]10\ stamp\ packets[/tex]
Step-by-step explanation:
Let
x-----> the number of packets that mark can buy
we know that
[tex]1.78x\leq 19[/tex] -----> inequality that represent the situation
Solve for x
Divide by [tex]1.78[/tex] both sides
[tex]x\leq 19/1.78[/tex]
[tex]x\leq 10.67\ stamp\ packets[/tex]
How many permutations are there of jack, queen, king, ace
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find three consecutive odd integers such that the square of the first plus the square of the third is 170
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x
x + 2
x + 4
x^2 + (x + 2) + (x + 4)^2 = 170
Take it from here.
You can jog around the block twice and the park once in 10 min. You can jog around the block twice and the park 3 times in 22 min. Write a system of linear equations that represents this situation. How long does it take to jog around the park?
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2b + p = 10 min 2 runs around the block takes 10 minutes
2b + 3p = 22 min 2 runs around the block plus 3 runs around the park takes 22 minutes
To solve, I will use substitution. First, I will divide the first equation by 2 to get b by itself and subtract p from both sides to get b by itself. Then, substitute 5 - 1/2p in for b in the second equation because they have equal values. Then, subtract 10 from both sides to eliminate it. Divide by 2 to both sides to get 'p' by itself.
2b + p = 10 min ---------→b + 1/2p = 5 ----------→ b = 5 - 1/2p
2(5 - 1/2p) + 3p = 22 ---------→ 10 -p + 3p = 22 --------→ 10 + 2p = 22
10 + 3p = 22 ----------→ 2p = 12
2p = 12 -------------→ p = 6
It takes 6 minutes to jog around the park
Hope this helps!