Using compound interest, it is found that:
a) The monthly payments are of $3,401.49.
b) The total of all monthly payments for 30 years is of $1,224,536.
c) The total interest is of $794,536.
d) The total interest is greater.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.For the parameters, we have that:
The Fortunato family is borrowing $430,000 to buy a home, hence P = 430000.30-year mortgage, hence t = 30.Rate of 3.55%, hence r = 0.0355.Yearly compounding, hence n = 1.For practicality, first we are going to solve item b.
Item b:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(30) = 430000\left(1 + \frac{0.0355}{1}\right)^{30}[/tex]
[tex]A(30) = 1224536[/tex]
The total of all monthly payments for 30 years is of $1,224,536.
Item a:
$1,224,536 is paid in 30 x 12 = 360 months, hence:
1224536/360 = $3,401.49.
The monthly payments are of $3,401.49.
Item c:
The interest is the total subtracted from the principal, hence:
1224536 - 430000 = $794,536.
The total interest is of $794,536.
Item d:
Loan of $430,000, interest of $794,536, hence the total interest is greater.
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What is the independent quantity?
A) not enough information
B) types of food I eat
Choose all options that apply. In the US Customary System, which of the following terms is used to measure volume? a) Cup b) Tablespoon c) Liter d) Fluid ounce
Answer:
D) Fluid ounce
Step-by-step explanation:
Fluid ounces are a unit used to measure volume, or how much space something takes up. This measurement is used for liquid ingredients, like water or milk. When a recipe calls for fluid ounces, go ahead and pull out your measuring cup; it's the most accurate way to measure this.
I hope this helps, and stay safe!! :)Answer:
A and D because yeah its right
Rory has 5 pounds of ground turkey to make meatballs. He uses 5/8 pound per meatball to make 7 meatballs. How many 1/8 pound meatballs can Rory with the remaining turkey?
Answer:
4/8
Step-by-step explanation:
because
Leah hangs 6 posters in a row, each 14 inches wide, on a bedroom wall. There are 4 inches between each poster. For the posters at each end, there are 3 inches between each poster and the end of the wall. What is an appropriate strategy for Leah to use to find the width of the wall?
Answer:
62 sq in of wall is covered
Step-by-step explanation:
6 x 14 = 84 -22 = 62
this is for the total
4 x 4 = 16
this is for the inches of the inside wall
2 x 3 = 6
this is for the inches of the outside wall
Leah can draw a picture showing each poster and space. Then she can add the measurements together to find the width of the wall option (C) is correct.
What is a rectangle?It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
Leah must add the widths of all the places and posters to get the breadth of the wall, so the best course of action is:
Leah can draw a picture showing each poster and space. Then she can add the measurements together to find the width of the wall.
Thus, the appropriate strategy for Leah to use to find the width of the wall is Leah can draw a picture showing each poster and space. Then she can add the measurements together to find the width of the wall option (C) is correct.
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State if the triangle are congruent by sss sas asa aas or not congruent
h e l p m e please its 20 points
Answer:
its just a rotation. its as simple as rotating it back to its origonal form and matching up the corners
Step-by-step explanation:
the general solution of the equation cos3x +cos2x =sin3x/2 + Sinx/2 is
Answer:
I am doiiiiiiinnnnggg just wait
What single percentage change is equivalent to a 14% increase followed by a 11% decrease?
Options:
4.54% decrease
26.54% increase
4.54% increase
1.46% decrease
26.54% decrease
1.46% increase
Answer:
1.46%
Step-by-step explanation:
Pretend you have a number as a test dummy. We'll go with 100 for simplicity. A 14% increase to 100 would be 114. Then we can decrease 114 by 11%. We can find 11% of 114 with an equation like so: x/114 = 11/100. We can then cross multiply to get this" 100x = 1254, which can be simplified to x=12.54. Now, we can subtract 12.54 from 114, which will get us 101.46. Because percentage is based on 100, we can simply subtract 100 from 101.46, which gives us 1.46. So, the answer is 1.46%.
HELP!! Will give brainliest
Answer:
my brother said it was
Step-by-step explanation:
1400.053...
how would you work out 0.5 is 1/100 of
0.5% of 100
is equivalent to multiplying them:
0.5% × 100 = 0.5
Solve for the values of x for each of the following exponential equations and inequalities.
1. 82− = 2
3. 5 = 25−2
4. 3+2 ≥ 27
5. 43 = 8−1
Answer:
8
2−x
=2
8^{2-x}=8^{1/3}8
2−x
=8
1/3
2-x=\dfrac{1}{3}2−x=
3
1
x=\dfrac{5}{3}x=
3
5
2.
(\dfrac{1}{2})^{x}<\dfrac{1}{8}(
2
1
)
x
<
8
1
(\dfrac{1}{2})^{x}<(\dfrac{1}{2})^{3}(
2
1
)
x
<(
2
1
)
3
x>3x>3
3.
5^x=25^{x-2}5
x
=25
x−2
25^{x/2}=25^{x-2}25
x/2
=25
x−2
\dfrac{x}{2}=x-2
2
x
=x−2
\dfrac{x}{2}=2
2
x
=2
x=4x=4
4.
3^{x+2}\geq273
x+2
≥27
3^{x+2}\geq3^33
x+2
≥3
3
x+2\geq3x+2≥3
x\geq1x≥1
5.
4^{3x}=8^{x-1}4
3x
=8
x−1
2^{6x}=2^{3x-3}2
6x
=2
3x−3
6x=3x-36x=3x−3
3x=-33x=−3
x=-1x=−1
Step-by-step explanation:
to the nearest 0.01cm3, what is the volume of this sphere?
Answer: Calculate the sphere volume, the volume of a spherical cap or of a hemisphere thanks to this sphere volume calculator.
Help or don’t eiether way you’re amazing
Answer:
267 (please double check this!!!)
Step-by-step explanation:
Separate the block into sections that you can find the volume for easily and figure out the measurements for each
the two smaller blocks on top will be symmetrical
the bottom area is 5 high and 3 deep and you get the length by adding 4+5+4 because that's the length of the whole thing
so 13*3*5 = 195
The two smaller blocks is just adding a *2 once you figure out the one
it's 3 deep still and 4 wide, if you subtract the total height from the height given of the bottom part you get 3
3*4*3 = 36
you have another one of those blocks so it'd be 36*2
then you add them both 72+195 = 267
pls help
its hw pls help
ill try to make brainiest
Answer:
1. 8. 2. 8. 3. 7/5. 4. 2/3.
Step-by-step explanation:
As you can see you just need to cross multiplication and use distirbitive property
Please give brainiest
The equation x^2+ (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real roots.
(a) Show that k satisfies k^2+2k-3>0
Step-by-step explanation:
For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,
b^2 - 4ac must be positive.
b^2 - 4ac > 0
(k - 3)^2 - 4(3 - 2k) > 0
k^2 - 6k + 9 - 12 + 8k > 0
k^2 + 2k - 3 > 0
To show that k satisfies k² + 2k - 3 > 0 ,the discriminant is given as Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]
How to prove the expressionTo have two distinct real roots, the discriminant of the quadratic equation must be positive. The discriminant is given by;
Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]
For two distinct real roots, Δ > 0. So, we have k² + 2k - 3 > 0. Thus, k satisfies the inequality k² + 2k - 3 > 0.
In summary, for the quadratic equation x² + (k - 3)x + (3 - 2k) = 0 to have two distinct real roots, the value of k must satisfy the inequality k² + 2k - 3 > 0
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HELP POINTS FOR Each answEr quantity 4 times x plus 3 end quantity divided by 5 equals quantity 8 times x minus 1 end quantity divided by 9.
[tex]\displaystyle \frac{4x+3}{5} ^{/9}=\frac{8x-1}{9} ^{/5} \\\\\\ 36x+27=40x-5 \\\\ 40x-36x=27+5\\\\ 4x=32 \\\\ \boxed{x=8 }[/tex]
Step-by-step explanation:
Given fractional expression:
(4x+3)/5 = (8x-1)/9
By doing cross multiplication, we get
⇛4x(9) + 3(9) = 8x(5) - 1(5)
⇛36x + 27 = 40x - 5
Now, combine the like terms in one side.
⇛27x - 40x = -5 + 36
⇛-13x = 31
⇛x = 31/-13 Ans.
The path of a skateboarder can be modeled by the equation (x – 3)2 = –8(y – 8), where distance is in feet and air resistance is insignificant. If the skateboarder makes a jump from a ramp at x = 0, what is her maximum height and how far is she horizontally from the end of the ramp when she lands?
Maximum height 3 feet; horizontal distance 16 feet
Maximum height 7 feet; horizontal distance 11 feet
Maximum height 8 feet; horizontal distance 11 feet
Maximum height 8 feet; horizontal distance 16 feet
Answer:
Maximum height 8 feet; horizontal distance 11 feet
Step-by-step explanation:
got it right
The maximum height and horizontal distance is required.
Maximum height 8 feet; horizontal distance 16 feet
The given path is [tex](x-3)^2=-8(y-8)[/tex]
If the skateboarder jumps at x = 0 she will land at y = 0. However there will be at horizontal displacement.
[tex](x-3)^2=-8(0-8)\\\Rightarrow (x-3)^2=8^2\\\Rightarrow x-3=\pm 8\\\Rightarrow x-3=8\\\Rightarrow x=11[/tex]
or
[tex]x-3=-8\\\Rightarrow x=-5[/tex]
The distance between -5 and 11 is [tex]11-(-5)=16[/tex]
Middle point would be [tex]\dfrac{16}{2}=8[/tex] from [tex]-5[/tex].
[tex]-5+8=3[/tex]
So, [tex]x=3[/tex]
The maximum height will be
[tex](3-3)^2=-8(y-8)\\\Rightarrow y-8=0\\\Rightarrow y=8[/tex]
The maximum height is 8 feet and the horizontal distance is 16 feet.
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choose all numbers that round to 30,000 when rounded to the nearest ten thousand
a. 28,5602
b. 20,347
c. 27,563
d. 22,547
Answer:
A & C
Step-by-step explanation:
in a set of 5 numbers the average of two is 12 the average of the other 3 is 7 what is the average of all five numbers. (fraction or whole number)
Answer:
The average of all 5 numbers is 9
Step-by-step explanation:
Two of the numbers average 12. That means that their total is 2*12 = 24
Three of the other numbers average 7. That means that their total is 7*3 = 21
The total score for the 5 numbers is 24 + 21 = 45
The average for all 5 numbers is 45/5 = 9
Will mark as brainlist
The title of the poem, "Poetry and Prose, 'is an example of antonyms. Poetry and prose are "opposite' ways of writing.
Search the poem to find the other antonym pairs. Ust the words in the order that they appear in the poem. There are
seven more pairs. Separate each word with a comma. For example: poetry, prose.
If it isn't a poem. It's prose:
And friends cannot be foes.
A package not heavy is light.
And after the day comes night.
if it's ap. it can't be down:
The country is never a town.
When asleep we aren't awake:
To give is never to take
ah, yes, college mathematics. how riveting
poem, prose
friends, foes
heavy, light
day, night
up, down
country, town
asleep, awake
give, take
I truly commend you on your pursuit of such higher level mathematics studies. Good luck!
Use the monthly payment formula to find the monthly payment for a $1,000, one year
loan at an APR of 7.5%
Step-by-step explanation:
The formula :
[tex]\displaystyle \rm S=A\cdot \left (1+\frac{N}{100} \right )^{\big r}[/tex]
where r is years ; N is the percentage by which we increase the price ; A is the original price
In our case :
[tex]\rm r=1 \ \ ; \ \ A=100 \ \ ; \ \ N=7,5\% \\\\ S=1000\cdot \bigg( 1+\dfrac{7,5}{100} \bigg)^1=1000\cdot 1,075=\boxed{1075\$}[/tex]
Then the monthly salary is equal to:
[tex]\dfrac{1075}{12} \approx 89,58 \$[/tex]
kia worked 30 hours and 15 minutes this weekend . if she makes $15.60 per hours ,how much did she make?
Answer:
$471.90 dollars
Step-by-step explanation:
First, we need to find out how many hours she's working.
There are 60 minutes in an hour so 15/60 is 0.25.
Thus, adding that to the 30 hours gives us 30.25.
If she makes $15.60 per hour we just multiply that by 30.25 hours and get the answer.
[tex]\frac{15.60}{hour}*30.25 hours = 471.9\\[/tex]
The [tex]\frac{}{hour}[/tex] comes from the wording of per hour, and since the unit is in the denominator, when we multiply it by the 30.25 hours, the units cancel out. Thus all we are left with is the amount of dollars made, which is $471.90.
The weight of two fish tighter is 16 kg. If one fish weight is 10.5 kg, find the ratio of
the weight of the smaller fish to that of the bigger fish.
what is the slope of the line? URGENT PLEASE
Answer:
when you have the two points of a line (-4,5) and (0,6) then you use the m = (y2-y1)/(x2-x1) and you get m = 1/4
Solve 3x + 4x = 2.
+
Answer: [tex]\frac{-2+\sqrt{10}}{3}[/tex]
Step-by-step explanation:
Dave determines the meal he ordered at the restaurant contains 29% of his daily
sodium intake. If the meal contains 251 mg of sodium, how many mg of sodium are in
Dave's daily diet?
Is 500 hrs a thing? Cause my question is: Every hour you get $10, how many hours till you get to $5,000? The answer should be 500 hrs, I don't know if that's an hour
Answer:
500 Hours
Step-by-step explanation:
Yes you are right, 500 hours is not an hour and I doubt anyone can work that much, there are only 168 hours in a single week.
If we're talking reality, it would take well over a few weeks.
If its just math then yeah you would get 500.
Either way, 500 is the right answer.
By which rule are these triangles congruent?
Answer:
S, S, S
Step-by-step explanation:
120 applications ? (Select all that apply.)
Which ratios are equivalent to the ratio
36 openings
The ratio equivalent to the ratio is 10:3. Therefore, option A is the correct answer.
The given ratio is 120:36.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Equivalent ratios are the ratios that are the same when we compare them.
120:36
= 20:6
= 10:3
The ratio equivalent to the ratio is 10:3. Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which of the following ratios is equivalent to the ratio of 120 to 36?
20 To 6, 12 To 3, 18 To 60, 84 To 1
A circle has a diameter of 24 yd. What is its circumference?
A circle has a diameter of 24 yd. What is its circumference?
Answer:
75.4
Step-by-step explanation:
Answer: 75.4 yd
Step-by-step explanation:
Using the formulas
C = 2 π r
d = 2 r
Solving for C
C = π d = π x 24 = 75.39822 yd
75.39822 rounded up is 75.4 so the answer is 75.4 yd.