Answer:
(a) [tex]A=1600(1+\frac{0.0375}{12})^{12t}[/tex]
(where [tex]A[/tex] is the account balance and [tex]t[/tex] is the time in years)
(b) $1,929.40
Step-by-step explanation:
Compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A is the amountP is the principalr is the interest rate (in decimal form)t is timen is the number of times the interest is compounded per unit of tGiven:
P = $1600r = 3.75% = 3.75/100 = 0.0375t = number of yearsn = 12 (as the interest is compounded monthly and t is number of years)Substituting these values into the formula:
[tex]\implies A=1600(1+\frac{0.0375}{12})^{12t}[/tex]
(where [tex]A[/tex] is the account balance and [tex]t[/tex] is the time in years)
Part (b)
Substitute [tex]t=5[/tex] into the equation created in part (a):
[tex]\implies A=1600(1+\frac{0.0375}{12})^{12\cdot 5}[/tex]
[tex]\implies A=1600(1.003125)^{60}[/tex]
[tex]\implies A=1929.404236...[/tex]
[tex]\implies A=1929.40[/tex]
Therefore, her account balance after 5 years will be $1,929.40
Use the grouping method to factor the polynomial below completely.
x3 + 2x2 + 5x + 10
O A. (x2 + 5)(x+5)
O B. (x2 + 5)(x+2)
O C. (x2 + 5)(x+5)
O D. (x2 + 5)(x+2)
Answer:
(x²+5)(x+2)
simple find the common factor between x³ and 2x² and the cf of 5x and 10
u will end up with these results then^
Gm!!! everyone (who see's this)
Answer:
GOODMORNING!!!
Step-by-step explanation:
I pray you, have a wonderful day!!
A DVD is regularly $19.99 but is on sale today for $15.99. What percent would you save if you bought the DVD on sale?
Answer:
the sale price will be 130% off
Step-by-step explanation:
URGANT PLEASE HELP!!
Solve the triangle for x. (1 point)
A) 41.8°
B) 89.6°
C) 48.6°
D) 90.4°
Answer:
it looks like c
Step-by-step explanation:
its not quite 50 but its extreemly close so its got to be c
[tex]12 {}^{2} = 9 {}^{2} + 8 {}^{2} - 2(9)(8)(cosx)[/tex]
[tex]144 = 81 + 64 - 2(72)(cosx)[/tex]
[tex]144 = 145 - 144(cosx)[/tex]
[tex] - 144(cosx) = 144 - 145[/tex]
[tex](cosx) = \frac{ - 1}{ - 144} [/tex]
[tex]arccos( \frac{1}{144} ) = > a = 89.6[/tex]
If you claim a dependent and have to pay for child
care while you're at work, you can claim a tax credit of
$780. If you owed $5,638 in federal income taxes, how
much do you owe after claiming that credit?
Answer:
4858
Step-by-step explanation:
5,638-780=4,858
Make
x
the subject of the formula
3
a
x
+
2
c
=
b
2
Answer:
x= (2b-2c)/3a
Step-by-step explanation:
3ax+2c=2b
or, 3ax= 2b-2c
Therefore, x= (2b-2c)/3a
I will mark brainliest please help ASAP :)
the distance a car travels d, is a function of t the time it travels a certain car travels 425 miles at a speed of 50 miles per hour. What are the domain range of the function described?
The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 50
The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 425
The domain is all real values from 0 to 50 and the range is all real values from 0 to 425
The domain is all real values from 0 to 425 and the range is all real values from 0 to 8.5
The domain and range of the linear function described are given as follows:
The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 425.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, the car travels 425 miles at a speed of 50 miles per hour, hence for the amount of miles left for the car to travel after t hours is given by a linear function with m = -50 and b = 425, that is:
d(t) = 425 - 50t.
The domain is the set of all possible values of the input, which considering that the car travels while the distance is greater than 0, is given by:
d(t) > 0 -> 425 - 50t > 0 -> t < 8.5.
The range is the set of all possible values of the input, which is the distance remaining, assuming real values from 0 to 425.
Hence, the correct option is:
The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 425.
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Given h(x)=x2-2, what is the value of h(-3)?
h(x) = x^2 - 2
h(-3) = (-3)^2 - 2
= 9-2
= 7
Myah is 4 feet 2 inches tall. Her sister, Ally,is 10 inches taller. Their little brother is half as tall as Ally. How tall is their little brother in feet and inches?
Answer:
2feet
Step-by-step explanation:
There brother is 2 feet and 6 inches
Formula: 12 inches = 1 foot
4'2 + 10 inches = 5 foot
Half of 5 foot would be 2'6 since there are 12 inches in a foot.
In a high school of 1000 students, 355 are playing sports and 233 are in a school band. If there are 175 students playing sports and are in a school band, how many are in neither activity?
Answer:
237
Step-by-step explanation:
1000 minus 355= 645
645 minus 233= 412
412 minus 175= 237
Answer:
237 students
Step-by-step explanation:
355 are playing sports
233 are in a school band.
175 in both
355 + 233 + 175 = 763
763 students are in sports, band or both
1000 - 763 = 237
237 students aren't participating in neither.
hope this helps :)
What is the resistance in a circuit when the current is 0.5 ampere? Ohms
Answer:
24 Ohms
Step-by-step explanation:
Resistance is a function of amperes. For each amp, there is one and only one value for resistance.
It works the other way, too.
E=IR (well-known relationship). If IR=12, R=12/I
R=E* (1/I)
When the current is 0.5 amp, R=12/0.5 - 24 ohms
What is the answer to 16 times 1/100
Answer:
16/100 or simplified is 4/25
Step-by-step explanation:
Are they functions or not ?
Answer:
10.) b. not a function
11.) a. function
Step-by-step explanation:
hope it helps. good luck :)
Solve the system of equations by graphing. Check the solution. y=-2x-3. y=2x+5. Graph each equation on the same coordinate plane. At what point do the graphs of the lines appear to intersect?
Answer:
[tex]\left \{ {{x=-2} \atop {y=1}} \right.[/tex]
Step-by-step explanation:
[tex]\left \{ {{y=-2x-3} \atop {y=2x+5}} \right.[/tex]
Substitute into one of the equations
[tex]-2x-3=2x+5[/tex]
Rearrange variables to the left side of the equation
[tex]-2x-2x=5+3[/tex]
Combine like terms
[tex]-4x=5+3[/tex]
Calculate the sum or difference
[tex]-4x=8[/tex]
Divide both sides of the equation by the coefficient of variable
[tex]x=-\frac{8}{4}[/tex]
Cross out the common factor
[tex]x=-2[/tex]
Substitute into one of the equations
[tex]y=-2\times\left(-2\right)-3[/tex]
Calculate
[tex]y=1[/tex]
The solution of the system is
[tex]\left \{ {{x=-2} \atop {y=1}} \right.[/tex]
I hope this helps you! Don't forget to check the picture I uploaded as well
:)
Answer:
[tex]\displaystyle [-2, 1][/tex]
Step-by-step explanation:
Use the Elimination method sinse both coefficients in the system are OPPOCITES:
[tex]\displaystyle \left \{{{y = -2x - 3} \atop {y = 2x + 5}} \right.[/tex]
2y = 2; 1 = y [Plug this y-coordinate back into the system to get the x-coordinate of −2 (−2 = x).]
I am joyous to assist you at any time.
Solve the following quadratic function by factoring
f(x)=4x^(2)-9
Both solutions are valid, so the solutions to the quadratic function [tex]f(x) = 4x^2 - 9[/tex] are x = -3/2 and x = 3/2.
To solve the quadratic function [tex]f(x) = 4x^2 - 9[/tex] by factoring, we set the expression equal to zero and then try to factor it.
Step 1: Set f(x) equal to zero:
[tex]4x^2 - 9 = 0[/tex]
Step 2: Factor the quadratic expression:
The expression [tex]4x^2 - 9[/tex] is in the form of a difference of squares, which can be factored as follows:
[tex]a^2 - b^2 = (a + b)(a - b)[/tex]
In our case, a = 2x and b = 3:
[tex]4x^2 - 9 = (2x + 3)(2x - 3)[/tex]
Step 3: Set each factor equal to zero and solve for x:
First factor: 2x + 3 = 0
Subtract 3 from both sides:
2x = -3
Divide both sides by 2:
x = -3/2
Second factor: 2x - 3 = 0
Add 3 to both sides:
2x = 3
Divide both sides by 2:
x = 3/2
Step 4: Check the solutions:
Plug the values of x back into the original equation to verify:
For x = -3/2:
[tex]f(-3/2) = 4(-3/2)^2 - 9\\f(-3/2) = 4(9/4) - 9\\f(-3/2) = 9 - 9\\f(-3/2) = 0\\For x = 3/2:\\f(3/2) = 4(3/2)^2 - 9\\f(3/2) = 4(9/4) - 9\\f(3/2) = 9 - 9\\f(3/2) = 0[/tex]
Both solutions are valid, so the solutions to the quadratic function f(x) = [tex]4x^2 - 9[/tex] are x = -3/2 and x = 3/2.
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Tyrell has a bankruptcy on his credit report and therefore pays higher interest rates on his current loans. he calculates that the extra money he pays in additional interest each year, if invested at the rate of 2.5% for one year, could earn him simple interest totaling $300. how much does tyrell pay in additional interest each month? a. $90 b. $100 c. $1,000 d. $12,000
Answer:
C. $1,000edge ⬇️
If invested at the rate of 2.5% for one year. The amount that tyrell pay in additional interest each month is: c. $1,000.
Additional interest each monthFirst step
Amount for one year=Simple interest amount/Interest rate
Amount for one year=$300/0.025
Amount for one year=$12,000
Second step
Additional interest each month=$12,000/12 months
Additional interest each month=$1,000
Therefore the amount that tyrell pay in additional interest each month is: c. $1,000.
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Kilani and Adrian are starting a nutrition program. Kilani currently consumes 1200 calories a day and will increase that number by 100 calories each day. Adrian currently consumes 3230 calories a day and will decrease that number by 190 each day. They will continue this pattern until they are both consuming the same number of calories per day. In how many days will that be? Be sure to define your variables, write an equation, and answer the question in context.
Answer:
7 days
Step-by-step explanation:
Let us represent the number of days = a
Kilani currently consumes 1200 calories a day and will increase that number by 100 calories each day.
1200 calories + 100 calories × a
1200 + 100a
Adrian currently consumes 3230 calories a day and will decrease that number by 190 each day.
3230 calories - 190 calories × a
3230 - 190a
The number of days that they would be consuming the same number of calories =
Kilani = Adrian
1200 + 100a = 3230 - 190a
Collect like terms
190a + 100a = 3230 - 1200
290a = 2030
a = 2030/290
a = 7 days
Therefore, the would be consuming the same number of calories in 7 days
Which expression is equivalent to 2(3 −4)−(8+3)?
Answer:
-40
Step-by-step explanation:
Answer:
-13
Step-by-step explanation:
CAN SOMEONE HELP ME OUT PLEASE AND THANK YOU
Answer:
10x+2
Step-by-step explanation:
2×(2x+1+3x)
4x+2+6x
10x+2
Answer:
10x + 2
Step-by-step explanation:
The perimeter is the sum of the 4 sides of the rectangle, where opposite sides are equal in measure, thus
perimeter = 3x + 3x + 2x + 1 + 2x + 1 = 10x + 2
HELP ME PLEASE EXPLAIN HURRY!!!!
Identify the angle type, the relationship, and the equation. Thank you!
An auto repair shop charged a customer $356 to repair a car. The bill listed $56 for parts and the remainder for labor. If the cost of labor is $50 per hour, how many hours of labor did it take to repair the car?
Answer:
6 hours
Step-by-step explanation:
356-56
=300
300/50
=6
Find the product of (4c-5)(7x^2m- 3x + 3)
Answer:
28cx2m−12cx+12c−35x2m+15x−15
Step-by-step explanation:
The perimeter of rectangle ABCD is 60 cm. The ratio of its length to its width is 3:2. Find the length,
width and area of the rectangle.
Length = cm
Width = cm
Area -cm
Answer:
Length = 18 cm
Width = 12 cm
Area = 216 cm^2
Step-by-step explanation:
The perimeter of a rectangle is twice it's length(l) plus twice it's width(w):
Perimeter = 2l + 2w
We are told that (l/w) = (3/2) [ratio of its length to its width is 3:2]
Therefore:
60cm = 2l + 2w
---
(l/w) = (3/2)
We can rewrite this as: l = (3/2)w
----
Now substitute this expression into the perimeter equation:
60 cm = 2l + 2w
60 cm = 2((3/2)w) + 2w
60 cm = 3w + 2w
60cm = 5w
w = 12 cm
l = (3/2)w
l = (3/2)*12
l = 18 cm
Area = 1*w
Area = (12cm)(18cm) = 216 cm^2
Tìm x,y nguyên dương 5x – xy + 3y = 22.
Answer:
x = 22-3y/5-y
y=-22-5x/x-3
Step-by-step explanation:
Solve for x:
1) Subtract 3y from both sides.
5x - xy = 22 - 3y
2) Factor out the common term x.
x(5 - y) = 22 - 3y
3) Divide both sides by 5 - y.
x = 22-3y/5-y
Solve for y:
1) Subtract 5x from both sides.
=xy + 3y = 22 - 5x
2) Factor out the common term y.
- y=(x-3)=22-5x
3) Divide both sides by x-3.
-y=22-5x/x-3
4) Multiply both sides by -1.
y=-22-5x/x-3
HELP ASAP THIS IS ABOUT “Multistep Pythagorean Theorem” HELP
Answer:
8.1
Step-by-step explanation:
The length of the missing side is 8.1 inches. You apply the pythagorean theorem to 5,b,10 and get 5sqrt3. Next, you apply the pythagorean theorem to 3, b, 5sqrt3 to get the square root of 66, which is 8.1, rounded to the nearest tenth.
Answer:
[tex]\displaystyle 8,1[/tex]
Step-by-step explanation:
Use the Pythagorean Theorem twise [first time for the reflexive edge and the second time for the longer leg of the other triangle]:
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ a^2 + 5^2 = 10^2 \hookrightarrow 100 = 25 + a^2 \hookrightarrow \sqrt{75} = \sqrt{x^2}; 5\sqrt{3}\:[or\:8,6602540378...] = a \\ \\ \\ \\ a^2 + b^2 = c^2 \\ \\ x^2 + 3^2 = 5\sqrt{3}^2 \hookrightarrow 75 = 9 + x^2 \hookrightarrow \sqrt{66} = \sqrt{x^2}; \sqrt{66}\:[or\:8,1240384046...] = x \\ \\ \boxed{\boxed{8,1 \approx x}}[/tex]
I am joyous to assist you at any time.
The diameter of a circle is 9 ft. Find the circumference and round it to the nearest tenth.
Answer:
9*3.14=28.26
Step-by-step explanation:
Hope this Helps!
Answer:
[tex]C\approx28.27ft[/tex]
Step-by-step explanation:
[tex]C=\pi d\\C=\pi(9)\\C=9\pi\\C\approx28.27[/tex]
Thus, your circumference is about 28.27 ft
Find the range of the data. 133,117,152,127,168,000,000
Answer:
168
Step-by-step explanation:
168 would be the range because the range is the highest number - the lowest number so 168=highest and 000=lowest
so 168-000 or just0=168
here's some extra answers.
The mean=100 rounded up to nearest 100
Mean= the average of the data set.
Median=127
The median is the middle number when the numbers in the data set are sorted least to greatest.
Mode=000 or just 0
The mode is the number that appear the most in the data set and 000 or just 0 appears twice rather than,all the other numbers only appear once.
Minimum=000 or just
The minimum is the lowest number in the data set and as for this one is is 0.
Maximum=168
The maximum is the highest number and the data set and 168 is the highest in this one.
Hope it helps have a great day:)
Find the value of x.
(2x + 21)
54°
(5x + 6)
Answer:
x= 9.3 but im not to sure this is right
Step-by-step explanation:
What is the equation of the line that passes through the point (-1,-5) and has a
slope of -1?
Answer:
5 x - 6 y - 8 = 0
Step-by-step explanation:
#5
A ball is kicked 5 feet above the ground with an initial vertical velocity of 50 feet per second. The function
h(t) = -16+ +50t + 5 represents the height h (in feet) of the ball after seconds. Using a graph, after how many seconds
is the ball 32 feet above the ground? Round your answers to the nearest tenth.
For
Answer:
Step-by-step explanation:
h(t) = 32 = -16t^2 + 50t + 5
-16t^2 + 50t - 27 = 0
Drawing a graph gives time = 0.7 seconds.
The ball is 32 feet above the ground after 2.9 seconds
We have,
To determine the time at which the ball is 32 feet above the ground, we can set the height function h(t) equal to 32 and solve for t:
h(t) = 32
-16t² + 50t + 5 = 32
-16t² + 50t + 5 - 32 = 0
-16t² + 50t - 27 = 0
We can solve this quadratic equation using various methods, such as factoring, completing the square, or the quadratic formula.
Let's use the quadratic formula:
t = (-b ± √(² - 4ac)) / (2a)
Plugging in the values a = -16, b = 50, and c = -27, we have:
t = (-50 ± √(50² - 4(-16)(-27))) / (2(-16))
Simplifying further:
t = (-50 ± √(2500 - 1728)) / (-32)
t = (-50 ± √(772)) / (-32)
Now, we can calculate the two possible solutions:
t ≈ (-50 + √772) / (-32) ≈ 2.85 seconds (rounded to the nearest tenth)
t ≈ (-50 - √772) / (-32) ≈ 0.18 seconds (rounded to the nearest tenth)
Based on the graph of the function, the ball is 32 feet above the ground after approximately 2.9 seconds (rounded to the nearest tenth).
Thus,
The ball is 32 feet above the ground after 2.9 seconds
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