$8400 is deposited at an APR of 5%. How much interest has been accrued after 6 years ?
Answer:
$2,856.80
Step-by-step explanation:
The formula for the balance of an account earning interest compounded annually is ...
A = P(1 +r)^t . . . . where P is the principal invested at annual rate r for t years
__
Using the given values, we find the account balance to be ...
A = $8400(1 +0.05)^6 ≈ $11,256.80
The excess over the initial investment is the interest earned:
$11,256.80 -8,400 = $2,856.80
The account has accrued $2,856.80 in interest after 6 years.
_____
Additional comment
If the account earns simple interest, it is computed using ...
I = Prt = $8400(0.05)(6) = $2,520
need help with geometry (number 20)
Answer: A
Step-by-step explanation:
Since diagonals of a rectangle are congruent and bisect each other, we know that the two opposite triangles formed by the diagonals are congruent by SAS.
Therefore, the measure of angle 1 is equal to 25 degrees.
If f(x) = x^3 - 2x^2 , which expression is equivalent to f(i)?
O -2 + i
O -2 - i
O 2 + i
O 2 - i
[tex]\text{Given that,}~f(x)=x^3-2x^2\\\\f(i)=i^3-2i^2\\\\~~~~~~=i^2 \cdot i -2(-1)~~~~~;[i^2=-1]\\\\~~~~~~=-i+2\\\\~~~~~~=2-i[/tex]
The expression equivalent to f(i) is 2-i.
What is expression?The expression is mathematical statement which consist of variables, numbers and connected by at least one operation.
Given that, a function f(x) = x³ - 2x², we need to find the expression equivalent to f(i),
To find the same we will put x = i,
So,
f(i) = i³ - 2i² [i = √-1]
= (√-1)³ - 2(√-1)²
= -i - 2(-1)
= -i+2
= 2-i
Hence, the expression equivalent to f(i) is 2-i.
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Which of the following functions is equal to f(x)=csc(x-9pi)+2 ? Select 3 answers
B. f(x) = csc(x - pie ) + 2 = - csc(x) + 2
C. f(x) = - csc(x - 2pie) + 2 = - csc(x) + 2
F. f(x) = - sec(x - 9pie/2 ) + 2 = - sec( x - 4pie - pie/2 ) + 2
= - sec(x - pie/2) + 2 = - csc(x) + 2
What’s the circumference of circles
Answer:
62.83185
Step-by-step explanation:
C=2πr=2·π·10≈62.83185
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Circumference of circle is :
[tex]\qquad \tt \dashrightarrow \:\pi d[/tex]
where,
d = diameter of circle[tex]\qquad \sf \dashrightarrow \:c = 20 \pi \: \: cm[/tex]
Now, let's plug approximate value of pi
[tex]\qquad \sf \dashrightarrow \:c = 20 \times 3.14\: \: [/tex]
[tex]\qquad \sf \dashrightarrow \:c = 62.8 \: \: cm[/tex]
how can I solve 1 4/5 x 1/2?
Answer:
[tex]\frac{9}{10}[/tex]
Step-by-step explanation:
first we write 1 4/5 as an improper fraction:
[tex]1 \frac{4}{5}=\frac{5}{5}+\frac{4}{5}=\frac{5+4}{5}=\frac{9}{5}[/tex]
Now we multiply :
[tex]\begin{aligned}1 \frac{4}{5} \times \frac{1}{2} &=\frac{9}{5} \times \frac{1}{2} \\&=\frac{9 \times 1}{5 \times 2} \\&=\frac{9}{10}\end{aligned}[/tex]
PLEASE ONLY ANSWER B. (GIVING BRAINLIEST THANKS)
Answer:
[tex][7\times(-2)]^5 = 7^5 \times (-2)^5[/tex]
Step-by-step explanation:
Use Descartes’s rule of signs to determine the possible number of positive and negative real zeros of f(x)=8x^4-6x^3-4x^2-7x+3
let's recall Descartes rule of signs, to get the Real Positive ones we start by checking the sign changes for f(x), and to get the Real Negative ones we check the sign changes for f( -x ).
Check the picture below.
The diagram represents the factorization of a2+8a+12.
A 2-column table with 2 rows. First column is labeled a with entries a squared, 2 a. Second column is question mark with entries 6 a, 12. First row is labeled a with entries a squared, 6 a. Second row is labeled 2 with entries 2 a, 12.
What is the missing number that will complete the factorization?
6
8
12
24
Answer:
The answer is 6
Step-by-step explanation:
Answer: 6
Step-by-step explanation: took the quiz
Which of the following are composite numbers? Select ALL that apply. 4 9 15 3 5 answers.
Answer:
4 and 9
Step-by-step explanation:
Composite numbers are whole numbers that can have more than 2 factors.
When a is greater than one the parabola ___
Answer:
parabola is open upwards
Please help as fast as possible
[tex]\rm Answer:[/tex]
20.125%
To find the relative frequency, divide the frequency(f) by the total number of data values (n).[tex]\rm \# KiroToshiroComeback[/tex]
A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she
might teach about the letter S or the letter U, but not the letter M.
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
What letters are CANT BE TAUGHT using this method? (There are 11.)
ОА
OB
Ос
OD
ОЕ
OF
OH
01
Answer:
01 she can teach alphabet using seven days name but not numbers.
Express the difference between 0.35 and 2/5 as a decimal
Help picture below problem 13
Answer:
B. Obtuse
Step-by-step explanation:
An obtuse angle is defined as one that extends beyond 90 degrees. An acute angle is defined as one that is less than 90 degrees. A right angle is one that is 90 degrees.
A club swimming pool is 22 ft wide and 44 ft long. The club
members want an exposed aggregate border in a strip of
uniform width around the pool. They have enough material for
432 ft squared. How wide can the strip be?
Answer:
968 is what they need and no they do not enough material
Step-by-step explanation:
What I always do on these questions is length times width and they need 536 more material
Find the area of right angled triangle at J, if ZJ = 14 and JW = 1.
Answer:
7 sq units
Step-by-step explanation:
Area of right angled triangle
= 1/2 * ZJ * JW
= 1/2 * 14 * 1
= 7 sq units
If you are traveling in your car at an average rate of r miles per hour for T hours, then the distance d in miles that you travel is described by the formula d=rt that is distance equals rate times time. A distance of 60 miles at an average rate of 40 miles per hour is covered in ___ hours?
Answer:
1.5 hr
Step-by-step explanation:
d = rt
re-arrange to
d/r = t
60 miles / 40 miles/hr = 1.5 hr
[50 points]
P(AB) = P(An B)/P(B)
Freshmen
Sophomores
Juniors
Seniors
Boys
3
1
4
2
Girls
7
9
5
1
P(Boy|Sophomore) =
Answer:
[tex]\sf \dfrac{1}{10}[/tex]
Step-by-step explanation:
From the table:
Total number of Sophomores = 10Total number of students = 37Total number of Boys who are Sophomores = 1[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]
[tex]\sf \implies P(Sophomore)=\dfrac{10}{37}[/tex]
[tex]\sf \implies P(Boy \cap Sophomore)=\dfrac{1}{37}[/tex]
[tex]\begin{aligned}\sf P(Boy | Sophomore) & = \sf\dfrac{P(Boy \cap Sophomore)}{P(Sophomore)}\\\\ & = \sf \dfrac{1}{37} \div \dfrac{10}{37}\\\\ & = \sf\dfrac{1}{37} \times\dfrac{37}{10}\\\\ & = \sf\dfrac{1}{10}\end{aligned}[/tex]
Answer:
1/10
Explanation:
Given Boy Sophomores: 1
Given Total Boy: 3 + 1 + 4 + 2 = 10
So
⇒ P(Boy|Sophomore)
⇒ Boy Sophomore/Total Boy
⇒ 1/10
3. The weight of cell phones is normally distributed. The mean weight of a sample of 300 cell phones is 112 grams, with a standard deviation of 2 grams. With a 95% confidence level, determine
the maximum error of estimate
18.99%
22.63%
1.31%
29.73%
The maximum error of estimate with a sample of 300 cell phones is 29.73%
Determining maximum error estimateThe formula for calculating the maximum error of the estimate is expressed as:
ME = √0.25/n
n is the total sample
Given the following parameters
n = 300
Substitute into the formula to have:
ME = √0.25/n
ME = √0.25/300
ME = 0.2973
ME = 29.73%
Hence the maximum error of estimate with a sample of 300 cell phones is 29.73%
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The weight of cell phones is normally distributed. The mean weight of a sample of 300 cell phones is 112 grams, with a standard deviation of 2 grams. With a 95% confidence level, determine
the maximum error of estimate
Answer:
29.73%
What are the domain and range of the function f(x) = 3x + 5
Step-by-step explanation:
Here,let x = 1,2,3 and 4
Then,
Domain =(1,2,3,4)
Again,
f(1)= 3*1 + 5
=3 + 5
=8
f(2)=3*2 + 5
=6 + 5
=11
f(3)=3*3 + 5
=9 + 5
=14
f(4)=3*4 + 5
=12 + 5
=17
Therefore, Range=(8,11,14,17)
What is the equation of the line that passes through the point(6,-2) And has an undefined slope
Answer:
X=6
Step-by-step explanation:
Josephine can correct her students' test papers in 9 hours, but if her teacher's assistant helps, it would take them 7 hours. How long, in hours and minutes, would it take the assistant to do it alone? (Write your answer in mixed units. Enter a zero in any unneeded blanks.)
Using the together rate, it is found that it would take the assistant 31 hours and 30 minutes to do it alone.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given as follows:
Josephine: 1/9.Assistant: 1/x.Together: 1/7.Hence:
[tex]\frac{1}{9} + \frac{1}{x} = \frac{1}{7}[/tex]
[tex]\frac{x + 9}{9x} = \frac{1}{7}[/tex]
[tex]9x = 7x + 63[/tex]
2x = 63
x = 31.5.
It would take the assistant 31 hours and 30 minutes to do it alone.
More can be learned about the together rate at https://brainly.com/question/25159431
can someone please help me out with this logarithm equation
[tex] \green{ - - - - - - - - - - - - - - - - - - }[/tex]
•— QUESTIONLogarithmic equation : log2 + log x = 1•— ANSWERThe answer is x = 5•— SOLUTIONlog¹⁰2+ log¹⁰ x = 1x >0log¹⁰2 + log¹⁰ x = 12x = 10[tex] \times \frac{10}{2} [/tex]x = 5•— Therefore, the answer is x = 5
[tex] \green{ - - - - - - - - - - - - - - - - - - }[/tex]
Tracy has 40 feet of material to make the perimeter of a rectangular sandbox for her little brother.
What rectangle with whole-number side lengths would give the sandbox with the greatest area?
Answer:
11 and 9
Step-by-step explanation:
With a width of 11 and a length of 9 the area of the rectangle would be
11 * 9 = 99
By adding 11 and 9, then mulitplying it by 2 we get the perimeter
11 + 9 = 20
20 * 2 = 40
A triangular swimming area is marked off by a rope.
a. If a woman swims around the perimeter of the swimming area, how far will she swim?
b. What is the area of the roped off section?
Δ perimeter of swimming area:
total length measure of all sides200√3 + 200√6 + 400 + 200( 200√3 + 200√6 + 600 ) m1436.3 mΔ area of roped off section:
1/2 base * height1/2 * (200+200√3)(200√3)20000√3 + 60000 m²94641 m²Can anyone help explaining step by step?
The height of a soccer ball in the air can be modeled by the equation h = -16t^2 +48f, where h is in feet of a ball that Cody kicks down the field.
How long is the ball in the air? (find the zeros).
What is the ball's max height? (find the vertex)
When will the ball reach its maximum height?
Answer:
3 seconds(0, 0), (3, 0)36 ft, (1.5, 36)Step-by-step explanation:
As the problem statement suggests, the question of time in the air can be answered by finding the zeros of the function. Similarly, the question of the ball's maximum height can be answered by finding the vertex. These findings are related by the fact that the vertex is on the line of symmetry, which passes through the midpoint between the zeros.
__
(a)The function can be factored as ...
h = -16t(t -3)
At any zero, one of the factors must be zero. (This is the "zero product rule.") The factors are zero for t=0 and for t=3.
The zeros are (0, 0) and (3, 0).
This tells you the height of the ball is zero initially (at t=0), and 3 seconds later (at t=3).
The ball is in the air for 3 seconds.
__
(b)The midpoint between the zeros is their average: (0 +3)/2 = 1.5. At that value of t, the ball will be at its maximum height.
The ball will reach its maximum height at t=1.5 seconds.
Using the above factored form to find the height, we get ...
h = -16(1.5)(1.5 -3) = 16(2.25) = 36 . . . feet
The ball's maximum height is 36 feet.
_____
Additional comment
The x-coordinate of the vertex of quadratic ax²+bx+c is found at the value ...
x = -b/(2a)
Here, that would be ...
t = -48/(2(-16)) = 3/2
__
A graphing calculator can answer all of these questions quite rapidly.
Please help me thank you so much!
Answer: the third one
Step-by-step explanation: how i know by guessing
A, B, C, D are points on a line.
AB = 1
BC = 2
CD = 4
Find the length of segment AD. Consider all possibilities.
So far, I've only gotten 7, 5, and 1. But I know there is one left. Can you guys help?
The points A, B, C and D are collinear points
The length of the segment AD is 7 units
How to determine the length AD?The given parameters are:
AB = 1
BC = 2
CD = 4
Because the points are on the same line, then the following is the possible equation
AD = AB + BC + CD
Substitute known values
AD = 1 + 2 + 4
Evaluate the sum
AD = 7
Hence, the length of the segment AD is 7 units
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Please help solve questions
Take some points
2x+3y<63y<-2x+6y<-2/3x+2As here < sign present line will be dashed and shading should be done below the line
So
(1,1)(1,0)(2,0)(-1,2)Graph attached
Answer:
Given inequality
[tex]\sf 2x + 3y < 6[/tex]
Rearrange to make y the subject
[tex]\sf \implies 2x + 3y < 6[/tex]
Subtract 2x from both sides:
[tex]\sf \implies 3y < -2x + 6[/tex]
Divide both sides by 3:
[tex]\sf \implies y < -\dfrac23x + 2[/tex]
When graphing inequalities
If the inequality sign is < or > then the line of the graph should be dashed.
If the inequality sign is ≤ or ≥ then the line of the graph should be solid.
If y < (less than) then the shading is below the line.
If y > (more than) then the shading is above the line.
Therefore, as the inequality is y < the line should be dashed and the shading should be below the dashed line.
To plot the line, substitute x = 0 and x = 3 into the equation:
[tex]\sf \implies -\dfrac23(0) + 2=2[/tex]
[tex]\sf \implies -\dfrac23(3) + 2=0[/tex]
Therefore, plot points (0, 2) and (3, 0). Draw a dashed straight line through the points. Shade below the dashed line.