Answer:
I reccommend using an AoPS book. You can learn more at aops.com
Step-by-step explanation:
Ivan put 500 000ISK (Icelandic Krona) and Blake put 700 000ISK into savings accounts
at different banks.
After 8 years, Ivan and Blake have the same amount of money in their accounts.
They both receive interest compounded quarterly and Blake has an annual interest rate
that is half of Ivan's annual interest rate.
Work out the annual interest rate that Blake receives.
Using compound interest, it is found that Blake receives an annual rate of 4.27%.
Compound interest:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
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.Ivan's parameters are given by:
Put 500 000 ISK, hence [tex]P = 500000[/tex]8 years, hence [tex]t = 8[/tex]Quarterly compounding, hence [tex]n = 4[/tex]Interest rate of r.Hence:
[tex]A_i(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A_i(t) = 500000\left(1 + \frac{r}{4}\right)^{32}[/tex]
[tex]A_i(t) = 500000(1 + 0.25r)^{32}[/tex]
Blake's parameters are given by:
Put 700 000 ISK, hence [tex]P = 700000[/tex]8 years, hence [tex]t = 8[/tex]Quarterly compounding, hence [tex]n = 4[/tex]Interest rate that is half of Ivan's, hence [tex]\frac{r}{2}[/tex]Thus:
[tex]A_b(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A_b(t) = 700000(1 + 0.125r)^{32}[/tex]
These amounts are equal, hence:
[tex]A_i(t) = A_b(t)[/tex]
[tex]500000(1 + 0.25r)^{32} = 700000(1 + 0.125r)^{32}[/tex]
[tex]\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32} = \frac{700000}{500000}[/tex]
[tex]\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32} = \frac{7}{5}[/tex]
[tex]\sqrt[32]{\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32}} = \sqrt[32]{\frac{7}{5}}[/tex]
[tex]\frac{1 + 0.25r}{1 + 0.125r} = \left(\frac{7}{5}\right)^{\frac{1}{32}}[/tex]
[tex]\frac{1 + 0.25r}{1 + 0.125r} = 1.01057023172 [/tex]
[tex]1 + 0.25r = 1.01057023172 + 0.12632127896r[/tex]
[tex]0.12367872103r = 0.01057023172 [/tex]
[tex]r = \frac{0.01057023172}{0.12367872103}[/tex]
[tex]r = 0.0854[/tex]
Blake's rate is:
[tex]\frac{r}{2} = \frac{0.0855}{2} = 0.0427[/tex]
Blake receives an annual rate of 4.27%.
A similar problem is given at https://brainly.com/question/24507395
How do you factor an expression to the 4 exponent.
Answer:
We can factor a difference of fourth powers (and higher powers) by treating each term as the square of another base, using the power to a power rule. For example, to factor x4 - y4, we treat x4 as (x2)2 and y4 as (y2)2. Thus, x4 - y4 = (x2)2 - (y2)2 = (x2 + y2)(x2 - y2) = (x2 + y2)(x + y)(x - y).
Answer: How do you factor variables with exponents? To do this, take the greatest common factor of the numbers and the smallest exponent of each variable. 2. Divide the original expression by the greatest common factor. To do this, divide the coefficients, and subtract the exponents of the variables.
Explanation: Expressions with fractional or negative exponents can be factored by pulling out a GCF. Look for the variable or exponent that is common to each term of the expression and pull out that variable or exponent raised to the lowest power. These expressions follow the same factoring rules as those with integer exponents.
Can someone solve 33 and 34 for me
Answer:
33. 320 (D)
34. 5 (A)
Step-by-step explanation:
33.
(14+3+3) x (10+3+3)
17+3 x 13+3
17x16
320
34.
P(28)=x+x+(x+4)+(x+4)
28=4x+8
-8 -8
20=4x
/4 /4
5=x
If you add the lengths of the focal radii of an ellipse, what other value will you produce?
Answer: the length of the major axis
Step-by-step found it on Quizlet and got it right on the quiz
If we add the lengths of focal radii of an ellipse the value of length of major axis will produce.
What is the major axis of an ellipse?
The major axis of an ellipse is the line segment connecting the two vertices.
Since, the sum of focal distances of a point on ellipse is constant.
And it is equals to the length of major axis.
Hence, if we add the lengths of focal radii of an ellipse the value of length of major axis will produce.
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Marco is working with the equation s=kw his teacher told him that’s a varies directly with w if Marco substitutes 300 for s and 60 for w which of the following would be valid
Answer:
S = kpq 280 = k(5)(7) 280 = 35k 8 = k
A group of 15 people are ordering pizza each person wants 2 slices and each pizza has 3 slices how many pizzas should they order
Answer:
Step-by-step explanation:
15*2=30
30/2=10
10 pizzas will evenly divide between 15 ppl and give each 2 slices with no extras.
Total number of pizzas will they order will be 10.
What are mathematics operations?
A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Here, it is given that :
A group of 15 people are ordering pizza each person wants 2 slices and each pizza has 3 slices.
Now, 15 person will eat = 15 x 2 = 30 slices of pizza
To Find the number of pizza divide total slice of pizza people wanted with slice per pizza :
number of pizza = 30/3 = 10 pizza.
Therefore, total number of pizzas will they order will be 10.
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2+4=? what does ? equal?
Answer:
= 6
Step-by-step explanation:
2+4 = 6
hope this helps.
ANSWER :
2+4 = 6
Step-by-step explanation:
Thanks for free point lol
Which of the following can be the sides of a right angled triangle?
(i) 1.5 cm, 2 cm, 3 cm (ii) 6 cm, 1.1 cm, 6.1 cm
Answer:
(ii) 6 cm, 1.1 cm, 6.1 cm
Step-by-step explanation:
Knowing that all right triangles obey the Pythagorean Theorem, we can test both sets of numbers. The longest of the 3, the hypotenuse, is substituted to the c value of the equation a^2 + b^2 = c^2. If the equation is still true after substituting and simplifying both sides, that combination of triangle lengths is the correct answer. In this case, 6^2 + 1.1^2 and 6.1^2 are both equal to 37.21, so the second set is correct.
PLEASEEE HELPPP ASAPP!!!!
Answer:
i gauth math NYU po meron yan
What is the sale price?
30 pts
Answer:
Sales Price = $8.75
Step-by-step explanation:
Original Price - Discount = Sale Price
=> 12.50 - 3.75 = Sales Price
=> Sales Price = $8.75
Hoped this helped.
Jayden’s rectangular garden is 5 3/4 feet long and 4 1/2 feet wide. What is the area, in square feet, of the garden
Answer:
The area is 25.875 square feet. Or it can be written as [tex]25\frac{7}{8}[/tex]
Step-by-step explanation:
You would simply multiply them by each other. 5 3/4 is aso 5.75. And 4 1/2 is also 4.5. So simply multiply 5.75 by 4.5
5.75*4.5 to get 25.875
On August 19, 2002, the ratio of stocks gaining value on the New York Stock
Exchange to stocks losing value was about 43 to 20. If 869 stocks lost value, how
many gained?
A)892
B)1953
C)1797
D)1868
Answer:
D: 1868
Step-by-step explanation:
43:20 ratio
43/20 = 2.15
869 * 2.15 = 1,868.35
round down to nearest whole number
1,868
Fave food. THIS IS FOR A GRAPH, PLEASE JUST COMMENT.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answer:
x2 + (y – 3)2 = 36
x2 + (y + 8)2 = 36
Step-by-step explanation:
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,
⇒ x² + (y - 3)² = 36
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Since, The standard form for finding the equation of a circle is expressed as;
⇒ (x - a)² + (y - b)² = r²
where;
(a, b) is the center of the circle
And, r is the radius of the circle
Given that;
Diameter = 12 units
And, Radius = 12/2 = 6 units
If the center lies on the y-axis, the center will be at (0, 3)
Substituting into the formula, we will have;
⇒ (x - 0)² + (y - 3)² = 6²
⇒ x² + (y - 3)² = 36
Thus, The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,
⇒ x² + (y - 3)² = 36
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In total there are 53,444 adults at a football match there are 4300 more women then men at the match how many men are at the match
Answer:
There are 24,572 men.
Step-by-step explanation:
Let men = m, let women = w.
m + w = 53,444
w = 4300 + m
m + (4300 + m) = 53,444
m + m + 4300 = 53,444
2m + 4300 = 53,444
2m = 53,444 - 4300
2m = 49144
m = 49144/2
m = 24,572
solve the system {2x+y=8 using substitution method.
{x-y=6 using elimination method
please answer my question
Answer:
y = -4/3
x = 14/3
Step-by-step explanation:
2x+y=8
x-y=6
First of all, we need the same coefficient, so we can make both of these 2x by multiplying the second one by 2.
2x+y=8
2x-2y=12
Then we need to subtract equation 1 from 2.
3y=-4
Solve normally
y = -1.33333 / -4/3
Substitute
x - (-4/3) = 6
x = 14/3
[tex]\large\huge\green{\sf{Answer:-}}[/tex]
[tex] \red {\mathbb{ \underline { \tt by \: elimination \: method \: s}}}[/tex]
2x+y=8________(i)x-y=6_________(ii)from equation (i):-
[tex]2x - y = 8 \\ x = \frac{8 - y}{2} [/tex]
put value of x in eq (ii)[tex]x - y = 6 \\ \frac{8 - y}{2} - y = 6 \\ \frac{8 - y - 2y}{2} = 6 \\ 8 - y - 2y = 12 \\ 8 - 3y = 12 \\ - 3y = 12 - 8 \\ - 3y = 4 \\ y = \frac{ - 4}{3} [/tex]
put value of y in eq (i)[tex]2x + y = 8 \\ 2x + ( \frac{ - 4}{3} ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ \frac{6x - 4}{3} = 8 \\ 6x - 4 = 8 \times 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = \frac{14}{3} [/tex]
now,
By elimination method:-[tex]2x + y = 8 \\ x - y = 6 \\ - - - - - - - \\ multiply \: eq \: (i) \: by \: 1 \\ and \: eq(ii) \: by \: 2 \\ \\ (2x + y = 8) \times 1\\ (x - y = 6) \times 2 \\ - - - - - - - \\2x + y = 8 \\ 2x - 2y = 12 \\ subtract \: these \\ 3y = - 4 \\ y = \frac{ - 4}{3} \\ [/tex]
put value of y in equation (i)
[tex]2x + y = 8 \\ 2x + ( \frac{ - 4}{3} ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ \frac{6x - 4}{3} = 8 \\ 6x - 4 = 8 \times 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = \frac{14}{3} [/tex]
What is the sale price of a $825 tablet that has a 1/4 discount
Answer:
206.25
Step-by-step explanation:
825/2=412.5
412.5/2=206.25
How would you solve for x and y and what are x and y? Not sure what to do.
Answer:
x = 26 2/3
y = 50
Step-by-step explanation:
you could set '2y-3x' equal to '-3x+y+50' because they are vertical angles
2y - 3x = -3x + y + 50
add 3x to each side to get:
2y = y + 50
y = 50
also, we know that (1/2y + 25) + (2y - 3x) = 180 because they form a straight line
3/2y + 25 - 3x = 180
subtract 25 from each side to get:
3/2y - 3x = 155
substitute 50 for 'y' to get:
3/2(50) - 3x = 155
75 - 3x = 155
-3x = 80
x = 26 2/3
Trust Officer Megan is the trust officer for an estate. If she
invests $15,000 into an account that carries an interest rate
of 8% compounded monthly, how long will it be until the
account has a value of $45,000 for Megan's client?
a
Answer:
????????
Step-by-step explanation:
i don't know if I can help with the subject line
Help me please with this question
Paul was thinking of a number.Paul doubles it and gets a answer of 13.1.What was the orginal number?
Answer:
See below:
Step-by-step explanation:
So first, Paul has a number that he got before he multiplied it, we can call that [tex]p[/tex], and for his answer after doubling it. we'll call it [tex]n[/tex].
So with this information, we know that [tex]n=13.1[/tex] so we can use that to make an equation.
[tex]p*2=n\\p*2=13.1[/tex]
We can solve it by first dividing on both sides and getting our answer.
[tex]p=\frac{13.1}{2} \\p=6.55[/tex]
Cheers! We get our final answer of 6.55.
The bearing of a point Q from a point P is 048 degree. find the bearing of P from Q.
Answer:
Vector PQ = 48 deg
Vector QP = -PQ = 48 + 180 = 228 deg
Note that 228 is 48 deg below the -x (180) axis
What is a trend line in math.
Answer:
Determining if a set of points exhibits a positive trend, a negative trend, or no trend at all.
A trend line, often referred to as a line of best fit, is a line that is used to represent the behavior of a set of data to determine if there is a certain pattern.
CAN SOMEONE HELP ME PLEASE ASAP!
Answer:
15lb
Step-by-step explanation:
1lb=453.59
Model with Math The 46 golf balls in Stavin's
golf bag have 15,180 dimples on them. Each
golf ball has the same number of dimples,
Use the bar diagram to write and solve an
equation to find the number of dimples on
each ball in Stavin's bag,
Answer:
Step-by-step explanation:
divide 15,180 and 46=330 dimples on each ball
Type your number answer in decimal form. Do not round.
0.6 kilograms = _______ grams.
0.6 KL = 600 grams
you can always use the ladder method
The mean age of 5 people in a room is 39 years. A person enters the room. The mean age is now 36. What is the age of the person who entered the room?
Answer:
21
Step-by-step explanation:
Mean is the average of the objects
With five people, the mean is the average age of these people so what did you divide 5 into to get 39.
5 × 39 = 195
After a person enter the room, total 6 in the room with a mean of 36.
6 × 36 = 216
Now the age of the person who entered the room 216 - 195 = 21
Corinne made apple jam and strawberry jam. She made enough apple jam to
fill 1 jars. If she made 3 times as much strawberry jam as apple jam, how
many jars will the strawberry jam fill?
Answer:
3
Step-by-step explanation:
1 ×3 =3
apple jam times strawberry
Prize Pooches charges a flat monthy lee or $22, plus $3.65 per hour. Daring Dogs
charges a flat monthly fee of $25, plus $3.40 per hour. After how many hours of
training, h, will Prize Pooches cost more than Daring Dogs?
A)h < 12
B)h = 12
C)h > 12
D)h> 0.75
Answer:
C.) H> 12
Step-by-step explanation:
1. At 12 hours Prize pooches has a total of $65.8
at Daring dogs it's rate is also $65.8.
2. Anything greater than 12 hours though, Prize pooches starts to have a higher total.
Could a circle have both a diameter of 7.2 inches and a circumference of 28 inches?
Answer:
no if the diameter was 7.2 inches the circumstance would be 22.62 :)