Answer:
The final balance is $10,792.14.
The total compound interest is $2,792.14.
Step-by-step explanation:
Final answer:
Explanation on calculating the amount of $8000 principal at 5% compounded annually after 6 years using compound interest formula.
Explanation:
The question: $8000 principal earning 5% compounded annually after 6 years.
Step-by-step explanation:
Use the compound interest formula: A = P(1 + r/n)^(nt) where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.
Plug in the values: P = $8000, r = 0.05, n = 1 (compounded annually), t = 6.
Calculate: A = $8000(1 + 0.05/1)^(1*6)
A = $10,720.77.
find the value of two numbers if their sum is 11 and the difference is 3
Answer:
7
4
Step-by-step explanation:
7+4=11
7-4=3
To find the value of two numbers if their sum is 11 and the difference is 3, we can use a system of equations. The two numbers are 7 and 4.
Explanation:To find the value of two numbers if their sum is 11 and the difference is 3, we can use a system of equations.
Let's call the two numbers x and y. We can set up the following equations:
x + y = 11
x - y = 3
Now we can solve this system of equations by adding the two equations together:
(x + y) + (x - y) = 11 + 3
Simplifying, we get:2x = 14
Dividing both sides by 2, we get:x = 7
Now we can substitute this value of x back into one of the original equations to solve for y:7 + y = 11
Subtracting 7 from both sides, we get:y = 4
So, the two numbers are 7 and 4.
A rectangle has side lenghs X +2 and 3X -1 write an expression that represents the perimeter of the rectangle then simplify the expression
Answer: Perimeter = 2(L + W) and
as a simplified expression is, 8x + 2
Step-by-step explanation: The length is represented by L and the width is represented by W in the expression above.
However, since we have been given the sides of the rectangle as x + 2 and 3x - 1, we shall substitute for the values of these in the expression representing the perimeter.
2(L + W) can now be written as
2( {x + 2} + {3x - 1} )
2(x + 2 + 3x - 1)
By collecting like terms, we now have
2(4x + 1)
8x + 2.
The expression can now be simplified as 8x + 2
As part of his retirement strategy, John plans to invest $210,000 in two different funds. He projects that the moderately high risk investments should return, over time, about 9% per year, while the low risk investments should return about 4% per year. If he wants a supplemental income of $11,400 a year, how should he divide his investments?
To achieve a supplemental income of $11,400 a year, John should allocate approximately $145,230 to the moderately high-risk investment and approximately $64,770 to the low-risk investment.
Explanation:To divide his investments and achieve a supplemental income of $11,400 a year, John can allocate a portion of his funds to the moderately high-risk investment and the remaining portion to the low-risk investment. Let's calculate the amounts:
Calculate the amount invested in the moderately high-risk investment:Therefore, John should allocate approximately $145,230 to the moderately high-risk investment and approximately $64,770 to the low-risk investment.
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what is the solution to this equation x-9=17
Answer:
26
Step-by-step explanation:
you add 17+9 and get 26.
Boden conjectures that in a right triangle, the sine of one acute angle is always equal
to the cosine of the other acute angle. Is Boden's conjecture correct? Choose the best
answer.
Answer:
Boden's conjecture is correct
Step-by-step explanation:
we know that
If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa.
A right triangle, has two acute angles.
The two acute angles are complementary
so
In any right triangle, the sine of one acute angle is equal to the cosine of the other acute angle
therefore
Boden's conjecture is correct
Answer:
Yes, because the leg opposite one of the acute angles is adjacent to the other acute angle
Step-by-step explanation:
What is the solution set of the quadratic inequality 6x2+1 <0?
o {x|x€ R}
Answer:
In my opinion i think ur answer would be: B
3a + 3b is equivalent to 3(a + 2b).
A true
B false
Answer:
B-false
Step-by-step explanation:
It is false because where the 2 is, has to be 3, other wise it won't make sense. Because it will not equal the same thing.
Final answer:
The expression 3a + 3b is not equivalent to 3(a + 2b). The first results in 3a + 3b, while applying the distributive property to the second expression gives 3a + 6b, clearly showing the expressions are different.
Explanation:
The statement 3a + 3b is equivalent to 3(a + 2b) is false. To show this, we can apply the distributive property of multiplication over addition, which states that for any real numbers a, b, and c, a · (b + c) = a·b + a·c. Using this property, we can expand 3(a + 2b) to get 3·a + 3·2b, which simplifies to 3a + 6b. This is not the same as 3a + 3b since 3b is not equal to 6b. Therefore, the expressions are not equivalent.
What is 85 divided by 4?
Answer:
Decimal form: 21.25
Mixed number: 21 1/4
Exact form: 85/4
What is the output, or dependent variable or
quantity?
X
f(x)
Y
Answer:
y or f(x), depends on the context.
Step-by-step explanation:
When graphing a function, we input a value, x, and output a value, y. This is why we have a coordinate plane.
For example, if we have y = 2x and x=2, our input, then y = 4, our output.
However, if written in function notation, f(x) = 2x, our output will still be 4, except that our output is f(x)
Answer:
f(x)
Step-by-step explanation:
1 3/4 + 1/6 + blank =7 1/2
Answer:
5 7/12
Step-by-step explanation:
7/4 + 1/6 +x = 15/2
Lowest Common denominator =12
21/12 + 2/12 + x = 90/12
23/12 +x= 90/12
x= 90-23 = 67/12 = 5 7/12
A card is drawn at random from a pack of 52 playing cards. Given that the card is a diamond, find the probability that the card is a King. Give your answer as a fraction in its simplest form.
================================================
Explanation:
Focus only on the diamond cards. There are 13 of them total. Out of the 13 diamond cards, there is one king of diamonds. So the probability of getting a king, if we know 100% the card is a diamond, is 1/13.
---------------
You can use a slightly longer method through a conditional probability
A = card is a king
B = card is a diamond
P(A and B) = probability of king and diamonds = 1/52
P(A \ B) = probability of event A happens given we know B happens
P(A \ B) = P(A and B)/P(B)
P(A \ B) = (1/52)/(13/52)
P(A \ B) = (1/52) ÷ (13/52)
P(A \ B) = (1/52) * (52/13)
P(A \ B) = 1/13
The probability that the card is a King is 1/13
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome
Given that a card is drawn at random from a pack of 52 playing cards, the total outcome is 52
If the card is a king, the expected outcome is 4
Pr(selecting a king) = 4/52 = 1/13
Hence the probability that the card is a King is 1/13
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Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n)=5+(n-1)(1/6)
Answer:
First term: A(1) = 5
Fourth term: A(4) = 5 1/2
Tenth term: A (10) = 6 1/2
Step-by-step explanation:
Let's find the first, fourth and tenth terms of the arithmetic sequence described by the given rule:
A(n) = 5 + (n-1) (1/6)
First term:
A(1) = 5 + (1-1) (1/6)
A(1) = 5 + (0) (1/6)
A(1) = 5
Fourth term:
A(4) = 5 + (4-1) (1/6)
A(4) = 5 + (3) (1/6)
A(4) = 5 + 3/6 = 5 3/6 = 5 1/2 (simplifying)
Tenth term
A(10) = 5 + (10-1) (1/6)
A(10) = 5 + (9) (1/6)
A (10) = 5 + 9/6 = 6 3/6 = 6 1/2 (simplifying)
The current rates for an 80/20 mortgage are 4.25% for the first mortgage and
9.75% for the second mortgage. On a $100,000 30-year mortgage, what is the
actual rate?
The actual rate of the mortgage is 5.27%.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Since, we're taking two mortgages for a total of $100,000 for 30 years,
Now, we can find the actual rate of the mortgage by finding the weighted average of the two rates.
Hence, The weights in this case will be the proportion of loan taken at each rate;
We have
Rates Weights Rates × Weights
4.15 0.80 4.15 x 0.80 = 3.32
9.75 0.20 9.75 x 0.20 = 1.95
Hence, The actual rate of the mortgage is,
⇒ 3.32 + 1.95
⇒ 5.27%.
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Answer:
mine was 5.45$
Step-by-step explanation:
[Image Attached] Which equation is equivalent to 4^x+3=64
Answer: 2^2x+6 = 2^6
Explanation:
looking at the right of the equal since we can see:
64 is the same as 4^3
but since that answer isn't shown in the multiple choice but we can notice that 64 is the same as 2^6
Now that we know the left side is 2^6 we can see there is similar an answer in the multiple choice. But let's double check that the right side is the same.
Its pretty simple, just make 4 into 2^2 then distribute the exponent of 2 (times the 2 in the exponent to the rest to x+3)
2^2(x+3)
2^2x+6
Answer:
Option B
Step-by-step explanation:
The other guy is correct I'm just making it simpler on edge people. :>
Is there a triangle that has a greater area than its perimeter?
Answer:
no
...
...
...
....
shajajs
Answer:
NO
A= 1/2 x B x H
P= A+B+C
Step-by-step explanation:
ex: triangle side 13, 6,8.5
high: 8
A= 52
P= 27.5
What is d,the common difference,in the arithmetic sequence 100,98,96,94,92...?
Answer: he is right the answer is -2
Step-by-step explanation:
The common difference (d) is -2.
In an arithmetic sequence, the common difference (d) is the constant value by which each term differs from the previous term.
To find the common difference in the sequence 100, 98, 96, 94, 92..., we can observe the difference between consecutive terms:
98 - 100 = -2
96 - 98 = -2
94 - 96 = -2
92 - 94 = -2
We see that each term is decreasing by 2. Therefore, the common difference (d) is -2.
What geometric shape best describes the sun? triangular prism cube cylinder sphere
Answer:
A sphere.
Step-by-step explanation:
The sun is a sphere.
The best geometric shape to describe the Sun is a sphere, as it appears as a circular disc in the sky and fits with observational data and theoretical models of its structure and the Earth's orbit around it.
Explanation:When considering the geometric shape that best describes the Sun, we assess its physical appearance and symmetry. The Sun is often depicted in diagrams as having a perfectly round, spherical shape, which aligns with our observations, as it appears as a circular disk in the sky. A sphere is a three-dimensional object where every point on the surface is the same distance from the center, which closely matches the Sun's observed shape. Unlike a triangular prism, cube or cylinder, a sphere has no edges, vertices, or faces, which makes it the best match for the Sun's shape.
Moreover, observations about the Sun, like those represented in figures discussing its structure as well as the Earth's orbit around the Sun, support the description of the Sun as being spherical. The orbit of the Earth itself is very close to a circle, which assumes central body - the Sun - of spherical form to exert a uniform gravitational pull. Additionally, the celestial sphere concept, although now known to be an incorrect model for the universe, also envisions stars, including our Sun, as points on a vast imaginary sphere, once more alluding to the spherical structure of these celestial bodies.
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Mick the monkey had 10 bananas he ate two fifth of them Mikey the monkey also had 10 bananas and he ate half of them which monkey ate more bananas step by step please
Answer: mikey ate more
Step-by-step explanation: mick ate 2/5 which is 4 out of ten mikey ate half which is 5 out of 10 so mikey ate more
brainliest plz
Final answer:
Mikey the monkey ate more bananas than Mick, consuming 5 compared to Mick's 4 bananas.
Explanation:
Let's calculate how many bananas each monkey ate. We'll start with Mick the monkey, who had 10 bananas and ate two fifths of them.
Calculate two fifths of 10 bananas: (2/5) × 10 = 4 bananas.
Mick therefore ate 4 bananas.
Now, let's calculate for Mikey the monkey, who also had 10 bananas and ate half of them.
Calculate half of 10 bananas: (1/2) × 10 = 5 bananas.
Mikey ate 5 bananas.
Mikey the monkey ate more bananas than Mick because 5 is greater than 4.
About 42% of a paint mix is white. A painter orders 18 gallons of paint mix. How much of it is white
Answer:
7.56 liters
Step-by-step explanation:
Total amount of paint mix ordered by the painter = 18 gallons
42% of the paint mix is white.
Representing this as a fraction, [tex]\[\frac{42}{100}\] [/tex] of total paint mix is white.
To find the amount of white paint, we need to multiply this fraction with the total amount of paint mix.
[tex]\[= \frac{42}{100} * 18\] [/tex]
[tex]\[= \frac{756}{100}\] [/tex]
[tex]7.56 liters[/tex]
Which group of three side lengths will form a triangle?
A. 11, 5, 4
B. 22, 17, 14
C. 28, 15, 10(maybe this)
D. 30, 15, 14
Answer:
D.30,15,14
Step-by-step explanation:
Solve for x in each problem 4x +2=42
Answer:
x = 10
Step-by-step explanation:
Given
4x + 2 = 42 ( subtract 2 from both sides )
4x = 40 ( divide both sides by 4 )
x = 10
Answer:
Step-by-step explanation:
4x+2=42
4x=42-2
4x=40
x=40/4
X=10
Alex paid $17,520 for a new car.he will make equal payments each month for 4 years. What will be Alex’s monthly car payments?
Answer:
$365.00
Step-by-step explanation:
4 years times 12 months equals 48 months.
$17520.00 / 48=$365.00
1. Find the geometric mean of 162 and 8.
46
Step-by-step explanation:
Geometric mean
[tex]= \sqrt{162\times 8}\\
=\sqrt{1296} \\
=36 [/tex]
Harper went into a movie theater and bought 10 bags of popcorn and 6 drinks,
costing a total of $79. Damian went into the same movie theater and bought 3 bags of
popcorn and 5 drinks, costing a total of $36.50. Write a system of equations that
could be used to determine the price of each bag of popcorn and the price of each
drink. Define the variables that you use to write the system.
Answer:
The price of a drink = $4
The price of a bag of popcorn = $5.5
Step-by-step explanation:
Let p represent popcorn and d represent drink
Harper bought 10 bags of popcorn and 6 drinks and paid $79 ➡ 10p + 6d = $79
Damian bought 3 bags of popcorn and 5 drinks and paid $36.50 ➡ 3p + 5d = $36.50
Now multiply first equation by -3 and second equation by 10
-3 × (10p + 6d) = $79 ➡ -30p - 18d = -$237
10 × (3p + 5d) = $36.50 ➡ 30p + 50d = $365
Now add the new equationd
30p + 50d -30p - 18d = $365 - $237 (-30p will eliminate 30p)
32d = $128 divide both sides of the equation by 32
32 ÷ 32d = 32 ÷ $128 ➡ d = 4
If d = 4 that means a drink costs $4 we can use this information to find the price of a bag of popcorn
3p + 5d = $36.50 (replace d with 4)
3p + 4×5 = $36.50
3p + 20 = $36.50
3p = $36.50 - 20
3p = 16.50 divide both sides by 3
p = $5.5
The question asked to set up a system of equations to determine the price of each bag of popcorn and each drink. Using the variables x and y to represent the price of popcorn and drinks respectively, the system of equations based on the information given is 10x + 6y = $79 and 3x + 5y = $36.50.
Explanation:To solve this problem, we need to setup a series of equations based on the information given. Let's say:
x is the price of each bag of popcorny is the price of each drinkAccording to the first scenario with Harper, we get:
10x + 6y = $79
From Damian's shopping, we have:
3x + 5y = $36.50
This gives us the system of equations which can be used to find individual prices of a bag of popcorn and a drink.
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Simplify (4х – б) + (5х + 1)
Step-by-step explanation:
[tex]9x {}^{2} + 4x - 30x - 6[/tex]
[tex]9 {x}^{2} - 26x - 6[/tex]
Answer: 9x-5
Step-by-step explanation:
Combine like terms
Which of the following are solutions to the quadratic equation below?
Check all that apply.
X2 + 7x=8
The solutions to quadratic equation are x = 1 and x = -8
Solution:
Given quadratic equation is:
[tex]x^2+7x = 8\\\\x^2 + 7x-8 = 0[/tex]
We have to find the solutions of equation
[tex]\mathrm{Quadratic\:Equation\:Formula:}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{Compare the given } x^2 + 7x - 8 = 0 \text{ with } ax^2 + bx + c = 0\\\\We\ get\\\\a = 1\\\\b = 7\\\\c = -8[/tex]
[tex]x=\frac{-7\pm \sqrt{7^2-4\cdot \:1\left(-8\right)}}{2\cdot \:1}\\\\x =\frac{-7 \pm \sqrt{7^2+4\cdot \:1\cdot \:8}}{2\cdot \:1}\\\\x = \frac{-7 \pm \sqrt{49 + 32}}{2}\\\\Simplify\ the\ equation\\\\x = \frac{-7 \pm \sqrt{81}}{2}\\\\x = \frac{-7 \pm 9}{2}[/tex]
Thus we get two solutions:
[tex]x = \frac{-7+9}{2} \text{ and } x = \frac{-7-9}{2}\\\\x = 1 \text{ and } x = -8[/tex]
Thus the solutions to quadratic equation are x = 1 and x = -8
what is 7/21 in simplest form
Answer:
1/3
Step-by-step explanation:
simplifying fractions can be easy.
In this case you just need to find a common number.
The common number between 7 & 21 just happens to be 7.
7 goes into 7 one time.
7 goes into 21 three times.
Therefore the answer is 1/3.
I hope this was helpful!
order of operation 36divided4+11x8
The answer for 36/4 + 11 [tex]\times[/tex] 8 = 97.
Step-by-step explanation:
The order of operation is done by using BODMAS rule.
B - bracket
O - of
D - division
M - multiplication
A - addition
S - subtraction
step 1 :
36 divided 4 + 11 [tex]\times[/tex] 8
The division operation must be done first.36/4 = 9step 2 :
9 + 11 [tex]\times[/tex] 8
After division, multiplication should be done next.11 [tex]\times[/tex] 8 = 88step 3 :
9 + 88
Finally addition is performed to get the answer.9 + 88 = 97∴ The answer for 36divided4+11x8 is 97.
Please help me. Thanks
Answer:
3.25 +7.25m
Step-by-step explanation:
The cost of membership in Jump Rope Gym can be modeled by ...
total cost = initial fee + m × (monthly fee)
j = 6.50 +17.50m
Likewise, the cost for Run Run Run Gym is ...
r = 9.75 +24.75m
Then the savings by joining the Jump Rope Gym is ...
r -j = (9.75 +24.75m) -(6.50 +17.50m) = 3.25 -7.25m . . . .savings
When D is divided by 15, the result is 6 with a remainder of 2.what is the remainder when D is divided by 6?
When number D (which is 92) is divided by 6, the remainder is 2.
Explanation:Based on the information given, when D is divided by 15, the result is 6 with a remainder of 2, so we can express D as 15*6 + 2 = 92. Now let's find out what happens when D (92) is divided by 6. When we do, we find that 92 divided by 6 gives us 15 with remainder 2. So, the remainder when D is divided by 6 is 2.
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