The sum of the capitals would be $530400.
What is the formula to calculate the simple interest?The formula to calculate the simple interest is -
I = PRT/100
Given is that a capitalist has two capitals that differ in $221,000. The largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces.
We can write the amount produced by largest as -
A = P(1 + rt)
A = 221000(1 + 0.2 x 3)
A = 221000 x 1.6
A = 353600
Amount generated by smallest -
a = 353600/2
a = 176800
Their sum would be -
A + a = 530400
Therefore, the sum of the capitals would be $530400.
To solve more questions on simple interest, visit the link below
https://brainly.com/question/25845758
#SPJ9
{Question in english -
A capitalist has two capitals that differ in S/. 221,000, the largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces. Find the sum of the capitals.}
hilary was examining the differences between perfect squares of numbers separated by 5. She made the following conjecture the differences always have the digit 5 in the ones place. for example: 17^2 - 12^2 = 289 -144 = 145
State another example that supports hilary's cpnjecture?
The another example that supports Hilary's conjecture are, 26² - 21²
What is subtraction?In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.
For example, if we take 4 pencils out of 10 then remaining pencils are 6
so this process is called subtraction.
Given that,
Hilary was examining the differences between perfect squares of numbers separated by 5.
The differences always have the digit 5 in the ones place.
Another example that supports Hilary's conjecture is:
= 26² - 21²
= 676 - 441
= 235
As we can see, the difference between the perfect squares of 26 and 21 is 235,
which ends in the digit 5 in the ones place, confirming Hilary's conjecture that the differences between perfect squares of numbers separated by 5 always have the digit 5 in the ones place.
To know more about subtraction check:
https://brainly.com/question/24326464
#SPJ9
Welding A welder finds that 2.1 cu ft of acetylene gas is needed to make one bracket. How much gas will be needed to make 27 brackets?
56.7 cubic feet of acetylene gas will be needed to make 27 brackets.
What is Total price?
In order to calculate the total price of something is by using this formula. Purchase Price = Cost Price + Margin.
To find out how much gas will be needed to make 27 brackets, we need to multiply the amount of gas required for making one bracket by the number of brackets to be made.
So, the total amount of gas needed to make 27 brackets would be:
2.1 cu ft * 27 = 56.7 cu ft
Therefore, 56.7 cubic feet of acetylene gas will be needed to make 27 brackets.
To know more about Total price visit,
https://brainly.com/question/29327002
#SPJ1
Write an equation for the polynomial graphed below
The equation of the polynomial is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2
How to determine the equation of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -3 A root of multiplicity 1 at x = -2A root of multiplicity 1 at x = 1A root of multiplicity 2 at x = 3y-intercept = 2A polynomial is represented as
P(x) = a * (x - zero)^multiplicity
Using the above as a guide, we have the following:
P(x) = a * (x + 3)(x + 2)(x - 1)(x - 3)^2
The y-intercept is 2
So, we have
a * (0 + 3)(0 + 2)(0 - 1)(0 - 3)^2 = 2
This gives
a = -1/27
Hence, the expression is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2
Read more about polynomial at
brainly.com/question/7693326
#SPJ1
Use interval notation to write the intervals over which fis (a) increasing, (b) decreasing, and (c) constant.
f is increasing on (-infty, -4) and (2,infty) since that's where you'd be walking uphill.
f is never decreasing.
f is constant on (-4,2), since that's where it's completely flat.
What is the correct answer answer asap for brainlist
According to the information, it can be inferred that the option that the quote explains is: The outcome... is situational irony because the opposite of what was expected is what happening.
How to identify the correct option that explains the quote?To identify the correct option that explains the quote we must read the text carefully and the options. Once we have read and understood this information, we can infer which option explains the quote.
In accordance with the above, option A would be the one that explains the quote because options B and C by discarding are fragments of the quote. So these fragments could not explain the same quote that is being used in the text. On the contrary, the paragraph of option A does explain the situation clearly.
Learn more about citation in: https://brainly.com/question/30066031
#SPJ1
Find the 66th
term in the following
arithmetic sequence
-92, -85, -78, -71, ...
Answer:
The [tex]66[/tex]th term is [tex]363[/tex].
Step-by-step explanation:
To find the [tex]n[/tex]th term, the formula is [tex]7n - 99[/tex]. Since we want to find the [tex]66[/tex]th term, we can plug [tex]n[/tex] for [tex]66[/tex]. So our expression is now [tex]7 \cdot 66 - 99 =[/tex] [tex]66[/tex]th term. Solving this we have
[tex]462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\[/tex]. Therefore, the [tex]66[/tex]th term is [tex]\boxed{363}[/tex].
Answer:
a₆₆ = 363
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then
a₆₆ = - 92 + (65 × 7)
= - 92 + 455
= 363
please help!!!!!!!!!
Answer:
yes
Step-by-step explanation:
2*(4+7) = ( 2 * 4 ) + ( 2 * 7 )
Write the first five terms of the arithmetic sequence. Find the common difference d and write the nth term of the sequence as a function of n.
a1
= 300, ак + 1 = ак - 20
The first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20
What is arithmetic sequence?An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.
Given is an arithmetic sequence, [tex]a_{k+1} = a_k-20[/tex] and [tex]a_1 = 300[/tex],
we need to find the first five terms,
a₂ = a₁-20
a₂ = 300-20
a₂ = 280
a₃ = a₂-20
a₃ = 260
a₄ = a₃ - 20
a₄ = 240
a₅ = a₄ - 20
a₅ = 220
aₙ = aₙ₊₁ - 20
d = 20
Hence, the first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20
Learn more about arithmetic sequence, click;
https://brainly.com/question/15412619
#SPJ1
Find the value of x
Answer:8
Step-by-step explanation:
Because Angle GJH is 90 degrees, Angle HJZ is also 90 degrees. (Because all right angles are 90 degrees)
Now, find Angle WJZ
90 - 18 = 72 degrees
By the Vertical Angles Theorem, Angle GJL is congruent to Angle ZJW
Now solve for x
72 = 9x
x = 8
You want to put a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden. The dirt store only sells topsoil by the cubic yard. How many cubic yards of topsoil will you need to order to fill this garden?
To fill a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden, you will need 79.33 cubic yards.
How is the volume determined?The volume is the product of the multiplication of the thickness, length, and width.
The thickness of the topsoil = 6 inches
12 Inches = 1 Feet
6 inches = 0.5 Feet (6/12)
The length of the garden = 28 feet
The width of the garden = 17 feet
The thickness of the soil = 0.5 feet
Volume of the topsoil = 28 x 17 x 0.5
= 238 ft³
3 Feet to 1 Yard
238 ft³ = 238/3 yards
= 79.33 cubic yards
Learn more about determining the volume at https://brainly.com/question/1972490
#SPJ1
Solve 4 x + 16 = y for x if y = 35
Answer:
Below
Step-by-step explanation:
So you have this:
4x + 16 = 35 subtract 16 from both sides of the equation
4x = 19 Divide by 4
x = 19/4
Answer:
The value of x is
[tex]x = 4.75[/tex]
Step-by-step explanation:
Greetings!!!
Given expression [tex]4x + 16 = y[/tex]Thus, the value of y is given as 35, substitute known value of y in expression and solve for x.
[tex]4x + 16 = 35[/tex]
Move the constant to the right
[tex]4x = 35 - 16 \\ 4x = 19[/tex]
Divide both sides of the expression by 4
[tex] \frac{4x}{4} = \frac{19}{4} [/tex]
solve
[tex]x = \frac{19}{4} [/tex]
or
[tex]x = 4 \frac{3}{4} [/tex]
or
[tex]x = 4.75[/tex]
Hope it helps!!!
can you please please please help me w this question!!! 40 points!!
The points K (1,3), L(-4,-3), M (2,-8), and N (7,-2) form quadrilateral KLMN. Where would these points be on the graph?
The location of the points for quadrilateral KLMN have been plotted in the graph shown in the image attached below.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapezoidNext, we would use an online graphing calculator to construct (plot) quadrilateral KLMN on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral KLMN on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a parallelogram.
Read more on quadrilateral here: brainly.com/question/6561516
#SPJ1
A rectangular pool has an area of 640 square feet. The length is 12 feet shorter than the width. The length of the pool is response area feet and the width of the pool is response area feet.
Let's assume the width of the rectangular pool is w. According to the problem, the length of the pool is 12 feet shorter than the width, so the length can be represented as w - 12.
The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. We know that the area of the pool is 640 square feet, so we can set up the equation:
A = L x W
640 = (w - 12) x w
Simplifying the equation:
640 = [tex]w^{2}[/tex] - 12w
[tex]w^{2}[/tex] - 12w - 640 = 0
We can solve for w by using the quadratic formula:
w = [-(-12) ± [tex]\sqrt{-12}^{2}[/tex]- 4(1)(-640))] / (2 x 1)
w = [12 ± [tex]\sqrt{(12^{2}+2560)[/tex]] / 2
w = [12 ± [tex]\sqrt{2596}[/tex]] / 2
w = [12 ± 51] / 2
We can ignore the negative solution, so:
w = (12 + 51) / 2
w = 31.5
Therefore, the width of the pool is 31.5 feet. We can use this value to find the length:
L = w - 12
L = 31.5 - 12
L = 19.5
Therefore, the length of the pool is 19.5 feet.
To know more about rectangular: https://brainly.com/question/21416050
#SPJ4
Given AC is the angle bisector of
proof below. Note that the last statement and reason have both been filled in for
you.
( must make AAS )
The proofing will be illustrated thus:
1. Seg. AC bisects ∠BAD 1. Given
2. (m=measure) m∠BAC=∠CAD 2. Definition of angle bisector
Therefore, m∠BAC≅∠CAD.
3. AC=AC 3. reflexive property
4. ∠ABC =∠ADC 4. Given
5. Triangle ABC≅Triangle ADC 5. Angle-Angle-Side (AAS postulate).
6. Therefore, BC=DC 6. CPCTC
What does AAS mean?It should be noted that AAS stands for Angle-Angle-Side. In this case, ehen two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
Corresponding parts of congruent triangles are congruent.
Here, the two pairs of angles correspond, but there is a shared side that is not between the angles.
Learn more about angles on:
https://brainly.com/question/25716982
#SPJ1
Given: AC bisects \angle BAD
Given: AC bisects \angle BAD
\angle ABC=\angle ADC
Write a two-column proof to prove= BC=DC
Note that JKLM has vertices J(1, 3), K(-4,2), L(-1,-5), and M(4,-4). Complete the following to determine if JKLM is a parallelogram.
Opposite sides JK and ML are equal and parallel (with slopes of -1/5 and 1/5, respectively), and opposite sides KL and MJ are equal and parallel (with slopes of 7/3 or 7). /3) We can conclude that JKLM is a parallelogram.
How to determine a parallelogram?To determine if JKLM is a parallelogram, we need to check if its opposite sides are parallel and equal in length.
First, we can find the lengths of the sides using the distance formula:
JK = [tex]\sqrt{(1 - (-4))^2 + (3 - 2)^2} = \sqrt{25} = 5[/tex]
KL = [tex]\sqrt{(-4 - (-1))^2 + (2 - (-5))^2} = \sqrt{58}[/tex]
LM = [tex]\sqrt{(-1 - 4)^2 + (-5 - (-4))^2} = \sqrt{26}[/tex]
MJ = [tex]\sqrt{(4 - 1)^2 + (-4 - 3)^2} = \sqrt{50}[/tex]
Next, we can find the slopes of the sides using the slope formula:
Slope of JK = (2 - 3)/(-4 - 1) = -1/5
Slope of KL = (-5 - 2)/(-1 - (-4)) = 7/3
Slope of LM = (-4 - (-5))/(4 - (-1)) = 1/5
Slope of MJ = (3 - (-4))/(1 - 4) = 7/3
Since opposite sides, JK and ML have the same length and are parallel (they have slopes of -1/5 and 1/5, respectively), and opposite sides KL and MJ have the same length and are parallel (they have slopes of 7/3 and 7/3, respectively), we can conclude that JKLM is a parallelogram.
To learn more about parallelogram visit:
https://brainly.com/question/1563728
#SPJ1
ning Page
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
14 cm
?
8 cm
16 cm
11 cm
6 cm
The missing side length from the given figure is 6 ft.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
From the figure,
Missing side = x
Now,
The expression we can make from the figure.
= 16 - 10
= 6 ft
Thus,
The missing side length is 6 ft.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
6. Part D
Another method of proving diagonals of a parallelogram bisect each other
uses a coordinate grid.
A.
P (r, t)
S (0, 0)
R (s, 0)
What could be shown about the diagonals of parallelogram PQRS to com
the proof?
PR and SQ have the same length.
PR is a perpendicular bisector of SQ.
PR and SQ have the same midpoint.
D. Angles formed by the intersection of PR and SQ each measu
B.
Q
(r+s, t)
Answer:
PR and SQ have the same midpoint.
Step-by-step explanation:
PR and SQ have the same midpoint.
simplify the expression (m^6)^-2/3 and write your answer using a positive exponent
We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is [tex]\mathrm{\dfrac{1}{m^4}}[/tex] .
What is expression?An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
It is possible to compare expressions to phrases. In language, a phrase by itself may contain an action, but it does not constitute a complete sentence.
The following are some examples of expressions and word phrases that they relate to:
Expression: 3 + 7
Given
⇒ [tex]\mathrm{(m)^6^{(-2/3)}}[/tex]
⇒ [tex]\mathrm{(m)^{(-12/3)}}[/tex]
⇒ [tex]\mathrm{(m)^{(-4)}}[/tex]
⇒ [tex]\mathrm{\dfrac{1}{m^4}}[/tex]
We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is [tex]\mathrm{\dfrac{1}{m^4}}[/tex]
To know more about expression click-
brainly.com/question/1859113
#SPJ1
The area of a rectangular wall of a barn is 110 square feet. Its length is 12 feet longer than twice its width. Find the length and width of the wall of the barn.
width= =feet
The length and width of the rectangular wall of a barn given the area is 22 feet and 5 feet respectively.
What is the length and width of the wall of the barn?Area of the rectangular wall of a barn = 110 square feet
Width of the barn = w
Length of the barn= 2w + 12
Area of a rectangle = length × width
110 = (2w + 12) × w
110 = 2w² + 12w
equate to 0
2w² + 12w - 110 = 0
w² + 6w - 55 = 0
using factorization method of solving quadratic equation
w² + 11w - 5w - 55 = 0
w(w + 11) - 5(w + 11) = 0
(w - 5) (w + 11) = 0
w = 5 or w = -11
The width of the rectangular barn cannot be negative
Therefore,
Width of the barn = w
= 5 feet
Length of the barn= 2w + 12
= 2(5) + 12
= 10 + 12
= 22 feet
Read more on area of rectangle:
https://brainly.com/question/25292087
#SPJ1
What is the volume 
Answer:
384 cm
Step-by-step explanation:
Simplify:
9 – 3 x 2 + 4
Answer:
2
:
5STEP
2
:
Trying to factor as a Difference of Squares:
2.1 Factoring: 5-3x2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Equation at the end of step
2
:
5 - 3x2 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : -3x2+5 = 0
Subtract 5 from both sides of the equation :
-3x2 = -5
Multiply both sides of the equation by (-1) : 3x2 = 5
Divide both sides of the equation by 3:
x2 = 5/3 = 1.667
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 5/3
The equation has two real solutions
These solutions are x = ±√ 1.667 = ± 1.29099
Two solutions were found :
x = ±√ 1.667 = ± 1.29099
which number line shows the solution to x + 8 > 15
7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The given inequality is:
x + 8 > 15
Subtracting 8 on both sides of the equation:
x + 8 - 8 > 15 - 8
x > 7
Here, 7 is not included and hence it is depicted using an open dot.
Hence, option B is the correct answer.
Learn more about inequality here:
https://brainly.com/question/28823603
#SPJ1
One snowy day 3/4 Ms staples class was late to school 1/3 of the late students brought notes what fraction of Mrs. Stanford class bra late notes that day
The fraction of Mrs. Stanford's class that came late and brought notes that day was 1 / 4
How to find the fraction of students ?To find the fraction of Mrs. Stanford's class that came late and brought notes that day, the relevant formula would be:
= Fraction of students who came late x Fraction of late students who brought notes
Fraction of students who came late = 3 / 4
Fraction of students who were late and brought notes = 1 / 3
The fraction of total students who were late and brought notes were ;
= 3 / 4 x 1 / 3
= 3 / 12
= 1 / 4
Find out more on fractions at https://brainly.com/question/26289507
#SPJ1
13. Solve the inequality.
12 ≤ 2x 4 <10
-
-10 ≤x < 4
-2
-4 ≤x≤ 3
-4 ≤x < 7
The solution of the inequality is -4≤x<7. Therefore, option D is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -12≤2x-4<10.
Here, -12≤2x-4
Add 4 on both the sides of an inequality, we get
-8≤2x
Divide 2 on both the sides of an inequality, we get
-4≤x
Now, 2x-4<10
Add 4 on both the sides of an inequality, we get
2x<14
Divide 2 on both the sides of an inequality, we get
x<7
So, the solution of the inequality is -4≤x<7
Therefore, option D is the correct answer.
To learn more about the inequalities visit:
https://brainly.com/question/20383699.
#SPJ9
whats the missing of the angle 104, 30?
Answer:46
Step-by-step explanation:
180=104+30+x
134+x=180
x=46
Some candles are in the shape of a right circular cylinder. For one such candle, the radius is 9 cm and the height is 26.5 cm. Find the volume of the candle. Round your answer to the nearest whole number. Do not type the units in the space below. (Be sure to use the pi button on your calculator to do the calculation.)
radius = 9 cm
height = 26,5 cm
as we know that
volume of cylinder = πr^2h
= 3,14x9x9x2x26,5
= 13.480 cm cubic
hand consists of 3 cards from a well-shuffled deck of 52 cards.
a. Find the total number of possible 3-card poker hands.
b. A black flush is a 3-card hand consisting of all black cards. Find the number of possible black flushes.
c. Find the probability of being dealt a black flush.
a)
The total number of possible 3-card poker hands is 22100
b)
The number of possible black flushes is 2600
c)
The probability of being dealt a black flush is 0.1176
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of cards = 52
Number of cards in hand = 3
Combination formula.
[tex]^nC_r[/tex] = n! / r! (n -r)!
a)
The total number of possible 3-card poker hands.
= [tex]^{52}C_3[/tex]
= (52 x 51 x 50) / (3 x 2)
= 22100
b.
Number of black cards (spades and clubs) = 13 + 13 = 26
The number of possible black flushes.
= [tex]^{26}C_3[/tex]
= (26 x 25 x 24) / (3 x 2)
= 2600
c.
The probability of being dealt a black flush.
From (a) and (b)
= 2600/22100
= 0.1176
Thus,
The total number of possible 3-card poker hands = 22100
The number of possible black flushes = 2600
The probability of being dealt a black flush = 0.1176
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ9
What is 0.738 that add up to 1
Answer:
0.262
Step-by-step explanation:
1 - 0.738 = 0.262
0, 738 + 0.262 = 1
What are the features of the function f(x) = -2 log_3 (x + 8) graphed below?
The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
Domain: The domain of the function is the set of all real numbers greater than -8, since the argument of the logarithm, x + 8, must be positive.
Range: The range of the function is all real numbers.
Asymptotes: The function does not have any vertical asymptotes.
Transformation: The function is a reflection of the standard logarithmic function over the x-axis, with a vertical scaling factor of -2. This means that the function will start from the origin and increase without bound.
Behavior near x = -8: As x approaches -8 from the right, the value of the function approaches negative infinity. As x approaches -8 from the left, the value of the function approaches positive infinity.
The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.
Given below is a sample question of function please refer the link
https://brainly.com/question/10439235
#SPJ1
