Answer:
We can use the formula for compound interest to calculate the amount and interest:
A = P * (1 + r/n)^(n*t)
I = A - P
Where:
P = Principal = $15,300
r = Rate = 8% = 0.08
n = Compounding frequency per year = 4 (since it is compounded quarterly)
t = Time period = 6 years
Plugging in the values, we get:
A = 15,300 * (1 + 0.08/4)^(4*6) = $23,659.28
I = 23,659.28 - 15,300 = $8,359.28
Therefore, the amount after 6 years is $23,659.28 and the interest earned is $8,359.28.
I hope this helps.
Solve the radical equation.
√3x-2-√11+x= -1
Answer:
[tex]x = \frac{(1 + \sqrt{11})( \sqrt{3 } - 1) }{2 } [/tex]
Find the lateral and total surface area round to the nearest hundredth if necessary
The lateral and total surface area of the prism are 1000 square feet and 1120 square feet.
How to determine the lateral and total surface area of a prismIn this problem we need to determine the lateral and total surface area of a prism with a triangular base. The lateral surface area is the sum of the areas of the three rectangles and the total surface area is the sum of the lateral surface area and the areas of the two triangles.
The area formulas for the triangle and the rectangle are, respectively:
Triangle:
A = s · √[s · (s - a) · (s - b) · (s - c)]
s = 0.5 · (a + b + c)
Where:
a, b, c - Sides, in feet.s - Semiperimeter, in feet.A - Area, in square feet.Rectangle:
A = w · h
Where:
w - Width, in feeth - Height, in feet.A - Area, in square feet.Now we proceed to determine each surface area:
Lateral surface area:
A = 2 · (20 ft) · (17 ft) + (20 ft) · (16 ft)
A = 1000 ft²
Total surface area:
s = 0.5 · (17 ft + 17 ft + 16 ft)
s = 25 ft
A = √[(25 ft) · (25 ft - 17 ft)² · (25 ft - 16 ft)] + 1000 ft²
A = 1120 ft²
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The area of a circle is 36π centimeters. What is the circumference of a circle in terms of π.
Solve for x. Round to the nearest tenth of a degree, if necessary.
The value of x it the nearest tenth of degree is 25.6°
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Sin(tetha) = opp/ hyp
cos( tetha) = adj/ hyp
tan( tetha) = opp/ adj
Here, the hypotenuse is 92 and adjascent to the to the angle x is 63
therefore to calculate x we use cosine function
cos x = 83/92
cos x = 0.902
x = cos^-1( 0.902)
x = 25.6° ( nearest tenth)
therefore the value of x is 25.6°
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According to the NOAA, the state of Oregon has just over 6 million feet of Pacific coastline. If the population of Oregon is approximately 3.8 million people, find the number of feet of coastline per capita in Oregon. Round your answer to the nearest hundredth
1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.
what is unitary method ?In statistics, the unitary approach is a way towards resolving proportional problems. It entails first determining the value of a single unit of either a statistic, and then applying that knowledge to determine the value of any other required number of units. Consider the scenario where we are aware that 5 bananas cost $2.50. We can employ the unitary technique to calculate the price of seven apples as follows: Determine the price of a single apple: 2.50 ÷ 5 = 0.50 .Divide the price of one banana by the quantity you want of apples. 0.50 × 7 = 3.50 .It follows that 7 bananas would cost $3.50. Additionally, this technique can be applied to more challenging issues requiring numerous ratios and proportions.
given
Divide the total number of feet of coastline by the state's population to get the amount of coastline per person in Oregon:
Total shoreline / Population equals coastline per person.
coastline divided by population (3,800,000) equals 6,000,000 feet.
1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.
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Help with this question please l need it
Answer:
(x+4)(x-9)!!!!!!!!!!!!!!!!!!
Write an equation that can be used to determine the angle measure, in degrees, of angle DBC. Let n represent the measure of angle DBC. Then determine the measure of n
An equation that can be used to determine the angle measure, in degrees, of angle DBC is 67 + n = 90.
The measure of n is equal to 23 degrees.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by the following mathematical equation;
∠ABD + ∠DBC = 90
∠ABD + n = 90
67 + n = 90.
n = 90 - 67
n = 23°
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
N Heracio's Computer Time Shopping Research 10% Videos 15% Homework 20% Games 20% Social dia 25% Heracio used the computer a total of 40 hours last week. How many more hours did Heracio use the computer to do homework than shop online?
Heracio used the computer 2 more hours to do homework than to shop online.
To solve the problem, we need to first calculate the number of hours Heracio spent on each activity:
Videos: 10% of 40 hours = 4 hours
Homework: 20% of 40 hours = 8 hours
Games: 20% of 40 hours = 8 hours
Social media: 25% of 40 hours = 10 hours
Shopping: 15% of 40 hours = 6 hours
To find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:
8 hours (homework) - 6 hours (shopping) = 2 hours
Therefore, Heracio used the computer 2 more hours to do homework than to shop online.
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Transactions on Furnell's credit card are shown for the month of June. The interest rate is 1.4% per month.
June 1 Balance $352.12
June 4 Sears $331.89
June 8 eBay $81.58
June 15 Outback $30
June 18 Payment $200
Find the average daily balance $
184.89
Find the interest for the month $
Find the balance for the following month $
The interest for the month is: $2.59
The balance for the month is: $598.18.
We have the information from the question is:
The interest rate is 1.4% per month.
June 1 Balance $352.12
June 4 Sears $331.89
June 8 eBay $81.58
June 15 Outback $30
June 18 Payment $200
Now, According to the question:
The average daily balance for June is $184.89.
To calculate the interest for the month,
Multiply the average daily balance by the interest rate:
$184.89 × 1.4% = $2.59.
To find the balance for the month :
Add the initial balance, transactions, and interest, then subtract the payment:
$352.12 + $331.89 + $81.58 + $30 + $2.59 - $200 = $598.18.
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If a1 =9 and an n-1 +2 then find the value of a5
Given that a₁ = 9 and aₙ = aₙ₋₁ + 2 , we can find the value of a5 by repeatedly applying the recursive formula to find a₂, a₃, a₄, and a₅.Using this method, we get a₅ is 17.
The given sequence is not defined explicitly. However, we can use the recursive formula to find the value of a5.
a₁ = 9 and aₙ = aₙ₋₁ + 2 for n > 1
To find a₂, we use the recursive formula
a₂ = a₁ + 2 = 9 + 2 = 11
To find a₃, we use the recursive formula
a₃ = a₂ + 2 = 11 + 2 = 13
To find a₄, we use the recursive formula
a₄ = a₃ + 2 = 13 + 2 = 15
To find a5, we use the recursive formula
a₅ = a₄ + 2 = 15 + 2 = 17
Therefore, the value of a₅ is 17.
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Among the products of a company, brand A has 40% of the market share. A market research firm finds that if a person uses brand A, the probability that he/she will be using it again next year is 30%. On the other hand if a person is not using the product at present, the probability that he/she will be using it next year is 60%. Required: a) Find the transition matrix. b) Find the percentage of the market share that brand A gets after two years. c) Want percentage of the market share will be handled by brand A on the long run, if the transition matrix does not change?
a) The transition matrix is [tex]\left[\begin{array}{ccc} 0.3&0.7 \\ 0.6&0.4\end{array}\right][/tex]
b) After two years, brand A is expected to have 40.4% of the market share.
c) Brand A is expected to have 37.5% of the market share.
a) The transition matrix can be constructed using the probabilities provided in the problem. Let P be the matrix where the (i, j)-th entry represents the probability of transitioning from state i to state j. In this case, there are two states: using brand A (state 1) and not using brand A (state 2).
Using the information given in the problem, we can fill in the entries of the matrix as follows:
P = [tex]\left[\begin{array}{ccc} 0.3&0.7 \\ 0.6&0.4\end{array}\right][/tex]
b) To find the percentage of the market share that brand A gets after two years, we need to multiply the initial market share vector (40% for brand A and 60% for other brands) by the transition matrix twice:
| 0.4 0.6 | × P × P = | 0.404 0.596 |
Therefore, after two years, brand A is expected to have 40.4% of the market share.
c) To find the long-run market share for brand A, we need to find the steady-state vector of the transition matrix P. This is the vector π such that:
πP = π
and
π ₁+ π₂ = 1
where π₁ is the long-run probability of being in state 1 (using brand A) and π₂ is the long-run probability of being in state 2 (not using brand A).
Solving the equations above, we get:
π = | 0.375 0.625 |
This means that in the long run, brand A is expected to have 37.5% of the market share.
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Given: rectangle MNPQ ~ rectangle RSTU
- find the perimeter of rectangle RSTU
- find the area of rectangle RSTU
The perimeter of rectangle RSTU is 21 cm.
The area of the rectangle RSTU is 27 cm².
How to find the perimeter and area of a rectangle?A rectangle is a quadrilateral that has opposite side equal to each other and opposite side parallel to each other.
Therefore, let's find the perimeter of the rectangle RSTU and the area of RSTU.
Hence,
Let's find the width of the rectangle MNPQ
14 = 2(4 + w)
14 = 8 + 2w
14 - 8 = 2w
2w = 6
w = 6 / 2
w = 3 cm
Therefore, using similar ratio,
4 / 6 = 3 / RU
cross multiply
4RU = 18
RU = 18 / 4
RU = 4.5 cm
Therefore,
Perimeter of the rectangle RSTU = 2(6 + 4.5)
Perimeter of the rectangle RSTU = 2(10.5)
Perimeter of the rectangle RSTU =21 cm
Area of the rectangle RSTU = 4.5 × 6
Area of the rectangle RSTU = 27 cm²
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Can someone help me please
The matrix formed by performing the row operation 2R₁ + R₂ — R₂ on M will have a new R₂ = [ -8 -1 -3]
What is the row of a matrixA rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.
performing the row operation 2R₁ + R₂ — R₂ on M, we have;
2(-3) + (-2) = -8 {row 2 column 1}
2(-1) + 1 = -1 {row 2 column 2}
2(-4) + 5 = -3 {row 2 column 3}
Therefore, the matrix formed by performing the row operation 2R₁ + R₂ — R₂ on M will have a new R₂ = [ -8 -1 -3]
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Convert the decimal 15.75 into a percent.
The decimal 15.75 into a percentage is 1575%
How to convert the decimal into a percentageFrom the question, we have the following parameters that can be used in our computation:
Decimal = 15.75
This means that
Number = 15.75
Multiply the number by 1
so, we have the following representation
Number = 15.75 * 1
Express 1 as 100%
This gives
Number = 15.75 * 100%
Evaluate the products of 15.75 and 100
So, we have
Number = 1575%
Hence, the percentage is 1575%
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Find value of X and BD
Look at picture
The measure of length of x of the parallelogram is x = 2.36 units
Given data ,
Let the parallelogram be represented as ABCD
Now , the measure of lengths of the sides are
The measure of AB = 13x - 20
The measure of CD = 2x + 6
The measure of BC = 5x + 4
Opposite sides are parallel
Opposite sides are congruent
So , AB = CD
13x - 20 = 2x + 6
Subtracting 2x on both sides , we get
11x = 26
Divide by 11 on both sides , we get
x = 2.36 units
Hence , the parallelogram is solved and x = 2.36 units
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4. The arithmetic mean of a data set is the measure of center is ….
A) that is found by adding the data values and dividing the total by the number of data values
B)that is the value midway between the maximum and minimum values in the original data set
C)that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude
D) that is the value that occurs with the greatest frequency
The correct statement is A) that is found by adding the data values and dividing the total by the number of data values
What is meant by adding?
Adding is an operation in which two or more numbers or quantities are combined to obtain a sum. It is represented by the symbol "+" and is one of the four basic arithmetic operations.
What is meant by dividing?
Dividing is an operation that separates a quantity or a number into equal parts or groups. It is represented by the symbol "÷" or "/" and is one of the four basic arithmetic operations.
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Encik Halim bought 108 lemons to sell at his grocery shop. He packed 3 lemons in small packets and sold at the price of RM6.80 per packet. If he made a total profit of RM88.20, calculate the price of each lemon bought by him.
Answer:
the price of each lemon bought by Encik Halim is RM1.45.
Step-by-step explanation:
Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.
Let's assume that the cost of each lemon bought by Encik Halim is x RM.
The total cost of 108 lemons would then be 108x RM.
Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.
We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:
Total cost = Total revenue - Profit
Total cost = RM244.80 - RM88.20
Total cost = RM156.60
We know that Encik Halim bought 108 lemons, so we can write:
Total cost = Number of lemons bought x Cost per lemon
RM156.60 = 108x
Therefore, the cost per lemon bought by Encik Halim is:
x = RM156.60/108
x = RM1.45
So the price of each lemon bought by Encik Halim is RM1.45.
Let H: X – Y be a mapping. The set Y is called the
Let H: X – Y be a mapping. The set Y is called the codomain of the mapping H: X – Y.
In mathematics, a mapping or function H: X – Y is a relation between two sets, where the set X is called the domain and the set Y is called the codomain.
The mapping H assigns each element in X to a unique element in Y. The codomain of the mapping H is the set Y, which contains all the possible outputs that can be obtained from the mapping.
It represents the range of the mapping H and provides a reference set for the outputs of the function. The actual range of the function may be smaller than the codomain, depending on the elements in X that are mapped to.
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The graph of f(x) = a × [tex]b^x[/tex] passes through (2,54) and (5,16).
What is the value of b?
The value of b when the graph of function f(x) = a*bˣ passes through (2,54) and (5,16), is given by, b = 2/3.
Given the function of the graph is,
f(x) = a*bˣ
It is given that the graph of the function passes through the points with coordinates (2, 54) and (5, 16). So this points must satisfy the given function.
Substituting the point (2, 54) in the given function we get,
f(2) = 54
a*b² = 54 ..................... (i)
Substituting the point (5, 16) in the given function we get,
f(5) = 16
a*b⁵ = 16 ..................... (ii)
So dividing equation (ii) by equation (i) we get,
(a*b⁵)/(a*b²) = 16/54
b³ = 8/27
b³ = (2/3)³
b = 2/3
Hence the value of b is 2/3.
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What is the area of one of the bases,b, of the prism b=_in2
Answer: 6
Step-by-step explanation:
Therefore, area of the base 'B' of given rectangular prism is equal to 6 in².
Answer:
Step-by-step explanation:
B= area of the triangle 1+area of triangle 2
(1/2*3*1)+(1/2*2*1)
=1.5+1
=2.5
At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 4.5% compounded
monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits
or withdrawals are made during this period?
i Click the icon to view some finance formulas.
The value of the account will be $
(Round to the nearest dollar as needed.)
4
Answer:
The value of the account will be $5,628
Step-by-step explanation:
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
therefore
The value of the account will be $5,628
Find the approximate radius of a circle with a circumference of 23.21 feet. Use 3.14 for π
. Round to the nearest hundredth if necessary.
Thee radius of the circle is 3. 696 feet
How to determine the radiusThe formula that is used for calculating or determining the circumference of a circle is expressed as;
C = 2πr
Given that the parameters for the formula are expressed thus;
C is the circumferenceπ takes the constant value of 3.14r is the radius of the circleFrom the information given, we have that;
Radius = 23.21 feet
Substitute the values, we get;
23.21 = 2× 3.14r
Multiply the values
r = 23.21/6.28
Divide the values
r = 3. 696 feet
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Solve the equation for the indicated variable
X= (simplify your answer)
B = (715x) / (h^2)
Step 1: Get rid of the denominator by multiplying both sides by h^2
(B)(h^2) = 715x
Step 2: Isolate x by dividing both sides by 715
(Bh^2) / 715 = x
Answer: x = Bh^2 / 715
Hope this helps!
An airplane is heading north at an airspeed of 550 km/hr, but there is a wind blowing from the southwest at 40 km/hr.
The plane will end up flying
degrees off course
The plane's speed relative to the ground will be
km/hr
Answer: To end up due north, the pilot will need to fly the plane 3.382 degrees east of north.
Step-by-step explanation:
don't know how to explain got it form chegg
What did Maleuvre write about Gauguin's views on Polynesian women?
According to Jean-Claude Maleuvre's book "Museum Memories: History, Technology, Art," Gauguin's views on Polynesian women were complex and contradictory. On the one hand, he was fascinated by their exotic beauty and saw them as a source of artistic inspiration. On the other hand, he objectified and exoticized them, portraying them as primitive and sexually available. Gauguin's depictions of Polynesian women have been criticized as perpetuating colonialist stereotypes and promoting a Westernized gaze.
Which statement is true about the system x - 3y = 5 and y = x - 7?
• (8, 1) is a solution to one equation but not the other one, so it is a solution to the system.
• (8, 1) is not a solution to either equation, so it is not a solution to the system.
• (8, 1) is a solution to one equation but not the other one, so it is not a solution to the system.
• (8, 1) is a solution to both equations, so it is a solution to the system.
The solution to the given equation is ( 8 , 1 )
Given data ,
To determine whether (8, 1) is a solution to the system, we need to check whether it satisfies both equations:
x - 3y = 5: 8 - 3(1) = 5, which is true
y = x - 7: 1 = 8 - 7, which is true
Since (8, 1) satisfies both equations, it is a solution to the system. Therefore, the correct answer is:
Hence , (8, 1) is a solution to both equations, so it is a solution to the system
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
4x^2 + 10 + x - 50 - x^2 + 4 + 11x
The factorization of the polynomial is determined as (x + 6)(x - 2).
What is the factorization of the polynomial?The factorization of the polynomial is calculated as follows;
4x² + 10 + x - 50 - x² + 4 + 11x
collecting similar terms, we will have;
3x² + 12x - 36
divide through by 3;
x² + 4x - 12
Factorize the expression as follows;
x² + 6x - 2x - 12
x (x + 6) - 2(x + 6)
(x + 6)(x - 2)
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An individual makes five annual deposits of $2000 in a savings account that
pays interest at a rate of 4% per year. One year after making the last deposit, the
interest rate changes to 6% per year. Five years after the last deposit, the accumulated
money is withdrawn from the account. How much is withdrawn?
could you solve this problem?
The total amount withdrawn from the account after five years is $24,927.38.
How do we calculate?The future value of a series of annual deposits of $2000) can be calculated using the following formula:
FV = [tex]PMT x (((1 + r)^n^-^ 1) / r)[/tex]
where FV = the future value, PMT= the payment amount = $2000 r = the interest rate per period = 4% n = the number of periods = 5
the interest rate and the number of periods are the same.
[tex]FV1 = $2000 x (((1 + 0.04)^5^-^ 1) / 0.04) = $11,025.52[/tex]
This is the amount that the deposits will grow to one year after the last deposit, at an interest rate of 4% per year.
We use compound interest:
FV = [tex]PV x (1 + r)^n[/tex]
we apply this formula with a present value of $11,025.52, an interest rate of 6%, and 4 periods, we get:
FV2 = [tex]$11,025.52 * (1 + 0.06)^4 = $13,901.86[/tex]
Therefore the total amount withdrawn = FV1 + FV2 = $11,025.52 + $13,901.86 = $24,927.38
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A toy car travels 12 centimeters per second ehich graph best best represents why the number of centimeters the toy var travels in x seconds
Answer: The graph that best represents the number of centimeters the toy car travels in x seconds would be a linear graph with a slope of 12. The equation for this graph would be y = 12x, where y represents the distance traveled in centimeters and x represents the time in seconds.
Step-by-step explanation:
PROJECT: INSCRIBED POLYGONS
You've learned about the different parts of a circle, as well as regular polygons and their angle measures. You've also learned how to use a protractor to measure angles.
In this project, you will apply this knowledge to inscribe regular polygons in a circle. If a polygon is inscribed in a circle, all of its vertices touch the circle. Here is an example of an equilateral triangle inscribed in a circle.
OBJECTIVES
Inscribe regular polygons in circles using a protractor, compass, and straight edge.
Materials
pencil and paper
protractor
compass
straight edge