The value of the principal investment (rounded to the nearest hundredth) is $9,000.39.
What is interest rate?Interest rate refers to the percentage amount charged or paid on a loan or investment, usually expressed as an annual percentage rate (APR). It represents the cost of borrowing or the return earned on an investment.
According to question:The equation you provided represents the compound interest formula:
A = P[tex](1 + r/n)^(n*t)[/tex]
Given that the annual interest rate is 6% and is compounded quarterly (i.e., n = 4), and the amount in the account after 15 years is $16,497.06, These values can be plugged into the equation to find P.
A = $16,497.06
r = 0.06 (6% expressed as a decimal)
n = 4
t = 15
$16,497.06 = P[tex](1 + 0.06/4)^(4*15)[/tex]
Dividing both sides by [tex](1 + 0.06/4)^(4*15)[/tex] to isolate P, we get:
P = $16,497.06 / [tex](1 + 0.06/4)^(4*15)[/tex]
Plugging in the values and solving for P using a calculator, we get:
P ≈ $9,000.39
So, the value of the principal investment (rounded to the nearest hundredth) is $9,000.39.
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aflati doua numere naturale stiind ca suma lor este 102 iar impartind numarul mare la cel mic obtinem catul 2 si restul 12
PLSSSS HELPPPPPPPOO
Write an expression in standard form that
represents the AREA of the square. A = s²
5y+3
Answer:
Step-by-step explanation:
The expression in standard form that represents the area of the square with side length s is given by:
A = s^2
However, if you want to substitute the value of s with the expression 5y+3, then the area expression becomes:
A = (5y+3)^2
Expanding the expression, we get:
A = 25y^2 + 30y + 9
Therefore, the expression in standard form that represents the area of the square with side length 5y+3 is 25y^2 + 30y + 9.
Ryan is installing new flooring in his house. Ryan can install 144 square feet of flooring in 3 hours. How much new flooring can Ryan install in 18 hours?
Here's what you need to do:
We know that Ryan can install 144 square feet of flooring in 3 hours.
So, if we take 144 square feet, and divide by 3 hours, 144 / 3, we end up with 48, meaning Ryan can install 48 square feet of flooring every hour.
Then, simply multiply 48 by 18, 48 x 18, and you end up with 864.
Meaning, in 18 hours, Ryan can install 864 square feet of flooring.
Answer: 864 square feet.
A number written without a sign is a _______ number.
Answer:
Positive
Step-by-step explanation:
It's a positive number
If it doesn't have a (-) it's a positive number
A rectangular prism has a volume of 840 cubic inches. The height of the prism is 6 inches and the width is 10 inches. Find the length of the prism and explain how you found it. ASAP
Answer:
14
Step-by-step explanation:
Volume = height x width x length
6 x 10 = 60
480 divided by 60 = 14
Suppose you have $50 in a savings account and deposit an additional $10 each week.
a) Write a recursive formula to represent the sequence.
b) Write an explicit formula to represent the sequence.
c) How much money do you have in savings after 26 weeks? Show all work.
According to the solving $310 money you have in savings after 26 weeks, we can use either the recursive or explicit formula:
Which equations are explicit?The explicit equations for L-functions are Riemann's relations between sums over an L-function's complex number zeroes and sums over prime powers for the Riemann zeta function.
According to the given information:a) Recursive formula:
Let S(n) be the amount of money in savings after n weeks. Then:
S(0) = 50 (initial amount)
S(n) = S(n-1) + 10 (deposit of $10 per week)
b) Explicit formula:
The explicit formula for this sequence is:
S(n) = 50 + 10n, where n is the number of weeks.
c) To find how much money you have in savings after 26 weeks, we can use either the recursive or explicit formula:
Using the recursive formula:
S(0) = 50 (initial amount)
S(1) = S(0) + 10 = 50 + 10 = 60
S(2) = S(1) + 10 = 60 + 10 = 70
S(3) = S(2) + 10 = 70 + 10 = 80
and so on, until:
S(26) = S(25) + 10 = 310
Therefore, after 26 weeks, you have $310 in savings.
Using the explicit formula:
S(26) = 50 + 10(26) = 50 + 260 = 310
after 26 weeks, you have $310 in savings.
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Weekly wages at a certain factory are
normally distributed with a mean of $400 and
a standard deviation of $50. Find the
probability that a worker selected at random
makes between $450 and $550.
250
350 400 450 500 550
P = [? ]%
Hint: use the 68- 95 - 99.7 rule.
300
There is a 15.74% chance that a randomly chosen employee will earn between $450 and $550.
Define probabilityThe study of random occurrences or phenomena falls under the umbrella of the mathematic discipline known as probability. It is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To find : the probability that a worker selected at random makes between $450 and $550
z = (x - μ) / б
where б is the standard deviation, μ is the mean, and x is the value we wish to normalize.
For $450, we have:
z₁ = (450 - 400) / 50 = 1
For $550, we have:
z₂ = (550 - 400) / 50 = 3
We can then use a standard normal distribution table or calculator to find the area under the standard normal curve between z₁and z₂:
P(z₁< z < z₂) = P(1 < z < 3) = 0.1574
This means that the probability that a worker selected at random makes between $450 and $550 is 15.74%.
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cost of jacket: $249.96 markup: 80% discount: 50% tax: 2%
Answer:249.98
Step-by-step explanation: i had a question like this before.
The vertex of the graph of the equation
y = -x² + 6x + 1 is
A. O neither a maximum nor a minimum
B. O both a maximum and a minimum
C. O a minimum
D. O a maximum
The vertex is ( 6 , 1 ). The vertex of the graph of the equation maximum.
What is parabola in math?
Each point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line. All of the parabola-related ideas are discussed here since it is a crucial component of the conic section subject.
the equation y = -x² + 6x + 1
Use the formula: -b/2a
= -6/-1
= 6
The x-coordinate of the vertex is 6
Plug the x value back into the original equation to find the y-coordinate of the vertex
y = -x² + 6x + 1
= -(6)² + 6 * 6 + 1
= -36 + 36 + 1
= 1
The vertex is = ( 6 , 1 )
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The equation P=20sin(2πt)+90 models the blood pressure, P , where t represents time in seconds. a. Find the blood pressure after 30 seconds. Enter the exact answer. The blood pressure is Number . b. What are the maximum and minimum blood pressures? Enter the exact answers. The maximum blood pressure is Number , and the minimum blood pressure is Number .
Which expression is equivalent to 5(2 + 1)?
Step-by-step explanation:
5(2 + 1) can be simplified using the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Using this property, we get:
5(2 + 1) = 5(2) + 5(1)
Simplifying the expression further, we get:
5(2) + 5(1) = 10 + 5 = 15
Therefore, 5(2 + 1) is equivalent to 15.
Ten cards numbered 1 thru 10 are placed in a box. If a card is de random from the box, what is the probability of drawing a prime a 10% b 25% c 40% d 50%
Answer:
a) There are four prime numbers between 1 and 10: 2, 3, 5, and 7. So the probability of drawing a prime number is 4/10 or 2/5, which is 20% and not 10%. Therefore, option (a) is not correct.
b) As we saw in part (a), the probability of drawing a prime number is 2/5 or 40% (since 2/5 is equivalent to 0.4). Therefore, option (b) is correct.
c) The probability of drawing a prime number is 2/5 or 40%, which is not 25%. Therefore, option (c) is not correct.
d) As we saw in part (a) and (b), the probability of drawing a prime number is 2/5 or 40%, which is not 50%. Therefore, option (d) is not correct.
So, the correct answer is (b) 25%.
Hope This Helps!
A gold and diamond bracelet sells for $1200. Find the sales tax and the total price if the sales tax rate is 3.5%.
Answer:42
Step-by-step explanation:
A fair coin is tossed 29 times. In how many outcomes do at least 3 tails occur?
a) 536,866,822
b) 1
c) 536,870,477
d) 536,870,476
e) 3,654
Answer:
The answer to your problem is, A. 536,866,822
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
The formula for calculating probability is expressed as:Probability = Expected outcome/Total outcomeIf a fair coin is tossed 29 times, the total number of outcomes will be expressed as: [tex]2^{29} = 536,870,476[/tex]
If at least 2 tails occur, the expected outcome will be 29 times
Pr(at least 2 tails occur) = [tex]2^{29} - 29 - 1[/tex]
Pr(at least 2 tails occur) = [tex]536,870,912 - 30 = 536,866,822[/tex]
Thus the answer to your problem is, A. 536,866,822
Parvati goes to the movies with $16 in her wallet. She buys
a ticket for $6.25 and two snacks for $2.25 each. How
much money does she have left?
Select the correct expression.
OA. 16-6.25-2-2.25
OB. 16-(6.25 +2.2.25)
O C. 16-2(6.25 +2.25)
OD. 16-6.25 +2.2.25
Answer:
[tex]16-(6.25+2*2.25)[/tex]
Step-by-step explanation:
To find the amount of money she has left, you want to subtract the price of the ticket and the price of the two snacks from the amount of money she starts with.
So we want to subtract 6.25 once and subtract 2.25 twice (because she bought two snacks) from 16
16-6.25-2*2.25
Or you can also do this by adding up the monetary value of the ticket and the snacks and subtract that from the initial amount of money that Parvati has
16-(6.25+2*2.25)
(I am assuming that the "2.2.25" is supposed to say [tex]2*2.25[/tex])
State the open intervals where the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
f(x) = 81 − x2
The function f(x) = 81 − x2 is increasing on the interval (−∞, 9) and decreasing on the interval (9, ∞).
What is parabola?Parabola is a type of curve which is defined by the quadratic equation. It has a distinct "U" shape, with the vertex of the curve being the highest or lowest point.
The point x = 9 is the vertex of the parabola, which marks the point at which the function changes from increasing to decreasing.
Since the function is a parabola, it is also a polynomial of degree 2, and it is always decreasing for points greater than the vertex, and increasing for points less than the vertex.
This means that the function is increasing on the interval (−∞, 9) and decreasing on the interval (9, ∞).
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Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is - 1/18.
The solution will be b=4, the number b such that the average rate of change of f on the interval [2, b] is - 1/18 if the provided assertion is correct.
What does interval look like in math?For instance, a range between 0 and 10 would include all of the integers between them, not just 1, 2, 3, 4, 5, 6, 7, 8, and 9. These would additionally incorporate fractional numbers like 1.3 and components like 1/10. We therefore have the job. We must determine b to the extent that the interval [2, b]'s average percentage of change or slope is -1/8. Discover f first(2).
f(2) = 1/(2) = 1/2
So, we have the point (2, 1/2)
At point b, f(b) = 1/b.
Let's plug this into the slope formula
We simply have to figure out b now. Let's start by multiplying the divisor and fraction by b.
Now, cross multiply.
Solve for b. Use the factors -4 and -2 to multiply.
Thus, b=4 or b=2.
However, b=2 cannot be the answer because the range [2,2] has no significance. Thus, b=4.
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X A A. B. C. D. B any of the perpendicular bisectors of the sides of the hexagon either diagonal of the square any of the perpendicular bisectors of the sides of the square there are no lines across which this figure can reflect onto itself....*******?Got answer off here and showing wrong ones in pic....thanks!
In a regular hexagon, where FGHIJK shares a common center with square ABCD on a coordinate plane. ||. It is Across any of the perpendicular bisectors of the sides of the square that the combined figure can reflect onto itself.
What is the explanation for the above response?
In Regular Hexagon FGHIJK, we have 6 lines of reflection across which the hexagon reflects onto itself. Those lines are:
3 perpendicular bisectors of sides i.e. perpendicular bisector of IJ , IH and GH
3 lines passing through vertices i.e. HK, IF and GJ.
While in Square, we have 4 line of reflection across which the square reflects onto itself. Those lines are:
2 perpendicular bisectors of sides AB and BC i.e. HK and perpendicular bisector of CD
2 diagonals of square i.e. AC and BD
Note as well that from figure we know that perpendicular bisector of CD and perpendicular bisector of IJ is the same line.
So, for combined figure we have to take common lines from both figures i.e. perpendicular of sides CD or IJ and line HK.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See the attached image and the questions below.
In a regular hexagon, FGHIJK shares a common center with square ABCD on a coordinate plane. || . Across which lines can the combined figure reflect onto itself?
A. any of the perpendicular bisectors of the sides of the hexagon
B. either diagonal of the square
C. any of the perpendicular bisectors of the sides of the square
D. there are no lines across which this figure can reflect onto itself
The length and breadth of a rectangular wire are 32 cm and 12 cm. It is bent into the shape of a circle. Find the radius of the circle. (Take p = 3.14)
The perimeter of the circle formed by bending the rectangular wire will be equal to the length of the wire.
Perimeter of the circle = Length of the wire
2πr = 2(l+b) where r is the radius of the circle, l is the length of the wire, and b is the breadth of the wire.
Substituting the given values, we get:
2 x 3.14 x r = 2(32 + 12)
6.28r = 88
r = 14 cm
Therefore, the radius of the circle is 14 cm.
Answer:
14.01 cm
Step-by-step explanation:
The length of the wire is equal to the perimeter of the rectangle. So, the length of the wire is:
2 × (32 + 12) = 88 cmWhen this wire is bent into a circle, its length becomes equal to the circumference of the circle. The formula for the circumference of a circle is:
(let r = radius)
2 × π × rSo, we can write:
2 × π × r = 88Solving for r, we get:
r = 88 ÷ (2 × π) = 14.01 cmSo, the exact value of the radius of the circle formed by bending this rectangular wire is 14.01 cm.
Saanvi recorded the number of math problems she did for homework each night for 10 days.
`0`, `5`, `5`, `4`, `5`, `10`, `5`, `6`, `50`, `0`
Calculate the mean and MAD of this data.
Answer:
Saanvi recorded the number of math problems she did for homework each night for 10 days.
Step-by-step explanation:
How many pieces of rope measuring 5/8 of a foot can be cut from a rope of 4 3/8 feet?
We can cut 6 pieces of rope measuring 5/8 of a foot from a rope of 4 3/8 feet, with some rope left over.
What is area?Area is a measurement of the size of a surface or a region in a two-dimensional space. It is expressed in square units, such as square inches (in²), square meters (m²), or square feet (ft²). To find the area of a shape, you need to multiply its length by its width, or use an appropriate formula depending on the shape. For example, the formula for the area of a rectangle is A = l × w, where A is the area, l is the length, and w is the width.
To find the number of pieces of rope measuring 5/8 of a foot that can be cut from a rope of 4 3/8 feet, we need to divide the length of the rope by the length of each piece of rope:
4 3/8 feet = 4 + 3/8 feet = 4 feet + (3/8) x 12 inches = 4 feet + 3 inches = 51 inches
Each piece of rope measures 5/8 of a foot, which is equivalent to 5/8 x 12 inches = 7.5 inches.
Now we can divide the length of the rope (in inches) by the length of each piece of rope (in inches) to find the number of pieces:
51 inches ÷ 7.5 inches ≈ 6.8
Therefore, we can cut 6 pieces of rope measuring 5/8 of a foot from a rope of 4 3/8 feet, with some rope left over.
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The graph of f passes through (-4,7) and is perpendicular to the line that has
an x-intercept of 2 and a y-intercept of - 4.
The equation of the function is ?
Answer:
f(x) = - [tex]\frac{1}{2}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 0 ) , x- intercept and (x₂. y₂ ) = (0, - 4) , y- intercept
m = [tex]\frac{-4-0}{0-2}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (- 4, 7 ) into the partial equation
7 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )
5 = c
y = f(x) = - [tex]\frac{1}{2}[/tex] x + 5 ← equation of function
helo please show work
Answer:
Step-by-step explanation:
Solution:
We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).
The GCF of 305 and 60 is 5.
Divide both terms by 5.
305 ÷ 5 = 61
60 ÷ 5 = 12
Therefore:
305 : 60 = 61 : 12
The Box Has A Volume Of 845. Find X
Answer: x=6.5
Step-by-step explanation: 13 x 10=130
845/130= 6.5
The polynomials (-3y²-y-8) + (-y² + 2y - 4) when added is:
Answers options
O -4y² + y - 12.
O -4y²-y-12.
O 4y² + y - 12.
O-4y2-3y - 12.
O 4y2-3y - 12.
Answer:
-4y2 +y - 12
Step-by-step explanation:
-3y2 - y2= -4y2
-y+2y= y
-8 - 4= -12
-4y2 + y - 12
Find the measures of angles a and b and of arc c Please
The measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.
In the given diagram, we can see that angle ACD is a right angle, since it is formed by the radius AC and tangent CD at point C.
Therefore, angle BCD is equal to angle ACD, which is 90 degrees.
Since angle BCD is an exterior angle of triangle BCF, it is equal to the sum of the two remote interior angles, which are angles BFC and FCB.
Angle BFC is equal to angle ABC (since they are opposite angles), which is 60 degrees.
Similarly, angle FCB is equal to angle ACF, which is also 60 degrees.
Therefore, angle BCD is equal to angle BFC + angle FCB, which is 60 + 60 = 120 degrees.
Now, since arc CD is subtended by angle BCD, its measure is also equal to 120 degrees.
Hence, the measure of arc CD is 120 degrees.
Similarly, angles ACF and FCB are opposite angles in the cyclic quadrilateral AFCB, so they are supplementary. Therefore, angle FCB is equal to 180 - angle ACF,
Which is also 180 - 60 = 120 degrees.
Now we can apply the exterior angle theorem to find the measure of angle BCD. We have:
angle BCD = angle BFC + angle FCB
= 120 + 120
= 240 degrees
Finally, we can conclude that the measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.
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what is Bethany's score on the test if she answered 23 out of 30 right?
part:
whole:
percent:
Answer: 76.67%
Step-by-step explanation:
Determine whether the relation represents y as a function of x: X^2+y^2=4
The relation is not a function, but rather a circle with center at the origin and radius 2.
Does the given relation represents y as a function of x?Given the relation in the question;
x² + y² = 4.
First, lets solve for y.
x² + y² = 4
Subtract x² from both sides
x² - x² + y² = 4 - x²
y² = 4 - x²
Take the squre root of both sides
y = ±√( 4 - x² )
This shows that for a given value of x, there are two possible values of y. One positive and one negative, that satisfy the equation.
Therefore, the relation is not a function.
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The picture is below
The surface area of the rectangular prism graphed is given as follows:
10.12 ft³.
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
Converting the mixed numbers to decimal, the dimensions of the rectangular prism are given as follows:
1.3 ft, 1.4 ft and 1.2 ft.
Hence the surface area of the prism is given as follows:
S = 2 x (1.3 x 1.4 + 1.3 x 1.2 + 1.4 x 1.2)
S = 10.12 ft³.
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Can someone help me with this please!!!
Using the graph of the picewise function we can see that:
i(-3) = 2i(-4) = 3How to evaluate the piecewise function?Here we have a piecewise function and we want to evaluate it in different values of x.
First we want to get:
i(-3)
Notice that at x = -3 we have a closed circle in the second line, the one constant at y = 2, so we need to use that value here:
i(-3) = 2
The closed dot means that the value belongs to that line, while a open one (like the one that is just above) means that the value does not belong.
For the second evaluation:
i(-4)
This time we just need to look at the line in the left, here we can see that: i(-4) = 3
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