The amount of money that needs to be deposited now into an account to obtain $6,200 in 15 years is $2,928.67.
How to determine the principal amount?Mathematically, continuous compounding interest can be calculated by using this mathematical expression:
P(t) = P₀e^{rt}
Where:
P(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.Substituting the given parameters into the continuous compounding interest formula, we have;
P(t) = P₀e^{rt}
$6,200 = P₀e^{0.05 × 15}
$6,200 = P₀e^{0.75}
Principal, P₀ = 6,200/e^{0.75}
Principal, P₀ = 6,200/2.11700001661
Principal, P₀ = $2,928.67.
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Find the angle of elevation
from point C to point A.
590
m
402 m
2
nm
B
Angle of elevation = [ ? ]0
The required angle of the elevation at point C to A is given as ∠C = 31°.
What is the angle of elevation?The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards to an object or point. In other words, it is the angle between the horizontal and an observer's line of sight to an object above the observer
Here,
A figure has been shown, Consider triangle ABC, where ∠A = 59, ∠B = 90°,
Since the sum of the angle in the triangle should be 180°.
∠A + ∠B + ∠C = 180
∠C + 90 + 59 = 180
∠C = 90 - 59
∠C = 31°
Thus, the required angle of the elevation at point C to A is given as ∠C = 31°.
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O Points: 0 of 1
Sav
Write the following phrase as an algebraic expression and simplify if possible. Let x represent the unknown number.
Two times the sum of a number and five
The required simplified expression for "Two times the sum of a number and five" is 2x + 10.
What is an algebraic expression?An algebraic expression is defined as when the expression is formed with help of variables such as x, y z, and so on. in the format of x + y + z or in any mathematical operation.
Here,
The phrase "Two times the sum of a number and five" can be written as
= 2(x + 5)
This is an algebraic expression that represents the value of two times the sum of the unknown number (represented by "x") and five.
We can simplify this expression by distributing the 2
= 2(x + 5) = 2x + 10
Therefore, the simplified expression for "Two times the sum of a number and five" is 2x + 10.
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Use the information provided to answer Part A through Part D.
One method that can be used to prove that the diagonals of a parallelogram bisect
each other is shown in the given partial proof.
S
ven: Quadrilateral PQRS is a parallelogram
ove:
PT= RT
ST= QT
1.
2.
7.
3.
4.
Statements
Quadrilateral PQRS is a
parallelogram
PQ || SR
PS || QR
ZPQS = ZRSQ
ZQPR ZSRP
?
5. ASRT AQPT
6.
PT=RT
ST=QT
Q
I
R
PT = RT
ST=QT
1. Given
2. Definition of
parallelogram
3.
4.
5.
Reasons
6.
2
?
Opposite sides of a
parallelogram are
congruent
?
Corresponding par
of congruent
triangles are
congruent
7. Definition of
congruent line
erop segments
Answer:
the anwser is 5
Step-by-step explanation: 5
Which inequality's solution is graphed here?
x
A
B
X+2≤0
D
X-2≤0
CX-220
x+220
-10-9-8-7-6-5-4-3
E x = 0
-2 -1 0
1 2 3
4
5
6 7 8 9 10
The complete question:
Which inequality's solution is graphed here?
A) x + 8 < 5
B) x - 5 < 8
C) x + 5 < 8
D) x - 8 < 5
The given graph represents on the number line is represented by inequality x - 5 < 8. So option B is correct.
What is a number line?Real numbers are represented by a straight line known as a number line. The distance between the dots on the line, which correlates to the magnitude of the numbers, is how the numbers are typically represented. Positive or negative numerals can be used, and they are normally marked at regular intervals.
Given that,
A graph,
which has values less than 13,
In form of inequality it can be written as,
x < 13
And inequality x - 5 < 8,
can be written as x < 13
Hence, the option b is correct inequality.
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If AB = 12 and BC = 19,
then what does AC equal?
The value of length AC is,
⇒ AC = 31
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
The lengths are,
AB = 12 and BC = 19
Now, If the points A, B and C are colinear.
Then, The value of length AC is,
⇒ AC = AB + BC
⇒ AC = 12 + 19
⇒ AC = 31
Thus, We get;
⇒ AC = 31
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13 Show that the equation (p+1)x² + (2p+3)x+ (p+2)=0 has real roots for all real values of p.
The equation (p+1)x² + (2p+3)x+ (p+2)=0 has real roots for all real values of p at x = -1, -2
What is a polynomial?A polynomial equation is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.
Given that:
(p+1)x² + (2p+3)x + (p+2) = 0
Open brackets;
px² + x² + 2px + 3x + p + 2 = 0
Move all terms not containing p to the right side of the equation.
px² + 2px + p = −x² − 3x − 2
Factor p out of px² + 2px + p.
p(x² + 2x + 1) = −x² − 3x − 2
Factor using the perfect square rule.
p(x+1)² = −x² − 3x − 2
Divide each term in p( x + 1 )² = −x² − 3x − 2 by (x + 1)² and simplify.
[tex]p= - \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}[/tex]
Set [tex]p= - \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}[/tex] to be equal to zero;
[tex]- \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}=0[/tex]
Solve for x;
-x² - 3x - 2 = 0
Factor the left side of the equation.
-(x + 1) (x + 2) = 0
x = -1
x = -2
The final solution is all the values that make -(x + 1) (x + 2) = 0 true
x = -1, - 2
Exclude the solutions that do not make [tex]- \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}=0[/tex] true.
Therefore, x = -2
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help me please i need help
Answer:
Step-by-step explanation:
The ansewr is C
Answer: 523.3cm^3
Step By Step Explanation:-The volume of a sphere can be calculated using the formula:
V = (4/3) * π * r^3
where r is the radius of the sphere. The diameter of the sphere is 10 cm, so the radius is half of that, or 5 cm.
Substituting the radius into the formula, we get:
V = (4/3) * π * (5 cm)^3
= (4/3) * π * 125 cm^3
= approximately 523.6 cm^3
So, the closest measurement to the volume of the sphere in cubic centimeters is approximately 523.3 cm^3.
what is the solution to | x | -2 <= -3
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 2.2 cubic feet of water weigh:
In pounds?
In tons?
So far I Havn't received the correct answer yet.
A bag contains 8 green marbles and 32 blue marbles. If a representative sample con
Because the ratio of green marbles to blue males is 1:4 in the population, the e
be 8 blue marbles.
Answer:
The expected number of blue marbles in a sample of 8 marbles would be 4 times the number of green marbles, so 4 * 8 = 32. Thus, the expected number of blue marbles in a sample of 8 marbles is 32.
Step-by-step explanation:
12. The point M(-6, -4) is translated 2 units right. What are the coordinates of the resulting point, M'?
(-4,0)
(2,-4)
(-4,-2)
(-4,-4)
Answer:
(-4,-2)
Step-by-step explanation:
Answer: (-4,-4)
Step-by-step explanation: the y- coordinate stays the same you would have to move the x-coordinate only which would give you -4. Because you are adding 2 to -6.
need help pls Choose ALL answers that describe the quadrilateral
Answer: A. Parallelogram
Step-by-step explanation: A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length.
What is the volume 
The volume of the composite figure is 2592 cubic feet.
What is composite figure?The area that any composite shape covers is known as the area of composite shapes. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These shapes or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.
The volume of the figure = Volume of the mounted object + Volume of the base object.
The volume of the mounted object is:
V = (l)(b)(h)
V = (9)(12)(6)
V = 648 cubic feet.
The volume of the base object is:
V = (l)(b)(h)
V = (27)(12)(6)
V = 1944 cubic feet.
The total volume of the composite figure is:
V = 648 + 1944
V = 2592 cubic feet
Hence, the volume of the composite figure is 2592 cubic feet.
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Graph the function y=x/4
Answer:
Step-by-step explanation:
A set contains the numbers 0,6,12 and 15. 2 different numbers are selected randomly from this set. What is the probability that the sum is greater than 12
Answer:
Step-by-step explanation:
To find the probability of the sum of two randomly selected numbers from a set being greater than 12, we need to first find the total number of possible combinations of two numbers and then count the number of combinations that result in a sum greater than 12.
The set contains four numbers, so there are 4 choose 2 possible combinations of two numbers, which is equal to (4! / (2! * (4 - 2)!)), or 6 combinations. These combinations are:
(0,6), (0,12), (0,15), (6,12), (6,15), (12,15)
Next, we'll count the number of combinations that result in a sum greater than 12. These combinations are:
(6,15), (12,15)
There are 2 combinations that result in a sum greater than 12.
Finally, to find the probability, we'll divide the number of favorable outcomes (combinations with a sum greater than 12) by the total number of outcomes (all possible combinations of two numbers), and express the result as a fraction:
probability = 2 / 6
Reducing the fraction, we get:
probability = 1 / 3
So, the probability that the sum of two randomly selected numbers from the set is greater than 12 is 1/3.
That's how you find the probability of the sum of two randomly selected numbers from a set being greater than a certain value. By counting the number of favorable outcomes and dividing by the total number of possible outcomes, you can find the probability of a certain event.
The
ages
of 5 women are
48, y, 52, 50 and (2y-5).
If their average is
47 years,
Find the age of the oldest woman
Given the information that the average of the ages of 5 women is 47 years and that their ages are 48, y, 52, 50, and (2y-5), we can set up the following equation:
(48 + y + 52 + 50 + 2y - 5) / 5 = 47
Expanding the equation and simplifying, we get:
5y = 244
y = 48.8
So the age of the woman whose age is represented by the variable y is 48.8 years.
The oldest woman is represented by the age of 52 years, which is the largest of all the ages.
Therefore, the age of the oldest woman is 52 years.
Maria is renting kayaks from a local shop that charges a $7 fee, plus an hourly rate of $5. 50. For how long can maria rent the kayak if she pays a total of $40?.
The number of hours Maria rent the kayak for the paid amount of $40 when hourly rate is $5.50 is equal to 6 hours.
Fees of renting charges paid for kayaks from a local shop = $7
Hourly rate = $5.50
Let 't' be the number of hours Maria rent kayak.
Total fees paid by Maria for renting kayak for 't' hours is equal to $40
Required equation to represents the above condition is
$40 = $7 + $5.50t
Simplify the expression to get the value of 't'
⇒ 5.50t = 40 - 7
⇒ t = 33 / 5.50
⇒ t = 6 hours
Therefore, for the number of hours Maria rent kayak by paying total of $40 is equal to 6 hours.
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This is a number sequence
2,3,5,9,17,33,65
what are the next two terms?
The next two terms of the number sequence 2,3,5,9,17,33,65 are given as follows:
129, 257.
How to obtain the next two terms of the number sequence?This is a recursive number sequence, as each term is obtained multiplying the previous term by 2 and then subtracting one.
Then the term after 65 is given as follows:
65 x 2 - 1 = 130 - 1 = 129.
The term after 129 is given as follows:
2 x 129 - 1 = 257.
Then the next two terms are 129 and 257.
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The function f (x) = 125,000 (1.028)x models the change in population of Pool City, where x represents the number of years since 2010. Which statement is NOT true?
A.) The domain of the function includes all real values of x .
B.) The point (1, 128500) represents the population of Pool City in 2011.
C.) The population of Pool City in 2010 is 125,000.
D.) The function has an asymptote at y = 125,000 .
Help!! Drag and drop a statement or reason to each box to complete the proof.
Given: PQ≅PR
Prove: ∠Q≅∠R
The triangles ΔPQM and ΔPRM are congruent. Then angle Q is identical to angle R.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The line segment PM is the median of the isosceles triangle ΔPQR.
Point M is the midpoint of QR by the definition of the median.
In triangles ΔPQM and ΔPRM, then we have
PQ = PR {Given}
QM = RM {Mid point}
MP = MP {Reflexive property}
The triangles ΔPQM and ΔPRM are congruent to each other by SSS postulates.
∠Q = ∠R
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The complete question is given below.
The line segment PM is the median of the isosceles triangle ΔPQR. Drag and drop a statement or reason to each box to complete the proof.
Given: PQ ≅ PR
Prove: ∠Q ≅ ∠R
On a partagé une somme entre trois personnes: la première en a reçu les deux tiers, la deuxième 300dirhams de moins que la deuxième. Chercher la somme et les trois parts
An investment of $65,000 is increasing at a rate of 3.2% per year. Which function represents how to find the value of the investment after t years?
Answer:
I honestly don't know I just need points
A scientist collected a sample of data on cactus heights. the data were rounded to the nearest foot. if the minimum score was 4 feet and the range was 6 feet, what was the maximum score? The answer is 9.
I found this question here on brainly but an expert said the answer is 10 but that is wrong. I tried commenting to say that the answer is 9 but couldn't figure out how to comment so I just posted this question with the answer for anyone who needs the answer. :) The answer is 9, I received points for it being correct.
Answer: the maximum score was 10 feet.
Step-by-step explanation:
here's a step-by-step explanation:
Identify the minimum score: The minimum score is given in the problem as 4 feet.
Identify the range: The range is also given in the problem as 6 feet.
Calculate the maximum score: To find the maximum score, we simply need to add the minimum score and the range.
Maximum score = Minimum score + Range
Maximum score = 4 feet + 6 feet
Maximum score = 10 feet
So the maximum score was 10 feet.
If the radius of one of the semicircles is 7 meters, what is the circumference of one of the semicircle? asap 70 Ponits!!!!!!!!!!
10.99 m
21.98 m
87.92 m
43.96 m
Answer:
The circumference of one of the semicircles with a radius of 7 meters would be approximately 21.98 meters.
Step-by-step explanation:
The circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference, π (pi) is approximately equal to 3.14, and r is the radius of the circle.
For a semicircle with a radius of 7 meters, the circumference can be calculated as follows: Because the semicircle is a half circle, then:
C = (2πr)/2= 3.14 × 7 = 21.98 meters
So, the circumference of one of the semicircles with a radius of 7 meters would be approximately 21.98 meters.
Answer:
The circumference of one of the semicircles is 21.98 m.
Step-by-step explanation:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
A semicircle is half a circle, therefore the length of the curved part of the circumference of a semicircle is half the circumference of a circle: πr.
Given the radius of one of the semicircles is 7 m and π ≈ 3.14, the circumference of the semicircle is:
⇒ C = 3.14 · 7
⇒ C = 21.98 m
Which number line best represents the solution to the inequality 3x+2≤4x+5≤9
?
The number line of the inequality is (d)
How to determine the number line of the inequalityfrom the question, we have the following parameters that can be used in our computation:
3x+2≤4x+5≤9
When this is expanded, we have
3x + 2 ≤ 4x + 5 and 4x + 5 ≤ 9
Evaluate the like terms
So, we have the following representation
-x ≤ 3 and 4x ≤ 4
Divide by the coefficient of x
x ≥ -3 and x ≤ 1
When combined, we have
-3 ≤ x ≤ 1
So x is between -3 and 1, inclusive.
This is represented by the number line (d)
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Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 232.36 square inches.
If the diameter of the tub is 8 inches, what is its height? Use π = 3.14.
6.75 inches
5.25 inches
3.375 inches
2.625 inches
If the diameter of the tub is 8 inches, then the height of gallon tube is, 5.25 inches
What is surface area ?Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.
The surface area of a cylinder can be expressed as:
SA = 2πr² + 2πr x h
where r is the radius of the cylinder, h is its height, and π is the constant pi (3.14).
The diameter of the tub is 8 inches, which means the radius is 4 inches. We are also given that the total surface area is 232.36 square inches.
So we can write:
232.36 = 2(3.14)(4²) + 2(3.14)(4)(h)
Simplifying and solving for h, we get:
232.36 = 100.48 + 25.12h
131.88 = 25.12h
h = 131.88/25.12
h ≈ 5.25 inches
Therefore, the height of the ice cream tub is approximately 5.25 inches.
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(ej a number is divisible by 2 and 3, it is divisible by 6. 64 is divisible by 2 but no Sh
What can be concluded from this?
64 is also divisible by 3
54 s dvisible only by 2
() 64 is also divisible by 6
(v) 64 is not divisite by 6
Answer:
64 is not divisible by 6 because although it is divisible by 2, it is not divisible by 3 so it is not divisible by 6.
Step-by-step explanation:
Translate the sentence into a mathematical equation.
Power equals current times voltage.
Let P represent power, current, and V voltage. Write the equation.
P=
On solving the Power equals Current times voltage as an equation we get power is P = VI
What is equation?A mathematical equation is a fοrmula that joins twο statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. For instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences οn either side of a letter is described by a mathematical fοrmula. Often, there is only οne variable, which also serves as the symbol. fοr instance, 2x – 4 = 2.
Given to write
Power equals current times voltage
in mathematical equation, i.e.
P = V × I
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Riding equation of the line that has the same slope as 3X minus 2Y equals 12 in the same y-intercept as 5Y +21 equals 4X
The linear equation can be written as:
y = (3/2)*x - 21/5
How to write the linear equation?
A general linear equation can be written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
First, we know that our line has the same slope than:
3x - 2y = 12
Rewriting that we will get:
3x - 2y = 12
3x - 12 = 2y
(3/2)x - 12/2 = y
So the slope of this line is (3/2).
And our lie has the same y-intercept as 5y + 21 = 4x
We can rewrite that to get:
5y = 4x - 21
y = (4/5)x - 21/5
The y-intercept is -21/5
Then the linear equation is:
y = (3/2)*x - 21/5
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Determine the truth value of the following statements if the universe of discourse of each variable is the set of real numbers. Enter your answer as Tor F.
1.∃x∀y(xy = 0)
2. ∃x (x^2 = -1)
The truth value for the logical proposition is 1) T 2) F 3) T 4) F 5) T
The rules of mathematical logic specify methods of reasoning mathematical statements. Greek philosopher, Aristotle, was the pioneer of logical reasoning. Logical reasoning provides the theoretical base for many areas of mathematics and consequently computer science. It has many practical applications in computer science like the design of computing machines, artificial intelligence, the definition of data structures for programming languages etc.
Propositional Logic is concerned with statements to which the truth values, “true” and “false”, can be assigned. The purpose is to analyze these statements either individually or in a composite manner
the truth value of the following statements if the universe of discourse of each variable is the set of real numbers. Enter your answer as T or F.
1) there exists x for all y xy=0 is true T
2) there exist x x2=-1 F
3) for all x2=y T
4) for all x there exist x=y2 F
5) for all x not equal to zero xy=1 T
The complete question is -
the truth value of the following statements if the universe of discourse of each variable is the set of real numbers. Enter your answer as T or F.
1) there exists x for all y xy=0 is true
2) there exist x x2=-1
3) for all x2=y
4) for all x there exist x=y2
5) for all x not equal to zero xy=1
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