This problem is related to the concept of continuous compounding, which is a method of calculating the interest earned on an account over a certain period of time. The formula for calculating the principal amount for a continuously compounded account earning 3.9% for 15 years is as follows:
P = A/ (1 + r)^t
Where P is the principal, A is the balance after 15 years, r is the rate of interest and t is the number of years.
In this problem, P = $4,768,549.11, A = $2,656,586.66, r = 3.9% and t = 15.
Therefore, the principal for the continuously compounded account earning 3.9% for 15 years is $4,768,549.11
Why is base e used in exponential functions?
Base e used in exponential functions because base e is the base rate of growth shared by all continually growing processes which lets us take a simple growth rate.
What does the base represent in an exponential function?In an exponential function, the base b is a constant. The exponent x is the independent variable in which the domain is the set of real numbers. There are two types of exponential functions, those are exponential growth and exponential decay. In the function f (x) = b^x when b > 1, the function represents exponential growth.
Base e allows us to take a simple growth rate, where all change occurs at the end of the year, and find the influence of compound, continuous growth, where every nanosecond or faster, we are growing slightly.
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hi please help me I’ll do the Brian list thing!!!
A set of eight cards were labeled with S, U, B, T, R, A, C, T. What is the sample space for choosing one card?
Os={A, B, C, R, S, U}
Os = {A, B, C, R, S, T, T, U}
Os = {A, U}
Os={T}
Which of the following equations are true? Select all that apply. A. 24 . 8 ÷ 10 2 = 0 . 248 B. 34 . 65 ÷ 1 , 000 = 0 . 3465 C. 193 . 5 ÷ 10 0 = 193 . 5 D. 6 . 24 ÷ 10 = 62 . 4 E. 160 . 4 ÷ 10 2 = 0 . 1604
I’ll give brainlist!!What is the restricted domain of the quadratic(y=x^2 +4) that would ensure that the inverse is a function? Justify the answer
We can restricted domain of the quadratic(y=x^2 +4) is {-∞,0} or {0,∞}.
What is Quadratic Equation?
Having the form ax^2 + bx + c = 0, quadratic equations are second-degree algebraic expressions. From the term "quad," which meaning square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way. A quadratic equation is employed in numerous situations. In addition, there are many uses for quadratic equations in physics, engineering, astronomy, etc.
There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are denoted as (, ) and are also known as the roots of the quadratic equations.
What is Domain?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
It cannot have an inverse function because the largest exponent is even (2), unless the domain is constrained.
We know that the vertex is at x = 0 since our equation is already in vertex form;
a(x - h)^2 + k, or 1(x - 0) + 4
In order to limit the domain to only one side of x = 0
either {-∞,0} or {0,∞}
Therefore, We can restricted domain of the quadratic(y=x^2 +4) is {-∞,0} or {0,∞}.
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Please help meee !?!,,,
Answer:
$3
Step-by-step explanation:
$13.99 is for one hour and one hour is for 3 children. This means they paid a total of 3 hours.
$13.99 * 3 = $41.97 for admission alone
Now our total is $50.97
Let's subtract that from admission to find sock price in total
$50.97-$41.97 = $9
Again, 3 children and each for a pair, so lets divide that $9 by 3 for each child.
$9/3 = $3
A vase is in the shape of a cone. The height is 12 inches and the diameter is 4.4 inches.
What is the lateral surface area to the nearest tenth of a square inch
The lateral surface area of the cone is:
A = 84.3 in²
How to get the lateral surface area of the vase?We know that for a cone of height H and a radius R, the lateral surface area is given by the formula:
A = pi*R*( √(H² + R²))
Where pi = 3.14
Here the height is 12 inches, and the diameter is 4.4 inches, then the radius is:
R = 4.4i/2 = 2.2 in
Then the lateral surface area is:
A = 3.14*2.2in*( √((12in)² + (2.2in)²))
A = 84.3 in²
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If triangles are similar what’s the scale factor
Answer:
1.5 on edg
Step-by-step explanation:
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1, Δ ABC∼ Δ DEF. Figure 1 Similar triangles whose scale factor is 2 : 1. The ratios of corresponding sides are 6/3, 8/4, 10/5.
What is the greatest common
factor (GCF) of 24 and 56?
Answer:
8
I wish you luck in your assignments.
Find the length of the third side, if necessary, write in simplest radical form.
Answer:
The length of the third side is 7.
Step-by-step explanation:
We can use the Pythagorean theorem to evaluate the length of the third side.
[tex]a^2+b^2=c^2[/tex]
Let the third side be [tex]a[/tex].
Lets solve for [tex]a.[/tex]
Subtract [tex]b^2[/tex] from both sides.
[tex]a^2=c^2-b^2[/tex]
Take the square root of both sides.
[tex]a=\sqrt{c^2-b^2}[/tex]
We are given
[tex]c=\sqrt{58} \\b=3[/tex]
Lets evaluate [tex]a[/tex].
[tex]a=\sqrt{(\sqrt{58} )^2-3^2}[/tex]
Simplify.
[tex]a=\sqrt{58-9}\\a=\sqrt{49} \\a=7[/tex]
Somebody help please I don’t understand!!
Answer:
1) y=0.56x
2)y=5x
3)y= 0.25x
Step-by-step explanation:
1) 2.24/4 = $0.56 (Cost per carton)
2) 15/3=5 ( miles ran per hour)
3) 3/12 = 0.25 (cost per ounce)
Martin is starting a new job. During training, he will earn $16 per hour. Once he starts, Martin will earn $20 per hour. What is the percent of change in Martin's pay from training to actually working?
Answer:
25%
Step-by-step explanation:
percent change = (new value - old value)/(old value) × 100%
percent change = (20 - 16)/(16) × 100%
percent change = 25%
What is the solution
the solutions for a system of equations is where the graphs of each equation meet or intersect.
for the picture above with two parallel lines, well, the lines are parallel and apart from each other, that means they never meet or intersect, and since they never intersect, they have no solution.
The probability of spinning an odd number, flipping heads, then spinning a yellow is
The probability of spinning an odd number, flipping heads, then spinning a yellow is of 1/9.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The probabilities for each case in this problem are given as follows:
Odd number: 2/3. (2 out of 3 regions in the spinner are odd numbers, 1 and 3).Heads: 1/2. (fair coin, equally as likely to be heads or tails).Spinning a yellow: 1/3.The events are independent, hence the probability is obtained multiplying each probability as follows:
p = 2/3 x 1/2 x 1/3 = 1/9.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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how do i graph this in the image attached?
The value of the equation is P ( 4 , 4 ) , where P is the point of intersection of the equations
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
4x - 2y = 8
Adding 2y on both sides of the equation , we get
2y + 8 = 4x
Subtracting 8 on both sides of the equation , we get
2y = 4x - 8 be equation (1)
Now , let the second equation be represented as B
Now , the value of B is
y = ( 3/2 )x - 2
On simplifying the equation , we get
2y = 3x - 4 be equation (2)
Now , subtracting equation (2) from equation (1) , we get
4x - 8 - ( 3x - 4 ) = 0
4x - 8 - 3x + 4 = 0
x - 4 = 0
Adding 4 on both sides of the equation , we get
x = 4
Substitute the value of x = 4 in equation ( 1 ) , we get
2y = 8
y = 4
So , the value of x = 4 and y = 4
The equations are plotted on the graph and the point of intersection is the solution to the equation , P ( 4 , 4 )
Hence , the equations are solved
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Write the rule for the linear function shown in the table I’ll give brainliest
Is there a factor on this pls help Questiob : 5x ^ 2 - 8x + 9
Answer:
(5x - 3)(x - 3)
Step-by-step explanation:
Yes, the expression "5x^2 - 8x + 9" can be factored.
One way to factor it is to find the two numbers that multiply to give 9 (the constant term) and add to give -8 (the coefficient of x). These two numbers are 3 and -3.
We can use these two numbers to factor out the common factor (x - 3) from the expression:
5x^2 - 8x + 9 = (5x^2 - 8x) + 9
= (5x^2 - 8x + 9) - 9 + 9
= (5x^2 - 8x + 9) - (3x - 3x)
= (5x - 3)(x - 3)
So the fully factored form of the expression is (5x - 3)(x - 3)
So, (5x - 3) and (x - 3) are the factors of the expression "5x^2 - 8x + 9"
The box-and-whisker plot below represents some data set. What is the value of the upper quartile?
The value of the upper quartile is 24.
What is quartile calculation method?This method is used to divide a data set into four equal parts and find the values of the quartiles.
To calculate the upper quartile, we first need to find the median (the middle value) of the data set.
This question involves the use of the quartile calculation method.
This can be done by arranging the data in numerical order and finding the middle value.
In this case, the median value is 20.
The upper quartile is then calculated by finding the median of the values above the median.
In this case, the values above the median are 22, 24, 28, and 30.
To find the upper quartile, we need to calculate the median of these values.
This is done by arranging the values in numerical order and finding the middle value, which is 24. Therefore, the upper quartile is 24.
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need help with math tyyy
Answer:
The answer is D!
Identify the equation of the line graphed
A
B
C
D
A. x + 2y = -2
B.
x-2y = 2
C. 2x + y = -1
D. 2x-y = 1
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
Step 1: m∠x + m∠y + m∠z = 180 degrees (sum of angles of a triangle)
Step 2: m∠w − m∠z = 90 degrees (corresponding angles)
Step 3: Therefore, m∠x + m∠y + m∠z = m∠w + m∠z
Step 4: So, m∠x + m∠y = m∠w
In which step did the student first make a mistake and how can it be corrected? (5 points)
a
Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (sum of corresponding angles)
b
Step 2; it should be m∠w + m∠z = 180 degrees (supplementary angles)
c
Step 1; it should be m∠x + m∠y + m∠z = 90 degrees (corresponding angles)
d
Step 2; it should be m∠w + m∠z = 90 degrees (alternate exterior angle)
Step 2 is the incorrect step and hence d is the correct answer.
What are Adjacent Angles?The two angles are said to be adjacent angles when they share the common vertex and side. The endpoint of the rays, forming the sides of an angle, is called the vertex of an angle. Adjacent angles can be a complementary angle or supplementary angle when they share the common vertex and side.
Given here: m∠w + m∠z = 90 but this is not true because they are adjacent angles and they lie on a line so they must supplement each other.
m∠w + m∠z = 180
Hence, Step 2 is the incorrect step and hence d is the correct answer.
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At the end of a snow storm, Nolan saw there was a lot of snow on his front lawn. The temperature increased and the snow began to melt at a steady rate. The depth of snow on Nolan's lawn, in inches, can be modeled by the equation S=-1.75t+14,S=−1.75t+14, where tt is the time, in hours, after the snow stopped falling. What is the yy-intercept of the equation and what is its interpretation in the context of the problem?
Answer:
r
Step-by-step explanation:
e
A magician asks a volunteer to think of two different positive integers without telling her what they are. She then asks him to calculate x, the sum of the larger number with the square of the smaller, and y, the difference between the numbers. The volunteer tells her that x = 9 and y = 3. Find the original numbers.
Answer: 2 and 5.
Step-by-step explanation: We can use algebra to solve for the original numbers. Let's call the smaller number "a" and the larger number "b". From the information given, we know that:
x = b + a^2
y = b - a
The volunteer tells the magician that x = 9 and y = 3. So we can use these values to create a system of equations:
b + a^2 = 9
b - a = 3
To solve for the original numbers, we can first add the two equations together to eliminate b:
a^2 + 2a + 2 = 12
a^2 + 2a = 10
a^2 + 2a - 10 = 0
(a + 5)(a - 2) = 0
This tells us that the two solutions for a are -5 and 2. But since a is a positive integer, we know that it must be 2.
We can now substitute this value of "a" back into the original equations to find "b":
b + a^2 = 9
b + 2^2 = 9
b + 4 = 9
b = 5
So the original numbers are 2 and 5.
Which equation can she use as statement 5? (3x + 24):3x = 85:51 (3x + 24):85 = 51:3x (3x + 24):51 = 3x:85 34:24 = 3x:51.
The equation that she can use as statement 5 is c) (3x + 24): 51 = 3x: 85.
To prove that x = 12, Dora must first prove that the segments ST and RQ are parallel. This can be done by showing that the angles formed by their intersection are congruent.
Since the angles, QRT and STP are congruent (statement 2) and the angles SPT and QPR are congruent (statement 3), the Triangle-Angle Angle Similarity Postulate can be applied to show that triangle SPT is congruent to triangle QPR (statement 4).
Now, the corresponding sides of the two triangles must be in proportion in order to prove that x = 12. For this, Dora can use the equation (3x + 24) : 51 = 3x : 85 (statement 5). This equation states that the ratio of the lengths of the corresponding sides of the two triangles is equal to the ratio of 3x to 51 and 3x to 85, respectively.
Since the ratio of the sides of the two triangles must be equal, then 3x + 24 must be equal to 85 and 3x must be equal to 51. Solving for x, we get x = 12, proving that if segment ST is parallel to segment RQ, then x = 12.
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The complete question
Look at the figure shown below. Dora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 12.
1.Segment ST is parallel to segment QR
Given
2.Angle QRT is congruent to angle STP
Corresponding angles formed by parallel lines and their transversal are congruent.
3.Angle SPT is congruent to angle QPR
Reflexive property of angles.
4.Triangle SPT is congruent to triangle QPR
Angle-Angle Similarity Postulate
5.?Corresponding sides of similar triangles are in proportion.
Which equation can she use as statement 5?
(3x + 24) : 3x = 85 : 51
(3x + 24) : 81 = 3x : 51
(3x + 24) : 51 = 3x : 85
34 : 24 = 3x : 51
After kicking, one coach likes to play practice games with 6 players on each
team. She doesn’t like any team to have more or fewer than 6 players and
she doesn’t like anyone to be left off a team. What are the possible numbers
of players who must show up to practice so that the coach can make these
teams?
Note that the question is about numbers in multiples of 6 or which can be divided equally by 6. Thus the likely number of people who must show up to practice so that the coach can make these teams are 6, 12, 18, 24, 30, 36, 48, and so on. The bottom line is that the number must be a common multiple of 6.
What is the proof that each of the numbers above will create teams of x players each?One way to show that each of the numbers above will equal an exact team of 6 without anyone left off is by dividing each by 6. If we get an integer, then we are correct. Thus:
6/6 = 1 Team12/6 = 2 Teams18/6 = 3 Teams24/6 = 4 Teams30/6 = 5 Teams36/6 = 6 teams48/6 = 8 Teams.Hence, the above Common Multiples are correct.
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Makena deposited the following
amounts in her savings account last
month: $6.74, $5.21, $5.53, and $3.52.
Divide the sum by 30 to find the average
amount she saved per day for the month.
Show your work.
Makena deposited $0.70 per day.
What is Average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Given:
The savings account last month: $6.74, $5.21, $5.53, and $3.52.
Makena deposited $6.74,$5.21,$5.53 and $3.52 in her saving account.
To find the average amount she saves per day.
We add all the deposited savings
= ( 6.74 + 5.21 + 5.53 + 3.52)
= $21.031
Now, Makena Saved per day for the month = $21.031/30
=$0.70
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Write the Expression “ x - 9” in words
Answer:
"x-9" can also be written as "x minus nine" or "nine subtracted from x"
A four-sided figure is resized to create a scaled copy. The proportional relationship between any given side length in the original figure, f, and the corresponding side length in the scaled copy, s, can be represented by the equation s can be represented by s= 11 over 2 f. What is the constant of proportionality from side lengths in the original figure to side lengths in the scaled copy
Constant of proportionality from side lengths in the original figure to side lengths in the scaled copy = 2/11
What is proportion?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol "::" or "=".
Given,
f is the length of side of original figure
And s be the side of copied figure
f ∝ s
⇒ f = ks --------(a)
where k is constant of proportionality
Proportion between side of original figure and its copy is such that
s = (11/2)f
f = (2/11)s -----------(b)
comparing equation (a) and (b)
k = 2/11
Hence, 2/11 is constant of proportionality from side lengths in the original figure to side lengths in the scaled copy.
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Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon. K = 1/2
The new coordinates of the polygon are J'(-5/2, 3/2), K'(1, 3/2), L'(1, -3/2), M'(-5/2, -3/2).
What is transformation?Transformation is the movement of a point in the coordinate plane. Types of transformation are reflection, rotation, translation and dilation.
Dilation is the enlargement or reduction in the size of a figure by a scale factor.
Given the coordinates of polygon J(-5, 3), K(2, 3), L(2, -3), M(-5, -3). For a dilation with a scale factor of 1/2, the new coordinates are:
J'(-5/2, 3/2), K'(1, 3/2), L'(1, -3/2), M'(-5/2, -3/2).
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What is the measure of 90,and measureof the inscribe angle
Answer: 45 degrees
Step-by-step explanation:
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.
what is y=2x-8 y=-x+1 on a graph
not sure if you need the solution too but if you do it’s (3,-2)