Using the compound interest formula, it is obtained that it would take approximately 9.9 years for the account balance to reach $20,000.
What is Compound Interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
We can use the formula for compound interest to solve this problem -
[tex]A = P(1 + \frac{r}{n})^{(nt)}[/tex]
where A is the account balance, P is the principal (the initial investment), r is the annual interest rate (as a decimal), n is the number of times per year the interest is compounded, and t is the time (in years).
In this case, we have P = 5000, r = 0.09 (9% annual interest), n = 4 (compounded quarterly), and A = 20000. We want to find t.
Substituting these values into the equation, we get -
[tex]20000 = 5000 \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]
Dividing both sides by 5000, we get -
[tex]4 = \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]
Taking the natural logarithm of both sides, we get -
ln(4) = 4t ln(1 + 0.09/4)
Solving for t, we get -
t = ln(4) / (4 ln(1 + 0.09/4))
Simplifying the equation, we get -
t ≈ 9.9
Therefore, the time value is obtained as 9.9 years.
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the figure below is dilated by a factor of 4 centered at the orgin. plot the resulting image
(where are the points pls im so confused)
The image that results from the dilation transformation is as shown in the attached file with coordinates as:
G'(0, -8)
H'(8, 0)
I'(-8, 4)
What is the coordinate of the triangle after dilation?A dilation is defined as a transformation that produces an image that is the same shape as the original, but is a different size.
The coordinates of the given triangle are:
G(0, -2)
H(2, 0)
I(-2, 1)
Now, when an object with coordinates is dilated by a factor about the origin, what we will do is to multiply each coordinate by that factor . The factor of dilation is 4 and as such we have:
G(0, -2) * 4 = G'(0, -8)
H(2, 0) * 4 = H'(8, 0)
I(-2, 1) * 4 = I'(-8, 4)
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The median of the data 10 16 12 15 7 is
What is the measure of a deciliter ?
Answer:A deciliter measures fluid volume equal to 1/10 of a liter.
Step-by-step explanation:
Answer:
A decilitre (dl) is a tenth of a litre.
Step-by-step explanation:
U・ᴥ・U
A furniture maker used 7/8 of a can of paint to paint some chairs. He used 1/8 of a can of paint for each chair. How many chairs did he paint?
Answes
djlkadmlke
wkdsjcnkslzmkcklask.dc
edskjhdiuwslnld
edsbkj,dw
What is the value of x? Enter your answer in the box. x = The figure shows 2 right triangles, triangle R S T with right angle S and triangle Q R T with right angle R. The measure of angle R T S is 60 degrees. The measure of angle Q T R is 45 degrees. The length of side R S is 2 square root 3. The length of side Q R is x.
The value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
using the trigonometric ratio of tan 45°
{recall that tan 45° = 1}
tan 45° = QR/RT {opposite/adjacent}
tan 45° = x/2√3
x = tan 45 × 2√3 {cross multiplication}
x = 1 × 2√3
x = 2√3
Therefore, the value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.
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Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ between 93 and 117.
The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.
What is probability?
Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.
To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.
The z-score formula is:
z = (x - μ) / σ
where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.
For the lower bound of 93, the z-score is:
z = (93 - 105) / 20 = -0.6
For the upper bound of 117, the z-score is:
z = (117 - 105) / 20 = 0.6
Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:
normalcdf(-0.6, 0.6, 0, 1)
This gives us a probability of 0.6827.
Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.
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[tex]2^{2} . 2^{3}[/tex]
Answer:
32
Step-by-step explanation:
add the exponents
2 + 3 = 5
2⁵ = 32
Can someone explain me how to do this task please? Thank you
Step-by-step explanation:
common multiples are numbers that can be divided without remainder by both numbers.
12. 3 and 5
3 and 5 are both prime numbers, so their common multiple are multiples of their product (3×5 = 15).
so,
1×15 = 15
2×15 = 30
3×15 = 45
13. 4 and 6
the prime factors of 4 are
2×2
the prime factors of 6 are
2×3
the last common multiple is the product of the longest chains of prime factors of the numbers :
2×2 × 3 = 12
6 has only one 2 factor, 4 has two 2 factors, so that is the longest chain. and 6 has one 3 factor, which makes it the longest chain for that.
the multiples for 4 and 6 and now the multiples of 12 :
1×12 = 12
2×12 = 24
3×12 = 36
4×12 = 48
14. 3 and 7
they are both again prime numbers, so we are looking for multiples of their product (3×7 = 21).
1×21 = 21
2×21 = 42
15.
what do we need to do to change the denominator by keep the overall value of the fraction ?
we need to multiply numerator and denominator by the same value (e.g. by 2/2, 3/3, 4/4, ...)
3/4 = 6/8 = 9/12 = 12/16
16.
as before.
2/3 = 4/6 = 6/9 = 8/12
17.
as before
4/5 = 8/10 = 12/15 = 16/20
18.
now we need to find the largest n/n factor hidden in the fraction. by eliminating that we get the core (simplified) value of the fraction.
4/12 = 1/3 × 4/4
so,
1/3 is the simplified fraction.
19.
as before
6/10 = 3/5 × 2/2
3/5 is the simplified fraction.
20.
as before
4/8 = 1/2 × 4/4
1/2 is the simplified fraction.
In the expression 5 a 5 a 5 a 5 a 5 you replace each of the four a symbols with either +, or –, or ×, or ÷. You can insert one or more pairs of parentheses to control the order of
operations. Find the second least whole number that CANNOT be the value of the resulting expression. For example, each of the numbers 25 = 5 + 5 + 5 + 5 + 5 and 60 = 5 + (5 + 5) × 5 + 5 can be the value of the resulting expression.
The final output of the algorithm is 42; being the second least entire numeral that cannot be acquired from the picked equation.
How to explain the informationIt should be noted that to accurately identify the solution to this predicament, one must understand all possible amalgamations of four elementary arithmetic operations and parentheses, then scrutinize each resulting expression to detect the second smallest whole number that is not attainable.
An efficient tactic to adopt during this process is to use an iterative function which conceptualizes each action and positioned pair of parenthesis, evaluates the created expressions, produces a set of accomplished values, sequences them in order, and at last locates the second minutest non-obtainable figure. The final output of the algorithm is 42; being the second least entire numeral that cannot be acquired from the picked equation.
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The equivalent expression
Ajustification for job training program is that they improve worker productivity
Answer:
Step-by-step explanation:
One justification for a job training program is that it can improve worker productivity. By providing training opportunities to workers, they can learn new skills, gain knowledge, and become more efficient in their work. This can lead to increased productivity, as workers can complete tasks more quickly and effectively.
Training can also improve the quality of work performed by employees. With proper training, workers can learn best practices, techniques, and procedures that can improve the quality of their work. This can lead to better outcomes, fewer errors, and more satisfied customers.
In addition, job training programs can lead to increased employee satisfaction and engagement. When workers feel that they are being invested in, they are more likely to be motivated and engaged in their work. This can lead to higher job satisfaction, better morale, and increased loyalty to the company.
Overall, job training programs can be a beneficial investment for companies. By improving worker productivity, quality of work, and employee engagement, companies can reap the benefits of a more efficient and effective workforce.
In addition to the benefits of improved worker productivity, job training programs can also have other advantages for both employees and employers, including:
Increased job satisfaction and motivation: By providing opportunities for growth and development, job training programs can help employees feel more engaged and invested in their work. This can lead to increased job satisfaction, motivation, and commitment to the company.
Improved employee retention: When employees feel that they are being invested in and have opportunities for advancement, they are more likely to stay with the company. This can lead to reduced turnover and the associated costs of recruiting, hiring, and training new employees.
Enhanced skills and knowledge: Job training programs can help employees develop new skills and knowledge that can be applied to their work. This can lead to increased efficiency, better quality work, and the ability to take on new responsibilities.
Adaptation to new technology and processes: As technology and processes evolve, job training programs can help employees stay up-to-date and adapt to new tools and methods. This can ensure that the company remains competitive and able to take advantage of new opportunities.
Improved safety and compliance: Job training programs can also help ensure that employees are aware of safety procedures and regulations, reducing the risk of accidents or legal violations.
Overall, job training programs can have a variety of benefits for both employees and employers, making them a worthwhile investment.
Explain why the nature of roots depends on the value of the dicriminant.
Answer:
The discriminant of a quadratic equation is the expression found under the square root sign in the quadratic formula, which is b^2 - 4ac. The discriminant reveals information about the nature of the roots of the equation.
If the discriminant is positive, the quadratic equation has two distinct real roots. This means that the equation can be factored into two linear factors, each of which can be set equal to zero to solve for the roots.
If the discriminant is zero, the quadratic equation has one real root, which is a repeated root. This means that the equation can be factored into a linear factor that occurs twice.
If the discriminant is negative, the quadratic equation has two complex (non-real) roots, which are conjugates of each other. This means that the equation cannot be factored into two linear factors with real coefficients.
In summary, the nature of roots of a quadratic equation is determined by the value of the discriminant, which depends on the coefficients of the quadratic equation.
Step-by-step explanation:
If 9% of a number equals 10, find 27% of that number.
Answer: 27% of the number is 30.
Step-by-step explanation:
Let's start by setting up an equation to solve for the number:
0.09x = 10
Here, x represents the number we are trying to find. To solve for x, we can divide both sides of the equation by 0.09:
x = 10 ÷ 0.09
x = 111.11...
So the number we are looking for is approximately 111.11.
To find 27% of this number, we can multiply it by 0.27:
27% of 111.11... = 0.27 × 111.11...
27% of 111.11... = 30
Therefore, 27% of the number is 30.
Help! Does the rule represent an exponential function?
y = -5x^7
If (-2,8) and (1,-10) are two anchor points on a trend line, then find the equation of the line
Answer:
The equation would be y = 3x - 7
Step-by-step explanation:
The equation of the trend line given the two coordinates is: y = -6x - 4
How to find the equation of a line?
The formula to find the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula to find the equation of a line between two coordinates is:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
From the given two coordinates, we can say that:
(y - 8)/(x + 2) = (-10 - 8)/(1 + 2)
(y - 8)/(x + 2) = -6
y - 8 = -6x - 12
y = -6x - 4
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write as a product: b^2*c^2-4bc-b^2-c^2+1
Answer:
(b*c+c-1+b)*(-c+b*c-b-1)
or
(b*c + c - 1 + b)*(-c + b*c - b -1)
put both in the same order:
(bc + b + c - 1)( bc - b - c - 1)
Turn the crank:
(bc)2 + b2c + bc2 - bc -b2c -b2 - bc + b -bc2 - bc - c2 + c -bc - b - c + 1
Cancel things....
(bc)2 - bc -b2 - bc - bc - c2 -bc + 1
(bc)2 - 4bc - b2 - c2 + 1
NO LINKS!!! URGENT HELP NEEDED!!!
Which additional point can be plotted so that the graph continues to represent y as a function of x?
a. (1 ,0)
b. (2, 2)
c. (3, 4)
d. (-4, 2)
Answer:
a. (1 , 0)
Step-by-step explanation:
A function is a special type of relationship where each input (x-value) is related to exactly one output (y-value).
From inspection of the given graph, the points on the graph of the function are:
(-4, 4)(-2, 3)(-1, -2)(0, 2)(2, -1)(3, 0)For the graph to continue to represent a function, any additional points cannot have the same x-value as any of the defined points.
Therefore, the only additional point that can be plotted so that the graph continues to represent y as a function is x is (1, 0).
Use the drop-down menus to explain if the
two figures below are congruent, similar, or
neither. If the figures are similar, state the
scale factor.
R
S
T
T
Q
12
11
10
9
8
7 N
6
5
4
3
2
1
onto Figure QRST.
S
-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
É Ổ có có ýó ơi Á có nó
-5
-6
-7
-9
-10
-11
-12
M
L
K_
1 2 3 4 5 6 7 8 9 10 11 12
Figure KLMN
◆ congruent to
Figure QRST because rigid motions
be used to map Figure KLMN
Figure KLMN
QRST because rigid motions and/or
dilations
be used to map
similar to Figure
Figure KLMN onto Figure QRST.
·x
Figure KLMN is congruent to Figure QRST because rigid motions can be used to map Figure KLMN onto Figure QRST.
Figure KLMN is similar to Figure QRST because rigid motions and/or dilations can be used to map Figure KLMN onto Figure QRST.
Since the figures are similar, the scale factor is 2.
What are similar geometric figures?In Mathematics, two (2) geometric figures are two (2) geometric figures are considered to be similar when the ratio of their corresponding side lengths are equal and the magnitude of their corresponding angles are congruent.
Generally speaking, the common ratio of the corresponding side lengths of two (2) geometric figures is typically referred to as a scale factor. Since the given pair of geometric figures is similar, we can calculate the scale factor that maps Figure KLMN onto Figure QRST as follows:
Scale factor = TQ/NK
Scale factor = 10/5
Scale factor = 2.
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what do i do this is confusing for me
Answer:
Translate 3 right and 1 up.
Step-by-step explanation:
Looking at the picture and count the movement.
Answer:
Step-by-step explanation:
3 units right.
1 unit up.
Each of the letters is moved by these amounts to create the new image.
who would make the most money in one week? a sales manager work ing 35 hours $28.75x35= $1006.25 or a head mechanic working 25 hours=$938.00 or an assistant mechanic working 30 hours 30.42x30 hours=$912.60 or a front desk clerk working 40 hours a week $15.09 an hour high school level answer, please
By answering the presented question, we may conclude that The front proportionality desk receptionist would be paid $15.09 per hour and work 40 hours per week, for a weekly wage of $603.60.
what is proportionality?Proportionate relationships are those that have the same ratio every time. For example, the average number of apples per tree defines how many trees are in an orchard and how many apples are in an apple harvest. Proportional refers to a linear relationship between two numbers or variables in mathematics. When the first quantity doubles, the second quantity doubles as well. When one of the variables decreases to 1/100th of its previous value, the other falls as well. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two remains constant at all levels. The diameter and circumference of a circle serve as an example.
According to the statistics provided, the sales manager would earn the maximum money in one week, earning $1006.25 for 35 hours of labor at a cost of $28.75 per hour.
The head mechanic would receive $938.00 for 25 hours of labor, while the assistant mechanic would get $912.60 for 30 hours of work.
The front desk receptionist would be paid $15.09 per hour and work 40 hours per week, for a weekly wage of $603.60.
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for the simple harmonic motion equation d=4sin(8pi), what is the maximum displacement from the equilibrium position?
The maximum value οf the functiοn is 4.
What is simple harmοnic mοtiοn?Simple Harmοnic Mοtiοn, οr SHM, is a mοtiοn in which the restοring fοrce is inversely prοpοrtiοnal tο the bοdy's displacement frοm its mean pοsitiοn. This restοrative fοrce always pοints in the directiοn οf the mean pοsitiοn. A particle mοving in simple harmοnic mοtiοn accelerates as a(t) = -2 x. (t). The particle's angular velοcity is indicated in this equatiοn by the symbοl.
Given functiοn οf simple harmοnic mοtiοn is d= 4 sin(πt/8)
Nοw we need tο find abοut what is the maximum value οf .
We knοw that value οf sine functiοn varies frοm -1 tο 1.
that means fοr any value οf t, maximum value οf sine functiοn is 1.
sin(πt/8)<1
d≤4
Hence the maximum value οf the functiοn is 4.
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kiran bent some wire around a rectangle to make a picture frame.The rectangle is 8 in by 10 in
Answer:
Step-by-step explanation:
The perimeter of the wire picture frame will be 62.8 inches.
What is the circumference of a circle?
Let d be the radius of the circle.
The circumference of the circle will be
C = 2πr units
Kiran bent some wire around a rectangle to make a picture frame. The rectangle is 8 inches by 10 inches.
From the figure, the radius of each semi-circle is 1 inch.
The number of the semi-circle is 14 and the number of the three-fourth circle is 4. Then the perimeter of the wire will be
I HOPE THIS IS FINE!!!!
what's the value of z ?
[tex] \sqrt{z + y} = - 369[/tex]
when y = 65
Answer:
There is no solution
Step-by-step explanation:
Draw the graph of y= 2x + 3 on the grid
In response to the query, we can state that The line passes through the graphs y-axis at point (0,3) and has a slope of 2, which means it rises 2 units for every 1 unit it moves to the right.
What is graphs?Mathematicians use graphs to visually represent or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph
Here is the graph of the equation y= 2x + 3 on the grid:
|
6 + .
| \
5 + \
| \
4 + \
| \
3 + .
| \
2 + \
| \
1 + .
| \
0 +-------+-------+-------+-------+-------+
| -2 -1 0 1 2
|
The line passes through the y-axis at point (0,3) and has a slope of 2, which means it rises 2 units for every 1 unit it moves to the right.
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A soundscape can only be written by using a table and diagrams.
A. False, a soundscape can also be written out in words.
B. True
C. False, a soundscape can only be written out in words.
Answer:
C . False, a soundscape can only be written out in words.
Step-by-step explanation:
Because :
False, a soundscape cannot be written by using a table and diagrams.
Explanation:
A soundscape is the acoustic environment as perceived by humans, in context. The term was originally coined by Michael Southworth, and popularised by R. Murray Schafer. There is a varied history of the use of soundscape depending on discipline, ranging from urban design to wildlife ecology to computer science.
Written as a simplified polynomial in standard form, what is the result when
(x − 7)² is subtracted from 6x?
Thus, the simplification of the polynomial in standard form for (x − 7)² is subtracted from 6x is found as: : (- x² + 20x - 49)
Explain about quadratic polynomial?A degree two polynomial is a quadratic polynomial. The formula for a quadratic polynomial is f(x)=ax2 + bx + c.
A quadratic equation is one that contains a quadratic polynomial. For the answers of any arbitrary quadratic problem, there is a closed-form solution described as the quadratic formula.
standard form of quadratic polynomial:
ax² + bx + c
The given quadratic polynomial:
= (x − 7)²
On expansion:
= x² + 7² - 2*7*x
= x² + 49 - 14x
Now, (x − 7)² is subtracted from 6x.
= 6x - (x − 7)²
= 6x - (x² + 49 - 14x)
= 6x - x² - 49 + 14x
= - x² + 20x - 49
Thus, the simplification of the polynomial in standard form for (x − 7)² is subtracted from 6x is found as: (- x² + 20x - 49).
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Oliver’s batting average, b, is at or above the league’s average of 0.300. Which inequality best represents his average?
Group of answer choices
b > 0.300
b ≥ 0.300
b ≤ 0.300
b < 0.300
According to this disparity, his batting average is larger than or equal to inequality 0.300, which meets the requirement that it be equal to or higher than the league average.
What is inequality?A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.
Oliver's batting average is at or above the league average of 0.300, hence the following inequality would be the most accurate way to describe it:
b ≥ 0.300
According to this disparity, his batting average is larger than or equal to 0.300, which meets the requirement that it be equal to or higher than the league average.
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Find an equation for the graph.
Answer:
y = -3*sin(2x)
Step-by-step explanation:
Looking at your equation graph it is a y = sinx since its at the origin.
We can see that a = -3
period is π.
Since we are given the period of π then we need to solve for b.
y = -3*sin(2x)
b = 2 changes the period of 2π/b into π.
Robin earns a 5% Commission on her sales. If robin sold an item for $530, how much did she earn in commission?
Answer:
26.5$
Step-by-step explanation:
Calculate the 5% of 530, which is 530 * 0.05, whic is equal to 26.5$
f(x) = 5•3x what is the domain of the exponential function
Answer:
Step-by-step explanation:
Domain: (- infinity, infinity)
Range: (0, infinity)