A function in terms of t that represents the situation of sales that is of $10,000 and increase by 65% each year is t = 10,000(1.65)ⁿ.
What is function?An element of one non-empty set and an element of another non-empty set are said to have a special relationship when they are connected by a function in mathematics.
An assignment of an element from set Y to each element of set X, where set X is the domain and set Y is the codomain, is what is meant when a function is applied from a set X to a set Y.
We have given that f(t) is given by the Sales of $10,000 increase by 65% each year, i.e.
As sales of $10,000 increase by 65% each year.
The situation is represented by an exponential growth function.
The initial amount a = 10,000
The rate of growth r = 65% = 0.65
Therefore, the function will be:
t = a(1 + r)ⁿ
Where,
t represents the final amount.
a represents the initial amount
r represents the rate of growth
1+r represents the growth factor
n represents the time.
⇒ t = a(1 + r)ⁿ
⇒ t = 10,000(1 + 0.65)ⁿ
⇒ t = 10,000(1.65)ⁿ
Thus, a function in terms of t that represents the situation of sales that is of $10,000 and increase by 65% each year is t = 10,000(1.65)ⁿ.
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Aaron has a loan of 1250£ He pays simple intrest 0.5% per month for eight months Calculate the total amount of interest Aaron pays
A graphing calculator is recommended.
Use the graphical method to find all solutions of the system of equations, rounded to two decimal places.
y=e^x+e^-x
y=5-x^2
Dont bother answering if you won't show how you got it
The solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)
How to solve the system of equations?The system of equations is given as
y=e^x+e^-x
y=5-x^2
See attachment for the graph of both equations
From the attached graph, the curve intersect at
(-1.189, 3.587) and (1.189, 3.587)
Hence, the solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)
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Q.3. The slope of line is ¾ and the y - intercept is equal to 4 . Write the equation of the line and draw the graph of the line.
help me now!!
The equation of line with the given slope and y-intercept is y = (3/4)x + 4.
What is the equation of the line?Given that;
Slope = 3/4y-intercept b = 4Equation of the line y = ?We use the formula for equation of line to determine the equation.
y = mx + b
Where m is the slope and b is the y-intercept.
We plug in our values
y = mx + b
y = (3/4)x + 4
Therefore, the equation of line with the given slope and y-intercept is y = (3/4)x + 4.
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A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as measured by Courtney). At the end of the trip, Courtney is 20 years old. How old is Andrea
The initial age of 10 years and the spaceship speed of 0.60•c, gives the Andrea's age at the end of the trip as 18 years.
How can Andrea's new age be calculated?The time dilation using the Lorentz transformation formula is presented as follows;
[tex]t' = \frac{t}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } } [/tex]
From the question, we have;
The spaceship's speed, v = 0.6•c
∆t = Rest frame, Courtney's time, change = 10 years
Therefore;
[tex]\delta t' =\delta t \times \sqrt{1 - \frac{ {(0.6 \cdot c)}^{2} }{ {c}^{2} } } = 8[/tex]
The time that elapses as measured by Andrea = 8 years
Andrea's age, A, at the end of the trip is therefore;
A = 10 years + 8 years = 18 years
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The probability of a student buying coffee before class is 30%. The probability of a student buying a muffin before class is 40%. The probability of a student buying tea before class is 20%. The probability a student buys coffee AND a muffin before class is 15%. The probability a student buys tea AND a muffin before class is 10%. What is the probability that a student buys coffee OR a muffin before class
The probability that a student buys coffee OR a muffin before class is 55%
How to determine the probability?The given parameters are:
P(Coffee) = 30%
P(Muffin) = 40%
P(Tea) = 20%
P(Coffee and Muffin) = 15%
P(Tea and Muffin) = 10%
The probability that a student buys coffee OR a muffin before class is
P(Coffee or Muffin) = P(Coffee) + P(Muffin) - P(Coffee and Muffin)
This gives
P(Coffee or Muffin) = 30% + 40% - 15%
Evaluate
P(Coffee or Muffin) = 55%
Hence, the probability that a student buys coffee OR a muffin before class is 55%
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The range, a measure of variability, Group of answer choices is the difference between the largest (L) and smallest (S) value in a list of scores is the most informative when used to describe data sets without outliers includes only two values in its computation, regardless of the number of scores in a distribution all of the above
The correct answer is all of the above.
Why is the range the most convenient measure of variability?
Your data's spread from the lowest to the greatest value in the distribution is indicated by the range. The calculation of this variability index is the simplest. Simply subtract the lowest value from the highest value in the data set to determine the range.How do you find the range?
The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response.Learn more about range
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The general term of a sequence is T(n)=n+2/n+3, find the value of T(1)*T(2)*T(3)*……….*T(100).
Answer:
T(1)=1+2(1)+3=6
T(2)=2+2(2)+3=9
T(3)=3+2(3)+3=12
T(100)=100+2(100)+3=303
These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
Help
simplest terms.
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer.
The probability of drawing two yellow balls if they're not replaced exists 1/45.
What is probability?
The probability exists in the analysis of the possibilities of happening of an outcome, which exists accepted by the ratio between favorable cases and possible cases.
Number of yellow marbles be 2
Number of pink marbles be 3
Number of blue marbles be 5
Total number of marbles = 2+3+5 = 10
The probability of removing the first yellow ball = 2/10
Since the ball exists not replaced, that indicates there choice be 9 balls left and 1 yellow ball left.
Probability of drawing the second yellow ball = 1/9.
Probability of drawing two yellow balls if they're not replaced
= 2/10 × 1/9
= 2/90
= 1/45
The probability of drawing two yellow balls if they're not replaced exists 1/45.
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Write the equation of the line that has a slope of -2 and passes through (-4, -5)
Answer: [tex]y+5=-2(x+4)[/tex]
Step-by-step explanation:
See attached image.
HELP PLEASE!)
A square pyramid has surface that is covered in dark glass. The sides of the pyramid are 456 feet in length. The slant height of the pyramid is 185 feet.
Find the lateral surface area to determine the square feet of glass needed to cover the surface of the pyramid.
Answer choices
376,656 ft^2
42,180 ft^2
337,440 ft ^2
168,720 ft^2
Nathan buys a bottle of water for $1.25, gum for $0.50, and a book for $3.95. the sales tax is 10%. what is the sales tax for the things he buys
Answer:
$0.75, which is
75 cents
Step-by-step explanation:
First add the cost of all the items.
1.25 + .50 + 3.95
= 5.70
To find 10% of 5.70, change the percent to a decimal and multiply.
10% is .10
5.70 × .10 = .57
The tax is 57 cents. This can be written as $0.57
A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true?
Based on the calculations, the true statements are:
A. The angular velocity is 10π rad/sec.
E. The angular velocity is 600π rad/min.
How to calculate the angular velocity?Mathematically, angular velocity can be calculated by using this formula:
ω = θ/t
Where:
ω is the angular velocity.θ is the angle.t is the time.Note: 1/2 revolution = 0.5 × 2π = π radians.
Substituting the given parameters into the formula, we have;
ω = θ/t
ω = π/0.1
ω = 10π rad/s.
Next, we would convert the time in seconds to minutes:
ω = 10π × 60
ω = 600π rad/min.
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Complete Question:
A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true? Check all that apply.
A. The angular velocity is 10π rad/sec.
B. The angular velocity is 10π rad/min.
C. The angular velocity is 60π rad/min.
D. The angular velocity is 600π rad/sec.
E. The angular velocity is 600π rad/min.
Answer:
A,
Step-by-step explanation:
Edge202
Which statement correctly describes the expression 19×4?
A. Both factors are negative, so the product will be positive.
B. One factor is positive and one factor is negative, so the product will be positive.
C. Both factors are positive, so the product will be negative.
D. Both factors are positive, so the product will be positive.
Answer:
D. Both factors are positive, so the product will be positive.
Quick Please
(order from least to greatest)
please and thank you
Answer:
√(3 , √(π , 2
Step-by-step explanation:
ascending order
John's dad is 30 years old than john. if john were three times ad old as he is now,he would still be younger than his dad. what is the oldest that john could be right now
john could be right now 45
What is word problem in math?
A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."
According to the question:
John's dad is 30 years old than john .In essence, x = y -30 .................equation 1And
john were three times ad old as he is now.y=3xSolution for the above equation:
[tex]x=y-30, y=3 x \quad\\ \quad x=15, y=45[/tex]
steps:
[tex]x=y-30 \\y=3 x[/tex]
Substitute :[tex]$y=3 x$[/tex]
[tex][x=3 x-30][/tex]
[tex]for $$x=3 x-30: \quad x=15[/tex]
For [tex]$y=3 x$[/tex]
Substitute: [tex]$x=15$[/tex]
[tex]y=3 \cdot 15[/tex]
Simplify:
[tex]y=45[/tex]
The solutions to the system of equations are: [tex]$x=15, y=45$[/tex]
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The ratio of the number of galleons to the number of galleys in the spanish armada is 5 : 1 . what missing information could be used to find the total number of galleons to galleys in the spanish armada ?
The amount of the galleys or the number of galleys.
If given the amount of galleons, you can find the amount of galleys by dividing the number of given galleons by 5.
If given the amount of galleys, you can find the amount of galleons by multiplying the number of given galleys by 5.
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There are 5 different families of triplets at a triplets convention. Each triplet shook hands with all the other triplets, except his or her siblings. How many handshakes took place?
There is a total of 90 handshakes.
How many handshakes took place?
There are 5 sets of triplets.
If we select one of the sets, each of the triplets will have one handshake with the other 12 people. So we have 36 handshakes at this point.
Now we only care for the other 4 sets.
We select one set again, each triple on that set will have one handshake with the other 9 people, so for the 3 triplets, we have a total of 27 new handshakes.
For the remaining 3 sets we do the same, this time we add 18 handshakes.
Finally, there are 2 sets of triplets, this time we add 9 new handshakes.
To get the total number of handshakes we need to add them all:
36 + 27 + 18 + 9 = 90
There is a total of 90 handshakes.
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Mr. Omwoyo, the principal of Maili Mbili Secondary would wish to cover the floor of the new administration block using square tiles. The floor is a rectangle of sides 12.8m by 8.4m. Find the area of the largest tiles in cm² which can be used to fit exactly without cutting.
Answer:
hi play truth and dare to with me in g met
What is the recursive formula for the geometric sequence with this explicit
formula?
The recursive formula for the geometric sequence is given as follows:
D.
[tex]a_1 = 9[/tex].[tex]a_n = a_{n-1} \times \left(-\frac{1}{3}\right)[/tex]What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
With a recursive formula, it is given by:
[tex]a_n = a_{n-1} \times q[/tex]
For this problem, the first term and the common ratio are:
[tex]a_1 = 9, q = -\frac{1}{3}[/tex]
Then the recursive formula is:
D.
[tex]a_1 = 9[/tex].[tex]a_n = a_{n-1} \times \left(-\frac{1}{3}\right)[/tex]More can be learned about geometric sequences at https://brainly.com/question/11847927
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Instructions: Given the coordinate points of the preimage, use the transformation given
to provide the points of the image.
The rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)
How to determine the coordinates
Note that rotation about in clockwise 90 degrees direction when M(h , k) rotated about the origin, the new rotation coordinates would be in the form M' (k , -h)
Coordinates of the preimage were given as;
H ( -3, -2)
I ( 1, 1 )
J ( 0, -4)
The coordinates after a 90 degrees rotation about the origin, would be
For H ( -3, -2)
h = - (-3) = 3
k = -2
H' = ( -2, 3)
For I ( 1, 1)
h = - (1) = -1
k = 1
I' = ( 1, -1)
For J ( 0, -4)
h = - (0) = 0
k = -4
J' = ( -4, 0 )
Thus, the rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)
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Which of the following terms is defined as a set of all points in a plane that are a given distance from a point?
O Circle
O Line segment
O Parallel line
O Ray
Answer:
circle
Step-by-step explanation:
any point on the circumference of a circle is equidistant from the centre.
FIRST CORRECT ANSWER WILL GET BRAINLIEST
Answer:
They are parallel.
Step-by-step explanation:
They have the same slope, 7, and different y-intercepts, 4, -1/4, so they are parallel.
An equilateral triangle and a square both have perimeters of 48 inches. What is the ratio of the length of the side of the triangle to the length of the side of the square
Answer: 4:3
Step-by-step explanation:
The side length of the triangle is 48/3 = 16.
The side length of the square is 48/4 = 12.
So, the ratio is 16:12 = 4:3.
Solve the linear equation
x/2 + 2y/3 = -1 and x - y/3 = 3
Multiply by 6
3x+4y=-6-»eq(1)And
x-y/3=3Multiply by 3
3x-y=9-»eq(2)eq(1)-eq(2)
5y=-15y=-3Then
3x+4(-3)=-63x-12=-63x=6x=2From Equation 1
[tex] \dfrac{x}{2} + \dfrac{2y}{3} = - 1 [/tex]
[tex] \dfrac{3x + 4y}{6} = - 1[/tex]
[tex]3x + 4y = - 6 [/tex]
From Equation 2
[tex]x - \dfrac{y}{3} = 3 [/tex]
[tex] \dfrac{3x - y}{3} = 3[/tex]
[tex]3x - y = 9[/tex]
By eliminating ;;
For that multiply equation 2 by 4
12x - 4y = 36 _(3)
By taking equation (1) and (3)
3x + 4y = -6
12x - 4y = 36
__________
15x = 30
x = 30/15
x = 2
Putting the value of x in 2
[tex]3(2) - y = 9[/tex]
[tex]6 - y = 9[/tex]
[tex]6 - 9 = y[/tex]
[tex]-3 = y[/tex]
So The value of x = 2 and y = -3
Use a model to solve six multiplied by seven eighths. Leave your answer as an improper fraction.
A. forty two forty eighths
B. thirteen eighths
C. thirteen fourteenths
D. forty two eighths
Let's see
seven eighths means 7/8
So
6(7/8)42/821/4Forty two eighths
1. What is the approximate area of circle A?
2. What is the approximate area of circle B?
3. What is the approximate area of the shaded region 1 (between the square and circle A)?
4. What is the approximate area of shaded region 2 (between circles A & B)?
The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.
The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.
The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.
The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.
How to estimate geometric areas
In this situation we have a square whose side length is known and two circles whose radii have to be estimated. By direct inspection we find that the diameter of circle A is two thirds of the length of the square side (l), in inches and the diameter of circle B is the half of the diameter of the former. Now we proceed to find the key dimensions of the figure:
Circle A
Diameter: 16 inches
Radius: 8 inches
Circle B
Diameter: 8 inches
Radius: 4 inches
The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.
The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.
The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.
The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.
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An athletic coach conducted an experiment to test whether a four-week stretching and flexibility program reduces the number of muscular injuries that occur during athletic events. the coach randomly selected 30 athletes from several sports and randomly assigned 15 athletes to the four-week program. the remaining 15 athletes did not participate in any type of flexibility program during the four weeks. which statements about this study are true?
Answer:
The remaining 15 athletes did not participate in any type of flexibility program
1. Find the Principal when S.l. = 100 Rate = 5% per annum Time = 2 years.
The principal is 1000
SI = PRT/100
Simple interest = 100
Rate = 5%
Time = 2 years.
SI = PRT/100
100 = (P × 5 × 2)/100
10000 = 10P
P = 10000/10
P = 1000
What is the -value in the solution to this system of linear equations?y
4 + 5 = −12xy
-2 + 3 = −16xy
The xy-value in the solution to the given system of linear equation shows that x = 2 and y = -4.
What is a system of linear equations?Whenever two or more linear equations operate simultaneously, we create a System of Linear Equations. These equations must contain one or more similar variables in order to operate together.
When solving a system of linear equations, our objective is to simplify two equations having two variables to a single equation having one variable. Because each equation in the system includes two variables, substituting an expression for a variable is one technique to minimize the number of variables in an equation.
From the given information:
4x + 5y = -12 --- (1)
-2x + 3y = -16 ----- (2)
From equation (1)
4x+5y+(−5y) = −12 + (−5y) (Add -5y to both sides)
4x = −5y − 12
Divide both sides by 4
[tex]\mathbf{\dfrac{4x}{4}= \dfrac{-5y-12}{4}}[/tex]
[tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]
Replacing the value of x in [tex]\mathbf{ \dfrac{-5}{4}y-3}[/tex] into equation (2); we have:
[tex]=\mathbf{-2(\dfrac{-5}{4}y-3)+3y=-16}[/tex]
[tex]\mathbf{\dfrac{11}{2}y+6 =-16}[/tex]
Simplifying both sides of the equation, we have:
[tex]\mathbf{\dfrac{11}{2}y+6-6 =-16-6}[/tex]
[tex]\mathbf{\dfrac{11}{2}y=-22}[/tex]
Cross multiply
11y = -44
y = -4
Replace the value of y = -4 into [tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]
[tex]\mathbf{x= \dfrac{-5}{4}(-4)-3}[/tex]
x = 2
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Which could be the entire interval over which the function, f(x), is positive? a 2-column table with 8 rows. the first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. the second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20.
The entire interval over which the function, f(x), is positive is (-∞,1).
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Each element of X receives exactly one element of Y when a function from one set to the other is used. The set X is referred to as the function's domain, while the set Y is referred to as the function's codomain.
According to the question,
The function has positive values corresponding to the interval from negative infinity to one.
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