The exponential function is P(t)=60(4)^t that can be expressed in terms of feature of the subsequent form: f ( x ) = a x.
Initial population 'a'=60 rabbits
After 1 year, the rabbit population is 240.
An exponential feature is a mathematical feature of the subsequent form: f ( x ) = a x. wherein x is a variable, and a is a regular known as the bottom of the feature.
Equation of the exponential function.
y=ab^x
Put x=0, y=60
60=ab^0
a=60
Put x=1, y=240
240=60(b)^1
b=4
Thus,
y=60(4)^x
P(t)=60(4)^t
To learn more exponential function check the link below:
https://brainly.com/question/2456547
#SPJ4
what is the point-slope form of -4,7?
An equation for this line in the point-slope form will be y-7 = -2(x + 4).
What is the Point-slope form?
The equation of the straight line has its slope and given point. If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation. Point-slope is a specific form of linear equations in two variables:
y - y₁ = m(x - x₁)
Which is the required equation of a line in a point-slope form.
We need to find the equation of the line that passes through (-4, 7) and whose slope is -2.
Well, we will simply plug m = -2, x₁= -4, and y₁ = 7 into point-slope form.
y-y₁ = m(x-x₁)
Now substitute;
y-7 = -2(x - (-4))
y-7 = -2(x + 4)
Therefore, an equation for this line in the point-slope form will be y-7 = -2(x + 4).
To learn more about slope visit,
brainly.com/question/2503591
#SPJ1
Timmy and Johnny's parents are very unfair. This year, Timmy received 5 Christmas presents, but his brother received 19. Their parents say that each year, Timmy will receive one more present than he did the last year, and Johnny will receive one less present that he did the last year. How many years will it take for them to receive the same amount of presents
Answer:
7 Years
Step-by-step explanation:
1 Year: 6,18
2 Years: 7,17
3 Years: 8,16
4 Years: 9,15
5 Years: 10,14
6 Years: 11,13
7 Years: 12,12
LOT OF POINTS!!
PLEASE NEED ANSWERS QUICKLY!!
By using the properties of angle,
The proof of ∠1 ≅ ∠3 has been given below
What is angle?
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle
1. ∠2 ≅ ∠4 [Given]
2. m∠2= m∠4 [Angle Congruence Postulate]
3. ∠2 and ∠3 are supplementary [Given]
4. m∠2+m∠3 = 180° [Definition of Supplementary angles]
5. ∠1 and ∠4 are supplementary [Angle on a straight line]
6. m∠1+m∠4 = 180° [Definition of supplementary angles]
7. m∠1+m∠4 = m∠2+ m∠3 [ Substitution from 4 and 6]
8. m∠1+m∠4 = m∠4+m∠3 [Substitution from 2]
9. m∠1=m∠3 [Cancellation property]
10. ∠1 ≅ ∠3 [Converse of angle congruence theorem]
To learn more about angles, refer to the link-
https://brainly.com/question/25716982
#SPJ1
f(t) = 2t; Find f (-3t)
Answer:
–6t
Step-by-step explanation:
f(t) = 2t
f(–3t) = 2( –3t )
= –6t
a campfire girls troop has 14 members. in how many different ways can the leader appoint 3 members to clean up camp?
The leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp in 364 ways.
The number of members in the campfire girls troop
= 14
The number of members the leader of the campfire girls troop can appoint at a time = 3
The number of ways to appoint r members out of n members
= nCr = n!/(r)!×(n-r)!
Therefore, the number of ways in which the leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp
= 14C3 = 14!/(3)!×(14-3)! = 364 ways
To know more about number of ways to appoint
https://brainly.com/question/16877119
#SPJ4
lagrange multiplier what are the points on the intersection of the ellipsoid with the plane that are respectively closest and furthest from the origin?
The points on the intersection of the ellipsoid with the plane that are respectively closest and furthest from the origin are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
Using Lagrange multipliers we attempt to find the extrema of f(x,y,z)=x2+y2+z2 given that g(x,y,z)=x−y+z−2=0 and that h(x,y,z)=x2+y2−4=0.
Given,
∇f=⟨2x,2y,2z⟩
∇g=⟨1,−1,1⟩
∇h=⟨2x,2y,0⟩
Extrema satisfy the condition that ∇f=μ∇g+λ∇h for some λ,μ∈R.
This is to say,
2x=2λx+μ
2y=2λy−μ
2z=μ
If λ=1 then μ=0 and so z=0, the g constraint tells us that x=y+2, and the h constraint tells us that y2+(y+2)2=4, meaning that either y=0 or y=2. This provides us with two crucial points in addition to the g constraint:
(2,0,0)
(0,−2,0)
Now assume λ≠1, and so
x=μ2−2λ
y=−μ2−2λ=−x
Since x=−y, we have that x=±2–√, y=∓2–√. Using the g constraint, our two critical points are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
And then it's east to determine which is the max and which is the min out of these four critical points.
To learn more about Lagrange multiplier
https://brainly.com/question/4609414
#SPJ4
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 54
Step-by-step explanation:
The 2 angles shown are vertical angles, so they are equal.
2x + 2 = 3x - 52
2x - 3x = -52 - 2
-x = -54
x = 54
They are 110° angles
Answer: x = -10
Step-by-step explanation:
1: Add: 2x+2 3x-52 = 5x -50
2: Divide both sides by the same factor: 5x - 50
------------
5 5
3: Level: x= -10
Find the sales tax. Sales Tax Selling Price Rate of Sales Tax Sales Tax
$40.00
8%
The sales tax is $
The sales tax on the good based on the selling price that is given will be $3.20.
How to calculate the sales tax?It should be noted that the sales tax simply means the tax that's levied on the goods and services that are sold by.
Based on the information given, the following can be deduced:
Sales tax Percentage = 8%
Price of good = $40
In this situation, in order to calculate the sales tax, we will have to multiply the sales tax percentage by the amount of the good which is the selling price. This will be:
Sales tax = Sales tax percentage × Price
Sales tax = 8% × $40
Sales tax = 0.08 × $40
Sale tax = $3.20
Therefore, the sales tax is $3.20.
Learn more about tax on:
brainly.com/question/25783927
#SPJ1
Elizabeth rents a home for $1,200 a month. The security deposit she paid is one months' rent. Renters insurance will cost $120 for the year. Elizabeth expects utilities to average $164 a month. What will be the total cost of renting the home for the first year (prior to any refund of her security deposit)? PLEASE SHOW WORK
Answer:
$17,688.00
Step-by-step explanation:
(1200 x 13) + 120 + (164 x 12)
17688
What is the answer to the picture I put below
The domain of the function y = √x + 4 is
0 ≤ x < ∞ How to find the domainAll of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.
The domain of a function are all possible values that will give output
For the function y = √x + 4
the domain are all positive real numbers which is shown by option C which is 0 ≤ x < ∞
these are numbers from zero to infinity. infinity is denoted by the symbol ∞
Hence the domain is 0 ≤ x < ∞
Learn more about range and domain at:
https://brainly.com/question/30068593
#SPJ1
if antonella has 3 more quarters than nickels and they have a combined value of 225 cents, how many of each coin does she have?
Antonella have a number of coins of quaters and nickels whose total value is 250.
The number of coins of nickel is 10 and the number of coins of quarters is 7.
Nickel and quarters are the coin based form of currency in the United States. The value of one nickel is 5 cents, while that of one quarter is 25 cents. We have given that
Antonella has 3 more quaters than nickles.
Let she has "x" number of quaters and "y" be number of nickels .
According to question,
y = 3+ x ---(1)
Combined value of all is 225 cents .
i.e 25 × x + y× 5 = 225 cents
plug the value of y from equation (1) to equation(2) we get,
25 x + 5(3+x) = 225
solve the equation
=> 25x + 15 + 5x = 225
=> 30x = 210
=> x = 7
put the value of x in equation (1)
y = x + 3 = 10
Hence, the number of nickels coins is 10 and numbers of quaters are 7.
To learn more about quaters and nickle, refer:
https://brainly.com/question/17127685
#SPJ4
Letting × represent the number of messages over 500, and y the total monthly charges, write equations representing the charges for plans A and B.
Then graph the equations for plans A and B on the same coordinate grid.
The system of equations representing the charges for plans A and B include the following:
y = 0.2x - 50
y = 0.3x - 105
A graph of the system of equations for plans A and B are shown in the image attached below.
How to write the system of equations representing the charges?In order to write the system of equations representing the charges, we would have to calculate the slope of the line based on the data points described above for each plans.
Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (66 - 50)/(580 - 500)
Slope, m = 16/80
Slope, m = 0.2
At point (500, 50), a linear equation for plan A can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
x and y are the points.m represents the slope.c represents the y-intercept.Substituting the given points into the point-slope form formula, we have;
y - 50 = 0.2(x - 500)
y - 50 = 0.2x - 100
y = 0.2x - 100 + 50
y = 0.2x - 50.
For plan B, the slope is as follows;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (69 - 45)/(580 - 500)
Slope, m = 24/80
Slope, m = 0.3
At point (500, 45), a linear equation for plan B can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
y - 45 = 0.3(x - 500)
y - 45 = 0.3x - 150
y = 0.3x - 150 + 45
y = 0.3x - 105.
Read more on slope here: brainly.com/question/1884491
#SPJ1
Complete Question:
Three cell phone plans, A, B, and C, each have a different flat monthly rate for the first 500 text messages and a different constant rate for every additional message over 500. These tables show the monthly charges for plans A and B when different numbers of messages are sent. Plan A Cell Phone Charges
Phone plans A and B each have a different flat monthly rate for the first 500 text messages and a different constant rate for every additional message over 500.
Plan A charges $50 monthly for 500 text messages and $66 monthly for 580 text messages.
Plan B charges $45 monthly for 500 text messages and $69 monthly for 580 text messages.
Letting x represent the number of messages over 500, and y the total monthly charges, write equations representing the charges for plans A and B. Then graph the equations for plans A and B on the same coordinate grid.
Can someone help me with making the x the subject of the formula100 point up for grabs pls helpppp I will make brainliest
y =xa+ b
y =xa− b
y =x + 2 divided by two
Answer:
x = [tex]\frac{y-b}{a}[/tex]
Step-by-step explanation:
y = xa + b ( subtract b from both sides )
y - b = xa ( isolate x by dividing both sides by a )
[tex]\frac{y-b}{a}[/tex] = x , that is
x = [tex]\frac{y-b}{a}[/tex]
-------------------------------------
y = xa - b ( add b to both sides )
y + b = xa ( isolate x by dividing both sides by a )
[tex]\frac{y+b}{a}[/tex] = x , that is
x = [tex]\frac{y+b}{a}[/tex]
--------------------------------------------
assuming you mean
y = [tex]\frac{x+2}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
2y = x + 2 ( subtract 2 from both sides )
2y - 2 = x , that is
x = 2y - 2
The Oakland Tigers are having team shirts made. One option is to pay Susan's Tees a $34 setup fee and then buy the shirts for $10 each. Another option is to go to City Printing, paying $23 for a setup fee and an additional $11 per shirt. The team parent in charge of the project notices that, with a certain number of shirts, the two options have the same cost. What is the cost? How many shirts is that?
To find the cost of the shirts, we need to set up a system of equations. Let x be the number of shirts.
Option 1: 34 + 10x = Option 2: 23 + 11x
We can solve this system of equations by subtracting the equations:
34 + 10x - 23 - 11x = 0
11x - 23 = 0
11x = 23
x = 23 / 11
Therefore, the cost is the same when the team orders 23/11 = 2 shirts.
what is the probability that a five-digit integer chosen at random is divisible by 5? (enter your probability as a percent.) %
The probability that a five-digit integer chosen at random is divisible by 5 is 13.1 %.
Given :
what is the probability that a five-digit integer chosen at random is divisible by 5 .
Probability :
Probability is a branch of mathematics that deals with the occurrence of a random event.
Probability = 9^3 * 8 * 2 / 9 * 10^4
= 729 * 8 * 2 / 9 * 10000
= 5832 * 2 / 9 * 10000
= 11809 / 90000
= 0.131
converting into percentage :
= 0.131 * 100 %
= 13.1 %
Therefore The probability that a five-digit integer chosen at random is divisible by 5 is 13.1 %
Learn more about the probability here:
https://brainly.com/question/11234923
#SPJ4
Solve the following system of equations using substitution
-3x+6y=12
2y=x+4
From the equation, 0 = 0. Therefore, the system of equation has infinite number of solutions.
How to solve system of equation?System of equation can be solved using different method such as elimination method, graphical method and substitution method.
Let's use substitution method to solve the system of equation as follows;
-3x + 6y = 12
2y = x + 4
x = 2y - 4
Hence, let's substitute the value of x in equation(i)
-3(2y - 4)+ 6y = 12
-6y + 12 + 6y = 12
-6y + 6y = 12 - 12
0 = 0
Therefore, the system of equations has infinite solutions.
learn more on system of equation here: https://brainly.com/question/15313209
#SPJ1
solving systems by Substitution
x-4y=15=3x-12y=12
Answer:
There is no solution
Step-by-step explanation:
x - 4y = 15
3x -12y = 12
Times the first equation by -3
-3x +12y = -45
3x - 12y = 12
0 = -33
So, there is no solution.
calculer.
a. 3x5-(5-12)
b. 5-(3-5x6)
c. 4x(2-3x9)+7
d. 9x(-2-4x5)-3
e. 63:(2-3x7+5x2)-11
f. 48:(2-12:4-7)-4
A.
3 × 5 - (5 - 12)
= (3 × 5) - (5 - 12)
= 15 - (5 - 12)
= 15 - (-7)
= 15 + 7
= 22
B.
5 - (3 - 5 × 6)
= 5 - (3 - (5 × 6))
= 5 - (3 - 30)
= 5 - (-27)
= 5 + 27
= 32
C.
4 × (2 - 3 × 9) + 7
= 4 × (2 - (3 × 9)) + 7
= 4 × (2 - 27) + 7
= 4 × (-25) + 7
= -100 + 7
= -93
D.
9 × (-2 - 4 × 5) - 3
= 9 × (-2 - (4 × 5)) - 3
= 9 × (-2 - 20) - 3
= 9 × (-22) - 3
= -198 - 3
= -201
E.
63 ÷ (2 - 3 × 7 + 5 × 2) - 11
= 63 ÷ (2 - (3 × 7) + (5 × 2)) - 11
= 63 ÷ (2 - 21 + 10) - 11
= 63 ÷ (-9) - 11
= (63 ÷ (-9)) - 11
= -7 - 11
= -18
F.
48 ÷ (2 - 12 ÷ 4 - 7) - 4
= 48 ÷ (2 - (12 ÷ 4) - 7) - 4
= 48 ÷ (2 - 3 - 7) - 4
= 48 ÷ (-8) - 4
= (48 ÷ (-8)) - 4
= -6 - 4
= -10
A toy is being constructed in the shape of a pyramid. The maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters. The height of the toy is double the side length. What are the maximum dimensions to the nearest square centimeter for a square base and for a hexagonal base?.
The maximum dimensions (side length and height) of the pyramid for a given square base is equal to 6.99cm and 13.98cm respectively.
As given in the question,
Maximum amount of material used to cover sides of pyramid and its bottom = 250cm²
Surface area of the ( sides + bottom ) = 250cm²
Base is square :
Let 's' represent the the side length
Then height 'h' of the toy = 2 ( side length)
= 2s
Surface area of Pyramid = s² + 2s√(s²/4) + h²
⇒ 250 = s² + 2s√(s²/4) + (2s)²
⇒250 = s² + 2s√(s² + 16s²)/4
⇒250 = s² + 2s√17s²/4
⇒250 = s² + 2s(s/2)√17
⇒250 = s²+ s²√17
⇒250 = s² ( 1+ √17)
⇒250 = s²( 1 + 4.123 )
⇒ 250 = 5.123s²
⇒s² = 250/5.123
⇒ s= 6.99cm
Height 'h' = 2(6.99)
= 13.98cm
Therefore, the side-length and height of the pyramid with square base is equal to 6.99cm and 13.98cm respectively.
Learn more about pyramid here
brainly.com/question/17615619
#SPJ4
if all sales are made on account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable. State True or False your answer:
a. True
b. False
If all sales are made on account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable.
It is False.
Information available from the question,
In the question:
If all sales are made on account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable.
The answer in TRUE/FALSE
Now, According to the question:
Accounting for cash transactions:
Daily cash sheet: If cash transactions are a significant part of your business, you should also prepare a daily cash sheet to reconcile your cash received and paid out for the day. If you use a daily cash sheet, you can reconcile your cash receipts with your daily deposit into your bank account.
So, The given statement is False.
Learn more about Accounts at:
https://brainly.com/question/14643061
#SPJ4
Write an equation in slope-intercept form for the line that contains the point (1, -1) and is parallel to y = 3x - 2.
Considering the definition of parallel line, the line that contains the point (1, -1) and is parallel to y = 3x - 2 is y= 3x -4.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts.
Equation of parallel line in this caseIn this case, the line is y= 3x -2
where:
the slope is 3.the ordinate to the origin is -2.Two lines are parallel if they have the same slope. So, the parallel line has a slope of 3.
The line passes through the point (1, -1). Replacing in the expression for a line:
-1= 3× 1 + b
-1= 3 + b
-1-3 = b
-4 = b
Finally, the equation of parallel line is y= 3x -4.
Learn more about parallel line:
brainly.com/question/7197064
brainly.com/question/11470863
brainly.com/question/7280013
#SPJ1
4700 people attended a football game. If 2% of the people who attended were
teenagers, how many teenagers attended the game?
Insert the values given in the problem then scale up or
down to find the missing value.
attendees
percent
100
The number of teenagers in the game are 94.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, 4700 people attended a football game.
Here, 2% of the people who attended were teenagers
So, the number of teenagers are
2% of 4700
= 0.02×4700
= 94
Therefore, there are 94 teenagers attended the game.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ1
Find the indicated critical value. z 0.03
The indicated critical value for significance level of 0.03 should be approximately 1.88.
In standard normal distribution, the critical value is the mark or point that seperates region of acceptance and rejection. In one-tailed test having significance level of 0.03, it will indicate the probability of getting a value that will be more than or equal to 0.03.
The calculation of critical value can be done in many ways. Either look through the standard table or use calculator for the same. The latter is done by using inverse function on standard normal cumulative distribution function. It should be around 1.88.
Learn more about critical value -
https://brainly.com/question/14040224
#SPJ4
Marcus has x songs downloaded on his phone. He downloads 20 more songs to his phone.
Enter an expression in the box to represent the number of songs Marcus now has on his phone.
Answer:
x + 20 = y
Step-by-step explanation:
x + 20 = y
where x= number of songs
y = total songs marcus has
Given that f(x) = x² + 3, work out the value of:
a) f(6)
b) f(-6)
The value of f(x) = x² + 3 at
(a) f(6) = 39
(b) f(-6) = 39
To work with these functions, we just need to put the value of x in the given function f(x) = x² + 3 i.e. substituting 6 and -6 into the equation per variable, then solving and simplifying as needed, to get the answer
(a) f(x) = x² + 3
f(6) = [tex]6^{2}[/tex] + 3
= 39
Hence, f(6) = 39
(b) f(x) = x² + 3
f(-6) = [tex](-6)^{2}[/tex] + 3
= 39
Therefore, the value of function f(x) = x² + 3 at f(6) and f(-6) is the same that is 39.
To learn more about functions:
brainly.com/question/2284360
help please i need it
Answer:
since a || b
<A = <ABb = 60°
in a triangle the sum of all angles is 180°
so,
30 + 60 + x = 180
x= 180-90
x= 90
Nevach and Michael are helping their friend Nabhitha move. If Nevaeh can
move 6 boxes for every 24 boxes that Michael moves, then how many boxes
can Michael move for every box that Nevaeh moves?
Michael boxes
24
Answer:
For every 1 box Naveah moves, Michael moves 4 boxes
point) The number of Drosophila fruit flies in controlled experiment assumes the following growth pattern when the food source is limited: 600 N(t) 1+ Me-0.3t where measured in days. A. How many fruit files were there in the beginning? What is the limiting number of fruit flies 600 C.At what time was the population increasing most rapidly? D. At what rate is the number of fruit flies increasing after days? 600/(1+11e
time was the population increasing most rapidly. At rate is the number of fruit flies increasing after days A. 600 B. 600 C. t=0 D. 0.09
The equation 600/(1+Me-0.3t) is a model for the population of Drosophila fruit flies, with time representing the number of days the experiment has gone on for. A. The population of fruit flies in the beginning is given by the equation as 600. B. The limiting number of fruit flies is also given by the equation as 600. C. The population is increasing most rapidly when t=0. D. After days, the number of fruit flies is increasing at a rate of 0.09, which can be calculated by taking the derivative of the equation with respect to t.
Learn more about time here
https://brainly.com/question/28050940
#SPJ4
Question 6 If z is a standard normal variable, find the probability. The probability that z is less than 1.13 a. 0.8708 b. 0.8907 c.0.1292 d.0.8485
If z is a standard normal variable, the probability that z is less than 1.13 is given by: A. 0.8708.
What is the standard normal distribution table?In Statistics, the standard normal distribution table is designed and developed to provide only the area to the left of a specified z-score.
Additionally, since z-score (z₁) and z-score (z₂) are generally symmetric about z = 0 and are negatives of one another, then, by symmetry, the area to the right of z-score (z₂) is always equal to the area to the left of z-score (z₁).
This ultimately implies that, the total areas under a standard normal distribution curve in two tails can be determined by calculating the area to the left of z-score (z₁) and multiplying the value by two (2).
From the z-score table, the area to the left of z-score (z₁ = 1.13) is the same as the probability that z is less than 1.13 and this is given by:
Area to the left of z-score (z₁ = 1.13) = 0.8708.
Probability, P(z ≤ 1.13) = 0.8708.
Read more on z-scores here: brainly.com/question/17180058
#SPJ1
X over 100 = 100
What is X?
Answer:
x is 1000
Step-by-step explanation:
hope this helps
