The population of a city can be modeled using the formula P=100,000e^(0.05t), where t is the number of years after 2012 and P is the city's population. Which of the following equations can be used to find the number of years after 2012 that the population will triple to 300,000?
Group of answer choices
t=3/(0.05e)
t=ln3/0.05
t=(ln200,000)/0.05
t=log3/0.05
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
Given,
The population of a city can be modeled using the formula P=100,000e^(0.05t)
t is the number of years after 2012
P is the population of the city
We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.
Here,
Substitute 300000 in for P and solve for t
300000=100000e^0.05t
Divide both sides by 100000:
We get,
3 = e^0.05t
Multiply both sides by the natural log (ln)
Then,
ln(3) = 0.05t
Now, divide 0.05 on both sides to get t by its self
t = ln(3) / 0.05
Therefore,
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
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If CE and FH are parallel lines and m/CDG =
are parallel lines and m/CDG = 128°, what is mZHGD?
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=990 and x=581 who said "yes." Use a 95% confidence level.
The 95% confidence interval for the proportion of respondents who say yes is of:
(0.5562, 0.6176)
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameters, which are the sample size and the estimate, are given as follows:
[tex]n = 990, \pi = \frac{581}{990} = 0.5869[/tex]
The lower bound of the interval is of:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 - 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.5562[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 + 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.6176[/tex]
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3.
A circular pool of oil grew so that its radius increased by 2 feet. The formula shown can
be used to determine the area of the circle.
A = π (r + 2)²
Which equation is equivalent to the formula solved for r in terms of A?
Or=√1-2
Or=√√√+2
Or=√√4+2
Or-√4-2
Equation which is equivalent to the formula solved for r in term of A is [tex]Or = \sqrt{\frac{A}{r}-2 }[/tex].
What is circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
A circle is also termed as the locus of the points drawn at an equidistant from the centre.
What is radius?
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.
What is circumference?
Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.
Given that;
[tex]A = \pi{({r+2})^{2}}[/tex]
[tex](r+2)^{2} =\frac{A}{\pi}[/tex] (equivalent transformation)
[tex]r + 2 = \sqrt{\frac{A}{\pi} }[/tex]
[tex]r = \sqrt{\frac{A}{\pi} -2}[/tex]
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Solve for x X/11=2
x=?
Answer:
x = 22
Step-by-step explanation:
Solve for x:
x/11 = 2
multiply both sides by 11:
11(x/11) = 11(2)
x = 22
Answer:
x = 22
Step-by-step explanation:
[tex] \sf \frac{x}{11} = 2[/tex]
Use cross multiplication.
[tex] \frac{x}{11} = \frac{2}{1} \\ \\ \sf x = 2 \times 11 \\ \\ \sf \: x = 22[/tex]
2
Linda paid $5.50 for 4 pounds of
strawberries. How much did she pay
per pound of strawberries?
She paid $1.375 per pound of strawberries.
What is the unit rate?
When expressed rate as a fraction, a unit rate has a denominator of 1.
Since 4 pounds cost $5.50, 1 pound of strawberries will cost 5.50/ 4 ≈ $1.375.
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HELP PLEASE ILL DO ANYTHING ONE MCRIB BURGER
The solutions for the graphed linear inequality are (-4, 0), (-1, 4), (0, 0), and (-2, 0). The correct options are A. (-4, 0), B. (-1, 4), C. (0, 0), and E. (-2, 0)
Determining the solutions of a linear inequality from a graphFrom the question, we are to determine all of the solutions for the linear inequality whose graph is given
To do this, we will find the points that fall in the solution region (shaded portion of the graph)
A. (-4, 0)The point (-4, 0) falls in the solution region. Thus, it is a solution for the linear inequality.
B. (-1, 4)The point (-1, 4) falls in the solution region. Thus, it is a solution for the linear inequality.
C. (0, 0)The poi0nt (0, 0) falls in the solution region. Thus, it is a solution for the linear inequality.
D. (4, -1)The point (4, -1) does not fall in the solution region. Thus, it is not a solution for the linear inequality.
E. (-2, 0)The poi0nt (-2, 0) falls in the solution region. Thus, it is a solution for the linear inequality.
F. (0, -2)The point (0, -2) does not fall in the solution region. Thus, it is not a solution for the linear inequality.
Hence, the solutions are (-4, 0), (-1, 4), (0, 0), and (-2, 0).
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How do work out 349 divided by 60
Answer:
5 with a remainder of 49
Step-by-step explanation:
Drag each tile to the correct box. Not all tiles will be used.
Consider the recursively defined function below.
f(1) = = 10
f(n) 2.2 f(n-1), for n = 2, 3, 4, ...
Create the first five terms of the sequence defined by the given function.
The first five terms of the sequence defined by the given function are f(1) = 10 f(2) = 22 f(3) = 48.4 f(4) = 106.48 and f(5) = 234.256.
What is a sequence?
A collection of events or items that occur one after the other in a specific order is referred to as a sequence.
Here, we have
Given the function is f(n) = 2.2 [ f(n-1) ] Here, f(1) = 10 then we have to create the first five terms of the sequence defined by the function.
Since f(1) = 10
f(2) = 2.2 [ f (2-1) ] = 2.2× [ f (1) ]
= 2.2 × 10 = 22
f (3) = 2.2 [ f (3-1)] = 2.2 × [ f (2) ]
= 2.2 × 22 = 48.4
f(4) = 2.2 [ f(4-1) ] = 2.2× [ f(3)]
= 2.2 × 48.4 = 106.48
f(5) = 2.2 [ f(5-1) ] = 2.2× [ f(4)]
2.2× 106.48 = 234.256
Hence the first five terms of the sequence defined by the given function are f(1) = 10 f(2) = 22 f(3) = 48.4 f(4) = 106.48 and f(5) = 234.256.
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Convert the expression (10) 1/3 to radical form.
Answer:
cubic root 10 power 1
Step-by-step explanation:
Apply the rule
x
m
n
=
n
√
x
m
to rewrite the exponentiation as a radical.
3
√
10
1
Anything raised to
1
is the base itself.
3
√
10
The result can be shown in multiple forms.
Exact Form:
3
√
10
Decimal Form:
2.15443469
…
find the amount on $ 6,250 at 8%p.a compounded annually for 2 years. also, find the compounded intrest
The Compound Interest is $7,290.00.
What is Compound Interest?In order to calculate compound interest, multiply the principal of the original loan by the annual interest rate multiplied by the number of compound periods minus one.
Given:
P= 6250
T= 2 years
r = R/100
r = 8/100
r = 0.08 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 6,250.00[tex](1 + 0.08/1)^{(1)(2)[/tex]
A = 6,250.00(1 + 0.08)²
A = $7,290.00
Hence, The Compound Interest is $7,290.00.
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The vertices of &ABC are A(2. 8), B(16, 2), and C(6, 2). The perimeter of aABC is____
units, and its area is_____
square units.
For the given triangle ABC,
The perimeter of ABC is 32.443 unit
The area of ABC is 30 unit^2
What is a vertex?
A triangle is created geometrically by the intersection of three line segments. Each side of a triangle has two ends, and the three sides' endpoints may intersect at three distinct places in a plane to form the triangle. The three locations where they cross each other are referred to as a triangle's vertices.
Solution explained:
The distances are found using the distance formula:
D=[tex]\sqrt{((y2-y1)^2+(x2-x1)^2)}[/tex]
Given A(2,8),B(16,2),C(6,2)
Now, calculate the distance
AB=[tex]\sqrt{((16-2)^2+(2-8)^2)}[/tex]=[tex]\sqrt{(14^2+6^2)}[/tex]=[tex]\sqrt{232}[/tex]
BC=[tex]\sqrt{((6-16)^2+(2-2)^2)}[/tex]=[tex]\sqrt{(10^2+0)}[/tex]=10
CA=[tex]\sqrt{((2-6)^2+(8-2)^2)}[/tex]=[tex]\sqrt{(4^2+6^2)}[/tex]=[tex]\sqrt{(16+36)}[/tex]=[tex]\sqrt{52}[/tex]
Perimeter=AB+BC+CA
=32.443 unit
For the area (we note that BC is horizontal (parallel to the x-axis)), so
Area = (1/2)base * height
=(1/2)10*(ya-yb)
=(1/2)10*(8-2)
=(1/2)10*6
=30 unit^2
Hence, the perimeter is 32.443 units and the area is 30 unit^2
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7. At time t seconds, the height, h, of a ball thrown vertically upward is modeled by the equation h = -5t² +33t+ 4. About how long will it take for the ball to hit the ground?
The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.
Quadratic equation :
An algebraic equation of the second degree in x is a quadratic equation.its standard form is ax2 + bx + c = 0where a and b are the coefficients, x is the variable, and c is the constant term.To solve the quadratic equation:
h(t) = 0 = -5t² +33t+ 4
[tex]t = \frac{-b \pm\sqrt{(b)^2 - 4ac}}{2a}[/tex]
[tex]t = \frac{-33 \pm\sqrt{(33)^2 - 4(-5)(4)}}{2(-5)}[/tex]
t = {(-33) ±√(1169)}/(-10)
t = -0.1190
t = 6.719
neglecting the negative term we get :
t = 6.719 seconds
This represents that the ball hits the ground after 6.719 seconds.
The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.
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Please help!! See screenshot attached below (100 pts)
Answer:
f(2) = 0
Step-by-step explanation:
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
Therefore, applying the factor theorem, if (x - 2) is a factor of a polynomial f(x) then f(2) = 0.
1. Solve the equation (9-6p) =
-11 for p.
Answer:
p=p=10/3
Explanation:
9-6p =-11=p=10/3
If y varies directly as x, find the constant of variation k and the direct variation equation for the situation.
y=2 when x= 10
Variation refers to differences in characteristics between individuals of the same species or between different genera or species. The formula is y = 0.25x.
What is meant by variation equation?A variation is a relationship between one set of values for one variable and another set of values for another variable. Variation in direct. If m is a nonzero constant and b = 0, then the function y = mx (often written y = kx) is a direct variation of the equation y = mx + b. If y varies directly as x and y = 6 when x = 2, the constant of variation is k = 3. As a result, the equation for this direct variation is y = 3x.The direct variation equation is a two-variable linear equation given by y = kx, where k is the constant proportionality. In a coordinate plane, the direct variation graph is a straight line.Therefore,
y=0.25 x
the initial statement is y ∝ x
to convert to an equation multiply by k the constant of
⇒ y=k x
to find k use the given condition
y=0.5 when x=2
[tex]$y=k x \Rightarrow k=\frac{y}{x}=\frac{0.5}{2}=0.25$$[/tex]
the equation is y = 0.25x
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The variation equation is [tex]y=\frac{1}{5} x[/tex]
What do you mean by direct variation?If two quantities change by the same amount, they are said to follow a direct variation. As a result, when one quantity changes, the other follows suit, increasing when the first changes and decreasing when the first changes. To put it another way, two quantities are said to be directly proportional to one another if the ratio of the first to the second is a constant term. The coefficient or constant of proportionality is the name given to this constant quantity.The mathematical relationship between the two quantities in the direct variation formula makes it so that one of the variables is a constant multiple of the other. The sign "∝" is used to indicate that two quantities are directly proportional to one another or directly varying from one another. Assuming that x and y are two quantities that are directly varying, they are stated as follows: y∝ xThe direct variation formula is expressed as follows when the proportionality sign is omitted.Calculation
Given, y =2 and x=10
we know the direct relation in y∝ x
so, y = kx, where k is the proportionality constant
2= k*10
k = [tex]\frac{2}{10} =\frac{1}{5}[/tex]
Therefore, the direct variation equation for this situation is [tex]y=\frac{1}{5} x[/tex]
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Division A of Aztec Manufacturing purchases materials to be used in production from an outside supplier for $20 per unit. The same materials are produced by Division B. Division B incurs variable costs of $10 per unit. Currently, Division B is able to sell only 320,000 units to outside buyers out of 400,000 units produced. In this situation, if a transfer price of $18 per unit is established between the two divisions and 80,000 units of materials are transferred to Division A, by what amount would Division B's operating income increase? a.$160,000 b.$960,000 c.$640,000 d.$800,000
The operating income of Division B will increase by $640,000
How to calculate the increase in Division B's operating income?
Given that: Division B incurs variable costs of $10 per unit and a transfer price of $18 per unit is established between the two divisions and 80,000 units of materials are transferred to Division A
This cost of production by division B is:
cost = $10 × 80,000 = $800,000
Division B uses a transfer price of $18 per unit. That is:
Selling price = $18 × 80,000 = $1,440,000
Operating income increase = Selling price - cost
Operating income increase = $1,440,000 - $800,000 = $640,000
Therefore, Division B's operating income increase will be $640,000
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6 sqrt 44z + sqrt 99z
Answer: 15√11z
Step-by-step explanation:
4x7 = 2x + 15
Does the equation have one
none, or infinite solutions?
Explain why.
Answer:
There is only one solution
Step-by-step explanation:
4x - 7 = 2x + 15
+7 +7
4x = 2x + 22
-2x -2x
2x = 22
divide by 2 into both sides
x = 11
Since there is only one answer, there is only ONE solution.
41% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
P(3)=
P(x >4)=
P(x<9)=
The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is;
(a) exactly three = 0.1314
(b) at least four = 0.7953
(c) less than eight = 0.93382
How to solve Binomial Probability Distribution Problems?The binomial probability distribution is the probability of exactly x successes on n repeated trials, with p probability. The formula is;
P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)
We are given;
p = 41% = 0.41
n = 12
Thus;
1) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is exactly three;
P(3) = ¹²C₃ * 0.41³ * (1 - 0.41)^(12 - 3)
P(3) = 0.1314
2) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is at least four;
P(x ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)
P(x ≥ 4) = 0.7953
3) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is less than eight using binomial probability calculator is;
P(X < 8) = 0.93382
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3 times 4 times 4 times 3 times 3 times 4 = 3 (to the power of x) times 4 (to the power of y)
The value of 3 times 4 times 4 times 3 times 3 times 4 in exponent is 3³ × 4³
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the expression given is 3 times 4 times 4 times 3 times 3 times 4. It should be noted that the 4 occurs three times as well as the 3.
Therefore, this will be 3³ × 4³.
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Calculate ending inventory and COGS using FIFO and LIFO methods for ABC Inc.
On April 1, 2022 the balance in inventory is 220 units at $50 each
April 5, 2022 purchased 100 units at $60 each
Purchased 50 units at $45 each on April 10, 2022
Sold 300 units at $80 each on April 16, 2022
Sold 20 units at $95 each on April 25, 2022
Purchased 200 units at $40 each on April 30, 2022
The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:
FIFO LIFO
Ending inventory $10,250 $12,800
Cost of goods sold $17,000 $14,450
How does FIFO differ from LIFO?FIFO, which means First-in, First-out, computes the cost of goods sold based on the assumption that the physical flow of goods sold depends on the earlier inventory in stock.
FIFO can be applied under both the perpetual and periodic inventory systems, unlike LIFO.
LIFO means Last-in, First-out, and as a cost flow assumption assigns the cost of goods sold based on the latest inventory purchases.
LIFO cannot be used under the perpetual inventory system.
Date Activities Units Unit Rate Total Cost
April 1 Beginning inventory 220 $50 $11,000
April 5 Purchases 100 $60 6,000
April 10 Purchases 50 $45 2,250
April 16 Sales -300 $80
April 25 Sales -20 $95
April 30 Purchases 200 $40 8,000
Total 570 $27,250
Units sold 320
Ending inventory 250
FIFO:
Ending Inventory = $10,250 (200 x $40 + 50 x $45)
Cost of goods sold = $17,000 ($27,250 - $10,250)
LIFO:
Ending Inventory = $12,800 (220 x $50 + 30 x $60)
Cost of goods sold = $14,450 ($27,250 - $12,800)
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How many dogs do they need to walk in order to pay for the box of treats?
hint:In the equation for the function representing the profit, substitute 5 for y and solve the equation for x.
hint:Round up to the nearest whole number of dogs.
The number of dogs do they need to walk in order to pay for the box of treats is 4
The function that representing the profit is
y = 3x - 5
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Here the cost for buying a box of treat = $5
Substitute the value in the function and find the number of dog that they need to walk
5 = 3x - 5
3x = 5 + 5
3x = 10
x = 10 / 3
x = 3.33
x ≈ 4
Hence, the number of dogs do they need to walk in order to pay for the box of treats is 4
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Joey has 80 pens and 30 of them are red. What percent are red?
Answer:
Step-by-step explanation:
What is the expected change in the dividend of a 6% preferred stock if the required rate of return drops instantly from 8% to 6%?
The expected change in the dividend of a 6% preferred stock is $75.
Given that, the required rate of return drops instantly from 8% to 6%.
What is the return?A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time.
The value of preferred stock = $100
Annual dividend = 100 × 6% = $6
Price of preferred stock when required return is 8% = Annual dividend / Required rate of return
= 6/8%
= 6 ×100/8
= $75
Therefore, the expected change in the dividend of a 6% preferred stock is $75.
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How many hour is 4:30 until 6:00
Answer: 1 hour and 30 minutes or 1.5 hours
Answer:
1 hour and 30 minutes
Step-by-step explanation:
Which represents the solutions of the graphed system of equations y=x2+2x-3 and y=x-1?
Answer:
second option
Step-by-step explanation:
the solution to the system of equations is at the points of intersection of the two graphs.
the graphs intersect at (- 2, - 3 ) and (1, 0 ) , then
the solutions are (- 2, - 3 ) and (1, 0 )
The probability that a 50-year-old male in the U.S. will die within one year is about 0.00142. An insurance company is preparing to sell a 50-year-old male a one-year, $60,000 life insurance policy. How much should it charge for its premium in order to have an expectation of $0 for the policy (i.e., make no profit and make no loss)? (Round your answer to the nearest dollar.)
They should charge for its premium in order to have an expectation of $0 for the policy is $85.
Given that, the probability that a 50-year-old male in the U.S. will die within one year is about 0.00142.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, probability of alive 100-0.00142
= 0.99858
P(A)=0.99858A+0.00142(A+60000)
Put A=0, in the obtained function, we get
P(0)=0.99858(0)+0.00142(0+60000)
=0.00142×(60000)
=$85.2
= $85
Therefore, they should charge for its premium in order to have an expectation of $0 for the policy is $85.
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rewrite 3x+4y>8 in slope intercept form
Answer: y > -3/4x + 2
Step-by-step explanation:
Lee.com accepted a $70,000, 634% , 120-day note on July 26. Lee discounted the note on October 28 at LB Bank at 6%. What proceeds did Lee receive? (Use Days in a year table) (Round your answer to the nearest cent.)
On October 28, Lee received proceeds of $71,153.66 from the discounted note.
What is note discounting?Discounting a note involves receiving immediate cash by selling it to a financial institution at a discount.
The implication of discounting a note is that the receiver gets less than the maturity value.
The maturity value is the face value of the note plus the computed interest.
Face value of the note receivable = $70,000
Interest rate = 6.34%
Note period = 120 days
July 26 - October 28 = 94 days
Maturity value of the note receivable = The Face Value + Interest
= $71,459.07 [$70,000 + ($70,000 x 6.34% x 120/365)]
Bank discount rate = 6%
The discount period from October 28 to Nov 22 = 26 days (120 - 94)
Bank discount = Maturity Value x Discount Rate x Discount Period
= $305.41 ($71,459.07 x 6% x 26/365)
Proceeds = Maturity value - Bank discount
= $71,153.66 ($71,459.07 - $305.41)
Thus, by discounting the note receivable at LB Bank at 6%, Lee received $71,153.66 instead of the $71,459.07 it would have received at maturity.
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