a) Let's say initial population is po and p = p(t) is the function that describes that population at time t. If it increases 10% each hour then we can write:
t = 0
p = po
t = 1
p = po + 0.1 . po
p = (1.1)¹ . po
t = 2
p = 1.1 . (1.1 . po)
p = (1.1)² . po
t = 3
p = (1.1)³ . po
and so on
So it has an exponential growth and we can write the function as follows:
p(t) = po . (1.1)^t
p(t) = 500 . (1.1)^t
Answer: p(t) = 500 . (1.1)^t
b)
We want the population for t = 2 hours, then:
p(t) = 500 . (1.1)^t
p(2) = 500 . (1.1)^2
p(2) = 500 . (1.21)
p(2) = 605
Answer: the population at t = 2 hours is 605 algae.
c)
Let's plug t = 4 in our function again:
p(t) = 500 . (1.1)^t
p(4) = 500 . (1.1)^4
p(4) = 500 . (1.1)² . (1.1)²
p(4) = 500 . (1.21) . (1.21)
p(4) = 500 . (1.21)²
p(4) = 732.05
Answer: the population at t = 4 hours is 732 algae.
In one year, the CPI increased from 106.3 to 108.9. How much money was required at the end of the year in order to have the same purchasing power as $1,000 at the beginning?
Based on the increase in CPI, the amount that would be required at year end to have the same purchasing power at the beginning of the year is $1,024.46.
How to find the change in purchasing power?First, find the inflation rate:
= (Current CPI - Beginning CPI) / Beginning CPI
= (108.9 - 106.3) / 106.3
= 2.446%
This means that the amount of money at the beginning of the year has lost a value of 2.446%.
In order to remain the same as the value of $1,000, a person would need:
= 1,000 x (1 + 2.446%)
= $1,024.46
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Which expression is equivalent to 8C +6 minus 3c minus 2
To simplify the expression above, simply combine similar terms.
The similar terms in the expression above are 8c and -3c as well as 6 and -2.
Let's combine the pairs of similar terms.
[tex](8c-3c)+(6-2)[/tex]So, 8c - 3c = 5c and 6 - 2 = 4. Hence, the answer is:
[tex]5c+4[/tex]The answer is 5c + 4. (Option A)
What is the value of 2(3x − 6) − 5y if x = −2 and y = 6?
−6 −18 −54 −78
Answer:
-54
Step-by-step explanation:
Finding a value means you will get a number answer. Since they said x
x = -2
fill in -2 in place of the x.
also they said
y = 6
so fill in 6 wherever you see a y.
2(3x - 6) - 5y
fill in -2 for x and 6 for y.
= 2(3•-2 - 6) - 5•6
Work on parentheses first. Multiply before adding or subtracting.
= 2(-6 - 6) - 5•6
= 2(-12) - 5•6
Again, multiply before adding or subtracting.
= -24 - 30
= -54
Which of the following transformations could be used to refute Anthony's claim? Select all that apply.
A parallelogram has rotational symmetry of order 2. This means that rotation transformation maps a parallelogram onto itself 2 times during a rotation of 360 degrees about its center.
And that is at 180 degrees and 360 degrees.
Hence, the only correct option is a rotation of 180 degrees clockwise about the center.
Answer:
Option D
Fraction multiplication 5/8 times 2/9 equals 10/72 how to simplify
So,
We're going to multiply:
[tex]\frac{5}{8}\cdot\frac{2}{9}[/tex]Multiplying numerators and denominators together, we obtain:
[tex]\frac{10}{72}[/tex]Now, to simplify, what we're going to do is to reduce the fraction dividing by a common number. Let's begin dividing by 2:
[tex]\frac{10}{72}=\frac{5}{36}[/tex]As you can see, we can't divide by a common number more times, so, the simplified fraction is 5/36.
Larry says all numbers that have a 2 in the one's place are composite numbers. Explain if Larry is correct or incorrect.
A composite number is defined as a whole number that have more than two factors; from this definition we conclude that all whole numbers that are not prime are composite numbers.
Since all even numbers are not prime we conclude that Larry is correct; all numbers that have a 2 in the one's place are composite. In fact all even numbers are composite with exception of 2 itself.
help meeeeeeeeee pleaseee !!!!!
The values for the composition of the functions are:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3x² + 15
How to Evaluate the Composition of Functions?To evaluate the composition of a function, the first thing to do is to evaluate the inner function, then use the output as an input to evaluate the outer function of the composition.
Given the following functions:
f(x) = x² + 5
g(x) = 3x
We are required to find (f o g)(x) and (g o f)(x).
To find (f o g)(x), replace g(x) for x in the outer function f(x):
(f o g)(x) = (3x)² + 5
(f o g)(x) = 9x² + 5
To find (g o f)(x), replace f(x) for x in the outer function g(x):
(g o f)(x) = 3(x² + 5)
(g o f)(x) = 3x² + 15
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I’m doing conversions and need to convert from years to months
Answer:
There are 126 months in 10 years and 6 months.
Explanation:
In a year there are 12 months.
[tex]1\text{ }year=12\text{ }months[/tex]Then, to know how many months are in 10 years, we multiply by 10:
[tex]10\cdot1\text{ }year=10\cdot12\text{ }months[/tex][tex]10\text{ }year=120\text{ }months[/tex]Now we add the additional 6 months:
[tex]120+6=126\text{ }months.[/tex]The answer is 126.
What is the volume in cubic feet of a corn crib that is 21 feet long, 9 feet wide, and 12 feet high?How many bushels of corn can be stored in the crib? (Note 1.25 cubic feet = 1 bushel)
Answer:
Volume = 2268 ft³
1814.4 bushels of corn
Explanation:
The volume of the corn crib can be calculated as:
Volume = Length x Width x Height
Then, the volume is equal to:
Volume = 21 ft x 9 ft x 12 ft
Volume = 2268 ft³
Finally, to know the number of bushels of corn that can be stored, we need to divide the volume of the corn crib by the volume of each bushel of corn. So:
[tex]\frac{2268ft^3}{1.25ft^3}=1814.4\text{ bushels of corn}[/tex]Therefore, the volume of the corn crib is 2268 ft³ and it can store 1814.4 bushels of corn.
Which of the following lists of data has the smallest standard deviation? Hint: you should not need to compute the standard deviation for each list.Select the correct answer below:11, 17, 9, 4, 4, 6, 6, 9, 8, 1829, 21, 21, 28, 28, 26, 24, 24, 17, 236, 8, 10, 6, 8, 8, 10, 7, 10, 1023, 19, 12, 19, 17, 18, 16, 10, 12, 2117, 12, 6, 6, 15, 16, 20, 20, 5, 17
Standard deviation is an important measure of spread or dispersion. It tells us how far, on average the results are from the mean.
The smallest standard deviation belongs to the dataset with the smallest range and almost no outliers. Closer the values are to the mean, less the value of the standard deviation.
Comparing those datasets, the one that fits this description is the third one.
[tex]\lbrace6,8,10,6,8,8,10,7,10,10\rbrace[/tex]find the coordinates of a point on a circle with radius 18 corresponding to an angle of 190°
The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).
What is transforming coordinates?
Polar coordinates (r,θ) are transformed into Cartesian coordinates (x, y) using the formulas x = r cos(θ), and y = r sin(θ).
This problem is under the concept of transforming polar coordinates (r,θ) to cartesian coordinates (x, y).
For this problem the polar coordinates are r = 18 and θ = 190°.
Convert these polar coordinates into a cartesian coordinates as,
x = r cos(θ) = 18 cos(190°) = -17.73
y = r sin(θ) = 18 sin(190°) = -3.13
The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).
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What is the area in square feet ( of the rectangle) of 4 3/4 feet and 6 4/5 feet
Recall the area of a rectangle is determined by the formula
[tex]\begin{gathered} A_{\text{rectangle}}=lw \\ \text{where} \\ l\text{ and }w\text{ are the dimensions of the rectangle} \end{gathered}[/tex]Given the following
w = 4 3/4 ft
l = 6 4/5 ft
Convert the following given into improper fraction first
[tex]\begin{gathered} w=4\frac{3}{4}\text{ ft}\Longrightarrow w=\frac{19}{4}\text{ ft} \\ l=6\frac{4}{5}\text{ ft }\Longrightarrow l=\frac{34}{5}\text{ ft} \end{gathered}[/tex]Next, substitute those values to the given formula for solving the area of the rectangle
[tex]\begin{gathered} A=lw \\ A=\frac{34}{5}\text{ ft}\cdot\frac{19}{4}\text{ft} \\ A=\frac{646}{20}\text{ ft}^2 \\ \text{Convert the final answer back into mixed fractions} \\ A=\frac{646}{20}\text{ ft}^2\Longrightarrow A=32\frac{3}{10}\text{ ft}^2 \\ \\ \text{Therefore, the area of the rectangle is} \\ 32\frac{3}{10}\text{ ft}^2 \end{gathered}[/tex]Please help!
How many solutions does the following equation have?
6 (c+4) = 6c + 30
zero solutions
one solution
infinitely many
solutions
The number of solutions that this equation have is: A. zero solutions.
What are zero solution?Generally speaking, an equation is said to have zero solution or no solution when the left hand side and right hand side of the equation are not the same or equal. This ultimately implies that, an equation would have zero solution or no solution when both sides of the equal sign are not the same and the variables cancel out.
How to determine the number of solutions?In order to determine the number of solutions that this equation have, we would simplify the equation by opening the bracket and then compare both sides of the equation as follows:
6(c+4) = 6c + 30
6c + 24 = 6c + 30
6c - 6c = 30 - 24
0 = 6 (no solution).
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write a system of equations that could be used to determine the number of liters of drink a maid and the number of liters of drink be made. Define the variables that you use to write the system.
ANSWER
Let x = liters of drink A
Let y = liters of drink B
System:
[tex]\begin{cases}x=y+30 \\ 0.2x+0.15y=100.5\end{cases}[/tex]EXPLANATION
We know that of the liters of drink A, 20% is real juice: 0.2x
and that of the liters of drink B, 15% is real juice: 0.15y
The sum of the amounts of real juice in each drink is 100.5, because it is said that 100.5 liters of real juice are use to make both drinks.
Also it is said that they make 30 more liters of drink A than of drink B, so the liters of drink A are 30 more than drink B: x = y + 30
The system is:
[tex]\begin{cases}x=y+30 \\ 0.2x+0.15y=100.5\end{cases}[/tex]write an algebraic model for the statement then solve the model the sum of a number and -9 is -21
Answer:
[tex]x + ( - 9) = - 21[/tex]
[tex]x - 9 = - 21[/tex]
[tex]x = - 12[/tex]
If Lanny spins the spinner below 70 times, how many times can he expect is to land on a number divisible by 3? *
From 1 to 10, there are 3, 6, and 9 are divisible by 3
Then we have 3 choices out of 10 numbers
Since the probability = an event/outcomes
Since the event is 3
Since the outcomes are 10, then
[tex]P(\frac{no}{3})=\frac{3}{10}[/tex]This is the probability for spinning the spinner one time
But we need to spin it 70 times
We will multiply 3/10 by itself 70 times, which means make it to the power of 70
[tex]P(\frac{no}{3})=(\frac{3}{10})^{70}[/tex]The answer is (3/10)^70 OR (0.3)^70
Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s newspaper. Assume the bond has a face value of $2,000 and the current date is April 19, 2021.
Company (Ticker) Coupon Maturity Last Price Last Yield EST volume (000s)
IOU (IOU) 6.3 April 19, 2037 112.97 ?? 1,857
a.
What is the yield to maturity of the bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b. What is the current yield? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
a) The yield to maturity of the IOU Corporation's bond is -0.39%.
b) The current yield of the IOU Corporation's bond is 5.58%.
What is the yield to maturity?The bond's yield to maturity (YTM) is the total rate of return earned by a bondholder with all interest payments and the original principal repaid.
We can compute the yield to maturity using the following YTM formula:
Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]
Where:
FV = Face Value of the Bond
Price = Current Market Price
Maturity = Maturity Period.
Bond's face value = $2,000
Current date = April 19, 2021.
Company (Ticker) Coupon Maturity Last Price Last Yield EST volume
(000s)
IOU (IOU) 6.3 April 19, 2037 112.97 ?? 1,857
Annual interest = $126 ($2,000 x 6.3%)
Maturity period = 16 (2037 - 2021)
Price = $2,259.4 ($2,000 x 112.97/100)
Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]
= [$126 + {($2,000 - $2,259.4)/16}] / [($2,000 + 2,259.4)/2]
= [$126 -$259.4)/16] / [($4,259.4)/2]
= -8.3375/2,129.7
= -0.39%
Current yield = Annual Coupon/Current Price
= 5.58% ($126/$2,259.4 x 100)
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a normal distribution has mean 62 and a standard deviation 20. find and interpret the z-score for x=46
The z - score of the normal deviation will be 0.8.
What is Standard deviation?
Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
A normal distribution has the mean = 62
Standard deviation = 20
Since, The formula for the z - score will be;
z = (x - μ) / σ
Where, σ is the standard deviation and μ is the mean of normal distribution.
Substitute all the values in above equation, we get;
z = (x - μ) / σ
z = (46 - 62) / 20
z = - 16 / 20
z = - 0.8
Therefore,
The z - score of the normal deviation will be 0.8.
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Determine whether the figure has line symmetry. If so, draw the line(s) of symmetry.
Yes
No
Yes, the given figure has the horizontal symmetry.
What is a line of symmetry?Line symmetry is a type of symmetry about reflections. When there is at least one line in an object that divides a figure into two halves such that one-half is the mirror image of the other half, it is known as line symmetry or reflection symmetry. The line of symmetry can be in any direction - horizontal, vertical, slanting, diagonal, etc.
The horizontal line of symmetry divides a shape into identical halves, when split horizontally, i.e., cut from right to left or vice-versa.
The given figure has horizontal symmetry.
Yes, the given figure has the horizontal symmetry.
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the jar's inner dimensions are approximately a rectangular prism with dimensions of 14cm by 12cm by 28cm. George estimates that the lowest amount of marbles possible to fill the jar 225 marbles and the highest amount is approximately 489 marbles. what is the reasonable lower limit and upper limit for the amount of marbles in the jar according to Fermi?
Given: the dimensions of the rectangular prism is 14 x 12 x 28 in cm
The point S is plotted on the coordinate grid below. Plot the point S', the reflection
of S over the x-axis.
Click on the graph to plot a point. Click a point to delete it.
Answer:
(1, -2)
Step-by-step explanation:
Reflecting a point over the x-axis means [tex](x,y) \longrightarrow (x, -y)[/tex].
Benjamin mows two lawns. The first lawn is 8 meters long and 7 meters wide. The second lawn has the same length, and a width that is 6 times as much as the first one. What is the total area of the two lawns?
Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.
what is square ?A square is a quadrilateral in geometry that has four equal sides and four right angles (90-degree angles). It is a unique kind of both a rhombus and a rectangle. A square is made up of four equal-length sides, two equal-length diagonals, and right-angle diagonal cuts. A square's area and perimeter can be calculated by multiplying one of its sides by itself (squared), and one of its sides by four, respectively. Because of their symmetry and regularity, squares are frequently employed in mathematics and building.
given
By multiplying the first lawn's length by its breadth, one may determine its area: 56 square metres is the size of the first lawn, which is 8 metres by 7 metres.
The second lawn's breadth is six times that of the first lawn's, so:
The second lawn's width is equal to 6 × 7 metres, or 42 metres.
The second lawn is the same length as the first one, so:
The second lawn is 8 metres long.
The second lawn's area is calculated by multiplying its length by its width:
The second lawn is 336 square metres in size (8 metres by 42 metres).
The first and second lawns' combined areas make up the overall area of the two lawns:
Total area equals the sum of the first and second lawns.
56 square metres + 336 square metres make up the total area.
Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.
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Suppose you want to have $400,000 for retirement in 25 years. Your account earns 4% interest.
a) How much would you need to deposit in the account each month?
$
b) How much interest will you earn?
$
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$400000 \\ pmt=\textit{periodic payments}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]
[tex]400000=pmt\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)[/tex]
[tex]\cfrac{400000}{\left[ \frac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)}=pmt\implies \cfrac{400000}{\left[ \frac{\left( \frac{301}{300} \right)^{300}-1}{\frac{1}{300}} \right]\left(\frac{301}{300}\right)}=pmt \\\\\\ \cfrac{400000}{515.84}\approx pmt\implies {\Large \begin{array}{llll} 775.43\approx pmt \end{array}}[/tex]
how much will it be in interest alone?
well, for 25 years every month you'd have been putting down that much, so we can just subtract what you put it from the 400,000 and what's left is the interest earned
[tex]400000~~ - ~~(25)(12)(775.43) ~~ \approx ~~ \text{\LARGE 167317}[/tex]
Billy is making a curtain for his kitchen window. He bought 2 1/2
yards of fabric. His total cost was $15. What was the cost per yard?
The fabric has a cost per yard of $6 per yard
How to determine the cost per yard of the fabric?From the question, the given parameters are:
Yards of fabric = 2 1/2 yards
Cost of the fabric = $15
The cost per yard of the fabric is then calculated as
Cost per yard = Cost of the fabric/Yards of fabric
Substitute the known values in the above equation
So, we have
Cost per yard = 15/(2 1/2)
Evaluate the quotient
So, we have
Cost per yard = 6
Hence, the cost per yard is $6 per yard
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22. This question has two parts.Aya sold printed T-shirts for $7.50 each at a carnival. She earned$187.50.Part A. Which equation represents the number of T-shirts, x, Aya sold atthe carnival?7.50x = 187.50187.50x = 7.50x + 7.50 = 187.50x - 7.50 = 187.50Part B. What is the number of T-shirts Aya sold at the carnival?0.04B25180195
Explanation
Step 1
Aya sold printed T-shirts for $7.50 each at a carnival. She earned
$187.50.
then
let x represents the number of T-shirts Aya sold.so, if she made $187.5 and the cost per T-shirt is $7.50
[tex]\begin{gathered} \text{total}=\text{ rate}\cdot\nu mber\text{ of T-shirt} \\ \text{replace} \\ 187.5=7.5x \\ or \\ 7.50x=187.50 \end{gathered}[/tex]therefore, for part A , the answer is
[tex]A)7.50x=187.5[/tex]
Step 2
What is the number of T-shirts Aya sold at the carnival?
to figure out this,we need to solve for x
[tex]\begin{gathered} 7.5x=187.5 \\ \text{divide both sides by 7.5} \\ \frac{7.5x}{7.5}=\frac{187.5}{7.5} \\ x=25 \end{gathered}[/tex]it means she sold 25 T-shirts at the carnival
I hope this helps you
Consider the following expression:3Step 2 of 2: Determine the degree and the leading coefficient of the polynomial.AnswerHow to enter your answer (opens in new window)KeybcPreviouDegree:Leading Coefficient:
Solution
We are given the expression
[tex]3[/tex]The image below shows the definition of a polynomial and some examples as well
Thus, given
[tex]3[/tex]Here;
Degree = 0
Leading coefficient = 3
15) If x and y satisfy both 9x + 2y = 8 and 7x + 2y = 4, then y =? * Hint: Use the elimination method to solve this system of equations
For the information given in the statement you have
[tex]\begin{cases}9x+2y=8\text{ (1)} \\ 7x+2y=4\text{ (2)}\end{cases}[/tex]Using the elimination method, multiply by -1 the equation (2) and then add the equations to eliminate one of the variables
[tex]\begin{cases}9x+2y=8\text{ (1)} \\ 7x+2y=4\text{ (2)}\cdot-1\end{cases}[/tex][tex]\begin{gathered} \begin{cases}9x+2y=8\text{ (1)} \\ -7x-2y=-4\text{ (2)}\end{cases} \\ ------------- \\ 2x+0y=4 \\ 2x=4 \\ \text{ Divide by 2 on both sides of the equation} \\ \frac{2x}{2}=\frac{4}{2} \\ x=2 \end{gathered}[/tex]Now plug the value of x found into any of the initial equations to find the value of y. For example in equation (1)
[tex]\begin{gathered} 9x+2y=8 \\ 9(2)+2y=8 \\ 18+2y=8 \\ \text{ Subtract 18 on both sides of the equation} \\ 18+2y-18=8-18 \\ 2y=-10 \\ \text{ Divide by 2 on both sides of the equation} \\ \frac{2y}{2}=\frac{-10}{2} \\ y=-5 \end{gathered}[/tex]Therefore, the solutions of the system of equations are
[tex]\begin{cases}x=2 \\ y=-5\end{cases}[/tex]Write the equation of a line containing (3,-7) that is parallel to the line given by the equation -4x+8y=3
Two lines are parallel is they have the same slope. In this case:
[tex]-4x\text{ + 8y = 3}[/tex]Solving the equation for y, and obtaining the slope-intercept equation for the line equation, we have:
[tex]8y\text{ = 3 + 4x}[/tex][tex]y\text{ = }\frac{3}{8}\text{ + }\frac{4}{8}x[/tex]Then,
The wholesale price for a pair of shoes is $3.50. A certain department store marks up the wholesale price by 60%. Find the price of the pair of shoes in the department store
Given
Wholesale price for a pair of shoes = $3.50.
Wholesale price by 60%.
Find
price of the pair of shoes in the department store
Explanation
Price in deparrtmental store is 60% more than wholesale
[tex](1+60\%\text{ \rparen of wholesale }[/tex]so ,
[tex]\begin{gathered} 1.6\times3.50 \\ 5.60 \end{gathered}[/tex]Final Answer
Therefore , the price of the pair of shoes in the department store is $5.60.
Can you please help me out with a question
AS shown in the figure:
The measure of arc RT = 27
The measure of arc FN = 105
The measure of angle FUN will be as follows:
[tex]m\angle\text{FUN}=\frac{1}{2}(105+27)=\frac{1}{2}\cdot132=66[/tex]So, the answer is option C. 66