The population of a pigeons in a city is 100 and is growing exponentially at 20% per year. Write a function to represent the population of pigeons after
t
t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent
Answers
Answer:
p(t) = 100×1.0153^(12t)1.53% per monthStep-by-step explanation:
In general, the function will be written ...
p(t) = (initial value)×(growth factor)^t
where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...
growth factor = 1 + growth rate
Here, the growth rate is given as 20% per year, so the growth factor per year is ...
1 +20% = 1.20
The initial value is given as 100, so we can write the exponential function as ...
p(t) = 100×1.20^t
__
The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.
p(t) = 100×(1.20^(1/12))^( 12t)
p(t) = 100×1.0153^(12t) . . . . population exponential function
This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...
1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change
Answers:
Function is \(P(t) = 100(1.0153)^{12t}\\\\\)Monthly growth rate is roughly 1.53%=====================================================
Explanation:
The population starts at 100 pigeons. After a year, the population goes up by 20%, meaning the population goes up by 20. It lands on 120 after a full year (100+20 = 120).
Dividing the "before" and "after" population amounts gets us 120/100 = 1.20
If we didn't worry about the monthly rate, and only cared about the annual rate of growth, then the population function would be
\(P(t) = 100(1.20)^t\)
where t is the number of years and P(t) is the population for that year number. Notice how the 1.20 is the base of the exponential to quickly tell the reader the annual rate of growth. We read off the .20 portion and that converts to 20% after moving the decimal 2 spots to the right.
If we were to plug t = 0 into that function, then we'd get P(0) = 100. Inputting t = 1 leads to P(1) = 120. This helps confirm we have the correct annual growth rate function.
---------------------
Unfortunately, your teacher doesn't want the annual growth rate function. Instead, they want you to write a function where the reader can easily pick out the monthly rate of change without having to do any math. This is due to the instructions that "the monthly rate of change can be found from a constant in the function". Let m be this constant.
Since t is the number of years, this means t = 1/12 represents 1/12 of a year, aka 1 month. If you were to compute P(1/12), then you should get roughly 101.530947049973
Divide this amount over the initial population to find m.
m = 101.530947049973/100 = 1.01530947049973
So we get m = 1.0153 after rounding to four decimal places.
The number m is in the form 1+x. Solving 1+x = m will lead to x = 0.0153 to indicate a monthly rate of change is roughly 1.53% since we move the decimal point 2 spots to the right to go from 0.0153 to 1.53%
The pigeon population is increasing by roughly 1.53% each month.
This is why computing this m value leads to the reader able to spot the monthly rate of change without having to resort to a calculator. All they have to do is read the digits to the right of the decimal point and convert that to percentage form.
---------------------
An alternative way to compute this value is to use this formula
m = (1+r)^(1/12)
We'll plug in the annual rate r = 0.20 to get:
m = (1+r)^(1/12)
m = (1+0.20)^(1/12)
m = 1.01530947049973
m = 1.0153
We get the same approximate value as earlier.
---------------------
Whichever method you use, you should get roughly m = 1.0153
We're given that A = 100 is the initial population
So we'll then be able to form this function
\(P(t) = A*(m)^{12t}\\\\P(t) = 100(1.0153)^{12t}\\\\\)
This represents the monthly growth of the population where t is in years. Note that after something like t = 3 years, we have 12t = 12*3 = 36 months pass by. So that's why the 12t is in the exponent rather than simply t.
Once again, for comparison we have...
\(P(t) = 100(1.20)^{t}\\\\\) for annual growth\(P(t) = 100(1.0153)^{12t}\\\\\) for monthly growthEach function has t represent the number of years. The difference is the base of each exponential to tell us the respective annual or monthly growth rate. Also, the exponent up top must be adjusted depending on which you go for.
---------------------
You may be wondering: "what if the exponent in the monthly growth rate function wasn't 12t?". Let's find out. We'll assume the monthly growth rate function is \(P(t) = 100(1.0153)^{t}\\\\\) and show that an error happens.
If we plugged in something like t = 1, we should get P(t) = 120 like mentioned earlier.
\(P(t) = 100(1.0153)^{t}\\\\P(1) = 100(1.0153)^{1}\\\\P(1) = 100(1.0153)\\\\P(1) = 101.53\\\\\)
That value of 101.53 is the approximate population number after 1 month, rather than 1 year. Making the exponent 12t will fix the issue.
Related Questions
help due in 7-8 minutes!!!!!!
Answers
Answer:
16.6 = 0.83×20
83% of 20 is 16.6
Hey I need help on this correct answer will get marked brainless
Answers
Answer:
\(\huge\boxed{\sf NO.}\)
Step-by-step explanation:
If the pair forms proportion, the cross multiplication of them should be equal to each other. Let's check it out!
\(\displaystyle \frac{3}{4} = \frac{5}{7} \\\\Cross \ Multiply\\\\3 \times 7 = 5 \times 4\\\\\boxed{35 \neq 20}\\\\\)
Hence, the given pair doesn't form a proportion.
\(\rule[225]{225}{2}\)
Hope this helped!
~AH1807a line intercepts the point ( -11, 4) and has a slope of -2 fill in the formula y - ? = ? (x - ? )
Answers
The point-slope form is;
\(y-4\text{ = -2(x+11)}\)Here, we want to write the slope intercept formula for the given line and point
We have the general point-slope form as;
\(\begin{gathered} y-y_1=m(x-x_1) \\ \\ m\text{ is slope = -2} \\ (x_1,y_1)\text{ = (-11,4)} \\ \\ y-4\text{ = -2(x-(-11))} \\ y\text{ - 4 = -2(x+11)} \end{gathered}\)A derivative is available with premium W(0)=1.34 when its underlying asset has value S(0)=36. This derivative will have expiry values W(1,↑)=0.64 and W(1,↓)=4.55, when the underlying asset has values S(1,↑)=57 and S(1,↓)=26, respectively. A writer sells 100 of these derivative and wants to set up a portfolio which will have zero cash flow, both at the time the derivative is sold and at the time the derivative expires. The portfolio will include 100 derivatives, borrowed or lent cash, and bought or short sold underlying assets. To ensure a zero cash flow, how many underlying assets should the writer have in the portfolio (with positive meaning bought assets and negative meaning short sold assets)? Give your answer to the nearest integer.
Answers
To ensure a zero cash flow in the portfolio, the writer needs to set up a portfolio that offsets the cash flow from selling the derivatives. The writer should have -3 underlying assets in the portfolio (meaning short sold assets)
The cash flow from selling 100 derivatives can be calculated as:
Cash Flow from selling derivatives = 100 * (Premium at time 0 - Expiry value)
Cash Flow from selling derivatives = 100 * (1.34 - 0.64) = 70
To offset this cash flow, the writer needs to include an equal and opposite cash flow from the underlying assets. Let's assume the writer buys ""x"" underlying assets.
Cash Flow from underlying assets = x * (Value at time 0 - Value at time 1)
Cash Flow from underlying assets = x * (36 - 57) = -21x
To make the cash flow from underlying assets equal to the cash flow from selling derivatives, we set up the equation:
-21x = 70
Solving this equation, we find:
x ≈ -3.33
Since the number of underlying assets must be an integer, we round -3.33 to the nearest integer, which is -3.
Therefore, the writer should have -3 underlying assets in the portfolio (meaning short sold assets).
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NEED HELP PLEASE. NO LINKS OR U WILL B REPORTED. WILL GIVE POINTS AND THE BRAINLIEST. THANKS!!
In a robotics competition, a robot must be built with a specific
maximum starting height, width, and depth. In order to meet the
height requirements, a robot must fit in the judge's plexi-glass box.
The box is a rectangular prism that has a surface area of 1 728 in”, a
width of 15 inches, and a length of 18 inches. The Mad Hatter robot
is 17.75 inches tall in its starting position. Does the Mad Hatter
meet the height requirement?
Answers
2*(15+18) + 2*(15H) + 2*(18H) = 540 + 30H + 36H
1,728 - 540 = 66H
1,188/66 = H = 18
so yes, it meets the height requirement 17.75 is less than 18
what is mathematics? your answer should be 10 marks
Answers
Answer:
a science of numbers.
Step-by-step explanation:
it helps us solve logical and theoretical problems in hidden and on sight sequence of life.....
You plan to purchase a house for 12.5 million baht, using a 30-year mortgage. You will make a down payment of 15 percent of the purchase price and you will not pay off the mortgage early. Ignore taxes in your analysis. Your bank offers you the following two options for payment.
Option 1: Mortgage rate of 7.25 percent and zero points.
Option 2: Mortgage rate of 6.75 percent and 4 points.
You would choose option ------- (1 or 2) because the Net Present Value of choosing option 2 is------ . (The answer can be negative. Do not round intermediate calculations and round your answer to two decimal places, e.g., 32.16.)
Answers
Option 2 has a lower NPV and thus should be chosen as it results in less total payment and better savings. Hence, you would choose option 2 as the Net Present Value of choosing option 2 is -9,903,615.48.
Given:
Purchase price = 12.5 million baht
Down payment = 15%30-year mortgage
We have to calculate the option which is best for us.
Option 1: Mortgage rate = 7.25%
Option 2:Mortgage rate = 6.75%
(a) Monthly Payment of Option 1:
Loan Amount = 12.5 * (100-15)%
= 10,625,000 baht
n = 30 * 12
= 360
i = 7.25%/12
= 0.006042857
Yearly Interest Paid = i * 10,625,000
= 64,515.48 baht
Monthly Interest Paid = 64,515.48 / 12
= 5,376.29 baht
EMI =\([P x R x (1+R)^n] / [(1+R)^n-1]\)
where P = Loan Amount, R= Interest Rate per month, n= total number of payments.
EMI = \([10,625,000 x 0.006042857 x (1+0.006042857)^360] / [(1+0.006042857)^360-1]\)
EMI = 69,677.31 baht
(b) Monthly Payment of Option 2:
Loan Amount = 12.5 * (100-15)%
= 10,625,000 baht
n = 30 * 12 = 360
i = 6.75%/12 = 0.005625
Yearly Interest Paid = i * 10,625,000
= 59,765.63 baht
Monthly Interest Paid = 59,765.63 / 12
= 4,980.47 baht
Point cost = 4% of Loan Amount
= 10,625,000 x 4/100
= 425,000 baht
Loan Amount after Deducting Points = 10,625,000 - 425,000
= 10,200,000 baht
EMI = \([P x R x (1+R)^n] / [(1+R)^n-1]\)
where P = Loan Amount, R= Interest Rate per month, n= total number of payments.
EMI =\([10,200,000 x 0.005625 x (1+0.005625)^360] / [(1+0.005625)^360-1]\)
EMI = 66,128.92 baht
(c) We have to calculate the NPV of the payments to decide which option is better.
We use the formula to calculate NPV:-
NPV = - \([B + (PMT / i) * (1 - (1 + i)^-n)] / ((1 + i)^t)\)
Where B = amount borrowed, PMT = monthly payment, i = interest rate, n = total number of payments, t = year.
NPV =\(- [10625000 + (69677.31 / 0.006042857) * (1 - (1 + 0.006042857)^-360)] / ((1 + 0.006042857)^30)\)
= -9,892,571.85 baht
NPV = \(- [10200000 + (66128.92 / 0.005625) * (1 - (1 + 0.005625)^-360)] / ((1 + 0.005625)^30)\)
= -9,903,615.48 baht
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A truck manufacturer wishes to test the safety of the six truck models they produce. The manufacturer randomly selects three trucks from each of the six models for safety testing. What type of sampling method is this? a. Simple random sampling b. Multistage sampling c. None of the above d. Convenience sampling e. Stratified random sampling Certainty 3 : C=1 (Unsure: <67% ) C=2 (Mid: >67%) C=3 (Quite sure: >80% )
Answers
The type of sampling method described, where three trucks are randomly selected from each of the six models for safety testing, is: b. Multistage sampling.
Multistage sampling involves a process where a larger population is divided into smaller groups (clusters) and then further sub-sampling is conducted within each cluster. In this scenario, the population consists of the six truck models, and the manufacturer first selects three trucks from each model. This can be considered as a two-stage sampling process: first, selecting the truck models (clusters), and then selecting three trucks from each model.
It is not simple random sampling because the trucks are not selected independently and randomly from the entire population of trucks. It is also not stratified random sampling because the trucks are not divided into distinct strata with proportional representation.
The sampling method used in this scenario is multistage sampling, where three trucks are randomly selected from each of the six truck models for safety testing.
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PLEASE HELP??!!
What is the end behavior of the function f(z)
2c2
1?
O As approaches infinity, f(r) approaches negative infinity. As I approaches
negative infinity, f(x) approaches infinity.
O As I approaches infinity, f(x) approaches infinity. As approaches negative
infinity, f(x) approaches negative infinity.
As I approaches infinity, f(x) approaches negative infinity. As I approaches
negative infinity, f(x) approaches negative infinity.
As I
approaches infinity. f(a) approaches infinity. As 2 approaches negative infinity, f(x) approaches infinity.
Answers
Answer:
d
Step-by-step explanation:
Can someone please teach me!!! :,( !!!!!!!!!!!!!!
and don't do it for the the points or i will have to report even if i do not want to
Graph this line using the slope and y-intercept: y= 1/7x+3
Answers
Which conversions go from a smaller unit to a larger unit? Select all that apply.
centimeters to millimeters
decimeters to meters
hectograms to kilograms
liters to centiliters
Answers
Answer:
decimeters to meters
Step-by-step explanation:
There are 10 decimeters in a meter.
Answer:
decimeters to meters
hectograms to kilograms
Step-by-step explanation:
. If a car can travel 38 miles on 2.4 gallons of gas, how many miles could the car travel on 6 gallons of gas?
I forgot how to do this
so if you could also explain with your answer please
Answers
Answer:
About 95 miles
Step-by-step explanation:
Let's set up a proportion using the following set up:
miles / gallons = miles / gallons
We know the car can travel 38 miles on 2.4 gallons of gas.
38 miles / 2.4 gallons = miles/ gallons
We don't know how far the car can travel on 6 gallons. Therefore, we can say the car travels x miles on 6 gallons of gas.
38 miles / 2.4 gallons = x miles /6 gallons
38/2.4=x/6
We want to find x (miles for 6 gallons). Therefore, we must isolate x.
x is being divided by 6. The inverse of division is multiplication. Multiply both sides by 6.
6*(38/2.4)=(x/6)*6
6*(38/2.4)=x
6*15.8333333=x
94.9999998=x
Let's round to the nearest whole number. The 9 in the tenth place tells us to round up.
95 ≈x
x ≈95 miles
The car can travel about 95 miles on 6 gallons of gas.
the base of a solid circle of radius a and is centered at the origin. each cross section perpendicular to the x-axis is a square. the solid has volume
Answers
The solid described is a cylinder with a circular base of radius "a" centered at the origin. Each cross-section perpendicular to the x-axis is a square. The volume of this solid can be determined.
To find the volume of the solid, we need to consider the properties of the cylinder. The base of the cylinder is a circle with radius "a," and its height extends infinitely along the y-axis. The cross-sections perpendicular to the x-axis are squares.
The volume of a cylinder can be calculated using the formula V = πr²h, where "V" represents the volume, "r" is the radius of the base, and "h" is the height.
In this case, since the base is a circle of radius "a," the volume of each cylinder is V = πa²h. As the height extends infinitely along the y-axis, the volume of the solid will also be infinite.
Therefore, the volume of the described solid is infinite, since each cross-section perpendicular to the x-axis forms a square and the height extends infinitely.
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!!!40 POINTS AND BRAINLIEST!!!ANSWER IT ONLY IF YOU KNOW THE ANSWER, MAKE SURE TO EXPLAIN!!!!
Answers
Write the equation of the line in slope intercept form that passes through the point (4,7) and is parallel to y = -7x + 8.
Answers
Answer:
y= -7x + 35
Step-by-step explanation:
(y - 7) = -7(x - 4)
y-7 = -7x + 28
y = -7x + 35
Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.
Year
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Median Age
25.1
24.6
24.3
24.3
22.8
22.8
23.2
24.7
26.1
26.8
Determine the average rate of change in median age per year from 1930 to 1960.
a.
-0.5 years of age per year
b.
20 years of age per year
c.
-0.05 years of age per year
d.
+0.05 years of age per year
Answers
-0.05 is the average rate of change in median age per year from 1930 to 1960.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, a data set that gives the median age of an American man at the time of his first marriage.
Year Median age
1910 25.1
1920 24.6
1930 24.3
1940 24.3
1950 22.8
1960 22.8
1970 23.2
1980 24.7
1990 26.1
2000 26.8
The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)
The average rate of change from 1930 to 1960 = -0.05
Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.
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I am stuck on the answer for this question
Answers
Answer:
12/13
Step-by-step explanation:
Trigonometric ratio:\(\sf Cos \ x = \dfrac{adjacent \ side \ to \ \angle x}{hypotenuse}\\\\\)
\(\sf = \dfrac{XY}{ZX}\\\\=\dfrac{36}{39}\\\\=\dfrac{36 \div3}{39 \div 3}\\\\=\dfrac{12}{13}\)
your anwer would be 12/13 love
answers and the work for them please
Answers
1) log2(x - 2) , when x = 10
log2 (10 - 2)
= log2 (8)
now we know that,
loga (b) = log b/ log a
so, = log 8/ log 2
= log (2)³/ log 2
we also know, log (a)^b = b log (a)
so,
= 3 log 2/ log 2 = 3
2) 6 r^t + 63 , when r = 4 and t = 2
so putting values,
6(4)² + 63
= 6(16) + 63
= 96 + 63 = 159
3) log25 (x) , when x = 5
log25 (5)
= log 5/ log 25
= log 5 / log (5)²
= log 5/ 2 log 5
= 1/5
Hope it helps...This is probably easy but I zoned out in class so yeah
Answers
Answer:
9+t= 54
Step-by-step explanation:
A triangle has coordinates of A(1, 2), B(4, 6), and C(4, -3).
1. If the triangle is translated 2 units right, what are the new coordinates?
2. If ΔABC is reflected over the x-axis, what are the new coordinates?
Please show all work and not just the answer.
Answers
1 = (3,2) B= (6, 6) C = (6, -3)
Move two to the right since left and right deals with the x axis, add two to the x’s
2 = (1, -2) B = (4, -6) C = (4, 3)
Reflecting across the x axis means the formula is (x, -y) so switch the sign of the y’s
Answer:
1) A (3,2), B (6,6), C (6,-3)
2) A (1,-2), B (4,-6), C (4,3)
Step-by-step explanation:
1) Each of the x-values goes up two.
A (1,2) becomes (3,2)
B (4,6) becomes (6,6)
C (4,-3) becomes (6,-3)
2). I assume they mean the ORIGINAL ABC, not the one you just translated 2 units to the right.
To do this, you just multiply each y-value times negative one.
A (1,2) becomes (1,-2)
B (4,6) becomes (4,-6)
C (4,-3) becomes (4,3)
Consider a $2 principal investment with a 10% annual simple interest rate. Enter the simple interest equation that represents the situation. Let t represent the time in years. A = __
Answers
The simple interest equation that represent the situation is A = t/5
What is simple interest?Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest. For example, when a person takes a loan of 500 dollars, at a rate of 10 per annum for two years, the person's interest for two years will be S.I. on the borrowed money.
Principal(P) borrowed = $2
Rate(R) in percentage = 10
time in years = t
Simple interest(A) = P X R X t / 100
A = 2 X 10 X t/ 100
After reducing 20/100 to the lowest term
A = t/5
In conclusion the simple interest(A) = t/5
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The number of minutes, m, that it takes to
print a batch of newspapers is inversely
proportional to the number of printers used,
n.
The equation of proportionality is m =
100
n
Calculate how long it will take to print a
batch of newspapers if 20 printers are
used.
If your answer is a decimal, give it to 1 d. p.
Answers
It will take 5 minutes to print a batch of newspapers if 20 printers are used.
What is proportionality?
Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.
We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:
m = k/n
where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:
m = 100/n
To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:
m = 100/20 = 5
So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.
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8. Which of the following statements
about the box plot is true?
HHH
0 2 4 6 8 10 12 14 16 18 20
♡ Minimum: 4
B Maximum: 16
© First quartile: 8
0 Third quartile: 16
1
IAS
Answers
Explanation:
Box = 12
A + C = 4 + 8 = 12
B - A = 16 - 4 = 12
D - A = 16 - 4 = 12
(C + D)/2 = (8 + 16)/2 = 24/2 = 12
(B + C)/2 = 24/2 = 12
Silvia has 20 tomato plants and 30 bean plants. She wants to put the plants in rows so that each row has the same number of tomato plants and the same number of bean plants. What is the greatest number of rows Silvia can plant?
Answers
The greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.
As given in the question,
Silvia is going to plant 20 tomato plants and 30 bean plants.
Total tomato plants = 20
Total bean plants = 30
If Silvia would like to plant, the plants in rows where each row has the same number of tomato plants and each row has the same number of bean plants.
Then, the greatest number of rows Silvia can plant is equal to greatest common factor of 20 and 30.
20 = 2×2×5
30 = 2×3×5
Greatest common factor of 20 and 30 = 2×5 = 10
Therefore, the greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.
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Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x^2/3 + y^2/3 = 4, (-3sqrt3, 1)
Answers
The equation of the tangent line to the curve at the point (-3sqrt3, 1) is y = (1/sqrt3)x + 4.
To find the equation of the tangent line to the curve at the given point, we will differentiate the equation implicitly with respect to x.
Differentiating both sides of the equation x^(2/3) + y^(2/3) = 4 with respect to x, we get:
(2/3)x^(-1/3) + (2/3)y^(-1/3) * (dy/dx) = 0
Now we need to find the value of dy/dx at the point (-3sqrt3, 1).
Substituting x = -3sqrt3 and y = 1 into the equation, we have:
(2/3)(-3sqrt3)^(-1/3) + (2/3)(1)^(-1/3) * (dy/dx) = 0
Simplifying, we get:
(2/3)(-1/sqrt(3)) + (2/3) * (dy/dx) = 0
Simplifying further, we have:
-2/(3sqrt3) + (2/3) * (dy/dx) = 0
Now we can solve for (dy/dx):
(dy/dx) = 2/(2sqrt3) = 1/sqrt3
So the slope of the tangent line at the point (-3sqrt3, 1) is 1/sqrt3.
Now we have the slope of the tangent line and the point (-3sqrt3, 1), we can use the point-slope form to find the equation of the tangent line. The equation is given by:
y - y1 = m(x - x1)
Substituting the values, we have:
y - 1 = (1/sqrt3)(x - (-3sqrt3))
Simplifying, we get:
y - 1 = (1/sqrt3)(x + 3sqrt3)
y - 1 = (1/sqrt3)x + 3
Finally, rearranging the equation, we have:
y = (1/sqrt3)x + 4
So the equation of the tangent line to the curve at the point (-3sqrt3, 1) is y = (1/sqrt3)x + 4.
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Zahra is driving on a long road trip. She wrote an equation to represent how many gallons of gas she has left in her tank, g=6.5-0.4hg=6.5−0.4h, where gg represents the number of gallons and hh represents time in hours. What is the meaning of the gg-value when h=1h=1?
Answers
Answer:
The number of gallons in the tank after one hour.
Step-by-step explanation:
g=6.5-0.4(1)=6.1
asmine is filling a small fish tank with water. The fish tank is in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in. What is the volume of this fish tank
Answers
The volume of the fish tank in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in is 90π cubic inches.
Therefore the answer is 90π in³.
Recognize that the fish tank is in the shape of a right circular cylinder.
Remember that the formula for the volume of a cylinder is
V = πr^2h
where r is the radius and h is the height.
Plug in the given values for the radius (r = 3 inches) and the height (h = 10 inches) into the formula.
Perform the calculation:
πr^2h
= π(3^2)(10)
= π×9×10
= 90π cubic inches
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Keyla traveled 2155 kilometers by car to visit some relatives. If 1 km is approximately 0.62 miles, then what is the number of miles Keyla traveled to the nearest unit? 1,336 miles 7,471 miles 2,877 miles 3,470 miles
Answers
Answer:
1336miles.
Step-by-step explanation:
From the question we are told that;
1km represents 0.62miles
1km = 0.62miles
We are to express 2155kilometers in miles.
2155km = x miles
Find x:
Divide both equations;
1/2155 = 0.62/x
Cross multiply;
1 * x = 2155 * 0.62
x = 1,336.1miles
Hence the correct option is 1336miles.
you turn over a card one by one from a deck. what is the expected number of cards that you need to flip before you see the first ace?
Answers
The expected number of cards that you need to flip before you see the first ace is known as the expected value or expected number of trials. To find the expected value, you can use the formula:
E = (probability of success) * (number of trials)
Where E is the expected value, probability of success is the probability of seeing an ace on a single card flip, and number of trials is the number of cards that you need to flip.
Since there are 4 aces in a deck of 52 cards, the probability of success is 4/52 = 1/13. Plugging this into the formula above, we get:
E = (1/13) * (number of trials)
To find the expected number of trials, we can solve for number of trials:
number of trials = E / (1/13) = 13 * E
So the expected number of cards that you need to flip before you see the first ace is 13.
Which table correctly identifies the sample space of spinning the spinner and then selecting a card?
Answers
The table that correctly identifies the sample of spinning the spinner and then selecting a card is Option A.
What is a sample?A sample is a random element that belongs to a population. Another way to state it is that, it is a set of all the outcomes that are possible from a given set of events.
What is the explanation for the above?Table A accurately depicts each potential result. Along the column on the left is where you'll see the card outcomes.
The spinner's output is shown along the top row. The intersection of the left and top results appears in each cell.
For instance, row 1, and column 3 include "red, purple" to show that you received a card with the color "purple" and the color "red" on the spinner.
The labels on each cell in table A are accurate. At least one cell in the other tables (B, C, and D) contains an incorrect label.Table B's middle cell in the top row reads "blue, green" when it should read "blue, purple."Table C's upper left corner reads "green, green" when it should be "green, purple."In the bottom middle cell of Table D, "blue, blue" appears where "blue, green" should. Since there isn't a blue card, it is impossible to say "blue, blue."We can rule out options B through D using the three things outlined above.Learn more about samples at;
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