The cylinder's surface area is S = 452.4 cm²
Given data ,
Let the surface area of the cylinder with one base be S
Now , Surface area of cylinder = 2πr ( r + h )
To find the surface area of a cylinder, we need to calculate the sum of the areas of the curved surface (lateral surface) and the two circular bases.
where r = 8 cm
h = 5 cm
The formula for the lateral surface area of a cylinder is given by:
Lateral Surface Area = 2πrh
where r is the radius of the cylinder and h is the height.
The formula for the area of a circle is given by:
Base Area = πr²
Now , S = πr² + 2πrh
On simplifying , we get
S = π ( 8 )² + 2 ( π ) ( 8 ) ( 5 )
S = 64π + 80π
S = 452.389 cm²
Hence , the surface area is S = 452.4 cm²
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(PEPPER FOOD DELIVERY) PLEASE READ FIRST
I just need to know how to do the math to answer the question. In the picture I am sending, it is not the full chart, but shows all the sections that are in it. I JUST NEED TO KNOW HOW TO DO THE MATH to answer this big question. DO NOT give me an answer because I did not provide all of the data to do the whole math problem since I can only post one photo at a time, just please tell me what I need to do for each part of this big question to properly answer it thats all.
following types of accounts (link):
• Asset Liability Equity • Revenue Expense $ J Calculate the following items using formulas in Excel (link)
• Total assets as of January 31, 2020 (put formula in Cell C84)
• Total liabilities as of January 31, 2020 (put formula in Cell 085) Revenues for the month ending January 31, 2020 (put formula in Cell C89) Expenses for the month ending January 31, 2020 (put formula in Cell C90)
• ● 4 • Net income for the month ending January 31, 2020 (put formula in Cell C91) Equity as of January 31, 2020 (put formula in Cell C86)Hint: Equity will be Common Stock + Retained Earnings + Net income - Dividends
4. Total liabilities and equity as of January 31, 2020 (put formula in Cell C87)Using your Excel worksheet and your answers to Requirement 2, answer the following questions:
a. What would the accounting equation (link) for Pepper Food Delivery be as of January 31, 2020?
b. What accounts would be found on Pepper Food Delivery's balance sheet (link) as of January 31, 2020?
c. What accounts would be found on Pepper's income statement (link) for the month ended January 31, 2020?
d. Did Pepper Food Delivery have a profitable month? How do you know?
e. What is the total amount that Pepper Food Delivery owes as of January 31, 2020?
4. What was Pepper Food Delivery's largest total expense for January?
You'll need to build Excel formulas using =SUM() function on specified cells in order to calculate total assets, total liabilities, revenue, and expenses. To calculate net income, subtract total expense from total revenue. Calculate Equity by summing common stock, retained earnings, and net income, then subtracting dividends. Finally, sum total liabilities and total equity.
Explanation:To answer these questions, you are required to have Excel skills and basic understanding of business accounting principles. Let's break it down per section:
Total assets as of January 31, 2020. You simply need to calculate the sum of all the Asset accounts for that date. You would use the SUM formula in Excel like this: =SUM(range of cells with asset values). Total liabilities as of January 31, 2020. The same as assets, you calculate the sum of all the Liability accounts for that date. The SUM formula is the same as the one used for assets. The Revenues for the month ending January 31, 2020. This is the total sales the business had during January. Again, use the SUM formula to add all the relevant revenue accounts together. Expense for the month ending January 31, 2020. You should add up all expense account figures within that time frame using the SUM formula. Net income for the end of January. This can be derived by subtracting Total Expenses (C90) from Total Revenues (C89). Equity as of January 31, 2020. This is calculated as common stock, plus retained earnings, plus net income, minus dividends. Total liabilities and equity as of January 31, 2020. This is achieved by summing the total liabilities (C85) and total equity (C86).Learn more about Business Accounting here:
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Find the distance around each figure. Use 3.14 as an approximation for π(pie)
30. The figure is made up of a rectangle and two identical semicircles.
Answer:
Step-by-step explanation:
Calculate: (a) the combined total of all items purchased, (b) total tax rate and (c) sales tax for the
items.
11. Andy Owens purchased a bicycle for $259.99 and a helmet for $62.99. The state sales tax rate is
8.25%, the local tax is 2.25%.
Answer:
356.89$
Step-by-step explanation:
259.9 + 62.99 = 322.98, 8.25% + 2.25 = 10.5 tax rate... So 322.98 + 10.5% = 356.89$
Find the x-coordinate of the inflection points for the function
guys pls help
After considering the given data we conclude that the x-coordinate of the inflection points for the function are x = - 2 and x = 2, which is option A.
To evaluate the x-coordinate of the inflection points for the function f(x) = ln(x² + 4) we need to evaluate the second derivative of the function and find for x when the second derivative equals zero.
The first derivative of f(x) is:
f' * (x) = (2x)/(x² + 4)
The second derivative of f(x) is:
f"(x) = 2(x² + 4)-4x² /(x²+4)² = 8 - 2x²/(x²+4)²
To evaluate the inflection points, we need to find the equation f'' (x) = 0 for x:
8 - 2x²/(x²+4)² = 0
After applying simplification this equation, we get:
8 - 2x² = 0
Evaluating for x, we get:
x = +/- √4) = +/- 2
Therefore, the x-coordinate of the inflection points for the function f(x) = ln(x² + 4)
x = - 2 and x = 2 .
The answer is A. x = - 2 and x = 2.
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mang pedro walks off a patch of garden for tomatoes. he walks 14feet north 7 feet west and 15 feet straight back to where he started .what is the area of mang pedro's tomato patch
Answer:
49 [tex]ft^{2}[/tex]
Step-by-step explanation:
a = 1/2 (bh)
a = 1/2(7x14)
a = 49
Helping in the name of Jesus.
Sam theows a ball up into the air and watches it come down. The equation for the height, h, in relation to time,t , is h=5f^2+25t. What is the range for height of the ball
Answer:
h = 5t²+ 25t
from projectiles
h = u²sin²∆ / 2g
taking the angle to be ∆
and range is u²sin2∆/g
Therefore integrate the equation h= 5t²+25t
R = 5t³/3 + 25t²/2 + t
help please which one of this is and what is the x and y
The value x, y and z from the given matrix are -3.65, -4.5 and 2.2 respectively.
From the given matrix,
[tex]\left[\begin{array}{ccc}-2&6&-7\\2&-7&-3\\6&-4&-6\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-47\\22\\-10\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-2x+6y-7z\\2x-7y-z\\6x-4y-6z\end{array}\right] =\left[\begin{array}{ccc}-47\\22\\-10\end{array}\right][/tex]
-2x+6y-7z=-47 -------(i)
2x-7y-z=22 ---------(ii)
6x-4y-6z=-10 ---------(iii)
Add equation (i) and (ii), we get
-2x+6y-7z+2x-7y-z=-47+22
-y-8z=-27 ---------(iv)
Multiply equation (ii) by 3, we get
6x-21y-3z=66 ---------(v)
Subtract equation (iii) from (v), we get
6x-21y-3z-(6x-4y-6z)=66-(-10)
6x-21y-3z-6x+4y+6z=76
-17y+3z=76 ---------(vi)
Multiply equation (iv) by 17, we get
-17y-136z=-216 ---------(vii)
Subtract equation (vi) from (vii), we get
-17y-136z-(-17y+3z)=-216-76
-133z=-292
z=-292/(-133)
z=2.2
Substitute z=2.2 in equation (vii), we get
-17y-136(2.2)=-216
-17y-292.6=-216
-17y=-216+292.6
-17y=76.6
y=-4.5
Substitute y=-4.5 and z=2.2 in equation (ii), we get
2x-7y-z=22
2x-7(-4.5)-2.2=22
2x+31.5-2.2=22
2x+29.3=22
2x=22-29.3
2x=-7.3
x= -7.3/2
x= -3.65
Therefore, the value x, y and z from the given matrix are -3.65, -4.5 and 2.2 respectively.
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Which measurement is equal to 2 1 2 gallons?
The Equivalent measurements of a given quantity can be useful in a variety of situations, such as when you need to convert between different units of volume
2 1/2 gallons is equal to various measurements depending on the context, but here are a few common conversions:
- 10 pints: There are 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 2 x 4 + 2 = 10 pints.
- 20 cups: There are 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 2 x 4 x 2 + 2 = 20 cups.
- 640 fluid ounces: There are 8 fluid ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 4 x 2 x 2 x 8 x 2.5 = 640 fluid ounces.
Knowing the equivalent measurements of a given quantity can be useful in a variety of situations, such as when you need to convert between different units of volume, or when you need to mix ingredients in a recipe.
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A rectangular pyramid has a base that is 14 yards long and 14 yards wide. The pyramid's slant height is 12 yards. What is its surface area?
The surface area of the rectangular pyramid is approximately 387.6 square yards.
To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of the four triangular faces.
The area of the base is:
Area of base = length x width
Area of base = 14 yards x 14 yards
Area of base = 196 square yards
To find the area of the four triangular faces, we need to first find the height of each triangle using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs (the two shorter sides) is equal to the square of the hypotenuse (the longest side).
In this case, the hypotenuse is the slant height of the pyramid, which is 12 yards. The legs are half the length and width of the base, which are both 7 yards.
So we have:
h² + 7² = 12²
h² + 49 = 144
h² = 95
h = √95
Now we can find the area of each triangular face using the formula:
Area of triangle = 1/2 x base x height
The base of each triangle is 14 yards, and the height is √95 yards. So we have:
Area of triangle = 1/2 x 14 yards x √95 yards
Area of triangle = 7√95 square yards
There are four triangular faces, so the total area of the four triangular faces is:
Total area of triangular faces = 4 x 7√95 square yards
Total area of triangular faces = 28√95 square yards
Finally, we can find the total surface area by adding the area of the base and the area of the four triangular faces:
Total surface area = Area of base + Total area of triangular faces
Total surface area = 196 square yards + 28√95 square yards
Total surface area ≈ 387.6 square yards (rounded to one decimal place)
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Qasim spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7200 feet. Qasim initially measures an angle of elevation of 16 ∘ ∘ to the plane at point � A. At some later time, he measures an angle of elevation of 38 ∘ ∘ to the plane at point � B. Find the distance the plane traveled from point � A to point � B. Round your answer to the nearest foot if necessary.
The plane traveled approximately 15,806 feet from point A to point B.
How to solve for the distancetan(angle) = opposite side / adjacent side
Let x be the horizontal distance from Qasim to point A and y be the horizontal distance from Qasim to point B. Then:
tan(16°) = 7200 / x
tan(38°) = 7200 / y
We can solve for x and y:
x = 7200 / tan(16°)
y = 7200 / tan(38°)
Now, we can calculate x and y:
x ≈ 7200 / 0.2878
= 25016.6 feet
y = 7200 / 0.7813
= 9210.7 feet
Finally, to find the distance the plane traveled from point A to point B, we take the difference between y and x:
distance = y - x
= 9210.7 - 25016.6
= -15805.9 feet
we take the absolute value:
distance = 15806 feet (rounded to the nearest foot)
approximately 15,806 feet from point A to point B.
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please help i been stuck on it forever i dont understand it at allll
Franklin got a Dino Delve activity set for his birthday there are eight dinosaur toys hidden in a large sand bin in Franklin must take to find them according to the manufacture each dinosaur toy has a 10% chance of being a T. rex how likely is it that at least one of the dinosaur toys in Franklin set is a T. rex
The chances that, at least, one of the dinosaur toys in Franklin's set is a T.rex is 57%.
Probability calculationWe can use the complement rule to find the probability that none of the dinosaur toys in Franklin's set is a T. rex, and then subtract this from 1 to get the probability that at least one of the toys is a T. rex.
The probability that a given toy is not a T. rex is 90%, or 0.9.
Since there are 8 toys in the set, the probability that none of them are T. rex is:
0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 0.43
So the probability that at least one of the toys is a T. rex is:
1 - 0.43 = 0.57, or 57%
In other words, it is 57% likely that at least one of the dinosaur toys in Franklin's set is a T. rex.
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Brenda sells balloon bouquets. She charges the same price for each balloon in a bouquet. The costs for several bouquets are shown in the table. Write an equation that relates the cost of a bouquet to the number of balloons in the bouquet.
The equation that relates the cost of a bouquet to the number of balloons in the bouquet is: Y = 5.75x
The bouquet with 6 balloons, and the cost per balloon is:
34.50 / 6 = 5.75
We can repeat this process for each bouquet to get:
6 balloons: cost per balloon = 5.75
9 balloons: cost per balloon = 3.83
12 balloons: cost per balloon = 3.04
we can write an equation of the form: Y = kx
where Y is the cost of a bouquet,
x is the number of balloons in the bouquet, and
k is a constant that represents the cost per balloon.
To solve for k, we can use any one of the bouquets to get:
34.50 = k(6)
Solving for k, we get:
k = 5.75
Therefore, the equation that relates the cost of a bouquet to the number of balloons in the bouquet is:
Y = 5.75x
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Complete question:
Brenda sells balloon bouquets. She charges the same price for each
balloon in a bouquet. The costs for several bouquets are shown in the
table. Write an equation that relates the cost of a bouquet to the number
of balloons in the bouquet.
Number of balloons,
(x= # of balloons)
6
9
12
(Y=cost)
3
4.50
6
What is the best name for the figure with the following coordinates?
(4, 1), (1, 1), (3,-2), and (0, -2)
A. rectangle
B. square
C. trapezoid
D. parallelogram
Please select the best answer from the choices provided
OA
OB
Answer: D. Parallelogram
Step-by-step explanation: Step 1. Input all the points on a graph, there's not really much to it, sorry if I didn't help but the answer is D
Find the surface area of
the prism.
The surface area isin.²
8 in.
15 in.
5 in.
Answer: A = 470 in²
Step-by-step explanation:
If the given prism is a rectangular prism, we can use the given formula to solve for the surface area of a rectangular prism.
A = 2((8 in)(15 in) + (5 in)(15 in) + (5 in)(8 in))
A = 2(120 in² + 75 in² + 40 in²)
A = 2(235 in²)
A = 470 in²
A water bottle is 3/4 full. Half of the water is drained. Now, 6 ounces of water remain in the bottle. What is the capacity of the bottle?
The capacity of the bottle is 16 ounces
Calculating the capacity of the bottle?From the question, we have the following parameters that can be used in our computation:
A water bottle is 3/4 full.
When half of the water is drained, we have
Remainder = 1/2 * 3/4x
Evaluate
Remainder = 3/8x
Where x is the capacity of the bottle
We understand that 6 ounces of water remain in the bottle.
This means that
3/8x = 6
So, we have
x = 8 * 6/3
Evaluate
x = 16
Hence. the capacity of the bottle is 16 ounces
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51. Trail running is one of the few outdoor sports that has been consistently increasing over the past few years. The number of people participating in trail running (in millions) from the years 2013 to 2018 is given by the equation y = 0.6x + 5.0, where x is the number of years after 2010.
a. use this equation to complete the ordered pair (7, )
b.write a sentence explaining the meaning of the answer to part a
c. if this trend continues, how many trail runners will there be in 2025? graph it
Give the parametric form of the circle x² + y² = 25
x(t) =
y(t) =
This is an exercise in parametric equations, which are a way of representing a curve or surface on the plane or in space using arbitrary values or a constant called a parameter instead of using an independent variable. In the case of circles, the points (x,y) can be expressed from a single variable θ, which is called a parameter. The parametric equations of a circle with radius r ≥ 0 and center (h,k) are given by x = h + rcosθ y = k + rsinθ, where 0 < θ < 2π. The parametric equation of a circle can be expressed from the angle θ of the point through the circle with respect to the x-coordinate axis. The parametric equations of the conics, including the circumference, can be deparameterized to obtain the canonical equation.
The parametric equation of a circle can be expressed from the angle θ of the point through the circle with respect to the x-coordinate axis. The angle can be expressed in radians (θ∈[0,2π]) or sexagesimal degrees (θ∈[0º,360º]). The parametric equation of a circle with center C=(-1,3) and radius r=2 cm is defined by x = -1 + 2cosθ and y = 3 + 2sinθ.
The parametric equations of a curve are expressed from the variable (or parameter) t, such that x = x(t) and y = y(t). Each value of t determines a point (x,y) in the plane. The parametric equations of a circle with radius r ≥ 0 and center (h,k) are given by x = h + rcosθ y = k + rsinθ, where 0 < θ < 2π. The parametric equation of a circle centered at the origin and with radius r is x² + y² = r².
The parametric equations for a curve are not unique. They represent the same circle with center at (0,0) and radius R. The parametric equations of the conics, including the circumference, can be deparameterized to obtain the canonical equation. To go from the parametric to the Cartesian equations, the parameter t must be eliminated. The parametric equations of a point on a circle of radius r at an angle θ are x = rcos(θ) and y = rsin(θ).
To get this parametric form of x² + y² = 25, we can use the trigonometric identities:cos²(t) + sin²(t) = 1
Multiplying both sides by 25, we get:
25 cos²(t) + 25 sin²(t) = 25
Which is equivalent to:
x² + y² = 25
Therefore, we can write:
x(t) = 5 cos(t), y(t) = 5 sin(t)
The parametric form of the circle x² + y² = 25 is:x(t) = 5 cos(t)y(t) = 5 sin(t)This means that for every value of t in the interval 0≤t≤2π, we can get a point on the circle.
Graphic attachedImmediate help would be much appreciated.
Two parallel lines are cut by a transversal.
If the measure of 4 is 110 degrees, what is the measure of 5?
The measure of 5 is 110°.
Given, Lines n and p are parallel to each other and have transversal t.
To find: The value of angle 5.
Therefore, the sum of these angles will be 180
Angle 4 = angle 5
Now, they are alternate interior angles.
Therefore,
angle 5 = 110
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Suppose y varies inversely with x, and y = 5 when x = 15. What is the value of y when x = 25 ?
The value of y is 3 when x = 25.
When two variables, x, and y, vary inversely, it means that as one variable increases, the other decreases in a proportional manner. In other words, their product is constant.
Mathematically, this relationship can be expressed as:
y = k/x
where k is the constant of proportionality.
To solve the problem, we are given that y = 5 when x = 15, which can be rewritten as:
5 = k/15
To find the value of y when x = 25, we need to first determine the value of k. We can do this by rearranging the equation above to solve for k:
k = 5 x 15 = 75
Now that we know the constant of proportionality, we can use it to find the value of y when x = 25:
y = k/x = 75/25 = 3
Therefore, when x = 25, y = 3. This means that as x increases from 15 to 25, y decreases from 5 to 3, in accordance with the inverse variation relationship between x and y.
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Snow-House sells a $1,248 snow thrower on the installment plan. The installment agreement includes a 20% down payment and 12 monthly payments of $116 each. What is the total cost of the snow thrower on the installment plan?
The total cost of the snow thrower on the installment plan is $1,641.60.
To find the total cost of the snow thrower on the installment plan, we will first calculate the down payment and then add the total monthly payments. Here's the step-by-step explanation:
1. Calculate the down payment:
Down payment = 20% of the original price
Down payment = 0.20 * $1,248
Down payment = $249.60
2. Calculate the total of the 12 monthly payments:
Total monthly payments = 12 * $116
Total monthly payments = $1,392
3. Calculate the total cost on the installment plan:
Total cost = Down payment + Total monthly payments
Total cost = $249.60 + $1,392
Total cost = $1,641.60
So, the total cost of the snow thrower on the installment plan is $1,641.60.
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What influenced Denis to write the first non-objective statement? (You must use one quote from his article the Definition of Neotraditionism)
What factors led Kandinsky to arrive at non-objective painting? (You must give at least one quote from Concerning the Spiritual in Art, and list the page number.
What did Kandinsky write about color? (You must give at least one quote from Concerning the Spiritual in Art - Part II. About Painting, VI: The Language of Form and Color and give the page number.)
Denis was told to write the first non-objective statement by the arising trend of Neotraditionism.
As he explains in his composition" The description of Neotraditionism,"" The thing of Neotraditionism is to make commodity new that isn't a dupe, nor a simple extension, nor a parody of the old"( Denis, 1911). He believed that this movement needed a new language of art, one that wasn't tied to emblematic forms.
Kandinsky's appearance atnon-objective oil was told by his spiritual beliefs and his desire to express the inner nature of effects. As he writes in Concerning the Spiritual in Art," The artist must have commodity to say, for mastery over form isn't his thing but rather the adapting of form to its inner meaning"( Kandinsky, 1977,p. 10). He believed that art should be a spiritual expression and that the inner world of the artist should be restated into visual language.
Kandinsky wrote considerably about color in Concerning the Spiritual in Art. He believed that color had its own language and could convey feelings and ideas. As he writes," Color is a means of plying direct influence upon the soul. Color is the keyboard. The eye is the hammer. The soul is the piano, with its numerous strings"( Kandinsky, 1977,p. 43). He believed that colors could be arranged in a way that would produce a symphony of feelings in the bystander.
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A university class has 27 students: 13 are history majors, 8 are accounting majors, and 6 are art majors. (Each student has only one of these majors.) The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is an accounting major and the second student is an art major?
Answer:
8/27
Step-by-step explanation:
There are a total of 27 students in the class, and 8 of them are accounting majors. Therefore, the probability of the first student selected being an accounting major is 8/27.
After the first student is selected, there will be 26 students remaining, out of which 6 are art majors. Therefore, the probability of the second student selected being an art major, given that the first student was an accounting major, is 6/26.
To find the probability of both events occurring together, we need to multiply the individual probabilities:
P(accounting major first) * P(art major second | accounting major first)
= (8/27) * (6/26)
= 48/702
= 8/117
Can you help me with this question please?
A. The initial size of the culture is 222.11
B. The doubling period is approximately 13.53 minutes.
C. The population after 100 minutes is 5807.76
D . The population will reach 13000 after approximately 44.59 minutes.
How did we get these values?Use the formula for exponential growth:
N = N0 × eʳᵗ
where N is the population size at time t, N0 is the initial population size, r is the growth rate, and t is the time elapsed.
Using the given data:
At t=10, N=500
500 = N0 × eʳ×¹⁰
At t=30, N=1500
1500 = N0 × eʳ׳⁰
To solve for N0 and r, we can divide the second equation by the first:
¹⁵⁰⁰/₅₀₀ = eʳ׳⁰ / eʳ×¹⁰
3 = eʳ× ²⁰
Taking the natural logarithm of both sides:
ln(3) = r × 20
r = ln³/₂₀
r ≈ 0.0513 (rounded to 4 decimal places)
Now we can use N = N0 × eʳᵗ to answer the remaining questions:
- The initial size of the culture is:
N0 = N / eʳᵗ = 500 / ₑ(0.0513×10) ≈ 222.11 (rounded to 2 decimal places)
- The doubling period is the time it takes for the population to double. Find this by setting N = 2N0 and solving for t:
2N0 = N0 × eʳᵗ
2 = eʳᵗ
ln(2) = rt
t = ln²/ᵣ
t ≈ 13.53 (rounded to 2 decimal places)
So the doubling period is approximately 13.53 minutes.
- The population after 100 minutes is:
N = N0 × eʳᵗ = 222.11 × ₑ(0.0513×100) ≈ 5807.76 (rounded to 2 decimal places)
- To find when the population reaches 13000, we can solve N = 13000 for t:
13000 = N0 × eʳᵗ
13000 = 222.11 × ₑ(0.0513t)
58.56 = ₑ(0.0513t)
ln(58.56) = 0.0513t
t ≈ 44.59 (rounded to 2 decimal places)
So the population will reach 13000 after approximately 44.59 minutes.
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ASAP!!!!!!!!!! Euler's formula, V – E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. How many faces does a polyhedron with 5 vertices and 8 edges have?
A. 7
B. 6
C. 4
D. 5
(55 points to who gets it first)
Answer:
5
Step-by-step explanation:
v - e + f =2
5 - 8 + f = 2
f = 2 - 5 + 8
= 5
The hypotenuse of a right triangle is 10 units, and one of the acute angles is 40°. To the nearest tenth, what are the lengths of the legs?
The lengths of the legs are 7.7 units and 6.4 units
How to determine the valueTo determine the lengths of the legs of the triangle, we have that;
We need to know the different trigonometric identities. These identities are expressed as;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
Using the sine identity;
sin θ = opposite/hypotenuse
Substitute the values
sin 40 = x/10
cross multiply the values, we get;
x = 6. 4 units
Using the cosine identity;
cos 40 = y/10
y = 7. 7 units
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The length of the other two legs are 6.4 and 7.6
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Since the hypotenuse is 10, we are going to find the other legs of the right triangle using the trig functions.
sin40 = opp/hyp
0.643 = opp/10
opp = 0.643 × 10
opp = 6.4
Cos 40 = adj/hyp
0.766 = adj/10
adj = 0.766 × 10
adj = 7.6
Therefore the length of other two legs are 6.4 and 7.6
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What is an equation of the line that passes through
the points (4, -3) and (2, 0)?
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{0 +3}{-2} \implies \cfrac{ 3 }{ -2 } \implies - \cfrac{3}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{4}) \implies y +3 = - \cfrac{3}{2} ( x -4) \\\\\\ y+3=- \cfrac{3}{2}x+6\implies {\Large \begin{array}{llll} y=- \cfrac{3}{2}x+3 \end{array}}[/tex]
Answer:
y = -1.5x + 3
Step-by-step explanation:
gradient = (-3 - 0) / (4 - 2) = -3/2 = -1.5.
equation on line through two points is given by
y - y1 = m (x - x1)
where y1 and x1 are the coordinates of the point and m is the gradient.
we can choose either point to use in the equation.
y - 0 = -1.5 (x - 2) = -1.5x + 3
y = -1.5x + 3
How many times does 12 go into 72
Answer:
6 times with a remainder of 0
how do u not know this
skipped basic math have u?
How do I solve this step by step?
9-5(x+4) = 12(x+1)
Answer:
9 - 5 (x + 4) = 12 (x + 1)
-5x - 11 = 12x + 12
-5x - 11 + 11 = 12x + 12 + 11
-5x = 12x + 23
-5x - 12x = 12x + 23 - 12x
x = -23/17
Answer:
x=−23/17
Step-by-step explanation:
Distribute: 9-5(x+4) = 12(x+1)
= 9+−5x+−20=12x+12
Combine like term 9&-220:
−5x+−11=12x+12
Subtract 12x:
−5x−11−12x=12x+12−12x
=−17x−11=12
Add 11:
−17x−11+11=12+11
=−17x=23
Divide by -17:
−17x/-17=23/-17
x=−23/17
.
What are the equivalent fractions for the following number? Show all your work.
The equivalent value of the fraction is A = 533 / 99
Given data ,
To find equivalent fractions for the repeating decimal 5.38383838..., we can use the concept of converting a repeating decimal to a fraction.
Let's denote the repeating decimal as x: x = 5.38383838...
Step 1:
Multiply x by a power of 10 to eliminate the repeating part.
100x = 538.38383838...
Step 2:
Subtract x from the product obtained in Step 1 to eliminate the repeating part.
100x - x = 538.38383838... - 5.38383838...
99x = 533
Step 3:
Solve for x by dividing both sides by 99.
x = 533 / 99
Hence , the fraction is A = 533 / 99
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