Answer:
≈ 3 minutes---------------------
The time is:
time = volume/rateThe rate is given - 2.3 ft³/min.
Find the volume of cylinder:
V = πr²h V = 3.14*(1.6/2)²*4 = 8.0384 ft³Find the required time:
time = 8.0384/2.3 = 3.49495652174 ≈ 3 min (rounded)A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1927 mailboxes this week. If each mailbox has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the value for 3.14 , and round up your answer to the next square meter.
Step-by-step explanation:
first we need to find how many square metres of aluminum we need to make 1 mailbox. to find the surface area of the mailbox we seperate it into the bottom cube and the top cylindir. the bottom cubes surface area is
[tex]0.55 \times 0.3 + 0.3 \times 0.4 \times 2 + 0.55 \times 0.4 \times 2 = 0.165 + 0.24 + 0.44 = {0.845m}^{2} [/tex]
the top half cylindirs surface area is
[tex]( {0.3}^{2} \times 3.14 \div 2 \times 2) + (0.3 \times 3.14 \times 0.55 = {0.2826m}^{2} + {0.5181m}^{2} = {0.8007m}^{2} [/tex]
then add both of them together and its
[tex] {0.8007m}^{2} + {0.845m}^{2} = {1.6457m}^{2} [/tex]
then multiply that by 1927 and its
[tex]1927 \times {1.6457m}^{2} = {3171.2639m}^{2} [/tex]
round that up to 3171m squared.
Answer:
2264 m²
Step-by-step explanation:
To calculate the total amount of aluminium needed to make the mailboxes, multiply the surface area of one mailbox by the total number of mailboxes.
The surface area of one mailbox is made up of the following areas:
Rectangular base with dimensions 0.3 m × 0.55 m.Two smaller rectangular sides with dimensions 0.3 m × 0.4 m.Two larger rectangular sides with dimensions 0.55 m × 0.4 m.Two half circular ends. Two half circles make a whole circle. Therefore, the area of the two half circular ends is the area of a circle with diameter 0.3 m. Since the diameter of a circle is twice its radius, the radius of the circle is 0.15 m.Half the curved area of a cylinder. The formula for the curved area of a cylinder is 2πrh, so the formula for half the curved area is πrh, where the radius is 0.15 m and the height is 0.55 m.Calculate the areas:
[tex]\begin{aligned}\textsf{Area of the rectangular base}&=0.3 \times 0.55\\&= 0.165\; \sf m^2\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Area of the 2 smaller rectangular sides}&=2(0.3 \times 0.4)\\&=2 \times 0.12\\&= 0.24 \; \sf m^2 \end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Area of the 2 larger rectangular sides}&=2(0.55 \times 0.4)\\&=2 \times 0.22\\&= 0.44 \; \sf m^2\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Area of the 2 half circular ends}&=\pi r^2\\& = 3.14 \times 0.15^2\\&=3.14 \times 0.0225\\& = 0.07065 \; \sf m^2\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Area of half the curved area of a cylinder}&=\pi rh\\&= 3.14 \times 0.15 \times 0.55\\&=0.471 \times0.55\\& = 0.25905 \; \sf m^2\end{aligned}[/tex]
Sum the areas to find the total surface area of one aluminium mailbox:
[tex]\begin{aligned}\textsf{Total S.A. of one mailbox}&= 0.165 + 0.24 + 0.44 + 0.07065 + 0.25905\\& = 1.1747 \; \sf m^2\end{aligned}[/tex]
Finally, to calculate the total amount of aluminium needed to make 1927 mailboxes, multiply the surface area of one mailbox by 1927:
[tex]\begin{aligned}\textsf{Aluminium needed to make 1927 mailboxes}&= \textsf{S.A. of one mailbox} \times 1927\\&=1.1747 \times 1927\\&= 2263.6469\\&= 2264 \; \sf m^2\end{aligned}[/tex]
Therefore, 2264 square meters of aluminium will be needed to make 1927 mailboxes (rounded up to the next square meter).
Statistics
TOPIC NAME
Weighted mean: Tabular data
no idea how to solve this i dont understand alek's explanation
Considering the information, the mean number of books read is approximately 3.06 books.
How to find the mean number of books read?We need to calculate the sum of the number of books read by each student and divide it by the total number of students:
Mean = (1 × 5 + 3 × 9 + 4 × 15 + 7 × 4) / (5 + 9 + 15 + 4)= 101 / 33≈ 3.06Therefore, mean, also known as the average, is a measure of central tendency that represents the sum of a set of values divided by the total number of values. In this case, we have a sample of 33 students, and we want to find the mean number of books they read. We can conclude that the mean number of books read is approximately 3.06 books.
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How many pounds of Brussels sprouts should you purchase if you want to serve five trimmed 12. sprouts to each of 200 guests?
You would need to purchase 16.67 to 20 pounds of Brussels sprouts to serve five trimmed 12 sprouts
Calculating the number of sprouts to purchaseIf you want to serve five trimmed 12 sprouts to each of 200 guests, you would need a total of:
5 sprouts/guest x 200 guests = 1000 sprouts
Assuming that the sprouts are sold by weight, it can be difficult to estimate the exact amount to purchase, as the weight of a given number of sprouts can vary depending on their size and density.
However, as a rough estimate, you can assume that 1 pound of Brussels sprouts contains approximately 50-60 sprouts.
Therefore, to serve 1000 sprouts, you would need approximately:
1000 sprouts / 50 sprouts/pound = 20 pounds of Brussels sprouts
or
1000 sprouts / 60 sprouts/pound = 16.67 pounds of Brussels sprouts
So, you would need to purchase approximately 16.67 to 20 pounds of Brussels sprouts to serve five trimmed 12 sprouts to each of 200 guests, depending on the size and density of the sprouts.
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Graph the image of △KLM after a dilation with a scale factor of 3, centered at the origin.
Therefore, The dilated triangle △K'L'M' is similar to the original triangle △KLM, but it is three times larger and centered at the origin.
How to graph the image?To graph the image of △KLM after a dilation with a scale factor of 3 centered at the origin, we can simply multiply the coordinates of each vertex by 3.
Assuming that the coordinates of the original triangle △KLM are [tex]K(1,1), L(3,2),[/tex] and [tex]M(2,4),[/tex] the coordinates of the dilated triangle △K'L'M' are:
[tex]K' = (3(1), 3(1)) = (3, 3)[/tex]
[tex]L' = (3(3), 3(2)) = (9, 6)[/tex]
[tex]M' = (3(2), 3(4)) = (6, 12)[/tex]
We can plot these new vertices on a coordinate plane to get the graph of the dilated triangle △K'L'M'.
Therefore, The dilated triangle △K'L'M' is similar to the original triangle △KLM, but it is three times larger and centered at the origin.
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Complete the statement with the correct term.
Among the roles in the digital media production team, the is in charge of overseeing the creative element.
Answer:
Step-by-step explanation:
Among the roles in the digital media production team, the creative director is in charge of overseeing the creative element.
A store sells two types of cleaning solutions. Brand X has 4 mL of white vinegar for
every 20 mL of water. Brand Y has 5 mL of white vinegar for every 30 mL of water
Which mixture has a higher concentration of vinegar?
Answer:
Brand X
Step-by-step explanation:
Brand X has 4mL of vinegar for every 20mL of water:
We can put this as 4/20=1/5=20%
Brand Y has 5mL of vinegar for every 30mL of water
We can put this as 5/30=1/6=16.6%
X 20. Yesterday, Tenser Inc. executed a 2-for-1 split. Kaylee was holding 500 shares of the stock before the split and each was
worth $34.12. How many shares did she hold after the split? What was the post-split price per share?
Points
0
/1
Answer:
Step-by-step explanation:
Kaylee held 1000 shares after the split. The post-split price per share was $17.06.
Explanation:
Before the split, Kaylee held 500 shares of the stock, and each share was worth $34.12. So, her total investment was 500 x $34.12 = $17,060.
After the 2-for-1 split, each share is split into 2 shares. So, the total number of shares she holds becomes 500 x 2 = 1000.
To find the post-split price per share, we divide the pre-split price by 2.
Post-split price per share = $34.12 / 2 = $17.06.
Find the equations of the lines that pass through the following pairs of points: (3,-5) and (2, -1)
An equation of the lines that pass through this pair of points (3,-5) and (2, -1) is equal to y = -4x + 7.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-1 + 5)/(2 - 3)
Slope (m) = 4/-1
Slope (m) = -4.
At data point (2, -1) and a slope of -4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-1) = -4(x - 2)
y + 1 = -4x + 8
y = -4x + 7
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What is it about how this pattern is formed that makes it always true??
The pattern that is formed that makes it always true is that the patterns were formed from triangles that are upside down as well as the use of Sierpiński triangle and lastly, with the use of black and white fillings.
What is the pattern about?The pattern of the Sierpiński triangle is one that comes up as a result of repeatedly removing certain triangles from an original equilateral triangle.
The Sierpiński triangle is known to be a kind of self-similar fractal equilateral triangle that is known to be made up of smaller equilateral triangles.
Note that It is a basic example of a mathematically generated pattern that can be reproduced at any magnification. It was named after Polish mathematician Wacław Sierpiński, but pre-dates his work as a decorative pattern.
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PLEASEEE HELPPPpppp
Step-by-step explanation:
[tex]( {2x}^{3} - {6x}^{2} + x - 8) - ( {2x}^{3} + 6x - 4) = - 12x - 4[/tex]
so the second polynomial is -12x-4
help with math quick pls
Answer:
the answer is
[tex] {13.5cm}^{2} [/tex]
5
Select the correct answer.
If the domain of the function, f, is restricted to x ≥ 0, which function is the inverse of f?
f(x) = 92² - 12, x ≥ 0
O A. g(x) = √√²+12
9
O B. h(r)
=
O c.
O D. g(x)
p(x) =
=
- 12
2-
3
√z-12
9
√z+12
3
The inverse of the function f(x) = 9x^2 - 12, x≥0 is q(x) = (√[x + 12])/3
Calculating the inverse of the functionFrom the question, we have the following function that can be used in our computation:
f(x) = 9x^2 - 12, x≥0
Replace f(x) with y
So, we have
y = 9x^2 - 12
Swap x and y
x = 9y^2 - 12
So, we have
9y^2 = x + 12
Divide by 9
y^2 = (x + 12)/9
Take the square roots of both sides
y = (√[x + 12])/3
Hence, the inverse function is
q(x) = (√[x + 12])/3
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Complete question
if the domain of the function,f, is restricted to x≥0, which function is the inverse of f? the function is f(x) = 9x^2 - 12, x≥0. A. p(x)=√z-12/9 B. q(x)=√x+12/9. C. h(x)=√x-12/3. D. g(x)=√x+12/3
Express each set using the roster method
A. The set of natural odd numbers greater than 2, but less than 11
B. {x|x€N and 4
The elements using rooster-method:
A){3,4,5,6,7,8,9,10}
B){5,6,7,8,9,10,11,12,13,14}
What is rooster-method?
By listing the items of a set inside brackets, the roster method may be used to display the elements of a set. One of three ways to describe a set is in rooster form. The items of a set are listed in the roster form between curly or following brackets, with commas separating each element. When items repeat in the set, the roster approach actually has an issue. Because the elements do not follow a pattern or have a specific order, it is impossible to describe the elements in roster notation if the set has a significant number of elements or any repeated elements.
A)Set of natural odd numbers greater than 2 but less than 11:
Let us represent the set using symbol O:
O = {3,4,5,6,7,8,9,10}
B){x| x∈ N and 4<x<15}
Given that x is a natural number greater than 4 but less than 15.
X={5,6,7,8,9,10,11,12,13,14}
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A pre-image has coordinates B(8, 4), U(6, 10) and N(5, −2). The image has coordinates B’(2, 1),
U’(1.5, 2.5) and N’(1.25, −0.5). Write the transformation rule used to create this image.
The transformation rule used to create this image is (x, y) → (1/4x + 1, 3/8y + k)
What is transformation?A transformation in geometry is the process of altering a geometric shape or object's position, orientation, or size.
This transformation involves moving a shape from one place to another without altering its size, shape, or orientation. To put it another way, the entire shape is moved a specific amount in one direction
Here we have
A pre-image has coordinates B(8, 4), U(6, 10) and N(5, −2). The image has coordinates B’(2, 1), U’(1.5, 2.5) and N’(1.25, −0.5).
To find the transformation rule, identify the type of transformation that maps the pre-image coordinates to the image coordinates.
One way to do this is to find the changes in the x-coordinates and y-coordinates between the pre-image and image points.
Let's start with point B.
The x-coordinate has decreased from 8 to 2, and the y-coordinate has decreased from 4 to 1.5.
This implies that there has been horizontal compression and vertical compression.
Here the x-coordinate has been compressed by a factor of 2/8 = 1/4, and the y-coordinate has been compressed by a factor of 1.5/4 = 3/8.
So, the transformation rule for point B is:
=> B(x, y) → B'(1/4x, 3/8y)
Using the same method for points U and N, we can find the transformation rules for those points:
U(x, y) → U'(1/4x, 3/8y + 7/8)
N(x, y) → N'(1/4x + 1, 3/8y - 1/4)
So, the overall transformation rule is:
(x, y) → (1/4x + 1, 3/8y + k)
where k is a constant that depends on the particular point being transformed.
Therefore,
The transformation rule used to create this image is
(x, y) → (1/4x + 1, 3/8y + k)
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We have 2 squares. One square is shaded 2/12 and the other shaded square in the diagram is 2/15 shaded. How much of the total diagram is shaded?
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
A rectangular prism has a length of 3 1/2 feet, a width of 5 1/3 feet, and a height of 12 feet. What is the volume of the prism?
Answer:
The answer is 1054ft³
Step-by-step explanation:
Volume of rectangular prism =1/3LWH
V=1/3×31/2×51/3×12
V=1054ft³
I need help please…………………
Answer:
≈ 63,4°
Step-by-step explanation:
Given:
A right triangle
AB = 2
BC = 1
Find: ∠C - ?
Use trigonometry:
[tex] \tan(∠c) = \frac{ab}{bc} [/tex]
[tex] \tan(∠c) = \frac{2}{1} = 2[/tex]
[tex] {tan}^{ - 1} (2) ≈63.4°[/tex]
if a population of a city decreased by 28% since it was last measured. if the current population is 30,600 what was the previous population
The calculated previous population of the city was 42,500.
Calculating the previous populationLet's denote the previous population as "x".
According to the problem, the current population is 28% less than the previous population, which can be represented as:
x - 0.28x = 30,600
Simplifying and solving for x, we have:
0.72x = 30,600
Divide by 0.72
x = 30,600 / 0.72
x = 42,500
Therefore, the previous population was 42,500.
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Expanding (3x - 2y)* yields:
A. x*-4x3y + 6x7y7 - 4xy3 + jt
B. x*+4x3 - 6x3y2 + 4xy3 - y*
C. 81x* - 216x3 + 216x2y2 - 96xy3 + 16y*
D. 81x* + 216x3y - 216x2y2 + 96xy3 - 16y4
The answer of the given question based on the Expression is , the answer is C. 81x* - 216x3 + 216x2y2 - 96xy3 + 16y*.
What is Expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations that represents a value or a mathematical relationship. Expressions can be as simple as a single number or variable, or as complex as a combination of several variables and operations.
To expand the expression (3x - 2y), we need to distribute the terms in the parentheses to get:
(3x - 2y) = 3x - 2y
Now, to expand the expression (3x - 2y)*, we need to multiply the expression (3x - 2y) by its conjugate, which is (3x + 2y):
(3x - 2y)*(3x + 2y) = 9x² - 6xy + 6xy - 4y²
Simplifying this expression, we get:
(3x - 2y)*(3x + 2y) = 9x² - 4y²
Therefore, the answer is C. 81x* - 216x3 + 216x2y2 - 96xy3 + 16y*.
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The expression used to determine the answer to the question is
[tex]81x^*-216x^3+216x^2y^2-96xy^3+16y^*[/tex]. option (c) is correct.
What is Expression?An expression in mathematics is a group of digits, variables, and mathematical operations that denotes a number or a mathematical relationship.
Expressions can range in complexity from being as simple as a single variable or number to being a complicated combination of numerous variables and actions.
By distributing the terms in the brackets, we can broaden the expression (3x - 2y) to obtain:
(3x - 2y) = 3x - 2y
We must now multiply the expression (3x - 2y)* in order to extend it
(3x - 2y) by its conjugate, which is (3x + 2y):
(3x - 2y)*(3x + 2y) = 9x² - 6xy + 6xy - 4y²
If we condense this phrase, we get:
(3x - 2y)*(3x + 2y) = 9x² - 4y²
Therefore, the answer is C. [tex]81x^*-216x^3+216x^2y^2-96xy^3+16y^*[/tex].
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Is 2 a solution of 3-p=1
Each of 184 guests at a Sunday brunch will be served ½ pound of peeled, diced cantaloupe. The average cantaloupe weighs 2 pounds. If cantaloupes come 12 to a case, how many cases of canta- loupe should you purchase? (For this question, round your answer up to a whole number.)
we must round up to a whole number, we need to purchase 4 cases of cantaloupe.
How to solve?
First, we need to calculate how many pounds of cantaloupe are needed in total:
184 guests ×0.5 pounds per guest = 92 pounds of cantaloupe
Next, we need to determine how many cantaloupes are needed. Since the average cantaloupe weighs 2 pounds, we can divide the total pounds of cantaloupe needed by the weight of one cantaloupe:
92 pounds of cantaloupe / 2 pounds per cantaloupe = 46 cantaloupes
Finally, we need to figure out how many cases of cantaloupe to purchase, given that they come 12 to a case:
46 cantaloupes / 12 cantaloupes per case = 3.83 cases
Since we must round up to a whole number, we need to purchase 4 cases of cantaloupe.
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Bear mountain summer camp opened last year and had 650 campers. after doing some advertising in the off season, the camp has enrolled 676 campers for this year, and enrollment is expected to continue increasing each year.
write an exponential equation in the form y = a(b) expounded x
There are campers y = 650(676/650)^x.
What is an exponential equation?The number of campers, y, x years after the camp opens, can be modeled using an exponential equation with the form y = a(b)x. Let's use x = 0 for the first year the camp was open (last year), and x = 1 for this year.
Then, we have:
y = a(b)^0 = 650 (when x = 0)
y = a(b)^1 = 676 (when x = 1)
These two points can be used to find the values of a and b.
We will first use the first equation to find a:
a = 650
Next, we'll use the second equation to solve for b:
676 = 650(b)^1
676/650 = (b)^1
b = 676/650
To describe the number of campers, an exponential equation of the type y = a(b)^x is needed.
y = 650(676/650)^x
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During a single day at the radio station WMZH, the probability that a particular song is played is 1/6. What is the probability that this song will be played on exactly 6 days out of 7 days? Round your answer to the nearest thousandth.
Around 0.000125 or 0.0125% of the time, the song will be played exactly six out of seven days.
Every day represents a trial in this binomial probability issue, and there are only two potential results:
either the music is played (a success), or it is not (failure). We're looking for the likelihood that exactly 6 out of 7 trials will be successful.
The likelihood of success (performing the song) is 1/6, while the likelihood of failure (not playing the song) is 1 - 1/6 = 5/6, on any given day.
We can use the binomial probability formula to find the probability of exactly 6 successes in 7 trials:
P(6 successes) = (7 choose 6) * (1/6)⁶ * (5/6)¹
where (7 choose 6) is the number of ways to choose 6 days out of 7 to play the song, and is calculated as:
(7 choose 6) = 7! / (6! * 1!) = 7
Plugging in the values, we get:
P(6 successes) = 7 * (1/6)⁶ * (5/6)¹
P(6 successes) ≈0.00012502
Therefore, the probability that the song will be played on exactly 6 days out of 7 is approximately 0.000125 or 0.0125%.
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6. In the figure at the right, what is m/1
if m/3 = 70°?
F. 180°
G. 110°
H. 90
I.
70°
3 2
4 1
6.
WILL GIVE BRAINLIEST
HURRY NEED ASAP
Angle 1 and angle 3 are vertically opposite angles.
We know that :
▪︎ Vertically opposite angles are always equal.
Which means :
Angle 1 = Angle 3
Thus, the measure of angle 3 = 70°
▪︎Therefore, the correct option is (I) 70
Expenditure (E)
30
20
MACRO-ECONOMIC MULTIPLIER
40
60
E=Y
E¹=30+0.5Y
Eo=20+0.5Y
Income (Y)
Calculate the multiplier for the above
Note that the multiplier in this scenario is 2.
What is the explanation for the above response?
To calculate the multiplier in this scenario, we need to use the formula:
Multiplier = ΔY / ΔE
where ΔY is the change in income and ΔE is the change in expenditure.
Here, we have two expenditure functions:
E¹ = 30 + 0.5Y
Eo = 20 + 0.5Y
To calculate the multiplier, we need to find the change in expenditure for a given change in income.
Let's assume that income increases by $1. In that case:
With E¹ function, expenditure increases by:
E¹(Y+1) - E¹(Y) = (30 + 0.5(Y+1)) - (30 + 0.5Y) = 0.5
With Eo function, expenditure increases by:
Eo(Y+1) - Eo(Y) = (20 + 0.5(Y+1)) - (20 + 0.5Y) = 0.5
Therefore, for a $1 increase in income, expenditure increases by $0.5 in both cases.
Now, we can calculate the multiplier:
Multiplier = ΔY / ΔE = 1 / 0.5 = 2
Therefore, the multiplier in this scenario is 2.
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Greg and Meg decide to set up a lemonade stand to raise money for their trip to Disneyland. The notice that when the temperature is higher 90 degree than
F, they sell 175
lemonades a day, and when the temperature is lower than
F, they sell
lemonades a day.
There is a
chance the temperature this week will be over
F. What is the expected number of lemonades Greg and Meg will sell in a day?
lemonades
Therefore, we can expect Greg and Meg to sell about 122 lemonades in a day, given that there is a chance the temperature will be over 90 degrees Fahrenheit. However, this is just an estimate.
To determine the expected number of lemonades Greg and Meg will sell in a day, we need to use the concept of conditional probability.
Let A be the event that the temperature is over 90 degrees Fahrenheit, and let B be the event that Greg and Meg sell lemonades in a day. We want to find P(B), the probability that they sell lemonades in a day, given that there is a chance the temperature will be over 90 degrees Fahrenheit.
We can use Bayes' theorem to express P(B) in terms of P(A) and P(B|A), the probability that they sell lemonades in a day given that the temperature is over 90 degrees Fahrenheit:
P(B) = P(A) * P(B|A) + P(not A) * P(B|not A)
where P(not A) is the probability that the temperature is not over 90 degrees Fahrenheit.
From the problem statement, we know that P(A) = the chance the temperature this week will be over 90 degrees Fahrenheit, and P(B|A) = 175, the number of lemonades they sell when the temperature is over 90 degrees Fahrenheit.
We don't have information about P(B|not A), the number of lemonades they sell when the temperature is not over 90 degrees Fahrenheit. But we can assume that it is some number less than 175, since the hotter weather tends to increase the demand for lemonade.
Assuming that P(B|not A) = 100, we can estimate P(not A) as follows:
[tex]P(not A) = 1 - P(A)[/tex]
Let's say that the chance of the temperature being over 90 degrees Fahrenheit this week is 0.3 (or 30%). Then:
[tex]P(A) = 0.3[/tex]
[tex]P(not A) = 0.7[/tex]
[tex]P(B|A) = 175[/tex]
[tex]P(B|not A) = 100 (assumption)[/tex]
Using these values in Bayes' theorem, we get:
[tex]P(B) = 0.3 * 175 + 0.7 * 100[/tex]
[tex]= 122.5[/tex]
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Submit a full solution (your final answer AND your work) to the problem below.
Suppose you take out a $10,000 student loan at 8% interest per year, compounding annually. After 4 years, what will be the total balance of this loan? (Hint: It'll be bigger than $10k...)
Step-by-step explanation:
after the first year its 10000÷100*8+10000=10800. after the second year its 10800÷100*8+10800=11664. after the third year its 11664÷100*8+11664=12597.12. and after the fourth year its 12597.12÷100*8+12597.12=13,604.8896$. If you want you can round it up to 13,605$
Help pls the question is the picture. 40 points
Answer:
Weight
Ant Team
Gorilla Team
Item
(in kilograms)
Empire State Building
no
no
Mount Everest
no
yes
Mount McKinley
no
no
Washington Monument
yes
yes
i-Ready
Linear Functions: Model from a Verbal Description - Instruction - Level H
A bike rental costs $2.50 per hour plus a fee for renting a helmet, which is required. The total cost
of renting a bike for 2 hours (h) is $13.
→ Write an equation for the total cost of renting
a bike, y, as a function of the hours, x.
y = ? x+ ?
Bike Rentals
$2.50 per hour
(additional fee for helmet rental)
Comparing with y = ? x+ ? this equation we get the first value is 2.50 and the second value is 8
What is equation?
An equation is a mathematical statement which is built by two expressions connected by an equal ('=') sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.
A bike rental costs $2.50 per hour plus a fee for renting a helmet, which is required. The total cost
of renting a bike for 2 hours (h) is $13.
If it rented for 2 hours then rental costs will be $(2×2.50)= $5
Let the number of hours be x
Then the equation will be
y= 2.50x+8 --------(1)
As the total cost is $13
c= 8 [as 13- 5 =8]
Hence, comparing with y = ? x+ ? we get the first value is 2.50 and the second value is 8.
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write the equation of the parabola in standard form.
8. y=3(x-1)² +2
9. y=-4(x+6)²-4
10. x=2(y+3)²-5
8. y=3(x-1)² +2 can be written in standard form as y = 3x² - 6x + 5. 9. y=-4(x+6)²-4 can be written in standard form as y = -4x² - 48x - 148. 10. x=2(y+3)²-5 can be written in standard form as 2(y+3)² = x + 5.
Describe parabola?A parabola is a two-dimensional geometric shape that is symmetrical around a vertical or horizontal axis. It is a type of conic section, which is formed by the intersection of a plane and a right circular cone. When the plane intersects the cone at an angle that is parallel to one of the sides, a parabola is formed.
A parabola is defined by a quadratic equation of the form y = ax² + bx + c, where "a" is a non-zero constant that determines the shape of the curve, "b" is the linear coefficient, and "c" is the constant term. The vertex of the parabola is located at the point (-b/2a, c - b²/4a), and the axis of symmetry is a vertical or horizontal line that passes through the vertex.
The shape of a parabola depends on the value of "a." If "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards. The vertex of the parabola is the maximum or minimum point of the curve, depending on the direction of the opening. Parabolas are commonly used in physics and engineering to model the trajectory of projectiles, as well as in optics to describe the shape of mirrors and lenses.
8. y=3(x-1)² +2 can be written in standard form as y = 3x² - 6x + 5.
9. y=-4(x+6)²-4 can be written in standard form as y = -4x² - 48x - 148.
10. x=2(y+3)²-5 can be written in standard form as 2(y+3)² = x + 5, which simplifies to (y+3)² = (1/2)(x+5).
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