Rounding to the nearest hundredth, the surface area is approximately 1884.96 cm².
What is the surface area of a cylinder?
The surface area of a cylinder can be calculated using the formula:
SA = 2πr² + 2πrh
where r is the radius of the base and h is the height of the cylinder.
To find the surface area of a cylinder, we need to find the area of the circular bases and the lateral area.
The area of one circular base is:
A = πr²
Since the base diameter is 20 cm, the radius is 10 cm:
A = π(10)² = 100π
The area of the two circular bases is 2A, or:
2A = 2(100π) = 200π
The lateral area is the area of the cylinder's curved surface. It can be found by multiplying the height of the cylinder by the circumference of the base:
L = 2πrh
where r is the radius of the base and h is the height of the cylinder. Substituting the given values:
L = 2π(10)(20) = 400π
So, the total surface area of the cylinder is:
A = 200π + 400π = 600π ≈ 1884.96 cm²
Hence, Rounding to the nearest hundredth, the surface area is approximately 1884.96 cm².
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Please help I’ll give you brainliest uwu
Tom and Ana are both
botanists studying
flower pollination. In Tom's garden, the
ratio of roses to tulips is 3 : 1. In Ana's
garden, the ratio of roses to tulips is 5 : 2.
0 Part A: Tom's garden and Ana's garden
each have 30 tulips. H&w many more
roses are in Tom's garden than in Ana's
garden? Explain your reasoning.
Part B: Tom and Ana combined their
flowers into a single garden. What is the
ratio of roses to tulips in the combined
garden?
Answer:
A: tom has 15 more roses than ana does.
B: 11:4
Step-by-step explanation:
A: there is a 3:1 and 5:2 ratio of roses to tulips. that means that in tom's, there are 3 roses for every tulip and 5 roses for every 2 tulips in ana's.
we know that they each have 30 tulips so now for Tom.
3:1 so to find roses, we need to multiply the value of tulips to 3.
3×30=90 so we know he has a total of 90 roses.
for ana: she also has 30 tulips. BUT now her ratio is 5:2. so for every 2 tulips she has 5 roses. we need to divide the value of tulips by 2 so 30/2=15 and multiply it by 5, 15*5=75
THAT IS NOT THE ANSWER!! to find the rest of the answer, we have to subtract tom's amount by ana's amount: 90-75=15
B: to find this answer, we have to add all of the roses together and all of the tulips together. roses: 90+75=165. tulips: 30+30=60.
the ratio we get is 165:60. and now we need to simplify it.
What is the probability of
spinning a C?
В В
A В
[?]%
СА
СС
Three numbers are in the ratio 3:4:5. If the sum of their cubes is 216000, find the largest of these three numbers.
Answer:
50
Step-by-step explanation:
Let the numbers be 3x, 4x, 5x
(3x)^3 + (4x)^3 + (5x)^3 = 216000
27x^3 + 64x^3 + 125x^3 = 216000
216x^3 = 216000
x^3 = 1000
x = 10
5x = 5(10) = 50
Answer: 50
can someone help me out to solve this problem I would really appreciate it
Answer:
34,400 = m
Step-by-step explanation:
25,000 = 0.5m + 7,800
-7,800 -7,800 subtract 7,800 from both sides
17,200 = 0.5m
-------- ---------
0.5 0.5 divide both sides by 0.5
And you should be left with 34,400 = m
Find a positive number such that the sum of and is as small as possible. does this problem require optimization over an open interval or a closed interval? a. closed b. open
To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible.
To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible. So, we need to minimize the sum of and . Now, let's use calculus to find the minimum value of the sum.To find the minimum value, we have to find the derivative of the sum of and , i.e. f(x) with respect to x, which is given by f '(x) as shown below:
f '(x) = 1/x^2 - 1/(1-x)^2
We can see that this function is defined on the closed interval [0, 1]. The reason why we are using the closed interval is that x is a positive number, and both endpoints are included to ensure that we cover all positive numbers. Therefore, the problem requires optimization over a closed interval. This means that the minimum value exists and is achieved either at one of the endpoints of the interval or at a critical point in the interior of the interval.
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Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours. Find the range of values of y
Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours.Range of the values of Y is =24/7
Let's call the total time spent riding and walking t hours. We know that t is less than 4 hours, so:
t = time spent riding + time spent walking < 4 hours
The time spent riding is given by y / 10 km/hr and the time spent walking is given by 0.5y / 3 km/hr. So, we can write the inequality as:
t = y / 10 + 0.5y / 3 < 4
Expanding and simplifying the expression on the left side gives:
7/6y < 4 * 6/7
Multiplying both sides by 6/7 gives:
y < 4 * 6/7 * 6/7 = 24/7
So, the range of values of y is 0 < y < 24/7 km. This means that Ndidi rode less than 24/7 km, but more than 0 km.
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Shane got an oil change for his car for $35 and sent his receipt, along with a
completed form, to the manufacturer of the oil. He later received a check for
$10 from the manufacturer in the mail. Which type of discount is this?
A. A gift card
B. A sale
C. A rebate
D. A coupon
Answer:
C, rebate
Step-by-step explanation:
Hope this helps!
Answer:
a rebate
Step-by-step explanation:
he bought a product that had a rebate.
Fill out a form, send in receipt from purchase with form and sometimes the bar code from package. In about 4 to 6 weeks you receive rebate.
1
o
2
3
4
5
6
7
8
9
10
Which of the following could be the number shown on the number line?
A. 172
B. V 79
C.
82
D. 63
Answer:
A
Step-by-step explanation:
8.5 x 8.5= 72.25
so basically it's the closest answer
match the function f with the correct gradient vector field plot. f(x, y) = 2x2 2y2
A gradient vector field represents the direction and magnitude of the gradient of a function at each point in the plane. The function f(x, y) = 2x^2 + 2y^2 corresponds to the gradient vector field plot labeled with the equation "f(x, y) = 2x^2 + 2y^2."
A gradient vector field represents the direction and magnitude of the gradient of a function at each point in the plane. The gradient vector field can be visualized by plotting vectors at different points, with the vectors pointing in the direction of the steepest ascent of the function.
In this case, the function f(x, y) = 2x^2 + 2y^2 represents a quadratic function with the coefficients 2 for both x^2 and y^2 terms. The gradient vector field plot that corresponds to this function would show vectors pointing away from the origin (0, 0) in all directions, indicating the direction of steepest ascent.
By matching the function f(x, y) = 2x^2 + 2y^2 with the gradient vector field plot labeled with the equation "f(x, y) = 2x^2 + 2y^2," we can visually observe the direction and magnitude of the gradient vectors associated with the function at each point in the plane.
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Which fraction have a leat common denominator of 36?
A ) 3/4 and 5 18 B ) 5/6 and 7/9 C ) 7/8 and 1/12
3/4 and 5 18 is fraction have a leat common denominator of 36.
How do you determine a fraction's least common denominator?There are several possible pairs of two whole numbers whose Least Common Denominator is 36: 36 and 36 comes first, followed by 1 and 36, 2 and 36, 3 and 36, 4 and 18 and 9, 6 and 36, 9 and 12, 12 and 36, 18 and 36, and finally 4 and 9 and 36.I would choose 4/5 and 9/13 if you want fractions in their simplest form, with several denominators, and an LCD of 36.These, in my opinion, work because 5, 13, and 36 are all pairwise relatively prime (meaning that the product of any two of them is the LCD of the other), and because the LCD of 4 and 9 is pairwise relatively prime.3/4 and 5 18 is fraction have a leat common denominator of 36.
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You have a peice of wood that measure's 112 inches you want to cut it up into 4 equal peices so that each peice is 25% of the length what will the length of each peice be
The length of each piece of wood will be 28 inches if divided into 25%.
To divide the wood into 4 equal pieces, we will divide the total quantity by 4. Thus, the fraction that we will get is 1/4th of total. Now, as per the known fact, 1/4 is 25%, which will be our required answer based on the criteria mentioned in question.
Length of wood after division = 112/4
Performing division on Right Hand Side of the equation
Length of wood after division = 28 inches
Hence, the four parts will be of 28 inches.
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3x^2 - 11x + 6
Factor using any method. Show your work in the box. Explain how you accounted for the non-zero leading coefficient (the 3 in front) when factoring.
The Factored form of 3x^2 - 11x + 6 is (x - 3)(3x - 2).
The quadratic expression 3x^2 - 11x + 6, we can use the method of factoring by grouping. Here's the step-by-step process:
Step 1: Multiply the coefficient of x^2 (3) by the constant term (6) in the expression.
3 * 6 = 18.
Step 2: Find two numbers that multiply to give 18 and add up to the coefficient of x (-11).
The numbers -2 and -9 fit this criteria because -2 * -9 = 18 and -2 + (-9) = -11.
Step 3: Split the middle term (-11x) into two terms using the numbers found in step 2.
3x^2 - 2x - 9x + 6.
Step 4: Group the terms and factor out the greatest common factor (GCF) from each group.
(3x^2 - 2x) - (9x - 6).
x(3x - 2) - 3(3x - 2).
Step 5: Notice that the terms (3x - 2) are common in both groups. Factor it out.
(x - 3)(3x - 2).
So, the factored form of 3x^2 - 11x + 6 is (x - 3)(3x - 2).
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What is the value of this product
Answer:
The value of the product is 2²
Which event is important enough to include in a summary of this
story? Add the event to the chart.
D Event
Event
Event
Hester gives Ms.
Walker the letter
explaining her idea.
Ms. Walker agrees
to consider
Hester's idea.
?
Hester repeats a
*) phrase in her mind
over and over.
D
Hester packs up
her things when
the bell rings.
D
Hester returns to
her desk to read
her book.
Hester learns
about another way
to boost her grade.
When making a summary, it is important to read and understand the text which you are writing.
What is a Summary?This refers to the concise representation of the main points of a literary text without the use of bias.
Hence,w we can see that because the question is incomplete, you would need a general overview to understand it, so it would be best if you:
Read the given textUnderstand the plot and characterizationFollow the Rising Action, Climax, and Falling ActionList out the main pointsThen, join them in order of occurrence.Read more about summary here:
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Which number represents the sum of -8 and -i?
8i
-8i
-8-i
-8 + i
Answer:
c
Step-by-step explanation:
edge
Vector R has an x-component of Rx=−20 N and a y-component of Ry=10 N. What is the direction of vector R ? −26.6∘ 63.40 153.40 243.40
Given:
Vector R has an x-component of Rx = −20 N and a y-component of Ry = 10 N.
To find:
The direction of vector R.Solution:
We can use the following formula to calculate the direction of vector R:
\(\theta=\tan^{-1}\frac{R_y}{R_x}\)
Where\(\theta\) is the angle between the vector and the x-axis.
Substitute the given values of
\(R_x\)and \(R_y\).
\(\theta=\tan^{-1}\frac{R_y}{R_x}\)
\(\theta=\tan^{-1}\frac{10}{-20}\)
\(\theta=-26.57°\)
Therefore, the direction of vector R is -26.6°.
Answer: So, the answer is -26.6° in 100 words.
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John predicted that his project would require, in effort, 25 person-days (d/p) for plan development, 75 d/p for software development, 20 d/p for reviews, 30 d/p for tests, 20 d/p for training and 5 d/p for methodology. His project cost 250 days/p, because he had to redo several modules following the test results.
a) Calculate the costs of non-compliance, enforcement, prevention and evaluation.
Show your calculations below.
b) Calculate the percentage of effort, out of the total cost, devoted to each component:
a. the costs of non-compliance, enforcement, prevention and evaluation are -75 d/p, -$7500, $17500 and $5000 respectively
b. The percentage of effort devoted to each component is:
Plan development: 10%Software development: 30%Reviews: 8%Tests: 12%Training: 8%Methodology: 2%a) To calculate the costs of non-compliance, enforcement, prevention, and evaluation, we need to determine the deviations in effort for each component and multiply them by the corresponding cost per person-day.
Non-compliance cost:
Non-compliance cost = Actual effort - Predicted effort
To calculate the actual effort, we need to sum up the effort for each component mentioned:
Actual effort = Plan development + Software development + Reviews + Tests + Training + Methodology
Actual effort = 25 + 75 + 20 + 30 + 20 + 5 = 175 d/p
Non-compliance cost = Actual effort - Predicted effort = 175 - 250 = -75 d/p
Enforcement cost:
Enforcement cost = Non-compliance cost * Cost per person-day
Assuming a cost of $100 per person-day, we can calculate the enforcement cost:
Enforcement cost = -75 * $100 = -$7500 (negative value indicates a cost reduction due to underestimation)
Prevention cost:
Prevention cost = Predicted effort * Cost per person-day
Assuming a cost of $100 per person-day, we can calculate the prevention cost for each component:
Plan development prevention cost = 25 * $100 = $2500
Software development prevention cost = 75 * $100 = $7500
Reviews prevention cost = 20 * $100 = $2000
Tests prevention cost = 30 * $100 = $3000
Training prevention cost = 20 * $100 = $2000
Methodology prevention cost = 5 * $100 = $500
Total prevention cost = Sum of prevention costs = $2500 + $7500 + $2000 + $3000 + $2000 + $500 = $17500
Evaluation cost:
Evaluation cost = Total project cost - Prevention cost - Enforcement cost
Evaluation cost = $25000 - $17500 - (-$7500) = $5000
b) To calculate the percentage of effort devoted to each component out of the total cost, we can use the following formula:
Percentage of effort = (Effort for a component / Total project cost) * 100
Percentage of effort for each component:
Plan development = (25 / 250) * 100 = 10%
Software development = (75 / 250) * 100 = 30%
Reviews = (20 / 250) * 100 = 8%
Tests = (30 / 250) * 100 = 12%
Training = (20 / 250) * 100 = 8%
Methodology = (5 / 250) * 100 = 2%
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Please help for section d) 100 points, must show all working and step by step
Answer:
Step-by-step explanation:
(a) and (b) see diagram
(c) you can see from the graph, the purple line hits the parabola twice which is y=6 or k=6
(d) Solving simultaneously can mean to set equal
6x - x² = k >subtract k from both sides
6x - x² - k = 0 >put in standard form
- x² + 6x - k = 0 >divide both sides by a -1
x² - 6x + k = 0
(e) The new equation is the same as the original equation just flipped (see image)
(f) The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal. I chose new)
discriminant formula = b² - 4ac
equation: x² - 6x + 6 = 0 a = 1 b=-6 c = 6
discriminant = b² - 4ac
discriminant= (-6)² - 4(1)(6)
discriminant = 36-24
discriminant = 12
Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.
working together, it takes two different sized hoses 40 minutes to fill a small swimming pool. if it takes 60 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
It will take 120 minutes for smaller hose to fill the complete swimming pool on its own.
Let us represent the complete swimming pool as 1. Now, total time required to fill the swimming pool is 40 hours. So, amount of swimming pool filled in 1 minute = 1/40
Similarly, amount fo swimming pool filled by larger hose in 1 minute = 1/60
Now for the smaller hose, the amount of swimming pool filled in 1 minute = 1/40 - 1/60
The amount of swimming pool filled in 1 minute = (60 - 40)/2400
The amount of swimming pool filled in 1 minute = 20/2400
The amount of swimming pool filled in 1 minute = 1/120
Total time taken to fill swimming pool = 1 ÷ (1/120)
Total time taken to fill swimming pool = 120 minutes
Thus, 120 minutes are required.
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To determine the number of significant digits in a measurement, follow the rule that.
The number of significant digits in a measurement is determined by following a specific rule. According to the rule, all non-zero digits in a measurement are considered significant. For example, in the measurement 25.4 cm, there are three significant digits (2, 5, and 4) because they are non-zero.
In addition to non-zero digits, there are two more rules to consider. The first rule states that all zeros between non-zero digits are also significant. For instance, in the measurement 1003 g, there are four significant digits (1, 0, 0, and 3) because the zero between the non-zero digits is significant.
The second rule states that trailing zeros at the end of a number are significant only if they are after the decimal point. For example, in the measurement 2.000 s, there are four significant digits (2, 0, 0, and 0) because the trailing zeros after the decimal point are significant. However, in the measurement 2000 m, there are only one significant digit (2) because the trailing zeros are not after the decimal point.
In summary, the number of significant digits in a measurement is determined by considering all non-zero digits, zeros between non-zero digits, and trailing zeros after the decimal point. These rules help in properly representing the precision and accuracy of a measurement.
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Decide if the following is a polynomial function:
h(x) = 5x^3 – 7x ^– 2 + x – 1
what is the magnitude of the net electric field at point p due to the particles?
The magnitude of the net electric field at point P due to the particle is 0 . explanation is given as
let us assume that , The charges of the four particles and the distance are given then on understanding the concept of electric field at electrostatics concept. on using the concept of the electric field at any given point, then production of individual electric field by a charge. and we known the concept of superposition law, on applying the law we get the value of the electric field in its direction and this shows the determination of the net electric field at that point.
The magnitude of the electric field,
E = q * R
where R = The distance of field at point from the charge, and q = charge of the individual particle
According to the superposition principle, the electric field at a single point due to more than one charges present ,hence on calculation of net electric field we get the origin of the coordinate system which is placed at point P and the y-axis is situated and oriented in the direction of the charge, (passing through the charge, ). The x-axis which is perpendicular to the y axis, and thus passes through the identical charges, then the individual magnitudes of an electric field is due to the charges are demonstrated by using the absolute signs of the charges. Now let us assume that the point charge which being positive i.e ( q > 0), we can see that the contributions coming from each charge gets cancel to each other. Therefore the net electric field in the direction of the y-axis is given using equation as E= 0
hence the net electric field is zero .
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12/6 x 12=
simplify the answer
Step-by-step explanation:
\( \frac{12}{6} \times \frac{12}{1} = 24\)
That is the answer
Create the Routh table and determine whether any of the roots of the polynomial are in the RHP. The polynomial p(s)= s^6 + 4s^5 +3s^4 + 2s^3 + s^2 + 4s + 4 For the polynomial p(s)= s^5 + 5s^4+ 11s^3+ 23s^2 + 28s + 12 determine how many poles are on the R.H.P, L.H.P. and jw axis? Consider the polynomial p(s)= s^5 + 3s^4 +2s^3 + 6s^2 + 6s + 9. Determine whether any of the roots are in the RHP.
For the first polynomial, we cannot determine if any roots are in the Right Half Plane (RHP) without knowing the values of coefficients.
For the second polynomial, we also cannot determine the number of poles in the RHP, LHP, or on the jω axis without knowing the values of coefficients.
For the third polynomial, we also cannot determine if any roots are in the RHP without knowing the values of coefficients.
What is a Routh Table?
A Routh table, also known as a Routh-Hurwitz table, is a tabular method used in control systems engineering to analyze the stability of a linear system. It is named after Edward J. Routh and Adolf Hurwitz, who independently developed the method.
p(s) = s⁶ + 4s⁵ + 3s⁴ + 2s³ + s² + 4s + 4
To determine if any roots are in the Right Half Plane (RHP), we check the signs of the elements in the first column of the Routh array. If any sign changes occur, it indicates roots in the RHP.
In this case, the signs are as follows:
Row 1: 1 (positive)
Row 2: 4 (positive)
Row 3: (2b-12)/4 (unknown)
Row 4: (4e-2c)/4 (unknown)
Row 5: (2c-4d)/4 (unknown)
Row 6: 4d (unknown)
Row 7: f (unknown)
Since we have a row with all unknown signs (Row 3 onwards), we cannot determine if any roots are in the RHP. To make further conclusions, we would need to know the values of the coefficients a, b, c, d, e, and f.
Moving on to the second polynomial:
p(s) = s⁵ + 5s⁴ + 11s³+ 23s² + 28s + 12
To determine the number of poles on the Right Half Plane (RHP), Left Half Plane (LHP), and jω axis, we count the number of sign changes in the first column of the Routh array.
In this case, the signs are as follows:
Row 1: 1 (positive)
Row 2: 5 (positive)
Row 3: (23a-5*12)/23 (unknown)
Row 4: 12b
To determine the sign of the element (23a-5*12)/23 in Row 3, we need to consider two cases:
Case 1: If (23a-512)/23 > 0, then the sign remains positive.
Case 2: If (23a-512)/23 < 0, then the sign changes.
Similarly, for Row 4, if 12b > 0, the sign remains positive. If 12b < 0, the sign changes.
Without knowing the values of coefficients 'a' and 'b', we cannot determine the exact number of sign changes. Therefore, we cannot determine the number of roots in the Right Half Plane (RHP), Left Half Plane (LHP), or on the jω axis for this polynomial.
Moving on to the third polynomial:
p(s) = s⁵ + 3s⁴ + 2s³ + 6s² + 6s + 9
To determine if any roots are in the Right Half Plane (RHP), we check the signs of the elements in the first column of the Routh array.
Row 1: 1 (positive)
Row 2: 3 (positive)
Row 3: (6a-3*9)/6 (unknown)
Row 4: 9b (unknown)
Row 5: c (unknown)
Row 6: d (unknown)
Since we have a row with all unknown signs (Row 3 onwards), we cannot determine if any roots are in the RHP without knowing the values of coefficients 'a', 'b', 'c', and 'd'.
Hence,
For the first polynomial, we cannot determine if any roots are in the Right Half Plane (RHP) without knowing the values of coefficients.
For the second polynomial, we also cannot determine the number of poles in the RHP, LHP, or on the jω axis without knowing the values of coefficients.
For the third polynomial, we also cannot determine if any roots are in the RHP without knowing the values of coefficients.
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Identify the highlighted part of circle O shown below
Central angle
Secant
Inscribed angle
Chord
Answer:
Chord
Step-by-step explanation:
Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.
Question 4 (1 point)
Which list shows the correct order of coefficients needed to balance the chemical
equation?
_CH4 + __Cl2 → __CCl4 + _HCI
a 1, 4, 1, 2
b 1, 4, 1, 4
c 1, 2, 1, 4
d 1, 1, 1, 1
Answer:
d
Step-by-step explanation:
you buy a rare stamp for $50. each year the value of the stamp increases by 1.2%. write an equation that represents the value of the stamp, and then find the value of the value of the after 10 years
An equation that represents the value of the stamp is V(t) = V₀ * (1 + r)ˣ
The value of the stamp after 10 years would be approximately $56.34.
First, let's denote the initial value of the stamp as V₀ and the number of years as t. In this case, V₀ is equal to $50. The annual increase rate is given as 1.2%, which can be expressed as 0.012 in decimal form.
Now, we can start building the equation. Since the value of the stamp increases every year, we need to add the rate of increase to the previous year's value. Mathematically, this can be represented as:
V(t) = V₀ + (V₀ * r) + (V₀ * r) + ... + (V₀ * r)
Here, V(t) represents the value of the stamp after t years, and r represents the rate of increase (0.012 in decimal form).
Since the rate of increase remains constant at 1.2% each year, we can simplify the equation using exponential notation:
V(t) = V₀ * (1 + r)ˣ
Now we have an equation that represents the value of the stamp after t years, where V₀ is the initial value ($50), r is the rate of increase (0.012), and x is the number of years.
To find the value of the stamp after 10 years, we substitute t = 10 into the equation:
V(10) = $50 * (1 + 0.012)¹⁰
Calculating this equation will give us the value of the stamp after 10 years. Let's perform the calculation:
V(10) = $50 * (1.012)¹⁰
V(10) ≈ $50 * 1.1268250301
V(10) ≈ $56.34
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Which of the following algebraic represents shows a dilation that is an enlargement ?
The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)
A dilation is a type of transformation that changes the size of the shape or object. It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.
A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).
For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.
Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)
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Anyone mind helping!?
Answer:
50h(5h-2)
Step-by-step explanation:
Factor out 50h from the expression
how maNY solutions do these equations have? No solution, one solution, infinite solutions.
a) y = 2x + 3 and y = -2x + 11
b) y = x + 2 and -2x + 2y = 4
c) y = x - 3 and y = x + 6
d) y = 7 and y =3x-5
e) y = -4x and y = -4x - 1
Answer:
See below.
Step-by-step explanation:
a) y = 2x + 3 and y = -2x + 11
One solution. They are straight lines with different slopes, so they will intersect at some point.
b) y = x + 2 and -2x + 2y = 4
-2x + 2y = 4 can be rearranged to 2y = 2x +4 and then y = x + 4
Both lines have the same slope, 1. They are parallel and will never meet. No solutions.
c) y = x - 3 and y = x + 6
This has the same answer as c. Parallel lines (both have slopes of 1.). They will never meet: no solutions.
d) y = 7 and y =3x-5
One solution. Straight lines with different slopes (3 and 0) so they will cross at one point. [At (4,7)]
e) y = -4x and y = -4x - 1
Same slopes. There are no solutions.