Answers
The rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex] when its length is 10 cm and its width is 6 cm, this is the case.
What is the rate of change?One quantity's rate of change with regard to another quantity is known as the rate of change function. In order to calculate the rate of change, one simply divides the amount of change in one item by the equivalent amount of change in another.
Let L and W represent the length and breadth of the rectangle, respectively, and A represents the area of the rectangle. Next, we have:
A = L * W
When L = 10 cm and W = 6 cm, we are interested in determining the rate of increase of the rectangle's area with regard to time, or dA/dt.
We can begin by finding the derivative of A = L * W with regard to time t for both sides of the equation:
Derivate the equation by both sides with respective t.
[tex]\frac{d}{dt} (L * W) = \frac{dA}{dt}[/tex]
Using the principle of product rule of derivative, we arrive at:
[tex]L * W + L * \frac{dw}{dt} = \frac{dA}{dt}[/tex]
To determine dA/dt when L = 10 cm and W = 6 cm, we are provided that [tex]\frac{dL}{dt}[/tex] = 8 cm/s and [tex]\frac{dw}{dt}[/tex]= 9 cm/s. Therefore, we replace these numbers in the previous equation to obtain:
[tex]\frac{dA}{dt}[/tex] = (8 [tex]\frac{cm}{s}[/tex]) * (6 cm) + (10 cm * 9 [tex]\frac{cm}{s}[/tex]).
[tex]\frac{dA}{dt} = 48 \frac{cm^{2}}{s} + 90 \frac{cm^{2}}{s} \\[/tex]
[tex]138 \frac{cm^{2} }{s} = \frac{dA}{dt}[/tex]
Since the rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex]when its length is 10 cm and its width is 6 cm, this is the case.
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Related Questions
The table shows the number of runs earned by two baseball players.
Player A
2, 1, 3, 8, 2, 3, 4, 3, 2
Player B
2, 3, 1, 4, 2, 2, 1, 4, 6
Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with an IQR of 1.5.
Player B is the most consistent, with an IQR of 2.5.
Player A is the most consistent, with a range of 7.
Player B is the most consistent, with a range of 5.
Answers
Player A has a smaller IQR and range, indicating less variability in their scores, therefore the correct option is: Player A is the most consistent, with an IQR of 1.5.
Baseball players' consistency explainedTo determine the best measure of variability for the data, we need to consider the nature of the data and what we want to measure. Since the data is quantitative and consists of individual values, measures like range, interquartile range (IQR), and standard deviation (SD) are commonly used.
The range is the difference between the highest and lowest values in the data. The IQR is the difference between the 75th and 25th percentiles of the data. The SD measures the average distance of the values from the mean.
For Player A:
Range = 8 - 1 = 7
IQR = Q3 - Q1 = 3 - 1.5 = 1.5
SD = 1.96 (approximate)
For Player B:
Range = 6 - 1 = 5
IQR = Q3 - Q1 = 4 - 1.5 = 2.5
SD = 1.61 (approximate)
Based on these measures, we can see that Player A has a smaller IQR and range, indicating less variability in their scores, while Player B has a larger IQR and range, indicating more variability. Therefore, Player A is the more consistent player.
So the correct option is: Player A is the most consistent, with an IQR of 1.5.
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What is the surface area of the geometric shape, in square centimetres?
Answers
The surface area of the given geometric shape(cube) is 24[tex]cm^2[/tex]. To find the surface area of a cube, you need to determine the total area of all the six faces of the cube.
Each face of a cube is a square with all sides equal in length to the edge length of the cube. The formula to find the surface area of a cube is:
Surface Area of Cube = 6 × (edge length[tex])^2[/tex]
Therefore surface are of the given cube = 6 x [tex](2cm[/tex][tex])^2[/tex]
= 6 x 4[tex]cm^2[/tex]
= 24[tex]cm^2[/tex]
Therefore, the surface area of the cube is 24 square centimeters.
To understand this conceptually, we have a cube with 2cm sides. It has six faces, and each face is a square with a side length of 2cm. Therefore, the area of each face is (2cm x 2cm) = 4[tex]cm^2[/tex]. The total surface area of the cube is obtained by adding up the area of all six faces, which gives us:
Total surface area = 6 x 4[tex]cm^2[/tex] = 24[tex]cm^2[/tex]
Therefore, the surface area of a cube with side length 2cm is 24 square centimeters.
The complete question is:
What is the surface area of the given geometric shape in the image, in square centimetres?
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on a separate sheet of paper, sketch the rectangle for each problem using any method round and estimate to check your answer problem 1 5 x 4,751
Answers
The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.
What is rounding of a number?Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.
The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.
1. 5 x 4751 ≈ 5 x 4800 = 24,000.
To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.
2. 7 x 6000 = 42,000.
To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.
3. 6 x 5214 ≈ 6 x 5200 = 31,200.
To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.
4. 8 x 3867 ≈ 8 x 3900 = 31,200.
To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.
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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.
What is rounding of a number?The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.
In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.
Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.
1. 5 x 4751 ≈ 5 x 4800 = 24,000.
To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.
2. 7 x 6000 = 42,000.
We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.
3. 6 x 5214 ≈ 6 x 5200 = 31,200.
By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.
4. 8 x 3867 ≈ 8 x 3900 = 31,200.
To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.
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A 4 m ladder leans against a
building. If the bottom of the
ladder is 1.3 m from the bottom of
the building, how far up the wall
will the ladder reach? Round your
answer to one decimal place.
Answers
solve using substitution method y = -3x 4x+y = 2
Answers
[tex]\Large\textbf{Please give complete questions}[/tex]
An airplane flies 55" east of north from City A to City B, a distance of 470 miles. Another airplane flies 7" north of east from City A to City C, a distance of 890 miles. What is the
distance between Cities B and C? Round to the nearest tenth of a mile.
The distance between City B and City C is about miles
Answers
Answer:
d = 523.8 miles
Step-by-step explanation:
law of cosines
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Step-by-step explanation:
The drawing attached represents the question. We create a triangle with the distances from each pair of cities, and we call the distance from B to C by 'd'.
First, we need to find the angle BAC:
55° + BAC + 7° = 90°
BAC = 28°
Then, we can use the law of cosines to find the value of d:
d^2 = 470^2 + 890^2 - 2*470*890*cos(BAC)
d^2 = 470^2 + 890^2 - 2*470*890*0.8829
d^2 = 274365.86
d = 523.8 miles
I need help asap!!!!!
Answers
Answer:
B
Step-by-step explanation:
You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x-3y=12 Equation 1 -2x+y=8 Equation 2 A. Add equation 2 to equation 1. B. Multiply equation 2 by 3. Then subtract the result from equation 1. C. Add the left side of equation 2 to the left side of equation 1.
Answers
Multiply equation 2 by 3. Then subtract the result from equation 1.
Explanation:
The 2nd equation given to us is -2x+y = 8
Triple both sides to get -6x+3y = 24
This means the original system
[tex]\begin{cases}2x-3y = 12\\-2x+y = 8\end{cases}[/tex]
is equivalent to
[tex]\begin{cases}2x-3y = 12\\-6x+3y = 24\end{cases}[/tex]
If we were to add the equations, then the y terms would cancel out because -3y+3y = 0y = 0.
Subtracting the equations will not cancel out the y terms.
-3y minus 3y = -3y -3y = -6y
Therefore the portion saying "Then subtract the result from equation 1." in answer choice B is not correct. It should be "add the equations" or "add the result to equation 1" after tripling both sides of the 2nd equation.
Answer choices A and C say the same thing more or less. Adding the original equations straight down will cancel out the x terms. Therefore, choices A and C are valid approaches to using elimination. We can cross choices A and C off the list.
What is the value of the expression below when w=9 and x=8
9w-7x
Answers
Answer:
25
Step-by-step explanation:
To find the value of the expression, all you have to do is plug 9 in for w and plug 8 in for x.
When you plug the numbers in, your equation should look like 9(9)-7(8)
Then you just simplify the expression and get your answer of 25
[tex]9(9)-7(8)\\81-56\\25[/tex]
The following shape has
1 pair of parallel sides. what is the area of the shape
Answers
The area of the following shape is 76 units.
What is a hexagon?
A regular hexagon is a closed shape polygon which has six equal sides and six equal angles. In case of any regular polygon, all its sides and angles are equal.
The structure in the figure is hexagon in which two parallel lines are present.
These parallel lines are dividing this hexagon into three parts:
1. Rectangular part with length = 8 units and width = 7 units
2. Triangle of height 2 units.
3. Triangle of height 3 units.
We know,
1. Area of rectangle = L x B
Area of rectangle = 8 x 7
Area of rectangle = 56 units
2. Area of triangle 1 = 1/2 x base x height
Area of triangle 1 = 1/2 x 2 x 8
Area of triangle 1 = 8 units
3. Area of triangle 2 = 1/2 x base x height
Area of triangle 2 = 1/2 x 3 x 8
Area of triangle 2 = 12 units
So, area of hexagon = area of rectangle + Area of triangle 1 + area of triangle 2
Area of hexagon = 56 + 8 + 12
Area of hexagon = 76 units
Therefore, the area of the shape is 76 units.
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if you have an 84% in a class and you get 100% on an assignment that’s worth 20% of your overall grade, what is your new grade?
Answers
Step-by-step explanation:
The 84 represents 80% of your grade and the 100 is 20 percent :
84 * 80% + 100 * 20% =
84 (.8) + 100(.2) = 87.2 %
(X+Y)(X-1) if x=-3 and y=-5
Answers
Answer: 16
Step-by-step explanation: Solve the parentheses inside first, which should be (3 + 5) (3 - 1). Solve the inside which the answer would be (8) (2). Multiply after (2x8) to get the answer 16
hope it helps!!
Using the table, what is the average daily balance of the credit card for the October 1 - October 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00. Day 1112131 Activity − Payment Purchase Purchase Adjustment −−2000+1500+1000 Closing Balance 100008000950010500
Answers
The balance based on the.data given in the table is shown below.
Balance from day 1 to 10 = 11000
Balance from day 11 to 21= 8000
Balance from day 21 to 30- 5500
Balance on day 31 7500
How to explain the balanceBalance from day 1 to 10= 11000
Balance from day 11 to 21= 8000 Balance from day 21 to 30 5500
Balance on day 31- 7500
The average daily balance of the credit card for the month of december is:
Average daily balance The ratio of total balance from each day in cycle to the total number of days in cycle.
Total balance from each day in cycle=
(11000 x 10)+(8000 × 10)+(5500 x 10) + (7500 x 1) = 104000
Average daily balance=104000 / 31
= 8145
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Why is it important to understand an index before deciding whether to trust it?
An index provides a simple way to
▼
made at different times or in different places based on
▼
an index value.
a reference value.
a rounding value.
a percentage value.
Understanding this value provides context to the index which can help determine if the index is trustworthy.
Answers
Also, we can contrast many indices and select the most pertinent and reliable one for our individual requirements.
A percentage is what?A percentage, which is denoted by the number 100, is a proportion, fraction, or piece of a whole. The Roman phrase per centum, which meaning "by the 100" or "per one hundred," is where the term "percent" originates. A numerical value and the percentage symbol (%) can be used to express percentages.
When deciding whether to believe an index, it's crucial to grasp it because it gives the data being provided context. A statistical measure known as an index reflects changes in a certain set of data across time, across several regions, or among various populations. However, the techniques, calculations, or underlying assumptions used by various indices might vary, which may have an impact on their validity and dependability.
An index, for instance, can be based on a tiny sample size, use biassed data sources, or employ an antiquated methodology that doesn't adequately reflect contemporary trends or circumstances. In certain situations, the index might not accurately represent the phenomenon being assessed, which could result in inaccurate judgements or decisions.
Hence, by comprehending the underlying information, methods, and constraints of an index, we may more accurately evaluate its validity and trustworthiness and make defensible choices according to the data it offers. Also, by contrasting many indices, we can select the one that best suits our unique requirements and is the most reliable.
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PLSSSSSSSSSSSSSSSSS HURRRYYYYYYYYYYYYYYYYYYYYYYY
A triangle with an area of 360 square meters was created from a triangle with an area of 2.5 square meters using a scale factor. What is the scale factor?
900:1
72:1
30:1
12:1
Answers
Answer:
Step-by-step explanation: Multiply all numbers and add all then divided by the lowest
Let x be the scale factor.
Then, the ratio of the areas of the two triangles is x².
We are given that the larger triangle has an area of 360 square meters and the smaller triangle has an area of 2.5 square meters. So we can set up the equation:
x²(2.5) = 360
Solving for x, we get:
x = sqrt(360/2.5)
x = sqrt(144)
x = 12
Therefore, the scale factor is 12:1. Answer: 12:1.
Courtney has a headache, and takes 250mg of Tylenol. The amount, A of Tylenol remaining in her body after n hours is given by the formula A=250(.73)^n. How much of the Tylenol remains in her body after 4 hours?
Answers
Approximately 106.79 mg of Tylenol remain in Courtney's body after 4 hours.
What is the capacity of taking medication?
When someone takes medication, it is important to understand how long the medication remains in their system. This can help ensure that the medication is effective and prevent unwanted side effects. In this case, Courtney has taken 250mg of Tylenol to relieve a headache. We are asked to find out how much of the Tylenol remains in her body after 4 hours.
To answer this question, we can use the formula A=250(.73)ⁿ, where A represents the amount of Tylenol remaining in the body after n hours. The value 250 represents the initial amount of Tylenol Courtney took, and 0.73 represents the percentage of Tylenol that is eliminated from the body per hour.
When we substitute n=4 into the formula, we get A= 250(.73)⁴. This means that after 4 hours, approximately 106.79 mg of Tylenol remain in Courtney's body. This calculation assumes that Courtney has not taken any additional Tylenol during this time period.
It is worth noting that individual factors such as age, weight, and metabolism can affect how long a medication remains in someone's system. Additionally, taking medications with other substances, such as alcohol or other medications, can also impact the body's ability to eliminate the medication. Therefore, it is always important to follow the advice of a medical professional and carefully read medication labels and instructions.
A = 250(.73)ⁿ
A = 250(.73)⁴ (substituting n=4)
A ≈ 106.79
In conclusion, we can calculate that after 4 hours, approximately 106.79 mg of Tylenol remains in Courtney's body. It is important to remember that medication elimination can vary based on individual factors, and it is always best to consult a healthcare professional if you have any concerns about medication use or potential side effects.
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A circle has a circumference of 153.86153.86153, point, 86 units.
What is the radius of the circle?
Use 3.14 for \piπpi and enter your answer as a decimal.
Answers
Answer:
The radius of the circle is 24.5 units
Step-by-step explanation:
The formula for the circumference of a circle is [tex]C=2\pi r[/tex]
Where [tex]C[/tex] is the circumference and [tex]r[/tex] is the radius.
Lets solve for [tex]r[/tex].
Divide both sides of the equation by [tex]2\pi[/tex].
[tex]\dfrac{C}{2\pi}=r[/tex]
Now we have an equation to evaluate the radius.
Numerical Evaluation
In this example we are given
[tex]C=153.86153\\\pi =3.14[/tex]
Substituting our values into our equation for the radius yields
[tex]r=\dfrac{153.86153}{2*3.14}[/tex]
[tex]r=\dfrac{153.86153}{6.28}[/tex]
[tex]r=\dfrac{153.86153}{6.28}[/tex]
[tex]r=24.5[/tex]
help pls show ur work
Answers
So, any positive value of x is 3for this triangle. correct answer is (A)
What is Triangle?A triangle is a three-sided polygon that is formed by connecting three straight lines or line segments. It is a basic geometric shape that is commonly studied in mathematics, geometry, and trigonometry. Triangles have a wide range of properties and characteristics that are important in various fields of study, including their angles, sides, and area. Triangles can be classified based on their angles (as acute, right, or obtuse triangles) or based on their sides (as equilateral, isosceles, or scalene triangles). The study of triangles is fundamental in many areas of mathematics and physics and is also important in practical applications such as engineering, architecture, and surveying.
by the question.
PC =7 and PQ= 14
PB = 9 and PR = 6X
Thel's theorem
[tex]PC/PQ =PB/PR\\7/14 = 9/6X\\42X = 126\\ X = 126/42\\ X= 3[/tex]
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Question
Prove the trigonometric identity.
csc x cos x / tan x + cot x =cos^2 x
Drag an expression to each box to correctly complete the proof.
Answers
Drag the following expressions accordingly to complete the proof:
1/sinx· cos x)/ (sinx/cosx + cosx/sinx) = cos²x
(cos x/sinx)/ ([sin²x/[sinx·cosx] + cos²x/[sinx·cosx]) = cos²x
(cos x/sinx)/ ([sin²x+cos²x] / sinx·cosx) = cos²x
(cos x/sinx)/ ( 1 / sinx·cosx) = cos²x
(cos x/sinx) · (sinx·cosx) = cos²x
How to prove the trigonometric identity?Given: (csc x cos x)/ (tan x + cot x) = cos²x
We want to prove the trigonometric identity.
We have:
(csc x· cos x)/ (tan x + cot x) = cos²x
Recall the following trig. expressions and substitute for them:
csc x = 1/sinx
tan x = sinx/cosx
cot x = cosx/sinx
(1/sinx· cos x)/ (sinx/cosx + cosx/sinx) = cos²x
(cos x/sinx)/ ([sin²x/[sinx·cosx] + cos²x/[sinx·cosx]) = cos²x
(cos x/sinx)/ ([sin²x+cos²x] / sinx·cosx) = cos²x
Recall sin²x+cos²x = 1. Subsitiute for it to get:
(cos x/sinx)/ ( 1 / sinx·cosx) = cos²x
(cos x/sinx) · (sinx·cosx) = cos²x
cosx · cos x = cos²x
cos²x = cos²x
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The graph of a proportional relationship contains the point (-12, 3).
What is the corresponding equation?
(A) y = 1/4x
(B) y = - 1/4x
(C) y = - 4/1x
(D) y = 4/1x
____
The variables x and y have a proportional relationship, and y=3 when x=4
Which equation represents this relationship?
(A) y = −12x
(B) y = 4/3x
(C) y = 7x
(D) y = 3/4x
____
correct answers gets brainliest
Answers
& Number two
A ( Y=-12x)
I need help for number 12
Answers
Evaluating the function f(x) = [x - 1] at different values of x, f(-1.30)=-3, f(-3)=-4, f(2.3)=1, f(4)=3, and f(7.1)=6
What is the evaluation of the functionGiven the function f(x) = [[x - 1]], we are asked to evaluate f at several values of x.
For x=-1.30, we have:
[tex]$f(-1.30) = [[-1.30 - 1]] = [[-2.30]] = -3$[/tex]
For x=-3, we have:
[tex]f(-3) = [[-3 - 1]] = [[-4]] = -4[/tex]
For x=2.3, we have:
[tex]$f(2.3) = [[2.3 - 1]] = [[1.3]] = 1$[/tex]
For x=4, we have:
[tex]$f(4) = [[4 - 1]] = [[3]] = 3$[/tex]
For x=7.1, we have:
[tex]$f(7.1) = [[7.1 - 1]] = [[6.1]] = 6$[/tex]
Therefore, f(-1.30)=-3, f(-3)=-4, f(2.3)=1, f(4)=3, and f(7.1)=6
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One third of the number of people attending a football game were admitted at 1/2 normal price of admission. How many people paid full price, if the gate receipts
were $42,000?
F. 2,800
G. 3,500
H. 5,000
J. 5,200
K. cannot be determined from the information given
Answers
Solving Systems of Quadratic Equations
5. Solve this nonlinear system of equations. Show your work.
a. Use substitution to combine equations. Rewrite so that one side is equal to 0. (1 point)
b. Factor your equation from Part a. (1 point)
c. Identify the x-values of the solutions. (1 point)
d. Identify the solutions to the system. (1 point)
Answers
Using equations,
A: y=-x²+6x-5
y=3
3=-x²+6x-5
y=0
B: (x-2) (x-4) =0
C: x-2=0 OR x-4=0
D: x=2 OR x=4
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, etc.
Y=-x²+6x-5
Y=3
Using substitution:
3 = - x²+6x- 5
x²- 6x+8 = 0
Now factor your equation:
x²- 6x+8 = 0
⇒ x² -2x - 4x + 8 = 0
⇒ x (x-2) -4(x-2) = 0
⇒ (x- 2) (x-4) =0
Identify the x-values of the solutions:
x-2=0 or x-4 =0
x=2 or x=4
Identify the solution to the system:
x=2 y=3 and
x=4 y=3
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Which series has a sum of 20?
Answers
a) [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex] series has sum of 20.
What is sum?
In mathematics, the sum of a series is the result obtained by adding together all the terms in a sequence of numbers.
The series that has a sum of 20 is [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex].
To see why, we can use the formula for the sum of an infinite geometric series:
[tex]S = \frac{a}{(1-r)}[/tex]
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, the first term is:
[tex]a = 5(\frac{3}{4} )^0 = 5[/tex]
And the common ratio is:
[tex]r = \frac{3}{4}[/tex]
So, the formula becomes:
[tex]S = \frac{5}{(1-\frac{3}{4} )}[/tex]
Simplifying the denominator, we get:
[tex]S = \frac{5}{\frac{1}{4}}[/tex]
Multiplying by the reciprocal, we get:
S = 20
Therefore, the sum of the series is 20, which means that the series [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex]
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Tell whether the statement is always, sometimes, or never true. Explain. Be sure to use an example in your explanation.
The absolute value of a number is equal to the opposite of that number.
Answers
Answer:
Step-by-step explanation:
this is a good aswer
Miguel’s coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Miguel $5.95 per pound, and type B coffee costs $4.65 per pound. This month’s blend used three times as many pounds of type B coffee as type A, for a total cost of $796.00. How many pounds of typeA coffee were used?
Answers
Answer:
Step-by-step explanation:
Let's start by setting up two variables to represent the number of pounds of type A and type B coffee used in the blend. Let:
x be the number of pounds of type A coffee used
3x be the number of pounds of type B coffee used (since there were three times as many pounds of type B used as type A)
The total cost of the blend is given as $796.00, so we can set up an equation based on the cost of each type of coffee and their respective amounts:
5.95x + 4.65(3x) = 796
Simplifying and solving for x, we get:
5.95x + 13.95x = 796
19.90x = 796
x = 40
Therefore, 40 pounds of type A coffee were used in the blend. To find the number of pounds of type B coffee, we can substitute x = 40 into our expression for the number of pounds of type B:
3x = 3(40) = 120
Therefore, 120 pounds of type B coffee were used in the blend.
Which of the following statements regarding local extrema is/are correct?
*A local extremum of a function is a maximum or minumum value of the function over some
open interval.
*A local extremum is an x-value.
*A local extremum of a function is a maximum or minimum value of the function over a given
closed interval.
*When a function is defined over a closed interval, a local extremum may occur at the endpoint
of the interval.
*The location of a local extremum is a y-value.
*A local extremum is a y-value.
*When a function is defined over a closed interval, a local extremum never occurs at the
endpoint of the interval.
*The location of a local extremum is an x-value.
Answers
The correct statements regarding local extrema are:
A local extremum of a function is a maximum or minimum value of the function over some open interval.What are local extrema?The point at which the function's highest or minimum value is reached in some open interval containing the point is known as the local extremum (or relative extremum) of the function.
The correct statements regarding local extrema are:
A local extremum of a function is a maximum or minimum value of the function over some open interval.When a function is defined over a closed interval, a local extremum may occur at the endpoint of the interval.The location of a local extremum is an x-value.Thus, the correct options are explained above.
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If you take any positive integer and apply the following infinitely:
If the number is even, divide by two
If the number is odd, multiply by 3 and add 1
Will every integer eventually fall back down into the 4, 2, 1 loop, or is there a positive integer that never falls down into that loop?
Answers
This is known as the Collatz Conjecture, and it remains an unsolved problem in mathematics. Despite extensive computational evidence suggesting that the conjecture is true, a proof or counterexample has yet to be found.
The conjecture states that no matter what positive integer you start with, applying the "3n+1" rule (multiply by 3 and add 1 if n is odd) or "n/2" rule (divide by 2 if n is even) repeatedly will eventually lead to the sequence 4, 2, 1, and then it will loop endlessly: 4, 2, 1, 4, 2, 1, and so on.
While the conjecture has been checked for all starting values up to at least 10^20, no one has been able to prove that it holds true for all positive integers. It is possible that there exists a starting value that does not eventually fall into the 4, 2, 1 loop, but no such value has been found.
can someone please explain how they got this answer
Answers
Step-by-step explanation:
138 = 10 log R
13.8 = log R anti-log both sides of the equation
10^13.8 = R Expand L side
6.3 x 10^13 = R
Hi i need help with this question
Answers
The measures of the numbered angles in the rhombus include the following:
m∠1 = 31°m∠2 = 90°m∠3 = 59°m∠4 = 59°m∠5 = 31°m∠6 = 59°What is a rhombus?In Mathematics and Geometry, a rhombus can be defined as a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal). Additionally, a rhombus typically has two (2) diagonals that bisect each other at right angles (90 degrees).
This ultimately implies that, the opposite sides of a rhombus are parallel and the sum of all the four (4) interior angles is equal to 360 degrees.
m∠3 + 90° + 31° = 180°
m∠3 + 121° = 180°
m∠3 = 180° - 121°
m∠3 = 59°
m∠3 ≅ m∠6 ≅ m∠4 = 59°
Since opposite angles are equal, we have:
m∠1 ≅ m∠5 = 31°
Since the two (2) diagonals bisect each other at right angles (90 degrees), we have:
m∠2 = 90°
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