To determine the actual height of the climbing frame, we need to know the scale factor of the model. If the scale factor is, for example, 1:50, it means that every 1 cm on the model represents 50 cm in real life.
Assuming that we have the scale factor, we can use the following proportion:
model height / actual height = scale factor
We know that the model height is 10 cm, and we want to find the actual height. Let's say the scale factor is 1:100. Then we have:
10 cm / actual height = 1/100
Multiplying both sides by the actual height, we get:
actual height = (10 cm) x (100/1) = 1000 cm
Therefore, the actual height of the climbing frame in this example is 1000 cm, or 10 meters.
Gina's class measured the weights of the pumpkins that they grew.
A line plot named “Pumpkin Weights” shows data from six to fourteen pounds. Six has three dots. Eight has five dots. Nine has one dot. Ten has seven dots. Twelve has four dots. Thirteen has two dots. Fourteen has one dot.
The weight of the pumpkins that Gina's class grew was measured.
a) There is a total of 23 pumpkins.
b) 7 pumpkins weigh 10 pounds.
c) The number of pumpkins that weigh 6 pounds is equal to 3 times the number of pumpkins that weigh 9 pounds.
Based on the given information, we can complete the sentences as follows:
a) There is a total of 23 pumpkins.
To get this number, we need to add up the number of dots for each weight:
3 + 5 + 1 + 7 + 4 + 2 + 1 = 23
b) 7 pumpkins weigh 10 pounds.
To find the weight with the most dots, we look for the peak in the line plot, which corresponds to 10 pounds, and count the number of dots on this peak, which is 7.
c) The proportion of pumpkins that weigh 6 pounds to those that weigh 9 pounds is 3 times.
To find the number of pumpkins that weigh 6 pounds, we count the number of dots on the peak corresponding to 6 pounds, which is 3. To find the number of pumpkins that weigh 9 pounds, we count the number of dots on the peak corresponding to 9 pounds, which is 1. Multiplying the number of pumpkins at 9 pounds by 3, we get 3 x 1 = 3, which is the same as the number of pumpkins at 6 pounds. Therefore, the statement is true.
The complete question is:-
Gina's class measured the weights of the pumpkins that they grew.
A line plot named “Pumpkin Weights” shows data from six to fourteen pounds. Six has three dots. Eight has five dots. Nine has one dot. Ten has seven dots. Twelve has four dots. Thirteen has two dots. Fourteen has one dot. Fill in the boxes to complete the sentences below to make each statement true.
a)there is a total of ____ pumpkins.
b) 7 pumpkins weigh _____ pounds.
c) the number of pumpkins that weigh ____ pounds is equal to 3 times the number of pumpkins that weigh 9 pounds.
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A point at (-5,7) is reflected across the x-axis. The new point is then reflected across he y-axis. What prdered pair names the third point? Explain.
Answer:
Step-by-step explanation:
Find the interest. All rates are annual interest rates.
3. Principal $200
Rate 9%
Time 1/2
O$9
OSIS
$36
$45
year
(1 point)
The interest is $9.To find the interest, we can use the simple interest formula:
I = P * r * t
what is interest ?
Interest is the amount of money charged by a lender to a borrower for the use of money, usually expressed as a percentage of the amount borrowed. In other words, it is the cost of borrowing money.
In the given question,
To find the interest, we can use the simple interest formula:
I = P * r * t
where I is the interest, P is the principal, r is the annual interest rate as a decimal, and t is the time in years.
Here, the principal is $200, the annual interest rate is 9%, and the time is 1/2 year.
Converting the annual interest rate to a decimal, we get:
r = 9% = 0.09
And, converting the time to years, we get:
t = 1/2 year
Substituting the values into the formula, we get:
I = $200 * 0.09 * (1/2) = $9
Therefore, the interest is $9.
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Consider the following polynomial.
q(x)=6x3+31x2+23x−20
Step 1 of 2 : Use the Rational Zero Theorem to list all of the potential rational zeros.
The potential rational zeros of the given polynomial are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±15, ±20, ±30, ±60, ±1/2, ±1/3, ±2/3, ±5/2, ±4/3, ±5/3, ±10/3, ±1/6, ±5/6, ±1/10, ±2/5, ±4/15, ±1/15, ±2/15.
How to calculate potential rational zeroes?
The Rational Zero Theorem states that if a polynomial with integer coefficients has any rational zeros, then they must have the form of a fraction p/q, where p is a constant term factor and q is a leading coefficient factor.
For the given polynomial q(x)=6x^3+31x^2+23x−20, the constant term is -20, and the leading coefficient is 6. Therefore, the potential rational zeros can be expressed as follows:
p/q = ± {factors of the constant term (-20)}/{factors of the leading coefficient (6)}
Possible factors of -20: ±1, ±2, ±4, ±5, ±10, ±20
Possible factors of 6: ±1, ±2, ±3, ±6
Therefore, the potential rational zeros are:
±1/1, ±2/1, ±4/1, ±5/1, ±10/1, ±20/1,
±1/2, ±2/2, ±4/2, ±5/2, ±10/2, ±20/2,
±1/3, ±2/3, ±4/3, ±5/3, ±10/3, ±20/3,
±1/6, ±2/6, ±4/6, ±5/6, ±10/6, ±20/6.
Simplifying and eliminating duplicates, we get:
±1, ±2, ±4, ±5, ±10, ±20,
±1/2, ±2/2, ±4/2, ±5/2, ±10/2, ±20/2 (which simplifies to ±1, ±2, ±3, ±5, ±10, ±20),
±1/3, ±2/3, ±4/3, ±5/3, ±10/3, ±20/3 (which simplifies to ±1/3, ±2/3, ±4/3, ±5/3, ±10/3),
±1/6, ±2/6, ±4/6, ±5/6, ±10/6, ±20/6 (which simplifies to ±1/6, ±1/3, ±2/3, ±5/6, ±5/3, ±10/3).
Therefore, the potential rational zeros of the given polynomial are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±15, ±20, ±30, ±60, ±1/2, ±1/3, ±2/3, ±5/2, ±4/3, ±5/3, ±10/3, ±1/6, ±5/6, ±1/10, ±2/5, ±4/15, ±1/15, ±2/15.
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Do the set of points in the figure represent a function?
A. Yes
B. No
Answer:
yes
Step-by-step explanation:
Solve the problem in the picture please!
Answer:
Step-by-step explanation:
d.
PLS HELP ME ASAP I NEED IT
Answer:
Step-by-step explanation:
Applying absolute value rule the solutions are:
x + 1/2 = 3/2/3 or x + 1/2 = -3 2/3
Changing to fractions:
x + 1/2 = 11/3 or x + 1/2 = -11/3
and then changing to a common denominator
x + 3/6 = 22/6 or x + 3/6 = -22/6
Solve left equation first:
x + 3/6 - 3/6 = 22/6 - 3/6
x = 19/6 or 3 1/6
Solve the right equation:
x + 3/6 - 3/6 = -22/6 - 3/6
x = -25/6 or -4 1/6
So the two solutions are:
19/6 and -25/6 as improper fractions
And
as mixed numbers: 3 1/6 and -4 1/6
Triangle POR with verlices P(- 13, -3). Q(-7, 3), and R(-6, 2) 270° counterclockwise rotation about C(-5, -4)
Therefore, the rotated triangle has vertices at (-5, -10), (-3, -1), and (-4, -2), which forms a new triangle.
Vertex?In mathematics, a vertex refers to a point where two or more lines, edges, or curves meet. In geometry, a vertex is a point where two or more edges of a polygon or polyhedron intersect. For example, in a triangle, each of the three points where the sides meet is a vertex.
A vertex is a fundamental unit of a graph, which is a collection of vertices connected by edges. Each vertex represents an entity or object, and the edges represent the relationships or connections between them. For example, in a social network graph, the vertices could represent individual users, and the edges could represent their friendships or connections with other users.
To perform a 270° counterclockwise rotation of a point about a center point, we can use the following formula:
[tex](x', y') = (x - a) * cos(theta) - (y - b) * sin(theta) + a, (x - a) * sin(theta) + (y - b) * cos(theta) + b[/tex]
where (x, y) is the original point, (x', y') is the rotated point, (a, b) is the center point, and theta is the angle of rotation in radians.
Let's first find the center point C(-5, -4) of the rotation. Then, we'll apply the formula to each vertex of the triangle to find its new location after the rotation.
[tex]Center point C = (-5, -4)[/tex]
Vertex P(-13, -3):
[tex]x' = (-13 - (-5)) * cos(270^{0} ) - (-3 - (-4)) * sin(270^{0} ) + (-5) = -5[/tex]
[tex]y' = (-13 - (-5)) * sin(270) + (-3 - (-4)) * cos(270) + (-4) = -10[/tex]
So, after the rotation, vertex P is at (-5, -10).
Vertex Q(-7, 3):
[tex]x' = (-7 - (-5)) * cos(270) - (3 - (-4)) * sin(270) + (-5) = -3[/tex]
[tex]y' = (-7 - (-5)) * sin(270) + (3 - (-4)) * cos(270) + (-4) = -1[/tex]
So, after the rotation, vertex Q is at (-3, -1).
Vertex R (-6, 2):
[tex]x' = (-6 - (-5)) * cos(270) - (2 - (-4)) * sin(270) + (-5) = -4\\y' = (-6 - (-5)) * sin(270) + (2 - (-4)) * cos(270) + (-4) = -2[/tex]
So, after the rotation, vertex R is at (-4, -2).
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(Need Help please and thank you!)
The equation of the graph is
d. y = sqrt(x) + 2How to complete the tableThe table is completed by substituting the x to the function y = sqrt(x) + 2
When x = 0:
y = sqrt(0) + 2
y = 0 + 2
y = 2
When x = 1:
y = sqrt(1) + 2
y = 1 + 2
y = 3
When x = 4:
y = sqrt(4) + 2
y = 2 + 2
y = 4
When x = 9:
y = sqrt(9) + 2
y = 3 + 2
y = 5
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the area of a trapizoid is 69.6in and the altude is 8.7 in. Find the perniniter of the trapizoid
Answer:
Step-by-step explanation:
area of trapezoid
[tex]= \frac{sum~of~parallel~sides}{2} \times altitude\\69.6=\frac{sum~of~parallel~sides}{2} \times 8.7\\139.2=sum~of~parallel~sides \times 8.7\\sum~of~parallel~sides=\frac{139.2}{8.7} =16[/tex]
minimum parameter=16+2(8.7)=16+17.4=33.4 in
Thanks to the help of insurance, non-
profits, family and friends, and
government, the Perez family was able
to make it through their time of need.
How did the family benefit (financially
and emotionally) from each of these
sources?
Insurance? Non-Profits? Family & Friends?
Government?
Overall, the Perez family likely benefited both financially and emotionally from each of these sources during their time of need.
The Perez family likely benefited in different ways from each of these sources during their time of need:
Insurance: If the Perez family had insurance, it is likely that they were able to receive financial assistance to cover some of their expenses. Depending on the type of insurance they had, they may have been able to receive money to pay for medical bills, property damage, or other expenses related to their time of need.
Non-profits: Non-profits may have provided the Perez family with resources such as food, clothing, and shelter during their time of need. These organizations may have also provided emotional support to the family, helping them feel less alone during a difficult time.
Family and friends: Family and friends likely provided the Perez family with emotional support during their time of need, as well as practical assistance such as meals, childcare, and help with household tasks. Financially, family and friends may have also helped the Perez family by providing loans or gifts of money.
Government: The government may have provided the Perez family with financial assistance through programs such as unemployment benefits, food stamps, or housing assistance. Additionally, the government may have provided emotional support to the family through counseling services or other resources.
Overall, the Perez family likely benefited both financially and emotionally from each of these sources during their time of need.
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Please help ASAP!! thanks!
The exact value of the trigonometric expression, given the conditions of sin and sec is -85/36.
The exact value of the trigonometric expression with u and v in Quadrant III is 304/425.
How to find the exact value ?We are given sin(u) = -3/5 with 3π/2 < u < 2π and cos(v) = 15/17 with 0 < v < π/2.
cos(v - u) = cos(v)cos(u) + sin(v)sin(u)
We are given cos(v) = 15/17 and sin(u) = -3/5. To find sin(v) and cos(u), we can use the Pythagorean identities:
sin^2(v) + cos^2(v) = 1
sin(v) = sqrt(1 - (15/17)^2) = 8/17
Similarly, for cos(u):
sin^2(u) + cos^2(u) = 1
cos(u) = -sqrt(1 - (-3/5)^2) = -4/5
Now we can find cos(v - u):
cos(v - u) = cos(v)cos(u) + sin(v)sin(u)
cos(v - u) = -36/85
Since sec(v - u) = 1/cos(v - u), we have:
sec(v - u) = 1/(-36/85) = -85/36
Since both u and v are in Quadrant III, sin(u) and cos(u) are both negative, and sin(v) and cos(v) are both negative. We are given sin(u) = -7/25 and cos(v) = -15/17.
To find sin(v) and cos(u), we can use the Pythagorean identities:
sin^2(u) + cos^2(u) = 1
cos(u) = -sqrt(1 - (-7/25)^2) = -24/25 (since u is in Quadrant III)
Similarly, for sin(v):
sin^2(v) + cos^2(v) = 1
sin(v) = -sqrt(1 - (-15/17)^2) = -8/17 (since v is in Quadrant III)
Now we can find cos(u + v):
cos(u + v) = (-24/25)(-15/17) - (-7/25)(-8/17)
cos(u + v) = 304/425
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in a recent year 23% of all college students were enrolled part-time. if 8.9 million college students were enrolled part-time that year, what was the total number of college students? round answer to the nearest million
The total number of college students is 204,700,000.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Here, Percentage of enrolled student for part time = 23%
Total enrolled students = 8.9 millions
Number of part time student = 23% x 8.9 million
[tex]= 0.23 \times 8900000[/tex]
[tex]=204,700,000[/tex]
Thus, the total number of college students is 204,700,000.
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The equation y = 1.5x can be used to determine y, The number of cups of water needed to cook x cups of rice. Which table shows the relationship between x and y?
Table A is showing the correct relation of equation y=1.5x
Define equationAn equation is a mathematical statement that asserts that two expressions are equal. It typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). They are used to model real-world phenomena, to solve problems, and to make predictions. Examples of equations include linear equations, quadratic equations, systems of equations, and differential equations.
Using the relation;
y=1.5x
Putting the value x=9
y=1.5×9
y=13.5
Putting the value x=11
y=1.5×11
y=16.5
On observing the tables, option A is satisfying the relation
Hence, Table A is showing the correct relation of equation y=1.5x.
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The complete question is:
Image is attached below.
Justin is younger than Hassan. Their ages are consecutive integers. Find Justin's age if the product of their ages is 210.
Justin is 14 years old, and Hassan is 15 years old.
What are integers?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Let's assume that Justin's age is x. Then, Hassan's age is x + 1, since their ages are consecutive integers and Hassan is older than Justin.
We are given that the product of their ages is 210:
x(x + 1) = 210
Expanding the left-hand side and simplifying, we get:
x² + x - 210 = 0
This is a quadratic equation in standard form. We can solve for x by using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -210.
Plugging these values into the formula, we get:
x = (-1 ± √(1² - 4(1)(-210))) / 2(1)
x = (-1 ± √(1 + 840)) / 2
x = (-1 ± √(841)) / 2
We take the positive root because x represents Justin's age, which is a positive integer. Therefore:
x = (-1 + 29) / 2 = 14
So, Justin is 14 years old, and Hassan is 15 years old.
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Solve for x.
x= units
(60 points)
Answer:
277.5
Step-by-step explanation:
first you multiply 37 * 90 then you get 3330 then you divide it by 12 and you get 277.5
1.
[(F v R). (Q = L)] > [Sv (r. M)]
[Sv (r. M)]
[(F v R). (Q = L)]
This argument is invalid because the premises do not logically lead to the conclusion. The conclusion is simply a repetition of the first premise and does not follow from the second premise. The argument lacks coherence and fails to establish a clear relationship between the premises and the conclusion. Therefore, we cannot accept the conclusion as a logical consequence of the premises.
Fill in the table to show the fifth multiple of each fraction.
Write your answers as fractions greater than 1.
Fraction. Fifth Multiple
2/6
7/10
3/8
5/12
7/6
The fifth multiple of each fraction is shown as follows:
1. 2/6 = 5/3
2. 7/10 = 7/2
3. 3/8 = 15/8
4. 5/12 =25/12
5. 7/6 = 35/6
What is the fifth multiple of the numbers?To get the multiple of a fraction, the best thing to do will be to multiply the fraction by the whole number in question. In this case, the whole number is five.
So, to get the right answers, you can begin by multiplying the functions with the whole number five. The values obtained are the fifth multiples. for the fraction, 2/6, the fifth multiple is 5/3.
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The right triangle on the right is a scaled copy of the right triangle on the lef
Identify the scale factor. Express your answer as a whole number or fraction
in simplest form.
10
10
20
20
scalar factor= 2, in order to find the scalar factor between two triangle we need to get the ratio between any of thier side of both the triangle on same side
what is scalar factor?
In mathematics, a scalar factor is a numerical value that scales or stretches a vector or a matrix by a certain factor. In other words, a scalar factor is a constant that is multiplied to a given vector or matrix to change its size or magnitude.
In the given question,
In mathematics, a scalar factor is a numerical value that scales or stretches a vector or a matrix by a certain factor. In other words, a scalar factor is a constant that is multiplied to a given vector or matrix to change its size or magnitude.
For instance, if we have a vector v = (x, y, z), then multiplying it by a scalar factor k will result in a new vector kv = (kx, ky, kz), which is stretched or shrunk according to the value of k. Similarly, if we have a matrix A, multiplying it by a scalar factor k will result in a new matrix kA, where each element of A is multiplied by k.
in order to find the scalar factor between two triangle we need to get the ratio between any of thier side of both the triangle on same side
scalar factor= opposite side of bigger triangle / opposite side of smaller triangle
scalar factor= 20/10
scalar factor= 2
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Calculate Average Rainfall with Total Rainfall and Average Temperature
The total rainfall is given as 16
Average rainfall is given as 1.23
The average temperature is given as 22.8
How to solve for the average rainfallwe would add all of the weekly rain values
2.6 + 1.6 + 10.2 + 1.4 + 0.2 = 16
The total rainfall is 16
The average rainfall would be 16 divided by the total number of days that we have here:
16 / 13
= 1.23
The average rainfall is 1.23
The average temperature calculationtotal temperature
22.9 + 28.5 + 24.6 + 36.2 + 19 + 20.8 + 19.4 + 22.8 + 22.6 + 21.6 + 19.6 + 19.9 + 18.3
= 296.2
average = 296.2 / 13
= 22.8
average temperature is given as 22.8
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X = 1/4 - 1/6
Determine the value of the x
The value of X in the given fraction is 1/12
What are improper fractions?A fraction is a mathematical expression that represents a part of a whole or a quotient of two numbers. It is expressed as one integer or number (called the numerator) divided by another integer or number (called the denominator), separated by a line or a slash.
Here, we are going to find the LCM of both 4 and 6 to determine the value of X.
LCM = 12
X = 1/4 - 1/6
X = (3 - 2)/12
X = 1/12
Therefore, we can conclude that the value of X in the given fraction is 1/12.
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The shaded face of a cuboid is a square. The length of the cuboid is 25 cm and its volume is 4900 cm³. Find the length of one side of the square face.
Answer: Let's denote the length, width, and height of the cuboid as l, w, and h, respectively. We know that the shaded face is a square, which means that two of its dimensions are the same. Without loss of generality, let's assume that the dimensions of the square face are l and w.
Since the volume of the cuboid is 4900 cm³, we have:
lwh = 4900
Substituting l = 25 - w (since the length of the cuboid is 25 cm) and simplifying, we get:
(25 - w)w h = 4900
Now, we use the fact that the shaded face is a square. Since two of its dimensions are the same, we have:
l = w
Substituting this into the equation above, we get:
(25 - l)l h = 4900
Simplifying further, we have:
25l^2 - 4900 = 0
Solving for l using the quadratic formula, we get:
l = 14 or -14/5
Since the length of the cuboid cannot be negative, we have l = 14. Therefore, the length of one side of the square face is 14 cm.
Step-by-step explanation:
write an equation of the line that is perpendicular to y= 1/3x +5 and passes through the points (-4,1)
Therefore , the solution of the given problem of equation comes out to be line passing through the spot (-4,1) and perpendicular to [tex]y = 1/3x + 5[/tex] is [tex]y = -3x - 11.[/tex]
What is an equation?Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a different method that could split 12 to two parts, consider the data supplied by y + 7,.
Here,
[tex]Y = mx + b[/tex], where m is the line's slope and b is its y-intercept, is the given equation in slope-intercept notation.
Provided that the slope of the provided line is 1/3, the slope of a line perpendicular to it will be the reciprocal of the negative of 1/3, or -3.
=> [tex]y - y_{1} = m(x - x_{1} )[/tex]
in which m [tex]= -3, x_{1} = -4,[/tex] and y1 = 1.
By replacing these numbers, we obtain:
=>[tex]y - 1 = -3(x - (-4))[/tex]
By condensing and figuring out x, we arrive at:
=> [tex]y - 1 = -3(x + 4)[/tex]
=>[tex]y - 1 = -3x - 12[/tex]
=> [tex]y = -3x - 11[/tex]
Consequently, the equation of the line passing through the spot (-4,1) and perpendicular to y = 1/3x + 5 is y = -3x - 11.
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{an}={((-1)^(n+1))/n} please how do you prove if this is convergent or divergent?
The series [tex]a_n=\frac{(-1)^{n+1}}{n}[/tex] is converges.
What is a series?
An n-arithmetic sequence is a sequence in which the difference d of successive terms is constant.
The general term of the arithmetic progression can be written using its first term [tex]a_1[/tex], tolerance [tex]d[/tex], and index [tex]n[/tex] as [tex]a_n=a_1+(n-1)d[/tex].
According to the alternating series test, if a sequence {b_n} satisfies the following three conditions:
[tex]b_n[/tex] is positive for all [tex]n[/tex].
[tex]b_n[/tex] is decreasing (i.e., [tex]b_n > = b_{n+1}[/tex] for all n).
[tex]\lim_{n \to \infty} b_n =0\\[/tex]
Then the alternating series [tex](-1)^n b_n[/tex] converges.
To apply the alternating series test to the sequence {a_n}, we first note that [tex]a_n = (-1)^{n+1}/n[/tex] satisfies condition 3, since [tex]\lim_{n \to \infty} \frac{1}{n} =0[/tex].
Next, we observe that [tex]a_n[/tex] is positive for n = 1, 3, 5, ... and negative for n = 2, 4, 6, ..., so [tex](-1)^n a_n = (-1)^{n+1}/n[/tex] is an alternating sequence.
Finally, we show that a_n is decreasing by considering the difference between successive terms,
[tex]a_{n+1} - a_n = (-1)^n/n - (-1)^{n+1}/(n+1)\\ = (-1)^{n} [(n+1)/(n(n+1))] \\= (-1)^{n}/n(n+1) < 0[/tex]
since n and n+1 are both positive. Therefore, a_n is decreasing.
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Standard Deviation. Find the Standard Deviation of the following set of data. You must fill out the table and show the ending calculations in order to get full credit here.
7.2, 8.9, 2.7, 11.6, 5.8, 10.2
show all steps
Answer:
Step-by-step explanation:
Scatterplots and correlation never prove __________
Fill in the blank
Scatterplots and correlation never prove causation. Causation may only be determined by well-designed experiments.
Give a brief account on scatterplots and correlation.A scatterplot is a type of graph commonly used to observe and visually represent the relationships between variables. Variable values are represented by dots. The position of the points on the vertical and horizontal axes indicates the value of each data point. Therefore, scatterplots use Cartesian coordinates to display the values of the variables in the dataset. A scatterplot is also called a scatter graphs, scatter charts, or scattergrams.
Correlation means association, and more specifically, it measures how well two variables are related. Correlation analysis have three possible outcomes: Positive correlation, negative correlation, no correlation.
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Can some help me? I have to find all possible solutions to that equation. I already found one thank you
The possible solutions to the equation are:
3π/4
π/4
How to solve trigonometric equations?Trigonometric equations involve trigonometric functions such as sine, cosine, tangent, etc. The goal is to solve for the unknown variable in the equation.
csc²x - 2 = 0
csc²x = 2
csc x = √2
sin x = 1/√2 (Remember: csc x = 1/sinx)
x = sin⁻¹(1/√2 )
x = 90° or 135° (sine is positive in 1st and 2nd quadrants)
x = π/4 or 3π/4
Thus, the possible solutions to the equation are x = π/4 or 3π/4.
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Calculate the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane.
the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113
The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
We have two points p=(-7,-2) and E=(1,-9)
then the distance between PE is
d=√(1+7)²+(-9+2)²
d= √(64+49)
d=√113
the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113
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each tank has a diameter of 6 ft and a height of 2 ft the cost is $5 per cubic use 3.14
It would cost $282.60 to fill a cylindrical tank with a diameter of 6 feet and a height of 2 feet.
What is cylinder?A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of equal size and shape, connected by a curved side.
According to given information:To calculate the cost of filling a tank with a diameter of 6 feet and a height of 2 feet, assuming a cost of $5 per cubic foot and using the value of pi as 3.14, we first need to calculate the volume of the tank.
The volume of a cylinder (which is the shape of the tank) is given by the formula:
V = π[tex]r^2h[/tex]
where V is the volume, r is the radius (half the diameter), and h is the height.
Since the diameter of the tank is 6 feet, the radius is 3 feet. Therefore:
V = 3.14 x [tex]3^2[/tex] x 2
= 56.52 cubic feet
Multiplying the volume of the tank by the cost per cubic foot gives us the total cost of filling the tank:
Total cost = 56.52 x $5
= $282.60
Therefore, it would cost $282.60 to fill a tank with a diameter of 6 feet and a height of 2 feet, assuming a cost of $5 per cubic foot and using the value of pi as 3.14.
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e want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately 29.6 . We would like to be 99.5% confident that the estimate is within 1 of the true population mean. How large of a sample size is required?
We need a sample size of at least 879 to be 99.5% confident that our estimate of the population mean will be within 1 of the true population mean.
To determine the required sample size, we use mathematical formula:
[tex]n = (z * σ / E) ^ 2[/tex]
Where:
n: sample size
z: z-score corresponding to desired level of confidence (99.5%)
σ: population standard deviation
E: margin of error (1 in this case)
Substitute given values into formula:
[tex]n = (2.807 * 29.6 / 1) ^ 2\\n = 878.3[/tex]
Hence, in order to be 99.5% confident that our estimate of the population mean would be within 1 of the actual population mean, we need a sample size of at least 879.
It's vital to remember that the estimate will be more accurate the larger the sample size. Larger sample numbers might, however, also be more costly and time-consuming to gather. Hence, while choosing the sample size, researchers must carefully weigh the trade-offs between the required level of confidence, the margin of error, and the resources at their disposal.
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