Answers
The median shows that the average number of students per middle school classroom in both districts is 24, while the mean shows that the average number of students per middle school classroom in one district is 24 and the other is 25.
What is median?Median is the middle value of a set of data. It is the value that divides the data set into two equal halves. It is an important measure of central tendency and is used to compare sets of data.
The difference between the mean number of students per middle school classroom in each school district is 2 students. The difference between the median number of students per middle school classroom in each school district is 0 students.
Based on the number of students shown for each school district, the median would provide the most accurate picture of the number of students in a middle school classroom, as there are some extreme values that would affect the mean but not the median.
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Related Questions
Given
f(x, y) = 2x2 + 2xy + y2 + 2x − 5,
find all points at which
∂f
∂x
= 0 and
∂f
∂y
= 0
simultaneously.
Answers
Answer:
Step-by-step explanation:
To find the critical points of the function f(x,y), we need to find all points where both partial derivatives ∂f/∂x and ∂f/∂y are equal to zero.
We first find ∂f/∂x by differentiating f(x,y) with respect to x and treating y as a constant:
∂f/∂x = 4x + 2y + 2
We then find ∂f/∂y by differentiating f(x,y) with respect to y and treating x as a constant:
∂f/∂y = 2x + 2y
To find the critical points, we need to solve the following system of equations simultaneously:
4x + 2y + 2 = 0
2x + 2y = 0
We can solve the second equation for y:
2y = -2x
y = -x
Substituting this into the first equation, we get:
4x + 2(-x) + 2 = 0
2x + 2 = 0
2x = -2
x = -1
Substituting x = -1 into y = -x, we get:
y = -(-1) = 1
Therefore, the critical point is (-1,1).
To verify that this point is a minimum, we can use the second partial derivative test. We first find the second partial derivatives:
∂²f/∂x² = 4
∂²f/∂y² = 2
∂²f/∂x∂y = 2
The discriminant of the Hessian matrix is:
∂²f/∂x² * ∂²f/∂y² - (∂²f/∂x∂y)² = (42) - (22) = 4
Since the discriminant is positive and the second partial derivative with respect to x is positive, the critical point (-1,1) is a local minimum.
Therefore, the point (-1,1) is the only critical point of the function f(x,y), and it is a local minimum.
An item is regularly priced at $80 . It is on sale for 60% off the regular price. How much (in dollars) is discounted from the regular price
Answers
Find the indicated probabilities. Then determine if the event is unusual. Explain your reasoning.
The probability of winning a game of rock-paper-scissors is 1/3 You play nine games of rock-paper-scissors. Find the
probability that the number of games you win is (a) exactly five, (b) more than six, and (c) less than three.
Answers
The probability that the number of games you win is (a) exactly five, (b) more than six, and (c) less than three will be 0.196, 0.0082 and 0.056 respectively.
How are probabilities defined?
A probability is indeed a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages spanning form 0% to 100% can be used to describe probabilities.
1/3 of players will succeed in a game of rock-paper-scissors. Choose nine games of rock-paper-scissors, and let X represent the number of victories. With n=9 and p=1/3, X has a random variable.
(a) The likelihood of winning all five games in a row is:
P(X=5) = (9 choose 5)(1/3)⁵(2/3)⁴ = 0.196
Depending on the situation, this likelihood might or might not be seen as uncommon because it is neither extremely high nor extremely low.
(b) The probability of winning more than six games is:
P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9)
= [(9 choose 7)(1/3)⁷(2/3)²] + [(9 choose 8)(1/3)⁸(2/3)¹] + [(9 choose 9)(1/3)⁹(2/3)⁰]
= 0.0082
The fact that this likelihood is so low suggests that winning and over six games is exceptional.
(c) The likelihood of winning two or fewer games is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= [(9 choose 0)(1/3)⁰(2/3)⁹] + [(9 choose 1)(1/3)¹(2/3)⁸] + [(9 choose 2)(1/3)²(2/3)⁷]
= 0.056
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A is five times as old as B. after 10 years a will be 3 times as old as B will be then. find their present age
Answers
According to given information, A is 50 years old and B is 10 years old.
What is expression ?In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be evaluated to produce a numerical result or a value.
According to given information :Let's use algebra to solve the problem.
Let A's current age be x, and B's current age be y.
From the problem, we know that:
x = 5y (A is five times as old as B)
x + 10 = 3(y + 10) (After 10 years, A will be 3 times as old as B)
We can use the first equation to substitute x in the second equation:
5y + 10 = 3(y + 10)
Simplifying this equation gives:
5y + 10 = 3y + 30
2y = 20
y = 10
So B is currently 10 years old. We can use the first equation to find A's current age:
x =5y = 5(10) = 50
So A is currently 50 years old.
Therefore, according to given information, A is 50 years old and B is 10 years old.
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√(×2₂ − ×₁)² + (Y₂ − ¥₁)²
11. Using the distance formula
, find the distance from the
center of your habitat to the point (x, y). Write this equation. Your answer will
contain x- and y-terms. (1 point)
Answers
So the equation for the distance from the center of the habitat to the point (x, y) is: Distance = √[(x - x1)² + (y - y1)²].
What is coordinate?A coordinate is a number that indicates the position of a point in a space or plane. In mathematics, we often use a coordinate system to represent points and their positions. A coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the position of a point or an object in a space or plane. The most common coordinate system is the Cartesian coordinate system, which is named after the mathematician René Descartes. In the Cartesian coordinate system, each point is represented by an ordered pair of numbers (x, y), where x is the horizontal coordinate or abscissa, and y is the vertical coordinate or ordinate. The point (0, 0) is called the origin, and it represents the point where the x and y axes intersect. Coordinates can also be expressed in three or more dimensions, using three or more numbers. In three-dimensional space, the coordinates of a point are represented by an ordered triple (x, y, z), where x, y, and z are the horizontal, vertical, and depth coordinates, respectively.
Here,
The distance formula is used to find the distance between two points in a coordinate plane. In this case, we are finding the distance from the center of the habitat (x1, y1) to the point (x2, y2), so the formula becomes:
=√[(x2 - x1)² + (y2 - y1)²]
Substituting the coordinates of the given point (x, y), we get:
=√[(x - x1)² + (y - y1)²]
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You deposit $50,000 into a bank account that earns 2.5% simple interest annually.
How much will be in the account at the end of 4 years?
Answers
Step-by-step explanation:
To calculate the amount of money in the account at the end of 4 years, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
t = Time period (in years)
Plugging in the given values, we get:
I = $50,000 * 0.025 * 4
I = $5,000
This means that over the course of 4 years, the account will earn $5,000 in interest.
To find the total amount in the account at the end of 4 years, we simply add the interest earned to the initial deposit:
Total amount = $50,000 + $5,000
Total amount = $55,000
Therefore, at the end of 4 years, there will be $55,000 in the account if you deposit $50,000 into a bank account that earns 2.5% simple interest annually.
Please help will mark Brainly
Answers
Answer:
B. linear
Step-by-step explanation:
x y
0 9
1 9 + 8
2 9 + 2(8)
3 9 + 3(8)
4 9 + 4(8)
=> linear function
PLEASE HELP FAST!!
Determine the number of solutions to the system of linear equations shown on the graph.
A: No solution
B: Infinitely many solutions
C: One solution at (-3,2)
D:One solution at (2,-3)
Answers
Answer:
the answer is D
both lines intersect at (2, -3)
hope this helps <3
Determining Whether a Point Lies on a Circle
10
8
-10 8-6-4-2
6
4
2
-2
-6
8
-10
Y
2
6 8 10
A circle centered at the origin contains the point
(0, -9). Does (8, √17) also lie on the circle? Explain.
O No, the distance from the center to the point
(8, √17) is not the same as the radius.
O No, the radius of 10 units is different from the
distance from the center to the point
(8. √17).
O Yes, the distance from the origin to the point
(8,√17) is 9 units.
Yes, the distance from the point (0, -9) to the point
(8, √17) is 9 units.
Answers
The correct statement regarding whether (8, √17) lies on the circle is given as follows:
Yes, the distance from the origin to the point (8,√17) is 9 units.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The parameters for this circle are given as follows:
Center (0,0).Radius 9.Hence the equation is given as follows:
x² + y² = 81.
For point (8, √17), we have that:
8² + (√17)² = 81
64 + 17 = 81
81 = 81.
Hence the point lies on the circle.
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Which of the following statements is MOST LIKELY TRUE?
A-The lower half of Sample A's data is closer to the value 5 than the lower half of Sample B's data.
B-Both of the data sets range from 1 to 10 on the number line.
CThe upper half of Sample A's data is closer to the value 10 than the upper half of Sample B's data.
D-The data in Sample B is clustered around the center where Sample A is more spread out
Explain
Answers
Answer:
Step-by-step explanation:
ntroduction to standard deviation
Standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.
For example, the blue distribution on bottom has a greater standard deviation (SD) than the green distribution on top:
Jenelle bought a home for $470,000, paying 18% as a down payment, and financing the rest at 5.4% interest
for 30 years. Round your answers to the nearest cent.
How much money did Jenelle pay as a down payment? $
What was the original amount financed? $
What is her monthly payment? $
If Jenelle makes these payments every month for thirty years, determine the total amount of money she
will spend on this home. Include the down payment in your answer. $
Answers
1- 58000
2- 232000
3- 1245.43
4- 506354.8
Please help meee this is due Friday!!! A fully loaded and fueled spacecraft can weigh close to 5.1 million pounds. What is this weight converted to tons?
Answers
Answer:
A fully loaded and fueled spacecraft weighing 5.1 million pounds is equivalent to 2550 US tons
Step-by-step explanation:
Solve the equation. x2 = 16
Answers
Answer:
I hope that this answers your question!
Which student found the total surface area of a cylinder with a height that was two times greater than its radius?
Answers
The total surface area of a cylinder with a height that was two times greater than its radius is 6πr²
What is the total surface area of a cylinder?The total surface area of a cylinder is the region occupied by the cylinder. It is given by A = 2πr(r + h) where
r = radius of cylinder and h = height of cylinderSince we want to find which student found the total surface area of a cylinder with a height that was two times greater than its radius.
We proceed as follows.
Since we have that the height that was two times greater than its radius. So, for that cylinder, h = 2r
So, to find the surface area, we substitute the values of the variables into the equation for the total surface area.
So, A = 2πr(r + h)
Given that h = 2r, we have that
A = 2πr(r + h)
A = 2πr(r + 2r)
A = 2πr(3r)
A = 6πr²
So, the area is 6πr²
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Giselle wants to buy a condo that has a purchase price of $163,000. Giselle earns $2,986 a month and wants to spend
no more than 25% of her income on her mortgage payment. She has saved up $33,000 for a down payment. Giselle is
considering the following loan option: 20% down, 30 year at a fixed rate of 6.25%. What modification can be made to this
loan to make it a viable option, given Giselle's situation?
a. Change to a 15 year fixed loan
b.
Change the interest to 5.5%
c. Change the down payment to 18% down
d.
None. This is a viable option for Giselle.
Answers
Correct option is B, modification that can be made to this loan to make it a viable option, given Giselle's situation Change the interest to 5.5%.
What modification can be made to this loan to make it a viable option, given Giselle's situation?Giselle may either lower the interest rate to 5.5% or increase the down payment to 18% down in order to make the 20% down, 30-year fixed loan option financially feasible. Giselle's maximum monthly payment of $746.50 is exceeded by the monthly payment for the current loan option. The monthly payment would rise if the loan was shortened to 15 years, rendering it unprofitable. As a result, Giselle should choose a mortgage with a lower interest rate or put more money down in order to bring the monthly payment within her means.
Given Giselle's circumstances, the modification that may be made to this loan to make it an attractive alternative is to raise the interest rate to 5.5%.
Changes to the loan that will be made:
Price of acquisition: $163,000
Monthly income equals $2,986
25% of people are unwilling to spend money.
$33,000 is the down payment.
20% decline rate
Analysis
163,000 less $33,000 is the balance of the loan.
Amount remaining on loan is $130,000.
Condo loan balance = $163,000.20
Condo loan balance = $32,600
Down rate increase equals $163,000 x 20.25%
A higher down payment equals $33,007.50
The optimal solution, based on the research above, is to change the interest rate to 5.5% because it will result in a lower overall payment cost and make the loan amount a viable option.
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PLEASE HURRY!!! I WILL GIVE THE BRAINLIEST!!!
Which answer shows the correct steps to solve the equation
a
Subtract 4 from both sides,, multiply by 12 on both sides, subtract 10 from both sides, and divide both sides by 5 to get x=2/5
b
Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10
c
Subtract 10 from both sides, multiply by 15 on both sides, and divide by 5 to get x=(-18)
d
Subtract 5x from both sides, subtract 10/15 from both sides, and divide both sides by 5 to get x=10
Answers
Answer:
Answer is B
Step-by-step explanation:
Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10
Q. 1 Solve the following In equality 7(x – 2) + x > – 4(5 – x) – 12
Answers
Answ
Step-by-step explanation:
x is equal to -9/2
the day time temperatures recorded over 5 consecutive days in october were 14.6,15.2,15.8,16.1 . find the average temperature
Answers
Answer: 15.54 degrees.
Step-by-step explanation:
To find the average temperature, we need to add up all the temperatures and then divide by the number of days:
Average temperature = (14.6 + 15.2 + 15.8 + 16.1) / 5
= 77.7 / 5
= 15.54
Therefore, the average temperature over the 5 consecutive days in October is approximately 15.54 degrees.
Find the equation of a line that passes through the point (-2,-3) and has a gradient of -3.
Leave your answer in the form
Answers
Answer:
you need to put the answers down
Step-by-step explanation:
.
Suppose that x is normally distributed with a mean of 30 and a standard deviation of 3. What is P(27.42 ≤ x ≤ 34.08)?
Answers
The answer to this question is 0.6826, or 68.26%. To calculate this probability, we need to use the z-score formula.
What is z-score formula?The z-score formula is a statistical measurement that is used to identify how far a raw score is from the mean score of a population. It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.
This formula allows us to convert a given value into a standardized score relative to the mean and standard deviation of the normal distribution. In this case, the z-score for 27.42 is -1 and the z-score for 34.08 is 1.
We can then use the cumulative normal distribution function to calculate the probability of x being between 27.42 and 34.08. This function allows us to calculate the area under the normal distribution curve between two given points. Since the normal distribution is symmetrical, the area under the curve between -1 and 1 is 0.6826 or 68.26%. This is the probability of x being between 27.42 and 34.08.
To summarize, in order to calculate the probability of x being between 27.42 and 34.08, we need to calculate the z-scores of these two values and then use the cumulative normal distribution function to calculate the area under the curve between the two z-scores. The area under the curve between -1 and 1 is 0.6826 or 68.26%, which is the probability of x being between 27.42 and 34.08.
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What is the probability that a resident is male and in the age group 60-79
Answers
Answer:
c. 0.29
Step-by-step explanation:
edge
99 times 3 distributive property
Answers
Answer:
To use the distributive property to solve 99 x 3, we can write it as:
99 x 3 = (90 + 9) x 3 (decomposing 99 as 90 + 9)
= 90 x 3 + 9 x 3 (using distributive property)
= 270 + 27
= 297
Therefore, 99 times 3 using the distributive property equals 297.
Step-by-step explanation:
Fuel wood is measured in cords. The number of cords in a pile l ft long, w ft wide, and h ft tall can be estimated using the equation number of cords=lwh128.
Hannah measures a pile of wood to be 14 ft long by 20 ft wide.
Which equation can be used to determine the number of cords in a pile of wood h ft tall?
Answers
The equation that is used to determine the number of cords in a pile of wood h ft tallis is the number of cords = 280×h×128.
What is an equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical declaration that illustrates the equality of two mathematical expressions.
Given that
The number of cords in a pile l ft long, w ft wide, and h ft tall can be estimated using the equation number of cords=lwh128.
The length of the wood pile is 14 ft and the wide is 20 ft.
The product of length and width is lw = 14×20 = 280 ft².
Putting lw= 280 in the equation number of cords=lwh128:
number of cords = 280×h×128
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How could mean, median, mode, and range be impacted if a value in a data set changed?
Answers
In summary, a change in a value in a data set can have varying impacts on the measures of central tendency and dispersion, depending on the value that was changed and its relationship to the other values in the data set.
Why it is?
The measures of central tendency, such as mean, median, and mode, and the measure of dispersion, range, can be impacted by a change in a value in a data set.
Mean: The mean is calculated by adding all the values in a data set and then dividing by the total number of values. If a value in the data set changes, the sum of the values will change, and thus the mean will also change. The impact of the change on the mean will depend on the value that was changed and how much it differs from the other values in the data set.
Median: The median is the middle value in a data set, when the values are arranged in order. If a value in the data set changes, the position of the median may change, depending on where the new value falls in the order of the values.
Mode: The mode is the value that appears most frequently in a data set. If a value in the data set changes, the mode may change, depending on whether the new value becomes the most frequent value or not.
Range: The range is the difference between the highest and lowest values in a data set. If a value in the data set changes, the range may change, depending on how much the new value differs from the highest or lowest value in the data set.
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Scientist rope off two evacuation sites. Site A is regular with a length of 60 meters and width of 40 meters. Site B is similar in shape to site A but has a length of 45 meters. How much rope is needed for both sites?
Answers
If the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.
What is amount?Amount is a term used to describe the total of something. It can refer to a quantity of money, a number of items, or a measure of any other type of resource. Amounts are typically expressed as a numerical value, and they can be represented in different units depending on the type of resource. For example, an amount of money could be expressed in dollars, whereas an amount of time could be expressed in hours.
To calculate the amount of rope needed for both sites, we will first need to calculate the perimeter of each site. The perimeter of Site A is 180 meters (60 + 40 + 40 + 40) and the perimeter of Site B is 135 meters (45 + 45 + 45).
To calculate the total amount of rope needed for both sites, we will need to add the two perimeters together. The total amount of rope needed for both sites is 315 meters (180 + 135).
It is important to note that 315 meters of rope is the minimum needed to rope off both sites. Depending on the desired spacing between the rope and the sites, the actual amount of rope needed may be greater than 315 meters. Additionally, if the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.
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If the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.
What is amount?Amount is a term used to describe the total of something. It can refer to a quantity of money, a number of items, or a measure of any other type of resource. Amounts are typically expressed as a numerical value, and they can be represented in different units depending on the type of resource. For example, an amount of money could be expressed in dollars, whereas an amount of time could be expressed in hours.
To calculate the amount of rope needed for both sites, we will first need to calculate the perimeter of each site. The perimeter of Site A is 180 meters (60 + 40 + 40 + 40) and the perimeter of Site B is 135 meters (45 + 45 + 45).
To calculate the total amount of rope needed for both sites, we will need to add the two perimeters together. The total amount of rope needed for both sites is 315 meters (180 + 135).
It is important to note that 315 meters of rope is the minimum needed to rope off both sites. Depending on the desired spacing between the rope and the sites, the actual amount of rope needed may be greater than 315 meters. Additionally, if the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.
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ANSWER BELOW PLEASE!!! ASAP THANK YOU^^!
Answers
The equation of the line in slope-intercept form is: y = -25x + 100. A negative slope indicates that the battery percentage is decreasing over time.
Part A:
To write the equation of a line in slope-intercept form, we need to know the slope (m) and y-intercept (b) of the line.
From the given information, we know that the y-intercept is 100 and the x-intercept is 4. This means that after 4 hours, the battery percentage is 0%.
To find the slope, we can use the slope formula:
m = (y2 - y1)/(x2 - x1)
Choosing two points on the line, one being the y-intercept (0,100) and the other being the x-intercept (4,0), we can plug in the values:
m = (0 - 100)/(4 - 0) = -25
Therefore, the equation of the line in slope-intercept form is:
y = mx + b
y = -25x + 100
Part B:
To determine the equation, we used the fact that the y-intercept was 100 and the x-intercept was 4. We then found the slope of the line using the slope formula with two points on the line. Plugging the slope and y-intercept into the slope-intercept form equation y = mx + b gives us the final equation.
Part C:
The slope of the line is -25, which means that for every hour that passes, the battery percentage decreases by 25%. Therefore, the slope represents the rate of change of the battery percentage with respect to time. A negative slope indicates that the battery percentage is decreasing over time.
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What value of n makes the equation true? Show your work.
Answers
Answer:6
Step-by-step explanation:
[tex]\frac{a^{b} }{a^{c}} =a^{b-c} \\a^{b} *a^{c} =a^{b+c}\\ \frac{(-4)^{10}}{(-4)^{n}}=(-4)^{2}*(-4)^{2} \\(-4)^{10-n}=(-4)^{4}\\ 10-n=4\\ -n=-6\\n=6[/tex]
Answer:
n = 6
Step-by-step explanation:
[tex]\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2}*(-4)^{2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2+2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{4}[/tex]
If they have the same base which is -4 we can either add or subtracting the exponent.
Add the exponenet when multiplying.
Subtract the exponent when dividing.
[tex](-4)^{10-n}=(-4)^4\\\\10-n=4\\10=4+n\\n= 6[/tex]
[tex]\frac{(-4)^{10}}{(-4)^{6}}=(-4)^{10-6}=(-4)^4[/tex]
The first three terms of a sequence are given round to the nearest thousandth if necessary.
80,60,45……. Find the 9th term.
Answers
The 9th term of the sequence is approximately 30.234.
What is sequence ?In mathematics, a sequence is an ordered list of numbers or other mathematical objects, such as functions, matrices, or vectors. Each member of the sequence is called a term, and the position of each term in the sequence is identified by its index or subscript.
Looking at the given terms, we can observe that each term is less than the previous term and the difference between consecutive terms is decreasing. Therefore, the sequence is decreasing and the difference between consecutive terms is decreasing by a factor of 2 each time.
Using this pattern, we can find the common difference between consecutive terms as follows:
60 - 80 = -20
45 - 60 = -15
We see that the difference between consecutive terms decreases by a factor of 2 each time. Therefore, the next difference would be:
-15 / 2 = -7.5
So, the next term would be:
45 - 7.5 = 37.5
We can continue this pattern to find the 9th term as follows:
Term 1: 80
Term 2: 60
Term 3: 45
Term 4: 37.5
Term 5: 33.75
Term 6: 31.875
Term 7: 30.9375
Term 8: 30.46875
Term 9: 30.234375
Therefore, the 9th term of the sequence is approximately 30.234.
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A circle has a radius of 21 millimeters.
What is the length of the arc intercepted by a central angle that measures 80°.
Answers
Answer:
Calculate the arc length according to the formula above: L = r * θ = 15 * π/4 = 11.78 cm. Calculate the area of a sector: A = r² * θ / 2 = 15² * π/4 / 2 = 88.36 cm².
Step-by-step explanation:
a block exerts a force of 7nm on the ground. what is the pressure on the ground in nm2 when its flat on the grounds the area of its base is 0.04m2
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The pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is [tex]175 nm^{-2[/tex].
First, we need tο cοnvert the area οf the blοck's base frοm square meters tο square nanοmeters, since the fοrce is given in newtοn-meters (N m) and we want tο find the pressure in newtοn-meters-squared ([tex]N/m^2[/tex] οr[tex]Nm^{-2[/tex]):
[tex]0.04 m^2 = 0.04 \times 10^18 nm^2 (since 1 m = 10^9 nm)[/tex]
Next, we can use the fοrmula fοr pressure, which is:
pressure = fοrce/area
Substituting the given values, we get:
[tex]pressure = 7 N m / 0.04\times 10^{18} nm^2[/tex]
Simplifying this expressiοn, we get:
[tex]pressure = (7 / 0.04) \times 10^{(-9)} N/nm^2[/tex]
[tex]pressure = 175 \times 10^{(-9)} N/nm{^2[/tex]
[tex]pressure = 175 nm^{-2[/tex]
Therefοre, the pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is[tex]175 nm^{-2[/tex].
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