simplest polynomial function with zeroes -2 and 3 is expanded form is f(x) = [tex]x^2 - x - 6[/tex].
To write a polynomial function with given zeros, we can use the factorization method. The zeros of a polynomial function are the solutions of the equation f(x) = 0. So, if we know the zeros of a polynomial function, we can use them to write the function in factored form.
For example, if the zeros of the polynomial function are -2 and 3, we can write the function as:
f(x) = (x + 2)(x - 3)
This function can be expanded into:
f(x) = [tex]x^2 - x - 6[/tex]
It's important to notice that the degree of the polynomial function is determined by the highest exponent of the variable in the equation, in this case 2.
It's also important to notice that the zeroes of the function are -2 and 3, as when you substitute them in the equation, the result is zero.
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The complete question is:
What is the simplest polynomial function with zeroes -2 and 3? Write the equation in the expanded form.
A 3-yard piece of cotton cloth costs $2.61. What is the price per foot?
The price per foot is $0.29
Given,
A 3-yard piece of cotton cloth costs = $2.61
1 Yard = 3 Foot
so, 3 Yard = 9 Foot
The Cost of cotton cloth per foot,
= 2.61/9
= 0.29
Therefore, the price per foot is $0.29
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the length of a rectangle is seven more than triple the width. if the perimeter is 166 inches , find the dimension
Answer:
Width = 3.773 inches
Length = 79.227 inches-
Step-by-step explanation:
g = 7(3w) Eq. 1
166 = 2(g+w) Eq. 2
g = length
w = width
From Eq, 1:
g = 21w Eq. 3
Replacing Eq. 3 in Eq. 2
166 = 2(21w + w)
166 = 2(22w)
166 = 44w
166/44 = w
w = 3.773
From Eq. 3
g = 21(3.773)
g = 79.227
Check:
From Eq. 2:
166 = 2(79.227 + 3.773) = 2 * 83
The random variable K has a geometric distribution with mean 16. Which of the following is closest to the standard deviation of random variable K ?a. 0.0625b. 0.9375c. 4d. 15.49e. 240
The standard deviation of random variable K is 15.49 (option D ) and this can be determined by using the formula of mean and standard deviation.
Given,
The mean of geometric distribution of random variable K = 16
Formulae for finding mean,
mean = 1/p
Substitute the value of the mean in the above formula in order to determine the value of 'p'.
[tex]16 =\frac{1}{p}[/tex]
[tex]p = 0.0625[/tex]
The formulae for standard deviation :
S.D.=[tex]\frac{\sqrt{1-p} }{p}[/tex]
Now substitute the value of p in the above equation,
S.D. [tex]= \frac{\sqrt{1-0.0625} }{0.0625}[/tex]
[tex]= 15.49[/tex]
Hence, the answer is option D.
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A florist divided f flowers equally among 6 vases. Choose the expression that shows how many flowers were in each vase.
Answer:
42 divided by 6=7 so in each vase there are 7 flowers
Step-by-step explanation:
The measure of a base angle of an isosceles tri-
angle is 13 more than 3 times the measure of the
vertex angle. How many degrees are in the vertex
angle?
The vertex angle of the isosceles triangle is 22°.
What is isosceles triangle?
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
We know that an isosceles triangle is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180degrees.
Base angle = 3vertex angle+13.
=> 2base angle + vertex angle = 180°
=> 2(3 vertex angle +13)+vertex angle = 180°
=> 6 vertex angle+26+vertex angle = 180
=> 7 vertex angle = 180-26
=> 7 vertex angle = 154
=> vertex angle = 154/7 = 22°.
Hence the vertex angle of the isosceles triangle is 22°.
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Atmospheric pressure P
in pounds per square inch is represented by the formula P=14.7e−0.21x
, where x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 8.164 pounds per square inch? (Hint: there are 5,280
feet in a mile)
The mountain is ___ feet high?
The peak of the mountain has a height of 14805 feet.
How to determine the height of a mountain according to atmospheric pressure model
In this problem we find the case of an exponential function for atmospheric pressure (p), in pounds per square inch, in terms of height (x), in miles, whose expression is introduced below:
[tex]p(x) = 14.7 \cdot e^{- 0.21\cdot x}[/tex], for x ≥ 0.
If we know that p(x) = 8.164 lb / in², then the height of the peak of a mountain is:
[tex]8.164 = 14.7\cdot e^{-0.21 \cdot x}[/tex]
[tex]0.555 = e^{-0.21\cdot x}[/tex]
Then, by relationship between exponential and logarithmic functions and logarithm properties:
㏑ 0.555 = - 0.21 · x · ㏑ 1
㏑ 0.555 = - 0.21 · x
x = - (1 / 0.21) · ㏑ 0.555
x ≈ 2.804
Finally, convert miles into feet:
x = 2.804 mi × (5,280 ft / 1 mi)
x = 14805.12 ft
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Help pls it’s imaginary numbers
Answer:
Why don't you use this app and take a picture and see if someone got the answer
I need help, please, I didn't understand you very well.
Answer:
30
Step-by-step explanation:
Answer: 30
Step-by-step explanation:
Use Pythagorean theorem a^2 + b^2 = c^2:
18^2 + 24^2 = c^2
324 + 576 = c^2
900 = c^2
c = 30
Given that the expression f(x)=2x³+px² 8x+q is exactly divisible by 2x²-7x+6, evaluate p and q and factorise completely
The values of p and q are given as follows:
p = 3.5, q = 6.
Hence the factored expression is given as follows:
2(x - 1.5)(x - 2)(x + 2).
How to obtain the values of p and q and factor the function?The function f(x) is divisible by 2x² - 7x + 6, which has the roots given as follows:
x = 1.5 and x = 2.
(using a quadratic equation calculator with coefficients a = 2, b = -7 and c = 6).
Hence the following relation holds true, considering the linear factors of the function:
2x³ + px² + 8x + q = 2(x - 1.5)(x - 2)(x - a).
In which a is the third root.
Hence:
2x³ + px² - 8x + q = 2(x² - 3.5x + 3)(x - a)
2x³ + px² - 8x + q = 2(x³ - x²(3.5 + a) + x(3.5a + 3) - 3a)
2x³ + px² - 8x + q = 2x³ - x²(7.5 + 2a) + x(7a + 6) - 3a.
Hence the system of equations is given as follows:
p = 7.5 + 2a.7a + 6 = -8.q = -3a.From the second equation, the value of a is given as follows:
7a = -14
a = -2
Then the value of q is given as follows:
q = -3a = 6.
The value of p is given as follows:
p = 7.5 - 4
p = 3.5
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evaluate the functions at 0, -2, and 1. f (x )equals x cubed minus 3 x squared plus 4
The functions are 0, -2 and 1 for the mentioned function is 4, - 16 and 2.
Firstly we will represent the function in equation form. Then we will calculate the result by keeping each value of function.
f(x) = x³ - 3x² + 4
Calculating result when function is 0
f(x) = 0³ - 3×0² + 4
f(x) = 0 - 0 + 4
f(x) = 4
Calculating result when function is -2
f(x) = (-2)³ - 3×(-2)² + 4
Finding square and cube
f(x) = -8 - 3×4 + 4
Performing multiplication
f(x) = - 8 - 12 + 4
Performing addition
f(x) = - 20 + 4
Performing subtraction
f(x) = - 16
Calculating result when function is 1
f(x) = 1³ - 3×1² + 4
f(x) = 1 - 3 + 4
Performing addition
f(x) = 5 - 3
Performing subtraction
f(x) = 2
Thus, functions are 4, -16 and 2.
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you have 10 bags full of coins. in each bag are infinite coins. but one bag is full of forgeries, and you can't remember which bag. but you do know that genuine coins weigh 1 gram, but forgeries weight 1.1 grams. you have to identify the bag with the forgeries in minimum readings. you are provided with a digital weighing machine.
If there are no forgeries, then total weight will be
= (1+2+3+4+5+6+7+8+9+10) = 55 grams
given that
they have 10 bags full of coins
in each bag are infinite coins.
but one bag is full of forgeries, and you can't remember which bag.
you know that genuine coins weigh= 1 gram
forgeries weight = 1.1 gram
now, we need to find which bag has forgeries in minimum readings
then take 1 coin from the first bag, 2 coins from the second bag . . . 10 coins from the tenth bag
If there are no forgeries, then total weight will be
= (1+2+3+4+5+6+7+8+9+10) = 55 grams
Therefore total weight should be 55 grams if the total weight is more than 55 grams then it has forgeries coins
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Total weight=55gm ,then there is no forgeries coin bag
1 bag with forgeries = take 1 coin from first bag
from 2 bag = take 2 coin
and similarly with all 10 bags.....
from 10th bag = take 10 coin
if there is no forgeries ,then total weight = (1+2+3+4+5+6+7+8+9+10)
=55gm
If bag weight 55.3 than we know that there are 3 forgeries.
So total weight=55 ,then there is no forgeries coin bag if weight is more than 55 than there is forgeries coin.
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which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?
The potential energy of the spring-mass system is equal to 1/2kx². Thus, figure I is a correct representation.
where x is the mass's deviation from the average location, or O.
Consequently, the graph would be symmetric about a vertical line that passes through O and would exhibit a quadratic variation with respect to x.
Thus, figure I is a correct representation.
The graph illustrates how the potential and kinetic energy of a block coupled to a spring that follows Hooke's law changes over time.
Due to the potential and kinetic energy's x2 variation, both graphs are parabolas.
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graphing y ≥ |x| - 4?
The graph for the given mode function, y ≥ |x| - 4 is attached below.
What is a modulus function?In mathematics, the modulus function is a function for which any input value of x, output will be always positive
Given that,
The modulus function,
y ≥ |x| - 4
We can write given function in a following two ways-
y ≥ x - 4
y ≥ -x - 4
So, for any value of x
y should be greater than modulus functions value
Plotting graph for y ≥ x - 4
So first draw line x - 4
Now, here we have inequality sign
So left side region will be our desired space
Similarly, Plotting graph for y ≥ -x - 4
So first draw line -x - 4
Now, here we have inequality sign
So right side region will be our desired space
Hence, Graph is drawn for the given function
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what is the slope through the line of (5, -6) and (2, 3)
Hello:
--> this problem wants us to calculate the slope between (5, -6) and (2, 3)
So we are given two points:
--> (x1, y1): (5, -6)
--> (x2,y2): (2, 3)
Let's consider our formula needed:
[tex]\text{Slope} = \dfrac{y2-y1}{x2-x1}=\dfrac{3--6}{2-5} =\dfrac{9}{-3} =-3[/tex]
Thus our slope is -3
Answer: -3
An ice cream cone with a 2cm radius has a volume of 75.36 cubic cm how tall is the ice cream cone
Step-by-step explanation:
reading the question thoroughly, we find out that volume (V) and radius (r) of the cone is given, and we just have to find out the length (h) of the cone
V = πr²h/3
Putting the given values in place,
V = 75.36 cm³
V = 75.36 cm³r = 2 cm
V = 75.36 cm³r = 2 cmπ = 3.14
Now, since we calculating for h, we can interpret the formula in the terms of h, i.e.
h = 3V/(πr²)
h = 3×75.36/(3.14×2²)
h = 226.08/12.56
h = 18 cm
Thus, the height of the ice cream cone is 18cm
Hope this helped!
Felipe has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Answer: 20 different total voting combination
Step-by-step explanation: So we have 5 bands. Lets called them A, B, C, D, and E.
If John has to vote on his favorite and second favorite that means we will be selecting 2 bands out of the 5 possible to choose from.
To find the TOTAL amount of different combinations we need to pair up bands and find all the combo's.
Here are the results/totals:
AB
AC
AD
AE
BA
BC
BD
BE
CA
CB
CD
CE
DA
DB
DC
DE
EA
EB
EC
ED
So this is 20 different total voting combinations.
If you want to do it simpler without listing you can take the the 5 bands and multiple by 4 since you know each initial band (A, B, C, D, and E) will be paired with another band other than itself.
during the first four summer olympic games attended by the united states, these medal counts were awarded. calculate the mean number of medals won during these olympic games. (round it to the nearest whole number.)
The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.
1904: 78 medals
1908: 82 medals
1912: 88 medals
1920: 94 medals
Mean = 86 medals
1. Add the total number of medals awarded to the US during the first four summer Olympic Games: 78 + 82 + 88 + 94 = 342
2. Divide the total number of medals by the number of Olympic Games (4): 342 / 4 = 85.5
3. Round the mean to the nearest whole number: 86 medals
The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.
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Justin has a savings account.
• He started with $50 in his account.
• He deposits $12 into the account each week.
• Let b represent the amount Justin has in the bank after w weeks.
Which equation can be used to determine the total amount in Justin's account?
Answer: The equation that can be used to determine the total amount in Justin's account is:
b = 50 + (12 * w)
This equation represents the total amount in Justin's account, b, after w weeks. The equation starts with the initial amount, $50, which is the amount Justin had in his account before making any deposits. Then, it adds the amount deposited each week, $12, multiplied by the number of weeks, w. This results in the total amount in the account after w weeks.
In this equation the variable "w" represents the number of weeks that have passed and "b" represents the total balance.
Step-by-step explanation:
It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear .Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear:1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et2. t2(d2y/dt2)+t(dy/dt)+2y=sin t3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t34. y''-y+y2=0You have 10 choices to choose for each problem:a. 1st. order linear differential equationb. 2nd. order linear differential equationc. 3rd. order linear differential equationd. 4th. order linear differential equatione. 5th. order linear differential equationf. 1st. order non-linear differential equation=g. 2nd. order non-linear differential equationh. 3rd. order non-linear differential equationi. 4th. order non-linear differential equationf. 5th. order non-linear differential equation
The coefficient of the second derivative (t2) is constant, so the equation is linear.
1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et2 -> 2nd. order non-linear differential equation
2. t2(d2y/dt2)+t(dy/dt)+2y=sin t -> 2nd. order linear differential equation
3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t3 -> 3rd. order non-linear differential equation
4. y''-y+y2=0 -> 2nd. order non-linear differential equation
The order of a differential equation is the highest derivative involved in the equation. For example, in the equation 1 + y2(d2y/dt2) + t(dy/dt) + y = et2, the highest derivative is the second derivative (d2y/dt2), so this equation is of 2nd order. Linearity is determined by whether the coefficients of each derivative are constants, or whether they depend on the function y and its derivatives. In this equation, the coefficient of the second derivative (1+y2) is not constant, so the equation is non-linear. Similarly, in equation t2(d2y/dt2)+t(dy/dt)+2y=sin t, the coefficient of the second derivative (t2) is constant, so the equation is linear.
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to help tyler identify the heights of the peaks, write down what you know about each peak from the first page of this activity (3 points: 1 point for each completed row).
The heights and locations of the three peaks in this activity are: Peak 1 is 4,064 meters (13,320 feet) and located in Ladakh, India; Peak 2 is 8,848 meters (29,029 feet) and located in Nepal; and Peak 3 is 8,611 meters (28,251 feet) and located in Pakistan.
Peak 1: Height: 4,064 m (13,320 ft), Location: Ladakh, India
Peak 2: Height: 8,848 m (29,029 ft), Location: Nepal
Peak 3: Height: 8,611 m (28,251 ft), Location: Pakistan
Peak 1: Height: 4,064 m (13,320 ft), Location: Ladakh, India
This means that the height of Peak 1 is 4,064 meters (13,320 feet) and it is located in Ladakh, India.
Peak 2: Height: 8,848 m (29,029 ft), Location: Nepal
This means that the height of Peak 2 is 8,848 meters (29,029 feet) and it is located in Nepal.
Peak 3: Height: 8,611 m (28,251 ft), Location: Pakistan
This means that the height of Peak 3 is 8,611 meters (28,251 feet) and it is located in Pakistan.
The heights and locations of the three peaks in this activity are: Peak 1 is 4,064 meters (13,320 feet) and located in Ladakh, India; Peak 2 is 8,848 meters (29,029 feet) and located in Nepal; and Peak 3 is 8,611 meters (28,251 feet) and located in Pakistan.
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We want to find how the volume. V. of a balloon changes as it is filled with air. We know V(r)=4/3 πr^3, wherer is the radius in inches and V(r) is in cubic inches. The expression v(3)-v(1)/3-1 represents (a) The average rate of change of the radius with respect to the volume when the radius changes from 1 inch to 3 inches. (b) The average rate of change of the radius with respect to the volume when the volume changes from 1 cubic inch to 3 cubic inches. (c) The average rate of change of the volume with respect to the radius when the radius changes from 1 inch to 3 inches. (d) The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches.
Option D is the correct answer that is The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches.
The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches is represented in v(3)-v(1)/3-1.
The difference in volumes is
V(r+3) - V(r) = 4π [tex](r+3)^{3}[/tex] /3 - 4π [tex]r^3}[/tex]/3
= 4π/3( (r+3)[tex]^{3}[/tex] - [tex]r^{3}[/tex])
= 4π/3( [tex]r^{3}[/tex]+ 9[tex]r^{2}[/tex]+ 27r + 27 - r∧3 )
= 4π/3(9 [tex]3^{3}[/tex] + 27r + 27 )
= 12π( [tex]r^{2}[/tex]+ 3r + 3 ) in cube
A balloon is a sphere shape. A sphere is a solid figure where each endpoint is equidistant from the center. It is like a 3-Dimensional version of a circle shape. The volume of a sphere is 4/3πr∧3 and its surface area is 4πr∧2. Here r is the radius of the sphere.
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skee ball refer to exercise 4. make a histogram of the probability distribution. describe its shape.
Ten to fifty is the range of the scores. The most frequent result is a 10 with a right-skewing bias.
Probability histogram
The height of each bar must be equal to the probability, the width of each bar must be the same, and the bars must be centered on the amount of money gathered.
The distribution is skewed to the right because the highest bar in the histogram is to the left and there is a tail of lower bars to its right.
The most frequent score is 10 due to the fact that the top bar in the histogram is centered at 10.
The result is:
Ten to fifty is the range of the scores.
The most frequent result is a 10 with a right-skewing bias.
Ten to fifty is the range of the scores.
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determine the number of cycles per day and the production quantity per cycle for this set of vehicles: product daily quantity a 18 b 16 c 6 d 14 click here for the excel data file use the sequence a-b-c-d.
The number of cycles per day and the production quantity per cycle.
Number of cycles per day = (Product Daily Quantity/Production Quantity per Cycle)
For Product A:
Number of cycles per day = (18/Production Quantity per Cycle)
For Product B:
Number of cycles per day = (16/Production Quantity per Cycle)
For Product C:
Number of cycles per day = (6/Production Quantity per Cycle)
For Product D:
Number of cycles per day = (14/Production Quantity per Cycle)
Using the data from the excel file, we can calculate the production quantity per cycle and the number of cycles per day.
For Product A:
Production Quantity per Cycle = 18/3.75 = 4.8
Number of cycles per day = 3.75
For Product B:
Production Quantity per Cycle = 16/2.5 = 6.4
Number of cycles per day = 2.5
For Product C:
Production Quantity per Cycle = 6/1.5 = 4
Number of cycles per day = 1.5
For Product D:
Production Quantity per Cycle = 14/2.25 = 6.2
Number of cycles per day = 2.25
Therefore, for this set of vehicles, the number of cycles per day and the production quantity per cycle are as follows:
Product A: 3.75 cycles per day, 4.8 units per cycle
Product B: 2.5 cycles per day, 6.4 units per cycle
Product C: 1.5 cycles per day, 4 units per cycle
Product D: 2.25 cycles per day, 6.2 units per cycle
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refer to the above table. if the consumer buys both product x and product y, how much will the consumer buy of each in order to maximize utility?
If the consumer buys both product X and product Y, the consumer buy of each to maximize utility will be 3X and 4Y.
Product X Product Y
Quantity MUx Quantity MUy
1 32 1 24
2 28 2 20
3 24 3 16
4 20 4 12
5 16 5 8
If the consumer can only buy product X, consumer buy and the total utility will be 5X and 120.
If the consumer buys both product X and product Y, the consumer buy of each to maximize utility will be 3X and 4Y.
When the consumer purchases the utility-maximizing
combination of product X and product Y, total utility will be 156.
A consumer is in equilibrium and is spending income in such a way that the marginal utility of product X is 40 units and Y is 16 units. The unit price of X is $5. The price of Y is: $2 per unit.
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The complete question is :
Based on the table below showing the marginal utility schedules for product X and product Y for a hypothetical consumer. The price of product X is $4 and the price of product Y is $2. The income of the consumer is $20. how much will the consumer buy of each in order to maximize utility?
Help pls! The question is in the the photo.
Step-by-step explanation:
after mixing 1 can of concentrate and 3 cans of water, we will have 4 cans of juice.
the volume of 1 can is (as for any cylinder or regular 3D object)
base area × height
for a cylinder the bar area is the area of a circle
pi×r²
r is the radius, which is half of the diameter.
in the picture it is not fully clear what is 2.25 in long : the diameter of the radius ?
I suspect it is the diameter.
so, the radius of our cans is 2.25/2 = 1.125 in
the volume of 1 can is
pi×1.125²×4.25
and the volume of all 4 cans of juice is then
4×pi×1.125²×4.25 = 17×3.14×1.265625 = 67.5590625 in³
≈ 68 in³
so, your answer is 68.
during the last 3 years consolidated oil company expanded its gasoline stations into convenience food stores (cfss) in an attempt to increase total sales revenue. the daily sales (in hundreds of dollars) from a random sample of 10 weekdays from one of its stores are:
One kind of average is the mean. It is calculated by dividing the total number of values in a list of values, such as measurements or numbers, by the total number of values in the list.
What is the mean in maths?There are various mean types in mathematics, particularly in statistics. Each mean helps to summarise a certain set of data, frequently to help determine the overall significance of a specific data set.The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.Only numerical variables—regardless of whether they are discrete or continuous—can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.Given data :
a ) Mean =
x = [tex]\frac{\left \{ {{i=10} \atop {i=1}} \right.}{n} Xi[/tex] = 101 / 10 = 10.1 hundreds of dollars
The median is the 50th percentile To determine the location index for the median (2nd
quartile (p =50) we do the following:
The index is
i = [tex]\frac{p}{100}[/tex] (n) = [tex]\frac{50}{100}[/tex] (10) = 5 integer
Since the index, 5, is an integer, the 2nd quartile is determined by finding the average of
the 5th and 6th values from the lower or higher end of the sorted data. This is:
Median = [tex]Q_{2}[/tex] = [tex]\frac{10 + 11}{2}[/tex] = 10.5 hundreds of dollar
Mode = most frequently occurring observation = 11 hundreds of dollars ( two times )
Here i attached graph
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"
el cociente de 5 y un número
Using Algebraic Expressions, The ratio of any two numbers is five: 5/x
What is algebra?Many students find algebra intimidating since it's the first math course they take where they have to deal with variables, abstract ideas, and problem-solving skills. Additionally, not enough is frequently done in the classroom to relate algebra to students' daily lives and explain why it is important to comprehend.
We take into consideration a number "x" for the algebraic expression.
Two numbers are divided to produce the quotient. The ratio between five units and any number "x" is what we have here.
a mathematical expression
Quantile = 5/x
We will get various quotient outcomes depending on the value we provide to the variable "x."
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Full question"
The ratio of 5 between any number.
Triangle ABC has sides that are 6 cm and 11 cm.The third is represented by the inequality 5 < ×
if Triangle ABC has sides that are 6 cm and 11 cm. The third is represented by the inequality 5 < 17.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that Triangle ABC has sides that are 6 cm and 11 cm
The third is represented by the inequality 5 < ×.
We know that the sum of sides of a triangle must be greater than the third side.
5<6+11
5<17
Hence, if Triangle ABC has sides that are 6 cm and 11 cm. The third is represented by the inequality 5 < 17.
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Tamela compared the rates of three cable companies. TV Watchers—$30.80 for 70 channels Tel-EVision—$46.40 for 145 channels Channels Galore—$40.80 for 120 channels Which cable company has the best rate of price per channel?
The cable company with the best rate of price per channel is
Tel-EVision.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
TV Watchers—$30.80 for 70 channels.
The unit rate.
= 30.80/70
= 0.44
Tel-EVision—$46.40 for 145 channels.
The unit rate.
= 46.40/145
= 0.32
Channels Galore—$40.80 for 120 channels
The unit rate.
= 40.80/120
= 0.34
Thus,
Tel-EVision cable company has the best rate of price per channel.
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Mid topic checkpoint chapter 4 for questions 3,and 4
Equation that represents the Marks and study hours of Adams is y = 7.5x + 60.
What is Linear equation?A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given a linear regression graph that has a linear equation.
Slope intercept form of a line
y = mx + c
where,
m is the slope
c is the y-intercept(Where x is zero)
In our case,
y-intercept = 60
Thus, the equation of line will be:
y = mx + 60
Coordinates of the line are given (4, 90). So, these points will Satisfy the equation.
90 = 4*m + 60
4.m = 30
m = 7.5
Thus, equation of the line will be:
y = 7.5x + 60
Adam's test score after studying for 6 hours:
y = 7.5 * 6 + 60
y = 45 + 60
y = 105
therefore, Equation that represents the Marks and study hours of Adams is y = 7.5x + 60.
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