No, it is not safe to stop the addition of terms when their magnitude falls below s, even if the desired absolute error is less than e.
This is because the magnitude of the terms in the series may not decrease monotonically, and there may be large fluctuations in the magnitudes of the terms.
Therefore, it is necessary to use convergence tests, such as the ratio test or the root test, to determine if the series converges absolutely.
For the series ∑ (0.99)^n, we can use the ratio test to check for absolute convergence:
lim (n → ∞) |(0.99)^(n+1)/(0.99)^n| = 0.99 < 1
Since the limit is less than 1, the series converges absolutely. However, we cannot simply stop adding terms when their magnitude falls below a certain value s, as the magnitude of the terms in the series may not decrease monotonically.
Instead, we need to use the convergence test to determine the number of terms required to achieve the desired absolute error e.
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For a project in her Geometry class, Madeline uses a mirror on the ground to measure the height of her school building. She walks a distance of 9.45 meters from the building, then places a mirror flat on the ground, marked with an X at the center. She then walks 2.75 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the school clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.55 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
Madeline's school building model is 5.33 meter.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, Madeline walks a distance of 9.45 meters from the building, then places a mirror flat on the ground, marked with an X at the center.
Use corresponding parts of similar triangles.
Madeline's eyes height/Madeline's distance from x = Buildings height/Buildings distance from X
1.55/2.75 = x/9.45
2.75x=1.55×9.45
2.75x=14.6475
x=14.6475/2.75
x=5.33
Therefore, Madeline's school building model is 5.33 meter.
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Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree to the nearest hundredth of a meter will be 6.40 meters.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.
Let h be the height of the tree in meters. Then, based on the similar triangles formed by Ethan, his shadow, the tree, and its shadow, we have:
h / x = Ethan's height/distance to Ethan's feet from the tree
and
h / (x + 28.45) = Ethan's height/distance to Ethan's feet from the tip of the shadows
where x is the length of Ethan's shadow in meters. We can solve for x using the first equation as follows:
x = (Ethan's height/distance to Ethan's feet from the tree) * h
Substituting the given values, we get:
x = (1.85 / 24.3) x h = 0.076 x h
We can now substitute this value of x into the second equation and solve for h:
h / (0.076 x h + 28.45) = 1.85 / 24.3
Multiplying both sides by 0.076h + 28.45, we get:
h = (1.85 / 24.3) x (0.076h + 28.45)
Expanding the right side and simplifying, we get:
h = 0.070 x h + 5.95
Subtracting 0.070h from both sides, we get:
0.930h = 5.95
Dividing both sides by 0.930, we get:
h = 6.40 meters (rounded to the nearest hundredth)
Therefore, the height of the tree is approximately 6.40 meters.
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convert the percent to a decimal: according to the local weather report, the probability of rain in boston on february 9 is 78%
Convert the percent to a decimal: according to the local weather report, the probability of rain in Boston on February 9 is 78% is 0.78%.
What is probability?Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability theory is used to study random phenomena, such as the outcome of a coin toss or the results of an election. It is also used to make predictions about the future, such as whether it will rain tomorrow.
The probability of choosing a student selected for the AP math class is 13/40 (6 girls and 7 boys selected for the AP math class). Therefore, the probability of choosing a boy or a student selected for the AP math class is 32/40 (19 boys plus 13 students selected for the AP math class out of 40 students).
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The complete question is: According to the local weather report, the probability of rain in Boston on February 9 is 78%. What is 78% converted to a decimal?
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = e^x, x = 0, y = 3Pie; about the x-axis V =
The x-axis V is if cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis is 488.061745.
V = π/2 [18π² ln[3π] - 9π² + 1]
v = 488.061744630
Volume of the region is V = 488.061745.
The area of a thin cylindrical shell with height dr and radius f(x), where f(x) is the equation of the boundary curve, needs to be integrated over the range of x in order to get the volume produced by rotating a region about the y-axis using the cylindrical shell method.
Here, the interval's lower and higher boundaries are denoted by the letters a and b, while the boundary curve's equation is written as f(x). To acquire the volume, the integration must be run across the specified time frame.
The basic idea behind the cylindrical shell method is to build a series of cylindrical shells by wrapping the area around the y-axis, measure the volume of each shell, and then add all the volumes to get the total volume.
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When the level of confidence decreases, the margin of error
a. Stays the same
b. Becomes smaller
c. Becomes larger
d. Becomes smaller or larger, depending on the sample size
When the level of confidence decreases, the margin of error c. Becomes larger
The margin of error is a gauge of how uncertain a sample-based estimate is. It is impacted by the sample size and level of confidence and shows the potential difference between the estimate and the true population value. The user selects a level of confidence, which is commonly given as a percentage, when we want to generate a confidence interval for a population parameter, such as a mean or proportion. By selecting a degree of confidence of 95%, for instance, we are expressing our confidence that the true population parameter falls inside the interval.
Based on the level of confidence, and sample size the margin of error is determined. In order to account for greater uncertainty, a higher level of confidence necessitates a bigger margin of error, whereas a lower level of confidence necessitates a smaller margin of error. As a result, the margin of error rises as the level of confidence declines, indicating a wider range of values within which the true population parameter is expected to fall.
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I need to find the length of JU, Triangle JTU is similar to JLK.
The measure of the side JU of the triangle will be 24 units.
Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.
Given that the two triangles ΔLKJ and ΔTUJ are similar. The sides LK 96 and the side JK = 64. The side JU = -4 + 4x and JT = 27.
From the similarity property, the length of the segment JU will be calculated as:-
LK / TU = JK / JU
96 / 36 = 64 / ( -4 + 4x )
96( -4 + 4x ) = 36 x 64
-384 + 384x = 2304
384x = 2688
x = 7
The value of JU will be,
JU = -4 + 4x
JU = -4 + 4 x 7
JU = -4 + 28
Ju = 24
Therefore, the length of JU will be 24 units.
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What is the solution, if any, to the inequality |3x| >=0?
Answer:
Step-by-step explanation:
The inequality |3x| >= 0 simply states that the absolute value of 3x must be greater than or equal to zero.
Since the absolute value of any number must always be non-negative, this inequality is always true. That means any real number x satisfies the inequality |3x| >= 0.
Therefore, the solution to the inequality |3x| >= 0 is x ∈ R, where R represents the set of all real numbers.
The average height and average weight of five students are presented in the table. Height (in cm) Weight (in kg) Student 1 172 62 Student 2 173 65 Student 3 175 64 Student 4 176 66 Student 5 177 65 The calculation for the correlation, r, for this set of five students is __________. Answer choices are rounded to the hundredths place.
The correlation coefficient for this set of five students is approximately 0.95.
How to calculate the correlation coefficient (r) for this set of data.
First we can use the formula:
r = [nΣ(xy) - ΣxΣy] / [√{nΣx^2 - (Σx)^2} √{nΣy^2 - (Σy)^2}]
Where
n is the sample size Σ represents the sum x and y are the variables of interest (in this case, height and weight)xy represents the product of x and y for each observationUsing the values given in the table, we can calculate the necessary sums and products:
n = 5
Σx = 173 + 172 + 175 + 176 + 177 = 873
Σy = 62 + 65 + 64 + 66 + 65 = 322
Σx^2 = 173^2 + 172^2 + 175^2 + 176^2 + 177^2 = 150367
Σy^2 = 62^2 + 65^2 + 64^2 + 66^2 + 65^2 = 20410
Σ(xy) = (172)(62) + (173)(65) + (175)(64) + (176)(66) + (177)(65) = 56209
Plugging these values into the formula for r, we get:
r = [5(56209) - (873)(322)] / [√{5(150367) - (873)^2} √{5(20410) - (322)^2}]
Simplifying the numerator and denominator:
r = [281045 - 280506] / [√{5(150367) - (873)^2} √{5(20410) - (322)^2}]
r = 0.95 (rounded to the hundredths place)
Therefore, the correlation coefficient for this set of five students is approximately 0.95.
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A pie chart should always show both the sum of all the pie pieces along with the data that comprise the pie slices.
True or False
The ideal pie charts should always show both the sum of all the pie elements along with the data that constitute the pie slices. Thus the statement in the question is true.
The circle diagram, often known as a pie chart, pie chart, or pie chart, is used to depict qualitative or discrete information. It is used to display the percentage of each variable's values' constituent parts.
To do this, divide the circle into sections proportionate to the relative frequency. Recognize the area of the circle that corresponds to each possible value of the variable as a component. It is characterized as an "exploded cake graph" because it divides the graph into its many components in order to shift one of the portions.
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which of the following is the warmest temperature?
5oF above zero, 6oF below zero, 10oF below zero 2oF above zero
Answer: 50 above zero
Step-by-step explanation:
[tex]\sqrt{8} \sqrt{3}[/tex]
We can write the equivalent value of the root expression √8√3 as 2√6.
What is square root of a number?The square root of a number is given by -
y = √x
y² = x
More specifically, we can write -
y = ± √x
Given is the root expression as -
√8√3
We can solve the expression as by finding the square roots of the numbers as -
√8√3 = √8 x √3
√8√3 = √(2 x 2 x 2) x √3
√8√3 = 2√2 x √3
√8√3 = 2√6
So, we can write that -
√8√3 = 2√6
Therefore, we can write the equivalent value of the root expression √8√3 as 2√6.
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let s(t) be the position of a particle in meters after t seconds. give the best approximate for the instantaneous velocity at 8 seconds. use this to approximate the position of the particle aftter 10 seconds.
The instantaneous velocity of the particle at 8 seconds is approximately the change in position over the change in time, or[tex]s(8+Δt) - s(8) / Δt[/tex]. If we use Δt = 0.1, then the instantaneous velocity is approximately s(8.1) - s(8) / 0.1. The approximate position of the particle after 10 seconds is then s(8) + (10-8) * (s(8.1) - s(8) / 0.1).
The instantaneous velocity of a particle is defined as the change in position over the change in time. This can be represented by the equation [tex]s(t+Δt) - s(t) / Δt[/tex]. Here, s(t) is the position of the particle at time t, and t is a small change in time. To approximate the instantaneous velocity at 8 seconds, we can use Δt = 0.1. This gives us an equation of s(8+0.1) - s(8) / 0.1. This equation gives us the velocity at 8 seconds. To approximate the position of the particle after 10 seconds, we can use the equation s(8) + (10-8) * (s(8.1) - s(8) / 0.1). This equation gives us an approximate position of the particle after 10 seconds, using the change in position over the change in time. This equation gives us a good approximation of the position of the particle after 10 seconds, given the information about the particle's position at 8 seconds.
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The Browns are moving across the country. Mr. Brown leaves 5 hours before Mrs. Brown. If he averages 50mph and she averages 90mph , how many hours will it take Mrs. Brown to catch up to Mr. Brown?
It takes Mrs. Brown 6 hours and 15 minutes to catch up to Mr. Brown.
What does average speed refer to?
The entire distance travelled by the object in a specific amount of time is its average speed.
What is a mile?
A common unit of measurement is the mile. It is typically used to describe the length of rivers, highways, and distances between cities. The unit mile is represented by the letter "mi."
Mr. Brown departs at 50 mph five hours early, giving him a 250mile head start.
So:
50n+250=90n
40n=250
n=6.25 hours after Mrs. Brown leaves before she overtakes Mr. Brown.
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A grocery store bought milk for $2.90 per half gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 14 half gallons. If the remaining milk is sold for $3.94 per half gallon, how many half gallons did the store buy if they made a profit of $46.76 ?
If the remaining milk is sold for $3.94 per half gallon, then the store initially bought 26 half gallons of milk for the profit of $46.76
What is meant by profit?
Profit is the term used to describe the financial gain experienced when the revenue from a company activity outpaces the costs, costs, and taxes incurred to support the activity in question.
Profit is the amount of money you have after paying for business expenses. Gross profit, operating profit, and net profit are the three basic categories of profit.
If the store bought x half gallons of milk at $2.90 per half gallon, the total cost of the milk would be:
total cost = 2.90x
Since the store stored the milk in two refrigerators, there were initially x/2 half gallons in each refrigerator.
Unfortunately, 14 half gallons were ruined, so the number of half gallons of milk remaining for sale is:
x - 14
The store then sells the remaining milk for $3.94 per half gallon, so the total revenue from the sale is:
total revenue = 3.94(x - 14)
The profit the store made is the difference between the total revenue and the total cost:
profit = total revenue - total cost
We know that the store made a profit of $46.76, so we can set up an equation:
46.76 = 3.94(x - 14) - 2.90x
Simplifying and solving for x:
46.76 = 3.94x - 55.16
102.92 = 3.94x
x = 26
So the store initially bought 26 half gallons of milk.
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Unit 1 Introduction
6 Dahlia's teacher asked her to decompose
the number 6,107. How can Dahlia write
this number in expanded form?
Answers:
Read the following statement: x + y = y + x. The statement demonstrates:
The given statement follows the commutative property.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is x+y=y+x
The commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.
Therefore, the given statement follows the commutative property.
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In Problems 9 and 10 determine whether the given first-order differential equation is linear in the indicated dependent variable by matching it with the first differential equation given in (7).
9. (y^2 - 1)dx + x dy = 0; in y; in x
10. u dv + (v + uv - ue^u) du = 0; in v; in u
8. M(x,y) and N(x,y) are functions of x and y, not just y, so the given differential equation is not linear in y.
9. Both M(u,v) and N(u,v) are functions of u, so the given differential equation is linear in u.
8. To match the given differential equation with the first differential equation given in (7), we need to write the given equation in the form of M(x,y)dx + N(x,y)dy = 0. If the resulting M(x,y) and N(x,y) are both functions of y, then the differential equation is linear in y.
Rewriting (y² - 1)dx + xdy = 0 as xdy = (1 - y²)dx and dividing by x(1 - y²), we get (1/x)dy - [(y² - 1)/(x(1 - y²))]dx = 0.
Therefore, we have M(x,y) = (y² - 1)/(x(1 - y²)) and N(x,y) = 1/x. Both M(x,y) and N(x,y) are functions of x and y, not just y, so the given differential equation is not linear in y.
9. To match the given differential equation with the first differential equation given in (7), we need to write the given equation in the form of M(u,v)du + N(u,v)dv = 0. If the resulting M(u,v) and N(u,v) are both functions of u, then the differential equation is linear in u.
We can rewrite the given equation as u dv + (v + uv) du - [tex]ue^u[/tex] du = 0.
Therefore, we have M(u,v) = v + uv - [tex]ue^u[/tex] and N(u,v) = u. Both M(u,v) and N(u,v) are functions of u, so the given differential equation is linear in u.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
2x² + 12x - 3 = 0
2x² + 12x = 3
divide through by 2
x² + 6x = ³/₂
Take half of coefficient of x, square it and add it both sides of the equation
(x + 3)² = ³/₂ + 3²
x² + 6x + 9 = 9 + ³/₂
2(x² + 6x + 9) = 18 + 3
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Divide 36x5 − 44x4 − 28x3 by 4x2.
Answer:-
36*5= 180
44*4= 176
28*3= 84
4*2=8
180-176-84= (-80)
-80/8=(-10)
Step-by-step explanation: Hope this helps. Mark me brainliest :)))
The average height of male basketball players is 79 inches with a standard deviation of 3.25 inches. We want to mass produce special caskets for the NBA that are long enough for all but the tallest 2% of male basketball players.
What is the inside length of the longer NBA caskets in inches (to 2 decimals)?
The inside length of the longer NBA caskets in inches is, 85.6745
What is standard deviation ?A statistical measure of the degree of variation or dispersion in a set of values is the standard deviation. It offers a way to measure how far apart the individual values in a data set are from the set's mean (average). The square root of the variance is used to calculate the standard deviation, which is denoted by the symbol (sigma).
We are given the distribution here as:
From standard normal tables, we have here:
P(Z < 2.0537) = 0.98
Therefore, P(Z > 2.0537) = 1 - 0.98 = 0.02
Therefore 2.0537 is the z score that would be used here. ( As we are given here that for tallest 2% of the male basketball players, the special caskets for the NBA would be too tall )
Therefore the longest length here is computed as:
= Mean + 2.0537xSD
= 79 + 2.0537x3.25
= 85.6745 inches is the required length here.
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Identify the domain of the function shown in the graph. A. x>0 B. x is all real numbers. C. -6≤x≤6 D. 0≤x≤8 16 11 EN 198 1 3 -8 15
The domain of the function is -6 ≤ x ≤ 6.
What is domain of a function?The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.
A function is defined as the relationship between input and output, Where each input has exactly one output. The inputs are the elements in the domain. The co-domain of the function is the set of output values.
From the graph given the possible input values of x lies from -6 to 6.
Hence, the domain of the function is -6 ≤ x ≤ 6.
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Use the confidence level and sample data to find a confidence interval for estimating the population mean, . Round your answer to the same number of decimal places as the sample mean.
Test scores: n = 175, x¯¯¯=81
, σ=11.8
, 98% confidence
ANSWER CHOICES
A.(77, 85)
B.(79, 83)
C.(76, 86)
D.(72, 90)
Answer:
Step-by-step explanation:
We can use the formula for a confidence interval for the population mean:
CI = x¯¯¯ ± z*(σ/sqrt(n))
where:
x¯¯¯ is the sample mean, which is 81.
σ is the population standard deviation, which is 11.8 (assuming the sample is drawn from a normally distributed population).
n is the sample size, which is 175.
z is the z-score corresponding to the desired level of confidence, which is 2.33 for a 98% confidence level.
Substituting the known values, we get:
CI = 81 ± 2.33*(11.8/sqrt(175))
Calculating this expression, we get:
CI ≈ (79, 83)
Therefore, a 98% confidence interval for the population mean is approximately (79, 83).
Therefore, the answer is (B) (79, 83).
A yogurt stand gave out 200 free samples of frozen yogurt, one free sample per person. The three sample choices were vanilla, chocolate, or chocolate & vanilla twist. 162 people tasted the vanilla and 115 people tasted the chocolate, some of those people tasted both because they chose the chocolate and vanilla twist. How many people chose chocolate and vanilla twist?
Answer:
77
Step-by-step explanation:
(V ∪ C) = V + C - (V ∩ C)
This is the same as: (V or C) = V + C - (V and C)
(V ∪ C) represents the number of people that chose chocolate or vanilla (or possibly both)
(V ∩ C) represents the number of people that chose chocolate and vanilla twist.
(V ∪ C) = V + C - (V ∩ C) ⇔ 200 = 162 + 115 - (V ∩ C)
(V ∩ C) = 162 + 115 - 200 = 77
Please assist,
2. Determine the scale factor of a dilation that maps Circle A onto a circle congruent to Circle B.
3. Determine the scale factor of a dilation that maps Circle C onto a circle congruent to Circle A.
4. Explain the relationship between dilations and similar figures
2. Scale factor of a dilation that maps Circle A onto a circle congruent to Circle B is: 4/3 . 3. Scale factor of a dilation that maps Circle C onto a circle congruent to Circle A is 1/2.
What is transformation?By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made. Transformational geometry, a fresh viewpoint on geometry, was first forth by Felix Klein in the 19th century.
The majority of geometric proofs rely on how objects change. Using transformations, we can change any image in a coordinate plane. By using transformational logic, it is possible to comprehend video game graphics more fully.
From the given figure we see that:
Diameter of A = 8
Diameter of B = 6
Diameter of C= 4
2. Scale factor of a dilation that maps Circle A onto a circle congruent to Circle B is:
8/6 = 4/3
3. Scale factor of a dilation that maps Circle C onto a circle congruent to Circle A is:
4/8 = 1/2
4. When a figure is dilated the new figure is similar to the pre-image. The segments, sides, edges, of the new image is dilated by scale factor.
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Can someone help me with these questions
The minimum wage increased by approximately 13.43% from 1987 to 1988.
The minimum wage increased by approximately 3.88% from 2004 to 2005.
How to find the percentage increasea) Assuming minimum wage increased from $3.35 per hour in 1987 to $3.80 per hour in 1988.
To calculate the percent increase, we can use the formula:
percent increase = (new value - old value) / old value * 100%
percent increase = (3.80 - 3.35) / 3.35 * 100% = 13.43%
b) Assuming minimum wage increased from $5.15 per hour in 2004 to $5.35 per hour in 2005.
percent increase = (5.35 - 5.15) / 5.15 * 100% = 3.88%
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Solve the system of linear equations using substitution. Use a pencil and paper. Which expression would be easier to substitute into the other equation, in order to solve this problem? Explain your reasoning.
x=4y-9
x+4y=3
Answer:
(- 3, 1.5)
--------------------------
Given system:
x = 4y - 9x + 4y = 3The first expression is ready to be substituted as no further operation is required to simplify it.
4y - 9 + 4y = 38y - 9 = 38y = 12y = 12/8y = 1.5Find x:
x = 4*1.5 - 9x = 6 - 9x = - 3Amount of butter
What was the difference between the highest guess and the lowest guess?
Write your answer as a fraction, mixed number, or whole number.
The difference between the highest and the lowest guess, on the whole number, is 120.
What is subtraction?Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.
Given:
A table that shows the amount of butter.
Amount of butter
120
130
150
240
From the table;
the highest guess is 240.
And the lowest guess is 120.
So, the difference between the highest and the lowest guess is,
= 240 - 120
= 120.
And here, 120 is a whole number.
Therefore, the required value is 120.
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Which one of the following statements is correct when the homoskedasticity assumption is violated while the rest of the OLS assumptions are correct.?
a.The beta parameter estimates can be calculated but they are wrong.
b.The beta parameter estimates are biased
c.The beta parameter estimates are unbiased because homoskedasticity assumption is not required for unbiasedness.
d.The beta parameter estimates cannot be calculated
The correct answer is option b. When the homoskedasticity assumption is violated, The beta parameter estimates are biased while the rest of the OLS assumptions are correct.
When the homoskedasticity assumption is violated, the ordinary least squares (OLS) estimator is still consistent but no longer efficient. This means that the estimates of the regression coefficients (beta parameters) are still unbiased, but they have higher variances and covariances.
In other words, the OLS estimator is no longer the best linear unbiased estimator (BLUE) and it may be biased when the errors are heteroscedastic. Therefore, option b is correct.
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Suppose the ratio of Lev's age to Mina's age is 1 : 2 and the ratio of Mina's age to Naomi's age is 3 : 4.
If the sum of all three ages is between 30 and 50, then how old is Mina?
Based on the given age ratio, Mina is 10 years old.
From the case, we know that the age ratio between these 3 people are:
L : M = 1 : 2
M : N = 3 : 4
L = 2M
N = 4/3 M
30 < L + M + N < 50
We can try to find Mina's age range as:
30 < 2M + M + 4/3 M < 50
30 < 13/3 M < 50
120 < 13M < 150
9 < M < 11
Please note that we round down the age range of Mina.
We take M = 10; then:
L = 2M = 2(10) = 20
N = 4/3 M = 4/3 (10) = 13
L + M + N = 20 + 10 + 13
L + M + N = 43 --> PROVEN!
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find the rank, nullity, and bases of the range spaces and null spaces for each of the following matrices. you must show your work, or explain your thought process; a correct numerical answer is not sufficient.
If A is a matrix of order m × n, then
Rank of A + Nullity of A = Number of columns in A = n
Now, According to the question:
What is rank nullity theorem and range?The rank-nullity theorem states that the dimension of the domain of a linear function is equal to the sum of the dimensions of its range (i.e., the set of values in the codomain that the function actually takes) and kernel (i.e., the set of values in the domain that are mapped to the zero vector in the codomain).
What is range and null space of a matrix?The range null-space decomposition is the representation of a vector space as the direct sum of the range and the null space of a certain power of a given matrix.
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The given question is incomplete,
So, The question is:
What is rank nullity theorem and range and null space ?