The matrix a is 13 by 91. give the smallest possible dimension for nul
a.
Final answer:
The smallest possible dimension for the null space of a 13 by 91 matrix is 78. This is determined using the Rank-Nullity Theorem, taking into account that the rank of a matrix cannot exceed the number of its rows.
Explanation:
The question pertains to the dimension of the null space (also known as the nullity) of a matrix 'a.' The dimensions of matrix 'a' are 13 by 91, which means it has 13 rows and 91 columns. The null space of a matrix 'a' is the set of all vectors that, when multiplied by 'a,' give the zero vector. The dimension of the null space is referred to as the nullity of 'a.'
To find the smallest possible dimension of the null space, we consider the Rank-Nullity Theorem, which states that for any matrix 'A' of size m by n, the rank of 'A' plus the nullity of 'A' is equal to n, the number of columns in 'A.' The maximum rank a matrix can have is limited by the smaller of the number of rows or columns, so for matrix 'a' with dimensions 13 by 91, the maximum rank is 13 since there are only 13 rows.
Using the Rank-Nullity Theorem, we can say:
Rank(a) + Nullity(a) = 91MaxRank(a) = 13 (Since there are only 13 rows)MaxRank(a) + Nullity(a) = 9113 + Nullity(a) = 91Nullity(a) = 91 - 13Nullity(a) = 78Therefore, the smallest possible dimension for the null space of matrix 'a' is 78.
4^2(2^3-3)^1+8(2-1)^10
Jean-pierre consumes only apples and bananas. he prefers more apples to less, but he gets tired of bananas. if he consumes fewer than 28 bananas per week, he thinks that one banana is a perfect substitute for one apple. but you would have to pay him one apple for each banana beyond 28 that he consumes. the indifference curve that passes through the consumption bundle with 31 apples and 40 bananas also pass through the bundle with x apples and 23 bananas, where x equals:
How to factor 4(x+5)^3(x-1)^2-(x+5)^4 • 2 (x-1) by grouping?
find the sum
5^71+5^72+5^73=?
If a boatman rows his boat 35km up stream and 55km downstream in 12 hours and he can row 30km upstream and 44 km downstream in 10hr , then the speed of the stream and that of the boat in still water
To solve this problem, let us assume linear motion so that we can use the equation:
t = d / v
where t is time, d is distance and v is velocity
First let us assign some variables, let us say that the velocity upstream is Vu while Velocity downstream is Vd, so that:
35 / Vu + 55 / Vd = 12 ---> 1
30 / Vu + 44 / Vd = 10 ---> 2
We rewrite equation 1 in terms of Vu:
(35 / Vu + 55 / Vd = 12) Vu
35 + 55 Vu / Vd = 12 Vu
12 Vu – 55 Vu / Vd = 35
Vu (12 – 55 / Vd) = 35
Vu = 35 / (12 – 55 / Vd) ---> 3
Also rewriting equation 2 to in terms of Vu:
Vu = 30 / (10 – 44 / Vd) ---> 4
Equating 3 and 4:
35 / (12 – 55 / Vd) = 30 / (10 – 44 / Vd)
35 (10 – 44 / Vd) = 30 (12 – 55 / Vd)
Multiply both sides by Vd:
350 Vd – 1540 = 360 Vd – 1650
10 Vd = 110
Vd = 11 km / h
Using equation 3 to solve for Vu:
Vu = 35 / (12 – 55 / 11)
Vu = 5 km / h
Answers:
Vu = 5 km / h = velocity upstream
Vd = 11 km / h = velocity downstream
A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time/4347395/f56da09a?utm_source=registration
For his long long distance phone service Chris pays a $6 monthly fee plus 8 cents per minute. Last month, Chris's long distance bill was $11.52. For how many minutes was Chris billed
total bill would be X=6.00 +0.08m
where m = minutes
X = total bill
so 11.52 = 6.00+0.08m
subtract 6 from each side
5.52 = 0.08m
now divide both sides by 0.08
5.52/0.08 = 69
he was billed for 69 minutes.
if 3×1=34 2×3=65 6×1=67 5×4=209 then 6×3=
Answer:
189 is the answer
Step-by-step explanation:
There are 50 competitors in the men’s ski jumping. 30 move on to the qualifying round. How many different ways can the qualifying round be selected?
To calculate the number of different ways 30 qualifiers can be selected from 50 competitors in a ski jumping event, use the combination formula C(n, k) = n! / (k!(n - k)!), where in this case n=50 and k=30.
Explanation:The question here is focused on finding the number of different combinations in which the qualifying round can be selected from a group of competitors in a sport event, specifically men’s ski jumping. This falls under the category known as combinatorics, which is a part of mathematics that deals with counting, both in a concrete and abstract way, as well as finding certain properties of finite structures.
The total number of different ways 30 competitors can be chosen from a group of 50 can be found using the combination formula, which is expressed as C(n, k) = n! / (k!(n - k)!), where "n" is the total number of competitors, "k" is the number of competitors to choose, "n!" signifies the factorial of "n", and "(n - k)!" is the factorial of the difference between "n" and "k".
In this situation, to find the number of different ways to select the 30 qualifiers from 50 competitors, we plug the values into the formula to calculate C(50, 30).
Final answer:
To find the number of different ways the qualifying round can be selected, you need to use combinations. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of competitors and r is the number of competitors moving on to the qualifying round.
Explanation:
To find the number of different ways the qualifying round can be selected, we need to use combinations. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of competitors and r is the number of competitors moving on to the qualifying round.
In this case, n = 50 and r = 30. Plugging these values into the formula, we get C(50, 30) = 50! / (30!(50-30)!). Simplifying this expression, we find that C(50, 30) = 211915132760.
Therefore, there are 211,915,132,760 different ways the qualifying round can be selected.
car rental in Thailand cost $35 per day when booked in advance. If rented locally you would be charged 1800 bahts per day. If the exchange rate is 40 bahts equals $1 how much cheaper is it to book in advance
Answer:
advance booking is cheaper by 400 bahts or $10.
Step-by-step explanation:
Car rental cost in advanced booking = $35 per day
and
when the rented locally it is charged = 1800 bahts per day
it is given that,
$1 is equal to 40 bahts.
now,
Car rental cost in advanced booking = 35 × 40
= 1400 bahts
hence, when booking is done advance
the cost is cheaper by 1800 - 1400 = 400 bahts
hence, advance booking is cheaper by 400 bahts or $10.
How can you use integers to represent the velocity and the speed of an object?
A plane flew for 4 hours heading south and for 6 hours heading east. If the total distance traveled was 3,370 miles, and the plane traveled 45 miles per hour faster heading south, at what speed was the plane traveling east?
The plane was traveling at 319 miles per hour heading east. This was determined by setting up equations for the distances covered in both directions, considering the speed difference, and solving for the eastward speed.
To find the speed at which the plane was traveling east, we need to set up two equations based on the given information.
Let's denote the speed of the plane heading east [tex]v_e[/tex] and the speed of the plane heading south [tex]v_s[/tex]. According to the problem, [tex]v_s[/tex] = [tex]v_e[/tex] + 45 mph. We also know that the plane flew south for 4 hours and east for 6 hours, covering a total distance of 3,370 miles.
To represent the sum of distances covered in both directions, we use the equation:
4[tex]v_s[/tex] + 6[tex]v_e[/tex] = 3,370
Substituting [tex]v_s[/tex] with [tex]v_e[/tex] + 45 in the equation yields:
4([tex]v_e[/tex] + 45) + 6[tex]v_e[/tex] = 3,370
By simplifying and solving for [tex]v_e[/tex], we find the speed of the plane traveling east. Let's solve it step by step:
4[tex]v_e[/tex] + 180 + 6[tex]v_e[/tex] = 3,370
10[tex]v_e[/tex] + 180 = 3,370
10[tex]v_e[/tex] = 3,190
[tex]v_e[/tex] = 319 mph
Therefore, the plane was traveling at 319 miles per hour heading east.
Mr. Wu is going to stock the concession stand for the Little League playoffs. He knows he will need at least twice as many hamburger buns as hotdog buns. Hamburger buns cost $0.45 each, and hotdog buns cost $0.40 each. He cannot spend more than $60 on buns. If x = the number of hamburger buns and y = the number of hotdog buns, which system of inequalities could be used to determine how many of each kind of bun Mr. Wu should purchase for the stand?
The system of inequalities to determine the number of hamburger and hotdog buns Mr. Wu should purchase is x \\geq 2y for the quantity requirement, and 0.45x + 0.40y \\leq 60 for the budget constraint.
To determine how many hamburger buns (x) and hotdog buns (y) Mr. Wu can purchase for the concession stand, we need to set up a system of inequalities based on the given conditions. Since he needs at least twice as many hamburger buns as hotdog buns, we can express this requirement as an inequality: x \\geq 2y. Additionally, considering the cost of hamburger buns is $0.45 each and hotdog buns are $0.40 each, the total spending should not exceed $60. This gives us a budget constraint inequality: 0.45x + 0.40y \\leq 60. Therefore, the system of inequalities that can be used to determine the number of each kind of bun Mr. Wu should purchase is:
x \\geq 2y0.45x + 0.40y \\leq 60Which expression is equivalent to 3(8 + 7)?
The expression 3(8 + 7) is equivalent to 45. The calculation follows the distributive property rule in mathematics, whereby we first simplify the expression inside the parentheses before multiplication.
Explanation:The mathematical expression of 3(8 + 7) is based on the principle of distribution in mathematics. This principle can be interpreted as 'spread' or 'distribute' and applies when you multiply a number by addends within parentheses.
For the given expression 3(8 + 7), do the operation inside the parentheses first. So 8 + 7 equals 15. Now the expression becomes 3(15).
To find the solution, just multiply 3 by 15, which equals 45. So, 3(8 + 7) is equivalent to 45.
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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.4 years, and standard deviation of 0.7 years. the 8% of items with the shortest lifespan will last less than how many years? give your answer to one decimal place.
To solve this problem, we make use of the z statistic. We are to look for the bottom 8% who has the shortest lifespan, this is equivalent to a proportion of P = 0.08. Using the standard distribution tables for z, the value of z corresponding to this P value is:
z = -1.4
Now given the z and standard deviation s and the mean u, we can calculate for the number of years of the shortest lifespan:
x = z s + u
x = -1.4 (0.7) + 2.4
x = -0.98 + 2.4
x = 1.42 years
Therefore the life span is less than about 1.42 years
What are the domain and range of f(x)=1/5x
Identify the domain of the exponential function shown in the following graph: (2 points) Exponential graph starting at point 0, 30000 and approaching the x axis as it moves left to right. Select one: a. all real numbers b. x ≥ 0 c. 0 ≤ x ≤ 30,000 d. 7 ≤ x ≤ 30,000
Answer: b. [tex]x\geq 0[/tex] , where x is the positive real numbers.
Step-by-step explanation:
We Know that, The Set of all Possible values of independent variable is called Domain of the function.
Since, Exponential graph starting at point (0, 30000),
Thus, the initial value of value of independent variable is 0.
Also, The given exponential function is approaching the x axis as it moves left to right.
Therefore, The Domain must contain the all positive real numbers.
Thus, the Domain of the given function is [tex]x\geq 0[/tex] , where x is the positive real numbers.
Therefore, Option b is correct.
Reducing the original price of an item is often called
Answer:
Price reduction.Step-by-step explanation:
The act of reducing the selling price of products in order to attract costumers is called Price Reduction. This comprehends a marketing strategy.
Find x. The units are in feet.
15 tan^3 x=5 tan x Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
The solutions to the equation 15 tan^3 x=5 tan x in the interval [0, 2π) are approximately x = 0.6155, x = 3.757, x =2.527, x = 5.669.
Explanation:The trigonometric equation provided in the question is 15 tan3 x=5 tan x. We can start solving this equation by dividing both sides by tan x, which gives 15 tan2 x = 5. Dividing again by 5, we get tan2 x = 1/3. The solutions to tan2 x = 1/3 are values of x in the interval [0, 2π) where the square of the tangent of x equals 1/3. However, these values cannot be easily computed, thus we use a calculator to approximate the results. We find the solutions to the equation by considering all angles whose tangent is either sqrt(1/3) or -sqrt(1/3). Therefore, the solutions for x in the interval [0, 2π) are approximately x = 0.6155, x = 3.757, x = 2.527, x = 5.669.
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for 2 hours, Lia drove at the speed of 60 mph ,and for the next 3 hours,at the speed of 50mph.What was Lia's average speed during this trip
Which system is equivalent to
y= 9x^2
x+y=5
?
Answer : Option A
Explanation:
we can clearly see that from x+ y=5 we can substitute y = 5-x in y = 9x^2
Option B is clearly incorrect x can not be y -5
Option C is incorrect because y can not be 5 +x
Option D is incorrect because its y = 9x^2 not y^2 =9x^2 so y can not be 3x
if its y^2 = 9x^2 then only implies y = 3x
Answer:
Option 1st is correct
[tex]5-x= 9x^2[/tex]
[tex]y = 5-x[/tex]
Step-by-step explanation:
Given the equations:
[tex]y = 9x^2[/tex] .....[1]
[tex]x+y = 5[/tex] .....[2]
We can write equation [2] as:
[tex]y = 5-x[/tex]
Now, substitute this y value in [1] we have;
[tex]5-x= 9x^2[/tex]
Therefore, the system which is equivalent to the given system equation is,
[tex]5-x= 9x^2[/tex]
[tex]y = 5-x[/tex]
the sum of two numbers is 8 if one number is subtracted from the other the result is -4
Which of the following nonlinear inequalities is graphed below? Picture included below!! PLEASE HELP ASAP!
Answer:
The correct option is A.
Step-by-step explanation:
The general form of an ellipse is
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Where, (0,0) is the center of ellipse, (±a,0) are x-intercepts and (0,±b) are y-intercepts.
From the given graph it is clear that the center of ellipse is (0,0), (±2,0) are x-intercepts and (0,±4) are y-intercepts. So, the equation of ellipse is
[tex]\frac{x^2}{(2)^2}+\frac{y^2}{(4)^2}=1[/tex]
[tex]\frac{x^2}{4}+\frac{y^2}{16}=1[/tex]
The shaded region is inside the ellipse, (0,0) lie in the solution set and the points lie on the ellipse are included in the solution set, therefore the sign of inequality is ≤.
[tex]\frac{(0)^2}{4}+\frac{(0)^2}{16}\leq 1[/tex]
[tex]0\leq 1[/tex]
This statement is true. The required inequality is
[tex]\frac{x^2}{4}+\frac{y^2}{16}\leq 1[/tex]
Therefore, the correct option is A.
ABCD is a parallelogram. If m
Answer:
65
Step-by-step explanation:
20 points PLEASE HELP WITH THIS QUESTION,, I WILL RANK HIGHEST TOO
Directions: Three families have purchased a large lot in the country and have built new homes on it. They plan to install a satellite dish on their lot. Locate the point on their lot that is equidistant (equal distance) from their 3 homes. Find the best location of the satellite dish. .
The best location for the satellite coordinates is
(Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3).
We have,
From the figure given,
Assume that the coordinates of the three families are:
Sanchez = (a, b)
Perez = (c, d)
Reyes = (e, f)
The point equidistant from all three families' coordinates can be calculated using the formula.
Midpoint = ((m + o) / 2, (n + p) / 2)
Where (m, n) and (o, p) are the coordinates.
Midpoint between Sanchez and Perez:
Midpoint(SP) = A = ((a + c) / 2, (b + d) / 2)
Midpoint between Perez and Reyes:
Midpoint(PR) = B = = ((c + e) / 2, (d + f) / 2)
Midpoint between Sanchez and Reyes:
Midpoint(SR) = C = ((a + e) / 2, (b + f) / 2)
Equidistant Point
= (Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3)
Where "Ax" represents the x-coordinate of the midpoint between Sanchez and Perez, Bx" represents the x-coordinate of the midpoint between Perez and Reyes, and Cx" represents the x-coordinate of the midpoint between Sanchez and Reyes. Similarly, Ay, By, and Cy" represent the y-coordinates of the respective midpoints.
Thus,
The best location for the satellite coordinates is
(Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3).
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What must be the contact area between a suction cup (completely evacuated) and a ceiling if the cup is to support the weight of an 80.0-kg student?
The question asks for the required contact area between a suction cup and a ceiling to support an 80.0 kg person. Using principles of physics pressure calculations, a suction cup with a minimum contact area of 7.74 cm² would be needed.
Explanation:The subject of your question is physics given it requires an understanding of pressure, force, and area relationships. To keep the suction cup adhered, the pressure difference between the lower (inside) of the suction cup and the outside (room pressure) must be large enough to support the weight of the person. This principle makes use of a simple physics equation: Pressure = Force/Area.
To support an 80.0-kg person, the force exerted due to weight would be mass multiplied by gravity or 80.0 kg * 9.8 m/s² = 784 N. The atmospheric pressure is about 101,325 Pascal (Pa) or N/m². Rearranging the equation for Pressure will give us the needed area: Area = Force/Pressure. So, the necessary contact area would be 784 N / 101325 Pa ≈ 0.00774 m² or 7.74 cm².
This means, that in ideal conditions and neglecting factors such as surface roughness, a suction cup with a contact area of at least 7.74 cm² would be needed to support an 80.0-kg person.
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Find the area of the shaded segment. Round your answer to the nearest square centimeter. Will make brainliest answer if correct :)
Draw a quadrilateral with the given description
A rhombus with 6-centimeter sides and two 80 degree angles
Answer:
Step-by-step explanation:
By definition, a quadrilateral is a general term for a parallelogram and a rhombus. They are both 4-sided two-dimensional shapes with two sets of parallel sides. However, a rhombus is a special case. It has equal sides. Consequently, all its angles are equal. Therefore, the resultant drawing is alike to what's in the attached picture. But technically, all its sides are equal to 6 cm and all its angles are equal to 80°.