Answer:
See Explanation
Step-by-step explanation:
(a)For matrices A and D, given that: [tex]AD=I_m[/tex].
We want to show that [tex]\forall b \in R^m[/tex], Ax=b has a solution.
If Ax=b
Multiply both sides by D
[tex](Ax)D=b \times D\\\implies (AD)x=bD$ (Recall: AD=I_m)\\\implies I_mx=Db $ (Since I_m$ is the m\times m$ identity matrix)\\\implies x=Db[/tex]
This means that the system Ax=b has a solution.
(b)Matrix A has a pivot position in each row where each pivot is a different column. Therefore, A must have at least as many columns as rows.
This means A cannot have more rows than columns.
The length of a rectangle is twice it’s breadth. if the perimeter is 72 meters, find the length and breadth of the rectangle
Perimeter of a rectangle = 2l + 2b
where
l = length
b = breadth
The length is twice it's breadth which is written as
l = 2b
Perimeter = 2(2b) + 2b
72 = 4b + 2b
72= 6b
Divide both sides by 6
b = 12 meters
Since l = 2b
l = 2(12) = 24 meters
The length of the rectangle is 24 meters and it's breadth is 12 meters
Hope this helps
Answer:
If breadth of a rectangle is 19m and perimeter is 80m, find the length of the rectangle.
Step-by-step explanation:
35% off a phone = £78 how much was the phone before the discount prices?
Answer:
£120
Step-by-step explanation:
Given that
The price after reduction = £78
So, 65% = £78.
We have to calculate 100 %
To do so, find 5% and multiply that by 20
65% = £78
5% = 78/13 = £6
So, 100% = 6 x 20 = £120
Hope this helps.
Good Luck
Please mark brainiest
some help a homie out in math
Answer:
1. A pentagonal Pyramid
2. Super Easy, tell me to draw one if you need but i am not gonna give in that much effort right now
La longitud de un rectángulo mide 3m mas que el doble de su ancho del rectángulo, escribe un polinomio que represente el perímetro del rectángulo y simplifica el polígono correspondiente.
Answer:
Step-by-step explanation:
El ancho es x, el largo es x+3
El perímetro es dos veces el largo más dos veces el ancho, es decir: 2(x) + 2(x+3) = 4x+6
El polinomio sería: P(x)=4x+6
Twenty-eight people in student council are running for the offices of president and vice-president. In how many different ways can those offices be assigned?
378
55
756
Answer: 756
Step-by-step explanation:
The president can be elected in 28 different ways. After a student is elected president, there are 27 students left to elect a vice president from. So there are 28 x 27 = 756 different arrangements.
What would be the most logical first step for solving this quadratic equation?
x2 + 2x- 14 = 6
A. Take the square root of both sides
B. Add 14 to both sides
C. Divide both sides by x
Ο Ο
D. Subtract 6 from both sides
Answer:
D
Step-by-step explanation:
So that you can have an equation equal to zero to solve for x
The length of a rectangle is a centimeters, the width of this rectangle is b centimeters. Write an expression for the perimeter of this rectangle.
Answer:
2a+2b
Step-by-step explanation:
I am pretty sure that if the length is a and width is b, you would add them twice together. I am actually not quite sure.
Hope this helped you
I am sorry if this was wrong, I am still a beginner at this
Please answer this quickly - just want the answers, explanation not needed!
Answer:
Step-by-step explanation:
3782Hi can you help me with this please
Answer:
x=13 degrees
Step-by-step explanation:
Supplementary angles: 180 degrees.
180-98=82
Vertical angles: congruent
Corresponding angles: congruent
We have 2 angles of the triangle, so we can find the third. (Angles in a triangle add to 180 degrees)
x=13
Please help! Question two
Answer:
4y+6
Step-by-step explanation:
Perimeter is adding up the outside
so.. there are y+y = 2y
y+3 + y+3 = 2y+6
2y+6 + 2y = 4y+6
Hope this helps :)
Evaluate 3(4-2) what would be the answer to this
Answer:
6
Step-by-step explanation:
3(4 - 2)
Expand brackets.
3(4) + 3(-2)
12 + - 6
= 6
━━━━━━━☆☆━━━━━━━
▹ Answer
6
▹ Step-by-Step Explanation
Follow PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
3(4 - 2)
3(2)
= 6
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Please answer this question now in two minutes
Answer:
u+43°=u_3°+u+3° (by exterior angle theorem)
u+43°= 2u
or, 2u_u=43°
or, u= 43°
is the value of u.....
Solve the simultaneous equations 3x+y=8 X-3Y=11
Answer:
(7/2, -5/2)
Step-by-step explanation:
We can solve this multiple ways: Algebraically (Substitution or Elimination) or Graphically
Step 1: Write 1st equation in terms of y
y = 8 - 3x
Step 2: Substitute y of 2nd equation
x - 3(8 - 3x) = 11
Step 3: Solve for x
x - 24 + 9x = 11
10x - 24 = 11
10x = 35
x = 7/2
Step 4: Plug x to find y
3(7/2) + y = 8
21/2 + y = 8
y = -5/2
Answer:
Step-by-step explanation:
let's organize our information :
3x+y=8x-3y=11The trick here is to multiply x-3y=11 by -3 then add it to 3x+y=8 to get rid of x and get a normal equation
we get : -3x+9y= (-33)
then after the addition : 3x+y-3x+9y=8-33⇔ 10y=(-25)
so y=(-25)/10= -5/2
let's replace y by -5/2 in 3x+y=8 3x-5/2 =8⇔ x= 21/6so y= (-5/2) and x= 21/6
When testing gas pumps for accuracy, fuel-quality enforcement specialists tested pumps and found that 1334 of them were not pumping accurately (within 3.3 oz when 5 gal is pumped), and 5663 pumps were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than 20% of the pumps are inaccurate. Use the P-value method and use the normal distribution as an approximation to the binomial distribution.
Answer:
We accept H0, Therefore we conclude that there is no evidence to support the claim that less than 20% of the pumps are inaccurate.
Step-by-step explanation:
We have,
x = 1334
n = 1334 + 5663 = 6997
we have to:
p = x / n = 1334/6997 = 0.1907
The hypothesis is:
H0: P = 0.20
H1: P <0.20
P = 0.2 and Q = 1 - P = 0.8
the test statistic is:
Z = (p - P) / [(P * Q / n) ^ (1/2)]
replacing:
Z = (0.1907 - 0.20) / [(0.2 * 0.8 / 6997) ^ (1/2)]
Z = -1.96
now, the p-value is
P = 0.0250, from normal table, attached
Here p-value> 0.01, so we accept H0, Therefore we conclude that there is no evidence to support the claim that less than 20% of the pumps are inaccurate.
Simple and easy question
please help
Answer:
A
Step-by-step explanation:
To find the volume we do 2 * 1.25 * 1.5 (i rewrote the fractions as decimals) which is 3.75 or 3 and 3/4 cubic inches.
Answer:
V = [tex]3 \frac{3}{4}[/tex]
Step-by-step explanation:
Hey there!
Well the volume "v" of a rectangular prism is,
V = l•w•h
Fill in
[tex]V = 2* 1 \frac{1}{4} * 1 \frac{1}{2}[/tex]
V = [tex]3 \frac{3}{4}[/tex]
Hope this helps :)
A construction company covered 3\8 of a road which is 10km long with asphalt in the first week and covered 7\18of the road in the second week with asphalt. what length of the road remained to be covered with asphalt?
Answer:
2.36 km
Step-by-step explanation:
First they covered 3/8 of the road, so in figures that is;
= [tex]\frac{3}{8} * 10km[/tex]
=3.75 km
The second week they covered 7/18 of the road which is;
= [tex]\frac{7}{18} * 10km[/tex]
= 3.89 km
If we combine the two distances, we get;
= 3.75 km + 3.89 km
= 7.64 km
Subtract this from the total distance and you get
= 10 km - 7.64 km
= 2.36 km
Which means 2.36 km of the road is left to be covered with asphalt.
determine (a) the volume and (b) the surface area of the three-dimensional figure. when appropriate, use pi key on your calculator.
Answer:
[tex] Volume = 150 yd^3 [/tex]
[tex] Surface Area = 150 yd^2 [/tex]
Step-by-step explanation:
Going by the dimensions of the given three-dimensional figure, we can conclude that the figure is that of a cube. The height, length and width are equal.
Volume of a cube is given as [tex] a^3 [/tex] , while surface area of a cube is given as [tex] 6a^2 [/tex]
Where, a = the side length = 5 yards
[tex] Volume = a^3 = 5^3 [/tex]
[tex] Volume = 150 yd^3 [/tex]
[tex] Surface Area = 6a^2 = 6(5)^2 [/tex]
[tex] Surface Area = 150 yd^2 [/tex]
Aubreys kitchen countertop is 2/3 meter by 3 4/5 meters she solves 2/3 multiply 3 4/5 to find the area of the countertop in square meters. Enter numers to conplete aubreys calculations for the area
Answer:
[tex]2\frac{8}{15}[/tex] or 2.5333
Step-by-step explanation:
Just multiply the numbers. please mark brainliest
PLEASE help me with this!! I need help!
Answer:
∠ BDG = 148°
Step-by-step explanation:
The tangent- chord angle BDG is half the measure of its intercepted arc DCG
The 2 arcs in the circle sum to 360°, thus
arc DCG = 360° - arc DG = 360° - 64° = 296° , thus
∠ BDG = 0.5 × 296° = 148°
Which of the following options correctly describes the graph below?
The option that correctly describes the graph below is A. Piecewise function.
What is a piecewise function?
A piecewise function is a function that reacts in different ways based on the input received at every point in time. This function has different intervals and funtions that apply to the respective domains.
Sometimes, these graphsa re recognized by the three main parts that they have. So, the function that is represented by the graph is the piecewise function.
Learn more about piecewise functions here:
https://brainly.com/question/27262465
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The Edward James Toy Company uses a Kanban system to make plastic wheels that are a component of several toys. The waiting time for a container of the wheels during production is 0.25 day; average processing time is 0.15 day per container. Each container holds 200 wheels. The company uses 2000 wheels a day in the production of its products. Using a policy variable of 5%, calculate the number of Kanban containers needed for the wheels.
Answer:
4.2 kanban containers required
Step-by-step explanation:
Given the following information :
Waiting time = 0.25 days
Average peocessing time = 0.15 days / container
Daily usage (Demand rate) = 2000 per day
Container capacity = 200 wheels
Policy variable ( Alpha) = 5% = 0.05
Therefore, number of kanban containers needed for the wheels can be calculated using:
(Number of containers(x) * container size) = (Demand rate (waiting time + processing time)*(1 + alpha))
x * 200 = 2000(0.25 + 0.15)*(1 + 0.05)
200x = 2000(0.40)*(1.05)
200x = 840
x = 840 / 200
x = 4.2
4.2 kanban containers required
Identify the property that justifies the following statement: I will make you a brainllest.
Answer:
reflexive property of simliarity
Step-by-step explanation:
the mean of five numbers is 8. when another number is added the mean is 7. find the number added
Answer:
[tex]\large \boxed{\sf \ \ 2 \ \ }[/tex]
Step-by-step explanation:
Hello,
The mean of five numbers is 8 so we can write
[tex]\dfrac{x_1+x_2+x_3+x_4+x_5}{5}=8[/tex]
When another number is added the mean is 7, let s note x the another number we can write
[tex]\dfrac{x_1+x_2+x_3+x_4+x_5+x}{6}=7[/tex]
From the first equation we can say
[tex]x_1+x_2+x_3+x_4+x_5=8*5=40[/tex]
So the second equation becomes
[tex]\dfrac{x_1+x_2+x_3+x_4+x_5+x}{6}=7\\\\<=> \dfrac{40+x}{6}=7\\\\<=>40 + x = 6*7=42\\\\<=> x = 42-40 = 2\\[/tex]
The solution is then 2
Hope this helps
A fair 6-sided die numbered 1 to 6 is rolled once. Find the probability that the number obtained is either even or a prime number. Define the event ME or MNE. If you can help me, I would be so thankful.
A box contains 5 blue, 4 red, and 3 yellow marbles. Two marbles are randomly drawn and not replaced. What is the probability of drawing a blue then a red marble?
Answer: Probability = 20/132
Step-by-step explanation: There is no replacement in the box, so, once the marble is taken out, there will be one less inside the bag:
Total = 5 + 4 + 3 = 12
Probability of Blue:
P(b) = 5/12
Probability of Red: Since the blue is already out, total will be one less:
P(r) = 4/11
Probability of taken one and then the other:
P(blue,red) = [tex]\frac{5}{12} . \frac{4}{11}[/tex]
P(blue,red) = [tex]\frac{20}{132}[/tex] ≈ 0.15
The probability of drawing a blue and then a red is 20/132.
Answer:
5/33
Step-by-step explanation:
Help please! How would i solve this?
Answer:
B is correct
Step-by-step explanation:
What is need to be done here is to set up an exponential equation for both scenario.
The exponential equation to set up is as follows;
V = P(1 + r)^t
It looks exactly like an equation used to get the amount on a compound interest after a stipulated number of years.
We have the following definitions;
V is the future value.
P is the present value
r is the rate in percentage
t is the time in years
So, for A, we have;
Kindly note that 4% = 4/100 = 0.04
110,000(1+0.04)^t = 110,000(1.04)^t
For B, we have;
6/100 = 0.06
100,000(1+0.06)^t = 100,000(1.06)^t
Now expected value of B is twice that of A.
The equation that defines this would look like;
100,000(1.06)^t = 2(110,000(1.04)^t)
leo, Kush and Mai share some money in the ratio 3 : 5 : 8. Kush receives £750 more than Leo. Calculate the total amount of money that they shared?
Answer:
£6000
Step-by-step explanation:
3:5:8
3+5+8=16
5-3 =2
Therefore 2=750
Therefore 1=375
16*375=£6000
Your friend swims on the school team. In her first four races, her times are 26.3, 28.4, 25.6 and 29.1. Which time listed for her next race would make the range larger? A. 25.2 B. 26.1 C. 28.0 D. 29.1
Answer:
A.) 25.2
Step-by-step explanation:
Given the following :
Times in first four races :
26.3, 28.4, 25.6 and 29.1
The range of a list of values is the difference between the maximum and minimum value of the list or data.
In her first four races :
Range = 29.1 - 25.6 = 3.5
Value of range in her first four races = 3.5
In other to make the range larger:
Either she has a value less than the least time in her previous four races or she has a value greater than the maximum value of her previous race in her next race.
With a time of 25.2 in her next race : least value in the data will be 25.2
Range = 29.1 - 25.2 = 3.9
With a time of 26.1 in her next race :
Range = 29.1 - 25.6 = 3.5
With a time of 28.0 in her next race :
Range = 29.1 - 25.6 = 3.5
With a time of 29.1 in her next race :
Range = 29.1 - 25.6 = 3.5
Answer:
25.2
Step-by-step explanation:
Your friend swims on the school team.
In her first four races, her times are 26.3, 28.4, 25.6, and 29.1 seconds.
Which time listed for her next race would make the range larger?
An evergreen nursery usually sells a certain shrub after 5 years of growth and shaping. The growth rate during those 5 years is approximated by dh/dt = 1.5t + 4, where t is the time in years and h is the height in centimeters. The seedlings are 12 centimeters tall when planted (t = 0). (a) Find the height after t years.
Answer:
[tex]h(t) = 0.75t^2 + 4t + 12[/tex]
Step-by-step explanation:
The equation given calculates the derivative of the height in relation to the time, that is, the rate of change of the height. To find the equation for the height, we need to integrate this equation:
[tex]dh/dt = 1.5t + 4[/tex]
Multiplying both sides by 'dt', we have:
[tex]dh = (1.5t + 4)dt[/tex]
Using the integral in both sides:
[tex]\int dh = \int (1.5t + 4) dt[/tex]
[tex]h = 0.75t^2 + 4t + h(0)[/tex]
[tex]h = 0.75t^2 + 4t + 12[/tex]
So the height after t years is represented by this equation:
[tex]h(t) = 0.75t^2 + 4t + 12[/tex]
The population of China was about 1,360,000,000 people in 2014. Which number best approximates the population as a single digit times a power of 10?
Answer: 1 * 10^9
Step-by-step explanation:
1*10^9 = 1,000,000,000, which is the closest you can get.
Hope it helps <3