We are given the matrices A and B
[tex]A = \left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right][/tex]
[tex]B = \left[\begin{array}{ccc}2\\1\\2\end{array}\right][/tex]
Multiplying these matrices:
We multiply matrices by taking the first column of the first matrix and the first row of the second matrix
we will multiply all the terms of the first column of the first matrix and multiply them by the terms of the first row of the second matrix, one by one
[tex]AB = \left[\begin{array}{ccc}2(2) + 3(1) + -1(2)\\0(2) + 2(1) + 5(2)\\2(2) + 4(1) + 0(2)\end{array}\right][/tex]
[tex]AB = \left[\begin{array}{ccc}5\\12\\8\end{array}\right][/tex]
9514 1404 393
Explanation:
Two matrices with dimensions (numbers of (rows, columns)) of (a, b) and (c, d) can only be multiplied if the number of columns in the left matrix is equal to the number of rows in the right matrix. That is, b=c. The dimensions of the product matrix will be (a, d).
For row i of the left matrix and column j of the right matrix, element a(i,j) of the product matrix is the dot-product of row i with column j. (The dot-product of two vectors is the sum of the products of corresponding elements.)
__
The example matrices have (row, column) dimensions (3, 3) and (3, 1), so can be multiplied with a result having dimensions (3, 1).
It is useful to refer to an element of a matrix by specifying the row and column in which it resides. An element of matrix 'A' in row 2 and column 3 can be referred to as A(2,3). Often, subscripts are used, as in ...
[tex]A_{i,j}[/tex]
For matrix C = A·B, the element C(1,1) will be the sum ...
A(1,1)B(1,1) +A(1,2)B(2,1) +A(1,3)B(3,1)
Calculators, apps, spreadsheets, and web sites are available that will perform this arithmetic for you. It can be a bit tedious to do by hand.
Here the product is ...
[tex]A\cdot B=\left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right] \cdot\left[\begin{array}{c}2&1&2\end{array}\right] =\left[\begin{array}{c}2(2)+3(1)+(-1)(2)&0(2)+2(1)+5(2)&2(2)+4(1)+0(2)\end{array}\right] \\\\=\left[\begin{array}{c}5&12&8\end{array}\right][/tex]
Using Suitable property Evaluate :
(10)3 – (2)³ – (8)3
Answer:
480
Step-by-step explanation:
(10)3- (2)3- (8)3
1000- 8- 512
= 480
Please mark mee brainlist....
If you have a right triangle with legs a =6 and b= 8, what is the value of the hypotenuse? show work.
Answer:
10
Step-by-step explanation:
1. [tex]6^{2} + 8^{2} = c^{2}[/tex]
2 [tex]100 = c^{2}[/tex]
3. c = 10
Danielle needs to walk 3 miles. If she wants to reach her destination in 45
minutes ( hour), how fast does she need to walk?
A. 135 miles
per hour
B. 2.25 miles per hour
C. 15 miles per hour
D. 4 miles per hour
Answer:
4 miles per hour
Step-by-step explanation:
3 miles
Change the 45 minutes to hours
45 minutes * 1 hour/60 minutes = 3/4 hour
3 miles ÷ 3/4 hour
Copy dot flip
3 * 4/3
4 miles per hour
Will mark BRAINLIEST !
Step-by-step explanation:
if u like this answer plz mark as brainlist
Angle formed by each blade = 40°
So, total angle formed by 3 blades
= 40° × 3 = 120°
Total angle of a circle = 360°
Ratio of angle formed by total circle to angle formed by the 3 blades
= 360° : 120°
= 360 : 120
= 3 : 1
Total area of circle
= πr²
= π(3m)²
= π9m²
Let the area of blades be x.
So, area of total circle : x = 3 : 1
= π9m² : x = 3 : 1
= π9m²/x = 3/1
= π9m²/3 = x/1
= π9m²/3 = x
= π3m² = x
So, the area of all three blades is π3m².
Does anyone know this?
Answer:
C
Step-by-step explanation:
Rationalize the denominator by multiplying [tex]\frac{\sqrt{5}}{\sqrt{5} }[/tex]. The denominator will become 5, while the numerator will be 3[tex]\sqrt{100}[/tex]. This is equal to 30/5, which is 6.
Hope this helps!
I’ll give you Brainliest if you answer this!
Answer:
17
Step-by-step explanation:
find z-score for the standard normal distribution with mean 0 and standard deviation 1 with the probability 0.9850
Answer:
z-score=2.17
Step-by-step explanation:
We are given that
Mean, [tex]\mu=0[/tex]
Standard deviation, [tex]\sigma=1[/tex]
Probability, p-value=0.9850
We have to find z-score for the standard normal distribution with mean 0 and standard deviation 1 with the probability 0.9850.
To find the z score for the standard normal distribution we will use z-table.
From z- table we get
p-value =0.9850 when z -score=2.17
[tex]\implies[/tex]z-score corresponding to p-value=2.17
Therefore, the z-score for the standard normal distribution with mean 0 and standard deviation 1 with the probability 0.9850=2.17
Find the missing length indicatedOk
Answer:
x = 135
Step-by-step explanation:
4.8 yd
6 yd
1
4.5 yd
5 yd
7 yd
Find the volume of the composite solid. Round your answer to the nearest hundredth.
A. 244.36 B. 264.79 C. 304.51 D. 330.84
Answer:
A
Step-by-step explanation:
The composite solid is made up of a cone and a rectangular prism.
Volume of the composite solid = volume of the cone + volume of the rectangular prism
✔️Volume of Cone = ⅓*π*r²*h
Where,
r = 4.8 yd
h = √(6² - 4.8²) = √12.96 = 3.6 yd
Substitute
Volume of cone = ⅓*π*4.8²*3.6
= 86.86 yd²
✔️Volume of rectangular prism = l*b*h
Where,
l = 7 yd
w = 5 yd
h = 4.5 yd
Substitute
Volume of prism = 7*5*4.5 = 157.5 yd²
✔️Volume of composite solid = 86.86 + 157.6 = 244.4 yd² (which is close to 244.36 yd²)
It's camping season! Ernie and Bert set up their tents 15 m from
each other. Ernie has Tent 1 and Bert has Tent 2. The angle
between the line of sight from Bert's tent to the shower and the
line of sight from Bert's tent to Ernie's tent is 78 degrees. If
Ernie's tent is 19m away from the shower, is Bert 's tent closer or
further away from the shower and by how much? In your
calculations, round your angles to the nearest whole degree and
side measurements to the nearest tenth of a metre.
1
2
Answer:
The answer is "21.6".
Step-by-step explanation:
Let A stand for tent 1
Let B stand for tent 2
Let C be a shower
Using cosine formula:
[tex]c= \sqrt{b^2 +a^2 - 2ab\cdot \cos(C)}\\\\[/tex]
[tex]= \sqrt{(19)^2 + (15)^2 - 2\cdot 19 \cdot 15 \cdot \cos(78^{\circ})}\\\\= \sqrt{361 + 225 - 570\cdot \cos(78^{\circ})}\\\\ = \sqrt{586- 570\cdot \cos(78^{\circ})}\\\\= 21.6\\\\[/tex]
Therefore, you need to reduce the similarity from B to C which is the length from tent 2 to shower:
Tent 2 Distance to Dusk = 21.6m
Bert's tent is 21.6m away from the shower
Let P(1,2,1), Q(1,0,-1), R(2,2,0) be the vertices of a parallelogram with adjacent sides PQ and PR. Find the other vertex S.
Given:
The vertices of a parallelogram are P(1,2,1), Q(1,0,-1), R(2,2,0).
PQ and PR are the adjacent sides of the parallelogram.
To find:
The coordinates of vertex S.
Solution:
We know that, the diagonals of a parallelogram bisect each other.
Let the coordinates of the vertex S are (a,b,c).
In the given parallelogram PS and QR are the diagonals. It means their midpoints are same.
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{1+2}{2},\dfrac{0+2}{2},\dfrac{-1+0}{2}\right)[/tex]
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{3}{2},\dfrac{2}{2},\dfrac{-1}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{1+a}{2}=\dfrac{3}{2}[/tex]
[tex]1+a=3[/tex]
[tex]a=3-1[/tex]
[tex]a=2[/tex]
Similarly,
[tex]\dfrac{2+b}{2}=\dfrac{2}{2}[/tex]
[tex]2+b=2[/tex]
[tex]b=2-2[/tex]
[tex]b=0[/tex]
And,
[tex]\dfrac{1+c}{2}=\dfrac{-1}{2}[/tex]
[tex]1+c=-1[/tex]
[tex]c=-1-1[/tex]
[tex]c=-2[/tex]
Hence, the coordinates of vertex S are (2,0,-2).
PLZZZZZZ HELP WILL GIVE BRAIN THING AND EXTRA POINTS !What is the least common denominator of the rational expressions below?
Answer:
D is the least common denominator
Triangle plz help me find B,b and c
Answer:
B = 55°
b = 17.1 (rounded to the nearest tenth)
c = 20.9 (rounded to the nearest tenth)
pleas help
given parallelogram ABCD find m<ADB
Answer:
∠ ADB = 19°
Step-by-step explanation:
Consecutive angles in a parallelogram are supplementary, sum to 180° , so
∠ CDA = 180° - ∠ DAB = 180° - 138° = 42°
Then
∠ ADB + ∠ CDB = 42° , that is
∠ ADB + 23° = 42° ( subtract 23° from both sides )
∠ ADB = 19°
Sixty out of every 100 pieces of candy is red. Which Indicates the
proportion of red candies? **
60
60/100
60/40
40/100
Answer:
The proportion of red candies is 60/100.
Step-by-step explanation:
Given that sixty out of every 100 pieces of candy is red, to determine which indicates the proportion of red candies, the following calculation must be performed:
60 red candies out of 100 total candies
60/100
Therefore, the ratio of red candies is 60/100.
please help, it’s urgent !
Answer:
f(-10) = 2 times -10 + 1
= -19
f(2) = 2^2
= 4
f(-5) = 2 times -5 + 1
= -9
f(-1) = (-1)^2
= 1
f(8) = 3-8
= -5
Step-by-step explanation:
PLEASE HELP ME NOW PLEASE
9514 1404 393
Answer:
x = 12
Step-by-step explanation:
Angle U is supplementary to the arc intercepted by the tangents.
5x +10 = 180 -110
5x = 60 . . . . . . subtract 10 and simplify
x = 12 . . . . . . . . divide by 5
A roller coaster descended 32.3 ft in one minute. How would you show this using an integer?
A. -32.3
B. +32.3
C. 32.3-
D. 32.3+\
Answer:
Step-by-step explanation:
a
Determine the difference. 3/4 – 5/16 =?
Answer:
[tex]\frac{3}{4} -\frac{5}{16} =\frac{3(4)}{4(4)} =\frac{5}{16} =\frac{12}{16} -\frac{5}{16} =\frac{7}{16}[/tex]
Answer:
7/16
Step-by-step explanation:
3/4 - 5/16
Get a common denominator of 16
3/4 *4/4 -5/16
12/16 - 5/16
7/16
Consider Line 1 with the equation: x = − 17 Give the equation of the line parallel to Line 1 which passes through ( 3 , 8 ) :
Answer:
what is thisssss
Step-by-step explanation:
Which expressions are equivalent to -7+3(-4e-3)
Choose all answers that apply:
A. -4(3e+4)
B. 12e
C. None of the above
Answer: A
-4(3e+4)=
-12e-16
Step-by-step explanation:
-7+3(-4e-3)=
-7-12e-9=
-12e-16
A baseball team plays in a stadium that holds 60000 spectators. With the ticket price at $11 the average
attendance has been 26000. When the price dropped to $8, the average attendance rose to 30000. Find a
demand function D(q), where q is the quantity/number of the spectators. (Assume D(q) is linear)
D(q)
(For best results, keep answers in fraction form, not decimals)
Answer:
D(q) = -(3)/(4,000)q+19.5
Step-by-step explanation:
Given:
overall capacity = 60000
price in point one = 11
spectators in first point = 26000
second point - price = 8
spectators = 30000
solution:
The demand of a product as a function of its price and other factors such as the prices of the substitutes and complementary goods, income is the expression known as demand function. It is represented by D(q)
we have two points in our line for given ques:
first point of line = (26,000, 11)
second point of line = (30,000, 8)
Slope = (11 - 8)/(26,000 - 30,000)
= (3)/(-4,000)
y = mx + b
here, b = factors influencing demand besides price
m = slope
x = price
10 = (3)/(-4,000) )(26,000) + b
b = 19.5
y = -(3)/(4,000)+19.5
D(q) = -(3)/(4,000)q+19.5
1. One half of a number added to a second
number equals 4. One half of the first
number decreased by the second number
equals zero. Find the two numbers.
Answer:
(4, 2)
Step-by-step explanation:
½x + y = 4
y = 4 - ½x
½x - y = 0
½x - (4 - ½x) = 0
½x - 4 + ½x = 0
x = 4
y = 4 - ½(4)
y = 2
Which of these statements is true for f(x) = 2 · 3x?
Answer:
the statement number D okay!
The y-intercept of the function will be at (0, 2). Then the correct option is A.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
The function is given below.
y = 2·(3)ˣ
The value of y at x = 0, we have
y = 2·3⁰
y = 2·1
y = 2
The y-intercept of the function will be at (0, 2).
Then the correct option is A.
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ5
What is the probability that the sample mean would differ from the true mean by greater than 1.9 dollars if a sample of 92 5-gallon pails is randomly selected
Answer:
The correct solution is "0.0226".
Step-by-step explanation:
The given question seems to be incomplete. Please find below the attachment of the complete query.
According to the question,
Mean
= 29
Standard deviation (s),
= 8
For sample size pf 92,
The standard error will be:
[tex]SE=\frac{s}{\sqrt{N} }[/tex]
[tex]=\frac{8}{\sqrt{92} }[/tex]
[tex]=0.834[/tex]
now,
⇒ [tex]1-P(\frac{-1.9}{0.834} < z < \frac{1.9}{0.834} )[/tex] = [tex]1-P(-2.28<z<2.28)[/tex]
or,
= [tex]1-(2\times P(z<2.28)-1)[/tex]
= [tex]2-2\times P(z<2.28)[/tex]
With the help of table, the normal distribution will be:
= [tex]2-2\times 0.9887[/tex]
= [tex]0.0226[/tex]
I need help answering this question
Answer:
I'm pretty sure it's D, sorry if I'm wrong
Step-by-step explanation:
Answer:
I think D
Step-by-step explanation:
Because an experiment is defined as a scientific procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact. This example is testing to see if the mouthwash is effective.
Javier jogs 3/4 of a mile in 8/1/2 minutes.
If he keeps the same pace, how many minutes will it take him to jog 1 mile?
Answer:
11 1/3 minutes per mile.
Step-by-step explanation:
3/4 miles jogged in 8 1/2 minutes.
So 1 mile jogged in: 8 1/2 divided by 3/4 = 8 1/2 x 4/3 = (17 x 4) / (2 x 3) = 11 1/3 minutes per mile
Answer:
x = 11 1/3 minutes
Step-by-step explanation:
We can write a ratio to solve
3/4 mile 1 mile
----------------- = --------------
8 1/2 minutes x minutes
Using cross products
3/4 *x = 8 1/2
Multiply each side by 4/3
4/3 * 3/4x = 8 1/2 * 4/3
x = 17/2 * 4/3
x = 34/3
x = 11 1/3
The side length of an equilateral triangle is x + 3. Write an expression for the perimeter of the triangle. *
Answer:
Perimeter = (x+3) * 3 = 3x+9
Step-by-step explanation:
(x+3) would be multiplied by 3 in order to account for each of the three sides of the equilateral triangle-
The expression for the perimeter of the triangle is 3x+9.To find the expression for the perimeter of the triangle.
What is the perimeter?Perimeter is the distance around the edge of a shape. The continuous line forms the boundary of a closed geometrical figure.In an equilateral triangle, all 3 sides are the same length, so the equation would look something like this:
P=the perimeter of the triangle
(x+3)=length of each side
P=3(x+3)
To simplify further, distribute the 3 to both the x and the 3 inside of the parentheses, getting
P=3x+9.
So, the expression for the perimeter of the triangle is 3x+9.
Learn more about perimeter here:
https://brainly.com/question/6465134
#SPJ2
Given the function, calculate the following values:
Answer:
Step-by-step explanation:
Camilla and Aisha are sisters and go to same school.Camilla bikes to school and Aisha walks. Camilla’s speed is 6.5 mph and Aisha’s is 2 mph. When Camilla reached school, Aisha was 1.5 miles behind. How far away from their house is the school?
Answer:
2 1/6
Step-by-step explanation:
6.5x=2x+1.6=1/3
1/3*6.5=2 1/6
