What is the value of a?
Enter your answer in the box. Enter your answer as a simplified fraction.
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Work Shown:
The scalar (2/5a+6) multiplies with the matrix on the left side to get the matrix on the right side
So this is what your steps could look like
[tex](\frac{2}{5}a+6)\begin{bmatrix}3 \\ -2 \\ 7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\\begin{bmatrix}(\frac{2}{5}a+6)*3 \\ (\frac{2}{5}a+6)*(-2) \\ (\frac{2}{5}a+6)*7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\[/tex]
[tex]\begin{bmatrix}\frac{2}{5}a*3+6*3 \\ \frac{2}{5}a*(-2)+6*(-2) \\ \frac{2}{5}a*7+6*7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\\begin{bmatrix}\frac{6}{5}a+18 \\ -\frac{4}{5}a-12 \\ \frac{14}{5}a+42\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\[/tex]
The last matrix equation leads to this system of equations
[tex]\begin{cases}\frac{6}{5}a+18=15 \\ -\frac{4}{5}a-12=-10 \\ \frac{14}{5}a+42=35\end{cases}\\\\\\[/tex]
If we pick any of those equations, and solve for 'a', then we'll get our answer.
---------------------
Let's say we pick the first equation
(6/5)a+18 = 15
(6/5)a = 15-18
(6/5)a = -3
a = -3(5/6)
a = -15/6
a = -5/2
--------------------
If we pick on the second equation, then,
(-4/5)a-12 = -10
(-4/5)a = -10+12
(-4/5)a = 2
a = 2(-5/4)
a = -10/4
a = -5/2
--------------------
Or we could solve the third equation for 'a'
(14/5)a+42 = 35
(14/5)a = 35-42
(14/5)a = -7
a = -7*(5/14)
a = -35/14
a = -5/2
-------------------
You only need to solve one equation to find 'a', though it's good practice to solve all three to see all three rows agreeing with one another.
The multiplication of the matrix by a constant will multiply for each term in the matrix value of the "a" given system of the matrix will be -2.5.
What is a matrix?A matrix is a collection of numbers lined up in rows and columns to produce a rectangular array.
In computer graphics, where they have been used to describe picture transformations and other alterations, matrices have vital applications as well in many sectors.
As per the given system of the matrix.
When we multiply anything in a matrix then it will multiply to each and every term of the matrix.
Therefore the (2/5)a + 6 will be multiplied by 3,-2, and 7 each.
So the first term of the left-hand side matrix becomes,[(2/5)a + 6]3
If we compare two matrices then each corresponding term will be the same.
Therefore, the first term of the left-hand matrix = first term of the right-hand matrix
[(2/5)a + 6]3 = 15
6a/5 + 18 = 15
6a/5 = -3
6a = -15
a = -15/6 = -2.5
Hence "The value of the "a" given system of the matrix will be -2.5".
For more about matrices,
brainly.com/question/11367104
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) A certain WSU curriculum committee consists of 11 members. In a regular meeting last year, seven members of the committee were in favor of a program proposal and the other four rejected it. If the committee members leave the meeting room in random order and each of the first three leaving the room is accosted by a reporter in quest of an interview, then let X be the number of committee members rejecting the proposal among those interviewed. 1. What is the probability that exactly two are from the membe
Complete Question
A certain WSU curriculum committee consists of 11 members. In a regular meeting last year, seven members of the committee were in favor of a program proposal and the other four rejected it. If the committee members leave the meeting room in random order and each of the first three leaving the room is accosted by a reporter in quest of an interview, then let X be the number of committee members rejecting the proposal among those interviewed.
1. What is the probability that exactly two are from the member favoring the acceptance of the proposal among those interviewed.
Answer:
The value is [tex]P(U) = 0.5091[/tex]
Step-by-step explanation:
From the question we are told that
The number of member is n = 11
The number of member who are in favor of the project is k = 7
The number of members who rejected the project is h = 4
Generally the number of way of selecting the first three member left out of the 11 members is mathematically represented as
[tex]F = ^n C _r[/tex]
Here r = 3 and C stand for combination , so using a combination calculator we have
[tex]F = ^{11} C _3 = 165[/tex]
Given that out of the first three members that left 2 of the members accepted the project i.e U = 2
The number of way of selecting the 2 members from the total 7 members that accepted the project is
[tex]G = ^{7} C _2[/tex]
=> [tex]G = 21[/tex]
Given that two members out of the first three accepted the project it means that the remaining one person rejected the project, the number of ways of selecting this one person from the 4 that rejected the project is mathematically represented as
[tex]U = ^4 C_1[/tex]
=> [tex]U = 4[/tex]
Generally the probability that exactly two are from the member favoring the acceptance of the proposal among those interviewed is mathematically represented as
[tex]P(U) = \frac{G * U}{F}[/tex]
[tex]P(U) = \frac{21 * 4}{165}[/tex]
[tex]P(U) = 0.5091[/tex]
Will give brainliest! Which linear equation has a slope of -2 and a y-intercept of -3?
a
y = 3x + 2
b
y = 3x - 2
c
u = - 2x + 3
d
y = -2x - 3
Answer:
D. y = -2x - 3
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m is slope
b is y-intercept
Step 1: Define variables
m = -2
b = -3
Step 2: Substitute
y = -2x - 3
Answer:
D
y = -2x -3
Step-by-step explanation:
Hey there!
A linear equation starts with y.
y =
The slope is X (-2)
y = -2x
The y-intercept is -3
y = -2x - 3
~I hope I helped you! :)~
Paper clips are sold in small boxes and in large boxes.
There is a total of 1115 paper clips in 4 small boxes and 5 large boxes.
There is a total of 530 paper clips in 3 small boxes and 2 large boxes.
Work out the number of paper clips in each small box and in each large box.
Answer:
Small boxes contain 60 paperclips and large boxes contain 175 paperclips.
Step-by-step explanation:
1. Set up two simultaneous equations:
Use s for small boxes and l for large boxes. (You could use any letters)
4s + 5l= 1115
3s + 2l= 530
2. Number the equations:
4s + 5l= 1115 (1)
3s + 2l= 530 (2)
3. Multiply both equations to get the same number of ls (for different questions the letters might be different):
(1) x 2:
8s + 10l= 2230 (3)
(2) x 5:
15s + 10l= 2650 (4)
4. Subtract one from the other to get rid of the ls:
(4) - (3)
8s + 10l= 2230
- 15s + 10l= 2650
7s =420
5. Solve for s:
s= 420/7= 60
6. Substitute the s value into one of the original equations to find l:
4 x 60 + 5l= 1115
240 + 5l= 1115
5l= 1115 - 240
5l= 875
l= 875/5= 175
6th grade math i mark as brainly
Step-by-step explanation:
i mean I never did that in six grade
3 units right and 4 units down
Answer:
(3, 4)
Step-by-step explanation:
If jimmy has 3 billion dollars and subtracts a dollar how much does he have
Answer:
2,999,999
Step-by-step explanation:
2,999,999
Step-by-step explanation:
dont need a explanation its obvious
3x= 5 + 2(3 + 4x)
How to solve this?
Answer:
Step-by-step explanation:
Simplifying
3x = 5 + 2(3 + 4x)
3x = 5 + (3 * 2 + 4x * 2)
3x = 5 + (6 + 8x)
Combine like terms: 5 + 6 = 11
3x = 11 + 8x
Solving
3x = 11 + 8x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-8x' to each side of the equation.
3x + -8x = 11 + 8x + -8x
Combine like terms: 3x + -8x = -5x
-5x = 11 + 8x + -8x
Combine like terms: 8x + -8x = 0
-5x = 11 + 0
-5x = 11
Divide each side by '-5'.
x = -2.2
Simplifying
x = -2.2
Answer:
x = -11/5
Step-by-step explanation:
3x = 5 + 2(3 + 4x)
~Distribute left side
3x = 5 + 6 + 8x
~Combine like terms on the left side
3x = 11 + 8x
~Subtract 8x to both sides
-5x = 11
~Divide -5 to both sides
x = -11/5
Best of Luck!
PLEASE HELP ILL GIVE BRAINLIEST!! IGNORE THE 6 POINTS THATS JUST HOW MUCH THE QUESTION IS WORTH IN THE GRADEBOOK
Answer:
100 degrees
Step-by-step explanation:
Jessie enjoys running every day for exercise. On Monday, he ran 3.30 miles. On Tuesday, he ran 3.09 miles. On Wednesday, he ran 2.98 miles. On what day did Jessie run the farthest? *
Answer:
monday
Step-by-step explanation:
Over a nine-month period, OutdoorGearLab tested hardshell jackets designed for ice climbing, mountaineering, and backpacking. Based on the breathability, durability, ver-satility, features, mobility, and weight of each jacket, an overall rating ranging from 0 (lowest) to 100 (highest) was assigned to each jacket tested. The following data show the results for 20 top-of-the line jackets (OutdoorGearLab website, February 27, 2013).
42 66 67 71 78 62 61 76 71 67
61 64 61 54 83 63 68 69 81 53
a. Compute the mean, median, and mode.
b. Compute the first and third quartiles.
c. Compute and interpret the 90th percentile.
Answer:
(a) The mean is 65.9, the median is, 66.5 and the mode is. 61.
(b) The first and third quartiles are 61 and 71 respectively.
(c) The value of the 90th percentile is, 78.3.
Step-by-step explanation:
The ratings of 20 top-of-the line jackets, arranged in ascending order are as follows:
S = {42 , 53 , 54 , 61 , 61 , 61 , 62 , 63 , 64 , 66 , 67 , 67 , 68 , 69 , 71 , 71 , 76 , 78 , 81 , 83}
(a)
Compute the mean as follows:
[tex]\bar x=\frac{1}{n}\sum\limits^{n}_{i=1}{x_{i}}=\frac{1}{20}\times 1318=65.9[/tex]
Compute the median as follows:
For an even number of values the median is the average of the middle two values.
[tex]M=\frac{10^{th}obs.+11^{th}obs.}{2}=\frac{66+67}{2}=66.5[/tex]
Compute the mode as follows:
The mode of a dataset is the term that occurs most of the time.
[tex]m=61[/tex]
Thus, the mean is 65.9, the median is, 66.5 and the mode is. 61.
(b)
The first quartile is the median of the first half of the data set.
S₁ = {42 , 53 , 54 , 61 , 61 , 61 , 62 , 63 , 64 , 66}
[tex]Q_{1}=\text{Median of }S_{1}=\frac{5^{th}obs.+6^{th}obs.}{2}=\frac{61+61}{2}=61[/tex]
The third quartile is the median of the second half of the data set.
S₂ = {67 , 67 , 68 , 69 , 71 , 71 , 76 , 78 , 81 , 83}
[tex]Q_{3}=\text{Median of }S_{2}=\frac{15^{th}obs.+16^{th}obs.}{2}=\frac{71+71}{2}=71[/tex]
Thus, the first and third quartiles are 61 and 71 respectively.
(c)
The pth percentile is a data value such that at least p% of the data set is less-than or equal to this data value and at least (100 - p)% of the data-set are more-than or equal to this data value.
Use the Excel formula "=PERCENTILE.INC(array,0.9)" to compute the 90th percentile.
The value of the 90th percentile is, 78.3.
This value implies that 90% of the ratings are less than 78.3.
the answer is 915 / 7
Answer:
If you want 915/7 simplified, it is 130.714285714.
Step-by-step explanation:
4617 divided by 23 as a mixed number
Answer:
200 17/23
Step-by-step explanation:
Mathxway.....
The Kroger Company is one of the largest grocery retailers in the United States, over 2000 grocery stores across the country. Kroger uses an online customer questionnaire to obtain performance data about its products and services and about what motivates its customers (Kroger website, April 2012). In the Kroger customers were asked if they would be willing to pay more for had each of the following four characteristics. The four questions were: pay more forproducts that have a brand name?products that are environmentally friendly?products that are organic?products that have been recommended by others?For each question, the customers had the option of responding Yes if they or No if they would not pay more.a. Are the data collected by Kroger in this example categorical orb. What measurement scale is used?
Answer:
A) Categorical
B) Nominal
Step-by-step explanation:
As we can see from the data that the question only had two answers i-e Yes or no so therefore they were categorical rather than quantitative in which he would have asked the user for how much money they were willing to pay more.
It's nominal because he asked in terms of more or less rather than some specific number
In math what number acts like a switch
Find the 125% of 600lb
Answer:
750
Step-by-step explanation:
of means multiply
125% * 600
change to decimal form
1.25 * 600
750
y=2/5xt 10 the rate of change and y intercept
Answer:
Below
Step-by-step explanation:
Rate of change (aka the slope) = 2/5
Y Intercept = 10
A recipe calls for 2 1/3 cups of flour, cups of white sugar, and cups of brown sugar. The recipe makes 6 servings.
How many cups of flour are there per serving?
Suppose you modify the recipe to triple the number of servings. How much flour do you need for the modified recipe? [PS]Can you show my how its done too?
Answer:
Lets find how much flour we need for just one serving.
2 2/3 ÷ 6
8/3 ÷ 6
8/3 * 1/6
8/18
4/9 cup of flour per serving
If we triple the recipe (6 * 3 = 18), we will have a total of 18 servings. Multiply the amount of flour we got for one serving to 18 servings.
4/9 * 18/1
72/9
8 cups of flour for 18 servings
Best of Luck!
Step-by-step explanation:
make me as brain liest
Consider the following simplified algebraic expression.
10x*y+6x - 7y2-6
Which could be the original expression?
8x*y+7x? - 5y?+3x-2+ 2x*y- x - 2y + 3x-4
Bx+y+ 7x? -5y?+3x-2+ 2x*y-x - 2y2 - 3x-4
8x*y+7x? - 5y2 + 3x+2+2xºy- x? - 2y3 - 3x-4
8x+y+7x2 - 5y2 + 3x-2-2x*y-x-2y? - 3x-4
Answer:
the answer is the second option hope this helped
Step-by-step explanation:
Answer:
b :)
Step-by-step explanation:
the width of a rectangle card is 2cm less than the length and the area is 35cm²
The width of a rectangle card is 2cm less than the length and the area of rectangle is 35cm²[tex].[/tex]
To Find :We have to find length and breadth of rectangle.
Solution :Let length of the rectangle be x cm.
Given that, width is 2cm less than the length.
∴ Width = (x - 2) cm
➤ Area of rectangle :
Area = Length × Width⭆ Area of rectangle = 35
⭆ length × width = 35
⭆ x × (x - 2) = 35
⭆ x² - 2x - 35 = 0
⭆ x² - 7x + 5x - 35 = 0
⭆ x(x - 7) + 5(x - 7) = 0
⭆ x = 7 or x = -5
We know that, length can't be negative.
∴ Length of rectangle = 7cm
Width = x - 2 = 7 - 2∴ Width of rectangle = 5cm
Hope It Helps!how to write number 11 in word form
Answer:
Eleven
Step-by-step explanation:
~I hope I helped you! :)~
What is the slope of this graph
Answer:
-7/8
Step-by-step explanation: If you use RISE/RUN, then you will see that they RISE is 7 and the RUN is 8 so therefroe,you would get 7/8. The graph is pointing down so, it is negative. Overall, your answer should be -7/8.
A basket ball player makes 12 out of 15 free throws. What is his shooting percentage?
Answer:
80%
Step-by-step explanation:
Please help me I’ll natal brainest I need help .
Answer:
B
Step-by-step explanation:
Next time, please show us the question! Luckily I know that the question is asking "which of these is a function" but not a lot of people can assume that. The answer is B because a function can't have repeating x values or more than 1 x value that's the same. None of the x values in B repeat so it's a function! Also, remember that y values CAN repeat, so if the y values repeat, it doesn't mean it isn't a function.
(5,9), (5-3)
what is the slope?
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
When you want to find out what the slope is, you have to remember what the formula is first....
[tex]m=\frac{y}{x} =\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
so in this case -3 would be the [tex]y_{2}[/tex] because it's the y in the ordered pair and it's the second one. Then one of the 5's would be [tex]x_{2}[/tex] and 9 would be [tex]y_{1}[/tex] and then the other 5 would be [tex]x_{1}[/tex].
now if we plug it in
[tex]\frac{-3-9}{5-5} =\frac{-12}{0}[/tex]
now we can tell that we can't divide by zero so the slope would be unidentified and that's it.
Estimate . Then find sum 25,211 plus 9,517
Answer: 34,728
Step-by-step explanation:
All your going to want to do here is add both numbers, and you will get your answer of 34,728. Hope this helps!
An airplane flies with a constant speed of 660 miles per hour. How long will it take to travel a distance of 2475 miles?
9514 1404 393
Answer:
3.75 hours
Step-by-step explanation:
Travel time can be found using the relation ...
time = distance/speed
time = (2475 mi)/(660 mi/h) = 3.75 h
It will take 3 3/4 hours to travel that distance.
7/10;1/3;5/6 ayuda es de matemáticas
Answer:
0.7 1/3 0.8333 repeating yo no hablo espanol
Step-by-step explanation:
7 / 10 is 0.7 , 1 / 3 is 1/3, 5 /6 is 0.8333 repeating
Graph f(x) =2/3x-3
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
f(x)=2/3.3=1/6=0,2
f(x)=0,2
Combine Like Terms. 2 x 2 − x 2 + 3 x 2 2x 2 −x 2 +3x 2
Answer:
The answer is 4x(exponent of 2)
Step-by-step explanation: