Week 4 Assignment: Solving Systems of Linear Equations by Eliminatio
Due Aug 2 by 11:59pm
Points 10
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Solve applications of systems of equations by elimination
Question
The sum of two numbers is -17. Their difference is 41. Find the numbers.
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Answer:
The two numbers are 12 and -29
Step-by-step explanation:
Let x and y be the two numbers
x+y = -17
x - y = 41
Add the two equations together
x+y = -17
x - y = 41
----------------
2x = 24
Divide by 2
x = 12
Now find y
x+y = -17
12 +y = -17
Subtract 12 from each side
y = -17-12
y = -29
30 points!!!!!!
There are 6 red marbles, 9 blue marbles, and 10 green marbles in a bag.
What is the theoretical probability of randomly drawing a red marble and then a green marble?
10%
9.6%
64%
16%
Answer:
A or B depending on whether replacement takes place
Step-by-step explanation:
Without replacementprobability of getting a red marble=6/25
probability of getting a green marble (considering no replacement of marble drawn has taken place)=10/24
probability of randomly drawing a red marble and then a green marble=(6/25)*(10/24)=0.1=10%
With replacementprobability of getting a red marble=6/25
probability of getting a green marble (considering replacement of marble drawn has taken place)=10/25
probability of randomly drawing a red marble and then a green marble=(6/25)*(10/25)=0.096=9.6%
2/3a - 1/6 =1/3 please help me
Answer:
[tex]a = \frac{3}{4}[/tex]
Step-by-step explanation:
Let's convert everything to sixths to make it easier to work with.
[tex]\frac{4}{6}a - \frac{1}{6} = \frac{2}{6}[/tex]
Add 1/6 to both sides:
[tex]\frac{4}{6}a = \frac{3}{6}[/tex].
Dividing both sides by 4/6:
[tex]a = \frac{3}{6} \div \frac{4}{6}\\\\a = \frac{3}{6} \cdot \frac{6}{4}\\\\a = \frac{18}{24}\\\\a = \frac{3}{4}[/tex]
Hope this helped!
simplify use the multiplication rule
Answer:
3
Step-by-step explanation:
[tex] \sqrt[4] {27} \cdot \sqrt[4] {3} = [/tex]
[tex] = \sqrt[4] {27 \cdot 3} [/tex]
[tex] = \sqrt[4] {3^3 \cdot 3^1} [/tex]
[tex] = \sqrt[4] {3^4} [/tex]
[tex] = 3 [/tex]
What expression is equal to6 e + 3 (e-1)
Answer:
9e -3
Step-by-step explanation:
Perform the indicated multiplication:
6 e + 3 (e-1) = 6e + 3e - 3
This, in turn, simplifies to
9e -3, or 3(3e - 1).
Answer:
ANSWER: 9e-3
Step-by-step explanation:
6e+3(e−1)
As we need to simplify the above expression:
First we open the brackets :
3(e-1)=3e-33(e−1)=3e−3
Now, add it to 6e.
So, it becomes,
$$\begin{lgathered}6e+3e-3\\\\=9e-3\end{lgathered}$$
Hence, equivalent expression would be 9e-3.
2. Imagine you are one of the people who left the luncheon with a contagious disease and interacted with an average of 9 different people each day. How many people could potentially be infected in 7 days
Answer:
63 people.
Step-by-step explanation:
If you have a contagious disease and met with 9 different people each day for 7 days, that'll be 63 people that have gotten infected. 9 x 7 = 63. Hope this helps you!
the dot plot above identifies the number of pets living with each of 20 families in an apartment building .what fraction of families have more than two pets
Answer:
B. ⅕
Step-by-step explanation:
Fraction of families having more than 2 pets = families with pets of 3 and above ÷ total number of families in the apartment
From the dot plot above, 3 families have 3 pets, and 1 family has 4 pets.
Number of families with more than 2 pets = 3 + 1 = 4
Fraction of families with more than 3 pets = [tex] \frac{4}{20} = \frac{1}{5} [/tex]
The fraction of families that have more than two pets is B. [tex]\frac{1}{5}[/tex]
Calculations and ParametersGiven that:
Fraction of families having more than 2 pets = families with pets of 3 and above/total number of families in the apartment
From the dot plot above:
3 families have 3 pets, 1 family has 4 pets.Number of families with more than 2 pets
= 3 + 1
= 4
Fraction of families with more than 3 pets = [tex]\frac{4}{20} = \frac{1}{5}[/tex]
Read more about dot plots here:
https://brainly.com/question/25957672
#SPJ5
A random variable is not normally distributed, but it is mound shaped. It has a mean of 14 and a standard deviation of 3. If you take a sample of size 10, can you say what the shape of the sampling distribution for the sample mean is
Answer:
Step-by-step explanation:
from the question,
the mean 14
the standard deviation is 3
and sample size is 10.
since the n which is the sample size is 10, then the distribution is mound shaped.
why?
this is due to the fact that the random variable from which we took the sample is mound shaped.
The sampling distribution of the mean is normally distributed although the question says the random variable is not normally distributed. so the shape is bell shaped and normally distributed.
the standard deviation of the mean is
3/√10
= 0.948
Last year, Rob set up the Road Runner Race for his school.
The race was 1,200 meters long and 188 people signed up to
run the race. 38 people did not show up to run. This year,
there will be 3 times as many runners as last year. How
many people will run the race this year?
Answer:
450 runners
Step-by-step explanation:
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and the number of sit-ups a person can do (y). The results were: y = a+bx b = -0.89 a = 23.65 r2 = 0.7038 If a person watches 14 hours of television a day, predict how many sit-ups he can do. What is the value of the correlation coefficient? Round to three decimal places.
Answer:
y = 11.19 ; 0.839
Step-by-step explanation:
Given the following :
relationship between hours of TV watched per day (x) and the number of sit-ups a person can do (y)
y = a + bx ; comparing with the linear regression model function
y = predicted variable
a = intercept
b = slope or gradient
x = independent variable
b = -0.89 a = 23.65 r2 = 0.7038
Therefore, if a person watches for 14 hours per day, that is x = 14, the number of sit-ups he can do will be :
y = 23.65 + (-0.89)(14)
y = 23.65 - 12.46
y = 11.19
About 11 sit-ups.
If the r^2 value = 0.7038
Then the Coefficient of regression = r
Will be the square root of r^2
r = sqrt(r^2)
r = sqrt(0.7038)
r =0.8389278 = 0.839
F(x)=2x+6,g(x)=4x^2 find (f+g)(x)
Work Shown:
(f+g)(x) = f(x) + g(x)
(f+g)(x) = 2x+6 + 4x^2
(f+g)(x) = 4x^2+2x+6
please help me asap!!!!!
Answer:
392
Step-by-step explanation:
1.49×10⁸/3.8×10⁵ = 392
2. In a 100m race, Luke was 2m ahead of Azam. Chandra was 3m behind Luke, Maggie was 7m ahead of Chandra. Luke was 5m behind Darren. Who was in the first place?
Answer:
luke won
Step-by-step explanation:
he is 2 meters ahead of azam witch is in 2dn place
Stephanie went to the shoe store and bought two pairs of flip-flops. One pair was $19.95, and the other was $23.55. If she has $50.00, how much will she have left after buying the shoes?
Answer:
$6.50
Step-by-step explanation:
First start by adding the prices of the pairs of shoes combined.
19.95+23.55=43.50
subtract the total price of both pairs of shoes from her total
50-43.50 = 6.50
how many wall are there in your room? what are the shape of the floor and ceiling in your room ? how can you find the area of each shape?prepare the answer. present the conclusion in the form of report. plz answer the question in right.how many wall are there in your room? what are the shape of the floor and ceiling in your room ? how can you find the area of each shape?prepare the answer. present the conclusion in the form of report. plz answer the question in right. plz answer the question steps by step.
Answer:
4 walls in my room. The shape of my room is square and my ceiling in square. By looking at it and measuring it. Thats how I found my answer.
I believe this is correct if it is can you mark brainliest? Hope I helped!!!! :)
Answer:
8 walls etc....
Step-by-step explanation:
Basketball A basketball player makes 8 of 12 free throws
in the first game of the season. If she shoots with the same
accuracy in the second game, how many of the 15 free
throws she attempts will she make?
Hey market sales six cans of food for every seven boxes of food the market sold a total of 26 cans and boxes today how many of each kind did the market sale
Answer:
It sold 14 cans boxes of food and 12 cans of food.
Step-by-step explanation:
The factor for the food cans depend upon every seven food boxes .So, the same no. of sets of food cans will be sold.
Let the no. of sets of food boxes be x.
According to the question,
6x+7x=26
13x=26
x=26/13
x=2
No. of food cans =6x=6×2=12 cans
No. of food boxes=7x=7×2=14 boxes
Please mark brainliest ,if it is truly the best ! Thank you!
Given m = - 1/4 & the point (4, 5)which of the following is the point slope form of the equation?
Answer:
y - 5 = -1/4(x - 4)
Step-by-step explanation:
Point slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
To find the point slope form, plug in the point given and the slope.
y - y1 = m(x - x1)
y - 5 = -1/4(x - 4)
BRAINLEST , If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.
Answer:
Question 18: B. 104
Question 19: [tex] x = \frac{3}{2} [/tex]
Step-by-step Explanation:
Question 18:
Step 1: express the inverse relationship with an equation
[tex] y = \frac{k}{x^2} [/tex] ,
where k is constant
y = 26 when x = 4,
Constant, k, = [tex] y*x^2 = k [/tex]
[tex] k = 26*4^2 = 416 [/tex]
The equation would be [tex] y*x^2 = 416 [/tex]
Step 2: use the equation to find y when X = 2.
[tex] y*x^2 = 416 [/tex]
[tex] y*2^2 = 416 [/tex]
[tex] y*4 = 416 [/tex]
Divide both sides by 4
[tex] \frac{y*4}{4} = \frac{416}{4} [/tex]
[tex] y = 104 [/tex]
Question 19:
[tex] \frac{x}{3} = \frac{x + 2}{7} [/tex]
Cross multiply
[tex] x(7) = 3(x + 2) [/tex]
[tex] 7x = 3x + 6 [/tex]
Subtract 3x from both sides
[tex] 7x - 3x = 3x + 6 - 3x [/tex]
[tex] 4x = 6 [/tex]
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{6}{4} [/tex]
[tex] x = \frac{3}{2} [/tex]
Answer: D.) 52
Explanation: I guessed and got it right lol
Câu 99: Cho hàm số f x xác định trên ℝ , bảng biến thiên của hàm số f x như sau.
x 1 1 3
f x | 0 |
f x
0 0
4
Mệnh đề nào dưới đây đúng?
A. Hàm số f x đồng biến trên 1;.
B. Hàm số f x đồng biến trên ; 1 và 3;.
C. Hàm số f x nghịch biến trên ; 1.
D. Hàm số f x đồng biến trên ; 1 3; .
Answer:
i doesn,t understand this language
What is the issue with the work? It is wrong. Please answer this for points!
Answer:
3 ( a ) : x = 3.6,
3 ( b ) : x = 5
Step-by-step explanation:
For 3a, we can calculate the value of x through Pythagorean Theorem, which seemingly was your approach. However, the right triangle with x present as the leg, did not have respective lengths 9.6 and 12. The right angle divides 9.6 into two congruent parts, making one of the legs of this right triangle 9.6 / 2 = 4.8. The hypotenuse will be 12 / 2 as well - as this hypotenuse is the radius, half of the diameter. Note that 12 / 2 = 6.
( 4.8 )² + x² = ( 6 )²,
23.04 + x² = 36,
x² = 36 - 23.04 = 12.96,
x = √12.96, x = 3.6
Now as you can see for part b, x is present as the radius. Length 3 forms a right angle with length 8, dividing 8 into two congruent parts, each of length 4. We can form a right triangle with the legs being 4 and 3, the hypotenuse the radius. Remember that all radii are congruent, and therefore x will be the value of this hypotenuse / radius.
( 4 )² + ( 3 )² = ( x )²,
16 + 9 = x² = 25,
x = √25, x = 5
How to evaluate this help me out so lost?
Answer:
5443
Step-by-step explanation:
Order of Operations: BPEMDAS
Always left to right.
Step 1: Add 68 and 5042
68 + 5042 = 5110
Step 2: Add 5110 and 333
5110 + 333 = 5443
And we have our answer!
Use the matrix tool to solve the system of equations choose the correct ordered pair -5x+6y=-3 6x-6y=12
Answer:
Hello,
x=9
y=7
Step-by-step explanation:
[tex]A*U=B\\\\\begin{bmatrix}-5&6\\6&6\\\end{bmatrix}*\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-3\\12 \end{bmatrix}\\\\\\A^{-1}=\begin{bmatrix}1&1\\1&\dfrac{5}{6}\\\end{bmatrix}\\\\\\A^{-1}*A*U=A^{-1}*B\\\\U=\begin{bmatrix}9\\7 \end{bmatrix}\\[/tex]
what is heavier ten tons of wool or ten tons of steel
A Markov chain has 3 possible states: A, B, and C. Every hour, it makes a transition to a different state. From state A, transitions to states B and C are equally likely. From state B, transitions to states A and C are equally likely. From state C, it always makes a transition to state A.
(a) If the initial distribution for states A, B, and C is P0 = ( 1／3 , 1／3 , 1／3 ), find the distribution of X2
(b) Find the steady state distribution by solving πP = π.
Answer:
A) distribution of x2 = ( 0.4167 0.25 0.3333 )
B) steady state distribution = [tex]\pi a \frac{4}{9} , \pi b \frac{2}{9} , \pi c \frac{3}{9}[/tex]
Step-by-step explanation:
Hello attached is the detailed solution for problems A and B
A) distribution states for A ,B, C:
Po = ( 1/3, 1/3, 1/3 ) we have to find the distribution of x2 as attached below
after solving the distribution
x 2 = ( 0.4167, 0.25, 0.3333 )
B ) finding the steady state distribution solving
[tex]\pi p = \pi[/tex]
below is the detailed solution and answers
nine times a number
Answer:
if we do 9 times a number that will be
9x
Answer:
9x
Step-by-step explanation:
9 times a number (a variable) = 9x
Solve each equation for the indicated variable. Solve for pi.
9514 1404 393
Answer:
π = 2A/r²
Step-by-step explanation:
Multiply by the inverse of the coefficient of π.
A = π(r²/2)
π = 2A/r²
Simplify the expression (6^4)^2
When raising a power inside parentheses to another power, multiply the numbers:
(6^4)^2 = 6^(4x2) = 6^8
Simplified = 6^8
6^8 = 1679616
Answer:
[tex] \boxed{ \purple{ {6}^{8} }}[/tex]Step-by-step explanation:
[tex] \mathsf{ ( { {6}^{4}) }^{2} }[/tex]
It is the example of Power to power law of indices.
Multiply the exponents
⇒[tex] \mathsf{ {6}^{4 \times 2} }[/tex]
Multiply the numbers
⇒[tex] \mathsf{ {6}^{8} }[/tex]
-------------------------------------------------------
[tex] \mathsf{\orange{ \underline{ power \: to \: power \: law \: of \: indices}}}[/tex]
If [tex] \mathsf{ ({x}^{a} )^{b}} [/tex] is an algebraic term then [tex] \mathsf{( {x}^{a} ) ^{b} = {x}^{a \times b} }[/tex]
i.e When an algebraic term in the index form is raised to another index , the base is raised to the power of two indices.
Hope I helped!
Best regards!!
Two fraction have the same denominator, 8.the some of two fraction is 1/2.if one of the fraction is added to five times the order, the result is 2,find the number.
Answer:
1/8, 3/8
Step-by-step explanation:
Let x and y represent the two fractions. Then we are given ...
x + y = 1/2
x + 5y = 2
Subtracting the first equation from the second, we get ...
(x +5y) -(x +y) = (2) -(1/2)
4y = 3/2 . . . . . simplify
y = 3/8 . . . . . . divide by 4
x = 1/2 -3/8 = 1/8
The two numbers are 1/8 and 3/8.
1 A. All master photographers are artists.
2. Ansel Adams is a master photographer.
Therefore, Ansel Adams is an artist.
B. 1. All master photographers are artists.
2. Ansel Adams is an artist.
Therefore, Ansel Adams is a master photographer.
Answer:
A is the appropriate option.
Step-by-step explanation:
The question given is a conditional statement.
With the condition that all master photographers are artist. This implies that any person who is a master photographer is automatically an artist.
A. Comparing the statement here, since Ansel Adam's is a master photographer, he is an artist.
B. Ansel Adams is an artist, but it is possible that not all artists are master photographer.
A is the correct option.
1. All master photographers are artists.
2. Ansel Adams is a master photographer.
Therefore, Ansel Adams is an artist.
Answer:
The correct answer is A.
Step-by-step explanation: