Use back-substitution to solve the system of linear equations.

Answer:

Step-by-step explanation:

percentage is per 100.

If we have to find x as percentage of y then

formula for percentage is given by = x/y*100

_______________________________________________

Given

total no. of shares = 50,000

Share bought by investor = 1,000

Percentage of share bought by investor

= Share bought by investor/total no. of shares *100

= (1000/50000)*100 = 2%.

It means that if  there are 100 shares for company then investor owns 2 shares of the company. This makes the qualitative analysis easy.

2% percent of the company does the investor own.

Answer:

65%

Step-by-step explanation:

Nadine mixes a juice solution that is made from 3 gallons of an 80% juice solution and 1 gallon of a 20% juice solution. What is the percent concentration of the final solution?

3 gallons of 80% juice solution contains this amount of juice:

80% * 3 gal = 0.8 * 3 gal = 2.4 gal

1 gallon of 20% juice solution contains this amount of juice:

20% * 1 gal = 0.2 * 1 gal = 0.2 gal

The total amount of juice in the final juice solution is

2.4 gal + 0.2 gal = 2.6 gal

The total amount of juice solution made is 3 gal + 1 gal = 4 gal

The 4 gal juice solution contains 2.6 gallons of juice.

2.6 gallons is what percent of 4 gallons?

2.6/4 * 100% = 0.65 * 100% = 65%

Answer: 65%

Answer:

65% i got the answer right on the question

Step-by-step explanation:

The question is incomplete. Here is the complete question.

In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each particpant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree", and these are assigned the numbers 1 or -1, respectively. pArticipnat's responses to the survey are encoded as a vector in R4, where coordinates coreespond to their answers to each question. Here are the questions:

Question #1: I prefer outdoor activities, rather than indoor activities.

Question #2: I prefer going out to eat in restaurants, rahter than cooking at home.

Question #3: I prefer texting, rather than talking on the phone.

Question #4: I prefer living in a small town, rather than in a big city.

Here are the results for the questionaire, with a group of 5 participants:

                        Question1     Question2   Question3       Question4

participant A           1                      1                   -1                      -1

participant B           -1                     1                    1                       1

participant C           -1                    -1                    1                       1

participant D           1                     -1                   -1                      -1

participant E            1                    -1                    1                       1

Two participants are considered to be "compatible" with each other if the angle between their compatibility vectors is 60° or less. Participants are considered to be "incompatible" if the angle between their compatibility vectors is 120° or larger. For angles between 60° or 120°, pairs of participants are warned that they "may or may not be compatible".

(a) Which pairs of paricipants are compatible?

(b) Which pairs of participants are incompatible?

(c) How would this method of testing compatibility change if the questionnaire also allowed the answer "Neutral", which would correspond to the number zero in a participant's vector? Would this be better than only

allowing  "Agree" or "Disagree"? Could anything go wrong if we allowed "Neutral" as an answer?

Answer: (a) Participants A and D; B and C; C and E.

(b) Participants A and B; A and C; A and E; B and D; C and D;

Step-by-step explanation: Vectors in R4 are vectors in a 4 dimensional space and are determined by 4 numbers.

Vectors form angles between themselves and can be found by the following formula:

cos α = [tex]\frac{A.B}{||A||.||B||}[/tex]

which means that the cosine of the angle between two vectors is equal the dot product of these vectors divided by the product of their magnitude.

For the compatibility test, find the angle between vectors:

1) The vectors magnitude:

Magnitude of a vector is given by:

||x|| = [tex]\sqrt{x_{i}^{2} + x_{j}^{2}}[/tex]

Since all the vectors have value 1, they have the same magnitude:

||A|| = [tex]\sqrt{1^{2} + 1^{2} + (-1)^{2} + (-1)^{2}}[/tex] = 2

||A|| = ||B|| = ||C|| = ||D|| = ||E|| = 2

2) The dot product of vectors:

A·B = 1(-1) + 1(1) + (-1)1 + (-1)1 = -2

cos [tex]\alpha_{1}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]

The angle that has cosine equal -1/2 is 120°, so incompatible

A·C = 1(-1) + 1(-1) + (-1)1 + (-1)1 = -4

cos [tex]\alpha _{2}[/tex] = -1

Angle = 180° --------> incompatible

A·D = 1(1) + 1(-1) + (-1)(-1) + (-1)(-1) = 2

cos [tex]\alpha _{3}[/tex] = 1/2

Angle = 60° ---------> COMPATIBLE

A·E = 1.1 + 1(-1) + (-1)1 + (-1)1 = -2

cos [tex]\alpha_{4}[/tex] = -1/2

Angle = 120° --------> incompatible

B·C = (-1)(-1) + 1(-1) + 1.1 + 1.1 = 2

cos [tex]\alpha _{5}[/tex] = 1/2

Angle = 60° -------------> COMPATIBLE

B·D = (-1)1 + 1(-1) + 1(-1) + 1(-1) = -4

cos[tex]\alpha_{6}[/tex] = -1

Angle = 180° -----------> incompatible

B·E = (-1)1 + 1(-1) + 1.1 + 1.1 = 0

cos[tex]\alpha _{7}[/tex] = 0

Angle = 90° -------------> may or may not

C·D = (-1)1 + (-1)(-1) + 1(-1) + 1(-1) = -2

cos[tex]\alpha_{8} =[/tex] -1/2

Angle = 120° ---------------> Incompatible

C·E = (-1)1 + (-1)(-1) + 1.1 + 1.1 = 2

cos [tex]\alpha_{9}[/tex] = 1/2

Angle = 60° ---------------> COMPATIBLE

D·E = 1.1 + (-1)(-1) + (-1)1 + (-1)1 = 0

cos [tex]\alpha_{10}[/tex] = 0

Angle = 90° -----------------> may or may not

(c) Adding zero (0) as a component of the vectors would have to change the method of compatibility because, to determine the angle, it is necessary to calculate the magnitude of a vector and if it is a zero vector, the magnitude is zero and there is no division by zero. So, unless the service change the method, adding zero is not a good option.

Answer:

I guess that the area we care about is the yellow area, delimited by the functions.

f(x) = 8*(x)^(1/4)

and the line with the slope s= 8/1 = 8 (as the line goes through the points (0,0) and (1, 8)).

g(x) = 8*x

then we want tofind the area between x = 0 and x = 1, of f(x) - g(x)

then we have:

[tex]I = \int\limits^1_0 {f(x)} \, dx = \int\limits^1_0 {8*\sqrt[4]{x} )} \, dx = (8*(4/5)*\sqrt[4]{1^5} - 8*(4/5)*\sqrt[4]{0^5}) = 6.4[/tex]

now, for the area under the g(x) we have:

[tex]I2 = \int\limits^1_0 {g(x)} \, dx = \int\limits^1_0 {8x} \, dx = (8/2)*1^2 - (8/2)*0^2 = 4.[/tex]

then I - I2 = 6.4 - 4 = 2.4

The yellow area is 2.4

And then, if we rotate this about the line AB, the volume will be:

B = 2*pi*2.4 = 2*3.14*2.4 = 15.075

The figure will be something like a half spheroid, with a hole in the shape of a cone inside of it.

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

Cross multiply.

10(4x + 1) = 15(2x)

Expand brackets.

40x + 10 = 30x

Add -30x and 10 on both sides.

40x - 30x = -10

10x = -10

Divide both sides by 10.

10/10x = -10/10

x = -1

Answer:

C. The term average is not used in statistics. The term "mean" should be used for the result obtained by adding all of the sample values and dividing by the total number of sample values.

Step-by-step explanation:

In colloquial language, the average is the result obtained when we add all the sample values and divide by the total number of sample values.

However, in statistics, the term which is used to represent this calculation is the "mean" of the sample data. The term average is not used.

The correct option is C.

Answer:

When x is 1, y=7

When x is 2, y=10

When x is 3, y= 13

Step-by-step explanation: Plug in each number for x and solve

Answer:

If x=1, y=7

If x=2, y=10

If x=3, y=13

Step-by-step explanation:

For every equation substitute x in y = 3x + 4, with the value you want.

For example the first one says when x=1, so simply substitute x with 1 in y = 3x + 4.

So it'll look something like this:

y = 3(1) + 4.

Simply solve the equation from there, and you'll get y=7, and we know that x is already equal to 1.

So if x=1, then y=7

Answer:

  87

Step-by-step explanation:

Such "find a pattern" problems can always be answered a number of ways.

Here, the alternating pattern (6, 12, 6, 12, ...) of first differences doesn't seem to hold. However, the first differences of alternate terms does seem to be constant: 33, 51, 69 all have a common difference of 18.

The next term in that sequence is 69+18 = 87.

___

The other terms seem to have increasing differences:

  57 -39 = 18

  84 -57 = 27

If that pattern continues, then the second missing term will be 84 +36 = 120.

___

So, one way to extend the sequence is ...

  33, 39, 51, 57, 69, 84, 87, 120, 105, 165, ...

The rule is that the sequence alternates a linear sequence and a quadratic one.

Answer:

June Financial Reports

a) Cost of goods available for sale = $5,250

b) Moving-Average unit cost for:

i) June 1:  = $5

ii)        12:  = $4.75

iii)       15: = $4.75

iv)      23:  = $5.75

v)       27:  = $5.25

Step-by-step explanation:

a) Calculations:

Date     Explanation   Units     Unit Cost    Total Cost   Moving Average Cost

June 1 Inventory          150        $4                $600         $4.000

      12 Purchase         450          5               2,250            4.750

      15 Sale                 500          7                      3,500     4.750

     23 Purchase         400          6               2,400            5.750

     27 Sale                 420          8                      3,360     5.250

     30 Inventory           80

Cost of goods available for sale = Cost of Beginning Inventory + Cost of Purchases = $5,250 + ($600 + 2,250 + 2,400)

b) Moving-Average unit cost for:

i) June 1: Cost of goods available/Units of goods available = $5 ($600/150)

ii)        12: Cost  of goods available/Units of goods available = $4.75 ($600 + 2,250/600)

iii)       15: Cost  of goods available/Units of goods available = $4.75 ($475/100)

iv)      23: Cost of goods available/Units of goods available = $5.75 ($475 + 2,400)/500

v)       27: Cost of goods available/Units of goods available = $5.25 ($420/80)

Answer:

The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.

Step-by-step explanation:

We have the standard deviation of the saple, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 50 - 1 = 49

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2\frac{1.3}{\sqrt{50}} = 0.4[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.

Answer:

Step-by-step explanation:

To find the relationship between the given lines, we have to find the slope of both lines using slope formula, which is

So for AB, we will get

And for CD , we will get

Since the slopes of the two lines are equal , and when slopes are equal , lines are parallel .

Answer: 8.6602540378

Step-by-step explanation:

Based on pythagorean’s theorem we have:

[tex]\sqrt{14^{2}-11^{2} } =\sqrt{75}=8.66025[/tex]

Answer:

19.49% probability that no more than 16 of them are strikes

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 30, p = 0.626[/tex]

So

[tex]\mu = E(X) = np = 30*0.626 = 18.78[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*(1-0.626)} = 2.65[/tex]

What is the probability that no more than 16 of them are strikes

Using continuity correction, this is [tex]P(X \leq 16 + 0.5) = P(X \leq 16.5)[/tex], which is the pvalue of Z when X = 16.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{16.5 - 18.78}{2.65}[/tex]

[tex]Z = -0.86[/tex]

[tex]Z = -0.86[/tex] has a pvalue of 0.1949

19.49% probability that no more than 16 of them are strikes

Answer:

(a) 780 students and 960 non-students  

(b) No. The maximum revenue is RM9000 from 1200 non-students.

(c). Revenue is maximum of RM9000 at 1200 non-students, decreasing by RM2.50 per student to a minimum of RM6000 at 1200 students

Step-by-step explanation:

 Let x = IIUM students and

and  y = non-IIUM students

You have two conditions

(a)          x +         y = total vehicles parked

(b) 5.00x + 7.50y = total gross receipts

(a) Wednesday

From your table,  

       x +          y = 1740

5.00x + 7.70y = RM11 100  

Solve the simultaneous equations

[tex]\begin{array}{rrcrl}(1) & x + y & = &1740&\\(2) & 5.00x + 7.50y & = & 11 100\\(3)& 5.00x + 5.00y & = & 8700 & \text{Multiplied (1) by 5}\\&2.50 y & = &2400 &\text{Subtracted (3) from (2)}\\(4)&y& = &\mathbf{960} &\text{Divided each side by 2.50}\\& x +960& = &1740& \text{Substituted (4) into (1)}\\& x& = &\mathbf{780}& \\\end{array}\\\text{There are $\large \boxed{\textbf{780 students and 960 non-students}}$}[/tex]

(b) Can 1200 vehicles bring in RM10000?

No. Even if all the cars were from non-students, the most you could get is  

1200 × 7.50 = RM9000

(c) Possible combinations for 1200 vehicles  

Revenue = 5.00x + 7.50y = 5.00x + 7.50(1200 -x) = 5.00x + 9000 - 7.50x =  

Revenue = 9000 - 2.50x

The maximum revenue of RM9000 occurs when there are no student cars and 1200 non-student cars.

For each student car that enters and displaces a non-student, the revenue drops by RM2.50.

Finally. when there are 1200 student cars and no non-students, the revenue has dropped to a minimum of RM6000.  

Answer:

slope = 2

Step-by-step explanation:

All four points lie on the same line.

Taking the first and fourth points, the slope can be found by the formula

slope, m = (y2-y1)/(x2-x1) = (3- -3) / (1- -2) = 6/3 =2

See attached diagram.

Answer:

2

Step-by-step explanation:

edge 2020

Answer:

n^2+3

Step-by-step explanation:

As we can see in the diagram

1st pattern consists from 1 square 1x1 +3 squares 1x1 each

2nd pattern consists from 1 square 2x2 +3 squares 1x1 each

3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each

4-th pattern consists from 1 square 4x4 + 3 squares 1x1  each

We can to continue :

5-th pattern consists from 1 square 5x5+3 squares 1x1 each

So the nth    pattern consists from 1 square nxn+3 squares 1x1 each

Or total amount of 1x1 squares in nth pattern N= n^2+3

The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."

From the given diagram

We can see that every term is made up with a square which side is n and three small square side is 1.

So,

1st term is 1 × 1 + 3 = 4

2nd term is 2 × 2 + 3 = 4

3rd term is  3 × 3 + 3 = 12

4th term is 4 × 4 + 3 = 19

So, nth term is [tex]n^{2} +3[/tex]

Hence, The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

Learn more about nth term of a sequence here

https://brainly.com/question/24306119

#SPJ2

Answer:

- 220° and 500°

Step-by-step explanation:

To find the coterminal angles add / subtract 360°, that is

140° - 360° = - 220°

140° + 360° = 500°

Answer:

- 220° and 500°

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

Number of students whose favorite class is Math:

60*0.85=51

Number of students whose favorite class is Science:

15% is equal to 0.15.

60*0.15=9

Subtract number of students who like science from number of students who like math.

51-9=42

42 more students in the survey prefer math over science.

Answer:

42

Step-by-step explanation:

85% math

15% science

Subtract

85-15 = 70

The difference is 70 %

70% of 60 students

.70 * 60 = 42

There is a 42 student difference

Answer:

y - 3 = (1/2)(x - 1)

Step-by-step explanation:

As we go from (1, 3) to (5, 1), we see that x (the run) increases by 4 and y (the rise) decreases by 2.  Hence, the slope is m = rise / run = 2/4, or m = 1/2.

Then the desired point slope equation is  y - 3 = (1/2)(x - 1).

Answer:

all real numbers

Step-by-step explanation:

Answer:

C. All real numbers

Step-by-step explanation:

x goes forever in both the positive and negative directions, so the domain is all real numbers.

Answer:

Step-by-step explanation:

We would assume a binomial distribution for the handedness of the population. Let x be a random variable representing the type of handedness in the population. The probability of success, p is that a randomly chosen person is left handed only. Then probability of failure is that a chosen person is not left handed only(right handed only or both).

p = 12/100 = 0.12

number of success, x = 20

n = 200

the probability that there are at least 20 left-handers is expressed as P(x ≥ 20)

From the binomial probability calculator,

P(x ≥ 20) = 0.84

Answer:

This is an arithmetic fraction written under the line that indicates the equal part, the divisor.

Step-by-step explanation:

Answer:denominator is the lower part of a fraction.

Step-by-step explanation:

Feel pleasure to help u...

Answer:

(115.2642, 222.7358).

Step-by-step explanation:

Given data:

type A: n_1=60, xbar_1=1827, s_1=168

type B: n_2=180, xbar_2=1658, s_2=225

n_1 = sample size 1, n_2= sample size 2

xbar_1, xbar_2 are mean life of sample 1 and 2 respectively. Similarly, s_1 and s_2 are standard deviation of 1,2.

a=0.05, |Z(0.025)|=1.96 (from the  standard normal table)

So 95% CI is

(xbar_1 -xbar_2) ± Z×√[s1^2/n1 + s2^2/n2]

=(1827-1658) ± 1.96×sqrt(168^2/60 + 225^2/180)

= (115.2642, 222.7358).

Answer:

0.1587

Step-by-step explanation:

According to the situation, the solution and the data provided is as follows

mean = 12.45 ounces

Standard deviation = 0.30 ounces

maximum = 12.75 ounces

More than ounces of soda = 12.75

Based on the above information, the probability is

[tex]Z=\frac{X-\mu }{\sigma } \\\\Z=\frac{12.75-12.45 }{0.30 } \\\\\Z=\frac{0.30 }{0.30 } \\\\Z= 1 \\\\P(X> 12.75)=1-P(X< 12.75) \\\\\P(X> 12.75)=1-P(Z< 1) \\\\[/tex]

As we know that

P(Z<1) = 0.8413

So,

P (X > 12.75) = 1 - 0.8413

= 0.1587

The program goes through the following steps when the input is 13

step 1) check to see if the age is less than 2. It is not, so we move on

step 2) check to see if the age is 2 to less than 12. It is not, so we move on

step 3) check to see if the age is 12 to less than 22. We are in the right range, so we execute the print statement "student admission is $8"

After this the program is done. It doesn't check to see if the age is greater than 22 (that only would apply if the other if statements were false).

So we have four steps. The first three are checking those "if" statements mentioned. The fourth statement is executing the print output to show the price.

Answer:

It would take 3 steps before executing

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

At the beggining, it says they are stacked in 5 layers which means the number of cubes is divisible by 5.

If the number of cubes equals x:

The least amount of sugar cubes the Jones family could have used is [tex]61*2[/tex] which equals 122. The most they couldve used is [tex]61*3[/tex] which equals 183.

Based on the information from the Jones family, x is between 122 and 183.

Based on the information from the Connor's, x is between 176 and 264.

Based on the information from both, x is between 176 and 183. The only number that is divisible by 5 between those numbers is 180 cubes.

Answer:

b: 4

Step-by-step explanation:

i took the test on edge 2020

The gallons of gasoline the car has left after it has traveled 330 miles is 4 gallons so option (B) will be correct.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given the table of the number of miles and gallons.

If we take two points of the number of miles and gallons.

Then,

1 st point = ( 0 ,15 )

2 nd point = ( 90 , 12)

Now since the relation is linear which can be seen by data.

So,

Linear equation joining points 1st and 2nd is

y - 15 = [(12-15)/(90-0)](x - 0)

y - 15 = -x/30

y = (450 - x)/30

So,

At x = 330 miles

y = (450 - 330 )/30

y = 4 gallons

Hence "The gallons of gasoline the car has left after it has traveled 330 miles is 4 gallons".

For more about the equation,

https://brainly.com/question/10413253

#SPJ2

Answer:

12.5

Step-by-step explanation:

This is the answer!

Answer:

50%

Step-by-step explanation:

Total Cards = 4

6 or even cards = 2

P( 6 or even) = 2/4

=> 1/2

In %age:

50%

Answer:

Sin(u-v)= (-119/169)

Step-by-step explanation:

Sin(a-b)= Sinacosb-cosasinb

Sin(u-v)= sinucosv-cosusinv

Sinu= 5/13

U = sin^-1(5/13)

U= 22.62

Sinv= 12/13

V= sin^-1(12/13)

V= 67.38

Fr right angle triangle

If sin u = 5/13

Cos u = 12/13

If sin v = 12/13

Cos v= 5/13

Sin(u-v)= sinucosv-cosusinv

Sin(u-v)=(5/13)*(5/13) -(12/13)*(12/13)

Sin(u-v)= 25/169 - 144/169

Sin(u-v) = (25-144)/169

Sin(u-v)= (-119/169)