5. What is the solution of the following linear system?
y= 3x + 1
2y = 6x + 2
O A. (5,-2)
OB. (34)
C. Infinitely many solutions
D. No solution

Answer:

80

Step-by-step explanation:

75                60

------     =      ------

100                x

100 x 60 = 6000

75x = 6000

x =  80

Answer:

0

Step-by-step explanation:

- 2×3= - 6

2×3=6

-6+6=0

Answer:

0

Step-by-step explanation:

first

(-2x3)+(3x2)

-6+6=0

Hi there! :)

Answer:

Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Step-by-step explanation:

To solve, we will need to set up a system of equations:

Let x = # of dramas, y = # of comedies, and z = # of documentaries:

Write equations to represent each person:

Gina:

x + y + z = 11

Sam:

2x + 3y + 2z = 27

Robby:

x + 2y + 2z = 19

Write the system:

x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Begin by subtracting the third equation from the second:

2x + 3y + 2z = 27

x + 2y + 2z = 19

-----------------------

x + y = 8

If x + y = 8, plug this into the first equation:

(8) + z = 11

z = 11 - 8

z = 3

We found the # of documentaries Gina rented, now we must solve for the other variables:

Subtract the top equation from the third. Substitute in the value of z we solved for:

x + 2y + 2(3) = 19

x + y + (3) = 11

-------------------------

y + 3 = 8

y = 5

Substitute in the values for y and z to solve for x:

x + 5 + 3 = 11

x + 8 = 11

x = 11 - 8

x = 3.

Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Answer:

B- x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Step-by-step explanation:

I took the quiz

Answer:  11 down and 9 right

Step-by-step explanation:

Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down

and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.

Given slope = -11/9

the numerator is -11 so the "rise" is  DOWN 11 units

the denominator is 9 so the "run" is RIGHT 9 units

Answer:

f(x) = (x - 3)² - 5

Step-by-step explanation:

equate equation to 0

(x - 3)² = 0

take the square root on both sides

x - 3 = 0

add 3

x = 3

If x = 3 then you are moving to 3 units to the right.

- 5 means you are going downward 5 units.

Answer:

2.7 in²

Step-by-step explanation:

Given:

∆BAC ~ ∆EDF

Area of BAC = 6 in²

EF = 2 in

BC = 3 in

Required:

Area of ∆EDF

SOLUTION:

Let x = area of ∆EDF

[tex] \frac{6 in^2}{x} = (\frac{3 in}{2 in})^2 [/tex] (theorem of area of similar triangles)

[tex] \frac{6 in^2}{x} = (\frac{3 in}{2 in})^2 [/tex]

[tex] \frac{6}{x} = \frac{9}{4} [/tex]

Cross multiply:

[tex] 6*4 = 9*x [/tex]

[tex] 24 = 9x [/tex]

Divide both sides by 9

[tex] \frac{24}{9} = x [/tex]

[tex] 2.67 = x [/tex]

Area of ∆EDF = 2.7 in²

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome of event/Total outcome.

If a video rental store keeps a list of their top 15 movie rentals each week, the total outcome is 15.

If the list for the week includes 6 action, 4 comedies, 3 dramas, and 2 mysteries and the store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store, the probability that she selected 2 comedies and 1 action movie will be calculated as shown;

Probability of selecting 2 comedies  = 4/15*4/15 = 16/225 (Note that the expected outcome in this case is 4).

Probability of selecting 1 action movie = 6/15 = 2/5

Hence, the probability that she selected 2 comedies and 1 action movie will be equivalent to 16/225*2/5 = 32/1125

Note that the rented movies will have to be returned hence reason for the replacement.

Answer:

Show that the statement is true for n=1

Step-by-step explanation:

Hey,

Show that the statement is true for n=1

You can check my other answer there which explains a little bit more the ideas.

https://brainly.com/question/17162256

thank you

Answer:

Standard deviation = 2.2360679774998

Step-by-step explanation:

We are asked to find the Standard deviation of a samples of speeches as an awards.

The formula for sample standard deviation is given as:

√[(x - μ)²/N - 1 ]

Step 1

We find the mean (μ)

The mean of the sample =>

= Sum of term/ Number of terms

= (3 + 7 + 5 + 4 + 1)/5

= 20/5

= 4

Step 2

Find the Standard deviation of the sample

√[(x - μ)²/N - 1 ]

N = number of samples or terms = 5

= √[(3 - 4) ² + (7 - 4)² + (5 - 4)² +(4 - 4)² +(1 - 4)²/ 4]

= √ (1 ² + 3² + -1² + 0² + -3²/4)

= √( 1 + 9 + 1 + 0 + 9/4)

= √20/5 - 1

= √5

= 2.2360679774998

The standard deviation of the sample = 2.2360679774998

Answer:

I thinksomething is wrong.

I'm getting another proving it's-tan thita.

I hope this is the one you are searching for..

Complete question is;

Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

Answer:

P(All three are not caused by firmware) = 83.84%

Probability that the entire batch will be accepted = 0.8384

Step-by-step explanation:

We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.

Thus,

Cases not caused by firmware = 8834 - 504 = 8330

So, probability of the first case not being affected by firmware is;

P(first case not caused by firmware) = 8330/8834

Also,

Probability of second case not being affected by firmware is given as;

P(second case not caused by firmware|first case not affected by firmware) = 8329/8833

Similarly,

Probability of third case not being affected by firmware is given as;

P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832

Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.

Thus, we will make use of the general multiplication rule which is;

P(A & B) = P(B) × P(A|B)

Thus;

P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)

Plugging in the relevant values, we have;

P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)

P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%

Answer:

Subtraction property

Step-by-step explanation:

Answer:

Subtraction

Step-by-step explanation:I took the test

Answer:

Question 1: 40 shirts and 40 magizines

Question 2: $4.4

Question 3: 6 gallons

Answer:

hello

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Given that:

y∞ xz

y=kxz. Where k is constant

When z=196 and x= 2 then y= 7

7=(196)(2)k

7=392k

k=1/56

There fore y=(1/56)xz

When x=3 and z =336

y=(1/56)xz

y=(1/56)(336)(3)

y=18

if value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2 then the value of y when x = 3 and z = 336 is 18.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Value of y varies jointly with x and z.

y ∞ xz

y=kxz.

Where k is constant

When z=196 and x= 2 then y= 7

Let us find the value of k

7=(196)(2)k

7=392k

Divide both sides by 7

k=1/56

y=(1/56)xz

When x=3 and z =336

y=(1/56)xz

y=(1/56)(336)(3)

y=18

Hence,  the value of y when x = 3 and z = 336 is 18.

To learn more on Ratios click:

https://brainly.com/question/13419413

#SPJ2

Answer:

The dimensions or Area of the rectangle is 1200cm².

The answer is $12792

Explanation:

It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:

1. Write the values you know and use x to represent the value you need to find

108 = 18        

  x =   82      

3. Cross multiply

x 18 = 8856

4. Find  the value of x by solving this simple equation

x = 8856 ÷ 18

x = 492 - Amount the employer pays every two weeks for Tessa's family coverage

Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.

1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks

52 ÷ 2 = 26

2. Finally, multiply the money paid by the employer every two weeks by 26

26 weeks x $492 = $12792- This is the total the employer pays annually

Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 p.m (6: 04 p.m.)

Explanation:

To solve this question, the first step is to calculate how much time does hiking to the lake, go fishing, and go back takes in total. This can be calculated by adding the time of the three activities. This means 1 hour 10 minutes + 3 hours 10 minutes + 1 hour 50 minutes which is equal to 6 hours 10 minutes. The detailed process is shown below.

Add the hours: 1 + 3 + 1 = 5

Add the minutes: 10+50 +10 = 70

Also, because the total of minutes is above 60 (each hour has 60 minutes) it is necessary to subtract 60 minutes and add 1 hour.

5 hours + 1 hour and 70 minutes - 60 minutes = 6 hours and 10 minutes

Now, to solve the question subtract the time of the activities to the time Lila needs to complete all the activities.

6: 05 p.m.  -  6 hours and 10 minutes = 11: 55 a.m

You can get this result by substracting first the hours and then the minutes

6: 05 p.m. - 6 hours = 12: 05 p.m.

12: 05 - 10 minutes = 11: 55 a.m.

According to this, Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 a.m because if she starts at 11: 54 a.m. she will be back at 6:04, which is a minute before 6:05 p.m.

Answer:

(a) 50%

(b) 47.5%

(c) 2.5%

Step-by-step explanation:

According to the honest coin principle, if the random variable X denotes the number of heads in n tosses of an honest coin (n ≥ 30), then X has an approximately normal distribution with mean, [tex]\mu=\frac{n}{2}[/tex] and standard deviation, [tex]\sigma=\frac{\sqrt{n}}{2}[/tex].

Here the number of tosses is, n = 2500.

Since n is too large, i.e. n = 2500 > 30, the random variable X follows a normal distribution.

The mean and standard deviation are:

[tex]\mu=\frac{n}{2}=\frac{2500}{2}=1250\\\\\sigma=\frac{\sqrt{n}}{2}=\frac{\sqrt{2500}}{2}=25[/tex]

(a)

To not lose any money the even rolls has to be 1250 or more.

Since, μ = 1250 it implies that the 50th percentile is also 1250.

Thus, the probability that by the end of the evening you will not have lost any money is 50%.

(b)

If the number of "even rolls" is 1250, it implies that the percentile of 1250 is 50th.

Then for number of "even rolls" as 1300,

1300 = 1250 + 2 × 25

        = μ + 2σ

Then P (μ + 2σ) for a normally distributed data is 0.975.

⇒ 1300 is at the 97.5th percentile.

Then the area between 1250 and 1300 is:

Area = 97.5% - 50%

        = 47.5%

Thus, the probability that the number of "even rolls" will fall between 1250 and 1300 is 47.5%.

(c)

To win $100 or more the number of even rolls has to at least 1300.

From part (b) we now 1300 is the 97.5th percentile.

Then the probability that you will win $100 or more is:

P (Win $100 or more) = 100% - 97.5%

                                   = 2.5%.

Thus, the probability that you will win $100 or more is 2.5%.

Answer: n = 52

Step-by-step explanation:

when we have two vectors (x,y) and (a,b) the distance between the vectors is:

D = √( (x - a)^2 + (y - b)^2)

now, we know that:

1) the distance between (x, y ) and the x-axis is 6 units.

The nearest point to (x, y) in the x-axis is the point (x, 0) so we have:

D = 6 = √( (x - x)^2 + (y - 0)^2) = √y^2

so y can be 6 or -6.

So we know that y = 6, and now we can write our point as (x, +-6)

2) The distance between our point and (8, 3) is 5 units:

D = √( (x - 8)^2 + (y - 3)^2) = 5.

And we know that the distance from the origin, (n, n) is:

D = √n = √(x^2 + y^2}

n = x^2 + y^2

Now, we should start with:

√( (x - 8)^2 + (y - 3)^2) = 5

first suppose that y = -6, then:

√( (x - 8)^2 + (-6 - 3)^2) = √( (x - 8)^2 + (-9)^2) = 5.

√( (x - 8)^2 + 81) = 5.

Then we must have that:

and we know that √25 = 5

so (x-8)^2 + 81 = 25

this can never happen, so we can discard y = -6

Now the second case, if y = 6,

√( (x - 8)^2 + (6 - 3)^2) = 5.

√( (x - 8)^2 + (3)^2) = 5.

√( (x - 8)^2 + 9) = 5.

here:

(x - 8)^2 + 9 = 25

(x - 8)^2 = 16

(x - 8) = √16 = +-4

So again we have two cases:

if x - 8 = 4, then:

x = 4 + 8 = 12

but we must have x < 8, so this can be discarded.

now, if x - 8 = -4 then:

x = -4 + 8 = 4, this is an acceptable answer, then our point is (4, 6)

And we have:

n = 4^2 + 6^2 = 16 + 36 = 52

Answer:

D. F(x) = ( (1/5)x)^2 - 4

Step-by-step explanation:

The standard transformation with a stretch and a shift is

F(x) = f(x/b) + k

The red curve has a vertex at (0,-4), and cuts the x-axis at (10,0)

That means that before the vertical shift (of k=-4), the vertex was at (0,0), and the curves passes through (10,4).

Substituting in the equation

F(10) = (10/b)^2 -4 = 0

solve for b

(10/b)^2-4 = 0

(10/b)= sqrt(4) = 2

b = 10/2 = 5

Therefore the transformation equation is

F(x) = (x/5)^2-4

The answer is

F(x) = ( (1/5)x)^2 - 4

Answer:

14/20 or .7 or 70%

Step-by-step explanation:

Total Number of cards: 20

Number of Red cards: 6

The leftover cards: 20 -6 = 14

The probability of not getting a red = 14/20

14/20 as a decimal = 14/20 = 70/100 = .7

14/20 as a percent = 14/20 = 70/100 = 70%

Answer:

the first  partial sum  [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]

the second partial sum  [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]

the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]

the fourth  partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]

the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]

the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]

Step-by-step explanation:

The term of the sequence are given as : [tex]\dfrac{1}{2}[/tex], [tex]\dfrac{1}{2^2}[/tex], [tex]\dfrac{1}{2^3}[/tex], [tex]\dfrac{1}{2^4 }[/tex] ,  .  .  .  

The nth term for this sequence is , [tex]\mathtt{a_n =( \dfrac{1}{2})^n}[/tex]

The nth partial sum of the sequence for [tex]\mathtt{a_1,a_2,a_3.... a_n}[/tex] is [tex]\mathtt{S_n}[/tex]

where;

[tex]\mathtt{S_n = a_1 +a_2+a_3+ ...+a_n}[/tex]

The first partial sum  is:  [tex]\mathtt{S_1= a_1}[/tex]

[tex]\mathtt{S_1= (\dfrac{1}{2})^1}[/tex]

[tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]

Therefore, the first  partial sum  [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]

The second partial sum is: [tex]\mathtt{S_2= a_1+a_2}[/tex]

[tex]\mathtt{S_2= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2}[/tex]

[tex]\mathtt{S_2= \dfrac{1}{2} + \dfrac{1}{4}}[/tex]

[tex]\mathtt{S_2= \dfrac{2+1}{4} }[/tex]

[tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]

Therefore, the second partial sum  [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]

The third partial sum is : [tex]\mathtt{S_3= a_1+a_2+a_3}[/tex]

[tex]\mathtt{S_3= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3 }[/tex]

[tex]\mathtt{S_3= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}}[/tex]

[tex]\mathtt{S_3= \dfrac{4+2+1}{8}}[/tex]

[tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]

Therefore, the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]

The fourth partial sum : [tex]\mathtt{S_4= a_1+a_2+a_3+a_4}[/tex]

[tex]\mathtt{S_4= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 }[/tex]

[tex]\mathtt{S_4= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}}[/tex]

[tex]\mathtt{S_4= \dfrac{8+4+2+1}{16}}[/tex]

[tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]

Therefore, the fourth  partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]

The fifth partial sum : [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5}[/tex]

[tex]\mathtt{S_5= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 }[/tex]

[tex]\mathtt{S_5= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}}[/tex]

[tex]\mathtt{S_5= \dfrac{16+8+4+2+1}{32}}[/tex]

[tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]

Therefore, the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]

The sixth partial sum: [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5+a_6}[/tex]

[tex]\mathtt{S_6= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 +(\dfrac{1}{2})^6 }[/tex]

[tex]\mathtt{S_6= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64} }[/tex]

[tex]\mathtt{S_6= \dfrac{32+16+8+4+2+1}{64}}[/tex]

[tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]

Therefore, the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]

Answer:

0.44

Step-by-step explanation:

11/25 = 0.44 = 44%

Answer:

11/25

Step-by-step explanation:

since there are 25 students, there will be 25 choices, and the 25 will be the denominator

and there are 11 guys so there will be 11 choices of guys and the 11 will go on top

George should be 150 mm taller than Martha.

Since George's height is 1.75 meters and Martha's height is 160 centimeters.

So here we convert the meters to mm

So,

[tex]= 1.75\times 100\\\[/tex]

= 1750 mm

Now 160 cm to mm

So,

[tex]= 160\times 10[/tex]

= 1,600 mm

So, the difference should be

= 1,750 - 1,600

= 150 mm

Therefore, George should be 150 mm taller than Martha.

Learn more about height here: https://brainly.com/question/15810288

Answer:

A consistent of equations has at least one solution,and an inconsistent system has no solution, watch an example of analyzing a system to see if its consistent or inconsistent.

Answer:  see below

Step-by-step explanation:

Consider the standard form of a linear equation in Slope-Intercept form:

        y = mx + b    where

A CONSISTENT system of equations is where the equations have different slopes OR the same slope and y-intercept.

This results in the lines crossing so they have at least one solution.

An INCONSISTENT system of equations is where the equations have the same slope but different y-intercepts.

This results in parallel lines so they have no solutions.

Answer:

[tex]\bold{n =2t-1}[/tex]

Step-by-step explanation:

Given table is:

[tex]\begin{center}\begin{tabular}{ c c}Term Number (t) & Number of triangles (n) \\ 1 & 1 \\ 2 & 3 \\ 3 & 5 \\ 4 & 7 \\\end{tabular}\end{center}[/tex]

i.e. when term number, t = 1, number of triangles (n) = 1

when term number, t = 2, number of triangles (n) = 3

when term number, t = 3, number of triangles (n) = 5

when term number, t = 4, number of triangles (n) = 7

If we closely look at the pattern, number of triangles (n) in each row are 1 lesser than twice of term number (t).

i.e. for [tex]t=1, n = 2\times 1 -1=1[/tex]

[tex]t=2, n = 2\times 2 -1=3[/tex]

[tex]t=3, n = 2\times 3 -1=5[/tex]

[tex]t=4, n = 2\times 4 -1=7[/tex]

Therefore, the number of triangles in the nth term will be given as:

[tex]\bold{n =2t-1}[/tex]

Answer:

an = 2t -1

Step-by-step explanation:

We are adding 2 each time

1+2 =3

3+2 = 5

5+2 = 7

an is the nth term in the sequence  and t is the number of triangle

an =1+ 2(t-1)

Distribute

an = 1 +2t -2

an = 2t -1

[tex]2.232\approx2.32[/tex]

Answer:

a y = 2

b.y = 14

c. y =56

Step-by-step explanation:

a .6 (1)- 4=2

y=2

b. 6 (3)- 4

=18-4

y=14

c. 6 (10) - 4

= 60 - 4 =56