Find the final output(s) of the circuits below:
ii.
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у
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Answer:

Option A

Step-by-step explanation:

Given equation is

=> 3y = 6x + 3

In slope-intercept form, it becomes

=> 3y = 3(2x+1)

=> y = 2x+1

So, Slope = m = 2

Parallel lines have equal slope, So any line parallel to the above line would have its slope equal to 2

=> Line parallel to 3y = 6x + 3 is y = 2x + 10

Answer:

Step-by-step explanation:

Looking at the Venn diagram,

The total number of students surveyed is 7 + 5 + 8 + 6 + 2 + 4 + 3 + 6 = 41

The number of children that studies none of the subjects is 6

The number of children that study only biology is 7

The number of children that study only physics is 5

The number of children that study only physics and biology is 2

Therefore, the number of students that do not study chemistry is 6 + 7 + 2 + 5 = 20

Probability = number of favorable outcomes/total number of outcomes

Therefore, the probability that a child chosen at random does not study chemistry is 20/41 = 0.49

Answer:  r represents a significant linear correlation.

Step-by-step explanation:

GIven : Linear correlation coefficient: r = 0.543

Sample size: n= 25

Significance levle: [tex]\alpha=0.05[/tex]

Degree of freedom : n-2 = 25-2=23

Now, we check r critical value table for value with df = 23 and [tex]\alpha=0.05[/tex].

Critical value = ±0.396  [From r critical value table]

Since r = 0.543 > 0.396, that means there is significant linear correlation.

Hence,  r represents a significant linear correlation.

Using the principle of hypothesis testing, the correlation Coefficient is greater than the critical value. Hence, the linear correlation Coefficient value is significant.

Given the Parameters :

Recall :

Decision Region :

Critical value at T0.05, 23 = ±0.396

Comparing the critical value and correlation Coefficient :

Hence, the correlation Coefficient is significant.

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Answer:

Ok, el jugador tiene:

J picas, 10 de tréboles.

En la mesa tenemos:

2 de corazones, 10 de diamantes, 10 de corazones, j de corazones y 5 de corazones.

Entonces, nosotros tenemos un full, que son tres 10 y dos J.

Ahora, en la mesa vemos una gran probabilidad de color, pero el full le gana al color, así que esto no nos amenaza.

Las combinaciones que le ganan al full son:

Poker (4 cartas iguales)

el único poker posible con las cartas de la mesa es si alguien tubiera 2 dieces en la mano, pero nosotros tenemos uno, así que hay un solo otro diez, entonces nadie puede tener poker.

Escalera de color u escalera real: (5 cartas seguidas del mismo palo.)

hay 4 corazones en la mesa, pero no estan a una distancia de de tal forma que nadie pueda hacer una escalera.

La única mano que nos podría empatar, es si otra persona también tubiera un diez y una jota.

Entonces no podemos perder esta mano, en el peor caso la podemos empatar. Esto implica que la mejor decisión es apostar todo.

Answer:

P10 = 27.4

P90 = 22.0

It helps the producer to know the higher (P10) and lower estimates (P90) for the amount of chocolate chips per cookie.

Step-by-step explanation:

In P10 and P90 the P stands for "percentile".

In the case of P10, indicates the value X of the random variable for which 10% of the observed values will be above this value X.

In the case of P90, this percentage is 90%.

In this case, we can calculate from the z-values for each of the percentiles in the standard normal distribution.

For P10 we have:

[tex]P(z>z_{P10})=0.1\\\\z_{P10}=1.2816[/tex]

For P90 we have:

[tex]P(z>z_{P90})=0.9\\\\z_{P90}=-1.2816[/tex]

Then, we can convert this values to our normal distribution as:

[tex]P10=\mu+z\cdot\sigma=24.7+1.2816\cdot 2.1=24.7+2.7=27.4 \\\\P90=\mu+z\cdot\sigma=24.7-1.2816\cdot 2.1=24.7-2.7=22.0[/tex]

Answer:

Lower Quartile: 62

Upper Quartile: 81

Interquartile Range: 19

Step-by-step explanation:

To find the lower quartile, you want to find the median from the minimum to the median.

49, 55, 62, 64, 67

The median of this is 62. Therefore, 62 is the lower quartile.

To find the upper quartile, you want to find the median from the median to the maximum.

76, 79, 81, 82, 83

The median of this is 81. Therefore, 81 is the upper quartile.

To find the interquartile range, you subtract the upper and lower quartile.

81-62=19

The difference is 19. Therefore, the interquartile range is 19.

Answer:

A) [tex]a_{1}[/tex] = 1, [tex]a_{2}[/tex] = 4

B) [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] + 2

C)    [tex]a_{n} = 2^{n-1} + 2^n -2\\a_{n} = 2^n + 2^{n-1} -2[/tex]

Step-by-step explanation:

For n ≥ 1 ,

S is a set containing 2^n distinct real numbers

an = no of comparisons to be made between pairs of elements of s

A)

[tex]a_{1}[/tex] = no of comparisons in set (s)

that contains 2 elements = 1

[tex]a_{2}[/tex] = no of comparisons in set (s) containing 4 = 4

B)  an = 2a[tex]_{n-1}[/tex] + 2

C) using the recurrence relation

a[tex]_{n}[/tex] = 2a[tex]_{n-1}[/tex] + 2

substitute the following values  2,3,4  .......... for n

a[tex]_{2}[/tex] = 2a[tex]_{1}[/tex] + 2

a[tex]_{3}[/tex] = 2a[tex]_{2}[/tex] + 2 = [tex]2^{2} a_{1} + 2^{2} + 2[/tex]

a[tex]_{4}[/tex] = [tex]2a_{3} + 2 = 2(2^{2}a + 2^{2} + 2 ) + 2[/tex]

    = [tex]2^{n-1} a_{1} + \frac{2(2^{n-1}-1) }{2-1}[/tex]   ---------------- (x)

since  2^1 + 2^2 + 2^3 + ...... + 2^n-1 =  [tex]\frac{2(2^{n-1 }-1) }{2-1}[/tex]

applying the sum formula for G.P

[tex]\frac{a(r^n -1)}{r-1}[/tex]

Note ; a = 2, r =2 , n = n-1

a1 = 1

so equation x becomes

[tex]a_{n} = 2^{n-1} + 2^n - 2\\a_{n} = 2^n + 2^{n-1} - 2[/tex]

Answer:

A

Step-by-step explanation:

9-2x≤3x+24

-15≤5x

-3≤x

so it's:

[-3,∞)

Answer:

16x^2 + 8x.

Step-by-step explanation:

To find the area of the walkway, you need to do the area of the whole thing minus the area of the pool.

The area of the whole thing is (8x - 3)(2x + 7) = 16x^2 - 6x + 56x - 21 = 16x^2 + 50x - 21.

The area of the pool is (8x - 3 - x - x)(2x + 7 - x - x) = (6x - 3)(7) = 42x - 21.

So, the area of the walkway is 16x^2 + 50x - 21 - (42x - 21) = 16x^2 + 50x - 21 - 42x + 21 = 16x^2 + 8x.

If you want, you can factor that and make it 8x(2x + 1).

Hope this helps!

Answer:

I graphed the inequality on the graph below.

Step-by-step explanation:

6x - 5y > 30

-6x         -6x        Subtract 6x from both sides

-5y > -6x + 30    Divide both sides by -5 and flip the inequality sign

y < 6/5x - 6

Answer:

56% shaded

Step-by-step explanation:

if there are 100 boxes, then every box it 1%

5 rows (50%) + 6 extra boxes (6%) = 56%

Answer:

m^4+(1/m^4)= 123.4641 or 118.6

Step-by-step explanation:

m-(1/m)=3

m² - 1= 3m

m² -3m -1= 0

m = (3-√13)/2 = -0.3

Or

m =( 3+√13)/2= 3.3

m^4+(1/m^4) for m = -0.3

= (-0.3)^4 + (1/(0.3)^4)

= 0.0081 + 123.456

= 123.4641

m^4+(1/m^4) for m = 3.3

= (3.3)^4 + (1/(3.3)^4)

= 118.5921 + 0.008432

= 118.6

Answer:

Step-by-step explanation:

No, it is not an even function.  The graph is not symmetric about the y-axis.

Answer:

<eba and <hbi are congruent angles

Step-by-step explanation:

They are vertical angles, therefore congruent

Answer:

(a) The probability you pass the exam is 0.0000501.

(b) The expected number of correct guesses is 7.5.

(c) The standard deviation is 2.372.

Step-by-step explanation:

We are given that you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. And you randomly guess on all 30 questions.

Since there is an assumption of only 1 correct choice out of 4 which means the above situation can be represented through binomial distribution;

[tex]P(X =x) = \binom{n}{r}\times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,3,......[/tex]

where, n = number of trials (samples) taken = 30

           r = number of success = at least 60%

           p = probbaility of success which in our question is the probability

                 of a correct answer, i.e; p = [tex]\frac{1}{4}[/tex] = 0.25

Let X = Number of questions that are correct

So, X ~ Binom(n = 30 , p = 0.25)

(a) The probability you pass the exam is given by = P(X [tex]\geq[/tex] 18)

Because 60% of 30 = 18

P(X [tex]\geq[/tex] 18) = P(X = 18) + P(X = 19) +...........+ P(X = 29) + P(X = 30)

= [tex]\binom{30}{18}\times 0.25^{18}\times (1-0.25)^{30-18} + \binom{30}{19}\times 0.25^{19}\times (1-0.25)^{30-19} +.......+ \binom{30}{29}\times 0.25^{29}\times (1-0.25)^{30-29} + \binom{30}{30}\times 0.25^{30}\times (1-0.25)^{30-30}[/tex]

= 0.0000501

(b) The expected number of correct guesses is given by;

  Mean of the binomial distribution, E(X) =  [tex]n \times p[/tex]

                                                                =  [tex]30 \times 0.25[/tex] = 7.5

(c) The standard deviation of the binomial distribution is given by;

      S.D.(X)  =  [tex]\sqrt{n \times p \times (1-p)}[/tex]

                    =  [tex]\sqrt{30 \times 0.25 \times (1-0.25)}[/tex]

                    =  [tex]\sqrt{5.625}[/tex]  =  2.372                

Answer:

SOLUTION SET={x/x>-1} and SOLUTION SET={x/x<-1}

Step-by-step explanation:

1)4x-39>-43

evaluating the inequality

adding 39 on both sides

4x-39+39>-43+39

4x>-4

dividing 4 on both sides

4x/4>-4/4

x>-1

SOLUTION SET={x/x>-1}

2)8x+31<23

evaluating the inequality

subtracting 31 on both sides

8x+31-31<23-31

8x<-8

dividing 8 on both sides

8x/8<-8/8

x<-1

SOLUTION SET={x/x<-1}

i hope this will help you :)

Answer: There are no solutions

Step-by-step explanation:Khan Academy

Answer:

Step-by-step explanation:

The complete statement would be "if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other".

The reason for this is because parallel lines have the same slope, that's the condition. On the other hand, parallel lines have opposite and reciprocal slopes.

So, if you think this through, if a line is perpendicular to another, then it's going to be perpendicular to all different lines which are parallel to the first one, because all their slopes are equivalent, and they will fulfill the perpendicularity condition.

Answer:

Parallel line

Step-by-step explanation:

Hope It Helps

Answer:

100%

Step-by-step explanation:

Total = 7

Odd or less than 7 = 6+1

=> 7

P(odd or less than 7) = 7/7

In %age:

100%

Answer:

100%

Step-by-step explanation:

Number of cards= 7

Odd or less than 7= 7

P= 7/7=1=100%

==================================================

Work Shown:

(-i)^5 = (-1*i)^5

(-i)^5 = (-1)^5 * i^5

(-i)^5 = (-1)^5 * i^2*i^2*i

(-i)^5 = (-1)^5 * (-1)*(-1)*i

(-i)^5 = -1 * 1 * i

(-i)^5 = -i

----------

A shortcut to quickly computing i^5 is to note the remainder of 5/4 is 1, so this means that i^5 = i^1 = i. Another example is i^25 would equal the same thing since 25/4 has a remainder of 1 as well.

Answer:

[tex]\huge\boxed{(-i)^5=-i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\to i^2=\left(\sqrt{-1}\right)^2=-1\\\\a^n\cdot a^m=a^{n+m}\\\\(ab)^n=a^nb^n\\=========================\\\\\text{We have:}\\\\(-i)^5=(-i)^{2+2+1}=(-i)^2(-i)^2(-i)^1=(-1\cdot i)^2(-1\cdot i)^2(-i)\\\\=(-1)^2(i)^2(-1)^2(i)^2(-i)=(1)(-1)(1)(-1)(-i)=-i[/tex]

Answer:

The equation is:

[tex]L=3\,\,d^2\\[/tex]

and a beam with 10 in diagonal will support 300 lb

Step-by-step explanation:

The mathematical expression that represents the statement:

"The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. "

can be written as:

[tex]L=k\,\,d^2[/tex]

where k is the constant of proportionality

To find the constant we use the data they provide: "A beam with diagonal 6 in will support a maximum load of 108 lb.":

[tex]L=k\,\,d^2\\108 = k\,\,(6)^2\\k=\frac{108}{36} \,\,\frac{lb}{in^2}\\ k = 3\,\,\frac{lb}{in^2}[/tex]

Now we can use the proportionality found above to find the maximum load for a 10 in diagonal beam:

[tex]L=3\,\,d^2\\L=3\,\,(10)^2\\L=300 \,\,lb[/tex]

Answer:

L=3d^2 the beam will support 300 pounds

Step-by-step explanation:

108=k x 6^2

Dividing by 6^2=36 gives k=3, so an equation that relates L and d is

L=3d^2 d=10 yields

3(10)^2=300

So a beam with a 10in diagonal will support a 300lb load.

Answer:

120

Step-by-step explanation:

As we can see that if we divide 120 by the 24, the remainder would be zero and the quotient be 5

As if we multiply 24 with the 5 it gives 120

And, the 4 is not a digit as it smaller than 24 so we have to carry the amount

Therefore if we insert 120 and divisible by 24 than it gives quotient 5 and the remainder is zero as it is completely divisible

Answer:

The 97% upper confidence limit for the proportion of green items is 0.502.

Step-by-step explanation:

We have to calculate a 97% upper confidence limit for the proportion.

The sample proportion is p=0.294.

[tex]p=X/n=5/17=0.294\\[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.294*0.706}{17}}\\\\\\ \sigma_p=\sqrt{0.01221}=0.11[/tex]

The critical z-value for a 97% upper confidence limit is z=1.881.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.881 \cdot 0.11=0.208[/tex]

Then, the upper bound is:

[tex]UL=p+z \cdot \sigma_p = 0.294+0.208=0.502[/tex]

The 97% upper confidence limit for the proportion of green items is 0.502.

Hey there! :)

Answer:

To graph y = -3x - 2, we can start by solving for some points. Plug in x values for x in the equation to solve for the y value:

X                   Y

-2                  4

-1                    1

0                   -2

1                     -5

2                    -8

Use these points to graph the line (Graphed below)

Answer:

0.49

Step-by-step explanation:

From the Venn diagram:

The number of students that study biology and physics = 2

The number of students that study biology and chemistry = 6

The number of students that study chemistry and physics = 4

The number of students that study only physics = 5

The number of students that study only biology = 7

The number of students that study only chemistry = 8

The number of students that study all 3 subjects = 3

The number of students that study none = 6

Therefore the total number of students = 2 + 6 + 4 + 5 + 7 + 8 + 3 + 6 = 41 students

The number of students that study chemistry = 8 + 6 + 3 + 4 = 21 students

The number of student that does not study chemistry = 41 - 21 = 20 students

the probability chosen at random that that child does not study chemistry =  number of student that does not study chemistry / total number of students  = 20/41 = 0.49

===================================================

Explanation:

Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.

Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.

Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.

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

Another approach

Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is

1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute

x = number of minutes

(combined rate)*(time) = number of jobs done

(1/24)*x = 1

x = 1*24

x = 24 is the time it takes if they worked together without getting in each other's way.

Effectively, we are solving the equation

1/A + 1/B = 1/C

with

A = time it takes Wilma to do the job on her own

B = time it takes Rocky to do the job on his own

C = time it takes the two working together to get the job done

The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.

So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.

Together they can mow the lawn in 24 minutes.

Time and efficiency are inversely proportional to each other.

Time and work are directly proportional to each other.

Given, Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes.

Assuming total work to be 120 as it is the LCM of 40 and 60.

So, The efficiency of Wilma is (120/60) = 2 and the efficiency of Rocky is

(120/40) = 3.

Now together their efficiency is (2 + 3) = 5.

∴ Together they can complete the work in (120/5) = 24 minutes.

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Answer:

unit rate of lemonade to cranberry juice

= 5:1

Step-by-step explanation:

A recipe for fruit punch calls for 1/2 liter of lemonada and 1/10 liter of cranberry juice

1/2 liter of lemonada= 0.5

1/10 liter of cranberry juice = 0.1

unit rate of lemonade to cranberry juice

= 0.5/0.1

unit rate of lemonade to cranberry juice

= (5*10^-1)/(1*10^-1)

unit rate of lemonade to cranberry juice

= 5/1 *(10^-1)/10^-1)

unit rate of lemonade to cranberry juice

= 5/1

unit rate of lemonade to cranberry juice

= 5:1

The unit rate of lemonade to cranberry juice is 5 : 1.

1/2 liters of lemonada are to be mixed with 1/10 litres of cranberry juice.

In ratio form this is:

1/2 : 1/10

To make it a unit rate of lamonada, you should divide both sides by the ratio of lamonada to cranberry juice in order to take lomonada's ratio to 1.

= 1/2 ÷ 1/2 :  1/10 ÷1/2

= 1 : 0.2

You then need to make the decimal a whole number by dividing both sides by the decimal:

= 1 ÷ 0.2 : 0.2 ÷0.2

= 5 : 1

The unit rate of lamonada to cranberry juice is therefore 5 : 1.

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Answer:

option 3 is the answer.

Answer:

The breadth is 16m because a square is a quadrilateral (four sided shape) that has all its side to be of equal measure.

Answer:

A. Reflectional symmetry

Step-by-step explanation:

If the shape is the same characteristics after being reflected, then it is A.

The type of symmetry is Reflectional symmetry.

Reflection symmetric is a symmetry that revolves around reflections. It is characterized as reflection symmetry if, at most, one line splits an image into two halves, with one half being the mirror reflection of the other.

Given that, we need to find that which is best described as the quality a design has if it maintains all of its characteristics when it is reflected over an axis lying in its plane,

So, according to the definition of the reflection symmetry the design will attain its exact position before and after the reflection when is reflected over an axis lying in its plane, is a reflection symmetry.

Hence, the type of symmetry is Reflectional symmetry.

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Answer:

1) 2/9

2)3/9

Step-by-step explanation:

sorry,thats what i know so far