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Find the value of i77.

A) 1

B) i

C) −1

D) −i

ANSWER

[tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]

EXPLANATION

Given;

[tex]4x-12y=1[/tex]

and

[tex]6x+4y=4[/tex]

The augmented matrix of the two linear equation is given by;

[tex]\left[\begin{array}{ccc}4&-12|&-1\\6\:&\:\:\:4|&4\end{array}\right][/tex]

We now perform row operations;

[tex]\frac{1}{4}\times R_1 \rightarrow R_1 [/tex].

This gives us

[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\6\:&\:\:\:4|&4\end{array}\right][/tex]

[tex]R_2-6R_1 \rightarrow R_2[/tex]

[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:22|&\frac{11}{2}\end{array}\right][/tex]

[tex]\frac{1}{22}R _2 \rightarrow R_2[/tex]

[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]

[tex]R_1+3R_2 \rightarrow R_1[/tex]

[tex]\left[\begin{array}{ccc}1&0|&\frac{1}{2}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]

Hence [tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]

Given that Mary has 2 bags of sweets. each of which contains same number of sweets.

Let us assume each bag contains x  number of sweets.

After eating 4 sweets, total number of sweets left in two bags = x+x-4=2x-4

But given 2x-4 = 30

                2x-4+4 = 30+4

                 2x=34

                [tex]x=\frac{34}{2} = 17[/tex]

Hence there are 17 sweets in each bag at starting.

Mary had two bags with an equal number of sweets. After eating 4 sweets, she had 30 left, which means each bag originally contained 17 sweets.

To solve the problem of determining how many sweets were in each bag to start with, we must consider that Mary had two bags with an equal number of sweets and ended up with 30 sweets after eating 4 sweets. We can represent the initial number of sweets in each bag as 'x'. So the equation for the total number of sweets after she eats 4 is 2x - 4 = 30.

Let's solve this equation step by step:

Add 4 to both sides: 2x = 30 + 4

Simplify: 2x = 34

Divide both sides by 2 to solve for x: x = 34 / 2

Therefore, x = 17

This means that initially, there were 17 sweets in each bag.

Remark

You could convert base two to base 10 and then convert base 10 to base 8. That's the long way. The procedure below is the short way.

Step One

Write the base 2 number in groups of 3 starting from the right and going left

11 100 111

Step Two

Convert the base 2 numbers in groups of 3 to base 8. The largest result will be a 7

11 = 2*1 + 1 = 2 + 1 = 3

100 = 1*2^2 = 4

111 = 1*2^2 + 1*2 + 1 = 7

Step Three

Read the answer going down.

347 is the answer

Answer

347(8) = C

Answer:

Option C)347(8) is correct. Below is the explanation for changing the base 2 number to the base 8

Step-by-step explanation:

Given:

      11100111(2)

To find:

      Number with base 8.

Let's convert the given base 2 number to a base 10 number or an integer. Then convert it to a base 8 number.

11100111(2) = 1* [tex]2^{7}[/tex]+1* [tex]2^{6}[/tex]+1*[tex]2^{5}[/tex] + 0*[tex]2^{4}[/tex] +0*[tex]2^{3}[/tex] +1* [tex]2^{2}[/tex]+1*[tex]2^{1}[/tex] +1*[tex]2^{0}[/tex]

Simplify it

                 =128 +64+32 +0+0+4+1+1

                 =231

Now, change this integer 231 to a base 8 number ( I have attached a file for this)

We get an answer of 347(8). Option C is correct!

You can learn more:

https://brainly.com/question/11454182.

Air bag manufactured by Aces(A)=57%

So, Probability [tex]P(A)=\frac{57}{100}[/tex]

Air bag manufactured by Best (B) =26%

So, Probability [tex]P(B)=\frac{26}{100}[/tex]

Airbag manufactured by Cool(C)=17%

So, Probability [tex]P(C)=\frac{17}{100}[/tex]

Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively.

Let K be the event which kill people.

Probability of Air bag made by A which kill people [tex]P(K/A)=\frac{1}{100}[/tex]

Probability of Air bag made by B which kill people [tex]P(K/B)=\frac{4}{100}[/tex]

Probability of Air bag made by C which kill people [tex]P(K/A)=\frac{13}{100}[/tex]

If an airbag kills a passenger, calculate the probability that the airbag was manufactured by Cool

Using Baye's theorem:

[tex]P(C/K)=\frac{P(K/C)P(C)}{P(K/A)P(A)+P(K/B)P(B)+P(K/C)P(C)}[/tex]

Substitute the values of probabilities into formula

We get,

[tex]P(C/K)=\frac{0.17\times 0.13}{0.57\times 0.01+0.26\times 0.04+0.17\times 0.13}[/tex]

Now we calculate it and get probability

So, [tex]P(C/K)=0.5785[/tex]

So, 57.85% of passenger kills if the airbag was manufactured by Cool.

The midpoint between -4 and 8 is answer B) 2

Answer:

All options are wrong.

Step-by-step explanation:

We have y > –3x + 3 and y > 2x – 2

Option A - (1,0)

          y > –3 x 1 + 3 = 0

         We have y = 0, which is not greater than 0.

         Option A is not correct.        

Option B - (–1,1)

          y > –3 x -1 + 3 = 6

         We have y = 1, which is not greater than 6.

         Option B is not correct.

Option C - (2,2)

          y > –3 x 2 + 3 = -3

         We have y = 2, which is greater than -3.

          y > 2 x 2 – 2  = 2

         We have y = 2, which is not greater than 2.

         Option C is not correct.  

Option D - (0,3)

          y > –3 x 0 + 3 = 3

         We have y = 3, which is not greater than 3.

         Option D is not correct.    

All options are wrong.

Answer:

The correct option is C.

Step-by-step explanation:

The height of the ball is defined by a parabolic function.

Let the equation of the parabola is

[tex]f(x)=a(x-h)^2+k[/tex]

Where, (h,k) is the vertex and a is stretch factor.

The maximum height of the ball is 15 feet in 2.2 seconds. So, the vertex is (2.2, 15).

The equation of the parabola is

[tex]f(x)=a(x-2.2)^2+15[/tex]

The initial height of the ball is 0.

[tex]f(0)=a(0-2.2)^2+15[/tex]

[tex]0=a(-2.2)^2+15[/tex]

[tex]a=-\frac{15}{(2.2)^2}[/tex]

[tex]a=-3.1[/tex]

The equation of the parabola is

[tex]f(x)=-3.1(x-2.2)^2+15[/tex]

The function takes 2.2 seconds to reach at maximum height, so after that it will take 2.2 seconds to reach at growth again.

[tex]2.2+2.2=4.4[/tex]

The ball will reach the growth at x=4.4.

The height can not be negative, therefore the value of x lies between 0 to 4.4. The domain of the function is

[tex]0\leq x\leq 4.4[/tex]

Therefore option C is correct.

Answer: P = -19, Q = 18

Step-by-step explanation:

Px + Q = -19x + 18

Px = -19x                Q = 18

÷x     ÷x      

P   = -19

Answer:

The factor form of given expression is (x-4)(x-2i)(x+2i).

Step-by-step explanation:

The given expression is

[tex]x^3-4x^2+4x-16[/tex]

It can be written as

[tex]f(x)=x^3-4x^2+4x-16[/tex]

According to the rational root theorem, all possible rational roots are in the form of

[tex]\frac{a_0}{a_n}[/tex]

Where, a₀ is constant term and [tex]a_n[/tex] is leading coefficient.

[tex]f(4)=4^3-4(4)^2+4(4)-16=0[/tex]

Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.

Use synthetic method to find the remaining factors.

[tex](x^3-4x^2+4x-16)=(x-4)(x^2+4)[/tex]

[tex](x^3-4x^2+4x-16)=(x-4)(x^2-(2i)^2)[/tex]

[tex](x^3-4x^2+4x-16)=(x-4)(x-2i)(x+2i)[/tex]

Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).

Answer:

(x-4)  (x-2i) (x+2i)

Step-by-step explanation:

x^3−4x^2+4x−16

I will factor by grouping

x^3−4x^2+  4x−16

The first group is the first 2 terms.  I can factor out an x^2

x^2 (x-4) + 4x-16

The second group I can factor out a 4

x^2 (x-4) + 4(x-4)

Now I can factor out (x-4)

(x-4)  (x^2 +4)

We know that x^2 + 4 factors into +2i and -2i  because

(a^2 -b^2) = (a-b) (a+b)  but  we have (a^2 + b^2)  = (a-bi)  (a+bi)

(x-4) (x-2i) (x+2i)

Answer:

$25.96

Step-by-step explanation:

We have been given that Ming took a cab across town. His fare was $22, and he leaves an 18% tip.

To find the total amount by Ming for cab ride will be equal to 22 plus 18% of 22.

[tex]\text{Total amount paid by Ming for the cab ride}=22+(\frac{18}{100}*22)[/tex]

[tex]\text{Total amount paid by Ming for the cab ride}=22+(0.18*22)[/tex]

[tex]\text{Total amount paid by Ming for the cab ride}=22+3.96[/tex]

[tex]\text{Total amount paid by Ming for the cab ride}=25.96[/tex]

Therefore, Ming paid a total amount of $25.96 to the cab driver.

Answer:

[tex]a_5=-4[/tex]

Step-by-step explanation:

[tex]a_n=a_{n-1}-3\\\\a_1=8\\\\a_2=a_1-3\to a_2=8-3=5\\\\a_3=a_2-3\to a_3=5-3=2\\\\a_4=a_3-3\to a_4=2-3=-1\\\\a_5=a_4-3\to a_5=-1-3=-4[/tex]

To find the value of a5, we subtract 3 repeatedly from the previous value starting with a1=8. After iterating this process four times, we find that a5 equals -4.

The sequence given is defined by a1 = 8 and an = an-1 - 3. To find a5, we need to apply the formula recursively starting from a1:

a2 = a1 - 3 = 8 - 3 = 5

a3 = a2 - 3 = 5 - 3 = 2

a4 = a3 - 3 = 2 - 3 = -1

a5 = a4 - 3 = -1 - 3 = -4

So, the value of a5 is -4.

A constant is a number that stays the same no matter what any outside variables are.  In this case, the variables are the number of hours of the event and the number of attendees.  However, it states in the problem that the event will be 5 hours so that becomes known; the only thing that might change is the number of attendees so you can eliminate any cost that will be affected by that.  You are left with Facility Rental, Musical Entertainment, and Cleaning Fee.  Furthermore, you can be sure that Musical Entertainment and Cleaning Fee must be included in the constant because they are described as "flat rates", which means they do not change.

The answer is D) It is the total cost for entertainment, facility rental, and cleaning.

Hope this helps!

The statement that best describes the constant in the expression

25n + 2,800 is:

It is the cost per person for food, linens, and food decorations.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Facility Rental = $150 per hour of the event

Linens = $2 per attendee

Food = $20 per attendee

Table Decorations = $3 per attendee

Musical Entertainment = $1,800

Cleaning Fee = $250

The total cost of the event.

= 25n + 2,800

Where n is the number of attendees.

Now,

25 is the total cost per attendee for food, linens, and table decorations.

Thus,

The constant in the expression is 25 which is the cost per attendee for food, linens, and table decorations.

Learn more about expressions here:

https://brainly.com/question/3118662

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Answer is 6 kg:

Given that Adam was asked to post a parcel.  The weight of the parcel was 12 lbs and 8 oz.

To convert the weight in kgs:

Let us convert oz into pounds first to make it uniform.

We have 16 0z. = 1 lb

Hence 8 oz. = 8/16 = 0.5 lbs

Weight of the parcel = 12.5 lbs.

We have the converting factor as

2.2 pounds make 1 kg.

Hence 12.5 pounds = 12.5/2.2 = 5.6818

So weight of the parcel in kg= 6. (after rounding off)

A small company plans to invest in a new advertising campaign.

There is a 20% chance that the company will lose $5,000 ,

50% chance of a break even, and a 30% chance of a $10,000 profit

So the expected value from the advertisement campaign is calculated as - 20% of 5000 + 0% of 5000 + 30% of 10,000

= -1000 + 0 + 3000

= 2000

The expected value from the advertisement campaign is $2000.

So the Company must go ahead with the campaign.

Answer : Option A

Hope it helps.

Thank you ..!!

The answer is B (-6,5) becuase C is located at (-3,4). -3 - 3 is -6... and 4 + 1 is 5

Answer:

C. |-9| = 9

Step-by-step explanation:

Distance is always non-negative. Distances in a negative direction are made positive by the use of the absolute value function. The distance from 0 to -9 is one such distance.

Answer:

At least 6907 people.

Step-by-step explanation:

Population std deviation = sigma= 10.6

Since population std deviation is known, we can use normal probability table to get sample size from confidence interval.

The sample mean weight loss is within 0.25 lb of the true population mean.

Hence  margin of error < 0.25

Margin of error = z critical (std dev/n) where n = sample size

Z critical for 95% = 1.96

Hence 0.25 >1.96(10.6)/sq rt n

Simplify to get

sq rt n > 1.96(10.6)/0.25 = 83.104

Square both the sides to get

n > 83.104 square = 6906.27

i.e. sample size should be atleast 6907.

The fraction equivalent to -84/-90 in the least common terms is 14/15, as both the numerator and the denominator can be divided by the common factor 6, resulting in a simplified positive fraction.

To find which fraction is equivalent to -84/-90 in the least common terms, we need to simplify the fraction by canceling out any common factors in the numerator and the denominator. We observe that both numbers are divisible by 6. When we divide the numerator and the denominator by 6, we get:

-84 / -90 = (-84 / 6) \/ (-90 / 6) = 14 / 15

Since a negative divided by a negative results in a positive number, we eliminate the negative signs and get the fraction in its least common terms as 14/15.

Lets say Alexis received 85, 89, 92, and x points in her four tests.

Average of a data set or the mean of a data set, we need to add all the values together and divide by the number of values in the set.

So here 85, 89, 92, and x are the values of the data set and the number of values are 4 (since there are 4 tests).

[tex]Avg=\frac{sum}{n}[/tex]

where 'n' represents the number of values and sum represents the total sum of the values.

Here we need to know how much Alexis need to score in her next test so that she can have an average of 90.

So we know the value of average that is 90.

Now,

[tex]90 = \frac{85+89+92+x}{4}[/tex]

Solving for 'x' we get:

[tex]90=\frac{266+x}{4}[/tex]

[tex]266+x=90 \times 4[/tex]

[tex]266+x=360[/tex]

Therefore,

[tex]x=360-266=94[/tex]

So, Alexis need to score at least 94 on her next test in order to have an average of at least 90.

Answer-

A. Brandon’s sound intensity level is 1/4th as compared to Ahmad’s.

Solution-

Given that, loudness measured in dB is

[tex]L=10\log \frac{I}{I_0}[/tex]

Where,

I   = Sound intensity,

I₀ = 10⁻¹² and is the least intense sound a human ear can hear

Given in the question,

I₁ = Intensity at Brandon's = 10⁻¹⁰

I₂ = Intensity at Ahmad's  = 10⁻⁴

Then,

[tex]L_1=10\log \frac{I_1}{I_0}=10\log \frac{10^{-10}}{10^{-12}}=10\log \frac{1}{10^{-2}}=10\log 10^{2}=2\times10\log 10=20[/tex]

[tex]L_2=10\log \frac{I_2}{I_0}=10\log \frac{10^{-4}}{10^{-12}}=10\log \frac{1}{10^{-8}}=10\log 10^{8}=8\times10\log 10=80[/tex]

[tex]\therefore \frac{L_1}{L_2} =\frac{20}{80} =\frac{1}{4}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

0.375 is answer

Step-by-step explanation:

Given that the  math teacher gave her students two tests. On the first test, 80% of the class passed the test.  But only 30% of the class passed both tests.

Let A - the students pass I test

B = students pass second test

Then P(A) = 80%=0.8 and P(AB) = 30% =0.30

Required probability =probability that a student passes the second test, given that they passed the first one

= P(B/A) = P(AB)/P(A)

= 0.30/0.80

=3/8

=0.375

Right answer is 0.375

The probability that a student passes the second test, given that they passed the first one, is 0.375.

The subject of this question is Mathematics, specifically focusing on the concept of conditional probability. The question asks about the probability that a student passes the second test, given that they passed the first one. Given that 80% of the class passed the first test and 30% passed both tests, we can use the formula for conditional probability P(B|A) = P(A and B) / P(A). Here, A represents passing the first test, and B represents passing the second test.

P(B|A) = P(A and B) / P(A) = 0.30 / 0.80 = 0.375.

Therefore, the probability that a student passes the second test, given that they passed the first one is 0.375.

Answer:

Total temperature change 104.25 f.

Step-by-step explanation:

Average temperature change is calculated by dividing total temperature change by the total hours it took for the change.

We have been given the average temperature change.

We have to multiply average temperature change by the total number of hours it took for the temperature to change we get the total temperature change.

⇒ Total temperature change =  Average temperature change * total hours

                                                = [tex]-4.17*25[/tex]

                                                 =104.25 f

The answer is B because you are takin away $50 a week. $200 is what she wants to have at the end off the summer. So that automaticly means it is ≥ 200. She is TAKING AWAY $50 a week. Meaning - 50w ≥ 200. Finally she has $800 to begin with. So, 800 - 50w ≥ 200.

Sorry if l am not very well at explaining this kind of stuff. Let me know if you need anymore help!!

Let's call the width of our rectangle [tex]w[/tex] and the length [tex]l[/tex]. We can say [tex]l = w + 4[/tex], since the length is equal to 4 cm greater than the width.

Also remember that the perimeter of a rectangle is the sum of two times the width and two times the length, or [tex]P = 2l + 2w[/tex]. To solve this problem, we can substitute in the information we know, as shown below:

[tex]150 = 2(w + 4) + 2w[/tex]

[tex]150 = 4w + 8[/tex]

[tex]142 = 4w[/tex]

[tex]w = \frac{71}{2}[/tex]

Now, we can substitute in the width we found into the formula for length, which is [tex]l = w + 4[/tex]:

[tex]l = \frac{71}{2} + 4[/tex]

[tex]l = \frac{79}{2}[/tex]

The width of our rectangle is [tex]\boxed{\frac{71}{2} \,\, \textrm{cm}}[/tex] cm and the length of our rectangle is [tex]\boxed{\frac{79}{2} \,\, \textrm{cm}}[/tex]

Final answer:

To calculate the average monthly weight loss of the black bear, divide the total weight loss by the number of hibernation months. The bear lost 0.1 pound per month during its 712 months of hibernation.

Explanation:

To find the average weight loss per month of the black bear, you need to divide the total weight loss by the number of months of hibernation. The black bear lost 64.4 pounds over 712 months.

First, we write out the calculation needed:
64.4 pounds ÷ 712 months.

When you perform the division, you get approximately 0.0904494382 pounds per month. Rounding to the nearest tenth gives us 0.1 pounds per month.

Therefore, the bear experienced an average weight change of 0.1 pound per month during hibernation.