The factors of 25x4 − 49y2 are

Answer: [tex]2\left(x-\frac{1}{4} \right)^{2}[/tex]

Step-by-step explanation:

[tex]2x^{2}-x+\frac{1}{8}\\\\=2\left(x^{2}-\frac{1}{2}x \right)+\frac{1}{8}\\\\=2\left(\left(x-\frac{1}{4} \right)^{2}-\frac{1}{16} \right)+\frac{1}{8}\\\\=2\left(x-\frac{1}{4} \right)^{2}-\frac{1}{8}+\frac{1}{8}\\\\=\boxed{2\left(x-\frac{1}{4} \right)^{2}}[/tex]

By definition of the binomial coefficient,

[tex]C(n,k) = \dfrac{n!}{k!(n-k)!}[/tex]

so we have

[tex]C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)[/tex]

as required.

The value of the investment in 5 years is $5805.9

Interest is the amount earned over years for the amount invested.

It is given that

Principal = $5000

Rate = 3%

Compounded Quarterly

Time = 5 years

Amount = ?

The Amount is given by the formula

Amount = P( 1 + (r/n))ⁿˣ

Here n = t = time period for which the investment has been done.

Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵

Amount = 5000 (1.16)

Amount = $ 5805.9

Therefore , The value of the investment in 5 years is $5805.9

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Answer:

e4fodor8rsidididi2f2

Answer:

9

Step-by-step explanation:

3:4

AB:12

cross multiply giving

3×12:4AB

36: 4AB

divide both sides by 4,thus

AB=9

Answer:

1.5 min

100 rotations

Step-by-step explanation:

to find 300 rotations time duration use the half-minute,

to find half of a minute divide the amount in one minute (200) by 2

200/2 = 100

then mutiply the 100 times 3 to find the time

100 * 3 = 300

therefore 30 sec (100 rot.) and 3 (3 times)

30 * 3 = 90

90 seconds minus 60 (one minute) is 30

so then it is equal to 1.5 minutes aka 1 min. 30 sec.

How long does it take to complete 300 rotations? 1.5 minutes (1 min. 30 sec.)

How many times does it rotate in a half minute?​ 100 rotations

hope this helps:)

Answer:

42 ft/s

Step-by-step explanation:

if superman travels 210 feet in 5 seconds, he will travel a fifth of 210 ft in 1 second

a fifth of 210ft is 210/5=42

hence 42ft/s is his rate.

Step-by-step explanation:

Let X be the mail arrival time to a department that follows uniform distribution over 0 to 60 minutes.

The probability function of X is:

f

(

x

)

=

1

60

,

0

<

x

<

60

Now, the probability that the mail arrival time is more than 40 minutes on a given day is calculated below:

P

(

X

>

40

)

=

∫

60

40

1

60

d

x

=

[

x

60

]

60

40

Answer: [tex]5x^3 - x^2 + 5x+2[/tex]

Step-by-step explanation:

[tex](f+g)(x)=(3x^2 + 5x-2)+(5x^3 - 4x^2 +4)=3x^2 + 5x-2+5x^3 - 4x^2 +4=\boxed{5x^3 - x^2 + 5x+2}[/tex]

The depth of the sea bed is 5104 fathom and 1.986 league

The bottom of an ocean , the ocean floor is called Seabed .

It is given that

The depth of a certain part of the Earth's seabed is 36,024 feet

The depth in fathom is given by =  depth in feet / 6

The depth in fathom is = 36024 / 6

= 5104 fathom

1 league = 6046.1 * 3 feet = 18138.1 feet

The depth in League (marine) = Depth in feet / 18138.1

The depth in League (marine) = 36024/18138.1

= 1.986 league

Therefore the depth of the sea bed is 5104 fathom and 1.986 league.

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The regression lines 3x+2y=26 and 6x+y=31 are linear regressions

The mean values are 4 and 7 and the correlation coefficient between x and y is 0.25

The standard deviation of x is 2/13

The mean value and the correlation

We have the equations to be:

3x+2y=26 and 6x+y=31

Make y the subject in the second equation

y = 31 - 6x

Substitute y = 31 - 6x in the first equation

3x+2[31 - 6x] = 26

Expand

3x+ 62 - 12x = 26

Collect like terms

3x - 12x = 26 - 62

Evaluate

-9x = -36

Divide by - 9

x = 4

Substitute x = 4 in y = 31 - 6x

y = 31 - 6 * 4

y = 7

This means that the mean values are 4 and 7

To determine the correlation coefficient, we make y the subject in 3x+2y=26 and x the subject in 6x+y=31.

So, we have:

y = 13 - 3x/2 and x = 31/6 - 1/6y

The above means that:

Bxy = -1/6 and Byx = -3/2

The correlation coefficient is then calculated as:

r^2 = Bxy * Byx

r = -1/6 * -3/2

r = 0.25

Hence, the correlation coefficient between x and y is 0.25

The standard deviation of x

We have:

Var(y) = 4

In (a), we have:

y = 13 - 3x/2

To solve further, we make use of:

Var(y) = Var(ax + b) = a^2Var(x)

This gives

Var(y) = Var(13 - 3x/2) = 13^2 * Var(x)

So, we have:

Var(y) = 13^2 * Var(x)

Substitute 4 for Var(y)

4 = 13^2 * Var(x)

Divide both sides by 13^2

4/13^2 = Var(x)

Express 4 as 2^2

(2/13)^2 = Var(x)

So, we have:

Var(x) = (2/13)^2

Take the square root of both sides

SD(x) = 2/13

Hence, the standard deviation of x is 2/13

Answer:

4y +x =18

Step-by-step explanation:

y - (-5) -1

----------- = ------

x - 2 4

4y +20 = -x+2

4y +x =18

Answer: 18, 24, 30

Step-by-step explanation:

For the segments to create a right triangle, they must satisfy the Pythagorean theorem.

The only set which satisfies the Pythagorean theorem, is 18, 24, 30, since [tex]18^{2}+24^{2}=30^{2}[/tex]

Answer:

11

Step-by-step explanation:

i don't know

Answer:

A.

Step-by-step explanation:

The other graphs answers have a point at (3, 1) which is not on the graph.

Answer:

Step-by-step explanation:

Jakub wants to build a new shed.

The area of the shed is 37 m².

The width of the shed is 5 m.

What is the length of the shed?

to find the side, having the area, you need to use the inverse formula Area = W * L

so

L = A: W

L = 37 : 5 = 7.4 m

If the area of the shed is 37 m²,width of the shed is 5 m as a result the length of the shed will be 7.4 m.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that, the area of the shed is 37 m². The width of the shed is 5 m.

Since the shed is rectangular. The length of width is found as,

Area = length × width

A = l × w

l=A/w

l=37/5

l=7.4 m

Thus, if the area of the shed is 37 m², the width of the shed is 5 m as a result the length of the shed will be 7.4 m.

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The answer is J. [tex](x+4)(x-2)=x\cdot x[/tex]

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:sin(\theta) = \cfrac{2}{3} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cos {}^{2} ( \theta) + \sin {}^{2} ( \theta) = 1[/tex]

[tex]\qquad \tt \rightarrow \: {\bigg( \cfrac{ \sqrt{5}}{3} \bigg) }^{2} + \sin {}^{2} ( \theta) = 1[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{5}{9} + \sin {}^{2} ( \theta) = 1[/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = 1 - \cfrac{5}{9} [/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = \cfrac{9 - 5}{9} [/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = \cfrac{4}{9} [/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \sqrt \cfrac{4}{9} [/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \pm \cfrac{2}{3} [/tex]

Generally, only positive value is taken :

[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \cfrac{2}{3} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

i dont speak English 3456

Answer:

m is not an element of real number

Considering the definition of probability:

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The probability of any event A is defined as the quotient between the number of favorable cases (that is, the number of times that event A may or may not occur) and the total number of possible cases:

[tex]Probability=\frac{number of favorable cases}{total number of possible cases}[/tex]

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

A complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

In first place, let's define the following events:

A: The event that a student owned a laptop.

B: The event that a student owned a car.

Then you know:

In this case, considering the definition of union of events, the probability that the student owns either a car or laptop is calculated as:

P(A∪B)= P(A) + P(B) -P(A∩B)

P(A∪B)= 0.78 + 0.46 -0.38

P(A∪B)= 0.86= 86%

Then, the probability that the student owns either a car or laptop is 86%.

On the other hand, considering the definition of the complementary event and its probability, the probability that the student owns neither a car nor a laptop is calculated as:

P [(A∪B)']= 1- P(A∪B)

P [(A∪B)']= 1 - 0.86

P [(A∪B)']= 0.14= 14%

Finally, the probability that the student owns neither a car nor a laptop is 14%.

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Answer:

A exponential equation is usually of the form f(x)=a (1±r)ˣ.

Our limitation: Initial Vale is 500.

Let's look at our options:

#1- Initial Value of 1000  --- WRONG!

#2- Initial Value of 1000  --- WRONG!

#3- Initial Value of 500 ---- Maybe

#4- Initial Value of 500 ---- Maybe

Let's look at 3 and 4:

#3- Fits Our Form of f(x)=a (1±r)ˣ ---- CORRECT!

#4- Does not fit Our Form of f(x)=a (1±r)ˣ, It's to the 2nd power, not the x power! ---- WRONG!

Hence, #3 Is correct!

Step-by-step explanation:

Well, I hope you understood, and I'd gladly explain anything that didn't make sense. A brainliest would be appreciated, thank you!

-Zylynn Jade Ardenne

Answer:

8 [units].

Step-by-step explanation:

if to see the given coordinates, then it is clear the x-coordinates are equal. It means, the required distance can be calculated:

d=5+3=8 [units].

Answer:

Step-by-step explanation:

x×4=2x²(x-1)

2x³-2x²-4x=0

2x(x²-x-2)=0

x≠0

x²-x-2=0

x²-2x+x-2=0

x(x-2)+1(x-2)=0

(x-2)(x+1)=0

x=2

or

x=-1 (rejected)

Answer:

Step-by-step explanation:

Formula

The following relationship exists between the parts of each chord.

(x - 1)(2x^2) = 4*x

Solution

The easiest way to start is to divide both sides of the equation by x.

(x - 1)(2x^2)/x = 4x / x                  Divide by x    

( x-1)(2x) = 4                                 Remove the brackets

2x^2 - 2x = 4                              Subtract 4 from both sides

2x^2 - 2x - 4 = 4 - 4                    Combine

2x^2 - 2x - 4 = 0                         Pull out the common factor

2(x^2 - x - 2) = 0                         Divide by 2

x^2 - x - 2 = 0                              Factor

(x - 2)(x + 1)

Answer:

x can be 2 or x can be - 1 on paper. The x on the upper right prohibits that. A line can't have a length of - 1. So - 1 is called an extraneous solution.

The answer is x = 2

Answer:

Hi! So, I'm pretty sure the answer is 1 (rounded).

However, I'm not sure if you're trying to find the answer to COS pi/10 or "the function in terms of cofunction of a complementary angle" which I'm not too sure about. I've given you the answer to the first part if this was not the right way to read the problem I deeply apologize.

Step-by-step explanation:

Using any calculator with the Cos, Sin, and Tan function, you can input

COS (pi / 10) which equals .9999849678 (which you can round as needed)

Answer:

To determine the most suitable candidate we will calculate their total scores and see who's the best.

first for mr X

work experience = 70

score = work experience x wieght = 70 x 4 = 280

Entrance = 78

score = 78 x 3 = 234

Interview = 70

score = 70 x 4 = 210

total score = 280 + 234 + 280 = 794

for mr Y

Work experience = 89

score = 89 x 4 = 356

Entrance = 83

score = 83 x 3 = 249

Interview = 89

Score = 89 x 4 = 356

Total score = 356 + 249 + 356 = 961

for mr Z

work experience = 85

score = 85 x 4 = 340

Entrance = 89

Score = 89 x 3 = 267

Interview = 85

Score = 85 x 4 = 340

Total score = 340 + 267 + 340 = 947

So as we can see Mr Y has best score therefore I think he's the best for the job.

Explanation:

[tex]\sf Average \ Result : \dfrac{sum \ of \ value \ of \ scores}{sum \ of \ weight}[/tex]

Workout:

[tex]\sf For \ candidate \ X = \dfrac{70 \ \cdot \ 4 \ + 78 \ \cdot \ 3 \ + 70 \ \cdot \ 4 }{4 + 3 + 4} = 72.18 \ \ average \ score[/tex]

[tex]\sf For \ candidate \ Y = \dfrac{89 \ \cdot \ 4 \ + 83 \ \cdot \ 3 \ + 89 \ \cdot \ 4 }{4 + 3 + 4} = 87.36 \ \ average \ score[/tex]

[tex]\sf For \ candidate \ Z = \dfrac{85 \ \cdot \ 4 \ + 89 \ \cdot \ 3 \ + 85 \ \cdot \ 4 }{4 + 3 + 4} = 86.09 \ \ average \ score[/tex]

Conclusion:

Among all of them, candidate Y has the best average score of about 87.36 whereas candidate Z has second best score of 86.09 average score and candidate X has the least average score of 72.18.

Candidate Y is the appropriate candidate for this position on the criteria.

The range, the mean, and standard deviation are mathematically given as

Participants ranged in age from 4 to 26.24 ( M = 26.24 , SD = 8.04 ). Option D.

Given the data presented below the given

A look at the result shows that the lowest and highest values are between 1s and 58, with a mean and standard deviation of 26.10 and 8.90, respectively.

Participants' ages varied from 18 to 58 (m-26.14, std dev = 8.01), hence option (d) is accurate.

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Answer:

Sorry I don't know the answer

The solution set of the inequality is:

w ∈ (-∞, -1] U [3, ∞)

The graphed parabola is f(w), and we have the inequality:

f(w) ≤ 0.

So we need to identify the intervals such that the parabola is below the horizontal axis. By looking at the graph, we can see that the two intervals are:

Left side:

(-∞, -1]

Right side:

[3, ∞)

Where the brackets are used because points x = -1 and x = 3 are solutions.

Then the solution set of the inequality is:

w ∈ (-∞, -1] U [3, ∞)

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The relation {(1,4), (2,5) (1,7)} is not a function because there is two mirror image of y for a single value of x option (D) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we know for every single value of x there should be only one image in y set.

If there are multiple images are there for a single value of x then the relation is not a function.

In a set of relations:

D. {(1,4), (2,5) (1,7)}

There is two mirror image of y for a single value of x:

Thus, the relation {(1,4), (2,5) (1,7)} is not a function because there is two mirror image of y for a single value of x option (D) is correct.

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