Which expression is equivalent to sec²x - 1?
O A. cot²x
OB. tan²x
OC. CsC²x
OD. cos²x

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \: - 2( {b}^{2} - 5c)[/tex]

( put the values )

[tex] \qquad❖ \: \sf \: - 2 \{( - 3) {}^{2} - 5( - 1) \}[/tex]

[tex] \qquad❖ \: \sf \: - 2(9 - (- 5))[/tex]

[tex] \qquad❖ \: \sf \: - 2(9 + 5)[/tex]

[tex] \qquad❖ \: \sf \: - 2 \times 14[/tex]

[tex] \qquad❖ \: \sf \: - 28[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

The probability that the mean fill is more than 84.8 ounces is 0.39358

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (84.8 - 84.5)/1.1

Evaluate the difference of 84.8 and 84.5

z = 0.3/1.1

Evaluate the quotient of 0.3 and 1.1

z = 0.27

The probability that the mean fill is more than 84.8 ounces is then calculated as:

P(x > 84.8) = P(z > 0.27)

From the z table of probabilities, we have;

P(x > 84.8) = 0.39358

Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358

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Answer:

The top left answer is correct.

Step-by-step explanation:

If you take each ordered pair and put them in the form y/x.  The top left corner is the only one where all of the equations are equivalent.

7/1 = 21/3 = 35/5 = 49/7

Answer:

Area = 32feet²

Step-by-step explanation:

Perimeter of a rectangule = 2(length+width)

Then:

g = 2w               Eq. 1

2(g+w) = 24       Eq. 2

g = length

w = width

From Eq. 2:

(2*g + 2*w) = 24

2g + 2w = 24      

2w = 24 - 2g            Eq. 3

Matching Eq. 1  and Eq. 3

g = 24 - 2g

g + 2g = 24

3g = 24

g = 24/3

g = 8 feet

From Eq. 1

g = 2w

8 = 2w

8/2 = w

w = 4 feet

Check:

From Eq. 2

2(g+w) = 24

2(8+4) = 24

2*12 = 24

Answer:

Area of a rexctangle = length * width

Then:

Area = 8feet * 4feet

Area = 32feet²

Step-by-step explanation:

sqrt(120) / sqrt(30) = sqrt(120/30) = sqrt(4) = 2

The quotient of √120 divided by √30 is 2.

Square root of a number is the value such that the value when multiplied to itself two times gives the original number.

It is denoted by the symbol √.

For example, square root of 16 is 4 since 4 × 4 = 16

The given numbers are √120 and √30.

We have to find the quotient when √120 is divided by √30.

Try to write each of the number as a product of perfect squares if possible.

√120 = √(4 × 30)

We know that √(ab) = √a √b

So, √120 = √4 × √30 = 2√30      (∵√4 =2)

√120 /√30 = 2√30 / √30 = 2    

Hence the required quotient is 2.

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The possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1

From the complete question, we understand that Mr. A wants to plays the game until he wins

This means that

He might win at the first game and he might win after n attempts

So, the values of X are

X = 0, 1, 2, 3, 4.......n

Hence, the possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1

The probability of x is represented as:

P(x) = nCx * p^x * (1 - p)^(n-x)

So, the probability that X = n is:

P(n) = nCn * p^n * (1 - p)^(n - n)

Evaluate the exponent

P(n) = nCn * p^n * 1

Evaluate the combination expression

P(n) = 1 * p^n * 1

This gives

P(n) = p^n

Hence, the probability that X = n is p^n

The distribution satisfies PMF conditions because

The expected value E(x) is calculated using

E(x) = n * p

So, we have:

E(x) = np

Hence, the value of E(x) is np

The variance V(x) is calculated using

V(x) = √n * p * (1 - p)

So, we have:

V(x) = √np(1 - p)

Hence, the value of V(x) is √np(1 - p)

The memoryless property of X is that each probability of X is independent

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Answer:

1. x = 20

2. x = 3

3. RST = 22 degrees

Step-by-step explanation:

1. Since QR bisects PQS, the measure of the angles PQR and PQS should be equal, so we can set their expressions equal to each other, and then solve.

4x-10 = -3x+130

4x = -3x +140

7x = 140

x = 20

2. Since there is a CAB has a right angle, the measure of angles CAD and BAD should add up to 90 degrees. So we can set the sum of their expressions equal to 90 degrees.

(5x+57) + (x+15) = 90

6x + 72 = 90

6x = 18

x = 3

3. I can't see where the R is but if it is on the empty line then we can find RST by subtracting the measure of angle TSU from angle RSU.

TSU - RSU = RST

91 - 69 = 22 degrees

RST = 22 degrees

Answer:

7.  m∠PQR =70°   m∠PQS = 140°

8.  m∠CAD = 18°    m∠BAD = 72°

9.  m∠RST = 22°

Step-by-step explanation:

Question 7

If QR bisects (divides into two equal parts) ∠PQS then:

⇒ m∠PQR = m∠RQS

⇒ 4x - 10 = -3x + 130

⇒ 4x - 10 + 10 = -3x + 130 + 10

⇒ 4x = -3x + 140

⇒ 4x + 3x = -3x + 140 + 3x

⇒ 7x = 140

⇒ 7x ÷ 7 = 140 ÷ 7

⇒ x = 20

Substitute the found value of x into the expression for m∠PQR:

⇒ m∠PQR = 4(20) - 10 = 70°

As QR bisects ∠PQS:

⇒ m∠PQS = 2m∠PQR = 2 × 70° = 140°

Question 8

From inspection of the given diagram, ∠BAC = 90°.

⇒ m∠CAD + m∠BAD = 90

⇒ x + 15 + 5x + 57 = 90

⇒ 6x + 72 = 90

⇒ 6x + 72 - 72 = 90 - 72

⇒ 6x = 18

⇒ 6x ÷6 = 18 ÷ 6

⇒ x = 3

Substitute the found value of x into the expressions for the two angles:

⇒ m∠CAD = 3 + 15 = 18°

⇒ m∠BAD = 5(3) + 57 = 72°

Question 9

From inspection of the given diagram (and assuming R is on the empty line segment):

   m∠RSU = m∠RST + m∠TSU

⇒ 91° = m∠RST + 69°

⇒ 91° - 69° = m∠RST + 69° - 69°

⇒ 22° = m∠RST

⇒ m∠RST = 22°

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Based on the data recorded by Isabella, it can be concluded the cube is rather fair.

Based on the data, here are the results:

This implies, in total Isabella got the same number between five and seven times. For example, the number 2 was obtained 5 times, but the number 3 was obtained 7 times.

Even though Isabella did not get the same number of times each number, the dice is rather fair because by rolling the dice thirty six times you will obtain the same number at least five times.

Moreover, there is not a big difference in the number of times you obtain each number.

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Answer:

converge

Step-by-step explanation:

the reason is : the individual terms of the series get smaller and smaller towards 0, and therefore the sum converges to a certain limit.

why do I know that the individual terms get smaller and smaller ?

because the terms are ultimately (with n getting very large the constant factors added constants become irrelevant)

n / (n^(3/2))

as sqrt(n³) = n^(3/2)

and n^(3/2) progresses much faster and stronger than n (or n¹), as 3/2 is larger than 1.

so, the denominator (bottom) of that fraction grows stronger than the numerator (top), and the terms go therefore against 0 with larger and larger n.

Answer: 10204 millimeters

Step-by-step explanation: A gallon = 3875 mm. A quart is 946. 946x 3 = 2838. A pint is around 473 mm which, when multiplied by 7, is 3311. Finally, there are 6 ounces which are approximately 30 mm. 6x30 = 180. We add all of this up : 3875 + 2838+ 3311 + 180 = 10204.

Answer: 4.9

Step-by-step explanation:

[tex]AB=\sqrt{(-4-3)^2 +(6-4)^2}=\sqrt{53}\\\\A'B'=\frac{2}{3}\sqrt{53} \approx \boxed{4.9}[/tex]

Answer:

Step-by-step explanation:

A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.

The attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.

The leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.

__

Additional comment

The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.

We know the x^2 coefficient is the opposite of the sum of the zeros:

  -(7 +(-2) +3) = -8 . . . . x^2 coefficient

And we know the constant is the opposite of the product of the zeros:

  -(7)(-2)(3) = 42 . . . . . constant

These checks lend further confidence that the zeros are those given.

(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)

The chances that NEITHER of these two selected people were born after the year 2000 is 0.36

The given parameters are:

Year = 2000

Proportion of people born after 2000, p = 40%

Sample size = 2

The chances that NEITHER of these two selected people were born after the year 2000 is calculated as:

P = (1- p)^2

Substitute the known values in the above equation

P = (1 - 40%)^2

Evaluate the exponent

P = 0.36

Hence, the chances that NEITHER of these two selected people were born after the year 2000 is 0.36

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In order to make 3 dimensional object to 4 dimensional object, it's important to draw the 4 dimensional shape in a way that gives the illusion of the 3 dimensional object.

It should be noted that shapes play an important part in geometry.

Here, to make make 3 dimensional object to 4 dimensional object, it's important to draw the 4 dimensional shape in a way that gives the illusion of the 3 dimensional object.

Also, it should be noted that a 4D tesseract can be used to project the image.

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If the price of 1 cubic foot of hay is $10 then the money needed is $15.

Given the price of 1 cubic foot of hay be $10 and the amount of hay be $1.50.

We are required to find the amount of money needed to buy the hay.

We know that the amount of money that can be spend on something is the product of price of one unit and number of units.

Product is the result when two numbers are multiplied with each other.

Total money =Price of 1 cubic foot*$1.50

=10*1.50

=$15

Hence if the price of 1 cubic foot of hay is $10 then the money needed is $15.

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Question is incomplete, the right question is as under:

1.5 cubic foot hay is required to fill a room completely. Calculate the amount we have to pay to fill the room completely if the price of 1 cubic foot is $10?

Answer: y = -1/4x + 4

Step-by-step explanation:

slope intercept form = y = mx + b

since you are given m and b, plug in the points into the formula

-1/4 goes in for m and 4 goes in for b

leaving us with:

[tex]y=-\frac{1}{4} x+4[/tex]

Answer:

[tex]y=-\frac{1}{4}x+4[/tex]

Step-by-step explanation:

Ok, so the slope-intercept form is generally expressed as: [tex]y=mx+b[/tex]

y-intercept:

Let's start by explaining why the "b" value represents the y-intercept. So I attached a graph to make this a bit more understandable, but the gist is that anywhere on the y-axis, is going to have x=0, any point on the y-axis can generally be expressed as (0, y).

This means, if we want to find the y-intercept, using the slope intercept form, we simply plug in 0 as x, since that's what x will always be equal to at the y-intercept.

We get the following equation: [tex]y=m(0) + b[/tex], and since anything times zero is just zero, we can simplify this to: [tex]y=b[/tex], meaning the y-intercept will be the "b" value in any slope-intercept form equation.

The slope:

By definition the slope is just how much the y-value changes as x increase by one. Whenever we increase the x-value by one, in the equation y=mx+b, we have one more "m", or the value is increasing by m.

Let's look at an example:

[tex]y=m(1) +b\implies m+b[/tex]

[tex]y=m(2) + b \implies m + m + b[/tex]

[tex]y = m(3) + b \implies m + m + m +b[/tex]

See how each time we increase the value "x" by one, the value of "y" increases by m. So by definition "m" is the value of the slope.

So putting this all together with your example, we get the following equation:

[tex]y=-\frac{1}{4}x+4[/tex]

The value |x−9|≤9 is equivalent to [18,0] in interval notation.

According to the statement

We have given that the distance of 9 from the number 9. and we have to find the all value of x between it.

So, For find all x value we use absolute value inequalities.

distance of 9 from number 9.

So, when we draw the number line

we see that the number will become

The distance from x to 9 can be represented using an absolute value symbol, |x−9|.

Write the values of x that satisfy the condition as an absolute value inequality.

So, it become

|x−9|≤9

Now write two inequalities then it become

x−9≤9 and x−9≥−9

x≤18  and x≥0

So, The solution set is x≤18 and x≥0,

then the solution set is an interval including all real numbers between and including 18 and 0.

So |x−9|≤9 is equivalent to [18,0] in interval notation.

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Answer

here

A={a,b,c,d}

B={c,d,e,f}

C={x,y,z}

A-B={e,f}

Answer:

39

Step-by-step explanation:

In a triangle, the sum of any two side lengths must exceed the length of the remaining third side. Therefore these 3 inequalities must be true.

5 + 19 > x

5 + x > 19

19 + x > 5

We can ignore the third inequality because, for any positive value of x, the inequality is true.

x < 26

x > 14

Now we know that x, the length of the third side, must be greater than 14 but less than 26. Since we are asked for the smallest whole number possible, the third side would be length 15. Therefore the perimeter is 5 + 19 + 15 = 39.

The number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.

Given that there are 60 students out of which 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities.

Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.

We're given the cardinalities of several sets:

total number of students n(U)=60, A applicants is n(A)=30, B applicants n(B)=25, W applicants n(W)=24, A and B applicants n(A∩B)=11, A and W applicants n(A∩W)=6, B and W applicants n(B∩W)=9 non-applicants n(U\(A∪B∪W))=4

The last cardinality tells us n(A∪B∪W),60-4=56 students applied anywhere at all.

We want to find n(A∩B∩W), the number of students that applied to each of the three universities.

By the inclusion/exclusion principle,

n(A∪B∪W)=n(A)+n(B)+n(W)-n(A∩B)-n(A∩W)-n(B∩W)+n(A∩B∩W)

56=30+25+24-11-6-9+n(A∩B∩W)

n(A∩B∩W)=3

Now, we will find the number of students that applied for at least two of the universities.

n(A∩B)=n(A∩B∩W)+n(A∩B∩W')

11=3+n(A∩B∩W')

8=n(A∩B∩W')

Similarly, we will find

n(A∩B'∩W)=3

n(A'∩B∩W)=6

n(A∩B'∩W')=16

n(A'∩B∩W')=8

n(A'∩B'∩W)=12

then the total number of students applied for at least two students is

n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B∩W)=20

Now, we will find the number of students that applied for atmost two universities, we get

n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B'∩W')+n(A'∩B∩W')+n(A'∩B'∩W)=53

now, we will find the number of students that applied for Addis Ababa but not Bahir Dar University is

n(A∩B')=n(A)-n(B)

n(A∩B')=30-25

n(A∩B')=5

hence, the total students is 60 and the number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.

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Answer:

c

Step-by-step explanation:

By the Pythagorean theorem,

[tex]28^2 + 15^2 = s^2 \\ \\ s^2 = 1009 \\ \\ s = \sqrt{1009}[/tex]

The solution to the original equation is 1, 1/6

Equations are expressions separated by mathematical operations.

Given the equation below

x/x − 1 = 6x + 1/x − 1

From the given expression, the least common denominator is x -1

Multiply both sides by x-1 to have;

x = 6x(x-1) +1

Expand

x = 6x^2-6x + 1

Equate to zero

6x^2-6x-x + 1 = 0

6x^2-7x +1= 0

The resulting quadratic equation in general form is 6x^2-7x +1 = 0

Factorize

6x^2 -6x-x + 1 = 0

Group the result

6x(x-1)-1(x-1) = 0

(6x-1)(x-1) = 0

6x - 1 = 0 and x -1 = 0

x = 1 and 1/6

Hence the solution to the original equation is 1, 1/6

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The length of third side of triangle is 4 or 14.

According to the statement

we have given that the two sides of the triangle which are 5 and 9 and we have to find the length of the third side of triangle.

So, For this purpose, we know that the

If we had a triangle with sides a, b and c, then we can say

b-a < c < b+a

where b is larger than 'a'. This is the triangle inequality theorem

In this case, a = 5 and b = 9 so,

b-a < c < b+a

9-5 < c < 9+5

4 < c < 14

Telling us that c is some number between 4 and 14, not including either endpoint. If c is a whole number, then c could be any value from this set.

And

We see that the numbers 4 and 14 are in this set. The values 2 and 7 are not in the set.

So, The length of third side of triangle is 4 or 14.

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Answer is b. ( -1, -5)

Answer is b. (-1, -5)

Step by step

Substitute the x and y values into both equations to find equality

 Answer b. Makes both equations equal

2x + y = -7

2(-1) + (-5) = -7

-2 -5 = -7

-7 = -7
it equals now let’s do the 2nd one

x - y = 4

-1 -(-5) = 4

4 = 4

This one equals too. I did the math on the other three answers and they did not equal. 

The slope of the curve described by the equation at the given point (0,1) as in the task content is; 4.

According to the task content, it follows that the slope of the curve can be determined by means of implicit differentiation as follows;

y⁵+ x³ = y² + 12x

5y⁴(dy/dx) -2y(dy/dx) = 12 - 3x²

(dy/dx) = (12 -3x²)/(5y⁴-2y)

Hence, since the slope corresponds at the point given; (0, 1); we have;

(dy/dx) = (12 -3(0)²)/(5(1)⁴-2(1))

dy/dx = 12/3 = 4.

Hence, slope, m = 4.

Consequent to the mathematical computation above, it can then be concluded that the slope of the curve, the line tangent to the curve at the given point is; 4.

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Answer:

Step-by-step explanation:

To do conversion change miles into feet and hour into second.

One foot is 5280 feet

And an hour is 3600sec

70 miles / Hour

70 * 5280feet / 3600 second

369600 feet / 3600seconds

Then simplify

102. 66 feet / Second

Speed given

1 mi=5280ft

1h=3600s

So convert

The given function is quadratic. The quadratic term is -18x², the linear term is 39x, and the constant term is -20. So, first option is correct.

A function in which the highest degree of the variable is 2, then that function is said to be a quadratic function.

The general form of a quadratic function is ax² + bx + c. Where the terms are:

ax² - quadratic term;

bx - linear term;

c - constant term;

A function in which the highest degree of the variable is 1, then that function is said to be a linear function.

The general form of a linear function is ax + c. Where the terms are:

ax - linear term;

c - constant term;

The given function is f(x) = (3x - 4)(-6x + 5)

Expanding the given function,

f(x) = (3x)(-6x) + (3x)(5) + (-4)(-6x) + (-4)(5)

     = -18x² + 15x + 24x - 20

     = -18x² + 39x - 20

Since the highest degree of the variable x in the obtained function is 2, it is a quadratic function.

The terms in the obtained quadratic function are:

quadratic term: -18x²

linear term: 39x

constant term: -20

Therefore, the first option is correct.

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Disclaimer: The question has a mistake in the function. The corrected question is here.

Question: Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.

f(x)= (3x - 4)(-6x + 5)

Answer:

Fufusyyigywngd, hdj4snwhsjtc

Bahr Ltd flu not ld6wlw

The slope-intercept form for the line is y = 1/3 x -5/3. and the option D is correct option.

According to the statement

we have given that the points (−4,1) and (2,3) and we have to find the slope-intercept form.

And we have to find the equation of line.

So, For this purpose,

The given points are:

(−4,1) and (2,3)

And the slope m become

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

So, put the values in it

then m= 3-1 / 2+4

m = 1/3

And and b point becomes (2+3) / (−4+1)

Then B = -5/3

Then the general equation of slope intercept form is y = mx +b

Then

y = 1/3 x -5/3.

So, The option D is correct and the slope-intercept form for the line is y = 1/3 x -5/3.

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