Given: BC ∥ AD ,
AC ∩ BD = O,
K ∈ BC ,
M ∈ AD ,
KM ⊥ BC ,
O ∈ KM ,
BC = 2, OK = 1, OM = 2
Find: AD

The log function is also called Logarithmic functions.

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The resulting religion Islam belongs to the class monotheism.

Monotheism is the class of religion where they believe in only one God.

Monotheism is the belief that there is one and only supreme power that is referred to as the universal God.

Given that according to Muslim tradition, the prophet Muhammad received his revelations from the only true God, whose name is Allah.

So there is only one God Allah that Islam believes in.

So Islam is a monotheistic religion.

Hence Islam is a monotheism.

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The c d f is (  1     : x≥4), b) mean is 2, c) the variance of x is 4/3 d) the value of f is 0.35 e) value of p is 0.375 and value of k is 1.4

a) F(x)=P(x ≤ x)=(  1     : x≥4

b) E(x)=∫^ (x)dx=2

c) ∫^4^0 x^ 2f(x)dx=4/3

d) f(x)=x/4,0<x<4)=0.35

e)P(1/2<X<2)=0.375

f)(p(x ≤ k)=F(K)=1.4

The pdf of x is
F(X)=1/4: 0<X<4
0 : otherwise


A) The c d f of x is
F(x)=P(x ≤ x)

=∫^ x f(t) αt
= ∫^ x1/4 αt
=1/4(t)^ x
=x/4,0<x<4
F(x)=(0: x≤0)        
      ( x/4:0<x<4)
     (  1     : x≥4)


B) We need, mean(x)
=E(x)=∫^ (x)dx

=1/4  ∫^4^ x dx
=1/4 (x^ 2/2)^ 4
=16/8
=2    

C) Here, E(X^2)          
=∫^4^0 x^ 2f(x)dx

=1/2∫^4^0 x^2 dx        
=1/4(x^ 3/3)^ 4^0
=16/3
Var(x)+E(X^2)-E^2(X)
=16/3-(2)^2
=4/3
       
d) F(1.4)=1.4/4   ∵   f(x)=(x/4,0<x<4)

=0.35


e)P(1/2<X<2)
=F(2)-F(1/2)

=2/4-1/2/4
=1/2-1/8=3/8              
=0.375

F) let R=35th percentile

so, we must have,
p(x ≤ K)=0.35           ∵  (p(x ≤ k)=F(K)
=K/4=0.35                    =k/4
k=1.4

Complete Question is given below

1. let x be a random variable with pdf . a) find the c d f f(x). b) find the mean of x. c) find the variance of x. d) find f (1.4). round to 3 decimal places. e) find P(1/2<X<2). f) find THE 35TH PERCENTILE.

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Jace should visit the theator 18 times for earning a free movie ticket.(inequality)

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

The stages of resolving inequities are as follows:

Let x be the number of visit in the theator to get at least 1 movie ticket

so the inequation is :

50 + 14.5*x > 310

x > 17.93

Jace should visit the theator 18 times for earning a free movie ticket.

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Answer:

6/8 = 9/12

Step-by-step explanation:

6/8 = 3/4

9/12 = 3/4

So, the answer is

6/8 = 9/12

The number of feet in 1 centimeter is 14 feet.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, in the scale drawing, the length of the cafeteria is 14 centimeters. the length of the actual cafeteria is 210 feet.

Here, 14 centimeters = 210 feet

1 centimeter =210/14 feet

1 centimeter =14 feet

Therefore, the number of feet in 1 centimeter is 14 feet.

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There are 10,000,000 (10 million) 7-digit combinations. A 7-digit combination is a combination of 7 different numbers (from 0-9). To calculate the total number of combinations, we can use the formula for combinations

A 7-digit combination is a combination of 7 different numbers (from 0-9). To calculate the total number of combinations, we can use the formula for combinations:

n!/(r!(n-r)!)

where n=10 (the number of possibilities for each digit) and r=7 (the number of digits).

10!/(7!(10-7)!) = 10!/7!3! = 10!/(7!3!) = 10 x 9 x 8 x 7 x 6 x 5 x 4/(7 x 6 x 5 x 3 x 2 x 1 x 3 x 2 x 1) = 10 x 9 x 8 x 7 x 6 x 5 x 4/(7 x 6 x 5 x 3 x 2 x 1) = 10 x 9 x 8 x 7 x 6 x 5 x 4/(7 x 6 x 5) = 10 x 9 x 8 x 7 x 6 x 5/7 = 10 x 9 x 8 x 7 x 6 = 10,000,000 (10 million)

Therefore, there are 10 million 7-digit combinations.A 7-digit combination is a combination of 7 different numbers (from 0-9). To calculate the total number of combinations, we can use the formula for combinations

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The equation of a sphere if one of its diameters has endpoints: (-6, 4, 0) and (0, 0, 6) will be (x+3)2+(y-2)2+(z-3)2=22

d2 = (xf-xi)2 + (yf-yi)2 +(zf-zi)2

d2 = (-6-0)2+(4-0)2+(0-6)2

d2=36+16+36=88

d=sqrt(88)

The radius is half the diameter

r=d/2

r=sqrt(88)/2

Use the center equation to get the diameter's middle.

(xf-xi)/2, (yf-yi)/2, (zf-zi)

(-6-0)/2, (4-0)/2, (0-6)/2

(-3,2,-3) Center

Apply the sphere equation now.

(x-xc)2+(y-yc)2+(z-zc)2=r2

(x+3)2+(y-2)2+(z-3)2=(sqrt(88)/2)2

(x+3)2+(y-2)2+(z-3)2=88/4

(x+3)2+(y-2)2+(z-3)2=22

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The rectangle of perimeter 174 unit that encloses the largest area is a square. [tex]\frac{87}{2}[/tex] unit on a side.

The perimeter of rectangle is 174, let the length of rectangle is x and the width of rectangle is y.

so, the perimeter of rectangle is.

Perimeter=2(x+y)

174=2(x+y)

x+y=87

y=87-x

now the area of rectangle is.

A=x × y

substitute value of y,

[tex]A=87x-x^2[/tex]

This is a quadratic equation whose graph is parabola. because the value of a is negative. the vertex is always located at the point x=-b/2a.

[tex]x=\frac{87}{2}[/tex] unit

[tex]y=87-\frac{87}{2}[/tex]

[tex]y=\frac{87}{2}[/tex]

the rectangle of perimeter 174 unit that encloses the maximum area is a square 87/2 unit on a side.

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A. Liam sets a goal to score a 720 on the GMAT test in October.

B. Liam develops an action plan to study for a month and take a practice test. After studying for a month, he takes a practice test and scores 40 points higher than he did on his first practice test.

C. Based on the average test scores of students at his target schools, Liam decides he wants to earn a 710 on the GMAT.

D. To achieve his goal, Liam will spend one hour each weeknight and three hours every Saturday and Sunday studying GMAT practice questions. He will also review progress regularly to ensure that he is on track to achieve his goal.

E. Finally, Liam will appraise his performance by comparing his scores on practice tests with his goal score of 710. If he finds that he is not making enough progress, he may adjust his study schedule or seek additional help.

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The solution of the system of linear equations 2x + y = 5 and 3x - 2y = 4 is x = 2, y = 1.

To find the solution of the pair of equations, 2x + y = 5 and 3x - 2y = 4, we can use different methods.

You can use elimination method to solve the system of linear equations. The elimination method consists of eliminating one of the variables by adding or subtracting the equations.

Multiply the first equation by 3 and the second equation by 2.

6x + 3y = 15

6x - 4y = 8

Subtract second equation from first:

7y = 7

y = 1

Substitute this value of y in the first equation:

2x + (1) = 5

2x = 4

x = 2

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Therefore , the solution of the given problem of number line comes out to be option D is correct .

The number line, a representation of real numbers integers in visual form, is a tool for teaching mathematics. An intensity line is depicted by it. Every actual number is used to represent a point just on real number, or every precise number is used to represent a position. The separations between increments on a number line are equation. The numbers on a line can only be replied in the manner indicated by those numbers. The number's intended usage will be determined by the question it answers.

Here,

Given :

Because multiplying two negative integers together

results in a positive number,

the meaning of -16 is not -4.

as a result: -4 will turn into 16

So, option D is correct .

Therefore , the solution of the given problem of number line comes out to be option D is correct .

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The percent of adults who are developmentally disabled by the criterion of an IQ score below 70 is approximately 2.28%

We can use the standard normal distribution in order to find the probability of an IQ score below 70.

We know the mean IQ score is 100 and the standard deviation is 15, so we can use the formula:

z = (70 - 100) / 15

z = -2

Using a normal probability table, we find that the probability of a score less than -2 is approximately 0.0228.

Therefore, we get that approximately 2.28% of adults are considered developmentally disabled by the criterion of an IQ score below 70.

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If you have 25 members and wish to pick a president, secretary, and treasurer, then we have 13,800 ways to choose the officers, if individual members may hold more than one office.

In the given question,

If you have 25 members and wish to pick a president, secretary, and treasurer, then we have to find how many ways can we choose the officers, if individual members may hold more than one office.

We have a total of 25 members.

They have a total of 3 positions president, secretary, and treasurer.

When the one position of president was filled then there were left 24 members for the secretary position.

When the one position of secretary was filled then there were left 23 members for the treasurer position.

So the possible ways to fill the position are found by multiplying 25,24 and 23. So

Possible ways=25*24*23

Possible ways=13,800

Hence, if you have 25 members, and wish to pick a president, secretary, and treasurer, then we have 13,800 ways to choose the officers, if individual members may hold more than one office.

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Answer: 6 + 2x

Step-by-step explanation:

Combine like terms:

= 6 + 2x

Answer: The perimeter of a shape is the sum of all its sides.

From the diagram, we can see that the shaded shape is composed of a square and a rhombus.

The square has 4 sides of equal length, which is the same as the length of one of the diagonals of the rhombus.

The rhombus has 4 sides with two sides of equal length (the diagonals) and two sides of equal length (the parallel sides).

We can call the length of the diagonals of the rhombus as "d" and the length of the parallel sides of the rhombus as "s".

So, the perimeter of the shaded shape is:

Perimeter = 4s + 4d

It is not possible to find the perimeter with out knowing the length of the sides of the rhombus and the square.

Step-by-step explanation:

Answer:

1 and - 2

Step-by-step explanation:

f(0) is asking what is the value of y when x = 0

locate x = 0 ( the origin), go vertically up the y- axis to meet the line at (0, 1)

then f(0) = 1

f(x) = 5 is asking what is the value of x when y = 5

locate y = 5 on the y- axis, go horizontally across to meet the line at (- 2, 5 )

then f(x) = 5 when x = - 2

8.4 of Susan's muffins weigh the same as 7 of Tom's muffins.

We can begin solving the problem by using the proportion:

(18 muffins) / (15 muffins) = (x muffins) / (7 muffins)

where x represents the number of Susan's muffins that weigh the same as 7 of Tom's muffins. To solve for x, we can cross-multiply and then divide:

18 muffins * 7 muffins = 15 muffins * x

x = (18 * 7) / 15

x = 8.4

Therefore, 8.4 of Susan's muffins weigh the same as 7 of Tom's muffins.

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Answer: 3

Step-by-step explanation: 77 - 2 = 75, 75/25 = 3

Answer:

hope I'm right-

Step-by-step explanation:

first row: 0.3

second row: 0.2

last row: 0.1

The value of function ƒ(10) is 340 if given ƒ(x) = 4x² – 4x – 20.

The concept of a function is used by mathematicians to describe a variety of operations, including addition and multiplication, transformations of geometric figures, relationships between variables, and many other things.

A function is a set of guidelines for matching things with one another. A function pairs the inputs with the outputs and has inputs and outputs. This pairing is subject to a crucial limitation: Each input can only be coupled with one output.

The value of x = 10

4x² – 4x – 20

Lets solve

ƒ(10) = 4(10)² – 4(10) – 20

ƒ(10) = 400 – 40 – 20

ƒ(10) = 340

Thus, The value of function ƒ(10) is 340 if given ƒ(x) = 4x² – 4x – 20.

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Answer: 4

Step-by-step explanation:

y wouldn't it be 4

so 2+2=4

ex: ii + ii = iiii (2+2 = 4)

Answer:

4

Step-by-step explanation:

2+2= 4

1+1=2 and 1+1=2

so if you add it together

you get 4

The value of x in simplest radical form is 8√3.    

A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "√" also known as root.

The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root.  

The radical and root of a number are the same thing.      

Here we have

Given triangle is a right-angled triangle

From trigonometric ratios,

Sin θ = [ Opposite side ]/[ Hypotenuse ]

=> Sin 30° = [ Opposite side ]/[ 16 ]  

As we know, Sin 30° = 1/2

=> [ Opposite side ]/[ 16 ] = 1/2

=> Opposite side = 8 units      

By the Pythagorean theory,

Hypotenuse² = Opposite side² + Adjacent side²  

=> 16² = 8² + x²  

=> 256 = 64 + x²

=> x² = 192  

=> x = √64 × 3  

=> x = 8√3      

Therefore,

The value of x in simplest radical form is 8√3.

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Suitable choices are (1), (2), (7), and (8). In a plane, lines that are consistently spaced apart from one another are referred to as parallel. Parallel lines don't ever intersect.

Given:

A and B are parallel lines.

Think of a | b and 'd' as a transversal,

Statements

Reasons

1. [tex]$\angle B X Z=\angle A Z P=58^{\circ}$[/tex]

Corresponding angles are equal

[tex]$\therefore \mathrm{m} \angle 2=58^{\circ}$[/tex]

2. [tex]$\angle B Y C=\angle X Y Z=(4 x-10) \cdot$[/tex] Vertically opposite angles are equal

Now, consider a | b and ' c ' be a transversal then,

Statements

Reasons

1. [tex]$\angle X Y Z=\angle Q Z U=(4 x-10)^{\circ}$[/tex]

Corresponding angles are equal  [tex]$\therefore \mathrm{m} \angle 1=(4 x-10)^{\circ}$[/tex]

2. [tex]$\angle P Z A+\angle P Z Q+\angle Q Z U=180^{\circ}$[/tex]

Sum of angles on a straight line is [tex]$180^{\circ}$[/tex]

3. [tex]$58^{\circ}+(3 x-1)^{\circ}+(4 x-10)^{\circ}=180^{\circ} \quad$[/tex]

Substitution property

4. [tex]$47^{\circ}+7 x=180^{\circ}$[/tex]

Combining like terms

5. [tex]$7 x=180^{\circ}-47^{\circ}$[/tex]

Subtraction property of equality

[tex]$\therefore 7 x=133^{\circ}$[/tex]

6. [tex]$x=19^{\circ}$[/tex]

Division property of equality

Plug in x = 19

in [tex]$(3 x-1)^{\circ}$[/tex]

and [tex]$(4 x-10)^{\circ}$[/tex]

we get [tex]$(3 x-1)^{\circ}=(3(19)-1)^{\circ}=56^{\circ}$[/tex]

[tex]$(4 x-10)^{\circ}=(4(19)-10)^{\circ}=66^{\circ}$[/tex]

So, [tex]$(3 x-1)^{\circ} \neq(4 x-10)^{\circ}$[/tex]

Hence, options (1), (2) , (7) and (8) are correct.

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Answer:

  9/4

Step-by-step explanation:

You want to simplify (6x^-2)^2(0.5x)^4.

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

We first work out the value of each set of parentheses, then form the product of the results.

  [tex](6x^{-2})^2(0.5x)^4=(6^2)(x^{-2\cdot2})(0.5^4)(x^4)=(36x^{-4})\dfrac{1}{16}x^4\\\\=\dfrac{36}{16}x^{-4+4}=\boxed{\dfrac{9}{4}}[/tex]

__

Additional comment

As you know, x^0 = 1, so the variable disappears when this is simplified.

Answer:

([tex]-\frac{7}{12}[/tex],-1)

Step-by-step explanation:

{(−2, 2), (−7, 7), (−1, 1), (−8, 8)} it is a function as every input has a single output. Therefore, option C is the correct answer.

In math, a relation defines the relationship between sets of values of ordered pairs. The set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.

A) {(1, −7), (2, −8), (−2, 7), (1, 8)}

Since the element  1 corresponds to two different images i.e., -7 and 8. So, this relation is not a function.

B) {(−2, 1), (−7, −1), (2, 8), (−7, −8)}

Since the element -7 corresponds to two different images i.e., -1 and -8. So, this relation is not a function.

C) {(−2, 2), (−7, 7), (−1, 1), (−8, 8)}

It is a function as every input has a single output.

So, -2, -7, -1 and -8 are the elements of the domain of the given relation.

D) {(−2, 1), (−2, 2), (−2, 7), (−2, 8)}

Since the element -2 corresponds to different images i.e., 1, 2, 7 and 8. So, this relation is not a function.

Therefore, option C is the correct answer.

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Answer:

No, you cannot fold the figure in half so that one side matches the other.

Step-by-step explanation:

The figure does not have any symmetry, so it cannot be folded in half so that one side matches the other.

The slope of the given coordinate points is -2. Therefore, option D is the correct answer.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinate points are (2, -8) and (-4, 4).

Here, substitute (x₁, y₁)=(2, -8) and (x₂, y₂)=(-4, 4) in slope formula, we get

m= (4+8)/(-4-2)

m= 12/(-6)

m= -2

Therefore, option D is the correct answer.

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