Construct a probability distribution for a discrete random variable uses the probability experiment of tossing a coin three times. Consider the random variable for the number of heads

Answer:

7/19

Step-by-step explanation: we could get two equations from the question if we set the denominator as x and the numerator as y:

1: x=2y+5

2:(y-3)/(x-3)=1/4

cross multiply

4(y-3)=1(x-3)

4y-12=x-3

x=4y-9

3: Then we can choose one of them and minus by another one

x-x=4y-2y-(9+5)

0=2y-14

2y=14

y=7

Then we only have to plug in

x=2*7+5

x=14+5

x=19

Given the points (3, -18) and (-5, -10)

Let the midpoint of the given coordinates is (x , y)

So, the coordinates of the midpoint is (-1 , -14)

1/100

To get the fraction of the square shaded we would use the rows and columns

For the row:

The total on the 1st row = 1

The first row is divided into 10. This means each box in the first row: 1/10

One of the box is shaded. This implies the fraction shaded in the first row is 1/10

For the column:

The total on the 1st column = 1

The column is also divided into 10 box which means each box represent 1/10

Since one of the box in the column is shaded, it represent 1/10

Fraction of the whole square shaded = fraction shaded in the row × fraction shaded in the column

Fraction of the whole square shaded = 1/10 × 1/10

Fraction of the whole square shaded = 1/100

In mathematical logic, the Law of Detachment says that if the following two statements are true:

( 1 ) If p, then q.

( 2 ) p

Then we can derive a third true statement:

( 3 ) q.

In our question, we have

( 1 ) If 0º< A <90º, then A is an acute angle.

( 2 ) The measure of A is 58º.

Then, from the first statement, we can affirm

( 3 ) A is an acute angle.

The quadrilateral has diagonals that are both congruent and perpendicular is square.

The correct option is (d)

Answer:

Its A

Step-by-step explanation:

Using the normal distribution, it is found that the measures are given as follows:

a) Proportion with less than 125 mg/dl: 0.16.

b) Percentage between 200 and 225 mg/dl: 2.35%.

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the cholesterol levels are given as follows:

[tex]\mu = 150, \sigma = 25[/tex]

The proportion below 125 mg/dl is the p-value of Z when X = 125, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (125 - 150)/25

Z = -1

Z = -1 has a p-value of 0.16, rounded with the Empirical Rule, which is the proportion.

The proportion with cholesterol levels between 200 and 225 mg/dl is the p-value of Z when X = 225 subtracted by the p-value of Z when X = 200, hence:

X = 225

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (225 - 150)/25

Z = 3

Z = 3 has a p-value of 0.9985.

X = 200

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (200 - 150)/25

Z = 2

Z = 2 has a p-value of 0.975.

0.9985 - 0.975 = 0.0235 = 2.35%, which is the percentage.

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To answer this question we will use the following property of sets:

(a) Since Ash has 153 cards in his collection (without any duplicates), Brock has 207 cards in his collection (also without any duplicates) and they have 91 cards in common, then:

Simplifying the above result we get:

(b) Expressing the above result using set notations:

Answer:

(a) There are 269 unique cards in between them.

(b)

Answer:

The function is given below as

Using the interval below

A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph).

Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).

Using a graphing tool, we will have the relative maximum and relative minimum to be

Hence,

The relative maximum is at

The relative minimum is at

The triangle is shown below:

Notice how this is an isosceles triangle.

We can find the lengths of the hypotenuse by using the trigonometric functions:

Then we have:

Therefore the hypotenuse is 29.7 ft.

The complete table using the given linear equation is x y

-4 -4

-2 0

0 4

2 8

A linear equation is one that has the form Ax+By=C. This definition comes from mathematics. It consists of two variables combined with a constant value that exists in each of them.

The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation.

Given the linear equation y = 2x + 4

If x = -4

y =2(-4) + 4

y = -4

If x = -2

y =2(-2) + 4

y = 0

If x = 0

y =2(0) + 4

y = 4

If x = 2

y =2(2) + 4

y = 8

Hence the complete table using the function is

x y

-4 -4

-2 0

0 4

2 8

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Complete question

Fill in the table using this function rule. y=2x -4

x y

-4 ?

-2 ?

0 ?

2 ?

Answer:

Step-by-step explanation:

1) -0.6 = -6/10

           = -3/5

2) -0.6*-2/5  = (-3/5)*(-2/5)

                     =(-3*-2)/(5*5)

ANSWER:

STEP-BY-STEP EXPLANATION:

To calculate the value of the midpoint, we use the formula of the midpoint which is the following:

Replacing and solving the midpoint:

we have the expression

y^3-5y^2+3y-15

Grouping terms

(y^3-5y^2)+(3y-15)

factor y^2

y^2(y-5)+(3y-15)

factor 3

y^2(y-5)+3(y-5)

factor (y-5)

The equation of the line in Slope-Intercept form is:

Where "m" is the slope and "b" is the y-intercept.

Let's solve for "y" from the equation of the line given in the exercise, in order to express it in Slope-Intercept form:

You can identify that:

By definition, the slopes of parallel lines are equal. Therefore, the slope of the line parallel to line given in the exercise, is:

Given: Different statement relating different quadrilateral

To Determine: If true or false statement

Solution

The image below summarizes the properties of a quadrilateral

From the above, we can conclude that

Answer:

Answers on attached image

Step-by-step explanation:

SOLUTION

(a) Now from the question, we want to find during what years the number of claims decrease. Let us make the graph of the function to help us answer this

We have

From the graph above, we can see that the function decreased at between x = 0 to x = 5.381

Hence the number of claims decreased between 1990 to 1995, that is 1990, 1991, 1992, 1993, 1994 and 1995

Note that 1990 was taken as zero

(b) The relative extrema from the graph is at 5.381, which represents 1995.

Hence the interpretation is that it is at 1995 that the minimum number of claims is approximately 1363.

Note that 1363 is approximately the y-value 1363.278

Answer:

96

Step-by-step explanation:

let the number be x then

1.2x=32

x=80/3

again

3.6x

3.6×80/3

96

The points (-4, -2) and (8, r) are located on a line of slope 1/4, We are asked to find the value of "r" that would make suche possible.

So we recall the definition of the slope of the segment that joins two points on the plane as:

slope = (y2 - y1) / (x2 - x1)

in our case:

1/4 = ( r - -2) / (8 - -4)

1/4 = (r + 2) / (8 + 4)

1/4 = (r + 2) / 12

multiply by 12 both sides to cancel all denominators:

12 / 4 = r + 2

operate the division on the left:

3 = r + 2

subtract 2 from both sides to isolate "r":

3 - 2 = r

Then r = 1

We are asked to identify the types of symmetries found in the given geometrical figure. Let's remember that asymmetry is a transformation that maps the figure onto itself. In this case the object has symmetry under reflections, also has symmetry under rotations around its center

If shown needs to reach a windowsill that is 10 feet above the ground and he placed his ladder 4 feet from the base of the wall.

Part a

The diagram of the right triangle formed by Shawn's ladder, the ground and wall has been plotted

Part b

The length of the Shawn's ladder is 10 foot

The distance between ladder base to the base of the wall = 4 feet

The distance between the wall base to the base of the window = 10 feet

Draw the right triangle using the given details

Part b

Using the Pythagorean theorem

[tex]AC^2= AB^2+BC^2[/tex]

Where AC is the length of the ladder

Substitute the values in the equation

AC = [tex]\sqrt{10^2+4^2}[/tex]

= [tex]\sqrt{100+16}[/tex]

= [tex]\sqrt{116}[/tex]

= 10.77

≈ 10 Foot

Hence, if shown needs to reach a windowsill that is 10 feet above the ground and he placed his ladder 4 feet from the base of the wall.

Part a

The diagram of the right triangle formed by Shawn's ladder, the ground and wall has been plotted

Part b

The length of the Shawn's ladder is 10 foot

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Reflection rule over y - axis is given as

(x , y) ------------ (-x, y)

This implies that the y - axis will remain the same and the x - axis will be negated

Pre image ABC at point (2, -1)

The reflection over y - axis will be

ABC A'B'C' A''B''C'' A'''B'''C'''

(2, -1) -----------------(-2, -1) ----------------------(2, -1) -------------------(-2, -1)

ABC A'B'C' A''B''C'' A'''B'''C'''

(2, -4) (-2, -4) (2, -4) (-2, -4)

Fund A, Jane invested $2000 and has a profit of 3%

Profit at Fund A is :

at Fund B, let $x be the amount she invested that gives her a profit of 10%

The profit at Fund B is :

It is said that the total amount she invested returned a 8% profit

The total amount she invested is :

and the 8% profit of her total investment is :

Now we need to equate the sum of her profits from Fund A and Fund B, and this must be equal to the 8% profit.

3% Profit at Fund A = $60

10% Profit at Fund B = $0.10x

8% Profit at both funds together = 160 + 0.08x

Therefore, the amount she invested in Fund B is $5000

To get x, we will use the equation below:

open the inner paremthesis

open the parenthesis

180 - x = 94

collect like term

180 - 94 = x

86 = x

They started the vacation with $426

After spending $198 the first three days, the remainder is $426 - $198 = $228

Given that there are 4 family members, we have to divide this remainder by 4, that is, $228/4 = $57

Each person has $57 to spend

Given: A conditional statement, "If a shape has four sides, then the

shape is a rectangle."

Required: To write the inverse of the statement.

Explanation: The given statement has two following statements:

The inverse of the statement will be

Hence the inverse statement is

Final Answer: The inverse statement is- "If the shape is not a rectangle, then the shape doesn't has four sides."

The result that can be gotten from the evaluation here is 6.625

We would have to solve the problem following the order that the operations are. The reason why it would have to be solve this way is because the operations are not in a bracket.

If it was in brackets, the brackets would have to be solved first using the bodmas rule

so we would have

7⋅5+42 = 49.5

49.5 - 23 = 26.5

26.5 / 4 = 6.625

The value that we got from the evaluation is 6.625

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ANSWER

2, 4 and 8

EXPLANATION

We have that in a triangle ABC, AB = 3 cm and BC = 5 cm.

To find the possible length of AC, we can apply the triangle inequality theorem.

It states that in any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

This means that:

So, we have that:

We have to disregard the third line, since the length of a triangle side can only be positive.

So, using the first 2 lines, we see that:

This means that from the options, the measure of AC can either be 2, 4 or 8.

The product of given complex number that is 8i and 4i will be -32 by the properties of complex number that states i*i will be -1 and 8*4 will be 32.

Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation i²=-1.

Commutative, Associative, Distributive Properties: All complex numbers are commutative and associative under addition and multiplication, and multiplication distributes over addition.

Here,

The product of 8i*4i=-32

as 8*4=32

and i²=-1

32*-1=-32

Due to the properties of complex numbers, which state that i*i will be -1 and 8*4 will be 32, the product of the given complex number, which is 8i and 4i, will be -32.

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Step-by-step explanation: