2
The probability distribution of the random variable X is shown in the following table.
0
3
1 2
0.12 0.16 9 0.22
-2
P(X=x) 0.08
X
-1
P
The mean of X is 1.05.
(i) Write down two equations involving p and q and hence find the values of p and q.
(ii) Find the variance of X.
[4]
[2]

2 congruent triangle can be drawn using any three of these six points as vertices.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape represented by three non-collinear points in a single plane.

Hence, 2 congruent triangle can be drawn using any three of these six points as vertices.

learn more about  triangle  click here:

https://brainly.com/question/1058720

#SPJ4

Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.

saddle point : a point on a curved surface at which the curvatures in two mutually perpendicular planes are of opposite signs

The function :

f(x , y) = x³ = y³ = - 3x² - 3y² - 9x

The first partial derivative with respect to x is:

f' x = 3x²-6x-9

And the partial derivative with respect to y is:

f' y = 3y²-6y

Now equate the above derivatives to zero, to obtain the system of equation:

3x²-6x-9 = 0

3y²-6y = 0

On solving the two equations:

The critical points are : A(-1,0), B(-1,-2), C(3,0) and D(3,2)

Now calculate the discriminant

D = f xx(x , y)f y(x , y)-f xy(x , y)²

Here,

f xx = 6x-6

f yy = 6y-6

f xy = 0

On putting the above values we get:

D = (6x-6)(6y-6)

At, A(-1,0)

D = -18<0

Hence , A(-1,0) is a local maximum point.

At, B(-1,2)

D = -72<0

Hence B(-1,2) is saddle point.

At, C(3,0)

D = -72

Hence C(3,0) is also a saddle point

At, D(3,2)

D = 12>0

Hence , D(3,2) is the minimum point.

Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.

To learn more about saddle point visit :

brainly.com/question/29526436

#SPJ4

98 degrees is approximately equal to 5.48 radians.

How to convert degree measure to radian measure?

To convert a degree measure to a radian measure, you can use the conversion factor of 180/π.

98 degrees is equal to (98*π)/180 radians

So, 98 degrees is approximately equal to 5.48 radians.

To learn more about degree measure to radian measure, Visit

https://brainly.com/question/29260735

#SPJ1

Answer:

Step-by-step explanation:

[tex]x^{2} -7x+c=(x+a)^{2}[/tex]

[tex]x^{2} -7x+c=x^{2} +2ax+a^{2}[/tex]

[tex]-7x=2ax\\a=-7/2[/tex]

[tex]a^{2} =c\\c=(-7/2)^{2} =49/4[/tex]

Answer:

a line

Step-by-step explanation:

y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2

Answer:

B)  A coordinate plane with one line that passes through the points (0, 4) and (2, 3) and another line that passes through the points (0, 0) and (2, 1)

Step-by-step explanation:

Given system of linear equations:

[tex]\begin{cases}y=\frac{1}{2}x\\x+2y=8\end{cases}[/tex]

Substitute the first equation into the second equation and solve for x:

[tex]\implies x+2\left(\dfrac{1}{2}x\right)=8[/tex]

[tex]\implies x+x=8[/tex]

[tex]\implies 2x=8[/tex]

[tex]\implies x=4[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]\implies y=\dfrac{1}{2}(4)[/tex]

[tex]\implies y=2[/tex]

Therefore, the solution to the given system of linear equations is:

The point of intersection is the solution to a graphed system of linear equations.  

Therefore, the graph that shows the solution to the given system of linear equations is the graph where the point of intersection of the two lines is (4, 2).

Therefore , the solution of the given problem of linear equation comes out to be  $105 is the total cost

A linear regression model is one that uses the equation y=mx+b. The slope is B, and the y-intercept is m. The preceding sentence is commonly referred to as a "math equation with two variables," despite the fact that both y and x are separate factors. The only variables in bivariate linear equations are two. In all circumstances, the solutions to linear equations' application domains are zero. Y=mx+b is the formula for a single linear equation.

Here,

The first company's equation is y = 10.5x.

Additionally, the second company's equation is y = 7.5x + 30.

Where

number of T-shirts equals x.

y = overall cost

For the overall cost to be the same for both businesses, we have to:

=> 10.5x = 7.5x + 30

=> 10.5 x - 7.5 x = 30

=> 3 x = 30

=> x = 30/3

=> x = 10

To make the T-shirts' prices equal, the volleyball team must purchase 10 from each vendor.

Total for each business:

=> 10.5x = 10.5 (10) = $ 105

OR

Totals for each company are calculated as follows:

=> 7.5x + 30 = 7.5(10) + 30 = 75 + 30

=> $105

Therefore , the solution of the given problem of linear equation comes out to be  $105 is the total cost.

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ4

A 3-regular graph is called a cubic graph. A strongly regular graph is a regular graph where every adjacent pair of vertices has an equal number of neighbors in common, and every non-adjacent pair of vertices has an equal number of neighbors in common.

In the mathematical field of graph postulate, a cubic graph is a graph in which all vertices have a degree of three. In other terms, a cubic graph is a 3-regular graph. Cubic graphs are also known as trivalent graphs.

A bicubic graph is called a cubic bipartite graph.

In graph theory, a regular graph is a graph where each vertex has an equal number of neighbors; i.e. every vertex has an equal degree or valency.

Read more about trivalent graphs :

https://brainly.com/question/29640291

#SPJ4

Answer:

0.75 is less than 1, so the portrait will be smaller than the actual head.

Step-by-step explanation:

The art teacher has said that the portrait will be 0.75 times as tall as the actual head.

0.75 is less than 1, so the portrait will be smaller than the actual head.

A ratio of 0.75 means that the portrait will be 3/4 the size of the actual head. So, if the actual head is 8 inches tall, the portrait will be 6 inches tall (8*0.75 = 6). Therefore, the portrait will be smaller than the actual head.

The correct option is A, the linear equation has no solutions.

Here we want to see how many solutions do the equation below has:

(1/4)*(8 - 24x) = 12 - 6x

Now let's try to solve that linear equation, we can start by simplifying the left side:

(1/4)*(8 - 24x) = 12 - 6x

8/4 - 24x/4 = 12 - 6x

2 - 6x = 12 - 6x

Now we can add 6x in both sides, so we will get:

2 - 6x + 6x = 12 - 6x + 6x

2 = 12

That is a false equation, thus, the equation has no solutions.

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Since, Four distinct fair coins are tossed. if it is known that at least one of the coins shows a head . The probability that all coins show heads is 3/4.

Probability:

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes for an event. In an experiment with 'n' outcomes, the number of favorable outcomes can be denoted by x. The formula for calculating the probability of an event is:

  Probability (Event) = Favorable Outcome / Total Outcome = x/n

The probability of an event can be calculated using the probability formula by simply dividing the number of favorable outcomes by the total number of possible outcomes. The value of the probability that an event will occur can range from 0 to 1. This is because the preferred number of outcomes can never exceed the total number of outcomes. Also, the resulting favorable number can never be negative.

Given that:

Four District fair coins are tossed.

So, possible outcomes are

    HH,HT,TH,TT

We know that:

Probability= total possible outcomes / favorable outcomes

Now,

​Favorable outcomes = HH,HT,TH

And,

Probability = 3/4

Therefore, ​the probability that all coins show heads is 3/4.

Learn more about Probability:

https://brainly.com/question/743546

#SPJ4

Answer:

Step-by-step explanation:

The formula for the sum of a geometric sequence is: S = a(1 - r^n) / (1 - r)

In this case, our a = -8, r = -3, and n = 10.

S = -8(1 - (-3)^10) / (1 - (-3))

S = -8(1 - (-59049)) / 4

S = -8(59049) / 4

S = -2362196

Answer:

The Sun has 1.0975 x 10^2  times the diameter of Earth

Step-by-step explanation:

Diameter of Sun = 1.4 x 10^9 m

Diameter of Earth = 1.2756 x 10^7 m

ratio between Diameter of Sun and Earth :-

Diameter of Sun/Diameter of Earth = 1.4 x 10^9/ 1.2756 x 10^7

= 1.0975 x 10^2

The area of shaded triangle is 20 square feet

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.

Area of triangle = 0.5*base*height

Area of whole triangle = 0.5*8*10 =  40 square feet

Area of unshaded triangle = 0.5*4*10 =  20 square feet

Area of shaded triangle

= Area of whole triangle  - Area of unshaded triangle

=  40 - 20

= 20 square feet

Thus, the area of shaded triangle is 20 square feet

To learn more about the area from the given link

https://brainly.com/question/25292087

#SPJ1

The equation 291 = 359 + 125m represents the given phrase, and the required value of m is 2.33

Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use. These symbols, known as variables in elementary algebra, indicate quantities with no set values. Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.

The equation 291 = 359 + 125m can be solved for m by subtracting 359 from both sides, resulting in:

291 - 359 = 125m - 359

-68 = 125m - 359

Adding 359 to both sides gives:

-68 + 359 = 125m

291 = 125m

Dividing both sides by 125 gives the solution for m:

291 / 125 = 125m / 125

2.33 = m

So, m is equal to 2.33.

To learn more about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

The question seems incomplete, the completed question would be as:

If 291 is the same as 359 increased by the product of 125 and m. what is the value of f?

The volume of a hemisphere with a radius of 44.9 m is approximately 189582.2 cubic meters, rounded to the nearest tenth.

To calculate the volume of a hemisphere, you can use the formula

V = (2/3)πr^3

where V is the volume, π is pi (approximately 3.14), and r is the radius. In this case, r = 44.9 m.

So, (2/3)π(44.9)^3 = 189582.234 cubic meters.

This is the exact volume, but since the question asked for the volume rounded to the nearest tenth, the final answer would be 189582.234 cubic meters. It's worth mentioning that a hemisphere is half of a sphere, thus, the volume of a full sphere with a radius of 44.9 m would be double of this value.

To know more about hemisphere click below:

https://brainly.com/question/13625065#

#SPJ4

Answer:

C. 14x^7-56x^6-126x^5+35x^4-140x^3-315x^2

I'm only providing an answer but if you need an explanation you can ask me because I did it in my journal.

Pls mark as brainliest ;)

The fraction of the books are hardback is 4 / 11.

In Mathematics, a fraction defined as the part of the whole thing. For example, a pizza is divided into four equal pieces, then each piece is represented by ¼. Fractions help to distribute and judge the numbers easily and make the calculation faster.

from given conditions, a boy ha 35 paperback book and 20 hardback book.

so, the total books are 35 paperback book + 20 hardback book = 55 books

fraction of books which are hardback book are,

20 / 55

= 4 / 11

Therefore, the fraction of the books are hardback is 4 / 11.

To learn more about fractions visit : brainly.com/question/8482939

#SPJ4

Answer: An array is a visual representation of a multiplication problem, and an area model is a way to represent a multiplication problem using rectangles. Both arrays and area models can be used to find factor pairs of a number.

Here's an example of how to use an array to find the factor pairs of 12:

Draw a rectangle that represents 12.

Divide the rectangle into smaller rectangles by drawing rows and columns.

Fill in the rectangles with the numbers 1 through 12.

Find the factor pairs by looking for the rectangles that have the same area as the original rectangle, 12.

The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4.

Here's an example of how to use an area model to find the factor pairs of 12:

Draw a rectangle that represents 12.

Divide the rectangle into smaller rectangles by drawing rows and columns.

Label the rectangles with the factors of 12, which are 1, 2, 3, 4, 6 and 12.

Find the factor pairs by looking for the rectangles that have the same area as the original rectangle, 12.

The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4.

Both arrays and area models are an effective way of finding the factor pairs of a number because they help you to visualize the multiplication problem and to see the relationship between the factors and the product.

Step-by-step explanation:

The ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the equivalent ratio 20 : 1/6.

By dividing both the antecedent and consequent values by a similar fraction, equivalent ratios can be reduced to the same value. In other words, two ratios are deemed equivalent if the bigger one in value can be expressed as a multiple of the other.

Therefore, we only need to multiply the two amounts by the same number to obtain the equivalent ratio of another ratio. Equivalent ratios and equivalent fractions both have similar ideas. Examples of equivalent ratios include 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, etc.

20 : 1/6

Multiply both by 6

120  : 1

Thus, 120 × 2/3  : 1 × 2/3

80 : 2/3

multiply by 3

80 × 3 : 2/3 × 3

240 : 2

120 : 2

When ratio is 120  : 1

divide both by 120

120/120  : 1/120

1 : 1/120

1 × 10 : 1/120 × 10

10 : 1/12

multiply by 12

120 : 1

1 × 90 : 1/120 × 90

90 : 3/4

multiply by 4

90 × 4 : 3/4 × 4

360 : 3

120 : 1

Thus, the ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the proportion 20 : 1/6.

Learn more about ratio

https://brainly.com/question/13419413

#SPJ1

​

Step-by-step explanation:

f(-1) = (1/8)^-1 = 1/(1/8) = 8

f(0) = (1/8)⁰ = 1 (a⁰ = 1 for any a)

f(1) = (1/8)¹ = 1/8 = 0.125

f(2) = (1/8)² = 1/64 = 0.015625

f(3) = (1/8)³ = 1/512 = 0.001953125

remember

(a/b)ⁿ = aⁿ / bⁿ

in the same way as

(a×b)ⁿ = aⁿ×bⁿ

Answer:

Step-by-step explanation:

I assume that the amount of peanut butter chips in original recipe is [tex]1\frac{1}{2}[/tex] c (the picture isn't clear!)

2( [tex]1\frac{1}{2}[/tex] + x ) = [tex]4\frac{1}{2}[/tex]

[tex]1\frac{1}{2}[/tex] + x = [tex]4\frac{1}{2}[/tex] ÷ 2

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

x = [tex]2\frac{1}{4}[/tex] - [tex]1\frac{1}{2}[/tex] = [tex]1\frac{5}{4}[/tex] - [tex]1\frac{2}{4}[/tex] = [tex]\frac{3}{4}[/tex]

There is [tex]\frac{3}{4}[/tex] of a cup of nuts in original recipe.

The value of x is 85°

A circular sector, also known as circle sector or disk sector is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector

A sector is a region bounded by two radii of a circle and the intercepted arc of the circle. The angle formed by the two radii is called a central angle. A sector with a central angle less than 180° is called a minor sector. A sector with a central angle greater than 180° is called a major sector.

The sector where x is the minor sector

The angular distance is x and it is measured in degrees (°)

Therefore the value of x is 85°

learn more about angle of a sector from

https://brainly.com/question/22972014

#SPJ

Answer:

90

Step-by-step explanation:

The symbol represented in the angle is the right angle symbol ∟

This means that the angle would be 90

Have a lovely day :)

Answer:

There's no m so I'm assuming you meant b.

The angle of b is 121

Step-by-step explanation:

The shape here is a heptagon. The formula for calculating the sum of interior angles is ( n − 2 ) × 180. *n represents the number of sides.

(7-2) × 180               There are 7 sides so plug that in.

(5) × 180 = 900       This means the shape's interior angles add up to 900.

Now, all we have to do is add up all the sides known and set it equal to 900.

c + d + e + f + g + a = 900

148 + 90 + 142 + 130 + 139 + 130 + b = 900

779 + b = 900              

now subtract 779 from both sides to isolate b.

b = 121

The confidence interval's upper and lower bounds, respectively, are 0.117 for the higher and 0.083 for the lower.

The interaction between two or much more quantities is the focus of the branch of mathematics known as ratio and proportion. A key component of GCSE mathematics, ratio and proportion comprehension has connections to several subjects in number, algebra, geometry, probability, and statistics. An equilibrium for two ratios is a percentage. We use proportions to construct comparable ratios and find solutions to problems involving unknown numbers.

[tex]\begin{aligned}\bar{p} & =\frac{x}{n}=\frac{120}{1200}=0.10 \\\frac{\alpha}{2} & =\frac{1-\text { Confidence } \%}{2}=\frac{1-0.95}{2}=0.025 \\z_{1-\alpha / 2} & =z_{0.975}=1.960 \Rightarrow \text { Use the Excel formula "=NORMSINV(0.975)" }\end{aligned}[/tex]

[tex]S . E .=z_{1-\alpha / 2} \sqrt{\frac{\bar{p}(1-\bar{p})}{n}}=1.960 \sqrt{\frac{0.1(1-0.1)}{1200}}=0.017[/tex]

The confidence interval's top bound: [tex]\bar{p}[/tex] + S.E = 0.10 + 0.017 = 0.117

The confidence interval's lowest bound: [tex]\bar{p}[/tex] - S.E. = 0.10 - 0.017 = 0.083

To know more about Proportion visit:

https://brainly.com/question/1496357

#SPJ4

Answer:

I would really like to help but I have no idea

Answer:

.5 or 1/2

Step-by-step explanation:

1-.5      .5

------=------- simplify= .5 slope is in fractions 1/2

2-1       1

The expressions that are equivalent to 5(4u) will be 20 u and 5(u + 3u).

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The expression that is equivalent to 5(4u) will be:

= 20 u

and

5(u + 3u)

= 20u

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

Answer:

84

Step-by-step explanation:

this is an isosceles triangle so the base angles are equal meaning <BAC= <BCA =48°

48° +48° =96°

180°- 96° = 84°

<ABC = 84°