A and B are independent events. Find P(A and B) P(A)=1/6, P(B)=2/5

According to the figure the side required to complete the requirements of SAS congruence theorem is

The SAS (Side-Angle-Side) Congruence Theorem is a criterion for determining when two triangles are congruent.

It states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In this case the included angle: angle GAE and angle LOD

and the side given to be equal is: side AE and side OD

The required part to complete the requirement for SAS congruence theorem is

side GA is congruent to side LO

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Answer:

I think its SAS

Step-by-step explanation:

AC is equal to CE

and BC is equal to CD

Answer:

sas

Step-by-step explanation:

the two lines on the sides mean that the sides are congruent and where the triangles meat show that the angles are also congruent because the angles are vertical and when the angles are vertical then they are equal to each other so its using side angle side congruency theorem which gives you two sides and one angle and

The length and width of the rectangular prism are (x + 5) and (x - 2) units respectively.

The volume of a rectangular prism is represented by the expression $6x^2 +18x-60$. The height of the prism is 6 units. Let l, w, and h be the length, width, and height of the rectangular prism respectively.

Then, Volume of a rectangular prism = l × w × h

the height of the rectangular prism is given to be 6 units.

So, we get,

l × w × 6 = $6x^2 +18x-60$lw = $\frac{6x^2 + 18x - 60}{6} = x^2 + 3x - 10$lw = (x + 5)(x - 2)

Therefore, the binomials that represent the length and width of the rectangular prism are (x + 5) and (x - 2).

Hence, the length and width of the rectangular prism are (x + 5) and (x - 2) units respectively.

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To find the probability of either event occurring, we can use the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Given that P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.25, we can substitute these values into the formula.

\(P(A or B) = P(A) + P(B) - P(A and B)\)
\(P(A or B) = 0.6 + 0.5 - 0.25\)
\(P(A or B) = 0.85 - 0.25\)
\(P(A or B) = 0.60\)
The probability of either event occurring is 0.60 or 60%.

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The probability of either event occurring can be found by adding the probabilities of the individual events and subtracting the probability of both events happening together. In this case, the probability of either event A or event B occurring is 0.6.

The probability of either event occurring can be calculated using the principle of addition. To find the probability of either event happening, we need to sum the individual probabilities of the events and subtract the probability of both events happening together.

Given:

p(a) = 0.6 (probability of event A occurring)
p(b) = 0.5 (probability of event B occurring)
p(a and b) = 0.25 (probability of both events happening together)

To calculate the probability of either event occurring, we can use the formula:

p(a or b) = p(a) + p(b) - p(a and b)

Substituting the given values into the formula:

p(a or b) = 0.6 + 0.5 - 0.25

p(a or b) = 0.85 - 0.25

p(a or b) = 0.6

Therefore, the probability of either event A or event B occurring is 0.6.

To understand this concept better, let's consider an example. Suppose event A represents rolling a fair six-sided die and getting an even number (2, 4, or 6). The probability of event A occurring would be 0.5. Now, let event B represent flipping a fair coin and getting heads. The probability of event B occurring would be 0.5.

If we want to find the probability of either rolling an even number or flipping heads, we can use the formula mentioned earlier. The probability of rolling an even number is 0.5, the probability of flipping heads is 0.5, and the probability of both happening together is 0.25. Plugging these values into the formula, we get:

p(A or B) = 0.5 + 0.5 - 0.25

              = 0.75

Therefore, the probability of either rolling an even number or flipping heads is 0.75.

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3150 miles in 14 hrs

225 mph

hope this helps!

As it's Given one two angles of triangle is 60°

let other angle be d

2 × 60° + d = 180°

d = 180° - 120°

d = 60°

All angles of triangle are equal

I.e 60°

.°. Triangle is equilateral and all sides are also equal.

\( \tt \: s = \dfrac{a + b + c}{2} \)

So:-

\( \tt \: s = \dfrac{3 \times 30}{2} \)

\( \\ \\ \)

\( \tt \: s = \dfrac{90}{2} \)

\( \\ \\ \)

\( \tt \: s = 45\)

Now Let's find Area:-

\( \\ \\ \)

\( \tt area = \sqrt{s(s - a)(s - b)(s - c)} \)

\( \\ \\ \)

\( \to \tt area = \sqrt{45(45 - 30)(45 - 30)(45 - 30)} \\ \)

\( \\ \\ \)

\( \to \tt area = \sqrt{45 \times 15 \times 15 \times 15} \\ \)

\( \\ \\ \)

\( \to \tt area =15 \sqrt{9 \times 5 \times 15} \\ \)

\( \\ \\ \)

\( \to \tt area =15 \sqrt{3 \times 3 \times 5 \times 15} \\ \)

\( \\ \\ \)

\( \to \tt area =15 \times 3 \sqrt{ 5 \times 15} \\ \)

\( \\ \\ \)

\( \to \tt area =15 \times 3 \times 5 \sqrt{3} \\ \)

\( \\ \\ \)

\( \to \tt area =15 \times 3 \times 5 \times 1.732\)

\( \\ \\ \)

\( \to \tt area =389.7\)

The equation of the blue graph is option B. G(x) = (x - 4)² + 1.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

The given function is f(x) = x².

From the figure, we can see that the graph of f(x) is shifted left to 4 units.

Then the function becomes (x - 4)².

Then the function is shifted up to 1 unit.

The resulting function is G(x) = (x - 4)² + 1.

Hence the correct equation of the graph is G(x) = (x - 4)² + 1.

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First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.

P = L + 2W

A = L * W

Now that we have our equations, we need to plug in what we know, which is the 40m of rope.

40 = L + 2W

A = L * W

Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.

L = 40 - 2W

Now, we can substitute the value for L into L in the area equation and get a quadratic equation.

A = W(40 - 2W)

A = -2W^2 - 40W

The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.

V = -b/2a

V = 40/2(2) = 40/4 = 10

Derivative:

-4w - 40 = 0

-4w = 40

w = |-10| = 10

To find the other dimension, use the perimeter equation.

40 = L + 2(10)

40 = L + 20

L = 20m

Therefore, the dimensions of the area are 10m by 20m.

Hope this helps!

Answer:

Width: 10 m

Length: 20 m

Step-by-step explanation:

Hi there!

Let w be equal to the width of the enclosure.

Let l be equal to the length of the enclosure.

1) Construct equations

\(A=lw\) ⇒ A represents the area of the enclosure.

\(40=2w+l\) ⇒ This represents the perimeter of the enclosure. Normally, P=2w+2l, but because one side isn't going to use any rope (sandy beach), we remove one side from this equation.

2) Isolate one of the variables in the second equation

\(40=2w+l\)

Let's isolate l. Subtract 2w from both sides.

\(40-2w=2w+l-2w\\40-2w=l\)

3) Plug the second equation into the first

\(A=lw\\A=(40-2w)w\\A=40w-2w^2\\A=-2w^2+40w\)

Great! Now that we have a quadratic equation, we can do the following:

4) Solve for w

\(A=-2w^2+40w\)

Factor out -2w

\(A=-2w(w-20)\)

For A to equal 0, w=0 or w=20.

The average of 0 and 20 is 10, so the width that will max the area is 10 m.

5) Solve for l

\(40=2w+l\)

Plug in 10 as w

\(40=2(10)+l\\40=20+l\\l=20\)

Therefore, the length of 20 m will max the area.

I hope this helps!

Therefore, the solution set for the inequality is x ≥ 4.75.

In mathematics, an expression is a combination of numbers, variables, and operators that are grouped together and evaluated to produce a value. It can consist of a single number or variable, or it can be a more complex combination of terms. Expressions can involve arithmetic operations such as addition, subtraction, multiplication, and division, as well as functions, exponents, and other mathematical operations. Expressions can be used to represent real-world problems and situations, and they are often used in algebra, calculus, and other areas of mathematics.

Here,

First, we simplify both sides of the inequality by performing the operations inside the parentheses and the brackets:

4(x-2)-3 ≥ −3(-2+7)+5

4x - 8 - 3 ≥ 3 + 5

4x - 11 ≥ 8

Next, we add 11 to both sides to isolate the variable term:

4x - 11 + 11 ≥ 8 + 11

4x ≥ 19

Finally, we divide both sides by 4 to solve for x:

4x/4 ≥ 19/4

x ≥ 4.75

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Answer:

-5 2/7

Step-by-step explanation:

i hope this helped you

Answer:

x=-6

Step-by-step explanation:

-24=7x+18

-7x-24=18                                         move variable to left and change the sign

-7x=18+24                                          add the numbers

-7x/-7 = 42/ -7                                    divide both sides by  -7

x=-6

The required total amount paid for magazine and pencil is 108p.

Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube  roots, plus and minus.

Now it is given that,

Costing of a magazine = 83p

Costing of pencil = 45p

Thus, Total costing = Costing of a magazine + Costing of pencil

Putting the values we get,

Total costing = 83p + 45p = 128p

Now voucher gives 20p off

So, Final Costing = Total costing - Voucher off

⇒ Final Costing = 28p - 20p

⇒ Final Costing = 108p

this is the equired total amount paid for magazine and pencil.

Thus, the required total amount paid for magazine and pencil is 108p.

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The value  of x for the given  triangle  is x = 8.4 units. 2. For the given triangle the value of x is 2941.17 m.

The opposing angles created by the junction of two lines are known as

vertical angles

or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is next are

supplementary angles

, meaning their sum is 180 degrees.

The given triangle is a right triangle.

Using the trigonometric functions we have:

tan (35) = opposite / adjacent = x / 12

0.7 (12) = x

x = 8.4

Hence, the value of x for the given triangle is x = 8.4 units.

For the second figure, using the alternate interior angles we have angle corresponding to the segment x as 10 degrees.

Using the trigonometric function we have:

sin (10) = opposite / hypotenuse = 500/x

x = 500/0.17

x = 2941.17

Hence, the value of x is 2941.17 m.

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The components of a number are the numbers that divide evenly into it. To find the factors of 13, divide 13 by each number from 1 to 13 and check whether or not the result is an integer. 13 is made up of two factors: 1 and 13.

Division is one of the four fundamental arithmetic operations that allows integers to be connected to produce new numbers. Addition, subtraction, and multiplication are the other operations. Division is the process of dividing a given amount into equal pieces in mathematics. For example, a group of 20 people can be divided into four groups of five people each, or five groups of four people each, and so on. Splitting anything involves dividing it into two or more equal halves, such as an area, class, category, group, or division. To divide something simply is to cut it in half and give it to a group.

Here,

A number's components are the numbers that split equally into it. To determine the factors of 13, divide 13 by each number from 1 to 13 and see if the result is an integer or not. 13 has two factors: 1 and 13.

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We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

-3/2

Step-by-step explanation:

\(m = \frac{7 - 4}{6 - 8} = \frac{3}{ - 2} = - \frac{3}{2} \)

Answer:

17.738

Step-by-step explanation:

to find x we’ll use sine

sin69=x/19

(remember that sine = opposite/hypotenuse)

so x = 19sin69

when typing this in your calculator you might need to change from radian to degree mode

Answer:

Just find the coordinate at the point where the x-coordinate is 3

Step-by-step explanation:

F(x) is just another term for Y. The variable of X is the value that you input into the f(x), which just stands for a function. Since the value that they asked for was 3, you know that they inputted the value of 3 as x. Just look where the coordinate at the point where the x-coordinate is 3 to find the answer.

Answer:

Sample Response: For f(3), the input is 3 and you are looking for the output. To determine the function's value when x = 3, go to the value of 3 on the x-axis and then locate the graph for that value of x. Determine the value of y from the y-axis at that location on the graph.

Step-by-step explanation:

answer on edge2020

Answer:

1st and 2nd options

Step-by-step explanation:

Using the method of completing the square to obtain standard form

(13)

Rearrange the given equation so x and y terms are together, that is

x² + 24x + y² + 30y + 353 = 0 ( subtract 353 from both sides )

x² + 24x + y² + 30y = - 353

To complete the square

add ( half the coefficients of the x/ y term)² to both sides

x² + 2(12)x + 144 + y² + 2(15)y + 225 = - 353 + 144 + 225

(x + 12)² + (y + 15)² = 16

(x + 12)² + (y + 15)² = 4² ← in standard form

with centre = (- 12, - 15 ) and radius = 4

---------------------------------------------------------------------

(14)

As in number 13

x² - 22x + y² + 16y = - 181

Complete the square

x² + 2(-11)x + 121 + y² + 2(8)y + 64 = - 181 + 121 + 64

(x - 11)² + (y + 8)² = 4

(x - 11)² + (y + 8)² = 2² ← in standard form

with centre = (11, - 8 ) and radius = 2

Answer:

It’s A

Step-by-step explanation:

You didnt write the whole question :)

If a jar containing 20 coins has a total value of $3.05, there are  13 dimes and 7 quarters in the jar

Total number of coins = 20 coins

Total value of coins = $3.05

The two types of coins are dimes and quarters

We know,

Consider x as the number of dimes and y as the number of quarts

Then the equations will be

x + y = 20

x = 20 - y

The second equation will be

0.10x + 0.25y = $3.05

Use the substitution method

0.10(20-y) + 0.25y = 3.05

2 - 0.10y + 0.25y = 3.05

0.15y = 1.05

y = 1.05 / 0.15

y = 7

Then find the value of x

x = 20 - y

x = 20 - 7

= 13

Therefore, there are 13 dimes and 7 quarters in the jar

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John's percentile rank is 60%.

The percentile rank is a measure used to indicate the percentage of scores that fall below a particular value in a given data set. To calculate John's percentile rank, we first need to determine how many students are below his rank.

In this case, John's rank is 120, which means that 119 students are ranked higher than him, and 300 - 119 = 181 students are ranked lower than him. To find John's percentile rank, we divide the number of students ranked below him by the total number of students and multiply by 100: (181/300) x 100 = 60%.

Therefore, John's percentile rank is 60%, indicating that he scored higher than 60% of the students in his class.

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Answer:

The answer is: -15 35/51 < -15.6 < - radical 245 < 154/10

The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

The diagonals of the rhombus will be the same as the dimension of the rectangle that is 8 cm and 6 cm.

Then the area of the rhombus is given as,

A = (Product of diagonal of rhombus) / 2

A = (8 x 6) / 2

A = 48 / 2

A = 24 square centimeters

The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

The diagram is shown below.

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If two lines form congruent adjacent angles, it indicates that the lines are perpendicular to each other.

This is known as the Perpendicular Adjacent Angles Theorem. According to this theorem, if two lines intersect and the adjacent angles formed by the intersection are congruent, then the lines are perpendicular to each other.

Congruent adjacent angles are angles that have the same measure and share a common vertex and a common side. When two lines intersect to form congruent adjacent angles, it implies that the lines are forming a right angle at their point of intersection. Thus, the lines are perpendicular to each other.

In summary, if two lines form congruent adjacent angles, it indicates that the lines are perpendicular.

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Answer:

1. Three fourths

2. 3/4

3. 0.75

4. 75%

Step-by-step explanation:

i dont know which one you want

Answer:

.75

Step-by-step explanation:

3 over 4 means \(\frac{3}{4}\), and a fraction is just a division problem. 3 ÷ 4 = .75

The correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.

To determine which angles are congruent in circle D, we need to analyze the given information about the measures of minor arcs. Since minor arcs are measured in degrees, we can use the following properties:

1. When two arcs are congruent, their corresponding central angles are also congruent.

2. The measure of a central angle is equal to the measure of its intercepted arc.

Given these properties, let's examine the answer choices:

A) EDH and FDG: We cannot determine their congruency based solely on the measures of the minor arcs.

B) FDE and GDH: These angles have the same intercepted arc, so they are congruent.

C) GDH and EDH: The intercepted arcs for these angles are different, so they are not congruent.

D) GDF and HDG: These angles have the same intercepted arc, so they are congruent.

Therefore, the correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.

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