The tree diagram represents an experiment consisting of two trials
What is P(A)

Answer:

See below

Step-by-step explanation:

48 + 3y = 90 degrees   so y = 14 degrees

3x + 2x + 12 = 90   so x = 78/5 = 15.6 degrees

The correct option regarding the minimum height reached by the toy is:

A height of -1.76 inches at 5.647 seconds.

The function for the height of the toy in the spring after x seconds is modeled as follows:

y = -cos(x) + 2cos(x)sin(x)

It is a trigonometric function, hence there is no rule to find the minimum value of the function as there is for a quadratic function, for example.

Since there is no rule, we have to sketch the graph of the function in the given domain of 0 < x < 6.

Using a graphing calculator, the graph of the function is given at the end of the answer, with minimum point at (5.647, -1.76), hence the correct option is:

A height of -1.76 inches at 5.647 seconds.

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The velocity of the body under simple harmonic motion is equal to - 5√3 / 2. (Correct choice: B)

Simple harmonic motion is a kind of self-sustained periodic motion that observed the following formula:

y = y' + Δy · cos ωt     (1)

Where:

The equation for the velocity of the body in simple harmonic motion is found differentiating (1):

v = - ω · Δy · sin ωt      (2)

If we know that ω = 1, t = 2π / 3 and Δt = 5, then the velocity of the body is:

v = - 1 · 5 · sin (2π / 3)

v = - 5 · sin (2π / 3)

v = - 5 · √3 / 2

v = - 5√3 / 2

The velocity is equal to - 5√3 / 2.

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To find h(-6), replace x = -6 into the function, as follows:

h(x) = -x - 3

h(-6) = -(-6) - 3

h(-6) = 6 - 3

h(-6) = 3

Answer:

use ASA

Step-by-step explanation:

since D=B, AB║CD

angle DEC=AEB (vertical angles)

AE=EC (given)

Given:

The distance between two stations in map, D= 9cm.

The distance between two stations in real life, d=3 km.

Now, to find the scale of the map take the ratio of D/d .

So, the scale of the map is 1 km=3 cm.

The absolute value inequality is given by | x-130745 | > 10000

and the possibility of Car B is  x < 120745  or  x > 140745

What is absolute value inequality?

Absolute value inequality are inequalities in algebra that involve algebraic expressions with absolute value symbols and inequality symbols. In simple words, we can say that an absolute value inequality is an inequality with an absolute value symbol in it. It can be solved using two methods of either the number line or the formulas.

x = price of car B

x-130745 = difference in price from car A to car B

If x is the larger price, then x-130745 will be positive. If x is the smaller price, then x-130745 is negative.

In short,

x-130745 > 0 when x > 130745

x-130745 < 0 when x < 130745

Using absolute value will give us

|x-130745| = positive difference in price

The result of an absolute value is never negative

We write the |x-130745| > 10000 to indicate that the difference in price is more than 10000 dollar

 | x-130645 | > 10000

Part b.

We'll use the idea that if |x| > k, then x < -k or x > k

to get the following

|x-130745| > 10000

x-130745 < -10000 or x-130745 > 10000

x < -10000+130745  or  x > 10000+130745

x < 120745  or  x > 140745

Car B has a price less than $120,745

OR

Car B has a price greater than $140,745

So basically anything that is not between 120745 and 140745. The price has to be positive of course.

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The correct answer is Tim

She drives at a variable speed for 2minutes

45 represents the slope while -900 is the y-intercept of the function

Here, we want to write the slope and y-intercept of the function that represents Patrick's elevation during his climbing

From the question, we are told that he averaged an elevation of 45 meters per hour

What the slope basically does is to measure a rate of change. As we can see from here, the change represents a rate and thus, we have this as our slope

To get the y-intercept of the function, we can see this as a distance of -900 meters

The reason for this is that we can see the summit of the mountain as 0 m

So we can represent the equation as;

1) Two points are the minimum number of points that need to be plotted to have instances of all four groups of numbers.

2) The sets that positive integers belong to among the available are;

possibilities

Choices A, B, C, and D

1) There are two basic categories into which numbers are often divided:

- Rational numbers

- Irrational numbers

The four examples above are all different categories of rational numbers.

Positive integers are now by definition also known as whole numbers and natural numbers. Whole numbers and natural numbers can therefore be displayed in one graphic.

Since integers may be both positive and negative, as well as include fractions, another plot will be needed to display them.

In order to plot the fewest number of points necessary to provide examples for each of the four sets of numbers

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[tex]y=14x[/tex], where x is the number of gallons used and y is the distance driven in miles.

Hence, the coordinates of other point (x, y) are (0,6).

i.e.  (x, y) → (0,6)

Let AB be the segment where

The coordinate M(2, 9) and C(4, 12)

and we have to find the point E.

Let us assume the other point is (x, y)

As we know that

The midpoint is halfway between the two end points, meaning midpoint coordinates are basically termed as the average of the corresponding endpoint coordinates.

Mid - point formula:

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

n = [tex]\frac{y_{1}+y_{2} }{2}[/tex]

So,

Substituting M(2, 9) into C(4, 12):

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

9 = [tex]\frac{12+y_{2} }{2}[/tex]

Solve the Equation:

[tex]x_{2} = 0\\y_{2} = 6[/tex]

Express solutions in ordered pairs:

(0,6)
Hence, the coordinates of other point (x, y) are (0,6).

i.e.  (x, y) → (0,6)

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The number of integers from 31 to 40 is 10

Integers are the set of positive whole numbers and negative whole numbers including zero. Examples are 5, 81, -56, 9, -2, 0, 17 etc.

From the question, we are to determine the number of integers there are from 31 to 40.

First, we will list all the whole numbers from 31 to 40.

The whole numbers from 31 to 40 are

31, 32, 33, 34, 35, 36, 37, 38, 39, and 40.

All of these numbers are positive whole numbers. Thus, they are integers.

The number of integers listed above is 10.

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mean = sum of the heights / number of grandchildren

Ratio means the quantitative relation between two amounts showing the number of times one value contains or contained in order

example 4 and 6

for example

if we have 4 men and 6 women

we can say the ratio of men to women is 4 to 6

that is 4 : 6

and ratio can also means division

for 4 and 6

= 4 / 6

= 2 / 3

= 2 : 3

that is, for every 2 men we have 3 women

Answer:

C

Step-by-step explanation:

- 2 = 5x + 3 ( subtract 3 from both sides )

- 5 = 5x ( divide both sides by 5 )

- 1 = x

The height is 9.875 feet from which the goalkeeper catches the ball.

The player kicks soccer from a height of 2 feet

x = 0 and y = 2

Maximum height of 20 feet after traveling 40 feet

x = 40, y = 20

So let y = a(x - 40)² + 20  ( the path of parabola)

Since x = 0 , y = 2

So, 2 = a(0 - 40)² + 20

2 = 1600a + 20

-18 = 1600a

a = - 9/800

Thus, y = -9/800(x - 40)² + 20

Since the soccer is caught by the goalkeeper 70 feet from where it was kicked

x = 70

So at this time,

y = -9/800 ( 70 - 40)² + 20

  = -9/800 × 900 + 20

  = - 81/8 + 20

  = 79/ 8

  = 9.875 feet

Therefore the height at which the goalkeeper catches the ball is 9.875 feet.

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P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.

An Independent Event is defined as if the outcome of one event has no bearing on the outcome of the other, the two events are said to be independent events. Or, we may say that an event is considered independent if it does not affect the probability of another event. Probability-independent events mirror actual occurrences.

Let B and C be two events such that P(B) = 0.25 and P(C) = 0.67.

To determine P (B U C),

Given that B and C are independent.

Since B and C are independent events, we can just multiply the probabilities together, 0.25 × 0.67 = 0.1675

To determine P (B U C),

Given that B and C are mutually exclusive.

Since B and C cannot both occur at the same moment by definition because they are mutually exclusive, the answer is 0.

Therefore, P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.

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The quadratic equation with roots -7, 3/4 in standard form is

4x² + 25x - 21 = 0.

A quadratic equation is an algebraic equation of degree two and has exactly two roots real or imaginary or complex.

We know the roots of a quadratic equation are also factors of a quadratic equation.

If x = a and x = b are two roots of a quadratic equation then x - a = 0 and

x - b = 0 are the factors of a quadratic equation that can be formed by multiplying the two factors (x - a)(x - b) = 0.

Given that -7 and 3/4 are the roots.

∴ { x - (-7)}{ x - 3/4) = 0.

(x + 7)(x - 3/4) = 0.

x² + 7x -(3/4)x - 21/4 = 0.

x² + (25/4)x - 21/4 = 0.

4x² + 25x - 21 = 0.

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Answer:

Bds $ 1.98

Step-by-step explanation:

1386 bds / $ 700   *  $ 1 = 1.98 Bds

The expression used to depict area will be 9 / (3x - 1).

A rectangle may be defined as a closed figure with four sides and four interior angles. The interior angles are 90°.

The given expression for area = 27x - 9

Factorize 27x - 9

Taking 9 as greatest common factor outside, we get

27x - 9 = 9(3x - 1)

We know that the area of rectangle with dimensions length by breadth is given by:-

Area = Length x Breadth

Hence, the possible dimensions of the rectangle will be 9 / (3x - 1).

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Complete Question:

What are possible dimensions of the rectangular area at the right? if area is 27x-9.

This will be his initial investment. The amount for 8% will be 84000, and the amount for 12% will be 204000.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the

value of the variable x is 7.

let x = the money invested at 8%

y = the money invested at 12%

an actor invests some money at 8% and 36,000 more than four times the amount at 12%

x = 36000 + 2y

total annual interest earned from the investment is 26400

0.08*x + 0.12*y = 26400

by solving the system of equations

x = 36000 + 2y

0.08*x + 0.12*y = 26400

solving the equations,

0.08(36000+2y)+0.12y=26400

2880+0.16y+0.12y=26400

y=84000

x=204000

The amount for 8% will be 84000, and the amount for 12% will be 204000.

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Answer:

Result of [tex] \tt{}(3 {x}^{2} + 2x - 5) - ( {5x}^{2} - 4x + 1)[/tex] is [tex]\tt{} - {2x}^{2} + 6x - 6.[/tex]

Step-by-step explanation:

[tex] \tt{}(3 {x}^{2} + 2x - 5) - ( {5x}^{2} - 4x + 1)[/tex]

[tex]\tt{} {3x}^{2} + 2x - 5 - {5x}^{2} + 4x - 1[/tex]

[tex]\tt{} - {2x}^{2} + 6x - 6[/tex]

Given: The figure shown

To Determine: The value of EF

Solution

Using intersecting chord theorem that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.

Applying the theorem to the given would give us

Therefore

2. Let us label the the image given

When a group of point is reflected across a line the distance of the points to the line must be equal, therefore the figure is inverted. With this in mind we can trace the intermediate step that is missing and finally draw the two lines.

Notice that the triangle get's inverted on each reflection around the lines.

Probability is expressed as

number of favorable outcomes/number of total outcomes

In a standard deck of cards, the total number of cards is 52.

There are 13 spades in a standard deck. Thus,

probability of selecting a spade = 13/52 = 1/4

There are 26 red cards in a standard deck of cards. Since the first card was replaced, the total number of cards remains 52.

probability of selecting a red card = 26/52 = 1/2

There are 4 queens in a standard deck of cards. Since the second card was also replaced, total number of cards is still 52. Thus,

Probability of selecting a queen = 4/52 = 1/13

Thus, the probability that the first card will be a spade, the second card will be a red card, and the third card will be a queen is

1/4 x 1/2 x 1/13

= 1/104

The solution to the equation g(x) = 6x - 9 whenx = -8b is g(-8b) = -48b - 9

From the question, the equation of the function is given as

g(x) = 6x - 9

Also, we have the value of the variable to be

x = -8b

So, we substitute -8b for x in the equation of the function

g(x) = 6x - 9

The above equation becomes

g(-8b) = 6(-8b) - 9

Open the brackets in the above expression

g(-8b) = -48b - 9

The above equation cannot be firther simplified

Hence, the solution is g(-8b) = -48b - 9

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Answer:

Find the following probabilities if you are dealt cards from a standard 52-card deck. Round your answers to three decimal places.

a. If a card is randomly selected, what is the probability that the card is a heart?

13/52 = 1/4

b. If a card is randomly selected, what is the probability that the card is either a club or a spade?

26/52 = 1/2

c. If a cards is randomly selected, what is the probability that the card is both a club and a spade?

0

d. If two cards are randomly selected, what is the probability of drawing a three first, then drawing a jack?

4/52·4/51 = 4/663 = 0.006033182503

e. If two cards are randomly selected, what is the probability of drawing a heart first, then drawing a diamond?

13/52·13/51 = 13/204 = 0.06372549019

f. If two cards are randomly selected, what is the probability of drawing a face card followed by drawing an ace?

12/52·4/51 = 4/221 = 0.01809954751

g. If two cards are randomly selected, what is the probability of drawing a diamond first, then drawing an eight?

12/52·4/51 + 1/52·3/51 = 1/52 = 0.01923076923

Given:

The equation is:

Find-:

Restrictions for this equation

Explanation:

The equation is:

The denominator is not equal to zero. If the denominator is zero, then the function is undefined.

Then the restriction is:

For the function value of x is:

The value of "x" is:

So above function value of x is possible only -6 and -1 then the restriction value is all real numbers except only -6 and -1