patricia will flip the coin 8 times. let a be the event that exactly 4 of the 8 flips are heads, and b be the event that the last two flips are tails. find p(a ∪ b).

Answer:

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

Step-by-step explanation:

- 3x + 6y = - 18 ( isolate the term in y by adding 3x to both sides )

6y = 3x - 18 ( divide through by 6 )

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

The relationship between the triangles are;

Δ ABC and Δ XYZ is related by ASA

Δ BAC and ΔRQP are related by SAS

The term congruency has to do with the fact that the triangles are similar. That is why another way that we could express congruent triangles is to call them similar triangles. These are the triangles that look alike in some ways. The triangles may be similar in the following ways;

1) Angle Angle Side

2) Side Side Side

3) Side Angle Side

4) Angle Side Angle

5) Angle Side Side

Having seen the various ways in which triangle could be similar we are asked to obtain the triangles that are similar by Angle Side Angle and  Side Angle Side.

A good look at the triangles as shown in the image attached to this answer would show us which of the triangles are similar on the basis of Angle Side Angle and  Side Angle Side.

We can see that;

Δ ABC and Δ XYZ is related by ASA

Δ BAC and ΔRQP are related by SAS

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Using the concept of the slope of a linear function, we have that:

A linear function is modeled by:

y = mx + b

In which:

Given two points in the graph of a function, the slope is given by change in y divided by change in x, hence:

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im still learning that

Step-by-step explanation:

The number shown on the number line could be related to the inexact irrational number √17.

In this problem we find the location of a point on a number line, which is related to an inexact irrational number, that is, an irrational number that is not equivalent to any rational number. The point is between two exact irrational numbers, that is, √16 = 4 and √25 = 5.

There are two options: (i) √17, (ii) √24. √24 is close to 5, but √17 is close to 4. Thus, the number shown on the number line could be related to the inexact irrational number √17.

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Answer: 12.8x^2

Step-by-step explanation:

3.2x * 4x=

3.2 * x * 4 * x=

3.2 * 4 * x * x=

12.8 * x^2=12.8x^2

According to the given statement the chi-square value in the test of this hypothesis is  10.111.

The correct option is C.

The chi-square statistic contrasts the actual values with what was anticipated. The discrepancy between the values observed and expected is tested using this test statistic to see if it is statistically significant.

Tall and purple flower observed valve = 860

Dwarf and purple flower observed valve  = 285

Tall and pink flower observed valve = 340

Dwarf and pink flower observed valve = 115

Total no. of flower = 860 + 285 + 340 + 115

                              = 1600

The ratio given is 9: 3: 3: 1

Expected no. for Tall and purple = 100(9/16) = 900

Expected no. for Dwarf and purple = 1600(3/16) = 300

Expected no. for Tall and pink   = 1600(3/16) = 300

Expected no. for Dwarf and pink = 1600(1/16) = 100

chi-square value  = ∑ (objered value - expected value)² /Expected value

                        = [tex]\begin{aligned}\frac{(860-900)^2}{900}+\frac{(285-300)^2}{300}+\frac{(340-300)^2}{300} +\frac{(115-100)^2}{100}\end{aligned}[/tex]

                         = 1.778 + 0.75 + 5.333 + 2.25

                         = 10.111

The value is 10.111

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I understand that the question you are looking for is:

A dihybrid plant was crossed; the F2 generation consisted of: 860 tall plants with purple flowers; 285 dwarf, purple plants; 340 tall, pink plants; and 115 dwarf, pink plants. The data remind you of a 9:3:3:1 ratio. What is the chi-square value in the test of this hypothesis?

a. 0.377;

b. 7.5;

c. 10.11;

d. 11.08;

e. 15.78

The algebraic equation that describes the relationship of the weights on both sides of the scale is: 2y + 3 = 4y + 2.

Using the weights on each side of the scale, we can create an algebraic equation that describes it.

Assume each weigh on the scale represents each side of an algebraic equation.

On left side, we can express the weights as: 2y + 3

On the right side, we can express the weight as: 4y + 2

Thus, expressing the relationship of the weights, we would have:

2y + 3 = 4y + 2

Thus, the algebraic equation that describes the relationship of the weights on both sides of the scale is: 2y + 3 = 4y + 2.

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Answer: x=7

Step-by-step explanation: hope this helps!!!

Answer:

x=7

Step-by-step explanation:

Answer:

p-65=114

Step-by-step explanation:

In this equation, "p" is the amount of pencils in the box before he starts drawing. he removes 65 pencils from the box, leaving 114 in the box. What he needs with 65 pencils at once, I can't fathom.

Answer:

I kinda want to say it's C

Answer:

Down below Explanation :) answer is [tex]x=-\frac{3-y}{2}[/tex]

Step-by-step explanation:

-6x+3y=9

Steps:

Subtract 3y From both sides.

-6x+3y-3y=9-3y

Simplify:

-6x=9-3y

Lastly; divide both sides by -6

[tex]\frac{-6x}{-6}=\frac{9}{-6}-\frac{3y}{-6}[/tex]

And your answer is

Answer:

151 shirts

Step-by-step explanation:

2578 divided by 17 is 151.647...

Answer:151

Step-by-step explanation:2578 divided by 17 equals 151.6470588. you cant have a partial shirt so you have to round down or you will go over your money

The new coordinates of the image A' will be  (-5, -9).

Here, we are given a point on the cartesian plane- A (-5, 9)

It is reflected along the x axis to form a new point A'

Originally, we can see that the point A will be in the 2nd quadrant as x is negative and y is positive.

Now, when it is reflected across the x axis, the point will shift from the 2nd quadrant to the 3rd quadrant.

In the third quadrant, both x and y values are negative. Thus the coordinates of the reflected point A' will become (-5, -9).

Note that the absolute values of the point will not change when it is reflected. It is only the signs that change.

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the expression can be negative under various circumstances.

An expression means to subtraction two numbers from a given number.

Let the numbers be a, b and c

Do, the expression will become:

a - b - c.

The expression can be negative if:

1. the value of b + c > a

For example: a = 4, b = 5 and c = 6

so, the expression will be

4 - 5 - 6 = - 7

2. The value can be negative if a - b < c

For example:

a = 2, b = 1 and c = 6

The expression will be:

2 - 1 - 6 = - 5

3. The value can be negative if a - c < b

For example:

a = 1, b = 6 and c = 2

The expression will be:

1 - 6 - 2 = - 7

Therefore, we get that the expression can be negative under various circumstances.

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Answer: Diego is correct, and X = 145

Step-by-step explanation:

The line that 35* and x* rest on must equal 180*. Elena cannot be right if we assume this, as 35 + 35 = 70. We must then move onto Diego's formula.

[tex]X + 35 = 180[/tex]

[tex]180 - 35 = X[/tex]

[tex]X = 145[/tex]

Solving this, we would subtract 35 from 180, leaving us with 145*. This must be correct as the solution would give us the total we need.

The expression that can be used to show a set of twenty book divided into 4 groups [tex]\frac{20}{5}[/tex]

Given,

The total number of books= 20

Number of books in each group= 4

We have to use division

Then, the expression used to represent a set of 20 books divided into four group =[tex]\frac{20}{5}[/tex]

So the result will be 4

Hence, the expression that can be used to show a set of twenty book divided into 4 groups is [tex]\frac{20}{5}[/tex]

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Yes, it is possible to draw a plane that contains a line and a point not in the line.

A plane is a flat two-dimensional surface that extends to infinity. Planes are points (0-dimensional), lines (1-dimensional), and the 2-dimensional analogue of 3-dimensional space. The plane has zero thickness, zero curvature, infinite width, and infinite length. It's actually difficult to imagine an airplane in real life. All the flat surfaces of a cube or cuboid, the flat surface of paper are all practical examples of geometric planes.

In any dimensional Euclidean space, a plane is uniquely defined by either: Use three non-collinear points. Use points and lines that are not on this line. Use two different lines that intersect.

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Answer:

B

Step-by-step explanation:

it grows b

The probability that all the 4 cards are

1) hearts = 0.0026

2) face cards = 0.0018

3) even cards = 0.0179

In a standard deck of cards, we have:

Total number of cards= 52

1) The probability that all the cards are hearts.

In a standard deck of cards, we have:

the number of Hearts = 13

When a card is selected, the number of cards reduces by 1.

So, the probability that all the 4 cards are hearts is:

P1 = 13/52 × 12/51 × 11/50 × 10/49

P1 = 0.25 × 0.2353 × 0.22 × 0.2041

P1 = 0.0026

2) The probability that all the cards are face cards.

In a standard deck of cards, we have:

Face card = 12

When a card is selected, the number of cards reduces by 1.

So, the probability that all the 4 cards are face cards.

P2 = 12/52 × 11/51 × 10/50 × 9/49

P2 = 0.2308 × 0.2157 × 0.2 × 0.1837

P2 = 0.0018

3) The probability that all the cards are even.

In a standard deck of cards, we have:

Even cards = 20

When a card is selected, the number of cards reduces by 1.

So, the probability that all the 4 cards are even.is:

P3 = 20/52 × 19/51 × 18/50 × 17/49

P3 = 0.3846 × 0.3725 × 0.36 × 0.3469

P3 = 0.0179

Hence, the probability that all the 4 cards are even is 0.0179

Therefore, the probability that all the 4 cards are

1) hearts = 0.0026

2) face cards = 0.0018

3) even cards = 0.0179

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Using a system of equations, the amounts of gems collected by each member is are given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

They collected a total of 182 gems, hence:

x + y + z + t + w = 182.

Alice collected 1 more than 3 times what Cecil did, hence:

y = 3x + 1.

Jaime collected 12 less than 3 times what Alice did, hence:

z = 3y - 12 = 3(3x + 1) - 12 = 9x - 9.

Amir collected 10 less than Cecil, hence:

t = x - 10.

Monte collected 5 more than Cecil, hence:

w = x + 5.

Replacing everything in the first equation, we can solve for x as follows:

x + y + z + t + w = 182.

x + 3x + 1 + 9x - 9 + x - 10 + x + 5 = 182.

15x = 195

x = 195/15

x = 13.

Hence the other variables are:

Thus the amounts of gems collected by each member is are given as follows:

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The simplified version of first expression is  y² + 10y + 25 and  simplified version of second expression is  y²  – 25

The first polynomial expression on the left is (y + 5)²

= y² + 2×y×5 + 5² (using the formula (a + b)² = a² + 2ab + b²)

= y² + 10y + 25

The second polynomial expression on the left is (y + 5)(y – 5)

= y(y – 5) + 5(y – 5)

= y² – 5y + 5y – 25

= y²  – 25

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The complete question is given below :

The polynomial expression on the left is (y + 5)², and the simplified version on the right for this polynomial is y² + 10y + 25.

The polynomial expression on the left is (y – 5)(y + 5), and the simplified version on the right for this polynomial is y² – 25.

The value of the inverse function f⁻¹(8) is  [tex]\frac{3}{2}[/tex] .

An inverse function in mathematics is a function that "undoes" another function.

To calculate the inverse of the function  f (x) = 2 x + 5 we simply  write the function in the form y = 2x + 5 .

Now we solve the equation for x.

∴ y = 2x + 5

or, 2x = y-5

or, x = (y-5)/2

Hence the inverse of the function is given as:

f⁻¹ (x) = (x - 5 ) / 2

Now we have to find the value of f⁻¹ (8).

f⁻¹ (8) = (8-5) / 2

or, f⁻¹ (8) = 3 / 2

Hence the value of f⁻¹ (8) is 3 / 2 .

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Disclaimer: the complete question is:

If f (x) = 2 x + 5 and three-halves are inverse functions of each other and f(x)=2x+5, what is f-1(8)?

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Answer: B

Step-by-step explanation: On Edge 2022

Answer:

n ≤ -1

Step-by-step explanation:

Inequality is a concept that refers to the unequal distribution of resources, opportunities, or status among individuals or groups. It can be measured in a number of ways, including income inequality, wealth inequality, and educational inequality.

For the Question:

Let's solve for 'n':

Given inequality:

[tex]\sf 9 + 8n \leq 1[/tex]

Subtract 9 from both sides:

[tex]\sf 9 + 8n -9 \leq 1 -9[/tex]

[tex]\sf 8n \leq -8[/tex]

Divide both sides by 8 (remember, since you're dividing by a negative number, the inequality sign flips):

[tex]\sf \dfrac{8n}{8} \leq \dfrac{-8}{8}[/tex]

n ≤ -1

So, the solution for 'n' that satisfies the inequality is n ≤ -1.

Let x be a rational number and y be an irrational number. This is the correct choice.

Allow xy=a.

Suppose an is a rational being.

A can be stated as q p since it is rational, where p and q are both integers.

Let x = n m, where n and m are both integers.

Then, xy=a

n \smy \s​ \s = \sq \sp \s​ \s .

When we cross multiply, we obtain,

⇒y= qm \spn \s​ \s .

Pn and qm are currently integers.

Consequently, qm pn is a rational number.

Y, however, is illogical.

Consequently, our assumption is unfounded.

Therefore, an irrational number is always the result of adding a non-zero rational number to an irrational number.

a number that cannot be written as the quotient of two integers and cannot be expressed as an infinite decimal with a series of consecutive digits repeating itself forever.

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Answer:

h = V/B

Step-by-step explanation:

[tex]\sf V \div B = h\\Reverse\\h = V \div B[/tex]

Answer:

D. h = V/B

Step-by-step explanation:

"Solve...for h" means get h all by itself on one side of the equation.

V = Bh

Divide both sides by B.

V/B = h

Turn it around and you can see the answer in the choices. D. h = V/B is the correct answer.

Answer:

96 cm

Step-by-step explanation:

14-10= 4.

So the base of the triangle is 4.

10*8=80

4*8*1/2=16

80+16 = 96

Answer:

32

Step-by-step explanation:

Answer:

Step-by-step explanation:

9.625 rounded is 10.

10 x $3.40 = $34

$3.99 rounded to the nearest cent is $4.

$34 + 4 = $38, so Bruno spends about $38 total.

The numerical length of KL = 10.

So,

Combine similar terms:

Take 2x off each side:

Add 11 for each side:

Therefore, the numerical length of KL = 10.

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