The probability of an event of P(A∪B) is 49/128.
In this question,
Patricia will flip the coin 8 times.
The sample space is the flipping of a coin 8 times.
⇒ n(s) = 2⁸
⇒ n(s) = 256
Let A be the event that exactly 4 of the 8 flips are heads
⇒ n(A) = [tex]8C_4[/tex] [∵ [tex]nC_r=\frac{n!}{r!(n-r!)}[/tex]]
⇒ [tex]\frac{8!}{4!4!}[/tex] = 70
Then, P(a) = [tex]\frac{n(a)}{n(s)}[/tex]
⇒ [tex]\frac{70}{256}[/tex]
Let B be the event that the last two flips are tails
⇒ n(B) = [tex]8C_2[/tex]
⇒ [tex]\frac{8!}{2!6!}[/tex] = 28
Then, P(a) = [tex]\frac{n(b)}{n(s)}[/tex]
⇒ [tex]\frac{28}{256}[/tex]
Now, P(A∪B) = P(A) + P(B)
⇒ P(A∪B) = [tex]\frac{70}{256} + \frac{28}{256}[/tex]
⇒ P(A∪B) = [tex]\frac{70+28}{256}[/tex]
⇒ P(A∪B) = [tex]\frac{98}{256}[/tex]
⇒ P(A∪B) = [tex]\frac{49}{128}[/tex]
Hence we can conclude that the probability of an event of P(A∪B) is 49/128.
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Find the area of the composite figure.
8 cm
10 cm
14 cm
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:
two f1 plants were crossed with each other and the f2 generation consisted of 860 tall plants with purple flowers; 285 dwarf, purple plants; 340 tall, pink plants; and 115 dwarf, pink plants (1600 total). a chi-square goodness-of-fit test is used to see if these data represent chance deviations from a 9:3:3:1 ratio. what will be the calculated chi-square value and what will be the degrees of freedom used to interpret the chi-square?
According to the given statement the chi-square value in the test of this hypothesis is 10.111.
The correct option is C.
What is chi-square value?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.
According to the given data: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
Which figure is missing in the pattern?
?
Answer:
B
Step-by-step explanation:
it grows b
Which expression can be used to show a set of twenty books divided into four groups?
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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- 3x + 6y =- 18 solve for y
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
given two points on a line and a third point not on the line, is it possible to draw a plane that includes the line and the third point?
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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create an equation from the model that describes the relationship between the weights on each side of the scale
The algebraic equation that describes the relationship of the weights on both sides of the scale is: 2y + 3 = 4y + 2.
How to Create an Algebraic Equation?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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Which line is perpendicular to y=−3x+2?
A. y = −3x+1/2
B. y =−1/3x+1
C. y = 3x−1/2
D. y =1 /3x−1
(Note: the selected answer is not guaranteed to be correct in the image)
Answer:
I kinda want to say it's C
Pls pls help whoever gets it right gets a crown
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
7 rationals and irrationals prove that the product of a non-zero rational number and an irrational number is irrational.
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.
What do you mean by 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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Use the figure to the right to find the value of PT.
PT= 4x+4 and TQ 6x-6
4 cards are drawn at random from a standard deck. find the probability that all the cards are hearts. find the probability that all the cards are face cards. note: face cards are kings, queens, and jacks. find the probability that all the cards are even. (consider aces to be 1, jacks to be 11, queens to be 12, and kings to be 13)
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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point k is on a line segment JL. given JK =2x-2, KL =x-9, and JL = 2x+8, determine the numerical length of KL
The numerical length of KL = 10.
What exactly is an equation?An equation, in its most basic form, is a mathematical statement demonstrating that two mathematical expressions are equal.3x + 5 = 14, for example, is an equation in which the expressions 3x + 5 and 14 are separated by a 'equal' sign.So,
JK + KL = JL2x – 2 + x – 9 = 2x + 8Combine similar terms:
3x -11 = 2x+8Take 2x off each side:
3x-2x -11 = 2x+8-2xx-11 = 8Add 11 for each side:
x-11+11 = 8+11x = 19KL = x – 9KL = 19-9KL = 10Therefore, the numerical length of KL = 10.
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If f (x) = 2 x + 5 and three-halves are inverse functions of each other and StartFraction 41 Over 8 EndFraction,
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.
In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹ .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
HELP !!
Elena and Diego each wrote equations to represent these diagrams. For each diagram decide which equation you agree with, and solve it. You can assume that angles that look like right angles are indeed right angles.
Elena: X=35
Diego: X+35=180
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.
An expression involves subtracting two numbers from a given number. Under what circumstances will the value of the expression be negative? Give an example
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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The table shows the numbers y (in thousands) of people in a city who regularly use sharable electric scootersx weeks after the scooters are introduced.
im still learning that
Step-by-step explanation:
If point A (-5, 9) is reflected across the x-axis, what will be the new coordinates of the image, A'?
please help! I am in the middle of a test! I am offering 30 points.
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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9+8n≤1 please help me with this
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.
Which square root could be the number shown on the number line?
O A. √15
O B. √17
O C. √26
O D. √24
The number shown on the number line could be related to the inexact irrational number √17.
What irrational number is associated with a point on a number line?
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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5 Bruno buys 9.625 gallons of gasoline at a gas station.
Each gallon costs $3.40. Bruno also buys a bag of ice
for $3.99. How much in total does Bruno spend at the
gas station to the nearest cent?
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.
Tyrell has a box of colored pencils. He uses 65 pencils and has 114 pencils left in the box. Write an equation showing how many pencils are in the box before he starts drawing.
p − 65 = 114
p = 114 − 65
65 + p = 114
114 + p = 65
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.
how to solve -6x+3y=9 by y?
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
[tex]x=-\frac{3-y}{2}[/tex]Match the polynomial expression on the left with the simplified version on the right.
(y + 5)²
(y - 5)(y + 5)
A
2-10
²-25
²+25
²-10y-25
²+10y + 25
Pls answer quick
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 pair of triangles that are congruent by the ASA criterion is . The pair of triangles that are congruent by the SAS criterion is .
The relationship between the triangles are;
Δ ABC and Δ XYZ is related by ASA
Δ BAC and ΔRQP are related by SAS
What is congruency of triangles?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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What is this supposed to mean!?!?!?!?
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.
The Rock Club members have collected 182 gems. How many did each
member collect if
a) Alice collected 1 more than 3 times what Cecil did.
b) Jaime collected 12 less than 3 times what Alice did.
c) Amir collected 10 less than Cecil.
d) Monte collected 5 more than Cecil.
How many gems didCecil collect?
How many gems did Alice collect?
How many gems did Jaime collect?
How many gems did amir collect
How many gems did Monte collect
Using a system of equations, the amounts of gems collected by each member is are given as follows:
Cecil: 13Alice: 40Jaime: 108Amir: 3Monte: 18.What is a system of equations?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:
Variable x: Number of gems collected by Cecil.Variable y: Number of gems collected by Alice.Variable z: Number of gems collected by Jaime.Variable t: Number of gems collected by Amir.Variable w: Number of gems collected by Monte.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:
y = 3(13) + 1 = 40.z = 9x - 9 = 9(13) - 9 = 108.t = x - 10 = 13 - 10 = 3.w = x + 5 = 13 + 5 = 18.Thus the amounts of gems collected by each member is are given as follows:
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solve the equation 4x -6 = 22
Answer: x=7
Step-by-step explanation: hope this helps!!!
Answer:
x=7
Step-by-step explanation:
pls help :) brainliest
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
Describe the similarities and differences between finding the slope of a linear equation from a graph that has x and y scales that are 1:1, and from a graph that has x and y scales that are not 1:1 (say your x and y scales are 2, 4, 6).
Using the concept of the slope of a linear function, we have that:
For a graph in a 1:1 scale, we can look at two consecutive values, y when x = a and y* when x = a + 1, and subtract y* by y. For a graph in another scale, we also do the same thing, but since the scale is not 1:1, we have to divide the subtraction of y* by y by the scale.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Given two points in the graph of a function, the slope is given by change in y divided by change in x, hence:
For a graph in a 1:1 scale, we can look at two consecutive values, y when x = a and y* when x = a + 1, and subtract y* by y. For a graph in another scale, we also do the same thing, but since the scale is not 1:1, we have to divide the subtraction of y* by y by the scale.More can be learned about linear function concepts at https://brainly.com/question/24808124
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