The probability that Larry wins the game is [tex]$\tfrac{1}{2}$[/tex].
The probability that Larry knocks the bottle off the ledge on his first throw is
[tex]$\tfrac{1}{2}$.[/tex]
The probability that Larry knocks the bottle off the ledge on his second throw, given that he did not knock it off on his first throw, is
[tex]$\tfrac{1}{2}$[/tex]
Therefore, the probability that Larry wins the game is
[tex]$\tfrac{1}{2} \times \tfrac{1}{2} = \tfrac{1}{2}$.[/tex]
By the law of total probability, we have:
[tex]$P(W) = P(W|F)P(F) + P(W|F^c)P(F^c)$[/tex]
[tex]$P(W) = 1 \times \tfrac{1}{2} + \tfrac{1}{2} \times \tfrac{1}{2}$[/tex]
[tex]$P(W) = \tfrac{1}{2}$[/tex]
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Select all pairs that are like terms.
1.) -4n and 18n
2.) 15ab and 2ab
3.) 17f and 17
4.) 3w and 3y
5.) 14h and -3h
6.) 5w and 5w²
All the pairs that are like terms are given as follows:
1.) -4n and 18n
2.) 15ab and 2ab
5.) 14h and -3h
What are like terms?Like terms are terms that share these two features:
Same letters. (algebraic variables).Same exponents.If two terms are like terms, then they can be either added or subtracted.
The like terms for this problem are given as follows:
1.) -4n and 18n -> algebraic variable of n, exponent of 1.
2.) 15ab and 2ab -> algebraic variable of ab, exponent of 1.
5.) 14h and -3h -> algebraic variable of h, exponent of 1.
For example, the pair in item 3 is of terms that are not like terms, as they have different algebraic variables, f and 1.
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Students are working on measurement principles. Kali measures a countertop in the classroom that is 5,743 mm long. Lauren finds that the distance on a map between New York City and Washington D.C. is drawn as 364.1 mm. How does the 3 in Kali's number compare to the 3 in Lauren's number
Based on the provided information regarding measurement, the way 3 in Kali's number compares to the 3 in Lauren's number is that Kali's digit is in the ones place and Lauren's digit is in the hundreds place.
Measurement refers to the process of comparing an unknown quantity with a standard of the same quantity. It quantifies the characteristics of an object or event, which we can compare with other things or events. It is the most commonly used term when dealing with the division of a quantity. When considering measurement, the value before decimals reads as ones, tens, hundreds etc. As Kali measures a countertop in the classroom that is 5,743 mm long or 5,743.0 mm the 3 just before the decimal is one place. As Lauren finds that the distance on a map between New York City and Washington D.C. is drawn as 364.1 mm, the 3 is hundreds place. Therefore, Kali's digit is 1/100 of the value.
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Please help:) 100 points
Which of the following is equivalent to the statement “(–3, 0) is an x-intercept"?
1. –3 is a root.
2. –3 is a zero.
3. x + 3 is a factor.
4. All of the above are equivalent statements.
Answer:
4. All of the above are equivalent statements.
Step-by-step explanation:
The x-intercept is the point at which a line crosses the x-axis.
The roots of a function are the x-values of the x-intercepts.
Therefore, if (-3, 0) is an x-intercept, then -3 is a root.
The zeros of the function are the x-values when y = 0.
(-3, 0) means x = -3 when y = 0.
Therefore, -3 is a zero.
According to the factor theorem, if f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
Given (-3, 0), then f(-3) = 0. Therefore, (x - (-3)) = (x + 3) is a factor.
Therefore, all given statements are equivalent statements.
A concert hall has 10 seats in the first row, 12 seats in the second row, 14 seats in the third row, and so on. If the pattern continues, how many seats are in the first 15 rows
There are a total of 360 seats in the first 15 rows.
Given that a concert hall had 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth.
We are to find the total number of seats in the concert hall.
Let us write the number of seats in the consecutive rows in a sequence as follows :
10, 12, 14, . . .
If a(n) denotes the number of seats in the n-th row, then we see that
a(2)-a(1)=12-10=2
a(3)-a(2)=14-12=2
. .
. .
So, there is a common difference of 2 in the consecutive terms of the given sequence. That is, the sequence is an arithmetic one.
The total number of seats will be equal to the sum of the first 15 terms of the sequence. We know that
the sum of the first n terms of an ARITHMETIC sequence with first term a and common difference d is given by
[tex]S_{n}=\frac{n}{2} (2a+((n-1)d)\\[/tex]
In our sequence, a = 10 and d = 2.
So, the sum of the first 15 terms will be
[tex]S_{15} =\frac{15}{2} (2*10+(15-1)*2)\\\\S_{15} =\frac{15}{2} (20+28)\\\\S_{15} =\frac{15}{2} (48)\\[/tex]
S15=360
Thus, there is a total of 360 seats in the auditorium.
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What is the result when the number 63 is increased by 1.3%
Answer:
63.819
Step-by-step explanation:
1.3% = 1.3/100 = 0.013
Then;
63 + 63*0.013 = 63 + 0.819
= 63.819
50 apples cost 25. How much would 75 apples cost?
75 apples would cost $37.50.
Explanation:
To find the cost of 75 apples, we can set up a proportion using the given information. Let's call the cost of 75 apples 'x'.
We know that 50 apples cost 25. This can be written as:
50 apples / 25 = 75 apples / x
To solve for 'x', we can cross-multiply:
50x = 75 * 25
Now, we can solve for 'x' by dividing both sides of the equation by 50:
x = (75 * 25) / 50
Calculating this, we find that:
x = 37.5
Therefore, 75 apples would cost $37.50.
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Here is Cho's logo.
They want to create stamps of their logo.
If the stamp is
3
5 inches wide, what does the height need to be?
Pls help ( need this by 9!!)
There is another part to this question look in the comments before solving
The height of the stamp should be proportional to the width, so if the width is 3 inches, the height should also be 3 inches.
What is proportional?Proportional refers to the relationship between two or more numbers, measurements, or quantities that are mathematically equivalent. In other words, when two or more values are proportional, a change in one value results in an equivalent change in the other. For example, if one quantity is twice as large as another, the two are said to be in a 2:1 proportion. Proportional relationships can also be expressed in equations, such as y=mx+b, where m is a constant factor of proportionality, and b is the y-intercept. Proportional relationships are a key component of algebra and geometry.
This will ensure that the logo looks the same size and shape when printed on the stamp.
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Two arithmetic sequences $A$ and $B$ both begin with 30 and have common differences of absolute value 10, with sequence $A$ increasing and sequence $B$ decreasing. What is the absolute value of the difference between the 51st term of sequence $A$ and the 51st term of sequence $B$
The difference between the 51st term of A and the 51st term of B is 1000.
the nth term of an arithmetic series is given by [tex]a_{n} = a_{0} (n-1)*d[/tex]
where [tex]a_{0}[/tex] is the first term of the arithmetic series, [tex]a_{n}[/tex] is the nth term of the series and d is the common difference
Given that, [tex]a_{0}=b_{0}=30[/tex]
Given that both series have common differences and have an absolute value of 10.
common difference of series a is 10 as this series is increasing
similarly common difference of series b is -10 as it is decreasing
putting the values in the above equation we get:
[tex]a_{n} = a_{0} (n-1)*d[/tex]
=> 30 + (51-1)*10
=> 30 + 500
=> 530
so. 51st term of A is 530.
Then, the 51st term of B = 30 + (51-1)*-10 => 30 -500 = -470
Hence the difference between the 51st term of A and B = 530-(-470)= 1000
Therefore, The difference between the 51st term of A and the 51st term of B is 1000.
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PLEASE HELP HURRY IM IN A BIG RUSH RN HELPPP
The expression that can be used to calculate the rate per second in which the machine launches the balls is given as follows:
A. 32/4.
What is a proportional relationship?A proportional relationship is a linear function with an intercept of zero modeled as follows:
y = kx.
In which k is the constant of proportionality.
As the graph of the function has a constant slope and an intercept of zero, it represents a proportional relationship.
The rate per second is equivalent to the constant of proportionality of the function.
From the graph, when x = 4, y = 32, meaning that the rate can be calculated as follows:
4k = 32
k = 32/4
k = 8.
Meaning that option A is correct.
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a straight line passes through the point P(-1,5). Another line which passes through Q(-4,4) intersects the first line at point R( µ,5) where µ is a constant . If <PRQ = 90° find the value of R
Answer:
[tex]\mu=-4[/tex]
Step-by-step explanation:
We know that [tex]\overline{PR} \perp \overline{QR}[/tex].
Since [tex]\overline{PR}[/tex] is horizontal, [tex]\overline{QR}[/tex] is vertical. Therefore, [tex]\mu=-4[/tex].
Lindsey went skydiving. When she jumped out of the plane, its elevation was 13,000 feet. She was in free-fall for 10,000 feet, and then she deployed her parachute. At what elevation did Lindsey deploy her parachute?
Answer:
3,000ft
Step-by-step explanation:
First set up the equation:
Start: 13,000 ft
Middle: 10,000 ft
End: ??
Lindsey started at 13,000ft, dropped 10,000ft, and then the remainder of it is what we are asked to find out. So all we have to do is 13,000 - 10,000 which equals 3,000.
Solve this system of equations by graphing. Graph the equations, then find the solution.
A. y = x + 1
B. y = -¾ x - 6
The solution to the system is: (-4, -3).
How to Solve a System of equations by Graphing?To solve a system of equations by graphing, you will need to:
Graph each equation on the same coordinate plane by plotting points that satisfy the equation and connecting them with a line.Look for the point of intersection between the two lines, which represents the solution of the system of equations.If the lines do not intersect, the system has no solution. If the lines are coincident, the system has infinitely many solutions.Once you find the point of intersection, you can substitute the x and y values back into the original equations to check that the solution is correct.Given the system of equations:
A. y = x + 1
B. y = -¾x - 6
Equation A is the red line on the image below while B is represented as the blue line. Both intersect each other at (-4, -3).
Therefore, the solution is; (-4, -3).
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Qualitative researchers focus intensive data collection on a small sample of participants in order to establish a wealth of data. What is a typical sample size for a qualitative study
Need to ensure there is enough, but not too much, data One review identified that samples of 20 and 30 were the most common with 25-30 being a typical recommendation.
Sampling means selecting the group that you will actually collect data from in your research.
Characteristics of Qualitative research and sample size:
no explicit, formal criteria, and sample size determined by informational needs.decisions to stop sampling guided by data saturation which to stop sampling if the reachdata quality can affect sample size, if have people that aren't good, need a larger sample size, ongoing analysis guiding design decisionsno predominant hypothesis, no theory trying to follow, doing more exploration and looking for the things that have to start understanding.To know more about Qualitative researchers and sample size:
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If b=9 inches and c=10 inches, what is the perimeter? If necessary, round to the nearest tenth.
Please help!!!
Answer:
19 + [tex]\sqrt{19}[/tex]
Step-by-step explanation:
So we have a right triangle right?
We use the Pythag. Theorem:
a^2 + 9^2 = 10^2
a^2 + 81 = 100
a^2 = 19
a = [tex]\sqrt{19}[/tex]
a + b + c = perimeter
[tex]\sqrt{9} + 9 + 10[/tex] = 19 + [tex]\sqrt{19}[/tex]
Roberta cites the following statement as evidence for a claim. "the chicken genome has about 17,000 genes, and the grape has about 30,000 genes. " which claim about human genes would be most strongly supported by this statement?.
The assertion that there aren't many extra genes in humans compared to other organisms would be the one this statement would most strongly support.
Genes are stretches of DNA that aid in the precise determination of each trait. The primary biological factor transmitted from parent to child. Genes are composed of DNA sequences and are organised sequentially at specified sites on chromosomes in the cell nucleus.
The human genome project estimates that we contain between 20,000 and 25,000 genes. Daphnia, a microscopic eating flea, contains 31,000 genes, the most of any animal.
Therefore, the claim that there are not particularly many genes in humans compared to other organisms would be most strongly supported by this statement.
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The claim that humans have more number of genes than chickens and grapes
The statement provided by Roberta states that the chicken genome has about 17,000 genes, and the grape has about 30,000 genes. This statement indicates that grapes have more genes than chickens. Therefore, it can be inferred that humans have more genes than chickens and grapes, as humans typically have more complex genomes than other species.
Roberta cites the following statement as evidence for a claim. "the chicken genome has about 17,000 genes, and the grape has about 30,000 genes. " From this statement, it can be inferred that humans have more genes than chickens and grapes. This is because humans typically have more complex genomes than other species, and the statement provided suggests that grapes have more genes than chickens. Therefore, the claim that humans have more number of genes than chickens and grapes would be most strongly supported by this statement.
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What are all the real zeros of the
function
y = −3(x + 1)³ + 9?
Answer:
∛3 - 1 which is 0.44 to the nearest hundredth.
Step-by-step explanation:
−3(x + 1)³ + 9 = 0
(x + 1)³ = -9/-3
(x + 1)³ = 3
x + 1 = ∛3
x = ∛3 - 1
= 0.44225
The cube root of 3 is positive, no negative real roots are possible.
Apply the skills you've learned in the tutorial in
a short project or investigation.
The tutorial feature such as begin thinking about the lesson’s main topic is important part.
What are the multi-step project in tutorial features?The multi-step project is one that can be utilized in leading different kinds of examination and they help in an examination as a lab project.
The student on the creatures and assists us with really taking a look at about the information by giving us similar warm-up questions and furthermore comprise of sorts of the illustration movement.
In this way the response to a short multi-project is a warm-up question.
Therefore, the undertaking incorporates different kinds of exercises and these should be visible in the inquiry, glossary joins, ace tests, and information checks.
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Correct question:
Drag each tutorial feature to its learning purpose.
Tiles
Warm-Up question
Glossary link
Knowledge check
Lesson Activity
Mastery test
Pairs
Begin thinking about the lesson’s
main topic.
arrowBoth
Make sure you’ve met the lesson’s
overall learning objective.
arrowBoth
View the definition of an important
lesson word.
arrowBoth
Do a short, multistep project or
investigation.
arrowBoth
See if you’re getting the main idea
or developing an important skill in
the lesson.
arrowBoth
A standard baseball diamond is a square 90 feet on each side. Find the distance of a throw made from the catcher 3 feet behind home plate in an attempt to throw out a runner trying to steal second base. Round to the nearest whole number.
Answer:
130 fr
Step-by-step explanation:
Distance (d) from home plate to second base:
d² = 90² + 90² = 16200
d = [tex]\sqrt{16200}[/tex] = 127.28 ≅ 127
Now add the 3 ft behind home plate:
127 + 3 = 130 ft
(√a + √8a)² = 54+b√2
a and b are positive integers. Find the value of a and the value of b.
The value of a is 6 and value of b is 24 for (√a + √8a)² = 54+b√2
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is (√a + √8 a)² = 54+b√2
Using algebraic identity (a+b) ²= a² + b ²+ 2ab
(√a )²+ ( √8 a )²+ 2×√a×√8a = 54 + b√2
a + 8 a + 2 ×√8 × √a x√a = 54 + b√2
a + 8a + 2×2√2 ×a = 54 + b √2
9a + 4a√2. = 54 + b√2
comparing above equations
9a = 54
a = 54/9
a = 6
4a = b
substituting a = 6
4×6 = b
b = 24
Hence, the value of a is 6 and value of b is 24.
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What is the largest share when $360 is divided in the ratio 2:7:9? Select one: O a. $180 O b. $140 O c. $120 O d. $200
The largest share is equivalent to 180.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that $360 is divided in the ratio 2 : 7 : 9.
We can write the equation as -
2x + 7x + 9x = 360
18x = 360
x = 20
For the largest share, the largest share is equivalent to 9x. The largest share will be -
9 x 20 = 180
Therefore, the largest share is equivalent to 180.
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Calculate the area of triangle abc with altitude bd, given a (−6, 0), b (0, 0), c (0, 6), and d (−3, 3). 18 square units 9 square units 18.5 square units 21 square units
Answer: 18 unit²
If BD is altitude, then AC is the base.
AC = BD =
The area is: A = 1/2bh
A = 1/2 * = 18 unit²
Step-by-step explanation:
What is an equation of the line that passes through the points (1, 3) and (7, -3)?
Answer:
y = -x + 4
Step-by-step explanation:
y = mx + b
You need the slope (m) and the y-intercept (b)
Slope
Change in y over the change in x
(1,3) (7,-3)
The y values are -3 and 3. You find the change by subtraction
-3 - 3 = -6
(1,3)(7, -3)
The x values are 7 and 1. You find the change by subtraction
7 - 1 = 6
You make a fraction by the change in y in the numerator and the change in x in the denominator.
[tex]\frac{-6}{6}[/tex] = -1
The slope is -1
y-intercept
Use the slope you just found -1 and one of the points given. I am going to use (1,3), but either point will work.
y = 3 From the point given (1,3)
x = 1 From the point given (1,3)
m = -1
Substitute these all in and solve for b
y = mx + b
3 = (-1)(1)+ b
3 = -1 + b Add 1 to both sides
3 + 1 = -1 + 1 + b
4 = b
The y-intercept is 4.
y =mx + b
y = -x + 4
Does someone mind helping me with this problem? Thank you!
Answer: ( 1, -2)
Step-by-step explanation: first number the equation as 1 and 2.
After that multiply 4 in equation 2 , then add both the equation
you will get x=1, y=-2,
answer = (1,-2)
Supervisor: "your salary is $25,000 and you will be receiving a 2.5% pay increase this year. what will your new salary be?"
In case of a 2.5% increase in your pay which is now $25,000, your new salary will be $25,625.
First, you need to determine the percent increase i.e.2.5% of 25,000 (old salary),
2.5% x 25,000 = ?
2.5/100 x 25,000 = 625
So, the $625 would be the increased amount in your salary which is equal to 2.5% of your old salary (i.e. 25,000).
In order to find out the amount of your new salary that you will be receiving, you have to add the increased amount to the amount of your old salary, as follows:
amount of the new salary = amount of the old salary + percent increase
= $25,000 + $625
= $ 25,625
When an increase of 2.5% is made in your salary which is now $25,000, then your new salary becomes $25,625.
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find a function f such that f '(x) = 5x3 and the line 5x + y = 0 is tangent to the graph of f.
The function f(x) is [tex]\frac{5x^{4} }{4}+\frac{15}{4}[/tex].
Given f'(x) = 5[tex]x^{3}[/tex]
We will first integrate to get f(x) = ∫5[tex]x^{3}[/tex]dx = [tex]\frac{5x^{4} }{4}[/tex] + C.
As given tangent line is y = - 5x,
Then f'(x) = 5[tex]x^{3}[/tex] = - 5,
[tex]x^{3}[/tex] = -1
x = -1
-1 is the x-coordinate of the tangent point.
Now y-coordinate of tangent point is f(-1) = [tex]\frac{5(-1)^{4} }{4}[/tex] + C
= 5/4 + C.
Now, equation of tangent line is y - 5/4 - C = - 5(x + 1),
y = - 5x - 15/4 + C.
So -15/4 + C = 0,
C = 15/4
Hence, f(x) = [tex]\frac{5x^{4} }{4}+\frac{15}{4}[/tex]
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What is the answer 184667230 x 273983
Answer:
Step-by-step explanation:
Bro just use a calculator... 5.0595682e+13
mr. muckle bought a new tv. the screen on his old TV measured 15 by 20 in, but the screen on his new TV measures 18 by 32 in. what is the persent of increase in the area of Mr.Muckle'a screen
Answer:
the answer is an increase by 28% sorry if i am incorrect
Fred, Jayne and Harry all inherit some money when their uncle passed away. In total they receive £186, 700. This is to be shared between them in the ratio 3: 2: 1. How much money does Jayne inherit?
Answer:
£64233.333333
Step-by-step explanation:
The ratio is 3:2:1
Let their inheritance be 3x, 2x ,x
Then, 3x + 2x + x = £186700
6x = £186700
x = £32116.6666
So, Jayne inherits 2x money or 2 x 32116.6666 = £64233.333333
Pls mark as brainliest if possible. Don't know why i need it, but i do. Cheers
i need help on 7, 9, 10
How do you solve 4n 9 =- 9?
The value of the unknown value n after simplifying the given equation
4n - 9 = -9 is Zero.
Simplifying the algebraic equation given, 4n - 9 = -9
Reorder the terms:
-9 + 4n = -9
Add '9' to each side of the equation i.e on both the sides :
-9 + 9 + 4n = -9 + 9
Combine like terms: -9 + 9 = 0 ( on left side )
0 + 4n = -9 + 9
4n = -9 + 9
Combine like terms: -9 + 9 = 0 (on right side )
4n = 0
Solving
4n = 0
Solving for variable 'n'.
Move all terms containing n to the left, all other terms to the right.
Divide each side by '4'.
Simplifying
n = 0
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