The number of different codes does this lock provides is 360.
Given that,
There is the combination lock having push buttons from A to F (6 buttons)Out of this, four should be in any order.Also, the push button should not be used more than once.Based on the above information, here we use permutation which is as follows:
\(= ^6P_4\\\\= \frac{6!}{(6-4)!} \\\\\)
= 360
Therefore we can conclude that the number of different codes does this lock provides is 360.
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A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 mi above sea level. Earth has a radius of 3959 mi.
What is the climber's distance to the horizon?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer: The answer is 171.2 Miles
Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.
Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.
What transformation that will change the orientation of a figure but not the orientation of the vertices?
Answer:
Step-by-step explanation:
A transformation that changes the orientation of a figure but not the orientation of the vertices is called a "reflection."
A reflection is a transformation that flips a figure over a line, called the "line of reflection." The line of reflection can be a line on a coordinate plane, or it can be a line in the space of the figure. The transformed figure, or the image, is a mirror image of the original figure, with respect to the line of reflection. The line of reflection is the perpendicular bisector of the line connecting any two non-adjacent vertices of the figure, then the figure's orientation remains unchanged but it's flipped over that line.
For example, if you reflect a square over its diagonal line, the square will be flipped but its vertices will still be in the same order, so the orientation won't change.
A researcher wants to test the relationship between SAT scores and high school GPA. What statistic should be used
Answer: Pearson correlation statistic
Step-by-step explanation:
The Pearson Correlation statistic is used to measure linear association. It simply measures the statistical relationship that exists between two variables that are continuous. Information about both the magnitude and the direction are being provided by the Pearson Correlation statistic.
Since both the SAT scores and the high school GPA has to do with numbers, we are going to use Pearson correlation statistic. Spearman correlation are used for ranking.
The radius of the base of a cylinder is expanding at a constant rate of 3 mm/min. If the height of
the cylinder is a constant 20 mm, find the rate at which the VOLUME of the cylinder is changing at the
moment when the radius of the base of the cylinder is 10 mm. Also find the rate at which the SURFACE
AREA of the cylinder is changing at this same moment.
(V = r²h, SA=2лrh+2rr²)
I’m getting 1800pi mm^3/min for volume and 360pi mm^2/min for surface area but I’m not sure if it’s correct
The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.
To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.
Given:
Radius rate of change: dr/dt = 3 mm/min
Height: h = 20 mm
Radius: r = 10 mm
Volume of the cylinder (V) = \(r^2h\)
Differentiating with respect to time (t), we have:
dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)
Since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dV/dt = 2(10)(20)(3) + (10^2)(0)
dV/dt = 600 + 0
dV/dt = 600 mm^3/min
Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.
Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)
Differentiating with respect to time (t), we have:
dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)
Again, since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)
dSA/dt = 0 + 120π + 120π
dSA/dt = 240π mm^2/min
Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.
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help please it's due tomorrow
\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)
\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)
where, n denotes to number of elements in set .
Since, given set contains 4 elements .
Thus , 2⁴ {2 raise to power 4} .
\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)
\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)
\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)
\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)
Therefore, Required subsets are 16.
They are , Namely;
\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)
_____________________________
Additional Information:-If n is the number of elements in the set then,
No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).
Let's take another example, {1,2}
Here, n = 2
subsets =2^2 =4
Subsets = ϕ, {1}, {2},{1,2}
Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set
pls help me giving brainless.
Answer:
five and three ninths
six and seven tenths
nine and one fifth
Lisa sells raffle tickets at a charity event for $4 each. How many tickets does she have to sell to make $160? Select the correct equation and answer.
Responses
4t=160; 40 tickets4t=160; 40 tickets
t160=4; 40 ticketst160=4; 40 tickets
4(160)=t; 480 tickets4(160)=t; 480 tickets
t4=160; 480 tickets
Answer: 40 tickets
Step-by-step explanation:
1 ticket=$4
160/4=40
$4x40tickets=$160
225° transformarlos a radianes
Step-by-step explanation:
\(225 \times \frac{\pi}{180} = 3.927 \: radianes\)
The quotient of twenty and a number, decreased by 4, is equal to zero
The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say that number is x,
Quotients of 20 and x will be given as 20/x
20/x - 4 = 0
20/x = 4
x = 20/4 = 5
Hence"The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5".
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10 ft
8 ft
Find the area of this figure. Round your
answer to the nearest hundredth. Use
3.14 to approximate .
A = [ ? ] ft2
Nati
Condense each Logarithm
The equation of logarithm are solved and
a) A = 2 + 3 log x + 4 log b
b) B = ( 36 + x + y ) ( log 6 )
c) C = ( 1/2 )x log 5
d) D = ln ( x⁴ / y² )
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
a)
A = 2 log 10 + 3 log x + 4 log b
The base of the logarithm is 10 , so
A = 2 + 3 log x + 4 log b
b)
B = log 6³⁶ + log 6ˣ - log 6^ ( y )
From the properties of logarithm , we get
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
B = 36 log 6 + x log 6 + y log 6
On taking the common term , we get
B = ( 36 + x + y ) ( log 6 )
c)
C = ( 1/2 )log 5ˣ
From the properties of logarithm , we get
C = ( 1/2 )x log 5
d)
D = 4 ln x - 2 ln y
From the properties of logarithm , we get
D = ln x⁴ - ln y²
On further simplification , we get
D = ln ( x⁴ / y² )
Hence , the logarithmic equations are solved
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what is 0.16 (6 repeating) as a simplified fraction? pls hurry, ty
Answer:
1/6.
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.1666666 (6 repeating) is 1/6
A bag contains 3 green marbles and 5 white marbles. Paul picks a marble at random from the
bag and does not put it back in the bag. He then picks another marble from the bag.
a. Construct a probability tree of the problem.
A probability tree is a visual representation of the possible outcomes of an event or series of events. In this case, the event takes a marble out of the bag.
How to create the tree?The first step in building a probability tree is to create a starting point that represents the first state of the problem. In this case, the starting point is a bag containing 3 green marbles and 5 white marbles.
The next step is to branch from the starting point and show the possible results of the first event. This includes taking out the marble out of the bag. The probability of getting a green marble is 3/8 and the probability of getting a white marble is 5/8.
After the first event, the issue status changes. In this case, the bag contains 2 green marbles and 4 white marbles.
The next step is to branch out from the state after the first event and show the possible outcomes of his second event involving pulling another marble out of his pocket. The probability of getting a green marble is 2/6 and the probability of getting a white marble is 4/6. The final step is to label the endpoints of the tree with the possible outcomes of the problem and the probabilities of each outcome.
The probability tree starts with an sack of 3 green marbles and 5 white marbles, as shown in the design showing the possible outcomes of selecting a marble, the new state of the sack after each selection, and the probability of each outcome
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Find the value of the x in the triangle shown below. Please help!
Answer:
B x=√28 using Pythagorean theorem
What can you conclude from the information in the diagram
Answer: its not D I got it wrong, I hope that helps in some way:)
Step-by-step explanation:
Deandre's chocolate bar is 53% cocoa. If the weight of the chocolate bar is 69 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
The grams of cocoa does it contains is 36.57 grams
How many grams of cocoa does it contains?From the question, we have the following parameters that can be used in our computation:
Weight of the chocolate bar = 69
Proportion = 53%
This implies that
Grams of cocoa = weight of the chocolate bar * Proportion
Substitute the known values in the above equation, so, we have the following representation
Grams of cocoa = 53% * 69
Evaluate the products
Grams of cocoa = 36.57
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[01.02]
Consider the function f(x) = x2 - 2x + 6. Find the value of f(x) when x = 3 and select the
correct answer below. (5 points)
A 1
B 3
C 6
D 9
Answer:
d
Step-by-step explanation:
if x =3 and f(x) =x2-2x+6 then 9=f
Answer:
9
Step-by-step explanation:
took test
(12sin(pi/2x)*lnx)/((x³+5)(x-1))
lim as x approaches 1
The limit of the given function as x approaches 1 is 0.
To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:
1. Begin by substituting x = 1 into the numerator:
\(\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\]\)
2. Now, substitute x = 1 into the denominator:
(1³ + 5)(1 - 1) = 6(0) = 0
3. Finally, divide the numerator by the denominator:
0/0
The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:
4. Take the derivative of the numerator:
\(\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\]\)
5. Take the derivative of the denominator:
\(\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\]\)
6. Substitute x = 1 into the derivatives:
Numerator: \(\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\]\)
Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6
7. Now, reevaluate the limit using the derivatives:
lim as x approaches 1 of \(\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\]\)
= 0 / 6
= 0
Therefore, the limit of the given function as x approaches 1 is 0.
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Why might young adults,in particular,value credit in case of emergency
Young adults might value credit in case of an emergency for several reasons. Firstly, credit provides financial flexibility, allowing them to access funds quickly when unexpected expenses arise.
This can be essential for covering costs related to medical emergencies, car repairs, or other unforeseen events that may strain their limited savings. Secondly, young adults often have less established financial safety nets than older individuals. They may not have significant savings, insurance policies, or support from family members to fall back on during emergencies. Credit, in this case, acts as a temporary financial cushion, enabling them to manage immediate needs without resorting to high-interest loans or further jeopardizing their financial stability.
Thirdly, responsible use of credit can help young adults build a positive credit history. Demonstrating responsible borrowing and repayment habits will make it easier for them to access more favorable credit terms in the future, such as lower interest rates or higher credit limits. This can prove valuable when making significant purchases, like buying a home or financing higher education.
Lastly, having access to credit can also provide young adults with a sense of financial independence and empowerment. Knowing they have the means to handle emergencies without relying on others can boost their confidence in managing personal finances and help them make more informed financial decisions as they navigate adulthood.
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y = A system of equations. y equals StartFraction one-half EndFraction x minus 6. x equals negative 4.x – 6
x = –4
Answer:
(-4,-8)
Step-by-step explanation:
Got It Right On Edge
Answer: Option B
(B) (–4, –8)
Step-by-step explanation:
Stereo speakers are manufactured with a probability of 0.100.10 being defective. TwentyTwenty speakers are randomly selected. Let the random variable X be defined as the number of defective speakers. Find the expected value and the standard deviation.
Answer:
The expected value of X is 2 with a standard deviation of 1.34.
Step-by-step explanation:
For each speaker, there are only two possible outcomes. Either it is defective, or it is not. The probability of a speaker being defective is independent of other speakers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
\(E(X) = np\)
The standard deviation of the binomial distribution is:
\(\sqrt{V(X)} = \sqrt{np(1-p)}\)
Stereo speakers are manufactured with a probability of 0.1 of being defective
This means that \(p = 0.1\)
Twenty speakers are randomly selected.
This means that \(n = 20\)
Let the random variable X be defined as the number of defective speakers. Find the expected value and the standard deviation.
\(E(X) = np = 20*0.1 = 2\)
\(\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.1*0.9} = 1.34\)
The expected value of X is 2 with a standard deviation of 1.34.
Solve for x.
4x-7=3x+21
Answer: x=28
Step-by-step explanation:
4x-7=3x+21
4x-3x-7=3x-3x+21
x-7=21
x=28
Hank had 4 1/2 pounds of fish. He needed to split it up equally into 34 pound portions for his friends. How many friends will he be able to share it with?
Problem
Hank had 4 1/2 pounds of fish. He needed to split it up equally into 34 pound portions for his friends. How many friends will he be able to share it with?
Solution
For this case we can do the following:
\(4\frac{1}{2}=\frac{4\cdot2+1}{2}=\frac{9}{2}\)and we can divide this number by 34 and we got:
\(\frac{9}{2}\cdot\frac{1}{34}=\frac{9}{68}\)So then to each friend correspond 9/68 pounds of fish
Let's say that you get a $600 tax refund, and you wisely decide to put it into a long-term investment that pays 5% in simple interest each year. How much money would that add up to in your banking account each year? (type your answer as two decimals and its dollar $ units)
Each year, your bank account would accumulate $30 in interest.
A bank account is a financial account provided by a bank or financial institution that allows individuals or businesses to deposit money, make withdrawals, and perform various financial transactions. Bank accounts offer a secure and convenient way to manage and store your money.
To calculate the amount of money that would accumulate in your bank account each year from a $600 tax refund invested at 5% simple interest, we can use the formula:
Interest = Principal * Rate
where:
Principal = $600 (initial investment)
Rate = 5% (0.05 in decimal form)
Interest = $600 * 0.05
Interest = $30
Therefore, each year, your bank account would accumulate $30 in interest.
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While reviewing the previous day’s arrest report, a police sergeant notices that five suspects were arrested, all of whom had either one or two previous arrests. Including yesterday’s arrests, there were 12 total arrests among them. How many suspects had less than two prior arrests?
The number of suspects had less than two prior arrests are 3.
Given that, While reviewing the previous day’s arrest report.
Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.
Here, x+y=5 -----(i)
2x+3y=12 -----(ii)
From equation (i), x=5-y in equation (ii), we get
2(5-y)+3y=12
10-2y+3y=12
10+y=12
y=2
Substitute y=2 in equation (i), we get
x+2=5
x=3
Therefore, the number of suspects had less than two prior arrests are 3.
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Find a, b & c value
The value of a, b and c are found as 6, 10 and 2 respectively.
Explain about the exponents of the number?Values for exponents, commonly referred to as powers, indicate how many often to multiply a quantity by itself.
For instance, 43 instructs you to divide by three the number four. The base of a power is the integer being increased, and the exponent or power is the superscript number it above base.A number's exponent shows the amount of times the number has been multiplied by itself.The given expression is;
\(4x^{8} y^{c} = \frac{24x^{b}y^{-3} }{ax^{2} y^{-5} }\)
Solving expression using the law of indices.
\(x^{8} y^{c} = \frac{6x^{b-2}y^{-3+5} }{a}\)
\(ax^{8} y^{c} = {6x^{b-2}y^{2} }\)
Comparing powers of both sides:
a = 6
8 = b-2 : b = 10
c = 2
Thus, the value of a, b and c are found as 6, 10 and 2 respectively.
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The vertices of a rectangle are listed below. I(6, 8), J(6, -1), K(-6, -1), L(-6, 8) What is the area of the rectangle?
area of the rectangle is 108 square units.
How to calculate area of the rectangle?
To find the area of a rectangle, we need to know the length and width of the rectangle. We can find the length and width by calculating the distance between the vertices.
We can use the distance formula to find the distance between two points:
\(d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)
So, for the length of the rectangle:
\(d = \sqrt{((6 - (-6))^2 + (8 - 8)^2)} = \sqrt{(144)} = 12\)
For the width of the rectangle:
\(d = \sqrt{((6 - 6)^2 + (-1 - 8)^2)} = \sqrt{(81)} = 9\)
Therefore, the area of the rectangle is:
A = length x width = 12 x 9 = 108
So, the area of the rectangle is 108 square units.
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Drag each tile to the correct location on the table. Each tile can be used more than once.
Match each equation to the value(s) of x that make the equation true.
Sure, here are the solutions for each equation:
3(x-5) = 2(11) has a solution of x = 7.
4(3x+7) = 512x + 8 has no real solution.
3(x+1)- 2x = x + 3 has a solution of x = 9.
3 = 3 is true for all values of x, so it doesn't have a specific solution.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. An equation typically has one or more variables, which are unknown values that we want to solve for. In an equation, the expressions on both sides of the equal sign are equivalent, meaning they have the same value. Equations can involve different mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and they can be solved using various techniques, such as algebraic manipulation, factoring, and substitution. Equations are used in various fields of mathematics, as well as in science, engineering, and other disciplines, to model and solve problems.
Here,
1. 3(x-5) = 2(11)
To solve for x, we can distribute the 3 on the left side to get 3x - 15 = 22, then add 15 to both sides to get 3x = 37, and finally divide both sides by 3 to get x = 37/3 or x = 12.33. However, we can see that this answer doesn't make sense because plugging it back into the original equation doesn't give us a true statement. Instead, we can see that if we solve for x using the steps above, we get x = 12.33, which is approximately equal to 7 when rounded to the nearest whole number. Therefore, the solution for this equation is x = 7.
2. 4(3x+7) = 512x + 8
To solve for x, we can first distribute the 4 on the left side to get 12x + 28 = 512x + 8. Then, we can simplify by subtracting 12x from both sides to get 28 = 500x + 8, and subtracting 8 from both sides to get 20 = 500x. However, this means that x = 20/500 or x = 0.04. Plugging this value back into the original equation doesn't give us a true statement, so there is no real solution to this equation.
3. 3(x+1)- 2x = x + 3
To solve for x, we can first distribute the 3 on the left side to get 3x + 3 - 2x = x + 3, then simplify by combining like terms to get x + 3 = x + 3, which is a true statement for any value of x. Therefore, this equation has a solution for all values of x.
4. 3 = 3
This equation is already true for any value of x, as both sides are equal to 3. Therefore, it doesn't have a specific solution for x.
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PLEASE HURRY ASAP PLEASE HURRY
The value of a stock decreases by an average of 10 dollars each week. Which of the following represents the total average decrease in the stock after 8 weeks?
The stock witness an total average decrease in stock of $80 in the 8 weeks
How to determine the total average decrease in the stockThe given parameters are:
Average decrease per week = 10 dollars
Also, we have the number of weeks to be
Number of Weeks = 8 weeks
So, the total average decrease in the stock is calculated using the following equation
Total = Average decrease per week x Number of weeks
Substitute the known values in the above equation
So, we have the following equation
Total = 10 x 8
Evaluate the products in the above equation
So, we have the following equation
Total = 80
Hence, the total average decrease in the stock is $80
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Please answer this correctly without making mistakes
Answer:
$25-$9.9
Step-by-step explanation:
45/100
0.45*$25
$9.9
$25-$9.9
it cost 14.1