The probability that the hacker guesses the password in first go is
[tex]\dfrac{1}{5^5}[/tex]
While statistics examines the frequency of previous events, probability deals with estimating the possibility of future events.
The primary goal of the theoretical branch of mathematics known as the probability is the investigation of the consequences of mathematical concepts. At its core, statistics is a field of mathematics that seeks to explain observations in the actual world.
Both topics are significant, pertinent, and helpful. However, they are distinct, and appreciating this difference is essential to correctly assessing the applicability of mathematical evidence.
Since sample space has 5⁵ possibilities.
The event space has only one possibility which is to successfully hack the password perfectly.
Hence, the probability is
[tex]\dfrac{1}{5^5}[/tex]
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Jimmy’s original account balance when he opened up his savings account was $3,450.00. In the last two years, he has made no other deposits and it has a current balance of $3,485.95. How much interest did he earn?
The interest that Jimmy's account has earned is $35.95.
What is the interest that Jimmy's account has earned?Interest is the total increase in excess of the amount deposited in the account. Interest earned can be determined by subtracting the amount deposited from the current balance.
Interest = current balance - amount deposited
$3,485.95 - $3,450.00 = $35.95
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Carnot heat engine receives heat at 900 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at 215 °C at a rate of 250 kJ/min and rejects it to the same environment at 300 K. Determine (a) the rate of heat supplied to the heat engine and (b) the total rate of heat rejection to the environment.
A heat engine is a device that turns heat into mechanical energy that may subsequently be utilized to do mechanical labour. The total rate of heat rejection to the environment is 298.4458 kJ/min.
What is a Heat Engine?A heat engine is a device that turns heat into mechanical energy that may subsequently be utilized to do mechanical labour. It accomplishes this by transferring a functioning ingredient from a higher to a lower state temperature.
For the following condition, the diagram can be made as shown below. Also, the Heat Engine Sink temperature, [tex]T_H[/tex] = 900 K
Heat Engine surrounding temperature, [tex]T_L[/tex] = 300 K
Refrigerator surrounding temperature, [tex]T'_C[/tex] = 215 C + 273 = 488 K
Refrigerator sink temperature, [tex]T'_H[/tex] = 300 K
The heat removed by the refrigerator, [tex]Q'_{in}[/tex] = 250 kJ/min
A.) For a Carnot refrigerator, the COP or the coefficient of performance is given by,
[tex]COP = \dfrac{T'_C}{T'_H-T'C}[/tex]
COP = (488)/(488-300)
COP = 2.596
The COP is also the ratio of the Heat input and the work output.
[tex]COP = \dfrac{Q'_{in}}{W}[/tex]
2.596 = 250/W
W = 96.302 kJ/min
The Carnot engine efficiency is expressed as,
[tex]\eta = 1- \dfrac{T_C}{T_H}[/tex]
η = 1 - (300/900)
η = 0.6667
Also, the Carnot engine efficiency is defined as,
[tex]\eta = \dfrac{W}{Q_{in}}\\\\[/tex]
[tex]0.6667 = \dfrac{96.302}{Q_{in}}\\\\Q_{in} = \rm 144.4458\ kJ/min[/tex]
Hence, the rate of heat supplied to the heat engine is 144.4458 kJ/min.
B.) The total work done by the engine is 96.302 kJ/min, while the heat input is 144.4458 kJ/min. Therefore, the heat output of the system is,
[tex]W = Q_{in} - Q_{out}\\\\Q_{out} = 48.1438\rm\ kJ/min[/tex]
Thus, the total rate of heat rejection to the environment,
[tex]\text{Total Heat rejection} = Q_{out}+Q'_{in}\\[/tex]
= 48.4458 kJ/min + 250 kJ/min
= 298.4458 kJ/min
Hence, the total rate of heat rejection to the environment is 298.4458 kJ/min.
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The area of one triangle is 270 square centimeters when its height is 30 centimeters and its base length is 18 centimeters. What
is the area of a triangle having a height of 25 centimeters and a base length of 16 centimeters?
Answer:
[tex]200 cm^2[/tex]
Step-by-step explanation:
A = (1/2)bh
A = (1/2)(18)(30)
A = 270 square cm
A = (1/2)(16)(25)
A = 200 square cm
Answer:
200 square centimeters
Step-by-step explanation:
The area of a triangle can be calculated using the formula: [tex]A = \frac{1}{2}bh[/tex] where b is the base and h is the height. So if the base is 16 cm and the height if 25 cm you simply plug the values into the equation to find the area
Plug Values In:
[tex]A = \frac{1}{2}(16 cm)(25 cm)[/tex]
Multiply 16 cm and 25 cm:
[tex]A = \frac{1}{2}(400 cm^2)[/tex]
Multiply by 0.5 (or technically divide by 2)
[tex]A = 200 cm^2[/tex]
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
Since the role of young Cosette is played by a child, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette, and alternate girls from night to night. (This is because of restrictions on working hours for children.) You have received headshots and resumes from 25 girls who wish to audition for young Cosette.
Does order matter when casting the 3 young Cosettes? (In other words, are young Cosette 1, young Cosette 2, and young Cosette 3 different parts?)
No, all three girls will play the same part.
Yes, even though they will all be playing the same part, it will be on different nights.
No, all three girls will get paid the same amount.
Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.
The inference based on the information about ordering is that D. Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.
What is an inference?It should be noted that a inference simply means the conclusion that can be deduced based on the information given.
In the role of young Cosette for the drama, 3 girls should be casted.
If three are being casted then there is need for different parts because for same role there may be different stages of character.
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simplify the expression 1-cos^2(t) / cos^2(t)
Answer: [tex]\tan^2 t[/tex]
Step-by-step explanation:
[tex]\sin^{2} t+\cos^2 t=1 \implies 1-\cos^2 t=\sin^2 t\\\\\implies \frac{1-\cos^{2}t}{\cos ^2 t}=\frac{\sin ^2 t}{\cos^2 t}=\tan^2 t[/tex]
How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters
(a) is allowed?
Your answer is :
Correct
(b) is not allowed?
Your answer is :
The number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
How to determine the waysFormula for permutation with repetition
[tex]^nPr = n^r[/tex]
Formula for permutation without repetition
[tex]^nPr = \frac{n!}{n-r!}[/tex]
We have = 5
r = 3
a. If repetition is allowed,
Permutation = [tex]5^3[/tex] = 125 ways
b. If repetition is not allowed,
Permutation = [tex]\frac{5!}{5-3!}[/tex]
Permutation = [tex]\frac{5*4*3*2*1}{2*1}[/tex]
Permutation = [tex]\frac{120}{2}[/tex]
Permutation = 60 ways
Thus, the number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
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MATH QUESTION HELP. Hhhhnh
Answer:
y
Step-by-step explanation:
that easy just isolate the variables
(b) Write the next whole number after A59C thirteen in the base-thirteen system.
In base 13, we use the digits 0-9 along with A for 10, B for 11, and C for 12.
Then the number that comes after A59C₁₃ is
A59C₁₃ + 1₁₃ = A59(C + 1)₁₃
… = A59(10)₁₃
… = A5(9 + 1)0₁₃
… = A5A0₁₃
where I use parentheses to indicate we're adding C and 1 in the same digits place, then carry the 1 into the next digits place.
What is the solution
Answer:
4
Step-by-step explanation:
5x + 2 = 2x + 14
5x-2x=14-2
3x=12
x=12/3
x=4
Answer:
The exact form: x = 4
A bird can fly 5 miles in 15 minutes how many miles can it fly in 60 minutes?
Please show the process
The number of miles the bird can fly for 60 minutes is 20 miles.
How to find rate and distance?A bird can fly 5 miles in 15 minutes.
Let's find the rate before we can find the number of miles the bird can fly in 60 minutes.
Therefore,
rate = distance / time
rate = 5 / 15 = 1 / 3 miles per minutes
Therefore,
1 / 3 = d / 60
cross multiply
60 = 3d
d = 60 / 3
d = 20 miles
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28 students; 14 students what is the percentage of it?
Answer:
The percentage of 28 students who are 14 students is 50%.
Step-by-step explanation:
Please help!! Find the solution for t in the equation:
Answer:
t = 1.322
Step-by-step explanation:
4×(2^t) = 10
2^t = 10/4 = 2.5
t = log2(2.5)
now, the logarithm to the base 2 of 2.5 must be larger than 1, as 2.5 is larger than 2.
so, it can be only the 4th answer option.
now, to actually calculate it :
log2(2.5) = log10(2.5) / log10(2) = 1.321928095... ≈
≈ 1.322
we were correct.
Answer:
t = 1.322
Step-by-step explanation:
Given equation:
[tex]4(2^t)=10[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4(2^t)}{4}=\dfrac{10}{4}[/tex]
[tex]\implies 2^t=2.5[/tex]
Method 1Take natural logs of both sides:
[tex]\implies \ln 2^t = \ln 2.5[/tex]
[tex]\textsf{Apply the natural log power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies t \ln 2 = \ln 2.5[/tex]
Divide both sides by ln 2:
[tex]\implies \dfrac{t \ln 2}{\ln 2} = \dfrac{\ln 2.5}{\ln 2}[/tex]
[tex]\implies t= \dfrac{\ln 2.5}{\ln 2}[/tex]
[tex]\implies t=1.321928095...[/tex]
Method 2[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]
[tex]\implies \log 2 (2.5)=t[/tex]
[tex]\implies t=1.321928095...[/tex]
SolutionTherefore, the solution that is nearest to the exact solution is t = 1.322
Median weekly earnings for women with some college for an associate degree. 1980.......$231 2013.............$657 Using today's dollars, the data in the bar graph can be described by the mathematical model W = 13n + 231, Where W represents median weekly earnings n years after 1980. Does the formula underestimate or overestimate the median weekly earnings in 2013? By how much?
Using the linear function given in this problem, the formula underestimates the median weekly earnings in 2013 by $3, as 657 < 660.
What is the linear function?The function that estimates the median weekly earnings n years after 1980 is:
W = 13n + 231.
2013 is 2013-1980 = 33 years after 2000, hence the estimate is given by W when n = 33, that is:
W = 13 x 33 + 231 = 660.
657 < 660, hence the formula underestimates the median weekly earnings in 2013 by $3.
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What happens to the surface area and volume if the lengths of the dimensions of the
prism are multiplied by a scale factor of 3?
Answer:
area is multiplied by 9volume is multiplied by 27Step-by-step explanation:
Area of a scaled figure is multiplied by the square of the scale factor; volume is multiplied by the cube of the scale factor.
AreaWhen dimensions are multiplied by 3, the area is multiplied by 3² = 9.
Area of the larger figure is 9 times that of the smaller one.
VolumeWhen dimensions are multiplied by 3, the volume is multiplied by 3³ = 27.
Volume of the larger figure is 27 times that of the smaller one.
__
Additional comment
In general, the area of a figure is the sum of the products of two orthogonal dimensions. If each of those is multiplied by 3, then the product is multiplied by 3 twice, or 3² = 9.
Similarly, the volume of a figure is the sum of products of three orthogonal dimensions. When those are each multiplied by 3, the product is multiplied by 3 three times, or 3³ = 27.
Complete the equation of this circle:
(x − [?])²+(y - [ ])²=[ ]
Answer:
(x+2)²+(y-4)²=36
Step-by-step explanation:
1) to determine the coordinates of the centre of the given circle. It is point A (-2;4);
2) to determine the length of the radius: to calculate the distance between the point A(-2;4) and any point on the circle, it is 6 [units];
3) to make up the required equation according to the scheme:
(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the coordinates of the centre, r - the length of the radius.
4) finally, (x+2)²+(y-4)²=6².
PS. for more details see the attachment.
Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.
Enter the correct answer in the box by replacing the values of m and b.
Answer:
[tex]y = -2x + 5[/tex]
m = -1
b = 5
Step-by-step explanation:
Hello!
Slope - Intercept Form: [tex]y = mx+b[/tex]
m = slopeb = y-interceptSlopeThe slope of the line is the rate of change, or how the graph changes in y as it changes in x.
Slope can be calculated by the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
We need two points on the line to get the x and y-values. I'm going to choose points (0,5) and (4,-3).
Calculate Slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]m = \frac{5 - (-3)}{0 - 4}[/tex][tex]m = -\frac{8}{4}[/tex][tex]m = -2[/tex]The slope is -2.
Y-interceptThe y-intercept of the line is where the graph touches the y-axis (x = 0). It can be found by looking at the intersection of the graph and the axis.
The intersection happens at point (0,5), so the y-intercept is 5.
EquationWe found m, the slope, to be -2 and b, the y-intercept, to be 5. We can just plug it into the equation format.
Equation: [tex]y = -2x + 5[/tex]
A person invested $7700 for 1 year, part at 8%, part at 9%, and the remainder at 12%. The total annual income from these investments was $811. The amount of money invested at 12% was $1100 more than the amounts invested at 8% and 9% combined. Find the amount invested at each rate.
The amount invested at 8% was $1400, $1900 was invested at 9% and $4400 was invested at 12% making a total annual income of $811.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of money invested at 8%, y represent the amount of money invested at 9% and z represent the amount of money invested at 12%
x + y + z = 7700 (1)
Total interest is:
(x * 1 * 0.08) + (y * 1 * 0.09) + (z * 1 * 0.12) = total interest
0.08x + 0.09y + 0.12z = 811 (
Also:
z = 1100 + x + y (3)
From equation 1, 2 and 3:
x = 1400, y = 1900 and z = 4400
T
The amount invested at 8% was $1400, $1900 was invested at 9% and $4400 was invested at 12% making a total annual income of $811.
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If we run the following program:
a = 2 + 6
b = 7 % 3
c = a - b
c = c * 5
print(c)
what gets printed?
If you run the program and print(c), your result will be: c = 35
Meaning of ProgramA program can be defined in terms of arithmetical functions as a set of instructions that are used to arrive at a solution.
A program guides the computer system on what the user wants.
Analysis
a = 2 + 6 = 8
b = 7 % 3 = 1
c = a - b = 7
c = c * 5 = 35
In conclusion, If you run the program and print(c), your result will be: c = 35
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Nine times the sum of a number and 3 is 6 .
Answer: -2 1/3
Step-by-step explanation:
First, change the word into equation
9*x+3=6
Do division first, so 6/9, simplify into 2/3 then subtract it by 3 which is -2 1/3
MATH: GRAPHING PIECE-WISE...HELP! 15 PTS
Answer:
Step-by-step explanation:
If it takes me 20 minutes to get to work while traveling at an average speed of 60 mph, but it took me 17 minutes to get to work today, what was my average speed today?
Answer:
if you are asking a real question the answer should be on your driving history on life 360 or maybe the average gps. How fast were you driving? I have no idea thats a answer only you know.
Step-by-step explanation:
Answer:
r = 70.59 miles / hour
Step-by-step explanation:
Comment
The first set of numbers gives you the distance you travelled.
Givens
t = 20 minutes = 20/60 = 1/3 of an hour
r = 60 miles / hour
d = ?
d = r * t
d = 60 * 1/3
d = 20 miles (The hours cancel)
So now you can find out what 17 minutes means
d = 20 miles
t = 17 minutes = 17/60 hours = 0.2833 hours.
r = d / t
r = 20 / 0.2833
r = 70.59 miles / hour
Determine whether the triangle is a scalene, isosceles of equilateral
Answer:
Equilateral triangle: All three sides are equal.
Isosceles triangle: All two sides are equal.
Scalene triangle: No sides are equal.
Step-by-step explanation: Step 1: Label the given points as A, B, and C, and plot them as vertices of a triangle with connecting lines to draw the triangle we are working to identify.
Step 2: Calculate the side length AB using the distance formula.
Step 3: Calculate the side length BC using the distance formula.
Step 4: Calculate the side length AC using the distance formula.
Step 5: Compare the side lengths AB, BC, and AC from the previous steps to define the triangle type.
How would you graph y-intercept is 8 and x-intercept is 9
Answer:
all shown below
Step-by-step explanation:
y-intercept means a dot's y coordinate is 8 and on the y axis, x-i intercept means a dot's x coordinate is 9 and on the x axis
Answer:
see the attached graph
Step-by-step explanation:
The intercepts are the points where a graph crosses the coordinate axes.
Y-interceptThe y-intercept is the the point where the graph crosses the y-axis. The value of x is zero there. The coordinates of the y-intercept are (0, 8).
X-interceptThe x-intercept is the point where the graph crosses the x-axis. The value of y is zero there. The coordinates of the x-intercept are (9, 0).
You graph these intercepts by plotting the points at these coordinates.
__
In the attached graph, the intercepts are blue dots, and we have drawn a line through them. The line is not part of the graph of the intercepts. It is merely an instance of a function that has these intercepts.
Which represents the inverse of the function f(x) = 4x?
• h(x) = X + 4
• h(x) =x-4
O h(x) = -x
• h(x) = x
32 randomly picked people were asked if they rented or owned their own home, 8 said they rented. Obtain a point estimate of the proportion of home owners.
Group of answer choices
0.250
0.600
0.750
0.200
0.500
Answer:
.750
Step-by-step explanation:
Expand. Your answer should be a polynomial in standard form. -p^2(p^2-p-1) =
Answer:
[tex]\huge\boxed{\sf -p^4+p^3+1}[/tex]
Step-by-step explanation:
Given expression:[tex]=-p^2(p^2-p-1)\\\\Distribute \\\\= -p^4+p^3+1\\\\\rule[225]{225}{2}[/tex]
graph y=1x. Sketch the graph below.
1. Select all phrases that fit the graph of y=1x.
curve
straight
y-intercept = 1
positive x-values
quadrant IV
quadrant III
point (1, 1)
x-intercept = 0
quadrant I
y-intercept = 0
no y-intercept
negative y-values
no x-intercept
quadrant II
x-intercept = 1
point (-1, -1)
The phrases that fit the graph of [tex]y = \sqrt x[/tex] are
curve positive x-valuespoint (1, 1) x-intercept = 0quadrant I y-intercept = 0How to select the phrasesThe equation of the function is given as:
[tex]y = \sqrt x[/tex]
Next, we plot the graph of the function (see attachment)
From the attached graph, we have the following highlights:
All points are in quadrant IThe function is a curveIt has an x-intercept of x = 0It has a y-intercept of y = 0It has only positive x valuesIt passes through (1,1)The above represents the phrases that fit the graph
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Complete questionUsing a graphing application, graph y = √x. Sketch the graph below.
Select all phrases that fit the graph of y = √x
curve straight y-intercept = 1 positive x-values
quadrant IV quadrant III point (1, 1) x-intercept = 0
quadrant I y-intercept = 0 no y-intercept negative y-values
no x-intercept quadrant II x-intercept = 1 point (-1, -1)
5. Gaur Grandeur is a society which has a garden of length 45 5/7 m and breadth 16 3/4m. Find area of garden
Step-by-step explanation:
Here,
given length= 45 5/7 m( mixed fraction)
= 320/7 m( simple fraction)
similar breadth= 16 3/4 m
= 67/4 m
Now,
Area= length* breadth
= 320/7 * 67/4
=5360/7 m²
Step-by-step explanation:
I guess this means the garden is a rectangle.
the area is
length × breadth (or width or ...)
so,
45 5/7 × 16 3/4 =
= (45×7 + 5)/7 × (16×4 + 3)/4 =
= 320/7 × 67/4 = 320×67 / 7×4 = 80×67 / 7 =
= 5360/7 = 765 5/7 m²
f: {whole numbers} → {whole numbers} Assign each whole number to its largest place value digit. For example, f(4) = 4, f(14) = 4, and f(194) = 9.
f (999)
Answer:
9
Step-by-step explanation:
Please help me out asap.
Using a calculator, the slope of the line of best-fit is of 7.2.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points are given as follows:
(-4,-32), (-2,-8), (0,10), (2,8), (4,32).
Using the calculator, the equation is:
y = 7.2x + 2.
Hence the slope is of 7.2.
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