Answer:
To find the dimensions of a rectangle
Step-by-step explanation:
perimeter=302
let width=x
length=x+47
p=2(L+W)
302=2(x+x+47)
302=2(2x+47)
302=4x+94
subtracting 94 from the other side we have
302-94=4x
208=4x
x=52
length=99
width=52
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
205, 201, 197, ...
Find the 35th term.
The first three terms of a sequence are given, so the 35th term is: [tex]a_n = 69[/tex]
What is sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts. A sequence is a list of elements that has been arranged in a certain way.
An ordered list of numbers is a sequence. The three dots indicate that the established pattern should go forward. A phrase is used to describe each number in the series. The first word in the order 1, 3, 5, 7, 9,... is 1, the second is 3, the third is 5, and so on.
The first three terms are : 205, 201, 197, .......
The general term through the pattern is:
[tex]a_n = - 4n+209[/tex]
or, [tex]a_n = - 4(35)+209[/tex]
here, n = 35
or, [tex]a_n = 69[/tex]
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The classroom outside bag had 5 frisbees in it. If 25% of the outside toys are frisbees, then how many total toys are in the bag?
The total number of toys in the bag is 20
How to determine the number of total toys in the bag?From the question, we have the following parameters that can be used in our computation:
Frisbees = 5
Proportion of these Frisbees = 25%
Using the above as a guide, we have the following:
Number of Frisbees = Total number of Frisbees * The proportion of these Frisbees
Substitute the known values in the above equation, so, we have the following representation
Total number of Frisbees * 25% = 5
Divide both sides by 25%
Total number of Frisbees = 20
Hence, the total is 20
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6(2x-3)-2(2x+1) please help me :)
8x-20
Step-by-step explanation:
12x-18-4x-2
8x-20
using division to find the ratios that are equivalent to 40:28 and please show the steps.
Answer:
10:7
Step-by-step explanation:
40:28 are both divisible by 4. 40/4 is 10. 28/4 is 7. So the ratio would be 10:7 since neither is divisible by both the same number, this is the final ratio.
help meeeeeeeeeee pleaseee
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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Find the area of the triangle below.
Be sure to include the correct unit in your answer.
10yd
4yd
7yd
The area of the triangle below 8 yards
What is triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Triangles are three-sided shapes. The many kinds of triangles go by various names. The size of the angles and the length of the sides determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.7-15=8
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An object was launched from the top of a hill with an upward vertical velocity of 100 feet per second. The height of the object can be modeled by the function h(t)=-16 t^2+100 t+300, where t represents the number of seconds after the launch. Assume the object landed on the ground at sea level. Find the answer using graphing technology,
The object's height was } \quad \text { when it was launched.
The object's height was 300 ft above sea level when it was launched.
What is a quadratic equation?
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as a[tex]x^{2}[/tex] + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
Given, the height of the object can be modeled by the function
h(t)=-16t^2+100 t+300
Height of object when it was launched
At the time of launched, t=0
h = -16(0)^2 + 100(0) + 300 = 300 ft above sea level
Hence, the object's height was 300 ft above sea level when it was launched.
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Use cylindrical shells to find the volume of the solid generated when the region enclosed by the curves y=x3, x=1, and y=0 is revolved about the y-axis.
To calculate the total volume of the solid we will divide it into n shell cyline thickness of [tex]$\Delta y$.[/tex]
The internal shell cylinder circumference C shall be[tex]$2 \pi r_i$[/tex]
where r is the in The shell cylinder internal area A shall be C.
where h is the height
The volume of the shell cylinder[tex]$\Delta v$[/tex] shall be[tex]$A \cdot \Delta y$.[/tex]
Then we will have:
[tex]\Delta v=A \cdot \Delta y=C \cdot h \cdot \Delta y=2 \pi r_i h \cdot \Delta y \Rightarrow d v=2 \pi r_i h \cdot d y$$[/tex]
The total volume of the solid shall be the summation of all n shell cylinders
[tex]\int d v=\int 2 \pi r_i h d y \Rightarrow V=\int_a^b 2 \pi r_i h d y \Rightarrow V=2 \pi \int_a^b r_i h d y$$[/tex]
[tex]\int d v=\int 2 \pi r_i h d y \Rightarrow V=\int_a^b 2 \pi r_i h d y \Rightarrow V=2 \pi \int_a^b r_i h d y[/tex]
[tex]The value $a$ is the value of $y$ at the point where $x=0$ then:For $x=0 \Rightarrow y=0^3 \Rightarrow y=0$ then $a=0$.The value $b$ is the value of $y$ at the point where $x=1$ then:[/tex]
[tex]For $x=1 \Rightarrow y=1^3 \Rightarrow y=1$ then $b=1$.Since the integration will be with variable $y$ we have to express the function $y=x^3$ in terms of $y$ :$$[/tex]
y=x^3 \[tex]Rightarrow x=\sqrt[3]{y}[/tex]
Substituting in V, we will have:
[tex]V= & 2 \pi \int_a^b r_i h d y=2 \pi \int_0^1(1-y)(1-\sqrt[3]{y}) d y=2 \pi[/tex]\[tex]int_0^1(1-y)\left(1-y^{\frac{1}{3}}\right) d y \\[/tex]
&[tex]1-y \\& \frac{1-y^{\frac{1}{3}}}{1-y} \\& \frac{-y^{\frac{1}{3}}+y^{\frac{1}{3}} \cdot y^{\frac{1}{1}}}{} \\[/tex]
[tex]& 1-y-y^{\frac{1}{3}}+y^{\frac{1}{3}+\frac{1}{1}}= \\& =1-y-y^{\frac{1}{3}}+y^{\frac{1+3}{3}}= \\[/tex]
[tex]& =1-y-y^{\frac{1}{3}}+y^{\frac{4}{3}}= \\& =y^{\frac{4}{3}}-y^{\frac{1}{3}}-y+1[/tex]
Substituting in V:
[tex]V=2 \pi \int_0^1\left(y^{\frac{4}{3}}-y^{\frac{1}{3}}-y+1\right) d y=2[/tex][tex]{1}{3}+1}}{\frac{1}{3}+1}-\frac{y^{1+1}}[/tex]{[tex]1+1}+y\right]_0^1=2[/tex] [tex]\pi\left[\frac{y^{\frac{4+3}{3}}}{\frac{4+3}{3}}[/tex]-[tex]\frac{y^{\frac{1+3}{3}}}{\frac{1+3}{3}}-\frac{y^2}{2}+y\right]_0^1$$[/tex]
Calculating the definite integral:
By definition[tex], $\int_a^b f(x) d x=\left.F(x)\right|_a ^b=F(b)-F(a)$[/tex] then:
[tex]& V=\frac{\pi}{14}\left[\left(12 \cdot 1^{\frac{7}{3}}-21 \cdot 1^{\frac{4}{3}}-14[/tex][tex]\cdot 1^2+28 \cdot 1\right)-\left(12 \cdot 0^{\frac{7}{3}}-21 \cdot[/tex] [tex]0^{\frac{4}{3}}-14 \cdot 0^2+28 \cdot 0\right)\right] \\[/tex]
& V=[tex]\frac{\pi}{14}[(12 \cdot 1-21 \cdot 1-14 \cdot 1+28 \cdot 1)-\underbrace{(12 \cdot 0-21 \cdot 0-14 \cdot 0+28 \cdot 0)}_0][/tex]
[tex]& V=\frac{\pi}{14}(12-21-14+28)=\frac{\pi}{14}(12+28-21-14)=\frac{\pi}{14}(40-35)=\frac{5 \pi}{14} \approx \frac{5 \cdot 3,1416}{14} \approx \frac{15,708}{14} \\& V \approx 1,122[/tex]
Answer:[tex]$V \approx 1,122 u . v$. (units of volume)[/tex]
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$4232 invested for 4 years at 6% compounded annually
The final amount of the money according to compound interest model is $ 5342.80.
What is the resulting amount after four years by compound interest model?
Herein we find a case of a money deposited that increases its amount in time by compound interest, that is, the amount increases continuously in time. The compound interest model is described below:
C' = C · (1 + r / 100)ⁿ
Where:
C - Initial amount.C' - Current amount. r - Interest rate, in percentage.n - Number of periods, in years.If we know that C = 4232, r = 6 and n = 4, then the final amount of the money is:
C' = 4232 · (1 + 6 / 100)⁴
C' = 5232.802
The final amount is $ 5342.80.
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When determining if triangles are congruent, what additional angles/sides should you mark in each triangle? Select all that apply.
Reflexive Angles
Reflexive Sides
Vertical Angles
nothing
Triangles are congruent, then there is no additional angles/sides should we mark in each triangle.
What is congruent triangles?
If and only if we can use rigid transformations to map one figure onto the other, then two figures are said to be congruent. All corresponding sides and angles are congruent because rigid transformations maintain distance and angle measure. Therefore, measuring all of the sides and angles of a pair of triangles would be one method of determining whether they are congruent.
Since reflexive angles means is an angle that is more than 180 degrees and less than 360 degrees.
And the reflexive sides means the reflexive property of congruence states that any shape is congruent to itself.
Vertical angles are angles opposite each other where two lines cross.
But to check the congruence of two triangles we only have the angles and sides of the two triangles are same.
So, there is no additional angles/sides should we mark in each triangle.
Hence, triangles are congruent, then there is no additional angles/sides should we mark in each triangle.
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Can you also mark the two points on the graph
Dontrell bought 5 1/2 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.
____________________
The equation for total amount to be paid represented as y and pounds of potatoes represented as x will be y = 0.64x
What is linear equation?Ax + By + C = 0 can be used to express a linear equation in two variables, where x and y are the two variables, and each has a degree of one.
Ex. -2x+3y=8
Total weight of potatoes in pounds Dontrell bought= x
Let total amount Dontrell he pays= $ y
It is given 5.5 pounds are bought by paying $3.52
5.5 pounds = $3.52
1 pound = $ 3.52/5.5
1pound=$0.64(Using Unitary method)
Dontrell buy x pounds potatoes and he pays $y
Therefore,
y=0.64x
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Write 0.00317 in scientific notation.
Answer:
3.17×10^3
Step-by-step explanation:
Hope it helps!
Immediate assistance needed, please
The jumper is in free fall for 7.07 s if the parachute is opens at 1000 ft
The jumper is in free fall for 7.29 s if the parachute is opens at 950 ft
The reasonable domain for the function h is
0 ≤ t ≤ 10
The reasonable range for the function h is
0 ≤ h ≤ 1800
How to find the time of free fallThe duration of free fall is calculated using the given function
h = -16t² + 1800
the parachute is opens at 1000 ft
h = -16t² + 1800
1000 = -16t² + 1800
16t² = 1800 - 1000
16t² = 800
t² = 800 / 16
t² = 50
t = √50
t = 7.07 s
the time at this situation is 7.07s
the parachute is opens at 950 ft
h = -16t² + 1800
950 = -16t² + 1800
16t² = 1800 - 950
16t² = 850
t² = 850 / 16
t² = 53.125
t = √53.125
t = 7.2887 s
the time at this situation is 7.29s
reasonable domain
minimum t = 0
for maximum t, h = -16t² + 1800 = 0
16t² = 1800
t = 10.61
0 ≤ t ≤ 10
the reasonable domain is 0 ≤ t ≤ 10
reasonable range
h = -16t² + 1800
at t = 0, h = 1800
at t = 10.606, h = 0
0 ≤ h ≤ 1800
the reasonable range is 0 ≤ h ≤ 1800
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8. 1/2.6+1/4.8+1/6.10+,..+1l20.24
The answer is 0.1657
Solution:
Given: [tex]\frac{1}{2*6}[/tex]+[tex]\frac{1}{4*8}[/tex]+ .. . . . . . . . +[tex]\frac{1}{20*24}[/tex]
∴ [tex]\frac{1}{12}[/tex] + [tex]\frac{1}{32}[/tex] + [tex]\frac{1}{60}[/tex] + [tex]\frac{1}{96}[/tex] + . . . . . . + [tex]\frac{1}{480}[/tex]
∴ [tex]\frac{40}{480}[/tex] + [tex]\frac{15}{480}[/tex] + [tex]\frac{8}{480}[/tex] + . . . . . . +[tex]\frac{1}{480}[/tex] --------- (multiplying the numerator with quotient of 480/denominators)
∴[tex]\frac{79.54}{480}[/tex]
= 0.1657
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After carefully calculating the sequence we have come to find that The answer of the given equation is 0.1657
What is a sequence?
A sequence is an ordered collection of enumerated objects in mathematics where repetitions are permitted. It has members, just like a set (also called elements, or terms). The length of the sequence refers to the total (possibly infinite) number of elements.
Contrary to a set, the same elements may appear more than once at various points in a sequence, and in contrast to a set, the order is important. The formal definition of a sequence is a function from natural numbers (the positions of the sequence's elements) to the elements at each position. A function from any index set is what is meant by an indexed family, which is a generalisation of the idea of a sequence.
[tex]\frac{1}{2\times6} + \frac{1}{4\times8} + \frac{1}{6\times10}.....\frac{1}{20\times24}[/tex] --------- (multiplying the numerator with quotient of 480/denominators)= 0.1657
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Find the interest rate for the given deposit and compound amount. $4200 accumulating to $5994.74, compounded monthly for 7 years. The interest rate is ___%. (Do not round until the final answer. Then round to the nearest hundredth as needed.)
The rate of interest monthly is 0.55%.
What is rate of interest?
An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the total loan amount.
Given that,
The deposit amount is $4,200.
The future value is $5,994.74
The number of months = 7(12) = 84.
The payment i.e. PMT = $0
Based on the above information, the calculation is as follows:
The formula is
= RATE(NPER,PMT,-PV,FV,TYPE)
After applying the above formula, the rate of interest monthly is 0.55%.
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Find the values of a b and c for the equation y = 4x2- 8x - 12
Answer:
[tex]a=4, b=-8, c=-12[/tex]
Step-by-step explanation:
Compare the given equation with the general form [tex]y=ax^2 + bx+c[/tex].
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is nine times the measure of the first angle. The third angle is 20 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
(X=60,Y=47,Z=73), the measures of the three angles.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.
The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question
x+y+z=180
The second and third angles' combined measurements equal twice the first angle's combined measurement, therefore
y+z−2x+y+z=2=0
Third angle has 26 more degrees than second angle, therefore
z−y+z=y+26=26
As a result, we obtain the equation system.
x+y+z=180−2x+y+z=0−y+z=26
(1)(2)(3)
By removing y and z, use equations (1) and (2) to determine x. To get rid of y and z, multiply equation (2) by one before adding it to equation (1).
x+y+z2x−y−z3xx=180=0=180=60(4)
To get rid of z, use equations (1) and 3). To get rid of z, multiply equation (3) by 1 and then add it to equation (1).
x+y+zy−zx+2y=180=−26=154(5)
To determine, substitute x=60 into equation (5).
x+2y(60)+2y2yy=154=154=94=47
In order to find, we can now change x=60 and y=47 in equation (1).
x+y+z(60)+(47)+zz+107z=180=180=180=73
Therefore, there is a solution.
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The sample space of an experiment involving graduating seniors is {No job offers, Exactly one job offer, Exactly two job offers, Exactly three job offers, More than three job offers}, where P(No job offers) = 0.33, P(One job offer) = 0.22, P(Two job offers) = 0.15, P(Three job offers) = 0.11, P(More than three job offers) = 0.19. Find the probability that a graduating senior receives two or three job offers. 0.26 0.36 0.46 0.56
0.26 is probability that a graduating senior receives two or three job offers.
What is probability in math?
Calculating or estimating how likely or "possible" something is to occur is the subject of probability. Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring.
Probabilities in mathematics are always represented as fractions, decimals, or percentages with values ranging from 0 to 1.
P(2 or 3 jobs)=P(2 jobs)+P(3 jobs)-P(2 jobs and 3 jobs)=P(2 jobs) + P(3 jobs) since a student can not have 2 jobs as well as three jobs at a time.
So,
P(2 or 3 jobs)=0.15+0.11 = 0.26
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= |4|+|−3|
= |1,2| − |−1,2|
= 2|4 − 10| + |7 − 5|
Answer:
Step-by-step explanation:
12=666
a number is between 58 and 60 it has prime factors between 2,3,and 5. what is the number?
Solution:
60
Step-by-step explanation:
60 is divisible by 2 -> 60 / 2 = 30
60 is divisible by 3 -> 60 / 3 = 20
60 is divisible by 5 -> 60 / 5 = 12
Hope that helped!Answer: 60
Step-by-step explanation:
60 has all prime factors of 2,3 and 5. :)
A right rectangular prism has the dimensions 4 by 6 by 3 feet. Enter the volume, in cubic feet, of the rectangular prism.
Determine whether the following statements are True or False. Then, explain why.
(a) Throughout a hypothesis test, the alternative hypothesis is assumed to be true.
(b) No matter what the conclusion of a hypothesis test is, neither the null or alternative hypothesis has been proven to be true.
(c) When drawing a conclusion to a hypothesis test, compare the calculated p-value to the calculated test statistic.
(d) As a p-value approaches 0 it is more likely the hypothesis test conclusion will be "reject the null hypothesis."
Throughout a hypothesis test, the alternative hypothesis is assumed to be true.
Answer :-FALSE
What is hypothesis test ?
in hypothesis test we compare p-value with level of significance and conclude our null hypothesis is true or not true.
p-value decided null hypothesis is true or not true.
p-value <= level of significance then null hypothesis is true.
We do not say alternative hypothesis is assumed to be true.
Therefore Correct Options
FALASE
No matter what the conclusion of a hypothesis test is, neither the null or alternative hypothesis has been proven to be true.
Answer :- TRUE.
Because,
Yes, no matter what was the conclusion of hypothesis test.
We set always our claim in alternative hypothesis and conclude about the null hypothesis.
We check null hypothesis is true or do not true.
That's reason Correct Options TRUE.
When drawing a conclusion to a hypothesis test, compare the calculated p-value to the calculated test statistic.
Answer :- FALSE
Because,
We Calculate the test statistic.
Using this test Statistic we calculate p-value
We compare p-value with level of significance and conclude it.
That's reason statement is false. We do to compare p-value and test statistic.
As a p-value approaches 0 it is more likely the hypothesis test conclusion will be "reject the null hypothesis.".
Answer :- TRUE
Because,
p-value is the probability that test hypothesis is accepted or rejected.
We compare always p-value with level of significance.
p-value < 0.05
We reject the null hypothesis.
In given problem p-value = 0
That is we reject the null hypothesis.
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If cos (∅)=-1/4 and ∅ is in the 3rd quadrant. find the exact value for sin (∅).
sin(∅)=
The exact value for sin (∅) is √15/4 if cos (∅)=-1/4 and ∅ is in the 3rd quadrant.
What are trigonometric functions?In mathematics, the trigonometric functions—also known as circle, angle, or goniometric functions—are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths. As some of the most basic periodic functions, they are frequently employed in Fourier analysis to examine periodic phenomena.
The sine, cosine, and tangent are the trigonometric functions that are most commonly utilized in contemporary mathematics. The cotangent, secant, and their less common reciprocals, the cosecant, are each of their reciprocals.
Given, cos (∅)=-1/4 and ∅ is in the 3rd quadrant.
cos²∅+sin²∅=1
sin²∅=1-cos²∅
sin²∅=(1-(-1/4)²)
sin²∅=1-(1/16)
sin²∅=15/16
sin∅=√15/4
Therefore, the exact value for sin (∅) is √15/4 if cos (∅)=-1/4 and ∅ is in the 3rd quadrant.
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NEED ASAP PLEASE
Determine the theoretical probability of rolling a two with one standard die. Write this probability in three equivalent forms: as a fraction, a decimal (rounded to three places), and a percentage (rounded to one decimal place).
Answer:
The theoretical probability of rolling a two with one standard die is 1/6. This can be written as a decimal by dividing 1 by 6, which is approximately 0.167. As a percentage, this is approximately 16.7%. Here are all three forms:As a fraction: 1/6As a decimal: 0.167As a percentage: 16.7%
Step-by-step explanation:
The following cards are dealt to three people at random, so that everyone gets the same number of cards. What is the probability that everyone gets a red card?
[There are three red cards and three blue cards]
The probability that everyone gets a red card will be 0.125.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The accompanying cards are managed by three individuals indiscriminately, so everybody gets a similar number of cards. There are three red cards and three blue cards.
Then the probability that everyone gets a red card is given as,
P = (3/6) × (3/6) × (3/6)
P = (1/2) × (1/2) × (1/2)
P = 1/8
P = 0.125
The probability that everyone gets a red card will be 0.125.
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the layers, in deep learning, represent the data processing that occurs in order to achieve the correct output. select one:
The layers, in deep learning, represent the data processing that occurs in order to achieve the correct output is true.
Deep learning is part of machine learning methods and is based on artificial neural networks with representation learning. It is a machine learning technique that teaches computers to carry out operations that comes naturally to humans: learn by example. Deep learning is a key technology behind driverless cars, enabling them to recognize a stop sign, or to distinguish a pedestrian from a lamppost. Deep learning networks learn by identifying intricate data structures in the data they experience. By developing computational models that are composed of multiple processing layers, the networks can create multiple levels of abstraction to represent the data. A layer is the highest-level building block in deep learning. A layer is a container that usually receives weighted input, transforms it with a set of functions through data processing and passes these values as output to the next layer.
Note: The question is incomplete. The complete question probably is: The layers, in deep learning, represent the data processing that occurs in order to achieve the correct output. select one: true false.
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estimate the difference between 3,894,256 and 756,533 by rounding each number to the nearest thousand. 4,561,000 3,137,000 3,138,000 3,139,000
The difference between 3894256 and 756533 by rounding each number to the nearest thousand is 3138000
The first number = 3894256
The second number = 756533
To find the difference between the numbers we have to use the subtraction
Difference between 3894256 and 756533 = 3894256 - 756533
Subtract the numbers
= 3137723
Rounding of a number is write the numbers to the nearest place values like tens, hundreds and thousand etc.
Here, the number is 3137723 and we have to round the number to nearest thousand
Round to nearest thousand = 3137000
Therefore, the result nearest to the thousand is 3138000
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Assume that x and y are both differentiable functions of t and are related by the equation y=cos(5x). Find [tex]\frac{dy}{dt}[/tex] when x= [tex]\frac{\pi }{10}[/tex], given
[tex]\frac{dx}{dt}[/tex] = -4 when x= [tex]\frac{\pi }{10}[/tex]
Enter an exact answer.
[tex]\frac{dy}{dt}[/tex]=______
Assume that x and y are both differentiable functions of t and are related by the equation y=cos(5x). The value of dy/dx is 25.
What is differentiable functions?
Differentiable simply means that the derivative exists at each location within its domain. As a result, the function must also exist (i.e., be continuous) on its domain in order for the derivative to exist. Because of this, a differentiable function can also be continuous.
Given that x, y are both differentiable function of t. and
[tex]y=\cos (5 x)[/tex]
Find [tex]\frac{d y}{d t}=$.[/tex] when [tex]$x=\frac{\pi}{10}$[/tex] given that [tex]$\frac{d x}{d t}=-5$[/tex], when [tex]$x=\frac{\pi}{10}$[/tex]
Given function is
[tex]$ y=\cos 5 x $[/tex]
[tex]$\frac{d y}{d t}=-\sin (5 x) \cdot \frac{d}{d t}(5 x) \text { (By chain } $[/tex]
[tex]$ =-\sin 5 x \cdot 5 \frac{d x}{d t} $[/tex]
[tex]$ \text { at } x=\frac{\pi}{10}$[/tex]
[tex]$ \frac{d y}{d t}=-\sin \left(8 \times \frac{\pi}{10}\right) \times 5 \times-5$[/tex]
[tex]$-\frac{d x}{d t}=-5 $[/tex]
[tex]$2^{20} $[/tex]
[tex]$\text { at } x=\frac{\pi}{10}$[/tex]
[tex]$ =25 \sin \frac{\pi}{2} $[/tex]
[tex]$=25 \times 1 $[/tex]
[tex]$ \frac{d y}{d t}=25 $[/tex]
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A cylinder that has an ideal piston contains one mole of hydrogen gas and undergoes an isobaric expansion that doubles its initial volume.
How much heat is transferred to or from the gas?
a) heat flows into the gas by an amount greater than the mechanical work W
b) heat flows into the gas by an amount less than the mechanical work W
c) heat flows out of the gas by an amount greater than the mechanical work W
d) heat flows out of the gas by an amount less than the mechanical work W
The option A is correct
In other words, the amount of heat entering the system must be greater than the amount of mechanical effort leaving the system.
Recall the first law of thermodynamics' ideas in order to comprehend this.
dQ = dU + dW
Assuming perfect conditions. There is no heat loss outside. No matter how much heat we give the gas dQ , some of it will be utilised to boost the gas's internal energy while the rest will be used to produce work. This must be less than dQ in turn.
Because of this extremely fundamental characteristic of all engines, none of them can operate at 100% efficiency. Even the "Carnot engine," the most ideal engine, is not entirely efficient.
The option A is correct
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