whats the area of a rectangle
:)
Answer:
Baguette. :)
Step-by-step explanation:
Answer:
I don't know you lollollollll
[tex]\huge{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=}}[/tex]
[tex]HOLA!![/tex]
Answer:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=e^{\frac{1}{3} } }}[/tex]
Explanation:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=}}[/tex]
For this we have to take into account:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{x^{n} }{n!} =e^{x} }}[/tex]
Using the properties of factorials and exponents we have:
[tex]n!=(n-1)n![/tex] Also. [tex]\frac{n^{x} }{ n^{y} }=n^{x-y}[/tex]
We replace:
[tex]{\boxed{ \sum_{n=1}^{\infty}\ \frac{1}{3^{n-1}.(n-1)! } }}[/tex]
Shape it:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} }}[/tex]
Finally:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} =e^{\frac{1}{3} } }}[/tex]
An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 30 feet up. The ladder makes an angle of 68° with the ground.
Find the length of the ladder. Round your answer to the nearest hundredth of a foot if
necessary.
Answer: [tex]32.36\ ft[/tex]
Step-by-step explanation:
Given
Ladder is leaned and make an angle of [tex]68^{\circ}[/tex]
Electric box is 30 ft up the ground.
Suppose x is the length of ladder
From the figure, we can write
[tex]\Rightarrow \sin 68^{\circ}=\dfrac{30}{x}\\\\\Rightarrow x=\dfrac{30}{\sin 68^{\circ}}\\\\\Rightarrow x=32.36\ ft[/tex]
The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The length of the ladder is 32.356 feet.
What is Sine (Sinθ)?The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
[tex]\rm{Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
As it is given that the height of the electric box from the bottom is 30 feet, while the ladder makes an angle of 68° with the ground.
The length of the ladder can be found using the trigonometric functions, therefore, the length of the ladder can be written as,
[tex]\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\\\\\Sine(\angle C) = \dfrac{AB}{\text{Length of the ladder}}\\\\\\{\text{Length of the ladder}}= \dfrac{AB}{Sine(\angle C) }\\\\\\{\text{Length of the ladder}}= \dfrac{30}{Sine(68^o) }\\\\\\{\text{Length of the ladder}}= 32.356\ feet[/tex]
Hence, the length of the ladder is 32.356 feet.
Learn more about Sine:
https://brainly.com/question/21286835
The distance between two points is 10 units, if the coordinates of one of the endpoints are (4, -7), find x if the coordinates of the other endpoint are (x, 1).
Answer:
10
Step-by-step explanation:
let the distance = d
d² = (x2-x1)² + (y2-y1)²
=>
10²= (x-4)²+(1+7)²
100 = (x-4)²+64
(x-4)²=100-64
= 36
x-4 = √36
x-4=6
x= 6+4
x= 10
I need help I’ll give u brainlest
Answer:
216 yd³
Step-by-step explanation:
Volume of a rectangular prism
= product of the three orthogonal sides
= 6yd * 6yd * 6yd
= 216 yd³
Answer:
216
Step-by-step explanation:
:)
You want to test the claim that the average age of students at Gorka College is greater than the average age of students at Yapoah College. You take a simple random sample of 53 people from Gorka and compute an average age of 21.2 (years) and a standard deviation of 1.1. Then you take a simple random sample of 46 students from Yapoah College and compute an average age of 20.7 and a standard deviation of 1.2.
Compute the t-statistic for testing the alternative hypothesis that the average age of Gorka students is greater than the average age of Yapoah students (set things up so that t is positive).
What are the degrees of freedom (using the conservative method)?
What is the P-value?
Is there significant evidence at the 0.05 level to support the hypothesis that the average age of Gorka students is higher than for Yapoah?
Answer:
Kindly check explanation
Step-by-step explanation:
The hypothesis :
H0 : μ1 = μ2
H1 : μ1 > μ2
Given :
x1 = 21.1 ; n1 = 53 ; s1 = 1.1
x2 = 20.7 ; n2 = 46 ; s2 = 1.2
The test statistic :
(x1 - x2) / √[(s1²/n1 + s2²/n2)]
(21.1 - 20.7) / √[(1.1²/53 + 1.2²/46)]
0.4 / 0.2326682
Test statistic = 1.719
The degree of freedom using the conservative method :
Comparing :
Degree of freedom = n - 1
Degree of freedom 1 = 53 - 1 = 52
Degree of freedom 2 = 46 - 1 = 45
Smaller degree of freedom is chosen ;
The Pvalue from Test statistic, using df = 45
Pvalue = 0.0462
Pvalue < α ; Hence, there is significant evidence to conclude that average age of Gorka student is higher than Yaphoa.
D(x, y) = (3x, 3y)
Preimage:P(1, -1), Q(2, 1), R(-2, 1)
Image: P'(,), Q'(,), R'(,)
Scale factor:
Step-by-step explanation:
I have no idea but here's thiss
A piece of office equipment purchased for dollar-sign 67,500 depreciates in value each year. Suppose that each year the value of the equipment is StartFraction 1 Over 15 EndFraction less than its value the preceding year.
Calculate the value of the equipment after 2 years.
The value of the equipment after 2 years is dollar-sign
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Answer:
$58,800
Step-by-step explanation:
Each year, the value is multiplied by 1-1/15 = 14/15. Then after 2 years, the initial value has been multiplied by (14/15)^2 = 196/225. The value after 2 years is ...
$67,500×196/225 = $58,800
Identify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 7500 households, and the data collected today will be used to determine the proportion of households tuned to a particular sports program. Which type of observational study is described in the problem statement?
Answer:
Cross sectional study
Step-by-step explanation:
Cross sectional study, also known as traverse or prevalence study caloukdnbe defined as a form of observational study which involves analysing a certain sample of data which is selected based on a variable of interest. This data is collected at a given point in time across the sample population. In the scenario described above, the record of viewing habit of 7500 household smoke obtained today(point in time) will be used to determine the proportion tuned to a particular sport programme. (data collected is based on the variable to be analyzed).
Byron is working in a lab testing bacteria populations. After starting out with a population of 288 bacteria, he observes the change in population and notices that the population triples every 16 minutes. Step 1 of 2 : Find the equation for the population P in terms of time t in minutes. Round values to three decimal places.
Answer:
[tex]P = 288 * 3^{(\frac{t}{16}) }[/tex]
Step-by-step explanation:
According to the Question,
Given that, Byron is working in a lab testing bacteria populations. After starting out with a population of 288 bacteria, he observes the change in population and notices that the population triples every 16 minutes.Therefore, the equation for the population P in terms of time t in minutes is[tex]P = 288 * 3^{(\frac{t}{16}) }[/tex] .
I need to know how to solve this completely not just the answers plz :)
HELP ME WITH THIS GEOMETRY QUESTION!!! 18 POINTS!
Answer:
72
72
96
120
Step-by-step explanation:
The arcs are in the ratio:
3 : 3 : 4 : 5
Add all numbers in the ratio:
3 + 3 + 4 + 5 = 15
In the ratio, the sum of all numbers is 15.
In the real circle, the sum of the measures of all the arcs is 360.
360/15 = 24
Multiply all numbers in the ratio by 24.
72 : 72 : 96 : 120
Answer:
72
72
96
120
8)
8x + 6
14x - 2
A) 11
C) 8
B) -9
D) -7
Answer:
C) 8
Step-by-step explanation:
Consecutive angles are equal to 180. So 22x+4+180. Solve that to get x=8. Hope I helped and post more questions :)
A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful, however he cannot try more than 3 times or the phone will lock him out. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experiment
Answer:
(S, FS, FFS, FFF)
Step-by-step explanation:
According to the Question,
Given, A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful.however, he cannot try more than 3 times or the phone will lock him out.Let, S denote a successful attempt and F denote a failed attempt.So, the sample space for this random experiment is
{S, FS, FFS, FFF}
The person stops trying when he successfully enters the code or when he has failed at all 3 attempts .
A calculator was used to perform a linear regression on the values in the
table. The results are shown to the right of the table.
х
y
1
9
N
6
LinReg
y = ax+b
0=-3.6
b=12.8
r2=.9969230769
r=-.9984603532
3
2
4
-2
5
-5
What is the line of best fit?
A. y = -3.6x + 12.8
O B. -0.998 = -3.6x + 12.8
O c. y = 12.8x - 3.6
D. y = -0.998x + 12.8
Answer:
Step-by-step explanation:
A y = -3.6x + 12.8
The line of best fit is,
⇒ y = - 3.6x + 12.8
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, Given that;
⇒ y = ax + b.
And, the best fitting line has values of a = - 3.6 and b = 12.8.
Hence, All you need do is put that into the general equation and try different values for it.
So you have y = - 3.6 x + 12.8
Now Let's run a couple of numbers.
The table shows 1 and 9 for the first entry. This means when x = 1, y should come pretty close to nine.
y = - 3.6(1) + 12.8
y = 9.2
Which is not a bad result for x = 1
You might want to check to see if anything else comes closer in your choices. If it does, then you have to try other points.
C
-0.998 = -3.6(1) + 12.8
This answer cannot work. We've already shown that x =1 will leave us close to 9 not -998
So, C is incorrect.
B
y = 12.8x - 3.6
Let x = 1
y = 12.8(1) - 3.6
y = 9.2 is right by coincidence. We must try another value. The hardest one is going to be 5 and - 5
y= 12.8*5 - 3.6
y = 64 - 3.6 which is no where's near - 5.
So B is wrong.
A
y = -0.998(1) + 12.8 Does this give 9 or anywhere near it? 11.802 You might argue that that is not a bad result. So let's try another pair.
x = 3. y should come to somewhere near 2.
y = -0.998 * 3 + 12.8 which comes to roughly nine. You can check this out.
It is not close enough to 2 to be acceptable.
Thus, The correct option is,
⇒ y = - 3.6x + 12.8
Learn more about the mathematical expression visit:
brainly.com/question/1859113
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a bag contains 16 red coins , 8 blue coins , and 8 green coins. A player wins by pulling a red coin from the bag. Is this game fair? Justify your answer
Answer:
Step-by-step explanation:
there are a total of 16+8+8=32 coins in bag
16 out of 32 are red
player wins by pulling a red coin
assume it is a single pull, the winning probability = 16/32 = 1/2
so it is 50/50 chance n hence a fair game
Step-by-step explanation:
yes it is a fair game because any one don't know what the coin will get, it is based on luck
three-fifths of a number increased by ten
Answer: [tex]\frac{3}{5} x+10[/tex]
Step-by-step explanation:
three-fifths of a number means multiply three-fifths by a variable [tex]\frac{3}{5} x[/tex]
increased by 10 means addition +10
together it is [tex]\frac{3}{5}x +10[/tex]
12.10.4 Test (CST): Income and Budgeting
Question 12 of 25
What is the y-intercept of the line passing through the point 5.-6) with a
slope of - 1/7?
A.47/7
B.37/7
C.-37/7
D.-47/7
Answer:
C.-37/7
Step-by-step explanation:
Given the following data;
Points (x, y) = (5, -6)
Slope, m = -1/7
Mathematically, the equation of a straight line is given by the formula;
y = mx + c
Where;
m is the slope.
x and y are the points
c is the intercept.
To find the y-intercept of the line, we would use the following formula;
y - y1 = m(x - x1)
y - (-6) = -⅐(x - 5)
y + 6 = -⅐x + 5/7
y = -⅐x + (5/7 - 6)
y = -⅐x - 37/7 = mx + c
Therefore, y-intercept (c) = -37/7
Can anyone help me with this question!
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Answer:
D. (x² -2x -3) +(-x² +4x +2)
Step-by-step explanation:
The tiles on the first row model (x² -2x -3).
The tiles on the second row model (-x² +4x +2).
If the difference is being modeled, it will show as ...
(x² -2x -3) -(-x² +4x +2) = (x -2x -3) +(x² -4x -2) . . . . . matches none
If the sum is being modeled, it will show as ...
(x² -2x -3) +(-x² +4x +2) . . . . . matches D
_____
Additional comment
As is often the case, you can select the correct answer without even any understanding of the question. You can do that because the correct answer is the only one that is a true statement. All of the other answer choices are incorrectly "simplified."
no spam pls
for which x is f(x)=-3
1. -7
2.-4
3. 4
4. 5
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Answer:
(a) -7
Step-by-step explanation:
You are given f(x) = -3. Look for -3 in the f(x) column. (You will find it in the first row.)
You want the corresponding value of x. It will be in the first row of the x column. The value there is -7.
The value of x for f(x) = -3 is -7.
A jet travels 5192 miles against a jetstream in 8 hours and 6072 miles with the jetstream in the same amount of time. What
is the rate of the jet in still air and what is the rate of the jetstream?
the answer is in the picture
Which
expression iS equivalent to (a^8)^4
Answer:
Step-by-step explanation:
What are the nasser choices
Answer:
a^32.
Step-by-step explanation:
Using one of the laws indices:
(a^8)^4
= a^(8*4)
= a^32.
The girls in Lana’s troop set a goal to sell 1,000 boxes of cookies this year. There are 13 girls in the troop. At least how many boxes of cookies should each girl sell to reach their goal?
Answer:
77 boxes each
Step-by-step explanation:
1,000/13
Answer:
Step-by-step explanation:
1000/13= 76.9 .... Each girl needs to sell 77 boxes
Total employment for sheet metal workers in 2016 is projected to be 201,000. If this is a 6.3% increase from 2006,
approximately what was the tctal employment in 2006?
a. 214,000
b. 187,000
C. 195,000
d. 189,000
Answer:
D 189,000
Step-by-step explanation:
Samples of rejuvenated mitochondria are mutated (defective) in 2% of cases. Suppose 12 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.
(a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
(c) is 0.00
Round your answers to two decimal places
Answer:
a) 0.7847 = 78.47% probability that no samples are mutated.
b) 0.9769 = 97.69% probability that at most one sample is mutated.
c) 0% probability that more than half the samples are mutated.
Step-by-step explanation:
For each sample, there are only two possible outcomes. Either they are mutated, or they are not. The probability of a sample being mutated is independent of any other sample, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
2% of cases.
This means that [tex]p = 0.02[/tex]
12 samples are studied
This means that [tex]n = 12[/tex].
(a) No samples are mutated.
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]
0.7847 = 78.47% probability that no samples are mutated.
(b) At most one sample is mutated.
This is:
[tex]P(X \geq 1) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]
[tex]P(X = 1) = C_{12,1}.(0.02)^{1}.(0.98)^{11} = 0.1922[/tex]
[tex]P(X \geq 1) = P(X = 0) + P(X = 1) = 0.7847 + 0.1922 = 0.9769[/tex]
0.9769 = 97.69% probability that at most one sample is mutated.
(c) More than half the samples are mutated.
This is:
[tex]P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,7}.(0.02)^{7}.(0.98)^{5} \approx 0[/tex]
So the others(greater than 7) wil be 0 too
0% probability that more than half the samples are mutated.
Mathematics
Evaluate the equations or inequalities. Write the Letter of your answer to the corresponding boxes at the bottom of the page to discover the answer to the title questions.
How does an ESP Expert send his mail?
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7 11 1 8 2 9 11 3 1 8 9 4 6 9 4 9 1 2 10 5
help po.
Step-by-step explanation:
ejdjbd x bxbx k wbu y DJ UK j HK JM dz
nb
Which choices are correct when determining the distance between −56 and −31?
Answer:
I dont know sorry so much
Find the P-value for the hypothesis test with a standardized test statistic z. Decide whether toreject the null hypothesis for the level of significance α.a. Left-tailed test, z = -1.32, α = 0.10b. Right-tailed test, z = 2.46, α = 0.01c. Two-tailed test, z = -1.68, α = 0.05
Answer:
1.) We don't reject the null
2.) We reject the Null
3.) We do not reject the null
Step-by-step explanation:
Obtaining p values using test statistic:
Given that ; we have a standardized test statistic and α - values ;
Let's define the decision region :
If Pvalue < α ; Reject H0 ; otherwise, fail to reject H0
A.)
Left tail , Z = - 1.32 ; α = 0.10
We can use the Pvalue calculator from Z score :
Pvalue = 0.934
Pvalue > α ; Hence, we fail to reject the null, H0
B.)
Right-tailed test, z = 2.46, α = 0.01
Pvalue from Zscore calculator ;
Pvalue = 0.0069
Pvalue < α ; Hence, we reject the null, H0
C.)
Two-tailed test, z = -1.68, α = 0.05
Pvalue from Zscore calculator ;
Pvalue = 0.093
Pvalue > α ; Hence, we fail to reject the null, H0
Of all the calls in the first quarter of year 5, how many were abandoned
I do not know what you mean, but ok.
Find the first three terms of the Maclaurin series for f(x) =
[tex]{e}^{ \frac{x}{2} } [/tex]
Step-by-step explanation:
Starting out with the Taylor series,
[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(a)}{n!}(x-a)^n[/tex]
where [tex]f^{(n)}[/tex] is the nth derivative of f(x) and if we set a = 0, we get the special case of the Taylor series called the Maclaurin series:
[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(0)}{n!}x^n[/tex]
Expanding this series up to the 1st 3 terms at a = 0,
[tex]f(x) = f(0) + \dfrac{f'(0)}{1!}x + \dfrac{f''(0)}{2!}x^2[/tex]
Let's find the derivatives of [tex]e^{\frac{x}{2}}[/tex]:
[tex]f'(x) = \frac{d}{dx} (e^{\frac{x}{2}}) = \frac{1}{2}e^{\frac{x}{2}} \Rightarrow f'(0) = \frac{1}{2}[/tex]
[tex]f''(x) = \frac{1}{4}e^{\frac{x}{2}} \Rightarrow f''(0) = \frac{1}{4}[/tex]
We can now write the Maclaurin series for [tex]e^{\frac{x}{2}}[/tex]as
[tex]e^{\frac{x}{2}} = 1 + \frac{1}{2} x + \frac{1}{8} x^2[/tex]
