Answer:
The probability is [tex]p(n ) = 3.18*10^{-5}[/tex]
Step-by-step explanation:
From the question we are told that
The population size is N = 31
The sample size n = 4
Generally the number of way by which the n can be selected from N is mathematically represented as
[tex]\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = 31465[/tex]
The number of ways of selecting a particular sample size is is [tex]k = 1[/tex]
Therefore the probability of each simple random sample in this case is mathematically evaluated as
[tex]p(n ) = \frac{1}{31465}[/tex]
[tex]p(n ) = 3.18*10^{-5}[/tex]
Write a rational number in fraction form that is equivalent to -1.\overline{5}
Answer:
[tex]\dfrac{-14}{9}[/tex].
Step-by-step explanation:
The given number is [tex]-1.\overline{5}[/tex].
We need to find a rational number in fraction form that is equivalent to given number.
Let [tex]x=-1.\overline{5}[/tex]
[tex]x=-1.555...[/tex] ...(1)
Multiply both sides by 10.
[tex]10x=-15.555...[/tex] ...(2)
Subtracting (1) from (2), we get
[tex]10x-x=-15.555...-(-1.555...)[/tex]
[tex]9x=-14[/tex]
Divide both sides by 9.
[tex]x=\dfrac{-14}{9}[/tex]
Therefore, the required rational number is [tex]\dfrac{-14}{9}[/tex].
arthur walks 5/8 mi to school jonathan rides a bus 8 times that far> How far does Jonathan ride to school
Answer:
Step-by-step explanation:
Distance walked by Arthur = 5/8 miles
Distance ride by Jonathan = 8 times that of Arthur
it means that Distance rode on bus by Jonathan is 8 multiplied by Distance walked by Arthur
Distance rode on bus by Jonathan = 8 * Distance walked by Arthur
Distance rode on bus by Jonathan = 8 * 5/8 = 5 Miles Answer
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5 . If there were 4545 no votes, what was the total number of votes?
Answer:
The total number of votes= 9999
Step-by-step explanation:
The ratio of vote specifically the ratio of yes to no vote in a city vote is 6 to 5.
There is a total of 4545 no votes.
Yes/no = 6/5
Yes= no(6/5)
Yes= 4545(6/5)
Yes= 5454
The total number of yes votes are 5454.
The total number of votes= yes votes+ no votes
The total number of votes= 5454+4545
The total number of votes= 9999
Factor.
x2 – 5x - 36
(x - 9)(x + 4)
(x - 12)(x + 3)
(x + 9)(x - 4)
(x + 12)(x - 3)
Answer:
The answer is option AStep-by-step explanation:
x² - 5x - 36
To factor the expression rewrite -5x as a difference
That's
x² + 4x - 9x - 36
Factor out x from the expression
x( x + 4) - 9x - 36
Factor out -9 from the expression
x( x + 4) - 9( x+ 4)
Factor out x + 4 from the expression
The final answer is
( x - 9)( x + 4)Hope this helps you
Answer:
[tex] \boxed{(x - 9) \: (x + 4) }[/tex]
Option A is the correct option.-
Step-by-step explanation:
( See the attached picture )
Hope I helped!
Best regards!
i will give brainliest and 5 stars if you help ASAP
Answer:
[tex] Area = 240 m^2 [/tex]
Step-by-step explanation:
The area of the right triangle above = [tex] \frac{1}{2}*base*height [/tex].
Where,
base = 16 m
height = 30 m
Plug in the above values into the area formula:
[tex] Area = \frac{1}{2}*16*30 [/tex]
[tex] Area = 8*30 [/tex]
[tex] Area = 240 m^2 [/tex]
Refer to the attachment for solution.
What Number is equivalent to 4^3
A. 7
B. 12
O C. 64
D. 81
Answer:
C
Step-by-step explanation:
4³ means 4 multiplied by itself 3 times, that is
4 × 4 × 4
= 16 × 4
= 64 → C
logx - logx-1^2=2log(x-1)
Answer:
x is approximately 2.220744
Step-by-step explanation:
This can be simplified a little using properties of logarithms, and then solve it by graphing:
[tex]log(x)-log(x-1)^2=2\,log(x-1)\\log(x)-2\,log(x-1)=2\,log(x-1)\\log(x)=4\,log(x-1)[/tex]
So we use a graphing tool to find the intersection point of the graph of [tex]log(x)[/tex], and the graph of [tex]4\,log(x-1)[/tex]
Please see attached image for the graph and solution.
The value of x is approximately 2.220744
Answer:
x = 2.32011574011
Step-by-step explanation:
The problem with your original equation is that it is a long way of saying ...
log(x) -log(x) -1 = 2log(x-1)
0 -1 = 2log(x-1)
which has the solution ...
-1/2 = log(x -1)
1/√10 = x -1
x = 1 + 1/√10 ≈ 1.3162278
__
We have asked for clarification, and what we got was ...
[tex]\log{(x)}-\log{(x-1^2)}=2\log{(x-1)}[/tex]
which, again, is a long way of saying ...
[tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]
The other reasonable interpretation of your 'clarified' equation is ...
[tex]\log{(x)}-\log{((x-1)^2)}=2\log{(x-1)}[/tex]
which you already have an answer to. You have declared that a "misconception."
So, we are left with the interpretation that the equation you want a solution to is ...
[tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]
_____
When solving these graphically, I like to write the equation as a function whose zero(s) we're trying to find. For this, when we subtract the right side, we get ...
[tex]f(x)=\log{(x)}-3\log{(x-1)}[/tex]
A graphing calculator shows that f(x) = 0 when ...
x ≈ 2.32011574011
__
If you don't like my interpretation, check out the second attachment. It has your x-1² as the argument of the middle term. You can see that the calculator interpreted that the same way I did (as required by the order of operations).
A random sample of 10 single mothers was drawn from a Obstetrics Clinic. Their ages are as follows: 22 17 27 20 23 19 24 18 19 24 We want to determine at the 5% significance level that the population mean is not equal to 20. What is the rejection region?
Answer:
0.09
Step-by-step explanation:
Let x = ages of mother
x : 22 17 27 20 23 19 24 18 19 24
N = 10
Mean = ∑x/N = 218/10 = 21.8
Difference in mean = 21.8 - 20 = 1.8
If significance level = 5% or 0.05
∴ Rejection region = 1.8 X 0.05 = 0.09
Write the equation of the line that passes through (−2, 6) and (2, 14) in slope-intercept form. (2 points)
Answer:
[tex]y = 4x + 14[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation we must first find the slope of the line
Slope of the line using points (−2, 6) and (2, 14) is
[tex]m = \frac{14 - 6}{2 + 2} = \frac{8}{2} = 4[/tex]
Now we use the slope and any of the points to find the equation of the line.
Equation of the line using point ( - 2, 6) and slope 4 is
[tex]y - 6 = 4(x + 2) \\ y - 6 = 4x + 8 \\ y = 4x + 8 + 6[/tex]
We have the final answer as
[tex]y = 4x + 14[/tex]
Hope this helps you
Un taxímetro inicia con 50 unidades y el banderazo o arranque es de $4500, las unidades comienzan a cambiar p0r cada kilometros recorrido. La función lineal que representa esta situación es y = 50x +4500 donde y representa el precio que cuesta la carrera y x la distancia recorrida en kilómetros. a) ¿ Cuanto cuesta una carrera si la distancia recorrida fue de 23 kilómetros?
Answer: $5650
Step-by-step explanation:
El precio de la carrera es:
y = ($50/km)*x + $4500.
Donde x representa la cantidad recorrida en Km.
Ahora se nos pregunta:
¿ Cuanto cuesta una carrera si la distancia recorrida fue de 23 kilómetros?
Para esto, debemos reemplazar la variable en la equacion por 23km:
x = 23km
y = ($50/km)*23km + $4500 = $5650
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 50 p = 0.2
Answer:
The mean, variance, and standard deviation of the binomial distribution are 10, 8, and 2.83 respectively.
Step-by-step explanation:
We have to find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p, i.e; n = 50 p = 0.2.
Let X = binomial random variable
So, X ~ Binom(n = 50, p = 0.2)
Now, the mean of the binomial distribution is given by;
Mean of X, E(X) = n [tex]\times[/tex] p
= 50 [tex]\times[/tex] 0.2 = 10
Now, the variance of the binomial distribution is given by;
Variance of X, V(X) = n [tex]\times[/tex] p [tex]\times[/tex] (1 - p)
= 50 [tex]\times[/tex] 0.2 [tex]\times[/tex] (1 - 0.2)
= 10 [tex]\times[/tex] 0.8 = 8
Also, the standard deviation of the binomial distribution is given by;
Standard deviation of X, S.D.(X) = [tex]\sqrt{\text{n} \times \text{p} \times (1 - \text{p})}[/tex]
= [tex]\sqrt{\text{50} \times \text{0.2} \times (1 - \text{0.2})}[/tex]
= [tex]\sqrt{8}[/tex] = 2.83
Combine like terms to simplify the expression: 2/5k - 3/5 +1/10k
━━━━━━━☆☆━━━━━━━
▹ Answer
1/2k - 3/5
▹ Step-by-Step Explanation
2/5k - 3/5 + 1/10k
Collect like terms:
2/5k + 1/10k = 1/2
Final Answer:
1/2k - 3/5
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
1/2k - 3/5
Step-by-step explanation:
Hey there!
Well the only fraction needed to combine are,
2/5 and 1/10.
To add them we need to make 2/5 have a denominator of 10.
To do that we multiply 5 by 2.
5*2 = 10
What happens to the denominator happens to the denominator.
2*2 = 4
Fraction - 4/10
4/10 + 1/10 = 5/10
5/10
simplified
1/2
1/2k - 3/5
Hope this helps :)
Diana paints 150 fence posts and chuck paints 130 fence posts. Diana paints 10 more fence posts than chuck. How many fence posts does chuck paint per hour?
Complete Question
The complete question is shown on the first uploaded image
Answer:
Step-by-step explanation:
From the question we are told that
The relationship is [tex]\frac{150 }{d} = \frac{130}{c}[/tex]
The number of fence post painted by chuck is [tex]l = 130[/tex]
The number of fence post painted by Diana is [tex]k = 150[/tex]
can paint 10 fences more than chuck so let say the of fence painted in an hour by chuck is [tex]g[/tex]
Then the number of fence post painted by Diana in one hour is
[tex]f = g+ 10[/tex]
So
[tex]\frac{150 }{ g + 10 } = \frac{130}{g}[/tex]
[tex]130 g + 1300 = 150g[/tex]
[tex]g = 65 \ m[/tex]
Find the length of a square with a perimeter of 48cmeter
Answer:
12
Step-by-step explanation:
Perimeter of a square:
4(L)
L = Length
=> 4(L) = 48
=> 4L = 48
=> 4L/4 = 48/4
=> L = 12
The length of the square is 12 cm.
Answer:
12
Step-by-step explanation:
Since the lengths of the sides of a square are equal, divide the perimeter by 4
Please answer this correctly without making mistakes
Answer:
5/12
Step-by-step explanation:
3/4-1/3=
9/12-4/12=
5/12
In your own words, define Quadratic Equation. How many solutions does a Quadratic Equation have?
Answer: an equation that has one term which is nameless and squared also no term which gets raised to higher power.
Step-by-step explanation:
What is 1/3 of 675 is left
if a salesman has a base salary of 35,000 per year makes 5% commission on each sales ,how much must he do in sales to make a total of 75,000 for the year
He must do a 8,00,000 sales to make total of 75000 for the year.
For salesman base salary = 35000, Salary to be atained is 75000. Having commission of 5% on every sales. Sales to be determine so the salesman attained 75000 for year.
In mathematics it deals with numbers of operations according to the statements.
Here, according to the statement.
Let x be sales,
35,000 + 5%x = 75,000
0.05x = 75000-35000
x = 40000/0.05
x = 8,00,000
Thus, he must do a 8,00,000 sales to make total of 75000 for the year
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23
Answer:
∠ H ≈ 23°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus
∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )
The points (-6,-4) and (3,5) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
The length of the radius is a
(Round to the nearest hundredth as needed.)
Answer:
40.5
Step-by-step explanation:
diameter^2 = (3 +6)^2 + (5+4)^2
or, d^2 = 9^2 + 9^2
or, d^2 = 81 +81
or,d^2 =162
or d=√ 162
• d= 81
then radius = d/2
r = 81/2
•r= 40.5 ans
What value does the 2 in the number 0.826?
Answer:
.02
Step-by-step explanation:
2 is in "Hundredths' place in .826
So, the number is multiplied with 1/100 or .01
=> 2 x 1/100
=> 2/100
=> .02
=> 2 x .01
=> .02
The value of 2 in .826 is .02
Given v(x) = g(x) (3/2*x^4 + 4x – 1), find v'(2).
Answer:
Step-by-step explanation:
Given that v(x) = g(x)×(3/2*x^4+4x-1)
Let's find V'(2)
V(x) is a product of two functions
● V'(x) = g'(x)×(3/2*x^4+4x-1)+ g(x) ×(3/2*x^4+4x-1)
We are interested in V'(2) so we will replace x by 2 in the expression above.
g'(2) can be deduced from the graph.
● g'(2) is equal to the slope of the tangent line in 2.
● let m be that slope .
● g'(2) = m =>g'(2) = rise /run
● g'(2) = 2/1 =2
We've run 1 square to the right and rised 2 squares up to reach g(2)
g(2) is -1 as shown in the graph.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's derivate the second function.
Let h(x) be that function
● h(x) = 3/2*x^4 +4x-1
● h'(x) = 3/2*4*x^3 + 4
● h'(x) = 6x^3 +4
Let's calculate h'(2)
● h'(2) = 6 × 2^3 + 4
● h'(2) = 52
Let's calculate h(2)
●h(2) = 3/2*2^4 + 4×2 -1
●h(2)= 31
■■■■■■■■■■■■■■■■■■■■■■■■■■
Replace now everything with its value to find V'(2)
● V'(2) = g'(2)×h(2) + g(2)× h'(2)
● V'(2)= 2×31 + (-1)×52
●V'(2) = 61 -52
●V'(2)= 9
What are the solution(s) of the quadratic equation 98 - x2 = 0?
x = +27
Ox= +63
x = +7/2
no real solution
Answer:
±7 sqrt(2) = x
Step-by-step explanation:
98 - x^2 = 0
Add x^2 to each side
98 =x^2
Take the square root of each side
±sqrt(98) = sqrt(x^2)
±sqrt(49*2) = x
±7 sqrt(2) = x
Answer:
[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]
Step-by-step explanation:
[tex]98-x^2 =0[/tex]
[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]
[tex]98=x^2[/tex]
[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]
[tex]\pm \sqrt{98} =x[/tex]
[tex]\sf Simplify \ radical.[/tex]
[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]
[tex]\pm 7\sqrt{2} =x[/tex]
[tex]\sf Switch \ sides.[/tex]
[tex]x= \pm 7\sqrt{2}[/tex]
There are $400$ pages in Sheila's favorite book. The average number of words per page in the book is $300$. If she types at an average rate of $40$ words per minute, how many hours will it take to type the $400$ pages of the book?
Answer:
50hours
Step-by-step explanation:
Given that there are 400 pages in Sheila's favorite book.
The average number of words per page in the book is 300
She types an average rate of 40words per minute.
So to type 400pages of the book
Total number of words in the pages = 400×300 = 120000 words
Typing rate : 40words ------- 1minute
120000 words ----------- x minutes
Hence we have 40 × X mins = 120000 × 1min
Make X the subject
40X = 120000minutes
X = 120000/40
X = 3000minutes
Since 60minutes = 1hour
3000minutes = 3000minutes/60
= 50hours
Hence it took her 50hours to type 400pages
Solution:
The total number of words in the book is 400 x 300. Sheila types at a rate of 40 words per minute, or 40 x 60 words per hour. The number of hours it takes her is equal to the number of words divided by her rate of typing, or 400x300/40x60 = 50 hours.
Manuel says that he can solve the equation 3n = 21 by multiplying both sides by ⅓. Explain why this is correct.
Step-by-step explanation:
はい、両側を削除して、3を掛けて7にします
Step-by-step explanation:
Given:
3n = 21
if we multiply both sides by 1/3, we will get:
3n = 21
3n x (1/3)= 21 x (1/3)
3n/3 = 21/3
n = 21/3
n = 7
Hence we can indeed solve for n by multiplying both sides by (1/3)
During the school year, there were 315 total points scored between basketball, soccer, baseball, and football. The baseball team scored 55 points. The soccer team scored twice as much as the baseball team. The football team scored 0.5 more than 1.5 times as much as the baseball team. How many points did the basketball team score?
Answer:
67.5p.
Step-by-step explanation:
315p in total.
- Baseball has 55p.
- Soccer teams points = 55x2 = 110p.
- Football team points = 110 x 0.5 = 55 x 1.5 = 82.5p.
So then you just do 315p - 82.5p - 55p - 110p = 67.5p
Given that
[tex]\sqrt{2p-7}=3[/tex]
and
[tex]7\sqrt{3q-1}=2[/tex]
Evaluate
[tex]p + {q}^{2} [/tex]
Answer:
Below
Step-by-step explanation:
The two given expressions are:
● √(2p-7) = 3
● 7√(3q-1) = 2
We are told to evaluate p+q^2
To do that let's find the values of p and q^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's start with p.
● √(2p-7) = 3
Square both sides
● (2p-7) = 3^2
● 2p-7 = 9
Add 7 to both sides
● 2p-7+7 = 9+7
● 2p = 16
Divide both sides by 2
● 2p/2 = 16/2
● p = 8
So the value of p is 8
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's find the value of q^2
● 7√(3q-1) = 2
Square both sides
● 7^2 × (3q-1) = 2^2
● 49 × (3q-1) = 4
● 49 × 3q - 49 × 1 = 4
● 147q - 49 = 4
Add 49 to both sides
● 147q -49 +49 = 4+49
● 147q = 53
Divide both sides by 147
● 147q/147 = 53/147
● q = 53/ 147
Square both sides
● q^2 = 53^2 / 147^2
● q^2 = 2809/21609
■■■■■■■■■■■■■■■■■■■■■■■■■
● p+q^2 = 8 +(2809/21609)
● p+q^2 = (2809 + 8×21609)/21609
● p+q^2 = 175681 / 21609
● p + q^2 = 8.129
Round it to the nearest unit
● p+ q^2 = 8
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2+5/2n
Answer: [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
Step-by-step explanation:
[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
Michael records the height of 1000 people. This data is a normal distribution and the sample mean was 0.75. Identify the margin of error for this data set.
Answer:
0.0284Step-by-step explanation:
The formula for calculating the Margin of error of a dataset is expressed as;
Margin of error = [tex]Z*\sqrt{\frac{p(1-p)}{n} } \\\\[/tex] where;
Z is the z-score of 95% confidence interval = 1.96
p is the sample proportion/mean = 0.75
n is the sample size = total number of people = 1000
Note that when the confidence interval is not given, it is always safe to use 95% confidence.
Substituting this values into the formula we have;
[tex]ME = 1.96*\sqrt{\frac{0.7(1-0.7)}{1000} } \\\\ME = 1.96*\sqrt{\frac{0.7(0.3)}{1000} } \\\\ME = 1.96*\sqrt{0.00021} } \\\\ME = 1.96*0.01449\\\\ME = 0.0284[/tex]
Hence the margin error for the dataset is 0.0284
A diameter that is perpendicular to a chord bisects the chord. True False
Answer:
[tex]\Large \boxed{\sf True}[/tex]
Step-by-step explanation:
[tex]\sf A \ diameter \ that \ is \ perpendicular \ to \ a \ chord \ bisects \ the \ chord.[/tex]
Answer:
True!!
I just did the assignment and got it right
