Answer:
Gloria is 3 years old and Ray is 21
Step-by-step explanation:
3+15=18
21+15=36
36÷18= 2
Which means he would be 2times older
Hope this helps..
The concentration of particles in a suspension is 50 per mL. A 5 mL volume of the suspension is withdrawn. a. What is the probability that the number of particles withdrawn will be between 235 and 265? b. What is the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52? c. If a 10 mL sample is withdrawn, what is the probability that the average number per mL of particles in the withdrawn sample is between 48 and 52? d. How large a sample must be withdrawn so that the average number of particles per mL in the sample is between 48 and 52 with probability 95%?
Answer:
(a) 0.6579
(b) 0.2961
(c) 0.3108
(d) 240
Step-by-step explanation:
The random variable X can be defined as the number of particles in a suspension.
The concentration of particles in a suspension is 50 per ml.
Then in 5 mL volume of the suspension the number of particles will be,
5 × 50 = 250.
The random variable X thus follows a Poisson distribution with parameter, λ = 250.
The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.
The mean of the approximated distribution of X is:
μ = λ = 250
The standard deviation of the approximated distribution of X is:
σ = √λ = √250 = 15.8114
Thus, [tex]X\sim N(250, 250)[/tex]
(a)
Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:
[tex]P(235<X<265)=P(\frac{235-250}{15.8114}<\frac{X-\mu}{\sigma}<\frac{265-250}{15.8114})[/tex]
[tex]=P(-0.95<Z<0.95)\\=P(Z<0.95)-P(Z<-0.95)\\=P(Z<0.95)-[1-P(Z<0.95)]\\=2P(Z<0.95)-1\\=(2\times 0.82894)-1\\=0.65788\\\approx 0.6579[/tex]
Thus, the value of P (235 < X < 265) = 0.6579.
(b)
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{5}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{5}})[/tex]
[tex]=P(-0.28<Z<0.28)\\=P(Z<0.28)-P(Z<-0.28)\\=P(Z<0.28)-[1-P(Z<0.28)]\\=2P(Z<0.28)-1\\=(2\times 0.64803)-1\\=0.29606\\\approx 0.2961[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.2961[/tex].
(c)
A 10 mL sample is withdrawn.
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{10}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{10}})[/tex]
[tex]=P(-0.40<Z<0.40)\\=P(Z<0.40)-P(Z<-0.40)\\=P(Z<0.40)-[1-P(Z<0.40)]\\=2P(Z<0.40)-1\\=(2\times 0.65542)-1\\=0.31084\\\approx 0.3108[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.3108[/tex].
(d)
Let the sample size be n.
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{n}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{n}})[/tex]
[tex]0.95=P(-z<Z<z)\\0.95=P(Z<z)-P(Z<-z)\\0.95=P(Z<z)-[1-P(Z<z)]\\0.95=2P(Z<z)-1\\P(Z<z)=\frac{1.95}{2}\\\\P(Z<z)=0.975[/tex]
The value of z for this probability is,
z = 1.96
Compute the value of n as follows:
[tex]z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241[/tex]
Thus, the sample selected must be of size 240.
Two points that are on the same line are called what?
A
coplanar
B
collinear
C
supplementary
D
parallel
Answer:
That would be B Collinear
Answer:
B: Collinear
Step-by-step explanation:
Let's look at the answer choices, shall we?
-Coplanar is two lines or points on the same plane.
-Supplementary is where two angles measure to 180 degrees
- Parallel lines are where two lines have the same slope and will never intersect
The only other option is collinear, which happens to have the definition of two points on the same line.
We want to factor the following expression: 25x^6-30x^3+9 We can factor the expression as (UVwhere Uand are either constant integers or single-variable expresSions 1) What are U and V?
Answer:
U = 5x^3
V = 3
(5x^3 - 3)^2
Step-by-step explanation:
(1) The value of U and V are U = 5x³ and V = 3.
(2) The factored form of 25x⁶ - 30x³ + 9 is (5x³3 - 3)²
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
We can factor the expression 25x⁶ - 30x³ + 9 by first noticing that each term is a perfect square:
25x⁶ = (5x³)²
30x³ = 2(15x³)
9 = 3²
Now we can write the expression as the difference of two squares:
25x⁶ - 30x³ + 9 = (5x³)² - 2(5x³)(3) + 3²
Let U = 5x³ and V = 3. Then we have:
(5x³3 - 3)²
Therefore, the factored form of 25x⁶ - 30x³ + 9 is (5x³3 - 3)².
To learn more about the quadratic equation;
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(2x+4) + (3x-9) simplify
Four friends went to the movies.
Each person bought a movie ticket, and the total the four friends spent on the tickets was $52.
Which equation can be used to find the cost of each tickets
A) 4+x=52
B) x - 4= 52
C) 4x=52
D)x/4=52
The equation that can be used to find the cost of each ticket is 4x = 52.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 6 is an equation.
We have,
Number of people who bought the tickets = 4
The total cost of tickets = $52
Now,
The cost of each ticket.
= 52 ÷ 4
= 13
Now,
Cost of one ticket = x
4x = 52
x = 52/4 = 13
Thus.
The cost of each ticket is $13.
Learn more about equations here:
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Which of the following expressions is not equivalent to -4.5 • -8?
-8 • -4.5
8 • 4.5
(8)(-4.5)
(4.5)(8)
Answer: (8)(-4.5)
Step-by-step explanation:
If you were to multiply-4.5 • -8 that would equal a positive number but if you were to divide (8)(-4.5) it would equal a negative number
Answer:
(8)(-4.5)
Step-by-step explanation:
please mark brainliest
what is 10 times 20,00x
Determine whether the lines are parallel, perpendicular, or neither. EM has the
slope of 5/6 and TC has the slope of 6/5
Answer:
Not sure, not good with lines, but I think I did it correctly. EM = Neither TC= Perpendicular.
Simplify: b3·b−5·b11
A) b9
B) b15
C) b19
D) b-165
Which of the following is the equation of the line that is parallel to
y= 3/5x+ 8 and goes through point (-10,4)?
Select one:
a. y = 5/3x + 20 2/3
b. y=-5/3x – 12 2/3
c.y= 3/5x + 10
d. y = -3/5x-2
Answer:
C
Step-by-step explanation:
We want to write the equation of a line that is parallel to:
[tex]y=\frac{3}{5}x+8[/tex]
And also passes through (-10, 4).
Remember that parallel lines have the same slope.
The slope of our old line is 3/5.
Therefore, the slope of our new line is also 3/5.
We know that it passes through (-10, 4). So, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's substitute 3/5 for m and let (-10, 4) be our (x₁, y₁). This yields:
[tex]y-(4)=\frac{3}{5}(x-(-10))[/tex]
Simplify:
[tex]y-(4)=\frac{3}{5}(x+10)[/tex]
Distribute on the right:
[tex]y-4=\frac{3}{5}x+6[/tex]
Add 4 to both sides:
[tex]y=\frac{3}{5}x+10[/tex]
So, our answer is C.
And we're done!
Step-by-step explanation:
Hey there!
The equation of a st.line passing through point (-10,4) is ;
(y-y1)= m1(x-x1) [one point formula]
Put all values.
(y - 4) = m1( x + 10)..........(i)
Another equation is; y = 3/5 + 8.............(ii)
From equation (ii)
Slope (m2) = 3/5 [ By comparing equation with y = mx+c].
As per the condition of parallel lines,
Slope of equation (i) = slope of equation (ii)
(i.e m1 = m2 )
Therefore, the value of m1 is 3/5.
Putting value of slope in equation (i).
[tex](y - 4) = \frac{3}{5} (x + 10)[/tex]
[tex](y - 4) = \frac{3}{5} x + \frac{3}{5} \times 10[/tex]
[tex](y - 4) = \frac{3}{5} x + 6[/tex]
[tex]y = \frac{3}{5} x + 10[/tex]
Therefore the required equation is y = 3/5x + 10.
Hope it helps...
What is the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5?
Expand the expression
3(x-6)
Answer:
3x-3(6) = 3x-18
Step-by-step explanation:
Find all solutions of the equation x^2+3x+5=0 and express them in the form a+ bi
Answer:
in you question there is the ans hibben
Step-by-step explanation:
x^2+3x+5=0 =a+ bi
What is the answer to 6x + 7= -x + 70
Answer:
x = 9
Step-by-step explanation:
6x + 7 = -x + 70
~Subtract 7 to both sides
6x = -x + 63
~Add x to both sides
7x = 63
~Divide 7 to both sides
x = 9
Best of Luck!
which is the equation of the line that passes through the points (-4,-8) and (1,3)
Answer:
−5x+13y=84
Step-by-step explanation:
I hope this is good :)
I buy a printer for $125 and ink cartridges cost $15 each. Explain the relationship between the cost of ink cartridges and the total cost.
Answer:
125+15c=t
Step-by-step explanation:
Every cartridge is worth $15, so that would be 15c aka 15 x however many cartridges you purchase. Then the printer is $125, and its not changing so there will be no variable. Put those two amounts together and you'll get the total cost. (Hopefully I explained this well enough.)
There are 35 students in art class and 57 students in dance class. Find the number of students who are either in art class or in dance class. Find
When two classes meet at different hours and 12 students are enrolled in both activities. ( 2marks)
When two classes meet at the same hour. ( 2 marks)
Answer:
a. 80 students
b. 92 students
Step-by-step explanation:
Represent arts students with A and Dance students with D.
So, we have,
n(A) = 35
n(D) = 57
Required
Determine n(A or D)
Solving (a):
Here, we have:
n(A and D) = 12
n(A or D) is calculated as thus:
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 12
n(A or D) = 80
b. From the given details
n(A and D) = 0 because both students are not mixed up as in (a) above
Using the same formula as (a).
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 0
n(A or D) = 92
Given m || n, find the value of x and y.
(3x-4)
(6x-5)
Answer:
X=21 and Y=121
Step-by-step explanation:
With these types of problems, we need to know our vertical angles and that lines are 180° when two angles on a line are next to each other.
To solve this problem algebraically we want to add (3x-4) and (6x-5) together so that they equal 180. The reason we do this is that they lie on the same line which is 180°. The equation would look like [tex]3x+6x-5-4=180[/tex]. We then want to add like terms which will leave us with [tex]9x-9=180[/tex]. Now we want to get 9x by itself by adding 9 on each side which leaves us with [tex]9x=189[/tex]. To isolate x we need to divide on each side by 9 which finally leaves us with [tex]x=21[/tex]
Now that we have the value of x (21) we can now utilize our knowledge of vertical angles (angles that are completely across and equal to one another.) We can find y by doing this equation: [tex]y=6x-5[/tex] and with the value of x found we can plug in the value to get [tex]y=6(21)-5[/tex] which simplifies to [tex]y=126-5[/tex] then to [tex]y=121[/tex].
what is meaning of integers
whole numbers, plus their counterparts less than zero, and zero
Negative integers(less than 0) being: –1, –2, –3 exc.
Positive integers(more than 0) being: 1, 2, 3 exc.
Answer:
Integers are whole numbers like -3, -2, -1, 1, 2, 3, 4. They can't be fractions or decimals though
Solve the following system of equations.
6x -5y=13 & 9y-15+2x=0
x = 3
y = 1
Step-by-step explanation:Hi !
6x - 5y = 13
9y - 15 + 2x = 0
6x - 5y = 13
2x + 9y = 15 | ×(-3)
6x - 5y = 13
- 6x - 27y = - 45
add
6x - 6x - 5y - 27y = 13 - 45
- 32y = - 32 | ×(-)
32y = 32
y = 1
replace y = 1
6x - 5(1) = 13
6x - 5 = 13
6x = 13 + 5
6x = 18
x = 3
Good luck !
Ming li spent $15 at the movies. She then earned $30 babysitting. She spent $12 at the bookstor. She now has $18 left. How much money did ming li have to begin woth
Answer:
$15
Step-by-step explanation:
30 - (12+15)
30-27=3
18-3=15
Hope this helps ;)
Simplify 3-8 divided by 3-2
Answer:
-5
Step-by-step explanation:
[tex] \frac{3 - 8}{3 - 2} [/tex]
[tex] \frac{ - 5}{1} [/tex]
[tex] - 5[/tex]
A = 2/3 * (B + C)
Solve for C
I think #1 is wrong but i can't figure it out
Answer:
Step-by-step explanation:
x=6
y=4
5x-y^2 :2
5×6 - 4 ^2 :2
30 - 16 :2
30 - 8
22 (the wright answer)
Circle the mistake :x =6 and y =4 it's not x=4 and y=6
Explain the mistake :when you calculed with x=4 and y=6 the final answer is wrong.
SUPER EASY, ILL GIVE A BRAINLIEST THINGY TO FIRST ANSWER. At the store, two brands are sold. Brand A is offered as 6 for $0.85. Brand B is offered as 8 for $1.00. Which brand is the better buy?
Answer:
8 for $1.00
step by step explanation:
Once cup of instant rice makes 1.5 cups of cooked rice. How many cups of cooked rice will 3 cups of instant rice make?
Answer:
2
Step-by-step explanation:
If 1 = 1.5
2 = 3
That is the answer
Answer: 3 cups will make 4.5 cups of cooked rice.
Step-by-step explanation: 3 * 1.5
Classify the following triangle. Check all that apply.
A. Right
B. Acute
C. Equilateral
D. Scalene
E. Obtuse
F. Isosceles
Solve for x: 2x-1-x+3=5
Answer:
given
2x-1-x+3=0
x+2=0
x= -2
hope it helps you mate
please mark me as brainliast...
Answer:
2x-1-x+3=5
subtract 3 both sides
add 1 both sides
after that now its
2x-x=3
2x-x= x
x=3 thats the answer
Which of the following list contains exactly 2 composite numbers and 2 prime numbers?
A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 31% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution?
Answer:
Explained below.
Step-by-step explanation:
A Binomial experiment has the following properties:
There are a fixed number of trials (n). Each trial are independent of the others. Each trial has only two outcomes: Success and Failure Each trial has the same probability of success (p).If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.
The number of employees selected is, n = 20.
Every employees response is independent of the others.
Each employees response is either: Yes or No.
The probability of an employee responding as "yes" is, p = 0.31.
Thus, the experiment being performed is a binomial experiment.
So, the probability distribution for the number of employees believing their company president has low ethical standards can be modelled by a binomial probability distribution.
But the number of years of experience cannot be modelled by a binomial probability distribution. Because every employee will have different answer for this question.