Answer:
The proportion of bottles that will have more than 30 ounces dispensed into them is 0.9772 = 97.72%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The amount dispensed has been observed to be approximately normally distributed with mean 32 ounces and standard deviation 1 ounce.
This means that [tex]\mu = 32, \sigma = 1[/tex]
Determine the proportion of bottles that will have more than 30 ounces dispensed into them.
This is 1 subtracted by the p-value of Z when X = 30, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 32}{1}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
1 - 0.0228 = 0.9772
The proportion of bottles that will have more than 30 ounces dispensed into them is 0.9772 = 97.72%.
State if the scenario involves a permutation or a combination. Then find the number of possibilities.
The student body of 290 students wants to elect a president and vice president.
Permutation/Combination:
Answer:
Answer:
Permutation. ; 83810 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 members (president and vice president) from 290 ; since order of arrangement does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
290P2 = 290! ÷ (290 - 2)!
290P2 = 290! ÷ 288!
290P2 = (290 * 289) = 83810 ways
Find the line integral with respect to arc length ∫C(9x+5y)ds, where C is the line segment in the xy-plane with endpoints P=(2,0) and Q=(0,7).
(a) Find a vector parametric equation r⃗ (t) for the line segment C so that points P and Q correspond to t=0 and t=1, respectively
(b) Rewrite integral using parametrization found in part a
(c) Evaluate the line integral with respect to arc length in part b
(a) You can parameterize C by the vector function
r(t) = (x(t), y(t) ) = P (1 - t ) + Q t = (2 - 2t, 7t )
where 0 ≤ t ≤ 1.
(b) From the above parameterization, we have
r'(t) = (-2, 7) ==> ||r'(t)|| = √((-2)² + 7²) = √53
Then
ds = √53 dt
and the line integral is
[tex]\displaystyle\int_C(9x(t)+5y(t))\,\mathrm ds = \boxed{\sqrt{53}\int_0^1(17t+18)\,\mathrm dt}[/tex]
(c) The remaining integral is pretty simple,
[tex]\displaystyle\sqrt{53}\int_0^1(17t+18)\,\mathrm dt = \sqrt{53}\left(\frac{17}2t^2+18t\right)\bigg|_{t=0}^{t=1} = \boxed{\frac{53^{3/2}}2}[/tex]
In this diagram,which equation could prove to be true in order to conclude that the lines are parallel?
Answer:
b/a = c/d (first option)
Step-by-step explanation:
Two lines:
f(x) = a*x +b
g(x) = m*x + s
are parallel if m = a, and s ≠ b.
So the lines must have the same slope and different y-intercept.
For the graphed lines is obvious that the y-intercepts are different, so let's look at the slopes.
Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
slope = (y₂ - y₁)/(x₂ - x₁)
So now let's look to our lines.
The top one, passes through (-a, 0) and (0, b)
Then its slope is:
a₁ = (b - 0)/(0 - (-a)) = b/a
The bottom line passes through the points (0, -c) and (d, 0)
Then the slope will be:
m₁ = (0 - (-c))/(d - 0) = c/d
Then the lines will be only parallel if the slopes are equal, which means that we must have
b/a = c/d
The correct option is the first one.
Please show work will mark you brainliest!
QUESTION:- An artist uses 200 tiles to create a tessellation design that covers a rectangle with dimensions 2 ft by 3 ft. He will cover a wall with dimensions 10 ft by 15 ft using the same design and tiles of the same size. How many tiles will he need to cover the entire wall?
ANSWER:-
CASE 1 :- NUMBER OF TILES USED -> 200AREA WHICH IS TO BE COVERED-> 2×3 ft² (given-> rectangle)CASE 2:-
AREA WHICH IS TO BE COVERED-> 10×15 ft² (given-> rectangle)NUMBER OF TILES:- TO FINDIT IS GIVEN THAT DESIGN AND SIZE OF TILES R SAME SO WE CAN CONSIDER THAT SAME NUMBER OF TILES WILL COVER SAME AREA IN BOTH CASE.
WE CAN USE UNITARY METHOD FOR SOLVING THIS:-
[tex]6ft² \: is \: covered \: using \: 200 \: tiles \\ 1ft² \: is \: covered \: using \: \frac{200}{6} \: tiles \\ 150ft² \: is \: covered \: using \: \frac{200 \times 150}{6} \: tiles \\ 150ft² \: is \: covered \: using \: \frac{200 \times \cancel{150}^{ \: \: 25} }{ \cancel6 {}^{ \: 1} } \: tiles \\ 150ft² \: is \: covered \: using \: 200 \times 25 \: tiles \\ 150ft² \: is \: covered \: using \: 5000 \: tiles[/tex]
The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student will answer to any one of Exam problems correctly. If the number of attempts for each question is unlimited, find the following probabilities
a. The student will correctly answer the first question after the 4th attempt.
b. The student will correctly answer three questions after 10 total attempts.
c. What is the average number and SD of attempts up to when the student answers all the questions correctly?
Solution :
a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.
P (correct in the 4th attempt)
= [tex]$(1-0.75)^3 \times 0.75$[/tex]
= 0.01171875
b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.
P( X = 3) for X = B in (n = 10, p = 0.75)
= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]
= 0.0031
c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :
There are = 6 success, p = 0.75.
Therefore, this is a case of a negative binomial distribution.
[tex]$E(X)=\frac{k}{p}$[/tex]
[tex]$=\frac{6}{0.75}$[/tex]
= 8
So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]
[tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]
= 1.6330
When is it appropriate to use the two-sample t-methods instead of the one sample t-methods? Choose the correct answer below. A. Use the two-sample t-methods when a sample was taken from each of two populations (i.e. two groups being compared) and the population standard deviations are not known. Use the one-sample t-methods when a sample was taken from one population. B. Use the two-sample t-methods when a random sample was not taken. Use the one-sample t-methods when a random sample was taken. C. Use the two-sample t-methods when the conditions for inference using the one-sample t-methods aren't satisfied. D. Use the two-sample t-methods when the population standard deviation is known. Use the one-sample t-methods when the population standard deviation is not known.
Answer:
A. Use the two-sample t-methods when a sample was taken from each of two populations (i.e. two groups being compared) and the population standard deviations are not known.
Step-by-step explanation:
T-distribution:
When the population standard deviation is not known, the t-distribution is used.
If a sample was taken from one population, we use the one-sample method, while if there is a comparison of two populations, the two-sample method is used, and thus, the correct answer is given by option A.
Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west at 18 mi/h. At what rate (in mi/h) is the distance between the cars increasing two hours later
Answer:
The rate at which the distance between the two cars is increasing is 30 mi/h
Step-by-step explanation:
Given;
speed of the first car, v₁ = 24 mi/h
speed of the second car, v₂ = 18 mi/h
Two hours later, the position of the cars is calculated as;
position of the first car, d₁ = 24 mi/h x 2 h = 48 mi
position of the second car, d₂ = 18 mi/h x 2 h = 36 mi
The displacement of the two car is calculated as;
displacement, d² = 48² + 36²
d² = 3600
d = √3600
d = 60 mi
The rate at which this displacement is changing = (60 mi) / (2h)
= 30 mi/h
Evaluate lim
x→0+
√x ln x
Answer:
vr
Step-by-step explanation:
konho bi m
Mr. Lamb has three children: two girls and one boy. After each meal, one child is chosen at random to wash dishes. Determine the probability that one boy and one girl will wash dishes after lunch and dinner on Saturday.You roll a die twice and add up the dots to get a score. What is the probability that your score is a multiple of 5?
Answer:
1/2 in fractions if you nees it in decimal just transfer
What is the equation of the parabola shown in the graph?
Answer:
[tex]-\frac{x^{2} }{4}[/tex] -2x - 7
Step-by-step explanation:
Never seen a phone with 3 cameras before or something but ok.
Took a while to use brainly's insert character thingie since fractions and the exponent kinda threw me off.
Use the given information to determine which of the following relationships
can be proved and why.
L= 20
ME ZP
ML = PO
A. ALMN - A OPQ, because of AAS.
B. ALMNE A OPQ, because of ASA.
C. We cannot prove any relationship based on these data.
D. ALMN=A OPQ, because of SAS,
Answer:
B. ∆LMN ≅ ∆OPQ because of ASA
Step-by-step explanation:
Two triangles are congruent if two angles and an included side of one triangle are congruent to two corresponding angles and a corresponding included side of the other.
From the information given, we have:
Two angles (<L and <M) in ∆LMN that are congruent to two corresponding angles (<O and <P) in ∆OPQ.
Also, included side in both triangles are congruent (ML ≅ PO).
Therefore, ∆LMN ≅ ∆OPQ by the ASA Theorem.
Question 1 of 10
What is the value of n?
144
O A. 36
O B. 23
O C. 95°
D. 590
Answer:
Option C, 95°
Step-by-step explanation:
180-121 = 59
180-144 = 36
third angle of the triangle is, 180-59-36 = 85,
missing angle n = 180-85 = 95°
Answered by GAUTHMATH
a special window in the shape of a rectangle with semicircles at each end is to be constructed so that the outside perimeter is 100 feet. find the dimensions of the rectangle tha tmaximizes the total area of the window
Answer:
The dimensions of the rectangle are length 25 feet and width 15.92 feet
Step-by-step explanation:
Let L be the length of the rectangle and w be the width.
The area of the rectangular part of the shape is Lw while the area of the two semi-circular ends which have a diameter which equals the width of the rectangle is 2 × πw²/8 = πw²/4. The area of each semi-circle is πw²/4 ÷ 2 = πw²/8
So, the area of the shape A = Lw + πw²/4.
The perimeter of the shape, P equals the length of the semi-circular sides plus twice its length. The length of a semi-circular side is πw/2. So, both sides is 2 × πw/2 = πw
P = πw + 2L
Since the perimeter, P = 100 feet, we have
πw + 2L = 100
From this L = (100 - πw)/2
Substituting L into A, we have
A = Lw + πw²/4.
A = [(100 - πw)/2]w + πw²/4.
A = 50w - πw²/2 + πw²/4.
A = 50w - πw²/2
Now differentiating A with respect to w and equating it to zero to find the value of w which maximizes A.
So
dA/dw = d[50w - πw²/2]/dw
dA/dw = 50 - πw
50 - πw = 0
πw = 50
w = 50/π = 15.92 feet
differentiating A twice to get d²A/dw² = - π indicating that w = 50/π is a value at which A is maximum since d²A/dw² < 0.
So, substituting w = 50/π into L, we have
L = (100 - πw)/2
L = 50 - π(50/π)/2
L = 50 - 50/2
L = 50 - 25
L = 25 feet
So, the dimensions of the rectangle are length 25 feet and width 15.92 feet
Working at home: According to the U.S Census Bureau, 34% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 170 were college graduates. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is .
Answer:
The answer is "0.340".
Step-by-step explanation:
[tex]n = 500\\\\x = 170[/tex]
Using formula:
[tex]\to \hat{p} = \frac{x}{n} = \frac{170}{500}=\frac{17}{50} =0.340[/tex]
In how many different ways can the letter of word
CORPORATION" be
arranged. So that the vowel always
come together"
Answer:
= 6 ways = Required number of ways = (120×6)=720
Which quadrilateral has equal diagonals
Select one:
a. trapezoid
b. rectangle
c. parallelogram
d. rhombus
Answer:
Option b: Rectangle
Explanation:
Give branliest pls ;)
Armando planted a 9-inch tall magical beanstalk. The height of the beanstalk increases by 13% each day. Write a function f that determines the height of the beanstalk in inches in terms of the number of days t since Armando planted the beanstalk.
Answer:
F(t) = 9(1 + 0.13)^t
Step-by-step explanation:
Given :
Height of beanstalk = initial height = 9 inches
Percentage increase in height per day = 13%
This plant exhibits an exponential increase in growth per day, hence, the function will be modeled using an exponential function.
Using an exponential function :
F(t) = initial height(1 + percentage increase)^t
Where, t = number of days since tree was planted.
The function is :
F(t) = 9(1 + 0.13)^t
 In one of the examples he is working on, he knows that the two coordinates (0,6) and
(8, 10) are on the function that he is deriving. Using the information from these two
coordinates, determine the slope and y-intercept of the function Mike is looking for, and
then write out the correct function.
9514 1404 393
Answer:
y = 1/2x + 6
Step-by-step explanation:
The slope m is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (10 -6)/(8 -0) = 4/8 = 1/2
The y-intercept is given by the formula ...
b = y -mx
b = 6 -(1/2)(0) = 6
Then the slope-intercept equation is ...
y = mx +b
y = 1/2x +6
Which of the following represents the factorization of the trinomial below?
- 4x3 - 4x2 +24 x
O A. -4(x2-2)(x+3)
B. -4(x2 + 2)(x+3)
O C. -4x(x + 2)(x+3)
D. -4x(x - 2)(x+3)
Answer:
D. -4x(x - 2)(x+3)
Step-by-step explanation:
We are given the following trinomial:
[tex]-4x^3 - 4x^2 + 24x[/tex]
-4x is the common term, so:
[tex]-4x(\frac{-4x^3}{-4x} - \frac{4x^2}{-4x^3} + \frac{24x}{-4x}) = -4x(x^2+x-6)[/tex]
The second degree polynomial can also be factored, finding it's roots.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
x² + x - 6
Quadratic equation with [tex]a = 1, b = 1, c = -6[/tex]
So
[tex]\Delta = 1^{2} - 4(1)(-6) = 25[/tex]
[tex]x_{1} = \frac{-1 + \sqrt{25}}{2} = 2[/tex]
[tex]x_{2} = \frac{-1 - \sqrt{25}}{2} = -3[/tex]
So
[tex]x^2 + x - 6 = (x - 2)(x - (-3)) = (x - 2)(x + 3)[/tex]
The complete factorization is:
[tex]-4x(x^2+x-6) = -4x(x - 2)(x + 3)[/tex]
Thus the correct answer is given by option d.
find the product of 8×53×(-125) by using suitable property
Answer:
-53,000
Step-by-step explanation:
Now to find this answer you use the PEMDAS rule now that stands for:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Now the first thing that you do is look for the parenthesis now there is but there is no equation in that so we go to the next one exponents and there are no exponents. So we go to the multiplication and we multiply everything and that is how you get that answer.
Hope it helped!
The lines shown below are parallel. If the green line has a slope of 5, what is a
the slope of the red line?
Answer:
A. 5
Step-by-step explanation:
Parallel lines have the same slope.
Answer:
5
Step-by-step explanation:
WORTH 15 POINTSSSSSSSSS
Answer:
15
Step-by-step explanation:
Difference in distances = 75-60 = 15 miles
So Car A travels 15 miles more than Car A in an hour
Answered by Gauthmath
I need help on this math problem
Answer:
for the first one, simply add g(x) and h(x) :
x+3 + 4x+1 = 5x + 4
the second one, you would multiply them :
(x+3)(4x+1) = 4x^2 + 13x + 3
the last one, you would subtract :
(x+3)-(4x+1) = -3x + 2
and then substitute 2 for 'x' :
-3*2 + 2 = -6 + 2 = -4
Answer:
1. 5x+4
2. [tex]4x^2+13x+3[/tex]
3. -4
Step-by-step explanation:
1. (x+3)+(4x+1)
Take off the parentheses and Add.
5x+4
2. (x+3)(4x+1)
Use the FOIL method to multiply.
[tex]4x^2+x+12x+3[/tex]
[tex]4x^2+13x+3[/tex]
3. First, set up the equation as (g-h)(x)
(x+3)-(4x+1)
x+3-4x-1
Solve.
-3x+2
Substitute in 2 for x.
-3(2)+2
-6+2
-4
Which of the following are exterior angles? Check all that apply.
Answer:
<5
Step-by-step explanation:
exterior angles + the corresponding interior angle of the triangle = 180º or a straight angle
the only exterior angle shown in the diagram is <5, which corresponds to the interior <2
hope this helps!
Answer:
<5
Step-by-step explanation:
everything else is matched up perfectly so it has to be <5
95% confident that the true mean difference in mean crying time after being given a vitamin K shot between infants using conventional methods and infants held by their mothers is between ____________and ___________________. In other words, the mean crying time of infants given vitamin K shot using conventional methods is anywhere from ______________ less than to _______________more than the mean crying time of infants given vitamin K shot using new methods.
Solution :
Two sample T-test and CI : Conventional methods, New methods
Two sample T for conventional method Vs new method
N Mean StDev Se Mean
Conventional mean 30 35.3 20.8 3.8
New methods 30 35.1 22.3 4.1
Difference = μ (conventional method) - μ (new method)
Estimate for difference : 0.17
95% CI for difference : (-10.976, 11.309)
T-Test of difference = 0(vs <): T-value = 0.03 P-value =0.5119 DF = 57
95% confident that the true mean difference in mean crying time after being given a vitamin K shot between infants using conventional methods and infants held by their mothers is between -10.976 and 11.309. In other words, the mean crying time of infants given vitamin K shot using conventional methods is anywhere from -10.976 less than to 11.309 more than the mean crying time of infants given vitamin K shot using new methods.
A group of friends try out a new game that uses a pair of ordinary, fair dice. Points are given to players based on the sum of the two numbers from the rolled pair of dice. If the sum is between 2 and 5, inclusive, the amount of points awarded is the sum minus 1. If the sum is between 6 and 9, inclusive, the amount of points awarded is the sum minus 3. If the sum is between 10 and 12, inclusive, the amount of points awarded is the sum minus 5. Calculate the probability of earning exactly 5 points.
Answer:
0.2222 = 22.22% probability of earning exactly 5 points.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Possible outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
If the sum is between 6 and 9, inclusive, the amount of points awarded is the sum minus 3.
Sum of 8 -> 5 points awarded. So
(2,6), (3,5), (4,4), (5,3), (6,2): 5 outcomes.
If the sum is between 10 and 12, inclusive, the amount of points awarded is the sum minus 5.
Sum of 10 -> 5 points awarded. So
(4,6), (5,5), (6,4): 3 outcomes.
Desired outcomes:
5 + 3 = 8
Calculate the probability of earning exactly 5 points.
[tex]p = \frac{D}{T} = \frac{8}{36} = 0.2222[/tex]
0.2222 = 22.22% probability of earning exactly 5 points.
What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward?
A)
K′ = (–2,0), L′ = (1,0), M′ = (1,–3), N′ = (–2,–3)
B)
K′ = (–2,2), L′ = (1,2), M′ = (1,–1), N′ = (–2,–1)
C)
K′ = (–0,0), L′ = (3,0), M′ = (3,–1), N′ = (0,–1)
D)
K′ = (–2,–2), L′ = (1,–2), M′ = (1,–5), N′ = (–2,–5)
9514 1404 393
Answer:
B) K′ = (–2,2), L′ = (1,2), M′ = (1,–1), N′ = (–2,–1)
Step-by-step explanation:
Translation 2 units right adds 2 to the x-coordinate.
Translation 4 units upward adds 4 to the y-coordinate.
The translation can be represented by the relation ...
(x, y) ⇒ (x +2, y +4)
__
You can choose the correct answer by looking at the translation of K.
K(-4, -2) ⇒ K'(-4+2, -2+4) = K'(-2, 2) . . . . . matches choice B
The graph shows the distribution of the number of text messages young adults send per day. The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.
A graph titled daily text messaging has number of text on the x-axis, going from 8 to 248 in increments of 30. Data is distributed normally. The highest point of the curve is at 128.
What percentage of young adults send between 68 and 158 text messages per day?
34%
47.5%
81.5%
95%
This value is approximate.
====================================================
Explanation:
We have a normal distribution with these parameters
mu = 128 = population meansigma = 30 = population standard deviationThe goal is to find the area under the curve from x = 68 to x = 158, where x is the number of text messages sent per day. So effectively, we want to find P(68 < x < 158).
Let's convert the score x = 68 to its corresponding z score
z = (x-mu)/sigma
z = (68-128)/30
z = -60/30
z = -2
This tells us that the score x = 68 is exactly two standard deviations below the mean mu = 128.
Repeat for x = 158
z = (x-mu)/sigma
z = (158-128)/30
z = 30/30
z = 1
This value is exactly one standard deviation above the mean
-------------------------------------------
The problem of finding P(68 < x < 158) can be rephrased into P(-2 < z < 1)
We do this because we can then use the Empirical rule as shown in the diagram below.
We'll focus on the regions between z = -2 and z = 1. This consists of the blue 13.5% on the left, and the two pink 34% portions. So we will say 13.5% + 34% + 34% = 81.5%
Approximately 81.5% of the the population sends between 68 and 158 text messages per day. This value is approximate because the percentages listed in the Empirical rule below are approximate.
Answer:
C. 81.5%
Step-by-step explanation:
X+y=11
Graphing which function
Answer:
Step-by-step explanation:
slopee -1
y-intercept (0,11)
x y
0 11
1 10
true or false?
please help me out
Answer:
true
Step-by-step explanation:
the incenter of a triangle is the common intersection of the angle bisectors.hence always remains inside the triangle.
