The probability of filling a cup between 22 and 33 ounces is 0.9371
The variable here is the machine's output which is normally distributed.
The normal distribution is defined by two parameters, namely, the mean and the standard deviation.
The population mean for this normal distribution is μ = 25 ounces per cup, and a population standard deviation of σ = 4 ounces (per cup).
calculate the z-score using this formula:
z = x-μ/σ
z is the z-score.
x is the raw score.
μ is the population mean.
σ is the population standard deviation.
The probability of filling a cup between 18 and 33 ounces
z = 18-25/4
z = -7/4
z = -1.75
P(Z< - 1.75) = 1 - P(Z > -1.75)
= 1 - 0.9599
= 0.0400
We can proceed in the same way to obtain the z-score and the associated probability with the raw score x = 33. We can see that this value is above the mean (positive).
z = 33-25/4
z = 8/4
z = 2
P(z<2) = 0.9772
P(18<x<33) = 0.9772 - 0.0400
P(18<x<33) = 0.9371
the probability of filling a cup between 22 and 33 ounces is 0.9371
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PLEASE HELP I DONR UNDERSTAND DENSITY CURVES AT ALL
As per the given graph, the correct statement is option (A) The median of the density curve is 3.
Median:
Basically, median refers the middle value in a set of data.
And it can be obtained by organize and order the data from smallest to largest. And to find the midpoint value, divide the number of observations by two. And then if there are an odd number of observations, round that number up, and the value in that position is the median.
Given,
Here we have the graph.
Now, we have to identify in with of the option is correct according to the given graph.
While we looking into the given graph,
We have identified that it form the triangle and as the middle point as 3.
So, based on this fact me have identified that the median density of the curve is 3.
Therefore, the option (A) The median of the density curve is 3.
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Drag the numbers below to put them in order from least to greatest:
6.426.42 6.536.53 6.4976.497 6.66.6 6.4536.453 6.486.48
The numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.
What is number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that the numbers are,6.42,6.53,6.497,6.66,6.453,6.486.
Ascending order refers to a list of numbers that are arranged from least to greatest. The numbers are arranged in ascending order in this form. The first figure must be less than the second figure. It is referred to in descending order when the numbers are listed from greatest to least.
Thus, the numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.
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What is one over four to the fifth power?
one over one thousand twenty-four
one over six hundred twenty-five
five over twenty
six over nine
Elaine roll 2 fair dice . What i the probability of both dice howing a prime number
The probability of both the dice showing prime numbers is 1/4.
Prime numbers:
The numbers which have only two factors, one and itself are known as prime numbers.
A dice has 6 faces numbering from 1 to 6.
Prime numbers from 1 to 6 are 2, 3, and 5.
Probability of one dice showing a prime number
= (number of favorable outcomes) / (total number of outcomes)
= 3/6
= 1/2
Probability of two dice showing a prime number = (1/2) x (1/2)
= 1/4
Therefore, the probability of both the dice showing a prime number is 1/4.
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Describe the transformations that map the
function y = 8* onto each function.
b) y = 84x
d) y = 8-2x
a) y = ( 1⁄2 8×18x
c) y = -8x
In the first function have vertical compression by 1/2, in second function have horizontal compresion by 1/4, in third compression have Vertical reflection and in fourth function have Horizontal reflection and horizontal compression by 1/2.
In the given question we have to find the transformations that map the function y = [tex]8^x[/tex] onto each function.
Since we have to find the transformation, so we know that in a transformation;
The transformation from the first equation to the second one can be found by finding a, h and k for each equation.
[tex]y=ab^{x-h}+k[/tex]
The horizontal is define by the value of h. The horizontal shift is defined as:
g(x)=f(x+h) - The graph is shifted to the left h units.
g(x)=f(x−h) - The graph is shifted to the right h units.
Horizontal Shift: None
The vertical shift define on the value of k. The vertical shift is defined as:
g(x)=f(x)+k - The graph is shifted up k units.
g(x)=f(x)−k - The graph is shifted down k units.
Vertical Shift: None
The value of a describes the vertical stretch or compression of the graph.
a>1 is a vertical stretch
0<a<1 is a vertical compression.
(a) The given first function is [tex](\frac{1}{2})8^{x}[/tex].
y = [tex]8^x[/tex]
Combine [tex]8^x[/tex] and 1/2.
y = [tex]8^x[/tex]/2
Assume that
y = [tex]8^x[/tex] is f(x)=[tex]8^x[/tex] and y= [tex](\frac{1}{2})8^{x}[/tex] is g(x)= [tex](\frac{1}{2})8^{x}[/tex].
On comparing the equation [tex]y=ab^{x-h}+k[/tex]
The value of a, h, and k for f(x)=[tex]8^x[/tex].
a=1, h=0, k=0
The value of a, h and k for g(x)=[tex](\frac{1}{2})8^{x}[/tex].
a=1/2, h=0, k=0
Since the value of h and k so tnere is no horizontal and vertical shift.
SInce the value of a changes from 1 to 1/2 and 1/2 is greater that 0 but less than 1 so there is vertical compression by 1/2.
(b) The given second function is [tex]8^{4x}[/tex].
y= [tex]8^{4x}[/tex] is g(x)= [tex]8^{4x}[/tex].
On comparing the equation [tex]y=ab^{x-h}+k[/tex]
The value of a, h and k for g(x)=[tex]8^{4x}[/tex].
a=1/4, h=0, k=0
Parent Function: f(x)=8^x
So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: None, Vertical Compression or Stretch: None, horizontal compresion by 1/4.
(c) The given third function is [tex]-8^{x}[/tex].
y= [tex]-8^{x}[/tex] is g(x)= [tex]-8^{x}[/tex].
The value of a, h and k for g(x)=[tex]-8^{x}[/tex].
a=-1, h=0, k=0
Parent Function: f(x)=8^x
So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.
Vertical reflection
(d) The given fourth function is [tex]8^{-2x}[/tex].
y= [tex]8^{-2x}[/tex] is g(x)= [tex]8^{-2x}[/tex].
The value of a, h and k for g(x)=[tex]8^{-2x}[/tex].
a=-1/2, h=0, k=0
Parent Function: f(x)=8^x
So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.
Horizontal reflection and horizontal compression by 1/2.
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In the function y = |x² - 4|, for
how many values of x does y = 3?
Answer:
4 answers
Step-by-step explanation:
y = |x² - 4|
3 = |x² - 4|
3 = x² - 4 and -3 = x² - 4
3+4=x² - 4 + 4 and -3+4=x² - 4 + 4
7=x² and 1=x²
x=[tex]\sqrt{7}[/tex] and x=-[tex]\sqrt{7}[/tex] since x²=7
x=-1 and x=1 since x²=1
x= -[tex]\sqrt{7}[/tex], [tex]\sqrt{7}[/tex], -1, 1 ==> 4 answers
Please help me!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
-24
Step-by-step explanation:
-3[-4(3-10)-12]/-2(-1)
-3[-4(-7)-12]/2
-3[28-12]/2
-3[16]/2
-48/2
-24
Hopes this helps
pls check and see if i'm wrong
Answer:
I think you are right.Because im sure
there are 32 students in categories a and b combined; 24 are in a, and 24 are in b. how many are in both a and b?
The number of students that are in both the Categories A and B are 16 students.
In the question ,
it is given that ,
the total number of students in category A and category B is 32 students .
which is represented as A union B ,
that is n(AUB) = 32 ,
the number of students in category A = n(A) = 24
the number of students in category B = n(B) = 24
we need to find the number of students that are in both category ,
that is n(A∩B) .
we know that ,
n(AUB) = n(A) + n(B) - n(A∩B)
Substituting the values , we get
n(A∩B) = 24 + 24 - 32
= 48 - 32
= 16
Therefore , The number of students that are in both the Categories are 16 students.
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a pole that is 3m tall casts a shadow that is 1.4m long. at the same time, a nearby tower casts a shadow that is 39.5m long. how tall is the tower? round your answer to the nearest meter.
The nearby tower that casts a shadow that is 39.5 m long is 85 m tall.
Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.
The ratio of the shadow of a pole to its length is 1.4 m : 3 m.
At the same time, the ratio of the shadow of a tower to its length should also be equal to the ratio of the shadow of a pole to its length, which is 1.4 : 3.
Let x = length of the tower
Using proportion, determine the length of the tower by solving for x.
1.4 : 3 = 39.5 m : x
x = 39.5(3)/1.4
x = 84.64
Round off to the nearest meter.
length of the tower = 85 meters
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teacher: how can we change the base of a logarithm? student:
We can change the base formula by:
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
The change of base formula is used to change the base of a logarithm. We know that "log" stands for a logarithm of base 10 and "ln" stands for a logarithm of base e. But there is no option to calculate the logarithm of a number with any other bases other than 10 and e.
The change of base formula solves this issue of changing base from e to 10, and from base 10 to e. Also, it is used in solving several logarithms problems.
Base Formula: -
The change of base formula is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm. This is a property of logarithms. You can see the change of base formula here.
Change of base formula
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
Change of Base Formula
Change of base formula can be represented as follows. Here the base of the given logarithm is also changed to a logarithm with a new base. The basic logarithm with a base is transformed to two logarithms with a new and same base. The change of base formula is:
logₐ b = [logₐ x] / [logₐ y]
In this formula,
The argument of the logarithm in the numerator is the same as the argument of the original logarithm.The argument of the logarithm in the denominator is the same as the base of the original logarithm.The bases of both logarithms of numerator and denominator should be the same and this base can be any positive number other than 1.Change of Base Formula Derivation
Change of base formula derivation can be understood from the following steps. Let us assume that
log ₐ b = p, logₙ a = q, and logₙ b = r.
By converting each of these into exponential form, we get,
a = [tex]b^{p}[/tex], a = [tex]x^{q}[/tex], and b = [tex]n^{r}[/tex]
From the first two equations,
[tex]x^{q}[/tex] = [tex]n^{r}[/tex]
Substituting b = [tex]n^{r}[/tex] (which is from third equation) here,
([tex]n^{r}[/tex])[tex]^{p}[/tex] = [tex]x^{q}[/tex]
[tex]n^{r}[/tex])[tex]^{p}[/tex] = [tex]x^{q}[/tex](Using a property of exponents)
p r = q
p = q / r
Substituting the values, we get,
logₐ b = [logₐ x] / [logₐ y]
For Example:
Evaluate the value of log₆₄ 8 using the change of base formula.
Solution:
We will apply the change of base formula (by changing the base to 10). Note that log₁₀ is same as log.
log₆₄ 8 = [log 8] / [log 64]
= [log 8] / [log 82]
= [log 8] / [2 log 8] [∵ log am = m log a]
= 1 / 2
Answer: log₆₄ 8 = 1 / 2
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the average starting salary of graduates of a large university (lu) is $20,000 with a standard deviation of $8,000. furthermore, it is known that the starting salaries are normally distributed. if 189 of the graduates have salaries of at least $32,240, how many students graduated from this university?
Total students who graduated this year from this university is 3000.
This is a normal distribution problem with
Mean , μ = $20,000
Standard deviation, σ = $8,000
If 189 of the recent graduates have salaries of at least $32240.
Then, We first find the percentage of LU graduates with salaries more than $32240.
Required probability = P(x ≥ 32240)
We first normalize or standardize $32,240, then as we know,
z = (x - μ)/σ
= (32240 - 20000)/8000 = 1.53
The required probability:
P(x ≥ 32240) = P(z ≥ 1.53)
We'll use data from the normal probability table for these probabilities
P(x ≥ 32240) = P(z ≥ 1.53) = 1 - P(z < 1.53)
= 1 - 0.93699
= 0.06301
= 6.301%
So, 6.301% of the graduates this year = 189
Total Number of graduates this year = (189/0.06301) = 2999.5 = 3000 graduates this year.
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What is the rectangular form of Θ = 3π/4?
x − y = 0
x − y = 1
x + y = 0
x + y = 1
The rectangular form of Θ = 3π/4 will be; y + x = 0.
What are Complex value?Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
On converting the rectangluar to polar form of the complex number;
x = rcosθ and y = rsinθ
z = r(cosθ+isinθ)
r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Given the Θ = 3π/4
Therefore, θ = tan⁻¹y/x = 3π/4
y/x = tan (3π/4)
Now multiply both side by x
yx/x = tan (3π/4) x
y = tan (3π/4) x
Thus, y = -x
in rectangular form y + x = 0
Hence, the rectangular form of Θ = 3π/4 will be; y + x = 0.
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aaliyah went into a grocery store and bought 5 peaches and 6 mangos, costing a total of $17.75. tristan went into the same grocery store and bought 2 peaches and 3 mangos, costing a total of $8. write a system of equations that could be used to determine the price of each peach and the price of each mango. define the variables that you use to write the system.
Answer:
Step-by-step explanation:
Define Variables:
Let p= the price of each peach
Let m=the price of each mango
One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangos cost 6m. The total cost 5p+6m equals $17.75:
5p+6m=17.75
Likewise, if 2 peaches and 3 mangos cost $8, then:
2p+3m=8
Write System of Equations:
5p+6m=17.75
2p+3m=8
System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.
Let p= the price of each peach
Let m=the price of each mango
One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangoes cost 6m. The total cost 5p+6m equals $17.75:
5p+6m=17.75
Likewise, if 2 peaches and 3 mangoes cost $8, then:
2p+3m=8
System of Equations:
5p+6m=17.75
2p+3m=8
Therefore System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.
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What is the value of (−13)4?
52
−52
28,561
−28,561
can anyone please help me? (pic attached)
Answer:
No, Eduardo made a mistake from Step 1 to Step 2. Eduardo should have subtracted 4 from 6 instead of evaluating the exponent. The order of operations says to perform all operations inside parentheses first.
If f (x) = 2x2 + 4x − 3, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
The difference quotient for the given quadratic equation is:
d = (2h + 4x + 4)
How to get the difference quotient for f(x)?Here we have the quadratic function:
f(x)= 2x² + 4x - 3
And we want to get the difference quotient that is defined as:
d = ( f(x + h) - f(x))/(h)
Replacing our function there, we get:
d = ( 2(x + h)² + 4*(x + h) - 3 - (2x² + 4x - 3)/h
d = (2x² + 2h² + 4xh + 4x + 4h - 3 - 2x² - 4x + 3)/h
d = (2h² + 4xh + 4h)/h
d = (2h + 4x + 4)
That is the difference quotient.
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-3/10 + 1 = 10 plsss
Select the correct answer.
Which graph represents this equation?
y − 4 = -3(x + 5)
A. The first graph
B. The second graph
C. The third graph
D. The last graph
( I know it is not the third graph)
what’s the question mark?
Answer:
? ≈ 5.01
Step-by-step explanation:
using the sine ratio in the right triangle
sin24.3° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2.06}{?}[/tex] ( multiply both sides by ? )
? × sin24.3° = 2.06 ( divide both sides by 24.3° )
? = [tex]\frac{2.06}{sin24.3}[/tex] ≈ 5.01 ( to 3 significant figures )
Solve each equation.
9^(x+2)=2^(5x-4)
Value of x is 1.411
Given Eq.
[tex]9^{x+2} = 2^{5x-4} \\\\[/tex]
Applying exponent rules
[tex](x+2)ln(9) = (5x-4)ln(2)\\[/tex]
Solving for x
[tex]x = \frac{4ln(6)}{5ln(2)-2ln(3)}[/tex]
[tex]x = \frac{1.791}{5(0.693)-2(1.098)}[/tex]
[tex]x = \frac{1.791}{3.465-2.196} \\[/tex]
[tex]x = \frac{1.791}{1.269}[/tex]
[tex]x = 1.411[/tex]
Value of x is 1.411
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What is the measure of ZD in the parallelogram below?
Check the picture below.
which of the following is not true of a chi squared test?(a) a chi-squared test can be used if one of the sample cells has a value of less than five
(b) the Chi-square test can be used to test how likely it is that an observed distribution is due to chance.
(c) a chi-square test can be used to analyze nominal data
(d) a chi-squared test can be used to test the probability of independence of a distribution of data
A) Chi-square test can be used if one of the samples has a value of less than five is the correct option.
Chi-square distribution and Chi-square test for independence:
A Chi-square distribution is the sum of squares of the standard normal deviates. The Chi-square test can be used for checking the association between categorical variables.The test can be used to decide whether the effect of one categorical data is dependent on the other variable or not on the basis of the critical value and p-value. The expected frequency of each categorical variable is calculated to compute the test statistic.The assumptions for the chi-square test are:
The frequency of each cell should be at least or more than 5.The variables should be categorical in nature and the observations should be independent of each other.Chi-square test can be used to analyze the nominal or categorical data. It can be used to test whether the observed data fits well with the expected frequency or not. It is used to test the independence of the data distribution by calculating probability.Hence, options (b), (c), and (d) are the assumptions that are true for chi-square test. Therefore, the options (b), (c), and (d) are considered incorrect.
The Chi-square test of independence can be used only if none of the frequencies of the sample cell is less than five.Hence, option (a), that is, “a Chi-square test can be used if one of the samples has a value of less than five” is the correct option.
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Every complex number can be written in the form a+bi. For the complex numbers 8-4i, identify the values of a and b
Answer:
C
Step-by-step explanation:
a baseball diamond is a square with side 90 feet. if a batter hits the ball and runs towards first base with a speed of 25 ft/sec, at what speed is his distance from second base decreasing when he is two thirds of the way to first base?
The rate when his distance from second base changes and it is two third of the way to first base is - 13.86 feet/s.
let us consider the following values
distance between batter to Second base = d feet
distance between batter to First base
= x feet
distance between first to second base
= 90 feet
Using the Pythagorean theorem:
d² = x² + 90²
Knowing that the velocity of the bat to first base is 25 ft/s,
the distance x can be written as: x
= 90 - 25t
The equation for is,d² = 90²+(90 -25t)²--(1)
we want to find the rate of change of d.
let it be d' and from implicit differentiation:
2d.d' = 2(90-24t) × (-25)
d' = -50(90 - 25t) / (2d)
d' = -25 (90 - 24t) / d ---(*)
We can determine t and d from the fact that the batter is two third to his first base: d = √90^2 + 60^2 = √1 = 108.2 feet
putting the values of d in (1) we get,
=> 90 - 25t = 60 => 25t = 30 => t = 6/5.
Substitute d' in the formula equation (*)
d' = -25 (90 - 24t) / d = -25(90-30)/108.2
d'= - 13.86
d' = - 13.86 feet/s
negative sign means decreasing distance from second base (as it approaches the first
bases, it approaches the second base).
Hence,The required speed is 13.86 feet/s
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1) How long will it take for the population of a certain country to double if its annual growth rate is 2%? Round to the nearest year.
Answer:
For example, a population with a 2% annual growth would have a doubling time of 35 years.Mar 24, 2015
Step-by-step explanation:
I need help ASAP!!!!!!!
Step-by-step explanation:
in that setup they will both explode after traveling the same distance.
A is just going faster and has to launch therefore a little bit later.
so, we need to make an equation based on distance traveled and find in that process the number of seconds needed to travel that distance.
speed is distance/time, so we need to multiply speed by time to get distance.
x = seconds for B
x - 0.25 = seconds for A
A is launched after B but explodes at the same time.
so, A's trip is of shorter time than B's trip.
(x - 0.25)×360 = x×320
360x - 90 = 320x
40x - 90 = 0
40x = 90
4x = 9
x = 9/4 = 2.25 seconds
both fireworks will explode 2.25 seconds after B launches (and 2.25 - 0.25 = 2 seconds after A launches).
the explosion will be at
320×2.25 = 360×2 = 720 feet height.
On a straight road, Jorge is 7 kilometers east of Peter, Jason is
10 kilometers west of Juan, and Juan is 13 east of Peter. how
many miles is Jorge from Jason?
Answer:
7x10x13=910=910 kilograms
Step-by-step explanation:
PLEASE HELP ME I FEEL LIKE THIS SHOULD BE SUPER EASY BUT MY BRAIN CAN NOT RN
Answer:
x = 62
y = 41
Step-by-step explanation:
y + 21 = x
x + y + 77 = 180
2y+77 = 180
2y = 82
y = 41
x = 62
Can anybody solve this for me?
Answer:
y = x + 6
Step-by-step explanation:
y = mx + c
2 = -4m + c
-2 = -8m + c
2 + 4m = c
-2 = -8m + 2 + 4m
-2 - 2 = -4m
-4 = -4m
-4/-4 = m
m = 1
2 + 4(1) = c
c = 6
y = x + 6