Answer:
The length that separates the top 8% is of 5.2162 centimeters, and the length that separates the bottom 8% is of 5.1038 centimeters.
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.
Mean of 5.16 centimeters and a standard deviation of 0.04 centimeters.
This means that [tex]\mu = 5.16, \sigma = 0.04[/tex]
Length that separates the top 8%
The 100 - 8 = 92th percentile, which is X when Z has a p-value of 0.92, so X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 5.16}{0.04}[/tex]
[tex]X - 5.16 = 1.405*0.04[/tex]
[tex]X = 5.2162[/tex]
Length that separates the bottom 8%
This is the 8th percentile, which is X when Z has a p-value of 0.08, so X when Z = -1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.405 = \frac{X - 5.16}{0.04}[/tex]
[tex]X - 5.16 = -1.405*0.04[/tex]
[tex]X = 5.1038[/tex]
The length that separates the top 8% is of 5.2162 centimeters, and the length that separates the bottom 8% is of 5.1038 centimeters.
67 2/3% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs?
Answer:
2/3
Step-by-step explanation:
2/3 is 66 2/3%
Diana is going to roll a 6-sided die. What's the probability she will role a 4 or
a 5? *
The probability of rolling any one number on a 6 sided die is 1/6
The probability of rolling a 4 is 1/6
The probability of rolling a 5 is 1/6
The probability of rolling a 4 or a 5 is the probability of rolling a 4 plus the probability of rolling a 5:
1/6 + 1/6 = 2/6 = 1/3
The answer is 1/3
Tính (1,5)4; ((-2)/3)3; (√3)5.
Step-by-step explanation:
câu trả lời là trong bức ảnh trên
please help its urgent
Answer:
Step-by-step explanation:
18x-6=120
18x=120+6
18x=126
x=126÷18
x=7
Is 69 square routed a even number
In mixture A of candy ingredients there are 3 parts of milk-chocolate for every Z parts peanut separate mixture B. there are 4 parts of nougat for every 3 parts of caramel equat parts of A and combined in one mixing bow what is the ratio of peanut butter to nougat in the bowl
Answer:
D. 7:10
Step-by-step explanation:
The Correct Answer
Select all the correct answers.
These examples show the application of the negative exponent property. Which two examples correctly apply this property?
Answer:
First one and Third one
Step-by-step explanation:
Answer is correct from Plato
The correct expressions are:
[tex]17^{-1/4}[/tex] [tex]= \frac{1}{17^{1/4}}[/tex]
[tex]y^{1/2}[/tex] [tex]= \frac{1}{y^{-1/2}}[/tex]
In the given expression,
Since we know that the rule of exponent,
[tex]a^{-n} = \frac{1}{a^n}[/tex]
Therefore,
For the given expression,
[tex]17^{-1/4}[/tex]
Using the above property of exponent we can write it,
[tex]= \frac{1}{17^{1/4}}[/tex]
Hence this is the correct expression.
For the given expression,
[tex]y^{1/2}[/tex]
Using the above property of exponent we can write it,
[tex]= \frac{1}{y^{-1/2}}[/tex]
Hence this is the correct expression.
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Find the length of side x
Answer:
Step-by-step explanation:
tan(30) = x/1
sqrt(3) / 3 = x/1
x= sqrt(3) / 2
The ice cream man just ended his shift for the day. Let 1/2x^2 6/11x + 8 represent the amount of chocolate ice cream bars he sold. Let 5/9x^2 + 2/3 represent the amount of vanilla ice cream bars he sold. Finally let 1/3x^2 + 4x + 4/3 represent the amount of strawberry ice cream bars he sold. Select all the statements that are true
a. The total amount of ice cream bars sold can be represented by the expression 25/18x^2+ 50/11x +10
b. The total amount of ice cream bars sold can be represented by the expression 25/18x^2 + 172/33x +28/3
c. He sold 1/6x^2 + 50/11x + 28/3 more chocolate than strawberry ice cream bars.
d. He sold 1/6x^2 - 38/11x + 20/3 more chocolate than strawberry ice cream bars.
Answer:
A and D
Step-by-step explanation:
Total ice cream bars sold = sum of chocolate sold , vanilla and strawberry ice-creams sold.
=(1/2)x2 + (6/11)x + 8 + (5/9)x2 + (2/3) +(1/3)x2 + 4x +(4/3) (Given in the question)
=(25/18)x2 + (50/11)x + 10 (Adding terms corresponding to x2,x ,constant respectively)
Difference in chocolate and strawberry bars =[ (1/2)x2 + (6/11)x + 8] - [(1/3)x2 + 4x +(4/3)]
= (1/6)x2 - (38/11)x +(20/3)
So, the correct options are A and D
Which of the following represents the factorization of the trinomial below?
x2 - 14x + 49
O A. (x-7)
O B. (x-7)(x+7)
O C. (x+7)
O D. (x+2)(x+7)
ANSWER ASAP!!
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: ( {x - 7})^{2} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] {x}^{2} - 14x + 49[/tex]
[tex] = {x}^{2} - 7x - 7x + 49[/tex]
Taking "[tex]x[/tex]" as common from first two terms and "7" from last two terms, we have
[tex] = x \: ( \: x - 7 \: ) - 7 \: ( \: x - 7 \: )[/tex]
Taking the factor [tex](x-7)[/tex] as common,
[tex] = ( \: x - 7\:) \: (\: x - 7\: )[/tex]
[tex] =( {x - 7})^{2} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
WILL GIVE BRAINLIEST Solve for x
Answer:
Step-by-step explanation:
sin x° = [tex]\frac{17}{19}[/tex]
x° = [tex]sin^{-1}[/tex] [tex]\frac{17}{19}[/tex]
x° ≈ 63°
Which expression can be modeled using the number line?
Answer:
7 x 1/10 = 7/10
Step-by-step explanation:
There are 7 "bumps" on the number line, and each "bump" moves the line 1/10.
This can also be modeled as
1/10 + 1/10 + 1/10 +1/10 +1/10 +1/10 +1/10 = 7/10
ANYONE KNOW THE ANSWER TO THIS??
Answer:
x = 14 is your answer
Step-by-step explanation:
76 = 7x-22, so to figure it out, you first move -22 to the other side and get
76+22 = 7x.
add them together and you get 98 = 7x
7x would be your equation, so divide 98 by 7 and you get your solution
x = 14 is your answer
A box has three balls, one white and two red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:
a. Let F= the event of getting the white ball twice.
b. Let G= the event of getting two balls of different colors.
c. Let H= the event of getting white on the first pick.
d. Are F and G mutually exclusive?
e. Are G and H mutually exclusive?
Answer:
See explaation
Step-by-step explanation:
Given
Represent the balls with the first letters
[tex]W =1[/tex]
[tex]R =2[/tex]
Solving (a): P(F) --- White balls twice
The event of F is:
[tex]F = \{(W,W)\}[/tex]
So:
[tex]P(F) = P(W) * P(W)[/tex]
[tex]P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(F) = \frac{1}{3} * \frac{1}{3}[/tex]
[tex]P(F) = \frac{1}{9}[/tex]
Solving (b): P(G) --- two different colors
The event of G is:
[tex]G = \{(W,R),(R,W)\}[/tex]
So:
[tex]P(G) = P(W) * P(R) + P(R) * P(W)[/tex]
[tex]P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(G) = \frac{1}{3} * \frac{2}{3} + \frac{2}{3} * \frac{1}{3}[/tex]
[tex]P(G) = \frac{2}{9} + \frac{2}{9}[/tex]
[tex]P(G) = \frac{4}{9}[/tex]
Solving (c): P(H) --- White picked first
The event of H is:
[tex]H = \{(W,R),(W,W)\}[/tex]
So:
[tex]P(H) = P(W) * P(R) + P(W) * P(W)[/tex]
[tex]P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(H) = \frac{1}{3} * \frac{2}{3} + \frac{1}{3} * \frac{1}{3}[/tex]
[tex]P(H) = \frac{2}{9} + \frac{1}{9}[/tex]
[tex]P(H) = \frac{3}{9}[/tex]
[tex]P(H) = \frac{1}{3}[/tex]
Solving (d): F and G, mutually exclusive?
We have:
[tex]F = \{(W,W)\}[/tex]
[tex]G = \{(W,R),(R,W)\}[/tex]
Check for common elements
[tex]n(F\ n\ G) = 0[/tex]
Hence, F and G are mutually exclusive
Solving (e): G and G, mutually exclusive?
We have:
[tex]G = \{(W,R),(R,W)\}[/tex]
[tex]H = \{(W,R),(W,W)\}[/tex]
Check for common elements
[tex]n(G\ n\ H) = 1[/tex]
Hence, F and G are not mutually exclusive
four times the difference of 15 and 6
Answer:
36
Step-by-step explanation:
9 is the difference
9 times 4 is 36
Subtraction is a mathematical operation. The statement "Four times the difference of 15 and 6" is equal to 36.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The statement "Four times the difference of 15 and 6" can be expressed as,
= 4 × (15 - 6)
= 4 × (9)
= 36
Hence, The statement "Four times the difference of 15 and 6" is equal to 36.
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find the equation of straight line passing through each of the following pairs of points
a) (2,4) and (7,2)
Answer:
The equation of the line is [tex]y = -\frac{2}{5}x + \frac{24}{5}[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Slope:
Having two points, the slope is given by the change in y divided by the change in x. Points (2,4) and (7,2), so:
Change in y: 2 - 4 = -2
Change in x: 7 - 2 = 5
Slope: [tex]m = \frac{-2}{5} = -\frac{2}{5}[/tex]
So
[tex]y = -\frac{2}{5}x + b[/tex]
(2,4)
This means that when [tex]x = 2, y = 4[/tex]. So
[tex]y = -\frac{2}{5}x + b[/tex]
[tex]4 = -\frac{2}{5}(2) + b[/tex]
[tex]b = 4 + \frac{4}{5} = \frac{20}{5} + \frac{4}{5} = \frac{24}{5}[/tex]
The equation of the line is [tex]y = -\frac{2}{5}x + \frac{24}{5}[/tex]
To solve the equation, Lorie applies the distributive property, combines like terms, then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible coefficients of x after Lorie has completed these steps?
10 (one-half x + 2) minus 5 = 3 (x minus 6) + 1
–32 and 2
–2 and 32
–2 and 2
–32 and 32
Answer:
-2 and -2
Step-by-step explanation:
subtract
a2-b2 from a2 +b2
Answer:
2b^2
Step-by-step explanation:
according to the question equation is
(a^2 + b^2 ) - (a^2 - b^2)
a^2 + b^2 - a^2 + b^2
plus a square and minus a square gets cancel
b^2 + b^2
since they are like terms they can be added
2b^2
Answer:
2b^2
Step-by-step explanation:
according to the question equation is
(a^2 + b^2 ) - (a^2 - b^2)
a^2 + b^2 - a^2 + b^2
= b^2 + b^2
like terms can be added
+2b^2
Please can you help me
Answer:
[tex]x = 24.75[/tex]
Step-by-step explanation:
Required
Find x
To find x, we have:
[tex]\angle PQR + \angle RPQ + \angle QRP = 180[/tex] -- angles in a triangle
Because [tex]\bar {PR}[/tex] is extended to S, then:
[tex]\angle QRS = \angle QRP[/tex]
So, we have:
[tex]2x + 6 + x - 7 + 5x -17 = 180[/tex]
Collect like terms
[tex]2x + x + 5x = 180 + 17 + 7-6[/tex]
[tex]8x = 198[/tex]
Divide by 8
[tex]x = 24.75[/tex]
06.04 find the area of the image below a.24.6 units b.25.8 units c.26.3 units d.27.5 units
What is the answer. I need it ASAP u have to choose 3 answers
Question 1 of 10
The number √3 goes on forever with no repeating pattern; therefore, it is
rational.
A. True
B. False
SUBMIT
Answer:
False
Step-by-step explanation:
Rational number :
A rational number is a number which can be represent as p/q of two integers where q is not equal to zero
Example: 2/3
[tex]\sqrt{3}[/tex] = 17320508075........ and it keeps extending. Since it does not terminate or repeated after the decimal point.
Therefore [tex]\sqrt{3}[/tex] is an irritational number,
Hence given statement is FALSE
A TRIANGLE HAS SIDE LENGTH 3, 8 AND 9. FIND THE ANGLE MEASUREMENTFOR THE ANGLE CROSS FROM THE SIDE WITH LENGTH OF 8.
Answer:tu culo
Step-by-step explanation:
Simplify
x×x×x×у×у and
2×x×x×3×y×y×y
Step-by-step explanation:
1.x³y²
2. 6x²y³
hope it helps
What is the volume in cubic centimeters of the figure below?
Answer:
so that you will multiply 15 * 4.
Step-by-step explanation:
15*4 = 60 now you divide 60 by 4 and the answer will be 15.
I need help please anyone
Answer:
20
Step-by-step explanation:
l*w*h
4*5*1= 20
solve for x 7_3x=2x_3
[tex]7 - 3x = 2x - 3 = [/tex]
[tex]7 - 3x = 2x - 3 \\ 7 - 3x - 2x = - 3 \\ 7 - 5x = - 3 \\ - 5x = - 3 - 7 \\ - 5 = - 10 \\ x = \frac{ - 10}{ - 5} \\ x = 2[/tex]
HOPE IT HELPS!!!I NEED BRAINLIEST ✌️ PLZWhich is equivalent to f/125)*? O 125+ 0 1254 125" C. 125/11
Answer:
I think choose (1)
[tex]125 ^{ \frac{1x}{3} } [/tex]
PLEASE HELP ASAP Determine the period.
Consider a species of bird that can be split into three age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years. The population is observed once a year. Given that the Leslie matrix is equal to
Answer: hello your question lacks some information attached below is the complete question
answer :
a) attached below
b) 65 students aged 1-2 years
Step-by-step explanation:
For a Leslie matrix ; there is a relation
Pn = L^n Po where ; Pn = population vector after n years , Po = initial population vector .
a) Initial population vector
attached below
[tex]\left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]
b) Number of birds aged 1-2 years are available after 10 years
i.e. P10 = L^10 Po
note : Po = Xo
∴ P10 = [tex]\left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]
we will apply MATLAB to resolve the above matrix
P10 = [tex]\left[\begin{array}{ccc}217.91\\65.24\\31.911\end{array}\right][/tex]
∴ Number of children between 1-2 years left after 10 years = 65.24 ≈ 65
The total number of birds aged between 1-2 years which are available after 10 years is 65 and this can be determined by using the Leslie matrix relation.
Given :
Consider a species of bird that can be split into three age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years. [tex]\rm L = \left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right][/tex]According to the given data, the initial population vector is given by:
[tex]x_0 = \left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]
Now, the total number of birds aged between 1-2 years which are available after 10 years is:
[tex]\rm P_{10} = \left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right] \left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]
Now, solve the above matrices in order to determine the value of [tex]\rm P_{10}[/tex].
[tex]\rm P_{10} = \left[\begin{array}{ccc}217.91\\65.24\\31.911\end{array}\right][/tex]
Therefore, the total number of birds aged between 1-2 years which are available after 10 years is 65.
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