Mariyam is designing shelves for a bookshop. The height, H cm, of books is modelled by the normal distribution with mean 25.1 cm and standard deviation 5.5 cm.
(a) Complete the statement H ~ N(_____, _____)
(b) Show that P(H > 30.8) = 0.15 correct to 2 decimal places.
(c) Hence find P(30.8 < H < 40.5).
Mariyam decided that the smallest 5% of books would not be placed on the shelves.
All the other books will be placed on the shelves.
(d) Using ( < ) = 0.005, find the minimum height of books (y) that will be placed on the shelves.
Answers
Answer:
its c
Step-by-step explanation:
Related Questions
When "b" = 6, solve for "a" using the following formula: a2 = 2b + 1
Answers
Answer:
sqrt(13)
Step-by-step explanation:
Assuming by a2 you mean a squared:
a^2=2b+1
a^2=2(6)+1
a^2=13
a=sqrt(13)
(if by a2 you mean 2*a then a=6.5)
Suppose that the functions q and r are defined as follows.
g(x)=x² +5
r(x)=√x+7
Find the following.
(roq)(2) = 0
&
X
(q or)(2) =
5
?
Answers
Answer:
(r o g)(2) = 4
(q o r)(2) = 14
Step-by-step explanation:
Given
\(g(x) = x^2 + 5\)
\(r(x) = \sqrt{x + 7}\)
Solving (a): (r o q)(2)
In function:
(r o g)(x) = r(g(x))
So, first we calculate g(2)
\(g(x) = x^2 + 5\)
\(g(2) = 2^2 + 5\)
\(g(2) = 4 + 5\)
\(g(2) = 9\)
Next, we calculate r(g(2))
Substitute 9 for g(2)in r(g(2))
r(q(2)) = r(9)
This gives:
\(r(x) = \sqrt{x + 7}\)
\(r(9) = \sqrt{9 +7{\)
\(r(9) = \sqrt{16}\){
\(r(9) = 4\)
Hence:
(r o g)(2) = 4
Solving (b): (q o r)(2)
So, first we calculate r(2)
\(r(x) = \sqrt{x + 7}\)
\(r(2) = \sqrt{2 + 7}\)
\(r(2) = \sqrt{9}\)
\(r(2) = 3\)
Next, we calculate g(r(2))
Substitute 3 for r(2)in g(r(2))
g(r(2)) = g(3)
\(g(x) = x^2 + 5\)
\(g(3) = 3^2 + 5\)
\(g(3) = 9 + 5\)
\(g(3) = 14\)
Hence:
(q o r)(2) = 14
please answer need help
Answers
The quotient of Sara’s score and 3.5 is 3. Write an equation that represents the situation, then find Sara’s score. Show your work.
c)The sum of Hamza’s score and 4.5 is equal to 7. Write an equation that represents the situation, then find Hamza’s score. Show your work.
d)4 less than Luna’s score is 4. Write an equation that represents the situation, then find Luna’s score. Show your work.
e)The sum of all scores must be at least 23 points. Write an inequality that represents the score of Mario, m, the fifth player. Access the following link where you can input the inequality you wrote and get it graphed. Attach a snip of the graph. Name
Mahdi score X
Sara score Y
Hamza score K
Luna score Z
Answers
Sara's score is 10.5; Hamza's score is 2.5; Luna's score is 8. The inequality for Mario's score is M ≥ 23 - X - Y - K - Z.
c) Let H be Hamza's score. Then we have the equation H + 4.5 = 7. Solving for H, we get:
H = 7 - 4.5 = 2.5
Therefore, Hamza's score is 2.5.
d) Let L be Luna's score. Then we have the equation L - 4 = 4. Solving for L, we get:
L = 4 + 4 = 8
Therefore, Luna's score is 8.
e) Let M be Mario's score. Then we have the inequality:
X + Y + K + Z + M ≥ 23
We can rearrange this inequality as:
M ≥ 23 - X - Y - K - Z
This represents the minimum score that Mario needs to achieve in order for the sum of all scores to be at least 23. Since we don't know the values of X, Y, K, and Z, we can't determine a specific value for M.
However, we can graph this inequality on a coordinate plane to see the possible values of M that satisfy the inequality.
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sum and difference of two terms (x+3)(x-3)
Answers
Answer:
x power 2 and -9 is the result
The value of a coin in 2010 was $40. The value of the coin has increased in value at a rate of 16.9% annually.
What was the value of the coin in 2019?
Enter your answer in the box rounded to the nearest dollar.
Answers
The value of the coin in 2019 would be approximately $132.
To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.
Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:
Value in 2019 = Initial value * (1 + Rate)^n
where Rate is the annual increase rate and n is the number of years between 2010 and 2019.
Plugging in the values:
Value in 2019 = $40 * (1 + 0.169)^9
Value in 2019 ≈ $40 * 2.996
Value in 2019 ≈ $119.84
Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.
However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.
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The graph below shows a translation of preimage hexagon with vertex A to image hexagon with Vertex A’. What is the vertical component of the translation?
Answers
Answer: you mightve done it already but c
Step-by-step explanation: i did it
HELP ME OUT PLEASE!!!!!!
Which table does NOT represent a function?
Α) Α
B) B
C) С
D) D
Answers
Answer:
d because it has the same number more than once. in the left column
adwoa received a commission of 20% on a bread she sold. in one week, Adwoa's commission was Gh¢540.00.
find
i. how much bread did she sell during the week.
ii. find her average daily commission
Answers
Answer:
tis is not confirmed aswer
Step-by-step explanation:
daily commission: 27%
At 9 a.m., Jessica started riding on the Red Mountain Parkway at the 40-mile marker.
At the same time, Kate started riding on the Red Mountain Parkway at the 10-mile
marker. Jessica rides her motorcycle at a rate of 30 miles per hour. Kate rides her
motorcycle at a rate of 40 miles per hour. If they are both riding in the same direction,
which graph shows the number of hours after 9 a.m. when Jessica and Kate will be in
the same position on the parkway?
Answers
Answer:
See below
Step-by-step explanation:
Start time = 9 A.M.
JessicaStart point- 40 milesSpeed - 30 mphEquation:
y = 40 + 30xKateStart point- 10 milesSpeed - 40 mphEquation:
y = 10 + 40xNote. There is no graph but see the attached. It should be similar graph for this case
The will meet after 3 hours at 130 miles mark
Solving the system of equations we get:
40+30x = 10 + 40x10x = 30x = 3And y is:
y = 40+3*30 = 130(3, 130) is the intersection of lines
Since it takes 3 hours for Jessica and Kate, it happens at 12 A.M.
The quotient of 50 and n
Answers
Answer:
D is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Which is a feature of function g if g(x)=-f(x-4)?
Answers
For the function, the x-intercept of g(x) is at (5,0).
What is the function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.
Given f(x) = ln(x)
and g(x) = -f(x - 4)
the function is
g(x) = -ln(x - 4)
when x = 5
g(x) = -ln(5 - 4)
g(x) = -ln1
g(x) = 0
the coordinates are (5, 0)
Hence the x-intercept is (5, 0).
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For what values of a and b is x^64 + ax^b +25 a perfect square for all integer values of x?
Answers
For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)
To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.
A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.
Let's examine the given expression: \(x^64 + ax^b\) + 25
For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.
So we have:\(x^64 + ax^64 + 25\)
Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)
By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)
Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)
From the second equation, we know that k = 25.
Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)
To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.
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what is the value of x
Answers
\( \large \mathfrak{Solution : }\)
By Applying Pythagoras theorem :
\(10 {}^{2} = {x}^{2} + {8}^{2} \)\(100 = {x}^{2} + 64\)\( {x}^{2} = 100 - 64\)\(x = \sqrt{36} \)\(x = 6\)therfore, the value of x = 6 units
Find the value of x.
12.1
17.6
12.4
6.3
Answers
Using Pythagorean theorem, the value of x is 12.4 units
What is the value of xTo find the value x, we need to find the radius of the circle from the diameter and then use Pythagorean theorem to find the unknown side or adjacent and then subtract the value from x.
radius = diameter / 2
radius = 44 / 2
radius = 22
Using Pythagorean theorem, the adjacent side will be;
22² = 19.8² + y²
y² = 22² - 19.8²
y = √(22² - 19.8²)
y = 9.6
The value of x will be
x = 22 - 9.6
x = 12.4
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The correct answer is 12.4
A central angle of a circle measures 42°. The arc intercepted by this central angle measures 12 inches.
Which value best approximates the radius of the circle?
8.67 in.
16.37 in.
17.34 in.
32.74 in.
Answers
\(\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ s=12 \end{cases}\implies 12=\cfrac{(42)\pi r}{180}\implies 12=\cfrac{7\pi r}{30} \\\\\\ 360=7\pi r\implies \cfrac{360}{7\pi }=r\implies 16.37\approx r\)
Answer:16.37 in.
Step-by-step explanation:
lian wants to advertise how many chocolate chips are in each big chip cookie at her bakery. she randomly selects a sample of 46 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 7.4 and a standard deviation of 2.7. what is the 95% confidence interval for the number of chocolate chips per cookie for big chip cookies? assume the data is from a normally distributed population. round answers to 3 decimal places where possible.
Answers
The big chip cookie's 95% confidence interval for the amount of chocolate chips per cookie is [8.325,6.474].
Given that,
The quantity of chocolate chips in each big chip cookie at Lian's bakery is something she wants to promote. She chooses a sample of 46 cookies at random and discovers that the average amount of chocolate chips per cookie has a standard deviation of 2.7 and a mean of 7.4.
We have to find what is the big chip cookie's 95% confidence interval for the amount of chocolate chips per cookie.
We know that,
The formula is
=x±Z(S/√n)
=7.4±2.326(2.7/√46)
=8.325 and 6.474
Therefore, the big chip cookie's 95% confidence interval for the amount of chocolate chips per cookie is [8.325,6.474].
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2. JOY leather, a manufacturer of leather Products, makes three types of belts A, B and C which are processed on three machines M1, M2 and M3. Belt A requires 2 hours on machine (M1) and 3 hours on machine (M2) and 2 hours on machine (M3). Belt B requires 3 hours on machine (M1), 2 hours on machine (M2) and 2 hour on machine (M3) and Belt C requires 5 hours on machine (M2) and 4 hours on machine (M3). There are 8 hours of time per day available on machine M1, 10 hours of time per day available on machine M2 and 15 hours of time per day available on machine M3. The profit gained from belt A is birr 3.00 per unit, from Belt B is birr 5.00 per unit, from belt C is birr 4.00 per unit. What should be the daily production of each type of belt so that the profit is maximum?
a) Formulate the problem as LPM
b) Solve the LPM using simplex algorithm.
c) Interpret the shadow prices
Answers
The shadow price of a constraint, the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.
What are constraints?A constraint is a condition of an optimization problem that should be satisfied the condition.
We can formulate this problem as a linear programming model (LPM):
Suppose X1 be the number of belt A produced per day, X2 be the number of belt B produced per day and X3 be the number of belt C produced per day
The objective function is to maximize the profit;
3X1 + 5X2 + 4X3.
The constraints are as :
The time spent on machine M1 must be less than or equal to 8 hours per day so we get;
2X1 + 3X2 <= 8
The time spent on machine M2 must be less than or equal to 10 hours per day so we get;
3X1 + 2X2 + 5X3 <= 10
The time spent on machine M3 must be less than or equal to 15 hours per day so we get
2X1 + 2X2 + 4X3 <= 15
Thus number of belts produced must be positive:
X1, X2, X3 >= 0
To solve this LPM using the simplex algorithm,
Also the objective function is to minimize the cost, and all constraints are in the form of "less than or equal to" a certain value.
The pivot row is the row that corresponds to the smallest positive ratio between (RHS) value and the corresponding pivot column element the constraint 2X1 + 3X2 ≤ 8.
Now Interpret the shadow prices.
The shadow price of a constraint is the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.
Here the value of the constraints in the LPM and how they contribute to the optimal solution.
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If there are 25 questions on the math test, and passing is 65%, What is the least amount of questions you need to get it right in order to pass? Explain your answer..
Answers
Answer:
17
Step-by-step explanation:
65% can be simplified to \(\frac{13}{20}\). Multiplying \(\frac{13}{20}\) by 25 gets 16.25 but since 16 would get you under 65%, you would need to correctly answer 17 questions.
Write an exponential function to describe the given sequence of numbers.
9, 27, 81, 243, 729, ...
Answers
Answer: 2187
Step-by-step explanation: Raise 3 to the power of 7 = 2187
the sumof 8pq and -17 pq is
Answers
Answer:
= -9pq
Step-by-step explanation:
=8pq + (-17pq)
=8pq-17pq
= -9pq
10. Grapes are on sale for
$2.36 per pound.
Pounds
0.75
1.25
2
2.5
Total Cost
Number 10
Answers
Answer:
.75 pounds= $1.77, 1.25 pounds=$2,95, 2 pounds=$4.72, 2.5 pounds= $5.90
Step-by-step explanation:
multiply each number in the pounds column by 2.36 to get the total cost
.75(2.36)=1.77
1.25(2.36)=2.95
2(2.36)=4.72
2.5(2.36)=5.9
If q stands for "This dog is big and r stands for "Lazy dogs do not play" write each of the following in symbolic form.
a. This dog is big and lazy dogs do not play-
b. Lazy dogs do not play or this dog is not big.
c. It is false that both this dog is big and lazy dogs do not play.
d. This dog is not big.
Answers
Step-by-step explanation:
in symbolic form:
V represents or
Λ represents and
~ it is not the case that/not true/false
a) qΛr
b) rVq
c) ~(qΛr)
d) ~q
if you have any questions, feel free to ask me!
-s.
Part G What is the ratio of the radius of circle A to the radius of circle B?
Course Activity: Proving That All Circles Are Similar
Edmentun Geometry
Answers
The ratio of the radius of Circle A to the radius of Circle B is given as follows:
0.6.
What is the radius of a circle?The radius of a circle represents the distance between the circle of the center to any point on the circumference of the circle.
From the circles given on the image presented at the end of the answer, the radius of each circle is given as follows:
Circle A: rA = 3.Circle B: rB = 5.Hence the ratio of the radius of circle A to the radius of circle B is calculated as follows:
rA/rB
Replacing the numeric values for each radius, the ratio is calculated as follows:
3/5 = 0.6.
Missing InformationThe circles are given by the image presented at the end of the answer.
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Select all lengths that are equal to 3 yards 16 inches.
Answers
The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).
To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.
1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).
Therefore, 3 yards is equal to 3 * 36 = 108 inches.
Now, we can compare 108 inches to 3 yards 16 inches.
108 inches is equal to 3 yards, so it matches the given length.
To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.
Therefore, 3 yards 16 inches is equivalent to:
3 yards
108 inches
3 yards 0.44 yards (or approximately 3.44 yards)
108 inches 0.44 yards (or approximately 108.44 inches)
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If the function m(x) has the point (1, 9) on its graph name a point that would be on the function 17n(x) + 2.
(1, 155)
(17, 11)
(2, 17)
(1, 11)
Answers
9514 1404 393
Answer:
(1, 155)
Step-by-step explanation:
Let f(x) = 17n(x) +2, where n(1) = 9.
Then we have ...
f(1) = 17n(1) +2 = 17×9 +2 = 153 +2
f(1) = 155
A point on the new graph would be (1, 155).
find the value of x and the measure of angle axc
Answers
Answer:
x = 4
m<AXC = 150
Step-by-step explanation:
m<1 + m<2 = m<AXC
102 + 10x + 8 = 6(6x + 1)
10x + 110 = 36x + 6
26x = 104
x = 4
m<AXC = 6(6x + 1)
m<AXC = 6(24 + 1)
m<AXC = 150
The length of a rectangular field is represented by the expression 14x-3x^2+2y . The width of the field is represented by the expression 5x-7x^2+7y . How much greater is the length of the field than the width?
Answers
The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)
1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)
2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).
3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).
4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)
5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)
6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)
7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)
8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)
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14. Jessica created a model of an ice cream cone by combining the shapes
of a cone and a hemisphere. Based on the dimensions shown in the figure
below, determine the volume of the model.
A.
B. 661 cm
C. 108 cm
D. 126 cm
Answers
Answer:A
Step-by-step explanation:trust me bro
While riding her bike to the ocean and back home 5 times, Mary timed herself at 69min, 51min, 66min, 50min, and 69min. She had set a goal of averaging 59minutes for her rides. How many minutes will she need to spend on her sixth ride to attain her goal?
Answers
If the timings of Mary are 69min, 51min, 66min, 50min, and 69min, then the timing at which Mary has to time herself to maintain average of 59 is 49 minutes.
Given that the timings at which Mary timed herself are 69min, 51min, 66min, 50min, and 69min and the average to be maintain is 59 minutes,
We are required to find the time at which Mary has to time herself to maintain average of 59 minutes.
Average is basically the sum of all the items divided by number of items.
Suppose the time at which Mary should time herself is x.
(69+51+66+50+69+x)/6=59
(295+x)/6=59
305+x=354
x=354-305
x=49
Hence if the timings of Mary are 69min, 51min, 66min, 50min, and 69min, then the timing at which Mary has to time herself to maintain average of 59 is 49 minutes.
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