Using the z-distribution, it is found that 3,007 passengers must be surveyed.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
In this problem, we desired a margin of error of M = 0.015, with no prior estimate, hence [tex]\pi = 0.5[/tex], then we solve for n to find the minimum sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.015 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.015\sqrt{n} = 1.645(0.5)[/tex]
[tex]\sqrt{n} = \frac{1.645(0.5)}{0.015}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645(0.5)}{0.015}\right)^2[/tex]
n = 3007.
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A farmer raises only cows and Sheep. He wants to raise no more than 16 animals, including no more than 12 sheep. He spends birr 5 to raise a cow and Br 2 to raise a sheep. He has Br 50 available for this purpose. Cows sell birr 100 and sheep birr 50. Required: How many of each animal should he raise to maximize profit? What is the maximum profit?
Answer:
1050 max profit
Step-by-step explanation:
cow 5brr 30br 600 × 6 cows 570
sheep 2brr 20br 500 ×10 sheeps 480
sheep&cows = 1050 max profit
What are the roots for the quadratic equation below?
3x^2+9x-2=0
Answer:
[tex]\sf{$a)$} \ x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Step-by-step explanation:
Quadratic formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Quadratic equation: ax² + bx + c = 0, where a ≠ 0
Given: 3x² + 9x - 2 = 0
⇒ a = 3, b = 9, c = -2
Substitute the given values into the formula and simplify:
[tex]x=\dfrac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)}\\\\x=\dfrac{-9\pm\sqrt{81+24}}{6}\\\\x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Therefore, the correct answer is A.
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What is the value of this expression when c = -4 and d = 10?
A.
2
B.
9
C.
21
D.
41
The complete question is
"What is the value of this expression when c= -4 and d= 10?
1/4 (c^3+d²)
A.2
B.9
C.21
D.41"
The value of this expression when c = -4 and d = 10 will be option B 9.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given expression is
[tex]1/4 (c^3+d^2)\\\\1/4 ((-4)^3+(10)^2)\\\\1/4 ( -64 + 100)\\\\1/4 (36)\\\\9[/tex]
Hence, the value of this expression when c = -4 and d = 10 will be option B 9.
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A carpenter wants to cut an 84 inches long board into two-pieces such that one piece is twice as long as the other piece. Set up an equation and find the length of each piece.
Answer:
small piece = 28 inches
large piece = 56 inches
Step-by-step explanation:
The carpenter has one piece of wood 84 inches long. He wants to cut that piece of wood into two pieces. One piece will be 2 times as long as the other. Let's let x = the small piece of wood
2x + x = 84
In this equation, the longer piece is 2 times the shorter piece and the shorter piece is added, which equals 84 inches. Lets solve:
2x + x = 84
3x = 84
3x/3 = 84/3
x = 28
This means that the shorter piece is 28 inches. To find the longer piece, multiply 28 by 2 because the longer piece is twice the shorter piece. Therefore the longer piece is
28 × 2 = 56
Finally, we figured out that the short piece is 28 inches and the longer piece is 56 inches
We can double check this by doing 56 + 28 and making sure it equals 84
4x² + 24x + 20
common factor =
3xy - ² + 4x for x = -2, y = - and = 6?
Answer:
See below
Step-by-step explanation:
Not sure what you are asking....do you want to know what y is when x = -2 and the equation = 6 ?
3 xy^2 + 4x = 6 or is that 3 xy^(-2) + 4x = 6
Could use some serious editing of your question if you are able ....
In the last three years Frederic’s basketball team win 40 more games than they lost
Answer:
Wht is the total matches they played?
Simplify the root below
\frac{a}{b} \sqrt[]{ \frac{405}{324} }
Answer:
(√5)/2
Step-by-step explanation:
To simplify the root, we remove perfect squares.
__
Factors that are the same in numerator and denominator cancel. A square under the radical can have its root brought out of the radical.
[tex]\sqrt{\dfrac{405}{324}}=\sqrt{\dfrac{9^2\cdot5}{9^2\cdot2^2}}=\boxed{\dfrac{\sqrt{5}}{2}}[/tex]
statement that is assumed to be true without proof is . A statement that has been shown to be true by vigorous application of logic is . is a statement that is believed to be true but hasn't been proven.
An axiom is a statement that is assumed to be true without proof.
What are the types of statements?In logic, a statement could be shown to be valid or true by the use of premises that lead to a sound conclusion.
The following terms can be used to describe the statements;
Axiom - a statement that is assumed to be true without proofTheorem - a statement that has been shown to be true by vigorous application of logicHypothesis - a statement that is believed to be true but hasn't been proven.Learn more about mathematical statements:https://brainly.com/question/17029275?
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Answer:
The answer is axiom, theorem, and then conjecture
Step-by-step explanation:
If Jenny walks 2 miles in 40 minutes, then Jenny will walk how far in 100
minutes if she walks at the same speed the whole time? If necessary, round
your answer to the nearest tenth of a mile.
Answer:
Five miles
Step-by-step explanation:
if 2=40 then 1=20 so 5=100
A comedy club's nightly revenue from the sale of x tickets is given by R = 15x and its
nightly costs are given by C= 1.25x + 495. How many tickets need to be sold each night
to break even? In other words, when will revenue equal costs?
Considering the given equations for the revenue and the cost, it is found that 36 tickets have to be sold each night to break even.
What is the break-even point?The break-even point is when the revenue and the costs are equal.
In this problem, the equations are given as follows:
R(x) = 15x.C(x) = 1.25x + 495.At the break-even point:
R(x) = C(x)
15x = 1.25x + 495
13.75x = 495
x = 495/13.75
x = 36.
36 tickets have to be sold each night to break even.
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what is golden ratio, and explain it's history
Answer:
The golden ratio is a proper term in the field of mathematics, but it finally covers more than the research in the field of mathematics. According to the current literature discussion, we can say that the discovery of the Golden ratio and how it evolved is still a mystery. But studies have shown that the Pythagorean school of ancient Greece in the 6th century BC studied the formation of regular 5-sided and regular 10-sided plots, leading modern mathematicians to conclude that the Pythagorean school had touched on and even mastered some of the rules of the golden ratio and also discovered irrational numbers. It focuses on the relationship from mathematics, to explore the principle of beauty and that beauty is harmony and proportion, according to the proportional relationship can form beautiful patterns, this is actually a digital proportional relations, the line is divided into two parts, a long and a short period of the ratio of the equal to the ratio of length to a long, their proportion is around 1.618:1, This mathematical principle is also embodied in the famous Frederikian sequence, in which everything in this proportion shows the harmony and balance of its internal relations.
In the 4th century BC, the Greek mathematician Eudoxus was the first to systematically study this problem and establish the theory of proportion. Around 300 BC, Euclid absorbed the research results of Eudoxus in writing The Elements of Geometry and further systematically discussed the Golden Section, which became the earliest treatise on the golden Section (i.e. the middle and the end ratio) [5].
After the Middle Ages, the golden ratio was shrouded in mystery. Italian mathematician Luca Pacioli called the middle and the end of the ratio sacred and wrote a book about it. The German astronomer Johannes Kepler called the divine ratio the Golden Ratio. Golden in the 19th century the name only gradually, and the evidence is that German mathematician Martin Ohm (English: Martin Ohm) wrote the second edition of the basic pure mathematics annotation wrote about the interpretation of the golden ratio: "people used to put any straight line along the way will be divided into two parts, the method of known as the golden mean". And in the ninth edition of the Encyclopaedia Britannica, published in 1875, Sully notes: "The interesting, experimental and strong idea put forward by Frederick... proclaimed the supposed superiority of the 'golden Section' in visual proportion." So the Golden Section was already popular. In the 20th century, American mathematician Mark Barr gave it the name Phi. The Golden Section has many interesting properties and has been widely used by humans to make it famous today. The most famous example is the golden ratio or 0.618 method in optimization, which is first proposed in 1953 by Jack Kiefer (English: Jack Kiefer), an American mathematician, and is promoted in China in 1970s.
Mrs. Juergen's class is building a model city from craft sticks. each house requires 267 sticks. the class will build 93 houses. About how many sticks will be needed?
g(x) f(x) = −6x − 3 cosine function with y intercept at 0, negative 3 h(x) = 2 cos(x + π) − 1 Using complete sentences, explain which function has the greatest y-intercept. (10 points)
full step by step process please.
A function assigns the values. The function that has the greatest y-intercept is h(x).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
There are three function, g(x){given in the graph below}, f(x)= -6x-3, and -3h(x) = 2 cos(x + π) − 1, the y-intercept of the function is the point at which the graph intersects the y-axis. Therefore, the y-intercept are,
g(x) = -3
f(x) = -3
h(x) = 1
Hence, the function that has the greatest y-intercept is h(x).
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What is the value of x?
E
(2x)°
xº
D
Answer:
30°
Step-by-step explanation:
Since ED = FD, the ∠DEF = ∠EFD
Since ∠DEF = 2x, ∠EFD is also equal to 2x
The sum of the 3 angles of a triangle is 180°
So x + 2x + 2x = 180
6x = 180
x = 30
Find the area of a 150° sector of a circle whose radius is 3.
Answer: [tex]\frac{15\pi}{4}[/tex]
Step-by-step explanation:
[tex]A=\pi(3^{2})\left(\frac{150}{360} \right)=\boxed{\frac{15\pi}{4}}[/tex]
Consider the two savings plans below. Compare the balances in each year after 14 years. Which person deposited more money in the plan? Which of the two investment strategies is better?
Yolanda deposits $250 per month in an account with an APR of 4%, while Zach deposits $3000 at the end of each year in an account with an APR of 4%
The balance in Yolanda's saving plan after 14 years is; $9,455.36
How to calculate future value?We want to find the balance in Yolanda's saving plan after 14 years.
For Yolanda;
PV = 0
PMT = 250
i% = 4%/12 = 0.33%
N = 14 yrs * 12 = 168
FV = ?
For Zach:
PV = 0
PMT = $3300
i% = 4%
N = 14 yrs
FV = ?
From online future value calculator, we have;
Yolanda FV = $9,455.36
Zach FV = $47,204.19
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Can anyone Help I have 25 questions, 2hr 40mins remaining,
Combining the like-terms, the result of the addition of polynomials f(x) and g(x) is given by:
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
How do we add polynomials?We add polynomials combining the like-terms, that is, adding terms with the same exponent.
In this problem, the polynomials are:
[tex]f(x) = 3x^{\frac{1}{2}} + 7x^{-\frac{1}{4}} + 8x^{-4}[/tex][tex]g(x) = -\frac{7}{4}x^{\frac{1}{2}} + 12x^{-\frac{1}{4}} - 21x^3[/tex]Combining the like terms, the addition is given by:
[tex]f(x) + g(x) = \left(3 - \frac{7}{4}\right)x^{\frac{1}{2}} + (7 + 12)x^{-\frac{1}{4}} + 8x^{-4} + 21x^3[/tex]
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
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Help me with this question please!! :)
Answer: 13/69
Step-by-step explanation:
13 students are female and got a B out of a total of 69 students, so the probability is 13/69
PLEASE HELPP!!!!!
Question 9 of 13
Which of the following scatterplots represents the data shown below?
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47),
(9,34), (10,3), (11, 33), (12, 35)
The attached graph below can represent the scatter plot of the points. the correct option is B.
How to find the function which was used to make graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
Given:
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47), (9,34), (10,3), (11, 33), (12, 35)
The above points would be plotted using the following scale such as:
x: axis -> 1 interval = 10 units
y: axis -> 1 interval = 10 units
The attached graph below can represent the scatter plot of the points. the correct option is B.
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HELP TO ASAP Compare the graph of f(x) with the graph of k(x) = 5(x-6)².
OA. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units right.
OB. The graph of k(x) is vertically stretched by a factor of 5 and shifted
6 units right.
OC. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units left.
Parent function
y=x²Now look the transformations
y=(x-6)²x is changed and shifted 6 units right
Then
y=5(x-6)²Horizontally Streched with a factor of 5
Answer:
B) The graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
Given functions:
[tex]f(x) = x^2[/tex]
[tex]k(x) = 5(x - 6)^2[/tex]
Parent function: [tex]f(x) = x^2[/tex]
Translated 6 units right: [tex]f(x-6)=(x-6)^2[/tex]
Then stretched vertically by a factor of 5: [tex]5f(x-6)=5(x-6)^2[/tex]
[tex]\implies 5f(x-6)=5(x-6)^2=k(x)[/tex]
Therefore, the graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.
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Is AABCDEF? If so, identify the similarity postulate or theorem that
applies.
A
B
16 105⁰
36
с
D
4
LLI
E
9
-105⁰
F
OA. Similar - AA
OB. Similar - SSS
OC. Similar - SAS
OD. Cannot be determined
4
Answer:
C
Step-by-step explanation:
C is the correct answer as both triangles have a similar angle of 105⁰ and both side lengths of triangle ABC are being divided by 4 to have the same two side lengths as triangle DEF
The triangles ΔABC and ΔDEF are similar triangles by SAS theorem
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔABC
The measure of side AB = 16
The measure of side AC = 36
And , the measure of ∠ABC = 105°
Let the first triangle be ΔDEF
The measure of side DE = 16
The measure of side DF = 36
And , the measure of ∠DEF = 105°
Now , the ratio of sides of the triangles is given by
AB / DE = AC / DF
4/16 = 9/36
1/4 = 1/4
So , corresponding sides of similar triangles are in the same ratio
And , the measure of angles = 105°
Therefore , by SAS , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , they are similar triangles
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Using Triangle Congruence Theorems
There are a total of five theorems congruent triangles. They are summarized as:
SASSSSAASRHS and ASA.What are the definitions of the Theorems of Congruent Triangles?SAS - Side Angle Side
According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.
SSS - Side Side Side Rule
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are proportional to the size three sides of the second triangle.
AAS - Angle Angle Side Rule
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the comparable angles and sides of another triangle.
ASA - Angle Side Angle rule
According to the ASA rule, two triangles are said to be congruent if any two angles and the side contained between the angles of one triangle are proportional to the size two angles and side included in between angles of the second triangle.
RHS - Right Angle- Hypotenuse side Rule
According to the RHS rule, two right triangles are said to be equivalent if their hypotenuses and one of their sides are identical to those of another right-angled triangle.
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Answer:
AD=BC (given)
DC=DC (reflexive property)
DE=CE (converse of isosceles triangle thm)
<BCD=<ADC (given)
<ECD=<EDC (CPCTC)
TriangleADC=TriangleBCD (SAS)
2
What is the equation of the line that is perpendicular to y=x+4 and that passes through (5,-4)?
--5v-20
K
Perpendicular lines have slopes that are negative reciprocals of each other, so since the slope of the given line is 1, the slope of the line we want to find is -1.
Substituting into point-slope form,
[tex]y+4=-1(x-5)\\\\y+4=-x+5\\\\\boxed{y=-x+1}[/tex]
evaluate -5+(-3)^2+2
Answer:6
Step-by-step explanation:at first calculate (-3)^2=9
then 9+2=11
finally the answer is 11-5=6
Answer:
6
Step-by-step explanation:
Given Problem:
[tex]-5+(-3)^2+2[/tex]
Using the PEMDAS order of operation:
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Thus, Solving in parentheses first.
[tex]-5+(-3)^2+2[/tex]
[tex](-3)^2=9[/tex]
[tex]-5+9+2=[/tex]
[tex]-5+11=[/tex]
[tex]6[/tex]
Hence, the answer to [tex]-5+(-3)^2+2=6[/tex]
RevyBreeze
The surface area of a square pyramid is 189 square inches. The side length of the base is 7. What is the value of the height?
The value of the height of the prism is 8.68 inches
Surface of a square pyramidThe surface area is the sum of the area of the faces.
The formula for calculating the surface area of the pyramid is;
TSA = [tex]a^2+2a\sqrt{\frac{a^2}{4} + h^2}[/tex]
where
a is the side length. = 7in
h is the height
Substitute
[tex]189=7^2+2(7)\sqrt{\frac{7^2}{2} + h^2} \\189=49+14\sqrt{\frac{49}{2} + h^2}\\140=14\sqrt{\frac{49}{2} + h^2}\\10=\sqrt{\frac{49}{2} + h^2}\\[/tex]
Square both sides to have
100 = 49/2 + h²
h² = 100 - 49/2
h² = 151/2
h² = 75.5
h = 8.68in
Hence the value of the height of the prism is 8.68 inches
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Work out the lengths of sides a and b.
Give your answers to 1 decimal place.
triangle a is a right angled triangle with a height | of 8cm base of 5cm and missing hypotenuse
triangle b is a right angled triangle with a height | of 12cm and a hypotenuse of 17cm with a missing base
The length of the missing sides of triangles A and B are 9.43 cm and 12.04 cm respectively.
Pythagoras theoremTriangle A:
Height = 8cmBase = 5cmHypotenuse = x cmHypotenuse² = height ² + base²
x² = 8² + 5²
= 64 + 25
x² = 89
x = √89
x = 9.43 cm
Triangle B:
Height = 12cmBase = x cmHypotenuse = 17 cmHypotenuse² = height ² + base²
17² = 12² + x²
17² - 12² = x²
289 - 144 = x²
145 = x²
x = √145
x = 12.04 cm
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Step-by-step explanation:
[tex]29 {}^{ \frac{x}{2} } [/tex]
[tex]((29) {}^{ \frac{1}{2} } ) {}^{x} [/tex]
The answer is A
Help me with this question please!!!
Answer: 98.5
Step-by-step explanation:
There were 942 people in total, 928 of which recognized Exxon.
So, the probability is 928/942, which is about 98.5%
The probability of random consumers knowing of exon will be 98.5%.
What is probability?Probability helps us to know the chances of an event occurring.
[tex]P =\dfrac{Desired \ Outcomes}{Possible outcomes}[/tex]
Given that:-
928 consumers knew exon and 14 did not.The probability will be calculated as:-
Total consumers are 942 out of which 928 knew exon and 14 did not.
P = 928 / 942
P = 0.985
P = 98.5%
Therefore the probability of random consumers knowing of exon will be 98.5%.
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Find the value of: (4/5)^1 A. 4/5 B. 1 C. 0 D. 16/25
Answer:
A. 4/5
Step-by-step explanation:
Answer:
4/5 (option a)
Step-by-step explanation:
by following the exponent rule of [tex]a^1 = a[/tex], we know that
[tex](\frac{4}{5} )^1[/tex] = [tex]\frac{4}{5}[/tex]
So, the value of
[tex]\frac{4}{5}^{1}[/tex] is 4/5
