As per the conditions given by the question, the 95% confidence interval of the true proportion who said that they would take a ride in a self-driving car is (53.3856%, 62.6144%).
Now, According to the question:
What is confidence interval?
A confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
To find the 95% confidence interval of the true proportion, we need to use the following formula:
point estimate +/- (margin of error * z-score)
The point estimate in this case is the sample proportion, which is 58%. The margin of error is 2.4%, and the z-score for a 95% confidence interval is 1.96.
Plugging these values into the formula, we get:
58% +/- (2.4% * 1.96)
This simplifies to:
58% +/- 4.6144%
So the 95% confidence interval is:
(53.3856%, 62.6144%)
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Activity
Luna I made the 3. 8 x 105 kilometers trip to the moon in 2. 16 x 10 minutes. In this activity, you will determine the average speed of Luna!
using division
Part A
Write an expression for the speed of Luna I In kilometers/minute. Represent this expression as a quotient of two numbers expressed in scientific
notation.
The average speed of Luna I is 1.78 x 10^-3 kilometers/minute.
To find the average speed of Luna I, we need to divide the total distance traveled (3.8 x 10^5 kilometers) by the total time it took to travel that distance (2.16 x 10^4 minutes). The quotient of these two numbers is 1.78 x 10^-3 kilometers/minute.
It's the ratio of distance covered to the time taken to cover that distance. The unit of speed is distance/time, which in this case is kilometers/minute. The speed of Luna I is in scientific notation, which is a way to express very large or very small numbers in a more manageable form.
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Look at the figure at the right. Explain one
thing that representing the area of the figure as 9(x + 3) - 6x tells
you about the situation. Then write an equivalent expression for
the area. Explain what information is in your expression that is not
in 9(x + 3) - 6x.
Answer:
3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18.
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Identify the inverse function of f(x)=√x - 2 + 3.
A) f-¹(x) = (x + 2)² - 3
B) f-1(x) = (x - 3)² + 2
C) f-¹(x) = √x + 2 - 3
D) ƒ-1(x) = √x + 3 − 2
Questi
The inverse of the function f(x) =√x - 2 + 3 is (x - 3)² + 2 so, option B is correct.
What is the function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given:
f(x)=√x - 2 + 3.
The inverse function can be found as shown below,
f⁻(x) = √(y - 2) + 3 (Replace x by y)
x = √(y - 2) + 3
solve the equation as shown below,
x - 3 = √(y - 2)
Squaring both sides,
(x - 3)² = [√(y - 2)]²
x² + 9 - 6x = y - 2
x² + 9 - 6x + 2 = y
y = x² - 6x + 11 or y = (x - 3)² + 2
Thus, the inverse of the function is (x - 3)² + 2.
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a survey was given to people who own a certain type of car. what percent of the people surveyed were completed satisfaction with the car?
The percent of the people surveyed who were completed satisfaction with the car will be 48%.
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100. The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %.
In this case, a survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car.
The percent of the people surveyed were completed satisfaction with the car will be:
= 24 / 50 × 100
= 48%
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Complete question
A survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car. what percent of the people surveyed were completed satisfaction with the car?
A rectangle has length x and width x - 3. The area of
the rectangle is 10 square meters.
Complete the work to find the dimensions of the
rectangle
Х
x(x - 3) = 10
x? - 3x = 10
x2 - 3x - 10 = 10 - 10
10 m2
X-3
(x + 2)(x - 5) = 0
What are the width and length of the rectangle?
O The width is 1 meter and the length is 10 meters.
O The width is 10 meters and the length is 1 meter.
The width is 2 meters and the length is 5 meters.
The width is 5 meters and the length is 2 meters.
The equation for dimensions of the rectangle is x(x - 3) = 10 and the width is 2 meters and the length is 5 meters.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
x(x-3)=10
x²-3x=10
x²-3x-10=0
x²-5x+2x-10=0
(x-5)(x+2)=0
x=-2,5
x=5 units
x-3=5-2
=2 units
The rectangle's dimensions are x(x - 3) = 10, with a width of 2 meters and a length of 5 meters.
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c) Mr. Gurung had Rs 3300. He purchased 5 kg of rice at Rs 70 per kg, 2 packets of oil at Rs 125 per packet and he gave Rs 2500 to his wife. If he divided the remaining sum between his son and daughter equally, find the share of each of them.
Answer:
Intial money=Rs 3300
final money=3300-(70×5)-(2×125)-2500
=3300-350-250-2500
=3300-3100=RS 200
Now,
share of each of them= 200/2=Rs100
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What is an inverse variation graph called?
The graph of the inverse variation equation is called a rectangular hyperbola.
A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.
An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.
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Find a polynomial which when added to the polynomial 3x^2+3x-1, is equaivelant to the following expressions: 1
The polynomials which, when added to the polynomial 3x²+3x-1, is equivalent to the following expressions: 1, 2x²-3, and x+5 include the following below:
P = 2 - 3x² -3x.P = -2 -x² -3xP = 6 -2x -3x².What is a Polynomial?This is referred to as algebraic expressions that consist of variables and coefficients.
For 1; it is calculated as:
3x²+3x-1 + P = 1.
P = 2 - 3x² -3x.
For 2x²-3, it is calculated as:
3x²+3x-1 + P = 2x²-3
P = -2 -x² -3x
For x +5; it is calculated as:
3x²+3x-1 + P = x +5
P = 6 -2x -3x².
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The full question is:
Find a polynomial which, when added to the polynomial 3x^2+3x-1, is equivalent to the following expressions: 1, 2x^2-3, and x+5
Reduce 22/154
to its lowest form.
Answer: 1/7
Step-by-step explanation: Find the GCD (Greatest Common Denominator) of the numerator and denominator. The GCD of 22 and 154 is 22. Divide both the numerator and denominator by the GCD = 22 ÷ 22; 154 ÷ 22. Reduced fraction: 1/7. Therefore, 22/154 simplified to lowest terms is 1/7.
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool
The number of units that tile will he need to surround his pool is 19.82units.
this question is of quadratic equation ,
The number of units of tile simply refers to the perimeter.
So, we need to find all the sides of the rectangle.
Now, we have,
AB = 4.24 units
BD = 7.07 units.
So, we can find AD using pythagoras theorem.
So,
(AD)² + 4.24² = 7.07²
(AD)² + 17.978 = 49.985
(AD)² = 49.985 - 17.978
AD = √32.007
AD = 5.66 units
AD = BC = 5.66 units
Likewise, AB = DC = 4.24 units
Thus,
perimeter = 2(5.66) + 2(4.24) = 19.8 units.
The number of units that tile will he need to surround his pool is 19.82units.
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In ΔSTU, = 670 inche, u = 630 inche and ∠U=67°. Find all poible value of ∠S, to the nearet degree
The measure of ∠S is 59.4° for trignometric identities
What are trigonometric identities?
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
ΔSTU:
s = 50 inches
t = 58 inches
u = 630 inches
Applying the cosines rule on ΔSTU.
s² = t² + u² - 2 x t x u x cos S
cos S = (t² + u² - s²) / 2tu
cos S = (58² + 27² - 50²) / (2 x 58 x 27)
cos S = (3364 + 729 - 2500) / 3132
cos S = 0.5086.
∠S = (0.5086)
∠S = 59.4°
Thus,
∠s angle value is 59.4°.
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what is an equation of the line that passes through the point (8,-7) and is parallel to the line 5x+4y=16
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]5x+4y=16\implies 4y=-5x+16\implies y=\cfrac{-5x+16}{4} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{4}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -5/4 and it passes through (8 , -7)
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{8}) \implies y +7= -\cfrac{5}{4} (x -8) \\\\\\ y+7=-\cfrac{5}{4}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{5}{4}x+3 \end{array}}[/tex]
Write 63 521. 769 correct to the nearest hundred
Triangle ABC was translated to form A’B’C’. Which describes the transformation? Check all that apply
Translation is a rigid transformation. As such, it preserves sizes and angles. Isometric is an alternative way to say the size is preserved. Hence; B, C and E are the correct choices.
What is a triangle?A triangle is a three-sided polygon. A closed shape consisting of three straight lines and three corners. The sum of the three angles of a triangle is always 180 degrees. Triangles come in a variety of shapes and sizes and can be classified according to their angles and sides. The most common type of triangle is the right triangle, which has 90 degree angles.
Translation is the transformation that happens when we move the image without changing anything in it. Therefore, the shape, size, and orientation remain the same.
In this case the triangle ABC has been transformed to A'B'C'. This means that the triangle has been moved in one direction to form a new triangle A'B'C' without changing its size or orientation. This is an example of translation transformation.
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The complete question is follows:
Triangle ABC was translated to form A’B’C’. Which describes the transformation? Check all that apply
A. It is non rigid
B. The size is preserved
C. It is rigid
D. The angles are not preserved
E. It is isometric
Which fraction is equivalent to fraction with numerator 6 and denominator negative 8 ? (5 points)
fraction with numerator negative 8 and denominator 6
fraction with numerator negative 6 and denominator 8
fraction with numerator negative 6 and denominator negative 8
fraction with numerator 8 and denominator 6
Answer:
A fraction is a mathematical expression that represents the division of two numbers, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the number of parts in the whole. A fraction with a numerator of 6 and a denominator of negative 8 can be simplified to -3/4. To find an equivalent fraction, we can multiply or divide both the numerator and denominator by the same number without changing the value of the fraction. In this case, the fraction with a numerator of negative 8 and a denominator of 6 is equivalent to -4/3.
Step-by-step explanation:
Angle of depression: A person standing on the top of the Petronas Tower I looks out
across the city and pinpoints her residence. If the angle of depression from the person's
eyes to her home is 5°, how far away (in feet and in miles) is the residence?
A field is in the shape of a square. The length of the field is 5x³y. What is the area of the field in terms of x and y? Write the variables in
alphabetical order. I really don’t know and I’m desperate :(
Answer:
25x^6y^2
Step-by-step explanation:
Since it is a square all sides are the same. So you multiply 5x^3y and 5x^3y together to get the area. That would get you 25x^6y^2.
I’d love you he help for all of it but i’ll take what I can get
Answer:
Parallelogram formula- 1/2 x base xheight
Step-by-step explanation:
An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a _____.
An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a contradiction.
What does the phrase "in contradiction" mean?a fact or assertion that contradicts what someone else said or that differs from another fact or assertion to the point where one of them must be incorrect.
What is an illustration of contradiction?A situation or set of ideas that contradict one another is called a contradiction. A contradiction would be saying out loud that you support the environment while never remembering to empty the recycling. A statement that contains opposing ideas is frequently referred to as a "contradiction in terms."
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 10
and DC = 4, what is the length of AD?
AC = 25 units is the length of AD.
A right triangle is divided into three equal halves by the height of the hypotenuseThe Geometric Mean (Altitude) Theorem (9.7) The hypotenuse of a right triangle is split into two pieces by the height from the right angle. The geometric mean of the lengths of the two hypotenuse segments determines how long the altitude is.
Length of BC = 10 units
Length of DC = 4 units
We will use geometric mean theorem in the given right triangle to get the length of side AC.
[tex]hypotenuse/leg=leg/projection\\AC/BC=BC/DC\\x/10=10/4\\x=25[/tex]
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WZ and XR are diameters of circle C. The diagram is not drawn to scale.
Circle C is shown.
Radii are drawn from point C to point R at the right, point Z at the upper right, point Y at the upper left, point X at the left, and point W at the lower left.
Angle Y C Z measures 112 degrees.
Angle X C W measures 63 degrees.
Points X, C, and R are all on the horizontal diameter of the circle.
What is the measure of convex arc upper Z upper W upper X?
A. 355º
B. 5º
C. 292º
D. 243º
The measure of convex arc upper Z is 243⁰ Option D
How to find the measure of the angle?We should be aware that a convex angle is the angles that are irregular in nature
Assume that the radius of the given circle is r.
The central angle of the lower arc ZWX = 41+180 = 221⁰
Note that then central angle of the upper arc ZWX = 360- 221⁰
This implies that the central angle of the upper arc ZWX = 360-221 = 139⁰
Recall that Lenght of arc = A/360 *2*π*r
Where A is the angle made by the radii, r= radius of the circle
Arc length of upper ZWX:
Arc length of upper ZWX = 139π/180*r
Arc length of upper ZWX = 139πr/180
The lenght is (139*22)/ 180*7
= 3058/2360
= 245⁰
In conclusion the measure of the convex upper is 245⁰
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Questions:
1. What did you do to the numerators? What did you do too to the denominators?
2. Did you find like terms among the collected terms of the numerator? What did you do
to terms?
3. What factoring techniques did you apply?
4. How did you simplify your sum?
The answers to all the subparts are shown:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
What is numerator and denominator?In a fraction, the number above the line is the numerator.
For instance, the numerator of the fraction 3/5 is 3.
A fraction's numerator displays the number of pieces that make up the whole while the denominator, or a number of equal parts, is displayed below the line.
So, we have the equation:
2x² + x/2x - 2 + x - 4/ 2x - 2
Now, answering questions taking the above-given equation into consideration:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
(3) We complete the square, but we can also use the straightforward factoring approach.
(4) We eliminate or simply cancel the factors in the numerator that are also present in the denominator to simplify the sum.
Therefore, the answer to all the subparts are shown:
(1) The numerator is simply added. The denominator is copied.
(2) Yes, it has; yet, we include them since that is what needs to be done.
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Which is the complete factorization of this expression?
-20x - 5y
A)5(4x+y)
B) 4(5x - y)
C) -5(4x + y)
D)-5(4x - y)
Factor -20 x-5 y, where x+y=4 and x+y=5. Our prime numbers become much, much harder to factor as we add a few extra digits.
What is meant by factorization ?When you factor in mathematics, you divide a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of an amount into its factors or divisors. The factorization of the integer 12, for instance, might be 3 times 4 or something similar. [tex]N = X^{a} * Y^{b} * Z^{c}[/tex] is used to represent the general factorization formula. In this instance, X, Y, and Z stand for a number's factors. Get a polynomial's GCF (Greatest Common Factor).
GCFs of polynomials should be factored out. By grouping the terms, factor a polynomial with four terms. trinomial of the form, and factor it. The size of our goods and the size of the data we use to check mean that each check takes an average amount of time longer. It is clear from this that factoring the product becomes significantly more difficult when we add a few digits to our prime integers.
Therefore the correct answer is option A)5(4x+y)
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solve for x: 2 < x + 4 < 4
Answer: −2<x<0
Step-by-step explanation: 2<x+4<4 2+−4<x+4+−4<4+−4 −2<x<0
2. The value of a machine depreciates by 5% every year. It is given that the initial value of the machine is RM100 000.
(a) Express its value, in RM, after n years.
(b) Hence, find its value after 10 years to the nearest ringgit.
Answer:
Step-by-step explanation:
Depreciation means wearing and tearing in the value of an asset over the years
(a) Given:
p = initial value of an asset
i% = depreciation per year
n = number of years
Depreciation after n years (d) = [tex]p(1-\frac{1}{100} )^{n}[/tex]
Value of machine after n years = p-d
(b) Given:
p = RM100000
i% = 5
n = 10
Depreciation after 10 years = [tex]100000(1-\frac{5}{100} )^{10} = 59873.69392[/tex]
Value of machine after 10 years = p-d = RM100000 - RM59873.69392 = RM 40123.30608
Value of machine after 10 years to nearest ringgit = RM40123
if the chosen significance level is α = 0.05, then ____________________________________________. A) there is a 5% probability of rejecting a true null hypothesis
B) there is a 5% probability of accepting a true null hypothesis
C) there is a 5% probability of rejecting a false null hypothesis
D) there is a 5% probability of accepting a false null hypothesis
C) there is a 5% probability of rejecting a false null hypothesis
Simply put, probability is the likelihood that something will occur.
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Testing hypotheses is a crucial component of empirical research and evidence-based medicine. A well-developed hypothesis is only half the solution to the research problem. Working understanding of fundamental statistical principles is preferred for this, as well as subject-specific knowledge gleaned through a thorough survey of the literature.
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On a assembly line, 2 parts can be made per minute. There are 8 parts already made. To determine how many more minutes (x) it will take to make y total parts, the equation y=2x + 8 is written. What is the description of a solution to this problem?
The description for the problem involving the linear function is given as follows:
The time it will take to make a total of 20 parts is of 6 minutes.
How to interpret this problem in the context of a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the y-intercept, representing the initial value.In this problem, the function is defined as follows:
y = 2x + 8.
In which the variables are given as follows:
x is the time in minutes.y is the number of pieces made.Hence the time needed to make 20 pieces is given as follows:
20 = 2x + 8
2x = 12
x = 12/2
x = 6 minutes.
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Solve the inequality n - 4/7> - 2/3
Answer:
N > -2/21
Step-by-step explanation:
Move -4/7 to the other side
n - 4/7 > - 2/3
n > - 2/3 + 4/7
Find a common denominator
n > - 14/21 + 12/21
Add
n > - 2/21
What is the GCF of 20x^76 and 8x^92
The GCF of the given expressions is 4x⁷⁶
What is the greatest common factor?The greatest common factor, abbreviated as GCF, of two numbers is the largest number that is a factor of, or divides evenly into, both of the numbers. When two numbers are relatively small, we have a quick and simple way to calculate their greatest common factor. We do this by listing all of the factors of each number, and then identifying the largest number that is in both lists.
Given here, The expressions 20x⁷⁶ and 8x⁹² and GCF(20,8)=4
and x⁷⁶ is a factor of 8x⁹²
∴ GCF(20x⁷⁶ , 8x⁹²) =4x⁷⁶
Hence, The GCF of the given expressions is 4x⁷⁶
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How do I find parameter?
Answer:
Depending of the figure that you are trying to find perimeter on, you just add up all the sides of that figure.
Answer:
The perimeter is the distance around a figure.
Step-by-step explanation:
For example, if I have a square where each side is 5 inches. The perimeter would be 20 inches. 5 + 5+ 5 + 5, a square has four sides and each side length is 5 inches.