Our confidence interval is (66, 102).
In statistics, 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. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.
Now, here:
Mean, μ = 84
Standard deviation, σ = 9
It is a 95% confidence interval. We know that, within 2 standard deviations of the mean lies 95% of the population. Hence, z = 2.
Now, calculating μ - z.σ and μ + z.σ to find the intervals.
μ - z.σ = 84 - 2x9 = 66
μ + z.σ = 84 + 2x9 = 102
Thus, our confidence interval is (66, 102).
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How do you construct a line segment half as long as the given line segment?
To steps to construct a line segment that is 1/2 the length of the given segment is:
Draw a line segment CD of any length.
Fix the compass's end on C and pencil on D. This gives the length of CD.
Now divide the length of CD by 2. That is the 1/2 the length of CD.
Draw a line 1. Mark a point A on line 1. Change compass's setting into 1/3 the length of CD, place the compass at A.
Make an arc on the line l which cuts l at B. Now, AB is a copy of CD which is 1/2 the length of CD.
What is line segment?
A line segment is bounded by two definite points on a line. We also can say a line segment is part of the line which connects two points. A line has no endpoints and extends immensely in both the direction but a line segment has two fixed or distinct endpoints.
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PLEASE HELP ASAP THERE ARE 3 QUESTIONS!!!!!! CORRECT ANSWER GETS BRAINLLEST!!! WORTH 100 POINTS. PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Case 2
The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)
Case 3
We need to add + 64 to both sides. (Correct choice: B)
Case 4
We need to add + 16 to both sides. (Correct choice: C)
How to use completing the square method
In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:
Case 2
x² - 14 · x + 48 = 0
x² - 14 · x + 49 = 1
(x - 7)² = 1
x - 7 = ± 1
x = 7 ± 1
The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.
Case 3
x² - 16 · x = - 21
x² - 16 · x + 64 = 64 - 21
(x + 8)² = 43
The first step consists in adding both sides by + 64.
Case 4
x² - 8 · x = 0
x² - 8 · x + 16 = 16
(x - 4)² = 16
The first step consists in adding both sides by + 16.
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Find the area enclosed by the curve x=t^2-2t , y = √t and the y axis.
The area enclosed by the curve x = t² - 2t, y = √(t), and the y-axis is 0.754 square units.
First, find the value of t at x = 0
x = t² - 2t
⇒ t² - 2t = 0
⇒ t(t - 2) = 0
Therefore, t = 0, t = 2.
Derivative of area, dA/dy
dA/dy = (0 - x)
dA = (0 - x) × dy
Since the curve has a negative x in this region.
y = √t (given)
dy/dt = (1/2)/√t
dA = [0 - (t² - 2t)] [(1/2)/√t]dt
dA = [2t - t²]/[(1/2)/√t]dt
dA = [[tex]t^{1/2}[/tex] - (1/2)[tex]t^{3/2}[/tex]]dt
Integrating to obtain A,
A = (2/3)[tex]t^{3/2}[/tex] - (1/5)[tex]t^{5/2}[/tex]
Now apply the limits t = 0 to t = 2
Area = [(2/3)[tex]2^{3/2}[/tex] - (1/5)[tex]2^{3/2}[/tex]] - [0]
Area = √[2(4/3 - 4/5)]
Area = √[2(8/15)]
Area = √(16/15)
Area = 0.754
Thus, the area enclosed by the given curves is 0.754 square units.
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if f(x) = 3x²+5x, then find f(2)
Answer: 22
Step-by-step explanation:
f(2)=3*2^2+5*2
=3*4+10
=12+10
=22
all of marcy's marbles are blue, red, green, or yellow. one third of her marbles are blue, one fourth of them are red, and six of them are green. what is the smallest number of yellow marbles that macy could have?
According to the concept of probability, the smallest number of yellow marbles that Marcy could have is 24
The term probability is known as the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
Here we have given that all of Marcy's marbles are blue, red, green, or yellow. one third of her marbles are blue, one fourth of them are red, and six of them are green.
Here we know that the 6 green marbles and yellow marbles form is calculated as,
=> 1 - 1/3 - 1/4 = 5/12 of the total marbles.
Here let us consider that the total number of marbles is x.
And here we know the number of yellow marbles is is written as,
=> 5/12x - 6 and a positive integer.
Now, we have to divide 12 by x, then we get,
Then we get the value of x as 24.
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Taylor and Raimi each earn an hourly wage. Taylor earns $308 for working 14 hours. Raimi earns $288 for working 12 hours. Which statement is true?
Answer:
Raimi earns more per hour than Taylor.
Step-by-step explanation:
lim x-> ∞ (sinh(x)/e^x)
Answer: [tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex][tex]= 0[/tex]
Step-by-step explanation:
[tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex]
[tex]\lim_{n \to \infty} \frac{sinh(\infty)}{e^(\infty)}[/tex]
As x approaches infinity, the exponential term e^x becomes much larger than the hyperbolic sine function sinh(x), so the entire expression sinh(x)/e^x becomes very close to zero.
Therefore, the limit of the expression as x approaches infinity is 0:
IF THE PROBABILITY OF WINNING IS 0.3 THEN WHAT IS THE PROBABILTY OF NOT LOSE?
Answer:
0.7
Step-by-step explanation:
if we set the total race of win and lose is 1
then we use 1-0.3=0.7
GDP Gross Domestic Product (GDP) is a measure of a country’s wealth. Indonesia had an estimated GDP in 2017 of 1,020,515,000,000. Madagascar had an estimated GDP of 10,372,000,000 in 2017. About how many orders of magnitude as great is Indonesia’s GDP?
The number of Empire State building‑height stacks of dimes required is 589,008.
What is the height of the Empire State building?The height of the Empire States Building including the antenna is 1,454 feet.
here, we have,
The height of a stack of 100 dimes is 5.3 inches.
The value of a stack of 100 dimes is 10 dollars.
The 2017 U.S. gross domestic product (GDP) = 19,390,604,000 dollars.
Number of stacks of dimes needed = $19,390,604,000 / $10 = 1,939,060,400 stacks of 100 dimes
Height of 1,939,060,400 stacks of 100 dimes in feet = 1,939,060,400 x 5.3/12
Height of 1,939,060,400 stacks of 100 dimes in feet = 856,418,343.3 feet
Number of Empire State building‑height stacks of dimes = 856,418,343.3 / 1,454
Number of Empire State building‑height stacks of dimes = 589,008
In conclusion, the number of Empire State building‑height stacks of dimes required is obtained from the height of the Empire State building and the height of a stacks of 100 dimes.
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On a coordinate plane, a red line, labeled g of x, begins on a negative slope, crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and crosses the x-axis on a positive slope at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 2) and the x-axis at (2, 0).
Which statement is true regarding the functions on the graph?
f(2) = g(2)
f(0) = g(0)
f(2) = g(0)
f(0) = g(2)
Which is the first error that Tomas made?
Tomas substituted the 3 for x when he should have substituted 6 for x.
Tomas added 6 to both sides of the equation instead of subtracting 6.
Tomas should have written the equation as .
Tomas substituted 3 for x when he should have substituted 3 for y.
The correct statement regarding the two functions in this problem is given as follows:
f(2) = g(2).
How to solve a system of equations graphically?The graphic solution of a system of equations is given by the point of intersection of all the equations that compose the system.
The points through which each function passes in this problem are given as follows:
g(x) = (-2,0), (0, -2) and (2,0).f(x) = (0,2) and (2,0).
The point that is common to both function is given as follows:
(2,0).
Meaning that the two functions intersect at x = 2, which is the solution to the system of equations, also meaning that they have the same numeric value at x = 2.
The fact that the two functions have the same numeric value at x = 2 means that the correct statement is given as follows:
f(2) = g(2).
Which is the first statement.
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write the expression as a single real number. Do not use decimal approximations
sin(pie/6)cos(pie/2)-cos(pie/60)sin(pie/2)
The expression as a single real number is [tex]\frac{1-\sqrt{3} }{2}[/tex] .
What is trignomentry ?
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of triangles and to solve problems involving angles and distances in two-dimensional space.
sin(π/6)cos(π/2) - cos(π/60)sin(π/2)
The first term in the expression, sin(π/6)cos(π/2), can be simplified as follows ,
sin(π/6) = √(3)/2, cos(π/2) = 0
so sin(π/6)cos(π/2) = (√(3)/2) * 0 = 0
The second term in the expression, -cos(π/60)sin(π/2) , can be simplified as follows ,
sin(π/2) = 1, cos(π/60) = sqrt(3)/2 - 1/2
so -cos(π/60)sin(π/2) = -(sqrt(3)/2 - 1/2) * 1 = -sqrt(3)/2 + 1/2
Now we can substitute the simplified values back into the original expression ,
0 - (-sqrt(3)/2 + 1/2)
and combining like terms, [tex]\frac{1-\sqrt{3} }{2}[/tex],
Hence , The expression as a single real number is [tex]\frac{1-\sqrt{3} }{2}[/tex] .
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mrs. johnson leaves on a trip planning to travel 24 mph.how fast must his son james travel to overtake himin 5 horus, if he starts 2.5 horus after his father?
Mr. Johnson leaves on a trip planning to travel with speed of 24 mph. His son leaves 2.5 hours after him. To catch his father in 5 hours, James must travel at 36 mph.
The relation between distance and speed is given by:
distance = speed x time.
In this case:
Ms' Johnson's speed = 24 mph
Mr Johnson's time = 2.5 + 5 = 7.5 hours
His travelled distance = 7.5 x 24 = 180 miles.
His son's time = 5 hours ( since he starts 2.5 hours after Mr Johnson left.)
He must catch distance of 180 miles in 5 hours. Therefore, his speed must be:
speed = distance / time
speed = 180 / 5 = 36 mph.
Hence, hisr son's speed is 36 mph.
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PLS HELP Choose 2 answers
Answer: C and D
Step-by-step explanation:
Plug in the X and Y from the coordinates into each equation. If both sides are equivalent, that means that the line passes through.
A mathematics class is given the following trinomial to factor using the grouping method. 6x2 + 11x - 10 Which of the following students has correctly identified the first step towards factoring this trinomial correctly
The factorise form of the trinomial 6x² + 11x - 10 is (3x - 2)(2x + 5).
How to factorise polynomial?Trinomials is a polynomial that has three terms. Let's factorise the trinomial by grouping as follows:
6x² + 11x - 10
The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.
Hence, let's find the factor of 6x² + 11x - 10
6x² + 11x - 10
let's find two numbers we can multiply to get -60 and add to get 11.
6x² + 15x - 4x - 10
3x(2x + 5) - 2(2x + 5)
Hence,
(3x - 2)(2x + 5)
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a piece of clothes was 5 m long,after washing it srank to 4.2m long find the percentage decrease in length
The length of the piece of clothing decreased by 16% after washing.
What is the percentage decrease?
To compute a percentage drop, first determine the difference (decrease) between the two values being compared. Then, divide the reduction by the original number and multiply the result by 100. The percentage change is expressed as a result of the alteration.
The percentage decrease in length of the piece of clothing can be calculated as follows:
Percentage decrease = (original length - new length) / original length * 100
Percentage decrease = (5 - 4.2) / 5 * 100
Percentage decrease = 0.8 / 5 * 100
Percentage decrease = 16%
Hence, the length of the piece of clothing decreased by 16% after washing.
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What is the DIFFERENCE in rates between the 2 people below:
The difference in rates between the 2 peoples is 2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
John y=5x
For sally we have to find the equation
m=28-14/4-2
m=14/2=7
14=7(2)+b
b=0
So for Sally y=7x
Hence, the difference in rates between the 2 peoples is 2.
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Circle O shown below has a radius of 9 inches. To the nearest tenth of an inch,
determine the length of the arc, x, subtended by an angle of 81°.
9 inches
10=81°
Answer:
[tex]\boxed{12.7\;inches}[/tex]
Step-by-step explanation:
For a circle of radius r, the circumference is given by the expression
C = 2πr
So for this circle of radius 9", the circumference is 2 x π x9 = 18π
The entire circle covers a total angle of 360°
If there is a sector of the circle that is subtended by an angle Ф, then the length of that arc will be Ф/ 360 x C
Here Ф = 81°
So length of arc is
[tex]\dfrac{81}{360} \times 18 \pi\\\\\\\textrm {Using a calculator this works out to }\\\\[/tex]
[tex]\dfrac{81}{360} \times 18 \pi = 12.72345\\\\[/tex]
Rounded to the nearest tenth of an inch this would be
[tex]\boxed{12.7\;inches}[/tex] ANSWER
How do you know if an absolute value graph opens up or down?
An absolute value graph is a V-shaped graph that opens either upwards or downwards, depending on the equation. To determine if an absolute value graph opens up or down, you need to examine the value of the constant k in the equation. If k is positive, the graph opens upwards and if k is negative, the graph opens downwards.
The general form of an absolute value equation is y = |x| + k, where k is a constant. The graph of this equation will open upwards if k > 0, and downwards if k < 0.
For example, if the equation is y = |x| + 2, the graph will open upwards and will have vertex at the point (0, 2)
On the other hand, if the equation is y = |x| - 2, the graph will open downwards and will have vertex at the point (0,-2)
The vertex of the graph is the point where the graph changes direction. The x-coordinate of the vertex is always 0 and the y-coordinate is the value of k.
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I WILL GIVE BRAINLEY TO PERSON WHO ANSWERS!! (Correctly) HELP
Answer:
it's the second
Step-by-step explanation:
i did this before and it was the second one
a basket contains 15 apples, of which two are rotten. a sample of three apples is selected at random. in how many ways can two rotten apples be chosen?
There are 6 ways to choose two rotten apples out of a sample of three.
What is algebra ?
Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include the manipulation of equations and formulas using the rules of arithmetic, the solution of equations, and the study of the properties and behaviors of functions.
There are two rotten apples out of 15 total apples, so the probability of choosing a rotten apple is 2/15. The probability of choosing two rotten apples out of a sample of three is (2/15) * (1/14) * (3 choose 2) = (2/455) * 3 = 6/455. So there are 6 ways to choose two rotten apples out of a sample of three.
Hence , There are 6 ways to choose two rotten apples out of a sample of three.
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A waterwheel has a radius of 4 feet, and the center of the wheel is 1 foot under the waterline. You notice a yellow mark at the top of the wheel. If the wheel rotates radians, how far above the water is the yellow mark?
1 foot
2 feet
3 feet
4 feet
The yellow mark is 1 foot above the water level.
This question can be answered using the concept of trigonometry.
According to the given question
radius of the waterwheel r= 4 feet
let OD is the part of the waterwheel that is submerged in the water and its value is to be determined.
From the figure we can see that
OA=OC=radius= 4 feet
Now
In triangle OAB
cos 60= [tex]\frac{OB}{OA}[/tex]
[tex]\frac{1}{2}= \frac{OB}{OA}[/tex]
OB= 2 feet
which means the length of the yellow mark above water is given by
OB-OD= 2-1= 1 feet.
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At a market, a pear cost bc and an apple cost 5 ¢ less than a pear. Mrs Ravi bought 5 pears and an apple. (a) (b) Find the total amount in cents Mrs Ravi paid in terms of b. If each pear cost 60 c, how much did Mrs Ravi pay? Leave your answer in cents.
Answer:
$355
Step-by-step explanation:
if each pear is 60c and apples are 5c less...
60×5=300
300+55=355
because 60-5=55
Vera wants to graph a line that passes through (0, 2) and has a slope of StartFraction 2 Over 3 EndFraction. Which points could Vera use to graph the line? Select three options.
The equation of the line is y = (2/3)x + 2, having a y intercept of 2 and slope of 2
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
The equation of a line with slope m passing through (x₁, y₁) is:
y - y₁ = m(x - x₁)
The line that passes through (0, 2) and has a slope of 2/3, hence:
y - 2 = (2/3)(x - 0)
y = (2/3)x + 2
The equation of the line is y = (2/3)x + 2
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a peer-reviewed (sometimes called refereed) journal article group of answer choices a) has been written by someone with a ph.d. b) is one that has found significant statistical results c) is one for which the author has been paid d) has been evaluated before publication by other researchers in the same field
Peer-reviewed (refereed or scholarly) journals: Before an article is published in a journal, it is examined by a number of other experts in the subject to guarantee that it is of a high caliber. (The paper is more likely to be valid from a scientific standpoint, draw fair conclusions, etc.)
Peer review is conducted on publications in refereed journals.Peer review has been conducted on the publications in a refereed journal. The papers were evaluated for quality by reputable academics or subject-matter experts before being approved for publication, so this tells us that they are of a high caliber. Also known as "scholarly" or "peer-reviewed," these pieces are published in journals.
5 Essential Qualities of writting JournalsAuthors having affiliations or credentials, such as a PhD (e.g. university professor)a particular emphasis on providing fresh, original research in a given field of study (often indicated through a long title)With complicated concepts and arguments, an impartial tone, and an analytical perspective, technical and formal languagematerial that is lengthy (at least 5 pages) and contains a lot of citations and referencesa simple look with barely any color, graphics, or photographs
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probability outcome: toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat? help
is the answer 3!=6
i dont understand how n! could be the way to go about this, if n! is for If you want to see how many ways you can order a certain number of things: n! (n factorial)
Answer:
There are 3! (3 factorial) ways for the toddler triplets to each choose a coat. However, we are only interested in the ways where exactly one of them ends up with their coat.
There are 3 ways for the first toddler to get their coat, 2 ways for the second toddler to get their coat, and 1 way for the third toddler to get their coat.
Therefore, there are 3*2*1 = 6 ways for exactly one of the toddler triplets to end up with their coat.
In other words, there are 6 possible scenarios in which exactly one of the toddler triplets get their coat.
For example, Red getting his coat, Green getting the wrong coat and Blue getting the wrong coat.
Boris runs 7 miles in 50 minutes. At the same rate, how many miles would he run in 75 minutes
Answer: 10.5 miles
Step-by-step explanation:
10.
(15x - 7)
х
37°
11.
Check the picture below.
Question
The understanding of history is molded by primary and secondary
sources. Describe how primary and secondary sources impact one's
understanding of the War of 1812 and its aftermath.
Find the general solution of the given differential equation.
(x + 1) dy/dx + (x + 2)y = 2xe?x
y=
Give the largest interval I over which the general solution is defined. (Think about the implications of any singular points.)
(??, ?)
(0, 1)
(?1, ?)
(0, ?)
(??, 1)
Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)
Solve the given initial-value problem. Give the largest interval I over which the solution is defined.
xy' + y = ex, y(1) = 8
y =
I
=
Solve the given initial-value problem. Give the largest interval I over which the solution is defined.
Ldi/dt + Ri = E, i(0) = i0, L, R, E, i0 constants
i =
I =
The whole response to the specified differential equation. (x + 1) dy/dx + (x + 2) y = 2xe is equal to y1(x), y2(x), f(x), and W(y1, y2), where dx = (ex)(1/2 e2x) = 1/ 2 e3x.
what is solution ?fixing a problem by an action or process; providing a solution explanation. an assortment of variable values that satisfy an equation, specifically Any value of a variable in an equation that fulfills the equality, that is, makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal, is the solution. Finding the solution(s) to an equation is what it means to solve it. The percentage of a solute in the solvent is one way to express a solution's concentration. the ratio of the mass of the solute to the mass of the solution
given
The characteristic equation is: r2 − 3r + 2 = 0
Factor: (r − 1)(r − 2) = 0
r = 1 or 2
So the general solution of the differential equation is y = Aex+Be2x
So in this case the fundamental solutions and their derivatives are:
Find the particular solution using the formula:
yp(x) = −y1(x)∫ y2(x)f(x) /W(y1, y2) dx + y2(x)∫ y1(x)f(x) /W(y1, y2) dx
4. First we solve the integrals:
∫ y2(x)f(x) / W(y1, y2) dx
= ∫ e2xe3xe3x dx
= ∫e2xdx
= 1 / 2 e2x
So:
−y1(x)∫ y2(x)f(x) / W(y1, y2) dx = −(ex)( 1/2 e2x) = − 1 / 2 e3x
the whole response to the specified differential equation. (x + 1) dy/dx + (x + 2) y = 2xe is equal to y1(x), y2(x), f(x), and W(y1, y2), where dx = (ex)(1/2 e2x) = 1/ 2 e3x.
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Pls help very urgent Write the rule for the linear function. Remember a function rule is written using f(z). 4 2- -2 2 X
