The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
Define confidence interval.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. The size of a 90% confidence interval for a given estimate is one way to gauge how "excellent" it is; the greater the interval, the more care must be used when utilizing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limits.
Given,
Data set: (33190, 31860, 32590, 26520, 33280, 32320, 33020, 32030, 30460, 32700, 23040, 30930, 32720, 33650, 32340, 24050, 30170, 28730, 31920)
The normal distribution's standard deviation, s = 3000 pounds
95% confidence interval
N = 20 observations were made.
Mean = 30,800
Margin of error :
z₇ × √3000².20
±1.314.8079
Confidence interval
= Mean + Margin of error
= 30,800 ±1.314.8079
= 29,485.192 , 32,114.8
The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
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Write the first four terms of the sequence defined by the explicit rule. f(n) = 3n + 6
The first four terms of the sequence would be -
9, 12, 15, 18
What is a Sequence?Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -
3, 6, 9, 12, 15
x, x + 2, x + 4, x + 6
We have the following sequence -
f(n) = 3n + 6
We can write the first four terms as -
f(1) = 3 x 1 + 6 = 9
f(2) = 3 x 2 + 6 = 12
f(3) = 3 x 3 + 6 = 15
f(4) = 3 x 4 + 6 = 18
Therefore, the first four terms of the sequence would be -
9, 12, 15, 18
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What does x equal to??
x is equal to 125° in the triangle
How to determine the value x in the triangle?The figure given here is a triangle. And we know that the sum of the angles in a triangle is 180°. So we can apply this concept by writing the expression below:
x + 25° + 30° = 180°
x + 55° = 180°
x = 180° - 55°
x = 125°
Therefore, the value of x is 125°. So x is equal to 125°
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Camilla borrows a book from the library for dd days. The library charges a late fee of 0. 10 dollars per day that the book is late. If Camilla returns the book more than 21 days after she borrowed it, the expression 0. 10(d-21) represents the total late fee Camilla owes
The expression represents the amount of total money. Then the total late fee Camilla owes will be $2.1.
What is Algebra?
Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
Camilla borrows a book from the library for d days.
The library charges a late fee 0.10 dollars per day that the book is late.
If Camilla returns the book more than 21 days after she borrowed it.
Then the expression will be 0.10d.
The total amount is given as
Total amount = 0.10 d
Total amount = 0.10 x 21
Total amount = $2.1
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Surface area of a rectangular prism 2cm 8cm 7 cm
The surface area of the rectangular prism is 172cm^2
What is a prism?Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross sections. The faces of the prism are parallelograms or rectangles.
The surface area of prism is 2A+ pH
where A is the base area
P is the perimeter of the base
and h is the height
for a rectangular prism, the base area is 2×8=16cm^2
perimeter of a rectangle= 2(l+b)
= 2(8+2)
= 20cm
surface area =( 2× 16) + 20× 7
= 32+ 140
= 172cm^2
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In thi quetion, aume that the car ue the ame amount of petrol for each mile it travel. A car ue 55 litre of petrol to travel 495 mile. How much petrol would the car ue on a trip of 160 mile?
Give your anwer to the nearet litre
The car use 6.67 liters of petrol to travel 160 miles of distance.
Given, the car use the same amount of petrol for each mile it travels.
A car use 55 liters of petrol to travel 495 miles.
we have to find the petrol used to travel 160 miles.
As, 55 liters = 495 miles
495 miles = 55 liters
1 mile = 55/495 liters
Now, 160 miles = 55/495×160 liters
160 miles = 6.67 liters
So, the car use 6.67 liters of petrol to travel 160 miles of distance.
Hence, the car use 6.67 liters of petrol to travel 160 miles of distance.
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Write and Solve the equation: A printing company charges $0.15 per copy in addition to a service fee of $3. Write an equation to represent the cost, y, the company charges for x numbers of copies. How much would 250 copies cost?
The equation representing the cost is y = 0.15x + 3 where x ix the number of copies and y is total cost.
Cost for 250 copies is $40.5
What is equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a printing company charges $0.15 per copy in addition to a service fee of $3,
Therefore, according to question, the total cost y for printing x copies is,
y = 0.15x + 3
For x = 250
y = 0.15*250 + 3
y = $40.5
Hence, The equation representing the cost is y = 0.15x + 3 where x ix the number of copies and y is total cost.
Cost for 250 copies is $40.5
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Transformation of functions f(x)=-7(x-8)^2 +2
Answer:
Step-by-step explanation:
I think this is the answer you were looking for but im not 100% sure
rewrite the function g(x)=2x^2+16x+6 in vertex form by completing the square
The vertex form of the function g(x)= 2[tex]x^2[/tex]+16x+6 is g(x)= 2[tex](x+4)^2[/tex]-26.
What is vertex form of the function?
The function's maximum or lowest possible output is represented by the vertex of the quadratic function's graph. When viewing a graph, the vertex is the highest or lowest point on the parabola. Utilizing the vertex formula is the simplest technique to discover the vertex. It is simple to locate the vertex of the parabola using the vertex form of a quadratic equation. Y=a(xh)2+k is the definition of the generic vertex form, where h is the x-coordinate and k is the y-coordinate of the vertex.
Here the given function is ,
=> g(x) = 2[tex]x^2[/tex]+16x+6
=> g(x) = 2([tex]x^2+[/tex]8x+3)
=> g(x) = 2([tex]x^2+[/tex]8x+16-16+3)
=>g(x) = 2 [[tex](x+4)^2[/tex]-13]
=> g(x)= 2[tex](x+4)^2[/tex]-26
Therefore vertex form of the function is g(x)= 2[tex](x+4)^2[/tex]-26 and vertex is (-4,-26).
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Answer:
g(x)=2(x+4)^2-26
Has a minimum value of -26
Step-by-step explanation:
i got it right!
A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 68 seconds at a speed of 0.8 feet per second.
She then ascends for 11 seconds at a speed of 3.8 feet per second.
Answer:
-11.8
Step-by-step explanation:
68x0.8
11x3.8
11x3.8=41.8
68x0.8=54.4
54.4-41.8=12.6
Now minus add a minus to it and you get -12.6 FT
< The concession stand at the baseball park sells food in value packs. The ratio in the value pack is 4 hot dogs 2 drinks: 1 bag of chips. A tape diagram representing the ratio of each item is shown. hot dogs drinks chips a. Describe what each small rectangle in the tape diagram represents b. What is the least total amount of items in a value pack? c. How many bags of chips are in a value pack if there are 10 drinks?
Answer:
someone answer please ive been waiting for 2 hours :skull:
Step-by-step explanation: please answer yall
=. A model plane is 24 cm in length. It represents a real plane that is 72 meters in
length. What is the scale used?
The scale used is 1 cm : 3m
a market research firm conducts telephone surveys with a 44% historical response rate. what is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? in other words, what is the probability that the sample proportion will be at least 150 400
The likelihood that at least 150 people will collaborate and react in a fresh sample of 400 telephone numbers is 0.9953.
Describe probability?The probability informs us of the likelihood that an event will occur. It is necessary for the likelihood to fall between 0 and 1. The likelihood of success is 1, whereas the probability of failure is 0.
Given, that the market research company has a history of having a 44% response rate for its telephone surveys.
Therefore, p=44%=0.44=μ
n=400
p=150/400
p=0.375
The standard deviation is then equal to,
σ=√(p(1-p))/n
σ=√(0.44(1-0.44))/400
σ=√(0.44×0.56)/400
σ=0.025
Using the z-table, the values are as follows:
z=(p-μ)/σ
z=(0.375-0.44)/0.025
z=-2.6
p(p>0.375)
=p(z>-2.6)
=1-p(z<-2.6)
=1-0.0047
=0.9953
=99.53%
Therefore, the likelihood that at least 150 people will participate and provide information in a new sample of 400 telephone numbers
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Rewrite x^3+8x^2+11x-20 as a product of linear factors. Explain how you found the factors.
The linear factors of the given cubic polynomial are (x-1)(x+4)(x+5).
What are linear factors?The linear factors of a polynomial are the first-degree equations that are the building blocks of more complex and higher-order polynomials.
Given a cubic polynomial, x³+8x²+11x-20
x³+8x²+11x-20 = (x-1)(x²+9x+20)
= (x-1)(x²+4x+5x+20)
= (x-1){x(x+4)+5(x+4)}
= (x-1)(x+4)(x+5)
Hence, The linear factors of the given cubic polynomial are (x-1)(x+4)(x+5).
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William leaves work at 16:00. He drives 36 kilometres from work to home at an average speed of 48 km/h. What time does William arrive home?
answer using the 24 hour clock.
William will arrive home at 16:45, it will take 45 min to reach home.
Given, that William leaves work at 16:00
Distance from work to home is 36 kilometres
Also, he drives at an average speed of 48 km/hr
Now, using distance-speed relation to find the time
So, as we know Distance = Speed × Time
On putting the values of distance and speed, we get
36 km = 48 km/hr × Time
On dividing both the sides by 48, we get
36/48 = (48×Time)/48
36/48 = Time
Time = 0.75
Hence, he will take 0.75 hr to reach home.
0.75 hr ≈ 45 minutes
As, 1 hr = 60 minutes
0.75 hr = 0.75 × 60 = 45 minutes
So, William will arrive home at 16:45
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Karama can paint a staircase banister in 50 minutes. Find the rate per minute at which Karama can paint banisters
The rate per minute at which Karama can paint banisters is 0.02.
In the given question,
Karama can paint a staircase banister in 50 minutes.
We have to find the rate per minute at which Karama can paint banisters.
Since we have to find the rate per unit. Rate per unit means how much Karama can paint in one minute.
To find the rate per unit we divide 1 by 50.
As we know that Karama can paint one staircase banister in 50 minute.
So we can write it as
50 minute = 1 staircase banister paint
Now in 1 minute.
1 minute = 1/50 staircase banister paint
Simplifying
1 minute = 0.02 staircase banister paint
Hence, the rate per minute at which Karama can paint banisters is 0.02.
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A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the
function S=18.95 +0.50M, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I=4.80 +0.15M.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
An equation relating C to M is (C) = 23.75 + 0.65M.
Given,
In the question:
The standard charge S (in dollars) is given by the
function S=18.95 +0.50M, where M is the number of miles driven.
The insurance charge I (in dollars) is given by the function I=4.80 +0.15M.
and, Let C be the total charge (in dollars) for a rental that includes insurance.
To find the An equation relating C to M.
Now, According to the question:
By the topic:
The total Charge (C) = The standard Charge (S) + The insurance charge (I)
Thus,
The total Charge (C) = 18.95 +0.50M + 4.80 +0.15M.
Combine like terms:
The total Charge (C) = 18.95 + 4.80 + 0.50M + 0.15M
The total Charge (C) = 23.75 + 0.65M
Hence, An equation relating C to M is (C) = 23.75 + 0.65M.
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5-(40/5)
Step A: 5+ (4)
Step B: 5+8
Step C: 13
In which step did the student first make an error? Be sure to include the correct value of
the expression in simplest form in your answer.
Explain your answer.
Answer:
5 - [tex]\frac{40}{5}[/tex] = 5 - 8 = -3
Step-by-step explanation:
The first mistake made by the student is in Step A where the problem was not copied down correctly.
De la comida que hay en la nevera, un tercio son alimentos sólidos. De estos un medio son vegetales, de los cuales tres quintos son frutas, de las que dos quintos son manzanas.
¿Qué fracción del total son manzanas?
Si X es la cantidad total de alimento en la heladera, (1/10)*X es la cantidad de manzanas, entoces vemos que la fraccion es 1/10.
¿Qué fracción del total son manzanas?Digamos que la variable X representa la cantidad total de comida en la heladera.
Sabemos que un tercio del total de los alimentos son solidos, entonces la cantidad de alimentos solidos es:
(1/3)*X
Luego 1/2 de estos son verduras, entonces la cantidad de verduras que tenemos es:
(1/2)*(1/3)*X
Finalmente, 3/5 de las verduras son manzanas, entonces la cantidad de manzanas es:
(3/5)*(1/2)*(1/3)*x = (1/10)*x
Asi hemos encontrado la fraccion.
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Find the equation of the straight line passing through the point (3, 5)
which is perpendicular to the line
y = 3x + 2
Answer:
y = -1/3x +6
Step-by-step explanation:
You want the equation of the line through (3, 5) perpendicular to the line y = 3x +2.
Perpendicular lineThe given equation is in slope-intercept form. This lets us identify its slope as 3.
y = mx + b . . . . . . line with slope m and y-intercept b
y = 3x +2 . . . . . . . line with slope 3 and y-intercept 2
The perpendicular line will have a slope that is the opposite reciprocal of this:
m = -1/3 . . . . slope of the perpendicular line
Point-slope formThe equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
The equation for a line with slope -1/3 through point (3, 5) is ...
y -5 = -1/3(x -3)
Slope-intercept formSolving for y gives us ...
y = -1/3x +1 +5 . . . . . eliminate parentheses, add 5
y = -1/3x +6 . . . . . equation of the desired line
<95141404393>
Please help with slope question
choose any 2 points on the graph
To calculate the slope use the formula:
slope = y (point 2)-y (point 1)/x (point 2)-x (point1)
substitute the choses points in
calculate your awnser
Write and equation in slope intercept form for the line that passes through the given point and is parallel to the graph of the equation
(4, -3); x = -5
The equation in slope intercept form is x =4 .
Given:
x = -5
x + 5 = 0
here slope m = ∞.
line equation passes through (4,-3) with m = ∞
-3 = 1/0(4) + c
4 + c = 0
c = -4.
y = (1/0)x - 4
x - 4 = 0
x = 4.
Therefore the equation in slope intercept form is x =4 .
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The identification of a relationship using
multiplication and the prediction of the value of one
quantity based on the value of another.
Utilizing multiplication to find relationships and predicting that value of one "Linear regression" is a quantity derived from the value of another.
Define the term Linear regression?The relationship in between magnitude of one parameter and that of a second is modeled by simple linear regression.
For instance, as X rises, Y also increases. or Y declines as X rises. 1 Regression defines the nature of the link, whereas correlation evaluates the strength of such a linking between two variables.Simple linear regression calculates the precise amount by which Y will alter when X alters by a specific amount. The variables X and Y remain interchangeable with the correlation coefficient. Regression uses a linear relationship, or a line, to try and predict any Y variable from the X variable:Y = b 0 + b 1 X.Thus, finding correlations via multiplication and assuming that the value of one "Linear regression" is a number obtained as from value of another
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Write an equation in slope-intercept form of the line that passes through the given points.
Equation in slope-intercept form of the line that passes through the given points is y = 2x - 1/2.
Given points:
(1, 1.5) and (2, 3.5)
slope m = 3.5 - 1.5 / 2 - 1
= 2/1
m = 2
substitute m and (1,1.5) in y = mx + c
1.5 = 2*1 + c
1.5 - 2 = c
c = -0.5
c = -1/2
y = mx + c
y = 2x - 1/2.
Therefore equation in slope-intercept form of the line that passes through the given points is y = 2x - 1/2.
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Find the measurement of X.
Answer:333
Step-by-step explanation:
Since this is a scalene triangle, two sides will equal the same, meaning two angles will equal the same. So 70 has an equal on the other side, meaning 70+70=140, and x will equal the remainder, meaning x=40.
Hope that helps.
Which of the following expressions is equivalent to 2y (3y^2 + 4y^4)
The expression that is equivalent to the given expression is 6y³ + 8y⁵
Evaluating an expression and determining an equivalent expressionFrom the question, we are to determine the expression that is equivalent to the given expression
The given expression is
2y (3y^2 + 4y^4)
This can be properly written as
2y (3y² + 4y⁴)
Now, to determine the expression that is equivalent to this expression, we will expand the expression by applying the distributive property.
2y(3y² + 4y⁴)
2y(3y²) + 2y(4y⁴)
Multiplying
6y³ + 8y⁵
Hence,
The expression is 6y³ + 8y⁵
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The radius of a circle is 15 inches. What is
the circumference of the circle? Write
your answer using T.
Answer:
C = 30pi inches
Step-by-step explanation:
The radius is 15 inches (said so in the question)
The diameter is 30 inches (The diameter is twice the radius)
The circumference is
C = pi•d
C = pi•30
C = 30pi
The circumference is 30pi inches.
For each sequence, decide whether it could be arithmetic, geometric, or
neither.
1. 27, 9, 3, ...
2. 4, 8, 12,...
3. 50, 56, 60, ...
4. 36, 12, 4, ...
5. 4, 24,...
1. Therefore, the sequence is geometric.
2. Therefore, the sequence is arithmetic.
3. Therefore, the sequence is neither arithmetic nor geometric.
4. Therefore, the sequence is geometric.
5. Therefore, the sequence is neither arithmetic nor geometric.
Explain sequences and seriesFor the arithmetic, geometric, and harmonic sequences, a collection of sequences and series formulas is provided below. The sequence and series formulas presented here contain formulas for determining the sum of the n terms in a series as well as the nth term of the sequence.
A common difference exists between two succeeding terms in an arithmetic series. There is a typical ratio between succeeding terms in a geometric series.
1. Given sequence is 27, 9, 3, ...
As the difference between the number is large.
So, we will check for geometric sequence.
[tex]r = \frac{27}{9} = \frac{3}{3} = \frac{1}{3}[/tex]
Therefore, the sequence is geometric.
2. Given sequence is 4, 8, 12, ...
As we can see there is uniform difference of 4
Therefore, the sequence is arithmetic.
3. Given sequence is 50, 56, 60, ...
As the difference between the number is not uniform.
So, we will check for geometric sequence.
[tex]r = \frac{50}{56} \neq \frac{56}{60}[/tex]
There, the sequence is neither arithmetic nor geometric.
4. Given sequence is 36, 12, 4, ...
As the difference between the number is large.
So, we will check for geometric sequence.
[tex]r = \frac{36}{12} = \frac{12}{4} = 3[/tex]
Therefore, the sequence is geometric.
5. Given sequence is 4, 24, ...
The number of terms is very less and hence we can't decide.
There, the sequence is neither arithmetic nor geometric.
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ERROR ANALYSIS Describe and correct the error in identifying congruent triangles. TUV=XYZ by the SSS Congruence Theorem.
The letters for XYZ are in the wrong order.
The correct statement should be [tex]\triangle TUV \cong \triangle ZYX[/tex]
============================================
Further Explanation:
The order of the letters matters when writing congruence statements.
The claim is that [tex]\triangle TUV \cong \triangle XYZ[/tex]
The first two letters of each are "TU" and "XY" in that order.
But notice how TU has a single tickmark, while XY has a double tickmark. The two sides are clearly different.
--------
Instead, the statement should be: [tex]\triangle TUV \cong \triangle ZYX[/tex] because of the following three facts:
TU = ZY (single tickmark)UV = YX (double tickmark)TV = ZX (triple tickmark)Notice that:
TU and ZY are the 1st two letters of TUV and ZYXUV and YX are the last two letters of TUV and ZYXTV and ZX are the 1st and 3rd letters of TUV and ZYXDetermine the value of x in the equation below.
16 - (x + 5) = 5
Answer:
x=6
Explanation:
16-(x+5)=15
open the bracket using 1 as an invisible number after the minus sign16-x+5=15You move -x to cross the equality sign and it change to + 16+5-15 =x+15 change to -15 because of the equality sign 21-15=6x=6what was the major flaw in the stanford prison experiment? question 9 options: a) the respondents wanted to leave, but zimbardo would not let them. b) the students were not randomly assigned. c) the study went on too long. d) zimbardo did not use a control group.
Zimbardo did not use a control group. Experiments are performed to reach meaningful conclusions using the appropriate research method. The correct answer is (A).
Experiments whether they are done in natural settings or in a controlled environment need to follow certain ethics. But the Stanford Prison Experiment is an exception. In this experiment, Philip Zimbardo, the Stanford psychologist, took paid participants and asked them to be “guards” in a mock prison at Stanford University.
As soon as the experiment began, the “guards” began mistreating the “prisoners,” in order to provoke evil circumstantially. The conclusion of the study suggested innocent people, thrown into a situation where they have power over others, will begin to misuse that power. And people who are put into a situation where they are powerless will be driven to submission.
The Stanford Prison Experiment has proved to be a Fraud. Philip Zimbardo, the Stanford psychologist who did the experiment, and interviews of the participants, offers convincing evidence that the guards in the experiment were trained to be cruel. This proves that the experiment’s most memorable moment of a prisoner screaming out of rage and proclaiming, “I’m burning up inside!” was the result of the prisoner's acting skills. Many of them think of this study as more of a dramatic demonstration with no real outcomes. The Zimbardo prison experiment is a classic study that has been recently reevaluated and exposed as a fraud.
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