The values of a, b and c in the mixed fractions are 1, 5 and 9 respectively.
How to simplify fractions?The fractions are mixed fractions . let's convert it to improper fraction be we simplify its.
A mixed fraction is a whole number and a proper fraction combined. Improper fractions are defined as fractions for which the numerator is greater than the denominator.
Therefore, let's solve the fractions as follows:
[tex]3\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
[tex]3\frac{1}{2} = \frac{7}{2}[/tex]
[tex]2\frac{1}{4} = \frac{9}{4}[/tex]
Therefore,
[tex]\frac{7}{2} (\frac{4}{9} ) = \frac{28}{18} = 1\frac{10}{18} = 1\frac{5}{9}[/tex]
Hence,
a = 1
b = 5
c = 9
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what is the value of underlined 5 fogit numbers?
In four digits number, if 5 is ones place, then the value is 5. It 5 is on tens place then the value will be 50. If the 5 is on hundred places then value will be 500. If 5 are on thousand places then value will be 5000.
In the given question, we have to find the value of underlined 5 in four digit numbers.
As we know that,
Place value labels like tens and ones notify us of a number appear digit's value. More than one digit can be used to create a number. As a result, to better understand the value of each digit, we employ place value labels such as ones, tens, hundreds, and thousands.
As we know that we count the numbers as ones, tens, hundreds and so on.
So if a 4 digit number is given and we have to find the value of underline 5, and then if 5 is ones place, then the value is 5. It 5 is on tens place then the value will be 50. If the 5 is on hundred places then value will be 500. If 5 are on thousand places then value will be 5000.
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a hippogriff rancher wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure below). he has 590 feet of fencing available to complete the job. what is the largest possible total area of the four pens?
The largest area is found to be 8702.5 [tex]ft^{2}[/tex].
We know that area of rectangle
A = xy ........ (1)
Perimeter of rectangle (given) = 590 ft
Using x and y as two variables ;
5x + 2y = 590
solve yb in term of x
y = -5/2 x + 295......(2)
Now we will get area only in one variable from (1) and (2)
A = x ((-5/2)x + 295)
A = -5/2 [tex]x^{2}[/tex] + 295x
differentiate it with respect gto x
A' = -5x + 295........ (3)
find the critical point to get your minima and maxima value.
Put A' = 0, x = 295/5 = 59
x = 59
then , from (2)
y= (-5/2 × 59) + 295 = 147.5
y = 147.5
again differentiate (3)
A'' = -5 < 0. i.e critical point x = 59 is point of maxima.
So, maximum area = 59 × 147.5
Largest area = 8702.5 [tex]ft^{2}[/tex]
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Let f(x) = 4x and g (x) = (4) ^x-1 + 2. Which transformations are needed to transform the graph f (X) to the graph of g (X)? Select each correct answer.
1. horizontal translation 2 units left
2. vertical translation 1 unit down
3. vertical translation 2 units up
4. horizontal translation 1 unit right
5. horizontal translation 1 unit left
6. vertical translation 1 unit up
complete the table of values y=x² - 4x - 2
Vector Vector P Q has an initial point at (3, 3) and its terminal point is at (5, 7).
Vector Vector R S has an initial point at (4, –6) and its terminal point is at (1, –5).
What is the component form of vector ?
The correct answer is: 5,3
Initial and terminal points of the vector [tex]\vec{PQ}[/tex] of (3., 3) and (5, 7) , and the initial and final point of the vector [tex]\vec{RS}[/tex] of (4, -5), and (1, -5), indicate that the the difference between the vectors is; 5·i + 5·j
What is a vector?
A vector is a quantity that has both magnitude and direction.
The specified vectors are;
The initial and terminal point on vector [tex]\vec{PQ}[/tex] are; (3, 3) and (5, 7)
The initial and terminal point of vector [tex]\vec{RS}[/tex] are (4, -6), and (1, -5)
Therefore, the vector [tex]\vec{PQ}[/tex] - [tex]\vec{RS}[/tex] is therefore;
The vector form of [tex]\vec{PQ}[/tex] = <5 - 3, 7 - 3> = <2, 4>
The vecror form of [tex]\vec{RS}[/tex] = <1-4, -5 - (-6)> = <-3, -1>
The difference between the vectors is therefore;
The vectors are therefore;
[tex]\vec{PQ}[/tex] = 2·i + 4·j
[tex]\vec{RS}[/tex] = -3·i - j
The difference between the vectors is therefore;
[tex]\vec{PQ}[/tex] - [tex]\vec{RS}[/tex] = (2 - (-3))·i + (4 - (-1))·j = 5·i + 5·j
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Help with these two problems will give branliest
Answer:
15. x = 4
16. x = 7
Step-by-step explanation:
15.
CD/ ED = DG / DF
48 / (5x - 2) = 40 / (2x + 7)
48 (2x + 7) = 40 (5x - 2)
96x + 336 = 200x - 80
200x - 96x = 336 + 80
104x = 416
x = 4
16.
ST / PL = TU / LM
(x + 1) / 72 = (2x - 3) / 99
99 (x + 1) = 72 (2x - 3)
99x + 99 = 144x - 216
144x - 99x = 99 + 216
45x = 315
x = 7
a random sample of 46 salespersons was asked how long on average they were able to talk to a potential customer. their answers revealed a mean of 8.90 with a variance of 6 minutes. construct a 95% confidence interval for the time it takes a salesperson to talk to a potential customer.
With 95% of confidence interval for the time it takes salesperson to talk to a potential customer is (12.42 , 5.38).
A Random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected, minimizing the risk of selection bias.
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by σ ² ,s² ,Var(X) , or V(X).
A confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level represents the long-run proportion of corresponding CIs that contain the true value of the parameter. For example, out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value.
Given in the question:
n = 46
x = 8.90
σ = 6
α = 0.95
As we know that:
[tex]X[/tex] ±[tex]Z_{\alpha /2} * \frac{\beta }{\sqrt{n} }[/tex]
putting the values we get,
8.90 ± Z (0.95/2) ×6/√46
Now, considering the positive sign, we get,
= 8.90 + 3.52
= 12.42
Now considering the negative sign,
8.90 ± Z (0.95/2) ×6/√46
= 8.90 - 3.52
= 5.38
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t the movie theatre, child admission is and adult admission is . on wednesday, twice as many adult tickets as child tickets were sold, for a total sales of . how many child tickets were sold that day?
The number of child ticket were sold on Wednesday is 236
The cost of child admission ticket = $6.10
The cost of adult admission ticket = $9.20
Consider the number of child ticket as x and the number of adult ticket as y
Twice times as many adult tickets as child tickets were sold
y = 2x
Then the equation will be
x + y = 707.70
Substitute the value of y in the equation
x + 2x = 707.70
Add the like terms
3x = 707.70
x = 707.70/3
Divide the terms
x = 235.9
x ≈ 236
Therefore, 236 child ticket were sold on that day
I have answered the question in general, as the given question is incomplete
The complete question is:
At the movie theatre, child admission is $6.10 and adult admission is $9.20 . On Wednesday, twice times as many adult tickets as child tickets were sold, for a total sales of $707.70 . How many child tickets were sold that day?
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tickets to movie cost $5 for adults and $3 for students. A group of friends purchased 18 tickets for $82.00. How many adults ticket did they buy
Answer: 14 Adult tickets
Step-by-step explanation:
The equation for the total number of tickets would be
x+y=18
5x+3y=82
y=18-x
5x+3(18-x)=82
2x=28
x=14
x= Number of adult tickets
what is distributional hypothesis in the context of distributional semantics? give a short explanation with some examples. g
Distributional semantics develops methods for measuring and classifying semantic similarity between language elements.
To quantify and classify semantic relatedness among linguistic items based on their distributional qualities in large samples of language data, distributional semantics is a field of study. The distributional hypothesis captures the fundamental principle of distributional semantics.
The semantic theory of language usage, states that terms used and occurring in comparable situations tend to have similar meanings is the basis for the distributional hypothesis in linguistics. For instance, the words "fire" and "dog" have very different meanings and aren't typically used together in a sentence. However, the terms "dog" and "cat" are occasionally used interchangeably, suggesting that they may have a similar connotation.
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Jessica bought a kitten from a pet store and recorded its weight at various times over a 6 month period.
She found the linear model that best fit the data was w = 0.45n + 0.12, where n is the number of months since Jessica bought the kitten and w is the kitten's weight in kilograms.
Drag and drop the correct numbers below to complete the sentence.
According to the model, the kitten gained approximately 0.45 kilograms every month and the kitten weighed approximately 0.12 kilograms when Jessica bought it from the store.
Linear functions: Completing a sentenceFrom the question, we are to drag and drop the correct numbers to complete the given sentence.
The given sentence is
According to the model, the kitten gained approximately ____ kilograms every month and the kitten weighed approximately ____ kilograms when Jessica bought it from the store.
From the given information,
The equation that fits the model is
w = 0.45n + 0.12
By comparing with the slope-intercept form a line,
y = mx + c
Where m is the slope
and c is the y-intercept
m = 0.45
and c = 0.12
This means the kitten gained approximately 0.45 kilogram every month and the initial weight of the kitten is 0.12 kilogram
Hence,
The kitten gained approximately 0.45 kilograms every month and the kitten weighed approximately 0.12 kilograms when Jessica bought it from the store.
Here is the complete question:
Jessica bought a kitten from a pet store and recorded its weight at various times over a 6 month period.
She found the linear model that best fit the data was w = 0.45n + 0.12, where n is the number of months since Jessica bought the kitten and w is the kitten's weight in kilograms.
Drag and drop the correct numbers below to complete the sentence.
According to the model, the kitten gained approximately ____ kilograms every month and the kitten weighed approximately ____ kilograms when Jessica bought it from the store.
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can you help with this question
Answer:
1. y=5
2. y=2x-1
3.y=-2x+1
4. y=-(1/2x)+1
Step-by-step explanation:
1. y=y-intercept. y=5.
2. 2x=mx=slope. -1=b=y-intercept
3. 2x=mx=slope. 1=b=y-intercept
4. -(1/2x)=mx=slope. 1=b=y-intercept
-Hope this helped
PLEASE! HELP ASAP GIVING 100 POINTS AND BRAINLEST!
Write a system of equations to compare these two scenarios:
1) You buy a grande café latte from Starbucks every day, which costs 3.65
2) You spend 300 to buy an espresso machine and purchase supplies for lattes, which cost an additional 1.35 a day.
a) After how many days will the price of buying lattes for Starbucks equal the price of making lattes at home?
b) How much money will you have spent at this point?
The equations used to compare the two scenarios are as follows:
3.65x
300 + 1.35x
What is an equation?Identifying which variables values result in equality is part of solving a variable equation. The variables for which the equation must be solved are known as unknowns, whereas the unknown values that fulfill the equality are known as equation solutions. A mathematical expression with two equal sides separated by an equal sign is known as an equation. 4 + 6 = 10. We can see 4 + 6 on the left and 10 on the right side of the equal symbol.
We already have,
1) You often purchase a grande cafe latte from Starbucks, which costs $3.65.
This formula is:
Number of days = x
Total cost after x days = 3.65x
2) You spend $300 on an espresso machine and ingredients for lattes, which cost an extra $1.35 per day.
This formula is:
Number of days = x
Total cost after x days = 300 + 1.35x
Now, three days later,
3.65 x 3 = $10.95
300 + 1.35 x 3 = 300 + 4.05 = $304.05
Thus,
The equations used to compare the two scenarios are as follows:
3.65x
300 + 1.35x
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Paul is making turkey burgers that are 1/4 pound each. He has 2.93 pounds of turkey how many turkey burgers can he make
Answer: 11 turkey burgers
Step-by-step explanation:
1/4 = 0.25
2.93 ÷ 0.25 = 11.72
You can't have a partial burger, so round down
He can make 11 turkey burgers
Answer:
12 burgers
Step-by-step explanation:
i just did this, you round up from the fraction you get
A ski lift rises at a 28° angle during the first 20 feet
up a mountain to achieve a height of 25 feet, which is the
height maintained during the remainder of the ride up
the mountain. Determine the length of cable needed for
this initial rise
The length of cable that is needed for the initial rise is; 41 feet.
How to use Law of Sines?The given parameters are as shown in the image of the triangle attached.
Where;
A = 28 , a = 25 ft, and b = 20 ft.
Now, if A is acute and a > b, it means that one solution exists. Using the
Law of Sines to find B;
a/sin A = b/sin B
Plugging in the relevant values gives;
25/sin 28 = 20/sin B
sin B = (20 sin 28)/25
sin B = 0.3756
B = sin⁻¹0.3756
B = 22.06°
Due to the fact that the two angles are now known, it means that the angle opposite x is 180 – (28 + 22.06 ) = 129.94 . Using the Law of Sines to find x;
a/sin A = x/sin X
25/sin 28 = = x/sin 129.94
solving fir x gives;
x = 40.83 ≈ 41 feet
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I WILL OPEN MY ALT AND COMENT AND GIVE YOU A BRINLIST OPEN IF YOU SHOWED YOUR WORK!!! OPEN THE IMAGE
Answer:
a = -5/4
Step-by-step explanation:
There are too many steps, it would take an hour to list it all....
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 9 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
are you sure this is correct tho?
Step-by-step explanation:
5. What must the complement of the supplement
of an obtuse angle be?
(A) an acute angle
(B) a right angle
(C) an obtuse angle
(D) a straight angle
(E) a reflex angle
**I’ll give 20 points!
Answer:
A Acute angle (Give me pointssss)
Step-by-step explanation:
Its right bc im smart
a variable is normally distributed with mean 23 and standard deviation 6. use your graphing calculator to find each of the following areas. write your answers in decimal form. round to the nearest thousandth as needed. a) find the area to the left of 25. 0.557 b) find the area to the left of 16. c) find the area to the right of 22. d) find the area to the right of 28. e) find the area between 16 and 30.
a) The area to the left of 25 is 0.63056
b) The area to the left of 16 is 0.12167
c) The area to the right of 22 is 0.56618
d) The area to the right of 28 is 0.20233
e) The area between 16 and 30 is 0.75666
Given,
The mean of the distribution = 23
Standard deviation = 6
We have to find the following areas
(a) Entering the values
Lower : -999999999Upper : 25Area (probability): 0.63056(b) Entering the values
Lower : -999999999Upper : 16 Area (probability): 0.12167(c) Entering the values
Lower : 22 Upper : 999999999 Area (probability): 0.56618(d) Entering the value
Lower : 28 Upper : 999999999 Area (probability): 0.20233(e) Entering the values
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values for the random variables or uncertain variable inputs to a simulation are a. randomly generated from the specified probability distributions b. equal to the most likely value c. selected by the decision maker d. calculated by fixed mathematical formulas e. controlled by the decision maker
The correct option is:
a. randomly generated from the specified probability distributions
Given,
In the question:
Values for the random variables or uncertain variable inputs to a simulation are:-
a. randomly generated from the specified probability distributions
b. equal to the most likely value
c. selected by the decision maker
d. calculated by fixed mathematical formulas
e. controlled by the decision maker
Choose the correct one.
Now, According to the question:
Let's Know:
How do you generate a random number from a probability distribution?
In general, generating a random number from a probability distribution means transforming random numbers so that the numbers fit the distribution. Perhaps the most generic way to do so is called inverse transform sampling: Generate a uniform random number in [0, 1].
The correct option is:
a. randomly generated from the specified probability distributions
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On Saturday, some adults and some children were in a theatre.The ratio of the number of adults to the number of children was 7:2
Each person had a seat in the Circle or had a seat in the Stalls.
of the children had seats in the Stalls.
124 children had seats in the Circle.
There are exactly 3875 seats in the theatre.
On this Saturday, what percentage of the seats had people sitting on them?
There are 72% percent of the seats had people sitting on them.
What are ratios and percentages?
A ratio is a comparison of two quantities that are similar. Given any two similar quantities a and b, so a:b ratio is defined as a:b = a/b, where b0. The percentage is an abbreviation for 'by the hundred' or 'divide by one hundred.' The percentage, which means 'per 100,' is also used to compare quantities.
Given data:
Ratio of adults to children = 7 : 2
The proportion of children that had sit in the stalls = 4/5
Number of children that had sit in the Circle = 124 children
Number of seats at the theatre = 3,875
Let x represent the number of children, we have;
The number of children in the stalls = (4/5).x
Then the number of children in the circle = x - (4/5).x = 124
Solving this, we get
x = 620
Given ratio is Number of adults/Number of children = 7:2
Number of adults/620 = 7/2
So the number of adults = 2,170
Total number of peoples = 2170 + 620 = 2790
The percentage of the seats had people sitting on them
[tex]=\frac{2790}{3875}\times100\\\\=72\%[/tex]
Hence, 72% percent of the seats had people sitting on them.
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2. loran is a long range hyperbolic navigation system. suppose two loran transmitters are located at the coordinates and , where unit distance on the coordinate plane is measured in miles a receiver is located somewhere in the first quadrant. the receiver computes that the difference in the distances from the receiver to these transmitters is 180 miles. what is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?
The path LORAN followed is hyperbolic.
The equation of the hyperbola is x²/8100 + y²/1900 = 1
Given,
These are the coordinates:
(x, y) = (-100, 0) (100, 0)
The hyperbola's center; (h, k) = (0, 0)
The following is the distance between the center and the focal points:
c = 100
Square both sides;
c² = 10000
The following is the distance between the transmitters and the receiver:
2a = 180
Divide 2 from both sides.
a = 90
Square both sides;
a² = 8100
We possess;
b² = c² - a²
This results in;
b² = 10000 - 8100
b² = 1900
A hyperbola's equation is as follows:
(x - h)²/a² + (y - k)²/b² = 1
We thus have:
(x - 0)²/8100 + (y - 0)²/1900 = 1
x²/8100 + y²/1900 = 1
As a result, the hyperbola's equation is: x²/8100 + y²/1900 = 1
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a 10 foot ladder is leaning against a wall when the base begins to slide away from the wall. when the base is 8 feet from the wall, the base is moving at the rate of 4 feet per second. how fast is the top of the ladder sliding down the wall, in feet per second?
40/3 feet /second fast the top of the ladder sliding down the wall.
What is ladder?
A ladder is a piece of gear used for climbing up or down objects that consists of repeated bars or steps (rungs) between two upright lengths of metal, wood, or rope.
Typically, these ladders work best for outdoor tasks like roof access or exterior painting. A straight ladder's reach is typically two feet higher than its height.
Given:
A 10 foot ladder is leaning against a wall when the base begins to slide away from the wall. when the base is 8 feet from the wall, the base is moving at the rate of 4 feet per second.
We have dx/dt = 4 feet per second
We want to find dy/dt.
From given information,
x^2 + y^2 = 10^2 ..(1)
When x = 8
⇒ y = √(10^2 - 8^2)
y = √(100 - 64)
y = √36
y = 6 feet
Now differentiate equation (1) with respect to t
[tex]2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\ x\frac{dx}{dt} + y\frac{dy}{dt} = 0\\ \frac{dy}{dt} = -\frac{x}{y} \frac{dx}{dt}[/tex]
Plug x = 8, y = 6 and dx/dt = 10
⇒
[tex]\frac{dy}{dt} = -\frac{8}{6}(10)\\ \frac{dy}{dt} = -\frac{40}{3}[/tex]
Hence, 40/3 feet /second fast the top of the ladder sliding down the wall.
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Which graph shows the solution of the inequality ? x+5_> 2
The graph of the solution of the inequality is shown in figure.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ x + 5 ≥ 2
Now,
Since, The inequality is,
⇒ x + 5 ≥ 2
Hence, Simplify the inequality as;
⇒ x + 5 ≥ 2
Subtract 5, we get;
⇒ x + 5 - 5 ≥ 2 - 5
⇒ x ≥ - 3
Thus, The graph of the solution of the inequality is shown in figure.
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The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon. A number of different independent variables were collected. The following regression output (with some values missing) was recently presented to the editors by the magazine's analysts:
Based on this output and your understanding of multiple regression analysis, what is the critical value for testing the significance of the overall regression model at a 0.05 level of statistical significance?
o Nearly F = 3.80
o About F = 5.92
o Approximately F = 2.50
o None of the above
Based on this output of multiple regression analysis, critical value for testing the significance of the overall regression model at a 0.05 level of statistical significance is Approximately F = 2.50.
What exactly is multiple regression analysis?A single dependent variable and a number of independent variables can be analyzed using multiple regression, a statistical approach. Using independent variables whose values are known, multiple regression analysis aims to predict the value of the single dependent value.
What is multiple regression analysis example?When doing multiple regression, each independent variable's value is taken into account in order to predict the value of the single dependent variable. Example: A researcher chooses to examine student performance at a certain school over time.
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
show your work.
(1/2 + 1/3)÷1/12 - 2^3
Answer: 2
Step-by-step explanation:
solve in parentesis than divide by 0.5 or 1/2 then 2^3= 4 so
that minus 4 equals 2
Select all the situations for which only zero or positive
solutions make sense.
Measuring temperature in degrees Celsius at an Arctic
outpost each day in January.
The height of a candle as it burns over an hour.
buns
The elevation above sea level of a hiker descending into a
canyon.
The number of students remaining in school after 6:00 p.m.
The temperature in degrees Fahrenheit of an oven used on a
hot summer day.
Answer: the last two situations
Step-by-step explanation:
there would be 0 students left in a school after 6 pm and the temperature in degrees fahrenheit has to be above 0 because it is a hot day and the oven is on
8. An organization published an article stating that in any one-year period, approximately 8.3 percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country.
Part (a)
Is this a test of one mean or proportion?
State the null and alternative hypotheses.
Is this a right-tailed, left-tailed, or two-tailed test?
What symbol represents the random variable for this test?
In words, define the random variable for this test.
Calculate the following.
(i) Enter your answer as a whole number.
x =
(ii) Enter your answer as a whole number.
n =
(iii) Enter your answer to two decimal places.
p' =
Part (g)
Calculate σx. (Round your answer to three decimal places.)
Show the formula set-up.
State the distribution to use for the hypothesis test.
Find the p-value. (Round your answer to four decimal places.)
[tex]z = \frac{0.08 - 0.083}{\sqrt{0.083 * 0.917/100} }[/tex]
= 0.108
pₐ = P( z < -0.108 ) = 0.4562
So the p-value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%)
Data given and notation
n = 100 represent the random sample taken
X=8 represent the people with depression or a depressive illness
p = 8/100 = 0.08 estimated proportion of people with depression or a depressive illness
p₀ = 0.083 is the value that we want to test
α = 0.05 represent the significance level assumed
Confidence = 83% or 0.83 assumed
z would represent the statistic (variable of interest)
pₐ represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportions of people with depression or a depressive illness is lower than the general adult population value of 8.3% or 0.083:
Null hypothesis:
p ≥ 0.083
Alternative hypothesis:
p < 0.083
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z = \frac{p- p_{0} }{\sqrt{p_{0} ( 1 - p_{0} )/ n } }[/tex] --------------------- (1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z = \frac{0.08- 0.083 }{\sqrt{0.083 ( 1 - 0.083 )/ 100 } }[/tex]
= - 0.083 / √ 0.0076
= -0.083 / 0.028
= -0.108
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level assumed is α = 0.05 . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
pₐ = P( z < -0.108 ) = 0.4562
So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%).
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an item is regulary priced at $40. Brian bought it at 40% off the regular price. HOw much did brian pay
Answer: Brian payed $24.00
How u do it:
Discount= original price x discount%/100
Discount = 40 × 40%/100
Discount = 40 x 0.4
You save = $16.00
Final Price = Original Price - Discount
Final Price = 40 - 16
Final Price = $24.00
Alto and Sheryl both worked hard over the summer. Together they earned a total of $500. Sheryl earned $100 more than Alto.
(a) Write a system of equations for the situation. Use s for the amount Sheryl earned and a for the amount Alto earned.
(b) Graph the equations of the system on the graph provided on the next page. a. Note: Insert->Shape will allow you to add lines, draw dots, and otherwise insert shapes in both Microsoft Word and LibreOffice. The graph should be big enough for you to easily plot points using this method. b. If you do not want to graph using the drawing tools built into Microsoft Word or LibreOffice you may also print out, graph by hand, and scan the page. Please note it’s perfectly okay to upload multiple files.
(c) Use Elimination or Substitution to solve the system.
(d) Use your graph to estimate how much each person earned, check your work with part C, and explain your results in complete sentences.
Alto earned $200 while Sheryl earned $300 over the summer.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Consider x represent the amount of money earned by Alto and y represent the amount of money earned by Sheryl
Together they earned a total of $500.
Hence the system of equations for the situation
x + y = 500 (1)
Sheryl earned $100 more than Alto:
y = x + 100
-x + y = 100(2)
Using Substitution to solve the system.
Solving equations 1 and 2 simultaneously gives:
x = 200 , y = 300
Therefore Alto earned $200 while Sheryl earned $300 over the summer.
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A data collection protocol calls for a questionnaire to be administered to patients having knee replacement surgery after the third physical therapy appointment. Errors can be introduced into the study by.
The way that errors can be introduced are;
Giving the questionnaire to all participants when they arrive for their appointment does not follow the protocol;
The participant could fill out the questionnaire before experiencing the therapy session.
How to identify errors in statistics study?Statistical errors are defined as errors that describe the difference that exists between a value obtained from a data collection process and the 'true' value for the population. Thus, the greater the error, the less representative the data will be of the population.
There are two main errors in this case which are type I error and type II error.
A type I error is called false-positive and it occurs if an investigator rejects a null hypothesis that is actually true in the population.
A type II error is called false-negative and it occurs if the investigator fails to reject a null hypothesis that is actually false in the population.
Now, from the question, since the data collection protocol alls for a questionnaire to be administered to patients having knee replacement surgery after the third physical therapy appointment, then we can introduce an error by;
Giving the questionnaire to all participants when they arrive.
The participant could fill out the questionnaire before experiencing the therapy session.
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Giving a questionnaire to all par-ticipants follows the timing of theprotocol.
BReading the questionnaire to par-ticipants with poor reading skillsfollows the timing of the protocol.
CGiving the questionnaire to allparticipants when they arrive fortheir appointment does not fol-low the protocol; the participantcould fill out the questionnairebefore experiencing the therapysession.
DGiving the questionnaire to theparticipants after the appoint-ment to be completed while theyhave a snack follows the timingof the protocol.