For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
A random sample of 5751 physicians in Colorado showed that 2954 provided at least some charity care (i.e., treated poor people at no cost).
(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
lower limit upper limit Give a brief explanation of the meaning of your answer in the context of this problem.
1% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care. 1% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care. 99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care. 99% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.
(c) Is the normal approximation to the binomial justified in this problem? Explain.
No; np < 5 and nq > 5. Yes; np < 5 and nq < 5. No; np > 5 and nq < 5. Yes; np > 5 and nq > 5.
Answers
a) The point estimate for p is given as follows: \(\pi = 0.5136\)
b) The 99% confidence interval for p is given as follows:
(0.4966, 0.5306).
The interpretation is given as follows:
99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.
c) The correct statement regarding the binomial approximation is given as follows: Yes; np > 5 and nq > 5.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.
The parameters for this problem are given as follows:
\(n = 5751, \pi = \frac{2954}{5751} = 0.5136\)
The lower bound of the interval is given as follows:
\(0.5136 - 2.575\sqrt{\frac{0.5136(0.4864)}{5751}} = 0.4966\)
The upper bound of the interval is given as follows:
\(0.5136 + 2.575\sqrt{\frac{0.5136(0.4864)}{5751}} = 0.5306\)
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Related Questions
Community Gym charges a $50 membership fee and a $70 monthly fee. Workout Gym charges a $200
membership fee and a $60 monthly fee. After how many months will the total amount of money paid to
both gyms be the same? What will the amount be?
After
months the amount paid to both gyms will be $
Answers
Answer:
community gym
50+(70×12)
=$890
workout gym
200+(60×12)
=$920
Find a power series representation for the function. (Give your power series representation centered at
x=0 .) f(x)= x/15x²+1
Answers
The upper bound of the 95% confidence interval for the average age in the U.S is 38.12.
To calculate the upper bound of the 95% confidence interval for the average age in the U.S, we have to follow the given steps:
Calculate the mean and standard deviation for the sample size of 1072 people
Randomly select 1072 people with replacement and repeat Step 1
Repeat step 2 many times (e.g., 5000) to get a distribution of sample statistics.
For the average age, the sample mean is 37.22 years, and the sample standard deviation is 14.96 years.
Using the formula for the standard error, the standard error of the mean is as follows:
SE = s/√n = 14.96/√1072 ≈ 0.46
CI = X± z(α/2) * (SE) = 37.22 ± 1.96 * (0.46) = 37.22 ± 0.90
The upper bound of the 95% confidence interval for the average age in the U.S is: 37.22 + 0.90 = 38.12
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Rosa Went to have a manicure that cost $25 she wanted to tip the technician and 15% and tax is 7% how much did she spend total for the manicure
Answers
The correct answer is $30.5 or $31 if rounded
Explanation:
To find the total Rosa spent on the manicure, it is necessary to calculate the money spent on taxes and the money she tipped to the technician. The process is shown below:
Taxes:
$25 represents 100% of the cost and 7% percent represents the total taxes.
1. Write the values using x as the value you want to know
25 = 100
x = 7
2. Use cross multiplication
x 100 = 175
3. Solve this equation
x = 175 / 100
x = 1.75 (Total price for taxes)
Tip:
Repeat the process but in this case calculate the 15% of $25
25 = 100
x = 15
x 100 = 375
x = 375 / 100
x = 3.75
Total: Finally, add the three values
$25 (cost of the manicure) + $ 1.75 (taxes) + $3.75 (tip) = $30.5 or $31 if rounded
An object is placed a distance r in front of a wall, where r exactly equals the radius of curvature of a certain concave mirror. At what distance from the wall should this mirror be placed so that a real image of the object is formed on the wall? Express your answer in terms of r. What is the magnification of the image? Follow the sign conventions. Express your answer using three significant figures.
Answers
The concave mirror should be placed at a distance of 2r from the wall to form a real image of the object on the wall. The magnification of the image is expressed using three significant figures is -0.500.
if the object is placed at a distance r in front of a concave mirror whose radius of curvature is also r, then the image is formed at the same distance r behind the mirror. This is a special case called the "center of curvature" configuration.
To form a real image on the wall, the mirror must be placed such that the object is beyond the mirror's focal point. The focal length of the mirror is half of its radius of curvature, so the focal length is f = r/2.
If the object is placed at a distance x from the mirror, then using the mirror equation:
1/f = 1/do + 1/di
where do is the distance of the object from the mirror and di is the distance of the image from the mirror. In this case, do = x and di = r, so we get:
1/r = 1/x - 1/f
Substituting f = r/2, we get:
1/r = 1/x - 2/r
Solving for x, we get:
x = 2r
Therefore, the mirror should be placed at a distance of 2r from the object to form a real image on the wall.
To find the magnification of the image, we use the magnification equation:
m = -di/do
where m is the magnification, di is the distance of the image from the mirror, and do is the distance of the object from the mirror. In this case, do = x = 2r and di = r, so we get:
m = -r/(2r) = -1/2
Therefore, the magnification of the image is -0.500.
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A rental car company charges $20 per day to rent a car and $0.10 for every mile driven. Addison wants to rent a car, knowing that: . She plans to drive 100 miles. She has at most $80 to spend. Write and solve an inequality which can be used to determine x, the number of days Addison can afford to rent while staying within her budget.
Answers
Answer:
80\(\leq\)20x+0.1(100)
Step-by-step explanation:
x for the number of days you are trying to find.
$20 to rent the car per day.
$0.1 for every mile driven and she wants to drive 100 miles so $0.1(100).
she cannot spend over 80 so the sign should be equal to $80 or less than.
There are 4 blue socks and 6 white socks in a drawer. You select one sock without looking and then return it to the drawer. Then you choose another sock. Is this an independent or dependent event?
Answers
Answer:
I am pretty sure it is dependent
Let me know if it is wrong.
(x=1)^2-4x=(x-1)^2 simplify and answer
Answers
Step-by-step explanation:
Firstly, there's a typing error at (x=1)². I assume it is (x-1)². If my assumption is correct,then:
x²-2x+1-4x=x²-2x+1
x²-6x+1-x²+2x-1=0
-4x=0
x=0
The slope of the line that passes through the point (2,4) and (3,8)is
Answers
Answer:
4
Step-by-step explanation:
x1 = 2, y1 = 4
x2 = 3, y2 = 8
from, (y2-y1)/(x2-x1) = m
m = (8-4)/(3-2)
m = 4/1
m = 4
Therefore, the slope of the line is 4
find the area....
please help
Answers
Answer:
12 yd*2
Step-by-step explanation:
\(a = l \times w\)
Use this next time!
The flight of a cannonball toward a hill is described by the parabola y=2+0.12x- 0.0004x^2
Answers
The computation shows that the placw on the hill where the cannonball land is 3.75m.
How to illustrate the information?To find where on the hill the cannonball lands
So 0.15x = 2 + 0.12x - 0.002x²
Taking the LHS expression to the right and rearranging we have:
-0.002x² + 0.12x -.0.15x + 2 = 0.
So we have -0.002x²- 0.03x + 2 = 0
I'll multiply through by -1 so we have
0.002x² + 0.03x -2 = 0.
This is a quadratic equation with two solutions x1 = 25 and x2 = -40 since x cannot be negative x = 25.
The second solution y = 0.15 * 25 = 3.75
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Complete question:
The flight of a cannonball toward a hill is described by the parabola y = 2 + 0.12x - 0.002x 2 . the hill slopes upward along a path given by y = 0.15x. where on the hill does the cannonball land?
What is the breakdown of this math problem? 8 2/5 - 6 7/10 =
Answers
let's first off, convert the mixed fractions to improper fractions.
\(\stackrel{mixed}{8\frac{2}{5}}\implies \cfrac{8\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{42}{5}}~\hfill \stackrel{mixed}{6\frac{7}{10}} \implies \cfrac{6\cdot 10+7}{10} \implies \stackrel{improper}{\cfrac{67}{10}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{42}{5}-\cfrac{67}{10}\implies \cfrac{(2)42~~ - ~~(1)67}{\underset{\textit{using this LCD}}{10}}\implies \cfrac{84-67}{10}\implies \cfrac{17}{10}\implies 1\frac{7}{10}\)
Suppose that X ~ Uniform(5, 10) and Y ~ Uniform(3, 8) are independent random variables, and let Z = 7X - 3Y. What is the value of the standard deviation of Z rounded to the nearest tenth?
Answers
The value of the standard Deviation of Z rounded to the nearest tenth is 2.9.
Let's first find the mean of ZLet Z = 7X - 3Y
Therefore, E(Z) = E(7X - 3Y) = 7E(X) - 3E(Y)
We know that X ~ Uniform(5, 10) and Y ~ Uniform(3, 8)E(X) = (a + b) / 2 = (5 + 10) / 2 = 7.5E(Y) = (a + b) / 2 = (3 + 8) / 2 = 5.5Therefore,E(Z) = 7E(X) - 3E(Y) = 7(7.5) - 3(5.5) = 26
Now, let's find the variance of Z:Var(Z) = Var(7X - 3Y) = 49Var(X) + 9Var(Y)
(because X and Y are independent)We know that X ~ Uniform(5, 10) and Y ~ Uniform(3, 8)Var(X) = (b - a)^2 / 12 = (10 - 5)^2 / 12 = 25 / 12Var(Y) = (b - a)^2 / 12 = (8 - 3)^2 / 12 = 25 / 12
Therefore, Var(Z) = 49Var(X) + 9Var(Y) = 49(25 / 12) + 9(25 / 12) = 25(49 + 9) / 12 = 100Var(Z) = 100 / 12 = 25 / 3
Now, the standard deviation of Z = √(Var(Z))= √(25/3)= 5/√3 ≈ 2.89
Hence, the value of the standard deviation of Z rounded to the nearest tenth is 2.9.
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Which inequality is graphed on the coordinate plane shown?
A
y≥2x−6
B
y<2x−6
C
y>2x−6
D
y≤2x−6
Answers
Answer:
y ≤ 2x-6
Step-by-step explanation:
First find the equation of the line
The y intercept is -6
The slope is 2
y = 2x-6
The line graphed is solid so we know that there is an equal sign
We are graphing below the line
y ≤ 2x-6
Applied (Word) Problems NoteSheet
Consecutive Integers
Consecutive numbers (or more properly, consecutive integers) are integers nrand ngsuch that
/h - nl = I, i.e., IJlfollows immediately after 17,.
Given two consecutive numbers, one must be even and one must be odd. Since the sum of an
even number and an odd number is always odd, the sum of two consecutive numbers (and, in
fact, of any number of consecutive numbers) is always odd.
Consecutive integers are integers that follow each other in order. They have a difference of 1
between every two numbers.
If n is an integer, then n, n+1, and n+2 wi II be consecutive integers.
Examples:
1,2,3,4,5
-3,-2,-1,0,1,2
1004, 1005, 1006
Answers
The concept of consecutive integers is explained as follows:
Consecutive numbers, or consecutive integers, are integers that follow each other in order. The difference between any two consecutive numbers is always 1. For example, the consecutive numbers starting from 1 would be 1, 2, 3, 4, 5, and so on. Similarly, the consecutive numbers starting from -3 would be -3, -2, -1, 0, 1, 2, and so on.
It is important to note that if we have a consecutive sequence of integers, one number will be even, and the next number will be odd. This is because the parity (evenness or oddness) alternates as we move through consecutive integers.
Furthermore, the sum of two consecutive numbers (and, in fact, the sum of any number of consecutive numbers) is always an odd number. This is because when we add an even number to an odd number, the result is always an odd number.
To generate a sequence of consecutive integers, we can start with any integer n and then use n, n+1, n+2, and so on to obtain consecutive integers. For example, if n is an integer, then n, n+1, and n+2 will be consecutive integers.
Here are some examples of consecutive integers:
- Starting from 1: 1, 2, 3, 4, 5, ...
- Starting from -3: -3, -2, -1, 0, 1, 2, ...
- Starting from 1004: 1004, 1005, 1006, 1007, ...
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3. Consider the sphere given by the equation x^{2}+2 x+y^{2}-4 y+z^{2}-11=0 . Determine the center and radius of the sphere. (3pts)
Answers
The standard form of the equation of the sphere is given by; (x−a)²+(y−b)²+(z−c)²=r² . Therefore, the center of the sphere is (-1, 2, 0) and its radius is 4 units.
The given equation of the sphere is x²+2x+y²-4y+z²-11=0.
To determine the center and radius of the sphere we have to express the given equation in standard form of the equation of the sphere as; (x−a)²+(y−b)²+(z−c)²=r²
The standard form of the equation of the sphere is given by; (x−a)²+(y−b)²+(z−c)²=r²
The given equation can be rearranged as follows;x²+2x+y²-4y+z²-11 = 0⇒ x²+2x+y²-4y+z² = 11
We will now complete the square for the x and y terms in the above equation as follows;
x²+2x+y²-4y+z² = 11
⇒ x²+2x+1+y²-4y+4+z² = 11+1+4
⇒ (x+1)²+(y-2)²+z² = 16
The standard form of the equation of a sphere is; (x−a)²+(y−b)²+(z−c)²=r²
The center of the sphere is given by (a, b, c) and the radius by r.The center of the sphere is (-1, 2, 0) and the radius of the sphere is √16 = 4 units.
Therefore, the center of the sphere is (-1, 2, 0) and its radius is 4 units.
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What should be done for an experiment to be considered verifiable?
Answers
We know that an experiment can be considered verifiable, meaning that its results can be trusted and used to inform future research and decision-making.
For an experiment to be considered verifiable, several things should be done. Firstly, the experiment should be designed in a way that allows others to replicate it and obtain the same results. This means that all procedures, materials, and variables used should be clearly documented and made available to others.
Secondly, the experiment should be conducted in a controlled environment, where all external factors that could influence the results are minimized or eliminated.
Thirdly, the data obtained from the experiment should be analyzed and interpreted objectively, without any bias or preconceived notions. Finally, the results should be subjected to peer review and scrutiny by experts in the relevant field to ensure that they are valid and reliable.
By following these steps, an experiment can be considered verifiable, meaning that its results can be trusted and used to inform future research and decision-making.
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Using the vertical angle image from problem 1, let ∠2 = 4x-4 and ∠4 = x+50.
A. What is the value of x?
B. What is the measure of ∠2?
C. Find the measure of ∠3.
Answers
Answer:
A) x = 18, B) ∠2 = 68°, C) ∠3 = 112°Step-by-step explanation:
According to vertical angles theorem, when two lines intersect the opposite angles are equal and adjacent angles are supplementary.
Given∠2 = 4x-4 and ∠4 = x+50A) Find the value of x:
4x - 4 = x + 504x - x = 50 + 43x = 54x = 54/3x = 18B) Find the measure of angle 2:
∠2 = 4*18 - 4 = 72 - 4 = 68C) Angles 2 and 3 are supplementary so their sum is 180°.
∠2 + ∠3 = 18068 + ∠3 = 180∠3 = 180 - 68∠3 = 112°Answer:
A. x = 18
B. m∠2 = 68°
C. m∠2 = 112°
Step-by-step explanation:
Given:
\(\angle 2=4x-4\)\(\angle4=x+50\)Part AVertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Therefore:
\(\implies \angle 2 = \angle 4\)
\(\implies 4x-4= x+50\)
\(\implies 4x-4-x= x+50-x\)
\(\implies 3x-4= 50\)
\(\implies 3x-4+4= 50+4\)
\(\implies 3x=54\)
\(\implies 3x\div 3=54 \div 3\)
\(\implies x=18\)
Part BTo find the measure of ∠2, substitute the found value of x into the given expression for ∠2:
\(\implies m\angle 2 =(4x-4)^{\circ}\)
\(\implies m\angle 2 =[4(18)-4]^{\circ}\)
\(\implies m\angle 2 =(72-4)^{\circ}\)
\(\implies m\angle 2 =68^{\circ}\)
Part CAngles on a straight line sum to 180°:
\(\implies m\angle 2 +m\angle 3=180^{\circ}\)
\(\implies 68 ^{\circ}+m\angle 3=180^{\circ}\)
\(\implies m\angle 3=180^{\circ}-68 ^{\circ}\)
\(\implies m\angle 3=112 ^{\circ}\)
What is the answer to this?
Answers
To find the y-intercept substitute x as 0
\(y = 1 \times {0}^{2} + 7 \times 0 - 5\)
\(y = 1 \times 0 + 0 - 5\)
\(y = 0 + 0 - 5\)
\(y = - 5\)
Thus, The y-intercept is -5...~We know that:
The y-intercept of an equation is the constant. Constants are the numerals in the equation.Finding the y-intercept.
In the equation provided, we can see only one constant.
=> y = 1x² + 7x - 5Thus, the y-intercept is -5.
question 19in this list of numbers, what is the median? 97, 96, 95, 93, 93, 90, 87, 86, 84, 78, 75, 74, 70, 68, 65.9383.48680
Answers
The median of the given list of numbers is 87.
To find the median of a list of numbers, we arrange them in ascending order and identify the middle value.
If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
First, let's arrange the numbers in ascending order:
65.9, 68, 70, 74, 75, 78, 84, 86, 87, 90, 93, 93, 95, 96, 97, 380, 486, 680
There are 17 numbers in the list, which is an odd number. The middle number is the 9th number in the list, which is 87.
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You have a mortagege of $275,000
after down payment with an interest
rate of 3% for 30 years.
What does P, r,n, and t are equal to?
Answers
Answer:
Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this
Step-by-step explanation:
what is the answer to 15-9:(-3)
Answers
Answer:
good questiion
Step-by-step explanation:
I need some help finding the volume of a sphere with a diameter of 18.6cm. Help would be greatly appreciated!
Answers
Answer:
\(V=3367.57\ cm^3\)
Step-by-step explanation:
The diameter of a sphere, d = 18.6 cm
Radius, r = 9.3 cm
We need to find the volume of the sphere. The formula for the volume of a sphere is given by :
\(V=\dfrac{4}{3}\pi r^3\\\\=\dfrac{4}{3}\times 3.14\times (9.3)^3\\\\=3367.57\ cm^3\)
So, the volume of the sphere is equal to \(3367.57\ cm^3\).
A B. C A3 x 3 matrix is above. It has a pattern going both horizontally across the rows and vertically down the columns. The pattern is not necessarily the same in both directions. There is one object that fits correctly in the bottom right corner of the matrix. Choose this object from the list below the matrix Select one: a. A ОБ. В Ос, с d. D e. E f.F 8.G h. H
Answers
We can conclude from answering the above question that the first two patterns of the matrix form a sequence in the third from top with the numbers 4-2-6.
what is matrix i?A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.
We can conclude from answering the above question that the first two patterns of the matrix form a sequence in the third from top with the numbers 4-2-6.
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which hypothesis or hypotheses about the relation between life satisfaction and job satisfaction has received the most empirical support?
Answers
Recent research has confirmed the Spillover Hypothesis by demonstrating a favourable association between life and job happiness.
According to the spillover hypothesis, behaviour or affect in a family system might flow immediately from one place or connection to another. Transfer takes place in the same valence, which means that one subsystem's negative affect is connected to another's negative affect, or stress at work spills over and intensifies stress at home. The compensatory hypothesis offers a different perspective by arguing that transfer between family subsystems occurs in the opposite valence, leading a person to seek fulfilment in one relationship or environment in order to make up for shortages in another.
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Ill give brainliest to the person who gets it right!!!!!!!
Answers
a line is perpendicular to y=-2x+5 and intersects the point (-4,2).What is the equation of this perpendicular line
Answers
Answer:
y = \(\frac{1}{2}\) x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 2x + 5 ← is in slope- intercept form
with slope m = - 2
given a line with slope m then the slope of a line perpendicular to it is
\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-2}\) = \(\frac{1}{2}\) , then
y = \(\frac{1}{2}\) x + c ← is the partial equation
to find c substitute the point (- 4, 2 ) into the partial equation
2 = \(\frac{1}{2}\) (- 4) + c = - 2 + c ( add 2 to both sides )
4 = c
y = \(\frac{1}{2}\) x + 4 ← equation of perpendicular line
Solve the given differential equation by undetermined coefficients. y'' 4y = 3 sin(2x)
Answers
To solve the differential equation y'' + 4y = 3sin(2x) using the method of undetermined coefficients, we assume a particular solution of the form \(y_p\)= A sin(2x) + B cos(2x).
The given differential equation is y'' + 4y = 3sin(2x). To find a particular solution, we assume it has the form \(y_p\) = A sin(2x) + B cos(2x), where A and B are undetermined coefficients that we need to determine. Taking the first and second derivatives of y_p, we have \(y_p\)'' = -4A sin(2x) - 4B cos(2x) and \(y_p\)' = 2A cos(2x) - 2B sin(2x).
Substituting these expressions into the original differential equation, we get (-4A sin(2x) - 4B cos(2x)) + 4(A sin(2x) + B cos(2x)) = 3sin(2x). Simplifying this equation, we have -4B cos(2x) + 4B cos(2x) = 3sin(2x).
Since the left-hand side of the equation cancels out, we are left with 0 = 3sin(2x). This equation holds true for all values of x if and only if the coefficient of sin(2x) on the right-hand side is zero. Therefore, we have -4A = 0, which implies A = 0.
Substituting A = 0 into the assumed particular solution, we obtain \(y_p\) = B cos(2x). Now, we differentiate \(y_p\) and plug it back into the original equation to solve for B. We find that B = -3/4.
Therefore, the particular solution is \(y_p\) = -3/4 cos(2x). The general solution of the differential equation is given by the sum of the particular solution and the homogeneous solution, which is obtained by solving the associated homogeneous equation y'' + 4y = 0. The general solution is y =\(y_p\) + \(y_h\) = C1 sin(2x) + C2 cos(2x) - 3/4 cos(2x), where C1 and C2 are arbitrary constants.
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Classify the following scenarios as one-sided or two-sided tests.
one-sided hypothesis test
test whether incoming students at a business school receive better grades in their classes if they've taken an on-line program covering basic material
test whether there is a difference between men's and women's usage of a mobile fitness app
two-sided hypothesis test
test whether the number of listeners of a streaming music service has changed after they changed the user interface
test whether users of a commercial website are less likely to make a purchase if they are required to set up a user account on the site
Answers
One-sided hypothesis test: Incoming students' grades based on the online program.
Two-sided hypothesis test: Men's and women's usage of mobile fitness app, listeners of a streaming music service based on user intappserface change, and users of a commercial website making a purchase based on user account requirement.
We have,
Classifying the scenarios as one-sided or two-sided tests:
One-sided hypothesis test:
Test whether incoming students at a business school receive better grades in their classes if they've taken an online program covering basic material.
Two-sided hypothesis test:
Test whether there is a difference between men's and women's usage of a mobile fitness app.
Two-sided hypothesis test:
Test whether the number of listeners of a streaming music service has changed after they changed the user interface.
One-sided hypothesis test:
Test whether users of a commercial website are less likely to make a purchase if they are required to set up a user account on the site.
Thus,
One-sided hypothesis test: Incoming students' grades based on the online program.
Two-sided hypothesis test: Men's and women's usage of mobile fitness app, listeners of a streaming music service based on user intappserface change, and users of a commercial website making a purchase based on user account requirement.
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Garden a rectangular garden is 12 feet across and 16 feet long. it is surrounded by a border of mulch that is a uniform width x. the maximum area for the garden, plus border, is 285square feet
Answers
The polynomial equation representing the situation is 4x² + 56x = 93 .
In the question ,
it is given that
the length of the rectangular garden is = 16 feet
the width of the rectangular garden is = 12 feet
we have to surround the border by mulch ,
the width of the border with mulch is = x
So the new length with mulch = 16 + x + x = 16 + 2x
and the new width with mulch is = 12 + x + x = 12 + 2x
also given that the area of garden plus border is = 285 square feet
we know that the area is = length × width
On substituting the values length and breadth , we get
285 = (16 + 2x)×(12 + 2x)
285 = 192 + 32x + 24x + 4x²
4x² + 56x + 192 = 285
4x² + 56x = 285 - 192
4x² + 56x = 93
Therefore , The polynomial equation representing the situation is 4x² + 56x = 93 .
The given question is incomplete , the complete question is
Garden a rectangular garden is 12 feet across and 16 feet long. it is surrounded by a border of mulch that is a uniform width x. the maximum area for the garden, plus border, is 285square feet . Write a polynomial equation to represent the situation ?
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\(\sf 8x+12-8x+15+15x-22-x\)
Answers
Let's get it done !
\(8x + 12 - 8x + 15 + 15x - 22 - x\)\(8x - 8x + 15x - x + 12+ 15 - 22\)\(14x + 5\)Answered by : " Unknown "