Answer:
The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
The randomly sampled 400 dogs from homes where an herbicide was used on a regular basis, diagnosing lymphoma in 230 of them.
This means that:
[tex]p_h = \frac{230}{400} = 0.575, s_h = \sqrt{\frac{0.575*0.425}{400}} = 0.0247[/tex]
Of 200 dogs randomly sampled from homes where no herbicides were used, only 25 were found to have lymphoma.
This means that:
[tex]p_n = \frac{25}{200} = 0.125, s_n = \sqrt{\frac{0.125*0.875}{200}} = 0.0234[/tex]
Distribution of the difference:
[tex]p = p_h - p_n = 0.575 - 0.125 = 0.45[/tex]
[tex]s = \sqrt{s_h^2+s_n^2} = \sqrt{0.0247^2 + 0.0234^2} = 0.034[/tex]
Confidence interval:
The confidence interval is:
[tex]p \pm zs[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower bound is [tex]0.45 - 1.96(0.034) = 0.3834[/tex]
The upper bound is [tex]0.45 + 1.96(0.034) = 0.5166[/tex]
The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).
x divided by 6 is what
Answer:x/6
Step-by-step explanation:
Here the value of x is not given and hence the answer to the question is
x/6
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9.
The table shows the number of pools sold by the Allied Pool company over a six month period.
Allied Pool Sales
Month
Number of
Pools Sold
Feb.
11
Mar.
10
Apr.
12
May
16
June
15
July
18
From the above table, what is the range in the number of pools sold during this period?
8 pools
According to the table, the Range of pools sold during this period is 8.
What is Range?The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.
Thus, the range could also be defined as the difference between the highest observation and lowest observation. The obtained result is called the range of observation. The range in statistics represents the spread of observations.
Range = Highest Value – Lowest Value
Range = 18 – 10
Range = 8
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Given the two triangles shown, find the value of x.
Answer:
the value of x would end up being 25
A cone with a radius of 6 cm has a volume of 1200 cm3. What is the height of the cone? (The volume of a cone is given by the formula V = 7er A) 8 cm B) 10 cm 12 cm D) 15 cm
Answer:
31.8 cmStep-by-step explanation:
Volume of a cone:
V = 1/3πr²hWe have:
V = 1200 cm³r = 6 cmh = ?Substitute values and solve for h:
1200 = 1/3*3.14*6²h1200 = 37.68hh = 1200/37.68h = 31.8 cm (rounded)None of the choices is correct
TRUE OR FALSES
No irrational numbers are integers.
All whole numbers are irrational numbers.
Some whole numbers are not rational numbers.
Some rational numbers are not whole numbers.
9514 1404 393
Answer:
T, F, F, T
Step-by-step explanation:
No irrational numbers are integers.
All integers are rational numbers. By definition, an irrational number is not a rational number. So it must be true that an irrational cannot be an integer.All whole numbers are irrational numbers.
Every whole number can be expressed as the ratio of two integers, hence is not an irrational number. The offered statement is false.Some whole numbers are not rational numbers.
Every whole number is rational. The offered statement is false.Some rational numbers are not whole numbers.
A reduced ratio of two integers with some number other than 1 in the denominator will not be a whole number. For example, 9/8 is not a whole number. The offered statement is true.PLEASE HELP
A fly makes a bee-line from one corner of Mrs. Tomasi's room
to the opposite corner. The room is 30x 32 feet and 9 feet tall.
What angle is the angle of elevation of the flight path if he flies
straight there?
The angle of elevation of the fly's flight path is approximately 57.74 degrees.
What is hypotenuse?In a right triangle, the hypotenuse is the side opposite the right angle. It is always the longest side of the triangle and is the side opposite to the 90 degrees angle. It is also the side that forms the "hypotenuse" of the right triangle.
What is Pythagorean theorem?The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2, where a and b are the legs of the triangle and c is the hypotenuse. This theorem can be used to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are known.
Let's call the angle we're trying to find "theta". The horizontal distance is 30 feet, the vertical distance is 32 feet and the height is 9 feet.
Using pythagorean theorem:
$c^2 = a^2 + b^2$
$c = \sqrt{30^2 + 32^2}$ = $\sqrt{900 + 1024}$ = $\sqrt{1924}$
Now we can use the tangent function:
$\tan(\theta) = \frac{opposite}{adjacent} = \frac{32}{30}$
Now we can find the angle, theta, by using the inverse tangent function:
$\theta = \tan^{-1}(\frac{32}{30})$
The angle of elevation of the fly's flight path is approximately 57.74 degrees.
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Choose all the pairs of fractions that are equivalent.
B and E Thank you for asking I'm good at fractions!!
In a recent year, 22.2% of all registered doctors were female. If there were 47,200 female registered doctors that year, what was the total number of registered doctors?
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Therefore , the solution of the given problem of percentage comes out to be 264414 doctors were registered that year.
What is a percentage?A% is a number that represents the percentage of 100 that it is, and it can also be stated as a decimal or a fraction. To convert a percentage to a fraction, place 100 in the denominator and the percentage number in the numerator.
Here,
"Female doctors make up 22.2% of all registered doctors," the inquiry states.
Consider the entire number of doctors who are registered as x; 22.2% of those doctors are women.
and 47,200 divided by 22.2% of x
=>22.2/100 * x = 47,200
in math
264414 doctors were registered that year, or
x = 58700* 100/22.2 x.
Therefore , the solution of the given problem of percentage comes out to be 264414 doctors were registered that year.
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Find the length of the third side if necessary round to the nearest tenth 6 and 7
Write and solve the inequality that represents
is greater than or equal to the product of 2 and a number.
5
3
The following is the proper response to this problem's inequality. The relationship between negative one fifth and negative two thirds is higher than or equal when y is bigger than or equal to three tenths.
what is inequality ?In mathematics, an inequality is a link between two expressions or values that is not equal. Thus, inequality arises as a result of imbalance. An inequality in mathematics describes the connection between two values that are not equal. Many simple inequalities can be eliminated by modifying both sides until just the variables are left. However, a number of things lead to inequality: On both sides, divide or add negative values. Toggle between left and right.
Given
One fifth less is -1/5.
When a negative two thirds is added to a number, the result is -2/3x. Since the value is unknown, we refer to it as x.
The following is the sign for more than or equal inequality:
The inequality is therefore: -1/5 -2/3x.
So that it will be easier for us to isolate x:
2/3x ≥ 1/5
2x ≥ 3/5
x ≥ 3/10.
Since y is more than or equal to three tenths, the right answer for the inequality is: negative one fifth is greater than or equal to negative two thirds y.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answer: To solve a quadratic equation of the form ax^2 + bx + c = 0, there are several steps that Inga could use. Here are three options:
She could complete the square to rewrite the equation in the form (x + p)^2 = q.
She could use the quadratic formula: x = (-b +/- √(b^2 - 4ac)) / (2a).
She could factor the equation to rewrite it in the form (x + r)(x + s) = 0.
Option 1: Completing the square
To complete the square, Inga could add and subtract (b/2)^2 to the equation to get:
a(x^2 + bx + (b/2)^2) - (b/2)^2 = 0
Then, she could rewrite the equation in the form:
a(x + (b/2))^2 = (b/2)^2
Option 2: Using the quadratic formula
To use the quadratic formula, Inga could substitute the values of a, b, and c into the formula to get:
x = (-12 +/- √(12^2 - 4 * 2 * -3)) / (2 * 2)
= (-12 +/- √(144 + 24)) / 4
= (-
Step-by-step explanation:
350 is what percent of 400??
Answer:
350 is 87.5% of 400
350/400 = 87.5%
Can someone help me solve this equation? will give brainliest
Answer:
a = -10
Step-by-step explanation:
33 - 4a = 73
To get a by itself, you must move 33 to the other side. To this, you must subtract it from both sides, canceling it out on the left side.
You will be left with: -4a = 73-33
Subtract 73 and 33, which will get you 40.
Now the equation is -4a = 40
To get a by itself, divide -4 into both sides. Doing this will isolate a.
The equation you will have after that is a = 40/-4.
Divide 40 by -4, which will get you -10.
Therefore, a = -10.
If one pound is $4.40 how much is 3/8's of a pound?
Answer:
1.65
Step-by-step explanation:
you said one pound is $4.40
and that how much is 3/8 of a pound
so 3/8 multiplied by 4.40
Answer:
$1.65
Step-by-step explanation:
1 pound -------------4.40
3/8 pounds------------x
cross multiplication
1x = 4.40 x (3/8) =
x = 1.65
156x2.2=?????Help fast
Answer:
343.2
Step-by-step explanation:
156 × 2.2
= (156 × 22)/10
= 3432/10
= 343.2
factorisé x2 + 14x +49
The expression is factorized to give (x + 7) and (x + 7)
What is factorization?Factorization described a mathematical methods that consists of writing a number or mathematical object as a product of several other factors that are mostly simpler or smaller objects of the same kind.
Given the quadratic equation;
x² + 14x +49
Find the pair factors of 49 that sum up to 14, the numbers are 7 and 7
Now, substitute the numbers in the expression
x² + 7x + 7x + 49
Make into two expressions, we have;
(x² + 7x) + (7x + 49)
factor out the common terms, we get;
x(x + 7)+ 7(x + 7)
Then, we have;
(x + 7)
(x + 7)
Hence, the factorized form is (x + 7) and (x + 7)
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the graph of linear function f passes through the point (1 -9) and has a slope of -3 brainly
Answer:
See attachment for graph
Step-by-step explanation:
Given
[tex](x_1,y_1) = (1,-9)[/tex] -- point
[tex]x = -3[/tex] --- slope
Required
Plot the graph
First, we determine the equatio using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = -3*(x - 1) -9[/tex]
Open bracket
[tex]y = -3x + 3 -9[/tex]
[tex]y = -3x -6[/tex]
See attachment for graph
Please need help asap, 50 points!!!!!!!!!!!!!!!!!!!!!!!!!!
Decide whether the triangles can be proven congruent by the given postulate or theorem. If not, state what information is needed.
17. The triangles can be proven congruent by the SSS theorem.
18. The triangles cannot be proven congruent by the HL theorem, as it is not known if the triangles are right triangles.
What are the congruence theorems?The side-side-side congruence theorem, abbreviated as SSS, means that if two triangles have three equal side lengths, then the triangles are congruent.
In item 17, we have that:
Sides JK and IH are equal.Sides JI and HY are equal.Side JH is common to both triangles, hence they are equal.As the three triangles are equal, then the SSS theorem can be used to prove the congruence of the two triangles.
The HL theorem represents the hypotenuse and leg theorem, which means that if two right triangles share a hypotenuse measure along with a leg measure, then they are congruent.
Hence item 18 cannot be proven congruent by the HL theorem, as there is no information regarding whether the triangles are right triangles.
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Write the coordinates of the vertices after a translation 2 units left and 5 units down. B(0,2). C(9-1) D(9,4) E(0,4)
Answer:
B'(-2, -3)
C'(7, -6)
D'(7, -1)
E'(-2, -1)
Step-by-step explanation:
When you move translate a coordinate horizontally, if it is to the left, you subtract the x value with how many units you move, and if its to the right, you add however many units you move to the x-value. and when you move vertically, if you move down, subtract the amount of units you moved from the y-value, and if you move up, add however many units you moved to the y-value.
Rewrite the following equation in slope-intercept form. 17x + y = –19
Answer: y = 17x - 19
Step-by-step explanation:
17x + y = -19
Subtract 17 on both sides
Y= -19 - 17x
Then put it in y= mx + b
Y= -17x - 19
Answer:
y = -17x -19
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
17x+y = -19
Solve for y
y = -17x -19
How many solutions does x^2=9 have
Answer:
Your answer is 1
Step-by-step explanation:
3² = 9 is the only possible solution.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{x^2=9}[/tex]
[tex]\large\text{TAKE the SQUARE ROOT}[/tex]
[tex]\mathsf{x =\pm \sqrt{9}}[/tex]
[tex]\large\text{REMEMBER this symbol }\mathsf{\pm}\large\text{ means plus or minus}[/tex]
[tex]\mathsf{ - \sqrt{9} = \boxed{\bf -3}}[/tex]
[tex]\mathsf{\sqrt{9}=\boxed{\bf 3}}[/tex]
[tex]\large\text{OR YOU COULD SAY THIS TO MAKE THIS SIMPLER TO}\\\large\text{SOLVE}\downarrow[/tex]
[tex]\large\text{-3}\mathsf{^2= \boxed{\bf -9}}[/tex]
[tex]\large\text{3}\mathsf{^2}\large\text{= \boxed{\bf 9}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore, your answer: \huge \bf x = -3 or x = 3 }}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the mean, median, and mode for the data set below.
weights of books (oz): 10 9 9 14 13 11
Answer:
Mean: 11
Median: 10.5
Mode: 9
There are 10 boys in Mr. Lee's class. If 40% of the class are boys, which is the total number of students in Mr. Lee's class?
Answer:
25
Step-by-step explanation:
2.5 =10%
2.5*4= 10
2.5*6=15
Answer:
25
Step-by-step explanation:
Using P=(%)w we can substitute the values. First, I will define the variables. P = part (is), % = percent, w = whole (of)
10 = (40%)w
The reason for this is because 10 is a PART and 40% is a PERCENT and we are solving for the unknown WHOLE. We now divide 10 by 0.40 because to convert a percent to a decimal you just move the point two places to the left:)
10 divided by 0.4 = 25. So, there is a total of 25 students in Mr. Lee's class. Now, we can check this by multiplying 25 and 0.4 to get 10! It is in fact correct.
PLEASE READ PRACTICE AND UNDERSTAND! DO NOT JUST TAKE THE ANSWER. KNOWLEDGE IS POWER :^)
Consider the graph of f(x). What is the domain of f(x)?
Answer:
(-infinity,+infinity)
Step-by-step explanation:
Any real value of x can be defined with a unique output in this function.
19,22,25,28 the 11nth term
Answer:
31 hecause the èattern is adding 3
Step-by-step explanation:
Rick claims that the equation
×2 + 5x + 9 = 0 has no solution. Jenny claims that there are two solutions. Explain how Rick could be correct, and explain how Jenny could be correct.
Answer: Both Rick and Jenny could be correct because we do not know what "x" is.
Step-by-step explanation:
The purpose of the variable "x" is to substitute it for an unknown number. Since we do not know what "x" is we can not solve the equation. We can only add like terms.
I hope this helps :)
Use the diagram to solve 3 ÷ 1/6
Answer:
A. 1/18
Step-by-step explanation:
Please Help! need this to pass :/
Answer:
c=66°
Step-by-step explanation:
a=51°
51+63=114°
180-114°= 66°
Answer:
66
Step-by-step explanation:
a° = 51° (corresponding angles)
a = 51
a° + c° + 63° = 180° (interior angle sum postulate of a triangle)
51° + c° + 63° = 180°
c° + 114° = 180°
c° = 180° - 114°
c° = 66°
c = 66
Brielle entered a contest at work that awards prizes to individuals who walk 10,000 steps a day. On the first day of the contest, Brielle checks her Fitbit at 12:00 PM and sees that she has already completed of the goal. How many steps has Brielle already walked at 12:00 PM? 3/8
Answer:
3750
I wish you luck in your assignments.
Item2
Item 2 6.66 points
Time Remaining 1 hour 23 minutes 43 seconds
01:23:43
Problem 10-4
Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed.
SAMPLE
1 2 3 4 5 6
79.2 80.5 79.6 78.9 80.5 79.7
78.8 78.7 79.6 79.4 79.6 80.6
80.0 81.0 80.4 79.7 80.4 80.5
78.4 80.4 80.3 79.4 80.8 80.0
81.0 80.1 80.8 80.6 78.8 81.1
Factors for three-sigma control limits for x¯x¯ and R charts
FACTORS FOR R CHARTS
Number of Observations in Subgroup,
n Factor for
x¯x¯ Chart,
A2 Lower
Control Limit,
D3 Upper
Control Limit,
D4
2 1.88 0 3.27
3 1.02 0 2.57
4 0.73 0 2.28
5 0.58 0 2.11
6 0.48 0 2.00
7 0.42 0.08 1.92
8 0.37 0.14 1.86
9 0.34 0.18 1.82
10 0.31 0.22 1.78
11 0.29 0.26 1.74
12 0.27 0.28 1.72
13 0.25 0.31 1.69
14 0.24 0.33 1.67
15 0.22 0.35 1.65
16 0.21 0.36 1.64
17 0.20 0.38 1.62
18 0.19 0.39 1.61
19 0.19 0.40 1.60
20 0.18 0.41 1.59
a. Using factors from above table, determine upper and lower control limits for mean and range charts. (Round your intermediate calculations and final answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)
Mean Chart Range Chart
UCL
LCL
Answer:
Kindly check explanation
Step-by-step explanation:
Sample 1 :
Mean = (79.2 + 78.8 + 80 + 78.4 + 81) / 5 = 79.48
Range = 81 - 78.4 = 2.6
Sample 2 :
Mean = (80.5 + 78.7 + 81 + 80.4 + 80.1) / 5 = 80.14
Range = 81 - 78.7 = 2.3
Sample 3 :
Mean = (79.6 + 79.6 + 80.4 + 80.3 + 80.8) / 5 = 80.14
Range = 80.8 - 79.6 = 1.2
Sample 4 :
Mean =(78.9 + 79.4 + 79.7 + 79.4 + 80.6)/5 = 79.6
Range = 80.6 - 78.9 = 1.7
Sample 5 :
Mean = (80.5 + 79.6 + 80.4 + 80.8 + 78.8)/5 = 80.02
Range = 80.8 - 78.8 = 2
Sample 6 :
Mean =(79.7 + 80.6 + 80.5 + 80 + 81.1)/5 = 80.38
Range = 81.1 - 79.7 = 1.4
Xbar = mean of the means
Xbar = (79.48+80.14+80.14+79.6+80.02+80.38) / 6 = 79.96
Rbar = Mean of the sample ranges
Rbar = (2.6 + 2.3 + 1.2 + 1.7 + 2 + 1.4) / 6 = 1.87
n =5 ;D4 = 2.11 ; D3 = 0
From table, D4 = 2.11 ; D3 = 0
Range chart :
Upper Control limit, UCL = D4 * Rbar ; 2.11*1.87 = 3.9457 = 3.95
Lower Control limit, LCL = D3 * Rbar ; 0*1.87 = 0
Mean chart :
Xbar ± A2 * Rbar
From the table :
n = 5 ; A2 = 0.58
Lower control limit(LCL) = Xbar - A2*Rbar
LCL = 79.96 - (0.58*1.87) = 78.8754 = 78.88
Upper Control Limit (UCL) = Xbar + A2*Rbar
UCL = 79.96 + (0.58*1.87) = 81.0446 = 81.04
(78.88 ; 81.04)
The value of Each sample mean falls within the mean interval, Hence, We can conclude that process is on control.