"National survey released in 2003 showed that among U.S. adults ages 70 and older, 21.1% had been told by a doctor that they had some form of cancer. Use this result as valid for the population of U.S. adults, 70 yrs. old and older. What is the probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer
Answers
Answer:
44.43% probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
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 \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)
In this question, we have that:
\(p = 0.211, n = 40\)
So
\(\mu = 0.211, s = \sqrt{\frac{0.211*0.789}{40}} = 0.0645\)
What is the probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer
This is 1 subtracted by the pvalue of Z when X = 22. So
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.22 - 0.211}{0.0645}\)
\(Z = 0.14\)
\(Z = 0.14\) has a pvalue of 0.5557
1 - 0.5557 = 0.4443
44.43% probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer
Related Questions
PLEASE HELP ITS MATH THANK YOU
Answers
Answer:
he needs 91 packets of seeds
Step-by-step explanation:
5214 divided by 66 gets 79 and then do 7189 divided by 79 to get 91
hi im doing homework i hate i-ready so yea can someone answer this please?
Answers
Weight of Omar after 4 weeks is 9.4375 pounds.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement.
For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
Weight of Omar at the time of birth = 8 pound 3 ounces
Weight gained by Omar in 4 weeks = 5 × 4 = 20 ounces
New weight of Omar
= (8 lb 3 ounces) + 20 ounces
= 8 lb + 23 oz
As, we know 16 ounces = 1 pound
23 ounces = 1.4375 pound
Now, total weight of Omar after 4 weeks = 8 lb + 23 oz
≈ 8 lb + (1.4375) lb
≈ 9.4375 pounds
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Polar coordinates: which is not the same?
Answers
Answer:
The first option is not the same point in polar coordinates as (-3, 1.236). This proves that inverting the signs of r and θ does not generally give the same point in polar coordinates.
Step-by-step explanation:
Let's think about the position of this point. As you can tell it lies in the 4th quadrant, on the 3rd circle of this polar graph.
Remember that polar coordinates is expressed as (r,θ) where r = distance from the positive x - axis, and theta = angle from the terminal side of the positive x - axis. Now there are two cases you can consider here when r > 0.
Given : (- 3, 1.236), (3,5.047), (3, - 7.518), (- 3, 1.906)
We know that :
7.518 - 1.236 = 6.282 = ( About ) 2π
5.047 + 1.236 = 6.283 = ( About ) 2π
1.236 + 1.906 = 3.142 = ( About ) 2π
Remember that sin and cos have a uniform period of 2π. All of the points are equivalent but the first option, as all of them ( but the first ) differ by 2π compared to the given point (3, - 1.236).
Pablo solved the polynomial equations given in the table. Determine whether each polynomial is correct. Select Correct or Incorrect for each equation.
Equation
(b²+7b-9)+(4b-6b²) = -8b² + 14b-9
(4a+6)-(3a²-9a+1)=-3a²+ 13a +5
(12c-8c²)+(5c²- 10c) = -3c²+2c
Answers
The first equation is incorrect.
The second equation is correct.
The third equation is correct.
Let's go through each equation and determine whether it is correct or incorrect:
(b²+7b-9)+(4b-6b²) = -8b² + 14b-9
To determine if this equation is correct, we need to simplify both sides and check if they are equal.
On the left side:
(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9
On the right side:
-8b² + 14b - 9
Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.
(4a+6)-(3a²-9a+1)=-3a²+ 13a +5
Again, we need to simplify both sides of the equation and check if they are equal.
On the left side:
(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5
On the right side:
-3a² + 13a + 5
Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.
(12c-8c²)+(5c²- 10c) = -3c²+2c
Again, let's simplify both sides and compare them.
On the left side:
(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c
On the right side:
-3c² + 2c
Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.
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What is the answer out of the options in the image?
Answers
Answer:
(fog)(x) = \( x \)
Step-by-step explanation:
Given:
\( f(x) = \frac{x - 1}{3} \)
\( g(x) = 3x + 1 \)
Required:
(fog)(x)
SOLUTION:
(fog)(x) = f(g(x))
Substitute 3x + 1 into \( f(x) = \frac{x - 1}{3} \)
f(g(x)) = \( \frac{(3x + 1)- 1}{3} \)
\( = \frac{3x + 1 - 1}{3} \)
\( = \frac{3x}{3} \)
\( = \frac{x}{1} \)
(fog)(x) = \( x \)
En 1 a 8, halla el valor de cada expresión cuando a = ;
1. 6a +4
5. 12a +c-b
WIN
2. 5a - 3
= 3b = 9, c= 5 y d = 10.
6.d+c²-b
3. 5d +c+2
7. d²+2c-b+3a
4. b²-9a
8. 3c+ b² +27a-d
Answers
sum of the geometric series 20-10+5-5/2
Answers
Decimal form is 12.5
Mixed number form is 12 1/2
To make marbled paper, Shannon filled a rectangular 279/10cm by 178/10cm dish with water. Then they gently swirled paint on top of the water. let a represent the area of the dish.
Select 1 multiplication and 1 division equation to represent the relationship.
choose 2 answers
A) 178/10 x a = 279/10
B) 178/10 x 279/10 = a
C) 279/10 ÷ 178/10 = a
D) a ÷ 178/10 = 279/10
Answers
The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:
a = (279/10) cm x (178/10) cm
Simplifying this expression, we get:
a = 4953/100 cm^2
So, the correct equations are:
B) 178/10 x 279/10 = a
and
D) a ÷ 178/10 = 279/10
Magic Realm, Inc., has developed a new fantasy board game. The company sold 15,000 games last year at a selling price of $20 per game. Fixed costs associated with the game total $182,000 per year, and variable costs are $6 per game. Production of the game is entrusted to a printing contractor. Variable costs consist mostly of payments to this contractor.
Required:
1) Prepare a contribution format income statement for the game last year and compute the degree of operating leverage.
2) Management is confident that the company can sell 18,000 games next year (an increase of 3,000 games, or 20%, over last year).
Compute:
a) The expected percentage increase in net operating income for next year.
b) The expected total dollar net operating income for next year.
Answers
The expected total dollar net operating Income for next year = $70,000
1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:
Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000
Variable expenses (15,000 × $6) = $90,000
Contribution margin = $210,000
Fixed expenses = $182,000Net operating income = $28,000
Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)
The expected percentage increase in net operating income for next year:
The expected sales in next year = 18,000
games selling price per game = $20
Therefore, Total sales revenue = 18,000 × $20 = $360,000
Variable expenses = 18,000 × $6 = $108,000
Fixed expenses = $182,000
Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses
= $360,000 – $108,000 – $182,000= $70,000
The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%
The expected total dollar net operating income for next year = $70,000
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A _____ curve shows larger increases in performance during early practice trails than in later trials.A. LinearB. Negatively acceleratingC. OgiveD. Positively accelerating
Answers
According to a negatively accelerated curve, early practice trials exhibit greater increases in performance than subsequent trials. Option B will be correct.
Negative acceleration occurs when an activity or function's rate of growth slows down as a result of practice or training. For instance, subsequent practice repetitions might result in decreased learning or performance increases.
The negatively accelerated curve indicates that performance on psychometric exams increases over time but at a diminishing rate. In other words, the pattern typically demonstrates significant improvement after early practice, followed by a decline in improvement with more exercise.
Therefore, the blank can be filled with negatively accelerated and the correct option is option B.
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Which is the graph of the cube root function f(x) = cube root of x
Answers
Answer:
The function is given below as
\(f(x)=\sqrt[3]{x}\)Step 1:
We will generate table of values for when x=0
\(\begin{gathered} f(x)=\sqrt[3]{x} \\ when\text{ x=1} \\ y=\sqrt[3]{1} \\ y=1 \\ (1,1) \end{gathered}\)When x=-1
\(\begin{gathered} f(x)=\sqrt[3]{x} \\ y=\sqrt[3]{-1} \\ y=-1 \\ (-1,-1) \end{gathered}\)when x=0
\(\begin{gathered} y=\sqrt[3]{0} \\ y=0 \\ (0,0) \end{gathered}\)When x=8
\(\begin{gathered} y=\sqrt[3]{x} \\ y=\sqrt[3]{8} \\ y=2 \\ (8,2) \end{gathered}\)When x=-8
\(\begin{gathered} y=\sqrt[3]{-8} \\ y=-2 \\ (-8,-2) \end{gathered}\)The table of values is given below as
Using a graphing calculator, we will have the graph be
13. Fast food restaurants sell food and beverages. Yesterday, 200 customers came into a fast food restaurant
during lunchtime. Of the 200 customers, 170 ordered food, 100 ordered a beverage, and 80 ordered both.
Suppose one of these customers is randomly selected.
Answers
(a) P(no food and no beverage) is 1/20.
(b) The probability that this person ordered food or a beverage is 19/20.
(c) The probability that they ordered a beverage given they ordered food is 8/17.
Given that,
Total customers = 200
Number of customers who ordered food = 170
Number of customers who ordered beverages = 100
Number of customers who ordered both = 80
(a) Number of customers who has not ordered food and beverage = 200 - [(170 - 80) + (100 - 80) + 80] = 10
P(no food and no beverage) = 10/200 = 1/20
(b) Probability that this person ordered food or a beverage is,
P = 1 - 1/20 = 19/20
(c) Given that person ordered food.
P(food) = 170/200 = 17/20
P(food and beverage) = 80/200 = 8/20
Probability that a customer ordered beverage given they ordered food is,
P = 8/20 ÷ 17/20 = 8/17
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The complete question is given below.
Fast food restaurants sell food and beverages.
Yesterday, 200 customers came into a fast food restaurant during lunchtime. Of the 200 customers, 170 ordered food, 100 ordered a beverage, and 80 ordered both.
Suppose one of these customers is randomly selected.
(a) Find P(no food and no beverage).
(b) What is the probability that this person ordered food or a beverage?
(c) If we know the person ordered food, what is the probability that they ordered a beverage?
Ms. Ortiz borrows $2.50 every day for a school week (5 days) to buy a bacon egg and cheese. How much does
she owe by the end of the week? (Use negative numbers to show how much she owes
It’s multiplying signed numbers
Answers
Answer: She will owe $12.50 at the end of the week, and her account balance will be -12.50 dollars.
Step-by-step explanation:
A school week is 5 days. If Ms. Ortiz borrows $2.50 every day, then we will have to multiply 2.50 by 5 to find how much Ms. Ortiz owes at the end of the week.
2.50 x 5 = 12.5, or $12.50.
Therefore, Ms. Ortiz owes $12.50 at the end of the week, and her account balance will be -12.50.
READ No link or bot and answer the question 20 points I give Brainliest to the best answer
Answers
Answer:
1- 5 to the 2nd power=25 / 25-11=14 / 14+2=16 /16+8=24
3- 6 to the 3rd power= 216/ 216-9= 207/207+1=208/ 208+4+8=220
4- 6-3=3/ 3x9=27/ 3x-9= -27/ -27+27=0
Step-by-step explanation:
I can't do all of them cuz im in 5th G but i can help u wit some
sorry i can tell this is very overwhelming also i'm am also sorry if this is wrong if this is not for work and your just practicing (thank god).
have a great day
Convert the angle 0=100 degrees to radians. What’s the exact answer??
Answers
an isosceles triangle the ratio ri/rc of the inscribed and circumscribed circumference is 1/2. determine the angles of the triangle.
Answers
9514 1404 393
Answer:
equilateral triangle: all angles 60°
Step-by-step explanation:
It can be shown easily that an equilateral triangle meets the requirement. It is a little more difficult to show that the requirement forces an equilateral triangle.
In an equilateral triangle, the incenter and the circumcenter are the same point: the centroid. The centroid is half as far from the side as it is from the vertex, so the requirement ri/rc = 1/2 is demonstrated by that property.
Answer:
the answer is all angles 60°
If a figure is dilated by a factor of 3, the sides of the pre-image will be _ of the image's sides.
A. one-ninth the size
B. one-third the size
C. nine times the size
D. three times the size
Answers
Cakculate the Length of line x
Answers
The length of line x in the figure of the cube given is 19.
Calculate the length of the base of the cube, which is the diagonal of the lower sides :
base length = √10² + 6²
base length = √136
The length of x is the diagonal of the cube
x = √baselength² + 15²x = √(√136)² + 15²
x = √136 + 225
x = √361
x = 19
Therefore, the length of line x in the figure given is 19.
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How many schools have fewer than 50 classrooms
Answers
Answer:
7 schools have fewer than 50 classrooms.
The growth of the population of Austin, Texas since 1900 can be modeled using the equation y = 25,145e0.0327x, where x is the time since 1900 and y is the population.
According the model, the population in 1940 was approximately
93,000
Using the model, the population will reach 1,221,796 in the year 2018
Answers
Answer:
93000 and 2018
Step-by-step explanation:
Marissa bought 60 party hats for $84.00. find the unit price for 1 hat
Answers
answer:
$1.40
step-by-step explanation:
so the price of one hat is your unknown variable, so let's make an equation out of it:
60*x=$84.00
let's let x stand for the price of one hat
the way i figured it out was to do 84 ÷ 60
which equals 1.4
and remember, since we're dealing with money you must add a zero at the end of the decimal
then if you want, just to ensure that this is correct you can multiply 60*1.40
good luck :)
i hope this helps
have a great day !!
|2x-5|+17=2 I don’t know how to do it what’s the answer
Answers
Answer:
x=-6,11
Step-by-step explanation:
Break down the problem into these 2 equations.
2x-5=17
-(2x-5)=17
2 Solve the 1st equation: 2x-5=17
x=11
3 Solve the 2nd equation: -(2x-5)=17
x=-6x
4 Collect all solutions.
x=-6,11
the table represents the radius, diameter, area, and circumference of different circles. circumference and area are in terms of n. complete the table by dragging values into the empty cells.
Answers
Answer:
Step-by-step explanation:
radius equation - πr^2
circumference equation - 2πr
diamet is twice radius
row 1 - diameter = 4 and area = 16πr
row 2 - radius = 8 , diameter = 16
row 3 - 36π
row 4 - circumference = 16π
row 5 - radius = 10 circumference = 20 π
What is the smallest positive integer $n$ such that $\sqrt[4]{56 \cdot n}$ is an integer?
Answers
The smallest positive integer n such that t \($\sqrt[4]{56 \cdot n}$\) is an integer is 686.
We have to find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer
To find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.
The prime factorization of 56 is:
56 = 2³ × 7
The prime factors of 56 need to be raised to multiples of 4.
Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.
To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴
The smallest value of n that satisfies this condition is:
n = 2 × 7³ = 2× 343 = 686
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What is the value of y in 8 + (6/y) = 53 ?
Answers
Answer:
y=2/15
Step-by-step explanation:
8+(6/y)=53
We move all terms to the left:
8+(6/y)-(53)=0
Domain of the equation: y)!=0
y!=0/1
y!=0
We add all the numbers together, and all the variables
(+6/y)+8-53=0
We add all the numbers together, and all the variables
(+6/y)-45=0
We get rid of parentheses
6/y-45=0
We multiply all the terms by the denominator
-45*y+6=0
We add all the numbers together, and all the variables
-45y+6=0
We move all terms containing y to the left, all other terms to the right
-45y=-6
y=-6/-45
y=2/15
hope this helps.
Ali has two options to decide where to save his money. He can save his money either at 9% compounded quarterly in bank A or at 8.5 % compounded monthly in bank B. Determine the effective rate for each of the nominal rates offered by the banks.
Answers
Answer:
Ali would earn more money if he saves his money in bank A as it offers a higher effective annual interest rate.
Bank A: 9.31%
Bank B: 8.81%
Step-by-step explanation:
The effective annual interest rate is the interest rate that is actually earned or paid on an investment, loan or other financial product due to the result of compounding over a given time period. The formula for calculating the effective annual interest rate is:
(1 + r/n)^n - 1
where r is the nominal interest rate and n is the number of times interest is compounded per year.
For bank A, the nominal interest rate is 9% compounded quarterly. Therefore, the effective annual interest rate would be:
(1 + 0.09/4)^4 - 1 = 9.31%
For bank B, the nominal interest rate is 8.5% compounded monthly. Therefore, the effective annual interest rate would be:
(1 + 0.085/12)^12 - 1 = 8.81%
So, Ali would earn more money if he saves his money in bank A as it offers a higher effective annual interest rate.
Choose the best graph that represents the linear equation:
-x = 2y + 1
Answers
The line slants downward from left to right, indicating that as x increases, y decreases.
The given linear equation is -x = 2y + 1. To represent this equation graphically, we need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.Rearranging the given equation, we get:2y = -x - 1
Dividing both sides by 2:y = (-1/2)x - 1/2
The slope of the line is -1/2, which means that for every unit increase in x, y decreases by 1/2 unit. The y-intercept is -1/2, indicating that the line intersects the y-axis at (0, -1/2).
Based on this information, the best graph that represents the linear equation y = (-1/2)x - 1/2 is a straight line with a negative slope of -1/2, starting at the point (0, -1/2) and extending infinitely in both directions.
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What is the probability that both events will occur? Two dice are tossed. Event A: the first die is a 5 or 6. Event B: The second die is not a 1
Answers
Answer: The probability that both events A and B will occur is 5/18 or 0.28.
Step-by-step explanation:
To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.
Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.
Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.
To find the probability that both events A and B occur, we multiply the probabilities:
Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.
name the quadrilateral with 2 pairs of consecutive congruent sides with diagonals that meet at a right angle
Answers
The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.
What is the best description of the relationship in the scatterplot below?A graph has an x-axis which ranges from 0 to 10, in increments of 1, and a y-axis, which ranges from 0 to 30 in increments of 5. Approximately 2 dozen points are scattered sporadically between x = 3 and x = 7 and between y = 12 and y = 28. All values estimated.112233445566778899551010151520202525yyxxChoose 1 answer:Choose 1 answer:(Choice A)APositive linear association(Choice B)BNegative linear association(Choice C)CNonlinear association(Choice D)DNo association
Answers
No association. Option D is correct
ExplanationsWhat is correlation?Correlation is the description of the relationship between two variables on a xy-plane. Correlation is important to determine the nature of a large body of data.
The closer the data points come when plotted to make a straight line, the stronger the correlation between the two variables in question. The type of correlation that we have include;
• Positive correlation
,• Negative correlation
,• Non-linear association
,• No correlation
According to the question, we are to describe the relationship in the scatterplot below. From the graph, we can see that as one variable moves away, another moves in an entirely different direction showing that the distributed points have no pattern. This shows that there is zero or no correlation between the x and y variables.
Hence we can conclude that the best description of the relationship in the scatterplot below is No association