Answers
Note that with respect to the above problem,
The z-score is 3.22The P-value is 0.001The conclusion is that there is evidence that the two proportions differ at the 0.10 significance level. (Option A)What is the justification for the above response?Plan:
Let P1 be the proportion for the treatment group (low-fat diet), and P2 the proportion for the control group (normal diet).
State the hypotheses for your test:
H₀: P1 = P2 (There is no significant difference in the proportion of women with a family history of breast cancer between the low-fat and normal diet groups)
Ha: P1 ≠ P2 (There is a significant difference in the proportion of women with a family history of breast cancer between the low-fat and normal diet groups)
To test this claim, we can use a two-sample z-test for proportions. We calculate the test statistic as follows:
z = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2))
where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and p is the pooled proportion. The pooled proportion is calculated as:
p = (x1 + x2) / (n1 + n2)
where x1 and x2 are the number of successes in each sample.
Using the given data, we have:
p1 = 1642/3311 = 0.495
p2 = 1480/3176 = 0.466
n1 = 3311
n2 = 3176
x1 = 1642
x2 = 1480
p = (1642 + 1480) / (3311 + 3176)
p = 0.480
Then, the test statistic is:
z = (0.495 - 0.466) / sqrt(0.480*(1-0.480)*(1/3311 + 1/3176))
z = 3.22
Using a standard normal distribution table or calculator, we find the p-value associated with a two-tailed z-score of 3.22 is approximately 0.001.
Therefore, the p-value is 0.001.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that there is a significant difference in the proportion of women with a family history of breast cancer between the low-fat and normal diet groups.
Answer: The difference between the sample proportions is significant at the 0.10 significance level. Therefore, we reject the null hypothesis and conclude that there is evidence that the two proportions differ.
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Related Questions
Pencil boxes cost $15 each. Calculators cost $24 each. Kelly bought a total of 100 pencil boxes and calculators for $2130. How many pencil boxes did she buy?
Answers
Answer:
Step-by-step explanation:
Kelly bought a total of 1500 pencil boxes.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answers
Therefore, the equations that represent circles with a diameter of 12 units and a center on the y-axis are x² + y² = 36 and (x + 6)² + y² = 36.
Which equations represent circles?The radius of a circle having a diameter of 12 units is 6 units. The center's x-coordinate is zero if its centre is on the y-axis.
To discover which equations describe circles with these characteristics, we may use the conventional version of the equation of a circle, (x - h)2 + (y - k)2 = r2, where (h, k) is the circle's centre and r is its radius.
When we enter h = 0 and r = 6, we obtain:
(x - 0)² + (y - k) (y - k)² = 6²\sx² + (y - k) (y - k)² = 36
As we are aware that the centre is on the y-axis, the center's y-coordinate is also 0. K thus equals 0.
With k = 0, we obtain:
x² + y² = 36\s(x - 4) (x - 4)² + y² = 36\s(x + 6)² + y² = 36
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A car travels at an average speed of 68 miles per hour. How long does it take to travel 357 miles?
Answers
If a car travels at an average speed of 68 miles per hour, it takes it 5 hours 15 minutes to travel 357 miles.
What is the average speed?The average speed is the unit rate.
The average speed is computed as the quotient of the total distance and the total time.
Conversely, the time is a function of the division of the total distance by the average speed.
The total distance traveled by the car = 357 miles
The average speed = 68 miles per hour (mph)
The time = Distance/Average speed = 357/68 = 5.25 hours
= 5 hours 15 minutes.
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Please help find the scale factor
Answers
Answer:
2.5
Step-by-step explanation:
for example, if you take two of the value of x's -- 5/2, it equals 2.5
2 x 2.5 = 5
Yesterday, a movie theater sold 290 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $566 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.
PLEASE HELP
Answers
Answer:
Step-by-step explanation:
Let's call the number of large bags of popcorn sold "L" and the number of small bags of popcorn sold "S".
We can set up two equations based on the information given:
L + S = 290 (the total number of bags of popcorn sold)
4L + S = 566 (the total revenue from popcorn sales)
We can use substitution or elimination to solve for L and S.
Substitution:
From the first equation, we know that S = 290 - L. We can substitute this into the second equation:
4L + (290 - L) = 566
Simplifying, we get:
3L + 290 = 566
3L = 276
L = 92
Then we can use the first equation to find S:
L + S = 290
92 + S = 290
S = 198
So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.
Elimination:
We can eliminate one variable by multiplying one of the equations by a constant to make the coefficients of one of the variables equal but with opposite signs.
In this case, we can multiply the first equation by 4 to make the coefficients of S equal but with opposite signs:
4L + 4S = 1160
4L + S = 566
Subtracting the second equation from the first, we eliminate L:
3S = 594
S = 198
Then we can use either of the original equations to find L:
L + S = 290
L + 198 = 290
L = 92
So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.
please help me :(
use the Remainder Theorem and synthetic division please
Answers
The value of the functions are,
⇒ f (- 10) = 20201
⇒ f (2) = 17
⇒ f (3) = 143
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The value of function is,
⇒ f (x) = 2x⁴ + x² - 10x + 1
Now, We can find all the values as;
At x = - 10;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (- 10) = 2 (- 10)⁴ + (- 10)² - 10 (- 10) + 1
⇒ f (- 10) = 20000 + 100 + 100 + 1
⇒ f (- 10) = 20201
At x = 2;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (2) = 2 (2)⁴ + (2)² - 10 (2) + 1
⇒ f (2) = 32 + 4 - 20 + 1
⇒ f (2) = 17
At x = 3;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (3) = 2 (3)⁴ + (3)² - 10 (3) + 1
⇒ f (3) = 162 + 9 - 30 + 1
⇒ f (3) = 143
Thus, The value of the functions are,
⇒ f (- 10) = 20201
⇒ f (2) = 17
⇒ f (3) = 143
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A researcher is investigating academic motivation among college students and their siblings. This type of study would be _______
Answers
Answer:
This type of study would be a comparative study, as it involves comparing the level of academic motivation between college students and their siblings.
Step-by-step explanation:
Answer this in this hour or no points.
A spinner has 3 equal sections colored blue, orange, and red. Determine the sample space for spinning the spinner two times.
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Blue Red
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Orange Blue
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Red Blue
Red Orange
Orange Blue
Orange Red
Answers
If the spinner is spinning two times then the sample space becomes { BB,B0,BR,OB,OO,OR,RB,RO,RR}.
What is sample space?In probability a sample space is a set of possible number of outcomes of a random experiment.
A spinner has three equal sections blue(B), orange(O), red(R).
The sample space will be
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Hence, If the spinner is spinning two times then the sample space becomes { BB, B0, BR, OB, OO, OR, RB, RO, RR}.
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Pleaseeee yelp meeeeee
Answers
Answer:
x ≤ 6.8
Step-by-step explanation:
1.25x + 6.50 ≤ 15
1.25x ≤ 8.5
x ≤ 6.8
So, the answer is x ≤ 6.8
Answer:
Below
Step-by-step explanation:
1.25x + 6.50 <= 15 SUBTRACT 6.50 from both sides of the equation
1.25x ≤ 8.50 DIVIDE both sides by 1.25
x ≤ 6.8
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $50.
If they offer a 2-year extended warranty for $7, what is the company's expected value of each warranty sold? Round your answer to the nearest cent.
Answers
Answer:
The expected value of each warranty sold is $23.8.
Write 4 3/20 as a decimal
Answers
Answer:
4.15 or
Step-by-step explanation:
100/20=5 times 3 is 15
so its 4.15 which equals 4 3/20
7 men build a house in 300 days how many men .working in the same rate can build the house in 70 days
Answers
Answer:
30 men
Step-by-step explanation:
7 men x 300 days = 2100 man-days to build 1 house)
(2100 man-days/house) x (1 house/70 days) = 30 men
x = 8 what is the value of 6(x - 3)
Answers
Answer: 30
Step-by-step explanation:
plug in x=8 to get: 6(8 - 3)
solve inside parenthesis: 6(8-3) = 6(5)
multiply: 6(5) = 30
Answer:
[tex] \sf \: 6(x - 3) = 30[/tex]
Step-by-step explanation:
Now we have to,
→ Find the value of 6(x - 3).
Given information,
→ x = 8
Let's solve the problem,
→ 6(x - 3)
→ 6(8 - 3)
→ 6(5)
→ 6 × 5
→ 30 => [solution]
Hence, the answer is 30.
fill in the blanks about determining if a property is sine,cosine, or both.
Answers
The functions are Identified as below
The domain is all real numbers for both
An x-intercept is (π, 0) for sin
The minimum value is -1 for both
An x-intercept is (π/2, 0) for cos
What are sin functions?Sin functions, or sine functions, are mathematical functions that describe a wave-like pattern that oscillates between a maximum and minimum value.
sin functions has x intercept of (π, 0), this can be checked by setting a calculator in radian and checking for sin π.This will give a value of of zero
For cos the x intercept is zero at π/2
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O Which point has the coordinates (-3.5, 4)? Point W Point Y Point X Point Z
Answers
The point which has the coordinates (-3.5, 4) is point Z.
What are Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given coordinate is (-3.5, 4).
This means that the point is at a distance of 3.5 to the left of the origin and at a distance of 4 units above the origin.
So in order to find the point, mark the point -3.5 in the exact middle of -3 and -4 on the X axis.
Mark the point 4 on the Y axis.
Draw perpendicular lines from both.
Intersecting point is the given point.
Here point Z indicates this.
Hence point Z indicates the coordinates (-3.5, 4).
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Your question lacks the graph showing the points and coordinates. The graph is given below.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
It is true that the graph contains the point (0, 0).
The following three assertions regarding the function and its graph are true:
The function's graph resembles a parabola.
The graph begins at the bottom.
The point is shown in the graph (0,0).
Explanation:
A second-degree polynomial function, the quadratic function f(x) = x2 - 5x + 12 has a parabola as its graph.
The parabola widens downward because the coefficient of x2 is positive (1 in this instance).
When we replace x with -10 in the given function, we obtain the value of f(-10) as (-10)2 - 5(-10) + 12 = 82. Hence, "f(-10) = 82" is true.
We substitute x = 20 in the given function, resulting in f(20) = 202 - 5(20) + 12 = 212, to see if the point (20, -8) is on the function's graph. The claim "The graph contains the point (20, -8)" is untrue since the point's y-coordinate is -8, which is not equivalent to f(20).
We substitute x = 0 in the given function to get f(0) = 02 - 5(0) + 12 = 12 to determine if the point (0, 0) is on the function's graph. The assertion "The graph contains the point (0, 0)" is true because the y-coordinate of the point (0, 0) is 0, which is equivalent to f(0).
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what is the exact circumference of a circle with a radius of 17mm (Answer options) 8.5
17
34
68
Answers
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=17 \end{cases}\implies C=2\pi (17)\implies C=34\pi[/tex]
The cost of 3 scarves is $86.25. What is the unit price?
Answers
In linear equation, $28.75 is the unit price .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
The cost of 3 scarves is $86.25
then,
the unit price is = $86.25/3 = $28.75
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I plan to deposit their annual profits in an investment account earning a 9% annual return. If the owner starts with their first deposit today for $22,000 and expects to make the same profit for the next 7 years, how much will be saved for retirement at that point?
Answers
Answer: We can use the formula for future value of an annuity to calculate how much will be saved for retirement:
FV = Pmt x (((1 + r)^n - 1) / r)
where:
FV is the future value of the annuity
Pmt is the payment made each period (in this case, the annual profit of $22,000)
r is the annual interest rate (9% or 0.09 as a decimal)
n is the number of periods (7 years)
Substituting the given values into the formula, we get:
FV = $22,000 x (((1 + 0.09)^7 - 1) / 0.09)
FV = $22,000 x (1.9904 / 0.09)
FV = $22,000 x 22.116
FV = $485,552
Therefore, the amount saved for retirement after 7 years will be $485,552.
Step-by-step explanation:
A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $80,000 saved up for when she goes to college in 15 years, assuming the account earns a 6% return.
Annual deposit: $
Answers
We can use the future value formula for an annuity to solve this problem:
FV = PMT * ((1 + r)^n - 1) / r
where:
FV is the future value of the annuity
PMT is the regular payment or deposit
r is the annual interest rate
n is the number of periods (in this case, the number of years)
We want to solve for PMT, so we can rearrange the formula to get:
PMT = FV * r / ((1 + r)^n - 1)
Plugging in the given values, we get:
FV = $80,000
r = 6% = 0.06
n = 15 years
So, the annual deposit required is:
PMT = $80,000 * 0.06 / ((1 + 0.06)^15 - 1) ≈ $3,782.58
Therefore, the man would need to deposit approximately $3,782.58 into the account each year in order to have $80,000 saved up for his granddaughter's college education in 15 years, assuming a 6% return.
10 workers can complete a piece of work in 18 days. How many workers are required to complete the work in 12 days?
Answers
The number of workers required = 15
Finding the number of workers:Observe the given problem and find out the relation between the number of workers and the number of days.
In given two one quantity decreased and the other quantity increased then both quantities are said to be in inverse proportions.
Here the product of two quantities will equal a constant.
Here we have
10 workers can complete a piece of work in 18 days
Let 'x' be the number of workers required to complete work in 12 days
Here when the number of days increases the number of workers will be decreased which shows the number of work is inversely proportional to the number of days
The relation can be represented as
=> 10 worker × 18 days = 12 days × x workers
=> 10 × 18 = 12x
=> x = 180/12
=> x = 15
Therefore,
The number of workers required = 15
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What is the unit rate? I need help.
Answers
Answer:
1/15
Step-by-step explanation:
Based on the given conditions, formulate: 2/3 divided by 10
Divide a fraction by multiplying its reciprocal: 2/3 x 1/10
Cross out the common factor: 1/3 x 1/5
Write as a single fraction: 1/3x5
Calculate the product or quotient:1/15
get the result:1/15
Answer:
1/15
1/15
Step-by-step explanation:
Based on the given conditions, formulate: 2/3 divided by 10
Divide a fraction by multiplying its reciprocal: 2/3 x 1/10
Cross out the common factor: 1/3 x 1/5
Write as a single fraction: 1/3x5
Calculate the product or quotient:1/15
get the result:1/15
Answer:
1/15
Terry takes a 800 mg Tylenol for his headache. Every hour that the Tylenol is in his system, a quarter of the medication dissolves in his body.
1. WRITE a function that models the amount of Tylenol in Terry’s body over time. Use x for hours, and y for the amount of Tylenol, in mg, remaining in the body.
2. When there is less than 100mg of medicine left in the body, it safe to take it again. HOW LONG will it take before Terry can take more medicine?
Answers
Therefοre, the sοlutiοn οf the given prοblem οf functiοn cοmes οut tο be Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.
What is functiοn?The curriculum fοr mathematics includes a wide range οf tοpics, such as numbers, numbers, and their cοmpοnents, as well as cοnstructiοn, building, and bοth actual and hypοthetical geοgraphic places. A wοrk discusses the relatiοnships between different variables that all wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that, when cοmbined, prοduce specific results fοr each input.
Here,
The functiοn can be written as fοllοws:
=> y = 800 * (0.25)ˣ
where y is the quantity οf Tylenοl still in Terry's system in milligrammes and x is the number οf hοurs since he last tοοk the medicatiοn.
When Terry's bοdy's cοncentratiοn οf Tylenοl gοes belοw 100mg, we need tο find οut hοw lοng it will be befοre he can take mοre medicatiοn.
The expοnential decay fοrmula frοm part 1 can be used tο find a sοlutiοn fοr this:
=> 800 * (0.25)ˣ = 100
by 800, divide bοth sides.
=> (0.25)ˣ = 0.125
Cοnsider the twο sides' lοgarithms:
=> lοg(0.25) * x = lοg (0.125)
tο find x:
=> lοg(0.125) / lοg (0.25)
=> x = 2.4
Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.
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What are the measures of all angles of a isosceles triangle.
Answers
Answer:
The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
Step-by-step explanation:
What does this equal?
5th grade math. Please answer quickly.
Answers
Answer
The answer is 60
Step-by-step explanation:
50 Points!!! Write a verbal sentence to represent 5n/n+3=n-8. Show as much work as possible please. Photo attached. (Only looking for answer to 12B)
Answers
Answer: Your welcome!
Step-by-step explanation:
5n / (n + 3) = n - 8
5n = n(n + 3) - 8(n + 3)
5n = n^2 + 3n - 8n - 24
n^2 - 5n - 24 = 0
n = 4 or n = -6
The verbal sentence to represent 5n/n+3=n-8 is "When n is 4 or -6, 5n divided by n plus 3 is equal to n minus 8."
Jan bought 7 liters of orange juice how many milliters did she buy
Answers
Answer:
The answer you're looking for is 7000ml
Step-by-step explanation:
Since there are 1000 millimeters inside a liter we can use the equation
x = 7×1000.
We need to first simplify all terms giving us this equation
x = 7000
With that, we are finished and that's how you do this question.
I hope this was helpful!
A service that repairs air conditioners sells maintenance agreements for $75 a year. The average cost of repairing an air conditioner is $350 and 2 in every 100 people who purchase maintenance agreements have air conditioners that need repair. Find the service’s expected profit.
Answers
The service's expected profit is $6,800.
What is the basic arithmetic operations?
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find the service's expected profit, we need to calculate the total revenue and the total cost, and then subtract the cost from the revenue.
First, let's calculate the total revenue. The service sells maintenance agreements for $75 a year, so for every 100 customers, the revenue will be:
100 customers x $75/customer = $7,500
Now, let's calculate the total cost. We know that 2 in every 100 people who purchase maintenance agreements have air conditioners that need repair, and the average cost of repairing an air conditioner is $350. So for every 100 customers, the cost of repairs will be:
2 customers x $350/customer = $700
Finally, let's calculate the expected profit:
Expected profit = Total revenue - Total cost
Expected profit = $7,500 - $700
Expected profit = $6,800
Hence, the service's expected profit is $6,800.
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Multiply f and 7. Then add 9 in expression
Answers
Bc it’s multiply so 7 x f = 7f
— 7f add 9
= 7f+9
- A state fair uses 32 pallets of lemons for lemonade and 32 pallets for
lemon ice. Which uses a greater amount of lemons?
Answers
Answer:
- A state fair uses 32 pallets of lemons for lemonade
Step-by-step explanation: