Using the z-distribution, it is found that there is enough evidence to conclude that taking a low-dose aspirin each day reduces the chance of developing cancer.
What are the hypotheses tested?At the null hypotheses, it is tested if there is no difference among the proportions, that is:
[tex]H_0: p_1 - p_2 = 0[/tex]
At the alternative hypotheses, it is tested if the aspirir proportion is lower, that is:
[tex]H_0: p_1 - p_2 < 0[/tex]
What is the mean and the standard error of the distribution of differences?For each sample, they are given by:
[tex]p_1 = \frac{15}{500} = 0.03, s_1 = \sqrt{\frac{0.03(0.97)}{500}} = 0.0076[/tex]
[tex]p_2 = \frac{26}{500} = 0.052, s_2 = \sqrt{\frac{0.052(0.948)}{500}} = 0.0099[/tex]
Hence, for the distribution of differences, they are given by:
[tex]\overline{p} = p_1 - p_2 = 0.03 - 0.052 = -0.022[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0076^2 + 0.0099^2} = 0.0125[/tex]
What is the test statistic?It is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which p = 0 is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
[tex]z = \frac{-0.022 - 0}{0.0125}[/tex]
z = -1.76.
What is the conclusion?Considering a left-tailed test, as we are testing if the proportion is less than a value, the critical value is [tex]z^{\ast} = -1.645[/tex]
Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that taking a low-dose aspirin each day reduces the chance of developing cancer.
More can be learned about the z-distribution at https://brainly.com/question/26454209
Solve the system of equations y=-x+3 and 2x+2y=6
Answer:
y = -x + 3
Step-by-step explanation:
1. Substitute "y = -x + 3" in for y in the second expression:
2x + 2(-x + 3) = 6
2. Simplify:
2x + (-2x) + 6 = 6
0 + 6 = 6
6 = 6
Because the values are equal, the solution of y = -x + 3 is a valid input.
hope this helps!
Answer:
Answer to the first equasion is y=2: 2=-1+3
Step-by-step explanation:
y=-x+3 (x=1)
-3 y=-x
-3=2
2=-1+3
y=2
Hope this helps and makes sence
Please help!!!
In the figure below, which is not drawn to scale, find x
A. 7.1
B. 14.2
C. 15
D. 7.5
Answer:
The answer is C. x=15
Step-by-step explanation:
PQ+PR+RQ=360°
(8x-10)°+(6x)°+(10x+10)°=360°
(8x+6x+10x)+(-10+10)=360°
24x+0=360°
[tex]x=\frac{360}{24}[/tex]
x=15
Amanda and Molly are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Amanda sold 3 rolls of plain wrapping paper and 3 rolls of shiny wrapping paper for a total of $60. Molly sold 1 roll of plain wrapping paper and 9 rolls of shiny wrapping paper for a total of $132. What is the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper? (no links please)
Answer:
Step-by-step explanation:
Solving system of symultaneous equation:
Let the cost of one roll of plain wrapping pair = x
Let the cost of one shiny wrapping paper = y
Amanda:
Cost of 3 rolls of plain paper + cost of 3 rolls of shiny paper = $ 60
3*x + 3*y = 60
3x + 3y = 60 ------------------(I)
Molly:
Cost of 1 roll of plain paper + cost of 9 rolls of shiny paper = $ 132
x + 9y = 132 ---------------------(II)
x = 132 - 9y ---------------(III)
Substitute x = 132 -9y in equation (I)
3*(132-9y) + 3y = 60
3*132 - 3*9y + 3y = 60
396 - 27y + 3y = 60
Combine like terms
396 - 24y = 60
Subtract 396 from both sides
-24y = 60 - 396
-24y = -336
Divide both sides by (-24)
y = -336/(-24)
[tex]\sf \boxed{y=14}[/tex]
Now, substitue y = 14 in equation (III)
x = 132 - 9*14
= 132 - 126
[tex]\sf \boxed{x = 6}[/tex]
cost of one roll of plain wrapping paper = $ 6
Cost of one roll of shiny wrapping paper = $ 14
The elements of a function of x are (-6, -7) (-2, -3) and (2, 3) What is the domain of the function?
A: {-7, -3, 3}
B: {-6,-2, 2}
C: {10}
D: {-7, -6, -2}
Answer:
B: {-6, -2, 2}
Step-by-step explanation:
Domain = input values (x-values)
Given elements: (-6, -7) (-2, -3) (2, 3)
The x-values of the given elements are: -6, -2 and 2
Therefore, the domain is {-6, -2, 2}
need the answer
Find (3x+7)2 .
Answer:
9x² + 42x + 49
Step-by-step explanation:
Identity
(x + a)² = x² + 2ax + a²In this case, x = 3x and a = 7, so substitute the values.
(3x + 7)²(3x)² + 2(3x)(7) + (7)²9x² + 42x + 49Answer:
[tex]9x^2 + 42x + 49[/tex]
Step-by-step explanation:
Step 1: Factor out the expression
[tex](3x + 7)^2[/tex]
[tex](3x + 7)(3x + 7)[/tex]
[tex](3x * 3x) + (3x * 7) + (7 * 3x) + (7 * 7)[/tex]
[tex]9x^2 + 21x + 21x + 49[/tex]
[tex]9x^2 + 42x + 49[/tex]
Answer: [tex]9x^2 + 42x + 49[/tex]
Becky says that when she simplifies the following expression, the value is 6 less than her age. What is Becky's age? (7+11) - 8÷2
20
14
26
11
With decimal is equivalent to 76/9
Answer:
8.4
Step-by-step explanation:
76 ÷ 9 = 8.44444444
= 8.4 (rounded)
hope this helps!
A science teacher recorded the pulse of each of the students in her classes after the students had
climbed a set of stairs. She displayed the results, by class, using the box plots shown.
Which class generally had the highest pulse after climbing the stairs?
The class which generally had the highest pulse of students recorded by the science teacher after climbing the stairs is class 3.
What is box plot representation of data?
Box plot is the way of representation of data which gives the graphical image of the data set to understand better.
The minimum and the maximum values in the box plot is plotted at the end points.
A science teacher recorded the pulse of each of the students in her classes after the students had climbed a set of stairs. She displayed the results, by class, using the box plots shown.
In this box plot, the class 3 has the highest value compare to all the box plot.
Thus, the class which generally had the highest pulse of students recorded by the science teacher after climbing the stairs is class 3.
Learn more about the box plot here;
https://brainly.com/question/14277132
#SPJ1
what is the answer to 1/3 + 3/4 + 2/5 =
Vivian and her friend Maddie are each baking apple pies and tarts for a bake sale, using the same recipes. Vivian baked 10 apple pies and 10 apple tarts, using a total of 130 apples. Maddie made 10 apple pies and 5 apple tarts, which used 100 apples. How many apples does each dessert require?
Answer:
6.5
Step-by-step explanation:
solve for x
42=x-2(x+4)
Answer:
-50
Step-by-step explanation:
42+=x-2x-8
42=-x-8
(add 8 to both sides)
50=-x
(divide by negative 1)
-50=x
Does anyone know the answers to this, I had to do this yesterday but I didn´t know any of the questions.
Answer:
(A)
(1) NO
(2) YES
(B)
(3) YES
(4) NO
(5) YES
Step-by-step explanation:
According to the triangle sum theorem, the three interior angles of any triangle add up to 180 degrees. So, if we add up the three angles given, to be a triangle, they have to add up to 180 degrees.
38 + 42 + 110 = 190
So, ( (1) 38, 42, 110 ) is not a triangle becuase it adds up to more than 180 degrees (1).
20 + 40 + 120 = 180
So, ( (2) 38, 42, 110 ) is a triangle because it adds up to 180 degrees (2).
For the lengths for a triangle, the length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides. This is saying:
A-B < C
A+B > C
So to find if they can be, simply plug in the values.
(3)
4-3 < 3
True : 1 < 3
4+3 > 3
True : 7 > 3
(3) is a triangle.
(4)
3-2 < 5
True : 1 < 5
3+2 > 5
False : 5 > 5
(4) is not a triangle
(5)
5-2.5 < 4
True : 2.5 < 4
5+2.5 > 4
True : 7.5 > 4
(5) is a triangle
explain how to do this
i forgot how to do it
Answer:
how i do it:
break the entire figure up into simple shapes ( there should be 4 separate figures once you do this )
find the missing / needed side lengths using the information already provided
multiply to get the area of each figure
add them all up
What is the mean absolute deviation of robin’s scores? m a d = startfraction 8 1 5 0 12 over 5 endfraction
The mean absolute deviation of the given scores of Robin as shown in the diagram atatched is: 5.2.
What is the Mean Absolute Deviation of a Data?The mean absolute deviation of a data set is determined by finding the average of the distance of each data point from the mean of the data set.
Given that the distance from the mean are: 8, 1, 5, 0, 12,
Mean absolute deviation = (8 + 1 + 5 + 0 + 12)/5
Mean absolute deviation = 26/5
Mean absolute deviation = 5.2.
Learn more about mean absolute deviation on:
https://brainly.com/question/447169
Help me I need now plese
Answer:
Ex1. SAS, ASA, SSS, SAS
Ex2. There are 2 heights and equal length
Dtu =uts and ut common side du=us
Rq=sd and sq common side rs=qd
Instructions: The following is the recorded earthquakes on South Carolina from August, 2016 to February, 2017. Use the data to find the residuals. Then draw a residual plot by hand. Use the residual plot to determine if the linear model is the best regression model for this data.
Magnitude Depth (km. )
[Table]
1. 7 2. 9
1. 1 0. 8
1. 4 1. 9
0. 7 3. 2
0. 8 4. 3
1. 9 4
1. 7 6. 3
1. 9 6. 9
1. 9 0. 9
1. 1 2
Source: USGS
x Residual (Round to nearest tenth)
1. 7 Answer
1. 1 Answer
1. 4 Answer
0. 7 Answer
0. 8 Answer
1. 9 Answer
1. 7 Answer
1. 9 Answer
1. 9 Answer
1. 1 Answer
Answer:
1.7 = -0.7
1.1 = -2.1
1.4 = -1.4
Unsure about 0.7
0.8 = 1.7
1.9 (unsure about both)
1.1 = -0.9
Step-by-step explanation:
Hope this helps :)))
The regression line is not a good model because the residuals are not randomly distributed.
What is the residual plot?For a residual plot to represent a good model, the points on the residual plot must be randomly distributed across the coordinates.
From a regression, the residual is the difference between the observed values and the predicted values.
Using the graph, we can see that the points that follow a pattern (or curve) regression line is not a good model because the residuals are not randomly distributed.
Read more about residual plots at:
brainly.com/question/16180255
#SPJ2
You roll a fair 66-sided die.
What is text P ( roll less than 4)
Answer:
1/22
Step-by-step explanation:
Answer:
P(<4)
Step-by-step explanation:
P(<4) means "What is the probability that the die shows a number less than 4?" Since each side has a probability of 1/6 of showing, we can simply sum these 3 probabilities.
What is the surface area of the following cylinder in square centimeters? 471 cm 2 31.4 cm 2 47.1 cm 2 54.95 cm 2
Answer:
54.95
Step-by-step explanation:just did the question and got it right.
Hope this helps!
A diagram of a rectangular prism filled with unit cubes is shown below. Each unit cube has
side lengths measuring 1 foot.
What is the volume, in cubic feet, of the rectangular prism?
A. 12
B. 13
C. 54
D. 72
The volume of the rectangular prism filled with unit cubes each measuring the value of the length given is 72ft³.
Hence, Option D) 72ft³ is the correct answer.
Rectangular Prism and Cube
A rectangular prism is simply a three-dimensional solid shape with six faces which are rectangles.
The volume of a rectangular prism is expressed as;
V = l × w × h
Where l is length, w is width and h is height of the prism
A cube is a three-dimensional solid with six equal square-shaped sides.
Given the data in the question;
Length of the sides of the cube = 1 footLength of the rectangular prism l = 4 cubes × 1 foot = 4ftWidth of the rectangular prism w = 3 cubes × 1 foot = 3ftHeight of the rectangular prism l = 6 cubes × 1 foot = 6ftTo determine the volume of the rectangular prism, we substitute our given values into the expression above.
V = l × w × h
V = 4ft × 3ft × 6ft
V = 72ft³
Option D) 72ft³ is the correct answer.
Hence, the volume of the rectangular prism filled with unit cubes each measuring the value of the length given is 72ft³.
In order to either condense or expand logarithms using their properties, what must be?
Group of answer choices
the need the same exponent
they need the same answer
the need to have the same base
Answer:
Answer C
Step-by-step explanation:
The rules of logarithmic functions require the two log functions to have the same base. If they do not have the same base, you cannot apply any of the rules.
Answer:
Last option
Step-by-step explanation:
They need same base inorder to apply any property
Like
log_a(bc)=log_a^b+log_a^clog_a(b/c)=log_a^b-log_a^cfactor the polynomials of 6x^2-7x-20
i need help math asap
Need help with this fast
Answer:
it says 20% under the math part
At school there is a ratio of 3 girls for every 2 boys. If there are 100 students in the school, how many are girls
Answer:
60 girls
Step-by-step explanation:
Which expression is equivalent to rootindex 4 startroot 144 a superscript 12 baseline b cubed endroot? assume a greater-than-or-equal-to 0 and b greater-than-or-equal-to 0.
An expression has numbers, variables, and mathematical operations. The expression that is equivalent to (144a¹²b³)⁰°⁷⁵ is 2a³(9b³)⁰°⁷⁵.
What is an expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression that is equivalent to [tex]\sqrt[4]{144a^{12}b^3}[/tex], this can be done in the following manner,
[tex]\sqrt[4]{144a^{12}b^3}\\\\= \sqrt[4]{2^4 \times 3^2 \times a^{12} \times b^3}\\\\= (2^4 \times 3^2 \times a^{12} \times b^3)^{\frac14}\\\\= 2^{(\frac14 \times 4)} \times 3^{(\frac14 \times 2)} \times a^{(\frac14 \times 12)} \times b^{(\frac14 \times 3)}\\\\= 2 \times 3^{(\frac12)} \times a^{3} \times b^{(\frac34)}\\\\[/tex]
[tex]= 2\times a^{3} \times 3^{(\frac12 \times \frac22)} \times b^{(\frac34)}\\\\= 2\times a^{3} \times 3^{(\frac24)} \times b^{(\frac34)}\\\\= 2\times a^{3} \times 9^{(\frac14)} \times b^{3(\frac14)}\\\\= 2\times a^{3} \times (9b^{3(\frac14)})\\\\=2a^3 \sqrt[4]{9b^3}[/tex]
Thus, The expression that is equivalent to (144a¹²b³)⁰°⁷⁵ is 2a³(9b³)⁰°⁷⁵.
Learn more about Expression:
https://brainly.com/question/13947055
Answer:
its a
Step-by-step explanation:
on edge 2022
Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
Answer:
area of triangle base ×height over 2= 10km×9.4 over 2
area rectangle l×w =10×10
Escribe una ecuación que represente la tabla.
por favor respondan ^^
What is the solution to the equation 9r=4/7
Answer:
r=4/63
Step-by-step explanation:
Divide each term in 9r=47 by 9 and simplify.
Answer:
[tex]r=\frac{4}{63}[/tex]
Step-by-step explanation:
1) Divide both sides by the same factor
[tex]9r=\frac{4}{7}[/tex]
[tex]\frac{9r}{9} =\frac{\frac{4}{7} }{9}[/tex]
2) Simplify
Cancel terms that are in both the numerator and denominator[tex]\frac{9r}{9} =\frac{\frac{4}{7} }{9}[/tex]
[tex]r=\frac{\frac{4}{7} }{9}[/tex]
Divide the numbers[tex]r=\frac{\frac{4}{7} }{9}[/tex]
[tex]r=\frac{4}{63}[/tex]
the answer is 1575 but I need to show my work! (find the total volume)
I WILL GIVE BRAINLIEST!!!!!
Answer: 1575
Step-by-step explanation:
Volume of Pyramid: b*l*h/2 = 21*9*7/3 = 441
Volume of Rectangular prism = V= lwh = (21*12*9)/2 = 1134 (divide by two because it is half of a rectangular prism)
441 + 1134 = 1575
1a. What formula would you use to find
the area of the rectangle below?
2 units
3 units
Answer:
Area = Width * Length
Step-by-step explanation:
This is the formula for a rectangle. If you plug in the values that were givin to you, the answer is 6 units^2.