(Round to three decimal places as needed)
Answer:
a) 95% Confidence interval = (0.026%, 0.037%) to 3 d.p
b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = (131/420076) = 0.0003118483 = 0.0312%
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 95% confidence interval for sample size of 420,076 is obtained from the z-tables because the sample size is large enough for the properties of the sample to approximate the population properties.
Critical value = 1.960 (from the z-tables)
Standard error = σₓ = √[p(1-p)/n]
n = sample size = 420,076
σₓ = √(0.0003118×0.999688/420076) = 0.0000272421 = 0.0000272
95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.000312 ± (1.96 × 0.0000272)
CI = 0.000312 ± 0.0000534
95% CI = (0.0002586055, 0.0003653945)
95% Confidence interval = (0.000259, 0.000365)
95% Confidence interval = (0.0259%, 0.0365%) = (0.026%, 0.037%) to 3 d.p
b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.
Hope this Helps!!!
Applying Math
8. Solve the equation to
show how I = v/r becomes
R= v/l Show your work
To solve the equation I = v/r and show how R = v/l, we can rearrange the equation I = v/r to solve for r, which gives r = v/I. Then substitute v/l for I to get r = v/(v/l) = l. Therefore, R = l.
Explanation:To solve for R = v/l, we can start by rearranging the equation I = v/r to solve for r. Multiply both sides of the equation by r to isolate it, which gives us I * r = v. Then divide both sides of the equation by I to solve for r, which gives us r = v/I. Now substitute v/l for I to get r = v/(v/l). Simplify the expression by multiplying the numerator and denominator by l, which gives us r = lv/v = l. Therefore, R = l.
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This shows how the original equation [tex]\( I = \frac{v}{r} \)[/tex]can be rearranged to solve for[tex]\( R \) (or \( r \))[/tex] in the form [tex]\( R = \frac{v}{I} \)[/tex]. It is important to note that in the context of physics, [tex]\( I \)[/tex] typically represents current, [tex]\( v \)[/tex]represents voltage, and [tex]\( R \)[/tex] represents resistance. The equation [tex]\( I = \frac{v}{r} \)[/tex] is Ohm's law, which relates the voltage, current, and resistance in an electrical circuit. The rearranged form [tex]\( R = \frac{v}{I} \)[/tex] is used to find the resistance when the voltage and current are known.
To solve the equation [tex]\( I = \frac{v}{r} \)[/tex] for [tex]\( R \)[/tex], we need to isolate [tex]\( R \)[/tex] on one side of the equation. Here are the steps to do so:
1. Start with the original equation:
[tex]\[ I = \frac{v}{r} \][/tex]
2. Multiply both sides of the equation by [tex]\( r \)[/tex] to eliminate the denominator:
[tex]\[ I \cdot r = v \][/tex]
3. Now, we want to solve for [tex]\( R \)[/tex], so we need to divide both sides of the equation by [tex]\( I \)[/tex] to isolate [tex]\( R \)[/tex] on one side:
[tex]\[ r = \frac{v}{I} \][/tex]
4. Notice that in the original equation, [tex]\( I \)[/tex] is used, but in the desired equation, [tex]\( R \)[/tex] is used. This seems to be a typo in the question, as [tex]\( I \)[/tex]and [tex]\( R \)[/tex] are likely meant to represent the same variable. Assuming [tex]\( I \)[/tex]and [tex]\( R \)[/tex] are the same, we can rewrite the equation as:
[tex]\[ R = \frac{v}{I} \][/tex]
5. Now, we have [tex]\( R \)[/tex] isolated on one side, which is the desired form of the equation.
Therefore, the final answer, assuming [tex]\( I \)[/tex] and [tex]\( R \)[/tex] represent the same variable, is:
[tex]\[ \boxed{R = \frac{v}{I}} \][/tex]
please help i will give brainleest
Really struggling! Will give 20 points to answers correctly
Answer:
8,820
Step-by-step explanation:
One candle:
½ × 10 × 7 × 6
= 210 cm³
42 candles:
42 × 210
= 8,820 cm³
Answer:
8820 cm^3
Step-by-step explanation:
Volume of one prism = A(base prism)*height(prism)
A(base prism)= A(triangle) = 1/2*(base triangle)*Height(triangle)= 1/2*10*7 = 35 cm^2
Volume of one prism(or one candle) = A(base prism)*height(prism)= 35*6=210 cm^3
Volume of 42 candles = 210*42= 8820 cm^3
Solve 41 = 1/2x + (-4)
Answers:
x = 70
x = 90
x=88
x=20
Answer:
x=90
Step-by-step explanation
multiply by two both sides -x=82-8 move terms -8-82=-x calculate x=90
In a certain Algebra 2 class of 30 students, 18 of them play basketball and 9 of them
play baseball. There are 10 students who play neither sport. What is the probability
that a student chosen randomly from the class plays both basketball and baseball?
Probability that a student will play both is 7/30
Step-by-step explanation:
Total students = 30
No. of students who play basketball = 18
Probability that a student will play basketball = 18/30
= 3/5
No. of students who play baseball = 9
Probability that a student will play baseball = 9/30
= 3/10
No. of students who play neither sport = 10
Probability that a student will play neither sport = 10/30
= 1/3
To find :
Probability that a student will play both = p(student will play both)
No.of students who play sport = 30 - 10
= 20
Out of 20 students 18 play basketball and 9 play baseball.
So, some students play both the sports.
No. of students who play both sports = 18 + 9 - 20
= 7
p(student will play both) = 7/30
Probability that a student will play both is 7/30
Mai is visiting Paris to see the Eiffel Tower. She is 80 feet away
when she spots it. To see the top, she has to look up at an angle of 85.7 degrees. How
Answer: height of the tower is 1064 feet
Step-by-step explanation:
We want to determine the height of the tower.
Assuming her line of sight of the top of the tower is a straight line, then a right angle triangle is formed. The height, h of the tower represents the opposite side of the triangle. Her distance from the foot of the tower represents the adjacent side of the triangle.
To determine h, we would apply the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side
Therefore,
Tan 85.7 = h/80
h = 80tan 85.7
h = 1064 feet
Answer:
The tower is 1063.97 feet.
Step-by-step explanation:
please see the attached files for details
What is the correct factorization of 6(x - 2) + y(x - 2)?
Answer:
( x − 2 ) ( 6 + y )
Step-by-step explanation:
Answer:
(x - 2)(6 + y)
Step-by-step explanation:
Given
6(x - 2) + y(x - 2) ← factor out (x - 2) from each term
= (x - 2)(6 + y) ← in factored form
HW HELP (also please explain how to do it too)
Answer: 14 + 24 + 24 = 62
Step-by-step explanation:
I got that answer by doing 24 x 7.
We know that the area is 168, so to get the area you divide the length in half; now you have 7. (The length is 14)
All you have to do now is 168 divided by 7 and you get 24. So, now you know the rest of the sides are 24. So, 24 x 2 + 14 = 62
Please let me know if the answer is wrong, thank you.
2. Fran bought sneakers for $54.26 and a shirt for $34.34. If Fran started with $100
about how much money does she have left?
Answer:
he has 11.4 dollars left
Step-by-step explanation:
54.26+34.34=88.6
100-88.6=11.4
Answer:
11.40
Step-by-step explanation:
I did the math.
54.26+34.34=88.6
100-88.6=11.40
Using the transformation T: (x, y) ➡️ (X + 2, y + 1) find the distance nammed
(I will get the picture in a moment)
Answer:
comment when you get the picture and i will try to answer !
Step-by-step explanation:
A landscape worker cares for 42 lawns in a 6-day work week. express his daily work unit rate.
Answer:
7 lawns per day
Step-by-step explanation:
42 ÷ 6 = 7
Answer the question fast!!
Answer:
A = bh, so the correct answer is A.
Nico wants to use a horizontal number line to compare 1
and 1.5. He is unsure how to do it and asks you for
help. How would you explain the process?
Answer:
Follow steps 1, 2 and 3.
Step-by-step explanation:
What we must do we will follow in the following steps:
1. Draw a line and make 5 vertical marks about 1/2 inch.
2. Label the middle one 0 and then label the right ones zero 1 and 1.5.
3. Perform the same procedure from step two on the left but negative.
Answer:
1 3 /4
is equal to 1.75. I would plot 1.5 and 1.75 between 1 and 2, but 1.75 would be closer to 2. Since 1.75 is further to the right, it is greater than 1.5.
Step-by-step explanation:
Simplify 12 + 3(2x - 3) + 4.
A.6x - 3
B.6x + 7
C.6x + 13
Step-by-step explanation:
12+6x-9+4
6x+7
option B
Answer:
6x + 7
Step-by-step explanation:
Let's simplify step-by-step.
12 + 3(2x−3) + 4
Distribute:
=12 + (3)(2x) + (3)(−3) + 4
=12 + 6x + −9 + 4
Combine Like Terms:
=12 + 6x + −9 + 4
=(6x) + (12 + −9 + 4)
=6x + 7
Can anyone help with this please?
Answer:
10
Step-by-step explanation:
Tyler is using the distributive property on the expression 9 - 4(5x – 6). Here is his
work:
9 - 4(5x - 6)
9+(-4)(5x +-6)
9 +-20x +-6
3 – 20x
Mai thinks Tyler's answer is incorrect. She says, "If expressions are equivalent then
they are equal for any value of the variable. Why don't you try to substitute the same
value for x in all the equations and see where they are not equal?"
a. Find the step where Tyler made an error.
b. Explain what he did wrong.
c. Correct Tyler's work.
Step-by-step explanation:
A Tyler made mistake in the third step
B Tyler didi not multiply 4 by 6
C 9 - 20x + 24
- 20x + 15
-5 (4x - 3)
Tyler is using the distributive property on the expression 9 - 4(5x – 6).
His work
9 - 4(5x - 6)
9+(-4)(5x +-6)
9 +-20x +-6
3 – 20x
What is the distributive property?The distributive property states that an expression that is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
A . Tyler made mistake in the third step
B . Tyler did not multiply 4 by 6
C. Correct steps are,
9 - 4(5x - 6)
9+(-4)(5x +-6)
9 - 20x + 24
- 20x + 15
-5 (4x - 3)
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The answer and the graph :)
Solve sin x + 2 sin x cos X = for 0°
Answer:
Step-by-step explanation:
hello :
sin x + 2 sin x cosx = 0 equivalent to : sinx(1+2cosx) =0
sinx=0 means : general solution is : x= kπ....k in Z
1+2cosx=0 means : cosx= -1/2 general solution is : x= ±π/6+kπ...k in Z
The question seems to involve solving a trigonometric equation with an incomplete equation provided. It suggests the use of trigonometric identities and basic values of sin and cos at 0 degrees to simplify and solve trigonometric equations.
Explanation:The question appears to be incorrectly phrased or incomplete. However, it seems to involve solving a trigonometric equation involving sine and cosine functions. To approach such equations, one common strategy is to use trigonometric identities to simplify the equation.
For instance the given expression sin x + 2 sin x cos x can be simplified using the double angle identity or factoring, allowing for easier solution. Yet, without a clear equation to solve or a specific value to find, it's challenging to provide a direct answer.
Solving trigonometric equations often requires understanding basic trigonometric functions like sin 0, which is 0, and cos, which is 1 at 0 degrees. These values are fundamental and help in simplifying equations to find solutions within a given domain, typically between 0° and 360° for high school mathematics problems.
If leo blew up 7 balloons and kathy blew up 5 ball what is the ratio of leo balloons to kathy balloons in ratio
Answer:
7 to 5 or 7/5
Step-by-step explanation:
A circle of radius 10cm had a hole cut out of its centre to form a ring. Find the radius of the hole if the remaining area is 50% of the original area. Round to one decimal place
Answer:
7.07cm
Step-by-step explanation:
A=πr2
= 100 π
= 314.159265359/2 (squared)
50% = 157.07963268cm ^2
We look for radius in the area formula
A=πr2
(A / π ) = 157.07963268/ 3.14159265359 = √50 = 7.07106781187
We do not need to half this as already has been squared.
What is the range of the dataset 12,12,12,12,12
Answer:
0
Step-by-step explanation:
Answer:
The range of the data set listed above would be 0.
Step-by-step explanation:
Because there is no greatest or least number, then its just 0. Just to make sure you could enter your data set into www.calculator.net. When I entered it, it said 0 :)
Please vote me brainliest.
Half of the tuna sandwich were on white bread. 25% of the ham sandwiches sold were on brown bread.
There were 20 more white breads sandwiches sold than brown bread.
Answer:
The frequency table is shown below.
Step-by-step explanation:
(i) Half of the tuna sandwich were on white bread = 21
On brown bread, tuna = 42 - 21 = 21
(ii) 25% of the ham sandwiches sold were on brown bread.
= 25% (32) = 8
On white bread, 32 - 8 = 24
Frequency table:
Tuna Cheese Ham Total
Brown 21 11 8 40
White 21 15 24 60
Total 42 26 32 100
which of the following algebraic represents shows a dilation that is an enlargement ?
Answer:
D: (5/2x, 5/2y)
Step-by-step explanation:
A dilation is an enlargement only when the dilation factor > 1
Only 5/2 is greater than 1
Others are less than 1
Dilation is a transformation that changes the size of a figure without changing its shape. It is represented algebraically as 'y=a*x' or 'y=a*x+b', where 'a' is the scale factor. If 'a' is greater than 1, it represents an enlargement.
Explanation:In algebra, a dilation is a transformation that changes the size of a figure without altering its shape. It can either enlarge (expansion) or reduce (contraction) a figure depending on the scale factor. If the scale factor is more than 1, the dilation is an enlargement. Any algebraic representation, such as 'y=a*x' or 'y=a*x+b' where 'a' is greater than 1, represents a dilation that is an enlargement. For instance, if we have y=2x, the '2' is the scale factor that determines the enlargement. The greater the number, the larger the image after dilation.
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Factor the algebraic expression
27x - 18y
Answer:9x
Step-by-step explanation: u would just do 27-18
Answer:hey there
Step-by-step explanation:
27x - 18y>9(3x-2y)>27x =3*3*3*x>-18 y= -(3*3*2*y)here 3 and 3 is common...so it is 9hope this helps uuuWhat is the area of the shaded region in the figure
shown below?
2 cm
2 cm
2 cm
Answer:
6 cm
Step-by-step explanation:
A county manager used a representative sample of two populations in the county to determine the number of pounds of trash thrown away per person per week. The results are shown in the dot plots below. Sample 1: A dot plot titled Sample 1. A number line going from 0.5 to 2.5 in increments of 0.5 is labeled Pounds of Trash. There is 1 dot above 0.5, 3 above 1, 4 above 1.5, 2 above 2, and 2 above 2.5. Sample 2: A dot plot titled Sample 2. A number line going from 0.5 to 2.5 in increments of 0.5 is labeled Pounds of Trash. There are 2 dots above 0.5, 3 above 1, 4 above 1.5, 2 above 2, and 1 above 2.5. The town manager uses the median to show that the average amount of trash thrown away per person per week in each sample is the same. What is the town manager’s error? The medians of the data sets are not the same. He should have used the mean to determine the average because the data sets are approximately symmetric. He should have used the IQR of the data sets to determine the average because the first data set has more large numbers than the second data set. He should have used the MAD to determine the average because the data sets do not contain outliers.
Answer: He should have used the mean to determine the average because the data sets are approximately symmetric.
Step-by-step explanation
Answer:
B
Step-by-step explanation:
Please help I am stuck on this equation
Answer:
Distribution
Step-by-step explanation:
On the second step he distributed the 1/4 to x, but not to twelve.
Answer:
Andre made a mistake in the first part of the equation when he was distributing.
Step-by-step explanation:
He got the 1/4x but forgot to distribute to the 12 which would have gotten him 1/4x + 3
A set of data collected to answer a statistical question has a distribution which can be described by its __________.
I. center
II. spread
III. overall shape
A.
I only
B.
I and II only
C.
III only
D.
I, II, and III
Answer:
its D. I, II, and III
Answer:
I, II, and III
Step-by-step explanation:
A set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
Ben starts his homework at 3:30 p.m. It takes him 45 minutes to do his homework.
What time does Ben finish his homework?
Is the equation xº -5x + 6 = 0 quadratic in form?
Explain why or why not.
Answer:
Step-by-step explanation:
No because the quadratic form is ax^2 + bx + c = 0. The equation, xº -5x + 6 = 0, is not in quadratic form because xº is not x^2, yet the rest of the equation follows the quadratic equation template.