Answer:
D. We are 98% confident that the proportion of adults in the United States, aged 18 or older, who are obese is between 0.2515 and 0.2805.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
26.6% of 5000 people reported a Body Mass Index (BMl) greater than 30
This means that [tex]\pi = 0.266, n = 5000[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.266 - 2.327\sqrt{\frac{0.266*0.734}{5000}} = 0.2515[/tex]
The upper limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.266 + 2.327\sqrt{\frac{0.266*0.734}{5000}} = 0.2805[/tex]
The correct interpreation is that we are 98% confident that the proportion of adults in the United States, aged 18 or older, who are obese is between 0.2515 and 0.2805, which means that the correct answer is given by option D.
in a math final please help asap
find the angle r show ur work
Answer:
The measure of angle R is 112 degrees
Step-by-step explanation:
Using the given markings, we can see that we have an isosceles triangle
so RT is also 3x-2
Mathematically, the sum of the interior angles of a triangle is 180:
Thus;
9x + 4 + (3x-2) + (3x-2) = 180
9x + 3x +3x + 4-2-2 = 180
15x = 180
x = 180/15
x = 12
Recall; Angle R is 9x + 4
= 9(12) + 4 = 108 + 4 = 112
Ethan is installing a new tile backsplash in his kitchen. The tile he likes costs $3.50 per square foot. The area he is tiling is 36.5 square feet. How much will Ethan pay for the tile for his backsplash?
Answer:
$127.75
Step-by-step explanation:
Multiply the cost by the area to find the total cost
Simplify the expression 3 (9+ 4z - 5)
Answer:
12x+12
Step-by-step explanation:
Multiply 3 to everything in the parenthesis
so it becomes
18+12x-15
=12x+12
3/4x × 12/11 ÷ 3x/22
Answer:
242/48
Step-by-step explanation:
What is the explicit formula for the geometric sequence 2, 6, 18, 54, …?
Answer:
3x
Step-by-step explanation:
You multiply the pervious number with 3 to get the next number
For example 2 times 3 = 6
6 times 3 = 18
18 times 3 =54
54 times 3= 162
So on and so forth
$2000 at 9% for 1 year
Answer:
$180
Step-by-step explanation:
9% = 0.09
2000 * 0.09 = 180
what is the answer to this question
Answer:
[tex]slope = \frac{2 - ( - 1)}{0 - ( - 1)} \\ = 3 \\ y = mx + c \\ 2 = (0 \times 3) + c \\ c = 2 \\ { \boxed{y = 3x + 2}}[/tex]
help solving inequalities true or false (middle school) first person to answer i’ll give brainliest please!!!
Answer:
aef true and bcd false
hope u get well in your exams
Step-by-step explanation:
Let z be inversely proportional to the cube root of y. When y =.064, z =3
a) Find the constant of proportionality k.
b) Find the value of z when y = 0.125.
Given:
z be inversely proportional to the cube root of y.
When y =0.064, then z =3.
To find:
a) The constant of proportionality k.
b) The value of z when y = 0.125.
Solution:
a) It is given that, z be inversely proportional to the cube root of y.
[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]
[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, z=3 when y=0.064. Putting these values in (i), we get
[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]
[tex]3=k\dfrac{1}{0.4}[/tex]
[tex]3\times 0.4=k[/tex]
[tex]1.2=k[/tex]
Therefore, the constant of proportionality is [tex]k=1.2[/tex].
b) From part (a), we have [tex]k=1.2[/tex].
Substituting [tex]k=1.2[/tex] in (i), we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]
We need to find the value of z when y = 0.125. Putting y=0.125, we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]
[tex]z=\dfrac{1.2}{0.5}[/tex]
[tex]z=2.4[/tex]
Therefore, the value of z when y = 0.125 is 2.4.
Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n}[/tex]
or
[tex]n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For the given case, it is given that:
[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]
Let the constant of proportionality be k, then we have:
[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]
It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:
[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]
Thus, the constant of proportionality k is 1.2. And the relation between z and y is:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]
Putting value y = 0.0125, we get:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]
Thus, for the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4Learn more about proportionality here:
https://brainly.com/question/13082482
15 point question!
Hi can you help? Thanks! *if you are gonna answer, actually answer please!*
Brainly if you get it right!
Answer:
The answer is 129
Step-by-step explanation:
5(exponent 4)/5 = 125 +4 equals 129
I think
Answer:
129
Step-by-step explanation:
5^4 / 5 + 4
We know that a^b / a^c = a^(b-c)
5^(4-1) +5
5^3 +4
125 +4
129
A quadrilateral is a parallelogram if each____ divides a parallelogram into two____.
Answer:
diagonal, congruent triangles
Step-by-step explanation:
The object below is made with six identical cubes. Each cube edge is 3 inches long.
As
3 in.
What is the surface area of the object in square inches?
Answer:
306 square inches.
Step-by-step explanation:
All surfaces of the cubes are exposed to the outside except 2 ( where 2 of the cubes join).
6 separate cubes have 6 * 6 faces exposed so this object has 36 - 2 = 34 surfaces exposed.
Each face of one cube = 3*3 = 9 in^2.
Therefore the surface area = 9 * 34 = 306 in^2.
solve the equation 4^y = 8
Answer:
y = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
4 = 2² and 8 = 2³ , then
[tex]4^{y}[/tex] = 8, can be written
[tex](2^2)^{y}[/tex] = 2³
[tex]2^{2y}[/tex] = 2³
Since bases on both sides are equal, both 2, then equate exponents
2y = 3 ( divide both sides by 2 )
y = [tex]\frac{3}{2}[/tex]
y = 1.5
Step-by-step explanation:
[tex] {4}^{y} = 8[/tex]
Take the logarithm of both sides and you will get
[tex] \log {4}^{y} = y \log4 = \log8[/tex]
or
[tex]y = \frac{\log8}{ \log4} = 1.5[/tex]
There are 5 red, 4 blue, and 3 green marbles in a bag. What are the odds of randomly pulling a blue marble out of the bag and then randomly pulling a green marble out of the bag? The blue marble is NOT replaced.
A - 7/2
B - 12/24
C - 1/12
D - 1/11
helpppp pleaseee its hard
Answer:
Ten thousands
Step-by-step explanation:
Replace all other digits with zero
This gives 40,000
Ten thousand (10,000) has the same amount of digits
Max bought three items for $18.95 each and two items for $26.71 each. How much change would he get from $500 ?
Answer:
$389.73 in change
Step-by-step explanation
500-( (18.95 x 3)+(26.71 x 2) )=
500-(56.85+53.42)=
500-110.27=
389.73
A car bought for $13,000 despreciates at 12% annually. What will the car be worth after 10 Years ?
Answer:
I think $3620.51
Step-by-step explanation:
If i did it right, the equation should be something like this?
13,000(.88)^10
Dana bought almonds at $8 per can and cashews at $12 per can. In total she bought 470 cans of nuts. Her total bill was $4260. How many cans of each type of nut did she buy? Use either substitution or elimination to solve this problem.
Answer:
almonds =345, cashews=125
Step-by-step explanation:
a=almonds, c=cashews
8a+12c=4260. Equation 1
a + c= 470 Equation 2
a=470-c. Isolate a from equation 2
8(470-c)+12c=4260 sub value of a from equation 2 into equation 1
3760-8c+12c=4260
4c=500
c=125
solve for a by substituting value of c into either equation
a+c=470
a+125=470
a=345
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+165x+69
Answer:
The rocket hits the gorund after approximately 10.71 seconds.
Step-by-step explanation:
The height of the rocket y in feet x seconds after launch is given by the equation:
[tex]y=-16x^2+165x+69[/tex]
And we want to find the time in which the rocket will hit the ground.
When it hits the ground, its height above ground will be 0. Hence, we can let y = 0 and solve for x:
[tex]0=-16x^2+165x+69[/tex]
We can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = -16, b = 165, and c = 69.
Substitute:
[tex]\displaystyle x=\frac{-165\pm\sqrt{(165)^2-4(-16)(69)}}{2(-16)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{-165\pm\sqrt{31641}}{-32}=\frac{165\pm\sqrt{31641}}{32}[/tex]
Hence, our solutions are:
[tex]\displaystyle x_1=\frac{165+\sqrt{31641}}{32}\approx 10.71\text{ or } x_2=\frac{165-\sqrt{31641}}{32}\approx-0.40[/tex]
Since time cannot be negative, we can ignore the first answer.
So, the rocket hits the gorund after approximately 10.71 seconds.
Answer:
10.71
Step-by-step explanation:
the person below was correct!
a study is planned to compare the proportion of men who dislike anchovies with the proportion of women who dislike anchovies. the study seeks to determine if the proportions of men and women who dislike anchovies are different. a sample of 41 men was taken and the p^ estimate for the true proportion of men who dislike anchovies was determined to be 0.67. a sample of 56 women was also taken and the p^ estimate for the true proportion of women who dislike anchovies was determined to be 0.84. are the requirements satisfied to perform this hypothesis test
Answer:
d. No because n·(1 - [tex]\hat p[/tex]) = 8.96 is less than 10
Step-by-step explanation:
Question options;
a. Yes because the sample sizes of both groups are greater than 5
b. Yes, because in both cases n·[tex]\hat p[/tex] > 10
c. Yes, because we know that the population is evenly distributed
d. No, because the n·(1 - [tex]\hat p[/tex]) is less than 10
Explanation;
The given data are;
The number of men in the sample of men, n₁ = 41
The proportion of men who dislike anchovies, [tex]\hat p_1[/tex] = 0.67
The number of women in the sample of women, n₂ = 56
The proportion of men who dislike anchovies, [tex]\hat p_2[/tex] = 0.84
The assumptions for an analysis of the difference between means using a T-test are;
1) The data should be from a random sample of the population
2) The variables should be approximately normal (n·[tex]\hat p[/tex] ≥ 10, and n·(1 - [tex]\hat p[/tex]) ≥ 10)
3) The scale of the data is a continuous ordinance scale
4) The sample size should be large
5) The sample standard deviations should be approximately equal
From the requirement for normality, we have;
For the sample of men, n₁·[tex]\hat p[/tex]₁ = 41 × 0.67 = 24.47 > 10
n₁·(1 - [tex]\hat p[/tex]₁) = 41 × (1 - 0.67) = 13.53 > 10
For the sample of women, n₂·[tex]\hat p[/tex]₂ = 56 × 0.84 = 47.04 > 10
n₂·(1 - [tex]\hat p[/tex]₂) = 56 × (1 - 0.84) = 8.96 < 10
Therefore, the for n₂·(1 - [tex]\hat p[/tex]₂), the sample does not meet the requirement for normality
The correct option is d. No because n₂·(1 - [tex]\hat p[/tex]₂) = 8.96 is less than 10
How many marble do you need to balance to scale
A. 4
B. 3
C. 2
D. 1
Answer: its B.
Step-by-step explanation:
have a good day hope this help
Answer:
B.3
Step-by-step explanation:
just divide 6 by 2
helpppp meee pleaseeeeewee
We can't see what you are talking about. send another one.
y-(-4) =m(x-(-5)) solve for m
Answer:
m = [tex]\frac{y+4}{x+5}[/tex]
Step-by-step explanation:
y-(-4) = m(x-(-5))
Simplify, distribute the negative sign outside of the parenthesis, remember negative times negative equals positive
y + 4 = m (x + 5)
Inverse operations, divide the equation by the value inside of the parenthesis
[tex]\frac{y+4}{x+5}[/tex] = m
Answer:
m=y+4x/x+5 your welcome !!
Peter gets 1 star for every 3 correct answers he gets on khan academy. What is the minimum number of correct answers Peter must enter if he wants to get 12 stars?
For full points you need to write an equation that uses a variable and division, show what work you did to solve it, and then give me a final answer.
Answer:
Peter needs to get 36 problems correct to get 12 stars
Step-by-step explanation:
for every 3 correct answers, Peter gets 1 star
1/3
if he wants 12 stars he will have to get 'x' amount of questions correctly
considering this is constant, 1/3 will have to equal 12/x
[tex]\frac{1}{3} = \frac{12}{x} \\\\1x = 36\\[/tex]
1x = x, so you don't need to do anything to 36
therefore the answer is that you need to get 36 problems correct to get 12 stars
The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room at a four-star hotel, beverages, breakfast, taxi fares, and incidental costs. Click on the datafile logo to reference the data. City Daily Living Cost ($) City Daily Living Cost ($) Bangkok 242.87 Mexico City 212.00 Bogota 260.93 Milan 284.08 Cairo 194.19 Mumbai 139.16 Dublin 260.76 Paris 436.72 Frankfurt 355.36 Rio de Janeiro 240.87 Hong Kong 346.32 Seoul 310.41 Johannesburg 165.37 Tel Aviv 223.73 Lima 250.08 Toronto 181.25 London 326.76 Warsaw 238.20 Madrid 283.56 Washington, D.C. 250.61 a. Compute the sample mean (to 2 decimals). b. Compute the sample standard deviation (to 2 decimals). c. Compute a confidence interval for the population standard deviation (to 2 decimals).
Answer:
[tex]\bar x = 260.1615[/tex]
[tex]\sigma = 70.69[/tex]
The confidence interval of standard deviation is: [tex]53.76[/tex] to [tex]103.25[/tex]
Step-by-step explanation:
Given
[tex]n =20[/tex]
See attachment for the formatted data
Solving (a): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}[/tex]
[tex]\bar x = \frac{5203.23}{20}[/tex]
[tex]\bar x = 260.1615[/tex]
[tex]\bar x = 260.16[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
[tex]\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}[/tex][tex]\sigma = \sqrt{\frac{94938.80}{19}}[/tex]
[tex]\sigma = \sqrt{4996.78}[/tex]
[tex]\sigma = 70.69[/tex] --- approximated
Solving (c): 95% confidence interval of standard deviation
We have:
[tex]c =0.95[/tex]
So:
[tex]\alpha = 1 -c[/tex]
[tex]\alpha = 1 -0.95[/tex]
[tex]\alpha = 0.05[/tex]
Calculate the degree of freedom (df)
[tex]df = n -1[/tex]
[tex]df = 20 -1[/tex]
[tex]df = 19[/tex]
Determine the critical value at row [tex]df = 19[/tex] and columns [tex]\frac{\alpha}{2}[/tex] and [tex]1 -\frac{\alpha}{2}[/tex]
So, we have:
[tex]X^2_{0.025} = 32.852[/tex] ---- at [tex]\frac{\alpha}{2}[/tex]
[tex]X^2_{0.975} = 8.907[/tex] --- at [tex]1 -\frac{\alpha}{2}[/tex]
So, the confidence interval of the standard deviation is:
[tex]\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }[/tex] to [tex]\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }[/tex]
[tex]70.69 * \sqrt{\frac{20 - 1}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{20 - 1}{8.907}[/tex]
[tex]70.69 * \sqrt{\frac{19}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{19}{8.907}[/tex]
[tex]53.76[/tex] to [tex]103.25[/tex]
Simplify the expression. 4^0
be careful i think this is a trick question
Answer:
1
Step-by-step explanation:
4^0
Any number raised to the 0 power is 1.
Answer:
1
Step-by-step explanation:
Anything raised to 0 is 1.
Help please! No links!
Answer:
It is placed to the left of –2
Please help?? I have an exam tomorrow
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
x² - 5xy + 6y² = x² - 3xy - 2xy + 6y²
= x(x - 3y) - 2y(x - 3y)
= (x - 3y)(x -2y)
x² - 4xy + 3y² = x² -xy - 3xy + 3y²
= x(x - y) - 3y(x - y)
= (x - y)(x - 3y)
x² - 3xy + 2y² = x² - xy - 2xy + 2y²
= x(x - y) - 2y(x - y)
= (x - y)(x - 2y)
Least common denominator = (x-y)(x - 2y)(x - 3y)
[tex]RHS = \frac{1*(x-y)}{(x-3y)(x-2y)*(x-y)}+\frac{a*(x-2y)}{(x-y)(x-3y)*(x-2y)}+\frac{1*(x-3y)}{(x-y)(x-2y)*(z-3y)}\\\\= \frac{x- y + ax - 2ay +x -3y}{(x-y)(x-2y)(x-3y)}\\\\= \frac{2x -4y +ax - 2ay}{ x^{3}-5x^{2}y+8xy^{2}-4y^{3}}[/tex]
279 students went on a field trip. Five buses were filled and 9 students traveled in cars. How many students were in each bus? PLEASEEEEE HELPPPPP ME you get 60 points i dont know if anyone cares but hey
Answer:
90 students.
Step-by-step explanation:
279-9=270, and 270 divided by 9 is 90.
how do you find x in this? I need help asap!!
Answer:
Step-by-step explanation:
According to the theorem, the angle measuring 110 is one-half the measure of the arc it intercepts. That means that the major arc (this arc of which I'm speaking) measures 110 * 2 = 220.
Since the outside of a circle, regardless of how big or small the circle is, has a degree measure of 360, then x = 360 - 220 so
x = 140°
