Given Information:
Mean percent of childhood asthma = μ = 2.23%
Sample size = n = 31
Standard deviation = σ = 1.24%
Required Information:
P(X > 2.6) = ?
Answer:
P(X > 2.6) = 0.0475 = 4.75%
Step-by-step explanation:
Let X is the random variable that represents percent of childhood asthma prevalence.
We want to find out the probability that the mean childhood asthma prevalence for the sample is greater than 2.6%
[tex]P(X > 2.6) = 1 - P(X < 2.6)\\\\P(X > 2.6) = 1 - P(Z < \frac{x - \mu}{\frac{\sigma}{\sqrt{n} } } )\\\\P(X > 2.6) = 1 - P(Z < \frac{2.6 - 2.23}{\frac{1.24}{\sqrt{31} } } )\\\\P(X > 2.6) = 1 - P(Z < \frac{2.6 - 2.23}{0.222} )\\\\P(X > 2.6) = 1 - P(Z < \frac{0.37}{0.222} )\\\\P(X > 2.6) = 1 - P(Z < 1.67)\\[/tex]
The z-score corresponding to 1.67 is 0.9525
P(X > 2.6) = 1 - 0.9525
P(X > 2.6) = 0.0475
P(X > 2.6) = 4.75%
Therefore, there is 4.75% probability that the mean childhood asthma prevalence for the sample is greater than 2.6%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.6)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.67 then go for 0.07 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
Using the normal distribution and the central limit theorem, it is found that that there is a:
0.0485 = 4.85% probability that the mean childhood asthma prevalence for the sample is greater than 2.6%. The interpretation is that when many samples of 31 are chosen, around 4.85% of them will have an asthma prevalence greater than 2.6%.
---------------------------------
When the distribution is normal, the z-score formula is used, with [tex]\mu[/tex] as the mean and [tex]\sigma[/tex] as the standard deviation.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. Each z-score has a p-value associated with it.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 p-value, we get the probability that the value of the measure is greater than X. For a sample of n observations, by the Central Limit Theorem, the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]---------------------------------
Mean of 2.23% means that [tex]\mu = 2.23[/tex]Standard deviation of 1.24% means that [tex]\sigma = 1.24[/tex]Sample of 31 means that [tex]n = 31, s = \frac{1.24}{\sqrt{31}} = 0.2227[/tex]---------------------------------
The probability of a sample mean above 2.6% is 1 subtracted by the p-value of Z when X = 2.6. Thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.6 - 2.23}{0.2227}[/tex]
[tex]Z = 1.66[/tex]
[tex]Z = 1.66[/tex] has a p-value of 0.9515.
1 - 0.9515 = 0.0485.
0.0485 = 4.85% probability that the mean childhood asthma prevalence for the sample is greater than 2.6%. The interpretation is that when many samples of 31 are chosen, around 4.85% of them will have an asthma prevalence greater than 2.6%.
A similar problem is given at https://brainly.com/question/22934264
Noah hopes to pick the winning ticket during her math class's raffle. The student who picks the ticket with a true statement will win. Which is the winning ticket?
a
2(x - 6) = -35 is equivalent to 2x = -23
b
8(x - 7) = 35 is equivalent to 8x = 28
c
9(x - 6) = -35 is equivalent to 9x = -29
d
4(x - 5) = 35 is equivalent to 4x = 40.
Answer:
Option a.
Step-by-step explanation:
We need to select correct statements form the given options.
[tex]2(x-6)=-35[/tex]
[tex]2x-12=-35[/tex]
[tex]2x=-35+12[/tex]
[tex]2x=-23[/tex]
Therefore, [tex]2(x-6)=-35[/tex] is equivalent to [tex]2x=-23[/tex].
[tex]8(x-7)=35[/tex]
[tex]8x-56=35[/tex]
[tex]8x=35+56[/tex]
[tex]8x=91[/tex]
Therefore, [tex]8(x-7)=35[/tex] is not equivalent to [tex]8x=28[/tex].
[tex]9(x-6)=-35[/tex]
[tex]9x-54=-35[/tex]
[tex]9x=-35+54[/tex]
[tex]9x=19[/tex]
Therefore, [tex]9(x-6)=-35[/tex] is not equivalent to [tex]9x=-29[/tex].
[tex]4(x-5)=35[/tex]
[tex]4x-20=35[/tex]
[tex]4x=35+20[/tex]
[tex]4x=55[/tex]
Therefore, [tex]4(x-5)=35[/tex] is not equivalent to [tex]4x=40[/tex].
Hence, option (a) is correct.
Answer:
A. 2(x - 6) = -35 is equivalent to 2x = -23
Step-by-step explanation:
just took the quiz
PLZ HELP ME HAS SOON HAS POSSIBLE?????
Answer:
- 7/2
Step-by-step explanation:
- sqrt(49/4)
We know that sqrt(a/b) = sqrt(a)/ sqrt(b)
- sqrt(49)/sqrt(4)
- 7/2
Select the statement that describes this expression: 1/2 x (734 − 246).
Answer:
The value of given expression is 244.
Step-by-step explanation:
The given expression is [tex]\dfrac{1}{2}\times (734 - 246)[/tex].
We need to simply the above expression.
First of all, we will subtract 246 from 734. By doing so, we get 488.
Now, we can divide 488 by 2.
As a result we get 244.
So, the value of given expression is 244.
The required statement is "[tex]\dfrac{1}{2}[/tex] the difference between 734 and 246".
Important information:
The given expression is [tex]\dfrac{1}{2}\times (734-246)[/tex].Phrase for Expression:(734-246) is the difference between 734 and 246.
[tex]\dfrac{1}{2}\times (734-246)[/tex] is [tex]\dfrac{1}{2}[/tex] the difference between 734 and 246.
Therefore, the required statement is "[tex]\dfrac{1}{2}[/tex] the difference between 734 and 246".
Find out more about 'Phrase for Expression' here:
https://brainly.com/question/25301924
3) Mrs. Noah’s bill, before tax, is $50. The sales tax rate is 3%. Mrs. Noah decides to leave a 2% tip for the gate keeper based on the pre-tax amount. How much will the total bill be, includingtax and tip?
Answer:
$52.50
Step-by-step explanation:
Start with $50
Add 2% Tip: $1 (50 x 0.02)
Add 3% Tax: $1.5 (50 x 0.03)
Total: $52.50
Answer:
52.50
Step-by-step explanation:
Because 3+2=5% and 5% of 50 dollars is 2.50 so 50+2.50 =52.50 dollars he is paying in total
Which of the following is not a property for all parallelograms?
A. Opposite sides are parallel.
B. All sides have the same length.
C. Opposite angles are congruent.
D. The diagonals bisect each other.
Answer:
B. All sides have that same length, would be the correct answer.
Step-by-step explanation:
Answers A,C, and D are all properties for all parallelograms.
Option B, which states that all sides have the same length, is not a property for all parallelograms. It is only true for rhombuses, which are a special type of parallelogram.
Explanation:Among the options given, the one that is not a property for all parallelograms is:
B. All sides have the same length.This statement is not true for all parallelograms; it is a specific property of a subset of parallelograms known as rhombi (singular: rhombus), where all four sides are congruent. However, a general parallelogram only requires opposite sides to be of equal length, not all four sides. To clarify further:
Opposite sides are parallel - True for all parallelograms.Opposite angles are congruent - True for all parallelograms.The diagonals bisect each other - True for all parallelograms.The key distinction here is understanding that while rhombi share all the properties of parallelograms, not all parallelograms are rhombi.
Hey i need help um pls ill give the crown
um im bad at math so
Rob says that this graph shows a proportional relationship. Is he correct? Explain.
Answer:
no, both lines increase at different angles
Answer:
No
Step-by-step explanation:
Because both of these functions have a constant, different growth, as one grows the other will grow at a slightly different rate, which will constantly change the ratio between their values. Since a proportional growth is one where the ratio between the values stays constant and this is not the case here, this is not a proportional relationship. Hope this helps!
in our own words describe 0.32 meters
Answer:
0.32 meters = 0.32 × 100
32 centimetres
0.32 meters is equivalent to 32 centimetres
Answer:
0.32 meters is a unit of measurement. It is equal to 32 centimeters, 3.2 decimeters, and 0.00032 kilometers. A meter is a unit used to measure length and one meter is around a yard. The width of most doorways is around the length of one meter. Therefore, 0.32 meters is a very small amount.
I’ll make sure to give you a brainliest
Answer:
Remove D
Step-by-step explanation:
The sum of the values would go from 0 to 3. Because there are 3 values when you remove one, the avg. of that would be 3/3 = +1
A water tank composed of a cylinder and 2 half spheres is shown below.
3ft high and 4ft long
The tank is being filled with drinking water by using a bucket that can hold 0.34 cubic feet of water. Emma is able to pour 5 full buckets into the tank every 3 minutes. How long will it take to fill the water tank completely at this constant rate? Use 3.14 for pi and round to the nearest whole minute.
The volume of the tank is __ cubic feet and it will be completely filled with water at the end of __ minutes.
Answer:
Hey i like your profile pic
Step-by-step explanation:
PLEASE HELP ! !
Identify the domain of the function.
A) (−2, 4)
B) (−3, 3)
C) [−2, 4]
D) [−3, 3]
Answer: A or C (i think A because its not including)
Step-by-step explanation:
How many solutions does -103x-6=-6x-103
Answer:
one solution
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Since this is a linear system, there can be 1, 0, or infinite solutions. In order to determine this, we need to solve this equation.
First, isolate the variables to one side:
0 = 97x -97
97x = 97
x = 1.
Thus there is one solution.
If we had gotten a statement such as 1 = 1, there would have been infinite.
If we had gotten a statement such as 1 = 0, there would have been no solution.
Find the midpoint m of AB
The midpoint m of line segment AB, with a length of 22 units, is located at 11. Assuming A and B are evenly spaced, the midpoint is found using the formula [tex]\( m = \frac{{A + B}}{2} \)[/tex].
To find the midpoint m of line segment AB, where AB has a length of 22 units, we use the midpoint formula: [tex]\( m = \frac{{A + B}}{2} \)[/tex].
Here, A and B are the coordinates of the endpoints of AB.
Since no specific coordinates are provided, let's assume A and B are equally spaced on the line.
If A = 0 and B = 22, the midpoint m would be [tex]\( \frac{{0 + 22}}{2} = 11 \)[/tex].
Therefore, the midpoint of AB is 11.
To find the midpoint of line segment AB, use the midpoint formula by averaging the x-coordinates and y-coordinates of the endpoints A and B.
Explanation:The midpoint of a line segment AB can be found by using the midpoint formula. The formula is:
(x1 + x2) / 2, (y1 + y2) / 2
where (x1, y1) and (x2, y2) are the coordinates of points A and B respectively.
Plug in the values for the coordinates of A and B, and calculate the midpoint coordinates.
The question asks to find the midpoint of a line segment AB. To find this midpoint, one would typically use the midpoint formula, which is derived from the average of the x-coordinates and y-coordinates of the endpoints of the segment. The question seems to be associated with a geometry or physics context, but the process to find the midpoint remains the same. It involves adding the x-coordinates of both endpoints and dividing by 2 to find the x-coordinate of the midpoint, and doing the same with the y-coordinates for the y-coordinate of the midpoint.
If x2 + nx + 18 = (x + 9)(x + 2), what is the value of n?
What is the standard form of (x+5)(x+5)
Answer:
x² + 10x + 25
Step-by-step explanation:
Given
(x + 5)(x + 5)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x + 5) + 5(x + 5) ← distribute both parenthesis
= x² + 5x + 5x + 25 ← collect like terms
= x² + 10x + 25 ← in standard form
Lydia is buying cupcake ls for he brother birthday party. She brought 36 cupcakes total.Of the cupcakes she bought,5/6 of them were vanilla cupcakes, which cost $1.50. The rest of the cupcakes were chocolate, which cost $2.25 each. What was the total Lydia spent on cupcakes
Answer:
58.50
Step-by-step explanation:
First find out how many were vanilla and chocolate
vanilla: 5/6 * 36 = 30
Chocolate = total - vanilla = 36-30 =6
Cost for vanilla = 1.50*30 =45
Cost for chocolate 2.25*6 =13.5
Add the cost together
45+13.50
58.50
Ellie bought 0.7kg of jelly beans from her local food festival for £1.89. She knows that to work out the price of a whole kg she simply needs to divide the price she paid by the quantity she bought.
Work out the price of 1kg of jelly beans.
Answer:
1.89£÷0.7kg=2.7£
To find the price of a whole kg you need to divide the price she paid by the quantity she bought.
Answer:
x = 2.7
Step-by-step explanation:
To find x
1) 1.89 ÷ 0.7 = 2.7
Thankyou
Solve for x if cos(2x+60)=-1
Answer:
x = 60°
Step-by-step explanation:
[tex] \cos \: (2x + 60) = - 1 \\ \cos \: (2x + 60) = \cos \: 180 \degree \\ 2x + 60 = 180 \degree \\ 2x = 180 \degree - 60 \degree \\ 2x = 120 \\ x = \frac{120}{2} \\ \huge \red{ \boxed{ x = 60 \degree}}[/tex]
the difference between Hawaii (12 degree) and south Dakota (-58 degree)
Answer:
Hawaii is 80 degrees warmer than Dakota.
Step-by-step explanation:
first you have to make the negative a positive by adding 58 degrees to it making it zero then you add the 12 degrees in Hawaii getting 80 degrees.
Quadrilateral D U C K is inscribed in circle O what is the measure of angle K?
Answer:
95°
Step-by-step explanation:
Find the circumference of the larger circle if the area of one of the smaller circles is 48 pi in^2.
A. [tex]4\sqrt{3\pi }[/tex] in.
B. [tex]8\sqrt{3 \pi }[/tex] in.
C. [tex]16\sqrt{3\pi }[/tex]in.
D. [tex]24\pi[/tex] in.
Answer:
C. 16√3π in.
Step-by-step explanation:
Circumference of a circle = 2πr where
r is the radius of the circle.
Given the area of one of the smaller circle to be 48π in², we can get the radius of one of the smaller circle.
If A = πr²
48π = πr²
r² = 48
r = √48 in
The radius of one of the smaller circle is √48.
To get the circumference of the larger circle, we need the radius of the larger circle. The radius R of the larger circle will be equivalent to the diameter (2r) of one of the smaller circle.
R = 2r
R = 2√48 inches
Since C = 2πR
C = 2π(2√48)
C = 4√48π in
C = 4(√16×3)π in
C = 4(4√3)π in
C = 16√3π in
Thw circumference of the larger circle is 16√3π in.
Step-by-step explanation:
Given two circa inscribed side by side inside a big circle, it is notice that the internal two circle are identical and diameter of the one the internal circles is equal to the radius of the big circle
So, we are given the area of one of the small circle, so from their we can find the radius of the small circle.
Area of small circle
A = 48π in²
Area of a circle is given as πr²
A = πr²
48π = πr²
Divide both side by π
48 = r²
Take Square root of both sides
r = √48 = √(16 × 3)
r = 4√3 in
Then, the diameter of the small circle is
d = 2r = 2 × 4√3
d = 8√3
So, the radius of the big circle is
R = d = 8√3
So, we want to find the perimeter of the big circle
The perimeter of a circle is calculated using
Perimeter = 2πr
P = 2πR
P = 2π × 8√3
P = 16π√3 in
So the correct option is C
P = 16√3 π in.
point
(Circles) What is the circumference of this circle, rounded to the nearest
tenth? Use 3.14 for T.
The radius of the cirde is 6 inches
6
in.
0
15.4 inches
18.8 inches
O
37.7 inches
O
113.0 inches
Answer:
37.68 or 37.7
Step-by-step explanation:
Circumference of a circle: 2πr
2 x 3.14 = 6.28
6.28 x 6 = 37.68 or 3.7
round 39.473 to the nearest tenth.
I need help fast please
Answer:
39.5
Step-by-step explanation:
If the number to the right of the number your rounding to is equal to or greater than 5 round up
Answer:
39.5
Step-by-step explanation:
Step 1: Round to the nearest tenth
39.473
Since the hundredths place is greater or equal to 5, we round up the tenth's place.
39.473
39.5
Answer: 39.5
Two farmhouses A and B are 10.3 km apart. A third farmhouse C is located such
that angle A=83◦ and angle B=59◦. How far is C from A?
Answer:
Distance between A to C is 16.62km
Step-by-step explanation:
See attached document to get a better illustration of the angle.
A = 83°
B = 53°
C = ?
180° = 83° + 53° + C (sum of angles in a triangle is equal to 180°)
180° = 142° + c
C = 180 - 142
C = 38°
To find the distance AC, we have to use sine rule.
a / sin(A) = b / sin(B) = c / sin(C)
a / sin(A) = c / sin(C)
a /sin83 = 10.31 / sin38
Cross multiply
10.31 * sin83 = a * sin38
10.23 = (0.61566)a
a = 10.23 / 0.61566
a = 16.616 km
a = 16.62km
The distance between A and C is 16.62km
Jackson purchases a new car for $48,000. The car's value can be modeled by the
following exponential function: y = 48000(0.76)^t where y represents the car's
value and t represents time in years. What is the decay rate expressed as a
percentage? *
We have been given that Jackson purchases a new car for $48,000. The car's value can be modeled by the following exponential function: [tex]y = 48000(0.76)^t[/tex] where y represents the car's value and t represents time in years. We are asked to find the decay rate as a percentage.
We know that an exponential decay function is in form [tex]y=a\cdot (1-r)^x[/tex], where,
y = Final value,
a = Initial value,
r = Decay rate in decimal form,
x = time.
Upon comparing our given function [tex]y = 48000(0.76)^t[/tex] with standard decay function [tex]y=a\cdot (1-r)^x[/tex], we can see that [tex]1-r=0.76[/tex].
Let us solve for r.
[tex]1-1-r=0.76-1[/tex]
[tex]-r=-0.24[/tex]
[tex]r=0.24[/tex]
Let us convert 0.24 into percentage.
[tex]0.24\times 100\%=24\%[/tex]
Therefore, the decay rate is 24%.
what’s the slope of this line?
Answer:
-1
Step-by-step explanation:
The formula for slope is: [tex]\frac{y_1-y_2}{x_1-x_2}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points
Plug in (-5,3) and (-3,1) into the equation, and you get:
[tex]\frac{-5-(-3)}{3-1} =\\\frac{-2}{2} =\\-1[/tex]
. You and a friend have dinner at a restaurant . Your meal costs $15.85 and you leave an 18% tip and your friend's meal cost $14.30 and he leaves a 20% tip. What is the difference in their total bills?
Answer:
$1.54
Step-by-step explanation:
18% of $15.85 is 2.853, so your total is $18.703
20% of $14.30 is 2.86, so their total is $17.16
So the difference is $1.543, rounded (since your dealing with money) would be $1.54
Two cars are 400 miles apart when they start moving towards each other. The speed of the first car is 30 mph. The the second car moves 20 mph faster than the first car. After how many hours will the cars meet?
Answer:
The number of hours it will take before both cars meet is 5 hours
Step-by-step explanation:
Here we have, speed of first car, A = 30 mph
Speed of second car, B = (30 + 20) mph = 50 mph
Therefore, we have
Let the point where both cars meet be X and the time before they meet be Y
Then for car A, 30 × Y = X....................(1)
For car B, 50 × Y = 400 - X..................(2)
From plugging the value of X from equation (1) into equation (2) we have;
50·Y = 400 - 30·Y
80·Y = 400
Y = 5 hours
Therefore the number of hours it will take before both cars meet = 5 hours.
Answer
t = 5 hrs
Step-by-step explanation:
let
speed of the first car = 30 mph
speed of the second car = 20 mph + 30 mph = 50 mph
When the cars meet we know both cars will have traveled a total distance of 400 miles.
Therefore,
let's make a distance equation
speed = distance/time
distance = speed × time
first car + second car = 400 miles
30t + 50t = 400
80t = 400
divide both sides b 80
t = 400/80
t = 5 hrs
Paco had 13 cookies. He ate 6 of them. How many cookies does Paco have left? Show how you can solve this problem in 2 different ways.
Answer:
He has 7 cookies left
Step-by-step explanation:
13-6=7 7+6=13
Answer:
Step-by-step explanation:
The first way you can explain is the simple standard way of subtraction using 13-6=7 or you can count up from 6 to 13 and see how many numbers are found in between.
A translation is shown on the grid below. On a coordinate plane, triangle A B C has points (negative 4, 2), (negative 4, negative 2), (negative 1, negative 2). Triangle A prime B prime C prime has points (1, 5), (1, 1), (4, 1). Which are true statements about the translation? The sides of the image and pre-image are congruent. The image is turned 90°. The angles in the image are different from the angles in the pre-image. The image is a slide of the pre-image. The image has a different shape than the pre-image. Each point has moved in a different direction. Each point has moved the same number of units.
Answer:
a, d, g
Step-by-step explanation:
Translation is one of the "rigid motions," along with reflection and rotation. Figures subject to rigid motions are congruent. No angles or segment lengths are changed. Translation is accomplished by adding the same vertical and horizontal offsets to every point of the original figure, effectively sliding the figure to a new location. Every image line segment is parallel to its corresponding pre-image line segment.
__
The statements shown in bold are true of any translation.
The sides of the image and pre-image are congruent. The image is turned 90°. The angles in the image are different from the angles in the pre-image. The image is a slide of the pre-image. The image has a different shape than the pre-image. Each point has moved in a different direction. Each point has moved the same number of units.Answer:
1,4,7
Step-by-step explanation:
1.) The sides of the image and pre-image are congruent.
4.) The image is a slide of the pre-image.
7.) Each point has moved the same number of units.
got 100
A square napkin is folded in half on the diagonal and placed on the diameter of a round plate (see diagram below). If the folded napkin spans the plate and the plate has an 18-inch diameter, what is the area of the space on the plate that is NOT covered by the napkin? Leave your answer in terms of .
Answer:
[tex]A=81(\pi-1)\ in^2[/tex]
Step-by-step explanation:
step 1
Find the area of the plate
The area of a circle is given by the formula
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=18/2=9\ in[/tex] ---> the radius is half the diameter
substitute
[tex]A=\pi (9)^{2}\\A=81\pi\ in^2[/tex]
step 2
Find the area of the square napkin folded (is a half of the area of the square napkin)
we know that
The diagonal of the square is the same that the diameter of the plate
Applying Pythagorean theorem
[tex]D^2=2b^2[/tex]
where
b is the length side of the square
we have
[tex]D=18\ in[/tex]
substitute
[tex]18^2=2b^2[/tex]
solve for b^2
[tex]b^2=162\ in^2[/tex] -----> is the area of the square
Divide by 2
[tex]162/2=81\ in^2[/tex]
step 3
Find the area of the space on the plate that is NOT covered by the napkin
we know that
The area of the space on the plate that is NOT covered by the napkin, is equal to subtract the area of the square napkin folded (is a half of the area of the square napkin) from the area of the plate
so
[tex]A=(81\pi-81)\ in^2[/tex]
simplify
[tex]A=81(\pi-1)\ in^2[/tex]