An exponential function is given by the formula:
\(f(x)=a\cdot b^x\)where a and b are numbers. b is always positive
We have that there are two ways of obtaining a decreasing exponential function:
1. if a is negative
2. if 0 < b < 1
We have that we have an increasing function if and only if
a is positive and b is higher than 1, b > 1
AnalysisWe have that:
In h(x) = 7 · 0.9ˣ
a = 7 and b = 0.9
Since 0 < 0.9 < 1, then it is a decreasing function.
In k(x) = 10 · (3/5)ˣ
a = 10 and b = 3/5 = 0.6
Since 0 < 3/5 < 1, then it is a decreasing function.
In n(x) = 4 · (7/6)ˣ
a = 4 and b = 7/6 = 1.166...
Since a is positive and b is higher than 1: 1 < 1.166...,
then it is an increasing function.
In p(x) = -10 · 8ˣ
a = -10 and b = 8
Since a is negative, then it is a decreasing function.
In j(x) = 2 · (1 + 0.03)ˣ
a = 2 and b = 1 + 0.03 = 1.03
Since a is positive and b is higher than 1: 1 < 1.03,
then it is an increasing function.
In g(x) = 0.25 · 6ˣ
a = 0.25 and b = 6
Since a is positive and b is higher than 1: 1 < 6,
then it is an increasing function.
In f(x) = 5 · 2ˣ
a = 5 and b = 2
Since a is positive and b is higher than 1: 1 < 2,
then it is an increasing function.
In m(x) = 3 · 4ˣ - 5
a = 3 and b = 4
Since a is positive and b is higher than 1: 1 < 4,
then it is an increasing function.
Answer- the increasing functions are:
Find the value of x.
78°
OA7
OB. 8
O C. 5
O D. 1
(12x+18)
Step-by-step explanation:
you can find the answer by vertical opposite angle
if the value of x is computed and it's equal to 78 you will find the answer
78=(12x+18)^
78=(12×5+18)
78=(60+18)
78=78 the problem is solved
may u get branliest please please
[50 POINTS + BRAINLIEST]
gary the fat boi ate 1000 pounds of "Sour patch kids". How much does gary weigh and does he have mega-evolved diabetes?
Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG. The measure of angle HGF is (9y + 3)°, and the measure of angle EFG is (8y + 5)°. What is the measure of angle HGF?
Answer:
21°
Step-by-step explanation:
In an sosceles trapezoid, the lower base and upper base angles are congurent
⇒ ∠HGF = ∠EFG
⇒ 9y + 3 = 8y + 5
⇒ 9y - 8y = 5 - 3
⇒ y = 2
⇒ ∠HGF = 9(2) + 3
= 18 + 3
= 21
The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.
Explanation:This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.
Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.
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Select the correct expanded form for (Two-thirds) Superscript 4.
Two-thirds times two-thirds times two-thirds times two-thirds
Two-thirds times two-thirds times two-thirds
Two-thirds + two-thirds + two-thirds + two-thirds
Two-thirds times 4
The correct expanded form using Laws of exponents is:
Two-thirds times two-thirds times two-thirds times two-thirds
How to use laws of exponents?Some of the laws of exponents are:
1) When multiplying like bases, keep the base the same and add the exponents.
2) When raising a base with a power to another power, keep the base the same and multiply the exponents.
3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.
Now, we want to solve the expression given as: (²/₃)⁴
When we expend this, we arrive at:
²/₃ × ²/₃ × ²/₃ × ²/₃
This among the options is Option A which is:
Two-thirds times two-thirds times two-thirds times two-thirds
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What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Answer:
mean = 24
Step-by-step explanation:
the mean is calculated as
mean = \(\frac{sum}{count}\)
the sum of the data set is
sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
there is a count of 7 in the data set , then
mean = \(\frac{168}{7}\) = 24
Work out the percentage change when a price of £40 is increased to £70.
give simple working out :)
Answer:
To calculate the percentage change when a price of £40 is increased to £70, we can use the following formula:
Percentage Change = (New Value - Old Value) / Old Value * 100
Plugging in the numbers:
Percentage Change = (£70 - £40) / £40 * 100 = £30 / £40 * 100 = 75%
So the price has increased by 75%.
In the division problem 18+ 3 = 6, is 18 the
quotient
divisor
dividend
remainder
Answer:
Dividened
Step-by-step explanation:
Because that is what is going into 3
have a great day!
brailiest is appreciated!
Find the midpoint of segment AB if A(-3, 8) and B (-7, -6).
Answer: (-5,1)
Step-by-step explanation: that should be right
If n = 4, all of the following expressions are equivalent except _____.
16
n -2
1/16
1/n ^ 2
karen purchased dvd 153.77 sale price the original price of dvd was 175.90 what is percent markd ou wn
Answer:
The price was marked down by 12.58%
Step-by-step explanation:
153.77 is a 12.581011938601% decrease of 175.90.
Percentage of decrease = |175.90 - 153.77|/175.90 = 22.13/175.90 = 0.12581011938601 = 12.581011938601%
Please help ASAP I rlly need this
The solution is, center = ( 0,0) & coefficient = 3
What is dilation?The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)
here, we have,
from the given figure,
we get,
length of MQ = 8.48
length of M'Q' = 2.82
so, dilation factor = 8.48/2.82
= 3
and, we get, the center of dilation = (0,0)
Hence, The solution is, center = ( 0,0) & coefficient = 3
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The beginning steps for determining the center and radius of a circle using the completing the square method are shown in the table.
Step 1
[original equation]: x2 + 8x + y2 − 6y = 11
Step 2
[group like terms]: (x2 + 8x) + (y2 − 6y) = 11
Step 3
[complete the square]:
Which of the following is the correct equation for Step 3?
Group of answer choices
(x2 + 8x + 4) + (y2 − 6y + 3) = 11 + 4 + 3
(x2 + 8x + 16) + (y2 − 6y + 9) = 11 + 16 + 9
(x2 + 8x + 16) + (y2 − 6y − 9) = 11 + 16 − 9
(x2 + 8x + 4) + (y2 − 6y − 3) = 11 + 4 − 3
The correct equation for Step 3 for completing the square method are shown in the table is,
⇒ (x² + 8x + 16) + (y² - 6y + 9) = 11 + 16 + 9
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
The beginning steps for determining the center and radius of a circle using the completing the square method are;
Step 1 [original equation]:
⇒ x² + 8x + y² - 6y = 11
Step 2 [group like terms]:
⇒ (x² + 8x) + (y² - 6y) = 11
Now, We ca complete the squares for determining the center and radius of a circle as;
Step 1 [original equation]:
⇒ x² + 8x + y² - 6y = 11
Step 2 [group like terms]:
⇒ (x² + 8x) + (y² - 6y) = 11
Step 3;
⇒ (x² + 8x + 16) + (y² - 6y + 9) = 11 + 16 + 9
Step 4;
⇒ (x + 4)² + (y - 3)² = 36
Thus, The correct equation for Step 3 for completing the square method are shown in the table is,
⇒ (x² + 8x + 16) + (y² - 6y + 9) = 11 + 16 + 9
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Using a calculator or statistical software, find the linear regression line for the data in the table below.
Using the regression with the values rounded to the nearest hundredth, find the value of y at x=7. Round your answer to the nearest hundredth if necessary.
x y
0 2.83
1 3.33
2 6.99
3 8.01
4 7.62
5 7.66
Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.
To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.
Using the provided data, the linear regression line equation is:
\(\[ y = 1.3642x + 3.2324 \]\)
To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:
\(\[ y = 1.3642(7) + 3.2324 \]\)
Simplifying the equation, we get:
\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)
In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.
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graph y+2=2(x+3). What is the x intercept?
x intercept :
The given equation is y + 2 = 2(x + 3) and the x-intercept is -2.
To find the x-intercept of the equation y + 2 = 2(x + 3), we need to set y equal to zero and solve for x. The x-intercept occurs when the value of y is zero, meaning the graph crosses the x-axis.
Let's substitute y with 0 in the equation:
0 + 2 = 2(x + 3)
Simplifying the equation:
2 = 2(x + 3)
Dividing both sides by 2:
1 = x + 3
Subtracting 3 from both sides:
-2 = x
The x-intercept is -2. This means that the graph of the equation y + 2 = 2(x + 3) crosses the x-axis at the point (-2, 0).
The x-intercept represents the value of x where the graph intersects or crosses the x-axis. In this case, it occurs when x is equal to -2, and the y-value is zero.
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6th grade math I mark as brainliest
Answer:
False
Step-by-step explanation:
2*2*2*2 is the correct answer
Answer:
False
Step-by-step explanation:
\(2^4=2\cdot 4\\\\Simplify\:\:2^4 =16\\Simplify\:\:2\cdot 4 = 8\\\\16=8\\\\\mathrm{The\:sides\:are\:not\:equal}\\\\\mathrm{False}\)
a + b=c make (a) the subject with working
Step-by-step explanation:
a= c-b pls let me know if it is correct or not
Country A has an exponential growth rate of 4.3% per year. The population is currently 4,079,000, and the land area of Country A is 19,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
The number of years it would it take for there to be one person for every square yard is 108,325.68 years.
How many years would it take for there to be one person for every square yard?When there is one person for every square yard, it means that the population and land area are equal in value.
Number of years = (In FV / PV) / r
FV = future populationPV = present populationr = rate of growth(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years
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a) b³(cm)³
b) x²(pulgadas)² 4x(pulg)
c)3x-9x
d)5b+4b
e) 3x+4-9x+7
f) (7x+3)+(3x-2)
AYUDA PLIS PARA AHORITA :)
Answer:
puedes decirme l indicación para poder resolverlo
Please answer this!!!!
Answer:
im not very sure but i believe that it is (40,4)
Answer:
for this on the equation will be y= -10x+40
Step-by-step explanation:
I hope this helps u :)
When comparing the two sets of data, what is a true statement
Answer:
b
Step-by-step explanation:
Answer:
the answer is b
Step-by-step explanation:
Mai's class volunteered to clean a park with an area of square mile. Before they took a lunch break, the class had cleaned of the park. How many square miles had they cleaned before lunch?
The class had cleaned x × A square miles before lunch.
Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).
If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:
Area cleaned before lunch = x × A
Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.
Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).
If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:
Before lunch, the area was cleaned = x A
We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.
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Exercise 1 (7 points)
The following data represent the scores of students in an Inferential
Statistics examination 5-12-8-14-11.
1. Determine the mean, variance and standard deviation of this population
2. How many simple random samples of size 2 can be constructed in an
exhaustive manner?
3. The sampling distribution of the sample means is studied, determine
the mean, variance and standard error of this sampling distribution.
4. Determine the variance of this sampling distribution.
5. This is considered to be data from a simple random sample, determine a
point estimate of the population mean and variance.
Answer: 1.To find the mean, we sum up all the scores and divide by the number of scores:
Mean = (5 + 12 + 8 + 14 + 11) / 5 = 50 / 5 = 10
To find the variance, we first find the deviation of each score from the mean:
5 - 10 = -5
12 - 10 = 2
8 - 10 = -2
14 - 10 = 4
11 - 10 = 1
We square each deviation and sum them up:
(-5)^2 + 2^2 + (-2)^2 + 4^2 + 1^2 = 26
Then, we divide by the number of scores to find the variance:
Variance = 26 / 5 = 5.2
Finally, we find the standard deviation by taking the square root of the variance:
Standard deviation = √5.2 = 2.28
2. To construct a simple random sample of size 2, we can choose any two scores from the population. The number of ways to do this is given by the combination formula:
C(5,2) = 5! / (2! * (5 - 2)!) = 10
Therefore, there are 10 simple random samples of size 2 that can be constructed.
3.The mean of the sampling distribution of the sample means is equal to the population mean, which we found to be 10. The variance of the sampling distribution is equal to the population variance divided by the sample size:
Variance of sampling distribution = Variance / Sample size = 5.2 / 2 = 2.6
The standard error of the sampling distribution is the square root of the variance:
Standard error = √2.6 = 1.61
4.The variance of the sampling distribution is 2.6, as we found in part
5. Since this is considered to be data from a simple random sample, we can use the sample mean as a point estimate of the population mean. Therefore, the point estimate of the population mean is 10.
Similarly, we can use the sample variance as a point estimate of the population variance. However, we need to correct for the bias in the sample variance by dividing by (n-1) instead of n:
Point estimate of population variance = Variance * (n / (n-1)) = 5.2 * (5 / 4) = 6.5
Step-by-step explanation:
Chapter 7: Solving Systems of Linear Equations and Inequalities
At least two linear inequalities in the same variables constitute a system of linear inequalities. The ordered pair that is a solution to all system inequalities is the linear inequality's solution, and the linear inequality's graph is the system's solution graph.
What are inequalities and systems of equations?A set of equations with the same variables is called a system of equations. The only difference is that you are working with inequalities rather than equations in a system of inequalities. Finding the variable values that simultaneously make each inequality true is necessary to solve such a system.
What are the three ways to solve equation systems?There are three methods for addressing frameworks of straight conditions in two factors:
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Lee and two of his friends purchased tickets to a school play. Tristan paid for all the tickets with a $100.00 bill and received $70.00 in change. If Tristan used a coupon for 45% off, what was the original price for one ticket?
Answer:
$54.55
Step-by-step explanation:
Elroy bought a $4210 custom video gam e/ virtual sound system on a special no-interest plan. He made
The amount of the last payment that Elroy will make is $710, which includes the $200 monthly payment and a balance of $510.
How is the last payment determined?The last payment amount is the result of the mathematical operations of subtraction and multiplication.
The first mathematical operation was the subtraction of the down payment from the total cost of the video game system.
Using multiplication, the monthly payments are determined to be $3,400 for 17 months. This is subtracted from the remaining balance to obtain the last payment amount.
The cost of a custom video game/virtual sound system = $4,210
Down payment = $100
The remaining balance for monthly payment = $4,110 ($4,210 - $100)
Payment period = 18 months (1¹/₂ years)
Monthly payments = $200
Payment for the first 17 months = $3,400 (17 x 200)
Last payment = $710 ($4,110 - $3,400)
Thus, if Elroy makes the minimum monthly payment of $200 till the last payment, then he will pay $710 to settle the account.
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Question Completion:He made a $100 down payment and agreed to pay the entire purchase off in 1 1/2 years The minimum monthly payment is $200 if he makes the minimum monthly payment up until the last payment what will be the amount of his last payment?
A line passes through (-2, 10) and (8.-9). Write an equation for the line in point-slope
form AND rewrite the equation in standard form using integers.
Merry Christmas and Happy Holidays!!! <3
Answer:
The Standard Form of the equation of a line is: Ax+By=C
Converting that, once and forevermore, into slope-intercept form, and remembering the result,
the slope m=(-A/B).
If the given slope is 8, the equation of the line is 8x-y=C and we a point to determine C. Use (2,10)
8(2)-10=C
6 = C
The equation of the line, in Standard Form, is: 8x - y = 6
A man wants to mesure the height of a nearby building. He places a 7ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building’s shadow is 162ft, the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot.
The height of the building is approximately 227 feet.
In the given question, a man wants to measure the height of a nearby building. He places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building.
The total length of the building's shadow is 162 ft, and the pole casts a shadow that is 5.5 ft long. We have to determine the height of the building.The given situation can be explained with the help of a diagram.
As shown in the figure above, let AB be the building and CD be the 7 ft pole. The height of the building is represented by the line segment AE, which is to be determined. Let the length of the shadow of the pole be CD and that of the building be BD.
Therefore, the length of the total shadow will be BC or CD + BD.According to the question, the shadow of the pole is exactly covered by the shadow of the building. This implies that the two triangles AEF and CDF are similar. Hence, the corresponding sides are proportional. Therefore, we have:AE/EF = CD/DF
On substituting the values from the given data, we get:
AE/(EF + 5.5) = 7/5.5.... (1)
Similarly, we can write from the given data:
BD/DF = 162/5.5.... (2)
From equations (1) and (2), we can write:
AE/(EF + 5.5) = BD/DF => AE/(EF + 5.5) = 162/5.5.... (3)
On solving the above equation for AE, we get:
AE = (7/5.5) × (162/5.5 - 5.5)≈ 226.6 ft
Therefore, the height of the building is approximately 227 feet.
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Enter the number that belongs in the green box
The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:
\(c^2 = a^2 + b^2 - 2ab*cos(C)\)
In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:
\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)
49 = 16 + 25 - 40*cos(C)
49 = 41 - 40*cos(C)
40*cos(C) = 41 - 49
40*cos(C) = -8
cos(C) = -8/40
cos(C) = -0.2
To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:
C = arccos(-0.2)
Using a calculator, we find that C ≈ 101.54 degrees.
Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
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Show all 4 steps of the following:
x - 3/5= 1/6
Answer: x=23/30
Step-by-step explanation: Hope this help :D
The mean percent of childhood asthma prevalence in 43 cities is 2.32%. A random sample of 32 of these cities is selected. What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.8%? Interpret this probability. Assume that sigmaequals1.24%. The probability is nothing.
Answer:
\( P(\bar X>2.8)\)
We can use the z score formula given by:
\( z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}\)
And replacing we got:
\( z=\frac{2.8 -2.32}{\frac{1.24}{\sqrt{32}}}=2.190 \)
And using the normal standard distribution and the complement rule we got:
\( P(z>2.190 )= 1-P(z<2.190) = 1-0.986=0.014\)
Step-by-step explanation:
For this case w eknow the following parameters:
\( \mu = 2.32\) represent the mean
\(\sigma =1.24\) represent the deviation
n= 32 represent the sample sze selected
We want to find the following probability:
\( P(\bar X>2.8)\)
We can use the z score formula given by:
\( z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}\)
And replacing we got:
\( z=\frac{2.8 -2.32}{\frac{1.24}{\sqrt{32}}}=2.190 \)
And using the normal standard distribution and the complement rule we got:
\( P(z>2.190 )= 1-P(z<2.190) = 1-0.986=0.014\)
Answer:
0.55% probability that the mean childhood asthma prevalence for the sample is greater than 2.8%. This means that a sample having an asthma prevalence of greater than 2.8% is unusual event, that is, unlikely.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. 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 pvalue, we get the probability that the value of the measure is greater than X.
If X is more than two standard deviations from the mean, it is considered an unusual outcome.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
\(\mu = 2.32, \sigma = 1.24, n = 43, s = \frac{1.24}{\sqrt{43}} = 0.189\)
What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.8%?
This is 1 subtracted by the pvalue of Z when X = 2.8. So
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{2.8 - 2.32}{0.189}\)
\(Z = 2.54\)
\(Z = 2.54\) has a pvalue of 0.9945
1 - 0.9945 = 0.0055
0.55% probability that the mean childhood asthma prevalence for the sample is greater than 2.8%. This means that a sample having an asthma prevalence of greater than 2.8% is unusual event, that is, unlikely.