The units of tile will he need to surround his pool is 13.42
The given parameters are:
[tex]AB =2.24[/tex]
[tex]BD =5[/tex]
Start by calculating the distance BC using the following Pythagoras theorem
[tex]BD^2 = AB^2 + BC^2[/tex]
So, we have:
[tex]5^2 = 2.24^2 + BC^2[/tex]
[tex]25 = 5 + BC^2[/tex]
Collect like terms
[tex]BC^2 = 25 - 5[/tex]
[tex]BC^2 = 20[/tex]
Take the square roots of both sides
[tex]BC = 4.47[/tex]
The unit of tiles is then calculated using the following perimeter formula
[tex]Tiles = 2 \times (AB + BC)[/tex]
So, we have:
[tex]Tiles = 2 \times (2.24 + 4.47)[/tex]
[tex]Tiles = 13.42[/tex]
Hence, the units of tile will he need to surround his pool is 13.42
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A bag contains 1p,20 and 5p coins 3/8 of the bag are 1p coins There are as many 5p coins as 1p coins in the bag. There are 640 coins in total. Work out the number of 20 coins in the bag
Answer:
160 off 20p coins
Step-by-step explanation:
1 p, 20 p, 5 p coins1 p= 3/8 of the bag5 p= 1 p= 3/8 of the bagtotal coins= 64020 p coins= 640 - 640*(3/8+3/8)= 640*(1- 6/8)= 640 * 2/8= 640* 1/4= 160
Which of the following is most likely the next step in the series?
Answer:
B
Step-by-step explanation:
They are increasing by 1 vertically. Hope this helps!! :)
The lifespan (in days) of the common housefly is best modeled using a normal curve having mean 22 days and standard deviation 5. Suppose a sample of 25 common houseflies are selected at random. Would it be unusual for this sample mean to be less than 19 days?
Answer:
Yes, it would be unusual.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 [tex]Z \leq -2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered unusual.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
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:
[tex]\mu = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]
Would it be unusual for this sample mean to be less than 19 days?
We have to find Z when X = 19. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{19 - 22}{1}[/tex]
[tex]Z = -3[/tex]
[tex]Z = -3 \leq -2[/tex], so yes, the sample mean being less than 19 days would be considered an unusual outcome.
1. You have a home business selling designer necklaces. You have done
some market research, which shows that at a price of $40 you can sell
500 per week, and at a price of $60 you can sell 400 per week. Assuming
that the relationship between price and quantity sold is linear, find the
price that maximizes revenue. You must use methods that we developed
and practiced in the course. You will be graded not only on your answer
but on the clarity of your presentation.
Answer:
The price that maximizes the profits from the sale of the product is $60.
Step-by-step explanation:
Since selling necklaces at $ 40 allows a total amount of 500 sales per week, while a price of $ 60 allows 400 sales at the same time, the following calculations must be made to determine the price that maximizes sales performance:
40 x 500 = $ 20,000
60 x 400 = $ 24,000
50 x 450 = $ 22,500
55 x 425 = $ 23,375
58 x 410 = $ 23,780
59 x 405 = $ 23,895
As can be seen from the calculations developed, the price that maximizes the profits from the sale of the product is $60.
PLEASE HELP ME GUYS!!
Answer:
[tex]\frac{7}{3}[/tex]
Step-by-step explanation:
csc(Ф) is equivalent to the inverse of sin(Ф)
[tex]csc = \frac{1}{sin}[/tex]Since sin(Ф) = 3/7, the inverse of this would be 7/3
So, [tex]csc = \frac{1}{\frac{3}{7} }=\frac{7}{3}[/tex]
Please answer this correctly
Answer:
=3651 km^2
Step-by-step explanation:
The rectangle at the top is 11 km by 32 km
The area is 11*32 =352
The rectangle at the bottom is 9 km by 11 km
The area is 9*11 = 99
Add the two areas together
352+99 =451 km^2
Which product represents the fraction of the circle that is shaded?
A
B
C
D
Answer:
B
Step-by-step explanation:
A boy is playing a ball in a garden surrounded by a wall 2.5 m high and kicks the ball vertically up from a height of 0.4 m with a speed of 14 m/s . For how long is the ball above the height of the wall.
Answer:
2.5 sec
Step-by-step explanation:
Height of wall = 2.5 m
initial speed of ball = 14 m/s
height from which ball is kicked = 0.4 m
we calculate the speed of the ball at the height that matches the wall first
height that matches wall = 2.5 - 0.4 = 2.1 m
using = + 2as
where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)
= + 2(-9.81 x 2.1)
= 196 - 41.202
= 154.8
v = = 12.44 m/s
this is the velocity of the ball at exactly the point where the wall ends.
At the maximum height, the speed of the ball becomes zero
therefore,
u = 12.44 m/s
v = 0 m/s
a = -9.81 m/s^2
t = ?
using V = U + at
0 = 12.44 - 9.81t
-12.44 = -9.81
t = -12.44/-9.81
t = 1.27 s
the maximum height the ball reaches will be gotten with
= + 2as
a = -9.81 m/s^2
0 = + 2(-9.81s)
0 = 196 - 19.62s
s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.
height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m
we calculate for the time taken for the ball to travel down this height
a = 9.81 m/s^2 (positive in downwards movement)
u = 0
s = 7.49 m
using s = ut + a
7.49 = (0 x t) + (9.81 x )
7.49 = 0 + 4.9
= 7.49/4.9 = 1.53
t = = 1.23 sec
Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec
We wish to find the probability that a child from this population who has inadequate calcium intake is 11 to 13 years old. In other words, if you know that a child has inadequate calcium intake, what is the probability that the child is between 11 and 13 years old
Answer:
Step-by-step explanation:
Look at the population statistics. Let's say it contains:
- data on the age groups available in the population
- data on the probability that a child in the population has inadequate calcium intake OR data that a child in the population does not have the deficiency. If you're given one of these, the other can be gotten by subtracting the probability value given from 1.
So let's say there are children from ages 5 to 15 in this population and the probability that a child in this population has the deficiency is 0.23 (not all the children in this population of 5-15 year olds may have the deficiency) while the probability that a child in this population does not have the deficiency is [1-0.23] = 0.77
So if you pick a child randomly from the population and he has this deficiency, what is the probability that he or she is between 11 and 13 years old?
From ages 5-15, ages 11, 12 and 13 are 3 ages. The total number of ages is 11 ages.
3÷11 = 0.2727
This is the probability that a child picked or selected at random from the population is 11, 12, or 13 years old.
0.2727 × 0.23 = 0.0627
This is the probability that a child picked at random is BOTH within the age bracket 11 to 13 AND has the deficiency!
Apply this.
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
Answer:
–2(5 – 4x) < 6x – 4
<=>
-10 + 8x < 6x - 4
<=>
2x < 6
<=>
x < 3
Hope this helps!
:)
Answer:
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
A. x < –3
B. x > –3
C. x < 3
D. x > 3
Step-by-step explanation:
The correct answer here is C. x < 3
Write the equation of the line in slope intercept form
Answer:
y=2x-2
Step-by-step explanation:
When writing the equation of a line in slope intercept form, you need to know two things; the slope, and the y intercept. The slope of the line can be found by seeing how steep the line is. For instance, here the line rises 2 units for every 1 unit it moves to the right, meaning that it has a slope of 2/1=2. The y intercept can be found by just seeing where the graph crosses the y axis, or where x is 0. Here it can be seen to be at -2. Therefore, the equation of this line is y=2x-2. Hope this helps!
Answer:
answer is : y = 2x + 2
Step-by-step explanation:
slope-intercept form is y= mx + b
the y-intercept is: (0, -2) and the x-intercept is (1,0)
the first thing you do is find the slope:
m = (y2-y1) / (x2-x1)
so : ( 0 - -2) / ( 1 - 0) or 2/1 therefore the slope is 2
y = 2x + ? is the next step
then you can substitute the x and y into the formula to find the (b) value
0 = 2 (1)
0 = 2 ?
since 0 equals two plus two the b value is 2.
so the answer is y = 2x + 2
Ronnie invested $1500 in an account that earns 3.5% interest, compounded annually. The formula for compound interest is A(t) = P{(1 + i)^t}A(t)=P(1+i) t . How much did Ronnie have in the account after 4 years?
Answer:
BStep-by-step explanation:
A= New amount
P= Principal or Original amount which is £1500
I= Interest
t= time period
3.5% as a decimal is 3.5÷100=0.035
time period= 4 years
so 1500(1+0.035)^4 = B
select the point that is a solution to the system of inequalities
This point is below both the red diagonal line and the blue parabola. We know that the set of solution points is below both due to the "less than" parts of each inequality sign.
In contrast, a point like (2,2) is above the parabola which is why it is not a solution. It does not make the inequality [tex]y \le x^2-3x[/tex] true. So this is why we can rule choice A out.
Choice C is not a solution because (4,1) does not make [tex]y \le -x+3[/tex] true. This point is not below the red diagonal line. We can cross choice C off the list.
Choice D is similar to choice A, which is why we can rule it out as well.
A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landing on 5? A. 1 over 13 B.1 over 8 C.5 over 13 D.5 over 8 PLEASE HURRY!!!!!!!!!!!!!!!!!
Answer:
B. 1 over 8
Step-by-step explanation:
To determine the probability of the spinner landing on 5, we need to first know what probability is,
probability = required outcome/all possible outcome
since the spinner is divided into 8 equal sections and each section contains number from 1-8, this implies there are total of 64 numbers on the spinner. This implies that all possible outcome = 64
In each section there is 5, since there are 8 sections on the spinner, the number of 5's on the spinner are 8.
This implies that the required outcome = 8
but
probability = required outcome/all possible outcome
probability (of the spinner landing on 5) = 8/64 =1/8
Answer:
b
Step-by-step explanation:
please hurry I’ll make brainiest
A ball is tossed into the air from a height of 6 feet above ground level,
with a velocity of 3.4 feet per second. Which function could be used to
model the height of the ball, after t seconds?
Answer:
I think it would be the first but not 100% sure
Step-by-step explanation:
Any help would be great
Answer:
88/57
Step-by-step explanation:
Answer: 88:57
Step-by-step explanation:
Length is 88 and width is 57
So the ratio is 88:57
Find the exact solution of 3x^2+7=28
[tex]\text{Solve:}\\\\3x^2+7=28\\\\\text{Subtract 7 from both sides}\\\\3x^2=21\\\\\text{Divide both sides by 3}\\\\x^2=7\\\\\text{Square root both sides}\\\\\sqrt{x^2}=\sqrt7\\\\x=\pm\sqrt7\\\\\boxed{x=\sqrt7\,\,or\,\,x=-\sqrt7}[/tex]
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. F(x) = 0.4x² - 1
Step-by-step explanation:
→The function F(x) has shifted downwards, meaning there has to be a 1 being subtracted.
→The function F(x) has grown wider, meaning there has to be a number of absolute value less than 1.
This means answer choice, "B," is correct.
Answer:
The answer is B
Step-by-step explanation:
→The function F(x) has shifted downwards, meaning there has to be a 1 being subtracted.
→The function F(x) has grown wider, meaning there has to be a number of absolute value less than 1.
This means answer choice, "B," is correct.
Banking fees have received much attention during the recent economic recession as banks look for ways to recover from the crisis. A sample of 41 customers paid an average fee of $12.22 per month on their interest-bearing checking accounts. Assume the population standard deviation is $1.86. Complete parts a and b below.
a. Construct a 95% confidence interval to estimate the average fee for the population.
b. What is the margin of error for this interval?
Answer:
a) The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79
b) $0.57
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{1.86}{\sqrt{41}} = 0.57[/tex]
So the answer for b) is $0.57.
The lower end of the interval is the sample mean subtracted by M. So it is 12.22 - 0.57 = $11.65
The upper end of the interval is the sample mean added to M. So it is 12.22 + 0.57 = $12.79
The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79
1. Mrs. Verner's class has
a total of 15 students. If 8
of them are girls, what
percentage are boys?
Answer:
46.7%
Step-by-step explanation:
Given:
Total number of students in Mrs. Verner's class = 15
Number of girls = 8
To find: percentage are boys
Solution:
Percentage of boys = ( Number of boys / Total number of students ) × 100
Number of boys = Total number of students - Number of girls = 15 - 8 = 7
So,
Percentage of boys = [tex]\frac{7}{15}[/tex] × 100 = 46.7%
Among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol. Suppose five 25- to 30-year-olds are selected at random. Complete parts (a) through (d) below. (a) What is the probability that all five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (b) What is the probability that at least one has not used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (c) What is the probability that none of the five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (d) What is the probability that at least one has used a computer while under the influence of alcohol? (Round to four decimal places as needed.)
Answer:
(a) The probability that all five have used a computer while under the influence of alcohol is 0.0021.
(b) The probability that at least one has not used a computer while under the influence of alcohol is 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is 0.1804.
(d) The probability that at least one has used a computer while under the influence of alcohol is 0.8196.
Step-by-step explanation:
We are given that among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol.
Suppose five 25- to 30-year-olds are selected at random.
The above situation can be represented through the binomial distribution;
[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = Five 25- to 30-year-olds
r = number of success
p = probability of success which in our question is probability that
people used a computer while under the influence of alcohol,
i.e. p = 29%.
Let X = Number of people who used computer while under the influence of alcohol.
So, X ~ Binom(n = 5, p = 0.29)
(a) The probability that all five have used a computer while under the influence of alcohol is given by = P(X = 5)
P(X = 5) = [tex]\binom{5}{5}\times 0.29^{5} \times (1-0.29)^{5-5}[/tex]
= [tex]1 \times 0.29^{5} \times 0.71^{0}[/tex]
= 0.0021
(b) The probability that at least one has not used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
Here, the probability of success (p) will change because now the success for us is that people have not used a computer while under the influence of alcohol = 1 - 0.29 = 0.71
SO, now X ~ Binom(n = 5, p = 0.71)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.71^{0} \times (1-0.71)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.29^{5})[/tex]
= 1 - 0.0021 = 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is given by = P(X = 0)
P(X = 0) = [tex]\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 \times 1 \times 0.71^{5}[/tex]
= 0.1804
(d) The probability that at least one has used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.71^{5})[/tex]
= 1 - 0.1804 = 0.8196
Given the function f(x) = 2|x + 6|- 4, for what values of x is f(x) = 6?
x=-1, x = 11
x=-1, x=-11
x = 14, x=-26
x = 26. x=-14
Answer:
solution is [tex]\boxed{x=-1,x=-11}[/tex]
Step-by-step explanation:
f(x)=2|x+6|-4
either x+6 is positive and then |x+6|=x+6
or it is negative and |x+6| = -(x+6)=-x-6
case 1: x>=-6
f(x)= 2x+12-4=2x+8
f(x)=6 <=> 2x+8=6 <=> 2x = 6-8=-2 <=> x = -1
case 2: x<=-6
f(x)=-2x-12-4=-2x-16
f(x)=6 <=> -2x-16=6 <=> 2x=-16-6 = -22 <=> x = -11
so to recap, the solutions are x=-1 and x=-11
The value of x from the modulus value function is x = -1 and x = -11
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = 2 | x + 6 | - 4 be equation (1)
On simplifying , we get
when the value of f ( x ) = 6
Substituting the value of f ( x ) = 6 , we get
6 = 2 | x + 6 | - 4
Adding 4 on both sides , we get
2 | x + 6 | = 10
Divide by 2 on both sides , we get
| x + 6 | = 5
And , If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
So , the two values of x are given by
when x + 6 = -5 and x + 6 = 5
x = -1 and x = -11
Hence , the values of x of modulus function is x = -1 and x = -11
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Devon wants to build a ramp with the dimensions shown. How much wood does he need?
The image of the ramp with dimensions is missing, so i have attached it.
Answer:
680 in² of wood is needed.
Step-by-step explanation:
The way to find how much wood would be needed by devon would be to find the total surface area of the ramp.
From the attached image,
Let's find the area of the 2 triangles first;
A1 = 2(½bh) = bh = 15 x 8 = 120 in²
Area of the slant rectangular portion;
A2 = 17 x 14 = 238 in²
Area of the base;
A3 = 15 × 14 = 210 in²
Area of vertical rectangle;
A4 = 8 × 14 = 112 in²
Total Surface Area = A1 + A2 + A3 + A4 = 120 + 238 + 210 + 112 = 680 in²
1. An LG Dishwasher, which costs $800, has a 20% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warrantee costs $112.10 on a dishwasher. What is the expected value of the extended warranty assuming it is replaced in the first 2 years?
2. Approximately 10% of all people are left-handed. Consider a grouping of fifteen (15) people.
a. State the random variable.
b. Write the probability distribution.
c. Draw a histogram.
d. Describe the shape of the histogram.
e. Find the mean.
f. Find the variance.
g. Find the standard deviation.
Step-by-step explanation:
The expected value of the extended warrant is calculated as follow.
Value of Waranty
= 800 x 20% − 112.10
= 800 x 20/100 − 112.10
= 47.9
The expected value of the extended warranty assuming it is replaced in the first 2 years is given as follow.
Expected value=800-112.10=>687.90
Therefore, required expected value of extended warranty is 687.90
2.
Given information:
Number of Trials (n) = 15
Probability of Success (p) = 0.10
a) Let X represents the number of left-handed people.
b) The probability distribution follows binomial distribution.
X ∼ Binomial distribution
The probability distribution is given as follow.
P(X = x) = ^nCx(p)^x(1 − p)^n − x
c)The histogram is given as follow. (See attachment)
d) The shape of histogram is skewed right.
e) The mean is calculated as follow.
Mean
=n x p
= 15 x 0.10
= 1.5
f) The variance is calculated as follow.
Variance
= n x p x q
= 15 x 0.10 x 0.90
= 1.35
g) The standard deviation is calculated as follow.
Standard deviation
=√n x p x q
=√15 x 0.10 x 0.90
= 1.162
What equation results from completing the square and then factoring? x^2+2x=9
a. (x+2)^2=8
b. (x+1)^2=8
c.(x+1)^2=10
d.(x+2)^2=10
Answer:
c.(x+1)^2=10
Step-by-step explanation:
Completing the square:
We use the following relation:
[tex](x + a)^{2} = x^{2} + 2ax + a^{2}[/tex]
In this question:
[tex](x + a)^{2} = x^{2} + 2ax + a^{2} = x^{2} + 2x + a^{2}[/tex]
We have to find a.
[tex]2a = 2[/tex]
[tex]a = \frac{2}{2}[/tex]
[tex]a = 1[/tex]
[tex]x^{2} + 2x + 1 = (x+1)^{2}[/tex]
Thus, we have to add 1 on the right side of the equality.
We end up with:
[tex](x+1)^{2} = 9 + 1[/tex]
[tex](x+1)^{2} = 10[/tex]
So the correct answer is:
c.(x+1)^2=10
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:
[tex] P(\bar X>2.8)[/tex]
We can use the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z=\frac{2.8 -2.32}{\frac{1.24}{\sqrt{32}}}=2.190 [/tex]
And using the normal standard distribution and the complement rule we got:
[tex] P(z>2.190 )= 1-P(z<2.190) = 1-0.986=0.014[/tex]
Step-by-step explanation:
For this case w eknow the following parameters:
[tex] \mu = 2.32[/tex] represent the mean
[tex]\sigma =1.24[/tex] represent the deviation
n= 32 represent the sample sze selected
We want to find the following probability:
[tex] P(\bar X>2.8)[/tex]
We can use the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z=\frac{2.8 -2.32}{\frac{1.24}{\sqrt{32}}}=2.190 [/tex]
And using the normal standard distribution and the complement rule we got:
[tex] P(z>2.190 )= 1-P(z<2.190) = 1-0.986=0.014[/tex]
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
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:
[tex]\mu = 2.32, \sigma = 1.24, n = 43, s = \frac{1.24}{\sqrt{43}} = 0.189[/tex]
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
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.8 - 2.32}{0.189}[/tex]
[tex]Z = 2.54[/tex]
[tex]Z = 2.54[/tex] 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.
Determine 6m 9m how much greater the area of the yellow rectangle is than the area of the gree rectangle 2m 5m
Step-by-step explanation:
multiple 6 by 9 then 2 by 5 then subtract them
Answer:
44
Step-by-step explanation:
(6*9) - (2*5)
54 - 10
44
Omar has three t shirts: one red, one green and one yellow. He has two pairs of shorts one black and red.
-How many different outfits can Omar put together?
-What is the probability of Omar’s outfits including a red T-shirt or red shorts?
Answer:
Omar can put together 6 outfits.
66.67% probability of Omar’s outfits including a red T-shirt or red shorts
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
-How many different outfits can Omar put together?
For each t-shirt, that are two options of shorts.
There are 3 t-shirts.
3*2 = 6
Omar can put together 6 outfits.
What is the probability of Omar’s outfits including a red T-shirt or red shorts?
Red t-shirt and red shorts
Red t-shirt and black shorts
Green shirt and red shorts
Yellow shirt and red shorts
4 desired outcomes.
4/6 = 0.6667
66.67% probability of Omar’s outfits including a red T-shirt or red shorts
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
D. Time ( length)
Step-by-step explanation:
The function is measuring the length of the race, and the time it took to complete. So, it would be D.
// have a great day //
Answer:
D. Time(length)
Step-by-step explanation:
→The time is on the outside because, according to the information that has been given/provided, the length of the race depends on the time taken to complete the race.
This means the correct answer is "D. Time(length)."
The sum of two fractions can always be written as a
Answer: decimal
Step-by-step explanation:
because i did this quiz