I need help with this question
Suppose that 29% of all residents of a community favor annexation by a nearby municipality. The probability that in a random sample of 50 residents at least 35% will favor annexation is
Let us say that,
X = the number of residents in the sample who favor
annexation.
X has a distribution which follows a binomial curve with parameters:
n=50 and p=0.29
Calculating for mean:
Mean of X = n * p = 50 * 0.29
Mean of X = 14.5
Calculating for standard deviation:
Standard deviation of X = sqrt(n * p * (1 - p))
Standard deviation of X = 3.2086
Now we are to find the probability that at least 35% favour
annexation:
35% * 50 = 17.5 residents
Normal approximation can be applied in this case since sample size is greater
than 31. Therefore,
Required Probability:
P(X>=17.5) = 1 - P(X<17.5)
1 - P(z<(17.5-14.5)/3.2086) = 1 - P(z<0.9350) = 1- 0.825106 = 0.174894
Answer:
0.175 or 17.5%
The probability that at least 35% of a sample of 50 residents favor annexation is approximately 0.1469.
To solve this problem, we are dealing with a situation where we need to find the probability that at least 35% of a random sample of 50 residents favor annexation, given that the true population proportion is 29%.
Let's denote:
- ( p = 0.29 ) as the population proportion favoring annexation.
- ( n = 50 ) as the sample size.
We are interested in finding [tex]\( P(X \geq 0.35 \times 50) \),[/tex] where ( X ) follows a binomial distribution[tex]\( X \sim \text{Binomial}(n=50, p=0.29) \).[/tex]
First, calculate [tex]\( 0.35 \times 50 \):[/tex]
[tex]\[ 0.35 \times 50 = 17.5 \][/tex]
Since we can't have half a person favoring annexation, we take the ceiling of 17.5, which is 18. So, we need to find [tex]\( P(X \geq 18) \).[/tex]
To find this probability, we can use the cumulative distribution function (CDF) of the binomial distribution or an appropriate normal approximation. Here, due to large ( n ) and ( p), we can use the normal approximation to the binomial distribution.
1. **Calculate mean and standard deviation for normal approximation:**
- Mean (( mu )) of the binomial distribution: ( mu = np = 50 x 0.29 = 14.5 )
- Standard deviation[tex](\( \sigma \)) of the binomial distribution: \( \sigma = \sqrt{np(1-p)} = \sqrt{50 \times 0.29 \times 0.71} \approx 3.34 \)[/tex]
2. **Approximate using normal distribution:**
Convert [tex]\( X \geq 18 \)[/tex] to the corresponding normal distribution:
[tex]\[ Z = \frac{18 - 14.5}{3.34} \approx 1.05 \][/tex]
3. **Find the probability using the standard normal distribution:**
[tex]\[ P(X \geq 18) \approx P\left(Z \geq \frac{18 - 14.5}{3.34}\right) = P(Z \geq 1.05) \][/tex]
Using standard normal distribution table or calculator,
[tex]\[ P(Z \geq 1.05) \approx 0.1469 \][/tex]
Therefore, the probability that in a random sample of 50 residents at least 35% will favor annexation is approximately [tex]\( \boxed{0.1469} \).[/tex]
Suppose that 19 inches of wire costs 57 cents.
At the same rate, how much (in cents) will 14 inches of wire cost?
(06.04 LC)
If x = 2.7, 5x = ____. (Input decimals only, such as 12.7.)
Best answer will get BRAINLIEST!!!
(-2)^2-(-8)*[(-2)-(-10)]
Indicate, in standard form, the equation or inequality that is shown by the graph. (0,4)(4,0)
Answer:
standard form y = -x + b.
Step-by-step explanation:
Given : Graph and points (0,4)(4,0).
To find : Standard form of equation .
Solution : We have given that points (0,4)(4,0).
Let [tex]x_{1}[/tex] = 0 , [tex]x_{2}[/tex] = 4
[tex]y_{1}[/tex] =4 , [tex]y_{2}[/tex] = 0.
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Plugging values
Slope = [tex]\frac{0 - 4}{4 - 0}[/tex].
Slope = -1 .
Standard form y = m x + b
y = -1 x + b.
Plug (0,4)
4 = -1 ( 0)+ b
4 = b .
Now , plugging values b= 4 , m = -1.
y = -x + b.
Therefore, standard form y = -x + b.
Gary mails 10 to 3 power flyers to clients in one week. How many flyers does Gary mail
which system of linear inequalities has the point (2 ,1) in its solution set?
Answer:
its the last one number 4
Step-by-step explanation:
The system of linear inequalities that includes the point (2, 1) in its solution set is y ≥ 2x - 3 and y ≤ -2x + 5.
Explanation:The system of linear inequalities that has the point (2, 1) in its solution set can be represented by the inequalities:
y ≥ 2x - 3y ≤ -2x + 5To determine if the point (2, 1) satisfies these inequalities, we can substitute the x and y values into each inequality and check if the resulting statements are true. In this case, 1 is indeed greater than or equal to 2(2) - 3, and 1 is also less than or equal to -2(2) + 5, so the point (2, 1) is indeed in the solution set of this system of linear inequalities.
Learn more about Solution of Linear Inequalities here:https://brainly.com/question/28484221
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What is the transformation shown in the graph?
90° rotation
180° rotation
270° rotation
reflection
Linda made $238 for 17 hours of work.
At the same rate, how many hours would she have to work to make $168?
8 men and 6 women arrive separately in a random fashion to a meeting. What is the probability that the first 4 people to show up are men?
First, you add 8 and 6 which will be 14. Since it's asking for the first four, it would be 4 over 14.
You can reduce that which is always a good idea and it comes out to be 2 over 7. That because you would divide both the top and bottom (like usual) by 2 each.
If you would want it as a percent, you would turn it into a decimal first. The decimal would be .02857. That's of course if you divide 2 and 7 like normal.
From there you would move the decimal point over two places making it 28.57 percent.
Hope this helps!!
3. Your teacher wants to make sure everyone has a pencil for class. She has 104 students in all of her classes. The office gave her 4 boxes of pencils. How many pencils were in each box if each of her students receives 1 pencil? Question 3 options: A 26 B 25 C 100 D 50
While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 40 degrees. After walking 450 ft closer, he guessed that the angle of elevation had increased by 18 degrees. Approximately how tall is the hill?
You are making bouquets to sell. You have 60 roses, 84 daisies, and 24 lilies. Each bouquet will have the same number of each kind of flower. You want to use all of the flowers. What is the greatest number of bouquets you can make?
Answer:
you can make 12 bouquets...each containing 5 roses, 7 daisies, and 2 lilies
Step-by-step explanation:
Solve for x
3x + 3 − x + (−7) > 6
The formula for the volume of a cylinder with a height of 5 units is V(r)=(5)(pi)(r^2) where r is the radius of the cylinder. What is the domain and range of this function?
Answer:
D=(-∞,∞) Range = [0, ∞)
Step-by-step explanation:
V(r) =5πr²
Firstly we have to work with π as ≈ 3.14 so that we can make it better, by doing this we reveal it more clearly its quadratic form
V(r)= 15.71r²
As there is no restriction algebraically speaking. The Domain is all the Real Line. This is a Total Function.
As for the Range, since any negative value plugged into x² will turn into a positive one we'll only have positive results for y to each entry of x. So the Range is f(x) ≥0
As you can check it below.
a relationship is linear if it has a(n) (negative, positive, constant, or undefined) rate of change.
Answer:
first one is (constant)
second answer is (slope)
the third answer is 2
Step-by-step explanation:
what else would need yo be congruent to show that EFG HIJ by SSS ?
Which statement belongs in the Perimeter section of the Venn Diagram?
A.The distance around a closed figure
B.The space or region of a closed figure
C.Base and altitude is found
D.Measured in units squared
A. The distance around a closed figure is the correct answer.
Explanation:
The definition of perimeter is : The summation of the outer sides of any closed figure. Like in a rectangle, its the sum of all the four sides. In a circle, its the measure of the outline of the circle also called the circumference.
Hence, the distance around a closed figure is called its perimeter.
Sue surveyed the students at her school to find out if they like sandwiches and/or tacos. The table below shows the results of the survey: Like Sandwiches Do Not Like Sandwiches Total Like Tacos 43 7 50 Do Not Like Tacos 27 23 50 Total 70 30 100 If a student likes sandwiches, what is the probability that student also likes tacos? 43% 61.4% 71.4% 86%
Answer:
61.4%
Step-by-step explanation:
There are a total of 43+27 = 70 students that like sandwiches.
Out of these, 43 also like tacos; this is
43/70 = 0.614 = 61.4%
Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown. R (1, 1) S (3, 1) T (1, 6) R' (–1, –1) S' (–3, –1) T' (–1, –6) Which best describes the transformation? The transformation was a 90° rotation about the origin. The transformation was a 180° rotation about the origin. The transformation was a 270° rotation about the origin. The transformation was a 360° rotation about the origin.
Answer:
B I took the test and got it right
Step-by-step explanation:
how much chocolate with each person get if 3 people share 1/2 lb of chocolate equally
Multiply (x – 4)(x2 – 5x – 6).
K(-5,-2), M(5,4), S(-3,6), T(3,-4)
One of two complementary angles is 8 degrees less than the other.
Which of the following systems of equations represents the word problem?
x + y = 90 and x - y = 8
x + y = 90 and 90 - x = 8
x + y = 90 and y = 8x
Answer: The correct option is
[tex](A)~~x+y=90,~~x-y=8.[/tex]
Step-by-step explanation: Given that one of the two complementary angles is 8 degrees less than the other.
We are to select the correct system of equations represents the given word problem.
Let x and y represents the two complementary angles where y is less than x.
Since one angle is 8 degrees less than the other and y is less than x, so we have
[tex]x-y=8.[/tex]
We know that the sum of two complementary angles is 90 degrees, so we get
[tex]x+y=90.[/tex]
Thus, the required system of equations representing the given word problem will be
[tex]x+y=90,\\\\x-y=8.[/tex]
Option (A) is CORRECT.
The population of a particular country was 28 million in 1985; in 1990, it was 36 million. The exponential growth function A=28e^{kt} describes the population of this country t years after 1985. Use the fact that 5 years after 1985 the population increased by 8 million to find k to three decimal places.
The value of k is 0.05.
The exponential growth function is: A = 28e^kt
Where
A = future value of population
e = 2.718
k = growth rate
t = time
The exponential growth function can be written as:
36 = 28 x e^k 5
log(36/28) ÷ log(e) ÷ 5 = 0.05
A similar question was answered here: https://brainly.com/question/1440123
Jim earned $140 during the summer doing chores. He bought 2 sets of pens worth $25 each using his chore money. How much money was left after he bought the pen sets?
25 x 2 = 50
140-50 = 90 dollars left
diana rode her stateboard at a average speed of 12mph what was her speed in feet per hour
Answer:
63,360 ft/h
Step-by-step explanation:
A line passes through (9, –9) and (10, –5). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers
Final answer:
a. The equation for the line in point-slope form is y + 9 = 4(x - 9), with a slope of 4.
b. The equation can be rewritten in standard form as 4x - y = 45.
Explanation:
a. To write the equation for the line in point-slope form, we need to determine the slope (m) and one point on the line (x1, y1).
The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1).
Taking the points (9, -9) and (10, -5), we can substitute the values into the formula to get m = (-5 - (-9)) / (10 - 9) = 4 / 1 = 4.
Now we can use the formula y - y1 = m(x - x1) with the point (9, -9) to get y - (-9) = 4(x - 9). Simplifying, we have y + 9 = 4x - 36.
b. To rewrite the equation in standard form, we need to bring the equation to the form Ax + By = C, where A, B, and C are integers.
Starting from the point-slope form, we can expand and simplify the equation to get y + 9 = 4x - 36 becomes y = 4x - 45.
To make all the coefficients integers, we can multiply the equation by 5 to get 5y = 20x - 225, rearrange the terms as -20x + 5y = -225, and divide every term by -5 to get the standard form 4x - y = 45.
Tara makes the following statement: "There is a 70% chance of sunny weather tomorrow and a 60% chance I will go to the beach." What is the probability that it will be sunny tomorrow and Tara will go to the beach? 42% 22% 11% 13%
Answer:
The probability is 42%
Step-by-step explanation:
The probability that A and B, two independent events, happens is given by:
P=P(A)*P(B)
In this case, lets call A the event in which there are sunny weather tomorrow and B the event in which Tara goes to the beach. Taking into account that they are independent, that means that one event doesn't affect the other, the probability P that it will be sunny tomorrow and Tara will go to the beach is:
P=0.7*0.6=0.42
Multiplying P by 100, we get:
P=42%
So, the probability that it will be sunny tomorrow and Tara will go to the beach is 42%