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]
For 6 consecutive days, Alejandro studied for 5 minutes more each day than he did the previous day. Which best represents the change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day?
The change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day is given by -30 minutes, the correct option is A.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
Alejandro studied for 6 consecutive days.
Let he studied for x minutes on the first day
Next day he studies (x + 5) minutes.
Each day the time is increasing by 5 minutes.
The equation for time he studied each day = x + 5 t
On last day he studied,
= x + 5 * 6
= x +30
The change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day is given by
x - x -30
= -30 minutes
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Answer:
A
Step-by-step explanation:
Sonya wants to know how much her annual take-home pay will be after she pays FICA taxes totaling 7.65% on an annual salary of $36,590.
Final answer:
Sonya's annual take-home pay, after FICA taxes of 7.65% on her annual salary of $36,590, would be $33,790.86.
Explanation:
To calculate Sonya’s annual take-home pay after FICA taxes, we first need to understand that FICA consists of two separate taxes: Social Security and Medicare. The total rate for these combined is 7.65% of the gross income. Sonya’s annual salary is $36,590.
First, we calculate the total FICA tax Sonya has to pay:
Social Security tax (6.2% of $36,590) = $2,268.58Medicare tax (1.45% of $36,590) = $530.56Add these two amounts to get the total FICA tax:
$2,268.58 (Social Security) + $530.56 (Medicare) = $2,799.14
Finally, subtract this total FICA tax from the annual salary to find Sonya’s take-home pay:
$36,590 (annual salary) - $2,799.14 (FICA taxes) = $33,790.86
answer correctly for brainliest
Which of the relations given by the following sets of ordered pairs is not a function?
a. {(5,2),(4,2),(3,2),(2,2),(1,2)}{(5,2),(4,2),(3,2),(2,2),(1,2)}
b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}
c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}{(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}
d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}
Answer:
The answer is the B)
Step-by-step explanation:
By the definition, in a function, a value in the first set of numbers only have a value in the second set of numbers, so for every pair of numbers, we have to review if the first number for this pair only appears one time in all the function.
All the set ot values agrees with this definition except the B, because the third and fourth pair have the same first value (3)
Suppose you are standing 500 feet away from a tree and you see a hawk hovering directly above that tree. The angle of elevation from you to the hawk is 24°. To the nearest foot, at what height is the hawk hovering?
choose the correct conic section to fit the equation (x-8)^2+(y-12)^2=25
a. Circle
b. Eclipse
c. Parabola
d. Hyperbola
Answer: a. Circle
Step-by-step explanation:
Given equation: [tex](x-8)^2+(y-12)^2=25[/tex] which is equivalent to [tex](x-8)^2+(y-12)^2=5^2[/tex]
This equation is of the form [tex](x-h)^2+(y-k)^2=r^2[/tex] which is the standard equation of a circle centered at (h,k) with radius r.
On comparing given equation to the standard equation of circle we have, h=8 and k=12 and r =2.
Therefore, given equation represent a circle centered at (8,12) and radius=5 units.
Which of these is a simplified form of the equation 6y + 4 = 8 + 2y + 2y? 6y = 8 10y = 12 2y = 4 4y = 12
what is the domain of the function on the graph?
a. all real numbers
b. all real numbers greater than or equal to - 2
c. all real numbers greater than or equal to - 5
d. all real numbers greater than or equal to 0
Answer:
Option a is correct.
Step-by-step explanation:
The given graph is of the function f(x)=|x|-2
Domain are the values that x will take in the given function x can take all the values whether fraction, integer the function will always be defined.
Hence, the domain of the function is all real numbers.
Therefore, Option a is correct.
Answer: Domain are all real number [a].
Step-by-step explanation:
Given : graph .
To find : what is the domain of the function on the graph.
Solution : We have given that a graph of function f(x) : |x| - 2.
Domain : The domain of a function is the set of its possible inputs,that is the set of input values where for which the function is defined.
Therefore, the domain are all real number [a].
A company manufactures and sells mini-recorders. A survey of office supply stores indicated that at a price of $82 each, the demand would be four hundred recorders, and at a price of $42 each, the demand would be nine hundred recorders. If a linear relationship between price and demand exists, which of the following equations models the price-demand relationship?
(Let x represent the price per mini-recorder and y represent the demand in hundreds.)
A. Y= -1/8x + 57/4
B. Y= -8x - 114
C. Y= -1/8x - 57/4
D. Y= -8x + 114
Final answer:
Using the two given points $(82, 4)$ and $(42, 9)$, the slope is calculated to be $-1/8$. Subsequently, by using the point-slope form of the line equation and simplifying, we find that the linear relationship between price and demand is described by $y = -1/8x + 57/4$, which corresponds to choice A.
Explanation:
To determine the linear equation that best models the price-demand relationship for the mini-recorders, we are given two points. At a price of $82, the demand is 400 recorders (4 hundred), and at a price of $42, the demand is 900 recorders (9 hundred). In the mathematical representation, these points are (82, 4) and (42, 9), where x is the price and y is the demand in hundreds.
To find the slope (m) of the line, we use the slope formula:
m = (y2 - y1) / (x2 - x1), which gives us m = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8.
Now, we can use the point-slope form to find the equation of the line. Let's use the point (82, 4):
y - y1 = m(x - x1)
y - 4 = (-1/8)(x - 82)
Multiplying out the right-hand side of the equation, we have:
y - 4 = (-1/8)x + (82/8)
y - 4 = (-1/8)x + 10.25
Moving 4 to the other side to get 'y' by itself, the equation becomes: y = (-1/8)x + 10.25 + 4
This simplifies to:
y = (-1/8)x + 14.25
Converting 14.25 into quarters gives us 14.25 = 57/4. Hence the equation becomes:
y = (-1/8)x + 57/4 which matches choice A.
Final answer:
The correct equation that models the price-demand relationship is y = -1/8x + 57/4, where y is the demand in hundreds and x is the price per mini-recorder.
Explanation:
To find the equation that models the price-demand relationship, we need two points to determine the line: (x1, y1) = (82, 4) and (x2, y2) = (42, 9). The demand, y, is in hundreds of recorders and x represents the price per mini-recorder. The slope (m) of the line is given by the change in demand over the change in price: m = (y2 - y1) / (x2 - x1) = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8. To find the y-intercept (b), we use one of the points and the slope in the linear equation formula y = mx + b. Using the point (82, 4), we have 4 = (-1/8)(82) + b. Solving this equation gives us b = 4 + (1/8)(82) = 4 + 10.25 = 14.25. Now the linear equation is y = -1/8x + 14.25. Since y needs to be in hundreds for the units to match the point given (400, 900), we must divide b by 100, resulting in b = 14.25 / 100 = 57/4. The final price-demand relationship is y = -1/8x + 57/4.
Which expression is equivalent to 5(2+7)?
Answer
b
Step-by-step explanation:
i got it on eduenity
Mrs. Patil bought 4 packs of pencils for her class. Then she bought 3 more packs of pencils. There are 12 pencils in a pack. How many pencils did she buy?
Marina can bicycle 19.5 miles in the same time it takes her to run 6 miles. She bikes 9 miles per hour faster than she runs. At what speed does Marina run? Distance Rate Time Bicycling 19.5 mc016-1.jpg mc016-2.jpg Running 6 r mc016-3.jpg
Running Speed = x
Cycling Speed = x + 9
19.5/x + 9 = 6/x
Cross multiply
19.5x = 6x + 54
19.5x - 6x = 54
13.5x = 54
x = 4
she runs 4 mph
Answer:
4 mph
Step-by-step explanation:
Is (-5, -1) a solution to y= -x + 4
Please help, I need the answer asap!
2 x 2 = 4 x 3 = 12
2 x 3 = 6 x 3 = 18
2 x 2 = 4 x 2 = 8 x 3 = 24 x 3 = 72
2x2 = 4 x 3 = 12 x 3 = 36
last one is the correct answer
The perimeter of the rectangle below is 86units . Find the length of side XY
A LIST OF 300 NUMBERS START AT 1.AFTER THAT EVERY NUMBER IS TRIPLED THE NUMBER WHICH IT HAD PRECEDES IT.THE 200TH NUMBER ON THE LIST IS
A:600
B:900
C:3 to the 199 power
D:3 to the 200 power
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −5 g(x)
0 −1 g(x) = 4x + 3
1 3
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
John draws a straight line in his notebook. What is the minimum number of points through which the line is drawn?
Final answer:
A straight line is determined by a minimum of two points. This is a fundamental concept in geometry and algebra, necessary for defining lines on any two-dimensional path or graph.
Explanation:
To determine the minimum number of points through which a straight line is drawn, we need to understand that a straight line is defined by only two points.
The minimum number of points through which a straight line is drawn is two. In geometry, a line extends infinitely in both directions but is determined by just two points. The concept of a line is fundamental in understanding various subjects such as algebra and geometry.
Can somebody please help me with this problem? Also please don't give me the final answer can you just like help me have an idea on how to do it. PLEASE AND THANK YOU
Fifty students in the fourth grade class listed their hair and eye colors in the table below: Brown hair Blonde hair Total Green eyes 16 12 28 Brown eyes 14 8 22 30 20 50 Are the events "green eyes" and "brown hair" independent?
The events "green eyes" and "brown hair" are not independent because the probability of a student having both green eyes and brown hair is not equal to the product of their individual probabilities.
Explanation:To determine whether the events "green eyes" and "brown hair" are independent, we need to look at the probabilities of each event occurring separately and together.
The probability of having green eyes (P(Green Eyes)) is the total number of students with green eyes divided by the total number of students, which is 28/50.
The probability of having brown hair (P(Brown Hair)) is the total number of students with brown hair divided by the total number of students, which is 30/50.
The probability of having both green eyes and brown hair (P(Green Eyes AND Brown Hair)) is the number of students with both green eyes and brown hair divided by the total number of students, which is 16/50.
Events A and B are independent if P(A and B) = P(A) * P(B). Using this formula, we can determine if the events are independent:
P(Green Eyes AND Brown Hair) = P(Green Eyes) * P(Brown Hair)
16/50 ≠ (28/50) * (30/50)
Since the probability of having both green eyes and brown hair does not equal the product of the probabilities of having green eyes and having brown hair, these events are not independent.
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What procedure can you use to convert a fraction to a decimal?
A.Numerator )denominator •100
B.numerator )denominator
C. denominator )numerator
D. Denominator )numerator •100
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 1/2 converted to a decimal is 0.5.
Explanation:To convert a fraction to a decimal, you use the method defined by option B: Numerator divided by Denominator (Numerator / Denominator). This will give you the decimal equivalent of the fraction. For example, if you have the fraction 1/2, you divide the numerator (1) by the denominator (2) to get 0.5, which is the decimal equivalent of the fraction 1/2.
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answer please!!!!!!!!!!!!!!!!!!
Maria is making a candle in the shape of a cylinder. She wants the candle to have a height of 3 cm and a radius of 2 cm. How much wax does Maria need?
volume = PI x r^2 x h
using 3.14 for pi
volume = 3.14 x 2^2 x 3
volume = 37.7 cubic cm of wax needed
Round answer as needed
Answer:
12Pi cm3
Step-by-step explanation:
On Tuesday, Pizza Hut sold 60 plain pizzas at $5 each; 20 meatball pizzas at $8 each; 25 Sicilian pizzas at $9 each; and 33 large crust supremes at $10 each. What were the total dollar sales for Pizza Hut on Tuesday? A. $790 B. $1,015 C. $1,115 D. $1,511
in the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with 80 degrees angle and the 60 degree angle. write and solve the equation to determine the measure of angle x
Plz Help me with this math problem
What is the LCM of 24a^3b and 36ab^2?
Answer:
The LCM of given expressions is [tex]72a^3b^2[/tex].
Step-by-step explanation:
The given expressions are
[tex]24a^3b[/tex]
[tex]36ab^2[/tex]
Find factor form of each expression.
[tex]24a^3b=2\times 2\times 2\times 3\times a\times a\times a\times b[/tex]
[tex]36ab^2=2\times 2\times 3\times 3\times a\times b\times b[/tex]
LCM is the product of all factors where common factors are considered only once.
[tex]LCM(24a^3b,36ab^2)=2\times 2\times 2\times 3\times 3\times a\times a\times a\times b\times b[/tex]
[tex]LCM(24a^3b,36ab^2)=72a^3b^2[/tex]
Therefore the LCM of given expressions is [tex]72a^3b^2[/tex].
Two systems of equations are shown below: System A System B 3x + 2y = 3 −x − 14y = 1 −2x − 8y = −1 −2x − 8y = −1 Which of the following statements is correct about the two systems of equations? The value of x for System B will be one−third of the value of x for System A because the coefficient of x in the first equation of System B is one third times the coefficient of x in the first equation of System A. The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. They will have the same solution because they represent the same lines when plotted on the coordinate axes. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.
The two linear equations represented in system A as :
3 x + 2 y =3 -------(1)
- 2 x - 8 y = -1 ------(2)
(1) × 2 + (2) × 3 gives
⇒ 6 x + 4 y - 6 x - 24 y = 6 -3
⇒ - 20 y = 3
⇒ y = [tex]\frac{-3}{20}[/tex]
Putting the value of y in equation (1), we get
[tex]3 x - \frac{6}{20}=3\\\\ 3 x= \frac{66}{20} \\\\ x=\frac{11}{10}[/tex]
Two linear equation represented in system B is:
3. -x - 14 y =1
4. - 2 x - 8 y = -1
-2 ×Equation (3) + Equation (4)=
2 x +28 y- 2 x - 8 y= -2 -1
⇒ 20 y = -3
⇒y =[tex]\frac{-3}{20}[/tex]
Putting the value of y in equation (3),we get
[tex]-x + \frac{42}{20}=1 \\\\ x=\frac{22}{20}=\frac{11}{10}[/tex]
As Two system , that is system (A) and System (B) has same solution.
By looking at all the options , i found that Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.
Answer:
(D)
Step-by-step explanation:
Two linear equations by system A is given as:
[tex]3x+2y=3[/tex] (1)
[tex]-2x-8y=-1[/tex] (2)
Multiply equation (1) with 2 and equation (2) with 3 and then adding, we get
[tex]6x+4 y-6x-24y=6-3[/tex]
[tex]-20y=3[/tex]
[tex]y=\frac{-3}{20}[/tex]
Putting the value of y in equation (1), we get
[tex]3x-\frac{6}{20}=3[/tex]
[tex]3x=\frac{66}{20}[/tex]
[tex]x=\frac{11}{10}[/tex]
Two linear equations by system B is given as:
[tex]-x-14y=1[/tex] (3)
[tex]-2x-8y=-1[/tex] (4)
Multiply equation (3) with -2 and adding equation (4), we get
[tex]2x+28y-2x-8y=-2-1[/tex]
[tex]20y=-3[/tex]
[tex]y=\frac{-3}{20}[/tex]
Putting the value of y in equation (3),we get
[tex]-x+\frac{42}{20}=1[/tex]
[tex]x=\frac{11}{10}[/tex]
As Two system , that is system (A) and System (B) has same solution.
Thus, Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.
What is the measure of a base angle of an isosceles triangle if its vertex angle measures 40°?
a) 70°
b) 65°
c) 140°
d) 75°
Answer:
The Answer Is A. edge 2020
Step-by-step explanation:
i have no clue what to do please help