in last 20 years, 238 couples have divorced out of a random sample of 500 couples in a certain city. find a 95% confidence interval for the rate of couples who divorced in that city. find the upper bound of the confidence interval (round off to second decimal place).
The upper bound of the confidence interval is 0.52
What is confidence interval?
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
Out of 500 couples in a given city, 238 couples had divorced in the past 20 years. As a result, the sample proportion is calculated as follows:
[tex]P=238/500 = 0.476[/tex]
As a result, the following 95% confidence interval is calculated for the city's divorce rate: [tex]P +(Z_{a}*(\sqrt{\frac{P(1-P)}{y} } )[/tex]
[tex]Z_{a}= 1.96[/tex]
the upper bound of confidence interval = 0.0438 + 0.476
= 0.52
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908 × 65 please help me with this question
Answer:
Step-by-step explanation:
59,020
Interest Earned over One Year
Answer: $300,000
Step-by-step explanation:
Help please.................
The solution to the expression ( √7 - √2 )² will be - 9 - 2√14. The value of the second part is 2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is ( √7 - √2 )². The expression will be solved as below,
E = ( √7 - √2 )²
E = (√7)² + (√2)² - 2 x √7 x √2
E = 7 + 2 - 2√14
E = 9 - 2√14
The second part will be calculated as,
2/5√(25x3)+(2-√(2x2x6)
2/5 x 5√3 + 2 - 2√3
2√3 + 2 - 2√3
2
The value of the third part will be calculated as,
[tex]\dfrac{(2+\sqrt{2})(\sqrt(10-\sqrt{5}}{(15-10\sqrt{2}}[/tex]
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hurry please!! - question on attached image
Answer:
the answer is y=2x+3 hope this helps
ou are offered a free play at the following game: ten balls are numbered 1 through 10. three are selected at random (each combination equally likely). before balls are drawn, players try to guess which three numbers are drawn by filling out a ticket. neither the order that the player selects the numbers nor the order in which the balls are drawn matters. how many outcomes are in the sample space for this experim
The outcome in sample space is equal to the no. of ways of selecting 3 balls at random from 10 distinct balls. So, number of outcomes in sample space = ¹⁰C₃.
Permutation:
Permutations are different ways of arranging objects in a particular order. This can also be expressed as rearranging the elements in linear order of an already ordered set. The symbol are used to denote the number of permutations of n distinct objects obtained for each r. Block bus, train and plane timetables, postcode and phone number assignments. These are some situations where permutations are used.
Example: There are 5 chairs and 3 people need to sit on them. There are 5 ways to place the first person. 2nd person 4 seats, 3rd person 3 seats. So to find the number of ways to place her 3 on 5 chairs, multiply these ways. Make 5×4×3 streets. So we can do it 60 ways. 5 × 4 × 3 is written as (5!) / (2!) (or) (5!) / (5 - 3).
Combination:A combination is a selection of elements from a set with different members, so the order of selection does not matter (unlike a permutation). For example, if he is given three fruits, such as apples, oranges, and pears, he has three binary combinations that he can draw from this set. An apple and a pear. apples and oranges. Or pear and orange. More formally, a k-combination of a set S is a subset of the k distinct elements of S. Two combinations are identical only if each combination has the same members.
According to the Question:
The outcome in sample space is equal to the no. of ways of selecting 3 balls at random from 10 distinct balls. So, number of outcomes in sample space = ¹⁰C₃.
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The school is having a fundraiser where each rose sold makes $1.25 in profit.
The school has to pay a flat shipping
cost of 50. How many roses must be
sold to earn a profit of $1000?
Answer: 800
Step-by-step explanation: 1.25$ x 800 is 1000
Answer:
840
Step-by-step explanation:
$1000+$50=$1050
$1050/$1.25=840
Answer=840
Liam has a points card for a movie theater.
• He receives 50 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 160 points for a free movie ticket.
Write and solve an inequality which can be used to determine , the number of visits
Liam can make to earn his first free movie ticket.
Answer:
x >= 9.
Step-by-step explanation:
To earn a free movie ticket, Liam needs at least 160 points. He already has 50 points from signing up, so he needs 160 - 50 = <<160-50=110>>110 more points.
Each visit to the movie theater earns Liam 12.5 points, so the inequality representing the number of visits he needs to make is:
12.5 * x >= 110
To solve this inequality, we need to divide both sides by 12.5:
12.5 * x / 12.5 >= 110 / 12.5
This simplifies to:
x >= 8.8
Thus, Liam needs to make at least 9 visits to the movie theater to earn his first free movie ticket.
Therefore, the solution to the inequality is x >= 9.
Answer:
9 visits
Step-by-step explanation:
12.5 x 9 = 112.5
112.5 + 50 = 162.5
1. The line parallel to y=2/3x+1
that passes through the point (3, 6)
The equation of the line is y = (2/3)x + 4
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line.
y = m(1)x + c
The line is parallel to y = (2/3)x + 1
It is in the form of y = m(2)x + c
This means,
m(1) = m(2)
m(1) = 2/3
Now,
The line passes through the point (3, 6).
(3, 6) = (x, y)
y = mx + c
6 = (2/3)3 + c
6 = 2 + c
c = 6 - 2
c = 4
The equation of the line.
y = (2/3)x + 4
Thus,
The equation of the line is y = (2/3)x + 4
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Lauren and Hazel's families provide money for their school lunch accounts. Hazel starts with $200 in her account. She spends $30 each week on lunches. Lauren starts with $50 in her account and does not spend any of it. Her family adds $20 each week to her account. Write an equation to represent how much money (y) Hazel has in her account after a number of weeks (x).
5. Lenore had a coupon
for 50 cents off each box
of cookies. She bought two
boxes that were $4.50
each and 4 cans of soup.
If her total bill was $16.00,
how much were the cans
of soup?
Answer: $8 for 4 cans of soup!
Step-by-step explanation:
We know that a box is $4.50 each, but Lenore had a coupon off 50 cents each, so the price of the box is $4
Lenore bought 2 box
4 times 2 = $8
16 - 8 =8
So the 4 cans of soup cost is $8 or $2 each can of soup
PLEASE HELP I NEED IT ASAP
Edgar wants to get ice cream for dessert. He looks up the prices at The Ice Cream Factory and Main Street Scoops. The Ice Cream Factory charges $1.75 per scoop and a $0.75 fee for unlimited toppings. Main Street Scoops charges $2 per scoop and a $0.25 fee for unlimited toppings. Which inequality can be used to find when Main Street Scoops would be the cheaper option?
A. 1.75x + 0.75 < 2x + 0.25
B. 1.75x + 0.75 > 2x + 0.25
C. 1.85 + 0.75x < 2 + 0.25x
D. 1.75x + 0.75 ≥ 2x + 0.25
1.75x + 0.75 < 2x + 0.25 inequality can be used to find when Main Street Scoops would be the cheaper option.
How do you explain inequality?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different individuals, it is prone to misunderstanding in public discourse. However, certain distinctions are universal.Related ideas include lifetime inequality (the distribution of incomes over a person's lifetime), inequality of wealth (the distribution of wealth across households or individuals at a particular point in time), and inequality of opportunity (the effects on income of factors that people cannot control, like.1.75x + 0.75 < 2x + 0.25 inequality can be used to find when Main Street Scoops would be the cheaper option.
1.75x + 0.75 < 2x + 0.25
1.75x + 0.75 -0.75 < 2x + 0.25 -0.75.
x< - 0.0068
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Translate a point (x,y) 3 units left and 5 units up. Then translate the image 5 units right and 2 units up. What are the coordinates of the point after the translations?
Answer:
[tex](x+2, y+7)[/tex]
Step-by-step explanation:
[tex](x,y) \longrightarrow (x-3, y+5) \longrightarrow (x+2, y+7)[/tex]
What additional information could you use to show that δstu ≅ δvtu using sas? check all that apply. uv = 14 ft and m∠tuv = 45° tu = 26 ft m∠stu = 37° and m∠vtu = 37° st = 20 ft, uv = 14 ft, and m∠ust = 98° m∠ust = 98° and m ∠tuv = 45°
Options A and D are both correct. UV = 14 feet and mTUV = 45 degrees D. ST = 20 feet, UV = 14 feet, and mUST = 98 degrees by using congruence of triangles.
What is congruence triangle?Two triangles are congruent if their corresponding sides are the same length and their corresponding angles are the same size.
What exactly is SAS congruence?According to the SAS criterion for triangle congruence, two triangles are congruent if they have two pairs of congruent sides and the included angle (the one between the congruent sides) in one triangle is congruent to the included angle in the other triangle.
Given
See the attachment for the triangle.
What evidence do you have?
SAS is used by STU and VTU.
To demonstrate their resemblance, we must examine the corresponding sides and angles of both triangles.
To begin, UST must equal UVT.
As a result, UST=UVT=98⁰.
Then, UV must equal US.
So:
UV = US = 14⁰
Furthermore, ST must equal VT.
So:
Furthermore, ST must equal VT.
As a result, ST = VT = 200.
Finally, TUV must be equal to TUS.
So: TUV = TUS = 450
Options A and D are both correct. UV = 14 feet and mTUV = 45 degrees D. ST = 20 feet, UV = 14 feet, and mUST = 98 degrees.
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A set of magical wand prices are normally distributed with a mean of 505050 dollars and a standard deviation of 444 dollars. A blackthorn wand has a price of 45. 2045. 2045, point, 20 dollars. What proportion of wand prices are lower than the price of the blackthorn wand?.
The proportion of wand prices as per normal distribution are lower than the price of the blackthorn wand is equal to 0.1151.
As given in the question,
Mean of the set of magical wand price 'μ' = 50dollars
Standard deviation 'σ' for normal distribution = 4 dollars
Price of blackthorn wand 'X' = 45.20 dollars
z-score = (x - μ)/σ
Proportion of wand prices be 'x'
P(x < X)
=P( x< 45.20)
=P [(x - μ)/σ < (X - μ )/σ]
=P[ z < (45.20 - 50)/4]
=P( z < -1.2 )
= 0.11507
=0.1151
Therefore, the proportion of the wand prices which are lower than the price of blackthorn wand using normal distribution is equal to 0.1151.
The complete question is:
A set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. A blackthor wand has a price of 45.20 dollars. What proportion of wand prices are lower than the price of the blackthorn wand? You may round your answer to four decimal places.
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a biologist had mice and rats run through a maze and recorded the number that finished the maze successfully and the number that did not. the table below shows the results of the study: mice rats finished: 22 25 did not finish: 26 12 suppose we use this data along with a .05 significance level to test the claim that the rodent type and the success of finishing the maze are not related. what can we conclude?
Answer:3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
Step-by-step explanation:For each time that the rat goes through the maze, there are only two possible outcomes. Either he fails it, or he succeds. The trials are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution:The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.In which is the number of different combinations of x objects from a set of n elements, given by the following formula.And p is the probability of X happening.
What is the probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt?Missing on the first six, each with 70% probability(P(X = 6) when p = 0.7, n = 6).Succeeding on the 7th attempt, with p = 0.3. So 3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
Lyme disease is an infection caused by bacteria. A test for Lyme disease may be affected by other medications and medical conditions. The testing results are summarized in the table.
Tested positive Tested negative Row Totals
Has Lyme disease 53% 17% 70%
Does not have Lyme disease12% 18% 30%
Column Totals 65% 35% 100%
What percentage of all patients who took the test had a true negative result?
35%
30%
18%
12%
Answer:
its 12%
Step-by-step explanation:
i took the test and got it right
Answer: 17%
Step-by-step explanation:
Which of these relations is a function?
last question!!!!!!!!
Answer: the top left is a function
How do you get 1/2 of a number?
Answer: to get 1/2 of a number, simply divide it by 2
Step-by-step explanation: the denominator, or the second digit after the numerator, is the one you use to divide a number. for example 1/3 of 33 = 11, as you divide 33 by 3, or 1/2 of 500 = 250.
The functions f(x) = x and h(x) = f(x + 7) are graphed on the same coordinate grid. Which
statement below is true? (select one)
a. The graph of f is steeper than the graph of h.
b. The graph of h is steeper than the graph of f.
C. To create h, f is translated 7 units to the right.
d. To create h, f is translated 7 units to the left.
Answer: d.
Step-by-step explanation:
To create h, f is translated seven units to the left.
Identify the measure of angle EHF:
Answer:
63
Step-by-step explanation:
h=90
90-27=63
Which description of a figure and its image match the transformation described by (x,y) → (-x+1,y+1)
Answer:
the figue which is translated one unit up and one unit to the right
Step-by-step explanation:
Ann work in a upermarket for $10. 00 an hour. If her pay i increaed to $12. 00, then what i her percent increae in pay?
Her pay will increase by 20% as a result of the percentage being the difference from the original.
What is Percentage ?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 78% grade if you answered 78 of 100 questions correctly on a test (78/100).
According to the given Information
Another name for the percentage is the signifying hundredths. As a result, 2% is equal to two hundredths, or 2%=2/100=0.02.
According to what has been stated,
Original price: $10
Pay increase = $12
% growth = (10 x 100 - (12 - 10))
⇒ 20%
Hence
Her pay will increase by 20% as a result of the percentage being the difference from the original.
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Help with question 13
The amount of stock that is wasted is given as follows:
1 - 21/64 inches.
How to obtain the amount of stock wasted?The total amount of stock is given as follows:
9 - 7/16 inches long = 144/16 - 7/16 = 137/16 inches long.
The total amount of stock used for the two punches is given by the sum of the two amounts, as follows:
4 - 1/64 + 4 - 3/32 = 8 - 7/64 = 505/64
Then the amount wasted is given by the subtraction of the total amount by the amount used, as follows:
137/16 - 505/64 = 548/64 - 505/64 = 43/64.
The decimal of this is of:
43/64 = 0.671875.
Hence the amount wasted is of:
1 - 43/64 = 64/64 - 43/64 = 21/64
Meaning that the third option is correct.
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Find the value of x.
x=
Find the vector v with the given magnitude and the same direction as u. Magnitude ||v|| = 51 Direction u = ⟨-8,15
The vector [v] whose direction is same as that of vector [u] is given as -
[v] = -24i + 45j.
What is an expression? What is a expression? What is a mathematical equation? What is vector?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A vector quantity is a quantity that has both magnitude and direction.
We have the a vector [v] with the given magnitude and the same direction as u.
We can write vector [u] as -
[u] = - 8i + 15j
Unit vector {u} along vector [u] -
{u} = [u] / |u|
{u} = (- 8i + 15j)/17
We can write vector [v] as -
[v] = 51 x (- 8i + 15j)/17
[v] = 3(- 8i + 15j)
[v] = -24i + 45j
Therefore, the vector [v] is given by [v] = - 24i + 45j.
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I need help with this question
Answer:b
Step-by-step explanation:
Is the coordinates of a point are 3 and 4?
The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)
The coordinates of point A = (-5, -4),
The coordinates of the point B = (-3, 3)
Let the point at the distance 3/4 from A to B = P
The coordinates of point 3/4 from A to B = P
At the x-coordinate, the distance from B to A is = -3-(-5) = 2 units.
At the y-coordinate, the distance from B to A is = 3-(-4) = 7 units.
Hence, the coordinates of P = (-5 + (3/4×(x-coordinate), -4 + 3/4×(y-coordinate)
P = (-5 + (3/4×(2), -4 + 3/4×(7))
P = (-3.5, 1.25)
Hence, the coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25).
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The complete question is -
What are the coordinates of the point 3/4 of the way from A to B?
Bill jumps off a diving board that is 12 feet above the surface of a swimming pool. Jumping upward and outward, he reaches a maximum height of 18 feet above the surface of the water when he has jumped outward 4 feet. Find f(x) an equation for his parabolic path and when he hits the water, how far out as he reached, to the nearest tenth of a foot.
The equation of the parabola is y = -0.25(x - 4)² + 16 and he reaches 12 feet outwards when he hits the water
How to determine the equation of the parabola?From the question, we have the following parameters that can be used in our computation:
Initial position = 12 feet above the surface
Maximum height = 18 feet at 4 feet outward
These parameters mean that
(h, k) = (4, 16) -- vertex
(x, y) = (0, 12)
A parabola is represented as
y = a(x - h)² + k
So, we have
y = a(x - 4)² + 16
Also, we have
12 = a(0 - 4)² + 16
This gives
12 = 16a + 16
So, we have
16a = -4
Divide
a = -0.25
Substitute a = -0.25 in y = a(x - 4)² + 16
y = -0.25(x - 4)² + 16
When it hits water, y = 0
So, we have
-0.25(x - 4)² + 16 = 0
This gives
0.25(x - 4)² = 16
So, we have
(x - 4)² = 64
Take square roots
x - 4 = 8
So, we have
x = 12
Hence, it is 12 feet outwards
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