The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). The y-coordinate is the value of b in the slope-intercept form. The Slope is - ⅖.
What is the Slope and Y-intercept of a Line?Y-intercept = (0, 4), where b = 4
Given the linear equation in standard form, 2x + 5y = 20, where A = 2, B = 5, and C = 20:
Start by transforming the standard equation into its slope-intercept form, y = mx + b, where m = slope, and b = y-intercept.
Subtract 2x from both sides:
2x -2x + 5y = - 2x + 20
5y = -2x + 20
Divide both sides by 5 to isolate y:
y = - ⅖x + 4 ⇒ This is the slope-intercept form where the slope, m = -⅖, and the y-intercept, b = 4. The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). The y-coordinate is the value of b in the slope-intercept form. Therefore, the y-intercept is (0, 4).
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onsider an economy with three industries: I1, I2, and I3. Consumer demand is currently
‚ 100 units from I1,
‚ 75 units from I2,
‚ 200 units from I3.
Also suppose that
‚ for every unit that I1 produces, it needs 0.5 units from I2 and 0.1 units from I3;
‚ for every unit that I2 produces, it needs 0.25 units from I1 and 0.2 units from I3;
‚ for every unit that I3 produces, it needs 0.3 units from I1 and 0.4 units from I2
Set up a system of equations
We have the following system of equations:
x₁ + 0.5x₂ + 0.1x₃ = 100
0.25x₁ + x₂ + 0.2x₃ = 75
0.3x₁ + 0.4x₂ + x₃ = 200
Define the term equation?Statement gives the equality of different mathematical expressions is called as an equation.
Let x₁, x₂, and x₃ be the outputs of I₁, I₂, and I₃, respectively. Then the total production must satisfy the following system of equations:
For I₁:
I₁ itself produces x₁ unitsIt requires 0.5 units of I₂ for every unit, so it requires 0.5x₂ unitsIt requires 0.1 units of I₃ for every unit, so it requires 0.1x₃ unitsTherefore, total demand from I₁ is x₁ + 0.5x₂ + 0.1x₃ = 100For I₂:
I₂ itself produces x₂ unitsIt requires 0.25 units of I₁ for every unit, so it requires 0.25x₁ unitsIt requires 0.2 units of I₃ for every unit , so it requires 0.2x₃ unitsTherefore, total demand from I₂ is x₂ + 0.25x₁ + 0.2x₃ = 75For I3:
I₃ itself produces x₃ unitsIt requires 0.3 units of I₁ for every unit, so it requires 0.3x₁ unitsIt requires 0.4 units of I₂ for every unit, so it requires 0.4x₂ unitsTherefore, total demand from I₃ is x₃ + 0.3x₁ + 0.4x₂ = 200Therefore, the system equations are:
x₁ + 0.5x₂ + 0.1x₃ = 100
0.25x₁ + x₂ + 0.2x₃ = 75
0.3x₁ + 0.4x₂ + x₃ = 200
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A blouse originally $29..99 is 15% off. Marlene has a coupon for an additional
20% percent off. What is the new price of the blouse before tax?
Answer:
20.39
Step-by-step explanation:
15% of 29.99 is 4.4985
so
29.99-4.5
=
25.49
subtract the 20%
20% of 25.49
=
5.1
lastly,
25.49-5.1
=
20.39
Formalize the following in terms of atomic propositions r, b, and w, first making clear how they correspond to the
English text. (a) Berries are ripe along the path, but rabbits have not been seen in the area.
(b) Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
(c) If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
(d) It is not safe to walk along the path, but rabbits have not been seen in the area and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to
pave been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area and berries are ripe along the path.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.
Given information and corresponding atomic propositions:
We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:
r: Rabbits have been seen in the area.
b: Berries are ripe along the path.
w: Walking on the path is safe.
Now, let us formalize each of the given statements in terms of these atomic propositions:
a) Berries are ripe along the path, but rabbits have not been seen in the area.
b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.
The formalizations in terms of atomic propositions are:
a) b ∧ ¬r.b) ¬r ∧ w ∧
b.c) (b → w) ∧ (¬r → w).
d) ¬w ∧ ¬r ∧
b.e) (¬r ∧ ¬b) → w.b ∧
Berries are ripe along the path, but rabbits have not been seen in the area.
This is formalized by using the ∧(logical and) operator.
(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
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Its not a quiz/test its homework thats due in a bit :)
Just to clear any misunderstandings that might arise
Answer:
MN = 25
Step-by-step explanation:
If LN=45, then the addition of both quantities will be 45.
LN = 3x + 2 + x + 19
3x + 2 + x + 19 = 45
4x + 21 = 45
4x = 45 - 21 = 24
x = 6
Now that we found the value of "x", we can find the lenght of MN
MN = x + 19
MN = 6 + 19
MN = 25
Hope it was helpful ;)
Answer: MN = 25
Step-by-step explanation:
Since the length is already given we just add the equations equal to it.
45 = 3x + 2 + x + 19 Combine like terms
45 = 4x + 21 Subtract 21 from both sides
24 = 4x Divide by 4
x = 6
Now we plug x into the equation needed.
X + 19
6 + 19 = 25
a circle in the coordinate plane passes through points (-3,-2) and (1,4). what is the smallest possible area of that circle?
The smallest possible area of the circle with the points (-3,-2) and (1,4) is 13π.
Given, the endpoints of the circle are given:
(-3,-2) = (x₁,y₁)
(1,4) = (x₂,y₂)
The circle with the smallest possible area that passes through the points (-3, -2) and (1, 4) is a circle with a diameter whose endpoints are these two points.
we are asked to determine the area of the circle = ?
first calculate the distance between the points:
distance = √(x₁-x₂)²+(y₁-y₂)²
d = √(-3-1)²+(-2-4)²
d = √(-4)² + (-6)²
d = √16+36
d = √52
d = 2√13
Thus, the radius has a length of r = √13,
and the area of the circle is A = π x (√13)²
= 13π.
Hence we get the area of the circle as 13π..
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Four friends took a road trip that lasted 50 hours round trip. Denny drove five times as long as Connor, while Pat and Seth drove the same amount of time. Connor drove half as long as Pat. How long did Denny drive?
Answer:
Denny drove for 25 hours
Step-by-step explanation:
Here, we want to calculate the amount of time Denny drove
Let the time Connor drove be c
Denny drove 5 times as this which is 5 * c = 5c
Conor drove half as long as Pat
So this means that Pat drove 2 times Conor = 2c
Seth is same as Pat which is also 2c
Adding all gives 50
c + 5c + 2c + 2c = 50
10c = 50
c = 50/10
c = 5 hours
Denny = 5 * c
= 5 * 5 = 25 hours
Set g is the set of positive integers divisible by 4, and set f is the set of perfect squares. list the first 5 elements of set h, which contains numbers in g that are also elements of f.
The first 5 elements of set H, which contains numbers in G that are also elements of F are {4, 16, 36, 64, 100}.
What is intersection of sets?The intersection of two sets has been the set that includes each of the elements which are shared by both sets.
The symbol for set intersection is "∩''. The intersection, A ∩ B (read as A intersecting B) lists all the items that really are present in both sets and constitute the common elements of A and B for any two sets A and B.
Now, according to the question;
Set G is the set of positive integers divisible by 4, and
Set F is the set of perfect squares;
Then,
G = {4; 8; 12; 16; 20; 24; 28; 32; 36; 40; 44; 48; 52; 56; 60; 64; 68; 72; 76; 80; 84; 88; 92; 96; 100; 104; ...}
F = {1; 4; 9; 16; 25; 36; 49; 64; 81; 100; ...}
So, by the intersection of the sets;
G ∩ F - a intersection of the two sets, that is, what numbers are present in both sets at the same time.
G ∩ F = {4; 16; 36; 64; 100}
Therefore, The first 5 elements of set H, which have the same numbers in G as elements of F are {4, 16, 36, 64, 100}.
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find the circumference, rounding your answer to 1d.p.
Answer:
Can't see the attached image
Step-by-step explanation:
Post another question and make sure it has the image on it :)
A shelf is supported with brackets as pictured in the diagram below. What is the
width of the shelf?
A 14 in.
B 16 in.
C 12 in.
D 10 in.
The width of the shelf is 10 inches. The correct option is D.
Describe Right Angled Triangle?A right-angled triangle is a triangle that has one angle measuring 90 degrees, which is known as the right angle. The sides adjacent to the right angle are known as the legs of the triangle, while the side opposite the right angle is known as the hypotenuse.
The Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, is one of the fundamental theorems of mathematics and is used extensively in various fields.
Let's call the width of the shelf "x". According to the given diagram, we have a right triangle where the base is x, the perpendicular is 10 inches, and the angle between the hypotenuse and the perpendicular is 45 degrees.
Using trigonometric ratios, we know that:
tan(45) = perpendicular/hypotenuse
tan(45) = 10/x
Since tan(45) is equal to 1, we can simplify the equation to:
1 = 10/x
Solving for x, we get:
x = 10
Therefore, the width of the shelf is 10 inches.
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You measure 31 randomly selected textbooks' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 10 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.
Give your answers as decimals, to two places.
The 95% confidence interval for the true population mean textbook weight is (61.68, 66.32) ounces.
To construct a confidence interval, we can use the formula:
Confidence Interval = sample mean ± (critical value) * (standard deviation / √sample size)
In this case, the sample mean weight is 64 ounces, and the population standard deviation is 10 ounces. Since the sample size is 31, we need to determine the critical value for a 95% confidence level.
The critical value can be found using a standard normal distribution table or a statistical calculator. For a 95% confidence level, the critical value is approximately 1.96.
Plugging the values into the formula, we have:
Confidence Interval = 64 ± (1.96) * (10 / √31)
Calculating the expression inside the parentheses:
10 / √31 ≈ 1.79
Multiplying 1.96 by 1.79:
1.96 * 1.79 ≈ 3.51
Finally, we can construct the confidence interval:
64 - 3.51 ≈ 61.68
64 + 3.51 ≈ 66.32
Therefore, the 95% confidence interval for the true population mean textbook weight is approximately (61.68, 66.32) ounces.
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Please help!
A building is constructed on top of a cliff that is 300 meters high. A person standing on level ground below the cliff observes that the angle of elevation to the top of the building is 72° and the angle of elevation to the top of the cliff is 63°.
a. How far away is the person from the base of the cliff?
b. What is the building’s height?
The distance from the person to the base of the cliff is 269.78 meters.
The height of the building from the base of the cliff is 829.37 meters
The situation forms right angle triangle.
The building is constructed on top the cliff that is 300 meters high.
Right angle triangle:Right angle triangle has one of its sides as 90 degrees. Therefore, the sides can be found using trigonometric ratios.
The height of the building from the cliff is 300m. let's find the hypotenuse side of the angle of elevation formed to the cliff.
Using sin rule,
300 / sin (72 - 63) = y / sin (180 - 162)
300 / sin 9 = y / sin 18
300 sin 18 = y sin 9
y = 300 sin 18 / sin 9
y = 92.7050983125 / 0.156
y = 594.230769231
Therefore, how far the person to the base of the cliff can be calculated as follows;
cos 63 = adjacent / hypotenuse
cos 63 = x / 594.2307
x = 594.2307 cos 63
x = 269.775092454
x = 269.78 meters
Therefore, the distance from the person to the base of the cliff is 269.78 meters.
height of the cliff / 269.78 = tan 63
height of cliff = 269.78 tan 63
height of cliff = 529.37493165
height of cliff = 529.37
The height of the building = 300 + 529.37 = 829.37493165 = 829.37 meters
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2. Simplify the expression. (x3)(x7)²
1
x18
x14
x126
Step-by-step explanation:
\( = ( {x}^{3} ) { ({x}^{7} )}^{2} \)
\( = {x}^{3} \times {x}^{7 \times 2} \)
\( = {x}^{3} \times {x}^{14} \)
\( = {x}^{3 + 14} \)
\( = {x}^{17} \)
Anita está asiendo pan de calabaza y tiene medio galón de masa ella planea verter la masa en un molde de vidrio con longitud de 9 pulgadas un ancho de 4 y una profundidad de cuatro determine si toda la masa cabra en el sartén
All the batter would fit into the pan as it has more volume than half a gallon.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
We know, One gallon is equal to 231 cubic inches.
Therefore, Half a gallon is equal to 231/2 cubic inches.
The volume of the pan is (9×4×4) cubic inches.
= 144 cubic inches.
Now, 144 > 231/2, so it would fit.
Q. Anita is baking pumpkin bread and has a half gallon of batter. She plans to pour the batter into a glass pan with a length of 9 inches, a width of 4 inches, and a depth of four. Determine if all the batter will fit in the pan.
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You find a slice of American cheese under a shelf in the garage. If the cheese has a shelf life of e t days, how old is the cheese you found if the slice was only 13.6% of the original size? 0.0386 after wa shelf life of e size?
The cheese slice you found in your garage is approximately 46.36 days old, based on the given decay rate and the percentage of its original size.
Let's start by denoting the initial size of the cheese slice as S, and the remaining size found as R. Given that the cheese slice is 13.6% of its original size, we can represent this as:
R = 0.136 * S
Now, let's consider the decay rate of the cheese, which is given as 0.0386. Assuming that the cheese decay follows exponential decay, we can write the formula for the decay as:
R = S * (1 - decay_rate) ^ t
Where 't' is the age of the cheese in days. We can now substitute the value of R in the decay formula:
0.136 * S = S * (1 - 0.0386) ^ t
Since we're interested in finding 't', we can simplify the equation by dividing both sides by S:
0.136 = (1 - 0.0386) ^ t
Now, to solve for 't', we can take the natural logarithm of both sides:
ln(0.136) = ln((1 - 0.0386) ^ t)
Using the logarithmic property, we get:
ln(0.136) = t * ln(1 - 0.0386)
Finally, divide both sides by ln(1 - 0.0386) to find 't':
t = ln(0.136) / ln(1 - 0.0386)
Using a calculator, we find that t ≈ 46.36 days.
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On the price is right, there is a game in which a bag is
filled with 3 strike chips and 5 numbers. let’s say that the
numbers in the bag are 0, 1, 3, 6, and 9. what is the probability of
selecting a strike chip or the number 1?
The probability of selecting a strike chip or the number 1 from the bag is 1/2 or 0.5.
The probability of selecting a strike chip or the number 1 from a bag that contains 3 strike chips and 5 numbers that are 0, 1, 3, 6, and 9 can be determined as follows:
Step 1: Determine the total number of chips in the bag.
There are 3 + 5 = 8 chips in the bag.
Step 2: Determine the number of chips that are either a strike chip or the number 1.
In the bag, there are 3 strike chips and 1 chip that is number 1.
Therefore, there are 3 + 1 = 4 chips that are either a strike chip or the number 1.
Step 3: Calculate the probability.
The probability of selecting a strike chip or the number 1 from the bag can be expressed as a fraction of the number of chips that are either a strike chip or the number 1 to the total number of chips in the bag.
This can be written as:
P (strike chip or 1) = 4/8
Simplifying the fraction gives
:P (strike chip or 1) = 1/2
Therefore, the probability of selecting a strike chip or the number 1 from the bag is 1/2 or 0.5.
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Help! (Solving quadratic equations by factoring)
m(m-3)=0
Answer:
m=0 and m=3
Step-by-step explanation:
there are two solutions
The table displays points please awnser the meadian for 10
Answer:520? for the mean?neareast answer and 75 for the median
Step-by-step explanation:
Two interior angles of a triangle each measure 34 degrees.What is the measure of the third interior triangle?
In a triangle with two interior angles that are both 34 degrees, the third interior angle is 112 degrees.
The measure of the third interior angle of a triangle can be found by subtracting the sum of the two given angles from 180 degrees.
In this case, if two interior angles of a triangle each measure 34 degrees, the measure of the third interior angle can be calculated as follows:
Finding the sum of the two given angles.
34 + 34 = 68 degrees
Subtracting the sum from 180 degrees.
180 - 68 = 112 degrees
Therefore, the measure of the third interior angle of the triangle is 112 degrees.
In conclusion, the third interior angle of a triangle has a measure of 112 degrees when the first two interior angles of the triangle each measure 34 degrees.
This can be determined by subtracting the sum of the given angles from 180 degrees, as the sum of the interior angles of a triangle is always 180 degrees.
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what’s the answer ???
The reasons for the steps are ;
step1 ; collect like terms
step2 : dividing both sides by 6
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
For example , in an equation 6x +5x = 3x + 24 , to find x in this equation we need to follow some steps;
First we collect like terms
6x +5x - 3x = 24
8x = 24
then we divide both sides by the coefficient of x
x = 24/8
x = 3
Similarly , solving 18 - 2x = 4x
collect like terms
18 = 4x +2x
18 = 6x
divide both sides by coefficient of x
x = 18/6 = 3
x = 3
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Select the correct answer from the options below. A box contains 3 blue socks, 8 black socks and 2 red socks. Find the probability that a sock selected at random is not black. A) 5/8 (B) 5/13 c) 3/8 (D) 8/14 E) I am unsure
The probability that a sock selected at random is not black is 5/13. Correct option is B.
To find the probability that a sock selected at random is not black, we need to calculate the ratio of the number of non-black socks to the total number of socks.
The total number of socks in the box is 3 (blue) + 8 (black) + 2 (red) = 13.
The number of non-black socks is 3 (blue) + 2 (red) = 5.
Therefore, the probability of selecting a non-black sock is 5/13.
The probability is typically expressed as a ratio or fraction, not as a decimal or percentage. The options (A), (B), (C), and (D) given in the question are expressed as fractions.
Comparing the calculated probability of 5/13 with the given options, we can see that the correct answer is (B) 5/13.
Therefore, the probability that a sock selected at random is not black is 5/13.
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Select the correct answer from the options below. A box contains 3 blue socks, 8 black socks and 2 red socks. Find the probability that a sock selected at random is not black. A) 5/8 (B) 5/13 c) 3/8 (D) 8/14
Question 4 of 10
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
□A. √2:√2
B. 15
□ C. √√√√5
□ D. 12
DE √3:3
OF. √2:√5
←PREVIOUS
SUBMIT
The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).
In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.
A. √2:√2
The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.
B. 15
This is a specific value and not a ratio. Therefore, option B is not applicable.
C. √√√√5
The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.
D. 12√3
This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.
E. √3:3
This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.
F. √2:√5
This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.
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Anna attends an art auction, and decides she’d like to buy a painting. She gives herself an upper limit of $3000 when starting the bidding process. The second-highest bidder offers $2200, and so Anna wins the painting by offering $2300. What is Anna’s consumer surplus?
$0
$700
$2200
$2300
$3000
Answer:
$700
Step-by-step explanation:
She's willing to pay up to $3000.
She pays only $2300.
consumer surplus = $3000 - $2300 = $700
Answer:
$700
Step-by-step explanation:
Anna's consumer surplus is the difference between her willingness to pay and the price she actually paid, which is $3000 - $2300 = $700.
Therefore, the answer is $700.
Write down the domain and range of: y = 2*
The domain is (-∝, ∝) and the range is y > 0
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
y = 2^x
The domain of the function is the set of all real numbers
This is so because there is no restriction on the input values
The range of the function is the set of positive real numbers
Since any positive number can be obtained by raising 2 to a power, and the function is never negative or zero.
We can write the range as y > 0.
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Which angle is vertical to DEA
The angle vertically opposite to ∠DEA is ∠BEC.
How to find vertical angles?Vertical angles are angles that are opposite of each other when two lines cross.
In other words, when line segment intersect each other, vertical angles are formed.
Vertical angles are congruent to each other.
Therefore, the angle vertical to angle DEA can be found as follows:
∠DEA is vertically opposite to ∠BEC
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Round 19.8 to 1 significant figure
Answer:
20
Step-by-step explanation:
the 0 is not significant since it is not sandwiched between 2 sigfigs and is not the last digit after a decimal
(a+b)^2hiiiiiiiiiiiiii
Answer:
a^2+2ab+b^2 is the formula
find the support and confidence of this transaction
A = I2, B = I3
Let 1 = {1,, I, I...... 1.} be a set of items, where I, denotes an item ID. Consider the transaction database D, defined in the table below: Transaction ID List of Items in the Transaction T₂ I, I,
For confidence interval: support of the association rule A to B is 0.5 and the confidence of the association rule A to B is 0.5.
For Support and confidence of the association rule A - B
To determine the support and the confidence of the association rule A → B, where A = {1, }, B = {1}, we use the formulas given below:
Support(A → B) = frequency of (A, B) / N
Confidence(A → B) = frequency of (A, B) / frequency of A
where N is the number of transactions in the database.
To find the frequency of (A, B) and the frequency of A.
Thus Frequency of (A, B) = 1
Since there is only one transaction in the database where both A and B occur, the frequency of (A, B) is 1.
Frequency of A = 2
The itemset {1, } occurs in two transactions T₁ and T₂.
Hence, the frequency of A is 2.
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16-?=2+6 solve for the missing number
Answer:
8
Step-by-step explanation:
trust
Answer:
8
Step-by-step explanation:
16-?=2+6
First, we add the right side .
16-?=8
Now that it's easier to solve, we can figure out you need to subtract 8 from 16 to get 8.
16-8=8
Solve for x in the equation x squared minus 12 x 36 = 90.
Answer:
x = ±3√58
Step-by-step explanation:
Given
x² - (12 x 36) = 90Solving
x² - 432 = 90x² = 522x² = 9 x 58x = ±3√58Answer:
\(x =\) ± \(22.85\)
Step-by-step explanation:
Step 1: Multiply 12 * 36
\(x^2 - (12 * 36) = 90\)
\(x^2 - 432 = 90\)
Step 2: Add 432 to both sides
\(x^2 - 432 + 432 = 90 + 432\)
\(x^2 = 522\)
Step 3: Square root both sides
\(\sqrt{x^2} = \sqrt{522}\)
\(x =\) ± \(22.85\)
Answer: \(x =\) ± \(22.85\)
a researcher found that out of 100 boys, 56 had dogs in their household, while only 43 out of 100 girls did. she plans to compute a confidence interval for the difference in proportions. compute the standard error to use in this formula.
The standard error to be used in the formula of a confidence interval for the difference in proportions is 0.07.
The estimated standard deviation of a statistical sample population is known as the standard error (SE) of a statistic.
By utilising standard deviation, the standard error is a statistical concept that assesses how well a sample distribution represents a population. In statistics, the difference between a sample mean and the population's actual mean is known as the standard error of the mean.
The standard error's primary function is to indicate how divergent the population mean will be from the sample mean. Because it aids in determining how well the standard data reflect the entire population, the standard error is significant. We may readily draw reliable conclusions by calculating the standard error in order to determine how representative our sample is of our population.
56 out of 100 boys = P1 = 0.56
43 out of 100 girls = P2 = 0.43
The formula for standard is given by,
\(S.E=\sqrt{\frac{P_1(1-P_1)}{n1} +\frac{P_2(1-P_2)}{n2} } \\=\sqrt{\frac{0.56(1-0.56)}{100} +\frac{0.43(1-0.43)}{100} } \\\\= \sqrt{\frac{0.2464}{100} +\frac{0.2451}{100} } \\\\=\sqrt{0.004915} \\=0.07\)
Therefore, the standard error is 0.07.
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