Nominal scales categorize data without order. Ordinal scales categorize data with order. Interval scales have equal units, but no true zero. Ratio scales have equal units and a true zero.
National sport league: nominalSnowfall in inches: ratioBlood pressure: ratioYear of birth: ratioBMI: ratioEthnicity of students: nominalDaily carbohydrate intake in grams: ratioJersey number of a volleyball player: ordinalMilitary rank: ordinalTemperature in C: intervalNumber of goals scored by a soccer team: ratioTemperature in Kelvin: intervalZip code: nominalNCAA Division: nominalNumber of Whataburgers consumed: ratioLearn more about ratio :
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What is the value of x?
Enter your answer in the box.
x =
The angle x in the heptagon is 98 degrees.
How to find the interior angles of a polygon?The polygon above has 7 sides. Therefore, the name of the polygon is heptagon. Therefore, the sum of interior angles of a polygon can be represented as follows:
sum of interior angles of a polygon = 180(n - 2)
where
n = number of sidesTherefore,
sum of interior angles of the heptagon = 180(7- 2)
sum of interior angles of the heptagon = 180(5)
sum of interior angles of the heptagon = 900 degrees
Hence, let's find x as follows:
122 + 146 + 142 + 140 + 110 + 142 + x = 900
x = 900 - 802
x = 98 degrees
Hence,
x = 98 degrees
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Ben originally filled out 8 more applications than
Henry. Then each boy filled out 3 additional
applications, bringing the total to 28. How many
applications did each boy originally fill out?
The number of applications filled by Henry is 7 and the number of applications filled by Ben is 15.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Ben originally filled out 8 more applications than Henry.
Let the number of applications filled by Henry be x.
Now, x+8
Then each boy filled out 3 additional applications, bringing the total to 28.
Here, x+3+x+8+3=28
2x+14=28
2x=14
x=7
So, x+8=15
Therefore, the number of applications filled by Henry is 7 and the number of applications filled by Ben is 15.
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Can someone please help me with this quick
Answer:
Minimum = -1
Maximum = 3
Step-by-step explanation:
∛-10+9 = ∛-1 = -1
∛18+9 = ∛27 = 3
The function S(t) = 4.5.3 models the growth of a tumor where t is the number of months since the tumor was discovered and Sis the size of the tumor in cubic millimeters. The size of the tumor when it was discovered was 4.5 cubic millimeters. Find the total change in the size of the tumor in the first 3 months and find the average rate of change in the size of the tumor in the first 3 months The total change in size of the tumor in the first 3 months was cubic millimeters. The average rate of change of the tumor in the first 3 months was cubic millimeters per month.
The total change in size of the tumor in the first 3 months is 13.5 cubic millimeters. The average rate of change of the tumor in the first 3 months is 4.5 cubic millimeters per month.
The total change in size of the tumor in the first 3 months can be calculated by subtracting the size at the beginning (4.5 cubic millimeters) from the size at the end of the 3-month period (S(3) = 4.5 * 3 = 13.5 cubic millimeters). Therefore, the total change in size of the tumor in the first 3 months is 13.5 cubic millimeters.
To calculate the average rate of change in the size of the tumor in the first 3 months, we need to divide the total change in size (13.5 cubic millimeters) by the time (3 months).
Therefore, the average rate of change of the tumor in the first 3 months is 4.5 cubic millimeters per month.
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A super large tank was initially filled with brine solution of 20 liters. At some point, fresh water starts to flow in at a rate of 8 liters per minute, and the well mixed solution flows out at half of the rate.Part I Set-up an Initial Value Problem to describe the above problem using: y(t) to represent the amount of salt in the tank t minutes after the process started. There was certain amount of salt in the tank initially,y0 to represent the initial amount.Part II Solve the above IVP to get y(t). Part III How much time (in minutes) will it take for the amount of salt in the tank be reduced to 20% of the initial amount?
The y(t) represents the amount of salt in the tank t minutes after the process started, and y(0) = 20 represents the initial amount. The y(t) is [tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex]. It will take approximately 6.875 minutes for the amount of salt in the tank to be reduced to 20% of the initial amount.
From the given data,
A super large tank was initially filled with brine solution of 20 liters.
At some point, fresh water starts to flow in at a rate of 8 liters per minute, and the well mixed solution flows out at half of the rate.
The initial value problem (IVP) to describe the above problem can be set up as follows:
⇒[tex]\frac{d}{dt} y(t)=\frac{1}{2} (8-y(t))[/tex]
⇒y(0)=20
Where y(t) represents the amount of salt in the tank t minutes after the process started, and y(0) = 20 represents the initial amount.
Part II:
To solve the IVP, we need to find y(t) for a given t. This can be done using numerical methods or analytical methods, such as separation of variables. Using separation of variables, we have:
⇒[tex]\frac{d}{dt} y(t)=\frac{1}{2} (8-y(t))[/tex]
⇒[tex]\frac{dy}{dt}=\frac{1}{2}(8-y)[/tex]
⇒2dy = (8 - y) dt
⇒2dy = (8 - y)dt
Integrating both sides with respect to t, we get:
⇒∫2dy = ∫(8 - y)dt
⇒2y = 8t - (1/2)y^2 + C
where C is a constant of integration. Using the initial condition y(0) = 20, we can find the value of C:
⇒[tex]2y=8t-\frac{1}{2}y^{2} +C[/tex]
⇒[tex]2y=8t-\frac{1}{2}y^{2} +20[/tex]
Solving for y, we get:
⇒[tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex]
Therefore, the y(t) is [tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex].
Part III:
To find the time it takes for the amount of salt in the tank to be reduced to 20% of the initial amount, we can solve for t when y(t) = 0.2 * y0:
⇒[tex]y(t) = 4 + 8t -\frac{1}{2}y^2 = 0.2 * y0[/tex]
⇒[tex]4 + 8t - \frac{1}{2} y^2 = 0.2 * 20[/tex]
Solving for t, we get:
⇒t =[tex]\frac{1}{8}[/tex](4 - 0.2 * 20) = approximately 6.875 minutes.
Hence, it will take approximately 6.875 minutes for the amount of salt in the tank to be reduced to 20% of the initial amount.
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A manager of a telemarketing firm wants to reward her best sales personnel. Each salesperson gets a list of customers to call. The data has been collected on the number of sales made per 100 calls. Now the manager wants to evaluate this data in order to decide what should be considered "exceptional" performance. Use Sales Record below to answer the question. Based on this data, what is the expected number of sales (per 100 calls)?
NOTE: Enter a numerical value only do not include the $ sign; and round your response to 2 digits after the decimal point.
Sales record- 14, 23, 18, 26, 25, 28, 24, 25, 23, 21, 22, 26, 17, 17, 23, 25, 24, 19, 28, 21, 19, 23, 20, 24, 32, 22, 31, 21, 25, 20, 19, 23, 22, 22, 20, 16, 25, 18, 27, 20, 25, 14, 11, 22, 28, 21, 18, 28, 21, 20,21, 15, 22, 16, 20, 22, 17, 20, 19, 22, 21, 26, 25, 18, 25, 16, 30, 20, 22, 14, 30, 25, 25, 21, 33, 19, 24, 18, 15, 30, 19, 34, 27, 26, 24
The expected number of sales (per 100 calls) can be calculated by finding the mean or average of the sales data. To find the mean, add up all the sales values and divide by the number of sales values.
To find the expected number of sales per 100 calls, we need to find the average sales made by the sales personnel. We can do this by adding up all the sales values and dividing by the number of sales values.
The sum of sales values is:
14 + 23 + 18 + 26 + 25 + 28 + 24 + 25 + 23 + 21 + 22 + 26 + 17 + 17 + 23 + 25 + 24 + 19 + 28 + 21 + 19 + 23 + 20 + 24 + 32 + 22 + 31 + 21 + 25 + 20 + 19 + 23 + 22 + 22 + 20 + 16 + 25 + 18 + 27 + 20 + 25 + 14 + 11 + 22 + 28 + 21 + 18 + 28 + 21 + 20 +21 + 15 + 22 + 16 + 20 + 22 + 17 + 20 + 19 + 22 + 21 + 26 + 25 + 18 + 25 + 16 + 30 + 20 + 22 + 14 + 30 + 25 + 25 + 21 + 33 + 19 + 24 + 18 + 15 + 30 + 19 + 34 + 27 + 26 + 24 = 1135
And the number of sales values is:
60
So, the mean or average sales per 100 calls can be calculated as follows:
1135 / 60 = 18.92
Rounding to 2 decimal places, the expected number of sales (per 100 calls) is 22.47.
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Help pls quickly it’s a answer I need fast thanks for help
Answer:
Step-by-step explanation:
D
find the ratio in which 2x 3y-5 duvudes tge kine segment joining (8, -9) and (2, 1). also, find the coorinates of the point of division
The ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1) is 8:1, and the coordinates of the point are 8/3 and -1/9
The given data is, the line 2x+3y-5= 0 and the points are (8, -9) and (2, 1)
Let us consider the ratio to be α: 1
To find the values of a and b we need to use the midpoint formula:
[tex]X=\frac{m_1x_1+m_2x_2}{m_1+m_2} ,\frac{m_1y_1+m_2y_2}{m_1+m_2}[/tex]
For Points (8,–9) and (2, 1) by applying the section formula we get,
[tex]X=\frac{2\alpha +8}{\alpha +1} ,y=\frac{\alpha -9}{\alpha -1}[/tex]
Given equation of line is 2x + 3y–5 = 0 substitute the values of x,y in the equation of line:
[tex]X=2(\frac{2\alpha +8}{\alpha +1} )+3(\frac{\alpha -9}{\alpha -1})-5=0[/tex]
4α+16+3α-27-5α-5
2α=16
α=8
Hence the ratio is 8:1.
Also, the coordinates are
[tex]X=\frac{2\alpha +8}{\alpha +1}=\frac{2(8) +8}{8+1}=\frac{24}{9}=\frac{8}{3} \\\\ y=\frac{\alpha -9}{\alpha -1}=\frac{8-9}{8-1}=\frac{-1}{9}[/tex]
∴ The coordinates are (x,y) = (8/3,-1/9).
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Ver en español
At a berry farm, Clayton picks 1 1 4
cups of blackberries and twice as many raspberries. He takes the berries home and uses them to make mixed-berry muffins. If Clayton needs
3 4 of a cup of mixed berries for each batch of muffins, how many batches can he make?
The number of batches of muffins she can make will be 5.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that at a berry farm, Clayton picks 1¹/₄ cups of blackberries and twice as many raspberries. He takes the berries home and uses them to make mixed-berry muffins.
The number of the batches of muffins can be calculated as:-
Number = ( 1¹/₄ + 2 x 1 ¹/₄ ) / ( 3 / 4 )
Number = [ ( 5 / 4 ) + ( 5 / 2 ) ] / ( 3 / 4 )
Number = [ ( 15 / 4 ) / ( 3 / 4 ) ]
Number = 5
Therefore, the number of batches of muffins will be 5.
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Which function is graphed
The function that is graphed is (c) y = x² + 2 if x < 1 and y = -x + 2 if x ≥ 1
How to determine the graphed functionFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the first curve is a quadratic function,
Also, it has an open circle at x = 1
So, we have:
x² + 2 if x < 1
Next, we have a linear equation with a closed circle at x = 1
So we have:
y = -x + 2 for x ≥ 1
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Using f(x) = 3x - 3 and g(x) = -x, find g(f(x)).
Answer:
Given f(x) = 3x - 3 and g(x) = -x, to find g(f(x)), we first need to substitute f(x) into g(x).
So, g(f(x)) = g(3x - 3) = -(3x - 3) = -3x + 3.
a square garden is 33 1/10 what is the length of each of its sides
Answer:
Step-by-step explanation:
if you mean 33 1/10cm2 then the side is square root of the number which is 5.753 but if the gardens side is 33 1/10 then all the sides are 33 1/10.maybe you typed the question wrongly or some
^^
Determine:
A) Graph the solution of each SIL inequality (separately) using a test point and a tabulation. (line graph)
B) The vertices that make up the solution region:
- Justify the process to find the coordinates of the vertices of the solution region.
- Determine in a table the coordinates of all the vertices that make up the solution region of the SIL.
The intersection point is the solution of inequalities is (15, 7.5).
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given system of inequalities are 13x+37y≤481 -----(i) and 27x+21y≤567 -----(ii)
Here, x≥4 and y≥2
From the graph we can see that, inequalities are intersecting at (15, 7.5)
Therefore, the intersection point is the solution of inequalities is (15, 7.5).
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Match each equation on the left to its solution on the right.
Some answer choices on the right will be used more than once.
The right expression will be -3x + 3 = 3( 1 - x ) for the given expressions.
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.
Given that there are different expressions the correct expression choice is calculated s below:-
-3x + 3 = 3( 1 - x )
-3x + 3 = 3 - 3x
-3x + 3 = -3x + 3
Hence, the correct ex[ression would be -3x + 3 = 3( 1 - x ).
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22000t + 70000r = 2000000
Solve for t
Solve for r
The equation given, when solved for t and r given expression, t = (1000-35r) / 11 and r = (1000-11t) / 35 respectively.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, 22000t + 70000r = 2000000, we are asked to solve it for, Solve for t and r
The given equation is
22000t + 70000r = 2000000
Solving for t, we get,
22000t + 70000r = 2000000
22000t = 2000000 - 70000r
22t = 2000 - 70r
11t = 1000 - 35r
t = (1000-35r) / 11
Solving for r, we get,
22000t + 70000r = 2000000
70000r = 2000000 - 22000t
70r = 2000 - 22t
35r = 1000-11t
r = (1000-11t) / 35
Hence, the equation given, when solved for t and r given expression, t = (1000-35r) / 11 and r = (1000-11t) / 35 respectively.
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How many yards are in two and three-fourths miles
There are 4840 yards in two and three-fourths miles.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know 1 mile is equal to 1760 yards.
Therefore, The number of yards in two and three-fourths miles can be obtained by multiplying the unit equivalent of one mile with two and three-fourths miles which is,
= 1760×[tex]2\frac{3}{4}[/tex] yards.
= 1760×(11/4) miles.
= 440×11 yards.
= 4840 yards.
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Answer: 4840
Step-by-step explanation:
A town’s population of children increased from 376 to 421 during the past year.
Which equation shows how to find the percent increase?
p = 421 - 376 / 376
p = 421 - 376 / 421
p = 376 / 421 - 376
p = 376 + 421 / 376
Answer:
the 3 answer is the right one
A hyperbolic mirror (used in some telescopes) has the property that a light ray directed at the focus will be reflected to the other focus. The focus of a hyperbolic mirror (see figure) has coordinates (17, 0). Find the vertex of the mirror if the mount at the top edge of the mirror has coordinates (17, 17). (Round your answers to two decimal places.) (x, y) = ()
The vertex of the hyperbolic mirror is (17, 8.5). To find the vertex of a hyperbolic mirror, you need to find the midpoint between its two foci.
In this case, the focus has coordinates (17, 0) and the mount at the top edge of the mirror has coordinates (17, 17). To find the midpoint, you average the x-coordinates and the y-coordinates.
The x-coordinate of the midpoint is: (17 + 17) / 2 = 17.
The y-coordinate of the midpoint is: (0 + 17) / 2 = 8.5
Therefore, the vertex of the hyperbolic mirror is (17, 8.5).
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We have two geometric sequences of positive real numbers:
6,a,b and 1/b,a,54
Solve for a
The value of a is 3√2 when the two geometric sequences of positive real numbers of 6, a,b and 1/b, a,54.
A sequence of the numbers in which all the numbers are arranged in such a manner so that the ratio of two successive numbers is always constant,
The geometric progression and the constant ratio are known as the common ratio (r).
A general G.P. can be represented as:
a,ar,ar²,ar³,...............,arⁿ⁻¹,........
Where a=First term, r is the Common ratio and the n=Number of terms.
The nth term of a G.P.:
an=arⁿ⁻¹
Some of the infinite terms of a G.P.:
S∞=a/1−r
Here r<1
Let:
[tex]a_n=a_1q^n^-^1\\a_n_-_1=a_1q^n^-^2\\a_n_+_1=a_1q^n[/tex]
Now multiply the last two equations:
[tex]a_n_-_1 a_n_+_1=a_1q^n^-^2a_1q^n\\\\a_n_-_1 a_n_+_1=a_1^2+q^n^-^2q^n\\\\a_n_-_1 a_n_+_1=a_1^2+q^n^+^n^-^2\\\\a_n_-_1 a_n_+_1=a_1^2+q^2^n^-^2\\\\a_n_-_1 a_n_+_1=a_1^2+q^2^(^n^-^1^)\\\\a_n_-_1 a_n_+_1=a_1^2+q^(^n^-^1^)^2\\\\\sqrt{a_n_-_1 a_n_+_1} =a_1^2+q^(^n^-^1^)\\\\\sqrt{a_n_-_1 a_n_+_1}=a_n[/tex]
Formula:
[tex]a_n=\sqrt{a_n_-_1a_n_+_1}[/tex]
a=√6b-----(1)
a=√1/b*54----(2)
By Equalating both equations:
6b=√1/b*54
b²=54/6
b²=9
b=3
substitute the b value in equation(1)
a=√6b
a=√6*3
a=√18
a=3√2
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An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 14 more than three times the length of the bottom of the triangle. The last side is 15 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
Answer:
P = 5x + 29
Step-by-step explanation:
Let's call the length of one side of the triangle "a".
According to the problem, another side is 14 more than three times the length of the bottom of the triangle, so it can be expressed as 3x + 14.
The last side is 15 more than the bottom of the triangle, so it can be expressed as x + 15.
The perimeter of the triangle is the sum of all three sides, so:
P = x + (3x + 14) + (x + 15)
Simplifying:
P = 5x + 29
Find the missing length indicated:
8
4
2
10
The missing length is 6.
How do we calculate?8
4
2
10
From the numbers shown above, it is found that the difference from one length to the other is 2.
Therefore, the missing length is 6.
Length is described as a measure of distance.
In the International System of Quantities, length is also a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived.
In conclusion, the base unit for length is the meter in the International System of Units system the base unit for length is the meter.
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Find the compound interest and the amount after twelve seconds if the interest is compounded every three seconds if the principal is $20,000 and the rate of interest is 800% per minute
The compound interest and the amount are $2349980000 and $2.35 * 10⁹
Finding the compound interest and the amountFrom the question, we have the following parameters that can be used in our computation:
Principal = $20,000
Rate = 800% per minute = 8
Duration = 12 seconds
n = 20 i.e. every 3 seconds
The amount is calculated as
A = P(1 + r/n)^(nt)
So, we have
A = 20,000(1 + 8/20)^(20*12)
A = 2.35 * 10⁹
So, we have
Interest = 2.35 * 10⁹ - 20000
Interest = 2349980000
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suppose a random sample of 40 houses are selected from the city. estimate the probability that the mean value of the 40 houses is less than $500,000 . show your work
a. Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71
b. the probability that the mean value of the 40 houses is less than $500,000 is 0.9863
a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.
To estimate the probability that a randomly selected house has a value less than $500,000:
P( x < 500,000)=P(x=0)+P(x=500)
=0.34+0.37+
=0.71
Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71
b. -since 40 is larger than or equal to 30, we assume a normal distribution.
-The probability can therefore be calculated as:
P(x')=P( z < (x' -u)/σ.sqrt(n)))
P(z< (500-403)/(578sqrt(40)))
=P(z<2.2068)
=0.986336
Hence, the probability that the mean value of the 40 houses is less than $500,000 is 0.9863
The complete question is -
a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.
(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.
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suppose a family has 3 children of di erent ages. we assume that all combinations of boys and girls are equally likely.a) Formulate precisely the sample space and probability measure that describes the genders of three children in the order in which they born.b) Supose we see the parents with two girls. Assuming we have no other information beyond that at least two of the children are girls, what is the probability that the child we have not yet seen is a boy?c). Suppose we see the parents with two girls, and the parents tell us that these are the two youngest children. What is probability that the oldest child we have not yet seen is a boy?
If a family has 3 children of different ages and all combinations of boys and girls are considered equally likely:
a) the sample space and probability measure that describes the gender of the three children in their birth order is: 1/8.
b) Assuming we see the parents with two girls and there is no other information beyond that, the probability that the child we have not yet seen is a boy is: 1/4.
c). If we see the parents with two girls, and the parents tell us that these are the two youngest children, the probability that the oldest child we have not yet seen is a boy is: 1/8
a) The sample space for the genders of three children can be represented as a set of strings of length 3, each consisting of B (for boy) or G (for girl).
The total number of combinations of boys and girls is 2^3 = 8. Each combination has the same likelihood of occurring, so each combination can be assigned a probability of 1/8. So the sample space and probability measure can be described as:
Sample space: {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}
Probability measure: P(BBB) = P(BBG) = P(BGB) = P(BGG) = P(GBB) = P(GBG) = P(GGB) = P(GGG) = 1/8
b) Assuming we see the parents with two girls, the possible combinations for the genders of the three children are:
GGB, GGBThe probability of the third child being a boy is 1/2. So, given two girls, the probability that the child we have not yet seen is a boy is:
P(third child is a boy) = P(GGB) + P(GGB) = 1/8 + 1/8 = 1/4c) Assuming we see the parents with two girls and they tell us that these are the two youngest children, the possible combinations for the genders of the three children are:
GBGThe only possible combination is GBG, so the probability of the oldest child being a boy is 1. So, given two girls and that they are the youngest children, the probability that the oldest child we have not yet seen is a boy is:
P(oldest child is a boy) = P(GBG) = 1/8 = 1/8Complete Question:
"Suppose a family has 3 children of different ages and all combinations of boys and girls are considered equally likely.
a) Precisely formulate the sample space and probability measure that describes the gender of the three children in their birth order.
b) Given that the parents have two girls and no other information is available, what is the probability that the remaining child is a boy?
c) If the parents have two girls and they inform us that they are the two youngest children, what is the probability that the oldest child is a boy?"
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make a factorial story
irene and her three sister plan to buy a gift for their mother birthday and split the cost equally the total cost of the gift must be less than 60$
An intelligence test for which the scores are normally distributed has a mean of 100 and a standard deviation of 15. Use this information to describe how the scores are distributed .
A score of 100 and a standard deviation of 15 for an intelligence test indicate that:
the scores are normally distributed, which means that the majority of scores are clustered around the mean (100) and the spread of scores decreases as the deviation from the mean increases.
Typically, in a normal distribution, 68% of scores fall within one standard deviation of the mean (85 to 115 in this case), 95% of scores fall within two standard deviations of the mean (70 to 130), and 99.7% of scores fall within three standard deviations of the mean (55 to 145).
This information can be used to describe how the scores are distributed as follows:
Most scores fall in the range of 85 to 115, with fewer scores as the deviation from 100 increases in either direction. There are relatively few scores that fall outside of the range of 70 to 130, and even fewer scores that fall outside of the range of 55 to 145.Therefore: the majority of scores are clustered around the mean (100) and the spread of scores decreases as the deviation from the mean increases.
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suppose a and b are integers that divide the integer c. if a and b are relatively prime, show that ab divides c. show, by example, that if a and b are not relatively prime, then ab need not divide c.
If a and b are integers that divide c and are relatively prime, then ab divides c. If a and b are not relatively prime, then ab need not divide c.
If a and b are integers that divide c, this means that c is divisible by both a and b. Additionally, if a and b are relatively prime, this means that they have no common factors besides 1. In this case, since a and b both divide c, then it follows that their product, ab, also divides c.
However, if a and b are not relatively prime, this means that they have common factors besides 1. In this case, the common factors of a and b may not divide c, so it is not necessarily true that ab divides c.
For example, if a = 6, b = 8, and c = 24, then 6 and 8 both divide 24, but 6 and 8 are not relatively prime (they have a common factor of 2). In this case, 6 * 8 = 48 does not divide 24.
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Which line best models line l?
y
F. x = 4
G. y = 4
H. x = 4y
x
J. y = x + 4
The line best models line l is x=4, the correct option is A.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
Given;
The graph shown in the figure.
Now,
On the graph the x coordinate is 4 throughout
So, x=4
On the graph the y coordinate is continous
Therefore, the graph function will be x=4
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The values of x are 13 and -1. Option A
How to factorize the expressionAlgebraic expressions are defined as expressions that have terms, variables, coefficients, constants and factors.
They are made up of arithmetic operations.
Given that;
(x - 7)²= 36
expand the bracket
x² - 7x - 7x + 49 = 36
collect like terns
x² - 14x + 49 = 36
x² - 14x + 13
Factorize the expression
(x² - 13x) + (x - 13)
Factor the common terms
x(x - 13) + 1(x - 13)
x = 13. x = -1
Hence, the values are 13 and -1
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