there are three age groups in a competition.
john wants to do a survey of the competitors.
he uses a stratified sample of exactly 50 competitors according to each age group.
work out the number of competitors in each age group that should be in his stratified sample of 50
There are 10 people in the 16-18 group , 22 people in the 19-24 group and 18 people who are 25+ in the stratified sample.
A method of sampling from a population that can be divided into subpopulations is known as stratified sampling in statistics. When subpopulations within a larger population differ in statistical surveys, it may be desirable to sample each subpopulation separately.
From the given table we can calculate the total of population:
population = 120 + 250 + 200 = 570 people
Now since it is a stratified sample, the ratio of each age group is equal in the sample as in the population.
∴Number of people in the 16-18 group :
[tex]=\frac{120}{570} \times 50\\\\=10.52[/tex]
∴Number of people in the 19-24 group :
[tex]=\frac{250}{570} \times 50\\\\=21.929[/tex]
∴Number of people in the 19-24 group :
[tex]=\frac{200}{570} \times 50\\\\=17.543[/tex]
Now as 10.52 is closer to 10 than 17.54 is closer to 17 , we will round off 10.52 to 10.
Hence there are 10 people in the 16-18 group , 22 people in the 19-24 group and 18 people who are 25+ in the stratified sample.
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Determine the probability of following event, drawing a card from a standard deck and not getting a diamond.
According to the question, to calculate the probability of the event which states that to draw a card from the standard deck but the condition is not getting the diamond.
The total number of the playing cards are [tex]52[/tex]
And total number of diamond cards are [tex]13[/tex]
Therefore, the total number of favorable outcomes in which diamond is not there is [tex]52-13 = 39[/tex]
As per question, the probability can be written as:
P(no diamond card) = [tex]\frac{39}{52} = \frac{3}{4}[/tex]
Hence, the probability of not getting a diamond card is [tex]\frac{3}{4}[/tex].
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Evaluate each expression 7^2
Answer:
PLEASE READ! Is that 7 to the second power? if so, here is your answer: 49
Step-by-step explanation:
a. Write the point-slope form of the line that passes through A(-3,12) and B(9,-4) . Use point A in the equation.
The equation of the line in point-slope form, which passes through the pair of points located at A(-3 , 12) and B(9 , -4), is y - 12 = -4/3(x + 3).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: A(-3 , 12) and B(9 , -4).
m = (y2 - y1)/(x2 - x1)
m = (-4 - 12)/(9 - -3)
m = -16/12
m = -4/3
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = -4/3 and (x1 , y1) = A(-3 , 12)
(y - 12) = -4/3(x - -3)
y - 12 = -4/3(x + 3)
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write integer for - 2 Feet taller
The integer value of the mathematical statement is -2
How to determine the integer value?The mathematical statement is given as:
- 2 Feet taller
- 2 Feet taller implies that we have a negative integer -2
i.e.
Value = -2
Hence, the integer value of the mathematical statement is -2
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Given f(x)=-2x-3, find f(-1).
Solve for x. It's telling me right but all have to ask is to just please answer quick
Answer: (7y+237) / 8 = x
Step-by-step explanation:
So your equation is:
(2y+50) + (7x-248) + (5y-17) + (x+44)
First thing to do is combine all the like terms. Lets start with y. So that would be 2y + 5y= 7y and 50 + -17 is 33. The new equation is:
(7y + 33) + (7x-248) + (x+44)
Now we will combine the x. We will do -248+44= -204
and 7x+x= 8x.
Now our new equation is:
(7y + 33) + (8x+-204)
Now we can subtract 33 from -204. That is 237.
Now we have 7y+237 = 8x
To isolate x we need to divide by 8. That will give us this:
(7y+237) / 8 = x
How do I find angle x?
By using the fact that the internal angles of a triangle always add up to 180°, we will see that x = 100°.
How to find the angle x?Remember that the sum of all the internal angles of a triangle is always equal to 180°.
On the image we can see two triangles, let's define the angle at the right as A. and the angle at the left as B
We can write:
A + B + x = 180°
And for the inner triangle the angles give:
A/2 + B/2 + 140° = 180°
So we have a little system of equations:
A + B + x = 180°
A/2 + B/2 + 140° = 180°
If we multiply the second equation by 2 we get:
A + B + 280° = 360°
With the first equation we can write:
A + B = 180° - x
And replace that in the above equation
(A + B) + 280° = 360°
180° - x + 280° = 360°
Now we can solve this to get the value of x:
180° + 280° - 360° = x = 100°
We conclude that the measure of angle x is 100°
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f(x) = 2x² + 5x - 3
g(x) = 4x - 5
Answer: 1.) 4x+5
2.) 4
Find the first differences for each data set, and write an equation to represent the data pattern
The first differences for each data set is 120 120 120 120 120 120, and the equation to represent the data pattern is y = 120
How to find the first differences for each data set, and write an equation to represent the data pattern?The table of values represents the given parameters
On the table of values, we have the following function range
60 180 300 420 540 660 780
Calculate the first differences for each data set
i.e. Difference = Tn - T(n-1) Where n > 1
So, we have
120 120 120 120 120 120
The numbers in the above pattern are the same
So, the equation can be represented as
y = 120
Hence, the first differences for each data set is 120 120 120 120 120 120, and the equation to represent the data pattern is y = 120
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What are 11y+1=-6x and 0=43-7x-4y written both in standard form (Ax+By=C) and what are the values for x and y?
Answer:
37777777777999999999999999
the set of all real numbers less than -8 or greater than or equal to -4 in set builder notation
Answer:
[tex]\{x \in \mathbb{R}|-4 \le x \le -8\}[/tex]
Step-by-step explanation:
Simplify each sum or difference. State any restrictions on the variables.
d-3 / 2d+1 + d-1 / 2d + 1
Simplification of the each sum or difference of the given equation [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex] is equal to 2(d-2)/(2d+1). Restriction on the variables is given by d≠ (-1/2).
As given in the question,
Given equation is [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex]
Simplify it by taking least common multiple of the denominator,
[tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}\\\\\\=\frac{d-3+d-1}{2d+1}\\ \\=\frac{2d-4}{2d+1}\\ \\=\frac{2(d-2)}{2d+1}[/tex]
Restriction on the variables is given by d≠ (-1/2).
Therefore, simplification of the each sum or difference of the given equation [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex] is equal to 2(d-2)/(2d+1).Restriction on the variables is given by d≠ (-1/2).
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A carpenter hollowed out the interior of a block of wood as shown at the right.
a. Express the volume of the original block and the volume of the wood removed as polynomials in factored form.
The volume of the original block and the volume of the wood removed as polynomials in factored form will be 2x³ + 15x² + 31x + 12 and (x + 2)(x + 1)(2x + 1).
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
A carpenter hollowed out the interior of a block of wood as shown on the right.
The volume of the original block will be
V = (2x + 1)(x + 3)(x + 4)
V = (2x + 1)(x² + 7x + 12)
V = 2x³ + 14x² + 24x + x² + 7x + 12
V = 2x³ + 15x² + 31x + 12
The volume of the wood removed as polynomials in the factored form will be
V = (x + 2)(x + 1)(2x + 1)
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The three books in a series have 234 pages .301 pages, and 293 pages .about how many pages are in the series?
Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
K(2,2,0) and L(-2,-2,0)
The midpoint is at (0,0,0,)
In the given statement is
To find the midpoint of the line segment joining the pair of points
K(2,2,0) and L(-2,-2,0)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2}[/tex])
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points K(2,2,0) and L(-2,-2,0)
Solving for the midpoint , we have,
m = ([tex]\frac{2+(-2) }{2} ,\frac{2+(-2)_{} }{2} ,\frac{0+0}{2}[/tex])
m = (0 , 0 , 0)
Therefore, the midpoint is at (0, 0, 0,)
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can someone please help
Answer: a) 4
Step-by-step explanation:
sides should be equal according to the shape.
7x-2=12x-22
Determine the probability of following event, rolling a pair of dice and not getting a 3
According to the question, the probability of the event in which rolling a pair of dice and not getting a 3 is as follows:
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
Probability of not getting 3= 1 - P(getting three)/Total number of events
Probability of not getting 3=1-2/36 = 1-1.18 =17/18
Hence, the probability of not getting three while rolling a pair of dice is 17/18 .
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Suppose you need to subtract a from b but mistakenly subtract b from a instead. How is the answer you get related to the correct answer? Explain.
answer:
it would be negative.
explanation:
when you subtract a value from a value, the result will be left to the larger number. if you subtract a larger number from a smaller number, the value will move left but since the value subtracted is more than the number minus itself, you would be subtracting from 0, therefore resulting in a negative number.
Determine whether y varies directly with x . If so, find the constant of variation.
y=-5 x
The required value of the constant of proportion is 5.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant of variation, rate of change, and constant ratio.
Solving for the value of constant of variation
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Given the relation is y = 5x —-- 2
On comparing both the equation 1 and 2, we have,
k = 5
Hence, the required value of constant of variation is 5.
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In the expression 5x6 + 3xy − 7yz2 + , which of the following choices is the numerical coefficient in -7yz2 ?
The numerical coefficient in -7yz² from the expression 5x⁶+3xy-7yz²+2y/z is -7 .
A Numerical Coefficient in an Algebraic Expression is defined as the integer value which is written along with the variable .
For Example : the numerical coefficient in 7xy is 7 , and in -5x is -5 as 7 and 5 are the only numerical value along with the variable y and x respectively.
In the question ;
the given Algebraic Expression is 5x⁶+3xy-7yz²+2y/z
the numerical coefficient in -7yz² is -7 , as -7 is the only numerical value in -7yz² .
Therefore , the numerical coefficient in -7yz² from the expression 5x⁶+3xy-7yz²+2y/z is -7 . the correct option is (d) -7 .
The given question is incomplete , the complete question is
In the expression 5x⁶+3xy-7yz²+2y/z , which of the following choices is the numerical coefficient in -7yz² ?
(a) 2
(b) 3
(c) 5
(d) -7
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Can you please help? Write an equation of a line in slope-intercept form with the given slope and y-intercept. slope: 7, y-intercept: 1
Answer:
Y=7x+1
Step-by-step explain
formula is y=mx+b
your slope is your M and the y-intercept is your B
Tamika has a points card for a movie theater. she receives 20 rewards points just for signing up. she earns 10.5 points for each visit to the movie theater. she needs 167 points for a free movie ticket. write and solve an equation which can be used to determine x, the number of visits tamika must make to earn a free movie ticket.
If Tamika receives 20 rewards points just for signing up and she earns 10.5 points for each visit to the movie theater and she needs 167 points for a free movie ticket, then an equation to determine x, the number of visits Tamika must make to earn a free movie ticket is 10.5x + 20 = 167 and the value of x is calculated to be 14.
The number of visits Tamika must make can be determined by using a linear equation with one variable.
As,
reward points for signing up = 20
points for each visit = 10.5
points needed for free movie ticket = 167
If we consider x to be the number of visits required, then the linear equation can be given as,
10.5x + 20 = 167
Solving for x,
10.5x = 167 - 20
10.5x = 147
x = 147/10.5 = 14
Hence, the number of visits Tamika must make to earn a free movie ticket is equal to 14.
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Please help !
- 20 POINTS
Answer:
184
Step-by-step explanation:
My mom is a teacher lol
10 Peter the baker sells bread rolls in packs of 6 for $2.30. Paul the baker sells bread rolls in packs of 10 for $3.50. I have $10 to spend on bread rolls. If I want to buy as many bread rolls as possible from one shop, which shop should I use? Show your working.
If you want to buy as many bread rolls as possible from one shop, you should use Paul the baker's shop.
Unit ratePeter:
$2.30 for 6 packs of bread rollsUnit rate = $2.30 / 6
= $0.383 per pack of bread rolls
Paul:
$3.50 for 10 packs of bread rollsUnit rate = $3.50 / 10
= $0.35 per pack of bread rolls
So,
Paul the baker bread rolls is cheaper than Peter the baker bread rolls.
Therefore, If you want to buy as many bread rolls as possible from one shop, you should use Paul the baker's shop.
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Q18.
In a company, the ratio of the number of men to the number of women is 3:2
40% of the men are under the age of 25
10% of the women are under the age of 25
What percentage of all the people in the company are under the age of 25?
When 32 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.
The negative solution of the given statement is - 4.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the unknown number be 'n'.
∴ When 32 is subtracted from the square of a number, is n² - 32 and the result is 4 times the number which is equal to 4n,
So, n² - 32 = 4n.
n² - 4n - 32 = 0.
n² - 8n + 4n - 32 = 0.
n(n - 8) + 4(n - 9) = 0.
(n - 8)(n + 4) = 0.
n - 8 = 0 Or n + 4 = 0.
n = 8 Or n = - 4.
So, the negative solution is - 4,
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each brick is 3 1/4 inches tall if martina makes a stack of 4 bricks how much inches tall will it be
Answer:
13 inches
Step-by-step explanation:
Convert to improper fraction and multiply
13/4 x 4/1 (4's cancel out)
13
I need this answered please
Simplify Expression-
( (pq) / (p^2-q^2) + (q) / (q-p) )
divide by
( (p-q) + (4q^2-p^2) / (p+q) )
pls help ;-;
When we divide [tex]\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}[/tex] by [tex](p-q) +\frac{4q^{2} -p^{2} }{q+p}[/tex] , we get simplified answer [tex]\frac{1}{3(q-p)}[/tex]
What are algebraic identities?
Algebraic identities are set of rules that are derived from binomial theorem and are used to solve algebraic expressions .
One such identity is [tex]a^{2} -b^{2} =(a+b)(a-b)[/tex] ....(1)
We have to divide [tex]\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}[/tex] by [tex](p-q) +\frac{4q^{2} -p^{2} }{q+p}[/tex], we get
=[tex]\frac{\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}}{(p-q) +\frac{4q^{2} -p^{2} }{q-p}}[/tex]
=[tex]\frac{\frac{pq}{(p-q)(p+q) } +\frac{q}{q-p}}{\frac{(p-q)(p+q)+4q^{2} -p^{2} }{q+p}}[/tex]
=[tex]\frac{\frac{pq+q(-1)(p+q)}{(p-q)(p+q) } }{\frac{(p-q)(p+q)+4q^{2} -p^{2} }{q+p}}[/tex]
=[tex]\frac{\frac{pq-q^{2}-pq }{(p-q)(p+q) } }{\frac{p^{2} -q^{2} +4q^{2} -p^{2} }{q+p}}[/tex]
=[tex]\frac{\frac{-q^{2} }{(p-q)(p+q) } }{\frac{3q^{2} }{q+p}}[/tex]
[tex]\frac{-q^{2}(q+p) }{3q^{2} (p-q)(p+q) }=\frac{-1}{3(p-q)}\\ =\frac{1}{3(q-p)}[/tex]
On dividing [tex]\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}[/tex] by [tex](p-q) +\frac{4q^{2} -p^{2} }{q+p}[/tex] and simplifying the answer we get [tex]\frac{1}{3(q-p)}[/tex].
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