It is a biased sample.
What is meant by a random sample?
Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.
A random sample is one in which each individual, thing, or event has an equal chance of being chosen. Compared to other types of samples, a random sample has a higher likelihood of being representative of the total population. A skewed sample is one that does not fairly represent the population as a whole.
Here Dorthy considered only the first 20 people and not the whole population so this is not a random sample and it is a biased sample.
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Buy 10 botttess spent $12 toles of sport drink which choice shows the money spent per sport drink bottle
Given that 10 bottles were bought for a total amount of $12, the price per bottle of sport drink is $1.20.
$12 divided by ten bottles equals $1.20.
By dividing the total amount paid ($12) by the quantity of bottles bought, the price per bottle of sport drink was determined (10). As a result, each bottle cost $1.20. According to the computation, the price of 10 bottles of sport drink came to a total of $12. The cost of individual goods or greater quantities of bottles can then be determined using this cost per bottle. The price per bottle can be used to compare the costs of various sport drink brands or sizes. Customers can choose and buy sport drinks with more knowledge if they are aware of the price per bottle.
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Could somebody please tell me what angles A and B equal along with X?
Answer:
x = 28
m∠A = 76°
m∠B = 104°
Step-by-step explanation:
Given the figure we can see that the two angles which measure
2x + 20 and 4x - 8 are adjacent linear angles and therefore they are supplementary angles which further means they add up to 180°
So
2x + 20 + 4x - 8 = 180
2x + 4x + 20 - 8 = 180\
6x + 12 = 180
6x = 180 - 12
6x = 168
x = 168/6
x = 28
We also have the property that angles that are vertically opposite each other at the vertex of the intersection of two lines are equal
So the angle represented by 2x + 20 = 2(28) + 20 = 56 + 20 = 76°
∠A is a vertically opposite angle to this angle and therefore the magnitude of ∠A denoted by m∠A = 76°
The angle represented by 4x - 8 = 4(28) - 8 = 112 - 8 = 104°
Since ∠B is a vertically opposite angle to this angle we have
m∠B = 104°
1. A worm moves down a path that is 1,3 m long. The worm starts moving at 9h12 and reaches the end of the path at 9h24. How fast is the worm travelling?
The worm is travelling at a speed of 0.0018 meter per second.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Total distance travelled by the worm = 1.3 m
The worm starts moving at 9 hour 12 minutes and reaches the end of the path at 9 hour 24 minutes.
Total time taken = 24 - 12 = 12 minutes
Speed = Distance / Time
Speed = 1.3 / 12
= 0.1083 meter / minute
= 0.0018 meter per second
Hence speed of the worm is 0.0018 meter per second.
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each of two persons tosses three fair coins. what is the probablity they obtain same number of heads
The probability of obtaining the same number of heads is 3/8 or 0.375 when each of two persons tosses three fair coins.
The probability that two persons will obtain the same number of heads depends on the number of possible combinations of heads and tails that can be obtained by each person.
Since each coin flip results in either a heads or tails, there are 2 possible outcomes for each flip. Therefore, for three coin flips,
there are 2^3 or 8 possible combinations of heads and tails.
Out of these 8 combinations, there are 3 in which both persons have the same number of heads (i.e., 0 heads, 1 head, or 3 heads).
So, the probability of obtaining the same number of heads is 3/8 or 0.375.
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The number of hours, h, it takes for a block of ice to melt varies inversely as the temperature, t. If it takes 3 hours for a square inch of ice to melt at 60 degrees, find the constant of proportionality
a.
150
c.
210
b.
180
d.
200
Please select the best answer from the choices provided
A
B
C
D
Answer is B
The constant of proportionality is 180.
What is the y-intercept (b) of the line that passes through (1,1)(2,5) You must solve for slope (m) first.
b=
Answer:
slope (m) is 4, y-intercept (m) is -3
Step-by-step explanation:
y=4x-3
use y¹-y² over x¹-x² to find slope, then use one of the points to fill in for x and y to find y-intercept
Mav is working two summer jobs, making
$15 per hour lifeguarding and making $10
per hour landscaping. In a given week, she
can work at most 12 total hours and must
earn no less than $140. If x represents the
number of hours lifeguarding and y
represents the number of hours
landscaping, write and solve a system of
inequalities graphically and determine
one possible solution.
Inequality 1: y ≥û
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
y
Inequality 2: y ≥û
0 1 2 3
4
5
switch shade
plot
6
switch shade
plot
7
8 9 10 11 12 13 14 15 16 17 18 19 20
Xx
This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.
What is inequality?
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
We can write the first inequality as x + y <= 12
This inequality represents the constraint that Mav can work at most 12 hours in total between both jobs.
The second inequality represents the constraint that Mav must earn no less than $140 in a given week, which can be written as:
15x + 10y >= 140
To graph the system of inequalities, we can plot the lines corresponding to x + y = 12 and 15x + 10y = 140 on the coordinate plane and shade the region that satisfies both inequalities.
The solution to the system of inequalities will be the values of x and y that lie in the shaded region.
One possible solution is x = 4 and y = 8, which means that Mav works 4 hours of lifeguarding and 8 hours of landscaping in a given week, earning a total of 15 * 4 + 10 * 8 = $120.
Hence, This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.
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Answer:
y ≤ 12 -xy ≥ 14 -1.5x(x, y) = (4, 8) — 4 hours lifeguarding, 8 hours landscapingStep-by-step explanation:
You want inequalities, their graph, and a possible solution satisfying Mav's requirement for at most 12 total hours spent lifeguarding at $15 per hour and landscaping at $10 per hour, with an income of at least $140.
SetupThe required relations can be written ...
x + y ≤ 12 . . . . . . . total hours
15x +10y ≥ 140 . . . . total earnings
InequalitiesThe inequalities need to be solved for y to match the answer format requirements.
inequality 1: y ≤ 12 -x . . . . . . . . . . subtract x
inequality 2: y ≥ 14 -1.5x . . . . . . divide by 10, subtract 1.5x
SolutionThe attached graph shows a couple of possible solutions. The solution space is the doubly-shaded area bounded by vertices ...
(4, 8), (12, 0), and (9 1/3, 0)
Mav will make the most money working 12 hours lifeguarding (x, y) = (12, 0).
She can just meet her income requirements by working 8 hours lifeguarding and 2 hours landscaping (x, y) = (8, 2).
One possible solution is 4 hours lifeguarding and 8 hours landscaping.
Mya uses a potato chip can to store small items. each cylindrical can has a radius of 2.5 inches and a height of 9 inches. what is the approximate surface area of the can? (use 3.14 for π.)
The approximate surface area of the can is 180.55 sq.inches
A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. Area of three-dimensional shapes often refers to surface area. Square units are used to denote the surface area. Examples include cm2, m2, and so forth. A group of circular discs placed on top of one another might be thought of as a cylinder. The cylinder has both surface area and volume since it is a solid with a three-dimensional geometry.
The area of the cylinder is determined by adding the areas of its two circular bases and curving surface.
The Surface Area of Cylinder = Curved Surface + Area of Circular bases
S.A. (in terms of π) = 2πr (h + r) sq.unit
Where, π (Pi) = 3.142 or = 22/7
r = Radius of the cylinder
h = Height of the cylinder
cylindrical can has a radius of 2.5 inches and a height of 9 inches
surface area =2πr (h + r) sq.unit
= 2π*2.5(9+2.5)
=180.55 sq.inches
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What is FG?
pls help this is hard
Answer:
FG = 18
Explanation:
There is a simpler solution:
It has to do with the interior angle bisector theorem. (the illustration with the angle marks and the line show that it is being bisected)
Which will divide the opposite side into segments whose lengths have the same ratio as the adjacent sides of the bisected angle.
x / 24 = x + 10 / 54 →
54x = 24(x + 10) →
54x = 24x + 240 →
30x = 240 →
x = 8.
Since the expression x + 10 represents the length of FG, it's length must be 18.
Choose the appropriate method for solving the following systems of equations.
The appropriate methods are
y = x + 8 and y = 4x + 2 - Substitution method
2x + 6y = 18 and x + 5y = 13 - Elimination method
y = 3x + 3 and y = x + 7 - Substitution method
4x + 7y = 10 and -3x + y = -1 - Elimination method
Elimination method:In this approach, the equation in one variable is obtained by either adding or subtracting the equations. We can add the equation to delete a variable if its coefficients are the same and have the opposite sign from the other variables.
Similarly to this, we can subtract the equation to get the equation in one variable if the coefficients of one of the variables are the same and their signs are the same.
From the given options, the system of equations
2x + 6y = 18 and x + 5y = 13
4x + 7y = 10 and -3x + y = -1
Can be solved using the Elimination method
Substitution method:The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.
From the given options, the system of equations
y = x + 8 and y = 4x + 2
y = 3x + 3 and y = x + 7
Can be solved by using the Substitution method
Therefore,
The appropriate methods are
y = x + 8 and y = 4x + 2 - Substitution method
2x + 6y = 18 and x + 5y = 13 - Elimination method
y = 3x + 3 and y = x + 7 - Substitution method
4x + 7y = 10 and -3x + y = -1 - Elimination method
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Arrange the digits 6, 0, 3, 2, and 4 to create the greatest possible five-digit number.
Answer:
The greatest possible five-digit number you can create with the numbers 6, 0, 3, 2, and 4 is 64,320.
Step-by-step explanation:
When it comes to creating the biggest number with a given set of digits, the one and only rule is to organize the digits from greatest to least, this way it ensures that you have the maximum possible values that aren't mitigated by having a small number before a larger one. Based on this, we can organize 6, 0, 3, 2, and 4 from greatest to least, which will be 64,320. Hence, the greatest possible five-digit number you can create with those given numbers is 64,320.
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What is the circumference of a circle with a diameter of 11 inches? (use 22/7 for pi)
The circumference of a circle with a diameter of 11 inches using π as 22/7 is 34.86 inches.
To find the circumference of a circle, we can use the formula:
C = πd
where C is the circumference, π is a mathematical constant (approximately 22/7), and d is the diameter of the circle.
The diameter of a circle is a straight line that passes through the center of the circle and touches two points on the edge of the circle. In this problem, we are given that the diameter of the circle is 11 inches.
To find the circumference, we can substitute this value for d in the formula:
C = πd = π(11 inches)
We can simplify this by using the approximation π ≈ 3.14 (or more precisely, π ≈ 22/7), to get:
C ≈ (3.14)(11 inches) = 34.54 inches
or
C ≈ (22/7)(11 inches) = 34.86 inches
So the circumference of the circle is approximately 34.54 inches or 34.86 inches, depending on which approximation of π is used.
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A right triangle has legs measuring 18 in. and 26 in. what is the length of the hypotenuse? round to the nearest tenth. responses 18.8 in. 18.8 in. 31.6 in. 31.6 in. 44.0 in. 44.0 in. 100.0 in.
The hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in, rounded to the nearest tenth. This is calculated by using the Pythagorean Theorem, which states that a2 + b2 = c2 and plugging in the values for a and b.
The hypotenuse of a right triangle is the longest side of the triangle and is always opposite of the right angle. To calculate the length of the hypotenuse, you need to use the Pythagorean Theorem. The theorem states that a2 + b2 = c2, where a and b are the legs of the triangle and c is the hypotenuse. In this case, a is 18 inches and b is 26 inches, so the equation would be 182 + 262 = c2. Plugging in the values, we get 324 + 676 = c2, which simplifies to 1000 = c2. To find the length of the hypotenuse, we need to take the square root of 1000, which is 31.6 inches. Rounded to the nearest tenth, the hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in.
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in a train yard there are tank cars, boxcars, and flatcars. how many ways can a train be made up consisting of tank cars, boxcars, and flatcars? (in this case, order is not important.)
There are 55 ways to form a train consisting of tank cars, boxcars, and flatcars by using concept of combinations.
If there are t tank cars, b boxcars, and f flatcars in the train yard, then the number of ways to form a train by selecting some of these cars is the same as the number of ways to distribute n = t + b + f identical objects into three distinct boxes, such that each box may receive any number of objects (including zero). The solution is given by the combination formula:
C(n + k - 1, k - 1)
where k is the number of boxes (in this case, k = 3). Therefore, the number of ways to form a train from t tank cars, b boxcars, and f flatcars is:
C(t + b + f + 3 - 1, 3 - 1) = C(t + b + f + 2, 2) = (t + b + f + 2)! / ((t + b + f)! * 2!)
There are 4 tank cars, 3 boxcars, and 2 flatcars in the train yard, then the number of ways to form a train is:
C(4 + 3 + 2 + 2, 2) = C(11, 2) = 55
Therefore, there are 55 ways to form a train consisting of tank cars, boxcars, and flatcars
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The figure on the right is a scaled copy of the figure on the left. Which side in the figure on the right corresponds to segment DF? What is the scale factor?
The side which corresponds to QS is VU, and the scale factor is 2.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Given that, the figure on the right is a scaled copy of the figure on the left.
We need to find the corresponding side of QS and scale factor,
The figure is 90° counterclockwise rotated,
Therefore,
The corresponding sides are:
PR ~ TW
RQ ~ VT
QS ~ UV
PS ~ WU
∵ the measure of QS = 4 units and the measure of UV = 2 units
∴ scale factor = 4/2 = 2
Hence, the side which corresponds to QS is VU, and the scale factor is 2.
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The question do not contain figure, the similar question is solved.
use elimination to solve the simulta
neous equations: 2x+7y)=3,
2x-y=3
Answer:
Step-by-step explanation: 2x+7y)=3,
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help plsssssssssssssss
Solve the right triangle table
The measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
We shall first evaluate for the angle m∠B as follows:
m∠A + m∠B + m∠C = 180° {sum of interior angles of a triangle}
49° + B + 90° = 180°
B + 139° = 180°
B = 180° - 139° {subtract 139° from both sides}
m∠B = 41°
12.7/sin90° = a/sin41
a = (12.7 × sin49)/sin90° {cross multiplication}
a = 9.5848
12.7/sin90° = b/sin49
b = (12.7 × sin49)/sin90 {cross multiplication}
b = 8.3319
Therefore, the measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.
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What is the average rate of change of the function -4≤x≤0
Answer:
The average rate of change of a function over an interval is a measure of how the function's value changes over that interval, given by the ratio of the change in the function's value to the change in the independent variable. To find the average rate of change of a function over an interval, we need to know the function's values at two points in the interval.
In the case of the function f(x) = x^2, the interval is -4 ≤ x ≤ 0. To find the average rate of change, we need to find the difference in the function's value between two points in this interval, and divide that by the difference in the x-values.
For example, if we compare the values of the function at x = -4 and x = 0, we have:
f(-4) = (-4)^2 = 16
f(0) = 0^2 = 0
The difference in the function's value is f(0) - f(-4) = 0 - 16 = -16.
The difference in the x-values is x2 - x1 = 0 - (-4) = 4.
So the average rate of change over this interval is the difference in the function's value divided by the difference in the x-values, or -16 / 4 = -4.
In other words, the average rate of change of the function f(x) = x^2 over the interval -4 ≤ x ≤ 0 is -4, meaning that for every 4 units of change in x, the function value decreases by 16 units.
Step-by-step explanation:
I think the difference 6.96 - 0.04 is greater or less than 7
The difference 6.96 - 0.04 is greater than 7.
does -6(x+1)+8x=2(x-3) have no solution one solution or all real numbers are solutions and if theres only one solution was does x=
The equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.
What is the equation in one variable?
An equation in one variable is a mathematical expression that contains a single variable, typically represented by x. The goal of solving an equation in one variable is to determine the value of the variable that makes the equation true.
To solve the equation -6(x+1)+8x=2(x-3), we can simplify the left-hand and right-hand sides of the equation and then solve for x. Here are the steps:
Distribute the -6 and 2 to the terms inside the parentheses: -6x - 6 + 8x = 2x - 6
Combine like terms on each side of the equation: 2x - 6 = 2x - 6
Subtract 2x from both sides of the equation: -6 = -6
At this point, we have a true statement (-6 = -6), but there is no variable present. This means that the equation has infinitely many solutions, and every real number is a solution to the equation.
Hence, the equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.
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What is m∠B?
There is a seven sided polygon ABCDEFG in which the measure of angle BCD is 148 degrees, the measure of angle DEF is 142 degrees, the measure of angle EFG is 130 degrees, the measure of angle FGA is 129 degrees, and the measure of angle GAB is 120 degrees. Angle CDE is a right angle.
For the polygon ABCDEFG, the measurement of ∠B is option D: 141°.
What is a polygon?
In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides).
The polygon ABCDEFG has angle measurements as -
Measurement of ∠BCD = 148°
Measurement of ∠DEF = 142°
Measurement of ∠EFG = 130°
Measurement of ∠FGA = 129°
Measurement of ∠GAB = 120°
Measurement of ∠CDE = 90°
Let the measurement of ∠ABC be x° .
In a heptagon (or polygon having seven sides) the sum of all angles is 900°.
So, for polygon ABCDEFG the equation will be -
∠BCD + ∠CDE + ∠DEF + ∠EFG + ∠FGA + ∠GAB + ∠ABC = 900°
Substitute the values in the equation -
148° + 90° + 142° + 130° + 129° + 120° + x = 900°
148° + 90° + 142° + 130° + 129° + 120° + x = 900°
759° + x = 900°
x = 900° - 759°
x = 141°
Therefore, the value of x is obtained as 141°.
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Amir notices that 3 out of every 50 cars that pass by his window
are green. If he observes 400 cars, what is the best estimate for how
many of them will be green?
Answer:
24 cars are green
Step-by-step explanation:
We know
Amir notices that 3 out of every 50 cars that pass by his window are green.
So, the ratio is 3:47
To get from 50 to 400, we time 8.
If he observes 400 cars, what is the best estimate of how many will be green?
We take
3 x 8 = 24 cars are green
So, there will be 24 cars that are green.
Solve for x *
est
45
O x = 50
O x = 8
O x = 48.2
O x = 40.5
20
S
18
R
The value of x for the similar triangles is given as follows:
x = 40.5.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.A bisection divides a triangle into two similar triangles, hence the proportional relationship for the side lengths is given as follows:
x/45 = 18/20
18/20 = 0.9, hence:
x/45 = 0.9
x = 45 x 0.9
x = 40.5.
Meaning that the fourth option is the correct option.
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The area of a square is given by x2, where x is the length of one side. Mary's original garden was in the shape of a square. She has decided to double the area of her garden. Part 1 Enter an expression that represents the area of Mary's new garden. An expression that represents the area is Part 2 out of 2 Evaluate the expression if the side length of Mary's original garden was 9 feet. The area of Mary's new garden is square feet
Part 1: If Mary doubles the area of her original square garden, the expression that represents the area of Mary's new garden is 2x^2.
Part 2: If the side length of Mary's original garden is 9 feet, the area of Mary's new garden is 162 square feet.
Part 1: If Mary doubles the area of her original square garden, the new area of her garden will be 2 times the area of her original garden.
If the area of her original garden is x^2, then the area of her new garden will be:
2(x^2) = 2x^2
So, the expression that represents the area of Mary's new garden is 2x^2.
Part 2: If the side length of Mary's original garden is 9 feet, then the area of her original garden is:
x^2 = (9 feet)^2 = 81 square feet
To find the area of Mary's new garden, we can substitute 81 for x^2 in the expression we found in Part 1:
2x^2 = 2(81 square feet) = 162 square feet
So, the area of Mary's new garden is 162 square feet.
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In a survey of 20 sophomores at a high school, 8 students said that they would prefer a class field trip to an amusement park, rather than a museum. The sophomore class has 150 students. Predict the number of sophomores who prefer a class trip to an amusement park.
Answer:
60 sopomores
Step-by-step explanation:
Let X denote the event prefer amusement park on a field trip
The probability that a sophomore will opt for a class trip to an amusement park would be 8/20 = 2/5 based on survey results
P(X) = 2/5
Based on this probability, if the number of sophomores is 150 then expected number of sophomores who prefer the amusement park trip
E(X) - P(X) x N where N is the total number of sophomores
E(X) = 2/5 x 150 = 60
ZABC and ZQRS are supplementary angles.
If the measure of ZABC = 170°, what is the
measure of ZQRS?
m/QRS = ?
Answer:
[tex]10^{\circ}[/tex]
Step-by-step explanation:
Supplementary angles have measures that add to [tex]180^{\circ}[/tex].
Help me please! So how do I put these from LEAST to GREATEST : -29/2, 14.25, -14.3, 14%
1) A function f(x), which contained the point (5,4) was transformed with the rule 2f (x-3) + 4. What would
be the new coordinates of that point?
(2,-2)
The solution is, point (5,4) will correspond to (5,8).
What is transformation?A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.
here, we have,
1) To find that the corresponding points, let'-s plug it into that formula:
(5,4)
If we plug 5 and we have output the number 4,
then f(x) is y=x-1
now,
2f(x-3)+4 is the function f(x) with a horizontal shift of 3 units to right, a vertical stretch 4, a reflection.
2) y=2(5-3)+4 then y=2(2)+4
y=8
So point (5,4) will correspond to (5,8)
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The point equidistant from the three sides of a triangle isA. CircumcentreB. CentroidC. IncentreD. Orthocentre
The point equidistant from the three sides of a triangle is (c) Incenter .
The Circumcenter of a triangle is defined as a point where perpendicular bisectors of sides of triangle intersect. It is also equidistant from 3 vertices of triangle .
The Centroid is defined as a point where 3 medians of the triangle intersect.
The Incenter is defined as a point where angle bisectors of the triangle intersect. It is equidistant from the three sides of the triangle, and is the center of the inscribed circle of the triangle .
The Orthocenter is defined as a point where the 3 altitudes of the triangle intersect.
So , by the definition of the Incenter , the correct option is (c) Incenter .
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The given question is incomplete , the complete question is
The point equidistant from the three sides of a triangle is
(a) Circumcenter
(b) Centroid
(c) Incenter
(d) Orthocenter
