Answer:
[tex]x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}[/tex]
Step-by-step explanation:
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Given quadratic equation:
[tex]x^2-3x-5=0[/tex]
Define the variables:
[tex]\implies a=1, \quad b=-3, \quad c=-5[/tex]
Substitute the defined variables into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{9+20}}{2}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Therefore, the exact solutions to the given quadratic equation are:
[tex]x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}[/tex]
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Answer:
[tex]\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}[/tex]
Step-by-step explanation:
Quadratic Formula :
[tex]\boxed {\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}}[/tex]
We are given the equation x² - 3x - 5 = 0.
Here,
a = 1b = -3c = -5Solving :
3 ± √3² - 4(1)(-5) / 2(1)3 ± √29 / 2Hence, the solutions are :
[tex]\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}[/tex]
(b) The co-ordinates of three points are A(7, 4), B(-1, -2) and C(3t, 5-4t). (i) Find the value of t if the three points are collinear.
Answer:
Step-by-step explanation:
To determine the value of t if the three points A(7, 4), B(-1, -2), and C(3t, 5-4t) are collinear, we can use the concept of slope. If the points are collinear, the slopes between any two pairs of points should be equal.
The slope between points A and B is given by:
m₁ = (y₂ - y₁) / (x₂ - x₁)
= (-2 - 4) / (-1 - 7)
= (-6) / (-8)
= 3/4
Now, let's calculate the slope between points B and C:
m₂ = (y₂ - y₁) / (x₂ - x₁)
= (5 - (-2)) / (3t - (-1))
= (7) / (3t + 1)
Since the points are collinear, the slopes m₁ and m₂ should be equal. Therefore, we can set up the equation:
3/4 = 7 / (3t + 1)
To solve for t, we can cross-multiply and solve the resulting equation:
4(7) = 3(3t + 1)
28 = 9t + 3
25 = 9t
t = 25 / 9
Therefore, the value of t that makes the points A(7, 4), B(-1, -2), and C(3t, 5-4t) collinear is t = 25/9.
Answer:
6/7
Step-by-step explanation:
If the three points are collinear, then the slope of the line passing through any two of the points should be the same as the slope of the line passing through the other two points.
Let's find the slope of the line passing through points A and B:
slope AB = (y2-y1)/(x2-x1)
= (-2-4)/(-1-7)
= -6/-8
= 3/4
Now let's find the slope of the line passing through points B and C:
slope BC = (y2-y1)/(x2-x1)
= (5-4t-(-2))/(3t-(-1))
= (7-4t)/(3t+1)
Since the three points are collinear, slope AB = slope BC:
3/4 = (7-4t)/(3t+1)
Cross-multiplying and simplifying:
12t + 4 = 28-16t
28t = 24
t = 24/28
t = 6/7
Therefore, the value of t is 6/7 if the three points A, B, and C are collinear.
which cellphone srvice provider was the first to be established in south africa
The first cellphone service provider to be established in South Africa was Vodacom. Vodacom was launched on April 1, 1994, and it became the country's first cellular network operator.
The company was a joint venture between Telkom, the national telecommunications company of South Africa, and Vodafone, a global telecommunications giant.
Vodacom introduced the GSM network to South Africa, providing mobile voice and data services to customers across the country. Its launch marked a significant milestone in the telecommunications industry in South Africa, as it brought mobile communication to the masses and revolutionized the way people connect and communicate.
Since its inception, Vodacom has played a pivotal role in the development of the telecommunications sector in South Africa. It has continually expanded its network coverage, introduced innovative services, and played an active role in bridging the digital divide in the country.
Today, Vodacom remains one of the leading mobile network operators in South Africa, providing a wide range of mobile services to millions of customers.
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The probable question may be:
Which cellphone service provider was the first to be established in south africa
The slope of a line of best fit is undefined when _____.
select all that apply
(1) the x values of the data set are constant
(2) the y values of the data set do not change when the x values change
(3) the slope of the line of best fit is vertical
(4) the slope is of the line of best fit is horizontal.
(5) the x values of the data set increase at an unspecified rate as the y values decrease
The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. This is because a horizontal line has a slope of zero
The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. A line of best fit is a straight line that is used to represent the data on a scatter plot. It is the line that best fits the data points in a scatter plot.
The slope of a line of best fit is the rate of change of the y-coordinate relative to the x-coordinate.. In other words, there is no rate of change of the y-coordinate relative to the x-coordinate when the line is horizontal.
The x values of the data set increase at an unspecified rate as the y values decrease. This means that the line of best fit has a negative slope. A negative slope means that the y-coordinate decreases as the x-coordinate increases.
In other words, there is a rate of change of the y-coordinate relative to the x-coordinate. The slope of the line of best fit is the value of this rate of change.
The slope of a line of best fit is used to determine the direction and strength of the relationship between two variables.
A positive slope means that the variables are directly proportional, while a negative slope means that they are inversely proportional. The slope of a line of best fit can be calculated using the formula y2 - y1 / x2 - x1.
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the martins bought a condominium for $85,000. assuming that the value of the condo will appreciate at most 5% a year, how much will the condo be worth in 5 years?
Answer:
Step-by-step explanation:
Answer:181,250
Step-by-step explanation:
Basically, the cost would go up 5 percent, and you’re asking how much it would go up in 5 years. So 5x5=25, so you’d multiply 145,000 by 25%, which is 36,250. So, you’d add that to 145,000 which would get you 181,250.
A solid figure is separated into 2 rectangular prisms. The volume of rectangular prism A is 75 cubic yards. Rectangular prism
B has a length of 7 yards and a width of 3 yards. The total volume of the solid figure is 180 cubic yards. What is the height of
rectangular prism B?
The height of rectangular prism B is 5 yards.
Let's first find the volume of rectangular prism B:
The volume of the solid figure = Volume of prism A + Volume of prism B
180 = 75 + length × width × height of prism B
105 = length × width × height of prism B
We know that the length of prism B is 7 yards and the width is 3 yards,
Substitute those values:
105 = 7 × 3 × height of prism B
105 = 21 × height of prism B
height of prism B = 105/21
height of prism B = 5
Therefore, the height of rectangular prism B is 5 yards.
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22. Which of the following is NOT a rational expression?
O(x+3)(2x-1)
x+3
O3x²+3x
4x+5
3x+4√x-7
2x+2
2x²-3x³+5
5x
The correct expression which is not a rational expression,
⇒ (x+3)(2x-1) / (x+3)
We have to given that;
All the expressions are,
⇒ (x+3)(2x-1) / (x+3)
⇒ (3x²+3x) / (4x+5)
⇒ (3x+4√x-7) / (2x+2)
⇒ (2x²-3x³+5) / 5x
Since, A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
Hence, We can simplify all the expressions as,
⇒ (x+3)(2x-1) / (x+3)
⇒ (2x - 1)
Hence, It is not a rational expression.
⇒ (3x²+3x) / (4x+5)
⇒ 3x (x + 1) / (4x + 5)
Hence, It is a rational expression.
⇒ (3x+4√x-7) / (2x+2)
⇒ (3x + 4√x - 7) / 2 (x + 1)
Hence, It is a rational expression.
⇒ (2x²-3x³+5) / 5x
Hence, It is a rational expression.
Thus, The correct expression which is not a rational expression,
⇒ (x+3)(2x-1) / (x+3)
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This may be hard to put together, but I need help with an angle equation. I'm looking for example equations and how to do these types of equations. *please note that this equation is completely random and probably ends with an ugly number. it's just an example of a type of problem*
Example: (2x - 4) x=7 so (2x (x=7) - 4) =18
Find the amount accumulated after
investing a principle P for t years at an
interest rate compounded k times per year.
P = $40,500 r = 3.8% t = 20 k = 12
Hint: A = P(1 + £)kt
A = $[?]
The solution is: the amount accumulated after investing a principle P for t years at an interest rate compounded k times per year is $86496.26.
Here, we know,
The whole sum borrowed (or invested), exclusive of interest and dividends.
We have,
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
The formula for the amount A accumulated after investing a principle P for t years at an annual interest rate r compounded k times per year is:
A = P * (1+r / k)^kt
given that,
P = $40,500 r = 3.8% t = 20 k = 12
Substituting the given values into this formula, we have:
A = $40,500 * (1 + 0.038 / 12)^12*20
A = $40,500 * 2.1357
A = $86496.2599
A = $86496.26 (rounded to the nearest cent)
Therefore, the amount accumulated after investing a principle P for t years at an interest rate compounded k times per year is $86496.26.
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A cruise ship can cover 19 nautical miles in 437 minutes. How many nautical miles will it travel in 345 minutes?
The cruise ship will travel approximately 15 nautical miles in 345 minutes.
How did we get the value?Use a proportion to solve this problem. Let "d" be the number of nautical miles the cruise ship will travel in 345 minutes. Then:
19 nautical miles / 437 minutes = d nautical miles / 345 minutes
To solve for "d", cross-multiply:
19 nautical miles x 345 minutes = d nautical miles x 437 minutes
Then, divide both sides by 437 minutes to isolate "d":
d nautical miles = (19 nautical miles x 345 minutes) / 437 minutes
Simplifying this expression, we get:
d nautical miles = 15 nautical miles (rounded to the nearest whole number)
Therefore, the cruise ship will travel approximately 15 nautical miles in 345 minutes.
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A bag contains 14 blue marbles, 6 green marbles and 8 purple marbles. What is the likelihood of randomly drawing a blue marble?
Answer:
0
Step-by-step explanation:
because 6 plus 8 eqaul 14
Write an expression to represent: 6 times the difference of 5 and x
Answer:
6 * (5 - x)
Step-by-step explanation:
This expression calculates the difference between 5 and x, and then multiplies it by 6. The difference is obtained by subtracting x from 5, and then the entire result is multiplied by 6.
4 3/8 + 5 1/2= in fractions
Answer:
9 7/8
Step-by-step explanation:
1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.
2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.
3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.
PLEASE HELP WITH THIS! PLEASE! SURFACE AREA. I HAVE NO CLUE!!
Answer: 626 yd^2
Step-by-step explanation: First you need to split the figure into 2 rectangular prisms (see attached image). The tallest rectangular prism has a length of 12 yd, a width of 3 yd, and a height of 11 yd. The shorter one has a length of 12yd, a width of 4 yd, and a height of 4 yd. The surface area equation is SA=2(wl+hl+hw). First solve for the taller rectangular prism. SA=2(3x12+11x12+11x3). SA=2(36+132+33). SA=2(201). SA=402 yd^2. Now solve for the smaller rectangular prism. SA=2(4x12+4x12+4x4). SA=2(48+48+16). SA=2(112). SA=224 yd^2. Lastly, add both values together. 402+224=626 yd^2.
Identify one example of each angle pair in the diagram to the right.
Alternate exterior angles are ∠9 and (∠1 + ∠2)
Consecutive interior angles are ∠7 and ∠4
Consecutive exterior angles are ∠9 and ∠∠3
Vertical angles are ∠2 and ∠5
Linear pairs are ∠7 and ∠8
We have,
Alternate exterior angles: Pairs of angles on opposite sides of a transversal line, formed by two parallel lines, and located outside the intersected lines.
Consecutive interior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located between the intersected lines.
Consecutive exterior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located outside the intersected lines.
Vertical angles: Pairs of non-adjacent angles formed by the intersection of two lines, sharing the same vertex and having equal measures.
Linear pair: A pair of adjacent angles formed by the intersection of two lines, sharing a common side, and whose measures add up to 180 degrees.
So,
Alternate exterior angles
= ∠9 and (∠1 + ∠2)
Consecutive interior angles
= ∠7 and ∠4
Consecutive exterior angles
= ∠9 and ∠∠3
Vertical angles
= ∠2 and ∠5
Linear pair
= ∠7 and ∠∠8
Thus,
Alternate exterior angles are ∠9 and (∠1 + ∠2)
Consecutive interior angles are ∠7 and ∠4
Consecutive exterior angles are ∠9 and ∠∠3
Vertical angles are ∠2 and ∠5
Linear pairs are ∠7 and ∠8
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How long must 100 be invested at a rate of 4% to earn 32.00 in interest
WhaYou is 1/5 divided by 2/6
100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
The required exact value of sin(585 degrees) is -0.707
The sine function is periodic with a period of 360 degrees.
Therefore,
= sin(585 degrees)
= sin(585 degrees - 360 degrees)
= sin(225 degrees).
The sine function has a negative value in the third quadrant, and 225 degrees is in the third quadrant.
Therefore,
sin(225 degrees) = -sin(45 degrees)
= -(1/sqrt(2)) = -0.7071.
Therefore, the exact value of sin(585 degrees) is -0.7071.
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Your brain needs caffeine! You decide to walk from home to the coffee shop located at point (-8,-5). What coordinate would you be standing on if you stood on a point “K” so that it directed the line segment in a ratio of 5:2?
The coordinates you would be standing on would be coordinate (-5.71, -3.57).
How to calculate the coordinatesTo discover the arrangement of point "K" that partitions the line section interfacing the beginning point to the coffee shop in a proportion of 5:2, we are able to utilize the concept of the area equation.
We should expect the starting point to be meant as A with orchestrates (- x1, - y1), and the café is implied as B with works with (- x2, - y2). The ratio of 5:2 suggests that segment AB is divided into two parts and five parts, each accounting for 7 percent of the length.
The x-direction of point K can be determined as:
xK = (5 * x2 + 2 * x1)/7
Basically, the y-direction of point K can be determined as:
yK = (5 * y2 + 2 * y1) / 7
Stopping within the arranges of the coffee shop (-8, -5) as (-x2, -y2) and accepting the beginning point as the beginning (0, 0), we have:
xK = (5 * (-8) + 2 * 0) / 7 = -40/7 ≈ -5.71
yK = (5 * (-5) + 2 * 0) / 7 = -25/7 ≈ -3.57
Hence, in case you stood on point K, you'd be around at coordinate (-5.71, -3.57).
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What is the intermediate step in the form (x+a)^2=b as a result of complementing the square for the following equations
The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.
To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.
Add the square of half of the coefficient of x to both sides of the equation:
x² + 2x + (2/2)² = 319 + (2/2)²
x² + 2x + 1 = 320
The left-hand side of the equation can now be factored as a perfect square:
(x+1)² = 320
This is the equation in the form (x+a)²=b, where a=1 and b=320.
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The complete question is as follows:
What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?
x² + 2x = 319
can somebody please help me with this asap!
The diameter of the second pile of phosphate is 53.5 ft.
We have,
Conveyor belt:
Cone shape:
Diameter = 48.6 ft
Radius = D/2 = 24.3 ft
Height = 15.3 ft
Volume.
= 1/3 x π x r² x h
= 1/3 x 3.14 x 24.3 x 24.3 x 15.3______(1)
Shorter conveyor belt:
Cone shape:
Diameter = D
Height = (15.3 - 2.7) = 12.6 ft
Volume.
= 1/3 x π x (D/2)² x h
= 1/3 x 3.14 x (D/2)² x 12.6_______(2)
Since (1) and (2) are equal.
24.3 x 24.3 x 15.3 = (D/2)² x 12.6
(D/2)² = 717.02
D²/4 = 717.02
D² = 717.02 x 4
D² = 2868.09
D = 53.55
D = 53.5 ft
Thus,
The diameter of the second pile of phosphate is 53.5 ft.
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Part of the population of 5,250 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected. How many elk are likely to be infected? Based on the sample, there will likely be infected elk in the wildlife preserve.
The likely population of the infected elk in the wildlife preserve is 840.
What is the likely population of the infected elk?A sample is a smaller group of the population. A sample is a representation of the population.
The fraction of infected elks in the sample to the total sample would be the same of the infected elks in the population to the total population of the elks.
Population of the infected elk = (infected elks in the sample / total sample) x number of elks in the preserve
(8/50) x 5250
= 0.16 x 5250 = 840
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15(2x -10) + 4x= -3(15x + 4)
The value of x in the equation 15(2x - 10) + 4x = -3(15x + 4) is 1.7
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
Given the equation:
15(2x - 10) + 4x = -3(15x + 4)
Solving the parenthesis:
30x - 150 + 4x = -45x - 12
Collect like terms:
30x + 4x + 45x = -12 + 150
79x = 138
Dividing both sides by 79:
x = 1.7
The value of x is 1.7
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Can someone please answer and provide an explanation for these problems?
The area of the sector is: 21) 177.0 cm² 22) 58.6 in.²
The missing sides are: 23) 12 24) 8
How to Find the Area of a Sector of a Circle?The area of the sector of any circle is given as:
Area = ∅/360 * πr², where r is the radius.
21. ∅ = 120°
r = 13 cm
Substitute:
Area = 120/360 * π * 13² = 177.0 cm²
22. ∅ = 105°
r = 8 in.
Substitute:
Area = 105/360 * π * 8² = 58.6 in.²
Since the lines appear tangents in the circles given, then the triangle formed is a right triangle, therefore, we will apply the Pythagorean Theorem in each case:
23. Missing side = √[(9 + 6)² - 9²]
Missing side = 12
24. Let the missing side be x. Therefore, we have:
12 + x = √(16² + 12²)
12 + x = 20
12 + x - 12 = 20 - 12
x = 8
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Ali has X paintings He buys two more paintings.
How many Paintings does he now have?
Answer:
X+2
Hope this helps
At a football game, a vender sold a combined total of 233 sodas and hot dogs. The number of hot dogs sold was 51 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
The vendor sold 142 sodas and 91 hotdogs.
According to the question:
The vendor sold 233 sodas and hotdogs combined
The number of hot dogs sold was 51 less number of sodas sold
To find:
Number of sodas sold(S)
Number of hotdogs sold(H)
From the question, it is clear that:
S + H = 233 ...(i)
S - H = 51 ...(ii)
These two are simultaneous linear equations.
Adding equations (i) and (ii):
S + H + S - H = 233 + 51
2S = 284
S = 284/2
S = 142
Substitute this value of S in equation (i):
142 + H = 233
H = 233 - 142
H = 91
Therefore, the vendor sold 142 sodas and 91 hotdogs.
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Hi
Please help on question asap if the answer is correct I'll rate you five stars a thanks and maybe even brainliest!
What do you notice about the values?
0.9 amps ÷0.03v=30 ohms.
1.9amps÷0.07v=27.149 ohms
3.1. amps ÷0.10v =31 ohms
3.9. amps ÷ 0.12v =032.5 ohms
5. amps ÷0.15v=33.33 ohms
6.1. amps ÷0.19v=32.1053 ohms
In the given data, current and voltage are directly proportional, while the resistance is constant.
What is the relationship between current and voltage?The relationship between the voltage, current, and resistance in an electric circuit is described by Ohm's Law.
The law states that the voltage across a circuit is directly proportional to the current flowing in the circuit.
V ∝ I
V = IR
where;
R is the resistance, the proportionality constantFrom the given data set we can see that for each division of current by voltage we have almost a constant value of 30 ohms.
Thus, if we observe the values given in the data set, we can conclude that;
current and voltage are directly proportional, while the resistance is constant.
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I just need someone to draw the tree diagram for the picture below not to much
According to the information, there are thousands of different lunch options in this restaurant.
How to calculate the number of different lunches in the restaurant?To calculate the number of different lunches in the restaurant we must carry out the following mathematical procedure. We must multiply the different options as shown below:
4 green options x 5 protein options x 8 vegetable options x 4 extra options x 6 topping options = 4 x 5 x 8 x 4 x 6 = 4,800 different lunch options.
Based on the above, we can infer that 4,800 different lunch options can be created with the available ingredients.
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area of a floor 19m by 12 m is
Answer:228m
Step-by-step explanation: 19m x 12m = 228m
Answer: 228m
Step-by-step explanation: Just multiply 19m by 12m. That's how you find area.
Before the new carpet is installed, all
the walls and the ceiling will be painted
with primer. If one gallon of primer
covers 300 square feet, how many
gallons of primer will be needed?
44 ft
8 ft
32 ft
You would need to purchase 6 gallons of primer.
Which of the following is an example of a statistical experiment?
A Twenty people in a neighborhood are asked if they want more streetlights on the street.
OB. More streetlights are installed on one street and people are then asked if they like the change.
OC. The number of accidents on the street is compared to last year's rate.
OD. People are asked to call a number to comment about the need for new streetlights.
Answer:
B. More streetlights are installed on one street and people are then asked if they like the change.
Step-by-step explanation:
An experiment is a type of research method that involves manipulating one or more variables and measuring their effects on other variables. In this case, the experiment is to change the color of the product packaging and see how many people like the change. This is because the outcome of the experiment (the number of people who like the change) depends on chance and can be measured using numerical data. The other options are not experiments, but surveys or observations. Surveys involve asking people questions and collecting their opinions or preferences. Observations involve watching and recording people's behavior or reactions without interfering with them.