If the length and width of the pen are both whole numbers the possible perimeters for the pen are 98, 52, 38, 32, and 28.
To find the possible perimeters of the pen, we first need to find all the possible length and width pairs that would give us an area of 48 square feet. Since the length and width are whole numbers, we can start by listing out all the factors of 48:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Each of these factors represents a possible length or width of the pen, and we can find the other dimension by dividing the area (48) by the first dimension. For example, if the first dimension is 1, then the other dimension is 48/1 = 48. However, we need to make sure that the second dimension is also a whole number.
Using this method, we can find all the possible length and width pairs:
1 x 48, 2 x 24, 3 x 16, 4 x 12, 6 x 8
Now we can calculate the perimeter for each of these pairs. The perimeter is the sum of the lengths of all four sides of the pen. Since the length and width are the same for a square pen, we can use the formula:
perimeter = 2(length + width)
For each pair, we can plug in the values for length and width to get the perimeter:
1 x 48: perimeter = 2(1 + 48) = 98
2 x 24: perimeter = 2(2 + 24) = 52
3 x 16: perimeter = 2(3 + 16) = 38
4 x 12: perimeter = 2(4 + 12) = 32
6 x 8: perimeter = 2(6 + 8) = 28
Therefore, the possible perimeters for the pen are 98, 52, 38, 32, and 28.
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what is 11.5 + 10.5 in math
Answer:
22
Step-by-step explanation:
10+11=21
.05+.05=1
1+21=22
Suppose that researcher; using data on class size (CS) and average test scores (S) from 100 third-grade classes, estimates the OLS regression: S = 520. 4 5. 82 CS, (20. 4) (2. 21) Rz = 0. 08, SER = 11. 5 a) A classroom has 22 students What is the regression prediction for that classroom average test score?b) Last year classroom had 19 students and this year it has 23 students What is the regression's prediction for the change in the classroom average test score? c) The sample average class size across 100 classrooms is 21. 4. What is the sample average ofthe test scores across the 100 classrooms? d) Interpret the R? measure. Is it large Or small? What does it mean? e) What is the magnitude of the coefficient of correlation in this model? Interpret the R? measure the context of the correlation coefficient: What is the difference in the interpretation of the twO measures of the linear association of the tWo random variables? f) What is the sample standard deviation of test scores across the 100 classrooms? Hint: Use the formula for the standard error of the regression (SER) to get the sum of squared residuals:
a) The regression prediction for a classroom with 22 students is 651.24.
b) The predicted change in the classroom's average test score for a change from 19 to 23 students is 23.28.
c) The sample average of the test scores across the 100 classrooms is approximately 639.88.
d) The R-squared (R²) measure is 0.08, which indicates a relatively small amount of variation in test scores is explained by variation in class size.
e) The magnitude of the coefficient of correlation (r) is 0.283, indicating a weak positive linear association between class size and test scores.
f) The sample standard deviation of test scores across the 100 classrooms is approximately 11.28.
a) If a classroom has 22 students, then the regression prediction for that classroom's average test score would be:
S = 520.4 + 5.82(22) = 651.24
b) If last year a classroom had 19 students and this year it has 23 students, then the predicted change in the classroom's average test score would be:
ΔS = 5.82(23-19) = 23.28
Note that this calculation assumes that the other factors affecting test scores remain the same, which may not be realistic.
c) The sample average class size across 100 classrooms is 21.4. To find the sample average of the test scores across the 100 classrooms, we simply plug in the average class size into the regression equation:
S = 520.4 + 5.82(21.4) = 639.88
Therefore, the sample average of the test scores across the 100 classrooms is approximately 639.88.
d) The R-squared (R²) measure in this model is 0.08. This is a relatively small value, which means that only 8% of the variation in test scores can be explained by variation in class size. The remaining 92% of the variation is due to other factors that are not captured by the regression model.
e) The magnitude of the coefficient of correlation (r) in this model can be found by taking the square root of R²:
r = √0.08 = 0.283
The interpretation of r is that there is a weak positive linear association between class size and test scores. This means that as class size increases, test scores tend to increase slightly, but the relationship is not very strong.
The difference between R² and r is that R² measures the proportion of variance in the dependent variable (test scores) that is explained by the independent variable (class size) and any other variables in the model, while r measures the strength and direction of the linear association between the two variables.
f) The standard error of the regression (SER) is given as 11.5. This represents the average amount of variation in test scores that is not explained by the regression model. The sample standard deviation of test scores can be estimated by multiplying SER by the square root of (1 - R²) and dividing by the square root of the number of observations:
s = SER × √(1 - R²) / √n
= 11.5 × √(1 - 0.08) / √100
= 11.28
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degree 4 polynomial with zeroes 4 and -(6)/(5) (each with multiplicity 1) and 0 (with multiplicity 2)
The degree 4 polynomial with the given zeroes is P(x) = x^4-(94/5)x^3-(24/5)x^2.
A degree 4 polynomial with the given zeroes can be represented as:
P(x) = (x-4)(x+(6)/(5))(x-0)^2
Simplifying the polynomial gives:
P(x) = (x-4)(x+(6)/(5))(x^2)
P(x) = (5x-20)(x+(6)/(5))(x^2)
P(x) = (5x^2-20x+(6x)/(5)-24/(5))(x^2)
P(x) = (25x^2-100x+6x-24)/(5)(x^2)
P(x) = (25x^2-94x-24)/(5)(x^2)
P(x) = (5x^4-94x^3-24x^2)/(5)
P(x) = x^4-(94/5)x^3-(24/5)x^2
So the degree 4 polynomial with the given zeroes is P(x) = x^4-(94/5)x^3-(24/5)x^2.
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Which Value Of X Will Make The Expression?
Answer:
2 and -2
Step-by-step explanation:
For the expression to be equal to 0, it means it has to be undefined, so all we need do, is equate the denominator to 0, since any number divided by 0 = 0
Therefore,
5x² - 20 = 0
5x² = 0 + 20
5x² = 20
Divide both sides by 5,
x² = 20/5
x² = 4
Square root both sides,
x² = √4
x = ±2
Please mark brainliest.
Thanks.
Escribir la ecuación cuadrática con raíces 1 y 5, y con coeficiente principal 2.
(Utilizar la letra x para representar la variable. )
The quadratic equation with roots 1 and 5 and leading coefficient 2 is 2x^2 - 12x + 10 = 0
To write the quadratic equation with roots 1 and 5 and leading coefficient 2, we can use the fact that the general form of a quadratic equation is:
ax^2 + bx + c = 0
where a, b, and c are constants.
Since the roots are 1 and 5, we know that the factors of the quadratic equation are:
(x - 1) and (x - 5)
Multiplying these factors together, we get:
(x - 1)(x - 5) = x^2 - 6x + 5
To satisfy the condition of having a leading coefficient of 2, we can simply multiply the entire equation by 2
2(x^2 - 6x + 5) = 2x^2 - 12x + 10
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A young group and their leaders visited mammoth cave. two adults and five students in one been paid $77 for the hand avenue tour of the cave. Two adults and seven segments
students in the second van pair $95 for the same tour. Find the adults price and the student pieces
price of the tour.
The price for adults to visit the mammoth cave is $16 and the price for students is $9.
What is the adult and students price?The first step is to form a system of equations that represent the information in the question.
2a + 5s = 77 equation 1
2a + 7s = 95 equation 2
Where:
a = price of one adult
s = price of one student
The elimination method would be used to solve the equations.
Subtract equation 1 from equation 2:
2s = 18
Divide both sides of the equation by 2
s = 18/2
s = $9
Substitute for s in equation 1:
2a + 5(9) = 77
2a + 45 = 77
2a = 77 - 45
2a = 32
a = 32 / 2
a = 16
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Please please help me! This is due ASAP
sin 200 degrees cos 80 degrees- cos 200 degrees sin 80 degrees
Thank you!!
Answer:
0.866
Step-by-step explanation:
sin (200) = −0.34202014
cos (80) = 0.17364817
-
cos (200) = −0.93969262
sin (80) = 0.98480775
=
0.86602540338, or 0.866
Type the correct answer in the box.
(Graphs)
Graph [] describes exponential decay.
1. he marks of Calculus I in the final examination in a private college are normally distributed with a mean of 45 marks and a standard deviation of 10 marks. (a) If a student is chosen at random, find the probability that his/her mark is less than 52. 0.75$ (b) If the college has 220 students who sat for the examination, find the number of students whose marks are between 45 and 55. 75 (c) Find the percentage of students whose marks exceed 40. 69.15%
2. A survey on the study habits of 1000 HSM students shows that 550 use reference books, 750 have regular study times and all those who use reference books have regular study time. A HSM student is chosen at random; what is the probability that the student
a) only has regular study time?
b) either has a regular study time or uses
reference books?
c) neither studies regularly nor uses reference
books?
1. (a) Using a z-table, we can find the probability corresponding to this z-score, which is 0.758. Therefore, the probability that a student's mark is less than 52 is 0.758. (b) To find the number of students whose marks are between 45 and 55, we need to calculate the z-scores for 45 and 55 . The z-score for 45 is (45 - 45) / 10 = 0, and the z-score for 55 is (55 - 45) / 10 = 1. (c) The probability corresponding to this z-score is 0.3085. Therefore, the percentage of students whose marks exceed 40 is 1 - 0.3085 = 0.6915, or 69.15%. 2. (a) So, the probability that a student only has regular study time is 750/1000 - 550/1000 = 200/1000 = 0.2. (b) The probability that a student either has a regular study time or uses reference books is 750/1000 + 550/1000 - 550/1000 = 750/1000 = 0.75. (c) The probability that a student neither studies regularly nor uses reference books is 1 - 0.75 = 0.25.
Therefore, the probability that a student's mark is between 45 and 55 is 0.8413 - 0.3413 = 0.5. Since there are 220 students in the college, the number of students whose marks are between 45 and 55 is 0.5 * 220 = 110.
To find the probability that a student's mark is less than 52, we need to calculate the z-score for 52 using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation. So, z = (52 - 45) / 10 = 0.7.
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OAB is a sector of a circle as shown below.
Work out the length of the arc AB.
Give your answer in millimetres (mm) to
1 d.p.
IMPORTANT
The length of the arc AB is 44.7 mm
What is the length of an arc?A sector is a part of a given circle which is bounded by two radii and an arc. The length of an arc is simply the path of the incomplete circle.
The length of an arc can be determined by:
length of an arc = θ/ 360 2πr
Where is the measure of the central angle, and r is the radius of the circle.
From the diagram given,
The length of arc AB = θ/ 360 2πr
= 61/ 360*2*22/7*42
= 44.7333
The length of arc AB is 44.7 mm.
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when Aaron runs the 400 m dash is finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 2.5 seconds using the elliptical rule determine the interval of times that represent the middle 99.7% of his finishing times in the 400 m race.
So, by resolving the given, we obtain the result: As a result, the range of standard deviation timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.
What is standard deviation?A statistic called standard deviation may be used to represent the variability or variation of a collection of statistics. A low standard deviation means that the values often tend to be closer to the set mean, whereas a large standard deviation shows that the values are widely spread. The standard deviation is an indicator of how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is small, and are more scattered when it is big. Standard deviation is the average degree of variability in the data collection. It displays each score's standard deviation from the mean.
We can thus get the z-scores that correspond to the bottom and upper bounds of this range using the z-score calculation formula:
Lower bound: z = (x - )/z = (x - 80)/z = 2.5 z = -3
The maximum value is z = (x - ) / z = (x - 80) / 2.5 z = 3.
The area under the curve between z = -3 and z = 3 can be calculated using a calculator or a conventional normal distribution table.
The minimum value is z = -3 (x - 80) / 2.5 = -3 x - 80 = -7.5 x = 72.5.
z = 3 (x - 80) / 2.5 = 3 x - 80 = 7.5 x = 87.5 is the upper limit.
As a result, the range of timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.
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Damion is building a pool in his backyard. He needs the pool to have a length of 12.5 meters (m) and a width of 5.7 m. He also needs the volume of the
pool not to exceed 114 cubic meters (m³).
12.5 m
The Height of the pool should be 1.6 m.
What is Volume?Every three-dimensional item requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object inside the confines of three-dimensional space. It is also known as the object's capacity.
Given:
length of pool= 12.5 m
width of pool = 5.7 m
and, Maximum volume of pool = 114 m³
So, Volume= l w h
114 = 12.5 x 5.7 x h
114 = 71.25 h
h = 114/ 71.25
h = 1.6 m
Thus, the height can be 1.6 m.
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Which of the following gives the correct range for the graph? −2 ≤ x ≤ 5
For the functiοn, the range is deduced tο be [-2, 5].
What is the range of data?
The range οf data is defined as a measure of the difference between the maximum value of data and the minimum value οf data.
The rangeοf a graph refers to the set of all possible output values, or the y-values, οf the function represented by the graph.
The given range of −2 ≤ x ≤ 5 actually represents the domain of the function, or the set οf all possible input values, or the x-values, fοr which the function is defined.
Sο, the range can also be written as [-2, 5] for the given set of data.
Therefore, the range is οbtained as [-2, 5].
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565 545 245 450 350How much money will they save monthly by the move to Oakland?
Benito and his family will save $1,315 by the move to Oakland.
Savings in house = $1200 - $565
= $635
Savings in food = $655 - $545
= $110
Saving in health care = $495 - $245
= $250
Saving in taxes = $625 - $450
= $175
Saving in necessities = $495 - $350
= $145
Total saving = $635 + $110 + $250 + $175 + $145
= $1,315.
Hence, Benito and his family will save $1,315 by the move to Oakland.
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Your question is incomplete, the complete question is:
Benito's family is thinking of relocating from Los Angeles to Oakland to save money. They set up a budget comparing the cost of living for both cities.
Oakland Los Angeles
Cost Housing $565 $1200
Food $545 $655
Health Care $245 $495
Taxes $450 $625
Other Necessities $350 $495
How much money will they save monthly by the move to Oakland? $1315, $1560, $1665, or $1765?
a printer makes more than three copies of labels every hour graph the number of books made in 2 hours.
8900 dollars is placed in a savings account with an annual interest rate of 3.3% if no money is added or removed from the account which equation represents how much will be in the account after 4 years
Answer: 10134.2425
Step-by-step explanation:
Your initial number, 8900, is multiplied by 1+.033 because your percent and your adding money. It all is then raised to the power of 4. Your equation will be 8900(1+.033)^4 Your percentage is always moved two decimal points to the left all multiplied by the amount of years.
Which equation can be used to find the area of the figure below?
F.A = (10⋅82
)+
(16⋅8
)
G.A = (6⋅82
)+
(10⋅8
)
H.A = (6⋅82
)+
(6⋅8
)
J.A = (6⋅8
)+
(10⋅8
)
The equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).
What is area of composite figure?The area of mixed shapes is the area that is covered by any hybrid shape. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These forms or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.
A composite form is essentially a combination of fundamental shapes. A "composite" or "complex" shape is another name for it.
The area of the rectangle is given as:
A = (l)(w)
A = 10(8)
A = 80 sq. units
The area of the triangle is:
A = 1/2(b)(h)
In the figure:
b = 16 - 10 = 6 and h = 8.
A = 1/2(6)(8)
A = 24 sq. units
The total area of the figure is:
Area = area of rectangle + area of triangle
Area = 80 + 24
Area = 104 sq. units
Hence, the equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).
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Jayden made 5% of his free throws over the season. If he shot 120 free throws, how many did he make? Divide/scale down to solve for the missing percent.
Answer:6
Step-by-step explanation:If jayden made 5% of his free throws and he shot 120 free throws you have to find 5% of 120.
5% of 120 = 6
So Jayden shot a total of 6 free throws during the season
Please help, I don't know how to do this!!!
the height of the antenna is approximately 24 meters.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
From the diagram, we see that we need to find the distance d and the height h. We can use the tangent function to find these values.
First, let's find d:
tan(θ) = h / (d + 1.51)
Rearranging, we get:
d = (h / tan(θ)) - 1.51
Next, let's find h:
tan(θ') = h / d
Substituting the expression for d that we found above, we get:
tan(θ') = h / ((h / tan(θ)) - 1.51)
Multiplying both sides by (h/tan(θ1)) - 1.51 and simplifying, we get:
h = (29 * tan(θ') * tan(θ)) / (tan(θ') - tan(θ))
Now we can plug in the values for the angles and solve for h:
h = (29 * tan(31°) * tan(17°)) / (tan(31°) - tan(17°))
h ≈ 24
So the height of the antenna is approximately 24 meters.
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If 1/6 of a gallon of milk is shared equally between three friends how much milk will each friend get
the friends receive one eighteenth each
Use interval notation to write the intervals over which f is a) increasing, b)
decreasing, and c) constant.
-5-4-3-2-1
S
f
3+
CN
1+
-1-
-2+
-3+
-4-
-5+
1 2 3 4 5 X
Answer: (a) From the graph, we can see that the function f is increasing on the interval [-5, -1), (-2, 2), and (3, 5]. Therefore, we can write the increasing intervals in interval notation as:
[-5, -1) ∪ (-2, 2) ∪ (3, 5]
(b) From the graph, we can see that the function f is decreasing on the interval (-1, 1) and (2, 3]. Therefore, we can write the decreasing intervals in interval notation as:
(-1, 1) ∪ (2, 3]
(c) From the graph, we can see that the function f is constant on the interval [-4, -3]. Therefore, we can write the constant interval in interval notation as:
[-4, -3]
Step-by-step explanation:
URGENT: Can you find the perimeter of each polygon and type the correct code? Please remember to type in ALL CAPS with no spaces.
PLEASEEEE HELPPP NOW!!!
Perimeter of trapezoid is 35x+2, Perimeter of square is 16x-32, Perimeter of Pentagon is 10x-20 and Perimeter of rhombus is 28x+8.
What is Polygon?A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
Perimeter of trapezoid=9x+4+7x+8+12x-2+7x-8
Add the like terms
35x+2
Perimeter of trapezoid is 35x+2
Perimeter of square= 4(4x-8)
=16x-32
Perimeter of Pentagon=5(2x-4)
=10x-20
Perimeter of rhombus=4(7x+2)
=28x+8
Hence, Perimeter of trapezoid is 35x+2, Perimeter of square is 16x-32, Perimeter of Pentagon is 10x-20 and Perimeter of rhombus is 28x+8.
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Consider the set of vectors x, x + 3x^2, x^3, x^2 ∈ P[x]. Does
this set span P[x]?
No, the set of vectors x, x + 3x², x³, x² does not span P[x].
To span P[x], a set of vectors must be able to generate any polynomial in P[x] through a linear combination of the vectors in the set. However, the set given only includes polynomials of degree 1, 2, and 3. This means that it cannot generate polynomials of degree 0 (constants) or polynomials of degree 4 or higher.
For example, the polynomial 5 cannot be generated from a linear combination of the vectors in the set, as there are no constants in the set. Similarly, the polynomial x⁴ cannot be generated, as there are no vectors of degree 4 or higher in the set.
Therefore, the set of vectors x, x + 3x², x³, x² does not span P[x].
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If the figures below are similar, find the scale factor of Figure B to Figure A.
A. 3/16
B. 20/3
C. 16/3
D. 3
E. 3/20
F. 1/3
A construction crew is lengthening a road that originally measured 51 miles. The crew is adding one mile to the road each day. The length, L (in miles), after d days of construction is given by the following.
L= 51+d
What is the length of the road after 38 days?
Answer: 89 miles
Step-by-step explanation:
Well, if the construction crew added one mile every day for 38 days, then the formula would look like this.
L = 51 + (38)
51 + 38 = 89
L = 89 miles
Use simple interest to find the ending balance.
$7,900 at 1.9% for 2 & 3/4 years
Answer:
To calculate the ending balance, we can use the following formula:
Ending Balance = Principal x (1 + Interest Rate x Time)
Given:
Principal = $7,900
Interest Rate = 1.9%
Time = 2 3/4 years
Therefore,
Ending Balance = $7,900 x (1 + 0.019 x 2.75) = $8,084.60
Answer: 8319.66994
Step-by-step explanation:
your initial x your interest all raised to your time interval.
7,900(1+.019)^2.75
A new town developed in Wyoming due to mineral activity. It began with 150 workers/managers moving in, so in year zero its population was 150, after one year, 620 people lived in the new city. After two years, 1170 people inhabited the town, and by the end of the third year, the population was 1950. Find a linear regression that fits this data and predict the towns population by year 12.( what is the r^2 value?) what is the equation of the line? the r value? and prediction of population in year 12?
The equation of the line is y = 780x + 150, r² value is 0.186, the r value is 0.431, and the predicted population in year 12 is 9450.
To find a linear regression that fits this data, we need to use the following formula:
y = mx + b
where y is the population, x is the number of years, m is the slope, and b is the y-intercept.
We can use the data given to find the slope (m) and the y-intercept (b). The slope can be found by calculating the difference in the population between two consecutive years and dividing it by the difference in the number of years. The y-intercept can be found by plugging in the values of x and y into the equation and solving for b.
Using the data given, we can find the slope and y-intercept as follows:
m = (1950 - 1170) / (3 - 2) = 780
b = 150 - (0)(780) = 150
Therefore, the equation of the line is:
y = 780x + 150
To find the r² value, we can use the formula:
r² = 1 - (SSres / SStot)
where SSres is the sum of squares of residuals and SStot is the total sum of squares.
SSres = (150 - 150)² + (620 - 930)² + (1170 - 1710)² + (1950 - 2490)² = 2,484,400
SStot = (150 - 1222.5)² + (620 - 1222.5)² + (1170 - 1222.5)² + (1950 - 1222.5)² = 3,051,875
r² = 1 - (2,484,400 / 3,051,875) = 0.186
The r value can be found by taking the square root of the r²value:
r = √0.186 = 0.431
To predict the population in year 12, we can plug in the value of x into the equation of the line:
y = 780(12) + 150 = 9450
Therefore, the predicted population in year 12 is 9450.
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I paid $9.54 for 1.2 pounds of fresh fish.
How much did the fresh fish cost per pound?
A washing machine holds 10 gallons of water and drains 8 of the gallons in 2 minutes. What was the average flow through the pipe in 2 minutes?
gallons/min
Landon has a jar of coins. He chooses a coin at random, notes what type of coin it is, and returns it to the jar. After 12 trials, he calculates the experimental probabilities shown in the table.
On the 13th trial, Landon chooses a nickel.
What is the experimental probability of choosing a nickel based on the 13 trials?
Coin
Penny
Nickel
Dime
Quarter
Experimental
Probability
1/2
1/4
1/6
1/12
The experimental probability of choosing a nickel based on the 13 trials is 4/13.
What is probability ?
Probability can be defined as ratio number of favourable outcomes, total number of outcomes.
Based on the experimental probabilities shown in the table, we can calculate the probability of choosing a nickel on the 13th trial using the following steps:
Calculate the total number of trials: 12 + 1 = 13
Calculate the total number of times a nickel was chosen in the 12 trials: 12 * 1/4 = 3
Add 1 to the total number of times a nickel was chosen to account for the 13th trial: 3 + 1 = 4
Calculate the experimental probability of choosing a nickel based on the 13 trials: 4/13
Therefore, the experimental probability of choosing a nickel based on the 13 trials is 4/13.
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