Answers
The relative frequency that a randomly selected student's favorite exhibit was either butterflies or trains is 0.025.
What is the formula for calculating the joint relative frequency?Assume you need to compute the joint relative frequency of a certain category inside a larger category.
Then there's the proportion of that specific category's frequency to the total frequency of that large category.
The sum of all the frequency of the survey is;
⇒12+25+17+6
⇒60
The relative frequency for butterflies:
⇒12/60
⇒1/5
⇒0.25
The relative frequency for the train:
⇒6/60
⇒1/10
⇒0.1
The relative frequency that a randomly selected student's favorite exhibit was either butterflies or trains is;
⇒0.25×0.1
⇒0.025
Hence the relative frequency that a randomly selected student's favorite exhibit was either butterflies or trains is 0.025.
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Related Questions
The entire graph of the function h is shown in the figure below.
Write the domain and range of h using interval notation.
Answers
Answer:
Step-by-step explanation:
Thomas earns extra money babysitting. He charges 45.50 for 5 hours and 72.80 for 8 hours. How much will thomas charge for 3 hours.
Answers
You take $45.50 and divide it by 5 to get the charge of one hour then times it by three.
You can also do $72.80 divided by 8 to get the charge of one hour, then times it by 3.
urgent help needed w this pls
Answers
Answer:
Based on the given information, we know the following:
Solid A is formed by joining one hemisphere to the frustum of a cone.
Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone.
The volume of solid A is 6 times the volume of solid B.
We can use the formulas for the volume of a hemisphere and a frustum of a cone to represent the volumes of solids A and B.
The volume of a hemisphere is (2/3)πr^3, where r is the radius of the hemisphere.
The volume of a frustum of a cone is (1/3)πh(R^2+r^2+Rr), where h is the height of the frustum, R is the radius of the larger base and r is the radius of the smaller base.
The volume of a cone is (1/3)πr^2h
Let's call the height of the frustum h, the radius of the large base R and the radius of the small base r
We can set up the equation: (2/3)πr^3 = 6((1/3)πr^2h + (1/3)πR^2h + (1/3)πRrh)
After simplifying, we get:
2h = 12r + 12Rh + 6Rr
We know k = (R/r)^(1/3)>(7)^1/3, we can substitute it into the equation:
2h = 12r + 12rk + 6rk^2
Solving for h, we get:
h = 6rk + 6rk^2
So h is expressed in terms of k and r.
if the parallel sides of a parallelogram are 2 cm apart and their sum is 10 cm then its area is
Answers
Answer:
10cm^2
Step-by-step explanation:
The parallel sides of a parallelogram is 2cm apart
Their sum is 10cm
Therefore the area can be calculated as follows
= 2 ×10/2
= 20/2
= 10 cm^2
Hence the area is 10cm^2
what value of h is needed to complete the square for the equation
Answers
To complete the square for the equation \(x^2 + 8x + 32 = (x - h)^2 + 16\),
we need to choose h = -2.
To complete the square for the given equation
\(x^2 + 8x + 32 = (x - h)^2 + 16\),
we need to express the left-hand side of the equation in the form
\((x - p)^2 + q\), where p and q are constants.
We can start by expanding the right-hand side of the equation:
\((x - h)^2 + 16 = x^2 - 2hx + h^2 + 16\)
Now we can compare the coefficients of \(x^2\), x, and the constant term on both sides of the equation:
\(x^2 + 8x + 32 = (x - p)^2 + q\)
=> \(p^2 = 0\) (since the coefficient of \(x^2\) is 1 on both sides)
=> -2hp = 8 (since the coefficient of x is 8 on the left-hand side)
=> h = -2 (solving for h)
=> q = \(h^2 + 16\) = 20 (since the constant term on the right-hand side is 16)
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The complete question may be:
What value of h is needed to complete the square for the equation \(x^2+8 x+32=(x-h)^2+16\) ?
Calculate the percentage by which the orangutan population has changed from 1900 when there were 85,000 orangutans to the present day when there are about 6,600 orangutans. Give your answer to 2 decimal places.
Answers
The percentage by which the orangutan population has changed is 92.23%
We know that the formula for the relative change.
R = |x2 - x1| ÷ x1
where x2 is the final value
and x1 is the initial value
R is the relative change
Here, the orangutan population has changed from 1900 when there were 85,000 orangutans to the present day when there are about 6,600 orangutans.
This means, x1 = 85000 and x2 = 6600
So, the relative change would be,
R = |6600 - 85000| ÷ 85000
R = 78400 / 85000
R = 0.9223
and the percentage change would be,
P = R × 100
P = 0.9223 × 100
P = 92.23%
Therefore, the percentage change = 92.23%
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you are examining three different containers. each holds 20cm^3 of water and each is 5cm high. the three containers are as follows: a cylinder a regular pentagon based prism a square based prism which container requires the least amount of material to make?
Answers
Comparing the surface areas of the three containers, we find that the cylinder requires the least amount of material to make, with a surface area of approximately 39.99 cm².
To determine which container requires the least amount of material to make, we need to compare the surface areas of the three containers: the cylinder, the regular pentagon-based prism, and the square-based prism.
1. Cylinder:
The formula for the lateral surface area of a cylinder is given by:
A_cylinder = 2πrh,
where r is the radius of the base and h is the height of the cylinder.
Given that the volume of the cylinder is 20 cm³ and the height is 5 cm, we can calculate the radius:
V_cylinder = πr²h,
20 = πr²(5),
r² = 4/π,
r ≈ 1.27 cm.
Substituting the values into the lateral surface area formula, we get:
A_cylinder = 2π(1.27)(5) ≈ 39.99 cm².
2. Regular Pentagon-Based Prism:
To find the surface area of a regular pentagon-based prism, we need to know the apothem (a line segment from the center of the polygon to the midpoint of one of its sides) and the height of the prism.
Since the container holds 20 cm³ of water and has a height of 5 cm, each layer of water has a volume of 20/5 = 4 cm³. As the prism is regular, we can find the side length of the pentagon by calculating the square root of the prism's volume:
side length = √(4/tan(π/5)) ≈ 2.12 cm.
The apothem of a regular pentagon can be calculated using the formula:
apothem = side length / (2tan(π/5)) ≈ 1.85 cm.
The lateral surface area of the pentagon-based prism is given by:
A_pentagon = 5 × (1/2 × perimeter × apothem) = 5 × (5 × 2.12 × 1.85) ≈ 49.17 cm².
3. Square-Based Prism:
Since the container holds 20 cm³ of water and has a height of 5 cm, each layer of water has a volume of 20/5 = 4 cm³. Thus, the base area of the square is 4 cm².
The lateral surface area of a square-based prism is given by:
A_square = 4 × side × height,
where side is the length of one side of the base and height is the height of the prism.
Given that the base area is 4 cm² and the height is 5 cm, we can calculate the side length of the square base:
4 = side²,
side ≈ 2 cm.
Substituting the values into the lateral surface area formula, we get:
A_square = 4 × 2 × 5 = 40 cm².
Comparing the surface areas of the three containers, we find that the cylinder requires the least amount of material to make, with a surface area of approximately 39.99 cm².
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HELPPPP PLEASE!!
Find the discounted price of a $90 calculator that is on sale for 25% off.
Answers listed:
$22.50
$67.50
$89.75
$65.00
Answers
Answer:
67.5
Step-by-step explanation:
ok easy it cost $90
90/100=0.9
0.9*25=22.5
90-22.5
67.5
Find the radius of the sphere. Use 3.14 for
V= 113.04
Answers
Answer:
square root of pie represent the triangularity of the polverinizing sphere which is V=12.^7aN(f>82
HURRY MY TIMES RUNNING OUT
Answers
Answer:
C
Step-by-step explanation:
Input x 6 = output for each of these numbers
3x6 =18
6x6 =36
11x6 = 66
12x6 = 72
the other options are incorrect. A is divided by 4, B is times 4, and D is divided by 6.
Name: Date: 6. A biased four-sided die is rolled. The following table gives the probability of each score. Score 1 21 3 Probability 0.28 k 0.15 0.3 a. Find the value of k. (2 marks) b. Calculate the e
Answers
The expected value of the die roll is 2.47. Finding the value of kProbability is the measure of the likelihood of an event taking place. The sum of the probability of all events occurring must equal one, otherwise, the set of events would be incomplete, which is not possible.
Therefore, we have 0.28 + k + 0.15 + 0.3 = 1 where k is the probability of getting 2 on the die.Solving for k:k = 1 - 0.28 - 0.15 - 0.3k = 0.27Therefore, the value of k is 0.27. b. Calculating the expected valueThe expected value of the die roll is the sum of each score multiplied by its probability of occurrence. This is also called the mean of the probability distribution, given by: E(X) = ΣxP(x)where X is the random variable and P(x) is the probability of X being equal to x.Using the given table of probabilities:E(X) = 1(0.28) + 2(0.27) + 3(0.15) + 4(0.3)E(X) = 0.28 + 0.54 + 0.45 + 1.2E(X) = 2.47Therefore, the expected value of the die roll is 2.47.
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Practice & Problem Solving
7. Leveled Practice Use the Pythagorean Theorem
to find the distance between points P and Q to the nearest tenth.
Label the length, in units, of each leg of the right triangle.
fy
c²=
10
8
6
4
2
P(3, 2)
Q(10, 10)
units
0
0 2 4 6 8 10
X
8. Express each of the side lengths
of triangle POR as a square root.
units
c²=
C=
Answers
The lengths of the legs of the right triangle and distance of between P and Q found using Pythagorean Theorem is about 10.6 units
The completed calculations used to obtain the distance between P and Q is presented as follows;
c² = 8² + 7²
c² = 64 + 49
c = √(113)
The distance between point P and point Q is about 10.6 units
What is Pythagorean Theorem?Pythagorean Theorem is a theorem that provides the relationship between the legs of a right triangle and the hypotenuse side of a right triangle. The Pythagorean Theorem states that the square of the hypotenuse side is equivalent to the sum of the square of the legs of the right triangle.
The figure in the question plotted on the graph is a right triangle
The coordinates of the point P on the graph is P(3, 2)
The coordinates of the point Q on the graph is Q(10, 10)
The coordinates of the third vertex point of the right triangle = (10, 2)
The lengths of the horizontal and vertical legs of the right triangle are;
Length of the horizontal leg = 10 units - 3 units = 7 units
Length of the vertical leg of the right triangle = 10 units - 2 units = 8 units
Where the length of the hypotenuse side of the right triangle, PQ = c, according to the Pythagorean Theorem, we get;
The square of the distance between P and Q, which is the square of the hypotenuse side, c² = The square of the length of the vertical side + The square of the length of the horizontal side
c² = 8² + 7² = 113
c² = 64 + 49 = 113
c = √(113) ≈ 10.6
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I NEED HELP ! I WILL CASH APP YOU !
Answers
Answer:B and D
Step-by-step explanation:big brain
Select the correct answer. Consider the graph of f(x) given below. The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)? A. g(x) = f(x - 5) B. g(x) = f(x) - 2 C. g(x) = f(x) - 5 D. g(x) = f(x + 2)
PLEASE OFFER ME YOUR ANSWER, I ASK OF YOU...PLS
Answers
The function that could represent g(x) is (c) g(x) = f(x) - 5
How to determine the function g(x)?The figure of the graph that completes the question is added as an attachment
From the attached graph, we have the equation of the function to be
y = f(x)
Also, the graph of the function f(x) has its intercept to be
y-intercept of f(x) = 3
From the question, we have
y-intercept of g(x) = -2
Subtract the intercepts
Difference = y-intercept of g(x) - y-intercept of f(x)
So, we have
Difference = -2 - 3
Evaluate
Difference = -5
The function g(x) is then represented as
g(x) = f(x) + Difference
So, we have
g(x) = f(x) - 5
Hence, the function g(x) is g(x) = f(x) - 5
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suppose that for budget planning purposes the city in exercise 12 needs a better estimate of the mean daily income from parking fees. a) someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. how would this interval be better for the city?
Answers
A 95% confidence interval is wider than a 90% confidence interval and so provides a better estimate of the population mean.
A confidence interval represents the range of values within which the population mean is estimated to lie with a certain degree of confidence. The wider the interval, the more certain we can be that the population mean lies within it. In other words, a 95% confidence interval provides a better estimate of the population mean than a 90% interval because it is wider and therefore more likely to contain the true population mean.
This increased accuracy is particularly important for the city in their budget planning as it allows them to make more informed decisions based on a more reliable estimate of their expected daily income from parking fees.
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Can someone please help me with this question
Answers
Answer:
I would think its 120
Step-by-step explanation:
Answer:
120*
Step-by-step explanation:
Help i cant get this wrong
Answers
Answer:
D
Step-by-step explanation:
I'm not the greatest in this subject, but I think that it's D/If the roof leaks, then the ceiling gets damaged because it clearly says that in the statement. It could be all of them, though, but this is my answer. Hope it helps!
Answer:
D. If it rains, then the ceiling gets damaged.
Explanation:
So, if it rains, then the roof leaks, and if the roof leaks, then the ceiling gets damaged, is the exactly the structure of the syllogism law that permits to conclude if it rains, then the ceiling gets damaged.
Pip was thinking of a number. Pip doubles it and gets the answer of 50.8. What was the original number?
Answers
Answer:
25.4
Step-by-step explanation:
If double of the number 'x' is 50.8, (2x=50.8)
Then the original number must be half of that value, (x=50.8/2)
50.8/2 = 25.4
I’m doing a review but I forgot how to do this can someone help?
Answers
Answer:
-3x+10=5x-8
so basically its like grouping.
so answer is
8x=18?
Step-by-step explanation:
sorry if incorrect
Answer:
x=2.25
Step-by-step explanation:
three -x make -3x and 10 +1s make +10 and 5 xs make 5x and 8 -1s make -8
which makes
-3x+10=5x-8
just solve
18=8x
2.25=x
Graph the solution to this inequality on the number line.
−4m+3>11
Answers
Subtract numbers
-4m>11-3
Evaluate and subtract
-4m>8
Divide by -4
Solution
M<-2
Answer: The person above me is correct. Here is a picture if you still dont get it..
Step-by-step explanation:
Solve each equation. Round to the nearest ten-thousandth. log x=log 2 x²-2
Answers
The solution to the equation log(x) = log(2x² - 2) is x ≈ 1.7321.
To solve the equation, we'll use the property of logarithms that states log(a) = log(b) if and only if a = b.
Given the equation log(x) = log(2x² - 2), we can equate the expressions inside the logarithms: x = 2x² - 2
Rearranging the equation: 2x² - x - 2 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Using a = 2, b = -1, and c = -2:
x = (-(-1) ± √((-1)² - 4(2)(-2))) / (2(2))
= (1 ± √(1 + 16)) / 4
= (1 ± √17) / 4
Approximating the solutions to the nearest ten-thousandth:
x ≈ (1 + √17) / 4 ≈ 1.7321
Therefore, the solution to the equation is x ≈ 1.7321.
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Helpppp I don’t get theseeee!!!!
Answers
Answer:
3,I guess
Step-by-step explanation:
7(b - 2) = -7
7b - 14 +7 =0
7b =14 + 7
7b =21
7b/7 =21/7
b = 3
7b - 14 = -7
7b = 14-7
7b = 7
b = 1
Solve with Quadratics
Answers
Answer:
x = 1 ± \(\sqrt{6}\)
Step-by-step explanation:
Given
2x² - 4x = 10 ( divide through by 2 )
x² - 2x = 5
Using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 1)x + 1 = 5 + 1
(x - 1)² = 6 ( take the square root of both sides )
x - 1 = ± \(\sqrt{6}\) ( add 1 to both sides )
x = 1 ± \(\sqrt{6}\) ← exact solutions
Answer:
\(x \pm\sqrt6 +1\)
Step-by-step explanation:
Hello!
Standard form of a quadratic: ax² + bx + c
Solve:
2x² - 4x = 102x² - 4x - 10 = 02(x² - 2x - 5) = 0x² - 2x - 5 = 0Now, complete the square:
Take the b-value in our equation (-2)Divide it by 2 (-1)Square it (1)Add and subtract that in our equation:
x² - 2x - 5 = 0x² - 2x + 1 - 5 - 1 = 0Factor the perfect square trinomial:
(x - 1)² - 6 = 0(x - 1)² = 6\(\sqrt{(x-1)^2} = \sqrt{6}\)x - 1 = ±√6x = ±√6 + 1The solutions are \(x \pm\sqrt6 +1\)
Find the surface area
Answers
Answer:
200.96
Step-by-step explanation:
2(3.14)2^2 + 2(3.14)2*14
8*3.14 = 25.12
56*3.14 = 175.84
175.84 + 25.12 = 200.96
i-solve the fraction 315+79 (show all steps)
Answers
Answer:
Step-by-step explanation:
step 1 Address input parameters & values.
Input parameters & values:
The fraction number = 315/79
step 2 Write it as a decimal
315/79 = 3.9873
3.9873 is the decimal representation for 315/79
For Percentage Conversion :
step 1 To represent 3.9873 in percentage, write 3.9873 as a fraction
Fraction = 3.9873/1
step 2 multiply 100 to both numerator & denominator
(3.9873 x 100)/(1 x 100) = 398.73/100
398.73% is the percentage representation for 315/79
Data that are accurate, consistent, and available in a timely fashion are considered: A) Oracle-based. B) Microsoft-based. C) high-quality. D) low-quality.
Answers
Data that are accurate, consistent, and available in a timely fashion are considered C) high-quality.
High-quality data is characterized as being reliable, consistent, and timely. High-quality data offers a strong foundation for analysis and decision-making because it is accurate, error-free, and consistent.
It is a valuable asset for organizations because it promotes accurate reporting and analysis, increases operational efficiency, and allows for informed decision-making. Although database management systems like Oracle and Microsoft SQL Server can assist with managing and storing data, the quality of the data is unrelated to the particular technology or program employed.
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Calculate the area of the shaded sector. KL = 20 ft
Answers
Answer:
415.39 \(ft^{2}\)
Step-by-step explanation:
3. Which name does not apply to the angle pair?
A. vertical
C. supplementary
B. adjacent
D. right angles
12
Answers
Answer:
D. right angle
Step-by-step explanation:
I think D is because
right angle is a an angle of exactly 90°
*adjacent angle is two angles with a common vertex, sharing a common side and no overlap
*supplementary angle is two angle, the sum of who's measure is 180
* vertical angle is two angle who's sides form two pairs of opposite rays (straight line)
Which expression is equivalent to -15x + 39?
Answers
Answer:
56x
Step-by-step explanation:
i think
Pls help me i’m on my test and i’m stuck
A car costs $45,000 new but depreciates at a rate of 19% per year. What is the value of the car after four years?
A
$19,371.02
B
$44,744.00
c.
$45,000.43
D.
$90,240.26
Answers
Answer:It is 19,371.02
Step-by-step explanation: If You Find out What 19 Percent of the number is then subtract it from your Number Then Repeat This 4 Times