A relative frequency of 0.56 means that out of the total number of observations in a given sample or population, 56% of those observations belong to a particular category or have a certain characteristic.
In other words, it is the proportion or fraction of the observations that fall into that particular category or have that characteristic, relative to the total number of observations. For example, if we had a sample of 100 people and 56 of them had brown hair, then the relative frequency of brown hair would be 0.56 or 56%.
To calculate relative frequency, you divide the frequency of a specific event or category by the total number of observations. In this case, the specific event or category occurs 56% as often as the total events or categories observed.
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Flying Home for the Holidays Does the airline you choose affect when you'll arrive at
your destination? The dataset DecemberFlights contains the difference between actual and
scheduled arrival time from 1000 randomly sampled December flights for two of the major North
American airlines, Delta Air Lines and United Air Lines. A negative difference indicates a flight
arrived early. We are interested in testing whether the average difference between actual and
scheduled arrival time is different between the two airlines.
a. Define any relevant parameter(s) and state the null and alternative hypotheses.
b. Find the sample mean of each group, and calculate the difference in sample means.
c. Use StatKey or other technology to create a randomization distribution and find the p-value.
d. At a significance level of a = 0. 01, what is the conclusion of the test? Interpret the conclusion in
context.
a
Relevant parameter is the difference between actual and scheduled arrival time. Also the difference in sample means is -1.70 minutes. We get a p-value of 0.017 and the conclusion is that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.
a. Relevant parameter: the difference between actual and scheduled arrival time.
Null hypothesis: The average difference between actual and scheduled arrival time is the same for Delta Air Lines and United Air Lines.
Alternative hypothesis: The average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.
b. Sample mean for Delta Air Lines: -2.31 minutes
Sample mean for United Air Lines: -4.01 minutes
Difference in sample means: -1.70 minutes
c. To create a randomization distribution, we can pool the data from both airlines and randomly assign them to two groups with the same sample sizes as Delta Air Lines and United Air Lines. We then calculate the difference in sample means for each random assignment. Repeating this process many times gives us a randomization distribution. Using StatKey with 10,000 iterations, we get a p-value of 0.017, which is less than 0.01.
d. At a significance level of 0.01, we reject the null hypothesis and conclude that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines. Specifically, the average difference for United Air Lines is greater than that of Delta Air Lines. This could have implications for travelers who prioritize arriving on time, as they may wish to consider
Delta over United.
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HELP! WILL GIVE BRAINLIEST!
A yard stick is placed on the table during a party game. A marker is placed at 11 inches, and labeled A, one labeled B at 24 inches, another labeled C at 26 and another labeled D at 36. A marble is shot toward the yard stick. What is the probability that the marble that hits the yard stick between A and D hits it between C and D? Write your answer as a percent
The required probability 40%
To find the probability that the marble that hits the yard stick between A and D hits it between C and D, we need to find the length of the interval between C and D, and divide it by the length of the interval between A and D.
The length of the interval between C and D is
36 - 26 = 10
The length of the interval between A and D is
36 - 11 = 25
The probability that a marble will strike a yardstick between A and D and C and D is
10/25 × 100 = 40%
Therefore, the probability that a marble will strike a yardstick between A and D and C and D is 40%
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The value of a sculpture depreciates by 20% each year. Today it is worth £650. How much was it worth 3 years ago? Give your newer to the nearest penny.
The sculpture was worth £332.80 three years ago when it depreciates by 20% each year
To determine how much the sculpture was worth 3 years ago, we need to apply the depreciation rate of 20% per year for the past three years.
First, we need to calculate how much the sculpture would be worth after one year of depreciation:
650 - (0.20)(650) = 520
This means that after the first year, the sculpture would be worth £520.
Next, we can calculate the value of the sculpture after the second year of depreciation:
520 - (0.20)(520) = 416
After two years, the sculpture would be worth £416.
Finally, we can calculate the value of the sculpture after the third year of depreciation:
416 - (0.20)(416) = 332.8
Therefore, the sculpture was worth £332.80 three years ago.
To check this answer, we can also use another method: We can calculate the value of the sculpture using the compound interest formula, where the initial value is £x, the annual depreciation rate is 20%, and the time period is three years:
650 = x[tex](1-0.20)^{2}[/tex]
Simplifying this equation, we get:
x = 650 / [tex]0.80^{2}[/tex] = 332.80
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Question 2 of 10
The graph of y=-2x + 10 is:
OA. a point that shows the y-intercept.
OB. a line that shows the set of all solutions to the equation.
OC. a line that shows only one solution to the equation.
D. a point that shows one solution to the equation.
Answer:
The graph of y = -2x + 10 is B) a line that shows the set of all solutions to the equation.------------------------------------------------
A linear equation is an equation of a straight line.
It describes the straight-line graph of a set of ordered pairs (x, y) that are solutions to the equation.
There are different forms of linear equations.
The slope-intercept form of a linear equation is y = mx + b.
The equation y = -2x + 10 is in slope-intercept form. Its graph is a line with slope -2 and y-intercept 10. It shows the set of all solutions to the equation.
As per description above, the correct answer choice is B, all the other options are false.
find the volume and the total surface area
The volume of a trapezoidal prism is 2362.5.
The total surface area is 852.
We have,
The volume of a trapezoidal prism.
V = ((a + b) / 2) × h × l
where:
a and b are the lengths of the two parallel sides (the bases) of the trapezoid
h is the height of the trapezoid (the perpendicular distance between the two bases)
l is the length of the prism (the distance between the two trapezoidal faces)
Now,
a = 9
b = 12
l = 15
Height h can be calculated using the Pythagorean theorem.
15² = (12 - 9)² + h²
h² = 225 + 9
h² = 234
h = √234
h = 15
Now,
The volume of a trapezoidal prism.
V = ((a + b) / 2) × h × l
V = ((9 + 12) / 2) x 15 x 15
V = 2362.5
And,
The surface area (A) of a trapezoidal prism can be calculated using the formula:
A = ph + 2B
where p is the perimeter of the trapezoidal base, h is the height of the prism, and B is the area of one of the bases.
So,
p = 12 + 8 + 12 + 8 = 44
h = 15
B = 12 x 8 = 96
Now,
Total surface area.
= 44 x 15 + 2 x 96
= 660 + 192
= 852
Thus,
The volume of a trapezoidal prism is 2362.5.
The total surface area is 852.
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QUESTION IN PHOTO I MARK BRAINLIEST
The value of x in the given circle is 13.9.
Given that a circle D, having an inscribed angle ∠CFE = 57° and the arc opposite it arc CE = 10x-25, we need to find the measure of x,
Using the inscribed angle theorem,
It states that the angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circumference of the circle.
So,
m ∠CFE = arc CE / 2
57 = 10x-25 / 2
10x-25 = 114
10x = 139
x = 13.9
Hence the value of x in the given circle is 13.9.
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If f(x) = 3x² - 3, find x = 2
Answer:
The answer is 9
Step-by-step explanation:
When x = 2,
f(2) = 3×2^2-3
f(2) = 3×4-3
f(2) = 12-3
f(2)= 9
Please answer the question correctly and neatly. Will upvote if
correct.
The temperatue of a town t months after January can be estimated by the function f(t) = – 20 cos (64) +66 Find the average temperature from month 1 to month 6
The average temperature from month 1 to month 6 is approximately 58.3 degrees Fahrenheit.
How to find the average temperature?The temperature of a town t months after January can be estimated by the function f(t) = –20 cos(64t) + 66. To find the average temperature from month 1 to month 6, we need to evaluate the integral of f(t) from t=1 to t=6 and divide by the number of months:
Average temperature = (1/6 - 1) ∫[1,6] f(t) dt
= (1/6 - 1) ∫[1,6] (-20 cos(64t) + 66) dt
= (1/6 - 1) [-5 sin(64t) + 66t] [1,6]
= (1/6 - 1) [-5 sin(646) + 666 - (-5 sin(641) + 661)]
= (1/6 - 1) [-5 sin(384) + 395]
≈ 58.3 degrees Fahrenheit
Therefore, the average temperature from month 1 to month 6 is approximately 58.3 degrees Fahrenheit.
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Jacob is building a square pyramid for a class project. He needs to cover the entire pyramid in aluminum foil. The base of the pyramid has a perimeter of 76 centimeters. The slant height of each triangular side is 28 centimeters. What is the surface area, in square centimeters, of Jacob’s pyramid?
The surface area of the pyramid is 390.8 cm².
What is the surface area of the triangular pyramid?The surface area of the triangular pyramid is calculated as follows;
S.A = base area + ¹/₂ (perimeter + slant height)
The height of the pyramid is calculated by applying Pythagoras theorem;
h = √ (28² - 14²)
h = 24.2 cm
Area of the base = ¹/₂ x 28 cm x 24.2 cm = 338.8 cm²
The surface area of the pyramid is calculated as follows;
S.A = 338.8 cm² + ¹/₂ (76 cm + 28 cm)
S.A = 390.8 cm²
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Answer:
1,425
Step-by-step explanation:
I got this one correct
A study was conducted to determine the relationship existing between the grade in english and the grade in mathematics. a random sample of 10 cte students in uc were taken and the following are the results of the sampling th a)compute for the pearson( r) - 10pts b) state null and alternative hypothesis- 5pts b)find equation of regression line- 5pts c) interpret and conclude results - 5pts student 1 2 3 4 5 6 7 8 9 10 english 75 83 80 77 89 78 92 86 93 84 mathematics 78 87 78 76 92 81 89 89 91 84
a) The Pearson correlation coefficient is 0.76.
b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)
Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)
c) The regression line is: y = 0.64x + 34.18
d) Interpretation and conclusion: The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.
Correlation analysis:
Using the Pearson correlation coefficient to measure the strength and direction of the linear relationship between two variables.
Hypothesis testing:
Setting up null and alternative hypotheses, and using the t-test to determine whether the correlation coefficient is statistically significant.
Linear regression:
Finding the equation of the regression line that best describes the relationship between the two variables.
Interpretation and conclusion:
Using the results of the analysis to draw meaningful conclusions about the relationship between the two variables and the sample population as a whole.
Here we have
A study was conducted to determine the relationship existing between the grade in English and the grade in mathematics. a random sample of 10 students in uc was taken and the following are the results of the sampling
Student 1 2 3 4 5 6 7 8 9 10
English 75 83 80 77 89 78 92 86 93 84
Mathematics 78 87 78 76 92 81 89 89 91 84
a) To compute the Pearson correlation coefficient (r), first calculate the mean, standard deviation, and covariance of the two variables:
Mean of English grades (x)
= (75+83+80+77+89+78+92+86+93+84)/10 = 83.7
Mean of Math grades (y)
= (78+87+78+76+92+81+89+89+91+84)/10 = 84.5
The standard deviation of English grades (Sx)
= √((75-83.4)²+(83-83.4)²+...+(84-83.4)²)/9) = 6.52
The standard deviation of Math grades (Sy)
= √((78-84.4)²+(87-84.4)²+...+(84-84.4)²)/9) = 5.47
Covariance of the two variables
= ((75-83.4)(78-84.4)+(83-83.4)(87-84.4)+...+(84-83.4)(84-84.4))/9 = 26.6
Using the formula, r = cov(X,Y)/(SxSy),
we can calculate the correlation coefficient as follows
r = 26.6/(6.52*5.47) = 0.76
Therefore,
The Pearson correlation coefficient is 0.76.
b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)
Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)
c) To find the equation of the regression line, we need to calculate the slope (b) and the intercept (a) of the line. The formula for the slope is:
b = r(Sy/Sx) = 0.76(5.47/6.52) = 0.64
The formula for the intercept is:
=> a = y - bx = 84.4 - 0.64(83.4) = 34.18
Therefore,
The equation of the regression line is:
y = 0.64x + 34.18
Interpretation and conclusion:
The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.
The p-value associated with this correlation coefficient can be used to test the null hypothesis.
The equation of the regression line shows that for every one-point increase in the English grade, the predicted increase in the Mathematics grade is 0.64 points.
Therefore,
a) The Pearson correlation coefficient is 0.76.
b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)
Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)
c) The regression line is: y = 0.64x + 34.18
d) Interpretation and conclusion: The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.
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Jackson makes fruit punch by mixing the ingredients listed below.
6 cups of orange juice
5 pints of fruit punch
8 cups of apple juice
How many quarts of fruit punch does Jackson make?
A.3
B.6
C.24
D.96
Answer: B
Step-by-step explanation:
First, let's convert the 5 pints of fruit punch to cups:
5 pints = 5 x 2 cups/pint = 10 cups
Now we can add up the cups of each ingredient:
6 cups of orange juice + 10 cups of fruit punch + 8 cups of apple juice = 24 cups
Since there are 4 cups in a quart, we can divide by 4 to get the number of quarts:
24 cups ÷ 4 cups/quart = 6 quarts
Therefore, Jackson makes 6 quarts of fruit punch.
The square below has an area of x^ 2 − 12 x + 36 What expression represents the length of one side of the square?
The length of one side of the square is x - 6 units
How to determine the lengthThe formula for calculating the area of a square is expressed as;
A = a²
Such that the a is the length of its side
From the information given, we have that;
Area = x^ 2 − 12 x + 36
solve the quadratic expression, we have that;
x² - 6x - 6x + 36
group in pairs
(x²- 6x) - (6x + 36)
factorize the terms
x(x - 6) - 8(x - 6)
Then, we have;
(x - 6) and (x - 6) units
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Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2. 6 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 12 minutes with each customer. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. Round your answers to four decimal places. Do not round intermediate calculations
There is a 95.52% chance that there are no customers in the system, a 9.93% chance that a customer has to wait in line, and a 31.20% chance that the server is busy.
λ = 2.6 guests per hour( Poisson appearance rate) μ = 1/ 12 hours per client( exponential service rate) c = 1 garçon( design adviser ) Using Little's Law, we can find the average number of guests in the staying line L = λ * W
where W is the average time a client spends in the system( staying and being served). To find W, we can use the formula
W = 1/( μ- λ) Using these formulas, we get
W = 1/(1/12-2.6) = 0.1154
hours = 6.92 twinkles
L = 2.6 *0.1154 = 0.3000 guests
So on average, there will be0.3 guests staying in line and each client will stay for6.92 twinkles before being served.
We can also cipher the probability that there are no guests in the system(P_0), the probability that a client has to stay(P_w), and the probability that the garçon is busy
(P_b) = 1- λ/ μ
= 0.9552
λ/ μ2 *( 1/( 1- λ/ μ)) = 0.0993 = λ/ μ = 0.3120
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PLEASE HELP ME AS SOON AS POSSIBLE WITH EXPLANATIONS PLEASE!!!!!
The statements true of the two-dimensional plane sections that could result from one of these slices made by Misha are B, C, D, E, and F.
What makes a two-dimensional plane sections?A. False. The only two-dimensional plane sections that could result from slicing a cube with a plane are squares or rectangles, but not triangles.
B. True. A plane section that is square could result from one of these slices through the cube.
C. True. A plane section that is rectangular but not square could result from one of these slices through the cube.
D. True. A plane section that is triangular could result from one of these slices through the pyramid.
E. True. A plane section that is square could result from one of these slices through the pyramid.
F. True. A plane section that is rectangular but not square could result from one of these slices through the pyramid.
Therefore, the correct statements are B, C, D, E, and F.
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7. If angle GFE ~ angle CBE, find FE.
The value of FE comes out to be 35.
What is angle?An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The measure of an angle is typically given in degrees or radians, and it describes the amount of rotation needed to move one of the rays or line segments to coincide with the other. Angles are used in many areas of mathematics, physics, engineering, and other sciences to describe and analyze various phenomena.
What is parallel line?Parallel lines have the same slope and will never meet, no matter how far they are extended. Parallel lines are important in geometry and other areas of mathematics, as well as in engineering, architecture, and other fields where precise measurements and constructions are required.
[tex]4x-1/x+5 = 60/24\\5x+25= 8x-2\\27= 3x\\x=9[/tex]
Therefore FE= 4×(9)-1
=35
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A boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 5 , before they draw closer. They measure the angle of elevation a second time from point
B at some later time to be 18∘ Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
If boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water, the distance from point A to point B is approximately 973 feet.
To find the distance from point A to point B, we can use trigonometry and the fact that the angles of elevation from both points are known.
Let x be the distance from point A to the lighthouse, and y be the distance from point B to the lighthouse. We can set up two equations using tangent function:
tan(5) = 119/x
tan(18) = 119/y
We can solve for x and y by isolating them in each equation:
x = 119/tan(5) ≈ 1343.44 feet
y = 119/tan(18) ≈ 370.79 feet
Therefore, the distance from point A to point B is approximately 1343.44 - 370.79 = 972.65 feet.
We rounded the final answer to the nearest foot, which is 973 feet.
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In ΔRST, s = 990 inches, ∠S=8° and ∠T=60°. Find the area of ΔRST, to the nearest square inch
The area of ΔRST, to the nearest square inch is,
Area = 29,17,735.54 square inches
We have,
In ΔRST, s = 990 inches, ∠S=8° and ∠T=60°.
Apply sine rule formula,
sin S / s = sin T / t
sin 8° / 990 = sin 60° / t
0.14 / 990 = 0.87 / t
0.14t = 990 x 0.87
0.14t = 861.3
t = 6,152 inches
Here, ∠R = 180° - (8 + 60)°
∠R = 180 - 68
∠R = 112°
sin S / s = sin R / r
sin 8° / 990 = sin 112° / r
0.14 / 990 = 0.92 / r
0.14r = 0.92 x 990
0.14r = 910.8
r = 910.8 / 0.14
r = 6505 inches
We use the formula
Heron's formula = √s(s - a)(s - b)(s - c)
Where s = a + b + c/2
Solving for s
s = 990 + 6505 + 6,152 /2
s = 6823.5
Solving for the area of the triangle
= √6823.5 × (6823.5 - 990) × (6823.5 - 6,152) × (6823.5 - 6505)
= √6823.5 x 5833.5 x 671.5 x 318.5
= 29,17,735.54 square inches
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Please help
jkl will be rotated 90° clockwise around the origin to form j'k'l
what are the coordinates of point j' after the rotation?
The coordinates of point j' after the rotation are (-y, x), where x and y are the original coordinates of point j
The coordinates of point j' after rotating point jkl 90° clockwise around the origin can be found by applying the following transformation:
j' = (cos(90°) * x - sin(90°) * y, sin(90°) * x + cos(90°) * y)
Since we are rotating 90° clockwise around the origin, we have cos(90°) = 0 and sin(90°) = 1, so the transformation simplifies to:
j' = (0 * x - 1 * y, 1 * x + 0 * y)
j' = (-y, x)
Therefore, the coordinates of point j' after the rotation are (-y, x), where x and y are the original coordinates of point j.
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Solve this: 12C11
And solve the others too
The values of the combination expressions are ¹²C₁₁ = 12, ¹²C₁₀ = 66, ¹²C₅ = 792, ¹²C₁ = 12, ¹²C₁₂ = 1, ⁵C₄ + ⁵C₃ = 15, ⁵C₃/⁵C₂ = 1 and 4⁷C₂ = 84
Also, the number of ways is 30045015
Solving the combination expressionsFrom the question, we have the following parameters that can be used in our computation:
¹²C₁₁
The formula for combination is
ⁿCₓ = n!/[(n - x)! * x!]
So, we have
¹²C₁₁ = 12!/[(12 - 11)! * 11!]
Evaluate
¹²C₁₁ = 12
Using the above as a guide, we have the following:
¹²C₁₀ = 12!/[(12 - 10)! * 10!]
¹²C₁₀ = 66
¹²C₅ = 12!/[(12 - 5)! * 5!]
¹²C₅ = 792
¹²C₁ = 12!/[(12 - 1)! * 1!]
¹²C₁ = 12
¹²C₁₂ = 12!/[(12 - 12)! * 12!]
¹²C₁₂ = 1
⁵C₄ + ⁵C₃ = 5!/[(5 - 4)! * 4!] + 5!/[(5 - 3)! * 3!]
⁵C₄ + ⁵C₃ = 15
⁵C₃/⁵C₂ = 5!/[(5 - 3)! * 3!] / 5!/[(5 - 2)! * 2!]
⁵C₃/⁵C₂ = 1
4⁷C₂ = 4 * 7!/[(7 - 2)! * 2!]
4⁷C₂ = 84
For the number of ways to get people hired, we have
n = 30
x = 10
So, we have
³⁰C₁₀ = 30!/[(30 - 10)! * 10!]
³⁰C₁₀ = 30045015
Hence, the number of ways to get them hired is 30045015 ways
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In a game of chance players spin the pointer of a spinner with six equal sized sections Anna 1 John 4 Carrie 4 Steve 1 Ethan 2 Liz 4 Jane 1 which outcome has a frequency closest to its expected frequency A (1) B (2) C (3) D (4)
The outcome with a frequency closest to its expected frequency is C (3).
Which outcome in a spinner game has a frequency closest to its expected frequency?In a spinner game where the pointer spins on a wheel with six equal-sized sections, the expected frequency of each section is 1/6 or 16.67%. Based on the given spinner, section A has an expected frequency of 1/6, section B has an expected frequency of 4/6, section C has an expected frequency of 4/6, section D has an expected frequency of 1/6, section E has an expected frequency of 2/6, and section F has an expected frequency of 4/6.
To determine the outcome with a frequency closest to its expected frequency, we need to compare the expected frequency to the actual frequency for each section.
Based on the given spinner, section A has an actual frequency of 1/18, section B has an actual frequency of 4/18, section C has an actual frequency of 4/18, section D has an actual frequency of 1/18, section E has an actual frequency of 2/18, and section F has an actual frequency of 4/18.
Calculating the difference between the expected and actual frequency for each section, we find that section C has the smallest difference, making it the outcome with a frequency closest to its expected frequency.
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What’s this answer in the picture
The sine function for the graph is given as follows:
y = sin(3x).
(a one should be placed on the green blank).
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(Bx).
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.The function oscillates between y = -1 and y = 1, for a difference of 2, hence the amplitude is obtained as follows:
2A = 2
A = 1.
The period is of 2π/3 units, hence the coefficient B is given as follows:
B = 3.
Then the equation is:
y = sin(3x).
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Estimate the solution to the system of equations. You can use the interactive graph below to find the solution.
7x−y=7
x+2y=6
Choose 1 answer:
(Choice A): x=1 1/3, y=1 1/3
(Choice B): x=2 1/3, y=2 1/3
(Choice C):x=2 1/3, y=1 1/3
(Choice D):x=1 1/3, y=2 1/3
Answer:
the answer is D
Step-by-step explanation:
Answer:
C. x = 2 1/3, y = 1 1/3.
Step-by-step explanation:
To solve this question, we need to plot the two equations on the graph and see where they cross. The graph below shows the two lines in different colors:
We can see that the point of intersection is somewhere between (1, 2) and (2, 1). Looking at the given options, we can see that only one of them is in that range. That is option C. x = 2 1/3, y = 1 1/3. Therefore, the answer is C. x = 2 1/3, y = 1 1/3.. The volume of a sphere is 6,000π m^3. What is the surface area of the sphere to the nearest square meter?
*
18850 m^2
33 m^2
1090 m^2
3425 m^2
The correct option is the last one, the surface is 3425 m²
How to get the surface area of the sphere?Remember that for a sphere of radius R, the volume is:
V = (4/3)pi*R³
S = 4pi*R²
Where pi = 3.14
Here the volume is 6,000π m³, then the radius will be:
R =∛( (3/4)*6,000m³)
R = 16.51 m
Then the surface area is:
[tex]S = 4*3.14*( 16.51 m)^2 = 3,424 m^2[/tex]
The option that is closser to it is the fourth one, so that is the correct option.
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A group of 150 dancers are auditioning for a dance show. 93 of the dancers trying out did not get on the show. What percentage of the dancers didn’t get in the show?
62% of the dancers did not get into the show.
To find the percentage of dancers who did not get into the show.
First, identify the total number of dancers auditioning and the number of dancers who did not get into the show.
In this case, there are 150 dancers in total, and 93 of them did not get in.
Next, divide the number of dancers who did not get into the show by the total number of dancers auditioning.
This will give us the proportion of dancers who did not get in.
Proportion = (Number of dancers who did not get in) / (Total number of dancers)
Proportion = 93 / 150
Finally, to find the percentage, multiply the proportion by 100:
Percentage = Proportion * 100
Percentage = (93 / 150) * 100.
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The surface area of a right-circular cone of radius r and height his S = πr √ r²+h² , and its volume is V = 1/3πr²h. (a) Determine h and r for the cone with given surface area S = 8 and maximal volume V. h = (4/(3pi^2))^(1/4) r = (1/(3p1^2))^(1/4) (b) What is the ratio h/r for a cone with given volume V = 5 and minimal surface area S? h/r = sqrt2 (c) Does a cone with given volume V and maximal surface area exist?
The height and radius of the cone with maximal volume V and surface area S = 8 are h = (4/(3π^2))^(1/4) and r = (1/(3π^2))^(1/4),
respectively.Explanation: To find the height and radius of the cone with maximal volume and surface area of 8, we need to use the formulas for the surface area and volume of a right-circular cone in terms of r and h. We can then use the method of Lagrange multipliers to find the values of r and h that maximize the volume subject to the constraint that the surface area is equal to 8.Using the formulas for the surface area and volume of a cone, we get:S = πr √(r²+h²)V = 1/3πr²hWe can then set up the Lagrangian function L(r,h,λ) = 1/3πr²h + λ(πr √(r²+h²) - 8), where λ is the Lagrange multiplier.Taking the partial derivatives of L with respect to r, h, and λ and setting them equal to zero, we get:∂L/∂r = 2/3πrh + λ(π√(r²+h²) + r²/√(r²+h²)) = 0∂L/∂h = 1/3πr² + λ(πh/√(r²+h²)) = 0∂L/∂λ = πr √(r²+h²) - 8 = 0Solving these equations, we get:h = (4/(3π^2))^(1/4)r = (1/(3π^2))^(1/4)Therefore, the height and radius of the cone with maximal volume and surface area of 8 are h = (4/(3π^2))^(1/4) and r = (1/(3π^2))^(1/4), respectively.(b) The ratio of height to radius for the cone with minimal surface area S and volume V = 5 is h/r = √2.Explanation: Using the formulas for the surface area and volume of a cone in terms of r and h, we can set up the following optimization problem:Minimize S = πr √(r²+h²)Subject to V = 1/3πr²h = 5Using the method of Lagrange multipliers, we can set up the Lagrangian function L(r,h,λ) = πr √(r²+h²) + λ(1/3πr²h - 5), where λ is the Lagrange multiplier.Taking the partial derivatives of L with respect to r, h, and λ and setting them equal to zero, we get:∂L/∂r = π√(r²+h²) + 2λr/3πh = 0∂L/∂h = πr²h/√(r²+h²) - 5λ/3π = 0∂L/∂λ = 1/3πr²h - 5 = 0Solving these equations, we get:h/r = √2Therefore, the ratio of height to radius for the cone with minimal surface area S and volume V = 5 is h/r = √2.(c) No, a cone with given volume V and maximal surface area does not exist.Explanation: Using the formulas for the surface area and volume of a cone in terms of r and h, we can set up the following optimization problem:Maximize S = πr √(r²+h²)Subject to V = 1/3πr²hUsing the method of Lagrange multipliers, we can set up the Lagrangian function L(r,h,λ) = πr √(r²+h²) + λ(1/3πr²h - V), where λ is the Lagrange multiplier.Taking the partial derivatives of L with respect to r, h, and λ and setting them equal to zero, we get:∂L/∂r = π√(r²+h²) + 2λr/3πh = 0∂L/∂h = πr²h/√(r²+h²) - λ/3πr² = 0∂L/∂λ = 1/3πr²h - V = 0Solving these equations, we get:h = rr³ = 3V/πSubstituting h = r into the surface area formula, we get:S = 2
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If f(x) = x2 − 6x − 4 and g(x) = 5x + 3, what is (f + g)(−3)? (1 point)
41
35
11
−35
The value of (f + g)(−3) given the functions f(x) = x² − 6x − 4 and g(x) = 5x + 3 is 11.
To find (f + g)(-3), we first need to add the functions f(x) and g(x) together, and then evaluate the resulting function at x = -3.
f(x) = x² - 6x - 4
g(x) = 5x + 3
Now, let's add f(x) and g(x):
(f + g)(x) = (x² - 6x - 4) + (5x + 3) = x² - x - 1
Now that we have the combined function, we can evaluate it at x = -3:
(f + g)(-3) = (-3)² - (-3) - 1 = 9 + 3 - 1 = 11
So, (f + g)(-3) = 11.
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Emilio draws an example of an obtuse triangle. Which triangle could be Emilio's drawing?
A.
Triangle with three angles less than 90 degrees.
B.
Triangle with one 90 degree angle and two angles less than 90 degrees.
C.
Triangle with two angles less than 90 degrees and one angle greater than 90 degrees.
D.
Triangle with three angles less than 90 degrees.
Answer:
C. An obtuse triangle has two angles less than 90 degrees and one angle greater than 90 degrees.
Calculate the derivatives of all orders: f'(x), F"(x), F"(x), f(4)(x), ..., f(n)(x), ... f(x) = (-2x + 1)3 f'(x) f''(x) = f''(x) = f(4)(x) = f(n) (x) for all n 25
The first derivative of f(x) is f'(x) = -12(-2x + 1)2. The second derivative is f''(x) =48(-2x + 1), and all higher derivatives have the form f^(n)(x) = (-1)n * 6 * n! * (-2x + 1)^(3-n).
To calculate the derivatives of all orders for f(x) = (-2x + 1)3, we first need to find the first derivative:
f(x) = (-2x + 1)³
f'(x) = 3(-2x + 1)²(-2)
f'(x) = 3(-2x + 1)²(-2)
f'(x) = -12(-2x + 1)2
Next, we find the second derivative:
f''(x) = d/dx(-12(-2x + 1)²)
f''(x) = 2(-2)(-12)(-2x + 1)
f''(x) = -12[2(-2x + 1)(-2)]
f''(x)= 48(-2x + 1)
We can continue this process to find the third and fourth derivatives:
f'''(x) = d/dx(96(-2x + 1))
f'''(x) = -384
f''''(x) = d/dx(-384)
f''''(x) = 0
Notice that the fourth derivative is 0, meaning that all higher derivatives will also be 0.
This is because the original function is a polynomial of degree 3, so its fourth derivative will be the derivative of a constant, which is 0.
Therefore, we can conclude that:
f(4)(x) = 0
f(n)(x) = 0 for all n ≥ 4.
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Ethan wrote the number below.
Lucy wrote another number in which the value of the digit 5 is 10 times larger than it is in Ethans number. Which number could be Lucy's number?
A. 4982.58
B. 4945.82
C. 4974.65
D. 4958.03
The answer would be D
Since Lucy's number has a digit of 5 which is 10x greater than Ethan's number, 5 x 10 = 50; so 50 would be in the tenth place, and option d is the only one with 5 in the tenth place.
The value of a number moves one decimal place to the left for each position it moves to the right. So, the number that Lucy could have written where the number 5 has a value 10 times larger than Ethan's number is 4974.65.
Explanation:In order for the value of the digit 5 to be 10 times larger in Lucy's number than it is in Ethan's, the '5' in Lucy's number should reside one place left compared to Ethan's. This means the 5 should be in the tens place, hundreds place, or beyond. So, we should look for a number having digit 5 at those places.
Let's examine the given options:
A. 4982.58 - '5' is in the hundredths place, which makes its value smaller, not larger.B. 4945.82 - '5' is in the ones place. No change in value.C. 4974.65 - '5' is in the tens place, making its value 10 times larger than if it were in the ones place.D. 4958.03 - '5' is in the thousands place, which makes its value even larger, but more than 10 times.Therefore, the correct answer is C. 4974.65.
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In circle O, mAD = 120 and mBC= 80. What is mBEC? :0 ;(
The measure of angle m<BEC is 80 degrees
How to determine the valueFrom the information shown, we have that;
m< AD = 120 degrees
m< BC = 80 degrees
To determine the value of m<BEC, we need to know that it is a minor arc in the circle.
Also, a minor arc is described as the shorter arc that connects two endpoints on a circle.
The measure of a minor arc is less than 180° , and is equal to the measure of the arc's central angle.
We can see than the angle measure of m<BC = m<BEC
Then,
m<BEC = 80 degrees
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