Answer:
perimeter of plot=119m
circumference of pond=44m
volume of house=9000 m^3
surface area of room=248 m^2
Step-by-step explanation:
Suppose the chance of rain on Saturday is and the chance of rain on Sunday is also. A student wants to run a simulation to estimate the probability that it will rain on both days. (Example 1) Date Go Online You can complete you Part A How can the student model the chance of it raining on each day? Design a simulation.
The student can model the chance of it raining on each day through a simulation that is designed with the help of a random number generator.
How to model the situation ?Use a random number generator to simulate the probability of rain for Saturday and Sunday, using the given probability as the likelihood of rain. For example, if the probability of rain is 0.3, the random number generator can generate a random number between 0 and 1, and if the number is less than 0.3, it is considered as rain, otherwise, it is considered as no rain.
Repeat step 1 a large number of times, say 10,000 or more, to obtain a sample of random outcomes for the probability of rain on each day. Count the number of times it rains on both days in the sample. The student can then divide the number of times it rains on both days by the total number of simulations to estimate the probability of it raining on both days.
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Jamal has 19 seeds. Kiara has 4 more seeds than Jamal.
Answer: Kiara has 23 seeds.
Step-by-step explanation:
Let k = the amount of seeds Kiara has.
If Kiara has 4 more seeds than Jamal, then you use the equation 19 + 4 = k.
19 + 4 = k
23 = k
Kiara has 23 seeds.
Hope this helps!!! :)
If p is a positive integer, then p(p + 1)(p − 1) is always divisible by
F. 7
G. 5
H. 4
J. 3
K. None of these
Answer:
K
Step-by-step explanation:
We can factor the given expression as:
p(p + 1)(p - 1) = p^3 - p
Notice that p^3 - p is the difference of two consecutive cubes. This can be factored further using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2):
p^3 - p = p(p^2 - 1) = p(p + 1)(p - 1)
So, we have shown that p(p + 1)(p - 1) is equal to p^3 - p, which is the product of three consecutive integers. By definition, this product is always divisible by 3.
However, we cannot conclude that p(p + 1)(p - 1) is divisible by 4, 5, or 7 for all positive integers p. Therefore, the answer is K) None of these.
The graph of y = 5x2 is
Answer:
................................
what the answer of this
The correct option for this question is (d) "No, none of the sides are parallel."
why it is and what is a Quadrilateral?
To determine if quadrilateral CDEF is a trapezoid, we need to check if it has exactly one pair of parallel sides.
We can find the slopes of the line segments CD and EF as follows:
slope of CD = (5 - (-6)) / (-8 - (-1)) = 11 / (-7) = -1.57 (approx.)
slope of EF = (8 - 5) / (3 - 4) = 3 / (-1) = -3
Since the slopes are different, CD and EF are not parallel, and therefore, CDEF is not a trapezoid.
Alternatively, we can also find the slopes of the line segments CF and DE as follows:
slope of CF = (-5 - (-6)) / (4 - (-1)) = 1/5
slope of DE = (8 - 5) / (3 - (-8)) = 3/11
Since the slopes are different, CF and DE are not parallel, and therefore, CDEF is not a trapezoid.
Therefore, the answer is option (d) "No, none of the sides are parallel."
A quadrilateral is a geometric shape that has four straight sides and four vertices (corners). It is a two-dimensional polygon with four sides and four angles. The sum of the interior angles of a quadrilateral is always 360 degrees.
There are many types of quadrilaterals, including squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.
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3.4 3.2 3.3 5m 3.142 Radius of semi-circie = 5.5m Area of cir Au 35m YOGA TWEM Define the word Perimeter in this context. Calculate the length of the swimming pool. If the circumference of the semi-circle is 17 3m. Calculate tl. total perimeter of the swimming pool. Calculate the total area of the floor of the swimm You may use the given formu
In the context of a semi-circle, the perimeter refers to the total distance around the curved edge of the semi-circle. It is calculated by adding the length of the straight edge (diameter) to half the circumference of the semi-circle.
The total area of the floor of the swimming pool is 23.86 square meters.
How to calculate the valueThe diameter of the semi-circle is twice the radius, so the diameter is 2 × 5.5m = 11m.
Therefore, the perimeter of the semi-circle is:
Perimeter = Diameter + Circumference/2
Perimeter = 11m + 17.3m/2
Perimeter = 20.3m
The length of the swimming pool is equal to the perimeter of the semi-circle, which is 20.3 meters.
To calculate the total area of the floor of the swimming pool, we need to find the area of the semi-circle. The formula for the area of a semi-circle is:
Area = πr²/2
where π is a constant approximately equal to 3.14 and r is the radius of the semi-circle.
In this case, the radius is 5.5m, so the area of the semi-circle is:
Area = π(5.5m)²/2
Area = 47.71m²/2
Area = 23.86m²
Therefore, the total area of the floor of the swimming pool is 23.86 square meters.
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Radius of semi-circle = 5.5m Define the word Perimeter in this context. Calculate the length of the swimming pool. If the circumference of the semi-circle is 17 3m. Calculate the total area of the floor of the swimming pool.
There are two coins. One of them is a biased coin such that P (head): P (tail) is 1 : 3 and the other coin is a fair coin. A coin is selected at random and tossed once. If the coin showed head, then find the probability that it is a biased coin.
Answer:
Step-by-step explanation:
Let B be the event that the selected coin is biased, and F be the event that the selected coin is fair. Let H be the event that the coin toss shows a head.
We want to find P(B|H), the probability that the selected coin is biased given that the coin toss shows a head. By Bayes' theorem, we have:
P(B|H) = P(H|B) * P(B) / P(H)
We know that P(H|B) = 1/4 (since the biased coin has a probability of 1/4 of showing a head), and that P(B) = 1/2 (since there are two coins, one of which is biased).
To find P(H), we can use the law of total probability:
P(H) = P(H|B) * P(B) + P(H|F) * P(F)
P(H) = (1/4) * (1/2) + (1/2) * (1/2)
P(H) = 3/8
Putting it all together:
P(B|H) = P(H|B) * P(B) / P(H)
P(B|H) = (1/4) * (1/2) / (3/8)
P(B|H) = 1/3
Therefore, the probability that the selected coin is biased given that the coin toss shows a head is 1/3.
Without an appointment, the average waiting time in minutes at the doctor's office has the probability density function f(t)=1/38, where 0≤t≤38
Step 1 of 2:
What is the probability that you will wait at least 26 minutes? Enter your answer as an exact expression or rounded to 3 decimal places.
Step 2 of 2:
What is the average waiting time?
The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.
Step 1:
The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:
P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38
= (38/38) - (26/38) = 12/38 = 0.316
So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.
Step 2:
The average waiting time can be calculated by finding the expected value of the probability density function:
E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt
= [(t²)/(238)] from 0 to 38
= (38²)/(238) = 19
Therefore, the average waiting time is 19 minutes.
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Find an equation for a sinusoidal function that has period 47, amplitude 1, and contains the point
(-л, 2).
Write your answer in the form f(x) = Asin (Bx + C) + D, where A, B, C, and D are real numbers.
f(x) =
The sine function with the desired features is given as follows:
F(x) = sin(3.5π(x + π/2)) + 1.
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are listed as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function has an amplitude of 1, hence the parameter A is given as follows:
A = 1.
The period is of 4/7, hence the coefficient B is given as follows:
2π/B = 4/7
4B = 14π
B = 3.5π.
The function contains the point (-π, 2), hence the phase shift and the vertical shift are given as follows:
c = π/2, as the function has it's maximum value at x = π, while the standard function has at x = π/2.d = 1, as the function oscillates between 0 and 2.Hence the function is:
F(x) = sin(3.5π(x + π/2)) + 1.
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You earned $1600 in a summer job and you were paid with a check. You are going to open a checking account at Hometown Bank and put $800 into the account. What amount would you fill in for each letter? Please include the letter and then the amount. If there isn't an amount you can write, for example, A) 0 or A) none
The amount in each letter for checking account is Bills - A = 0, Coin B = 0, Checks C = $800, Total D = $1600, Less cash E = $800, and Net deposit F = $800.
What is checking account?A checking account is a type of bank account that enables regular deposits and withdrawals of money by account holders. Checking accounts frequently come with amenities like check writing, debit cards, and internet banking, making them practical for daily usage. Checking accounts typically do not pay interest on the account balance, in contrast to savings accounts. Yet, many checking accounts don't have to maintain a minimum balance and permit unrestricted withdrawals, which makes them perfect for daily transactions.
Given that, you earn $1600, and put $800 in a checking's account thus,
Bills - A = 0
Coin B = 0
Checks C = $800
Total D = $1600
Less cash E = $800
Net deposit F = D - $800 = $1600 - $800 = $800.
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The table below shows a set of dataWhich statement about the table is true?
The correct option A) There is a cluster, and as x decreases, y increases.
The table represents a set of data containing two variables, x and y. By analyzing the data, we can observe a cluster of values around x = 4 with corresponding y values in the range of 42-45. As we move towards smaller x values, there is a general trend of increasing y values. However, there are a few outliers. Based on these observations, statement A is the most accurate description of the data in the table. It is important to note that the accuracy of the statement is limited to the given data, and further analysis or additional data may reveal a different trend or pattern.
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Complete question:
The table below shows a set of data. Which statement about the table is true?
x: 1.6, 1.9, 2.3, 3.4, 3.8, 4.2, 4.3, 4.6, 4.8.
y: 39, 38, 42, 40, 41, 44, 42, 45, 44
Which statement about the table is true?
A) There is a cluster, and as x decreases, y increases.
B) There is a cluster, and as x increases, y increases.
C) There is not a cluster, and as x increases, y increases.
D) There is not a cluster, and as x decreases, y increases.
If An = 4(2)^n-1 , what is Sa?
The sum of the geometric progression is the sum S₃ = 32
What is sum of terms of a geometric progression?The sum of terms of a geometric progression is given by
Sₙ = a(rⁿ - 1)/(r - 1) where
a = first term ,r = common ratio and n = number of termsGiven the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then
a = first term = 4 and r = common ratio = 2Now, we desire S₃, that is Sₙ when n = 3.
So, S₃ = a(r³ - 1)/(r - 1)
= 4(2³ - 1)/(2 - 1)
= 4(8 - 1)/1
= 4(8)
= 32
So, the sum S₃ = 32
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the measures of the angles in a triangle are in the extended ratio of 1:4:7 find the measures of the angles
The angles of the triangle measure 15 degrees, 60 degrees, and 105 degrees.
Let the measures of the angles in the triangle be x, 4x, and 7x, where x is a constant.
According to the properties of a triangle, the sum of the angles is 180 degrees. So we have
x + 4x + 7x = 180
Simplifying this equation, we get
12x = 180
Dividing both sides by 12, we get
x = 15
Therefore, the measures of the angles are:
x = 15 degrees
4x = 4 × 15
Multiply the numbers
= 60 degrees
7x = 7 × 15
Multiply the numbers
= 105 degrees
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IF 1 POUND OF RAW SPAGHETTI NOODLES MAKES 5 CUPS OF COOKED SPAGHETTI NOODLES, HOW MANY POUNDS OF RAW SPAGHETTI NOODLES WOULD BE NEEDED TO MAKE 30 CUPS OF COOKED NOODLES
Answer: 6 pounds
Step-by-step explanation:
If 1 pound of raw spaghetti makes 5 cups of cooked spaghetti, then we can set up a proportion:
1 pound raw spaghetti : 5 cups cooked spaghetti = x pounds raw spaghetti : 30 cups cooked spaghetti
To solve for x, we can cross-multiply and simplify:
1 * 30 = 5 * x
30 = 5x
x = 6
Therefore, 6 pounds of raw spaghetti noodles would be needed to make 30 cups of cooked noodles.
Find the values of a and b such that 4x^2+12x=4(x+p)^2-q
Answer: p = 1.5 and q = 9
Step-by-step explanation:
Expand the right side then compare the coefficients of like terms on both sides, that is
4(x + p)² - q ← expand (x + p)² using FOIL
= 4(x² + 2px + p²) - q ← distribute parenthesis
= 4x² + 8px + 4p² - q
Comparing coefficients of like terms on both sides
8p = 12 ( coefficients of x- terms ) ← divide both sides by 8
p = 1.5
4p² - q = 0 ( constant terms ), that is
4(1.5)² - q = 0
9 - q = 0 ( subtract 9 from both sides )
- q = - 9 ( multiply both sides by - 1 )
q = 9
If point c is between points A and B the. __+CB=AB
Help please! I have no idea!!!!
By shifting the appropriate numbers to the appropriate locations, the equations become true with [tex]f(-6) = 5, f(x) = 3[/tex] , and [tex]x = -5,[/tex] and [tex]f(7) = 8[/tex] .
What is equation?An equation is a claim that two expressions are equivalent in mathematics. Usually, it has one or more factors, which stand in for the unknowable elements we're trying to figure out how to calculate.
Equations can be used to depict actual-world circumstances or to explain relationships between various mathematical things.
For instance, the equation [tex]"x + 3 = 7"[/tex] indicates that the total of the constant "3" and the variable "x" equals 7. By taking 3 out of both parts of the equation, we can find "x" and get [tex]"x = 4"[/tex] as a result.
Given
To make the equations true, move the right values to the right places in the table below:
[tex]f(-6) = 5[/tex]
[tex]f(x) = 3; x = -5[/tex]
[tex]f(7) = 8[/tex]
By shifting the appropriate numbers to the appropriate locations, the equations become true with [tex]f(-6) = 5, f(x) = 3,[/tex] and [tex]x = -5[/tex] , and [tex]f(7) = 8[/tex] .
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The complete question is :- Use the table below to drag the correct numbers to their appropriate spots to make the equations true:
(Fill in the blank)
X f(x)
-6 8
7 3
4 -5
3 -2
-5 12
What is the difference between the longest and
shortest pieces of scrap wood?
The difference in length between the two pieces of scrap wood is 7/8 inches.
What is the difference between the longest and shortest pieces of scrap wood?
To get the difference we just need to take the difference between the two lenghs.
Remember that we only have pieces of scraph wood if we have an "x" over the correspondent value in the line diagram.
By looking at it we can see that the longest pice measures 5 inches, while the shortest one (there are two of these) measure (4 + 1/8) inches.
The difference is:
5 - (4 + 1/8) = 7/8
The longest piece is 7/8 inches longer.
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The table shows some points on the graph of exponential function g(x)
0 1 2 3 4 g(x) 1 3 9 27 81 What is the range of g?
the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
How to solve and what is graph?
The range of a function refers to the set of all possible output values. Looking at the table, we can see that the output values of g(x) increase rapidly as x increases.
In fact, the output values of g(x) are the result of raising 3 to the power of x, which means that g(x) can never be negative. Therefore, the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
A graph is a visual representation of data or mathematical functions. It is a diagram made up of points, lines, and curves that show the relationship between different variables or data points.
Graphs are used to display and analyze data, to illustrate trends and patterns, and to communicate complex information in an easily understandable way. There are many different types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more, each suited to different types of data and analysis.
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Can some please help
Answer:
1.5
2.28
3.quadrilateral
4.heptagon
5.hexagon
6.15
7.54mm
8.25cm
9.im not sure
15. Math. The poissonier receives 30 lb.. 4 oz. of
dressed mahi-mahi. After filleting and skinning.
13 lb.. 12 oz. of fillets were produced. What
is the yield percentage of the fillets? If the
whole dressed mahi-mahi was purchased
for $5.85/b.. what is the per pound cost of
the fillets?
Answer:
To find the yield percentage of the fillets, we need to divide the weight of the fillets by the weight of the dressed mahi-mahi and then multiply by 100 to get a percentage:
Yield percentage = (Weight of fillets / Weight of dressed mahi-mahi) x 100%
First, we need to convert the weights to a common unit, such as ounces:
Weight of dressed mahi-mahi = 30 lb. 4 oz. = 484 oz.
Weight of fillets = 13 lb. 12 oz. = 220 oz.
Now we can calculate the yield percentage:
Yield percentage = (220 oz. / 484 oz.) x 100% = 45.45%
So the yield percentage of the fillets is 45.45%.
To find the per pound cost of the fillets, we need to divide the total cost of the dressed mahi-mahi by its weight in pounds, and then multiply by the yield percentage to get the cost per pound of fillets:
Total cost of dressed mahi-mahi = 30.25 lb. x $5.85/b. = $176.96
Weight of dressed mahi-mahi in pounds = 30.25 lb.
Weight of fillets in pounds = 13.75 lb.
Cost per pound of fillets = (Total cost of dressed mahi-mahi / Weight of dressed mahi-mahi) x Yield percentage / 100%
Cost per pound of fillets = ($176.96 / 30.25 lb.) x 45.45% = $3.04/lb.
Therefore, the per pound cost of the fillets is $3.04/lb.
Standard Error of the Mean =
Confidence Interval Estimate for the Mean
Margin of Error E= Z
= Z. V
±Z
You want to rent a one-bedroom apartment near BCIT for next term. The mean monthly rent for a random sample of 36 apartments advertised for rent on Craigslist is $1,235. Assume that the population standard deviation is $150.
(a) Give the point estimate of the true mean monthly rent for one-bedroom
apartments available for rent near BCIT.
Answer=$
(b) At the 95% confidence level, what is the margin of error on your estimate of the true mean monthly rent for one-bedroom apartments available for rent near
BCIT.
Answer=$
(c) Construct a 95% confidence interval for the true mean monthly rent for one-bedroom apartments.
Lower value=$
Upper value=$
Choose the correct statement to interpret the confidence interval.
• I am totally confident that the population mean belongs to this confidence interval.
• I am 95% confident that the true population mean belongs to this confidence interval.
(d) A friend claims the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300. Based on your confidence interval do you agree?
• Yes
• No
(e) What is the z-score used to construct a 92% confidence interval?
Answer= (Enter a positive value in 2 decimal places)
"I am 95% convinced that the true population mean corresponds to this confidence interval," is the appropriate sentence to use when interpreting the confidence interval.
What does the statistical term "population" mean?Each whole group that shares at least one trait is referred to be a population. People do not make up all populations. Individuals, animals, groups, organisations, edifices, edifices, buildings, houses, farms, items, or events can all be considered populations.
As a rough estimate, the true mean monthly rent is $1,235.
At a 95% confidence level, the critical value (Z) for a two-tailed test is 1.96. The margin of error can be calculated as follows:
The 95% confidence interval can be obtained as follows:
CI = 1235 1.96*(150/36) CI = X Z*(n/n)
Lower value: 1.96 * (150/36) * 1235 = $1,175.20
Higher value: $1,294.80 = 1235 + 1.96 * (150/36).
Higher value: $1,294.80; Lower value: $1,175.20
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Find the slope of the line that passes through the pair of points.
(5, 4), (8, –1)
Answer:
m = -5/3
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (5, 4) (8, –1)
We see the y decrease by 5 and the x increase by 3, so the slope is
m = -5/3
help quick pls im stuck
If necessary Therefore, the value of x is √2, in radical form.
What is radical ?Radical is a term used to describe ideas, actions, and attitudes that are extreme or break with tradition. It is often used to refer to a political or social movement that advocates for drastic change in society. Radicals challenge the status quo, often by challenging the existing power structures and existing norms. They are often willing to take extreme measures in order to create change.
Given: ^2−2=0
Solution: To find the value of x, we need to solve the given equation.
We can solve the equation by taking the square root of both sides.
√(^2−2)=0
Since the square root of a number squared is equal to the number itself, we can rewrite this equation as:
=√2
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For the given figure of right angled triangle, the value of x in radical form is √168.
Give a brief account on Pythagorean theorem.The Pythagorean theorem, the well-known geometric theorem that the sum of the squares crossing the sides of a right triangle equals the square crossing the hypotenuse (opposite the right angle) – or in common algebraic notation, a² + b² = c².
Name the given triangle as mentioned below:
Now, in triangle ABC:
AB² + AC² = BC² [Using Pythagoras theorem]
AB² + AC² = 24²
AB² = 24² - AC² [eq. 1]
In triangle AOB:
AO² + OB² = AB² [Using Pythagoras theorem]
x² + 17² = AB² [eq. 2]
In triangle AOC:
AO² + OC² = AC² [Using Pythagoras theorem]
x² + 7² = AC² [eq. 3]
Using eq. 1 and 2
24² - AC² = x² + 17²
Since, AC² = x² + 7²
24² - (x² + 7²) = x² + 17²
576 - x² + 49 = x² + 289
625 - x² = x² + 289
625 - 289 = 2x²
336 = 2x²
168 = x²
x = √168
x = 12.96
x ≈ 13
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The area of a rectangular living room is 144 square feet. The length of the room is four times its width. Find the length and width of the living room.
quiz I need help D:
Answer:
Length equals 6
Width equals 24
Step-by-step explanation:
if you do 6 x 4 you get 24 and
24 x 6 equals 144.
FILL IN THE BLANK.A point that moves on a coordinate line is said to be in simple ___ ___ if its distance d from origin at time t is given by either d=a sinωt or d=a cosωt.
"A point that moves on a coordinate line is said to be in simple harmonic motion if its distance d from origin at time t is given by either d = a sinωt or d = a cosωt."
Any function which is written in the form 'a sin(ωt+Ф)' and 'a cos(ωt+Ф)' is said to be a simple harmonic motion.
One definition of a periodic motion is a straightforward harmonic motion. The acceleration of the particle at any location is directly proportional to the displacement from the mean position in simple harmonic motion, which is an oscillatory motion.
Simple harmonic motion, or SHM, is a specific type of repeated or periodic motion that describes the motion of the pendulum. The oscillating object's location changes sinusoidally over time.
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Individuals who identify as male and female were surveyed
regarding their diets.
Meat-
eater
Male 35
Female 37
Total 72
.
Vegetarian Pescatarian Vegan Total
12
23
35
24
14
38
18
27
45
89
101
190
What is the probability that a randomly selected
person is a pescatarian or vegetarian? Round your
answer to the hundredths place.
Answer:
The number of individuals who are either pescatarians or vegetarians is 12 + 27 = 39.
The total number of individuals surveyed is 190.
Therefore, the probability of selecting a pescatarian or vegetarian at random from the survey is:
39/190 ≈ 0.21
Rounding to the hundredths place, the probability is approximately 0.21.
What is the value of 2/2 exponent -3
Answer:1
Step-by-step explanation:
2/2=1
1^-3=1
1/1times1times1
Answer:
1
Step-by-step explanation:
[tex]\frac{2}{2}[/tex] = 1
[tex]1^{-3}[/tex] To make a negative exponent positive, put it under one.
[tex]\frac{1}{1^{3} }[/tex] = [tex]\frac{1}{1}[/tex] = 1
Helping in the name of Jesus.
3) ____ is the expression,
which tells the nature of the roots of a quadratic equation of the form
3) ____ is the expression,
which tells the nature of the roots of a quadratic equation of the form
A rain gutter is made of sheets of metal 9 inches wide. The gutters have a 3 inch base and two 3 inch sides, folded up at an angle of . What angle will maximize the cross sectional area of the rain gutter?
The value of angle that maximizes the cross sectional area is 60°
What is the cross sectional area of a solid?The cross sectional area of a solid is the two dimensional surface formed when the solid is sectioned by a plane.
The shape of the cross sectional area of the gutter is a trapezoid
Area of a trapezoid = ((Sum of the lengths of the parallel sides)/2) × Height
Let a and b represent the parallel sides of the trapezoid, and let a represent the base of the trapezoid we get;
A = ((a + b)/2) × h
a = 3 inches
b = The longer parallel side
h = The height of the trapezoid
The angle formed by the sides of a trapezium and the horizontal = θ
Therefore;
h = 3 × sin(θ)
b = 3 + 2 × 3·cos(θ)
A(θ) = ((3 + 3 + 2 × 3·cos(θ)) × 3 × sin(θ))/2 = 9·sin(θ)·cos(θ) + 9·sin(θ)
At the extremum value of θ, we get;
A'(θ) = 18·cos²(θ) + 9·cos(θ) - 9 = 0
Solving, we get;
cos(θ) = 0.5 or cos(θ) = -1
Therefore;
θ = arccos(0.5) = 60° and θ = arccos(0.5) = 180°
When θ = 60°, we get;
A(max) = 9·sin(60)·cos(60) + 9·sin(60) ≈ 11.69
The cross sectional area when θ is 60° is about 11.69 square inches which is larger than the 9 square inched when θ = 90°
The angle that maximizes the cross sectional area is θ = 60°
Learn more on the maximum value of a function here: https://brainly.com/question/7352919
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