A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the height h of water in the tank in feet after t seconds is described by dh dt А. 2gh AW where A and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition in terms of the symbols Awr An, and H. Use g = 32 ft/s2. (4„VH – 44,4) h(t) = osts 4A 4VĀ By hand, sketch the graph of h(t). h h H H/2 t h h H/2H H t (b) Suppose the tank is 11 ft high and has radius 2 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty? (Round your answer to two decimal places.) sec
The height of water in the tank in feet after t seconds can be expressed as h(t) = H - (Aw/Ah) 2gh t2, where Aw and Ah are the cross-sectional areas of the water and the hole in square feet respectively,
and g is the gravitational acceleration (32 ft/s2). The interval of definition for h(t) is 0 ≤ t ≤ H/2gh.
The graph of h(t) is a parabola with its vertex at (H/2gh, H) and is symmetric about the line t = H/2gh. It starts at (0, H) and gradually decreases to (H/2gh, 0).
Given the tank is 11 ft high, has radius 2 ft and the circular hole has radius in, and it is initially full, the time it will take to empty can be calculated as: t = √(2H/gAh) = √(22/(32 x π(0.52))) = 3.87 seconds. Therefore, it will take approximately 3.87 seconds to empty.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer:
The perimeter of the shape is 53km.
Answer : 53km
Step-by-step explanation: To find the perimeter you need to add all the sides so 8+18+18+9=53 and dont forget the unit km! Have a great day! And good luck!
14. Two angles of a triangle measure 57º and 46°. What is the measure of the
largest exterior angle of the triangle?
Answer:
103
Step-by-step explanation:
57° + 46° =103°
This shows that the third angle in the triangle is 180°-103°=77°
Therefore the largest exterior angle is 180°-77°=103°
Consider the validity of the statement "A Triangle with side lengths 20,21, and 28 is a right triangle"
the statement "A Triangle with side lengths 20,21, and 28 is a right triangle" is invalidated.
As, You may simply rule out the first three options if you are familiar with specific Pythagorean triples and other triangle relationships.
Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular. The smallest and most important triplets are (3,4,5).
So,
20² +21² = 400 +441 = 841 = 29²
The appropriate choice is 20, 21, and 29
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Water flows into a lake at a constant rate.
Grace recorded that 400 litres of water flowed into the lake in 1 minute.
She recorded the number of litres to the nearest 20 litres.
She recorded the time to the nearest
10 seconds.
Calculate the upper bound for the rate at which the water could have flowed into the lake.
Give your answer in litres per second to 2 d.p.
The upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.
What is an upper bound?An upper limit is a value that is larger than or equal to all the values in a set. In mathematics, it is used to specify a cap or a maximum value for a collection of data. For instance, an upper bound is frequently employed in optimization issues to place a cap on the highest value that a function or variable may take. Upper limits are used in statistics to specify a data set's maximum range which may be used to spot outliers or other abnormalities in the data. In calculus, upper bounds are used to specify a sequence's or series' limit, or the highest number that it may possibly approach.
Given that, 400 liters of water flowed into the lake in 1 minute.
The upper bound of water flow will be the maximum amount of water.
For the nearest measures taken by Grace the amount of water needs to ne more than 400, while the time must be less than 10 seconds from the recorded 1 min.
That is time must be 60 - 10 = 50 seconds.
Approximating the values we have:
410/50 = 8.2 liters per second.
Hence, the upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.
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g in acid base reactions, the hydrogen ions from the acid and the hydroxide ions from the base neutralize each other. khp has one ionizable hydrogen; this means that one mole of sodium hydroxide neutralizes one mole of khp. from experiment 1, calculate the exact molarity of the sodium hydroxide. (hint: use the mass of khp and do a stoichiometry problem.....) tip: khp is not the chemical formula. khp stands
In the following question, among the conditions given, the statement is said to be, the exact molarity of the NaOH solution is 0.0960 M.
The question is asking to calculate the exact molarity of the sodium hydroxide from Experiment 1.
KHP stands for potassium hydrogen phthalate, and one mole of sodium hydroxide (NaOH) will neutralize one mole of KHP. To solve the problem, use the mass of KHP and a stoichiometry problem.
First, calculate the number of moles of KHP:
Moles KHP = (Mass KHP (g) / Molar Mass KHP (g/mol))
Then, calculate the moles of NaOH:
Moles NaOH = (Moles KHP * Mole Ratio NaOH/KHP)
Finally, calculate the molarity of NaOH:
Molarity NaOH = (Moles NaOH / Volume NaOH (L))
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How to find x? I am not sure what equation to use to get the correct answer?
Consider a hash table, a hash function of key % 10. Which of the following programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation? O c1 = 1 and 2 = 0 O c1 = 5 and c2 = 1 O c1 = 1 and c2 - 5 O c1 = 10 and 2
D: "[tex]c_{1} = 10[/tex] and [tex]c_{2} = 2[/tex]" are programmer-defined constants for quadratic probing that cannot be used in a quadratic probing equation. Option D is correct answer.
The quadratic probing equation is defined as:
h (k, i) = (h′(k) + [tex]c_{1}[/tex] * i + [tex]c_{2}[/tex] * i^2) mod m,
where h′(k) is the hash value of key
k and m is the size of the hash table.
The constants [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are programmer-defined constants that are used to compute the new hash index when a collision occurs in the hash table.
The given hash function is h(k) = k % 10.
Therefore, the hash value of any key will be between `0` and `9`.Now, let's check which of the given programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation:
Option A: `c1 = 1 and c2 = 0`This option can be used in the quadratic probing equation. It means that linear probing is being used.
Option B: [tex]c_1 = 5[/tex] and [tex]c_2 = 1[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 5i + i^2) mod m`.
Option C: [tex]c_1 = 1[/tex] and [tex]c_2 = 5[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + i + 5i^2) mod m`.
Option D: [tex]c_1 = 10[/tex] and [tex]c_2 = 2[/tex] This option cannot be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 10i + 2i^2) mod m`.
Since [tex]c_{1}[/tex] is greater than or equal to `m`, this equation will always result in a hash index that is greater than or equal to `m`. Therefore, it is not possible to use `[tex]c_{1}[/tex]= 10` in the quadratic probing equation. Hence, the correct option is D.
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Raj went to the theatre to watch a traditional Indian dance performance with his family. The theatre had 1050 seats. There were 50% fewer $50-seats than $30-seats. 90% of the $30-seats and some $50-seats were sold. A total of $34 650 was collected. How many seats were unsold?
Total number of seats that remain unsold are 168.
What is statistics?
The branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.
Let's start by defining some variables to represent the unknowns in the problem:
Let x be the number of $30-seats.Let y be the number of $50-seats.From the problem, we know that:
The total number of seats is 1050: x + y = 1050.There were 50% fewer $50-seats than $30-seats: y = 0.5x.90% of the $30-seats and some $50-seats were sold, which means that the revenue from the $30-seats is 0.9(30x) = 27x, and the revenue from the $50-seats is 0.9(50y) = 45y.We also know that the total revenue collected is $34,650:
27x + 45y = 34650
Now we can substitute y = 0.5x from the second equation into the third equation and simplify:
27x + 45(0.5x) = 34650
27x + 22.5x = 34650
49.5x = 34650
x = 700
So there were 700 $30-seats and 350 $50-seats.
The number of sold $30-seats is 0.9(30x) = 567, and the number of sold $50-seats is 0.9(50y) = 315.
Therefore, the total number of seats sold is 882, and the number of unsold seats is:
1050 - 882 = 168
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If thrice a number increased by 11, the result is 35. What is the number?
If thrice a number increased by 11 and the result is 35, then the number is 8
Let's call the number we're trying to find "x".
According to the problem, "thrice a number increased by 11" is equal to 35. So we can write this as an equation:
3x + 11 = 35
To solve for x, we need to isolate it on one side of the equation. We can start by subtracting 11 from both sides:
3x + 11 - 11 = 35 - 11
Simplifying the left side and evaluating the right side, we get:
3x = 24
Now we can solve for x by dividing both sides by 3:
3x/3 = 24/3
x = 8
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The rectangular garden is 175 m long and 96 m broad . find the cost of fencing it at 17.50per m.also find the cost of ploughing it at 4.50 paise per square metre
Hence, the cost of fencing the garden is ₹9485. Hence, the cost of plowing the garden is ₹756.
What is perimeter?Perimeter is the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of all its four sides, whereas the perimeter of a circle is found by multiplying the diameter by π (pi). Perimeter is usually expressed in units of length, such as meters, centimeters, feet, or inches.
Here,
The perimeter of the rectangular garden is twice the sum of its length and width. So, the length of the fence needed to enclose the garden is:
2 × (length + width) = 2 × (175 m + 96 m) = 542 m
Therefore, the cost of fencing the garden at 17.50 per meter is:
Cost of fencing = length of fence × cost per meter
= 542 m × 17.50
= 9485
Hence, the cost of fencing the garden is ₹9485.
To find the cost of plowing the garden, we need to first calculate its area, which is given by:
Area = length × width
= 175 m × 96 m
= 16800 m²
Therefore, the cost of plowing the garden at 4.50 paise per square meter is:
Cost of plowing = area of garden × cost per square meter
= 16800 m² × 0.045
= 756
Hence, the cost of plowing the garden is ₹756.
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Water freezes at 0º Celsius and 32º Fahrenheit. It boils at 100ºC and 212ºF. a) Find a linear function C that expresses temperature in the Celsius scale in terms of degrees Fahrenheit. b) Use this function to convert 110ºF into Celsius.
a) To find a linear function that expresses temperature in Celsius in terms of degrees Fahrenheit, we need to use the formula for converting Fahrenheit to Celsius:
C = (F - 32) * 5/9
This formula shows that to convert Fahrenheit to Celsius, we first subtract 32 from the Fahrenheit temperature, then multiply by 5/9.
If we rearrange this formula, we can solve for C in terms of F:
C = (F - 32) * 5/9
C = 5/9 * F - 5/9 * 32
C = 5/9 * F - 160/9
So the linear function C that expresses temperature in Celsius in terms of degrees Fahrenheit is:
C = 5/9 * F - 160/9
b) To use this function to convert 110ºF to Celsius, we simply substitute F = 110 into the equation:
C = 5/9 * F - 160/9
C = 5/9 * 110 - 160/9
C = 61.11ºC
Therefore, 110ºF is equivalent to 61.11ºC.
Answer:
a) To find a linear function that expresses temperature in Celsius in terms of degrees Fahrenheit, we can use the formula:
C = (F - 32) * 5/9
where C is the temperature in Celsius and F is the temperature in Fahrenheit.
b) To convert 110ºF to Celsius, we can plug in F = 110 into the formula above and simplify:
C = (110 - 32) * 5/9
C = 78 * 5/9
C = 43.33ºC
Therefore, 110ºF is equivalent to 43.33ºC in Celsius.
(please mark my answer as brainliest)
LetR=[0, 4]×[−1, 2]R=[0, 4]×[−1, 2]. Create a Riemann sum by subdividing [0, 4][0, 4] into m=2m=2 intervals, and [−1, 2][−1, 2] into n=3n=3 subintervals then use it to estimate the value of ∬R (3−xy2) dA∬R (3−xy2) dA.Take the sample points to be the upper left corner of each rectangle
The Riemann sum is:Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.
We can create a Riemann sum to estimate the value of the double integral ∬R (3-xy²) dA over the rectangular region R=[0, 4]×[-1, 2] by subdividing [0, 4] into m=2 intervals and [-1, 2] into n=3 intervals. Then we can evaluate the function at the upper left corner of each subrectangle, multiply by the area of the rectangle, and sum all the results.
The width of each subinterval in the x-direction is Δx=(4-0)/2=2, and the width of each subinterval in the y-direction is Δy=(2-(-1))/3=1. The area of each subrectangle is ΔA=ΔxΔy=2*1=2.
Therefore, the Riemann sum is:
Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.
Evaluating the function at the upper left corner of each subrectangle, we get:
(3-0*(-1)²)2 + (3-20²)2 + (3-21²)2 + (3-41²)*2 = 2 + 6 + 2 + (-22) = -12.
Thus, the estimate for the double integral is -12.
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How does the volume of a square pyramid change if the base edge is multiplied by 6?
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Lwh}{3} ~~ \begin{cases} L=\stackrel{base's}{length}\\ w=\stackrel{base's}{width}\\ h=height\\[-0.5em] \hrulefill\\ L=6L\\ w=6w \end{cases}\implies V=\cfrac{(6L)(6w)h}{3}\implies \stackrel{ \textit{36 times the volume} }{V=\cfrac{Lwh}{3}(36)}[/tex]
Tyra will flip a red and yellow counter and spin a spinner labeled A-E. If Tyra flips the counter and spins the spinner, then list only the outcomes in which a red counter and a vowel are spun. (Select all that apply)
red, A
red, E
yellow, A
yellow, E
red, B
There are two possible outcomes where a red counter and a vowel are spun: a)red, A and b) red, E.
To see why, we can make a table listing all the possible outcomes of flipping a red or yellow counter and spinning a spinner labeled A-E:
A B C D E
Red A B C D E
Yellow A B C D E
We can then circle the outcomes that satisfy the condition of spinning a red counter and a vowel: red, A and red, E.
Therefore, the selected outcomes are:
red, A
red, E
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the classification of student class designation (freshman, sophomore, junior, senior) is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a parameter.
The classification of student class designation (freshman, sophomore, junior, senior) is an example of a categorical random variable. The correct option is A.
What is a random variable?A random variable is a numerical or categorical quantity whose value is unknown but whose behavior can be forecast based on data that has been measured or observed. Random variables are typically used to represent quantities that fluctuate over time or are subject to chance occurrences.
The types of random variables are as follows:
i) Categorical random variable: This type of variable contains categorical data or data that are descriptive in nature. It is used to classify items or events into categories, which can be named or identified. For example, a set of data that includes categories like gender, eye color, or country of origin.
ii) Discrete random variable: This type of variable takes on discrete values, which means it can only take on whole numbers. For example, the number of cars sold at a dealership on any given day is a discrete random variable because it can only take on integer values.
iii) Continuous random variable: This type of variable takes on continuous values, which means it can take on any value within a given range. For example, the temperature in a room can take on any value between a certain minimum and maximum value.
Therefore, the correct option is A.
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17. When preparing a sweet, sugar and flour are mixed in the ratio 2:3 and flour and butter are mixed in the ratio 3:1. If 200 g of sugar is used, find the mass of butter used to make the sweet.
Step 1: Calculate the total amount of flour used.
200 g of sugar is used, so the amount of flour used is 300 g (because it follows the ratio 2:3).
Step 2: Calculate the amount of butter used.
Since flour and butter are mixed in the ratio 3:1, for every 3 units of flour, 1 unit of butter is used. So for 300 g of flour, 100 g of butter should be used.
Therefore, the mass of butter used to make the sweet is 100 g.
I need help! I need the graph drawn and the steps to how I got the answer but I don’t know it! Please help me!
Answer:
25 computers per hour
Step-by-step explanation:
look ate the point 2 hours corresponding to 50 computers
50/2 = 25/1 or 25 computers per hour
A triangle has sides with lengths of 7 inches, 14 inches, and 16 inches. Is it a right triangle?
Answer:
No, is not a right triangle
Step-by-step explanation:
If it is a right triangle Pythagoras theorem do apply.
Since the hypotenuse is the side with 16in, sides are 7 and 14 inches
notice
[tex]\sqrt{7^{2} +16^{2} } = \sqrt{245} \neq 16[/tex]
A telephone pole is secured with a cable as shown. The cable makes an angle of 80° with the ground and is secured 7 m from the bottom of the pole. A second cable is attached from the top of the pole and secured to the ground three times as far from the pole as the first cable and on the same side. Find the angle the second cable makes with the ground, rounded to the nearest degree. 80° 7 m
The angle the second cable makes with the ground is 68° (rounded to the nearest degree).
Given that:A telephone pole is secured with a cable as shown. The cable makes an angle of 80° with the ground and is secured 7 m from the bottom of the pole. A second cable is attached from the top of the pole and secured to the ground three times as far from the pole as the first cable and on the same side.The required:Find the angle the second cable makes with the ground, rounded to the nearest degree.Step-by-step explanation:Let AB be the telephone pole and P be the point at which the first cable is attached to the pole such that PB = 7m and angle APB = 80°Let QC be the second cable and Q be the point at which the second cable is attached to the ground, such that CQ = 3PB = 3 × 7 = 21mWe need to find the angle QCB (let this angle be x)AC = AB + BC = AB + CQAB = AC - BC = 21 sec 80° - 21 tan 80° = 197.239 - 9.3646 = 187.8745mNow in right ΔABCtan 80° = BC/ABBC = AB tan 80° = 187.8745 tan 80° = 46.1883mIn right ΔQCBtan x = BC/CQBC = CQ tan x = 21 tan x = 46.1883/21x = tan -1 (46.1883/21) = 68.2959°≈ 68°Hence, the angle the second cable makes with the ground is 68° (rounded to the nearest degree).
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Most exposures and outcomes used in correlational studies are in the form of:
A. Individual data
B. Aggregate data
C. Average data
D. Relative data
Most correlational studies use d)relative data, which compares two variables.
This means that one variable is being measured against another, often in the form of ratios or percentages. For example, one might compare the number of people who smoke cigarettes with the number of people who develop lung cancer, in order to determine whether there is a correlation between the two.
Relative data allows researchers to examine the relationship between variables, allowing them to assess the strength of the relationship between them.
In order to compare variables, correlational studies rely on either primary or secondary data. Primary data is collected through direct observation and experimentation, while secondary data is obtained from existing sources.
In most cases, correlational studies use secondary data, such as survey results or statistics from public databases. This data is often in the form of relative data, such as percentages or ratios.
By using relative data, correlational studies can determine the strength of the relationship between two variables. This information can be used to better understand how the variables are related, as well as to draw conclusions about their relationship. For example, the relationship between smoking and lung cancer can be examined using relative data, allowing researchers to identify patterns and draw conclusions about the correlation between the two variables.
Hence Option D is correct.
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Write a quadratic function in standard form to represent the data in the table.
Ordered pairs arranged in a table. From left to right the pairs are: 2, 3, and 4, 1, and 6, 3, and 8, 9, and 10, 19.
y = x2 − x +
The length of a rectangular room is 9 feet longer than twice the width. If the room's perimeter is 150 feet, what are the room's dimensions?
Answer:
Length = 53 feet
Width = 22 feet
Step-by-step explanation:
Perimeter = 2(length + width)
Then:
a = 2w + 9 Ec. 1
150 = 2(a + w) Ec. 2
a = length
w = width
From Eq. 1:
a - 9 = 2w Eq. 3
From Eq. 2:
150 = 2*a + 2*w
150 = 2a + 2w
150 - 2a = 2w Eq. 4
Equalizing Eq. 3 and Eq. 4
a - 9 = 150 - 2a
a + 2a = 150 + 9
3a = 159
a = 159/3
a = 53
From Eq. 1:
a = 2w + 9
53 = 2w + 9
53 - 9 = 2w
44 = 2w
44/2 = w
w = 22
Check:
From Eq. 2
150 = 2(a+w)
150 = 2(53+22)
150 = 2*75
math question please help
Answer:
Step-by-step explanation:
only the 1st and 5th statements are true
When Beth returns from holiday she changes €120 back into pounds. The exchange rate is now £1 = €1.16 (b) Work out how many pounds (£) Beth receives.
Beth receives £103.45 when she changes €120 back into pounds.
What is exchange rate?An exchange rate is the value of one currency expressed in terms of another currency. In other words, it is the rate at which one currency can be exchanged for another currency.
What is pound?Pound is a unit of currency that is used in several countries, including the United Kingdom, Egypt, Lebanon, and Sudan, among others. The pound symbol is "£".
In the given question,
If the exchange rate is £1 = €1.16, this means that for every euro, Beth will get £1/€1.16.
Therefore, the number of pounds Beth receives when she changes €120 back into pounds is:
120 euros * £1/€1.16 = £103.45 (rounded to two decimal places)
So Beth receives £103.45 when she changes €120 back into pounds.
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Elouise finds a woodlouse that is 8 mm long. When she views it under the microscope it
appears 12 cm long.
What is the magnification?
Answer:
Step-by-step explanation:
This can be solved by taking X as the magnification
8*x = 12cm *10
x= 120/8
x= 30/2= 15
the magnification = 15 times
What is the slope of a line that is perpendicular to the line y = –14 x – 1 ?
Answer:
m= 1/14
Step-by-step explanation:
If the slope is perpendicular, the rule say that it must be reciprocal (turned around) and with the opposite sign.
Therefore, if the original slope is -14/1.
It must be changed to positive, and swap numerator and denominator.
m2= 1/14
he mean salary at a local industrial plant is $27,600 with a standard deviation of $5400 . the median salary is $25,200 and the 61st percentile is $29,100 . step 5 of 5: if tom's salary has a z-score of 0.7 , how much does he earn (in dollars)?
He mean salary at a local industrial plant is $27,600 with a standard deviation of $5400 . the median salary is $25,200 and the 61st percentile is $29,100, The amount Tom earns (in dollars) is $31,590.
How do we calculate the amount Tom earns?Given that, the mean salary at a local industrial plant is $27,600The standard deviation of salary is $5400The median salary is $25,200The 61st percentile is $29,100We have to find the amount that Tom earns (in dollars) if Tom's salary has a z-score of 0.7.
We need to calculate the z-score using the formula,[tex]Z = (X - \mu) / \sigma[/tex], where X is the value, μ is the mean and σ is the standard deviation. [tex]z = (X - \mu) / \sigma 0.7 = (X - 27,600) / 5,400[/tex] Multiplying both sides by 5,400, we get,0.7 × 5,400 = X - 27,600 Add 27,600 on both sides, we get, [tex]X = (0.7 * 5,400) + 27,600= 3,780 + 27,600= $31,590[/tex] Therefore, The amount Tom earns (in dollars) is $31,590.
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I need help asap I just need atleast one of these explained and I can do the rest
Answer:
To factor 30b³-54b², we can factor out the greatest common factor of 6b² to get:
30b³-54b² = 6b²(5b-9)
To factor 35-48y³, we can notice that it is a difference of cubes:
35-48y³ = (5)³ - (4y)³ = (5-4y)(25+20y+16y²)
To factor x³+8, we can use the sum of cubes formula:
x³+8 = (x+2)(x²-2x+4)
To factor 3-64, we can use the difference of squares formula:
3-64 = (1)² - (8)² = (1+8)(1-8) = -7(-9) = 63
To factor 8c³+343, we can use the sum of cubes formula:
8c³+343 = (2c)^3 + 7³ = (2c+7)(4c²-14c+49)
To add or subtract complex polynomials, we simply combine like terms. For example:
(3x²+2x-5) + (4x²-3x+7) = 7x²-x+2
To multiply complex polynomials, we can use the distributive property and FOIL method. For example:
(2x+1)(3x-4) = 6x²-5x-4
To factor complex polynomials, we can use various methods such as factoring out the greatest common factor, using the difference of squares formula, using the sum or difference of cubes formula, or factoring by grouping.
The formulas provided are for factoring the sum or difference of cubes:
(a + b³) = (a + b)(a² - ab + b²)(a - b³) = (a - b)(a² + ab + b²)These formulas can be useful for factoring complex polynomials that have a cube term or a constant term in addition to the quadratic and linear terms.
Michelle asked 30 people entering a movie theater how many movies they had seen over the past year. Here are the results of her poll. 0, 5, 3, 2, 6, 8, 10, 12, 11, 16, 0, 3, 4, 7, 2, 0, 1, 9, 6, 4, 4, 8, 14, 16, 17, 18, 5, 3, 6, 8 (a) Create a frequency table for the data with 5 classes. (b) Create a histogram from your frequency table. Label the axes and give the histogram a title. Answer: (c) Number of movies Frequency
Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b) .
what is histogram ?A graph that displays the distribution of a collection of continuous data is called a histogram. It is composed of a number of bars, each of which represents a set of values, and whose height denotes the frequency or number of data points that lie within a given range. Histograms are used to depict a distribution's shape, centre, and spread graphically. They are frequently used to find patterns and trends in data in areas like statistics, data analysis, and scientific study.
given
(A) We must first identify the data's range before dividing it into 5 intervals of equal width in order to construct a frequency table with 5 classes. The values are in the range of 0 to 18.
(b) We plot the class intervals on the x-axis and the frequency on the y-axis to generate a histogram from the frequency chart. The counts are used to illustrate how frequently each class interval occurs.
Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b).
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