There are three primary sorts of operations done on sets in a set theory, such as:
Sets' union (∪)
Sets intersecting (∩)
Set difference (- )
Why are the above important?Sets help in the identification of related groupings of objects. Set operations such as relations and functions are used to connect and manipulate sets.
Bowls, glasses, cups, and saucers are kept separate from plates, while pans and utensils have their own compartments. Cooking utensil sets and other collections are separated in storage. As seen above, there are countless examples of sets in our daily lives.
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3. Alaska is 3,186 miles from California and 2,774 miles from Florida.
Assuming the roads between the three States made a right triangle, find the
distance from California to Florida.
Answer: 4224.413805 miles
Step-by-step explanation:
First, we use The Pythagorean Theorem equation to find the distance between California and Florida
Equation: [tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]
[tex]3186^{2}[/tex]+[tex]2774^{2}[/tex]=[tex]c^{2}[/tex]
So, we are trying to solve for c.
The first thing we do is evaluate the expression.
10,150,596+7,695,076=[tex]c^{2}[/tex]
Add like terms
17,845,672=[tex]c^{2}[/tex]
Then, do inverse operations and square root 17,845,672
You would then get 4224.413805 miles.
Write the equation of the line that passes through the points (-2, -1) and (2, 11)
The equation of the line that passes through the points (-2, -1) and (2, 11) will be y = 3x + 5.
Given that:
Points, (-2, -1) and (2, 11)
Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The equation that passes through (-2, -1) and (2, 11) is calculated as,
(y + 1) = [(11 + 1) / (2 + 2)](x + 2)
y + 1 = 3x + 6
y = 3x + 5
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how do i find the sample size of x-bar chart in order to find A2 from upper control limit and lower control limit formulas?
(i hope this makes sense)
It should be noted that to discover the required sample size for an x-bar chart, you must first determine the values of the upper and lower control limit (UCL & LCL) based on the process descriptions and the desired level of restriction.
How to determine the sampleThe equations for UCL and LCL are:
UCL = x + A2R
LCL = x - A2R
Where x denotes the average of the mean samples, R represents the ambit of the means, and A2 stands for a constant value rooted in the amount of the sample..
Utilizing these values, then one can apply the formulas of UCL & LCL to solve for the constant A2, which is utilized to calculate the boundaries of the chart.
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What is the perimeter of a square that has an area of 595.36 square feet?
Answer :
97.6 feetStep-by-step explanation:
It's given that, Area of square is 595.36 square feet.
As we know that area of square is calculated by,
Area = side²
Substituting the values,
595.36 = side
side =√595.36
side = 24.4 feet
Hence, the side of the square is 24.4 feet.
Now,
Perimeter (square) = 4 × side
Perimeter = 4 × 24.4
Perimeter = 97.6 feet
Therefore, The perimeter of the square is 97.6 feet
Consider functions fand g.
f(x)= log (x-1)
g(x)= 1/3x2 - 4
Which statement gives the best approximation of the solutions of the equation f(x) = g(x)?
=
OA.
The solutions are where the graphs of the functions cross the x-axis at ≈ -3.464and ≈ 3.642.
OB. The solutions are where the graphs of the functions intersect at
-3.464and ≈ 3.464.
OC. The solutions are where the graphs of the functions intersect at
land ≈ 3.642.
OD. The solutions are where the graphs of the functions cross the x-axis at ≈ -4and ≈ 0.422.
d
The solutions are where the graphs of the functions intersect at x = 1 and the value at x ≈ 3.642
Given data ,
Let the first function be f ( x )
Now , the value of f ( x ) = log ( x - 1 )
Let the second function be g ( x )
g ( x ) = ( 1/3 )x² - 4
On simplifying the equation , we get
f ( x ) = g ( x )
On plotting the graph , we get the point of intersection at x = 1 and x = 3.642
Hence , the solution of equations are x = 1 and x = 3.642
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Answer:
x = 1 and x = 3.642
Step-by-step explanation:
Plato/Edmentum
What is the net income from the following income statement? Income Statement Sales Returns $12,800 ($360) Net Sales COGS Gross Profit Overhead ($2,500) Net Income ($8,000) net income = $ [?]
The net income from the given income statement is $7,440. This is calculated by subtracting the overhead expenses from the gross profit.
To calculate the net income, we need to subtract all expenses from the gross profit.
First, we need to calculate the Net Sales by subtracting the Sales Returns of $360 from the Sales of $12,800
Net Sales = Sales - Sales Returns
Net Sales = $12,800 - $360
Net Sales = $12,440
Next, we can calculate the Gross Profit by subtracting the Cost of Goods Sold (COGS) from the Net Sales
Gross Profit = Net Sales - COGS
Gross Profit = $12,440 - $2,500
Gross Profit = $9,940
Now, we can calculate the Net Income by subtracting the Overhead expenses from the Gross Profit
Net Income = Gross Profit - Overhead
Net Income = $9,940 - $2,500
Net Income = $7,440
Therefore, the net income from the given income statement is $7,440.
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Find surface area
LOTS OF POINT**
The surface area of the cone is 763.02 cm²
What is surface area of a cone?A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex.
The surface area of a cone is expressed as;
SA = πr( r+l)
where l is the slant height and r is the radius
Incase l is not given ;
l = √h²+r²
The radius of this cone = diameter/2
= 18/2 = 9cm
SA = 3.14 × 9( 9+18)
SA = 28.26 × 27
SA = 763.02 cm²
therefore the surface area of the cone is 763.02 cm²
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point(s) possible
Find the area of the shaded region. The graph depicts the standard
normal distribution with mean 0 and standard deviation 1.
Click to view page 1 of the table. Click to view page 2 of the table.
The area of the shaded region is.
(Round to four decimal places as needed.)
Submit test
z = 0.22
Q
Note that the area of the shaded region is 0.4129. See how it was derived.
How did we arrive at this ?Using the standard normal distribution table, the area to the left of
z = 0.22 is 0.5871.
Therefore, the area of the shaded region to the right of z = 0.22 is
1 - 0.5871 = 0.4129
Rounding to 4 decimal places, the area of the shaded region is 0.4129.
The shaded region's area is the difference between the area of the complete polygon and the area of the polygon's unshaded portion.
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Miss Wan and Miss Lim left their school at 2.50 p .m and drove along the same
route to Orchard Road. Miss Wan drove at an average speed of 60 Km/h and
reache Orchard Road 30 min later. Meanwhile, Miss Lim was still 5 km away from Orchard
Road.
a) What was the Miss Lim's average speed for the whole journey?
b) What time would Miss Lim reach Orchard Road?
Answer and explanation:
a) To find the average speed of Miss Lim for the whole journey, we need to use the formula:
Average speed = Total distance ÷ Total time
Let's first calculate the total distance traveled by both Miss Wan and Miss Lim. We know that Miss Wan drove at an average speed of 60 km/h and reached Orchard Road 30 minutes later. So, the total distance traveled by her would be:
Distance = Speed × Time
Distance = 60 km/h × (30/60) h
Distance = 30 km
Now, we also know that Miss Lim was still 5 km away from Orchard Road when Miss Wan reached there. Therefore, the total distance traveled by both of them would be:
Total distance = Distance covered by Miss Wan + Distance left for Miss Lim
Total distance = 30 km + 5 km
Total distance = 35 km
Next, let's calculate the total time taken by both of them. We know that Miss Wan took 30 minutes less than Miss Lim to reach Orchard Road. So, if we assume that Miss Lim took t hours to reach Orchard Road, then Miss Wan took (t - 0.5) hours. Therefore, the total time taken by both of them would be:
Total time = Time taken by Miss Wan + Time taken by Miss Lim
Total time = (t - 0.5) h + t h
Total time = 2t - 0.5 h
Now, we can use the formula to find the average speed of Miss Lim:
Average speed = Total distance ÷ Total time
Average speed = 35 km ÷ (2t - 0.5) h
Therefore, the average speed of Miss Lim for the whole journey is 35/(2t-0.5) km/h.
b) To find out what time Miss Lim would reach Orchard Road, we can use the formula:
Time taken = Distance ÷ Speed
We know that Miss Lim was 5 km away from Orchard Road when Miss Wan reached there. Therefore, the distance left for Miss Lim to cover would be:
Distance = 5 km
We also know that Miss Lim's average speed for the whole journey is 35/(2t-0.5) km/h. Therefore, the time taken by her to cover the remaining distance of 5 km would be:
Time taken = Distance ÷ Speed
Time taken = 5 km ÷ 35/(2t-0.5) km/h
Time taken = (2t - 0.5) ÷ 7 h
Now, we need to add this time to the time when Miss Wan reached Orchard Road, which was 30 minutes past 2.50 p.m. So, the time when Miss Lim would reach Orchard Road would be:
Time = Time when Miss Wan reached Orchard Road + Time taken by Miss Lim
Time = 2.50 p.m. + 30 min + (2t - 0.5) ÷ 7 h
Simplifying this equation, we get:
Time = (14t + 11) ÷ 14 p.m.
Therefore, Miss Lim would reach Orchard Road at (14t + 11) ÷ 14 p.m.
Answer:
a) 50 km/h
b) 3:26 p.m.
Step-by-step explanation:
You want to know Miss Lim's average speed and arrival time at Orchard Road if Miss Wan gets there in 30 minutes at 60 km/h, starting at 2:50 pm.
DistanceThe distance Miss Wan traveled is ...
distance = speed × time
distance = (60 km/h) × (1/2 h) = 30 km
a) SpeedIn the same 30 minutes that Miss Wan traveled 30 km, Miss Lim traveled 5 km less, so 30 -5 = 25 km. Miss Lim's speed was ...
speed = distance/time
speed = (25 km)/(1/2 h) = 50 km/h
Assuming Miss Lim maintained that speed for the remaining 5 km, her average speed for the journey was 50 km/h.
b) TimeMiss Lim's travel time is ...
time = distance/speed
time = (30 km)/(50 km/h) = 3/5 h = 36 min
The clock time 36 minutes after 2:50 pm is 3:26 pm.
Miss Lim reached Orchard Road at 3:26 p.m..
plot and connect the points in the order listed below when you are done find the area of the resulting figure (-5,5) (-2,5) (-2,8) (9,8) (9,-3) (-2,-3) (-2,2) (-5,2) area= units
Check the picture below.
1. Fill in the balance sheet below with each of Rosa's assets and liabilities. Calculate (add up) her total assets and total liabilities. Then calculate her net worth. (15 points) Cash Assets ($) Checking account Liabilities ($) Student loans Credit card(s) balance(s) Net Worth ($) TOTAL ASSETS - TOTAL LIABILITIES
Answer:
Balance Sheet:
Cash Assets ($)
Checking account: $2,000
Liabilities ($)
Student loans: $10,000
Credit card(s) balance(s): $500
Total Assets: $2,000
Total Liabilities: $10,500
Net Worth: Total Assets - Total Liabilities
Net Worth: $2,000 - $10,500
Net Worth: -$8,500
Therefore, Rosa's total assets are $2,000, her total liabilities are $10,500, and her net worth is -$8,500. This indicates that her liabilities exceed her assets, and she has a negative net worth.
1. A probability experiment which outputs a single number is a(n) _______________ ________________.
(two words)
2. A discrete random variable can output either a finite or a(n) ______________(countably, uncountably)
infinite number of values.
3. A continuous random variable has its values in one or more __________________. An example is the __________________ distribution whose density function is the horizontal line from X=a to X=b.
4. The _________________ __________________ (two words) of a discrete random variable lists every possible value that the variable can assume and the corresponding probabilities.
5. For a(n) _________________ random variable, a sample is drawn with replacement, or there is a large population size. Successive trials are independent of each other. There is a categorical variable with 2 possible values. The ________________(population, sample) is of a fixed size n.
6. For a ____________________ random variable, a sample is drawn without replacement. Successive trials are dependent on each other. There is a ____________________ (population, sample) of finite size N and a categorical variable with 2 possible values. The sample is of a fixed size _______ (N, n, p, q, r).
7. For each blank, include both the formula and the exact answer; do not use a calculator.
Given a uniform distribution with the sample space [1, 4], the height of its density function is ________________ and it has mean ________________ and standard deviation __________________.
8. The ___________________ ____________________ (two words) distribution has a density function that is bell shaped and symmetric. Its mean is 0 and its standard deviation is 1.
9. The ___________________ is also known as the average, expectation and expected value.
10. The ___________________of a discrete random variable can be found by taking the product of each outcome and its probability and then summing.
11. The ______________________ (one word!) of a discrete random variable can be found by subtracting the square of its mean from the expectation of the square of the random variable.
Write the angle in degrees and minutes. 20 1/2°
After considering the given data we come to the conclusion that the evaluated angle of 20 1/2° can be placed in degrees and minutes as 20° 30'.
Angles are generally measured in degrees, also known as a unit of measurement for angles, arcs, and circles, in geometry and trigonometry. A degree is 1/360th of a full circle's revolution, and it is typically designated by the sign.
Angles can be gradually divided into minutes and seconds, which are smaller units of measurement when they are presented in degrees. One degree has 60 minutes, and one minute has 60 seconds. Then, 360 degrees, 0 minutes, and 0 seconds can be used to express a full circle.
For instance 20 1/2°, we first apply the entire number (20) to represent the number of degrees before multiplying the fraction (1/2) by 60 to represent the number of minutes.
The angle may be exposed as 20 degrees and 30 minutes since this provides us with 30 minutes. It should be helpful to express angles in degrees and minutes (or seconds) in a variety of contexts, including engineering, astronomy, and navigation.
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Please help answer the attached image
The collusive outcome is better for both firms than the Bertrand outcome.
How to explain the informationSetting the price equal to marginal cost gives us:
P = $100
Substituting into the demand function, we get:
Q = 140 - (100/0.5) = 40
Therefore, each firm will sell 20 units of service, for a total of 40 units sold. The market price will be $100, and each firm will earn zero profit
The market demand function is:
P = 70 - 0.5Q
Total revenue for the monopoly is:
TR = P*Q = (70 - 0.5Q)*Q = 70Q - 0.5Q^2
The marginal revenue function is:
MR = dTR/dQ = 70 - Q
Setting marginal revenue equal to marginal cost (which is still $100), we get:
70 - Q = 100
Q = 30
Therefore, the monopoly will sell 30 units of service. Each firm will sell half of this quantity, or 15 units. The market price will be:
P = 70 - 0.5Q = $55
Each firm's total revenue will be:
TR = P*Q = $1,650
Each firm's total cost will be:
TC = 100*15 = $1,500
Therefore, each firm will earn a profit of:
π = TR - TC = $150
Note that this collusive outcome is better for both firms than the Bertrand outcome,
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Rita draws an angle with a measure of 20 degrees. Which statement about Rita's angle
is true?
A It turns through 20 one-degree angles.
B
It turns through 20 360-degree angles.
C
It turns through one-twentieth of a circle.
D
It turns through one-twentieth of a protractor.
The statement "It turns through one-twentieth of a circle" is accurate. Then the correct option is C.
Given that:
Rita draws an angle with a measure of 20 degrees.
An angle is a unit of rotation created when two rays share the same vertex or endpoint. Since an angle is a measurement of rotation, it may also be measured in degrees. A circle has 360 degrees of arc.
360 degrees is the length of a circle's complete rotation. The rotation of one-twentieth (1/20) of a full revolution, or one-twentieth of a circle, is equivalent to a measurement of 20 degrees.
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I WILL GIVE BRAINLEST
The surface area of the footrest is 1018 inches squared.
1 yard square of fabric will completely cover the footrest.
How to find the surface area of a rectangular prism?Alicia wants to cover a footrest in the shape of a rectangular prism with cotton fabric . The footrest is 19 inches, 11 inches and 10 inches.
She has only 1 square yard of fabrics.
Hence, let's check if she can cover the footrest completely.
Therefore,
surface area of the rectangular prism = 2(lw + hw + lh)
Hence,
surface area of the rectangular prism = 2(19 × 11 + 19 × 10 + 10 × 11)
surface area of the rectangular prism = 2(209 + 190 + 110)
surface area of the rectangular prism = 2(509)
surface area of the rectangular prism = 1018 inches squared
Therefore, the footrest has a surface area of 1018 inches squared.
1296 inches² = 1 yard²
1018 inches² = ?
surface area of the footrest in yards squared = 1018 / 1296
surface area of the footrest in yards squared = 0.79 yard²
Therefore, the fabric will completely cover the footrest.
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Harper is getting ready to plant corn on his family's farm. The table shows the number of pounds of seed she needs to buy depending on the number of hectares she will plant. Hectares, h 10 15 25 50 Pounds of seed, p 200 300 500 1000 a. Write an equation that shows how to find the pounds of seed, p, needed for h hectares of land. b. Write an equation that shows how many hectares, h, Harper can plant with p pounds of seed.
An equation that shows how to find the pounds of seed, p, needed for h hectares of land is p = 20h.
An equation that shows how many hectares, h, Harper can plant with p pounds of seed is h = p/20.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this table;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (300 - 200)/(15 - 10)
Slope (m) = 100/5
Slope (m) = 20
At data point (10, 200) and a slope of 20, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 200 = 20(x - 10)
y = 20x - 200 + 200
y = 20x ≡ p = 20h
Making h the subject of formula, we have:
h = p/20
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After 1 year, $400 deposited in a savings account with simple interest had earned $16 in interest. What was the interest rate?
The population of a town is modeled by the function f(x) = 465(1 + 0.003) x, where x is the time in years. What type of change does this function represent?
The function represents an exponential growth.
What type of change does this function represent?A general exponential function can be written as:
y = A*(1 + r)^x
Where A is the initial value and r is the rate of change, and if r > 0 we have a growth, if -1 < r < 0 we have a decay.
Here f(x) = 465(1 + 0.003)^x is the population function, we can see that the value of r is positive, thus, the function is an exponential growth.
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Professor Dorsey is grading papers in the teachers' lounge. She has already finished grading 21 assignments, and is grading 2 more assignments per hour. Her teaching assistant just came in to help her. She can grade at a rate of 9 assignments every hour. At some point, they will be finished and will have graded the same number of papers. How many assignments will they each have graded? How long will that take?
Professor Dorsey and her assistant both will have graded ___ assignments in
___hours.
HELPPP
find the surface area of the figure
The calculated value of the surface area of the cylinder is 1056π
From the question, we have the following parameters that can be used in our computation:
Slant height, l = 40 mm
Height, h = 32 mm
Calculate the radius r using
(2r)² = 40² - 32²
So, we have
(2r)² = 576
r = 12
using the above as a guide, we have the following:
SA = 2πr(r + h)
Substitute the known values in the above equation, so, we have the following representation
SA = 2π * 12(12 + 32)
Evaluate
SA = 1056π
Hence, the surface area of the cylinder is 1056π
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Need help putting the angle pairs in their right spot!!!
The angle relationships are as follows:
Corresponding angles → ∠5 and ∠13 and ∠3 and ∠11
Alternate interior angles → ∠4 and ∠9 and ∠7 and ∠14
Alternate exterior angles → ∠5 and ∠16
Consecutive interior angles → ∠3 and ∠9
How to find angle relationships?When parallel lines are crossed by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, adjacent angles, same side interior angles, vertically opposite angles etc.
Therefore, let's classify the angle relationships in the diagram.
Hence,
∠5 and ∠13 and ∠3 and ∠11 are corresponding angles
∠4 and ∠9 and ∠7 and ∠14 are alternate interior angles.
∠5 and ∠16 are alternate exterior angles.
∠3 and ∠9 are consecutive interior angles.
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What’s 80% of $500 worth items
Answer:
$400
Step-by-step explanation:
80% = 80/100 = 8/10 = 0.8
0.8(500)=400
Eli has 38 in cash and 72 on gift card he says that when he rounds to the nearest 10 tickets he has about a $100 is he correct explain
Eli's statement is incorrect. Since $10 is greater than $5, we cannot round $110 to $100 when rounding to the nearest 10.
To determine if Eli is correct, we need to add the amount of cash he has with the value of his gift card;
$38 + $72 = $110
Since Eli says that he has about a $100 when he rounds to the nearest 10, we need to check whether $110 rounds to $100 or not. To round to the nearest 10, we look at the last digit of the number, which is 0 in this case. If the last digit is 5 or greater, we round up to the next multiple of 10. If the last digit is less than 5, we round down to the previous multiple of 10.
Since the last digit of $110 is 0, we don't need to round up or down. $110 is already a multiple of 10. Therefore, Eli is incorrect in saying that he has about a $100 when he rounds to the nearest 10. He actually has $110.
Alternatively, we can check if $110 is within $5 of $100, which is the threshold for rounding to the nearest 10.
$110 - $100 = $10
Therefore, Eli's statement is incorrect.
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The average GPA of a random sample of 31 college students who take evening classes was calculated to be
2.74 with a standard deviation of 0.07. The average GPA of a random sample of 18 college students who
take daytime classes was calculated to be 2.73 with a standard deviation of 0.03. Test the claim that the
mean GPA of night students is larger than the mean GPA of day students at the .05 significance level.
Claim: Select an answer which corresponds to [Select an answer
Opposite: [Select an answer which corresponds to [Select an answer
The test is: Select an answer
The test statistic is: t-
The P-value is: Select an answer
Based on this we: Select an answer
(to 2 decimals)
Conclusion There Select an answer appear to be enough evidence to support the claim that the mean
GPA of night students is larger than the mean GPA of day students.
The results of the two-sample t-test, there does not appear to be enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students.
To test the claim that the mean GPA of night students is larger than the mean GPA of day students, we can perform a two-sample t-test. The null hypothesis is that there is no difference in the mean GPAs between the two groups, while the alternative hypothesis is that the mean GPA of night students is larger than the mean GPA of day students.
Using the given data, we can calculate the test statistic as follows:
t = (2.74 - 2.73) / sqrt((0.07^2 / 31) + (0.03^2 / 18)) = 0.45
The degrees of freedom for this test are 31 + 18 - 2 = 47. Using a t-table or calculator, we can find that the p-value for this test is approximately 0.326.
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.05 significance level.
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Good-afternoon everyone! This past week I've managed to finish up some math work. However, I want to make sure I didn't make any errors in the process of solving and if I did, I want to know how to fix them and make sure I don't make those errors next time. If anyone would be willing to check my work, I would deeply appreciate it! Basically, the question is asking to give the error that the student made and to find the correct area & volume of the cone. For the surface area, I got an answer of 1244.1 meters squared. For the volume, I got an answer of 2787.6 meters squared. Thank you so much for your time and help! :)
you're correct, Jan used the height instead of the slant-height, which is needed for the SA, so hmm well, we really don't know the slant-height, hmmm let's find it, keeping in mind the slant-height is just the hypotenuse of either triangular cross-section
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{L}\\ a=\stackrel{adjacent}{11}\\ o=\stackrel{opposite}{22} \end{cases} \\\\\\ L=\sqrt{ 11^2 + 22^2}\implies L=\sqrt{ 121 + 484 } \implies L=\sqrt{ 605 }\implies L=11\sqrt{5} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{surface area of a cone}\\\\ SA=\pi rL + \pi r^2~~ \begin{cases} r=radius\\ L=slant~height\\[-0.5em] \hrulefill\\ r=11\\ L=11\sqrt{5} \end{cases}\implies SA=\pi (11)(11\sqrt{5})+\pi (11)^2 \\\\\\ SA=121\pi \sqrt{5}+121\pi \implies \boxed{SA\approx 1230.14~m^2} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=11\\ h=22 \end{cases}\implies V=\cfrac{\pi (11)^2(22)}{3}\implies \boxed{V\approx 2787.64~m^3}[/tex]
Use the given zero to find the remaining zeros of the function.
h(x)=x²-12x³ +28x² + 196x-1845
zero: 4-5i
Enter the remaining zeros of h.
(Use a comma to separate answers as needed.)
The remaining zeros of h based on the function will be 9 and -5.
What is a function?A function in math represents the correlation between two groups of numerical data, known as domain and range. The input value is drawn from the first set or domain, while the resulting output value belongs to the second set or range.
It should be noted that to specify, a formal breakdown states that a function f operates from X into Y whereby each component x of X possesses an exclusive element y in Y referred to by the mentioning of f(x) = y. Here, it's clear that 'x' applies to input with its respective contribution being labeled as 'y', which denotes the result of the equation belonging to set Y.
In this case, the remaining zeros of h based on the function will be 9 and -5.
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Find the value of X for the following
Answer:
x = 8.1
Step-by-step explanation:
According to Euclidean theorem:
10² = 12 × (2x - 8)
Multiply inside the parenthesis with 12.10² = 24x - 96
Find the second power of 10.100 = 24x - 96
Add 96 to both sides.100 + 96 = 24x
Add the expressions.196 = 24x
Divide both sides by 24.8.1 = x approximately
Help me!!!!!! I have to turn this in in a few min
The following data were used in a regression study.
Observation 1 2 3 4 5 6 7 8 9
xi
2 3 4 5 7 7 7 8 9
yi
4 5 4 6 4 6 9 6 11
(a)
Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.)
ŷ =
The estimated regression equation for these data is ŷ = 0.69x + 2.15
Developing an estimated regression equation for these dataFrom the question, we have the following parameters that can be used in our computation:
Observation 1 2 3 4 5 6 7 8 9
xi 2 3 4 5 7 7 7 8 9
yi 4 5 4 6 4 6 9 6 11
Using a graphing tool, we have the following calculation summary
Sum of X = 52Sum of Y = 55Mean X = 5.7778Mean Y = 6.1111Sum of squares (SSX) = 45.5556Sum of products (SP) = 31.2222Regression Equation: ŷ = bX + a
Where
b = SP/SSX = 31.22/45.56 = 0.68537
a = MY - bMX = 6.11 - (0.69*5.78) = 2.15122
So, we have
ŷ = 0.68537x + 2.15122
Rounding the numerical values to two decimal places, we have
ŷ = 0.69x + 2.15
Hence, the estimated regression equation for these data is ŷ = 0.69x + 2.15
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