Answers
Note that one advantage of the given Linear equation over the graph given above is that the whereas from the equation, we can immediately tell what the slope (m)is and what the y-intercept (b) is, this is not given in the above graph.
What is the Y-intercept and the slope as given in the above Linear Equation?Note that every linear equation takes the following form:
y = mx + b
Where:
the variable b denotes the y-intercept of the graph of the line; and variable m denotes the slope of the line.Since we have the given linear equation to be:
y = 6/1x + 100
m here = 6/1 or 6 which is the slope; while
b here = 100, that is the y-intercept.
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Related Questions
Let V and W be vector spaces over a field F. Let Z = {(v, w): v ∈ V and w ∈ W}. Prove that Z is a vector space over F with the operations(v1, w1)+(v2, w2)=(v1 + v2, w1 + w2) and c(v1, w1)=(cv1, cw1).
Answers
Z is a vector space over F with the operations(v1, w1)+(v2, w2)=(v1 + v2, w1 + w2) and c(v1, w1)=(cv1, cw1) is proved.
A vector is a mathematical object that can be added and multiplied by a number, also known as a scalar.
In this case, we have two vector spaces, V and W, which are sets of vectors that can be added and scaled in a certain way, with the scalars taken from a field F.
=> (v1, w1)+(v2, w2)=(v1 + v2, w1 + w2)
We then define a new set, Z, which consists of ordered pairs of vectors, one from V and one from W. With the operations of adding two vectors element-wise and scaling a vector by a scalar, we can show that Z is also a vector space over F.
=> c(v1, w1)=(cv1, cw1).
To do this, we need to verify that Z satisfies the properties of a vector space, such as closure under addition and scalar multiplication, associativity and commutativity of addition, the existence of an additive identity and inverse, and distributivity of scalar multiplication over vector addition.
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35. Find the perimeter and area of each composite figure. 10 in 6 in 14 in
Answers
WILL GIVE BRAINLEST, PLEASE HELP
Which of the following gives the correct range for the graph?
A coordinate plane with a segment going from the point negative 3 comma 2 to 0 comma 1 and another segment going from the point 0 comma 1 to 5 comma negative 4.
−4 ≤ x ≤ 2
−3 ≤ x ≤ 5
−4 ≤ y ≤ 2
−3 ≤ y ≤ 5
Answers
The range of the graph is -4 ≤ y ≤ 2.
Option C is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
A coordinate plane with a segment going from the point (-3, 2) to (0, 1) and another segment going from the point (0, 1) to (5, -4).
This means,
(-3, 2) to (5, -4)
The range of the graph is the y-coordinate.
So,
-4 to 2
This can be written as,
-4 ≤ y ≤ 2
Thus,
The range is -4 ≤ y ≤ 2.
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For each inequality, how it on the number line and write all one-digit integer that atify it. K<0
Answers
Any pair of real numbers or algebraic expressions that are equivalent by the symbols ‘<’, ‘>’, ‘≤’ or ‘≥’ constitute an inequality.
A mathematical concept used to compare quantities is inequality. By highlighting the area that the inequality pertains to, we can graph the inequality on a number line.
Let's examine the number line graphing of inequality. Look at the illustration below, which shows the following disparities on a number line:
x ≥ 5, x > 5, x ≤ 5, and x < 5.
It should be noticed that if the inequality indicates that a certain number is included, we mark a filled circle on that specific number; nevertheless, if the inequality indicates that a certain number is excluded, we mark an empty circle on the number.
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I WILL GIVE Y'ALL ANYTHING LIKE ANYTHING PLEASE HELP
Question 1(Multiple Choice Worth 2 points)
(Likelihood MC)
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
Question 2(Multiple Choice Worth 2 points)
(Likelihood MC)
Three softball players discussed their batting averages after a game.
Probability
Player 1 seven elevenths
Player 2 six ninths
Player 3 five sevenths
Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
Question 3(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
10%
30%
50%
90%
Question 4(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
0.25
0.35
0.50
Question 5(Multiple Choice Worth 2 points)
(Theoretical Probability LC)
Question 6(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on blue, P(not blue).
0.375
0.625
0.750
0.875
Question 7(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
Question 8(Multiple Choice Worth 2 points)
(Likelihood MC)
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
Question 10(Multiple Choice Worth 2 points)
(Experimental Probability MC)
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a gold marble from the bag.
The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 11.5%.
The theoretical probability, P(gold), is 25%, and the experimental probability is 25%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 13.0%.
Question 11(Multiple Choice Worth 2 points)
(Experimental Probability LC)
A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number greater than 4.
17 over 60
18 over 60
24 over 60
42 over 60
Question 12(Multiple Choice Worth 2 points)
(Likelihood MC)
The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 15%, interpret the likelihood of randomly selecting a terrier from the shelter.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Question 15(Multiple Choice Worth 2 points)
(Experimental Probability MC)
Answers
Answer:
unlikely
Step-by-step explanation:
25% of the cookies are chocolate chip, so the other 75% would be oatmeal raisin and sugar cookies. 0.25 is equal to 25%, so it is unlikely you will get a chocolate chip cookie.
From the data regarding the no. Of children core
0,0,2,5,4,3,2,3,4
Tabulate the following
Answers
The cumulative frequency is the running total of the frequency; each value in the cumulative frequency column is the sum of the previous and current frequency values.
From the data on the number of children, the following can be calculated:
Table of Frequency:
No. of Children | Frequency 0 | 1 2 | 2 3 | 2 4 | 2 5 | 1
Table of Relative Frequency:
Children | Frequency | Relative Frequency 0 | 1 | 1/9 2 | 2 | 2/9 3 | 2 | 2/9 4 | 2 | 2/9 5 | 1 | 1/9
Table of Cumulative Frequency:
Child Count | Frequency | Cumulative Frequency
0 | 1 | 1 \s2 | 2 | 3 \s3 | 2 | 5 \s4 | 2 | 7 \s5 | 1 | 8
Because the cumulative frequency is the frequency's running total, each value in the cumulative frequency column is the sum of the previous and current values in the frequency column.
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in which of these rows of the truth table is the compound proposition (p ∧ r) → ¬(q ∨ p) true? The row where both p and q are true, but ris false. The row where both p and rare true, but q is false. The row where p q and rare all false. The row where p, q and r are all true.
Answers
By using the truth table The correct options are (a) The row where both p and q are true, but r is false and (c) The row where p, q and r are all false.
Given, (p ^ r) -> ~(q v p)
Creating truth table:
=> p ^ r will return true if both the values of p and r are true else will return false.
=> q v p will return true if at least one of the values of q or p is true else will return false.
=>~(q v p) will return true if the truth value of q v p is false else will return false.
=>(p ^ r) -> ~(q v p) will return false if truth value of p ^ r is true and truth value of ~(q v p) is false else will return true.
p q r (p ^ r) (q v p) ~(q v p) (p ^ r) -> ~(q v p)
F F F F F T T
F F T F F T T
F T F F T F T
F T T F T F T
T F F F T F T
T F T T T F F
T T F F T F T
T T T T T F F
=> Option (a) is correct because according to the row number 7 where p = q = T and r = F, the result = T
=> Option (b) is wrong because according to row number 6, where p = q = T and q = F, the result = F
=>Option (c) is correct because according to row number 1, where p = q = r = F the result = T
=>Option (d) is wrong because according to the row number 8 where p = q = r = T the result = F
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Algebraically determine the limit. (Note: This exercise corresponds to the subsection Algebraically Determining Limits.) lim (4 + b)2-82 DO h
Answers
Limit, (4 + b)² - 8², Algebraically Determining Limits, h approaches 0, Expansion Formula for Square, Lim [(4 + b + h)² - 8² = (4 + b)² - 64.
To algebraically determine the limit, we can use the definition of a limit.
The limit of (4 + b)²-8² as h approaches 0 is equal to the limit of (4 + b + h)² - 8² as h approaches 0 minus (4 + b)² - 8².
Using the expansion formula for a square, we can write:
(4 + b + h)² - 8² = (4 + b)² + 2(4 + b)h + h² - 64
Now, taking the limit as h approaches 0:
lim [(4 + b + h)² - 8²] = lim [ (4 + b)² + 2(4 + b)h + h² - 64 ] = (4 + b)² - 64
So,
lim (4 + b)² - 8² as h approaches 0 = lim [(4 + b + h)² - 8²] - (4 + b)² + 64 = lim [(4 + b + h)² - 8²]
Hence,
lim (4 + b)² - 8² as h approaches 0 = lim [(4 + b + h)² - 8² = (4 + b)² - 64.
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What is another way to write the expression x(14 + 19) + 30
Answers
Answer:
The answer could be x * 33 + 30.
Step-by-step explanation:
In this expression, the parentheses indicate that 14 and 19 are to be added together first, which equals 33. The expression x * 33 means that 33 is being multiplied by x. Finally, 30 is being added to this product. So both expressions represent the same mathematical operation.
Here's how to check our answer:
First, we simplify the expression inside the parentheses:
x(33) + 30
Next, we multiply x and 33:
x * 33 + 30
Finally, we add 30 to the product of x and 33:
x * 33 + 30
So, the expression x * 33 + 30 is equivalent to the expression x(14 + 19) + 30.
I would greatly appreciate Brainliest.
Have a nice day.
x(14+19)+ 30 =
33 + 30
33x+30
Two pools are being filled with water. To start, the first pool contains 1272 liters of water and the second pool contains 1600 liters of water. Water is being added
to the first pool at a rate of 31.5 liters per minute. Water is being added to the second pool at a rate of 21.25 liters per minute.
After how many minutes will the two pools have the same
amount of water?
minutes
How much water will be in each pool when they have the i
same amount?
liters
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Answers
1. After 32 minutes the two pools will have the same amount of water.
2. 2,280 liters of water will be in each pool when they have the same amount.
Let's call the time in minutes when the two pools have the same amount of water "t". Getting into variables here.
At time t, the first pool will have 1272 + 31.5t liters of water, and the second pool will have 1600 + 21.25t liters of water.
For the two pools to have the same amount of water, we need:
1272 + 31.5t = 1600 + 21.25t
10.25t = 328
t = 32 minutes
I underlined all the answers if you don't want to read the entire thing, lol.
Question 1: So, 32 minutes after starting, the two pools will have the same amount of water.
Question 2: The amount of water in each pool will be:
1272 + 31.5 * 32 = 1600 + 21.25 * 32 = 1600 + 680 = 2,280 liters.
michelle and themba are travelling from Cape Town to Johannesburg by car. They travel 30km in 18 minutes and continue at a constant speed. how far will they have to travel in 1hour 24minutes
Answers
A shipping company charges a $5.75 handling fee in addition to $0.31 per pound to ship a package. Using X for the weight in pounds and for the cost of shipping in dollars, write a linear function that determines the cost of shipping based on weight.
Answers
The Shipping Company Cost, y=$(5.75+0.31x) is a linear function that determines the cost of shipping based on weight.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
A shipping company charges a $5.75 handling fee in addition to $0.31 per pound to ship a package.
Using X for the weight in pounds and for the cost of shipping in dollars
Let the number of pounds being shipped=x
Shipping Company charges $5.75 plus an additional $0.31 per pound to ship a package.
Shipping Company Cost = $5.75 + ($0.31 X Number of Pounds)
Shipping Company Cost, y=$(5.75+0.31x)
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Isaac owns a food truck that sells tacos and burritos. He only has enough supplies to make 130 tacos or burritos. He sells each taco for $4.25 and each burrito for $8.50. Isaac must sell a minimum of $850 worth of tacos and burritos each day. If x represents the number of tacos sold and y represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
Answers
By solving linear equation, it can be calculated that x = 60 , y = 70 is one possible solution of the linear equation.
What is linear inequation?Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by <, >, ≤, ≥
A one degree inequation is known as linear inequation.
Let the number of tacos sold be $x and the number of burrito sold be $y
He only has enough supplies to make 130 tacos or burritos.
x + y ≤ 130 ... (1)
He sells each taco for $4.25 and each burrito for $8.50.
Isaac must sell a minimum of $850 worth of tacos and burritos each day.
4.25x + 8.5y ≥ 850
x + 2y ≥ 200 ... (2)
The inequalities has been solved graphically as;
One possible solution is x = 60, y = 70
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the function g is given by g(x)=1x2−4x 5. the function h is given by h(x)=2x2−8x 10x2−4x 6. if f is a function that satisfies g(x)≤f(x)≤h(x) for 0
Answers
One possible solution is to define f(x) as the average of g(x) and h(x), which would be: f(x) = (g(x) + h(x)) / 2
The function g(x) = 1x^2 - 4x + 5 and the function h(x) = 2x^2 - 8x + 10x^2 - 4x + 6 are quadratic functions. To find a function f(x) that satisfies the inequality g(x) ≤ f(x) ≤ h(x) for all x >= 0, we need to find a function that lies between these two functions for all x >= 0.
One possible solution is to define f(x) as the average of g(x) and h(x), which would be: f(x) = (g(x) + h(x)) / 2
The intuition behind this choice is that if f(x) is the average of g(x) and h(x), it should be located between these two functions for all x >= 0. To confirm this, we can graph g(x), h(x), and f(x) on the same coordinate plane and see if they satisfy the inequality.
It's important to note that this solution is just one possible choice and there may be other functions that satisfy the inequality g(x) ≤ f(x) ≤ h(x) for all x >= 0.
Therefore, One possible solution is to define f(x) as the average of g(x) and h(x), which would be: f(x) = (g(x) + h(x)) / 2
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The sum of two numbers is 97. The difference is 19. Find the numbers
Answers
To solve
Create a system of equations.
Say one number is X and the other is Y.
X+Y=97
X-Y=19
Use the first equation to find the value of either X or Y. I’m going to find it in terms of Y.
Subtract X from both sides.
X+Y=97 —> Y=97-X
Now, use that Y value and replace it in the second equation.
X-Y=19 —> X-(97-X)=19
Now solve for X.
1. Distribute terms in the parenthesis
X-97+X=19
2. Combine like terms.
2X-97=19
3. Add 97 to both sides
2X=116
4. Divide both sides by 2
X=58
Now, we can plug the X value in to any of the two first equations to solve for Y.
X+Y=97
58+Y=97
Subtract 58 from both sides and you get Y=39
X=58 and Y=39
The breed. Com moondhedegas dome tetembe eggs to find the Seed Yes creo A5x4 OON 8. 9x8 Ore O No Yes No C 5 -- D8x9 O O No L-8X9 Yes No Yes No P A bookstore has 7 copies of their top selling book in their window display. The store has 10 times the amount in stock. If the store sells 17 of the books, how many books would be left in stock? Cicle the equations you can use to solve the problem. Then circle the solution 10 + 7 First, solve 2x17 - Then solve 119 - 17 - b. 7x10 70 There are 10 books left in stock 53
Answers
The answer to the question is: 10 books left in stock.The equation that used to solve this problem is 7 + 10 = x - 17.
This question can be solved by using an equation. The equation that used to solve this problem is 7 + 10 = x - 17. This equation can be solved by first multiplying both sides by 2. This will give us 2x17 = x. Then, subtract 17 from both sides, which gives us x = 119 - 17. Finally, subtract 7 from both sides to get 10 = x - 17. Therefore, the answer to the question is 10 books left in stock.
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What do the center and the scale factor need to be in order to transform ACE to triangle ABD?
Answers
A shape must cross a line in order to be reflected.
Because a reflection across BA will map ABC to ABD, the true statement is (c).
What is transformation?A translation only moves a shape up, down, or from side to side; it has no effect on how it appears. An illustration of a transformation is translation. A transformation is a technique for moving or repositioning a shape.
here, we have,
Sides AC and AD of both triangles are congruent
Sides BD and BC of both triangles are congruent
The triangles share a common side AB
This means that a reflection over line AB will map both triangles.
Hence, the true statement is (c)
The complete question is given below.
Is there a rigid transformation that maps triangle ABC to triangle ABD? If so, which transformation?
yes, because a translation to the right will map ΔABC to ΔABD
yes, because a rotation about point B will map ΔABC to ΔABD
yes, because a reflection across BA will map ΔABC to ΔABD
no, because no rigid transformation will map ΔABC to ΔABD
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monica wants to cut a cake into identical pieces. if the cake has rectangular form and 21 inches by 35 inches, what is the least number of square pieces he can cut without wasting a cake?
Answers
The least number of square pieces that Monica can cut from a rectangular cake without wasting any cake is 15 pieces, each 7 inches on a side.
Monica wants to cut a cake into identical square pieces without wasting any cake. To find the least number of square pieces that can be cut from a rectangular cake, we need to find the greatest common divisor (GCD) of the lengths of the sides.
In this case, the GCD of 21 and 35 is 7. This means that we can cut the cake into 7-inch square pieces, and there will be no waste. The number of pieces can be found by dividing each side of the rectangular cake by the side length of the square pieces.
For the 21-inch side, the number of pieces is
21 / 7 = 3
For the 35-inch side, the number of pieces is
35 / 7 = 5
Therefore, the total number of pieces that can be cut from the rectangular cake is
3 * 5 = 15.
In conclusion, the least number of square pieces that Monica can cut from a rectangular cake without wasting any cake is 15 pieces, each 7 inches on a side.
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how much sugar is needed to make 200 grams of 15% sugar syrup
Answers
Let's call the amount of sugar needed to make 200 grams of 15% sugar syrup "s".
From the information given, we know that 15% of the syrup is sugar, so 200 grams * 15% = 200 grams * 0.15 = 30 grams of the syrup is sugar.
Therefore, the amount of sugar needed is equal to 30 grams, or s = 30 grams.
What are all values of x for which the function f defined by f(x) = (x2 - 3)e-x is increasing?.
Answers
The function f is increasing for x > 3/2.
To determine the values of x for which the function f is increasing, we need to find the critical points of f, which are the values of x where the function changes from increasing to decreasing or vice versa.
The first step is to find the derivative of f:
f'(x) = (2x - 3)e-x
Next, we need to find the critical points by setting f'(x) = 0 and solving for x:
(2x - 3)e-x = 0
2x - 3 = 0
x = 3/2
This is the only critical point of f. To determine the behavior of f near this critical point, we need to find the second derivative of f:
f''(x) = (2 - 3e-x)
For x < 3/2, f''(x) < 0, which means f is concave down and f'(x) is decreasing. This means that f is decreasing for x < 3/2.
For x > 3/2, f''(x) > 0, which means f is concave up and f'(x) is increasing. This means that f is increasing for x > 3/2.
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A hemisphere fits snugly inside a cylinder with a radius of 8 cm. A cone fits snugly inside the same hemisphere.
a. What is the volume of the cylinder?
b. What is the volume of the cone?
c. Estimate the volume of the hemisphere by calculating the average of the volumes of the cylinder and cone.
Answers
Answer:
guys i have no idea
Step-by-step explanation:
The volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Given that, a hemisphere fits snugly inside a cylinder with a radius of 8 cm. A cone fits snugly inside the same hemisphere.
Since, all of them are tightly packed in one another therefore, radius of all them will be equal,
And, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.
r = radius of cylinder = 8 cm and
h = height of cylinder = radius of hemisphere = 8 cm
We know that,
Volume of a cylinder = π × radius² × height
Volume of a cone = 1/3 × π × radius² × height
Therefore,
a) The volume of cylinder =
π × 8² × 8 = 512π cm³
b) The volume of cone =
1/3 × π × 8² × 8 = 170.6π cm³
c) Volume of the hemisphere = (512π + 170.6π) / 2
= 341.3π cm³
Hence, the volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.
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Is "Johann Sebastian Bach is the greatest of all the Baroque composers" a proposition? Why?
Answers
"Johann Sebastian Bach is the greatest of all the Baroque composers"
a proposition, The proposition is a meaningful statement. without any question,
Mathematical reasoning techniques are laid forth in the rules of mathematical logic. The father of logical reasoning was the Greek philosopher Aristotle. The theoretical foundation for many branches of mathematics, and hence computer science, is provided by logical reasoning. It is used in the design of computing devices, artificial intelligence, the definition of data structures for programming languages, and many other practical areas of computer science.
Statements to which the truth values "true" and "false" can be given are the focus of propositional logic. The objective is to evaluate these claims, either singly or collectively.
"Johann Sebastian Bach is the greatest of all the Baroque composers"
a proposition
The proposition is a meaningful statement. without any question,
in our case, Johann is the greatest composer, is truth statement,
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Square ABCD has vertices at A(-2,1), B(2,7), C(8,3), and D(4, -3).
ch
1
2
3
4
5
© 2016 Strong Mind. Created using GeoGebra.
How many units is the perimeter of square ABCD?
104
1615
24
Answers
The perimeter of square ABCD is 8 [tex]\sqrt{13}[/tex] units.
Coordinates of the vertices are A(-2, 1), B(2, 7), C(8, 3) and D(4, -3)
A square's perimeter is equal to the sum of its four sides or the product of four and one of its sides.
Therefore, the square's perimeter is equal to a + b + c + d.
4 × any of the sides because the sides of a square are equal to one another.
Since ABCD is a square:
Perimeter of a square = 4 × (length of a side)
=4 × AB
Formula to calculate the distance between two points [tex]$\left(x_1, y_1\right)$[/tex] and [tex]$\left(x_2, y_2\right)$[/tex] is, [tex]$\mathrm{d}=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$[/tex]
Therefore, distance between two points A(-2, 1) and B(2, 7) will be,
AB = [tex]\sqrt{(2+2)^2+(7-1)^2} \\[/tex]
AB = [tex]\sqrt{4^2+6^2} \\[/tex]
AB = [tex]\sqrt{52} \\[/tex]
AB = 2[tex]\sqrt{13}[/tex]
Hence the perimeter of square ABCD can be calculated as 4 × AB
Now Perimeter of a square ABCD = 4 × 2[tex]\sqrt{13}[/tex]
= 8 [tex]\sqrt{13}[/tex] units
Therefore the answer is 8 [tex]\sqrt{13}[/tex] units
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Square ABCD has vertices at A(−2,1), B(2,7), C(8,3), and D(4,−3). How many units is the perimeter of square ABCD?
we are all pretty familiar with ""means"" or ""averages""…why do we need more information than that? what is the point of calculating variance?
Answers
Variance is a useful tool for gaining a deeper understanding of a dataset beyond just the mean.
Variance is a measure of how far the individual values in a set of data are from the average value.
The variance is calculated by first finding the difference between each value in the dataset and the mean, squaring these differences, and then averaging the squared differences.
The result is a non-negative number that indicates how far, on average, each value deviates from the mean. If the variance is small, it means that most of the values are close to the mean, while a large variance indicates that the values are widely spread out.
One important use of variance is in statistical inference, where it is used to make predictions about a population based on a sample of data. Variance also plays a role in hypothesis testing, where it is used to determine whether the differences between two sets of data are statistically significant.
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the helix r(t) = cos(pi t/2), sin (pi t/2) , t) intersects the sphere x^2 y^2 z^2 =2
Answers
The helix r(t) = (cos(πt/2), sin(πt/2), t) intersects the sphere x² + y² + z² = 2 in two points and the angle of intersection at every point is 0°.
Let's assume that the central axis of the helix is z
Given r(t) = (cos(πt/2), sin(πt/2), t)
Put this point in the sphere equation
cos²(πt/2) + sin²(πt/2) + t² = 2
1 + t² = 2
t² = 1
t = +1, -1
Now, let f = x² + y² + z² - 2
Δf = (fx, fy, fz)
Δf = (2x, 2y, 2z)
At (cos(πt/2), sin(πt/2), t), Δf = (2cos(πt/2), 2sin(πt/2), 2t)
Angle of intersection at t = 1
Δf = (0, 2, 2) and r = (0, 1, 1)
Using dot product:
cosθ = (0, 2, 2).(0, 1, 1)/ √(2² + 2²) √(1² + 1²)
cosθ = 1
θ = 0°
Angle of intersection at t = -1
Δf = (0, -2, -2) and r = (0,-1, -1)
Using dot product:
cosθ = (0, -2, 2-).(0, -1, -1)/ √((-2)² + (-2)²) √((-1)² + (-1)²)
cosθ = 1
θ = 0°
Hence, the angle of intersection at every point is 0°
The given question is incomplete. The complete question is
"The helix r(t) = (cos(πt/2), sin(πt/2), t) intersects the sphere x² + y² + z² = 2 in two points. Find the angle of intersection at each point."
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Seventy-five (75) customers at Crummy Burger today were entered in a drawing. Three names will be drawn, and each will win a prize.
Determine the number of ways that the prizes can be distributed if all 3 prizes are a $10 gift card.
Bonus**** If a pair of fair six-sided dice are tossed, what is the probability that the sum is even OR greater than 7?
Answers
The number of ways in which the prizes are allocated is 67,525.
Combinations are the various ways in which objects from a set may be selected, generally without replacement, to form subsets.
Given that
Number of customers = 75
Number of prizes = 3
And, the value of the gift card = $10
Based on the above information,
The number of ways in which the prizes are allocated is shown below:
=⁷⁵C₃
=[tex]\frac{75!}{(3!*(75-3)!}[/tex]
After solving this the number of ways that came is 67,525
Hence, the number of ways in which the prizes are allocated is 67,525
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What i the lope of the line that pae through the point (2, 8)(2,8) and (-3, 14)(−3,14)? Write your anwer in implet form
Answers
The slope of the line that passes through points (2, 8) and (-3, 14) is -1.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Given:
The coordinates of point = (2, 8) and (-3, 14),
Calculate the slope of the line from the formula given below,
m = (y₂ - y₁) / (x₂ - x₁)
Here m is the slope.
Substitute the values,
m = (13 - 8) / (-3 - 2)
m = −1
Therefore, the slope of the line that passes through points (2, 8) and (-3, 14) is -1.
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The Luxor as a square pyramid and Trump Tower as a rectangular prism. Round your answer to the nearest whole number without commas!
350 ft.
646 ft.
646 ft.
Luxor Hotel Base width: 646 ft. Height: 350 ft.
The trump tower Base width is:290 ft. base length is : 125ft. and the hight is 622ft.
Answers
The minimum amount of glass used for the exterior 615340.84 m ²
How to find the minimum amount?We must calculate the lateral area which is given by:
A = (1/2) * pb * Ap
Where,
pb: perimeter of the base
Ap: Apotema
Calculating the apothem we have:
Ap = root ((646/2) ^ 2 + (350) ^ 2)
Ap = 476.27 feet
Calculating the perimeter of the base we have:
pb = 4 * (646)
pb = 2584 feet
Substituting values:
A = (1/2) * pb * Ap
A = (1/2) * (2584) * (476.27)
A = 615340.84 m ^ 2
The minimum amount of glass used for the exterior is:
A = 615340.84 m ²
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Correct question:
The luxor hotel in las vegas is a square base pyramid that is 646 feet wide at the base and 350 feet tall. if the outer walls of the hotel are covered in glass, what was the minimum amount of glass used for the exterior?
Among the contestants in a competition are 45 women and 25 men. If 5winners are randomly selected, what is the probability that exactly two are men?
Answers
When 5 winners are randomly selected, the probability that they are all men is 0.0045
How to solve for the probability?Among the contestants in a competition are 45 women and 25 men.
Total persons are = 45+25 = 70
When one winner is chosen, there are 69 people left, when second winner is chosen there are 68 people left and so on.
So, the probability that they are all men is given by:
25/70 *24/69 * 23/68 * 22/67 * 21/66 = 0.0045
Therefore, when 5 winners are randomly selected, the probability that they are all men is 0.0045-
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If b = 5.4 yards and c = 7.5 yards, what is the perimeter? If necessary, round to the nearest
tenth.
Answers
The perimeter of the triangle would be 18.1 yards.
What is Pythagorean theorem ?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between the three sides of a right triangle in Euclidean geometry. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.
Given the information in the problem, we can use the Pythagorean theorem to find the length of the other leg, a:
[tex]c^2 = a^2 + b^2\\\\7.5^2 = a^2 + 5.4^2\\\\56.25 = a^2 + 29.16\\\\56.25 - 29.16 = a^2\\\\27.09 = a^2\\\\a = \sqrt{27.09} \\\\a = 5.2\ yards[/tex]
The perimeter of the triangle is the sum of the lengths of all its sides:
Perimeter = a + b + c
Perimeter = 5.2 + 5.4 + 7.5
Perimeter = 18.1 yards (rounded to the nearest tenth)
Therefore, The perimeter of the triangle would be 18.1 yards.
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