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If u is a square matrix such that u^tu = i what can we say about det(u)
Please Help....Which statements include two quantities in the real world that are additive inverses? Select each correct answer. A plane ascends 500 yards and descends 100 yards. Twenty gallons of water leak from a pool and 20 gallons are put back into the pool. A driver drives 40 miles north and 30 miles south. A person deposits $100 in to her bank account and then withdraws $100 from the same account.
Answer: Second and Fourth options are correct.
Step-by-step explanation:
Since we know that
Additive inverse means
[tex]a+(-a)=0[/tex]
so, -a is the additive inverse of a.
So, according to options, we get that
A plane ascends 500 yards and descends 100 yards.
Ascends = (+)500 yards
Descends = (-) 100 yards
So, -100 is not an additive inverse of +500.
Twenty gallons of water leak from a pool and 20 gallons are put back into the pool.
Number of gallons are leaked out = (-)20
Number of gallons are put back = (+)20
So, we can write
+20-20=0
So, -20 is the additive inverse of +20.
A driver drives 40 miles north and 30 miles south.
Number of miles towards north = +40
Number of miles towards south = -30
So, -30 is not additive inverse of +40.
A person deposits $100 in to her bank account and then withdraws $100 from the same account.
Amount he deposited into her bank = $100
Amount he withdraws from bank = -100
So, we can write as
+100-100=0
So, -100 is an additive inverse of 100.
Hence, Second and Fourth options are correct.
Group a contains 157 students. of these, 51 students in group a have taken math 2a, 80 have taken math 2b, and 70 have taken math 2c. 15 have taken both math 2a and 2b, 20 have taken both math 2a and 2c, and 13 have taken both math 2b and 2c. how many students in group a have taken all three classes?
Answer:
86
Step-by-step explanation:
The stock market decreased by 135 points during a 5 day week.
What was the average daily change in the market for that week?
Tan (pi/5) - tan (pi/30) / 1+tan (pi/5)tan (pi/30)
I need help please ❓❓
(b) if the length, width, and height are increasing at a rate of 0.1 ft/sec, 0.2 ft/sec, and 0.5 ft/sec respectively, find the rate at which the surface area of the box is changing when x = 20 ft, y = 15 ft, and z = 25 ft.
Final answer:
By applying the derivative of the surface area of a rectangular prism formula with respect to time, it is found that the surface area of the box is increasing at a rate of 61 ft^2/sec when the dimensions are 20 ft by 15 ft by 25 ft.
Explanation:
The question involves calculating the rate of change of the surface area of a box with respect to time using derivatives, a concept from calculus. Given the rates at which the length (x), width (y), and height (z) are increasing, we can find the rate at which the surface area S is changing by using the surface area formula for a rectangular prism, S = 2(xy + xz + yz), and differentiating with respect to time.
At the given dimensions (x = 20 ft, y = 15 ft, z = 25 ft), and rate of increase (dx/dt = 0.1 ft/sec, dy/dt = 0.2 ft/sec, dz/dt = 0.5 ft/sec), the rate of change of surface area dS/dt is calculated by:
dS/dt = 2( (dy/dt)z + y(dz/dt) + (dx/dt)z + x(dz/dt) + (dx/dt)y + x(dy/dt) )
dS/dt = 2( (0.2)(25) + (15)(0.5) + (0.1)(25) + (20)(0.5) + (0.1)(15) + (20)(0.2) )
dS/dt = 2(5 + 7.5 + 2.5 + 10 + 1.5 + 4)
dS/dt = 2(30.5)
dS/dt = 61 ft2/sec
Therefore, the surface area of the box is increasing at a rate of 61 ft2/sec when the dimensions x, y, and z are 20 ft, 15 ft, and 25 ft respectively.
What is the slope of the line that passes through th epoints (26, 7) and (-39, 12)?
Suppose that a person rolls two balanced dice three times in succession. determine the probability that on each of the three rolls, the sum of the two numbers that appear will be 7.
The number of combinations that will result in a sum of 7 is:
1 + 6
6 + 1
2 + 5
5 + 2
3 + 4
4 + 3
For a total of 6 combinations per roll. While the total number of combinations per roll are:
6 * 6 = 36
Hence the probability that the sum is 7 would be:
Probability = 6 / 36 = 1 / 6
For a succession of three times, the overall probability that each three rolls will be a sum of 7 is:
Overall probability = (1/6) * (1/6) * (1/6)
Overall probability = 1/216 = 4.63 x 10^-3 = 0.463%
Final answer:
The probability of rolling a sum of 7 three times in succession using two balanced dice is 1/216.
Explanation:
To determine the probability that on each of the three rolls of two balanced dice, the sum of the two numbers that appear will be 7, we first need to identify the probability of rolling a sum of 7 with a single roll of two dice. There are six ways to roll a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of possible outcomes when rolling two dice is 6*6 = 36. Therefore, the probability of rolling a sum of 7 on one roll is P(sum=7) = 6/36 = 1/6.
Since each roll is independent of the others, the probability of this event occurring three times in succession is the product of the individual probabilities. Thus:
P(First roll is 7) = 1/6P(Second roll is 7) = 1/6P(Third roll is 7) = 1/6Therefore, the probability of all three rolls resulting in a sum of 7 is:
P(Three 7's in a row) = P(First roll is 7) * P(Second roll is 7) * P(Third roll is 7) = (1/6) * (1/6) * (1/6) = 1/216.
A rectangular flower box holds 1232 in3 of soil. Find the height of the box if it is 22 in. long and 7 in. wide
The image shows a portion of a bridge supported by two vertical pillars built from the points B and C on the slope below. The length of the bridge between pillar B and pillar C is BLANK feet.
Answer:
The length of the bridge between pillar B and pillar C is 56 feet.
Here's the answer from the plato.
3.5 times (5.8 - 7.09)
The value of the expression simplified using PEMDAS rule is -4.515.
What is PEMDAS?"The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)".
For the given question,
The expression is 3.5 times (5.8 - 7.09).
PEMDAS rule is used to simplify this expression.
The expression is simplified as [tex]3.5[/tex] × [tex](5.8 - 7.09)[/tex]
⇒[tex]3.5[/tex] × [tex](-1.29)[/tex]
⇒[tex]-4.515[/tex]
Hence we can conclude that the value of the expression simplified using PEMDAS rule is -4.515.
Learn more about PEMDAS rule here
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Norfolk va has a population of 242,628 people. Baltimore, Md has 376,865 more people than Norfolk. Charleston,SC has 496,804 less than Baltimore. What is the total population of all 3 cities?
The total population of Norfolk, VA, Baltimore, MD, and Charleston, SC is 984,810 people. This is calculated by adding the respective populations of the three cities together.
Explanation:The total population of the three cities can be found by adding their respective populations together. Given that Norfolk, VA has a population of 242,628 people, and Baltimore, MD has 376,865 more people than Norfolk, we calculate the population of Baltimore by adding these two figures together to get 619,493 people. Charleston, SC has 496,804 less than Baltimore, so its population is found by subtracting 496,804 from 619,493 to get 122,689 people. To find the total population of all 3 cities, we add the populations of Norfolk, Baltimore and Charleston together, giving us 984,810 people in total.
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In a scale diagram, 0.125 inch represents 125 feet. How many inches represents 1 foot?
Middle school has 450 students vanlue school has 600 students which school has a greater percent of girls explain
Find the slope of the line that passes through (90, 93) and (-4, 49).
If l is a line whose equation is y=5x-3, find the equation of the image of l under each of the following translations a. (x,y) --> (x, y-6) b. (x,y) --> (x+2,y)
True or false: the population proportion and sample proportion always have the same value.
Let z ∼ norm(0, 1). use the normal table and also r's "pnorm" function to find (a) p r(z ≤ 1.45) (b) p r(z > −1.28) (c) p r(−0.674 ≤ z < 1.036) (d) p r(z > 0.836)
To find the probabilities using the normal table and R's pnorm function, follow these steps: (a) p r(z ≤ 1.45) is 0.9265 or 92.65%. (b) p r(z > −1.28) is 0.8997 or 89.97%. (c) p r(−0.674 ≤ z < 1.036) is 0.6017 or 60.17%. (d) p r(z > 0.836) is 0.2013 or 20.13%.
Explanation:To find the probabilities using the normal table and r's pnorm function, we can follow these steps:
For (a) p r(z ≤ 1.45), we can use the normal table or the pnorm function in R to find the area to the left of 1.45. The area is 0.9265 or 92.65%.
For (b) p r(z > -1.28), we can find the area to the left of -1.28 using the normal table or the pnorm function in R, which is 0.1003 or 10.03%. To find the area to the right of -1.28, we subtract this value from 1. The area is 0.8997 or 89.97%.
For (c) p r(-0.674 ≤ z < 1.036), we can find the area to the left of -0.674 using the normal table or the pnorm function in R, which is 0.2514 or 25.14%. To find the area to the left of 1.036, we can use the normal table or the pnorm function in R, which is 0.8531 or 85.31%. The difference between these two values gives us the area between the z-scores, which is 0.8531 - 0.2514 = 0.6017 or 60.17%.
For (d) p r(z > 0.836), we can find the area to the left of 0.836 using the normal table or the pnorm function in R, which is 0.7987 or 79.87%. To find the area to the right of 0.836, we subtract this value from 1. The area is 0.2013 or 20.13%.
You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?
using a paid membership card to buy it at a 10 percent discount
buying it online at a 10 percent discount with a $5 shipping charge
buying it at a 10 percent discount without sales tax
Answer:
C.
buying it at a 10% discount without sales tax
Step-by-step explanation:
A linear function has a slope of -7/9 and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y+11=-7/9(x-18)
Answer:
A
Step-by-step explanation:
it has the same slope and the same y-intercept
The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132. Lara wrote the following step to find the length of the unknown leg: Length of the unknown leg = 1572 – 1322 = 24,649 – 17,424 = 7,225 units Which statement best explains whether Lara's step is correct or incorrect? It is correct because the length of the unknown side is the difference of the lengths of the sides. It is correct because the length of the unknown side is the difference of the squares of the sides. It is incorrect because the length of the unknown side is the square root of 42,073. It is incorrect because the length of the unknown side is the square root of 7,225.
the correct answer for this is the last choice:
It is incorrect because the length of the unknown side is the square root of 7,225.
Answer:
It is incorrect because the length of the unknown side is the square root of 7,225.
Step-by-step explanation:
what is the slope of the line represented by the equation 2x+ 3y= -12
Answer:
Slope: -2/3
Step-by-step explanation:
In order to solve this we first have to clear the equation for Y:
[tex]2x+ 3y= -12\\3y=-12-2x\\y=\frac{-12-2x}{3}\\ y=-4-\frac{2}{3} x[/tex]
Remember that the equation in the form of Y is represented in this way:
y=mx+c
Where M is the slope and C is the constant, so the slope is the number that is multiplying x, in the equation, in this case -2/3 is the number that is multiplying x, sot eh slope of the equation is -2/3
Train “A” leaves Westtown and travels at 50 mph toward Smithville, 330 miles away. At the same time, Train “B” leaves Smithville and travels at 60 mph. After how many hours do the two trains meet?
train A travels at 50 mph
train B travels at 60 mph
60 +50 = 110
330/110 = 3
they will meet in 3 hours
An unknown number x is at most 30. Which graph best represents all the values of x?
Number line graph with closed circle on 30 and shading to the right.
Number line graph with closed circle on 30 and shading to the left.
Number line graph with open circle on 30 and shading to the left.
Number line graph with open circle on 30 and shading to the right
Answer:
b
Step-by-step explanation:
Use the distributive property to simplify the following expression 4x(2x-6)
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - -
[tex]\textsf{Using the distributive property, \textbf{a(b+c)=ab+ac}, expand the given expression:}[/tex]
[tex].\qquad\bullet\sf{4x(2x-6)=4x*2x-4x*6=8x^2-24x}[/tex]
[tex]\sf{\bf{$Answer: 8x^2-24x}}[/tex]
[tex]\Large\underbrace{\overbrace{\boldsymbol{Reflection - RoSe}}}^\star_\star[/tex]
0.006 is greater than 0.1
Is this true?
The table shows the annual profits (in thousands of dollars) of a county fair from 2008 to 2012.what must the 2012 profit be ( in hundreds of dollars ) to brake even over the five year period?
44 tens is the same as