Find the matrix A' for T relative to the basis B' = {(1, 1, 0), (1, 0, 1), (0, 1, 1)). T: R3-R? T(x, y, z)=(-3x, -7y, 52) 0-70 A'= -3 70 3 75] 0 --5 -4 -6 A= 2 1 -2 4-1 -0 -3 -7 0 A'= -3 05 005] --3-30 A'= -7 00 0 55 2 2 A'= -4 6 1 -6 4-1

Answer:

y(y-1)

Step-by-step explanation:

the common factor of both of these is y so you divide by y for both of these problems to get

y-1 and then you multiply by y since you took y out

y(y-1)

hopes this helps please mark brainliest

Answer:

y(y-1)

Step-by-step explanation:

hope this helped

The mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

The mean of a geometric distribution is given by:

Mean = 1/p

Here, p is the probability of success on a single trial.

In this case, p = 0.80

So, the mean of the geometric distribution = 1/0.80 = 1.25

The variance of a geometric distribution is given by:

Variance =\((1-p) / p^2\)

By substituting the value of p = 0.80, we get:

Variance = \((1-0.80) / 0.80^2 = 0.20 / 0.64 = 0.3125\)

So the variance of the geometric distribution = 0.3125

Therefore, the mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

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Answer: The expression is 7/2.

The rate of change of the circle diameter with respect to the radius is a constant value of 2.

The diameter of a circle is twice the radius, so we can write:

Diameter = 2 * Radius

To find the rate of change of the diameter with respect to the radius, we can take the derivative of both sides of this equation with respect to the radius:

diameter/d(radius) = d(2 * radius)/d(radius)

The derivative of 2*radius with respect to radius is simply 2, so we can simplify the equation:

diameter/d(radius) = 2

Therefore, the rate of change of the circle diameter with respect to the radius is a constant value of 2. This means that if we increase the radius by a small amount, the diameter will increase by twice that amount. Conversely, if we decrease the radius by a small amount, the diameter will decrease by twice that amount.

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Answer:

Step-by-step explanation:

Mean income of 99 people = $ 400

Sum of income of 99 people = 400 * 99 = $ 39600

Income of a woman = $ 1500

Income of 100 people = 39600 + 1500 = $41100

Mean of 100 people = 41100/100 = $411

411 - 400 = $11

Mean income increases by $11

Answer:

\(\huge\boxed{\sf x=\frac{2}{y-f}}\)

Step-by-step explanation:

xy - fx = 2

Take x common

x(y - f) = 2

Divide y-f to both sides

\(\displaystyle x=\frac{2}{y-f} \\\\\rule[225]{225}{2}\)

Answer:

B: 3,0,-3,-6

Step-by-step explanation:

An arithmetic sequence has constant adding or subtracting. In this case, 3 is being subtracted as a constant.

Reserve Requirement

Took the test got 100

Answer:

Its D

Step-by-step explanation:

Reserve Requirement I got it right on my test

The f-test can be used to test the linear hypothesis, except for the β2. The linear hypothesis mentioned can be tested using the f-test, except for the β2

In hypothesis testing, the f-test is used to determine if there is a significant difference between the variances of two or more groups or conditions.

It is commonly used in analysis of variance (ANOVA) tests. The f-test compares the variability between groups to the variability within groups. To conduct an f-test, you need to calculate the f-statistic by dividing the mean square between groups by the mean square within groups. The resulting f-statistic is then compared to the critical value from the F-distribution. If the calculated f-statistic is greater than the critical value, the null hypothesis is rejected, indicating that there is a significant difference between the groups. In this case, the linear hypothesis can be tested using the f-test, but the exception is the β2 group of answer choices. This means that the β2 coefficient is not involved in the hypothesis being tested using the f-test. In conclusion, the f-test can be used to test the linear hypothesis, except for the β2 group of answer choices.

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Therefore, the volume of a cycle that is shaped like a cylinder with a height of 150 feet and a radius of 35 feet is 576975 ft^3.

They are asking us to calculate the volume of a cycle, formed by a cylinder (The cycle is shaped like a cylinder).

To calculate the volume, we apply the formula:

We know that the height you have is 150 feet, and the radius is 35 feet, we solve:

V = 3.14 × (35 ft)² × 150 ft

V = 3.14 × 1225 ft² × 150 ft

V = 576975 ft³

Therefore, the volume of a cycle that is shaped like a cylinder with a height of 150 feet and a radius of 35 feet is 576975 ft^3.

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Answer:

The distance between each sign would be 1/8th of a mile.

Step-by-step explanation:

To find where each should be placed and the distance between them we would have to multiply 1/2 by 1/4 because there are 4 signs.

1/2 * 1/4 = 1/8

Each sign should be placed 1/8 of a mile away from each other.

So, the first sign would be placed at 1/8 of the half mile, the second sign would be placed at 1/4 of the half mile, the third sign should be put at 3/8 mark of the half mile, and then the fourth sign would be placed at the 1/2 mile mark.

Fraction form:

Sign 1: 1/8 mile

Sign 2: 1/4 mile

Sign 3: 3/8 mile

Sign 4: 1/2 mile

In decimal form it would be:

Sign 1: 0.125 mile

Sign 2: 0.25 mile

Sign 3: 0.375 mile

Sign 4: 0.5 mile

Hope this helps!!

The value of function f' (2) would be,

f′(2) = 0

For the value of f′(2), we need to take the derivative of the function f(y) with respect to y and then evaluate it at y = 2.

Using the quotient rule, we have:

f′(y) = [2(1/y²)h(y) - 2(2/y³)h(y)]/y⁴

Simplifying this expression by factoring out 2/y⁴, we get:

f′(y) = [h(y)/y² - 2h(y)/y³]

Now, we can substitute y = 2 and use the given information about h(2) and h′(2) to evaluate f′(2).

f′(2) = [h(2)/2² - 2h(2)/2³]

f′(2) = [5/4 - 10/8]

f′(2) = [5/4 - 5/4]

f′(2) = 0

Therefore, the answer is B. 0.

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We simplify fractions because doing so always makes them easier to work with or compute.

A fraction is a piece of the entire. The number is shown as a quotient in mathematics, where the numerator and denominator are split. Both are integers in a straightforward fraction. A fraction appears in a complex fraction's numerator or denominator. The numerator of a valid fraction is smaller than the denominator. A fraction is a mathematical concept that denotes a component of a whole or, more generally, any number of equal parts. As employed in conversational English, a fraction—such as one-half, eight-fifths, and three-quarters—indicates the number of components of a particular size. With fractions, smaller portions of a whole are represented. The whole may be made up of one thing or several things. In any case, they collectively constitute what is referred to as a whole.

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the uniform distribution does not have the memoryless property. In our example, we calculated P(X>0.5) = 0.5 and P(X>0.7|X>0.2) = 0.375.

First, let's define the terms:

1. Distribution: A function that describes the probability of a random variable.
2. Property: A characteristic or feature of a distribution.
3. Parameters: Values that define a specific distribution.

Now, let's answer the questions:

Question 3: To find P(X>0.5) for a uniform distribution with parameters 0 and 1, we need to calculate the probability of X being greater than 0.5. Since it's a uniform distribution, the probability is the same for all values in the range [0,1]. So, P(X>0.5) is equal to the length of the interval (1-0.5) = 0.5.

Answer 3: P(X>0.5) = 0.5

Question 4: To find P(X>0.7|X>0.2), we need to calculate the probability of X being greater than 0.7, given that X is already greater than 0.2. Since X follows a uniform distribution, we can calculate the conditional probability by finding the length of the remaining interval and dividing by the length of the conditioning interval.

Remaining interval: (1-0.7) = 0.3
Conditioning interval: (1-0.2) = 0.8

Answer 4: P(X>0.7|X>0.2) = (Remaining interval) / (Conditioning interval) = 0.3 / 0.8 = 0.375

Now, let's discuss the memoryless property. A distribution has the memoryless property if P(X>s+t|X>s) = P(X>t) for all s, t ≥ 0. The exponential distribution and the geometric distribution are two examples of memoryless distributions.

However, the uniform distribution does not have memoryless property. In our example, we calculated P(X>0.5) = 0.5 and P(X>0.7|X>0.2) = 0.375. If the uniform distribution were memoryless, these two probabilities would be equal, but they are not.

Conclusion: The uniform distribution does not have the memoryless property.

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Answer:

-4-26=6x-x   or,-30=5x Therefore , x=-6

Step-by-step explanation:

Step-by-step explanation:

\(x-4=6x+26\)

\( \longrightarrow \: x - 6x = 26 + 4\)

\(\longrightarrow \: - 5x = 30\)

\(\longrightarrow \: - x = \frac{30}{5} \)

\(\longrightarrow \fcolorbox{green}{red}{ x = - 6}\)

To prove that the x = -6

putting the value of x

\(x-4=6x+26\)

\(\longrightarrow \: ( - 6) - (4) = 6 \times ( - 6) + 26\)

\(\longrightarrow \: - 10 = - 36 + 26\)

\(\longrightarrow \: - 10 = - 10\)

\(\longrightarrow \fcolorbox{blue}{green}{ LHS=RHS }\)

hence its proved

Answer:

72.5

Step-by-step explanation:

70=-2.5x

+2.5 +2.5

x =72.5

Answer:

-28 for x

Step-by-step explanation:

the equation is supposed to be multiplied but you have to find x first so i think you have to divide 70 and -2.5 to find x then check your work by multiplying -2.5 and the answer which is -28 to get 70.

Answer:

  f = 2.75p

Step-by-step explanation:

You can see that the amount of flour for 6 cakes is double the amount for 3 cakes, so the amount of flour is proportional to the number of cakes. An equation for a proportional relationship will have the form ...

  f = kp

We can find the value of k from any column in the table.

  8.25 = k(3) . . . . using the values in the first column

  8.25/3 = k = 2.75 . . . . . divide by 3

The equation is ...

  f = 2.75p

_____

Additional comment

If the input doubles, but the output does not, then the relationship is not proportional. We ordinarily expect recipes to have proportional relationships.

Answer:

Megan hired the canoe for 2 hours

Step-by-step explanation:

Given:

Cost(h) = 6h+15 = 27

Solution

6h+15 = 27

6h = 27-15 = 12

h = 2

Answer:

1500 - 30x

Step-by-step explanation:

Aquí, queremos obtener una función que describa la cantidad de litros que quedan en la piscina a las x horas después de abrir la salida de drenaje.

De la pregunta, la capacidad total de la piscina. es de 1.500 litros.

La tasa de goteo es de 0,5 litros por minuto.

x horas es lo mismo que 60 * x = 60x minutos

La cantidad de litros caídos en 60x minutos será 60x * 0,5 litros = 30x litros.

Entonces el número de litros que quedan será; 1500 - 30x

The correct hypothesis statement for this golfer to prove his claim would be:

\(H_{0} :u\geq 90\)

\(H_{1} :u < 90\)

The golfer claims that his average score is less than 90.

Therefore, the null hypothesis is the opposite of what he claims

Null hypothesis \(H_{0}\) is average score \(u\) is greater than or equal to 90:

\(u \geq 90\)

\(H_{0} :u\geq 90\)

Alternative hypothesis \(H_{1}\) is then the opposite of null hypothesis.

Hence alternate hypothesis \(H_{1}\) is u< 90

\(H_{1} :u < 90\)

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(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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If three cards are drawn from a standard deck of 52 cards , then the probability that all the cards are of same rank is  1/425  .

The number of cards in the standard deck is = 52 cards ;

thee cards are drawn from the deck ,

we have to find the probability that they all are of the same rank , that means ( e.g. all 3 are queens ) ;

we have to draw 3 cards from 4 suits. which means 1 card is taken from the 13 numbers.

the number of favorable outcomes (all from same rank) = ⁴C₃×13

= 52  ;

total number of outcomes is = ⁵²C₃ = 22100 ;

the required probability is = 52/22100  ;

= 1/425 .

Therefore , the probability that all 3 cards are of same rank is 1/425  .

The given question is incomplete , the complete question is

The three cards were randomly drawn from a standard deck of 52 cards.

What is the probability they are all the same rank ?

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Answer:

It would 85

Step-by-step explanation:

The easiest way to think about it is that the angle looks a little smaller than a right angle (90 degrees) therefore 85 degrees is correct.

Answer:

Spiders=8

Ants=12

Step-by-step explanation:

Spider(s)=8 legs

Ants(a)=6 legs

Total legs=136

Total heads=20

8s+6a=136 (1)

s+a=20 (2)

From (2)

s=20-a

Substitute 20-a into (1)

8s+6a=136

8(20-a)+6a=136

160-8a+6a=136

160-2a=136

-2a=136-160

-2a=-24

a= -24/-2

a=12

Substitute a=12 into (2)

s+a=20

s+12=20

s=20-12

s=8

To use the quadratic formula, we need to identify the values of a, b, and c.

1. In this case, the equation is 4x² - 3x - 8 = 0, so a = 4, b = -3, and c = -8.

2. x = (-b ±√(b² - 4ac))/2a.

3.  x = (3 ±√137)/8.

The Quadratic Formula is a mathematical equation used to solve second-degree equations.

To use the quadratic formula, we need to identify the values of a, b, and c in the equation ax² + bx + c = 0.

In this case, the equation is

4x² - 3x - 8 = 0,

so a = 4, b = -3, and c = -8.

Once the values of a, b, and c are known, we can substitute them into the Quadratic Formula:

x = (-b ±√(b² - 4ac))/2a.

In this equation, a = 4, b = -3, and c = -8, so the equation becomes

x = (-(-3) ±√((-3)² - 4(4)(-8)))/2(4).

Simplifying, we get x = (3 ±√(9 + 128))/8.

Finally, solving for x yields x = (3 ±√137)/8.

Therefore, the solution to the equation is

x = (3 ±√137)/8.

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The equivalent expression of 15x+10+ 20x can be written as 35x+10.

In mathematics, an expression is a combination of numbers, symbols and operations such as addition, subtraction, multiplication and division that may be evaluated to produce a single number, a variable or a set of numbers. Expressions can be complex, and often appear in the form of equations or formulas. Examples of expressions include equations, polynomials, functions, matrices and more.

This expression can be further simplified by multiplying the 35x and 10 with the variable x, resulting in 35x²+10x.

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Answer:

let angle 1 = angle 2 = x

as ad perp to bf they make 90 degrees at BOD

so

angle 1 + angle 2 = 90 degree

x + x = 90

2x = 90

x = 45

so angle 1 = 45° options c

Lori made a cake. Her brother ate 3 quarters of it. What decimal best represents 3/4?

We can calculate 3/4 in decimal form by dividing 3 by 4.

This gives us:

Also, we can think of it like that: each quarter is 0.25 of the cake. If he ate 3 quarters, it means that he ate 3*0.25 = 0.75 of the cake.

The answer is option F: 0.75.

C. If random samples of nine employees were repeatedly selected from the population of all employees from this position, then 95% of the time the sample mean income would be between $1371 and $1509.

This interpretation refers to the concept of a confidence interval, which gives a range of values within which the true population mean is likely to fall. In this case, the interval ($1371, $1509) was obtained from a sample of data and suggests that the true mean weekly income for all senior level workers in the automobile industry is likely to be within this range with 95% confidence. Option A is incorrect as it implies that all employees in this position have income within this range, which is not necessarily true. Option B is incorrect as it only refers to the sample mean, not the population mean. Option D is incorrect as it refers to the population mean, which cannot be determined from a sample alone.

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Answer to the multi-step equation:  11x+7

(Or try 7+11x)

Step-by-step explanation:

Solve the steps in this order: Parenthesis, Exponents, Multiply/Divide, Add/Subtract

Put the like terms together..

2 ^ 2 = 4.

4+3 = 7

11x + 7