true or false: if and are mutually exclusive and exhaustive with and , and is an event in , then

The probability that Andre, Olivia, and Zach all win gift cards that are at least $25 is 0.

Since the value of the gift cards is determined by chance, it is impossible to calculate the probability of this exact outcome. Instead, we can calculate the probability of any one person winning a gift card that is at least $25, which is 0.5.

The probability of them all winning would be the product of the individual probabilities, which is 0.5 x 0.5 x 0.5 = 0.125. However, since this is impossible, the probability of this exact outcome is 0.

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She should use the equation k = P/x². The correct answer would be an option (D).

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

The potential energy, P, in spring is represented using the formula, as follows:

P = kx²

Solve for variable k and we get the equation:

k = P/x²

When we compare this equation to the provided possibilities, we can easily see that it corresponds to the last option.

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We will add 2 ml of klotrix to the orange juice for a 20.5kg patient.

We know that , 1 kg=2.20462 pounds

Therefore, 20.5kg=20.5x2.20462 pounds= 45.195 pounds or 45.195 lb

Additionally we have, 1 lb = 0.35 mEq

Therefore, 45.195 lb=  0.35 mEq × 45.195 = 15.818 mEq.

Also, 8mEq=1 mL

By using unitary method,

1 mEq=1/8 mL

Converting 15.818 mEq to mL, we get

15.818mEq = 15.818 ÷ 8 = 1.9 mL

Thus, 15.818mEq  = 1.9 mL

Rounding off the answer we get,

The amount of klotrix required to add to the orange juice for a 20.5 kg patient is 2mL

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Yes, Chris has enough money to buy 30 folders and 30 pens.

The cost of the stationaries Chris bought are as follows:

Chris wants to buy 30 pens and 30 folders and he has only £60.

Let's check If he has has enough money to buy the products.

Therefore,

3 pens cost £2.25

1 pen  = ?

cost of 1 pen = 2.25 / 3 = 0.75 dollars

5 folders cost £5.80

1 folder = ?

cost of 1 folder = 5.80 / 5 = 1.16 dollars

Hence,

30(0.75) + 30(1.16) = 22.5 + 34.8 = 57.3 dollars

Therefore, he has enough money to buy 30 folders and 30 pens

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An equation in point slope form for the line that passes through (-4, 3) and whose slope is 3 is equal to y - 3 = 3(x + 4).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (-4, 3) and has a slope of 3 by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 3(x - (-4))

y - 3 = 3(x + 4)

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x = 1

Answer:

-----------

3x + 1 = 4x

4x = 3x + 1

4x - 3x = + 1

x = 1

With the help of algebraic expression, there were 8 small tables and 4 large tables in the local cafe.

Algebraic expressions serve as the mathematical statement when operations such as addition, subtraction, multiplication, division, etc. are performed on variables and constants. Let's imagine that while playing with matchsticks, James and Natalie came up with the idea to arrange the sticks into patterns that represented numbers.

James drew a four in the air with four matchsticks. Natalie was able to make a pattern with two 4s by putting three more matchsticks on the board. They realised they could proceed to add three matchsticks each round until they had a total of four. This led them to the conclusion that, in general, 4+ 3(n-1) sticks are needed to make a pattern with n numbers of 4s. This sentence makes reference to the algebraic expression 4+ 3(n-1).

The total no. of tables are 32

Let x be the no. of Small tables = 2x

And y be the no. of Large tables = 4y

Total no. of tables = 12

2x + 4y = 32

And

x + y = 12

x = 12 - y

Putting the value of x in first equation

2(12 - y) + 4y = 32

24 - 2y + 4y = 32

4y - 2y = 32 - 24

2y = 8

y = 4

And Putting the value of y in 2nd equation

x = 12 - (4)

x = 8

Thus, With the help of algebraic expression, there were 8 small tables and 4 large tables in the local cafe.

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The approach used to solve equations with integer coefficients & constants can also be used to solve equations with fractional / decimal coefficients and constants.

An equation is a mathematical statement that expresses the equality of two expressions. It is a relationship between two or more variables, such as x + y = z. Equations are used to solve a wide variety of problems in mathematics, physics, chemistry, engineering and other scientific fields.

The main difference is that when solving equations with fractional or decimal coefficients and constants. For example, if you have an equation with a decimal coefficient, divide both sides by the coefficient to make the coefficient 1 before you can use the same steps to solve the equation.

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The acute angle formed by the hands of a clock at 4:20a.m is 10°.

For the minute hand, we can compute that, for its every move, it covers 6 degrees. And for the hour hand, each move covers 30 degrees.

A clock is a circle, and a circle always contains 360 degrees. Since there are 60 minutes on a clock, each minute mark is 6 degrees.

The angle between the hour's hand and the minute hand when the clock shows 4:20 pm can be calculated by using the formula:

Angle=|11/2 M-30H|

where M= minute H= hour's

Here M=20 H=4

Therefore we get the angle |11/2(20)- 30*4|=|110-120|=|-10°|=10°

Hence, 10° is the correct answer.

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W = 6 is a solution to the inequality.

In mathematics, Inequality is an unequal comparison between two or more algebraic terms or expressions. The solution of an inequality is a numerical value that will satisfy the given expression.

The signs that we use in Inequality expression are  

'>' - greater than

'<' - less than

'≥' - greater than or equal to

'≤' - less than or equal to

Here we have

Inequality 8 > W

Where the symbol '>' less than indicates 8 is greater than W

or the value of W is less than 8  

As we can see that 6 < 8

Therefore,

W = 6 is a solution to the inequality.

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Answer:x<1

Step-by-step explanation:

move constant -5x>-2-3

Add alike numbers (-2 and -3)

-5x>-5

Divide both sides by -5

Then flip the inequality sign

x<1

Answer:

Step-by-step explanation:

Add 3 to the -2

-5x > 1

Divide by -5 the sign switches because of the negative

x < - 1/5 or X < -0.2

Using the similarity rectangle theorem, the value of FG is approx 23.

We determine the value of FG using the using the similar rectangle theorem.

Two rectangles must have proportional sides in order for them to be identical (form equal ratios). The two shorter sides should be proportionately equal to the two longer sides.

The rectangle ABCD and FGEH are both have same shape.

As we know that the rectangle same two sides equal. So

FG/EF = AD/DC

FG/15 = 18/12

Multiply by 15 on both side, we get

FG = 18/12 * 15

FG = 3/2 * 15

FG = 22.5

FG = 23 (approx)

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The complete question is:

Square 1 ABDC square 2 FGEH. AD= 18 DC=12 FE= 15. How do I find the square factor FG?

The multiplication of the numbers given to the reduced form is 10/7.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

The given expression is 5 × 2/7

One of the number is a whole number and the other is a fraction.

We can write 5 as 5/1 in terms of fraction and then multiply the numerators and the denominator.

(5/1) × (2/7) = (5×2) / (1 × 7) = 10/7, which is in the lowest form.

Hence the solution of the multiplication is 10/7.

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Answer:

Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of a function is the set of values that we are allowed to plug into our function. While a functions range, is the set of values that the function can take.

To be more precise, he domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

A relation's domain can also be discussed, where one element in the domain may be mapped to more than one element in the range.

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If the force is changed to 50N, the acceleration of the object becomes 10m/s²

From the information given, we have that force is directly varies as the acceleration.

Given that;

This is represented as;

F ∝ a

Then, the constant is

F= ka

Now, make 'k' the subject of the formula, we get;

k = F/a

substitute the values to determine the value of k

k = 40/8 = 5

If the value of the force, F of the object changes to 50N, then the acceleration is given as;

a = F/k

Substitute the values into the formula

a = 50/5

Divide the values

a = 10m/s²

Hence, the value is a = 10m/s²

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Answer:

Step-by-step explanation:

ham 3.45x

The eigenvectors of AAH are called the left-singular vectors of A and the eigenvectors of AHA are the right-singular vectors of A . They are called this way because of their use in singular value decomposition. Say A=UΣVH , then the columns of U are the left-singular vectors and the columns of V are right-singular vectors.

We know that the non-zero eigenvalues of AAH  and AHA are the same, they are the squares of the singular values of A . A singular of value of A is a value σ such that Av=σu   AHu=σv where u is a left-singular vector and vs a right-singular vector. This can be taken as the definition of singular value, left-singular vector (which is an eigenvector of AAH) and right-singular vector (which is an eigenvector of AHA).the left-singular and right-singular vector pair works with AAH and AHA

AAHu=σAv=σ2u

AHAv=σAHu=σ2v

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Q: What is the relationship between the eigenvectors of AAT and ATA?

Answer: A: what would be population equal 100 years from now?

Step-by-step explanation: I hope this helps!

The total 7 two-player games and 6 six-player games were played.  

Here the total games = 13

And the total number of athletes participated = 50

Let us assume that x represents the total 2-player games played and y represents the total 6-player games played.

The neighborhood holds 13 total games.

So, we get an equation,

x + y = 13                    ................(1)

There are 50 athletes signed up for a neighborhood basketball competition.

So, we get an equation,

2x + 6y = 50                 .............(2)

From equation (1)

x = 13 - y                   ..........(3)

substitute above value of x in equation (2)

2(13 - y) + 6y = 50

26 - 2y + 6y = 50

4y = 24

y = 6

Substitute above value of y in equation (3)

x = 13 - 6

x = 7      

Thus, we can conclude that the total 7 two-player games and 6 six-player games were played.  

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Using division we know that each person will have 1/4 pound of Skittles.

In mathematics, the division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed.

For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

The division sign, "," or occasionally "/," is used in computer code.

So, we know that:

Lauren and Shayla have 1/2 pound of Skittles

They will share it with 2 more people.

Then, each will have:

(1/2)/2

1/2 / 2

1/2 * 1/2

1/4

Therefore, using division we know that each person will have 1/4 pound of Skittles.

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Taking into account the definition of wavelength, frecuency and propagation speed, the wavelength of a wave with a frequency of 4.11×10⁴ Hz is 7299.27 m.

Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).

Frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).

The propagation speed is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.

The propagation speed relate the wavelength (λ) and the frequency (f) using the following equation:

v = f×λ

In this case, you know:

v= 3×10⁸ m/s

f= 4.11×10⁴ Hz

λ= ?

Replacing:

3×10⁸ m/s= 4.11×10⁴ Hz× λ

Solving:

λ= 3×10⁸ m/s ÷ 4.11×10⁴ Hz

λ=7299.27 m

In summary, the wavelength of the wave is 7299.27 m.

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Answer:

Hi, my name is Za'Riah! I will gladly help you with your problem. (see explanation)

Step-by-step explanation:

There really isn't much to explain or step out with this problem.

60% of 150 is 90

150 + 90 = 240 inches

The truck is 240 inches long.

Answer:

240

The equation of the line, given the ordered pair and the y - intercept, is y = -2 x + 2

The slope ( m ) is - 2

The equation for a linear model takes the form :

y = mx + b

m =  slope

b = y - intercept

As we have the ordered pair, and the y - intercept, we can find the slope:

y = mx + b

- 4 = 3 x slope + 2

3 x slope = - 4 - 2

Slope = - 6 / 3

Slope = - 2

The equation is therefore:

y = -2 x + 2

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The SAS congruency is applied here.

Hence,

[tex] \frac{TR}{JK} = \frac{RS}{JL} = \frac{TS}{KL} \\ \frac{24}{x} = \frac{12}{6} = \frac{y}{15} \\ \frac{24}{x} = 2 \\ x = 48 = JK[/tex]

[tex] \frac{y}{15} = 2 \\ y = 30[/tex]

Perimeter =

[tex]6 + 30 + 48 \\ 36 + 48 \\ = 84[/tex]

(x - h)^2 + (y - k)^2 = r^2 is the equation for a circle with center (h, k) and radius (r).

What exactly is a math equation?

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."

So, an equation that represents a circle with center (5, -1) and radius of 16 units is:

(x - 5)^2 + (y + 1)^2 = 16^2

or

(x - 5)^2 + (y + 1)^2 = 256

The graph of this equation will be a circle centered at the point (5,-1) with a radius of 16 units.

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Complete the pyramid with the corresponding values

Since each number is the product of the two numbers directly below it. Then the pyramid can be completed as follows:

Check the attached image for labeling.

j = -1 × -1 = 1

h = -2 × j = -2 × 1 = -2

y = h × -1 = -2 × -1 = 2

j × n = -1

1 × n = -1

n = -1

n × m = 2

-1 × m = 2

m = -2

w = -1 × 2 = -2

t = y × w = 2 × -2 = -4

-1 × k = n

-1 × k = -1

k = 1

k × l = m

1 × l = -2

l = -2

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The expression is equivalent is 6x/4 + 24y/12

Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.

These expressions also consisting of mathematical operations, such as;

Given the expression;

1/4(3x+4y) + 3(1/4x+ 2/3y)

expand the bracket

3x/4 + 4y/4 + 3/4x + 3/3y

collect like terms

3x/4 + 3/4x + 4y/4 + 3/3y

add like terms

3x + 3x/4 +  12y + 12y /12

add the numerators

6x/4 + 24y/12

Hence, the expression is 6x/4 + 24y/12

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The class midpoint of the first class in the case of table of quantitative data is 0-4 and the second class is 5-9 is 2.5

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