what is the length of the diagnal of a cube with a side length of 5 cm

The questions are:

Is the prize in the first five boxes?

Is the prize in the first two and a half boxes?

Is the prize in the first or second box?

To find the prize with the fewest number of questions, we can use the binary search algorithm.

The algorithm works as follows:

Ask if the prize is in the first five boxes or the last five boxes.

Based on the answer, eliminate half of the boxes from consideration.

Repeat this process until only one box remains.

The fewest number of questions you can ask is log base 2 of the number of boxes, which in this case is log base 2 of 10, or approximately 3 questions.

The questions are:

Is the prize in the first five boxes?

Is the prize in the first two and a half boxes?

Is the prize in the first or second box?

Note that the exact wording of the questions may differ depending on the specific rules of the game show, but the principle remains the same.

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To find the map's scale, use the formula below:

In this exercise,

map distane = 9 inches

distance on the ground = 3 miles.

So, the map scale is:

Dividing both numerator and denominator by 3:

The map scale is: 3 inches : 1 mile.

Answer:

537.64

Step-by-step explanation:

Here are some suggestions:

The exercise you're doing.

How frequent are you exercising.

The duration of exercise.

Fitness goals.

Location.

Time.

etc

answer: c. l =p-2b/2

step by step:

p=2(1-b)

p=2l-2b

p+2b/2=2l/2

l =p-2b/2

In research studies, an extraneous variable refers to a variable other than the independent variable that seems to have influenced the dependent variable.

These variables are sometimes also called "confounding variables" as they can create confusion or distortion in the relationship between the independent and dependent variables.

Extraneous variables can arise due to various factors such as measurement errors, participant characteristics, or environmental conditions. They have the potential to introduce bias and obscure the true effect of the independent variable on the dependent variable. To ensure accurate and valid results, researchers need to identify and control for these extraneous variables.

One common approach is to use statistical techniques such as regression analysis to account for the effects of extraneous variables by including them as covariates in the analysis. By doing so, researchers can isolate the specific impact of the independent variable on the dependent variable, while holding constant the influence of extraneous variables.

Overall, recognizing and managing extraneous variables is crucial in research to establish a clear cause-and-effect relationship between the independent and dependent variables and enhance the internal validity of the study.

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The statement "When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events" is true.

When two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event. In such cases, the joint probability of both events can be found by multiplying their individual probabilities. Mathematically, this can be expressed as P(A ∩ B) = P(A) * P(B). This rule holds true for independent events and is a fundamental concept in probability theory.

Now, let's examine the other statements:

1. The probability of the union of two events can exceed one:

This statement is false. The probability of an event is always between 0 and 1, inclusive. When you consider the union of two events, the probability of their combined occurrence cannot exceed 1. It is possible for the sum of the individual probabilities of the two events to exceed 1, but the probability of their union will never be greater than 1.

2. When events A and B are mutually exclusive, then P(A ∩ B) = P(A) + P(B):

This statement is false. Mutually exclusive events are events that cannot occur at the same time. If events A and B are mutually exclusive, their intersection (A ∩ B) will be an empty set, and therefore, the probability of their intersection is 0 (P(A ∩ B) = 0). The correct statement for mutually exclusive events is P(A ∪ B) = P(A) + P(B), where P(A ∪ B) represents the probability of the union of events A and B.

3. The union of events A and B consists of all outcomes in the sample space that are contained in both event A and B:

This statement is false. The union of events A and B, denoted as A ∪ B, consists of all outcomes that belong to either event A or event B or both. In other words, it includes all outcomes that are in A, in B, or in both A and B. The intersection of events A and B (A ∩ B) represents the outcomes that are contained in both A and B.

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Answer:

45 because it is what I think

To find \(\(X\)\) such that \(\(AX = B\)\), where \(\(A\) and \(B\)\) are given matrices, we can use the formula \(\(X = A^{-1}B\), where \(A^{-1}\)\) represents the inverse of matrix \(\(A\)\).

To find \(\(X\)\), we need to multiply matrix \(\(A\) with \(X\)\) such that the result is matrix \(\(B\)\). In other words, we are looking for a matrix \(\(X\)\) that satisfies the equation \(\(AX = B\)\).

To solve this equation, we can multiply both sides by the inverse of matrix \(\(A\)\). The inverse of a matrix \(\(A\)\) is denoted as \(\(A^{-1}\)\) and has the property that \(\(A^{-1}A = I\)\), where \(\(I\)\) is the identity matrix.

By multiplying both sides of the equation \(\(AX = B\) by \(A^{-1}\)\)0

\(\(A^{-1}(AX) = A^{-1}B\)\)

Since \(\(A^{-1}A = I\)\), the left side simplifies to:

\(\(I(X) = A^{-1}B\)\)

Therefore, we have:

\(\(X = A^{-1}B\)\)

By evaluating the matrices \(\(A\) and \(B\)\) and finding the inverse of matrix \(\(A\)\), we can perform the matrix multiplication to find the value of \(\(X\)\) that satisfies the equation \(\(AX = B\)\).

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The probability of P(x < 4) is 0.6922 or approximately 69.22%.

The exponential distribution is often used to model the time between events that occur randomly and independently at a constant rate over time. The probability density function of the exponential distribution with parameter λ is given by f(x) = λe^(-λx) for x ≥ 0.

In this case, X ~ Exp(0.75) means that the parameter λ is 0.75. To find P(x < 4), we need to calculate the area under the curve of the probability density function to the left of 4. This can be done by integrating the function from 0 to 4 as follows

P(x < 4) = ∫₀⁴ λe^(-λx) dx

= [-e^(-λx)]₀⁴

= -e^(-0.75 * 4) + 1

= 0.6922

Therefore, the probability that X is less than 4 is 0.6922 or approximately 69.22%.

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Answer:

Hi! The answer to your question is 176,868 Square Inches

Step-by-step explanation:

\(Area = Length * Width\)

\(8.5 * 12 * 12 *8.5 * 17 = 176,868\)

☆*: .｡.｡.:*☆☆.*: .｡..｡.:*☆☆*: .｡.｡.:*☆☆.*: .｡..｡.:*☆

☁Brainliest is greatly appreciated!☁

Hope this helps!!

- Brooklynn Deka

Explanation:

The blue rectangle has area of 4a^2*6a^2 = 24a^4

The red rectangle has area 4a^2*9a = 36a^3

The green rectangle has area 4a^2*3 = 12a^2

The total area is 24a^4 + 36a^3 + 12a^2

The probability that the transistor will last between 12 and 24 weeks is 0.424

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

X~gamma(\(\alpha ,\beta\))

E(X)= \(\alpha \beta\)                 \(\beta\)= \(12^{2}/24\)=6 weeks

V(x)= \(\alpha \beta ^{2}\)                \(\alpha\)=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X, \(\alpha\), \(\beta\), False)

P(\(12\leq X\leq 24\))

P(\(12/6\leq G\leq 24/6\))

P(\(2\leq G\leq 4\))

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:

Step-by-step explanation:

0.424 is the probability that the transistor will last between 12 and 24 weeks.

X= lifetime of the transistor in weeks E(X)= 24 weeks

Standard deviation= 12 weeks

Finding the parameters alpha and beta X~gamma(αβ)

E(X)= αβ             β =6 weeks

V(x)=αβ^2           α =24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,α,β,False)

P(12≤X≤24)

P(12/6≤G≤24/6)

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:

45%

Step-by-step explanation:

Here, we want to know the probability of a randomly selected yard having 6 or more than 6 trees

To get this, we simply add up the probability of 6 yards and above

That is the probability of 6, 8 , 10 and 12 yards

This is obtainable from the histogram

We then proceed to add up from the graph

What we have is;

0.05 + 0.25 + 0.10 + 0.05

= 0.10 + 0.10 + 0.25 = 0.45

This is same as 45/100 which is otherwise 45%

The probability that a randomly selected yard will have 6 or more trees is 45%.

Probability of having 0-2 tree = 0.35

Probability of having 2-4 tree = 0.20

Probability of having 4-6 tree = 0.05

Probability of having 6-8 tree = 0.20

Probability of having 8-10 tree = 0.10

Probability of having 10-12 tree = 0.05

Probability is to quantify the possibilities or chances.

So, probability of having 6 or more trees

= (2*0.05 + 2*0.25 + 2*0.10 + 2*0.05)/(0.35*2+0.20*2+2*0.05 + 2*0.25 + 2*0.10 + 2*0.05)

=0.9/2

=0.45

=45%

So,  probability of having 6 or more trees =45%

Therefore, the probability that a randomly selected yard will have 6 or more trees is 45%.

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Answer:

Step-by-step explanation:

Prime factorization requires dividing by primes starting with smallest prime number

402/2=201

201/3=67, 67 is prime so we cannot go further so the prime factorization of 402 is

2X3X67

A population of scores has µ = 80. in this population, a score of x = 86 corresponds to z = 2.00. The population standard deviation is 03.

In statistics, the standard deviation is a measure of the variability or spread of an outcome. [1] A low standard deviation indicates that the value is close to the mean of the cluster (also called the expected value), while a high standard deviation indicates that the results are very interesting.

The standard deviation can be abbreviated as SD and is often used in mathematics and equations with the Greek letter σ (sigma) for population standard deviation or the Latin letter s for different sample sizes.

The standard deviation of a variable, such as a population, a data set, or a probability, is the basis of its variance. Algebraically it is easier than the mean absolute difference, but in practice, it is lower than the mean absolute difference. The useful feature of standard deviation is that it is expressed in the same unit as the data, unlike the difference.

Here we can use the Z-score formula:

Z = (X - µ) / σ

where Z is the Z-score, X is the individual score, µ is the population mean, and σ is the population standard deviation. In this case, we are given Z = 2.00, X = 86, and µ = 80. We need to find σ.

2.00 = (86 - 80) / σ

Now, solve for σ:

σ = (86 - 80) / 2.00 = 6 / 2.00 = 3

The population standard deviation (σ) is 3.

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Answer:

  see attached

Step-by-step explanation:

The formulas given work perfectly.

It might help you to think of the tax rate as a percentage. For example, $2.37 per $100 is a rate of 2.37/100 = 0.0237 = 2.37%

Each dollar value is the product of the previous two columns.

  $400,000 × 0.19 = $76,000; $76,000 × 0.0237 = $1801.20 (tax)

  $235,000 × 0.10 = $23,500; $23,500 × 0.0993 = $2333.55 (tax)

  $215,000 × 0.15 = $32,250; $32,250 × 0.1240 = $4000.00 (tax)

__

Where the rates are missing (as on the third line), they can be found by dividing the dollar value on the right of it by the dollar value on the left of it.

  32,250/215,000 = 0.15 = 15%

  4000/32,250 = 0.1240 = $12.40 per $100

_____

Additional comment

To get a tax of exactly $4000 on the last line, the tax rate needs to be specified to 4 decimal places: $12.4031 per $100. Otherwise the value rounds to something less than $4000.

(a) To determine the probability of finding the particle at a distance between r and r+dr from the origin, we need to calculate the volume of the spherical shell centered at the origin with an inner radius of r and a thickness of dr.

The volume of a spherical shell can be calculated as V = 4πr²dr, where r is the radius and dr is the thickness.

In this case, the wave function is given as (x, y, z) = Ae^(-a(z²+y²+x²)), and we need to find the probability density function |ψ(x, y, z)|².

|ψ(x, y, z)|² = |Ae^(-a(z²+y²+x²))|²

            = |A|²e^(-2a(z²+y²+x²))

To find the probability of finding the particle at a distance between r and r+dr from the origin, we need to integrate |ψ(x, y, z)|² over the volume of the spherical shell.

P(r) = ∫∫∫ |ψ(x, y, z)|² dV

     = ∫∫∫ |A|²e^(-2a(z²+y²+x²)) dV

Since the wave function is spherically symmetric, the integral simplifies to:

P(r) = 4π ∫∫∫ |A|²\(e^{-2a}\)(r²)) r² sin(θ) dr dθ dφ

Integrating over the appropriate ranges for r, θ, and φ will give us the probability of finding the particle at a distance between r and r+dr from the origin.

(b) To find the value of r at which the probability in part (a) has its maximum value, we can differentiate P(r) with respect to r and set it equal to zero:

dP(r)/dr = 0

Solving this equation will give us the value of r at which the probability has a maximum.

However, the value of r at which the probability has a maximum may not be the same as the value of r for which |ψ(x, y, z)|² is a maximum. This is because the probability density function is influenced by the absolute square of the wave function, but it also takes into account the volume element and the integration over the spherical shell. So, while the maximum value of |ψ(x, y, z)|² may occur at a certain r, the maximum probability may occur at a different r due to the integration over the spherical shell.

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The property of adaptive immunity enables a person to have the chicken pox when he or she is six years old and still be immune to chicken pox at age 45 exists Memory.

Specificity and memory are two crucial properties that determine adaptive immunity. Both specificity and memory pertain to the adaptive immune system's capacity to recognize and attack certain diseases, as well as to promptly react to pathogens to which it has already been exposed.

Adaptive immunity can offer an enduring defense, perhaps for the duration of a person's lifespan. In certain circumstances, such as with chickenpox, it does not confer permanent protection; for instance, a person who recovers from measles is now protected against measles for the rest of their life.

Specificity, diversity, specialization, memory, and self/non-self identification are the immunologic characteristics that define adaptive immunity, and these cells both create and show antigen-binding cell surface receptors.

The property of adaptive immunity enables a person to have the chicken pox when he or she is six years old and still be immune to chicken pox at age 45 exists Memory.

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Answer:

he needs 3 bags i did this test

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

£9095

Step-by-step explanation:

Given data

P=£8500

T= 3 years

R= 2.3%

The compound interest formula is

A= P(1+r)^t

substitute

A=8500(1+0.023)^3

A=8500(1.023)^3

A=8500*1.07

A=£9095

Hence the savings after 3 years is £9095

Answer:  

The answer is y=0.4

The value of the equation is A = ⁵√32,768 is A = 8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ⁵√32,768   be equation (1)

On simplifying the equation , we get

A = 8 x 8 x 8 x 8 x 8 = 32,768

So , the 5th root of ( 32,768 ) is 8

Therefore , the value of A = 8

Hence , the equation is A = 8

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Answer:

4,5

Step-by-step explanation:

I hope this helps

We will try to leave the letter \(r\) alone by modifying the given equation.

This equation is defined with the following expressions.

Ans: \(r=\frac{3t}{t-1}\)

Answer:

20%

Step-by-step explanation:

To solve, we can calculate how much 1,600,000 is of 8,000,000 as a decimal and then solve from there.

Let's say our missing value is x.

x of 8,000,000 = 1,600,000

"x of something", in this case, can be rephrased as "x * something", so we have

x * 8,000,000 = 1,600,000

divide both sides by 8,000,000 to isolate x

x = 1,600,000/8,000,000 = 0.2

to convert from a decimal to percentage, multiply by 100

0.2 * 100 = 20

20% is our answer

Answer:

Step-by-step explanation:

The area formula for a parallelogram is the same as the area formula for a rectangle or square. A = bh.

Our base is 5 1/4 and the height, which drops perpendicular to the base, is 4 1/5.  So the formula for the area is

\(A=(4\frac{1}{5})(5\frac{1}{4})\)

Choice D

There are four outcomes that can occur when two players flip fair coins: both coins must be heads (HH), both must be tails (TT), or one coin must be heads and the other must be tails (HT or TH).

Because these are the only outcomes in which both players receive the same outcome, the probability that they will have the same outcome is equal to the sum of the probabilities of getting HH and TT. The likelihood of receiving HH or TT is:

HH or TT, where P(HH) = P(HH) + P(TT) = 1/4 + 1/4 = 1/2

As a result, the likelihood that they arrive at the same conclusion can be expressed as 1/2, a fraction with a coprime denominator and numerator.

As a result, a+b has the value:

a + b = 1 + 2 = 3

So, the response is 3.

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Answer:

y=2(x+4)-3

Step-by-step explanation:

To make it parallel to y=2x+4, the slope needs to be the same

Point-slope form is: y=m(x-x1)+y1

In this case,

m = 2

x1 = -4

y1 = -3

So when put into point-slope form, it is y=2(x+4)-3