Order these numbers from least to greatest.

Answer:

Step-by-step explanation:

\( { ({6}^{2} )}^{x} = 1 \\ { ({6}^{2}) }^{x} = {6}^{0} \\ {6}^{2 \times x} = {6}^{0} \\ 2x = 0 \\ x = \frac{0}{2} \\ x = 0 \\ \)

\( {( {6}^{0} )}^{x} = 1 \\ { ({6}^{0} )}^{x} = {6}^{0} \\ {6}^{0 \times x} = {6}^{0} \\ 0 \times x = 0 \\ x = 0\)

To find the probability distribution for Y, the number of errors detected by the auditor, we can use the binomial distribution formula. The binomial distribution is used when there are only two possible outcomes, success or failure, and each trial is independent.

In this case, the probability of success (detecting an error) is 5% or 0.05, and the probability of failure (not detecting an error) is 1 - 0.05 = 0.95.

a. To find the probability distribution for Y, we can use the formula for the binomial distribution:

P(Y = y) = (nCk) * p^k * (1-p)^(n-k)

where n is the number of trials (3 in this case), k is the number of successes (errors detected), p is the probability of success (0.05), and (nCk) is the combination formula.

For y = 0:
P(Y = 0) = (3C0) * (0.05)^0 * (0.95)^(3-0) = (1) * (1) * (0.95)^3 = 0.857375

For y = 1:
P(Y = 1) = (3C1) * (0.05)^1 * (0.95)^(3-1) = (3) * (0.05) * (0.95)^2 = 0.135375

For y = 2:
P(Y = 2) = (3C2) * (0.05)^2 * (0.95)^(3-2) = (3) * (0.05)^2 * (0.95)^1 = 0.007125

For y = 3:
P(Y = 3) = (3C3) * (0.05)^3 * (0.95)^(3-3) = (1) * (0.05)^3 * (0.95)^0 = 0.000125

So the probability distribution for Y is:
Y = 0 with probability 0.857375
Y = 1 with probability 0.135375
Y = 2 with probability 0.007125
Y = 3 with probability 0.000125

b. To construct a probability histogram for p(y), you can create a bar graph where the x-axis represents the number of errors detected (Y) and the y-axis represents the probability (P(Y = y)). Each bar will have a height corresponding to the probability.

c. To find the probability that the auditor will detect more than one error, we need to calculate the sum of the probabilities for Y = 2 and Y = 3:

P(Y > 1) = P(Y = 2) + P(Y = 3) = 0.007125 + 0.000125 = 0.00725

Therefore, the probability that the auditor will detect more than one error is 0.00725.

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The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Answer:

BC = 28

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{BC}{EF}\) = \(\frac{AB}{DE}\) ( substitute values )

\(\frac{BC}{7}\) = \(\frac{16}{4}\) = 4 ( multiply both sides by 7 to clear the fraction )

BC = 4 × 7 = 28

In this case this "of" means we will multiply the two fractions "4/5 × 3/4" exists 3/5.

That operation exists utilized to 'simplify' a fraction (reduce it to lower terms).

When there exists no number that goes into both the top and bottom numbers, then the fraction is in simplest form (lowest terms).

We are looking for 4/5 of 3/4. In this case this "of" means we will multiply the two fractions. To multiply fractions, we multiply

top × top and bottom × bottom

4/5 × 3/4 exists 4 × 3 on top and 5 × 4 on the bottom.

= (4 × 3)/(5 × 4)

= 12 / 20

= 3 / 5

Therefore, the correct answer is 3/5.

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At $ 10 per mug you will not get any money; the maximum possible revenue is $ 175, which will be obtained by selling the mugs for $ 5; and to get at least $ 70 in revenue the mugs must be sold for $ 2.

Since you could give away 70 coffee mugs without charging anything, and if you charge $ 10.00, nobody will buy the coffee mugs, and you also figured out that your sales will be decreasing following straight line, and your job is to find the maximum possible revenue from selling the coffee mugs, to determine at which price per coffee mug do you not make any money; the price per coffee mug that makes the most revenue; how many coffee mugs must be sold to maximize the revenue; what is the maximum revenue; and what price per coffee mug you should charge to collect at least $ 70 in revenue; the following calculations must be performed:

Therefore, at $ 10 per mug you will not get any money; the maximum possible revenue is $ 175, which will be obtained by selling the mugs for $ 5; and to get at least $ 70 in revenue the mugs must be sold for $ 2.

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we have that

A quadratic equation that will have a solution of only x = 0 is given by the equation

Answer:

792600

Step-by-step explanation:

For this question you can add four zeroes to the back of 792.6 andmove the decimal to get you the answer, hope this helps

It's also good to know that if the exponent was positive the answer would be 0.07926

SOLUTION STEPS

10 ^−4/792.6

​

Calculate 10 to the power of −4 and get  

10000

1

​

.

10000

1

​

792.6

​

Divide 792.6 by  

10000

1

​

 by multiplying 792.6 by the reciprocal of  

10000

1

​

.

792.6×10000

Multiply 792.6 and 10000 to get 7926000.

7926000

hopefully i helped

Answer:

1. =2.5759 ; 2. =0.8290 ;  3. =2  ; 4. =1.7959 ; 5. = 3.9138

Step-by-step explanation:

1. Taking logarithm with base 3 on both sides, we get:

b = log₃(17)

b ≈ 2.5759

2. Taking logarithm with base 12 on both sides, we get:

r = log₁₂(13)

r ≈ 0.8290

3. Taking logarithm with base 9 on both sides, we get:

n = log₉(49)

n = 2

4.Taking logarithm with base 16 on both sides, we get:

v = log₁₆(67)

v ≈ 1.7959

5.Taking logarithm with base 3 on both sides, we get:

a = log₃(69)

a ≈ 3.9138

Answer:

m∠VUS = 122

Step-by-step explanation:

m∠TUX = 122°

∴m∠VUS = 122°(vertically opposite angles are equal)

hope this helps you!!

The solution is, m∠VUS = 122

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

We know that, a ray is a line that continues on forever inn one direction with a point at it's start.

here, we have,

from the diagram, we get,

m∠TUX = 122°

∴m∠VUS = 122°

(vertically opposite angles are equal)

Hence, The solution is, m∠VUS = 122.

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An equation for the ellipsoid which is centered at (3, 0, −5) and has a radius of 3 in the x-direction, a radius of 5 in the y-direction, and a radius of 1 2 in the z-direction is:

(x - 3)²/9 + y²/25 + (z + 5)²/0.25 = 1

An equation for an ellipsoid is a mathematical expression that describes the shape of an ellipsoid in terms of its size and orientation. An ellipsoid is a three-dimensional geometric shape that looks like a stretched sphere or an egg. It is defined as the surface generated by an ellipse rotating about one of its principal axes.

The equation for an ellipsoid centered at (h, k, l) with a radius of a in the x-direction, b in the y-direction, and c in the z-direction is:

(x - h)²/a² + (y - k)²/b² + (z - l)²/c² = 1

Substituting in the given values for h, k, l, a, b, and c, we get:

(x - 3)²/3² + (y - 0)²/5² + (z + 5)²/(1/2)² = 1

Simplifying, we get:

(x - 3)²/9 + y²/25 + (z + 5)²/0.25 = 1

This is the equation for the ellipsoid centered at (3, 0, −5) with a radius of 3 in the x-direction, 5 in the y-direction, and 1/2 in the z-direction.

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Answer:

-2/3

Step-by-step explanation:

Rise= -2

Run= 3

-2/3

Answer:

adult tickets 15

child tickets  12

Step-by-step explanation:

2x + 2y = 54   L1

3x + 5y = 105  L2

3L1 - 2L2

6x + 6y = 162

-6x - 10y = -210

-4y = -48

y = -48/-4

y = 12

2x + 2y = 54

2x +2(12) = 54

2x + 24 = 54

2x = 54 - 24

2x = 30

x = 15

The radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base is 6.6 feet.

To determine the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base, we can use similar triangles.

The given cone has a height of 10 feet and a diameter of 22 feet. The radius of the given cone is half of the diameter, so it is 22/2 = 11 feet.

When a horizontal plane passes through the cone at exactly 4 feet from the base, it divides the cone into two parts: the smaller cone and the frustum (the remaining part of the cone).

The height of the smaller cone is the distance from the 4-feet mark to the top of the cone, which is 10 - 4 = 6 feet.

Since the two cones are similar, their corresponding dimensions are proportional. The ratio of the corresponding heights is the same as the ratio of the corresponding radii.

So, we can set up the following proportion:

(r_small / r_given) = (h_small / h_given)

Substituting the values we have:

(r_small / 11) = (6 / 10)

Cross-multiplying:

10 * r_small = 11 * 6

r_small = (11 * 6) / 10

r_small = 66 / 10

r_small = 6.6 feet

Therefore, the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base is 6.6 feet.

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Step-by-step explanation:

4 -0 / -1 - -3.

4/2 = 2

m = 2 (slope)

Answer:

inteager

Step-by-step explanation:

temperature can express both positive and negative

Answer: 361

Step-by-step explanation:

The inequalities that represent the problem is 5h + 2.50t ≤ 60

Each hamburger costs $5 and each taco costs $2.50.

He has a total of $60 to spend on hamburgers and tacos.

The inequalities that would be used to  represent the possible values for the number of hamburgers purchased, h, and the number of tacos purchased, t is as follows:

Therefore,

h = number of hamburgers purchased

t = the number of tacos purchased

Hence,

5h + 2.50t ≤ 60

Therefore, the inequalities that represent the problem is 5h + 2.50t ≤ 60

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Answer:

6

Step-by-step explanation:

A=hbb/2=4·3/2=6

To find a triangle's area, use the formula area = 1/2 * base * height. Choose a side to use for the base, and find the height of the triangle from that base. Then, plug in the measurements you have for the base and height into the formula

or

The area of a triangle is the space enclosed within the three sides of a triangle. It is calculated with the help of various formulas depending on the type of triangle and is expressed in square units like, cm2, inches2, and so on.

No, it does not make sense that the probability of cats falling from the 5th floor would be greater than those of the 4th. The force of gravity is the same regardless of the floor, so the number of cats falling should be the same no matter what floor they start from.

The force of gravity is a constant force that is the same on all floors. This means that the same amount of force is acting on the cats, no matter which floor they start from. Therefore, the number of cats falling from the 5th floor should be the same as the number falling from the 4th floor. The number of cats falling from a higher floor may be greater if there are extra factors, such as wind, that could affect their fall, but the force of gravity does not change with the floor. Therefore, it does not make sense for the number of cats falling from the 5th floor to be greater than those of the 4th

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The union of two sets is to avoid counting the same elements twice.

The mathematical logic subfield of set theory investigates sets, which can be loosely defined as collections of objects. Although any object can be combined into a set, set theory, as a mathematical discipline, focuses primarily on those that are relevant to mathematics as a whole.

Given union of set

(A ∪ B),

The set of all objects that are members of either A or B, or both, is the union of the sets A ∪ B.

let us take example,

A = { 1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

(A ∪ B) = { 1, 2, 3, 4} ∪  {3, 4, 5, 6, 7}

we can simply write all of A and B's elements in a single set to avoid duplicates to find A U B.

(A ∪ B) = {1, 2, 3, 4, 5, 6, 7}

Hence the  union of two sets is a set that contains all the elements of both set and avoid duplicates.

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The remaining amount of the element after 5 minutes after exponential decay is approximately 114.26 grams.

To find out how much of the element is remaining after 5 minutes, we can use the formula for exponential decay.

First, we need to calculate the decay factor. The decay factor is equal to 1 minus the percentage decay rate, which is 25.5%, converted to decimal form (0.255). So, the decay factor is 1 - 0.255 = 0.745.

Next, we can calculate the remaining amount of the element by multiplying the initial amount (330 grams) by the decay factor raised to the power of the number of minutes (5 minutes).

Remaining amount = 330 grams * (decay factor)^(number of minutes)
Remaining amount = 330 grams * 0.745^5

Calculating this expression, we find that the remaining amount of the element after 5 minutes is approximately 114.26 grams.

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one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

The question is not complete, so i have attached it.

Answer:

Option A - The data may not be reliable because there is an outlier.

Step-by-step explanation:

Looking at the question attached and the number of the gorrila vis - a - vis the time to interact, we can see that majority of the time to interact falls between 2.5 and 3.4.

However, we have a time of 8.3 days which is for gorrila 3.

This 8.3 is far higher than the range of the other values. Thus, we have an outlier because an outlier is a value is much more smaller or larger than most of the other values in a set of given data.

Thus, the data may not be reliable because there is an outlier.

Magada's loan factor is approximately 0.006367. This means that for every $1 borrowed, Magada will have to pay approximately $0.006367 per month for the next 25 years to repay the loan with an interest rate of 10.75%.

To calculate the loan factor, we first need to calculate the monthly interest rate and the total number of monthly payments.

Monthly interest rate = Annual interest rate / 12

= 10.75% / 12

= 0.8958%

Monthly payments = Number of years * 12

= 25 * 12

= 300

Now, we can use loan factor formula, which is:

Loan factor = [monthly interest rate * (1 + monthly interest rate)^n] / [(1 + monthly interest rate)^n - 1]

Substituting the values, we get:

Loan factor = [0.008958 * (1 + 0.008958)^300] / [(1 + 0.008958)^300 - 1]

= 0.006367

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Answer:

1047.2 cubic inches

Step-by-step explanation:

V = 4(pi)(r³/3)

V = 4(pi)(125/3)

V = 523.6 cubic inches (1 ball)

V = 2(523.6) = 1047.2 cubic inches (total)

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

slope of line perpendicular to the line y=-1/4x-1 is 4.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Let us write the given equation  y=-1/4x-1

If we compare the given equation with slope intercept form

We get to know slope of line m is -1/4.

It two lines are perpendicular then the product of their slopes will be -1

-1/4×m=-1

m=4

Hence slope of line perpendicular to the line y=-1/4x-1 is 4.

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