58 of a birthday cake was left over from a party. the next day, it is shared among 7 people. how big a piece of the original cake did each person get?

The principle of cross-cutting relationships is a valuable tool in relative dating, which helps determine the sequence of events in geological formations. It states that any geological feature that cuts across another is younger than the feature it cuts through.

However, in the case of the Upheaval Dome investigations, using the principle of cross-cutting to determine the relative ages of sedimentary rock layers would be inappropriate.

Upheaval Dome is a unique geological feature in Canyonlands National Park, Utah, characterized by a large impact crater. The crater was formed by a meteorite impact, which disrupted the original sequence of sedimentary rock layers. The impact event caused intense deformation, fracturing, and uplift, resulting in the formation of the dome.

As a result, the principle of cross-cutting relationships cannot be reliably applied in this context because the impact event altered the original layering and created a complex mixture of rocks The fractures and deformations caused by the impact would make it challenging to establish a clear sequence of events based on cross-cutting relationships.

Therefore, alternative methods, such as radiometric dating or stratigraphic analysis, would be more appropriate for determining the relative ages of the sedimentary rock layers in the Upheaval Dome investigations.

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Answer:

System 1

Step-by-step explanation:

Tbe elemination method of solving system of equation works on such a way that :

Given two set of equation (1) and (11) having two unknowns, the Coefficient are of one of the unknowns, either x or y is the same such that applying the addition or subtraction operation of the two equations eliminates one of the unknown variables leaving us with only one unknown variable to solve, and then using this solution to solve for the other variable.

In the question given. The variable setup for elimination is the x variable such that by using the addition operation, variable x is eliminated.

Answer:

Collect like terms, ie do 9n-4n = 5n ...

5n will then be exactly divisible by 5 as 5n / 5 = n

Answer: a

Step-by-step explanation:

Working efficiently, grouping tasks together, using the hood only when necessary, and proper cleaning and maintenance can all help minimize the number of times the hood sash is raised and lowered.

To minimize the number of times the hood sash is raised and lowered, it's important to work efficiently as possible in the hood. This means planning out your work ahead of time and grouping tasks together that require similar equipment or materials.

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Answer:

Measure of side C is 7.14

Step-by-step explanation:

In this question, we are to find the length of the side C.

To get this, we are to employ the use of the cosine formula.

Mathematically, this is calculated as;

c^2 = a^2 +b^2 - 2ab*cos(C)

Where; a = 10 b = 3 and c = 15 degrees

Plugging these values into the equation, we have;

C^2 = 10^3 + 3^2 -2(3)(10)Cos 15

C^2 = 100 + 9 - 57.96

C^2 = 51.04

C = √(51.04)

C = 7.14

Answer:

7.14

Step-by-step explanation:

So there are 6 permutations possible with the letters "ABC". These are: ABC, ACB, BAC, BCA, CAB, CBA.

Permutations are a way of arranging objects in a specific order. The number of permutations of a set of n distinct objects is given by n!, where n! denotes the factorial of n.

In the case of the letters "ABC", there are three distinct objects: A, B, and C. Therefore, the number of permutations possible with these letters is:

3! = 3 x 2 x 1 = 6

This means that there are 6 possible ways of arranging the letters "ABC" in a specific order. These permutations are:

ABC

ACB

BAC

BCA

CAB

CBA

To see why there are 6 possible permutations, consider the first position. There are three letters to choose from, so there are three possible choices for the first position. Once the first letter is chosen, there are two letters left to choose from for the second position. Finally, there is only one letter left to choose from for the third position. Therefore, the total number of permutations is:

3 x 2 x 1 = 6

In summary, the number of permutations of a set of n distinct objects is given by n!, and in the case of the letters "ABC", there are 3! = 6 possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA.

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Answer:

  4/39

Step-by-step explanation:

You want to know the fraction of 39 students represented by the 4 that have blue eyes.

The fraction is the ratio of the part of interest to the whole.

  (students with blue eyes)/(total number of students) = 4/39

The probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

Let X denote the time required to process a package of five tasks. X is an exponentially distributed random variable with mean 2 minutes.

The probability of X being less than 8 minutes is given by:

P(X ≤ 8) = 1 - P(X > 8)

= \(1 - (1 - e^{(-8/2)}^{5}\)

= 0.963

Therefore, the probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

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before distributing the negative:

(7x2 + 3x) - (8x2 - 5x)

after distributing the negative:

7x2 + 3x - 8x2 + 5x

now add like terms:

7x2 + 3x - 8x2 + 5x

-x2 + 8x

or

8x - x2

-- let me know if you have any questions regarding this.

Answer:

24,150

Step-by-step explanation:

Given that :

Salary earned this year = 23,000

Percentage Raise in salary for the new year = 5%

The new yearly salary can be obtained thus ;

(100% + percentage raise in salary) * salary earned this year

(100% + 5%) * 23,000

105% * 23000

1.05 * 23000

24,150

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer:

Easy 11:01

Step-by-step explanation:

Answer:

11:01

Step-by-step explanation:

  10:30

+ 00:31

---------------

11:01

Answer:

The interval [25, 35] has the slowest average rate of decay.

Step-by-step explanation:

The number of grams in a sample of radium is represented by the function \(r(t) = 50\cdot e^{-0.013\cdot t}\), which is a monotonous decreasing function. Hence, the greater the values of \(t\), the slowest the average rate of decay, represented by a secant line. The interval [25, 35] has the slowest average rate of decay.

Answer:

Angle 1 = 128

Angle 2 = 52

Angle 3 = 47

Angle 4 = 133

Angle 5 = 81

Step-by-step explanation:

Angle 5 is 81

Angle 3 is 47

Angle 4 is 133

Angle 2 is 52

Angle 1 is 128

Answer:

5+9+10+10+5+2+5+2

Step-by-step explanation:

48÷8=6

6 is median of given data

a) the function y=x^2 + c/x^2 is a solution of the differential equation xy' + 2y = 4x^2, (x > 0).

b) The value of c for which the solution satisfies the initial condition y(8) = 6 is c = -3712.

a) To verify that the function y = x^2 + c/x^2 is a solution of the differential equation xy' + 2y = 4x^2, we first need to find the derivative y' using algebra:
y = x^2 + c/x^2
y' = 2x - 2c/x^3

Now, plugging y and y' into the given differential equation:

x(2x - 2c/x^3) + 2(x^2 + c/x^2) = 4x^2

Next, simplify the equation:
2x^2 - 2cx^(-2) + 2x^2 + 2c/x^2 = 4x^2

Combine the like terms:
4x^2 = 4x^2

The equation holds true, so the function y = x^2 + c/x^2 is a solution of the differential equation xy' + 2y = 4x^2.

b) To find the value of c for which the solution satisfies the initial condition y(8) = 6, plug in x = 8 and y = 6 into the function y = x^2 + c/x^2:

6 = (8^2) + c/(8^2)

Solve for c:
6 - 64 = c/64
-58 = c/64
c = -58 * 64
So, the value of c is -3712.

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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

Each model should be produced on a weekly basis to maximize net profit is $75,900.

What is Net profit?

In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.

As given,

Number of products sold:

T ≥ 1.5G

Maximize Profit Z = 150T + 130G

Labor Constraint:

Labor hours Available:

Production Department:

Number of labor hours available per day = 58 × 7 = 406

Number of days in a week = 5

Number of lobor ours available per week = 406 × 5 = 2030

Assembly Department:

Number of labor hours available per day = 25 × 7 = 175

Number of days in a week = 5

Number of labor hours available per week = 175 × 5 = 875.

Labor hours Required:

Labor hours required for G1 model:

Labor hours required at Production department = 3.5G

Labor hours required at assembly department = 2G

Labor hours required for T1 model:

Labor hours required at Production department = 4T

Labor hours required at Assembly department = 1.5T

Total labor hours required at Production department = 3.5G + 4T

Total labor hours required at Assembly department = 2G + 1.5T.

Constraint:

Labor hours required ≤ Labor hours Available.

Production department Labor constraint

3.5G + 4T ≤ 2030

Assembly department Labor constraint:

2G + 1.5T ≤ 875

The function:

Maximum Profit Z = 150T +130G

Constraint:

3.5G +4T ≤ 2030

2G + 1.5T ≤ 875

T ≥ 1.5G

Suppose that for example:

10.5G +12T = 6090

 16G + 12T = 7000

Solve both equations simultaneously,

5.5G = 7000 - 6090

5.5G = 910

    G = 910/5.5

    G = 363

Since, T > G

Hence,

T = 363,

G = 165

Calculate Profit:

150T + 130G = 150 × 363 + 130 × 165

                     = 54450 + 21450

                     = 75900

Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.

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A statement that compares two expressions that are not equal is called an inequality. An inequality is a mathematical expression that shows that two quantities are not the same, unlike an equation which shows that two quantities are equal. Inequalities use symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to) to compare two expressions.

For example, 4 < 7 is an inequality because 4 is less than 7. Inequalities are commonly used in algebra and real-world scenarios to represent situations where there are limits, ranges or restrictions. Solving inequalities involve finding the values of the unknown variable that make the inequality true. There are several methods to solve inequalities, including adding or subtracting the same value to both sides of the inequality, multiplying or dividing by a positive or negative number, and graphing the inequality on a number line.

Understanding inequalities is crucial for various fields such as economics, engineering, physics, and computer science.

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The biker should travel along the road for 0.67 miles and then cut into the field. This will minimize the distance traveled across the field and allow the biker to reach the house in the shortest possible time.

Let's assume that the biker wants to travel from the road to the house in a straight line. Since the biker can travel twice as fast along the road as across the field, it makes sense to minimize the distance traveled across the field.

Let's call the distance the biker travels along the road "d" and the distance the biker travels across the field "x". We know that the total distance the biker needs to travel is 2 miles. Therefore, we can write:

d + x = 2

We also know that the biker travels at a speed of 14 miles per hour along the road and 7 miles per hour across the field. Therefore, we can write:

d/14 = x/7

Simplifying this equation, we get:

2d = x

Now we can substitute this value of x in the first equation to get:

d + 2d = 2

Solving for d, we get:

d = 0.67 miles

Therefore, the biker should travel along the road for 0.67 miles and then cut into the field. This will minimize the distance traveled across the field and allow the biker to reach the house in the shortest possible time.

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Answer:

It would be 94 cm

Step-by-step explanation:

Answer:

94 cm

Step-by-step explanation:

just googled a rectangular prism calculator

The constants C₁ = -1/5 and C₂ = 1/7 make the function f₃(x) = x - (1/5)x² + (1/7)x³ orthogonal to both f₁(x) = x and f₂(x) = x⁶ on the interval [−4, 4].

Given two functions, f₁(x) = x and f₂(x) = x⁶, which are orthogonal on the interval [−4, 4], we need to find constants C₁ and C₂ such that a third function f₃(x) = x + C₁x² + C₂x³ is also orthogonal to both f₁ and f₂ on the same interval.

To determine the constants C₁ and C₂, we need to use the property of orthogonality, which states that the integral of the product of two orthogonal functions over a certain interval is equal to zero. Mathematically, this can be written as:

\(\int^a_b\) f₁(x) * f₃(x) dx = 0

\(\int^a_b\) f₂(x) * f₃(x) dx = 0

We can use this property to find the values of C₁ and C₂ that satisfy the condition for orthogonality. Let's start with the first integral:

\(\int^{-4}_4\) x(x + C₁x² + C₂x³) dx = 0

Expanding the integrand and solving for C₁, we get:

C₁ = -1/5

Similarly, for the second integral:

\(\int^{-4}_4\) x⁶(x + C₁x² + C₂x³) dx = 0

Expanding the integrand and solving for C₂, we get:

C₂ = 1/7

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These are the polynomial equations:

A = x^ (1/4) - ∛x + 4√x - 8x + 16

B = 3x² - 5x⁴ + 2x - 12

C = x³ - 7x² + 9x - 5x⁴ - 20

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

These are the non-polynomial equations:

E = 4/x⁴ + 3/x³ - 2/x² - 1

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.

Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.

Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.

In the equation, we can solve for other values to obtain:

Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.

A = x^ (1/4) - ∛x + 4√x - 8x + 16

This polynomial exists.

B = 3x² - 5x⁴ + 2x - 12

This polynomial exists.

C = x³ - 7x² + 9x - 5x⁴ - 20

This polynomial exists.

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

It is a polynomial.

E = 4/x⁴ + 3/x³ - 2/x² - 1

It is not a polynomial.

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

A polynomial is not what it is.

The polynomials are thus resolved.

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The a = 0.01 critical value for the chi - square statistic with 13 degrees of freedom is given by 27.688.

Hence the correct option is (A).

Here given distribution is Chi - squared distribution.

two parameters of chi - squared distribution are given by ' a ' and ' d ' where d is degree of freedom.

The critical value against chi squared distribution changes according to the change of the values of a and d.

The table chi squared distribution is given by,

Here we have to find the critical value for the chi - squared statistic with 13 degrees of freedom when a = 0.01.

Therefore, a = 0.01 and d = 13

From the given table we can see that when a = 0.01 and d = 13 the critical value is given by 27.688.

Hence the correct option is (A).

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Answer:

A cuboid has 6 faces. 4 are lateral.

Answer:

a cuboid has 6 faces

Step-by-step explanation:

Step-by-step explanation:

Welll.... there are EIGHT of them that total 1080

1080 / 8 = 135 degrees each

The value of ∠GFH=59°, in the given question.

What do you mean by angle?

Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet.

According to the data in the given question,

We have :

∠EFH=127°

∠EFG=(8x-4)°

∠GFH=(5x+14)°

Now, we have to solve the value of ∠GFH,

∠EFG+∠GFH=∠EFH

Putting the values given and solve for x,

(8x-4)°+(5x+14)°=127°

8x°-4°+5x°+14°=127°

13x°+10°=127°

13x°=127°-10°

13x°=117°

x=9

Then, putting the value of x in ∠GFH,

∠GFH=(5x+14)°

=(5(9)+14)°

=(45+14)°

=59°

Therefore, the value of ∠GFH=59°.

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