Morgan ran 5 miles in 57 days and a half minutes. How long did it take her to run each mile

The values of given differential equation  constant r are  = 1/5 and -3.

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x)

Here “x” is an independent variable and “y” is a dependent variable.

For example, dy/dx = 5x A differential equation contains derivatives which are either partial derivatives or ordinary derivatives.

The derivative represents a rate of change, and the differential equation describes a relationship between the quantity that is continuously varying with respect to the change in another quantity.

There are a lot of differential equations formulas to find the solution of the derivatives.

As y = e power rx

y¹= dy/dx= re power rx

and y'' = r²e power rx

Hence 5y'' +14y' – 3y = 0 can be written as

5r²e - 14re** - 3e¹² - 0

or 5r2 + 14r - 3 - 0

or 5r2 + 15r - r - 3 - 0

or (5r − 1)(r + 3) = 0

r=1/5 or r= -3

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Answer:

Step-by-step explanation:

refreh it

So 213 employees left in the company after 13 years.

Given

Number of employee in the company=630

Decreasing rate in the company per year =8%

Time= 13 years

Let the number left in the company be x

Since the decrease rate is 8% we use 0.08

So after 13 years the employee left are

630(1-0.08)¹³=x

630(0.92)¹³=x

630*.338= 212.94

We can take approx as 213

so x= 213

So 213 employees left in the company after 13 years.

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The composite translation for this problem is represented as follows:

<3, -9>

The four translation rules are defined as follows:

Another notation is the <x,y> notation, in which:

For the composition of translations, we add the movements, hence:

Meaning that the first option is the correct option.

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The statement does not makes a sense because i is an imaginary unit and has fixed value √-1.

What is meant by value ?

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The required length of a side of the rhombus is 10 cm.

A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.

Let diagonals intersect each other at o,

In ΔROQ

RQ = [tex]\sqrt{OR^{2}+OQ^{2}}[/tex]

RQ =[tex]\sqrt{36+64} =\sqrt{100}[/tex]

RQ = 10 cm

Thus, required length of the side of rhombus is 10 cm.

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Complete question:

PQRS is a rhombus. The shorter diagonal PR measures 12 units and QS = 16 units. The measure of angle PQR = 60°. Find the length of a side of the rhombus.​

For the gumballs in Julia's bag

Sample space = lemon-lime, watermelon, grape.

The correct option is B.

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.

Given,

Number of lemon limes gumballs in the bag = 2 lemon-lime gumballs

Number of watermelon gumball in the bag = 1 watermelon gumball

Number of grape gumballs in the bag = 3 grape gumball

Sample space is the set of all the possible outcomes the experiment

Here, Julia has 1 watermelon, 2 lemon-lime, and 3 grape gumballs

Sample space = lemon-lime, watermelon, grape

Hence { lemon-lime, watermelon, grape} is the sample space for gumballs in Julia's bag.

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Answer unzipped,new bases, sealed

Step-by-step explanation:

The length of Mid segment QT is 57.56 units.

The incenter of a triangle can be discovered by drawing the triangle's angle bisectors and then locating the location of their intersection. This is possible with the aid of a compass.

The three line segments and the three lines that include those segments are equally spaced from the incenter and constitute each of the three sides of the triangle.

the single point where the three internal angle bisectors of a triangle meet and which also serves as the circumference of the circle around which it is inscribed.

The three line segments and the three lines that include those segments are equally spaced from the incenter and constitute each of the three sides of the triangle.  

ΔQUT is right triangle

QU = 55

UT= 17

Using Pythagoras Theorem

QT² = QU² + UT²

QT² = 55² + 17²

QT = √3314

QT = 57.56

Thus, The length of Mid segment QT is 57.56 units.

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The coordinates of the rotated image are:

A' = (1, 1)

B' = (1, 3)

C' = (-2, 1)

Option A is the correct answer.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

Triangle ABC.

A = (1, 1)

B = (3, 1)

C = (1, 4)

When rotated 90 degrees counterclockwise around (1, 1).

A = (1, 1) will stay the same.

B = (3, 1) will change into B' = (1, 3)

C = (1, 4) will change into C' = (-2, 1)

Now,

The coordinates of the image after reflection are:

A' = (1, 1)

B' = (1, 3)

C' = (-2, 1)

This image is found in option A.

Thus,

The rotated image of the triangle is in option A.

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Answer: a. The independent variable in the equation C(a) = 5a is a. It represents the number of art classes Amir attends.

b. The dependent variable in the equation C(a) = 5a is C(a). It represents the cost Amir incurs as he attends art classes. The dependent variable is dependent on the independent variable because the cost will change as the number of classes attended changes.

Christian is making a circular pizza. The diameter of the pizza is 12 inches. The pizza crust on the outside will be about 12 inches thick.

The formula for determining a pizza's circumference is C = 2πr, where C is the circumference, pi is a constant that is roughly equivalent to 3.14, and r is the pizza's radius.

We must determine the pizza's circumference in order to locate the crust on the pizza's outer edge. C = 2πr is the formula for a circle's circumference, where C is the circumference, pi is a constant that is roughly equivalent to 3.14, and r is the circle's radius.

The pizza has a diameter of 12 inches, so the radius, or 6 inches, is half of that. Thus, the pizza's circumference is:

                 C= 2π6 = 12π

The pizza's circumference represents the crust's outer edge. C = 26 inches = 12 inches As a result, the pizza's crust on the outside measures about 12 inches.

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The mean is 120 and the standard deviation is 20.

How to find the mean and standard deviation?

We must calculate the mean and standard deviation from the curve in the preceding graph.

As we can see from the normal distribution curve that the center is at 120.

As a result, 120 is the distribution's mean.

From the above curve:

Mean + Standard deviation = 140

We know that the Mean = 120.

120 + Standard Deviation = 140

Standard Deviation = 20

Therefore, 20 is the standard deviation.

Therefore, from the given data we can find that the Mean is 120 and the Standard deviation is 20.

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The given value of 157 pounds is a statistic.

This is because it is a numerical measurement describing a characteristic of a sample. A statistic is a value calculated from a sample, whereas a parameter is a value calculated from a population. In this case, the sample is the 40 randomly selected members of the health and fitness club, and the statistic is the average weight of those members. This statistic is used to make inferences about the larger population of all members of the health and fitness club, but it is not the same as the parameter, which would be the true average weight of all members of the club.

Therefore, The given value of 157 pounds is a statistic.

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The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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Answer: 7

Step-by-step explanation:

yarn = 4 1/5 = 21/5

measure of one piece = 3/5

no. of pieces of yarn = 21/5÷3/5

= 21/5×5/3

= 105/15 = 7

So the number of pieces of yarn cut will be 7

Answer:

7

Step-by-step explanation:

4.2' yarn

cut into 0.6' pieces

4.2/0.6 =7

A.BC BD must be true in order to demonstrate that triangles ABD and ABC are congruent by SSS.

The SSS Congruence Theorem requires three pairs of corresponding sides to be congruent for two triangles to be considered congruent to one another.

We may infer the two triangles' characteristics from the provided image by looking at them:

AB ≅ AB (reflexive property) (reflexive property)

AC ≅ AD (provided) (given)

The two pairs of corresponding congruent sides are so present. As a result, for SSS to demonstrate that ABD ABC, the following must be true: A. BC BD.

A.BC BD must be true in order to demonstrate that triangles ABD and ABC are congruent by SSS.

The complete question is,

Have a look at the triangles below. In order to demonstrate that ABDABC, which of the following would also need to be true?

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The average rate of change of these function f(x), g(x), h(x) on interval [4, 7] from least to greatest is f(x)<g(x)<h(x) with values A1 = -7.5 < A2 = -6 < A3 = -3.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

Average rate of change of any function say S(x) on [a,b] is -

A = [S(b) - S(a)]/b-a....(1)

Now. for function f(x) on interval [4, 7].

Here, use values of f(4) and f(7) from graph and find value of f(x)=y for x=4 and value of f(x)=y for x=7.

f(4) = -10, f(7) = 5

Substitute the values in equation (1) -

A1 = [f(7) - f(4)]/(4 - 7)

A1 = [5 - (-10)]/-2

A1 = 15/-2

A1 = -7.5

Average rate of change for function g(x) on interval [4, 7].

Here, use the values of g(4) and g(7) from table.

g(4) = 7, g(7) = 19

Substitute the values in equation (1) -

A2 = [g(7) - g(4)]/(4 - 7)

A2 = [19 - 7]/-2

A2 = 12/-2

A2 = -6

Average rate of change for function h(x) = x² - 9x + 5 on interval [4, 7].

Here, use the values of h(4) and h(7) by putting x = 4 and x = 7 in function h(x).

h(4) = x² - 9x + 5

h(4) = (4)² - 9(4) + 5

h(4) = 16 - 36 + 5

h(4) = -15

h(7) = x² - 9x + 5

h(7) = (7)² - 9(7) + 5

h(7) = 49 - 63 + 5

h(7) = -9

Substitute the values in equation (1) -

A3 = [h(7) - h(4)]/(4 - 7)

A3 = [-9 - (-15)]/-2

A3 = [-9 + 15]/-2

A3 = 6/-2

A3 = -3

Now, average rate of change of these function f(x), g(x), h(x) from least to greatest is f(x)<g(x)<h(x).

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In 2009, Florida would have 558 hospitals if it had the same hospital beds per million residents as Texas. This is a little more than what Florida's real number of hospitals was in 2009. (343).

A mathematical technique called proportional reasoning is used to compare the ratios of two or more identical quantities.

The proportionate reasoning theory is being used in this query.

In this instance, we're contrasting Florida's hospital density per million residents with Texas' hospital density per million residents.

We may predict the number of hospitals in Florida given the same ratio as Texas by comparing these two ratios.

1. Determine Texas's hospital density per million residents: 428 hospitals divided by 26.4 million residents equals 16.2 hospitals per million residents.

2. Determine Florida's hospital density per million residents: 343 hospitals / 19.5 million residents = 17.6 hospitals per million residents.

3. Multiply the population of Florida (19.5 million) by the number of hospitals per million of the population of Texas (16.2) to arrive at 315.3 hospitals: 19.5 million people x 16.2 hospitals per million of the population.

The result should be rounded to the next whole number: 315 hospitals are equal to 315.3 hospitals.

5. Contrast Florida's actual hospital count in 2009 with the expected number of hospitals there (315). (343).

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Answer:

Step-by-step explanation:

Answer: To determine which loan(s) meet Jeremy's criteria of no more than an effective rate of 7.000% annually, we need to calculate the effective rate for each loan.

The effective rate is the true annual interest rate that a borrower will pay on a loan, taking into account the frequency of compounding.

Loan A: 6.785% normal rate compounded semi-annually

To calculate the effective rate, we can use the formula:

(1+ (nominal rate/2))^2 - 1

Effective rate = (1+ (6.785/2))^2 - 1 = 6.897%

Loan B: 6.795% nominal rate compounded, manually

Since the loan is compounded manually, the effective rate is the same as the nominal rate.

Effective rate = 6.795%

Loan C: 6.659% nominal rate, compounded weekly

To calculate the effective rate, we can use the formula:

(1+ (nominal rate/number of compounding periods per year))^(number of compounding periods per year) - 1

Effective rate = (1+ (6.659/52))^52 - 1 = 6.759%

Since 6.897% > 7.000% and 6.795% > 7.000% and 6.759% < 7.000%. So Loan C with 6.659% nominal rate, compounded weekly meets Jeremy's criteria.

Step-by-step explanation:

Answer: Based on the information provided, it appears that the graph represents a linear equation, which is a straight line. The equation of a straight line can be represented in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line, we need two points on the line. We can use the points (x1, y1) and (x2, y2) to calculate the slope of the line, m, using the formula:

m = (y2 - y1) / (x2 - x1)

Without knowing the coordinates of the points on the graph it is not possible to give the equation of the line.

To find the cost of ordering 6 pounds of mushrooms, we would substitute 6 for x in the equation of the line and solve for y.

y = mx + b

y = m(6) + b

Without the equation of the line, it's not possible to find the cost of ordering 6 pounds of mushrooms.

Step-by-step explanation:

a. The total cost C as a function of the number of units produced is C = $12.13x + $92,000

b. The revenue R as a function of the number of units sold is R = $17.10x

c. The profit P as a function of the number of units sold is P = $5.97x - $92,000

(A) The total cost for a business is the sum of the variable cost and the fixed costs.

The variable cost per unit is $12.13, so the total variable cost for x units produced is $12.13x.

The fixed costs are $92,000 and do not change with the number of units produced, so the total cost C as a function of the number of units produced is given by -

C = $12.13x + $92,000

(B) The revenue is the total amount of money earned from selling the product. The product sells for $17.10 per unit, so the revenue R as a function of the number of units sold is given by -

R = $17.10x

(C) The profit is the difference between the revenue and the total cost. Using the equations from (A) and (B), the profit P as a function of the number of units sold is given by -

P = R - C = $17.10x - ($12.13x + $92,000) = $5.97x - $92,000

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D. 19 elements are in ALB.

| A | =6 and | B | = 13,

4 elements are common to sets A and B.

but | A ∪ B | ≠ 6 + 13.

Image search results for Set A has six components, set B has thirteen, and sets A and B share four elements.

A. 14 B. 15 C. 16 D. 19.The formula for A union B complement is (A U B)’ = A’ B’ or (A U B)c = Ac Bc, where or c represent the complement of a set. As one of De-Laws Morgan’s of Union of Sets, this formula of A union B complement is named after the mathematician De-Morgan. A U B (which denotes the union of two sets A and B) is a set that contains all of the components of A and B.

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The total average monthly expenditure in 2020 was £2400.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The expenditure in 2020 will be calculated as:-

Average monthly expenditure in 2020 = 600 + 500 + 400 + 300 + 200 + 100 = £2400

So, the total average monthly expenditure in 2020 was £2400.

The complete question is given below:-

Average monthly expenditure (£)

600

500

400

300

200

100

The total average monthly expenditure in 2010 was £1200. What was it in 2020?

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The authors argue that Cypher's decision to go back into the Matrix was a betrayal of his friends because it showed that he was willing to abandon his beliefs and betray those closest to him in order to return to a life of comfort and ease within the Matrix.

By doing so, he effectively gave up his freedom and became a tool of the machines once again, thereby betraying the ideals of the rebellion and those who had fought alongside him to achieve it. Hence, The authors argue that Cypher's decision to go back into the Matrix was a betrayal of his friends.

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Answer:

Step-by-step explanation:

Exercise 2:

1.To construct the triangle ABC, start by drawing a line segment BC of length 5cm. Using a protractor, measure and mark an angle of 80° at B and an angle of 40° at C. Connect the two marked angles with a line to form triangle ABC.

2.The bisector of angle ABC cuts the line segment AC at M.

a. To calculate MBC, we can use the Angle Bisector Theorem, which states that the ratio of the lengths of the bisector of a given angle of a triangle to the sides of the triangle is equal to the ratio of the other two sides of the triangle. So, MBC/AC = BC/AB. Since angle B=80° and angle C=40°, angle A is (180-(80+40))=60°. Therefore, AB/BC = MC/MB.

b. Using the Angle Bisector Theorem again, we can see that MBC/AC = BC/AB, which means that MBC/5 = 5/AB. And since AB/BC = MC/MB, we can deduce that MB = MC. Therefore, triangle MBC is an isosceles triangle.

c. As we know that MB=MC, we can say that triangle MBC is an isosceles triangle.

Note: To construct the triangle in a more accurate way, you may need a ruler and a compass, and the angles and sides should be measured and drawn with more precision.

For the given condition number of laps "l" is the independent variable.

A symbol (often a letter) is used in mathematics to represent an unknowable numerical value in an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.

Given The amount of time, t, to finish a race and the number of laps, I,

there are two types of variables,

dependent and independent variables,

In an algebraic equation, an independent variable is one whose values are not impacted by changes. When there are two variables in an algebraic equation, x and y, and each value of x depends on every other value of y, x is an independent variable, and y is a dependent variable.

for the given condition,

the time taken to finish the race directly varies with the number of laps,

so time is dependent on the number of laps and a number of laps "l" is the independent variable.

Hence the independent variable is the number of laps, "l".

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The complete question is,

The amount of time, t, to finish a race and the number of laps, l, around a track. What is the independent variable?

In reality, only 55% of the calories produced by crops around the world are consumed directly by humans. Animal feed accounts for an additional 36% of usage.

The Complete Question.

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14.3 percentage of the trees were oaks, The total number of trees have increased by: 15/28.

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