Scarlett usually rides her bike about 1 and 1/5 hours every day. The distance between the library and school is 7/8 mile. Yesterday the bike had a problem and Scarlett only rode her bike 2/3 of the way from school to the library and walked the rest of the way. How far did she ride her bike

The inequality for number of hours Aman worked

90.9 hour < h < 127.27 hour

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Amar travel expenses will cost between $1,800 and $2,400 total.

He has $300 In savings, and he earns $16.50 per hour at his job.

let the number of hours be represented by h.

So, 300 + 16.5h = 1800

16.5h = 1500

h = 90.9

and, if the expense exceeds to $2400

300 + 16.5h = 2400

16.5h =  2100

h = 127.27

Thus, the inequality is

90.9 hour < h < 127.27 hour

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Answer:

m = 5/4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0, -3) (4,2)

We see the y increase by 5 and the x increase by 4, so the slope is

m = 5/4

The value that 50% of the data, is 50 the median.

An illustration of variation in a set of data is called a box and whisker plot. A histogram analysis usually gives an adequate display, but a box and whisker plot can add more detail while enabling the display of different sets of data on the same graph.

Given Data: 42, 44, 50, 54, and 56

The median can be referred to as the second quartile (Q2) or 50th percentile of the data set.

The median value shows that 50% of the data set is above it while 50% is below it also.

So, 50 is the median, and this means that 50% of the data lie above 50.

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The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes.

In this case, the favorable outcome is that the customer had a high level of satisfaction and used the company more than five times per month. The total number of possible outcomes is the total number of customers in the study, which is 700.

Therefore, the desired probability can be calculated as:

P(High satisfaction and more than 5 times per month) = 70 / 700

And the answer is P(High satisfaction and more than 5 times per month) = 70 / 700 = 1/10.

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The rational functions with the given asymptotes are presented as follows:

1. y = 1/(x³ + x² - 6x).

2. y = 1.5x²/(x² + 0.5x - 0.5).

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

For item 1, due to the vertical asymptotes, the denominator is given as follows:

x(x + 3)(x - 2) = x(x² + x - 6) = x³ + x² - 6x.

As the horizontal asymptote is of zero, the numerator has a lower degree than the denominator, hence it can be constant, and the function is given as follows:

y = 1/(x³ + x² - 6x).

For item 2, the denominator is given as follows:

(x + 1)(x - 0.5) = x² + 0.5x - 0.5.

Due to the horizontal asymptote of 3/2, the degree of the numerator must be the same as the denomiator, with a coefficient 3/2 that of the denominator, hence the numerator is given as follows:

3x²/2 = 1.5x².

Meaning that the function is:

y = 1.5x²/(x² + 0.5x - 0.5).

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The expression when rewritten is 3^1/2

From the question, we have the following parameters that can be used in our computation:

(3^3/4  * 3^3/8)^4/9

Apply the law of indices

So, we have

(3^9/8)^4/9

Simplify the exponent

3^1/2

Hence, the solution is 3^1/2

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The expression can be rewritten as 3^1/2 = √3

We want to simplify the expression below:

(3^3/4  * 3^3/8)^4/9

Remember that we can add these exponents, so we get:

3/4 + 3/8 = 9/8

Then we can rewrite this as:

(3^9/8)^4/9

Takin the product between the exponents we will get:

(3^9/8)^4/9 = 3^(4/8) = 3^1/2

the solution is 3^1/2

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Answer:

$119.25.

Step-by-step explanation:

Let's call the deposit amount "D".

Starting balance: $654.98

Check amount: -$321.45

Deposit: +D

Ending balance: $452.78

So, we can set up an equation:

$654.98 - $321.45 + D = $452.78

Solving for D:

$654.98 - $321.45 + D = $452.78

$333.53 + D = $452.78

D = $119.25

So the deposit amount was $119.25.

Answer:

see below

Step-by-step explanation:

area of a door = length * width = 7* width = 7x-14

so width = ( 7x-14 ) / 7 =  x-2

when x=6 width = 4

area = 4*7 = 28

perimeter = (4+7)*2 = 22

An inequality that best represents this situation is: x - 1300 > 2500.

a) Let x be the amount of money Sara has in savings. We know that the amount she wants to spend on vacation is $1300, so we have x - 1300 > 2500.

b) To solve for x, we can add 1300 to both sides: x > 3800.

c) The value of x in this situation represents the amount of money Sara has in savings.

The inequality x > 3800 means that Sara must have more than $3800 in savings in order to spend $1300 on a vacation while following the financial planner's suggestion to spend less than $2500.

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If a pair of linear equations in two variables have no solution then the pair of lines are​ inconsistent or parallel lines.

Depending on the number of variables and type of equations there are 3 types of solutions to an equation.

1. Unique Solution (One solution):

When there is only one variable then the linear equation will have a Unique Solution or One solution. In the case of pair of linear equations, the linear equation will have a unique solution when the straight lines are intersected at a single point.

2. No solution:

When the given pair of linear equations is inconsistent equations the linear equation will have no solutions in common or we can say that the given lines are non-intersected lines. Usually, a pair of parallel lines will have no solutions.

3. Infinite Solutions (Many solutions):  

When the given lines are overlapped on each other or coincident with each other the given lines will have Infinite Solutions. These intersected lines.    

Therefore,

If a pair of linear equations in two variables have no solution then the pair of lines are​ inconsistent or parallel lines.  

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The solution is :

1. How much change did he get from 1500-pesos bill.

2. 2 t-shirt 249.95 pesos pants for 675.95 pesos .

3. 2 t-shirt and pair of pants.

4. 249.95 pesos + 675.95 pesos  and subtraction 1500-pesos bill.

5. Seventy-four and twenty cents.

6. 74.20 pesos.

Arithmetic is one of the oldest and elementary branches of mathematics, originating from the Greek word ‘Arithmos’, which means ‘number’. Arithmetic involves the study of numbers, especially the properties of traditional operations, such as: Addition, Subtraction, Multiplication, Division.

The arithmetic operators based on these operations are ‘+’, ‘-’, ‘×’ and ‘÷’.

as given, Bobby bought:

2 shirts bought at 249.95 each

Pair of pants for 675.95

So,

How much change did he get from his 1500 peso bill ? (correction : 1500 peso)

2 shirts for 249.95 each.

249.95 * 2 = 499.9

Total spent on the shirts : 499.9

A pair of pants bought for: 675.95

Total money spent = 675.95 + 499.9 = 1175.85

In order to determine the final solution we have to subtract the total amount from 1500.

1500 - 1175.85 =324.15

He will getting a change of 324. 15 pesos .

Therefore, The solution is :

1. How much change did he get from 1500-pesos bill.

2. 2 t-shirt 249.95 pesos pants for 675.95 pesos .

3. 2 t-shirt and pair of pants.

4. 249.95 pesos + 675.95 pesos  and subtraction 1500-pesos bill.

5. Seventy-four and twenty cents.

6. 74.20 pesos.

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Bob received 824.15 pesos as change from his 1 000-peso bill.

What is asked?

The question asks for the change Bob received from his 1 000-peso bill.

What are given?

The given information is that Bob bought 2 t-shirts at 249.95 pesos each and a pair of pants for 675.95.

What is/are the hidden question?

The hidden question is: How much did Bob spend in total?

What operations will you use to solve the problem?

To solve the problem, you need to find the total amount that Bob spent, and then subtract it from his 1 000-peso bill to get his change.

What is the number sentence?

The number sentence would be: change = 1 000 pesos - (2 * 249.95 pesos + 675.95 pesos)

What is the answer?

To find the answer, you can calculate the expression in the number sentence:

change = 1 000 pesos - (2 * 249.95 pesos + 675.95 pesos)

change = 1 000 pesos - (499.90 pesos + 675.95 pesos)

change = 1 000 pesos - 1175.85 pesos

change = 824.15 pesos

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The value of this expression is 576/365

What is Expression?

A phrase, also known as an expression in some circumstances, is a group of words or a single word that functions as a grammatical unit. For instance, the English word "the very joyful squirrel" is a noun phrase which contains the adjective phrase "extremely happy". Phrases can be made up of a single word or a whole sentence.

(3x³y⁻²)² = 576/365

Given,

x = -2

y = 5

Applying property of exponents to simplify the expression.

Property: [tex](a^{b} )^{c}[/tex] =[tex]a^{bc}[/tex]

So, we have : (3x³y⁻²)²

= 3²x⁶y⁻⁴

= 9x⁶y⁻¹

Property : a⁻ᵇ

= 1/aᵇ

= 9x⁶ / y⁴

Now, plugging in values of x and y

= 9 (-2)⁶ / 5⁴

= 9*64/625

= 576 / 365

This phrase has a value of 576/365.

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The value of this expression is 576/365

What is Expression?

A phrase, also known as an expression in some circumstances, is a group of words or a single word that functions as a grammatical unit. For instance, the English word "the very joyful squirrel" is a noun phrase which contains the adjective phrase "extremely happy". Phrases can be made up of a single word or a whole sentence.

(3x³y⁻²)² = 576/365

Given,

x = -2

y = 5

Applying property of exponents to simplify the expression.

So, we have : (3x³y⁻²)²

= 3²x⁶y⁻⁴

= 9x⁶y⁻¹

Property : a⁻ᵇ

= 1/aᵇ

= 9x⁶ / y⁴

Now, plugging in values of x and y

= 9 (-2)⁶ / 5⁴

= 9*64/625

= 576 / 365

This phrase has a value of 576/365.

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The solution to the ODE dy/dx = x^6 * (y - 2)^2 with initial condition y(0) = -1 is a complicated expression involving the antiderivative of a complex function, which may not have a closed-form solution.

What is function ?

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

1) Rewrite the ODE into a separable form:

dy/dx = x^6 * (y - 2)^2

2) Integrate both sides of the equation:

∫(dy/dx)dx = ∫x^6 * (y - 2)^2 dx

3) Solve for y on one side of the equation and integrate the other side:

y = 2 + √((C - ∫x^6 * (y - 2)^2 dx)/x^6)

where C is an arbitrary constant of integration.

4) Use the initial condition y(0) = -1 to find the value of C:

-1 = 2 + √((C - ∫0^0 * (y - 2)^2 dx)/0^6)

5) Solve for C:

C = (1 - 2)^2 = 1

6) Substitute C back into the solution for y:

y = 2 + √((1 - ∫x^6 * (y - 2)^2 dx)/x^6)

7) The solution y(x) is a complicated expression that involves the antiderivative of a complex function. It may not have a closed-form solution, but it can be approximated numerically using numerical methods.

The solution to the ODE dy/dx = x^6 * (y - 2)^2 with initial condition y(0) = -1 is a complicated expression involving the antiderivative of a complex function, which may not have a closed-form solution.

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The probability that all 5 customers order pepperoni pizza is 0.2457 and the probability that at least 1 customer doesn't order pepperoni pizza is 0.7543.

We can calculate the probability that all 5 customers order pepperoni pizza by multiplying the probability that each individual customer orders pepperoni pizza.

The probability of each customer ordering pepperoni pizza is 72%. Therefore, the probability that all 5 customers order pepperoni pizza is (0.72)^5 = 0.2457.

We can calculate the probability that at least 1 customer doesn't order pepperoni pizza by subtracting the probability that all 5 customers order a pepperoni pizza from 1.

Hence, The probability that at least 1 customer doesn't order pepperoni pizza is 1 - 0.2457 = 0.7543.

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The expected acceleration of an object is based on the acceleration due to gravity, which is a constant value of 9.8 m/s2. To calculate the expected acceleration, we use the equation: Expected acceleration = (5/7)gsin(θ), where θ is the angle at which the object is moving.

This equation takes into account the angle of the object and uses the acceleration due to gravity to calculate the expected acceleration. In this equation, the acceleration due to gravity is multiplied by a fraction, which is determined by the angle at which the object is moving. Therefore, the higher the angle at which the object is moving, the greater the expected acceleration.

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The function g(x) graphed here, the limit of g(x) as x approaches -2 is -1, the limit of g(x) as x approaches -1 is 2, and the limit of g(x) as x approaches 0 is 3.

a. limx→−2g(x)

= g(-2)

= -1

Therefore, the limit of g(x) as x approaches -2 is -1.

b. limx→−1g(x)

= g(-1)

= 2

Therefore, the limit of g(x) as x approaches -1 is 2.

c. limx→0g(x)

= g(0)

= 3

Therefore, the limit of g(x) as x approaches 0 is 3.

d. There is no limit of g(x) as x approaches infinity because the graph of the function is not defined at infinity. However, there is no limit of g(x) as x approaches infinity because the graph of the function is not defined at infinity.

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Answer:

10

Step-by-step explanation:

All possible permutations except those that are not shown by the clock.

Eg:92:02

Step-by-step explanation:

First, we need to calculate the area of the pond by using the formula for the area of a circle: πr^2, where r is the radius. In this case, the radius is 3 feet.

3^2 = 9

π * 9 = 28.27 square feet

Now, we need to find the volume of the pond to find the finished area by using the formula for the volume of a cylinder: πr^2h, where r is the radius, h is the height/depth.

28.27 * 2 = 56.54 cubic feet

Finally, we need to convert the square feet to square meters and multiply it by the cost per square meter.

56.54 square feet * 0.092903 square meters/square foot = 5.24 square meters

5.24 square meters * $175.85/square meter = $924.99.

So, the cost of cementing the bottom and sides of the circular pond would be $924.99

Given quadratic equation has same solution set as -x=x²+12x+36 i.e. C.

A second-degree algebraic equation in x is a quadratic equation. Ax2 + bx + c = 0 is the quadratic equation in its standard form, with a and b acting as coefficients, x acting as the variable, and c acting as the constant term.

The coefficient of x2 must not be zero (a 0) for an equation to qualify as a quadratic equation. The x2 term comes first, followed by the x term, and finally the constant term when stating a quadratic equation in standard form. Instead of being written as fractions or decimals, the numerical values a, b, and c are frequently expressed as integral values.

Now,

Given equation is √-x=x+6

-x = (x+6)²

-x = x² +36+12x

x² + 11x + 36 = 0

As it is same quadratic equation as given in option C.

Hence,

         Given quadratic equation has same solution set as

-x = x² + 12x + 36.

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Answer:

can u screenshot the question then ill solve it!!

Step-by-step explanation:

The height of the tree is 6.77 meters.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.

Given that, the height of the person is 1.25 meters, the length of the tree's shadow is 24.65 meters, and the distance between the person and the tree is 20.1 meters.

Let the height of the tree be x.

Note that the scenario makes two similar triangles.

Since the ratio of the side lengths of similar triangles is proportional, it follows:

(24.65 - 20.1)/1.25 = 24.65/x

3.64 = 24.65/x

x = 24.65 / 3.64

x = 6.77

Hence, the height of the tree is 6.77 meters.

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the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get: ∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is illustrated in the figure below.

b. ∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is the area bounded by the two parabolas y= 2x2 and y= 1 x2. This can be seen in the sketch below.

b. To evaluate the integral ∫∫ df(x,y)dxdy, we need to evaluate the integral of the function f(x,y) = x2y over the region D. We can do this by setting up the integral as follows:

∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy

Next, we can evaluate the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get:

∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

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Step-by-step explanation:

to solve an equation with a variable we want to transform the equation, so that in the end we have the variable alone on one side of the equation, and everything else on the other side.

so, when we look at

(n + 8)/2 - 4 = 16

what blocks us from reading the value of n ?

several things on the left side.

I would start with the "- 4".

to get rid of that from the side of the variable we need to add 4. and to keep the equality true, we need to add this on both sides :

(n + 8)/2 - 4 + 4 = 16 + 4

and we get

(n + 8)/2 = 20

what blocks us now ?

I would say the fraction, this division by 2.

how do we get rid of that ?

by multiplying everything by 2 :

2×(n + 8)/2 = 2×20

and we get

n + 8 = 40

still, something is blocking us from reading the value of n : the "+ 8".

how do we get rid of that ?

by subtracting 8 from both sides :

n + 8 - 8 = 40 - 8

and we get

n = 32

that's it. we are finished. goal achieved.

The joint probabilities are: P(A and B) = 0.36, P(A and C) = 0.1, P(AC and B) = 0.07.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. An event with probability 0 cannot occur, and an event with probability 1 is certain to occur. The probability of an event A is usually written as P(A) and is calculated as the number of favorable outcomes divided by the total number of possible outcomes in the sample space. For example, if a fair six-sided die is rolled, the sample space is the set of all possible outcomes (1, 2, 3, 4, 5, 6), and the probability of rolling a 4 is 1/6. Probability is used in many fields to make predictions, draw inferences, and make decisions under uncertainty.

We can use the formula for conditional probability to calculate the joint probabilities:

P(A and B) = P(B | A) * P(A) = .4 * .9 = .36

P(A and C) = P(A) * P(C | A) = .9 * P(C) / P(A) = .9 * .1 / .9 = .1

P(AC and B) = P(B | AC) * P(AC) = .7 * .1 = .07

So, the joint probabilities are:

P(A and B) = .36

P(A and C) = .1

P(AC and B) = .07

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A function which has the same horizontal asymptote as the function graphed above include the following: A. f(x) = 4^{x + 2} - 3.

In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

In this context, the line passing through the ordered pair (0, 3) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 3, as shown in the image attached below.

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The general solution for d^2y/dt^2 - 2dy/dt - 15y = e^4t is a sum of a homogeneous solution (c1e^(r1t) + c2e^(r2t)) and a particular solution (Ate^4t).

What is differentiation ?

Differentiation is a method of finding the derivative of a function. Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.

The general solution for the second-order homogeneous linear ordinary differential equation d^2y/dt^2 - 2dy/dt - 15y = 0 can be found using the characteristic equation:

r^2 - 2r - 15 = 0

The characteristic equation has two roots, which are the eigenvalues of the corresponding homogeneous linear system. Let r1 and r2 be the roots of the characteristic equation, then the general solution for the homogeneous equation is:

y(t) = c1e^(r1t) + c2e^(r2t)

where c1 and c2 are arbitrary constants.

y(t) = c1e^(r1t) + c2e^(r2t) + Ate^4t

The general solution for d^2y/dt^2 - 2dy/dt - 15y = e^4t is a sum of a homogeneous solution (c1e^(r1t) + c2e^(r2t)) and a particular solution (Ate^4t).

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The generatrix of a cylinder is intersected by a plane parallel to its axis to determine the shape of the hole in the cylinder, while the generatrix of a cone is intersected by a plane via its vertex.

We select cutting planes that intersect both surfaces along their generatrixes in order to construct the intersection points of a cone and a cylinder. A cylinder's generatrix is intersected by a plane parallel to its axis, and a cone's generatrix is intersected by a plane via its vertex.

Since the line passing through the cone's vertex is parallel to the axis of the cylinder, the system of planes that intersect both surfaces in their generatrixes is a pencil-shaped arrangement of planes.

The cone and the cylinder are both intersected by every plane of that pencil in two different generatrixes.

In contrast to the vertices of the surfaces, the junction curve has four points that are intersections of these four lines.

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Calculating the mean amount of time that these students spent on the internet yesterday it is not appropriate because sample is a convenience sample to determine condition for population mean.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode.

The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

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