how many trains would pass from 6:00 to 6:30

Answer:

32

Step-by-step explanation:

1/3 of 60 is 20, so 60-20=40.

1/5 of 40 is 8, so 40-8=32.

32 fliers havent been posted

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

Answer:

g(-2) = 3

x = -2.535 and -0.131

Step-by-step explanation:

Answer:

25 and 31, respectively

Step-by-step explanation:

1. Divide the number of miles (77 1/2) by the number of gallons (3 1/10).

2. Whatever number you get is where you place your dot

Tip: Converting fractions to decimals can make the work easier (in this case [77 1/2=77.5], [3 1/10=3.1], [99 1/5=99.2], and [3 1/5=3.2]

The correct answer of the operation is option B: 4x^2 - 9.

To perform the operation (2x-3)(2x+3), we can use the FOIL method, which stands for First, Outer, Inner, Last. Let's go through the steps:

First: Multiply the first terms of each binomial.

(2x)(2x) = 4x^2

Outer: Multiply the outer terms of each binomial.

(2x)(3) = 6x

Inner: Multiply the inner terms of each binomial.

(-3)(2x) = -6x

Last: Multiply the last terms of each binomial.

(-3)(3) = -9

A binomial is a two-term algebraic expression that contains variable, coefficient, exponents and constant, a binomial is an expression that has two unlike terms connected through an addition or subtraction operator in between.  

Now, let's combine the like terms:

4x^2 + 6x - 6x - 9

Notice that the terms 6x and -6x cancel each other out.

Simplifying further, we have:

4x^2 - 9

The correct answer is option B: 4x^2 - 9.

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Answer:

\(\{x=\frac{19-\sqrt{409} }{2}\ , \ x=\frac{19+\sqrt{409} }{2}\}\)

Step-by-step explanation:

x² = 19x + 12

⇔ x² - 19x - 12 = 0

Calculating the discriminant :

b² - 4ac = (-19)² - 4×1×(-12) = 409

The discriminant is positive ,then the equation has two solutions.

\(x=\frac{19-\sqrt{409} }{2} \ \ or\ \ x=\frac{19+\sqrt{409} }{2}\)

Using the normal distribution, given the graph at the end of this problem, we have that:

a. 99.74% of the homes are on the market between 14 and 86 days.

b. 0.1587 = 15.87% probability that a home is on the market for 62 days or more.

c. Approximately 95 homes were on the market between 26 and 50 days.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

Item a:

The proportion is the p-value of Z when X = 86 subtracted by the p-value of Z when X = 14, hence:

X = 86:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{86 - 50}{12}\)

\(Z = 3\)

\(Z = 3\) has a p-value of 0.9987.

X = 14:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{14 - 50}{12}\)

\(Z = -3\)

\(Z = -3\) has a p-value of 0.0013.

0.9987 - 0.0013 = 0.9974.

0.9974 = 99.74% of the homes are on the market between 14 and 86 days.

Item b:

The probability is 1 subtracted by the p-value of Z when X = 62, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{62 - 50}{12}\)

\(Z = 1\)

\(Z = 1\) has a p-value of 0.8413.

1 - 0.8413 = 0.1587.

0.1587 = 15.87% probability that a home is on the market for 62 days or more.

Item c:

The proportion is the p-value of Z when X = 50 subtracted by the p-value of Z when X = 26, hence:

X = 50:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{50 - 50}{12}\)

\(Z = 0\)

\(Z = 0\) has a p-value of 0.5.

X = 26:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{26 - 50}{12}\)

\(Z = -2\)

\(Z = -2\) has a p-value of 0.0228.

0.5 - 0.0228 = 0.4772.

Out of 200 homes:

0.4772 x 200 = 95.4

Approximately 95 homes were on the market between 26 and 50 days.

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Answer:

The theorem requiring proof;

A transversal perpendicular to one of two  parallel lines is also perpendicular to the other parallel line

The two column proof is as follows

Statement      \({}\)                                               Reason

RS ⊥ CD     \({}\)                                                   Given

AB ║ CD     \({}\)                                                  Given

The Slope of AB = The slope of CD    \({}\)       definition of parallel lines

The Slope of RS = -1/(The slope of CD)    \({}\) definition of perpendicular lines

The Slope of RS = -1/(The slope of AB)    \({}\) transitive property of equality

The Slope of RS = -1/(The slope of AB)    \({}\) definition of perpendicular lines

RS ⊥ AB

Step-by-step explanation:

Answer:

i dont know

Step-by-step explanation:

Answer:

The first one

\( log_{11} \: (x)\)

Step-by-step explanation:

f(x) = 11^x

Here are the steps to find the inverse of a function:

1. Let f(x)=y

2. Make x the subject of formula.

3. Replace y by x.

\(11 {}^{x} = y \\ \: log(11 {}^{x} ) = log(y) \\ x log(11) = log(y) \\ x = \frac{ log(y) }{ log(11) } = log_{11}(y) \\ f {}^{ - 1} (x) = log_{11}(x) \)

The solution to the initial value problem is √x = (1/3) \(y^{\frac{3}{2} }\) + 2/3.

Given: dx/dy = -2y, y = 3 when x = 0

To solve this, we'll separate the variables and integrate:

dx = -2y dy

Integrating both sides:

∫ dx = ∫ -2y dy

x = - \(y^{2}\) + C

Now we can apply the initial condition y = 3 when x = 0:

0 = - \(3^{2}\) + C

C = -9

Therefore, the solution to the initial value problem is x = - \(y^{2}\) - 9.

Given: dx/dy = xy, y = 1 when x = 0

We'll again separate the variables and integrate:

dx = xy dy

Integrating both sides:

∫ dx = ∫ xy dy

x = (1/2)\(y^{2}\) + C

Applying the initial condition y = 1 when x = 0:

0 = (1/2) \(1^{2}\) + C

C = -1/2

Thus, the solution to the initial value problem is x = (1/2)\(y^{2}\) - 1/2.

Given: dx/dy = \(e^{x+y}\), y = 0 when x = 0

Separating the variables and integrating:

dx = \(e^{x+y}\) dy

∫ dx = ∫ \(e^{x+y}\) dy

x = \(e^{x+y}\) + C

Using the initial condition y = 0 when x = 0:

0 = \(e^{0+0}\) + C

C = -1

Hence, the solution to the initial value problem is x = \(e^{x+y}\) - 1.

Given: dx/dy = √(y/x), y = 1 when x = 1

Again, separating the variables and integrating:

dx/√x = √y dy

Integrating both sides:

2√x = (2/3)\(y^{\frac{3}{2} }\) + C

Simplifying:

√x = (1/3)\(y^{\frac{3}{2} }\) + C

Applying the initial condition y = 1 when x = 1:

1 = (1/3)\(1^{\frac{3}{2} }\) + C

C = 2/3

Therefore, the solution to the initial value problem is √x = (1/3) \(y^{\frac{3}{2} }\) + 2/3.

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The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

4

Step-by-step explanation:

Answer:

The greatest common factor of 36 and 68 is 4

Step-by-step explanation:

36÷4=9

68÷4=17

The particular solution to the given differential equation is y_p = A + Bx + Cx^2 + D cos(x)

To solve the differential equation by undetermined coefficients, we assume a particular solution of the form:

y_p = A + Bx + Cx^2 + D cos(x) + E sin(x)

where A, B, C, D, and E are constants to be determined.

Now, let's find the derivatives of y_p:

y_p' = B + 2Cx - D sin(x) + E cos(x)

y_p'' = 2C - D cos(x) - E sin(x)

y_p''' = D sin(x) - E cos(x)

Substituting these derivatives into the differential equation:

(D sin(x) - E cos(x)) - 6(2C - D cos(x) - E sin(x)) = 4 - cos(x)

Now, let's collect like terms:

(-12C + 5D + cos(x)) + (5E + sin(x)) = 4

To satisfy this equation, the coefficients of each term on the left side must equal the corresponding term on the right side:

-12C + 5D = 4 (1)

5E = 0 (2)

cos(x) + sin(x) = 0 (3)

From equation (2), we get E = 0.

From equation (3), we have:

cos(x) + sin(x) = 0

Solving for cos(x), we get:

cos(x) = -sin(x)

Substituting this back into equation (1), we have:

-12C + 5D = 4

To solve for C and D, we need additional information or boundary conditions. Without additional information, we cannot determine the exact values of C and D.

Therefore, the particular solution to the given differential equation is:

y_p = A + Bx + Cx^2 + D cos(x)

where A, B, C, and D are constants.

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The probability of selecting a human character randomly in the game is \(\frac{1}{3}\)

The probability that a human character will be chosen when the player selects a character randomly can be calculated by dividing the number of human characters by the total number of available characters.

There are 8 animal characters and 4 human characters, making a total of 12 characters to choose from. Therefore, the probability of selecting a human character randomly is:

P(Human) = Number of human characters / Total number of characters

P(Human) = 4 / 12

Simplifying this fraction, we find:

P(Human) = 1 / 3

Therefore, the probability of selecting a human character randomly is 1/3 or approximately 0.333.

In the given scenario, there are a total of 8 animal characters and 4 human characters, making a total of 12 characters to choose from. When a player selects a character randomly, each character has an equal chance of being chosen. Since there are 4 human characters, the probability of selecting one of them is determined by dividing the number of human characters (4) by the total number of characters (12).

When we simplify the fraction 4/12, we find that it is equal to 1/3.

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Answer:

The vertex form is \(y=-(x+2)^2+4\)

Step-by-step explanation:

The statement that It is sufficient to test an analogy by asking what are its relevant similarities is false.

Analogy refers to the process of comparison of two or more items such that it explains some idea, or classification or familiarity and representativeness. Studying the analogies helps in enhancing, strengthening and reinforcing the skills in areas such as reading comprehension, homophones, deductive reasoning and logic.

Testing an analogy only by relevant similarities will produce partial results which might not be suitable to fully explain the reason. Hence, both relevant similarities and differences are to be considered for more detailed review. Different kind of analogies used to explain the differences or similarities are synonym and antonym, symbol and reference, degree of differences.

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The unit of measurement for coding the length of lacerations d)centimeters.

Centimeters are the most common unit of measurement used to code the length of lacerations. This is because they are a small enough unit of measurement that they can accurately describe even the smallest of lacerations.

Centimeters are also the most commonly used metric unit of length, making them the most useful when coding lacerations for medical records. In addition, centimeters are a more precise unit of measurement than inches and are accepted internationally as a unit of measurement, making them the best choice when coding lacerations.

Finally, centimeters are consistent units of measurement, making it easy to compare laceration lengths between different patients and different medical records.

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The value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

R = x^2/y

Where

y = 3.8 x 10^5

x = 5.9 x 10^4

Substitute y = 3.8 x 10^5 and x = 5.9 x 10^4 in the equation R = x^2/y

So, we have

R = (5.9 x 10^4)^2/3.8 x 10^5

Evaluate the exponent in the above equation

So, we have

R = 34.81 x 10^8/3.8 x 10^5

Evaluate the quotient in the above equation

So, we have

R = 9.16052631579 x 10^3

Approximate the above expression

So, we have

R = 9.2 x 10^3

Hence, the value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

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Answer:

The ratios 2.56/32 and 0.48/6 are equivalent; y = 0.08x.

Step-by-step explanation:

$2.56 for 32 oz is a unit price of $2.56/(32 oz) = $0.08/oz

$0.48 for 6 oz is a unit price of $0.48/(6 oz) = $0.08/oz

The unit prices are equal, so the cost of both sizes are proportional.

If x is the weight in oz, multiply the weight by 0.08 to get the cost, y, in dollars.

y = 0.08x

The ratios 2.56/32 and 0.48/6 are equivalent; y = 0.08x.

The value of x in the first question is 11 and the value of y is 3.

The value of x in the second question is 4 and the value of y is 4.

The value of x in the third question is -5 23/26 and the value of y is -1/13

2x + y = 25 equation 1

2x - 3y = 13 equation 2

The first step is to subtract equation 2 from equation 1:

-4y = -12

Divide both sides of the equation by -4

y = -12 / -4

y = 3

Substitute for y in equation 1:

2x + 3 = 25

2x = 25 - 3

2x = 22

x = 22 / 2

x = 11

-3x + 4y = -18 equation 1

x = -2y - 4

x + 2y = -4 equation 2

Multiply equation 2 by 2

2x + 4y = -8 equation 3

Subtract equation 3 from equation 2:

-5x = -20

Divide both sides of the equation by -5

x = -20 / -5

x = 4

Substitute for x in equation 2:

4 + 2y = -4

4 + 4 = 2y

8 = 2y

y = 8/2

y = 4

-2x + 3y = -15 equation 1

3x + 2y = -23 equation 2

Multiply equation 1 by 3 and equation 2 by 2

-6x + 9y = -45 equation 3

6x + 4y = -46 equation 4

Add equation 3 and equation4 together

13y = -1

y = -1/13

Substitute for y in equation 1:

-2x + 3(-1/13) = -15

-2x  -3/13 = -15

-2x = -15 + 3/13

-2x = 11 10/13

x = 11 10/13 ÷ -2

x = 153/13 x -1/2

x = -153/26

x =-5 23/26

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Answer:

11. D

12. C

Step-by-step explanation:

11. We need to find 2 numbers where the sum is -15 and the product is 56. Those two numbers are -7 and -8 so the answer is D.

12. Like the previous problem, we need to find 2 numbers where the sum is -9 and the product is 14. Those two numbers are -2 and -7 so the answer is C.

The solution to given differential equation is dx/dy = −2y−9x+1/2x−9y−6.

Differentiate implicitly to find dx/dy. x^2−9xy+y^2−6x+y−6=0

The implicit differentiation can be defined as a method of differentiating implicitly by considering y as a function of x. The implicit differentiation is used when it is hard to differentiate y explicitly with respect to x.

Given, x²− 9xy + y² − 6x + y − 6 = 0

Differentiating both sides with respect to y, we get

2x(1.dy/dx) - 9y - 9x(dy/dx) + 2y(1.dy/dx) + 1.dy/dx - 6 + 0= 0

Simplifying the above equation we get,

2x(dy/dx) - 9y - 9x(dy/dx) + 2y(dy/dx) + dy/dx = 6 - y

Now, take dy/dx common and simplify.

2x - 9x + 2y + 1 = dy/dx(-9) + (2y)

dx/dy = 2y-9x+1/2x+9y+6.

dx/dy = 2y+9x+1/2x+9y-6.

dx/dy = −2y+9x+1/2x+9y-6.

dx/dy = −2y−9x+1/2x−9y−6

The above solution explains the process of differentiating implicitly to find dx/dy. The given equation is differentiated with respect to y. The chain rule and the power rule are used to differentiate the equation. After simplifying the equation, we get the value of dx/dy.

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The total cost of repayment over 5 years is $23,300.

A loan repayment refers to the act of paying back money previously borrowed from a lender.

To get total cost of repayment, we must principal amount, the interest rate and the duration of the loan.

The formula to get total cost of repayment is given by \(Total Cost of Repayment = Principal + Interest\)

Interest = Principal * Interest Rate * Time

Given:

Principal amount is $20,000

Interest rate is 3.3%

Duration is 5 years.

Interest = $20,000 * 0.033 * 5

Interest = $3,300

Total Cost of Repayment = Principal + Interest

= $20,000 + $3,300

= $23,300.

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The camper should take 3 units of food, 1 first-aid kit, and 1 piece of clothing within the given constraints.

To determine the optimal number of each item the camper should take, we need to maximize the total benefit while considering the capacity constraint of the backpack.

Let's assume the camper takes x units of food, y first-aid kits, and z pieces of clothing.

The backpack has a capacity of 9 ft^3, and each unit of food takes up 2 ft^3. Therefore, the constraint for food is 2x ≤ 9, which simplifies to x ≤ 4.5. Since x must be a whole number and the camper needs at least one unit of food, the camper can take a maximum of 3 units of food.

Similarly, for first-aid kits, since each kit occupies 1 ft^3 and the camper must take at least one, the constraint is y ≥ 1.

For clothing, each piece takes 3 ft^3, and the constraint is z ≤ (9 - 2x - y)/3.

Now, we need to maximize the total benefit. The benefit of food is assigned as 7, first aid as 5, and clothing as 6. The objective function is 7x + 5y + 6z.

Considering all the constraints, the possible combinations are:

- (x, y, z) = (3, 1, 0) with a total benefit of 7(3) + 5(1) + 6(0) = 26.

- (x, y, z) = (3, 1, 1) with a total benefit of 7(3) + 5(1) + 6(1) = 32.

- (x, y, z) = (4, 1, 0) with a total benefit of 7(4) + 5(1) + 6(0) = 39.

- (x, y, z) = (4, 1, 1) with a total benefit of 7(4) + 5(1) + 6(1) = 45.

Among these combinations, the highest total benefit is achieved when the camper takes 3 units of food, 1 first-aid kit, and 1 piece of clothing.

Therefore, the camper should take 3 units of food, 1 first-aid kit, and 1 piece of clothing to maximize the total benefit within the given constraints.

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Answer:

(1/3)y= -2

Step-by-step explanation:

I don't have a step-by-step explanation but I hope this helps!!!

Answer:

All the lines have the same slope, m = 0, showing that they are all parallel.

Step-by-step explanation:

PLATO

Answer:

The fact that all of the lines have the same slope, m = 0, indicates that they are all parallel.

Step-by-step explanation:

the Greatest Common Divisor is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.

The greatest common divisor (GCD) is the biggest positive integer that divides two or more integers without leaving a remainder. It's also referred to as the greatest common factor (GCF) or the highest common factor (HCF). The Euclidean procedure, which continually divides the greater of the two integers by the smaller until a remainder of zero is obtained, is one way to calculate the GCD. The GCD is a crucial idea in mathematics, notably in number theory, and it has several applications in other disciplines, such as computer science and encryption. Finding the greatest common divisor of the coefficients of a linear equation in two variables is another popular geometry task.

How to solve?

The Greatest Common Divisor of 6,066 and 2,286 can be expressed as 252 = 6,066 * (-2) + 2,286 * 3. So, the GCD is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.

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The magnitude of the correlation coefficient, regardless of the sign, provides information about the strength of the linear relationship between variables.

The sample correlation coefficient, r, ranges between -1 and 1. A value of 1 or -1 indicates a perfect linear relationship, where all data points lie precisely on a straight line. On the other hand, a value close to 0 indicates a weak or no linear relationship.

In the given scenario, r = .40 indicates a moderate positive linear relationship. Although the correlation is not perfect (not equal to 1), it still suggests a moderate degree of association between the variables. The positive sign indicates that as one variable increases, the other tends to increase as well, but not necessarily in a strictly linear fashion.

On the other hand, r = -.60 indicates a stronger linear relationship, albeit in the negative direction. The negative sign signifies an inverse relationship, meaning that as one variable increases, the other tends to decrease, but again, not necessarily in a perfectly linear manner. The magnitude, which is the absolute value of the correlation coefficient, indicates a stronger relationship compared to r = .40.

Therefore, it is important to consider both the magnitude and the sign of the correlation coefficient to assess the strength and direction of the linear relationship between variables.

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