Every 12 minutes, Bus A completes a trip from P to X


to S to X to P. Every 20 minutes. Bus B completes a


trip from Q to X to T to x to Q. Every 28 minutes,


Bus C completes a trip from R to X to U to X to R. At


1:00 p. M. , Buses A, B and C depart from P. Q and R.


respectively, each driving at a constant speed, and each


turning around instantly at the endpoint of its route.


Each bus runs until 11:00 p. M. At how many times


between 5:00 p. M. And 10:00 p. M. Will two or more buses


arrive at X at the same time?

In the given formula we have variables:

If we have to solve it for P then it should be called 'Principal' or 'Loan amount'.

If we have to solve it for n then it should be called 'Number of payments' or 'Number of installments'.

Since n is the power of a number we need logarithm to solve it for n.

Answer:

"Principal (loan amount)"

"Term of the loan (in months)" or "Number of monthly payments"

Logarithms

Step-by-step explanation:

Monthly Payment Formula

\(M=\dfrac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\)

where:

If we solve for P, the name of the formula is "Principal (loan amount)".

If we solve for n, the name of the formula is "Term of the loan (in months)" or "Number of monthly payments".

When solving for n, we need to use logarithms:

\(\boxed{\begin{aligned}M&=\frac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\\\\M(\left(1+r\right)^n-1)&=Pr\left(1+r\right)^n\\\\\frac{\left(1+r\right)^n-1}{\left(1+r\right)^n}&=\frac{Pr}{M}\\\\1-\frac{1}{\left(r+1\right)^n}&=\frac{Pr}{M}\\\\\frac{1}{\left(r+1\right)^n}&=1-\frac{Pr}{M}\\\\\left(r+1\right)^{-n}&=1-\frac{Pr}{M}\\\\\ln \left(r+1\right)^{-n}&=\ln \left(1-\frac{Pr}{M}\right)\\\\-n\ln(r+1)&=\ln\left(1-\frac{Pr}{M}\right)\\\\n&=\frac{-\ln\left(1-\frac{Pr}{M}\right)}{\ln(r+1)}\end{aligned}}\)

The next three terms in the sequence are 116 , 159 and 209

We are supposed to find the next 3 terms in the sequence:

5, 6, 14, 29, 51, 80, ___, ___, ___.

Here we can are first supposed to find the pattern which is as follows:

\(6-5=1\\14-6=8\\29-14=15\\51-29=22\\80-51=29\\\)

Therefore difference between the numbers is 7 more than the previous one i.e,

\(1+7=8\\8+7=15\\15+7=22\\22+7=29\)

Let required three numbers be x, y and z

So \(x-80=29+7=36\\x=116\)

    \(y-116=36+7=43\\y = 159\)

and \(z-159=43+7=50\\z=209\)

Hence x = 116, y = 159 and z = 209

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If the resulting F-statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the variances are significantly different.

The F-test is a statistical test used to compare the variances of two groups.

In this problem, we will use it to compare the variance of the value added by the manufacturer and the variance of the cost of materials in manufacturing. The F-test is performed by dividing the larger variance by the smaller variance. The resulting F-statistic is then compared to the critical value of an F-distribution with degrees of freedom equal to the sample size minus one for each group.

Before we can perform the F-test, we need to determine which variable will be group 1. Typically, the variable with the smaller mean is designated as group 1. This is because we want to minimize the chance of making a type II error, which is failing to reject the null hypothesis when it is false. If we designated the variable with the larger mean as group 1, we might not detect a significant difference between the groups, even if one exists.

Once we have designated which variable will be group 1, we can perform the F-test. If the resulting F-statistic is greater than the critical value of the F-distribution, we reject the null hypothesis and conclude that the variances are significantly different.

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The dimensions of the rectangle are 10 feet (length) and 8 feet (width).

To find the dimensions of the rectangle with an area of 80 square feet and a width that is 2 feet less than the length,

follow these steps:

1. Let the length of the rectangle be L feet and the width be W feet.

2. According to the given information, W = L - 2.

3. The area of a rectangle is calculated by multiplying its length and width: Area = L × W.

4. Substitute the given area and the relationship between L and W into the equation: 80 = L × (L - 2).

5. Solve the quadratic equation: 80 = L² - 2L.

6. Rearrange the equation: L² - 2L - 80 = 0.

7. Factor the equation: (L - 10)(L + 8) = 0.

8. Solve for L: L = 10 or L = -8 (since the length cannot be negative, L = 10).

9. Substitute L back into the equation for W: W = 10 - 2 = 8.

So, the dimensions of the rectangle are 10 feet (length) and 8 feet (width).

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The volume of the given prototype is calculated as: Option D: 300in³

We are told that a watch company is developing packaging for its new watch. the designer uses an octagonal prism with a base area of 30 in² and rectangles with a length of 10 in to create a prototype for the new package.

Since the designer uses octagons with a base area of 30 in² and rectangles with a length of 10 in to create a prototype for the new package.

So here the volume is

= 30(10)

= 300

Therefore, The volume of the prototype is 300in³

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The probability that strictly more than 5 customers arrive in a given hour is approximately 0.8335 (or 83.35%).

Let's denote the random variable representing the number of customers arriving in an hour as X, which follows a Poisson distribution with a mean of 11.

To calculate P(X > 5), we need to sum the probabilities of X being greater than 5 for all possible values of X greater than 5.

P(X > 5) = 1 - P(X ≤ 5)

Using the Poisson distribution formula, we can calculate the cumulative probability of X being less than or equal to 5:

P(X ≤ 5) = Σ [e^(-λ) * (λ^k) / k!] for k = 0 to 5

Substituting the mean λ = 11 into the formula, we get:

P(X ≤ 5) = Σ [e^(-11) * (11^k) / k!] for k = 0 to 5

P(X ≤ 5) ≈ 0.1665

Finally, calculating P(X > 5) using the complement rule:

P(X > 5) = 1 - P(X ≤ 5)

P(X > 5) ≈ 1 - 0.1665

P(X > 5) ≈ 0.8335

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2 of 6 can be written as 2/6 or simplified as 1/3, which means that two parts out of six parts represent one-third of the whole.

To solve 2 of 6, we need to understand the basic concepts of fractions and division.

The formula that we can use to solve 2 of 6 is: 2/6 = 1/3

Fraction is a numerical value that represents a part of the whole.

A fraction consists of two parts: the numerator and the denominator.

The numerator is the number above the fraction line, and

the denominator is the number below the fraction line.

For example, in 2/6, 2 is the numerator, and 6 is the denominator.

To solve 2 of 6, we need to divide 2 by 6.

In other words, we need to find out how many parts of the whole 2 represents out of 6 equal parts.

The formula to divide fractions is:

a/b ÷ c/d = ad / bc.

To solve 2 of 6, we can rewrite it as 2/6 ÷ 1/1.

Then we can use the formula as follows:

2/6 ÷ 1/1 = 2/6 × 1/1 = 2/6

Therefore, 2 of 6 can be written as 2/6 or simplified as 1/3, which means that two parts out of six parts represent one-third of the whole.

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The lateral surface area of the frustum with a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches is 45π sq. inches is 45π sq. inches

The lateral surface area of the frustum is calculated using the given formula:

Lateral surface area of frustum = π × (sum of the radii) × √(difference of radii²  + height²)

Lower base radius of frustum = 6 inches

Upper base radius of frustum = 3 inches

Height of frustum = 4 inches

Lateral surface area of given frustum = π × (6 + 3) × √[(6 - 3)² + 4²]

                                                              = π × 9 × √[(9 + 16]

                                                              = 9π × 5

                                                              = 45π sq. inches

Hence, the lateral surface area of the given frustum is 45π sq. inches

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Answer:

Solving it mentally :-

It says 25% × 44. When we have a percent, change it to decimal and solve which would be easy to do it mentally.

25% = 0.25

0.25 × 44 = 11 *Answer is bolded.*

Solving it on paper :-

I have attached a picture of me doing it on paper.

Hope this helps, thank you :) !!

(a) The cost of 1 kg of turnips is £71.95, and

(b) The cost of 1 kg of mushrooms is £89.50.

To solve this problem, let's assign variables to the unknowns.

Let the cost of 1 kg of mushrooms be 'm' and the cost of 1 kg of turnips be 't'.

According to the given information:

Equation 1: 2m + 2.5t = 8.55

Equation 2: 3m + 4t = 13.10

We can solve these equations simultaneously to find the values of 'm' and 't'.

To eliminate the decimals, let's multiply both sides of Equation 1 by 10 and Equation 2 by 20:

20m + 25t = 85.50

60m + 80t = 262.00

Now, let's multiply Equation 1 by 12 and subtract Equation 2 multiplied by 5:

240m + 300t - (60m + 80t) = 1026.00 - 1310.00

180m + 220t = -284.00

We have a new equation:

180m + 220t = -284.00 ---(3)

Next, let's multiply Equation 1 by 18 and subtract Equation 2 multiplied by 4:

36m + 45t - (60m + 80t) = 154.35 - 524.00

-24m - 35t = -369.65

We have another new equation:

-24m - 35t = -369.65 ---(4)

Now, we have a system of linear equations with two variables. Let's solve this system by eliminating one variable.

Multiply Equation 3 by 35 and Equation 4 by 220:

6300m + 7700t = -9940.00 ---(5)

-5280m - 7700t = -81323.00 ---(6)

Adding Equations 5 and 6, we eliminate 't':

1020m = -91263.00

m = -91263.00/1020

m = -89.50

Substituting the value of 'm' back into Equation 3:

180(-89.50) + 220t = -284.00

-16110 + 220t = -284.00

220t = -284.00 + 16110

220t = 15826.00

t = 15826.00/220

t = 71.95.

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The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.

To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:

S(n) = 70000(1.2)

S(n) = 84000

The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)

S(1) = 84000

The percent increase of her salary is: S(n) = 70000(1.2)n

S(n) - S(n-1) / S(n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = 20%

Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.

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Answer:

Step-by-step explanation:its 27

The margin of error for a 95% confidence interval for the true mean mercury concentration in the Lower Willamette River is 0.02566.

The margin of error represents the range within which the true population mean is likely to fall. In this case, with a 95% confidence level, it means that we are 95% confident that the true mean mercury concentration in the Lower Willamette River falls within a specific range. The margin of error is calculated by multiplying the standard error (a measure of the variability of the sample mean) by a critical value, which is determined based on the desired confidence level and the sample size. In this case, the margin of error is rounded to five decimal digits and given as 0.02566.

It's important to note that the provided margin of error (0.02566) matches none of the options given (0.02566, 0.00199, 0.00261, none of the above). Therefore, the correct answer is "none of the above." It's crucial to carefully read and compare the options provided to ensure the accurate selection of the margin of error.

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Answer:

d>0

Step-by-step explanation:

brainliest please

The average value of x^2 for the given function f(x) is approximately 1.47.

To find the average value of x^2 for the given function f(x), we need to calculate the definite integral of x^2 multiplied by f(x) over the given range [0, 2], and then divide it by the integral of f(x) over the same range.

The average value of x^2 is given by:

Average value of x^2 = (1/(2-0)) * ∫[0, 2] (x^2 * f(x)) dx / ∫[0, 2] f(x) dx

Let's calculate the integrals:

∫[0, 2] (x^2 * f(x)) dx = ∫[0, 2] (x^2 * (9.6 / (-x^4 + 8x))) dx

= 9.6 * ∫[0, 2] (x^2 / (-x^4 + 8x)) dx

∫[0, 2] f(x) dx = ∫[0, 2] (9.6 / (-x^4 + 8x)) dx

Now, we can evaluate these integrals numerically.

Using numerical integration methods or a symbolic math software, we find:

∫[0, 2] (x^2 * f(x)) dx ≈ 3.99

∫[0, 2] f(x) dx ≈ 1.36

Finally, we can calculate the average value of x^2:

Average value of x^2 ≈ (1/(2-0)) * 3.99 / 1.36 ≈ 1.47

Therefore, the average value of x^2 for the given function f(x) is approximately 1.47.

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Answer:

it is 48 yards

Step-by-step explanation:

what You would do is this 12x4, which would equal 48

Answer:

32 yards

Step-by-step explanation:

First we need to know what perimeter is. It's similar but not the same as area. The perimeter is the length around the entire area, or in this case, a garden. We know 2 side lengths of the garden and because it is a rectangle we just have to add another width and length the same as these and add them all together.

4 + 4 + 12 + 12

8 + 24

32

So, the perimeter of the rectangular garden is 32 yards.

Hope this helps! If you have any additional questions please don't hesitate to ask me or your teacher to be sure you master the subject. :) Stay safe and please mark brainliest!

Answer:

1/2 is BIGGER than 20%

Step-by-step explanation:

1/2 is the same as 50% and 50% is greater than 20%

(Percent is out of 100 so half of 100 is 50.)

Hope that helps and have a great day!

Answer:

Well if it is a sale taking place then 1/2 off is less than 20% off

However if the prices are being increased then 1/2 more is bigger than 20% more.

Step-by-step explanation:

Step-by-step explanation:

a) given slope=m1=a/3

slope of parallel line=m2=5/6

parallel lines have equal slopes:

m1=m2

a/3=5/6

a=5/6×3

a=5/2

b) m1=a/3

m2=-2/9

lines are parallel:

m1=m2

a/3=-2/9

a=-2/9×3

a=-2/3

c)m1=a/3

m2=6

Slopes are perpendicular:

m1×m2=-1

a/3×6=-1

a×2=-1

a=-1/2

d)m1=a/3

m2=6/7

lines are perpendicular:

m1×m2=-1

a/3×6/7=-1

a×2/7=-1

a=-7/2

x - 2y = 2. …………(1). and x + y^2 =10. ………………(2).

Subtracting eqn. (1) from eqn. (2).

y^2 + 2y = 8.

or, y^2 +2y - 8 =0.

or, (y +4).(y-2)=0.

or, y = -4 , 2. and x = -6 , 6.

Thus, A(-6,-4) and B(6,2). let the mid point of AB is M , M((-6+6)/2,(-4+2)/2)

or, M(0, -1).

slope of AB = (2+4)/(6+6) = 1/2.

Slope of the perpendicular bisector of the line AB= -2.

Hence, the eqn. of the perpendicular bisector of AB is:-

y. +1 = - 2.(x - 0).

or, 2.x + y + 1 = 0. Answer.

Answer:

no

Step-by-step explanation:

the arrow is between 140 and 130 so it will be 135. If it was between 140 and 150 then it could be 145 degrees.

Option C, y = e^(x+y) + x^2 + 3x - 2, requires the use of implicit differentiation to find dy/dx.

The expression that requires the use of implicit differentiation to find dy/dx is option C: y = e^(x+y) + x^2 + 3x - 2.

Implicit differentiation is a technique used to differentiate equations where the dependent variable y is not explicitly expressed as a function of x. It involves differentiating both sides of the equation with respect to x, treating y as an implicit function of x.

Let's apply implicit differentiation to option C:

Starting with the equation: y = e^(x+y) + x^2 + 3x - 2

To find dy/dx, we differentiate both sides of the equation with respect to x:

d/dx(y) = d/dx(e^(x+y) + x^2 + 3x - 2)

Using the chain rule on the right side of the equation, we get:

dy/dx = d/dx(e^(x+y)) + d/dx(x^2) + d/dx(3x) - d/dx(2)

The derivative of e^(x+y) with respect to x requires the use of implicit differentiation. We treat y as an implicit function of x and apply the chain rule:

d/dx(e^(x+y)) = e^(x+y) * (1 + dy/dx)

The derivatives of the remaining terms on the right side are straightforward:

d/dx(x^2) = 2x

d/dx(3x) = 3

d/dx(2) = 0

Substituting these derivatives back into the equation, we have:

dy/dx = e^(x+y) * (1 + dy/dx) + 2x + 3

Next, we isolate dy/dx on one side of the equation by moving the term involving dy/dx to the left side:

dy/dx - e^(x+y) * dy/dx = e^(x+y) + 2x + 3

Factoring out dy/dx, we get:

(1 - e^(x+y)) * dy/dx = e^(x+y) + 2x + 3

Finally, we solve for dy/dx:

dy/dx = (e^(x+y) + 2x + 3) / (1 - e^(x+y))

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Answer:

\( KS = 12 \)

Step-by-step explanation:

Given that ∆KLM ~ ∆RSK, \( \frac{KL}{KR} = \frac{KM}{KS} \) (similarity theorem)

KL = 65

KR = 65 - 52 = 13

KM = 60

KS = ?

\( \frac{65}{13} = \frac{60}{KS} \)

Cross multiply

\( 65*KS = 60*13 \)

\( 65*KS = 780 \)

\( \frac{65*KS}{65} = \frac{780}{65} \)

\( KS = 12 \)

The values of x which satisfies the fractional inequality (x - 1) / (2 - x) ≥ 0 is x ≥ 1

(x - 1) / (2 - x) ≥ 0

This is a fractional inequality whose numerator is (x - 1) and the denominator is (2 - x)

(x - 1) / (2 - x) ≥ 0

cross product

(x - 1) ≥ 0 × (2 - x)

(x - 1) ≥ 0

x - 1 ≥ 0

Add 1 to both sides

x ≥ 1

Therefore, x ≥ 1 satisfies the inequality.

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The ball reaches its maximum height after 2 seconds.

To determine when the ball reaches its maximum height, we need to find when its velocity changes from positive to negative. The velocity of the ball is given by the derivative of its height, which is the function h'(t) = -16t. The ball's velocity is 0 when h'(t) = 0, so we need to solve -16t = 0.

The solution to this equation is t = 0. When t = 2, h'(t) = -32, which is negative, indicating that the ball is moving downward. So, the maximum height is reached when the velocity changes from positive to negative, which is at t = 2 seconds.

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Taking into account the definition of proportion, 12 students said their favorite color was blue.

The ratio is the comparison of two quantities and is measured from the division of two values. In other words, the ratio between two magnitudes is defined as their ratio or division; that is, given the quantities a and b, the ratio between them is a÷b.

The result of this division can be understood as how many times one quantity is in another.

The relationship of equality that exists between two ratios, that is, between two comparisons between two determined quantities, is known as a proportion. So if a/b corresponds to the ratio, then a/b = c/d equals a proportion.

At school, the teacher surveyed the color preferences of 21 students. Out of every 7 students surveyed, 4 said they liked blue the best. This can be expressed as a proportion as follow:

4÷7= x÷ 21

where x is the number of students of the 21 students surveyed who like blue.

Solving:

(4÷7)×21= x

12= x

Finally, 12 students said their favorite color was blue.

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Answer:

-1.3333

-1/2

3.25

Step-by-step explanation:

Ion need an explanation

Answer:

B: 9 outcomes

Step-by-step explanation:

you have 3 possibilites in the left pocket, and 3 in the right. Multiply the number of possibilites in each pocket to find how many total possibilites there are.

The third outer loop execution (i = 3), the loop compares the third element (12) with the remaining elements in the list (13, 14, 15) for a total of 3 comparisons

Assuming the outer loop is a standard loop that iterates through the list from the first to the second-to-last element, the number of comparisons made during the third outer loop execution (i = 3) would be 3.

During the first outer loop execution (i = 1), the loop compares the first element (10) with the rest of the elements in the list (11, 12, 13, 14, 15) for a total of 5 comparisons.

During the second outer loop execution (i = 2), the loop compares the second element (11) with the remaining elements in the list (12, 13, 14, 15) for a total of 4 comparisons.

During the third outer loop execution (i = 3), the loop compares the third element (12) with the remaining elements in the list (13, 14, 15) for a total of 3 comparisons.

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Assuming you are using a standard bubble sort algorithm, during the third outer loop execution (i = 3), there will be 3 comparisons made.

The given list (10, 11, 12, 13, 14, 15) and the number of comparisons made during the third outer loop execution (i = 3):

In the first outer loop iteration (i = 1), there will be 5 comparisons (comparing elements at positions 1-2, 2-3, 3-4, 4-5, and 5-6).

In the second outer loop iteration (i = 2), there will be 4 comparisons (comparing elements at positions 1-2, 2-3, 3-4, and 4-5).

In the third outer loop iteration (i = 3), there will be 3 comparisons (comparing elements at positions 1-2, 2-3, and 3-4).

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Answer:

456 drinks

Step-by-step explanation:

just multiply 11.40×40 and you get 456. that's how many drinks you can afford. hope i helped.