The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 318 people entered the park, and the admission fees collected totaled 952.00 dollars. How many children and how many adults were admitted?

True. Recursion is often necessary to solve certain types of problems that exhibit a recursive structure or require repeated subproblem solving.

Recursion is a programming technique where a function calls itself in its own definition. It allows for the decomposition of complex problems into smaller, more manageable subproblems that can be solved recursively. Recursion is particularly useful when problems exhibit a recursive structure, such as tree traversal, backtracking, or divide-and-conquer algorithms.

For example, problems like computing the factorial of a number, calculating Fibonacci numbers, or traversing a binary tree can be elegantly and efficiently solved using recursion. These problems can be broken down into smaller instances of the same problem until a base case is reached, and then the solutions are combined to solve the original problem.

However, it's worth noting that not all problems require recursion for their solution. There are alternative approaches, such as iterative loops or dynamic programming, which can be used depending on the problem's characteristics and requirements.

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The surface area of a polygon will be 4LW + 2W² square units.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

If the two sides of the rectangle become the same that is W = H. Then the surface area of the prism is given as,

SA = 2(LW + W × W + WL)

SA = 2(2LW + W²)

SA = 4LW + 2W²

The surface area of a polygon will be 4LW + 2W² square units.

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The vector product (cross product) of M and N is -10j + 155k - 362j - 6k + 24i.

The vector product (cross product) of two vectors M and N is calculated using the determinant method. The cross product of M and N is denoted as M x N. To calculate M x N, we can use the following formula,

M x N = (2 * (-1) - (-4) * (-6))i + ((-4) * 61 - 31 * (-1))j + (31 * (-6) - 2 * 61)k

Simplifying the equation, we get,

M x N = -10j + 155k - 362j - 6k + 24i

Therefore, the vector product M x N is -10j + 155k - 362j - 6k + 24i.

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Answer:

Interest at the end of the first year is $105.93

Step-by-step explanation:

$800 at 12.5% APR compounded monthly.

Interest at the end of the year

= $800 *( (1+0.125/12)^12 - 1 )

= $800 * 0.132416

= $105.93

Answer:

\(24 \times \frac{1}{3} = \frac{24}{3} = 8\)

8 pupils like football

\(24 \times \frac{1}{4} = \frac{24}{4} = 6\)

6 pupils like basketball

\(24 \times \frac{3}{8} = \frac{72}{8} = 9\)

9 pupils like athletics

and how many liked swimming?

8 + 9 + 6 = 23 pupils

24-23 = 1 pupils liked swimming

GOOD LUCK ツ

Here are the step-by-step workings for simplifying 3/7 (1+ square root of 36)^2 - (5- 1)^3:

1) square root of 36 = 6

2) (1 + 6)^2  = 49

3) (1 + square root of 36)^2 = 49

4) (5 - 1)^3 = (4)^3  = 64

5) 3/7(49) - 64 = 23 - 64= -41

Therefore, the simplified expression is:

3/7 (1+ square root of 36)^2 - (5- 1)^3 = -41

The workings are as follows:

- We calculate the square root of 36, which is 6.

- We then square (1 + 6), which gives us 49.

- Therefore, (1 + square root of 36)^2 =  49.

- We calculate (5 - 1)^3, which is (4)^3 = 64.  

- We multiply 3/7 by 49,  which gives us 23.

- Finally, we subtract 64 from 23 to get -41.

So the full expression simplifies to -41.

Let me know if you have any questions! I'm happy to provide any clarification or additional worked examples.

Answer:

Ice Cream= 2/7

Soccer: 3/14

Book= 5/14

Coin= 1/7

Answer: 88

Step-by-step explanation:

So we have 220:2.5, since 30 seconds is half a minute we can make that .5, so to get unit rate it’s formula is front divided by back,

220/2.5 = 88!

The given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3.

What is the linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

The equation 4x=3y-7

So, here we can solve this equation for the x as well as y equals,

Firstly we will solve for x:

4x = 3y - 7

dividing the whole equation by 4 we get,

4x/4 = (3y - 7)/4

x = (3y - 7)/4

Similarly, we will solve for y:

4x = 3y - 7

3y = 4x + 7

dividing the whole equation by 3 we get,

3y/3 = (4x + 7)/3

y = (4x + 7)/3

Hence, the given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3

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Answer:

y=-3x+4

Step-by-step explanation:

The researcher is measuring the reliability of a self-report test that measures anxiety in a group of participants. This is because if the test is not reliable, then we can not rely on the answers that participants give.

To measure reliability, the researcher is using split-half reliability by computing the correlation between the scores for the first 10 questions and the scores for the last 10 questions for each participant. This type of reliability measurement is commonly used with self-report tests and helps to determine how consistent the answers to the questions on the test are. If the two halves are highly correlated, then we can be more confident that the test is reliable.

An alternative measure of reliability is test-retest reliability, which assesses the consistency of a test over time. Test-retest reliability is calculated by administering the same test to the same group of participants on two different occasions and computing the correlation between the two sets of scores. If a test is reliable, then the scores obtained on the test should be relatively consistent over time.

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The derivative of\(-log_e(2x - 3) \ is\ 1/(2x - 3).\)

To find the derivative of\(-log_e(2x - 3)\), we can use the chain rule of differentiation. The chain rule states that if we have a composition of functions, f(g(x)), then the derivative of f(g(x)) with respect to x is given by \(f'(g(x)) * g'(x).\)

In this case, our outer function is\(-log_e(u)\), where u = 2x - 3. The derivative of \(-log_e(u)\) with respect to u is -1/u, using the derivative of the natural logarithm.

Next, we need to find the derivative of the inner function u = 2x - 3 with respect to x. Taking the derivative of 2x - 3 gives us 2.

Now, applying the chain rule, we multiply the derivative of the outer function by the derivative of the inner function:

\(-1/(2x - 3) * 2\)

Simplifying the expression, we get:

1/(2x - 3)

Therefore, the derivative of \(-log_e(2x - 3) is 1/(2x - 3).\)

The derivative of\(-log_e(2x - 3) \ is\ 1/(2x - 3)\). This result is obtained using the chain rule of differentiation, which allows us to differentiate composite functions. By applying the chain rule to the natural logarithm function and the inner function 2x - 3, we find that the derivative of the logarithm term is -1/(2x - 3), and the derivative of the inner function is 2. Multiplying these derivatives together gives us -2/(2x - 3). Simplifying further, we obtain 1/(2x - 3), which is the final derivative.

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Answer:

She earned $288 this week

Step-by-step explanation:

x = 12

Work = 2(12) + 8

24 + 8 = 32 hours

Earned = (12) - 3 = 9 per hour

32 × 9 = $288

I hope this helps!

We can writey + dy = 2x1x2 / (x1+x2) + 2x1Δx2/ (x1+x2) + 2x2Δx1/(x1+x2)+ 2Δx1Δx2/ (x1+x2)On subtracting y from both sides, we getdy = 2x1Δx2/ (x1+x2) + 2x2Δx1/ (x1+x2) + 2Δx1Δx2/ (x1+x2)

Given y= x1/(x1+x2)  we need to find the total differential of y.It is given that, y= x1/(x1+x2)Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we get + dy = (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)We know that dy = y - (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)

On further simplification, we get,dy = (Δx1(x2+Δx2))/(x1+Δx1+x2+Δx2)²-(Δx1x2)/((x1+Δx1+x2+Δx2)²)Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y= x1/(x1+x2) is given by dy = (-x1x2/(x1+x2)²) dx1 + (x1²/(x1+x2)²) dx2. Note: x1 and x2 are independent variables.

Therefore, dx1 and dx2 are their differentials.Given y=2x1x2 /(x1+x2) Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we gety + dy = 2(x1 + Δx1)(x2 + Δx2)/ (x1 + Δx1 + x2 + Δx2)On simplifying, we gety + dy = (2x1x2+2x1Δx2+2x2Δx1+2Δx1Δx2)/(x1+Δx1+x2+Δx2)

Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y=2x1x2 /(x1+x2) is given by dy = (2x2/(x1+x2)²) dx1 + (2x1/(x1+x2)²) dx2.

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Answer:

p=11

Step-by-step explanation:

let A(3,7),B(-6,1),C(9,p) be the points.

or

B(-6,1),A(3,7),C(9,p) are the points in the same line.

let A divides BCin the ratio k:1

\(3=\frac{9k+1(-6)}{k+1} \\3k+3=9k-6\\3k-9k=-6-3\\-6k=-9\\k=\frac{-9}{-6} =\frac{3}{2} \\so~ratio~is~\frac{3}{2} :1\\or\\3:2\\again\\7=\frac{3p+2(1)}{3+2} \\5*7=3p+2\\3p=35-2=33\\p=\frac{33}{3} =11\)

Answer:

86

Explanation:

3² × (2³ + 4) - 22

9 × (8 + 4) - 22

9 × 12 - 22

108 - 22

86

The 90 %confidence interval for the mean waste recycled per person per day for the population of Texas is (0.9, 1.5)

We will solve the problem in the following way,

Let us first assume that the population of Texas is approximately normal.

We will then find the critical value that will be used in constructing the confidence interval.

We have been given the following values:

The sample mean waste recycled per person per day= x'= 1.2 pounds

The sample Standard Deviation= s= 0.99 pounds

The sample size of residents of the state of Texas= n= 24 residents

The significance level= α= 0.1

The critical value that we get is t' = 1.714

Now we will calculate the Standard Error.

The formula for Standard error is

Error= \(\frac{s}{\sqrt{n} }\)

Substituting the values we know, we get

Error = \(\frac{0.99}{\sqrt{24} }\)

Error = 0.2021

Now we will calculate the margin of error

The formula for the Margin of error is

Margin= \(t' *\)\(\frac{s}{\sqrt{n} }\)

Substituting the known values, we get

margin= 1.714*0.2021

margin= 0.3463

Now we will calculate the lower limit and upper limit

Lower limit= x' - margin of error

= 1.2 - 0.3463

= 0.9

Upper limit = x' + margin of error

= 1.2 + 0.3463

=1.5

The 90% confidence interval is (0.9, 1.5) or 0.9 ≤ μ ≤ 1.5

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A collection of two or more inequalities in one or more variables is known as a system of inequalities.

Two or more inequalities in one or more variables make up a system of inequalities. When a problem calls for a variety of answers and those answers are constrained by multiple factors, systems of inequalities are used.

The intersection region of every solution in the system of inequalities is the system's solution.

Comparable to solving a system of linear equations, solving a system of linear inequalities involves locating the point (or points) of intersection, however this is not the case with inequalities. Instead, the area that fulfils each linear inequality will make up the solution set.

An inequality system's graph shows how the inequalities are resolved.

The system of inequality needs to be fixed by \($y > \frac{2}{3}$ \\ and $x \leq \frac{16}{3}$\)

Following is a description of the inequality system:

\($y > 2 x+4$$x+y \leq 6$\)

The charts for these are in the attached.

\($y > 2 x+4$ and $x+y \leq 6$\)

The graph shows us:

\($y > \frac{2}{3}$$x \leq \frac{16}{3}$\)

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The value of the integral ∫√x/(x - 4) dx from 9 to 16 is 3.022

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

∫√x/(x - 4) dx from 9 to 16

The above expression can be integrated using integration by parts method

When integrated, we have

∫√x/(x - 4) dx = 2(√x - ln(√x + 2) + ln(|√x - 2|))

Recall that the x values are from 9 to 16

This means that

∫√x/(x - 4) dx = 2(√16 - ln(√16 + 2) + ln(|√16 - 2|)) - 2(√9 - ln(√9 + 2) + ln(|√9 - 2|))

So, we have

∫√x/(x - 4) dx = 2(4 - ln(4 + 2) + ln(|4 - 2|)) - 2(3 - ln(3 + 2) + ln(|3 - 2|))

Solving further, we get

∫√x/(x - 4) dx = 2(4 - ln(6) + ln(2)) - 2(3 - ln(5) + ln(1))

Evaluate

∫√x/(x - 4) dx = 3.022

Hence, the value of the integral is 3.022

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By identifying and minimizing these uncertainties, it is possible to improve the accuracy of the data and obtain more reliable results.

Experimental uncertainties refer to the errors or variations that may occur in the process of conducting an experiment. There are several sources of experimental uncertainties that can affect the accuracy of the data, specifically:

1. Instrument uncertainties: These uncertainties arise from the limitations of the instruments used in the experiment. For example, if a measuring device has a limited resolution or if it is not properly calibrated, it can lead to inaccuracies in the measurements.

2. Operator uncertainties: These uncertainties arise from the variations in the way different people conduct the experiment. For example, if different people are measuring the same quantity, they may have different techniques, which can lead to variations in the measurements.

3. Environmental uncertainties: These uncertainties arise from the variations in the environment in which the experiment is conducted. For example, if the temperature or pressure of the environment changes during the experiment, it can affect the measurements.

Each of these sources of experimental uncertainties can affect the accuracy of the data by introducing errors or variations in the measurements. By identifying and minimizing these uncertainties, it is possible to improve the accuracy of the data and obtain more reliable results.

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Equilibrium potential increases by 2.303 times when Na is increased by factor 10.

Equilibrium potential increases by 4.606 times  Na is increased by factor 100.

Equilibrium potential decreases by 4.606 times Na is decreased by factor 100.

Given,

Sodium ion

Here,

Using nernst equation,

E = RT/nF \(ln\frac{Na_{ex} }{Na^+_{in} }\)

E = 58mV

When \({Na_{ex}\) increased by a factor of 10,

E' = RT/nF ln(10 Na)/Na

E/E' = 1/ln(10)

E/E' = 1/2.303

E' = 2.303E

Thus equilibrium potential increases by 2.303 times.

Now when Na is increased by a factor of 100

E' = 4.606E

Equilibrium potential increases by 4.606 times.

Now when Na is decreased by a factor of 100

E' = 4.606E

Equilibrium potential decreases by 4.606 times.

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Complete question is attached below.

The operations that would increase the value of a given number include the following:

A. Multiply the number by 10.

D. Divide the number by 0.1.

The operations that would decrease the value of a given number include the following:

B. Multiply the number by 0.1.

C. Divide the number by 10.

Multiplication is a mathematical operation which can be used to increase the value of a given number, especially by multiplying the number by a value that is greater than 1. Similarly, the value of a given number can also be increased by dividing it by a number that is lesser than 1 such as 0.1

Multiplication is a mathematical operation which can be used to decrease the value of a given number, especially by multiplying the number by a value that is lesser than 1. Similarly, the value of a given number can also be decreased by dividing it by a number that is greater than 1 such as 10.

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Answer:

x^4 +y+1

Step-by-step explanation:

The quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, -17) is \(-17(x-1)^{2}\).

The vertex form of a quadratic function is \(f(x) = a(x-h)^{2} + k\) where a, h, and k are constants and (h, k ) is the vertex of the graph of the function.

According to the given question we have

The graph has the vertex is (1, 0) and passes through (2, -17)

Since, the general form of a quadratic function in a vertex form  is

\(y = a(x-h)^{2}+ k\)

substitute, h = 1 and k = 0 in the above equation

⇒ \(y = a(x-1)^{2} +(0)^{2}...(i)\)

Also, the graph passes through the point (2, -17)

⇒ \(-17 = a(2-1)^{2}\)

⇒ -17 = a or a = -17

Substitute the value of a in equation (i).

⇒\(y = -17(x-1)^{2}\)

Therefore, the quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, -17) is \(-17(x-1)^{2}\).

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Answer:

(A.) & (D.) are your answers i hope you have a great day

Step-by-step explanation:

The answer is D. East Hills HS is negatively skewed, and Southview HS is positively skewed.

In order to compare the shapes of the distributions, we need to look at the skewness of the distributions.

Skewness is a measure of the asymmetry of a probability distribution. A distribution is said to be negatively skewed if the tail on the left-hand side of the probability density function is longer or fatter than the right-hand side. Conversely, a distribution is said to be positively skewed if the tail on the right-hand side of the probability density function is longer or fatter than the left-hand side.

Based on the answer choices, we can eliminate options B and C, as they both indicate that one of the distributions is symmetric, which is not possible if the other is skewed.

Now, we need to determine which distribution is positively skewed and which is negatively skewed.

Option A indicates that East Hills HS is negatively skewed, and Southview HS is symmetric. This is not possible since a negatively skewed distribution cannot be symmetric.

Option D indicates that East Hills HS is negatively skewed, and Southview HS is positively skewed. This is a valid comparison since it is possible for one distribution to be negatively skewed while the other is positively skewed.

Therefore, the correct answer is D. East Hills HS is negatively skewed, and Southview HS is positively skewed.

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Answer:

2.36lb/$

Solution:

(26lb) ÷ (11$) = 2.36lb/$

Answer: 2200 yards

Step-by-step explanation:

First find the unit rate, 660/3 = 220

So, Owen can jog 220 yards in one minute.

220 times 10 to find how much Owen can jog in 10 minutes.

220*10 = 2200.

Answer:

2200

Step-by-step explanation: