On a certain hot summer's day, 344 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $537.00. How many children and how many adults swam at the public pool that day?​

Evaluating this expression will give us the value of f(3).

To find the value of f(3), we need to integrate the second derivative of f(x) twice and use the given initial conditions to determine the constants of integration.

Step 1: Integrate the second derivative f''(x) with respect to x to find the first derivative f'(x):

∫(f''(x)) dx = ∫(9x + 5sin(x)) dx

f'(x) = (9/2)x^2 - 5cos(x) + C1

Step 2: Use the given initial condition f'(0) = 2 to find the constant C1:

f'(0) = (9/2)(0)^2 - 5cos(0) + C1

2 = 0 - 5 + C1

C1 = 7

Step 3: Integrate f'(x) with respect to x to find the function f(x):

∫(f'(x)) dx = ∫[(9/2)x^2 - 5cos(x) + 7] dx

f(x) = (9/6)x^3 - 5sin(x) + 7x + C2

Step 4: Use the given initial condition f(0) = 3 to find the constant C2:

f(0) = (9/6)(0)^3 - 5sin(0) + 7(0) + C2

3 = 0 - 0 + 0 + C2

C2 = 3

Now we have the function f(x):

f(x) = (9/6)x^3 - 5sin(x) + 7x + 3

To find f(3), substitute x = 3 into the function:

f(3) = (9/6)(3)^3 - 5sin(3) + 7(3) + 3

Therefore, Evaluating this expression will give us the value of f(3).

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Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Answer:

The closest measurement is 69 meters.

Step-by-step explanation:

We already know that 22 meters is the diameter and to find the circumference you need to multiply the diameter with π. We don't know π, so we are going with 3.14. When you multiply 22 and 3.14 together, you get 69.08 meters. You round the answer to the nearest meter, so it's 69 meters. So, the closest measurement is 69 meters.

Only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.

The second-order homogeneous linear differential equation is given as:y'' - 9y' + 18y = 0This differential equation is a linear homogeneous equation. We will have two roots of the characteristic equation: r1 = 3, r2 = 6So, the general solution to the differential equation is given as:y = c1e3x + c2e6xwhere c1 and c2 are arbitrary constants.a. y(x) = e6x is a solution because it is a part of the general solution of the differential equation.y(x) = e−x, y(x) = 0, y(x) = 6x, y(x) = 3x, y(x) = ex are not solutions because they don't satisfy the differential equation. Hence, the correct options are:a. y(x) = e6xTherefore, only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.

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Answer:

2, 3, & 5 are reflections, the others are rotations.

Answer:

F=45

Step-by-step explanation:

G is 90 degrees and FC angles combined is 90 and divided is 45 each

Answer:

Negative

Step-by-step explanation:

From the scatter plot displayed, we could clearly observe the direction of the trend line as it produces a negative slope. For high values of y, the values of x are low and similarly, high values of x have low y values. Therefore, this kind of relationship between the two variables is considered negative.

Part a:Here, In be the number of n-digit quinary (0, 1, 2, 3, 4) sequences with(i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's).Since there is at least one 3 in the n-digit sequence, we start the sequence by selecting one of the 5 digits. There are five ways to do this.The next digits are chosen according to one of the three cases shown below:1) A string of (n-1) digits where no 0's are included in the string.2) A string of (n-1) digits where at least one 0 appears in the string before the first 3.3) A string of (n-1) digits where 3 appears before the first 0 in the string.The first string in case 1 can be formed in 4 different ways because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). There are 5 choices for the first digit and thus 5*4 quinary sequences of length n with at least one 3 and no 0's that start with the selected digit.The first string in case 2 can be formed in 5 different ways because the first 3 can appear in any position before the first 0. The remaining digits are chosen in n-2 positions because the first digit is already chosen (which is 3) and n-1 digits are left. There are 4 choices for each of the remaining n-2 positions because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). Thus, there are 5*5*4^(n-2) quinary sequences of length n with at least one 3 and at least one 0 that start with the selected digit.The first string in case 3 can be formed in n-1 different ways because the first 3 can appear in any position before the first 0. The remaining digits are chosen in n-2 positions because the first digit is already chosen (which is 3) and n-1 digits are left. There are 4 choices for each of the remaining n-2 positions because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). Thus, there are 5*(n-1)*4^(n-2) quinary sequences of length n with at least one 3 and at least one 0 that start with the selected digit.Therefore, the number of n-digit quinary sequences with (i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's) is the sum of the number of sequences in each of the three cases above, i.e.In = 5*4^(n-1) + 5*5*4^(n-2) + 5*(n-1)*4^(n-2)Part b:Recurrence: qn = 3q(n-1) + 4^(n-1) + 2.   q1 = 1. Let's see if qn = 39(n-1) + 5(n-1) satisfies this recurrence.q1 = 1 = 3(1-1) + 4^(1-1) + 2 = 0 + 1 + 2 = 3(0) + 5(1-1) + 1 = 0 + 0 + 1Thus, q1 = 1 satisfies the recurrence.qn+1 = 3qn + 4^n + 2 = 3(39n-1 + 5n-1) + 4^n + 2= 117(n-1) + 15(n-1) + 4^n + 2= 132(n-1) + 4^n + 3Using this formula, we can see that q2 = 91.Part c:Here, we need to finish the induction proof of this fact 2 that In = (n > 1).Induction Hypothesis: Assume true for n = k, i.e., Pk = Ik = 5*4^(k-1) + 5*5*4^(k-2) + 5*(k-1)*4^(k-2)Induction Step: To show that it is true for n = k+1, we need to show that the formula given above holds. The first digit can be any of the 5 digits (0, 1, 2, 3, 4) and the remaining digits can be selected in one of the three ways discussed in part (a).Case 1: n-1 digits with no 0'sThere are 4 choices for each of the n-1 digits, since 0 cannot be used. Therefore, there are 4^(n-1) such sequences with no 0's.Case 2: n-1 digits with at least one 0 before the first 3The first 3 can be in any of the n-1 positions, and the digits before it must be chosen from the set {0,1,2,4}. The remaining digits can be chosen in any of the 4 choices. Therefore, there are 5*(n-1)*4^(n-2) such sequences.Case 3: n-1 digits with 3 before 0We start by selecting one of the n-1 positions for the 3, then the remaining digits are chosen from the set {0,1,2,4}. There are (n-2) positions left for the remaining digits. There are 4 choices for each position, since 0 cannot be used. Therefore, there are 5*(n-1)*4^(n-2) such sequences.Thus, the total number of n-digit quinary sequences with at least one 3 and with the first 3 before the first 0 isIn = 5*4^(n-1) + 5*5*4^(n-2) + 5*(n-1)*4^(n-2) = qn+1 - qn = 132(n-1) + 4^n + 3 - (39(n-1) + 5(n-1)) = 93(n-1) + 4^n + 3which completes the induction proof.Part d:Since qn = 39n-1 + 5n-1, we haveqn+1 - qn = 132n - 39n - 5n = 88nTherefore, qn+1 = qn + 88nSubstituting qn = 39n-1 + 5n-1, we getqn+1 = qn + 88n = 39n-1 + 5n-1 + 88n = 39n + 5n + 88(n-1)Simplifying, we getqn+1 = 132(n-1) + 4^n + 3Therefore, en = In - In-1 = 93(n-1) + 4^n + 3 - 93(n-2) - 4^(n-1) - 3= 93n - 93(n-1) - 4^(n-1)= 93 - 4^(n-1)Thus, the closed form for en is en = 93 - 4^(n-1).

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The correct answer is: c. The n-th error term (e_n) can be predicted with e_n = 0.91 * e_n - 1.

This statement indicates that there is a correlation or relationship between consecutive error terms, where the n-th error term can be predicted based on the previous error term. In a simple linear regression model, the error terms are assumed to be independent and have no correlation with each other.

However, if there is a correlation between the error terms, it violates the assumption of independence, which can lead to biased and unreliable regression results. Therefore, this condition suggests that the result from the simple linear regression model could be potentially misleading.

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Answer:

2.08

Step-by-step explanation:

We know 2 is a whole number.

8/100 would be converted to the hundredths place.

0.000

     /\

      |

This is the hundredths place.

So the decimal is 2.08

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hope it helps

Answer:

hello your question is incomplete attached below is the complete question

a) Histogram shows positive skewness and the box plot depicts the fact that the median of the 3-iron club is bigger while the variance of the 5-wood club is more than that of 3-iron club when compared to their distance

b)The Median is a better choice because it is not affected by skewness or outliners

c) Josh should use Club 3 iron.   Reason : it has less variance

Step-by-step explanation:

A) Histogram and box plot is attached below

Histogram shows positive skewness and the box plot depicts the fact that the median of the 3-iron club is bigger while the variance of the 5-wood club is more than that of 3-iron club when compared to their distance

B) The Median is a better choice because it is not affected by skewness or outliners

Typical distance when Josh hits with a wedge  = 4 , distance when Josh hits with an 8 iron = 10.5

c) Josh should use Club 3 iron.   Reason : it has less variance

Answer:

The time the object will hit the ground is 2 s.

Step-by-step explanation:

Given;

h(t) = (-4.9t + 29.4)(t + 2)

Open the bracket;

h(t) = -4.9t² + 29.4t  -9.8t + 58.8

h(t) = -4.9t²  + 19.6t + 58.8

When the  object hit the ground, the final velocity will be zero;

[tex]v = \frac{dh}{dt} = 0 \\\\\frac{dh}{dt} = -9.8t + 19.6 = 0\\\\9.8t = 19.6\\\\t = \frac{19.6}{9.8} \\\\t = 2 \ s[/tex]

Therefore, the time the object will hit the ground is 2 s.

The solution is the zero function for all values of x and t.

To solve the heat equation u_t = 60u_xx with the given boundary and initial conditions, we can use separation of variables. We assume that u(x, t) can be written as a product of two functions, X(x) and T(t), such that u(x, t) = X(x)T(t).

Substituting this into the heat equation, we have:

X(x)T'(t) = 60X''(x)T(t)

Dividing both sides by 60X(x)T(t), we get:

T'(t)/T(t) = 60X''(x)/X(x)

The left side of the equation only depends on t, while the right side only depends on x. Since both sides are equal to a constant, we can set them equal to -λ², where λ is the constant.

T'(t)/T(t) = -λ²

X''(x)/X(x) = -λ²

Now, let's solve these two equations separately:

T'(t)/T(t) = -λ²

This is a separable ordinary differential equation. Integrating both sides with respect to t, we get:

∫ T'(t)/T(t) dt = ∫ -λ² dt

ln|T(t)| = -λ²t + C₁

Taking the exponential of both sides, we have:

T(t) = e^(-λ²t + C₁)

T(t) = e^(C₁) * e^(-λ²t)

T(t) = A * e^(-λ²t), where A = e^(C₁)

Now, let's solve the second equation:

X''(x)/X(x) = -λ²

This is also a separable ordinary differential equation. Integrating both sides with respect to x, we get:

∫ X''(x)/X(x) dx = ∫ -λ² dx

∫ (X''(x)/X(x)) dx = -λ²x + C₂

Using the fact that X''(x) = d²X(x)/dx², we can rewrite the equation as:

∫ (d²X(x)/dx²)/X(x) dx = -λ²x + C₂

∫ (d²X(x)/dx²) / X(x) dx = ∫ -λ² dx

∫ (1/X(x)) d²X(x)/dx² dx = -λ²x + C₂

Integrating both sides again, we have:

ln|X(x)| = -λ²x + C₂x + C₃

Taking the exponential of both sides, we get:

X(x) = e^(-λ²x + C₂x + C₃)

X(x) = e^(-λ²x) * e^(C₂x) * e^(C₃)

X(x) = B * e^(-λ²x) * e^(C₂x), where B = e^(C₃) * e^(C₂x)

Putting the solutions for T(t) and X(x) together, we have:

u(x, t) = X(x)T(t)

u(x, t) = (B * e^(-λ²x) * e^(C₂x)) * (A * e^(-λ²t))

We can combine the constants A and B into a single constant C:

u(x, t) = C * e^(-λ²x) * e^(C₂x) * e^(-λ²t)

Applying the boundary condition u(0, t) = 0, we have:

u(0, t) = C * e^(-λ²0) * e^(C₂0) * e^(-λ²t) = 0

This implies that C * e^(-λ²t) = 0. Since e^(-λ²t) is never zero, we must have C = 0.

Therefore, the solution to the heat equation with the given boundary and initial conditions is: u(x, t) = 0

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0 -18 is the answer to your question

A non-empty relation on set A which satisfies all the condition is {(10, 20), (20, 30), (30, 10)}.

To find a non-empty relation on set A = {10, 20, 30} that satisfies the given conditions (not reflexive, not transitive, and antisymmetric), we can define the following relation:

R = {(10, 20), (20, 30), (30, 10)}

Explanation:

Not Reflexive: A relation R on set A is reflexive if for every element x in A, (x, x) is in R. In this case, (10, 10), (20, 20), and (30, 30) are not present in the relation R, which makes it not reflexive.

Not Transitive: A relation R on set A is transitive if for every (x, y) and (y, z) in R, (x, z) is also in R. In this case, we have (10, 20) and (20, 30) in R, but (10, 30) is not present. Therefore, the relation R is not transitive.

Antisymmetric: A relation R on set A is antisymmetric if for every (x, y) and (y, x) in R, where x ≠ y, then x and y are not the same element. In this case, we have (10, 20) and (20, 10) in R, but 10 is not equal to 20. Similarly, we have (20, 30) and (30, 20) in R, but 20 is not equal to 30. Therefore, the relation R is antisymmetric.

By defining the relation R as {(10, 20), (20, 30), (30, 10)}, we satisfy all three conditions simultaneously: not reflexive, not transitive, and antisymmetric.

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Answer:

6

Step-by-step explanation:

do 9-6 then

The limit of the given expression as x approaches infinity is negative infinity. The limit of (4[tex]x^2[/tex] + 2) as x approaches negative infinity is positive infinity. The limit of (2x + 5x + 3) divided by (2x + 3) as x approaches negative infinity is 7/4.

In the first limit, as x approaches infinity, the dominant term in the expression is 2x^2. Since x^2 grows without bound as x becomes larger, the value of 2x^2 will also increase without bound, resulting in a limit of negative infinity.

In the second limit, as x approaches negative infinity, the dominant term in the expression is 4x^2. Similar to the first limit, since x^2 grows without bound as x becomes more negative, the value of 4x^2 will increase without bound, leading to a limit of positive infinity.

In the third limit, as x approaches negative infinity, both the numerator and denominator have the dominant term of 5x. Dividing the numerator and denominator by 5x, we get (2 + 5/x) divided by (2 + 3/x). As x approaches negative infinity, the terms with x in the denominator become negligible, resulting in the limit simplifying to 2/2, which equals 1. Therefore, the limit of (2x + 5x + 3)/(2x + 3) as x approaches negative infinity is 7/4.

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Answer:

[tex]178.98\ \text{m}^2[/tex]

Step-by-step explanation:

d = Diameter of flower bed = 16 m

Thickness of sidewalk = 3 m

r = Radius of flower bed = [tex]\dfrac{d}{2}=\dfrac{16}{2}=8\ \text{m}[/tex]

R = Radius of flower bed with sidewalk = [tex]8+3=11\ \text{m}[/tex]

The required area is given by

[tex]A=\pi(R^2-r^2)\\\Rightarrow A=3.14\times (11^2-8^2)\\\Rightarrow A=178.98\ \text{m}^2[/tex]

The radius of the sidewalk is [tex]178.98\ \text{m}^2[/tex].

The longest racial grouping of respondents to the 2012 GSS was non-Hispanic white, with 78.7%. The second-largest grouping was Black or African American, with 15.6%.

The General Social Survey (GSS) is a nationally representative survey of American adults that has been conducted annually since 1972. The GSS collects data on a wide range of topics, including race and ethnicity. In 2012, the GSS asked respondents to identify their race and ethnicity. The results showed that the largest racial grouping in the United States was non-Hispanic white, followed by Black or African American. in the 2012 GSS or any other related information, it is recommended to refer to the official documentation or reports from the General Social Survey (GSS).

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Answer:

m = 58°

x = 64°

Step-by-step explanation:

When a puck touches one side of the air hockey table,

All the angles formed are located at a point on a straight line.

Therefore, sum of angles formed is 180°.

m° + m° + 64° = 180°

2m + 64 = 180

2m = 180 - 64

2m = 116

m = 58°

m∠y = m = 58° [Alternate interior angles]

Similarly, on the other side of the table,

58° + y° + x° = 180°

58° + 58° + x° = 180°

x + 116° = 180°

x = 180 - 116

x = 64°

Answer:

C

Step-by-step explanation:

Add like terms to get

4.5a + 4b + 3.5c

Answer:

A. x = -2, x = 1.25

Step-by-step explanation:

Use the quadratic formula

x = [tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

4x² + 3x - 10 = 0

a = 4

b = 3

c = - 10

x = [tex]\frac{-3+\sqrt{3^{2}-4x4(-10) } }{2x4}[/tex]

Simplify

Evaluate the exponent

x = [tex]\frac{-3+\sqrt{9-4x4(-10)} }{2x4}[/tex]

Multiply the numbers

x = [tex]\frac{-3+\sqrt{9+160} }{2x4}[/tex]

Add the numbers

x = [tex]\frac{-3+\sqrt{169} }{2x4}[/tex]

Evaluate the square root

x = [tex]\frac{-3+13}{2x4}[/tex]

Multiply the numbers

x = [tex]\frac{-3+13}{8}[/tex]

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x = [tex]\frac{-3+13}{8}[/tex]

x = [tex]\frac{-3-13}{8}[/tex]

Solve

Rearrange and isolate the variable to find each solution

x = - 2

x = 1.25

Answer:

A. x = -2, x = 1.25

Step-by-step explanation:

Use the sum-product pattern

4x² + 3x - 10 = 0

4x² + 8x - 5x - 10 = 0

Common factor from the two pairs

(4x² + 8x) + (-5x - 10) = 0

4x (x + 2) - 5 (x + 2) = 0

Rewrite in factored form

4x (x + 2) - 5 (x + 2) = 0

(4x - 5)(x + 2) = 0

Create separate equations

(4x - 5)(x + 2) = 0

4x - 5 = 0

x + 2 = 0

Solve

Rearrange and isolate the variable to find each solution

x = 1.25

x = - 2

Answer:

Convert the decimal to a percentage by multiplying the decimal by  

100 .

500%

700%

900%

400%

Answer:

The answer is C

Step-by-step explanation:

The mean of math is 84, and the Mean of science is 85.

so, science is clearly one point higher

Answer:-3/4

Step-by-step explanation:

5x+2=x-1

5x-x=-1-2

4x=-3

X=-3/4

Here's an Overleaf PDF I created with an explanation for your question:

The true intercept and slope are both different from the estimated values based on statistical significance.

The p-value of the intercept coefficient and that of the slope coefficients are 0 and 0.02(2%) respectively. This means that they are statistically significant. Thus we can infer that the true intercept and slope is not equal to 0.

The standard error of the intercept coefficient is 6, which means that the true intercept is likely to be within 6 units of the estimated intercept. The standard error of the slope coefficient is 1, which means that the true slope is likely to be within 1 unit of the estimated slope.

Therefore, the true slope and intercept will be different from the estimated slope and intercept.

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Answer:

Yes it is possible. Start at (0,0) which is the orgin and go right on the x-axis 3 spaces, and go up on the y-axis 7 spaces to get to the ordered pair of (3,7).

Step-by-step explanation: