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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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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:

Option 4: 4¹¹

Step-by-step explanation:

Looking at the problem, I need to work out 4⁴ squared first, which is the same as 4⁸. Then multiply that by 4³ to get 4¹¹. What I did was simply add 3 + (4 * 2), which is 11.

Answer:

the 1 one

Step-by-step explanation:

Answer:

113.4=x(18)

x=6.3

Step-by-step explanation:

It says the product of a number, x, and 18 is 113.4. Since it says product there will be multiplication. The word "is" tells us that x and 18 equals 113.4. Is x= 6.3, 6.3 times 18 equals 113.4. This is a true equation.

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 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:

5, -4

Step-by-step explanation:

midpoint = x1 + x2/2 ,y1 + y2/2

= 0 + 10 /2 , -2 + -6/2

= 10/2 , -8/2

midpoint = 5, -4

Answer:-3/4

Step-by-step explanation:

5x+2=x-1

5x-x=-1-2

4x=-3

X=-3/4

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 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:

The probability is 7/11

Step-by-step explanation:

This is because there are 7 blue coins that you can grab out of 11 coins in total.

Answer:

1.8 inches

Step-by-step explanation:

Create a proportion where x is the distance on the map

[tex]\frac{1}{55}[/tex] = [tex]\frac{x}{99\\}[/tex]

Cross multiply and solve for x

55x = 99

x = 1.8

So, the distance on the map is 1.8 inches

Answer:

1.8 inches

Step-by-step explanation:

Scales on a map always represent the direct proportion.

Compare the distances as fractions:

Inches on the map

________________  =  [tex]\frac{1}{55} = \frac{x}{99}[/tex]

Miles on the ground

[tex]x = \frac{1x99}{55}[/tex]

[tex]x = \frac{99}{55}[/tex]

[tex]x = \frac{9}{5} = 1\frac{4}{5}[/tex]

x = 1.8 inches

Answer:

No

Step-by-step explanation:

Say n was equal to 2

7(2) + 6 =20

13(2) = 26

a) The determination of the equivalent units of production for materials and conversion costs is as follows:

                                                       Units       Materials       Conversion

Completed and transferred out  12,500        12,500            12,500

Ending work in process                2,850         2,850                1,710

Total equivalent units                  15,350       15,350              14,210

b) The calculation of the unit costs is as follows:

                                      Direct Materials     Conversion Costs

Production costs                $42,980                 $34,104

Total equivalent units           15,350                    14,210

Unit costs                              $2.80                      $2.40

c) The preparation of the cost reconciliation schedule is as follows:

                                         Direct Materials  Conversion Costs  Total Costs

Beginning work in process      $0                        $0                     $0

Cost to be accounted for       $42,980                 $34,104          $77,084

Total production costs           $42,980                 $34,104          $77,084

Costs accounted for units:

Completed / transferred out $35,000               $30,000         $65,000

Ending work in process          $7,980                   $4,104          $12,084

Total costs accounted for    $42,980                 $34,104         $77,084

Equivalent units are the multiplication of the number of physical (or actual) units on hand by the percentage of completion of the units.

1. Completed and transferred out 12,500 units.

2. Beginning work in process = $0

Ending work in process = 2,850 units 60% complete

Production Costs

Direct materials costs = $42,980 100% complete in terms of materials at July 31.

Direct labour = $15,700

Manufacturing overhead = $18,404

Total conversion costs = $34,104 ($15,700 + $18,404)

Equivalent units of production:

                                                       Units       Materials       Conversion

Completed and transferred out  12,500        12,500            12,500

Ending work in process                2,850         2,850 (100%)    1,710 (60%)

Total equivalent units                  15,350       15,350              14,210

Unit costs:

                                      Direct Materials     Conversion Costs

Production costs                $42,980                 $34,104

Total equivalent units           15,350                    14,210

Unit costs                              $2.80                      $2.40

                                 ($42,980 ÷ 15,350)    ($34,104 ÷ 14,210)

Cost Reconciliation Schedule:

                                         Direct Materials  Conversion Costs  Total Costs

Beginning work in process      $0                        $0                     $0

Cost to be accounted for       $42,980                 $34,104          $77,084

Total production costs           $42,980                 $34,104          $77,084

Costs accounted for units:

Completed / transferred out $35,000               $30,000         $65,000

                                 (12,500 x $2.80)              (12,500 x $2.40)

Ending work in process          $7,980                   $4,104          $12,084

                                   (2,850 x $2.80)              (1,710 x $2.40)    

Total costs accounted for    $42,980                 $34,104         $77,084

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Answer:

3 bagel recipe and 2 doughnut recipes are needed

Step-by-step explanation:

Given the expression

3d + 5b = 21 .. 1

d + b = 5 .... 2

We can use the expression to look for the amount of doughnut recipe and bagel recipe needed by solving the equations simultaneously

Multiply equation 1 by 1 and 2 by 3 to have;

3d + 5b = 21 .. 3

3d + 3b = 15 .... 4

Subtract 3 from 4

5b - 3b = 21 - 15

2b = 6

b = 6/2

b = 3

Substitute b = 3 into equation 2;

From 2,

d = b = 5

d + 3 = 5

d = 5 - 3

d = 2

Hence 3 bagel recipe and 2 doughnut recipes are needed

Answer:

The highest temperature was 33C warmer  than the lowest temperature.

Step-by-step explanation:

In order to find how many degrees warmer was the highest temperature, you have to calculate the difference between both temperatures:

23-(-10)

According to the sign rule, you have to change the subtraction sign  to addition and then, change the sign on the umber after that and add the numbers, which is:

23+10=33

According to this, the answer is that the highest temperature was 33C warmer  than the lowest temperature.

Answer:

90°

Step-by-step explanation:

Formula to find EACH interior angle:

[tex]\frac{(n-2) *180}{n}[/tex]

Given:

n (number of sides) = 4

Work:

[tex]\frac{(n-2) *180}{n} \\\\\frac{(4-2) *180}{4} \\\\\frac{(2) *180}{4} \\\\\frac{360}{4} \\\\90[/tex]

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.

Answer:

12/5

Step-by-step explanation:

Pythagorean theorem=> adjacent side=5

tanx=oppx/adjx

tanx=12/5

Answer:

Kala's first step.

Step-by-step explanation:

Solving linear equations.

But Kala did not do that. Instead, she skipped the first stages and moved on ahead, making her equation invalid.

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

Answer:

6

Step-by-step explanation:

because  i had the same question and the departments where 6

Answer:

Hey! I can teach you this.

The range is the distance between the highest and lowest numbers.

In this case, the lowest number is 3, and the highest is 54, making the range 54 - 3, which is 51.

Because 3 is 51 away from 54. I hope this helps you!

A hose will be needed vertical walls to run along the entire outer edge of the floor and up around the door of the greenhouse 88 feet .

To calculate the length of the hose needed to run along the entire outer edge of the floor and up around the door of the greenhouse, we need to consider the perimeter of the floor and the additional distance around the door.

The perimeter of the floor is the sum of the lengths of all four sides of the rectangle. Since the greenhouse is 20 ft long and 16 ft wide, the perimeter of the floor is:

Perimeter of floor = 2(length + width) = 2(20 ft + 16 ft) = 2(36 ft) = 72 ft

In addition to the floor perimeter, to account for the distance around the door. The door is 8 ft wide, so the additional distance around the door is:

Distance around door = 2(width of door) = 2(8 ft) = 16 ft

calculate the total length of the hose needed by adding the perimeter of the floor and the distance around the door:

Total length of hose = Perimeter of floor + Distance around door = 72 ft + 16 ft = 88 ft

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Answer:

Step-by-step explanation:

The formula for the sequence is an = [tex]2^n[/tex], where n is a positive integer. This formula is proven correct using mathematical induction.

To find a formula for the sequence defined by a1 = 1 and ak = 2ak-1, we can use mathematical induction to establish a pattern and then derive the formula. Here's how we can solve it step by step:

Step 1: Base case:

For k = 1, we have a1 = 1.

Step 2: Assume the formula holds for some positive integer n, where n ≥ 1.

Assume that an = [tex]2^{n-1[/tex] for some positive integer n.

Step 3: Use the assumption to prove the formula for the next term.

Now, let's prove that an+1 = [tex]2^n[/tex] holds.

Using the recursive formula ak = 2ak-1, we have:

an+1 = 2an

Substituting the assumed formula an = [tex]2^{n-1[/tex], we get:

an+1 = 2([tex]2^{n-1[/tex])

To simplify, we have:

an+1 = [tex]2^n[/tex]

Step 4: Conclusion:

Based on the assumption and the proof for the next term, we can conclude that the formula an = [tex]2^n[/tex] holds for all positive integers n ≥ 1.

Therefore, the formula for the sequence defined by a1 = 1 and ak = 2ak-1 is an = [tex]2^n[/tex].

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Answer:

Lol its in total of 34

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Add like terms to get

4.5a + 4b + 3.5c