Ki Tae uses 54 meters of fencing to make a 6-sided outdoor dog pen. Two of the sides of the dog pen are each 15 meters long. The remaining 4 sides each have the same length.

The equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is[tex](x^2/289) + (y^2/225) = 1.[/tex]

To determine the equation of an ellipse given its foci and the length of its major axis, we need to use the standard form equation for an ellipse. The standard form equation for an ellipse centered at the origin is:

[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]

where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.

In this case, we know that the distance between the foci is equal to 2a, which means a = 34/2 = 17. The foci of the ellipse are given as (7, 17) and (7, -13). The foci lie on the major axis of the ellipse, and since their y-coordinates differ by 30 (17 - (-13) = 30), the length of the major axis is equal to 2b, which means b = 30/2 = 15.

Now we have the values of a and b, so we can substitute them into the standard form equation:

[tex](x^2/17^2) + (y^2/15^2) = 1[/tex]

Simplifying further, we have:

[tex](x^2/289) + (y^2/225) = 1[/tex]

Therefore, the equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is:

[tex](x^2/289) + (y^2/225) = 1.[/tex]

This equation represents an ellipse centered at the point (0, 0) with a semi-major axis of length 17 and a semi-minor axis of length 15.

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Answer:

The equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is

To determine the equation of an ellipse given its foci and the length of its major axis, we need to use the standard form equation for an ellipse. The standard form equation for an ellipse centered at the origin is:

where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.

In this case, we know that the distance between the foci is equal to 2a, which means a = 34/2 = 17. The foci of the ellipse are given as (7, 17) and (7, -13). The foci lie on the major axis of the ellipse, and since their y-coordinates differ by 30 (17 - (-13) = 30), the length of the major axis is equal to 2b, which means b = 30/2 = 15.

Now we have the values of a and b, so we can substitute them into the standard form equation:

Simplifying further, we have:

Therefore, the equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is:

This equation represents an ellipse centered at the point (0, 0) with a semi-major axis of length 17 and a semi-minor axis of length 15.

Step-by-step explanation:

a linear relationship or function is described in general as

y = f(x) = ax + b

Because the variable term has the variable x only with the exponent 1, this makes this a straight line - hence the name "linear".

here f(x) is P(x) :

P(x) = ax + b

now we are using both given points (ordered pairs) to calculate a and b :

20 = a×170 + b

2820 = a×220 + b

to eliminate first one variable we subtract equation 1 from equation 2 :

2800 = a×50

a = 2800/50 = 280/5 = 56

now, we use that in any of the 2 original equations to get b :

20 = 56×170 + b

b = 20 - 56×170 = 20 - 9520 = -9500

so,

P(x) = 56x - 9500

Answer:

5.9

Step-by-step explanation:

sin Θ = opp/hyp

sin 36° = x/10

x = 10 × sin 36°

x = 5.88

Answer: 5.9

Answer:

a. To fill in the missing data in the table, we can use the information given in the table along with the fact that the total number of employees is 186.

For value A: Since the total number of employees with no college credit is 28, and the total number of men is 79, we can subtract the number of men with some college (C) and college graduates (15) from the total number of men to find the missing value A. So A = 79 - C - 15.

For value B: Since the total number of women is 186, we can subtract the number of women with some college (D) and college graduates (22) from the total number of women to find the missing value B. So B = 186 - D - 22.

For value C: Since the total number of employees with some college is 81, and we have already determined the values A and D, we can subtract A and D from the total number of employees with some college to find the missing value C. So C = 81 - A - D.

For value D: Similarly, we can subtract B and E from the total number of women to find the missing value D. So D = 186 - B - E.

For value E: Since the total number of college graduates is 37 (15 men + 22 women), we can subtract the number of college graduates among men (15) from the total to find the missing value E. So E = 37 - 15.

For value F: Since the total number of employees is 186, we can subtract the total number of men (79) from the total to find the missing value F. So F = 186 - 79.

b. Joint relative frequency refers to the proportion of individuals that fall into a particular combination of categories. For example, the joint relative frequency of men with no college credit is the number of men with no college credit divided by the total number of employees (28/186). These data are joint and relative because they represent the proportion of individuals in a specific category combination relative to the total population.

c. To summarize the data using conditional relative frequency, we can calculate the proportion of individuals in each category given a specific condition. For example, we can calculate the conditional relative frequency of women who are college graduates by dividing the number of women who are college graduates (22) by the total number of women (186). Similarly, we can calculate the conditional relative frequency of men with some college by dividing the number of men with some college (C) by the total number of men (79).

To summarize the data using marginal relative frequency, we can calculate the proportion of individuals in each category by dividing the number of individuals in that category by the total number of individuals. For example, we can calculate the marginal relative frequency of men by dividing the total number of men (79) by the total number of employees (186). Similarly, we can calculate the marginal relative frequency of college graduates by dividing the total number of college graduates (37) by the total number of employees (186).

d. The data in the table can be analyzed to determine if there is an association or relationship between the variables. If the values in the table change depending on the categories of the other variable, then the variables are dependent. In this case, the data is dependent because the number of individuals with certain educational levels (no college credit, some college, college graduate) varies based on their gender. For example, there are different proportions of men and women in each educational category, indicating a relationship between gender and education level.

Step-by-step explanation:

The missing values in the two-way frequency table are filled based on the given values and the composition of the table. The table represents joint relative frequency, which is the proportion of specific groups in the total population. We can summarize the data using marginal and conditional relative frequencies, and the data are considered dependent because an employee's education level depends on their gender.

To fill in the missing values of the two-way frequency table, we need to use the given numbers and the rules of the two-way frequency table. Here are the strategies used for filling in the values for A through F:

The table will also represent joint relative frequency because each cell represents the joint occurrence of two categories (gender and education level). For example, the number of male employees with no college credit (28) divided by the total number of employees (186) is a joint relative frequency.

We may summarize the table data using conditional relative frequency and marginal relative frequency. The marginal relative frequency is the total of each row or column divided by the grand total. The conditional relative frequency would be, for example, the proportion of women among those with no college credit.

The data are dependent because the education level depends on whether the employee is a man or a woman.

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The solution to the system of equations using the inverse matrix method is x = -1, y = 2, z = 3.

To solve the system of equations using the inverse matrix method, we need to represent the system in matrix form.

The given system of equations can be written as:

| 5 -4 1 | | x | = | 12 |

| 1 7 -1 | [tex]\times[/tex]| y | = | -9 |

| 2 3 3 | | z | | 8 |

Let's denote the coefficient matrix on the left side as A, the variable matrix as X, and the constant matrix as B.

Then the equation can be written as AX = B.

Now, to solve for X, we need to find the inverse of matrix A.

If A is invertible, we can calculate X as [tex]X = A^{(-1)} \times B.[/tex]

To find the inverse of matrix A, we can use the formula:

[tex]A^{(-1)} = (1 / det(A)) \times adj(A)[/tex]

Where det(A) is the determinant of A and adj(A) is the adjugate of A.

Calculating the determinant of A:

[tex]det(A) = 5 \times (7 \times 3 - (-1) \times 3) - (-4) \times (1 \times 3 - (-1) \times 2) + 1 \times (1 \times (-1) - 7\times 2)[/tex]

= 15 + 10 + (-13)

= 12.

Next, we need to find the adjugate of A, which is obtained by taking the transpose of the cofactor matrix of A.

Cofactor matrix of A:

| (73-(-1)3) -(13-(-1)2) (1(-1)-72) |

| (-(53-(-1)2) (53-12) (5[tex]\times[/tex] (-1)-(-1)2) |

| ((5(-1)-72) (-(5(-1)-12) (57-(-1)[tex]\times[/tex](-1)) |

Transpose of the cofactor matrix:

| 20 -7 -19 |

| 13 13 -3 |

| -19 13 36 |

Finally, we can calculate the inverse of A:

A^(-1) = (1 / det(A)) [tex]\times[/tex] adj(A)

= (1 / 12) [tex]\times[/tex] | 20 -7 -19 |

| 13 13 -3 |

| -19 13 36 |

Multiplying[tex]A^{(-1)[/tex] with B, we can solve for X:

[tex]X = A^{(-1)}\times B[/tex]

= | 20 -7 -19 | | 12 |

| 13 13 -3 | [tex]\times[/tex] | -9 |

| -19 13 36 | | 8 |

Performing the matrix multiplication, we can find the values of x, y, and z.

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Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

[tex]\boxed{I = \frac{P \times R \times T}{100}}[/tex],

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

[tex]6180 = \frac{P \times 6.12 \times 28}{100}[/tex]

⇒ [tex]6180 \times 100 = P \times 171.36[/tex]     [Multiplying both sides by 100]

⇒ [tex]P = \frac{6180 \times 100}{171.36}[/tex]    [Dividing both sides of the equation by 171.36]

⇒ [tex]P = \bf 3606.44[/tex]

Therefore, James needs to invest $3606.44.

Answer:

Step-by-step explanation:

Let's calculate the expression step by step:

93 - (15 × 10) + (160 ÷ 16)

First, we perform the multiplication:

93 - 150 + (160 ÷ 16)

Next, we perform the division:

93 - 150 + 10

Finally, we perform the subtraction and addition:

-57 + 10

The result is:

-47

Therefore, 93 - (15 × 10) + (160 ÷ 16) equals -47.

┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈

✦ The number is - 5

┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈

[tex]\begin{gathered} \; \sf{\color{pink}{Let \; the \; other \; number \; be \; (x)::}} \\ \end{gathered}[/tex]

Atq,,

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x + ( - 7) \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x - 7 \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x - 21 = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 36 + 21} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 15} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{x = \dfrac{\cancel{ - 15}}{\cancel{ \: 3}}} \qquad \bigg \lgroup \sf{Cancelling \: by \: 3} \bigg \rgroup \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink} :\dashrightarrow \underline{\color{pink}\boxed{\colorbox{black}{x = - 5}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]

The answer is:

Work/explanation:

The product means we multiply two numbers.

Here, we multiply 3 and a number increased by -7; let that number be z.

So we have

[tex]\sf{3(z+(-7)}[/tex]

simplify:

[tex]\sf{3(z-7)}[/tex]

This equals -36

[tex]\sf{3(z-7)=-36}[/tex]

[tex]\hspace{300}\above2[/tex]

[tex]\frak{solving~for~z}[/tex]

Distribute

[tex]\sf{3z-21=-36}[/tex]

Add 21 on each side

[tex]\sf{3z=-36+21}[/tex]

[tex]\sf{3z=-15}[/tex]

Divide each side by 3

[tex]\boxed{\boxed{\sf{z=-5}}}[/tex]

Approximately 76.5% of the student body at Walton High School loves math.

To determine the percentage of the student body that loves math, we need to consider the proportions of males and females in the Walton High School student body and their respective percentages of loving math.

Given that 45% of the student body are males, we can deduce that 55% are females (since the total percentage must add up to 100%). Now let's calculate the percentage of the student body that loves math:

For the females:

55% of the student body are females.

90% of the females love math.

So, the percentage of females who love math is 55% * 90% = 49.5% of the student body.

For the males:

45% of the student body are males.

60% of the males love math.

So, the percentage of males who love math is 45% * 60% = 27% of the student body.

To find the total percentage of the student body that loves math, we add the percentages of females who love math and males who love math:

49.5% + 27% = 76.5%

As a result, 76.5% of Walton High School's student body enjoys maths.

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Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

Answer:

113.1 is the answer. I used the arbitory height of 4 so the volume of both are now 314.16 and 201.06

314.16-201.06=113.1

Answer:

arc LKF = 208°

Step-by-step explanation:

the angle FLX between the tangent and the secant is half the measure of the intercepted arc LKF , then intercepted arc is twice angle FLX , so

arc LKF = 2 × 104° = 208°

Let's use the fact that the sum of the angles of a triangle is always 180 degrees to solve this problem. Let the two equal angles be x, then the third angle is x + 45.Let's add all the angles together:x + x + x + 45 = 180Simplifying this equation, we get:3x + 45 = 180Now, we need to isolate the variable on one side of the equation. We can do this by subtracting 45 from both sides of the equation:3x = 135Finally, we can solve for x by dividing both sides of the equation by 3:x = 45Therefore, the value of x is 45 degrees.

Answer:

Step-by-step explanation:

180 = x + x + x + 45

180 - 45 = 3x

135 = 3x

x = 135 : 3

x = 45°

------------------

check

180 = 45 + 45 + 45 + 45

180 = 180

same value the answer is good

Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.

Alonso has $21.00 to spend on eggs and avocados. He buys eggs that cost $2.50, which leaves him with $18.50. Since the store only sells avocados in bags of 3, he will need to find the cost per bag in order to calculate how many bags he can buy.

First, divide the cost of 3 avocados by 3 to find the cost per avocado. $5.00 ÷ 3 = $1.67 per avocado.

Next, divide the money Alonso has left by the cost per avocado to find how many avocados he can buy.

$18.50 ÷ $1.67 per avocado = 11.08 avocados.

Since avocados only come in bags of 3, Alonso needs to round down to the nearest whole bag. He can buy 11 avocados, which is 3.67 bags.

Thus, he will buy 3 bags of avocados.Let's test our answer to make sure that Alonso has spent all his money:

$2.50 for eggs3 bags of avocados for $5.00 per bag, which is 9 bags of avocados altogether. 9 bags × $5.00 per bag = $45.00 spent on avocados.

Total spent:

$2.50 + $45.00 = $47.50

Total money had:

$21.00

Remaining money:

$0.00

Since Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.

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When 2 items are selected without replacement from a population of 6 items, there are 15 possible samples that can be formed. Option A.

To determine the number of possible samples when 2 items are selected at random without replacement from a population of 6 items, we can use the concept of combinations.

The number of combinations of selecting k items from a set of n items is given by the formula C(n, k) = n! / (k! * (n-k)!), where n! represents the factorial of n.

In this case, we have a population of 6 items and we want to select 2 items. Therefore, the number of possible samples can be calculated as:

C(6, 2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5 * 4!) / (2! * 4!) = (6 * 5) / (2 * 1) = 15. Option A is correct.

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Answer:

f(3r - 1) = -6r + 6

Step-by-step explanation:

To find f(3r - 1), we substitute 3r - 1 for x in the expression for f(x) and simplify:

f(x) = 4 - 2x

f(3r - 1) = 4 - 2(3r - 1)

= 4 - 6r + 2

= -6r + 6

So, f(3r - 1) = -6r + 6.

Answer:

the first 2

Step-by-step explanation:

let me know if it is wrong

The exact circumferences of the inscribed and circumscribed circles for the given polygons are 8π cm and 15π cm, respectively.

To find the exact circumference of a circle inscribed or circumscribed by a polygon, we can use the Pythagorean theorem to determine the diameter of the circle.

In the case of an inscribed polygon, the diameter of the circle is equal to the diagonal of the polygon. Let's consider the polygon with a diagonal of 8 cm. If we draw a line connecting two non-adjacent vertices of the polygon, we get a diagonal that represents the diameter of the inscribed circle.

Using the Pythagorean theorem, we can find the length of this diagonal. Let's assume the sides of the polygon are a and b. Then the diagonal can be found using the equation: diagonal^2 = a^2 + b^2. Substituting the given values, we have 8^2 = a^2 + b^2. Solving this equation, we find that a^2 + b^2 = 64.

For the circumscribed polygon with a diagonal of 15 cm, the diameter of the circle is equal to the longest side of the polygon. Let's assume the longest side of the polygon is c. Therefore, the diameter of the circumscribed circle is 15 cm.

Once we have determined the diameter of the circle, we can calculate its circumference using the formula C = πd, where C is the circumference and d is the diameter.

For the inscribed circle, the circumference would be C = π(8) = 8π cm.

For the circumscribed circle, the circumference would be C = π(15) = 15π cm.

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Answer:

x = 2

Step-by-step explanation:

We are given the following equation:

[tex]\sqrt{x+7} -1=x[/tex], which we want to solve for x.

To do this, we should isolate the square root on one side, then square both sides. We can then solve the equation as normal, but then we have to check the domain in the end for any extraneous solutions.

Start by adding 1 to both sides.

[tex]\sqrt{x+7} -1=x[/tex]

            +1      +1

________________________

[tex]\sqrt{x+7} = x+1[/tex]

Now, square both sides.

[tex](\sqrt{x+7} )^2= (x+1)^2[/tex]

We get:

x + 7 = x² + 2x + 1

Subtract x + 7 from both sides.

x + 7 = x² + 2x + 1

-(x+7)   -(x+7)

________________________

0 = x² + x - 6

This can be factored to become:

0 = (x+3)(x-2)

Solve:

x+3 = 0

x = -3

x-2 = 0

x = 2

We get x = -3 and x = 2. However, we must check the domain.

Substitute -3 as x and 2 as x into the original equation.

We get:

[tex]\sqrt{-3+7} -1 = -3[/tex]

[tex]\sqrt{4} -1 = -3[/tex]

2 - 1 = -3

-1 = -3

This is an untrue statement, so x = -3 is an extraneous solution.

We also get:

[tex]\sqrt{2+7} -1 = 2[/tex]

[tex]\sqrt{9}-1=2[/tex]

3 - 1 = 2

2 = 2

This is a true statement, so x = 2 is a real solution.

Our only answer is x = 2.

Answer:

45 inches represent 55 miles on the scale drawing.

Step-by-step explanation:

To solve this proportion, we can set up the following ratio:

9 inches / 11 miles = x inches / 55 miles

We can cross-multiply to solve for x:

9 inches * 55 miles = 11 miles * x inches

495 inches = 11 miles * x inches

Now, we can isolate x by dividing both sides by 11 miles:

495 inches / 11 miles = x inches

Simplifying the expression:

45 inches = x inches

Answer: D. 145°

Step-by-step explanation:

Since it is a parallelogram given by the symbol, then angle B is equal to angle D which is 145°.

The shape is represented as below

The figure is of three shapes, the firs two are whole numbers then the last is a fraction.

Adding them results to

shape 1 + shape 2 + shape 3

1 + 1 + 1/4

As one fraction

= 9/4

as a mixed number

= 2 1/4

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Answer:

Hope this helps and have a nice day

Step-by-step explanation:

To find the value of x, we can use the formula:

Time = Distance / Speed

Let's calculate the time taken to travel from Q to P and back to Q.

From Q to P:

Distance = 12 km

Speed = 6 km/h

Time taken from Q to P = Distance / Speed = 12 km / 6 km/h = 2 hours

From P to Q:

Distance = 12 km

Speed = (6 + x) km/h

Time taken from P to Q = Distance / Speed = 12 km / (6 + x) km/h

Given that the total time taken for the round trip is 3 hours 20 minutes, we can convert it to hours:

Total time = 3 hours + (20 minutes / 60) hours = 3 + (1/3) hours = 10/3 hours

According to the problem, the total time is the sum of the time from Q to P and from P to Q:

Total time = Time taken from Q to P + Time taken from P to Q

Substituting the values:

10/3 hours = 2 hours + 12 km / (6 + x) km/h

Simplifying the equation:

10/3 = 2 + 12 / (6 + x)

Multiply both sides by (6 + x) to eliminate the denominator:

10(6 + x) = 2(6 + x) + 12

60 + 10x = 12 + 2x + 12

Collecting like terms:

8x = 24

Dividing both sides by 8:

x = 3

Therefore, the value of x is 3.

Answer:

x = 3

Step-by-step explanation:

speed  = distance / time

time = distance / speed

Total time from P to Q to P:

T = 3h 20min

P to Q :

s = 6 km/h

d = 12 km

t = d/s

= 12/6

t = 2 h

time remaining t₁ = T - t

= 3h 20min - 2h

=  1 hr 20 min

= 60 + 20 min

= 80 min

t₁ = 80/60 hr

Q to P:

d₁ = 12km

t₁ = 80/60 hr

s₁ = d/t₁

[tex]= \frac{12}{\frac{80}{60} }\\ \\= \frac{12*60}{80}[/tex]

= 9

s₁ = 9 km/h

From question, s₁ = (6 + x)km/h

⇒ 6 + x = 9

⇒ x = 3

Trent will need approximately 2.86 bottles of waterproof spray to cover his tent.

To calculate the number of bottles of waterproof spray Trent will need to cover his tent, we first need to find the surface area of the tent.

The surface area of a square-based pyramid is given by the formula:

Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)

The base of the pyramid is a square with a side length of 14 feet, so the base area is:

Base Area = (Side Length)^2 = 14^2 = 196 square feet

To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by one side of the base, the height of the pyramid, and the slant height. The height of the pyramid is given as 8 feet, and half the length of the base is 7 feet.

Using the Pythagorean theorem:

[tex]Slant Height^2 = (Half Base Length)^2 + Height^2[/tex]

[tex]Slant Height^2 = 7^2 + 8^2Slant Height^2 = 49 + 64Slant Height^2 = 113Slant Height ≈ √113 ≈ 10.63 feet[/tex]

Now we can calculate the surface area of the tent:

Surface Area = 196 + (0.5 x 4 x 10.63)

Surface Area = 196 + (2 x 10.63)

Surface Area = 196 + 21.26

Surface Area ≈ 217.26 square feet

Since each bottle of waterproof spray covers 76 square feet, we can divide the total surface area of the tent by the coverage of each bottle to find the number of bottles needed:

Number of Bottles = Surface Area / Coverage per Bottle

Number of Bottles = 217.26 / 76

Number of Bottles ≈ 2.86

Therefore, Trent will need approximately 2.86 bottles of waterproof spray to cover his tent. Since we can't have a fraction of a bottle, he will need to round up to the nearest whole number. Therefore, Trent will need 3 bottles of waterproof spray to fully waterproof his tent.

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The computed mean of 52.4 and the actual mean of 52.7 suggest a close relationship in terms of central tendency.

A computed mean is a statistical measure calculated by summing up a set of values and dividing by the number of observations. In this case, the computed mean of 52.4 implies that when the values are averaged, the result is 52.4.

The actual mean of 52.7 refers to the true average of the population or data set being analyzed. Since it is higher than the computed mean, it indicates that the sample used for computation might have slightly underestimated the true population mean.

However, the difference between the computed mean and the actual mean is relatively small, with only a 0.3 unit discrepancy.

Given the proximity of these two values, it suggests that the computed mean is a reasonably accurate estimate of the actual mean.

However, it's important to note that without additional information, such as the sample size or the variability of the data, it is difficult to draw definitive conclusions about the relationship between the computed mean and the actual mean.

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What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D

Given that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.

We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..

ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.

In ΔABC, side between ∠A and ∠C is AC,

in ΔXYZ, side between ∠X and ∠Z is XZ.

Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.

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Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).

The given functions are f(x) = 3x² and g(x) = -2².

To understand the difference between their graphs, let's examine the characteristics of each function individually:

Function f(x) = 3x²:

The coefficient of x² is positive (3), indicating an upward-opening parabola.

The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.

The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.

Function g(x) = -2²:

The coefficient of x² is negative (-2), indicating a downward-opening parabola.

The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.

The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.

Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.

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