2. Decide whether enough information is given to prove that the triangles are congruent using
the HL Congruence Theorem. Explain how you have concluded your answer.

Answer:

Rise and run

Step-by-step explanation:
Lets have it in slope intercept form
y=3/5x

Therefore our slope is 3/5 and y-intercept is (0,0)

Now we can start to graph. Start on our Y-intercept which is zero. Let's count 3 spaces up, which is our rise, then lets count 5 spaces to our right, which is our positive run, and plot a dot on our final point. You can do the same negative to graph our opposing points. Start on our 0,0 y-intercept, and count down 3 spaces. Then count 5 spaces to the left, and plot a dot on your final point. Now, let's draw a line through our points (-5, -3), (0,0), and (5,3)!

Answer:8/3

Step-by-step explanation:

Total number of hours: 24

Total number of guards: 9

Equation: Total number of hours/ total number of guards

24/9= 8/3 hour shifts or 2.66667 hour shifts for each guard.

The equation of the line of best fit is a mathematical representation of the relationship between two variables. It is typically written in the form,

y = mx + b.

where m is the slope and b is the y-intercept. To find the equation of the line of best fit for a set of data, you can use a graphing calculator or statistical software to calculate the slope and y-intercept.

      Alternatively, you can use the formula for the slope of a line (m = (y2 - y1)/(x2 - x1)) and the point-slope form of a line (y - y1 = m(x - x1)) to find the equation of the line of best fit. Once you have the slope and y-intercept, you can plug these values into the equation y = mx + b to find the equation of the line of best fit.

For more such questions on Equation of line, visit:

brainly.com/question/21511618

#SPJ11

The solution for u is 36.

To solve for u using the multiplicative property of equality, we need to isolate u on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction that is attached to u. The reciprocal of (5/6) is (6/5), so we can multiply both sides of the equation by (6/5) to get:

(6/5) * 30 = (6/5) * (5/6) * u

Simplifying the right side of the equation gives us:

(6/5) * 30 = u

Multiplying the fraction and the whole number gives us:

(180/5) = u

Simplifying the fraction gives us:

36 = u

Therefore, the solution for u is 36.

For more such questions on Multiplicative property of equality.

https://brainly.com/question/9070018#

#SPJ11

Answer: $12.45.

Without a calculator, we can first round a dinner bill of $83.44 to the closest whole figure and estimate a 15% tip. In this instance, $83.44 can be rounded up to $83.

Then, we can calculate 15% of $83 by using a quick technique. In order to do this, we must first calculate 10% of $83, or $8.30. After that, we can calculate 5% of $83 by subtracting 50% of 10%, or $4.15.

Finally, we can add 10% and 5% together to get an estimate of 15% of $83:

$8.30 (10%) + $4.15 (5%) = $12.45

So, a 15% tip on a dinner bill of $83.44 would be approximately $12.45.

For more such questions on Ratios, proportions and percentages, visit:

brainly.com/question/19306970

#SPJ11

About 71 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected. The mean is 0.71. Standard Deviation is 0.043. The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.

1) Mean:
The mean of a proportion is simply the proportion itself, so the mean is 0.71.

2) Standard Deviation:
The standard deviation of a proportion is given by the formula:
σ = √(p(1-p)/n)
where p is the proportion, and n is the sample size. Plugging in the values given in the question:
σ = √(0.71(1-0.71)/110)
σ = 0.043

3) To find this probability, we need to use the normal distribution. We will use the z-score formula:
z = (x - μ) / σ
where x is the proportion we are interested in (0.8), μ is the mean (0.71), and σ is the standard deviation (0.043). Plugging in the values:
z = (0.8 - 0.71) / 0.043
z = 2.09
Using a z-table, we find that the probability of getting a z-score greater than 2.09 is 0.0183. So the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.

Learn more about probability at https://brainly.com/question/30052626

#SPJ11

The soap from Seventh Generation brand cost less than Method brand.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

The Method brand that is $5. 49 for 36 oz

So, the unit rate of soap

= 5.49 / 36

= $ 0.1525

and, The Seventh Generation brand that is $3. 39 for 25 oz

So, the unit rate of soap

= 3.39/ 25

= $0.1356

So, the soap from Seventh Generation brand is cheaper.

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ1

The area of the given isosceles trapezoid is 120 square units.

An isosceles trapezoid is a quadrilateral formed by a trapezium whose base angles are equal due to which the left and right sides are also equal in length.

In the given question,

Length of left/right side = 10

Length of bigger base = 21

Length of smaller base = 9

If we join the edges of the smaller base to the bigger base in such a way that we get 2 right-angled triangles formed by the legs of the trapezoid and the base,

we can say that the length of the base would be

=(bigger base-smaller base)/2

=(21-9)/2

=6

and we know that the length of the legs is 10

So to the Pythagorean theorem,

the height of the trapezoid would be

h=√(10² - 6²) = √64 = 8

Now that we know all the variables, we can easily calculate the area of the trapezoid by the formula

= height × (bigger base+smaller base)/2

= 8 ×(21+9)/2

= 4 × (30)

= 120 square units

To learn more about isosceles trapezoids visit,

https://brainly.com/question/12854321

#SPJ4

The only value of y that is a solution to the equation 40=5-7y is y=-5.

To identify solutions to a linear equation in one variable, we can plug in the given values of y and see if the equation is true.

For the first value of y, let's plug in y=1:
40=5-7(1)
40=5-7
40=-2

This equation is not true, so y=1 is not a solution to the equation.

Now let's try y=2:
40=5-7(2)
40=5-14
40=-9

This equation is also not true, so y=2 is not a solution to the equation.

Finally, let's try y=-5:
40=5-7(-5)
40=5+35
40=40

This equation is true, so y=-5 is a solution to the equation.

Know more about solution here:

https://brainly.com/question/17145398

#SPJ11

Cοrmac cοuld use 1/3 cup οf milk and 1 1/2 cups οf water, a mixture with a tοtal οf 1 5/6 cups, where the amοunt οf milk is less than 1/2 the amοunt οf water, represented by the sοlutiοn pοint (1/3, 1 1/2) tο the system οf inequalities x + y <= 2 and x < 1/2 * y.

An inequality is a mathematical statement that cοmpares twο values, expressing the relatiοnship between them using οne οf several symbοls, such as "<" (less than), ">" (greater than), "<=" (less than οr equal tο), ">=" (greater than οr equal tο), οr "!=" (nοt equal tο).

The pοint (1/3, 1 1/2) is a sοlutiοn tο Cοrmac's system οf inequalities, which means that it satisfies bοth inequalities. In this case, the inequalities are:

x + y <= 2

x < 1/2 * y

If we plug in x = 1/3 and y = 1 1/2, we can check if it satisfies bοth inequalities:

1/3 + 1 1/2 = 2 (satisfies x + y <= 2)

1/3 < 1/2 * (1 1/2) (satisfies x < 1/2 * y)

Therefοre, the sοlutiοn is (1/3, 1 1/2) since it satisfies bοth inequalities.

Sο, the statement that explains what the pοint (1/3, 1 1/2) represents is:

Cοrmac cοuld use 1/3 cup οf milk and 1 1/2 cups οf water, a mixture with a tοtal οf 1 5/6 cups, where the amοunt οf milk is less than 1/2 the amοunt οf water.

Hence, Cοrmac cοuld use 1/3 cup οf milk and 1 1/2 cups οf water, a mixture with a tοtal οf 1 5/6 cups, where the amοunt οf milk is less than 1/2 the amοunt οf water, represented by the sοlutiοn pοint (1/3, 1 1/2) tο the system οf inequalities x + y <= 2 and x < 1/2 * y.

To learn more about inequality, visit:

https://brainly.com/question/24372553

#SPJ1

Answer: All questions and answers from the Mathematics Part I (solutions) Book of Class 9 Math Chapter 4 are provided here for you for free.

Step-by-step explanation:

By using the slope-intercept form it can be concluded that:

The slope-intercept form of an equation is represented as follows:

y = mx + c    or     y - y₁ = m(x - x₁)  , where

m = slope

c = y-intercept

(x₁, y₁) = point on the line

The slope of the line when given two points can be calculated as follows:

m = (y₂ - y₁) / (x₂ - x₁)

1. Given f(2) = - 7 and f(6) = - 17. To find f(x), we need to use the slope-intercept form of a linear function: f(x) = mx + b. First, we need to find the slope of the line by using the two given points:

m = (y₂ - y₁) / (x₂ - x₁)

   = (f(x₂) - f(x₁)) / (x₂ - x₁)

   = (-17 - (-7)) / (6 - 2)

   = (-10) / (4)

   = -2.5

Now, we can plug in one of the points to find the y-intercept:

f(x) = mx + b

f(2) = (-2.5)(2) + b

 -7 = -5 + b

  b = -2

Therefore, the equation of the line is f(x) = -2.5x - 2.

2. To find the slope of the line passing through points A(6,3) and B(15,-3), we use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

   = (-3 - 3) / (15 - 6)

   = (-6) / (9)

   = -2/3

Therefore, the slope of the line is -2/3.

3. To find the equation of the line that contains point A(5,-3) and has slope m=3/5, we use the point-slope form of a linear function:

  y - y₁ = m(x - x₁)

y - (-3) = (3/5)(x - 5)

 y + 3 = (3/5)x - 3

       y = (3/5)x - 6

Therefore, the equation of the line is y = (3/5)x - 6.

4. To find the equation of the line that contains the point A(4,-8) and is parallel to the graph of the function f(x)=1/4x+3, we know that the slope of the new line will be the same as the slope of the given function, which is 1/4. We can use the point-slope form of a linear function to find the equation of the new line:
  y - y₁ = m(x - x₁)

y - (-8) = (1/4)(x - 4)

 y + 8 = (1/4)x - 1

       y = (1/4)x - 9

Therefore, the equation of the line is y = (1/4)x - 9.

5. To find the zero of the function f(x) = 4x - 2, we need to set the function equal to zero and solve for x:

    f(x) = 0

4x - 2 = 0

     4x = 2

       x = 2/4

          = 1/2

Therefore, the zero of the function is x = 1/2.

To learn more about slope-intercept form click here: https://brainly.com/question/1884491

#SPJ11

Answer:

a)  The angle subtended by the chord at the centre of the circle is 120°.

b)  The length of the minor arc is 12.57 cm (2 d.p.).

The perimeter of the minor segment formed by a chord and minor​ arc is 22.96 cm (2 d.p.).

Step-by-step explanation:

The chord of a circle is the base of an isosceles triangle, where its congruent sides are the radii of the circle.

The height of the isosceles triangle is the perpendicular bisector of the chord from the central angle.

The angle subtended by the chord at the centre of the circle is twice the angle formed by the radius and the perpendicular bisector (marked θ on the attached diagram).

To find the measure of angle θ, use the cosine trigonometric ratio.

[tex]\begin{aligned}\implies \cos \theta&=\sf \dfrac{adjacent\;side}{hypotenuse}\\\\\cos \theta &=\sf \dfrac{3}{6}\\\\\cos \theta &=\sf \dfrac{1}{2}\\\\\theta &=\arccos\left(\sf \dfrac{1}{2}\right)\\\\\theta &=60^{\circ}\end{aligned}[/tex]

As the angle subtended by the chord at the centre of the circle is twice angle θ:

[tex]\implies 2\theta=2 \cdot 60^{\circ}=120^{\circ}[/tex]

Therefore, the angle subtended by the chord at the centre of the circle is 120°.

A minor arc is less than 180° and is equal to the central angle.

Therefore, as the angle subtended by the chord at the centre of the circle is 120°, the minor arc is the part of the circumference between the two endpoints of the chord (marked in red on the attached diagram).

To find the length of the minor arc, use the arc length formula.

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $= \dfrac{\pi r\theta}{180^{\circ}}$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\implies \textsf{Arc length}&= \dfrac{\pi \cdot 6 \cdot 120^{\circ}}{180^{\circ}}\\\\&= 4 \pi\\\\&= 12.57\; \sf cm\;(2\;d.p.)\end{aligned}[/tex]

Therefore, the length of the minor arc is 12.57 cm (2 d.p.).

To calculate the perimeter of the minor segment formed by the chord and minor​ arc, we need to calculate the length of the chord.

[tex]\boxed{\begin{minipage}{10.2 cm}\underline{Chord length}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle (in degrees) subtended at the center by the chord.\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\implies \textsf{Chord length}&= 2 \cdot 6 \cdot \sin \left(\dfrac{120^{\circ}}{2}\right)\\\\&= 12 \cdot \sin \left(60^{\circ}\right)\\\\&= 12 \cdot \dfrac{\sqrt{3}}{2}\\\\&= 6\sqrt{3}\; \sf cm\end{aligned}[/tex]

Therefore, the perimeter of the minor segment formed by the chord and minor​ arc is:

[tex]\begin{aligned}\implies \textsf{Perimeter}&=\textsf{Minor arc length}+\textsf{Chord length}\\&=4 \pi + 6 \sqrt{3}\\&=22.96\; \sf cm\;(2\;d.p.)\end{aligned}[/tex]

To find f(i), we will substitute i for x in the given function and simplify:

f(i) = (i^{26} + i^{24} + 2i^{22})/(i-1)
= ((i^{22})(i^4 + i^2 + 2))/(i-1)
= ((i^{22})(1 + (-1) + 2))/(i-1)
= ((i^{22})(2))/(i-1)
= (2i^{22})/(i-1)
= (2i^{22})/((-1)(1-i))
= (2i^{22})/((-1)(1-i)) * ((1+i)/(1+i))
= (2i^{22})(1+i)/((-1)(1-i)(1+i))
= (2i^{22})(1+i)/((-1)(1^2 - i^2))
= (2i^{22})(1+i)/((-1)(1 - (-1)))
= (2i^{22})(1+i)/(2)
= i^{22} + i^{23}
= i^{22}(1 + i)
= (i^{22})(1 + i)
= (1)(1 + i)
= 1 + i

Therefore, the answer is (d) (1+i).

To know more about function refer here:

https://brainly.com/question/28193994

#SPJ11

Function Family: quadratic

Domain: all real numbers

x-int: (0,0) and (2,0)

y-int: (0,0)

The scale factor that Sidney used for the drawing is approximately 0.00333.

To determine the scale that Sidney utilised for the drawing, we can put up a proportion. The ratio will compare the drawing's shown volleyball court's width to the actual court's width:

Scale factor = width in drawing / real width

The scaling factor will be x. Next, we have:

3 cm / 900 cm = x

By multiplying 9 metres by 100, we may convert them to centimetres:

9 metres equals 9 times 100, or 900 centimetres.

By condensing the proportion, we obtain:

x = 0.00333

Thus, Sidney utilised a scale factor for the drawing that is roughly 0.00333. As a result, each centimetre on the drawing corresponds to 0.00333 metres, or 3.33 millimetres, on the volleyball court in real life.

To know more about Meters Visit:

https://brainly.com/question/29367164

#SPJ1

The coordinates of point B' after the translation are given as follows:

B'(1,-2).

A translation happens when either a figure or a function are moved horizontally or vertically.

The meaning of the translation for this problem is given as follows:

The coordinates of point B are given as follows:

B(5,1).

Hence the coordinates of point B' are given as follows:

Meaning that the last option is correct.

More can be learned about translations at brainly.com/question/28174785

#SPJ1

[tex]\huge\begin{array}{ccc}A=75ft^2\end{array}[/tex]

The formula:

[tex]\huge\boxed{A=l\cdot w}[/tex]

[tex]l[/tex] - length of a rectangle

[tex]w[/tex] - width of a rectangle

[tex]l=25ft,\ w=30ft[/tex]

substitute:

[tex]A=25\cdot30=750ft^2[/tex]

The length of the rectangular prism is 13 centimetres.

The volume of a rectangular prism is 208 cm³. The area of one end is 16 cm². The length of the rectangular prism can be found as follows:

Therefore,

volume of a rectangular prism = lwh

where

Hence, let's find the length

volume of a rectangular prism = lwh

208 = 16 × l

16l = 208

divide both sides by 16

l = 208 / 16

l = 13 cm

Therefore,

length of the prism = 13 cm

learn more on rectangular prism here: https://brainly.com/question/24460838

#SPJ1

The length of QS to 3 significant figures is 26.9 cm. QS is the side of the triangle that is adjacent to the angle of 27°.

An adjacent angle is an angle that shares a common side and a common vertex with another angle. Adjacent angles are commonly seen when two lines intersect, forming four angles.

QS is the side of the triangle that is adjacent to the angle of 27°. To calculate the length of this side, we can use the Law of Sines. The Law of Sines states that for any triangle with sides a, b and c and angles A, B and C respectively, the following equation holds true:

a/sin A = b/sin B = c/sin C

Therefore, for our triangle, we can use the equation as follows:

11/sin 27° = QS/sin 90°

Rearranging this equation, we can solve for QS:

QS = (11/sin 27°) x sin 90°

QS = 26.9 cm

Therefore, the length of QS to 3 significant figures is 26.9 cm.

For more questions related to the Law of Sines,

https://brainly.com/question/17289163

#SPJ1

To find the level of production that maximizes the manufacturer's total revenue, we need to find the quantity, q, that maximizes the revenue function, R(q) = p*q.

First, we need to find the revenue function by substituting the demand function for p in the revenue function:
R(q) = p*q = (−0.13q+156)*q = -0.13q^2 + 156q
Next, we need to find the quantity that maximizes this function. To do this, we can take the derivative of the revenue function and set it equal to zero:
R'(q) = -0.26q + 156 = 0
Solving for q, we get:
q = 600
This means that the quantity that maximizes the manufacturer's total revenue is 600 units.
To find the maximum revenue, we can plug this quantity back into the revenue function:
R(600) = -0.13(600)^2 + 156(600) = 46,800

Therefore, the maximum revenue is $46,800.

To know more about it refer here:

https://brainly.com/question/30529157

#SPJ11

The trinomial in standard form is x^2 + 10x + 25.

To express (x+5)^(2) as a trinomial in standard form, we need to expand the expression using the distributive property.

First, we will distribute the first term, x, to each term inside the parentheses:

(x+5)(x+5) = x(x) + x(5) + 5(x) + 5(5)

Next, we will simplify the terms:

= x^2 + 5x + 5x + 25

Finally, we will combine like terms to get the trinomial in standard form:

= x^2 + 10x + 25

Therefore, the trinomial in standard form is x^2 + 10x + 25.

Learn more about Trinomial

brainly.com/question/16347049

#SPJ11

The length of the side x in the triangle is approximately 7.5.

A right-angled triangle is a geometric shape that consists of three sides and three angles. One of the angles in a right-angled triangle measures 90 degrees, which is called a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called the legs or catheti.

The Pythagorean theorem is a fundamental property of right-angled triangles that states that the sum of the squares of the two shorter sides (legs) is equal to the square of the hypotenuse. This can be written as:

a² + b² = c²

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Right-angled triangles also have many real-world applications, such as in construction, engineering, architecture, and navigation. They are used to calculate distances, heights, angles, and other measurements in many different contexts.

Using trigonometry, we can solve for x:

sin(32°) = x/14

x = 14 * sin(32°)

x ≈ 7.5 (rounded to the nearest tenth)

Therefore, the length of the side x in the triangle is approximately 7.5.

To know more about sin visit:

https://brainly.com/question/28711469

#SPJ1

The two integer values of a for which the quadratic equation x² + ax + 8a = 0 have integer solutions are

A quadratic equation is an polynomial in which the highest power of the variable is 2.

Since we have the equation x² + ax + 8a = 0, we desire to find how many integer values of a that will make the equation have integer solution.

To do that, we use the discriminant of a quadratic equation

D = b² - 4ac where

Now, for a quadratic equation to have real solutions D ≥ 0

So, b² - 4ac ≥ 0

Now from the equation we have that

So, substituting the values of the variables into D, we have that

D = b² - 4ac

a² - 4(1)(8a) ≥ 0

a² - 32a ≥ 0

For integer values of a

a² - 32a = 0

a(a - 32) = 0

a = 0 or a - 32 = 0

a = 0 or a = 32

So, we have two integer values of a which are

Learn more about quadratic equation here:

https://brainly.com/question/28038123

#SPJ1

You can write an equivalent fraction with a smaller numerator and denominator.

When we take a fraction with the ratio of two integers =

Let the odd numerator be 3, and

Let the odd denominator be 9

therefore, now that we have to determine if one can write an equivalent fraction with a smaller numerator and denominator, the ratio will be as follows:

3:9 or we can similarly say 3/9

when we further simplify it, we will be getting the value of 1:3 or 3/9

hence, this shows that you can write an equivalent fraction with a smaller numerator and denominator.

To learn more about fractions, click here:

brainly.com/question/10354322

#SPJ1

The model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2

The Body Mass Index (BMI) of a person can be calculated using the formula:
BMI = (weight in pounds)/(height in inches)^2

In this case, the BMI varies directly as a person's weight in pounds and inversely as the square of the person's height in inches. This means that as the weight increases, the BMI increases and as the height increases, the BMI decreases.

To find a model for the BMI of a person, we can use the formula:
BMI = k(weight in pounds)/(height in inches)^2

Where k is a constant of proportionality. To find the value of k, we can use the given information that a 6ft 6in tall person has a BMI of 25.

First, we need to convert the height from feet and inches to inches. 6ft 6in is equivalent to 78 inches. Then, we can plug in the values into the formula and solve for k:

25 = k(weight in pounds)/(78 inches)^2
25(78 inches)^2 = k(weight in pounds)
152100 = k(weight in pounds)

Therefore, the model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2

This model can be used to calculate the BMI of a person given their weight in pounds and height in inches.

Learn more about BMI

brainly.com/question/18697844

#SPJ11

Based on the ratio of red to white paint in making pink paint of 1:3, the total cost to Robert to buy enough paint to make 12 liters is $54.

The Ratio refers to the relative size of one quantity compared to another.

Ratios are expressed in standard ratio form using (:) with one value in relation to another.

Ratios can also be depicted in percentages, fractions, and decimals.

The Ratio of mixing red and white paint = 1:3

The sum of ratios = 4 (1 + 3)

To mix 12 liters of pink paint, the quantity of red paint = 3 liters (12 x 1/4)

To mxi 12 liters of pink paint, the quantity of white paint required = 9 liters (12 x 3/4)

Cost of red paint per 500ml = £5

The cost of 1 liter of red paint = £10 (£5 x 2)

The total cost of 3 liters of red paint = £30 (£10 x 3)

Cost of white paint per 3 liters = £8

The total cost of 9 liters of white paint = £24 (£8 x 9/3)

The total cost of 12 liters of pink paint mixture = £54 (£30 + £24)

Learn more about ratios at https://brainly.com/question/2328454 and https://brainly.com/question/12024093.

#SPJ1

The 99.5% confidence interval for the population mean μ is (23.140, 38.260), accurate to 3 decimal places.

The 99.5% confidence interval for a sample of size 54 with a mean of 30.7 and a standard deviation of 19.8 can be calculated as follows:

1. Find the critical value for the 99.5% confidence level using a z-table or a t-table. For a 99.5% confidence level, the critical value is 2.807.
2. Calculate the standard error of the mean by dividing the standard deviation by the square root of the sample size:
SE = 19.8 / √54 = 2.694
3. Multiply the critical value by the standard error to find the margin of error:
ME = 2.807 * 2.694 = 7.560
4. Subtract the margin of error from the sample mean to find the lower bound of the confidence interval:
LB = 30.7 - 7.560 = 23.140
5. Add the margin of error to the sample mean to find the upper bound of the confidence interval:
UB = 30.7 + 7.560 = 38.260
6. Write the confidence interval as an open-interval using parentheses:
(23.140, 38.260)

Therefore, the 99.5% confidence interval for the population mean μ is (23.140, 38.260), accurate to 3 decimal places.

Know more about population mean here:

https://brainly.com/question/30727743

#SPJ11

Answer:

area = (1/2) · (p + q) · h

Step-by-step explanation: