Answer:
1 metre = 100 centimetres
Step-by-step explanation:
The length of the base edge of a pyramid with a regular hexagon base is represented as x. The height of the pyramid is 3 times longer than the base edge. The height of the pyramid can be represented as . The of an equilateral triangle with length x is units2. The area of the hexagon base is times the area of the equilateral triangle. The volume of the pyramid is x3 units3.
Answer: 1: 3x
2: area
3: six
4: 3/2
Step-by-step explanation:
The height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.
What is a pyramid that has a hexagonal base?The pyramid has a hexagonal base with six isosceles triangular faces known as a hexagonal base pyramid. It is also called a heptahedron.
We have,
The length of the base edge of a pyramid = x units
The height of the pyramid is three times longer than the base edge ie.
The height of the pyramid = 3x
The area of an equilateral triangle with base length x units is [tex]\rm x\sqrt{3}[/tex] square units square(let's assume)
Then the area of the hexagon base = 6×[tex]\rm x\sqrt{3}[/tex] ⇒ 6[tex]\rm x\sqrt{3}[/tex] square units.
Because the hexagon base has a six-equilateral triangle.
Let's assume the area of a hexagonal base is Y times the equilateral triangle.
[tex]\rm 6x\sqrt{3} = Y \times x\sqrt{3}[/tex]
Y = 6 times
We know the volume of a hexagonal pyramid = [tex]\frac{\sqrt{3} }{2} a^2h[/tex]
Where a is the base length and h is the height of the hexagonal pyramid.
Here a = x units and h = 3x units
Then Volume:
[tex]\frac{\sqrt{3} }{2} x^2(3x)\\\\\frac{{3} }{2} \sqrt{3}x^2[/tex]
Thus, the height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.
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The university is on a bearing of 050 degrees from the stadium and 300 degrees from the hospital. Mark the position of the university on the map with a cross
The position of the university marked x is shown in the attachment.
Given that university is on a bearing of 050 degrees from the stadium and 300 degrees from the hospital.
so we can say that the university position is gotten relative to the the position of the stadium and hospital.
The university is 50° from the stadium and then 350° from the hospital.
I.e it is N 50° E from the stadium and N 60° W from hospital.
The angle forms will be 50+60 = 110°
The point where the two lines intersect is the position of the university. Mark this point with a cross on the map.
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Match each mathematical expression with its simplified form.
(2 +9+4)
(3 + 1 + 4 + 8)
Answer:
15 and 16
Step-by-step explanation: To get simplified form, you add the numbers in parentheses together. (2+9+4)= 15 and (3+1+4+8)=16
For problem 1. 2+9=11 11+4=15
For problem 2. 3+1=4 4+4=8 8+8=16
Hopefully this helped, and please add me as brainliest.
Final answer:
The simplified forms of the expressions (2 + 9 + 4) and (3 + 1 + 4 + 8) are 15 and 16, respectively. The placement of parentheses affects the outcome of mathematical operations significantly, and careful evaluation following the order of operations is essential for accurate simplification, particularly when nested expressions are involved.
Explanation:
The question requires matching each mathematical expression with its simplified form. Let's simplify the given expressions:
(2 + 9 + 4) simplifies to 2 + 9 + 4 = 15.
(3 + 1 + 4 + 8) simplifies to 3 + 1 + 4 + 8 = 16.
Now, to address your example concerning the importance of the placement of parentheses, consider the expression 2 + (3 x 5). If the parentheses are around (2 + 3), the result is different than if the parentheses are around (3 x 5). Without any parentheses, the order of operations dictates that multiplication is done before addition. Hence:
(2 + 3) x 5 = 5 x 5 = 25 (since addition within parentheses is done first, followed by multiplication).
2 + (3 x 5) = 2 + 15 = 17 (since multiplication within parentheses is done first, followed by addition).
What is the rate of the interest on $560 for two years is $145.60?
The rate of interest is 13%.
Step-by-step explanation:
Given,
Principal (P) = $560
Interest (I) = $145.60
Time (T) = 2 years
To find the rate of interest
Formula
If P principal was invested for T years at r% simple interest, the interest will be I = [tex]\frac{PTr}{100}[/tex]
So,
Putting the values of P, I, T we get,
145.60 = [tex]\frac{560X2Xr}{100}[/tex]
or, r = [tex]\frac{145.60X100}{2X560}[/tex]
or, r = 13%
Hence,
The rate of interest is 13%.
Which of the following equations was used to graph the line shown?
Graph where both the axes run from minus sux to plus six and beyond. Straight lines intersect the aves at (6, 0) and (0, 6)
A. y = 6 + x
B. y = 6 – x
C. y = x – 6
D. y = 6x
The answer would be D since it forms a straight line along the x-axis
What is circumference? Please select all that apply:
A) distance around the circle
B) the space inside the circle
C) To find the circumference C of a circle if you know the diameter d is to multiply pi by the diameter
D) To find the circumference if you know the radius, replace d with 2r in the formula
E) the formula for circumference is C=pi + r
Answer:
A, C and D are correct.
\
Step-by-step explanation:
A is correct.
B is false; that space is the "area" of the circle.
C is true. C = πd
D is true. C = 2πr
E is false. Way off.
Final answer:
Circumference is the distance around a circle, calculated as C = πd or C = 2πr, depending on whether the diameter or radius is known. (Option A,C,D)
Explanation:
Circumference is the term used to describe the distance around a circle. When calculating the circumference, you can use different formulas depending on the information you have about the circle. If you know the diameter (d), the circumference (C) can be found by multiplying the diameter by pi (π), using the formula C = πd. Alternatively, if you know the radius (r) of the circle, you can use the formula C = 2πr since the diameter is twice the radius (d = 2r).
The correct answers to the question are:
A) distance around the circleC) To find the circumference C of a circle if you know the diameter d is to multiply pi by the diameterD) To find the circumference if you know the radius, replace d with 2r in the formulaIt's important to note that the space inside the circle is referred to as the area, not the circumference, and the formula for circumference is not C = pi + r as stated in option E, but rather C = πd or C = 2πr.
Help please please help
Answer:
A, 61 degrees
Step-by-step explanation:
Since the two angles are supplementary, this means that they add up to 180 degrees. m=180-119=61 degrees, or option A. Hope this helps!
Answer:
A. 61
Step-by-step explanation:
The line AOB is a 180 degree line. That means that both the angles have to add up to 180. Angle AOc is 119. 180-119= 61. You can check by doing 119 + 61 does it equal 180.
Hope this helps!
All tickets for a concert are the same price as the ticket agency as a fixed fee to every order a person who orders five tickets pays $93 a person who orders three tickets pays $57 a hint you'll need to calculate the slope of your first line. what is the cost per ticket?
Answer:
$18 is the cost per ticket ordered
Step-by-step explanation:
We proceed as follows;
Let the cost per ticket be $x while the fixed fee be $y
For the person that ordered 5 tickets, we can have his mathematical representation as;
5(x) + y = 93 •••••••••(i)
For the person that ordered 3 tickets, we can have his mathematical representation as;
3(x) + y = 57 ••••••••(ii)
From the first equation, we can have;
y = 93 - 5x
Let’s plug this into ii
3x + 93 - 5x = 57
-2x = 57 -93
2x = 36
x = 36/2
x = $18
This means that the cost per ticket ordered is $18
If you double president Reagans age at the time of his first inauguration and subtract his age at the time he died,the result is 45 years. How old was president Reagan when he died?
Answer:
93
Step-by-step explanation:
Let's say President Reagan was x years old when he died. He was 69 years old at his first inauguration
(2*69)-x = 45
Wait. But how will we find x in that equation?
--> (2*69)-45 = x
That's better.
2*69 = 138
138-45 = 93
x=93
At time t is greater than or equal to zero, a cube has volume V(t) and edges of length x(t). If the volume of the cube decreases at a rate proportional to its surface area, which of the following differential equations could describe the rate at which the volume of the cube decreases?
A) dV/dt=-1.2x^2
B) dV/dt=-1.2x^3
C) dV/dt=-1.2x^2(t)
D) dV/dt=-1.2t^2
E) fav/dt=-1.2V^2
Answer:
A) dV/dt=-1.2x^2
Step-by-step explanation:
The rate of change of volume is given by dV/dt. Surface area is proportional to x^2. Since the volume is decreasing, the constant of proportionality between surface area and rate of volume change will be negative. Hence a possible equation might be ...
dV/dt = -1.2x^2
Answer:
C
Step-by-step explanation:
V(t) = [x(t)]³
A(t) = 6[x(t)]²
dV/dt = k × 6[x(t)]²
Where k < 0
From the options,
taking k = -0.2
dV/dt = -1.2[x(t)]²
Can 4 cm, 7 cm, 9 cm be a right triangle
Answer:
No
Step-by-step explanation:
For it to be a triangle c² = a² + b²
The longest side is c (9)
and 81 ≠ 49 + 16
Can I get brainliest
Answer:
No
Step-by-step explanation:
Since it might be a right triangle, we can test the values using the Pythagorean theorem.
[tex]a^2+b^2=c^2[/tex]
a and b are the legs, and c is the hypotenuse.
We know that 4 and 7 are the legs, or a and b. This is because they are two smaller sides. We know that 9 is the hypotenuse, or c. This is because it is the longest side.
[tex]4^2+7^2=8^2[/tex]
Solve the exponents
[tex]16+49=81[/tex]
65=81
[tex]65 \neq 81[/tex]
Since 65 does not equal 81, this cannot be a right triangle
jazzy...respond pls..A box contains different-colored marbles that are all the same size. The table below shows the colors and amount of each marble in the box:
Color of Marble Number
Red 4
Blue 8
Green 3
Pink 5
Allen selects a marble from the box randomly, without looking, and then tosses a fair coin. What is the probability that Allen will select a red marble and the coin will land heads up?
Answer:
well is a 50 50 chains that Allen will get a red marble and
a 50 50 that the coin will land heads up.
Step-by-step explanation:
If you invest $12,000 and one year later your investment has grown to $13,188, then the rate of return on your investment was ____ %. (Round your answer to the nearest tenth of a percent.) Type in your numerical answer only; do not type any words or letters with your answer.
what makes 2 figures congruent
Two polygons are congruent if they are the same size and shape
Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour
of use to rent a paddle boat. Write an equation to find out how many
hours, h, they rented the Boat if the total cost was $33,
Answer:
y=2x+15
Step-by-step explanation:
h=9
The equation to find the number of hours the boat was rented is $33 = $15 + ($2 imes h). After subtracting the deposit fee and dividing by the cost per hour, the solution is h = 9, indicating the boat was rented for 9 hours.
The equation to find out how many hours, h, the boat was rented for when the total cost was $33 can be represented as follows:
Total cost = Deposit fee + (Cost per hour imes Number of hours)
Substituting the given values, we have:
$33 = $15 + ($2 imes h)
To solve for h, we subtract $15 from both sides of the equation:
$33 - $15 = $15 - $15 + ($2 imes h)
So, $18 = $2 imes h
Next, we divide both sides of the equation by $2 to solve for h:
$18 \/ $2 = ($2 imes h) \/ $2
h = 9
This means they rented the boat for 9 hours.
we started something new and I'm competely lost
Given:
Triangle ABC is similar to triangle XYZ.
The measures of the sides are AB = 6 cm, BC = 18 cm and XY = 12 cm
We need to determine the measure of side YZ.
Measure of YZ:
Since, ABC and XYZ are similar triangles, by using similar triangles property, we have;
[tex]\frac{AB}{XY}=\frac{BC}{YZ}[/tex]
Let the length of YZ be x.
Substituting the values, we get;
[tex]\frac{6}{12}=\frac{18}{x}[/tex]
Cross multiplying, we get;
[tex]6x=12 \times 18[/tex]
[tex]6x=216[/tex]
Dividing both sides by 6, we have;
[tex]x=36[/tex]
Thus, the value of x is 36.
Hence, the measure of the side YZ is 36 cm.
A coin is flipped and a normal dice is rolled.
a)
How many possible outcomes are there?
b)
What is the probability of getting a tail and a five?
c)
What is the probability of getting a number less than five and a head?
Total possible outcomes if a coin is flipped and a normal dice is rolled are 12
Probability of getting a tail and a five will be 1/12
The probability of getting a number less than five and a head is 1/3
What is probability?Probability is the chance of happening of an event.Probability is always ≤ 1How to find out how many possible outcomes are there?If a coin is tossed 2 possible outcomes will be there. Either it will be a Head or a Tail.If a normal dice is rolled 6 possible outcomes will be there.∴ Total possible outcomes = (6 x 2) = 12
How to know the probability of getting a tail and a five?As we know that there will be 12 possible outcomes .Getting a five and a tail will be one of those possible outcomes.∴ Probability of getting a tail and a five will be 1/12
How to know the probability of getting a number less than five and a head?We know that probability of getting a head when a coin is flipped is 1/2 Probability of getting a number less than five is a dice is rolled is = 4/6∴ The probability of getting a number less than five and a head = (1/2)(4/6) = 4/12 = 1/3
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Having trouble with this problem. Please help
Answer:
A) 33 3/4°
Step-by-step explanation:
The supplement of an angle is the difference between 180° and the angle measure:
supplement of 146 1/4° = 180° -(146 1/4)°
= (180° -146°) -1/4° = 34° -1/4°
= 33 3/4° . . . . supplement of the given angle
Which graph shows the solution set for Negative 4.4 greater-than-or-equal-to 1.6 x minus 3.6?
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded.
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the right of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the left of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.
Answer:
A
Step-by-step explanation:
right on Edge.2020
The graph that shows the solution set for -4.4 ≥ 1.6x - 3.6 is A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded, the correct option is A.
What is an Inequality?An Inequality is a statement that is formed when two expressions are joined using an inequality operator.
-4.4 ≥ 1.6x - 3.6
The value of x is
-4.4+3.6 ≥ 1.6x
x ≤ -0.5
The number line of any length, which has a closed circle at -0.5 and the left side of the point -0.5 is shaded is the graph of the inequality.
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If the campers at Camp Grilled Meat prefer hot dogs to hamburgers by a ratio of 4:3, and they need 500 hot dogs, how many hamburgers will they need?
Answer:
375
Step-by-step explanation:500 equals 100% divide by 4 its 125 times 3 equals 375, your welcome
Answer:
They will need 375 hamburgers.
Step-by-step explanation:
Keeping the ratio in mind, we solve this problem by cross multiplying. Set up the ratio 4/3 and set it equal to the greater ratio of 500/(an unknown number of hamburgers, represented by x). Cross multiply to end up with the equation 4x=1500. (Cross multiplying is multiplying each numerator by the opposite denominator). Solve for x in the above equation using SADMEG. You divide 1500 by 4 and end up with 375 hamburgers.
A net has a square at the center and 4 triangles on the sides. The square has side lengths of 4 millimeters. The triangles have a base of 4 millimeters and height of 7 millimeters. Complete the statements about the net of this pyramid. The net will have square face(s). The net will have triangular face(s). The triangular faces are . The net will have a total of faces.
Answer:
The net will have 1 square face
The net will have 4 triangular faces
The triangular faces are identical
The net will have a total of 5 faces.
Step-by-step explanation:
If you look at the picture, count the triangular faces, you will see 4.
Count the square on the bottom, its 1.
All the triangular faces are identical, if they weren't the picture would be all over the place.
Add 1+4 and it equals 5. The net will have a total of 5 faces.
(Hope you got it right, cause I took it and got it right!! Also I'm not good at explaining math lol)
Stay safe and social distance :DD
The net will have one square face, four triangular faces, the triangular faces are identical.
The net will have a total of five faces.
What is a square pyramid?"It is a three-dimensional geometric shape that has a square base and four triangular sides that are joined at a vertex."
What is net?"It is a two-dimensional structure which forms a three-dimensional geometric structure by folding."
According to the problem,
The base of the square pyramid has a square and if a three dimensional structure of a net formed into a pyramid is looked at, we can see 1 face of the square at the base.
A pyramid is comprised of 4 triangles joined together at the vertex.
Again, if a three dimensional structure of a pyramid is looked at, we can see 4 faces of the pyramid.
Now in order to align into a single unit to be joined at the vertex, the triangles have to be identical. They will have similar faces with the same base and slant height.
Therefore, 1 square face and 4 triangular faces adds up to five total faces.
Hence, we can conclude that the net will have one square face, four triangular faces and a total of five faces with the triangular faces being similar.
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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 8 large boxes and 3 small boxes has a total weight of 187 kilograms. A delivery of 2 large boxes and 5 small boxes has a total weight of 102 kilograms. How much does each type of box weigh?
Answer:
Weight of large box = 18.5 Kg
Weight of small box = 13 Kg
Step-by-step explanation:
Let the weight of large box be X kg
Let the weight of small box be Y kg
So weight of 8 large boxes = 8X
weight of 3 small box be = 3Y
According to question
8 large boxes and 3 small boxes has a total weight of 187
mathematically it can be represented as
8X + 3 Y = 187
_________________________________________________
Second condition
weight of 2 large boxes = 2X
weight of 5 small box be = 5Y
According to question
2 large boxes and 5 small boxes has a total weight of 102 kilograms
mathematically it can be represented as
2X + 5Y = 102
--------------------------------------------------------------------------
we have two equation
8X + 3 Y = 187 -------------------A
2X + 5Y = 102 -------------------B
multiplying equation B with 4 on both side of equation we have
4*(2X + 5Y) = 4*102
=> 8X + 20Y = 408 -------------------C
Now subtracting equation A and C on both sides we have
8X + 3 Y - (8X + 20Y ) = 187 -408
8X - 8X + 3 Y - 20Y = -221
-17Y = -221
=> Y = -221/-17 = 13
Now substituting value of Y in equation B we have
2X + 5*13 = 102
=> 2X + 65 = 102
=> X = (102-65)/2 = 18.5
______________________________
Weight of large box = 18.5 Kg
Weight of small box = 13 Kg
The large box weighs 17 kg and the small box weighs 13 kg.
Explanation:Let's denote the weight of a large box as x and the weight of a small box as y. We can set up a system of equations to solve for the weights:
8x + 3y = 187 (equation 1)
2x + 5y = 102 (equation 2)
To solve the system, we can multiply equation 1 by 2 and equation 2 by 8 to eliminate x:
16x + 6y = 374 (equation 3)
16x + 40y = 816 (equation 4)
Subtracting equation 3 from equation 4, we get:
34y = 442
Solving for y, we find y = 13.
Substituting this value back into one of the original equations, we find x = 17.
Therefore, the large box weighs 17 kilograms, and the small box weighs 13 kilograms.
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Rewrite the expressie
sohe.
1) 6(5 + 3)
Answer:
48
Step-by-step explanation:
6*5+6*3=30+18=48
distubutive property
What single decimal multiplier would you use to increase by 7% followed by a 9% increase?
Answer:
The decimal multiplier is 1.1663
Step-by-step explanation:
Since the increases are done successively we can find decimal numbers for each one and multiply both to have a single decimal representing the whole operation. When there's a increase this means that we have the original value (100%) summed by some other value, in this case 7%, so the new value would be 100% + 7% = 107%, we can transform this to a decimal number by dividing it by 100, so 107/100 = 1.07. The same applies to the 9% increase, so we would have 109/100 = 1.09. We can now multiply both to obtain a single decimal multiplier, we have:
1.07*1.09 = 1.1663
Sharon has 72 beads. She has twice as many sphere beads as cylinder beads. How many of each kind of bead does Sharon have? How did you solve the problem? How can you check your check.
Answer:
Sphere=48 beads
Cylinder=24 beads
Step-by-step explanation:
Let the number of cylinder beads be y and since she has twice as many sphere beads, the sphere beads will be 2y
The sum of sphere and cylinder beads will be y+2y=3y
This sum is equivalent to the total number given as 72
Therefore, equating 3y to be equal to 72 we obtain the equation
3y=72
Dividing by 3 on both sides we obtain that
Y=72/3=24 beads for cylinder
Since the sphere is 2y then 2*24=48
To confirm, it is evident that 48+24=72
Also, the number 48 is double/twice the number 24
.If a golf ball has a diameter of 4.3 centimeters and a tennis ball has a diameter of 6.9 centimeters. Find the difference between the volumes of the two balls.
Answer:
130.43 cm³
Step-by-step explanation:
To find the difference between the volumes of the balls, we must first find the volumes of the balls. To find the volume of each ball, we must first determine their shape. We understand that both balls are spherical.
The volume V of a sphere wit radius r is given as
V = 4/3 πr³
where r is the result when the diameter of the sphere is divided by 2.
Hence the radius of the Golf ball
= 4.3cm/2
= 2.15cm
radius of the tennis ball
= 6.9cm/2
= 3.45cm
The difference between the volumes of the two balls
= 4/3 π (3.45³ - 2.15³)
= 130.43 cm³
Line I and line m are straight lines , which statements are true regarding the angles in the figure!! Select 2 options .
Answer:2(B) and 4(D) are your answers!!
Step-by-step explanation:
hope this helped youu!!have a terrific Tuesday!
Two sides of a triangle measure 8 cm and 15 cm. Which could be the length of the third side?
6 cm
18 cm
24 cm
28 cm
Answer:
Option 2 is correct
Since only 18 is less than 23 and greater than 7, therefore the possible length of third sides is 18 cm and option 2 is correct.
In which number does the digit 8 have a value that is 1,000 times greater than the digit 8 in the number 349,257.83?
Answer:
349,257,830
Step-by-step explanation:
Multiply 349,257.83 by 1000
The required number where the digit 8 has a value that is 1,000 times greater than the digit 8 in the number 349,257.83 is 349,257,830.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the number x,
According to the question, [An approximate calculation]
x / 1000 = 349,257.83
x = 1000 [349,257.83]
x = 349,257,830
Thus, the required number where the digit 8 has a value that is 1,000 times greater than the digit 8 in the number 349,257.83 is 349,257,830.
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A data set includes 103 body temperatures of healthy adult humans having a mean of 98.9degreesf and a standard deviation of 0.67degreesf. construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. what does the sample suggest about the use of 98.6 degreesf as the mean body temperature?
A 99% confidence interval for the mean body temperature can be calculated using the sample mean, standard deviation, and the t-score corresponding to the confidence level. The findings may suggest that the commonly accepted average body temperature of 98.6°F could be reconsidered if it does not fall within this interval.
Constructing a 99% Confidence Interval
To construct a 99% confidence interval for the mean body temperature of all healthy humans, we use the sample mean, standard deviation, and the t-distribution since the population standard deviation is not known. With a mean of 98.9°F, a standard deviation of 0.67°F, and a sample size of 103, we can calculate the margin of error using a t-score that corresponds to the 99% confidence level.
First, we find the t-score from the t-distribution table for 102 degrees of freedom (n-1) that corresponds to a 99% confidence level. Then, we calculate the margin of error using the formula:
Margin of Error (E) = t-score * (standard deviation / sqrt(n))
This margin of error is then added and subtracted from the sample mean to obtain the confidence interval:
Lower Limit = Mean - Margin of Error
Upper Limit = Mean + Margin of Error
This confidence interval provides a range within which we can be 99% confident that the true mean body temperature of all healthy humans lies.
Implications for 98.6°F as Average Body Temperature
The sample suggests that the mean body temperature of 98.6°F might not be accurate for all individuals. If the constructed 99% confidence interval does not contain the traditional mean of 98.6°F, it could indicate that the average body temperature is different than what has been historically taught.
The 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.
To construct a 99% confidence interval for the mean body temperature of all healthy humans, we'll use the formula:
[tex]\[ \text{Confidence Interval} = \bar{x} \pm z \left( \frac{s}{\sqrt{n}} \right) \][/tex]
Let's calculate the confidence interval:
[tex]\[ \text{Confidence Interval} = 98.9 \pm 2.576 \left( \frac{0.67}{\sqrt{103}} \right) \]First, let's calculate \(\frac{s}{\sqrt{n}}\):\[ \frac{s}{\sqrt{n}} = \frac{0.67}{\sqrt{103}} \approx 0.0662 \][/tex]
Now, we can find the margin of error:
[tex]\[ \text{Margin of Error} = 2.576 \times 0.0662 \approx 0.1706 \]Finally, construct the confidence interval:\[ \text{Confidence Interval} = 98.9 \pm 0.1706 \][/tex]
So, the 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.