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.
The net below can be folded to form a square pyramid.
A square pyramid. The square base has side lengths of 9 inches. The triangular sides have a height of 6.1 inches and side length of 7.6 inches.
What is the surface area of the pyramid?
190.8 square inches
217.8 square inches
300.6 square inches
354.6 square inches
Answer:
190.8 square inches
Step-by-step explanation:
The area of one of its triangular sides is given by A = bh/2 were b = base = 9 inches and h = perpendicular height = 6.1 inches.
A = bh/2. Since we have 4 triangular sides, the total area of its sides A₁ = 4A = 4bh/2 = 2bh = 2 × 9 × 6.1 = 109.8 square inches.
The area of is base is the area of a square = 9² = 81 square inches.
So te total surface area is 109.8 square inches + 81 square inches = 190.8 square inches
Answer:
190.8
Step-by-step explanation:
In this circle, AB is tangent to the circle at point B, AC is tangent to the circle at point C, and point D lies on
the circle. What is m BAC ?
a. 264
b. 84
c. 96
d. 90
Answer:
c. 96
Step-by-step explanation:
Answer:
96
Step-by-step explanation:
Jami is keeping track of the weather for a class project she recorded data on 16 days out of 16 days 1/4 were clear blue skies how many days had clear blue skies
Answer:
4 days
Step-by-step explanation:
She recorded date for 16 days, and 1/4 of the days were clear blue skies.
One way to find this is to multiply 16 and 1/4
16*1/4=4
Another way is to first convert 1/4 to a decimal
1/4=0.25
Then multiply 16 and 0.25
16*0.25 =4
So, 4 out of 16 days had clear blue skies
The data plot represents the hours student each week in two different classrooms
Answer:
Could you put a link or image or pic
Step-by-step explanation:
We can not see
Answer:
the mean number of hours a student in Mr. Hart’s class studies is hours 4.6
The mean number of hours a student in Ms. Perry’s class studies is 2.8 hrs
A typical student in Mr. Hart’s class studies a typical student in Ms. Perry’s class.more than
Step-by-step explanation:
just took the test
Australian glitter ants reproduce so that their population doubles every 15 days. If there are 3 ants initially, the equation is represented by y=3(2)^t/15, where t represents the number of days. Rewrite the equation in the form y=a(1+r)^t and find the daily increase rate represented by r.
Answer:
4.73%
Step-by-step explanation:
y = 3×2^(t/15) = 3×(2^(1/15))^t = 3×1.0472941^t
In this form, ...
1 +r = 1.0472941
r = .0472941 ≈ 4.73%
The daily increase is about 4.73%.
If f(x) = 2(3x) + 1, what is the value of f(2)?
Answer:
when x is 2. f(2)=3(2)+1. f(2)=6+1. f(2)=7.
Step-by-step explanation:
Determine which of the following graphs does not represent a function.
(Help me ASAP)
Answer:
D
Step-by-step explanation:
one way to determine whether or not something is a function is to use the vertical line test
You can draw vertical lines all along the figure and if the same vertical line touches 2 parts of the graph we know this is not a function due to there being 2 outputs for the same x value
d is a vertical line and therefore will not pass this test
can someone help me with this geometry plz??? will mark brainliest and 20 points!!
Answer:
A unique
Step-by-step explanation:
2 triangles are similar if they have the same angle measures, by the law of triangle similarity.
That means that given 2 angles measures, we can find our third angle measure and create infinitely many triangles with those 3 angles. however we have a given side length. changing the length of this will not satisfy the given conditions
9. Betsy's softball team won 47 games, lost
15 games, and tied none. What fractional
part of the games played did the team
win?
Answer:
47/62
Step-by-step explanation:
62 total games won 47 therefore 47/62
Final answer:
The fractional part of the games won by Betsy's softball team is 47/62, representing the number of games won out of the total games played.
Explanation:
To calculate the fractional part of the games won by Betsy's softball team, you need to divide the number of games won by the total number of games played. The team won 47 games and lost 15 games, giving a total of 47 + 15 = 62 games played.
The fraction representing the part of the games won is therefore 47/62. When simplified, this fraction may be reduced to a simpler form by finding the greatest common divisor and dividing both the numerator and the denominator by it. However, as 47 is a prime number and does not divide evenly into 62, the fraction can't be simplified further. Therefore, the fractional part of the games won by the team is 47/62.
Write the number 54300 in standard form
Answer:
5.4300 x 10 with a small 4
Step-by-step explanation:
Answer:
5.43*10^4
Step-by-step explanation:
You donate 8 baseballs to a local baseball team. Your uncle donates 12 baseballs. If a total of 50 baseballs are donated, what is the probability that the first pitch of the season uses one of your baseballs or one of your uncle’s baseballs?
The required probability that the first pitch of the season uses one of your baseballs or one of your uncle's baseballs is 2/5.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
There are 20 baseballs donated between you and your uncle and a total of 50 baseballs, so the probability that the first pitch of the season uses one of your baseballs or one of your uncle's baseballs is:
P(your baseball or uncle's baseball) = (number of your baseballs + number of uncle's baseballs) / total number of baseballs
= (8 + 12) / 50
= 20/50
= 2/5
Therefore, the probability that the first pitch of the season uses one of your baseballs or one of your uncle's baseballs is 2/5.
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The probability that the first pitch of the season uses one of the baseballs donated by the student or their uncle is 2/5 or 40%.
To calculate the probability that the first pitch of the season uses one of your baseballs or one of your uncle's, we first need to figure out the total number of baseballs donated by you and your uncle. You donated 8 baseballs and your uncle donated 12 baseballs. Hence, together you both donated 8 + 12 = 20 baseballs.
Since there are a total of 50 baseballs donated, we can now calculate the probability. The probability of picking either one of your baseballs or one of uncle's baseballs is the total number of your combined baseballs divided by the overall total number of baseballs, which is 20/50. This can be simplified to 2/5 or 40%.
Therefore, the probability that the first pitch of the season uses one of the baseballs donated by you or your uncle is 2/5.
Line k is parallel to line l. Lines k and l are parallel. Lines m and n intersect to form 2 triangles. The top triangle has angles 1, 2, 3 and the bottom triangle has angles 4, 5, 6. Which angle is congruent to Angle 4? Angle 1 Angle 2 Angle 5 Angle 6
Answer:
The line that is congruent to angle 4 is angle 1
hope this helped :)
Angle 4 is congruent to Angle 2 because they are alternate interior angles formed by the transversal intersecting two parallel lines.
Given that lines k and l are parallel, and lines m and n intersect to form two triangles, we need to determine which angle is congruent to Angle 4.From geometry, we know that alternate interior angles are congruent when two parallel lines are cut by a transversal. Here, lines m and n intersecting parallel lines k and l can be visualized as forming such alternate interior angles.Since Angle 4 is within the lower triangle, the angle in the upper triangle that is on the 'opposite' side of the transversal, corresponding to the same spot, is Angle 2.Congruence of Angles
Angle 4 ≈ Angle 2 (alternate interior angles)
Gabriella and her children went into a grocery store and where they sell apples for $1 each and mangos for $0.50 each. Gabriella has $15 to spend and must buy at least 19 apples and mangos altogether. If Gabriella decided to buy 13 mangos, determine the maximum number of apples that she could buy.
Answer:
Step-by-step explanation:
Let x represent the number of apples that she wants to buy.
The grocery store sells apples for $1 each and mangos for $0.50 each.
If Gabriella decided to buy 13 mangos, it means that the cost of buying x apples and 13 mangoes is expressed as
x + 13 × 0.5 = x + 6.5
If she buy at least 19 apples, it means that
x + 13 ≥ 19
x ≥ 19 - 13
x ≥ 6
Gabriella has $15 to spend. It means that
x + 6.5 ≤ 15
x ≤ 15 - 6.5
x ≤ 8.5
Therefore, the maximum number of apples that she can buy is 8
Final answer:
After purchasing 13 mangos, Gabriella can spend the remaining $8.50 on apples, which allows her to buy a maximum of 8 apples while also meeting the minimum requirement of 19 fruits in total.
Explanation:
If Gabriella decided to buy 13 mangos at $0.50 each, she would spend $6.50 on mangos. She has $15 to spend, so after buying the mangos, she would have $15 - $6.50 = $8.50 left. Since apples cost $1 each, Gabriella could buy a maximum of $8.50/ $1 per apple = 8 apples. However, she must buy at least 19 apples and mangos altogether. Since she has already bought 13 mangos, she would need to buy 19 - 13 = 6 apples to meet the minimum requirement. Therefore, the maximum number of apples she can buy is 8, which also satisfies the minimum quantity of fruit required.
If you meet a person online there is a 50% chance that they aren't who they say they are. There is a 75% chance that part of what they tell you is the truth. What are the chances that they are who thy say they are.
ASAP show work please
Answer:
20 degrees
Step-by-step explanation:
Because lines CB and DA cross in the center of the circle, they are vertical angles and they are equidistant from arcs AB and CD. This means that CD and AB are congruent, and that therefore CD=AB=20 degrees. Hope this helps!
Any help is appreciated! Question in picture.
Answer:
Step-by-step explanation:
1.65
Answer:
1.65
Step-by-step explanation:
choose $16.50 / 10 pounds = $1.65
Determine o período, a imagem e construa o gráfico de cada uma das funções abaixo: a) f(x) = 3sen(x) b) f(x) = 1 - sen(3x) c) f(x) = -1+2sen(0,5x)
Answer:
Please read the answer below
Step-by-step explanation:
The general form of a sinusoidal function is given by:
[tex]f(x)=Asin(\omega x)[/tex] (1)
where A is the amplitude, and the period is given by:
[tex]T=\frac{2\pi}{\omega}[/tex]
The image of a function is the available values of the function f(x) in the domain of f(x). For sinusoidal function the image of f(x) is determined with the aid of the amplitude. For example, in the case of (1), f(x) varies from -A to A.
Due to the information given above you have (the plots are attached below):
a)
[tex]f(x)=3sin(x)\\\\T=\frac{2\pi}{1}=2\pi\\\\Im\ f(x)=[-3,3][/tex]
b)
[tex]f(x)=1-sin(3x)\\\\T=\frac{2\pi}{3}\\\\Im\ f(x)=[0 \ ,2][/tex]
in the last case the first term of f(x) modifies the image of f(x) because the sinusoidal function is displaced to y=1.
c)
[tex]f(x)=-1+2sin(0.5x)\\\\T=\frac{2\pi}{0.5}=4\pi\\\\Im\ f(x)=[-3,1][/tex]
What are the zeros of this function?
Answer:
Answer:
X=3 and X=6
Step-by-step explanation:
When y is zero
Step-by-step explanation:
Answer:
Its b
Step-by-step explanation:
What is the median of 4,3,5,9,3,4
Answer:
THE ANSWER IS 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
3, 3, 4, 4, 5, 9
The median is 4
A gym charges a $615 yearly fee for membership plus $50 for each hour of personal training. What is the average total cost per hour of training if a member works with a personal trainer for 30 hours in a year? Do not include the dollar sign ($) in your answer.
Answer:
The average total cost per hour of training is $70.5
Step-by-step explanation:
The form of the linear function is f(x) = m x + b, where
m is the average rateb is the initial value∵ The gym charges a $615 yearly fee for membership plus
$50 for each hour of personal training
- That means the initial amount is 615 and the average rate is 50
∴ m = 50 dollars per hour
∴ b = 615 ⇒ fixed fee
- Substitute m and b in the form of the linear function
∴ c(x) = 50 x + 615, where c(x) is the cost per year for x
training hours
∵ A member works with a personal trainer for 30 hours in a year
- That means x = 30
∴ x = 30
- Find the total cost of this year by substituting x by 30
∴ c(30) = 50(30) + 615
∴ c(30) = 1500 + 615
∴ c(30) = 2115
∴ The total cost of this year is $2115
To find the average cost per hour divide the total cost by the number of the training hours
∵ Average cost per hour = 2115 ÷ 30
∴ The average cost per hour = 70.5 dollars
∴ The average total cost per hour of training is $70.5
Based on the number of hours and the cost per hour of using the trainer, the average cost per hour is $70.50 per hour.
First find the total cost of using a trainer for 30 hours.
= Fixed membership cost + (Cost per hour x Number of hours)
= 615 + (50 x 30)
= $2,115
The total cost for the year is $2,115.
The average cost per hour will be:
= Total cost / Number of hours
= 2,115 / 30
= $70.50
In conclusion, the total average cost per hour is $70.50.
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A game increased in price by 1/2.. After the increase it was priced at £27. What was the original price of the game? I am very confused (hegarty maths)
The original price of the game was £18. This is derived by understanding a 1/2 increase equates to a 50% increase, thus making £27 150% of the original price. To get the original price, divide £27 by 1.5.
Explanation:To solve this problem, you need to understand that an increase of 1/2 equals a 50% increase. If the game price were £27 after increasing by 50%, that means £27 represents the original price plus an additional half (50%) of the original price, in other words, it represents 150% of the original price. We can set up the equation like this:
Original Price(1.5) = £27
To solve for the original price, we divide £27 by 1.5, resulting in £18.
So, the original price of the game was £18.
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Does anyone get this??
Answer:
The distance from the feet to the wall is 9 ft
Step-by-step explanation:
Using trig,
We must use cosine to find the missing side.
The equation is cos 60 = [tex]\frac{adjacent}{18}[/tex]
The cosine of 60 is 1/2
So, we multiply 1/2 by 18
to get 9
Hope this helps!
Branliest would really be nice!
Which of these is equal to 50 + 21?
The question is asking for the sum of 50 and 21. This is a mathematical operation known as addition. Following the steps of addition, the sum of 50 and 21 equals 71.
Explanation:The question is essentially asking for the sum of 50 and 21. In Mathematics, when we talk about 'equal to', we are referring to the result of an equation or mathematical operation.
So, to find out what is equal to 50 + 21, you simply add these two numbers together. The process is as follows:
Start by lining up the numbers by their place value.Add the ones place (0 + 1).Then, add the tens place (50 + 20).
After following these steps, you will find that 50 + 21 equals 71.
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One circle is 1962.5ft.It’s 32 circles. So how many ft is that ?
I’m not sure of what to do ,can u please help me ?
Please I’ve been stuck on this for hours.
Answer:
Out of 240,000 feet² of the field 62,800 feet² was being watered.
Step-by-step explanation:
We have a figure with 32 circles and diameter of each circle is 50 feet. We have to find how much area is being watered. Assuming that each circle represents the Area of the field which is being watered.
We can find the area of one circle and multiply that by 32 to find the area of all 32 circles. This will give us the area of the field that is being watered.
Since, radius is half of the diameter, the radius of each circle will be r = 25 feet.
Area of a circle is calculated as:
Area = πr²
Substituting the value of r = 25 and π = 3.14, we get:
Area of one circle = 3.14 x (25)² = 1962.5 feet²
Since area of 1 circle is 1962.5 feet² , area of 32 circles will be = 32 x 1962.5 = 62,800 feet²
The field is rectangular in shape with length = 600 feet and width = 400 feet.
Area of a rectangle is the product of its length and width. So area of the entire field will be:
Area of field = 600 x 400 = 240,000 feet²
This means, out of 240,000 feet² of the field 62,800 feet² was being watered.
write an expression for " the quotient of q and 9
Answer:
q/9
Step-by-step explanation:
The quotient is an number or variable that is the product of division. My answer may be reversed or wrong, but it should be close to the correct one.
does x^2-6x+3 have solutions that are real numbers
Answer:
X=10.8 and X=1.1
Step-by-step explanation:
Δ= b^2-4ac
= (-6)^2-4(1)(3)
=24
X1=
[tex] \frac{6 + \sqrt{24} }{ {1}^{2} } [/tex]
=10.8
X2=
[tex] \frac{6 - \sqrt{4} }{ {1}^{2} } [/tex]
=1.1
Mrs. Wilton is planning a rectangular flower box for her front window. She wants the flower box to hold exactly 16 cubic feet of soil.How many flower boxes with different-size bases will hold exactly 16 cubic feet of soil, using whole-number dimensions?flower boxes with different-size bases will hold exactly 16 cubic feet of soil. please no fake answers or you not getting nothing
There are 4 different flower boxes with different-size bases that can hold exactly 16 cubic feet of soil when using whole-number dimensions. These consist of dimension combinations of 1x1x16, 1x2x8, 1x4x4, and 2x2x4 feet.
Mrs. Wilton is planning a rectangular flower box that should have a volume of 16 cubic feet. To find how many flower boxes with different-size bases can hold exactly 16 cubic feet of soil, we need to find all the possible combinations of whole-number dimensions (length, width, and height) that when multiplied together equal 16 cubic feet. We must remember that volume is calculated as Length x Width x Height. Since 16 is the volume in cubic feet, we look for whole-number factors of 16.
Here are the possible whole-number dimension sets (in feet) for a volume of 16 cubic feet:
1 x 1 x 16 (Height can be 1, 16, or any factor of 16)
1 x 2 x 8 (Height can be 2, 8, or any factor of 16)
1 x 4 x 4 (Height can be 4 or any factor of 16)
2 x 2 x 4 (These dimensions are interchangeable)
Each of these dimensions gives a different base size for the flower box, and all ensure the volume is 16 cubic feet. Thus, there are 4 different flower boxes with different-size bases that will hold exactly 16 cubic feet of soil.
Which inequality statement describes the two numbers on a number line?
"−7 and a number 5 units to the right of −7"
A) 5 < −7
B) 5 > −7
C) −7 > −2
D) −7 < −2
Answer:
Option C)
[tex]-7<-2[/tex]
Step-by-step explanation:
We are given the following in the question:
"-7 and a number 5 units to the right of -7"
The nubmer 5 units to the right of -7 will be:
[tex]=-7 + 5\\=-2[/tex]
The number line shows the two marked points.
As observed from the number line, we can write the inequality:
[tex]-7<-2[/tex]
Thus, the correct option is
Option C)
[tex]-7<-2[/tex]
Answer:
its d not c so -7<-2 is the awnser
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C (x) = 0.5x^2-130x+17,555. What is the minimum unit cost?
The minimum unit cost to manufacture a car for the given quadratic cost function C(x) = 0.5x^2 - 130x + 17,555 is found by using the vertex formula. The x-coordinate of the vertex is -(-130)/(2*0.5) = 130, which yields the minimum unit cost of $9,105 when substituted back into the function.
Explanation:To find the minimum unit cost for manufacturing cars in the given scenario, we need to analyze the cost function C(x) = 0.5x2 - 130x + 17,555. This is a quadratic function, which is parabolic in shape, generally either opening upwards or downwards. In this case, we have a positive coefficient for the x2 term, which means the parabola opens upwards and the vertex of this parabola will give us the minimum point or the minimum cost for producing cars.
The vertex of a quadratic function expressed in the form ax2 + bx + c can be found using the formula -b/(2a) for the x-coordinate of the vertex. In this case, a = 0.5, b = -130, so the x-coordinate of the vertex is -(-130)/(2*0.5) = 130. Plugging this value into the original function will give us the minimum unit cost C(130).
The calculation is as follows:
C(130) = 0.5 * (130)2 - 130 * (130) + 17,555
C(130) = 0.5 * 16,900 - 16,900 + 17,555
C(130) = 8,450 - 16,900 + 17,555
C(130) = 9,105
Therefore, the minimum unit cost to manufacture a car in this scenario is $9,105.
Find the point, M, that divides segment AB into a ratio of 2:1 if A is at (-1, 2) and B is at (8, 15). A) (6, 8) B) (6, 26 3 ) C) (5, 32 3 ) D) (5, 26 3 ) 27)
Answer:
Hence, the coordinate of point M that divides the line segment AB is [tex](5, \frac{32}{3} )[/tex].
Step-by-step explanation:
Given that,
AB is the line segment, and M divides the line segment AB into a ratio of 2:1.
Coordinate of point A is [tex](-1, 2)[/tex] and Coordinate of point B is [tex](8, 15)[/tex].
Let, the coordinate of point M is [tex](x. y)[/tex].
Now,
The coordinate of a point M, which divides the line segment AB internally in the ratio [tex]m_{1}:m_{2}[/tex] are given by:
[tex]\frac{m_{1}x_{2}+m_{2}x_{1} }{(m_{1}+m_{2}) } ,\frac{m_{1}y_{2}+m_{2}y_{1} }{(m_{1}+m_{2}) }[/tex]
[tex]x[/tex] coordinate of point M is [tex]\frac{(2\times 8)+(1\times -1)}{(2+1)}[/tex] = [tex]\frac{(16-1)}{3} =\frac{15}{3} =5[/tex]
[tex]y[/tex] coordinate of point M is [tex]\frac{(2\times 15)+(1\times 2)}{(2+1)}[/tex] = [tex]\frac{30+2}{3} = \frac{32}{3}[/tex]
Hence, the coordinate of point M that divides the line segment AB is [tex](5, \frac{32}{3} )[/tex].