Answer:
The 95% confidence interval = (98.225, 98.655)
Step-by-step explanation:
The formula for Confidence Interval =
Mean ± z × standard deviation/√n
Where Mean = 98.44°F
Standard deviation = 0.30°F
n = number of samples is 10
Because our number if samples is small, we use the t score confidence interval formula
Mean ± t × standard deviation/√n
Degrees of Freedom = n - 1
= 10 - 1 = 9
We find the t score of 95% confidence interval and degrees of freedom 9
= 2.262
Hence,
Confidence interval = 98.44 ± 2.262 × 0.30/√10
= 98.44 ± 0.214592162
Confidence Interval
98.44 - 0.214592162
= 98.225407838
≈ 98.225
98.44 + 0.214592162
= 98.654592162
≈ 98.655
The 95% confidence interval = (98.225, 98.655)
The 95% confidence interval for the mean of all body temperatures is [98.2255, 98.6545] (in degree Fahrenheit)
How to calculate confidence interval for population mean from small sample?If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.
Let the sample mean given as [tex]\overline{x}[/tex] andThe sample standard deviation s, andThe sample size = n, and The level of significance = [tex]\alpha[/tex]Then, we get the confidence interval in between the limits
[tex]\overline{x} \pm t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}[/tex]
where [tex]t_{\alpha/2}[/tex] is the critical value of 't' that can be found online or from tabulated values of critical value for specific level of significance and degree of freedom = n - 1
For this case, we have:
The sample mean given as [tex]\overline{x}[/tex] = 98.44° FThe sample standard deviation s = 0.30° F, andThe sample size = n = 10, and The level of significance = [tex]\alpha[/tex] = 100% - confidence level = 100% - 95% = 5% = 0.05The degree of freedom(d.f.) is n-1 = 10-1=9
At d.f. 9, at level of significance 0.05, the critical value of t is [tex]t_{\alpha/2} = 2.262[/tex]
Thus, the limits of the confidence interval is calculated as;
[tex]\overline{x} \pm t_{\alpha/2}\times \dfrac{s}{\sqrt{n}} = 98.44 \pm 2.262 \times \dfrac{0.3}{\sqrt{10}} = 98.44 \pm 0.2145[/tex]
This shows that the confidence interval is [98.44 - 0.2145, 98.44 + 0.2145] which is [98.2255, 98.6545] (in degree Fahrenheit)
Thus, the 95% confidence interval for the mean of all body temperatures is [98.2255, 98.6545] (in degree Fahrenheit)
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1. Simplify by combining
like terms.
j + 3t + 8 + 7j + 2t
select the correct description for the expression 5(x-7)
A the product of a number and a sum
B the quotient of a difference and a number
C the quotient of a sum and a number
D The product of a number and a difference
PLSSS HELP
Answer:
d
Step-by-step explanation:
i got it
Answer:
The correct answer is D
Step-by-step explanation:
My reason for giving this answer is because this problem is written in expression form. Since there is a variable in the expression, You cannot solve X-7 without outside information on the value of X. So D would be the answer because The answer to a multiplication problem is called the product, Then the answer to a subtraction problem is a difference. Answer D says "The product of a number and a difference", Which would mean multiplication and subtraction.
Hope this helped!
PLEASE HELP 15 POINTS WILL BE GIVEN TO THE CORRECT ANSWER!
Answer:
but where is the question
kindly attach it
What is the answer to the question?
A jar contains four orange marbles numbered one to four. The jar also contains four green marbles numbered one
to four. You randomly pick a marble. It is orange or has a number less than three.
Determine if the scenario involves mutually exclusive events. Then find the probability.
Answer:
1/4
Step-by-step explanation:
Probability of (mutually exclusive events) randomly pick a orange or number less than three is P(A or B) = ( 3/ 4).
What is mutually exclusive event?
" Two events 'A' and 'B' are said to be mutually exclusive events if and only if they are not happening at the same time. It is written as P(A or B)."
Formula used
Probability = (Number of favourable outcome) / Total outcomes
For Mutually exclusive event
P(A or B) = P(A) + P(B)
P(A∩B) = 0
According to the question,
Let O₁, O₂, O₃, O₄ be the orange balls numbered one to four.
Let G₁, G₂, G₃, G₄ be the green balls numbered one to four.
As per condition,
Randomly pick a ball which is orange or numbered less than three is mutually exclusive event.
Let A represents the event ball to be orange.
Let B represents the event ball to be number less than three.
Number of total outcomes = 8
Favourable outcome for event A =4
Favourable outcome for event B =2
Therefore,
P(A) = 4 / 8
P(B) = 2 /8
Substitute the value in the formula of mutually exclusive event P(A or B) we get,
P(A or B) = ( 4 / 8) + ( 2 / 8)
= ( 6 / 8)
= ( 3 / 4)
Hence, probability of ball to be orange or number less than 3 is
P(A or B) = 3 /4.
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solve by using the quadratic formula
x^2-4x=-2
Answer:
x=2+[tex]\sqrt[]{2}[/tex] or x= 2-[tex]\sqrt[]{2}\\[/tex]
Step-by-step explanation:
Jaden measured the length of a book to be 29 cm. The actual length of the book is 27 cm.
What is the percent error for Jaden's measurement?
Answer:
About 7%
Step-by-step explanation:
He got 27/29 cm correct which is about 93% so he was off by 7%.
Write this in expression: Three less than five times a number....Use x for the number i will give out points to whoever answers quick!
Answer:
5x-3
Step-by-step explanation:
three less than 5 so three will come after the 5. and the number (x) is being multiplied by 5
The imaginary coefficient of 18 + 15i is?
Answer:
I bc it has an invisible 1 at the side
Find the exact value of cos (α+β), given π/2<α<π, π/2<β<π
tan α = -15/8, sin β = 5/13
I need an explanation on how to do it too. Thank you.
Answer:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{21}{221}[/tex]
Step-by-step explanation:
First, we can draw two right triangles to represent the given information.
Please refer to the attachment.
We will ignore the negatives for now.
The triangle on the left represents the ratio:
[tex]\displaystyle \tan(\alpha)=\frac{15}{8}[/tex]
And the triangle on the right represents the ratio:
[tex]\displaystyle \sin(\beta)=\frac{5}{13}[/tex]
And the unknown side, c and d, were determined using the Pythagorean Theorem.
We want to find:
[tex]\displaystyle \cos(\alpha+\beta), \; \pi/2<\alpha<\pi, \; \pi/2<\beta<\pi[/tex]
So, both α and β are in QII.
Using the Sum Identity, we can write our expression as:
[tex]\displaystyle\cos(\alpha+\beta) =\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)[/tex]
Now, we will use our triangles and what we know about our angles and quadrants.
Since α and β are in QII, cosine is always negative, sine is always positive, and tangent is always negative.
Now, we can use our trig ratios. Recall SohCahToa.
According to the first triangle, cos(α) is 8/17.
However, since α is in QII, cos(α) must be -8/17.
Likewise, according to the second triangle, cos(β) is 12/13.
Since β is in QII, cos(β) is -12/13.
Now, we can determine our sine ratios.
According to the first triangle, sin(α) is 15/17.
And since α is in QII, this stays positive.
And, sin(β), as given to us, is 5/13.
Therefore, we will substitute this into our equation. So:
[tex]\displaystyle \cos(\alpha+\beta)=(-\frac{8}{17})(-\frac{12}{13})-(\frac{15}{17})(\frac{5}{13})[/tex]
Evaluate:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{96}{221}-\frac{75}{221}[/tex]
Hence:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{21}{221}[/tex]
Solving equations
-2(x+3)=3(2x-10)
Answer:
x=3
Step-by-step explanation:
nine bo6s can paint a house in 3 hours how long would one boy take working at the same rate
Answer:
1 boy can work about 0.3 hours
Step-by-step explanation:
The answer is about 0.3 because 3 divided by 9 is 0.333 but rounded its just 0.3
P.S Can I have brainliest?
Which situation can be simulated by rolling a six-sided die once?
selecting one person from a group of four boys and two girls
picking one pair of jeans from four distinct pairs
selecting 1 of 12 boys as the captain of the baseball team
selecting one of two smartphones
Answer:
A. Selecting one person from a group of four boys and two girls.
Step-by-step explanation:
A dice has six sides and here we have six people we're trying to choose from. If each person is assigned a number on the dice rolling the dice once will pick out of the six of them.
Answer:
A and D
Step-by-step explanation:
A is pretty obvious becuase there are four girls and two boyd which add up to six
Now D would be correct because you have two options so you can split it up 50/50 to get your answer!
HOPE this helps you!
Answer the question that is in the picture please!
Answer:
55
Step-by-step explanation:
180-125= 55
Answer:
55
Step-by-step explanation:
Line DCF is 125. A straight line is 180. So, if you are missing a degree of an angle when you have another angel given to you, then just subtract 180 from the degree that was given. So it's more like this: 180 - 125 = 55.
Vernon downloads games on his phone every month. Each game costs the same amount.
Month
Games Downloaded
Cost
January
14
$56
February
23
$92
March
?
$116
April
19
$76
How many games did Vernon download in March?
O 31 games
29 games
27 games
25 games
Answer:
29 games
Step-by-step explanation:
Simply divide the amount spent by the number of games.
For January, it would be 56/4 = $4 each game
The same goes on for the following months, even March since the problem states that each game costs the same amount.
So $116/$4 = 29 games.
Vernon downloaded 29 games in March.
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Month Games Downloaded Cost
JAN 14 $56
FEB 23 $92
MAR __ $116
APR 19 $76
Now, In January the price for each game
=56 /15
=$4 each game
In February the price for each game
=92/23
=$4 per game
So, In March
= $116/ $4
= 29 games.
Hence, Vernon downloaded 29 games in March.
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• The first customer paid $12 for 14 postcards and 5 large envelopes.
• The second customer paid $24.80 for 10 postcards and 15 large envelopes.
What was the cost in dollars of each large envelope?
Answer:
$1.42
Step-by-step explanation:
The cost of postcard is $0.35 and the cost of large envelope is $1.42.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have -
first customer paid $12 for 14 postcards and 5 large envelopes.second customer paid $24.80 for 10 postcards and 15 large envelopes.We can write -
14x + 5y = 12
10x + 15y = 24.80
Now, solving the equation graphically, we get -
x = 0.35
y = 1.42
Therefore, the cost of postcard is $0.35 and the cost of large envelope is $1.42.
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plz help I have only 5 minutes
From point A to point C, we can see there's a wide range between 0 and -10. It's not possible for the answer to be B or D, since the point lays between -10 and 0, and those points are both beyond -10. Between A and C, the best answer would be C. -8.45, since the point is much closer to 10 that it is to the center, around where -5.8 would be.
Find the measure of the indicated angle to the nearest degree
Please show all steps ty
Answer:
71 degrees
Step-by-step explanation:
1. We know that the angle is unknown as demonstrated by '?'
2. The 17 side is opposite of the unknown angle
3. The 18 side the hypotenuse (not in contact with the right angle)
4. Therefore sine will be used where, sine(degree) = opposite/hypotenuse
5. The equation should be sine(degree) = 17/18
6. Since we don't know the degree we bring sine to the left and has a negative power of 1
7. The equation now becomes degree = sine^-1 (17/18)
8. The answer to this is 70.811... which equals 70 degrees and 48 minutes which rounds to the nearest degree of 71
please help me with this I'll give brainliest to best answer!
Answer:
Liner
Step-by-step explanation:
17,21,18,20,24
WILL GIVE BRAINLIEST!!!!!
solve for y,
y=3x-2
Answer:
-2
Step-by-step explanation:
Y=3x-2
y=3x0-2
y=-2
Four ingredients costing $320 per kg, $240 per kg, $160 per kg and $80 per kg are mixed so that their masses are in the ratio 4:1:3:2. Calculate the average cost per kg of the mixture.
Answer:
$2160
Step-by-step explanation:
(320*4)+(240*1)+(160*3)+(80*2) = 2160
Four ingredients costing $320 per kg, $240 per kg, $160 per kg and $80 per kg are mixed so that their masses are in the ratio 4:1:3:2. The average cost per kg of the mixture, would be $2160.
What is average?The average is defined as the mean value of the given data which is equal to the ratio of the sum of the data value to the total number of units present in the data.
It is given that
Four ingredients costing $320 per kg, $240 per kg, $160 per kg and $80 per kg are mixed so that their masses are in the ratio 4:1:3:2.
(320 x 4) = 1280
(240 x 1) = 240
(160 x 3) = 480
(80 x 2) = 160
The averege cost per kg of the mixture,
1280 + 240 + 480 + 160
= 2160
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Brainiliest
Solve For x.
x
_ = 4
40
A) 16
B) 36
C) 160
D)176
Answer:
It would be 160 (C)
Step-by-step explanation:
160 is the only one that works if u rplace x with 160.
Answer:
160
This is how I got my answer I divided each answer by 4 to see if it equaled 40 and 160 divided by 4 equals 40 so 160 is your answer
Given if logan eats his vegetables then he can have bowl of ice cream logan eats his vegetables..
Guyssss I really need help on this high school and up. I’m doing corrections so it’s not c
Answer:
B~48
Step-by-step explanation:
I think its 48....let me know if right or wrong sorry if wrong..
A graph of a function in the photo, all blanks have these same answer choices.
PLEASE ANSWER
Answer:
did you try google ? I usally search up things when I dont usally know i dont know to be honest try to search it up if you already did then good luck I hope someone answers
12 more than 3 times a number is 4
How to write it in equation form?
Answer:
3n + 12 = 4
Step-by-step explanation:
hope this help, pls mark brainliest :D
3 1/2 - 2 5/9 still for the same test XD
Answer: 17/18
Step-by-step explanation:
I need help guys?.....
x=15
if this is not right, please report me
eeeeeee someone help
Answer:
C
Step-by-step explanation:
The he has to pay 40$ a month (40*m or 40m) + the intial amount of 75. So put together this equation would be C. Hope this helps!!! :)
Answer: C t = 40m +75
Step-by-step explanation:
plz guys help and DONT ignore me plz
Answer:
Object b
Step-by-step explanation:
So you see that when you look at the graph it shows two point and you would think A is bigger because its higher. So when looking closely it look that object B is a lot farther that object A making it greater than object A because A is a lot higher but time is shorter than abject B.
This might be wrong so sorry I tried.
:)
Answer:
A
Step-by-step explanation:
You could do a calculation.
A: d/t = 10 / 2 = 5 m/s
B: d/2 = 4/3 = 1.33 m/s
A has the greater unit rate.
