Answer:
The margin of error is [tex]E = 6.9 [/tex]
The 95% confidence interval is [tex] 26.5 < \mu < 40.3 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 31
The mean is [tex]\mu = 33.4 \ ng/ml[/tex]
The standard deviation is [tex]\sigma = 19.6 \ ng/ml[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{19.6 }{\sqrt{31 } }[/tex]
=> [tex]E = 6.9 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 33.4 - 6.9 < \mu < 33.4 + 6.9 [/tex]
=> [tex] 26.5 < \mu < 40.3 [/tex]
Help guyssssssssssssss
Answer:
1
Step-by-step explanation:
what is 3+5 divided by 6/7?
Answer:
8 divided by 6/7. I will give you the answer in fraction form and in decimal form. 56/6 can be simplified to 28/3. 28/3 is an improper fraction and should be written as 9 1/3.
Step-by-step explanation:
You add 3+5 together and then divide. After that you simplify your answer
Hope this helped, Have a Great Day!!
ONLY DO THE THE ONES THAT HAVE BLUE NEXT TO THEM!!!
Answer:
You need to have an attachment or question for us to help you. :3
Step-by-step explanation:
10 POINTS AND BRAINLIEST TO THE CORRECT ANSWER A restaurant has a group of seats at the counter and t individual tables, where each table has the same number of seats. If 3t + 15 represents the total number of seats in the restaurant, what does 3
represent?
O the number of seats at each table
O the number of seats at the counter
O the total number of customers in the restaurant
O the total number of tables in the restaurant
Answer:
I think A
Step-by-step explanation:
The correct explanation for the number 3 will be;
⇒ the number of seats at each table.
Option A is true.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The mathematical expression is;
⇒ 3t + 15
Where, t represent the individual tables.
And, The expression represents the total number of seats in the restaurant.
Now,
Since, 't' represent the individual tables.
Hence,
3t = Number of tables for 3 seats
Clearly, 3 represent the number of seats at each table.
Therefore,
The correct explanation for the number 3 will be;
⇒ the number of seats at each table.
Option A is true.
Learn more about the expression visit:
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PLEASE HELP
A car dealer offers a 15% discount off the list price x for any car on the lot. At the same time, the manufacturer offers a $1500 rebate for each purchase of a car.
a. Write a function f(x) to represent the price after the discount is applied.
b. Write a function g(x) to represent the price after the rebate is applied.
Suppose the list price of a car is $19,000. Use a composite function to find the price
of the car:
C. if the discount is applied before the rebate;
D. if the rebate is applied before the discount
Answer:
A) f(x) = 0.85x
B) g(x) = x - 1500
C) g(f(x)) = $14650
D) f(g(x)) = $14875
Step-by-step explanation:
A) The list price is x and a 15% discount is applied.
Thus;
f(x) = x - 15%x
f(x) = 0.85x
B) We are told that the manufacturer offers a $1500 rebate for each purchase of a car.
Thus, the function g(x) to represent the price after the rebate is applied is;
g(x) = x - 1500
C)if the discount is applied before the rebate, the function is;
g(f(x))
Now,
f(x) = 0.85(19000)
f(x) = 16150
g(x) = x - 1500
Thus;
g(x) = 16150 - 1500
g(x) = $14650
D) If discount after rebate, then we have; f(g(x))
g(x) = 19000 - 1500
g(x) = 17500
f(g(x)) = 0.85(17500)
f(g(x)) = $14875
Four hot air balloons each descend 295 feet per minute for 7 minutes. Find the total change in altitude for all 4 balloons.
The total change in altitude for all 4 balloons is
(blank) feet.
Answer:
There is descending of 8260 feet in altitude for all 4 balloons.
I dont understand even where to begin on this, please help!
Answer:
-17
Step-by-step explanation:
The average rate of change is synonymous to the slope of a function.
We want to find the average rate of change for the function:
[tex]f(x)=-2x^2-3x-8[/tex]
For the interval [3, 4]
So, we simply have to calculate the values of the function at the endpoints and then find the slope between them.
Our endpoint values are x=3 and x=4. So:
[tex]\begin{aligned} f(3)&=-2(3)^2-3(3)-8 \\ f(3)&=-18-9-8 \\ f(3)&=-35\end{aligned}[/tex]
And:
[tex]\begin{aligned} f(4)&=-2(4)^2-3(4)-8 \\ f(4)&=-32-12-8 \\f(4)&=-52\end{aligned}[/tex]
So, we have the two points (3, -35) and (4, -52).
Now, we can use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Calculate the slope:
[tex]m=\frac{-52-(-35)}{4-3}=-17/1=-17[/tex]
Hence, the slope or the average rate of change for our function for the interval [3, 4] is -17.
How many pounds of chocolates that cost $7 per pound must be mixed with 3 pounds of caramels that cost $3.50 per pound to make a candy mix that
cost $5.25 per pound?
Answer:
You know somw things are changed i can't even answer that so please answer it yourself because hahhahaahahaahahhahahahha hello
Step-by-step explanation:
Because i dont know how to answer that ok?! Tell that to ur mom haha
What Is 55 > -7x + 6 ?
Answer:
x>−7
Step-by-step explanation:
55−6>−7x
49>−7x
−
7
49
<x
−7<x
x>−7
8. Three gases found in Earth's atmosphere are carbon dioxide, nitrogen, and oxygen. What is their
order of abundance from greatest to least?
A. nitrogen, oxygen, carbon dioxide
B. nitrogen, carbon dioxide, oxygen
C. oxygen, nitrogen, carbon dioxide
D. carbon dioxide, oxygen, nitrogen
Answer:
carbon dioxide,oxygen,nitrogen
answer choices are
A:45°
B:180°
C:61°
D:119°
Answer:
Option c: 61° is the correct answer
Step-by-step explanation:
By the diagram attached with the question, we can conclude that a transversal is interesting two parallel lines which results in formation of 8 angles.
Angle 3 and angle 5 are interior angles on same side of transversal.
When a transversal intersects two parallel lines, the interior angles on same side of transversal are supplementary angles i.e. their sum is 180°
So using this
m∠3+m∠5 = 180°
m∠3 + 119° = 180°
m∠3 = 180°-119°
m∠3 = 61°
Hence,
Option c: 61° is the correct answer
Change 10/25 to a decimal
Answer:
0.4
Step-by-step explanation:
→ Convert fraction to a denominator of 100
10 / 25 ⇔ 40 / 100
Answer:
0.4
Step-by-step explanation:
An easy way to do this is to get the fraction over 100
So, multiply the fraction by 4 (because 25*4=100)
then you get 40/100 which is 0.4 in decimal form
I need an answer quick. I am trying to finish this fast.
Answer:
D, m<4 is 137°
Step-by-step explanation:
The answer would be D, because m<4 would be supplementary with the angle that's 43 degrees. Supplementary angles add up to 180, so this could be found through the following equation.
x + 43 = 180
x would represent <4
You would now subtract 43 from both sides.
x = 137
Answer:
D. The m<4 is 137°
Step-by-step explanation:
The rest of the angles are not correct because if you add 142+56 (adjacent angles) or the unknown angles (angle 1 + angle 2), it doesn't equal 180. You can picture it as angle 3 and its adjacent angle (56°) equal to 180 sience there sharing one straight line thus being 180°
If f(x) = 3[x] + 5, find f(x) if x = 4.3
PLS ANSWER I HAVE TO TURN IN SOON
Answer:
F(x) = 17.9
Step-by-step explanation:
Plug in x. 3(4.3) + 5 = 17.9
List what you are thankful for! (It's Thanksgiving! Answer if you bake! Or if you like cakes pies cookies and treats!!! )
Answer:
I'm thankful for everything :3
I do not know how to bake but I love cookies UvU
Step-by-step explanation:
Answer:
My family!
Step-by-step explanation:
I am baking cheesecake
Which expression is equivalent to (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) )?
d
Step-by-step explanation:
Answer:
the answer is d
Step-by-step explanation:
What is 11/12 divided by 1/3
Answer:
Step-by-step explanation:
11/12 ÷ 1/3 = 2 3/4, or 11/2 as a improper fraction
hope this helps
Answer:
11/12 divided by 1/3 is the same as 11/12 * 3/1, which is 33/12.
Step-by-step explanation:
Which number is divisible by 3?
A) 1,794
B) 1,912
C) 1,270
D) 473
Answer:
Step-by-step explanation:
should be A.
-5x=-6
what is the value of x?
Answer: x=6/5
Step-by-step explanation:
Answer:
6/5
Step-by-step explanation:
An equilateral triangle and a regular hexagon have the same area. The ratio of the side length of the regular hexagon to the side length of the equilateral triangle can be written as m/√n. What is m+n?
Help me plz!
Answer:
7
Step-by-step explanation:
Let a and b be the sides of the equilateral triangle and the regular hexagon respectively as shown in figures (1) and (2).
The area of the equilateral having side a is
[tex]A_T= \frac {\sqrt3}{2}a^2\cdots(i)[/tex]
Now, join all the 6 corner points of the regular hexagon to the center of the hexagon as shown in figure (3).
As there are 6 equal sides, so angle subtended by each side at the center is 360/6=60 degrees.
Considering the triangle POR:
[tex]\angle POR= 60[/tex] degree [angle at center]
As sides PO=RO, so [tex]\angle OPR = \angle ORP = 60[/tex] degree.
Hence, triangle POR is an equilateral triangle.
Similarly, all the remaining 5 triangles are equilateral triangles.
So, the area of hexagon = 6 x Area of triangle POR
As the length of sides of the triangle POR is b,
so the area of the triangle POR [tex]= \frac {\sqrt3}{2}b^2[/tex].
Hence, the area of the regular hexagon,
[tex]A_H = 6 \times \frac {\sqrt3}{2}b^2\cdots(ii)[/tex]
As the equilateral triangle and a regular hexagon have the same area, so from the equations (i)and (ii), we have
[tex]A_T=A_H\\\\\frac {\sqrt3}{2}a^2=6 \times \frac {\sqrt3}{2}b^2\\\\\Rightarrow a^2=6b^2\\\\\Rightarrow \frac {b^2}{a^2}=\frac 1 6\\\\\Rightarrow \frac {b}{a}=\frac {1}{\sqrt 6}\cdots(iii)[/tex]
Given that the ratio of the side length of the regular hexagon to the side length of the equilateral triangle, b/a= m/√n.
On comparing with the equation (iii), we have
m=1 and n=6
Hence, m+n=1+6=7.
Slope is known as the run over the rise. True or False
Answer:
false. slope is calculated by rise over run
Answer:
FALSE
Step-by-step explanation:
Slope is known as the RISE OVER RUN.
Can I get brainliest? Plz!!!
Nebi has already typed 250 words. He then starts a timer and finds that he types 150 words in 3 minutes. If nebi types at a constant rate, write a linear equation to represent the number of words w that nebi types m minutes after starting the timer
Answer:
[tex]w=250+50m[/tex]
Step-by-step explanation:
Number words Nebi has typed = 250
t = Duration of typing = 3 minutes
Number of words typed in 3 minutes = 150
Rate of typing in 3 minutes
[tex]\dfrac{150}{3}=50\ \text{words/minute}[/tex]
So the linear equation representing the situation would be
[tex]w=250+50m[/tex]
Where
w = Number of words
m = Number of minutes after starting the timer
The linear equation to represent the number of words w that nebi types m minutes after starting the timer is w = 250 + 50m
Given:
Words already typed = 250 words.
Words typed in 3 minutes = 150 words
Words typed per minute = 150 words / 3 minutes
= 50 words per minute
w = Total words typed
m = number of minutes
The equation:
Total words typed = Words already typed + (Words typed per minute × number of minutes )
w = 250 + (50 × m)
w = 250 + 50m
Therefore, linear equation to represent the number of words w that nebi types m minutes after starting the timer is w = 250 + 50m
Read more:
https://brainly.com/question/16450098
If 4 gal of the premium unleaded gasoline costs $16.24, how much would it cost to completely fill a tank whose capacity is 7 gal?
Answer:
$4.06 per gallon $4.06 x 7 = $28.42
Step-by-step explanation:
Identify the following as an identity, a contradiction, or a conditional equation.
3(x + 2) = 3x + 2
PLS I NEED HELPPP
(if u don’t mind pls explain ur answer)
How to reduce 0.35 to the lowest term
A car travels 20 miles in half an hour at constant speed is
What is the equation of a line that is perpendicular to 2x+y=−4 and passes through the point (2, −8) ?
Answer:
y=1/2z-9= Perpendicular line
y=-2x-4= parrallel
Step-by-step explanation:
Answer:
y = [tex]\frac{1}{2}[/tex] (x) - 9
Step-by-step explanation:
Set the given equation to standard form: y = -2x -4
Set the slope of the given equation's slope to the reciprocal ( -2 --> 1/2).
Thus, you will have y = 1/2x + b
Insert the given information: (2, -8)
-8 = 1/2 (2) + b
Half of 2 is 1: subtract it on both sides...
-8 = 1 + b
-1 -1
-9 = b
So, the equation will be y = 1/2(x) - 9
Ivy wants to see 20 birds on her hike. So far, she has seen 8. How many more birds does she need to see.
Answer:
12
Step-by-step explanation:
20-8=12
helppppp please I will give brainliest
Answer:
y = -1/2x
Step-by-step explanation:
The slope is negative and 1/2, and y-intercept is 0