Answer:
a) The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.
b)
The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.
c) They are respected, as the upper bound of both intervals is below the new FAA recommendations.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve these questions.
Question a:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 100 - 1 = 99
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9842
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.9842\frac{20}{\sqrt{100}} = 4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 183 - 4 = 179 pounds.
The upper end of the interval is the sample mean added to M. So it is 183 + 4 = 187 pounds.
The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.
Question b:
Critical value is the same(same sample size and confidence level).
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.9842\frac{23}{\sqrt{100}} = 4.6[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 190 - 4.6 = 185.4 pounds.
The upper end of the interval is the sample mean added to M. So it is 190 + 4.6 = 194.6 pounds.
The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.
c. The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from Parts (a) and (b).
They are respected, as the upper bound of both intervals is below the new FAA recommendations.
pls help i’ll give brainliest
Answer:
94
Step-by-step explanation:
So
376= x + 3x
Where x is the hambugers and 3 x is cheeseburgers
so it is the same as
376= 4x
divide both sides by 4
x= 94
we can check by tripling x = 283 and adding the hamburgers we found to be 94 which gives us 376
what is equivalent to 2/8
Answer:
1/4,
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
2-3(3x+1)=2(7-6x) - SOLVE THE FOLLOWING EQUATION
Answer: X=5
Explaination: Did the problem.
what is the correct factorization of 100^12
Answer:
GCF of 12 and 100 by Prime Factorization
Prime factorization of 12 and 100 is (2 × 2 × 3) and (2 × 2 × 5 × 5) respectively. As visible, 12 and 100 have common prime factors. Hence, the GCF of 12 and 100 is 2 × 2 = 4.
GCF of 12 and 100 by Listing Common FactorsFactors of 12: 1, 2, 3, 4, 6, 12Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
There are 3 common factors of 12 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 100 is 4.
help plz it due in an hour
Answer:
4√3/3
Step-by-step explanation:
This is a 30,60,90 triangle. Therefore, small side (X) is equal to 4/√3 or X√3. In this case, it is 4/√3. This is equal to 4/√3 times √3/√3. This means the answer will be 4√3/3. Therefore, X=4√3/3
If this helps please mark as brainliest
Prove that for any natural n: a the number 7^(n+4) −7^n is divisible by 30.
For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.
What is mathematical induction?An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.
Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.
Let, n = 0.
Therefore,
7⁴ - 7⁰.
= 2401 - 1.
= 2400.
= 30×80, Divisible by 30.
Similarly for n = 1 we have,
7⁵ - 7¹.
= 16807 - 7.
= 16800.
= 30×560.
Hence by induction, the cycle will continue.
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2 cm
A glass bead has the shape of a rectangular prism with a smaller rectangular
prism removed. What is the volume of the glass that forms the bead?
]
2 cm
4 cm
7 cm
4 cm
(The figure is not to scale.)
The volume of the glass that forms the bead is cm3.
Answer:
80
Step-by-step explanation:
What is the area of the figure below? 7 cm 8 cm 3 cm 4 cm
Anna wants to buy 4 sweaters. The sweater come at a discount rate. If you buy one sweater regular price the other sweater is 40% off. How much percent is off of each sweater?
Answer:
20%------------------------
If you buy a sweater, the second one is at 40% discount.
Divide the discount between the two to get:
40%/2 = 20%You get a discount of 20% for each sweater.
Answer:
Discount percentage = 20%
Step-by-step explanation:
Discount of the sweaters,
→ first sweater = 0%
→ other sweater = 40%
The average discount percent is,
→ (first sweater + other sweater)/2
→ (0% + 40%) ÷ 2
→ (0 + 40)/2
→ 40/2
→ 20% off
Hence, the answer is 20% off.
1. The backdrop of the altar in a church is triangular in shape. It has a base of 10.5 meters
and a height of 8.5meters. The priest instructed the layman to cover it from the center with
a white rectangular cloth measuring 4.5 meters long and 4 meters wide. How big was the uncovered backdrop?
A. 26.63 m² B. 18 m²
C. 44.63 m² D. 89.25 m²
------------------------------------
2. A circular portion of a cardboard having 7.6 centimeters radius was being cut out from the entire
squarepiece of a cardboard having a side of 34 centimeters. How big was the remaining piece of
a cardboard?
A.181.37 m² B.974.63 m²
C. 1156 m² D. 219.6 m²
Answer:
#1
Area of triangle backdrop:
A = 1/2bh = 1/2(10.5)(8.5) = 44.63 m²Area of the cloth:
A = 4.5*4 = 18 m²Uncovered area:
44.63 - 18 = 26.63 m²Choice A
#2
Area of the cut piece:
A = πr² = 3.14*7.6² = 181.37 cm²Area of the square piece:
A= a² = 34² = 1156 cm²Remaining piece is:
1156 - 181.37 = 974.63 cm²Choice B
Explain what an exponential form is but leveled down for high schoolers
The required exponential function is given as y = aˣ where the value of a should be positive always.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
here,
Since from the above definition exponential function is given as y = aˣ,
This shows the exponential increase and decrease, by means of exponential increase and decrease, a sudden in increase and sudden decrease of function as the value of a varies, see in the graph after the answer. And the value of an always remains positive.
Thus, the required exponential function is given as y = aˣ where the value of a should be positive always.
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paper costs $1.50, which inequality is used to find how many rolls of paper could be purchased with less than $12?
Answer:
1.50x < 12 (the inequality would just be "less than")
Step-by-step explanation:
17v = 62 (exponential equations with logarithms, solve)
Therefore v = log(62) / log(17) is the solution for v, the unknown variable in the equation.
Define log(Logarithm).The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.
What is a function?A function in mathematics is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
To solve this exponential equation, we can use the logarithms property that is log(a^b) = b*log(a).
Given the equation 17v = 62, we can take the logarithm base 17 of both sides:
log(17^v) = log(62)
v*log(17) = log(62)
Dividing both sides by log(17) gives us:
v = log(62) / log(17)
This is the solution for v, the unknown variable in the equation.
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Question #2
What is the value of the expression
35
?
23 – 1
A 5
B 7
C 12
Answer:
A. 5
Step-by-step explanation:
just use calculator tbh
let sets a and b defined as follows
A is c,d,e,f,g
b is the set of odd numbers greater than 5 and less than 13
Answer:
The set A is defined as the set containing the elements c, d, e, f, and g.
The set B is defined as the set of odd numbers greater than 5 and less than 13. This set includes the elements 7, 9, and 11.
Step-by-step explanation:
The square of a number minus six times a number equals negative five.
The equation is ?
The solutions to the equation is ?
Equation [tex]x^{2}-6x=-5[/tex]
Solving:
[tex]x^2 - 6x+5=0\\\\(x-5)(x-1)=0\\\\x=1, 5[/tex]
PLEASE BE FAST
Find the constant of proportionality for the proportional relationship shown in the graph.
graph of a line going through 0 comma 0 and one half comma 5
p = 10
p = 5
p = 0.5
p = 0.1
The constant of proportionality is 10 for the proportional relationship shown in the graph.
What is the constant of proportionality?The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.
The proportional relationship is shown in the given graph.
As per the given graph, we take two points (1, 10) and (2, 20)
So, the constant of proportionality will be as:
⇒ (20 - 10)/(2-1)
⇒ 10/1
⇒ 10
Hence, the correct answer would be option (A).
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Here is the graph of a quadratic function f.
Select all equations that could define the function f.
Answer:
A B and D
Step-by-step explanation:
Given the parabola is opening downward, the function has to be negative. Therefore, A B and D are correct.
The following equations could define the given quadratic function.
1. -1(x-1)²+9
4. -x²+2x+8
6. (x+2)(x-4)
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c.
1. The function -1(x-1)²+9 represents a downward-facing parabola.
The vertex of the parabola is at point (1, 9), and it opens downward because the coefficient of the squared term (-1) is negative.
4. The function -x²+2x+8 represents a downward-facing parabola as well.
6. The parabola intersects the x-axis at x = -2 and x = 4.
Hence, the correct answer is options 1, 4, 6.
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help help help help pls
Answer:
67
Step-by-step explanation:
42+90=132
180-132=48
<A=48
if u use the 113 that you got than
113+48=161
180-161=19
<B= 19
48+19=67
gretchen buys a sweater at a clearance sale for $35.74. The original price of the sweater was $59.99. Find the percent discount.
Answer:
59.5765%
Step-by-step explanation:
$35.74/$59.99
-15 POINTS-
How many sides does a regular polygon have if one interior angle measures 144°
Answer: 10 sides
Step-by-step explanation:
You can always use the given formula to calculate but I (personally) find it much easier to calculate the number of sides using the exterior angle.
To calculate the exterior angle, it is 180 - the interior angle.
In this example, the exterior angle would be 180-144 = 36°
Because it is a regular polygon, we know that all the angles in the shape are the same.
In all polygons, the exterior angles always add up to 360 degrees.
So divide 360 by 36 (the size of each exterior angle), and you get 10.
360/36 = 10
< 8. If m M = (8x - 56) and mNP = (5x + 22), find mLP. M39 degrees
Answer:
I think 42 is the answer...
The function f is defined by f(x) = 2x2 -7.
Find f(5x).
Answer:
10fx-7
Step-by-step explanation:
(:
Can y’all help me on question 20?!
Answer:
A. 84
Step-by-step explanation:
84 / 4 = 21
Answer:
Its a(84)
Step-by-step explanation:
a line has a slope of 7/10 and a y intercept of (0,-4) what is the equation of the line in standard form
Considering the definition of a line, the equation of the line in standard form is y - 7/10x= -4
What is Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.The standard form of a linear equation is Ax + By = C. In this type of equation, x and y are variables and A, B, and C are integers.
Equation in this caseIn this case, you know:
A line has a slope of 7/10.A line has a y-intercept of (0,-4).So, the line can be expressed as:
y=7/10x -4
Expresed in standard form:
y - 7/10x= -4
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Determine if the graph is a function.
Answer:
1. not a function
2. function
3. function
Step-by-step explanation:
ask yourself..."does it pass the vertical line test?"
If a= m2 + 2, what is the value of a when m=-3?
0-7
-4
11
00
Answer:
a=11
Step-by-step explanation:
a=m2 +2
a= (-3)2+2
a=9+2
a=11
The square of a number minus six times a number equals negative five.
The equation is ?
The solutions to the equation is ?
Answer:
x² - 6x = -5
x = {1, 5}
Step-by-step explanation:
The square of a number minus six times a number equals negative five.
x² - 6x = -5
Add 5 to both sides
x² - 6x + 5 = 0
Factor
(x - 1)(x - 5) = 0
x = {1, 5}
Answer:
[tex]x^{2} - 6x = -5[/tex]
x = 1 or x = 5
Step-by-step explanation:
Let x = the no.
[tex]x^{2} - 6x = -5\\x^{2} - 6x + 5 = 0[/tex]
(x - 1)(x - 5) = 0
x = 1 or x = 5
Find the missing numbers 46 62 87 123 ---- 236
Answer:
The missing numbers are 74, 105, and 178.
please only right answers
Answer:
what is the full question? 4 units left or right or?