Final answer:
To find the equation of a line perpendicular to 2x - 3y = 13 and passing through (-6, 5), first find the slope of the given line, then its negative reciprocal for the perpendicular line, and finally apply the point-slope formula with the new slope and given point.
Explanation:
To find the equation of a line perpendicular to 2x - 3y = 13 that passes through the point (-6, 5), follow these steps:
Rewrite the given equation in slope-intercept form (y = mx + b) to find its slope.
Calculate the slope of the perpendicular line using the negative reciprocal of the given line's slope.
Use the point-slope formula with the slope from step 2 and the given point to find the equation of the perpendicular line.
Rewriting the given equation: 2x - 3y = 13 → -3y = -2x + 13 → y = (2/3)x - 13/3. The slope (m1) is 2/3. The slope of the perpendicular line (m2) is -3/2 (the negative reciprocal of m1). Using the point-slope formula with the perpendicular slope and the point (-6, 5), we get: y - 5 = (-3/2)(x + 6), which simplifies to y = (-3/2)x - 4. This is the equation of the line perpendicular to 2x - 3y = 13 that passes through (-6, 5).
A manufacturing company is shipping a certain number of orders that need to weigh between 187 and 188 pounds in order to ship. Use the dot plot data below to answer the following questions.
187, 187.1, 187.2, 187.3, 187.4, 187.5, 187.6, 187.7, 187.8 ,187.9 ,188
1. How many orders did the company ship between 196 and 197 pounds?
2. What was the most common order weight?
3. Was the average weight for this sample of orders closer to 196 pounds or 197 pounds?
The dot plot shows the distribution of order weights. There were no orders between 196 and 197 pounds. The most common order weight was 187.5 pounds, and the average weight was closer to 196 pounds.
Explanation:1. To find the number of orders between 196 and 197 pounds, we need to look at the dot plot. From the given data, there are no orders between 196 and 197 pounds.
2. The most common order weight from the dot plot is 187.5 pounds.
3. To determine if the average weight is closer to 196 or 197 pounds, we need to calculate the mean of the data. The mean weight is calculated as the sum of the weights divided by the total number of weights. In this case, the mean weight is closer to 196 pounds.
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In the auditorium, there are 21 seats in the first row and 29 seats in the second row. Ths number of seats in a row continues to increase by 8 with each additional row.
Answer:
813 seats
Step-by-step explanation:
Given that,
In the auditorium, the number of seats in the 1st row = 21
In the auditorium, the number of seats in the 2nd row = 29
Therefore, the increasing number of seats in each of the row = 8.
According to the question,
The number of seats in a row continues to increase by 8 seats with each additional row. For example, 29, 37, 45 etc.
To find the number of seats in the 100th row, we have to use statistical formula.
As 21 is the total seats in the 1st row, and there is an increase of 8 seats, the formula should be = 21 + (n - 1) × 8
we have to deduct 1 so that we get 99th rows seat numbers as we have to add 21 with that to find the 100th number row.
As the question is to determine the number of seats in the 100th row, therefore, n = 100.
The number of seats in the 100th row = 21 + (100 - 1) × 8 = 21 + 99 × 8
= 21 + 792 = 813 seats.
What is the most plausible value for the correlation between spending on tobacco and spending on alcohol? 0.99 − 0.50 −0.50 0.80 0.08
Answer:
Option c) 0.80
Step-by-step explanation:
We have to approximate the most possible correlation between spending on tobacco and spending on alcohol.
Correlation is a technique that help us to find or define a relationship between two variables.A positive correlation means that an increase in one quantity leads to an increase in another quantity A negative correlation means with increase in one quantity the other quantity decreases. Values between 0 and 0.3 tells about a weak positive linear relationship, values between 0.3 and 0.7 shows a moderate positive correlation and a correlation of 0.7 and 1.0 states a strong positive linear relationship. Values between 0 and -0.3 tells about a weak negative linear relationship, values between -0.3 and -0.7 shows a moderate negative correlation and a correlation value of of -0.7 and -1.0 states a strong negative linear relationship.a) 0.99
This shows almost a perfect straight line relationship between spending on tobacco and spending on alcohol. Thus, this cannot be the right correlation as the relationship between spending on tobacco and spending on alcohol is not so strong.
b)-0.50
This shows a negative relation between spending on tobacco and spending on alcohol which cannot be true as they share a positive relation.
c) 0.80
This correlation shows a strong positive correlation between spending on tobacco and spending on alcohol which is correct because the relationship between spending on tobacco and spending on alcohol is positive
d)0.08
This correlation shows a very weak positive correlation between spending on tobacco and spending on alcohol which cannot be true.
A swimmer swam 3 5/16 miles today and 2 7/16 miles yesterday.
Answer: 5&3/4ths
Step-by-step explanation:
[tex]5+\frac{5}{16} +\frac{7}{16} \\\\5+\frac{5+7}{16} \\\\\5\frac{12}{16}=5\frac{3}{4}[/tex]
Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!
- Cutiepatutie ☺❀❤
Which of the following best represents the highest potential for nonresponse bias in a sampling strategy? Describe why this option should be considered nonresponse a. Surveying a population on Sunday mornings for a new needs assessment b. Submitting a post online advertising the need for participants in a new study c. Asking people leaving a local election to take part in an exit poll d. Posting a leaflet in the elevator of a university asking for students to take part in a paid study
Answer:
c. Asking people leaving a local election to take part in an exit poll
Step-by-step explanation:
Asking people leaving a local election to take part in an exit poll best represents the highest potential for nonresponse bias in a sampling strategy because of the importance of the local election compared to the exit polls.
It is worthy of note that nonresponse bias occurs when some respondents included in the sample do not respond to the survey. The major difference here is that the error comes from an absence of respondents not the collection of erroneous data. ...
Oftentimes, this form of bias is created by refusals to participate for one reason or another or the inability to reach some respondents.
Evaluate the function
k
(
x
)
=
−
x
2
+
6
k
(
x
)
=
-
x
2
+
6
at two different inputs and state the corresponding points.
Answer:Evaluate the function
k
(
x
)
=
−
x
2
+
6
k
(
x
)
=
-
x
2
+
6
at two different inputs and state the corresponding points.
Step-by-step explanation:
You’re trying to calculate the conversion rate on one of your forms. 600 people visited your landing page, but only 50 visitors submitted the form. What is the conversion rate of your form?
Answer: [tex]\dfrac{1}{12}[/tex] or 8.33%
Step-by-step explanation:
The conversion rate is given by :-
Conversion rate =(number of conversions ) ÷( total number of visitors)
As per given , we have
600 people visited your landing page, but only 50 visitors submitted the form..
i.e . Total number of visitors= 600
Number of conversions = 50
Then , the conversion rate would be:-
Conversion rate = (50) ÷ 600 [tex]=\dfrac{50}{600}=\dfrac{1}{12}[/tex]
Hence, the conversion rate of your form = [tex]\dfrac{1}{12}[/tex]
In percentage , the conversion rate= [tex]\dfrac{1}{12}\times100=8.33\%[/tex]
The conversion rate is calculated by dividing the number of form submissions by the total number of visitors to the page and multiplying by 100. In this case, the conversion rate is 8.33%.
Explanation:The conversion rate is central to tracking the effectiveness of your landing page. It's calculated by dividing the number of conversions (in this case, form submissions) by the total number of visitors to the page, then multiplying by 100 to get a percentage. In this case, the formula would look like this: (Number of forms submitted / Total visitors) x 100.
Plugging in your numbers, we get: (50 / 600) x 100 = 8.33%. So, the conversion rate of your form was 8.33%.
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Rationalize denominator when a monomial is in the denominator.Please show steps
Answer:
[tex]\frac{\sqrt[3]{90 x^2 y z^2} }{6 y z}[/tex]
Step-by-step explanation:
step 1;-
Given [tex]\frac{\sqrt[3]{5 x^2} }{\sqrt[3]{12 y^2 z} }[/tex]
now you have rationalizing denominator (i.e monomial) with
[tex]\frac{\sqrt[3]{5 x^2} }{\sqrt[3]{12 y^2 z} } X \frac{\sqrt[3]{(12 y^2 z)^{2} } }{\sqrt[3]{(12 y^2 z)^2} }[/tex]
By using algebraic formula is
[tex]\sqrt{ab} = \sqrt{a} \sqrt{b}[/tex]......(a)now [tex]\frac{\sqrt[3]{5 x^2)(12 y^2 z)^2} }{\sqrt[3]{12 y^2 z)(12 y^2 z)^2} }[/tex][tex]\frac{\sqrt[3]{720 x^2 y^4 z^2} }{\sqrt[3]{(12 y^2 z)^{3} } }[/tex]....(1)again using Formula [tex]\sqrt[n]{a^{n} } =a[/tex]now simplification , we get denominator function
[tex]\frac{\sqrt[3]{720 x^2 y^4 z^2} }{12 y^2 z}[/tex]again you have to simplify numerator term
[tex]\frac{\sqrt[3]{2^3 y^3 90 (x^2 y z^2)} }{12 y^2 z}[/tex]now simplify
[tex]\frac{2 y\sqrt[3]{90 x^2 y z^2} }{12 y^2 z}[/tex]cancelling y and 2 values
we get Final answer
[tex]\frac{\sqrt[3]{90 x^2 y z^2} }{6 y z}[/tex]
a pair of fair dice is rolled. what is the probability that the second die lands on a higher value than the first?
Answer:
The required probability is [tex]\dfrac{5}{12}[/tex].
Step-by-step explanation:
If a fair dice is rolled then total outcomes are
{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
We need to find the probability that the second die lands on a higher value than the first.
So, total favorable outcomes are
{(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)}
Formula for probability:
[tex]Probability=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]Probability=\dfrac{15}{36}[/tex]
[tex]Probability=\dfrac{5}{12}[/tex]
Therefore, the required probability is [tex]\dfrac{5}{12}[/tex].
Translate the following English statements into a logical expression with the same meaning.
a. All friendly people at HTS are knowledgeable.
b. Nobody at HTS is friendly, helpful, and knowledgeable.
c. Someone at HTS is helpful.
d. There is no one at HTS who is both friendly and helpful.
e. No friendly person at HTS is helpful.
Answer:
C makes most sence
Step-by-step explanation:
What are the factors of the function represented by this graph? the graph of a quadratic function y = (1/4)(x + 4)(x - 8) with a maximum value at the point (2,9) A. (x − 4) and (x − 8) B. (x − 4) and (x + 8) C. (x + 4) and (x − 8) D. (x + 4) and (x + 8)
Answer:
option C. (x + 4) and (x − 8)
Step-by-step explanation:
A factor is one of the linear expressions of a single-variable of the polynomial.
Given: y = (1/4)(x + 4)(x - 8)
When y = 0
∴ (1/4)(x + 4)(x - 8) = 0 ⇒ multiply both sides by 4
∴ (x + 4)(x - 8) = 0
So, the factors of the function are (x+4) and (x-8)
The answer is option C. (x + 4) and (x − 8)
The structure ABECD is loaded with P = 100 lbs and F = 125 lbs. Determine the internal loads (forces and moments) at section E, which is mid‐way between points B and C.
Answer:
P = 100 lbs in tension
F = 125 lbs in shear force downward direction
Moments are: 50 lb-ft and 125 lb-ft both in counter clockwise direction
Step-by-step explanation:
Forces
If we consider the entire structure as a system with two external forces P and F acting on it.
Translating these forces at point E,
Hence point E experiences the following forces:
P = 100 lbs in tension
F = 125 lbs in shear force
Moments
The bending moments are caused by the forces acting at respective offsets from point E
P = 100 lbs causes a bending moment of Mp = 100 lbs * (6/12) ft = 50 lb-ft
F = 125 lbs causes a bending moment of Mf = 125 lbs*(12/12)ft = 125 lb-ft
Moments are: 50 lb-ft and 125 lb-ft
Find the surface area
Answer:
Step-by-step explanation:
3. the diagram has 3 rectangles, 2 triangles
the surface area is the area of each shape
for the first rectangle = length x breadth = 8 x 6 = 48
for the second rectangle = length x breath = 6 x 6 = 36
for the third rectangle = length x breath = 6 x 6 = 36
for the triangles
(base x height )/2 = (8 x 4.5) /2 = 4 x 4.5 = 18
Surface Area = 48 + 18 + 36 + 36 = 138
4. there are 4 identical rectangles and a base rectangle
4 x (5 x3 ) + ( 5 x5) = 4 x 15 + 25 = 60 + 25 = 85 ft
5. there are 2 triangles of 6 x 8 and a rectangle of 10 x 8
surface area = 2 x( (base x height)/2) + 10x8
2 x ((6 x8) /2 ) + 80 = 2 x (48/2) + 80 = 48 + 80 = 128ft
The half-life of Carbon 14 (C-14) is 5230 years. Determine the decay-rate pa-rameterλfor C-14.
Answer:
λ = 1.3252 x 10⁻⁴
Step-by-step explanation:
Since we are already given the half-life, the decay expression can be simplified as:
[tex]N(t) = N_0*e^{-\lambda t}\\\frac{N(half-life)}{N_0}=0.5[/tex]
For a half-life of t =5230 years:
[tex]0.5 = e^{(-\lambda t)} \\ln(0.5) = -\lambda * 5230\\\lambda = 1.3252*10^{-4}[/tex]
The decay-rate parameter λ for C-14 is 1.3252 x 10⁻⁴
Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor.4xy dx (4y 6x2) dy
Answer:
y=1/6 · ln |x|+c .
Step-by-step explanation:
From Exercise we have the differential equation
4xy dx= (4y6x²) dy.
We calculate the given differential equation, we get
4xy dx= (4y6x²) dy
xy dx=6yx² dy
6 dy=1/x dx
∫ 6 dy=∫ 1/x dx
6y=ln |x|+c
y=1/6 · ln |x|+c
Therefore, we get that the solution of the given differential equation is
y=1/6 · ln |x|+c .
The differential equation presented can be rewritten and solved using an integrating factor. The integrating factor in this case is 1, yielding the solution x^2 y = C.
Explanation:To solve the given differential equation, we first need to rewrite it in a recognizable form namely, in the form Mdx + Ndy = 0. The given differential equation can be rewritten as 4xy dx + (4y - 6x2 ) dy = 0.
Now, we need to find an integrating factor which is e^∫(M_y - N_x) / N dx. In this case, M = 4xy, N = 4y - 6x2, M_y = 4x and N_x = -12x. Substituting these values into the equation ∫(M_y - N_x) / N dx, we find that the integrating factor is e^0=1.
With the integrating factor being 1, the given differential equation can be rewritten as d(x2y) = 0. Integrating both sides of this equation, we get x2y = C.
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The price of gas at the local gas station was $5.00 per gallon a month ago; today it is $5.50 per gallon. Suppose the price of gas goes down by the same percentage amount over the next month as it went up over the last month. What will the price of gas be then?
$4.95
Step-by-step explanation:
Initial price of gas was $5.00 a month ago
Today price of a gas is $5.50 per gallon
Increase in price= $5.50-$5.00=$0.50
%increase= 0.50/5.00 *100 =10%
Current price= $5.50
decrease current price by 10% is by multiplying the current price by 90%
90/100 * 5.50 = $4.95
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Which equation could be used to find the number of days, d, in h hours?
Answer: In my opinion, I would say b is the correct answer
Step-by-step explanation:
What’s the answer I will do 50 points first person to answer
Answer: 1. Route ABC is a right triangle.
2. Route CDE ia not a right triangle.
3. Distance HJ= 23.32miles
4. Distance GE = 17
5. Missing length= 35
6. The sides 16, 60, 62 do NOT belong to a right triangle.
Step-by-step explanation:
Going by Pythagoras theorem, for triangle to be proven to be a right triangle, the condition below must be satisfied.
Hypotenuse² = Opposite² + Adjacent²
For question 1,
Hyp =13, opp = 5, Adj is 12
Going by Pythagoras rule.
Since 13²= 5² + 12²
Then triangle ABC is a right triangle.
For question 2,
Using the same Pythagoras theorem to prove,
In triangle CDE,
Hyp= 22, opp= 18, Adj = 14
Since 22² is not = 18² + 14²
then CDE is not a right triangle.
For question 3,
For triangle HIJ, since it is confirmed to be a right triangle, then we use the Pythagoras theorem to calculate the missing side.
Longest side if the triangle= IJ = hypotenuse = 25
HI = 9.
IJ² = HI² + HJ²
HJ²= IJ² - HI²
HJ² = 25² - 9²
HJ² = 625 - 81
HJ= √544
HJ = 23.32miles
For question 4,
FGE is also shown to be a right triangle and the missing side GE is the longest side which is also the hypotenuse.
FG= 8, FE =15
Using the Pythagoras theorem,
Hyp² = FG² + FE²
GE² = 8² + 15²
GE² = 289
GE = √289
GE = 17.
For question 5,
The hypotenuse is given as 37, one side is given as 12, let's call the missing side x
Going by Pythagoras theorem,
37² = 12²+ x²
x²= 37² - 12²
x²= 1225
x=√1225
x=35.
The missing side is 35inches.
For number 6,
The numbers given are 16, 60, 62
To know if three sides belong to a right angle, we simply put them to test using Pythagoras theorem.
It is worthy of note that the longest side is the hypotenuse.
This brings us to the equation to check below that since:
62² Is not = 60² + 16²
Then the side lengths 16, 60, 62 do not belong to a right angle.
Multiple-choice questions each have four possible answers (a comma b comma c comma d ), one of which is correct. Assume that you guess the answers to three such questions. a. Use the multiplication rule to find P(CWW), where C denotes a correct answer and W denotes a wrong answer.
Answer:
0.140625
Step-by-step explanation:
Given that multiple-choice questions each have four possible answers (a comma b comma c comma d ), one of which is correct. Assume that you guess the answers to three such questions.
Each question is independent of the other with constant probability
p = Prob for correct guess = 1/4 = 0.25
q = prob for wrong guess = 1-p = 0.75
Hence
[tex]P(CWW)\\= P(C)*P(W)*P(W)[/tex], since each question is independent of the other
=[tex]0.25*0.75*0.75\\= 0.140625[/tex]
the number of ways 8 cars can be lined up at a toll booth would be computed from
a. 8 to the 8th power
b. (8)*(8)
c. 8!
d. 8!/7!1!
Answer: c. 8!
Step-by-step explanation:
We know , that if we line up n things , then the total number of ways to arrange n things in a line is given by :-
[tex]n![/tex] ( in words :- n factorial)
Therefore , the number of ways 8 cars can be lined up at a toll booth would be 8! .
Hence, the correct answer is c. 8! .
Alternatively , we also use multiplicative principle,
If we line up 8 cars , first we fix one car , then the number of choices for the next place will be 7 , after that we fix second car ,then the number of choices for the next place will be 6 , and so on..
So , the total number of ways to line up 8 cars = 8 x 7 x 6 x 5 x 4 x 3 x 2 x1 = 8!
Hence, the correct answer is c. 8! .
If v lies in the first quadrant and makes an angle π/3 with the positive x-axis and |v| = 4, find v in component form.
Answer:
v = <2, 2√3>
Step-by-step explanation:
Let v be the vector of form <x,y>
Since its determinant is |4|, then:
[tex]x^2 +y^2 =4^2=16[/tex]
If it makes a π/3 angle with the positive x-axis, then the tangent relationship yields:
[tex]tan(\pi/3) = 1.732=\frac{y}{x}\\3x^2=y^2[/tex]
Replacing in the first equation:
[tex]x^2 +3x^2 =16\\x=2\\y=\sqrt{16-4}\\ y=2\sqrt 3[/tex]
Therefore, v can be represented in component form as v = <2, 2√3>.
The vector [tex]v[/tex] that lies in the first quadrant, makes an angle of [tex]\frac{\pi}{3}[/tex] with the positive x-axis, and has a magnitude of [tex]4[/tex] is:
[tex]v = 2i + 2\sqrt{3}j[/tex]
To find the vector v in component form, we start by understanding the relationships between the angle, magnitude, and components of a vector in the Cartesian coordinate system.
Given Data:
Angle with positive x-axis, [tex]heta = \frac{\pi}{3}[/tex]Magnitude of vector, [tex]|v| = 4[/tex]Vector Components:
In the first quadrant, the components of vector [tex]v[/tex] can be calculated using the following formulas:
Calculating Components:
For the x-component:
[tex]v_x = 4 \cdot \cos\left(\frac{\pi}{3}\right)[/tex]
The cosine of [tex]\frac{\pi}{3}[/tex] is [tex]\frac{1}{2}[/tex], so:
[tex]v_x = 4 \cdot \frac{1}{2} = 2[/tex]
For the y-component:
[tex]v_y = 4 \cdot \sin\left(\frac{\pi}{3}\right)[/tex]
The sine of [tex]\frac{\pi}{3}[/tex] is [tex]\frac{\sqrt{3}}{2}[/tex], so:
[tex]v_y = 4 \cdot \frac{\sqrt{3}}{2} = 2\sqrt{3}[/tex]
Resulting Vector:
Thus, the vector [tex]v[/tex] in component form is:
[tex]v = v_x i + v_y j = 2i + 2\sqrt{3} j[/tex]
A physical fitness researcher devises a test of strength and finds that the scores are Normally distributed with a mean of 100 lbs and a standard deviation of 10 lbs. What is the minimum score needed to be stronger than all but 5% of the population
Answer:
116.45 is the minimum score needed to be stronger than all but 5% of the population.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 100
Standard Deviation, σ = 10
We are given that the distribution of score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.05
P(X > x)
[tex]P( X > x) = P( z > \displaystyle\frac{x - 100}{10})=0.05[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{x - 100}{10})=0.05[/tex]
[tex]=P( z \leq \displaystyle\frac{x - 100}{10})=0.95 [/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<1.645) = 0.95[/tex]
[tex]\displaystyle\frac{x - 100}{10} = 1.645\\x =116.45[/tex]
Hence, 116.45 is the minimum score needed to be stronger than all but 5% of the population.
The Insurance Institute for Highway Safety publishes data on the total damage caused by compact automobiles in a series of controlled, low-speed collisions. The following costs are for a sample of six cars:
$800, $750, $900, $950, $1100, $1050.
1. What is the five-number summary of the total damage suffered for this sample of cars?
Answer: [tex]Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100[/tex]
Step-by-step explanation:
The five -number summary consists of five values :
Minimum value , First quartile [tex](Q_1)[/tex] , Median , Third Quartile [tex](Q_3)[/tex] , Maximum value.
Given : The Insurance Institute for Highway Safety publishes data on the total damage caused by compact automobiles in a series of controlled, low-speed collisions.
The following costs are for a sample of six cars:
$800, $750, $900, $950, $1100, $1050.
Arrange data in increasing order :
$750,$800, $900, $950, $1050, $1100
Minimum value = $750
Maximum value = $1100
Median = middle most term
Since , total observation is 6 (even) , so Median = Mean of two middle most values ($900 and $950).
i.e. Median[tex]=\dfrac{900+950}{2}=\$925[/tex]
First quartile [tex](Q_1)[/tex] = Median of lower half ($750,$800, $900)
= $800
, Third Quartile [tex](Q_3)[/tex] = Median of upper half ($950, $1050, $1100)
= $1050
Hence, the five-number summary of the total damage suffered for this sample of cars will be :
[tex]Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100[/tex]
In the following hypothetical scenarios, classify each of the specified numbers as a parameter or a statistic. a. There are 100 senators in the 114th Congress, and 54% of them are Republicans. b. The 54% here is a In a 2011 Gallup poll of 1008 adults living in the United States, 11% said they are satisfied with the condition of the national economy. c. The 11% here is a A survey of hospital records in 120 hospitals throughout the world shows the mean height of 180 cm for adult males. d. The mean height of 180 cm is a The 59 players on the roster of a championship football team have a mean weight of 248.6 pounds with a standard deviation of 44.6 pounds. e. The 44.6 pounds is a In a random sample of households in the United States, it is found that 51% of the sampled households have at least one high‑definition television.
Answer:
a) Parameter
b) Statistic
c) Statistic
d) Parameter
e) Statistic
Step-by-step explanation:
For this case we need to remmber that a parameter describe a population of interest is fixed and not changes , and a statistic is a value that describe the sample size selected and can change between samples.
a. There are 100 senators in the 114th Congress, and 54% of them are Republicans.
The 54% here is a parameter since represent the proportion for all the population of interest on this case.
b. In a 2011 Gallup poll of 1008 adults living in the United States, 11% said they are satisfied with the condition of the national economy.
The 11% here is a statistic since we have a random sample and from this sample we calculate the proportion of interest for this case.
c. A survey of hospital records in 120 hospitals throughout the world shows the mean height of 180 cm for adult males.
The mean height of 180 cm is a statistic since we have a survey not all the population of interest
d. The 59 players on the roster of a championship football team have a mean weight of 248.6 pounds with a standard deviation of 44.6 pounds.
The 44.6 pounds is a parameter since we are interested on all the possible players and we have the info for all of them
e. In a random sample of households in the United States, it is found that 51% of the sampled households have at least one high‑definition television.
The 51% here is a statistic since we have a result from a sample not from the population
An analyst for a large credit card company is going to conduct a survey of customers to examine their household characteristics. One of the variables the analyst will record is the amount of purchases on the card last month. The analyst knows that for all customers that have this card the average was $1622. In the sample of 500 customers the average amount of purchases last month was $1732. In this example the number 1732 is
Answer:
We can conclude that the value of 1732 is a statistic who represent the sample selected. And the value of 1622 represent the population mean from all the customers with the previous data.
Step-by-step explanation:
Previous concepts
A statistic or sample statistic "is any quantity computed from values in a sample", for example the sample mean, sample proportion and standard deviation
A parameter is "any numerical quantity that characterizes a given population or some aspect of it".
Solution to the problem
For this case the analyst knows that from previous records that the mean for all the customers (that represent the population of interest) is [tex] \mu = 1622[/tex]
He have a random sample of n =500 customers from the previous month and he knows that 1732 represent the sample mean for the selected customers calculated from the following formula:
[tex] \bar X = \frac{\sum_{i=1}^{500} X_i}{500}= 1732[/tex]
So on this case we can conclude that the value of 1732 is a statistic who represent the sample selected. And the value of 1622 represent the population mean from all the customers with the previous data.
Final answer:
The number 1732 represents the sample mean of monthly credit card purchases for a sample of 500 customers, distinct from the population mean of $1622.
Explanation:
The number 1732 in the scenario given refers to the sample mean, which is the average amount of money spent on purchases last month by the 500 customers in the sample. This contrasts with the population mean, which the analyst knows to be $1622 for all customers holding the credit card. The difference between the sample mean and the population mean can be a subject of further statistical analysis to understand customer behavior and spending patterns better.
g Determine if the statement is true or false. A linear system with three equations and five variables must be consistent. True False Justify your answer.
Final answer:
A linear system with three equations and five variables does not have to be consistent. The statement 'A linear system with three equations and five variables must be consistent' is false
Explanation:
A linear system with three equations and five variables does not have to be consistent. In fact, it is possible for the system to be inconsistent.
The statement that a linear system with three equations and five variables must be consistent is False. In linear algebra, the consistency of a system depends on whether there are any contradictions among the equations. For a system to be consistent, it must have at least one solution.
For example, consider the system of equations:
x + y + z = 5
2x + 3y + 4z = 10
5x + 2y + 3z = 8
Since there are more variables than equations, there will be infinitely many solutions if the system is consistent. But if the system is inconsistent, there will be no solution.
Therefore, the statement 'A linear system with three equations and five variables must be consistent' is false
The initial value of a quantity Q (at year t = 0) is 112.8 and the quantity is decreasing by 23.4% per year. a) Write a formula for Q as a function of t. 2 Edit b) What is the value of Q when t-10? Round to three decimal places.
Answer:
a) [tex]Q(t) = 112.8*(0.766)^{t}[/tex]
b) When t = 10, Q = 7.845.
Step-by-step explanation:
The value of a quantity after t years is given by the following formula:
[tex]Q(t) = Q_{0}(1 + r)^{t}[/tex]
In which [tex]Q_{0}[/tex] is the initial quantity and r is the rate that it changes. If it increases, r is positive. If it decreases, r is negative.
a) Write a formula for Q as a function of t.
The initial value of a quantity Q (at year t = 0) is 112.8.
This means that [tex]Q_{0} = 112.8[/tex].
The quantity is decreasing by 23.4% per year.
This means that [tex]r = -0.234[/tex]
So
[tex]Q(t) = 112.8*(1 - 0.234)^{t}[/tex]
[tex]Q(t) = 112.8*(0.766)^{t}[/tex]
b) What is the value of Q when t = 10?
This is Q(10).
[tex]Q(t) = 112.8*(0.766)^{t}[/tex]
[tex]Q(t) = 112.8*(0.766)^{10} = 7.845[/tex]
When t = 10, Q = 7.845.
Jesse takes a 3-day kayak trip and travels 72 km south from Everglades City to a camp area in Everglades National Park. The trip to the camp area with a 2-km/hr current takes 9 hr less time than the return trip against the current. Find the speed that Jesse travels in still water.
Answer: The speed that Jesse travels in still water is 6 km/hr.
Step-by-step explanation:
Let the speed that Jesse travels in still water be 'x'.
Distance = 72 km
The trip to the camp area with a 2-km/hr current takes 9 hr less time than the return trip against the current.
Speed of current = 2 km/hr
According to question, we get that
[tex]\dfrac{72}{x-2}-\dfrac{72}{x+2}=9\\\\\dfrac{x+2-(x-2)}{x^2-4}=\dfrac{9}{72}\\\\\dfrac{4}{x^2-4}=\dfrac{1}{8}\\\\32=x^2-4\\\\32+4=x^2\\\\x^2=36\\\\x=\sqrt{36}\\\\x=6[/tex]
Hence, the speed that Jesse travels in still water is 6 km/hr.
Jesse's speed in still water is determined by setting up a system of equations using the distance equals rate times time formula for both downstream and upstream travel. By accounting for the time difference and the current speed, we solve for the variable representing Jesse's speed in still water.
Explanation:Jesse takes a kayak trip traveling 72 km with and against a current, and we need to find Jesse's speed in still water. Let's denote the speed in still water as v (km/hr) and the current speed as 2 km/hr. The trip downstream increases Jesse's speed to (v + 2) km/hr, and upstream decreases it to (v - 2) km/hr.
Using the distance equals rate times time formula (d = rt), we can write the following equations for the time taken downstream (td) and upstream (tu):
72 = (v + 2)td72 = (v - 2)tuGiven that it takes 9 hours less to travel downstream, we have tu = td + 9.
By solving these linear equations, we find the system:
td = 72 / (v + 2)td + 9 = 72 / (v - 2)Combining these gives us:
72 / (v + 2) + 9 = 72 / (v - 2)
By solving this equation, we find the value of v, Jesse's speed in still water.
Learn more about Speed in Still Water here:https://brainly.com/question/29248237
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Find the approximate probability that the total number of credits earned by a random sample of 484 students from that school in that semester was less than 6650.
Answer:
The correct answer is B=0.0262
Step-by-step explanation:
91÷3525 = 0.0262
The attached picture below gives a step by step explanation of how I arrived at my answer.
Please let's endeavor to always upload complete questions to avoid wrong answers.
Let X1, X2, ... , Xn be a random sample from N(μ, σ2), where the mean θ = μ is such that −[infinity] < θ < [infinity] and σ2 is a known positive number. Show that the maximum likelihood estimator for θ is θ^ = X.
Answer:
[tex] l'(\theta) = \frac{1}{\sigma^2} \sum_{i=1}^n (X_i -\theta)[/tex]
And then the maximum occurs when [tex] l'(\theta) = 0[/tex], and that is only satisfied if and only if:
[tex] \hat \theta = \bar X[/tex]
Step-by-step explanation:
For this case we have a random sample [tex] X_1 ,X_2,...,X_n[/tex] where [tex]X_i \sim N(\mu=\theta, \sigma)[/tex] where [tex]\sigma[/tex] is fixed. And we want to show that the maximum likehood estimator for [tex]\theta = \bar X[/tex].
The first step is obtain the probability distribution function for the random variable X. For this case each [tex]X_i , i=1,...n[/tex] have the following density function:
[tex] f(x_i | \theta,\sigma^2) = \frac{1}{\sqrt{2\pi}\sigma} exp^{-\frac{(x-\theta)^2}{2\sigma^2}} , -\infty \leq x \leq \infty[/tex]
The likehood function is given by:
[tex] L(\theta) = \prod_{i=1}^n f(x_i)[/tex]
Assuming independence between the random sample, and replacing the density function we have this:
[tex] L(\theta) = (\frac{1}{\sqrt{2\pi \sigma^2}})^n exp (-\frac{1}{2\sigma^2} \sum_{i=1}^n (X_i-\theta)^2)[/tex]
Taking the natural log on btoh sides we got:
[tex] l(\theta) = -\frac{n}{2} ln(\sqrt{2\pi\sigma^2}) - \frac{1}{2\sigma^2} \sum_{i=1}^n (X_i -\theta)^2[/tex]
Now if we take the derivate respect [tex]\theta[/tex] we will see this:
[tex] l'(\theta) = \frac{1}{\sigma^2} \sum_{i=1}^n (X_i -\theta)[/tex]
And then the maximum occurs when [tex] l'(\theta) = 0[/tex], and that is only satisfied if and only if:
[tex] \hat \theta = \bar X[/tex]