Answer:
a. The point estimate was of $44,600.
b. The sample size was of 16.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
a. What is the point estimate of the mean salary for all college graduates in this town?
Mean of the bounds, so:
(38737+50463)/2 = 44600.
The point estimate was of $44,600.
b. Determine the sample size used for the analysis.
First we need to find the margin of error, so:
[tex]M = \frac{50463-38737}{2} = 5863[/tex]
Relating the margin of error with the sample size:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.64.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
For this problem, we have that [tex]\sigma = 14300, M = 5863[/tex]. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5863 = 1.645\frac{14300}{\sqrt{n}}[/tex]
[tex]5863\sqrt{n} = 1.645*14300[/tex]
[tex]\sqrt{n} = \frac{1.645*14300}{5863}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2[/tex]
[tex]n = 16[/tex]
The sample size was of 16.
HELP PLEASE!! I WILL MARK BRAINLIST
Answer:
D
Step-by-step explanation:
Have a nice day :)
Solve 2x2 + 8 = 0 by graphing the related function.
There are no real number solutions.
There are two solutions: V8.
There is one solution: 2
There are two solutions: 2 and -2.
Answer:
there are no real number solutions
Step-by-step explanation:
2x² + 8 = 0
x² + 4 = 0
x² = -4
these solutions all involve "i", the imaginary or complex numbers, as normally the square of any number has to be positive (and cannot be negative).
I need help please someone help me
Answer:
We know that the height equation is given by:
H(t) = -16*t^2 + 108*t + 28
in ft.
First, we want to find the maximum height of the ball.
The first thing we can see is that the leading coefficient of the quadratic equation is negative, this means that the arms of the graph will open downwards, so the vertex of the quadratic equation is the maximum.
We also know that the ball will reach its maximum height when its velocity is zero (this means that the object stops going upwards at this point).
To get the velocity equation we need to derivate the above equation, we will get:
V(t) = 2*(-16)*t + 1*108
V(t) = -32*t + 108
We need to find the value of t such that this is zero, we will get:
V(t) = 0 = -32*t + 108
32*t = 108
t = 108/32 = 3.375
So the ball reaches its maximum height after 3.375 seconds.
Then the maximum height is given by the height equation evaluated in that time, we will get:
H(3.375) = -16*(3.375)^2 + 108*3.375 + 28 = 210.25
Then the maximum height of the ball is 210.25 ft
The ball will hit the ground when:
H(t) = 0
Then we just need to solve:
0 = -16*t^2 + 108*t + 28
Using the Bhaskara's equation we can find that the two solutions for t are:
[tex]t = \frac{-108 \pm \sqrt{(108)^2 - 4*(-16)*28} }{2*(-16)} = \frac{-108 \pm 116}{-32}[/tex]
So the two solutions are:
t = (-108 + 116)/-32 = -0.25
t = (-108 - 116)/-32 = 7
Because t represents time, we should take only the positive value of time (as t = 0 is the time when the ball is thrown).
Then we can conclude that the ball hits the ground after 7 seconds.
If any of the graphs below have a Hamiltonian circuit, list the vertices of the complete circuit. There may be many possibilities. For full credit, just list one for each graph, if the circuit exists
9514 1404 393
Answer:
ABHGEFDCAdoes not existECBADFEStep-by-step explanation:
A Hamiltonian circuit visits each node once and returns to its start. There is no simple way to determine if such a circuit exists.
__
For graph 2, if there were a circuit, paths ACB, ADB, and AEB would all have to be on it. Inclusion of all of those requires visiting nodes A and B more than once, so the circuit cannot exist.
__
For graph 3, the circuit must include paths BAD and DFE. That only leaves node C, which can be reached from both nodes B and E, so path ECB completes the circuit.
Determine the angles. There’s only two answers.
A. 90 clockwise
B. 90 counterclockwise
C. 180
D. 270 clockwise
E. 270 counterclockwise
Answer:
its would be a and d
Step-by-step explanation:
6 times 5
When doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial samples of different blood specimens. If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture, assuming the probability of an individual blood sample testing positive for the virus is 0.06.
Answer:
0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.
Step-by-step explanation:
For each test, there are only two possible outcomes. Either it is positive, or it is negative. The probability of a test being positive or negative is independent of any other test, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability of an individual blood sample testing positive for the virus is 0.06.
This means that [tex]p = 0.06[/tex]
If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture.
It will be positive if at least one of the tests is positive, that is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.06)^{0}.(0.94)^{3} = 0.8306[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8306 = 0.1694[/tex]
0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.
One pair of parallel sides proves a quadrilateral to be a parallelogram
True
False
Which of the following logarithmic expressions have been evaluated correctly, to the nearest hundedth? Select all that apply.
A. log3 8 = 0.43
B. log3 6 = 1.63
C. log4 5 = 1.16
D. log2 32 = 1.51
Answer:
b
Step-by-step explanation:
ive done it before
order 520, 475, 720, 580, 310, 170, 370, 220, 140 and 15 from least to greatest
Answer:
15,140,170,220,310,370,475,520,580,720
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
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Find the value of y
A) 9.850
B) 18.610
C) 65.825
D) 125.365
Answer:
B) 18.610
Step-by-step explanation:
Using SOHCAHTOA (trig ratios), the tangent of 28° is the ratio of its opposite length to its adjacent.
in this scenario, the side opposite to 28°, and the side adjacent to it is 35°
tan 28° = y/35
Using inverse operations, multiply both sides by 35
y = 35 * tan 28
Solve your answer using your calculator.
I attached a picture that can help you later to recognize what function to use depending on the sides given.
96 sq meters
144 sq meters
84 sq meters
102 sq meters
Pls show work I get different answers from people every time
Answer:
84 sq meters
Step-by-step explanation:
First, divide the shape in 2 or more parts so that you can find it step by step
Divide this shape in three parts:
One part (blue): 2 m and 3 m rectangle
Second part (orange): 5 m and 12 m rectangle
Third part (red): 6 m and 3 m rectangle
(you can also see this below: in the pic there are three parts so you figure out that which is the correct value for the sides)
Now, find area of each shape by multiplying its values:
1st shape: 3 x 2 = 6
2nd shape: 5 x 12 = 60
3rd shape: 6 x 3 = 18
As you have the area of all the different shapes,
add all of them:
6 + 60 + 18 = 84 sq meters
I hope this helps :)
An auto repair shop charged a customer $170 to repair a car. The bill listed $50 for parts and the
remainder for labor. If the cost of labor is $30 per hour, how many hours of labor did it take to repair
the car?
The answer is attached. I hope this helps answer your question!
I’ll mark brainliest
Answer:
B
Step-by-step explanation:
they said 2 hours for each final
There are four pairs of different types of shoes in a bag: a pair of boots a pair of sandals a pair of sneakers a pair of flip-flops If you pick shoes from that bag (in the darkness), what is the minimum number of shoes you should pick to be certain that you will have a pair of matching shoes
Answer:
5
Step-by-step explanation:
Quantitative - Column chart
Quantitative - Line chart
Qualitative - Histogram
Qualitative - Pie chart
Answer:
A. Qualitative - Column chart
Step-by-step explanation:
Data could either be qualitative or quantitative. Quantitative data are usually given in a definite number, i.e it can be counted. While qualitative deals with characteristics, i.e it can be collected either by the use of questionnaires, or any similar method.
Therefore for the given question, the data survey is qualitative. And since the result would be presented as a graph showing the percentage users for each application, a column chart would be appropriate.
Thus for the data and its presentation, the answer is A. Quantitative - Column chart
The fencing William chooses costs $29.53 per foot, including installation. What will the fencing cost? Show your work.
Answer:
[tex]C = 29.53x[/tex]
Step-by-step explanation:
Given
[tex]Unit\ cost = \$29.53[/tex]
Required
The cost of fencing (C)
The cost is calculated as:
[tex]C = Unit\ Cost * Perimeter\ of fencing[/tex]
Let:
[tex]x \to Perimeter\ of fencing[/tex]
So, we have:
[tex]C = Unit\ Cost * x[/tex]
[tex]C = 29.53 * x[/tex]
[tex]C = 29.53x[/tex]
The question cannot be solved further since the dimension of the fence is not given
If you know the dimension, calculate the fence perimeter and substitute the value for x
Which side lengths form a right angle?
Choose all answers that apply:
A) 3, square root 27, 6
B) 8, 15, 17
C) 5, 5, square root 50
Answer:
B and C
Step-by-step explanation:
Using the Pythagorean theorem a²+b²=c², those are the correct answers
A basketball player made 80 out of 100 attempted free throws. What percent of free throws was made?
I need a correct answer asap!
Percent of free throws = (number of free throws made / total attempts) x 100
Percent = (80/100) x 100 = 80%
The answer is 80%
Answer:
80%
Step-by-step explanation:
What is the perimeter of Quadrilateral ABCDwith vertices at A(−11, −6), B(−3, 0), C(1, 0), and D(1, −6)?
Answer:
32 units
Step-by-step explanation:
the perimeter =
(1 -(-3)) +(0-(-6)) + (1 -(-11) + (√(12-4)²+6²)
= (1+3) +(0+6) +(1+11) +(√(64+36))
= 4+6+12 + 10
=32 units
Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <2,-4>, v = <6,3> (5 points)
===========================================================
Explanation:
For any two vectors defined as follows
u = <a,b>
v = <c,d>
the dot product is computed by
u dot v = a*c + b*d
If the dot product of the vectors is 0, then the vectors are orthogonal. Meaning they are perpendicular to one another.
-------------------
Let's find the dot product of these two given vectors
u = < 2, -4 >
v = < 6, 3 >
u dot v = 2*6 + (-4)*3
u dot v = 12 - 12
u dot v = 0
Therefore, these two vectors form a right angle and are orthogonal
-------------------
Extra info:
If we can show that u = <a, b> and v = <ka, kb> for some real number k, then we have shown that vectors u and v are parallel.
Find the volume of the figure shown below.
A)42 1/2 units^3
B)11 1/4 units^3
C)14 1/4 units^3
D)80 1/4 units^3
E)None of these answers are correct
Answer:
A. 42½ units
Step-by-step explanation:
the volume = 5×2×4¼ = 10×4¼ = 42½
the measure of an exterior angle of a triangle is greater than the measure of either of its remove interior angles
Answer:
what do u want exactly or it us a theorem
Answer
Step-by-step explanation:
What is the volume of a cylinder, in cubic feet, with a height of 3 feet and a base diameter of 18 feet?
Answer:
763.41 ft
Step-by-step explanation:
V=π(d/ 2)2*huse formula
What's 60 in the ratio 1 : 4
Answer:
15/240 = 5/80= 1:16. helpful answer
Answer:
1+4=60
5=60
60/5
12#
Step-by-step explanation:
or,let it be X
1x+4x=60
5x=60
X=60/5
there fore
X=12#
What is the sum of the factors?
Two factors of -48 have a difference of 19. The factor
with a greater absolute value is positive.
-19
-13
13
16
Answer:
13
Step-by-step explanation:
The two factors 16 and -3.
Solve the equation for x
2(x - 7) = 10x + 18
Hi there!
»»————- ★ ————-««
I believe your answer is:
x = -4
»»————- ★ ————-««
Here’s why:
We will use inverse operations to solve for 'x'.⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x':}}\\\\2(x-7)=10x+18\\------------\\\rightarrow 2x-14 = 10x + 18\\\\\rightarrow 2x - 14 + 14 = 10x + 18 + 14\\\\\rightarrow 2x = 10x + 32\\\\\rightarrow 2x-10x=10x-10x+32\\\\\rightarrow-8x=32\\\\\rightarrow\frac{-8x=32}{-8}\\\\\rightarrow \boxed{x=-4}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1.
Answer:
The equation of the parabola is y = x²/4
Step-by-step explanation:
The given focus of the parabola = (0, 1)
The directrix of the parabola is y = -1
A form of the equation of a parabola is presented as follows;
(x - h)² = 4·p·(y - k)
We note that the equation of the directrix is y = k - p
The focus = (h, k + p)
Therefore, by comparison, we have;
k + p = 1...(1)
k - p = -1...(2)
h = 0...(3)
Adding equation (1) to equation (2) gives;
On the left hand side of the addition, we have;
k + p + (k - p) = k + k + p - p = 2·k
On the right hand side of the addition, we have;
1 + -1 = 0
Equating both sides, gives;
2·k = 0
∴ k = 0/2 = 0
From equation (1)
k + p = 0 + 1 = 1
∴ p = 1
Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;
(x - 0)² = 4 × 1 × (y - 0)
∴ x² = 4·y
The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;
y = x²/4.
whats 926 divided by 30
[tex]30.87[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{926}{30} \\ = 30 \frac{26}{30} \\ ( \: or \: ) \\ = 30.8666 \\ = 30.87 [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
The yearbook staff receive 75 submissions for yearbook articles. Paul will acceptſ of all submissions. Currently, Paul plans for the yearbook to have 156
pages.
How many more pages will Paul need to add to the yearbook to have 2 articles on every 13 pages? Show your work and explain your thinking.
Answer:
The correct answer is - 332 pages.
Step-by-step explanation:
Given:
number of articles submissions - 75
number of pages in the yearbook on current plan = 156
pages required for two articles = 13 pages.
The number of pages to add = ?
Solution:
1 article takes pages in the yearbook = 13/2
= 6.5
the number of pages required for 75 articles = 75*6.5
= 487.5
The number of pages to add in the yearbook = 487.5 - 156
= 331.5 or 332.
Thus, the correct answer is - 332 pages.
A pupil dilates from 4.5 millimeters to 8 millimeters. What is the scale factor of the dilation?
Answer:
[tex]\frac{80}{45} =k[/tex]
Step-by-step explanation:
image/actual= 8/4.5
8(10)/4.5(10)= 80/45