Answer:
Step-by-step explanation:
Try to use the distance formula to determine whether the sides are congruent. So take every pair of consecutive vertices and apply the distance formula. So you will have which, in any, sides are congruent.
Use the slope formula to determine which sides are parallel or perpendicular or neither of those. If the slopes are equal the sides are parallel, if the product of the slopes is - 1 the sides are perpendicular. In any other case the sides are neither parallel nor perpendicular.
With that and the definitions of the shapes you will be able to classify shapes.
To write a full example would be very long .
An easy one might be this as an example:
Given the points (0,0), (2,0), (2,2) and (0,2), classify the shape.
When you apply the distance formula: you will find 2 for all the sides, so they are all congruent.
When you apply the slope formula you will find two pair of parallel sides, and the sides that intersects are perpendicular.
Therefore... the classification of the shape is a square.
Assume that IQ scores are normally distributed, with a standard deviation of 16 points and a mean of 100 points. If 60 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points
Answer:
The probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points is 0.67
Step-by-step explanation:
Please check attachment for complete solution and step by step explanation
Please help, much needed. A lot of points
Answer:
A. -9
Step-by-step explanation:
If one of the variables were negative than, it would not be able to equal 2/7.
What is the inverse of the function
Answer:
A
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = [tex]\frac{19}{x^3}[/tex] ( multiply both sides by x³ )
x³y = 19 ( divide both sides by y )
x³ = [tex]\frac{19}{y}[/tex] ( take the cube root of both sides )
x = [tex]\sqrt[3]{\frac{19}{y} }[/tex]
Change y back into terms of x, then
[tex]f^{-1}[/tex] (x) = [tex]\sqrt[3]{\frac{19}{x} }[/tex] = [tex]\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex] → A
Find the amount necessary to fund the given withdrawals. Semiannual withdrawals of 850 for 6 years,interest rate is 4.7% compounded semiannually.
Answer:
The amount necessary to fund the withdrawal is $8798.820
Step-by-step explanation:
Here, we are interested in calculating the necessary amount to fund the withdrawal given in the question.
From the question, we can identify the following;
Principal amount, P= $850
Here, Period rate, i = 0.047/ 2 =0.0235
n = 6*2 = 12
Mathematically;
Present Value of an annuity, Ao=P* [1-(1+i)^{-n}]/i
Ao=850* [1-(1+0.0235)^{-12}] /0.0235
Ao = $8798.820
Lengths of pregnancies (in humans) have a mean of 267.6 days and a standard deviation of 15.4 days. A woman tracked her pregnancy and found it to be 309 days. Find the z score for 309 days. Is such a length unusual?
Answer:
The z-score is [tex]z = 2.65[/tex]
The length of days is not unusual
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 267.6 \ days[/tex]
The standard deviation is [tex]\sigma = 15.4 \ days[/tex]
The value considered is [tex]x = 309 \ days[/tex]
The z-score is mathematically represented as
[tex]z = \frac{x - \mu}{\sigma }[/tex]
[tex]z = \frac{309 - 267.6}{15.6 }[/tex]
[tex]z = 2.65[/tex]
Now given that the z-score is not greater than 3 then we can say that the length of days is not unusual
(reference khan academy)
Can two events with nonzero probabilities be both independent and mutually exclusive? Choose the correct answer below. A. Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities add up to one. B. No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero. C. Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities are equal. D. No, two events with nonzero probabilities cannot be independent and mutually exclusive because independence is the complement of being mutually exclusive.
Answer:
Step-by-step explanation:
B. No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero.
For two mutually exclusive events , with non- zero probabilities , when one occurs , the other can not happen . In this way they become dependent events . In this way , for two events to be both independent and mutually exclusive , at least one of the two events must have zero probability .
It should be noted that two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero.
Mutually exclusive events simply means the events that cannot take place at the same time. The occurrence of one of the events will prevent the other event from occuring.
Therefore, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero.
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In triangle abc what is the value of cos b A 5/13 B 12/13 C 5/12 D 13/12
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
In the triangle,
Hypotenuse = 13
Opposite = Perpendicular = 5
Adjacent = Base = 12
Now,
Cos B = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Cos B = 12/13
If the triangle is just like in the attached file!
Answer:
B) 12/13
Step-by-step explanation:
conditinal probability question. please help! :)
Answer:
P(A|B) = 1 / 6
Step-by-step explanation:
Assuming two fair sided dice with faces numbered 1 to 6.
By intuition, there can only be 6 possible outcomes, so probability is 1/6.
Illustration how to use conditional probability.
Given two events A, B, following is the equation of conditional probability
that A happens given B has already happened and observed.
P(A|B) = P( A intersect B ) / P(B)
In the given problem,
A = casting a double-six
B = casting a double
P(A) = (1 / 6) * (1 / 6) = 1/36
P(B) = (6/6) * (1/6) = 1/6
P(A|B) = 1/36 / (1/6) = 1/6
QUESTION 4 (10 MARKS)
A retired couple requires an annual return of $2,000 from investment of $20,000. There are 3
options available:
(A) Treasury Bills yielding 9%;
(B) Corporate bonds 11%;
Junk Bonds. 130%
How much should be invested in each to achieve their goal? Give 3 sets of options that can
achieve their goal.[10 Marks]
Answer:
(T, C, J) = (in dollars)
(10000, 10000, 0),
(15000, 4915.97, 84.03),
(18181.82, 1680.67, 137.51)
Step-by-step explanation:
There are a number of ways to approach this question. We have chosen an approach that determines the investments required to achieve interest rate targets.
__
For an overall interest rate of I, the proportion that must be invested at rate I1 < I < I2 is ...
proportion at I1 = (I2 -I)/(I2 -I1)
Similarly, the proportion that must be invested at I2 is what's left over. It can be computed similarly:
proportion at I2 = (I -I1)/(I2 -I1)
__
We want an overall interest rate of $2000/$20000 = 10%.
Given available interest rates of 9%, 11%, and 130%, we need to have investments at a rate lower than 10% and at a rate higher than 10%.
If we use only the options for 9% and 11% (no junk bonds), then we can compute ...
proportion at 9% = (11 -10)/(11 -9) = 1/2
proportion at 11% = (10 -9)/(11 -9) = 1/2
1st Option:
$10,000 in treasury bills; $10,000 in corporate bonds
__
Suppose we want to achieve a 13% return on our investments at 11% and 130%. Then the proportion invested at 9% will use this value for I2:
proportion at 9% = (13 -10)/(13 -9) = 3/4
Of the remaining 1/4 of the money, we can achieve a 13% return by mixing the investments like this:
proportion at 11% = (130 -13)/(130 -11) = 117/119
proportion at 130% = (13 -11)/(130 -11) = 2/119
2nd option:
$20,000 × 3/4 = $15,000 in treasury bills
$5000 × 117/119 = $4,915.97 in corporate bonds
The remaining amount, $84.03 in junk bonds
__
Let's suppose we want a 20% return on our investment in junk bonds and corporate bonds. Then the proportion of the money invested at 9% will be ...
proportion at 9% = (20 -10)/(20 -9) = 10/11
And the proportion at 11% will be ...
proportion at 11% = (130 -20)/(130 -11) = 110/119 . . . (of the remaining 1/11 of the funds)
3rd option:
$20,000 × 10/11 = $18,181.82 in treasury bills
$1,818.18 × 110/119 = $1,680.67 in corporate bonds
The remaining amount, $137.51 in junk bonds
_____
Additional comment
The most that could be invested in Junk Bonds is $165.29. If the remainder is invested in Treasury Bills, then the overall return will be $2000. (You could consider this to be a 4th option.)
a test consists of 10 true false questions to pass a test a student must answer at least six questions correctly if a student guesses on each question what is the probability that the student will pass the test A. 0.172 B. 0.205 C. 0.828 D. 0.377
Answer:
[tex] P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)[/tex]
And using the probability mass function we got:
[tex]P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205[/tex]
[tex]P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117[/tex]
[tex]P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439[/tex]
[tex]P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098[/tex]
[tex]P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977[/tex]
And adding the values we got:
[tex] P(X\geq 6) = 0.377[/tex]
The best answer would be:
D. 0.377
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=10, p=0.5)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
For this case in order to pass he needs to answer at leat 6 questions and we can rewrite this:
[tex] P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)[/tex]
And using the probability mass function we got:
[tex]P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205[/tex]
[tex]P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117[/tex]
[tex]P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439[/tex]
[tex]P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098[/tex]
[tex]P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977[/tex]
And adding the values we got:
[tex] P(X\geq 6) = 0.377[/tex]
The best answer would be:
D. 0.377
Find the solution(s) of the quadratic equation 2x2 – 3x – 35 = 0
Answer: x = 5, x = -7/2
Step-by-step explanation:
2x² - 3x - 35 = 0
Step 1: Find two values whose product = 2(-35) and sum = -3: -10 & 7
Step 2: Replace the b-value of -3x with -10x + 7x:
2x² - 10x + 7x - 35 = 0
Step 3: Factor the first two terms and the second two terms:
2x(x - 5) +7(x - 5) = 0
Step 4: Write the factored form:
Notice that the parenthesis are identical. This is one of the factors. The outside values are the other factor:
Parenthesis: (x - 5)
Outside: (2x + 7)
Factored form: (x - 5)(2x + 7) = 0
Step 5: Set each factor each to zero and solve for x:
x - 5 = 0 2x + 7 = 0
x - 5 [tex]x=-\dfrac{7}{2}[/tex]
The solutions of the quadratic equation given as 2x² - 3x - 35 = 0 are x=5 and x =-3.5.
Given that:
2x² - 3x - 35 = 0
This is a quadratic equation.
It is required to find the solutions of this equation.
The solution of the quadratic equation of the form ax² + bx + c = 0 can be found using the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
From the given equation:
a = 2
b = -3
c = -35
Substitute to the quadratic formula.
[tex]x=\frac{-(-3)\pm \sqrt{(-3)^2-4(2)(-35)}}{2(2)}[/tex]
[tex]=\frac{3\pm \sqrt{9+280}}{4}[/tex]
[tex]=\frac{3\pm \sqrt{289}}{4}[/tex]
[tex]=\frac{3\pm 17}{4}[/tex]
So, the solutions are:
[tex]x=\frac{3+ 17}{4}=5[/tex], and [tex]x=\frac{3-17}{4}=-3.5[/tex]
Hence, the solutions are x =5, -3.5.
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67.805 what is the value of the 0 help please asap!
Answer:
hundreths
Step-by-step explanation:
After the decimal there is tenths, hundreths thousandnths, tens of thousands e.t.c
Answer:
Hello! The answer will be hundredths.
Step-by-step explanation:
The 5 means the thousandths.
The 0 means the hundredths.
The 8 means the tenths.
The 7 means the ones
And the 6 means the tens.
Hope this helps! :)
( below I attached a picture, which might be helpful.)
A manufacturer claims that the mean tensile strength of thread A exceeds the average tensile strength of thread B. To test his claim, 16 sample pieces of each type of thread are tested under similar conditions. Type A thread had a sample average tensile strength of 185 kg with a standard deviation of 6 kg, while type B thread had a sample average tensile strength of 178 kg with a standard of 9 kg. Assume that both populations are normally distributed and the variances are equal. Test the manufacturers claim using a = 0.05 level of significance.
The complete part of the first sentence is;
A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kilograms.
Answer:
we fail to reject the null hypothesis and conclude that the difference of the average tensile strength of thread A and thread B is less than 12
Step-by-step explanation:
We are given;
n_A = 16
n_B = 16
x'_A = 185 kg
x'_B = 178 kg
s_A = 6 kg
s_B = 9 kg
Let μ_A denote the population average tensile strength of thread A
Also, Let μ_B represent the population average tensile strength of thread B
Thus;
Null Hypothesis; H0;μ_A - μ_B ≤ 12
Alternative hypothesis;H1; μ_A - μ_B > 12
From the image attached, with a significance level of 0.05, the critical value for right tailed is 1.645. So we will reject the hypothesis is z > 1.645
Formula for z is;
z = (x'_A - x'_B - d_o)/√((s_A²/n_A) + (s_B²/n_B))
Plugging in the relevant values, we have;
z = (185 - 178 - 12)/√((6²/16) + (9²/16))
z = -5/2.7041634566
z = - 1.849
Since the z-value is less than 1.645,we fail to reject the null hypothesis and conclude that the difference of the average tensile strength of thread A and thread B is less than 12
Y+15<3 what is the solution
Answer:
y < -12
Step-by-step explanation:
Step 1: Subtract 15 on both sides
y + 15 - 15 < 3 - 15
y < -12
This inequality means the any number smaller than -12 would work. So:
-123415235 would work
-1234 would work
-46527 would work
2 would NOT work
6 would NOT work
Answer:
[tex]y < - 12[/tex]Step-by-step explanation:
[tex]y + 15 < 3[/tex]
Move constant to RHS and change its sign:
[tex]y < 3 - 15[/tex]
Calculate the difference
[tex]y < - 12[/tex]
Hope this helps..
Good luck on your assignment..
What is the focus of the parabola? y=−1/4x2−x+3
Answer: Focus = (-2, 3)
Step-by-step explanation:
[tex]y=-\dfrac{1}{4}x^2-x+3\\\\\rightarrow a=-\dfrac{1}{4},\ b=-1[/tex]
First let's find the vertex. We do that by finding the Axis-Of-Symmetry:
[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(-1)}{2(\frac{-1}{4})}=\dfrac{1}{-\frac{1}{2}}=-2[/tex]
Then finding the maximum by inputting x = -2 into the given equation:
[tex]y=-\dfrac{1}{4}(-2)^2-(-2)+3\\\\y=-1+2+3\\\\y=4[/tex]
The vertex is: (-2, 4)
Now let's find p, which is the distance from the vertex to the focus:
[tex]a=\dfrac{1}{4p}\\\\\\-\dfrac{1}{4}=\dfrac{1}{4p}\\\\\\p=-1[/tex]
The vertex is (-2, 4) and p = -1
The focus is (-2, 4 + p) = (-2, 4 - 1) = (-2, 3)
Which statement is true about the function f(x)= -x?
O The domain of the graph is all real numbers.
The range of the graph is all real numbers.
O The domain of the graph is all real numbers less than or equal to 0.
The range of the graph is all real numbers less than or equal to 0.
Answer:
The domain of the graph is all real numbers less than or equal to 0.
Step-by-step explanation:
Hello,
We know that we cannot take square root of negative numbers, so we must have
[tex]-x\geq 0 \ \text{ ***multiply by -1, it changes the inequality, so*** } \\ \\\large \boxed{\sf \ \ x\leq0 \ \ }[/tex]
So the domain of the graph is all real numbers less than or equal to 0.
For information, I attached the graph so that we can verify it.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
If we assume that asset X has an expected return of 10 and a variance of 10, then its coefficient of variation is:
Answer: Its coefficient of variation = 0.316
Step-by-step explanation:
The formula to find the coefficient of variations:
Coefficient of variation: [tex](\dfrac{\sqrt{\text{variance}}}{\text{return}})[/tex]
Given: Asset X has
Variance = 10
Expected return = 10
then, coefficient of variation [tex]=\dfrac{\sqrt{10}}{10}=\dfrac{1}{\sqrt{10}}\approx0.316[/tex]
Hence, its coefficient of variation = 0.316
Which of the following is an exterior angle of triangle BHE? Yes or no
Answer:
Im not 100% sure, but I think it is:
No
No
No
Yes
Find one solution for the equation. Assume that all angles involved are acute angles. tangent (3 Upper B minus 32 degrees )equals cotangent (5 Upper B plus 10 degrees )
Answer:
Step-by-step explanation:
Equation given
tan(3B-32 ) = cot ( 5B +10 ) = tan [ 90 - ( 5B + 10 ) ]
tan(3B-32 ) = tan (90 - 5B - 10 )
(3B-32 ) = (90 - 5B - 10 )
8B = 32 + 80
B = 14° .
Compute P7,2. (Enter an exact number.)
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Answer:
42
Step-by-step explanation:
The permutation formula is P(n, r) = n! / (n - r)!. We know that n = 7 and r = 2 so we can write:
7! / (7 - 2)!
= 7! / 5!
= 7 * 6 * 5 * 4 * 3 * 2 * 1 / 5 * 4 * 3 * 2 * 1
= 7 * 6 (5 * 4 * 3 * 2 * 1 cancels out)
= 42
Answer:
[tex]\boxed{42}[/tex]
Step-by-step explanation:
Apply the permutation formula.
[tex]P(n,r)=\frac{n!}{ (n-r)!}[/tex]
[tex]P=number \: of \: permutations\\n=total \: number \: of \: objects \: in \: the \: set\\r=number \: of \: choosing \: objects \: from \: the \: set\\[/tex]
[tex]n=7\\r=2[/tex]
Plug in the values and evaluate.
[tex]P(7,2)=\frac{7!}{ (7-2)!}[/tex]
[tex]P(7,2)=\frac{7!}{ (5)!}[/tex]
[tex]P(7,2)=\frac{5040}{120}[/tex]
[tex]P(7,2)=42[/tex]
Question 20 of 21
In the triangle shown below, what is the approximate value of X?
12
O A. 20.78 units
O B. 26.83 units
O c. 12 units
D. 18 units
Answer:
O A. 20.78 units
Step-by-step explanation:
APEXX
7x-x combine the like terms to create an equivelent expression
Answer:
6x
Step-by-step explanation:
7x - x
Factor out x
x( 7-1)
6x
Answer:
6x
Step-by-step explanation:
7x - x
Apply rule : a = 1a
x = 1x
7x - 1x
Factor out x.
(7 - 1)x
(6)x
Which of the following functions best describes this graph ?
Answer:
answer D
Step-by-step explanation:
Lets have a look to the graph and to the each of given functions.
As we can see in graph it intersects X in points (-3;0) and (-6;0) that means the function has the roots x1=-3 and x2=-6
Function A has the roots x1=+3 and x2=+6 => doesn' t fit
Function B has only 1 root x=2 , so can be factorized y=(x-2)^2 => doesn' t fit
Function C has 2 roots x1=4 and x2=-5 => doesn' t fit
Function D can be factotized as y=(x+6)*(x+3) so has 2 roots x1=-6 x2=-3 => exactly what we need!!!
We can also notice that the coefficient near x² is equal to 1 and is positive.
That means the legs of the graph directed up,- this is exactly like in our graph. It gives us extra argument why we choose D.
The population density, D, in people/square mile (p/mi²), for the large city Westport is related to the distance x (in miles) from the city’s center by the equation:________.
D=4300x /x^2 + 40.
a. Describe what happens to West-port's population density as the distance from the city’s center changes from one mile to six miles. What may explain this phenomenon?
b. Describe what happens to West-port's population density as the distance from the city’s center changes from ten miles to thirty miles.
c. Describe the end-behavior of this function? What may explain this phenomenon?
d. In what areas of the city is the population density below 200 p/mi²?
Answer:
Step-by-step explanation:
D=4300x /x² + 40.
x = 1
D = 4300 / 41 = 104.88 p / mi²
x = 6
D = 25800 / 76
= 339.47 p / mi²
Population density increases as we go away from city's centre .
b )
x = 10
D=4300x /x² + 40.
D = 307.14 p/ mi²
x = 30
D = 137.23 p / mi²
Population decreases .
c )
when x is very high , density will decrease due to squared denominator whose value increases very fast .
d )
D < 200
4300x /x² + 40 < 200
4300 x < 200 x² + 8000
43 x < 2 x² + 80
2 x² - 43 x + 80 > 0
( x - 19.44 ) ( x - 2.05 ) > 0
Range x < 2.05
x > 19.44
2.4.6.8. 10.... geometrical,arithmetic or neither?
Answer:
This is an arithmetic sequence.
Step-by-step explanation:
The difference between the consecutive terms is constant => sequence is arithmetic.
4-2 = 2
6-4= 2
8-6 = 2
10-8 = 2
Step-by-step explanation:
It's an arithmetic sequences.
Formed by the n th term 2n.
As the difference is 2 between them.
let's find it, by formulae.
n th term = 2n
t1= 2×1=2t2 = 2×2=4t3=2×3=6t4=2×4=8and so on.....
Therefore, it's an arithmetic sequence.
Hope it helps..
Mia agreed to borrow a 3 year loan with 4 percent interest to buy a motorcycle if Mia will pay a total of $444 in interest how much money did she borrow how much interest would Mia pay if the simple interest rate was 5 percent
Answer:
a) $3700
b) $555
Step-by-step explanation:
The length of the loan is 3 years.
The interest after 3 years is $444.
The rate of the Simple Interest is 4%.
Simple Interest is given as:
I = (P * R * T) / 100
where P = principal (amount borrowed)
R = rate
T = length of years
Therefore:
[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]
P = $3700
She borrowed $3700
b) If the simple interest was 5%, then:
I = (3700 * 5 * 3) / 100 = $555
The interest would be $555.
A college administrator predicts that the proportion of students that are nursing majors is greater than 40%. To test this, a group of 400 students are randomly selected and it's determined that 190 are nursing majors. The following is the setup for this hypothesis test:
H0:p=0.40
Ha:p>0.40
In this example, the p-value was determined to be 0.001. Find the conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)
Answer:
Step-by-step explanation:
Using the following data:
H0:p=0.40 (null hypothesis)
Ha:p>0.40 (alternative hypothesis)
The p-value was determined to be 0.001.
a significance level of 5%
Since the p value (0.001) is less than the significance level (0.05), we will reject the null hypothesis and then we would conclude that the proportion of students that are nursing majors is greater than 0.4.
Answer:
p value= 0.131
Step-by-step explanation:
Since we have calculated the test statistic, we can now proceed to find the p-value for this hypothesis test.Using the test statistic and since the hypothesis test is a left tailed test, the p-value will then be the area under the standard normal curve to the left of the test statistic of -1.12.Using the Standard Normal table given above, the area under the standard normal curve to the left of the test statistic of -1.12 is 0.131 (rounded to 3 decimal places.Thus the p-value = 0.131.
A researcher is interested in determining the mean energy consumption of a new
compact florescent light bulb. She takes a random sample of 41 bulbs and determines
that the mean consumption is 1.3 watts per hour with a standard deviation of 0.7.
When constructing a 97% confidence interval, which would be the most appropriate
value of the critical value?
A) 1.936
B) 2.072
C) 2.250
D) 2.704
E) 2.807
Answer:
The most appropriate value of the critical value is 2.289.
Step-by-step explanation:
We are given that a researcher takes a random sample of 41 bulbs and determines that the mean consumption is 1.3 watts per hour with a standard deviation of 0.7.
We have to find that when constructing a 97% confidence interval, which would be the most appropriate value of the critical value.
Firstly, as we know that the test statistics that would be used here is t-test statistics because we don't know about the population standard deviation.
So, for finding the critical value we will look for t table at (41 - 1 = 40) degrees of freedom at the level of significance will be [tex]\frac{1 - 0.97}{2} = 0.015[/tex] .
Now, as we can see that in the t table the critical values for P = 1.5% are not given, so we will interpolate between P = 2.5% and P = 1%, i.e;
[tex]\frac{0.015 - 0.025}{0.025-0.01}= \frac{\text{Critcal value}-2.021}{2.021-2.423}[/tex]
So, the critical value at a 1.5% significance level is 2.289.
Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $21.51 and a 95% confidence interval of [$20.52, $22.48]. Which of the following statements is a valid interpretation of the confidence interval?
a. 95% of all taxi fares are between $20.52 and $22.48.
b. We are 95% confident that a randomly selected taxi fare will be between $20.52 and $22.48.
c. We can report that the average taxi fare between Logan Airport and downtown Boston will fall between $20.52 and $22.48.
d. With 95% confidence
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x =[/tex]$21.51
The 95% confidence level interval is [$ 20.52 , $22.48]
Generally the 95% confidence level interval is mathematically represented as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
Where MOE is the margin of error which defines in percentage the amount by which the sample mean taxi fare(for the 7 taxi ) will differ from the average taxi fare between Logan Airport and downtown Boston will fall between
Also [tex]\mu[/tex] is the average taxi fare between Logan Airport and downtown Boston
So we see that the this 95% confidence level interval tells us that the average taxi fare between Logan Airport and downtown Boston will fall between $20.52 and $22.48.
The coldest temperature ever recorded in New York City was -15F on Feb 9, 1934. The next day, the temperature rose
Write an expression for the temperature on Feb 10
Answer:
x = -15 + y
Step-by-step explanation:
Let next days temperature be x and the temperature rise be y
=> x = -15 + y
The next day's temperature will be more since it "rose".
Answer:
[tex]\boxed{x=-15+y}[/tex]
Step-by-step explanation:
Let the temperature on Feb 10, 1934 be x.
Let the temperature increase be y.
On Feb 9, the temperature was -15F.
On Feb 10, the temperature increased.
[tex]x=-15+y[/tex]