Answer:
See explanation below
Step-by-step explanation:
1) Prove or disprove that if [tex] x^y[/tex] is an irrational number, then x or y is also an irrational number.
Let's take the following instances:
i) When x= 2 and y=[tex] \sqrt{2} [/tex] we have: [tex] 2^\sqrt^{^2^} [/tex]
ii) When [tex] x=2\sqrt{2} [/tex] and y=3, we have: [tex] (x=2\sqrt{2})^3 [/tex]
iii) When [tex] x=2\sqrt{2} [/tex] and [tex] y = \sqrt{2}[/tex], we have: [tex] (2\sqrt{2})^\sqrt^{^2^}[/tex]
It is proven because, in scenario
i) x is rational and y is irrational
ii) x is irrational and y is rational
iii) x and y are irrational
2) Prove tha x² is irrational, then x is irrational.
Use contradiction here.
Thus, x² is irrational and x is rational.
[tex] x =\frac{b}{a} [/tex] when x is rational, a & b are integers.
Therefore, [tex] x^2 =\frac{b^2}{a^2} [/tex]. This x² is rational.
This contradicts the statement that x² is irrational.
Therefore, if x² is irrational, x is also irrational.
Keith Rollag (2007) noticed that coworkers evaluate and treat "new" employees differently from other staff members. He was interested in how long a new employee is considered "new" in an organization. He surveyed four organizations ranging in size from 34 to 89 employees. He found that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
A) In this study, what was the real range of employees hired by each organization surveyed?
B) What was the cumulative percent of "new" employees with the lowest tenure?
Answer:
a) Real range of employees hired by each organization surveyed = 56
b) The cumulative percent of "new" employees with the lowest tenure = 30%
Step-by-step explanation:
a) Note: To get the real range of employees hired by each organization, you would do a head count from 34 to 89 employees. This means that this can be done mathematically by finding the difference between 34 and 89 and add the 1 to ensure that "34" is included.
Real range of employees hired by each organization surveyed = (89 - 34) + 1
Real range of employees hired by each organization surveyed = 56
b) It is clearly stated in the question that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
Therefore, the cumulative percent of "new" employees with the lowest tenure = 30%
A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000 women reported drinking alcohol and 552 of 1000 men reported drinking alcohol. What is the 95% confidence interval of the drinking alcohol percentage difference between women and men
Answer:
The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).
Step-by-step explanation:
We want to calculate the bounds of a 95% confidence interval of the difference between proportions.
For a 95% CI, the critical value for z is z=1.96.
The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.
[tex]p_1=X_1/n_1=494/1000=0.494[/tex]
The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.
[tex]p_2=X_2/n_2=552/1000=0.552[/tex]
The difference between proportions is (p1-p2)=-0.058.
[tex]p_d=p_1-p_2=0.494-0.552=-0.058[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022[/tex]
Then, the margin of error is:
[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014[/tex]
The 95% confidence interval for the difference between proportions is (-0.102, -0.014).
solve for x
2x/3 + 2 = 16
Answer:
2x/3 + 2= 16
=21
Step-by-step explanation:
Standard form:
2
3
x − 14 = 0
Factorization:
2
3 (x − 21) = 0
Solutions:
x = 42
2
= 21
Which are the right ones?
Answer:
20 4/5
Step-by-step explanation:
13/5 times 8/1
104/5
which is simplify
to 20 4/5\
hope this helps
For what values (cases) of the variables the expression does not exist: a / a−b
Answer:
a=b
Step-by-step explanation:
When the denominator is zero, the expression is undefined
a-b=0
a=b
1. A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head
Answer:
See below in bold.
Step-by-step explanation:
We can write the equation as
y = a(x - 28)(x + 28) as -28 and 28 ( +/- 1/2 * 56) are the zeros of the equation
y has coordinates (0, 32) at the top of the parabola so
32 = a(0 - 28)(0 + 28)
32 = a * (-28*28)
32 = -784 a
a = 32 / -784
a = -0.04082
So the equation is y = -0.04082(x - 28)(x + 28)
y = -0.04082x^2 + 32
The second part is found by first finding the value of x corresponding to y = 22
22 = -0.04082x^2 + 32
-0.04082x^2 = -10
x^2 = 245
x = 15.7 inches.
This is the distance from the centre of the door:
The distance from the edge = 28 - 15.7
= 12,3 inches.
Use Green's Theorem to evaluate ?C F·dr. (Check the orientation of the curve before applying the theorem.)
F(x, y) =< x + 4y3, 4x2 + y>
C consists of the arc of the curve y = sin x from (0, 0) to (p, 0) and the line segment from (p, 0) to (0, 0).
Answer:
Step-by-step explanation:
given a field of the form F = (P(x,y),Q(x,y) and a simple closed curve positively oriented, then
[tex]\int_{C} F \cdot dr = \int_A \frac{dQ}{dx} - \frac{dP}{dy} dA[/tex] where A is the area of the region enclosed by C.
In this case, by the description we can assume that C starts at (0,0). Then it goes the point (pi,0) on the path giben by y = sin(x) and then return to (0,0) along the straigth line that connects both points. Note that in this way, the interior the region enclosed by C is always on the right side of the point. This means that the curve is negatively oriented. Consider the path C' given by going from (0,0) to (pi,0) in a straight line and the going from (pi,0) to (0,0) over the curve y = sin(x). This path is positively oriented and we have that
[tex] \int_{C} F\cdot dr = - \int_{C'} F\cdot dr[/tex]
We use the green theorem applied to the path C'. Taking [tex] P = x+4y^3, Q = 4x^2+y[/tex] we get
[tex] \int_{C'} F\cdot dr = \int_{A} 8x-12y^2dA[/tex]
A is the region enclosed by the curves y =sin(x) and the x axis between the points (0,0) and (pi,0). So, we can describe this region as follows
[tex]0\leq x \leq \pi, 0\leq y \leq \sin(x)[/tex]
This gives use the integral
[tex] \int_{A} 8x-12y^2dA = \int_{0}^{\pi}\int_{0}^{\sin(x)} 8x-12y^2 dydx[/tex]
Integrating accordingly, we get that [tex]\int_{C'} F\cdot dr = 8\pi - \frac{16}{3}[/tex]
So
[tex] \int_{C} F cdot dr = - (8\pi - \frac{16}{3}) = \frac{16}{3} - 8\pi [/tex]
divide and simplify x^2+7x+12 over x+3 divided by x-1 over x+4
Answer:
[tex]\dfrac{x^2+8x+16}{x-1}[/tex]
Step-by-step explanation:
In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...
[tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]
wo cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a nine and then selecting an eight. The probability of selecting a nine and then selecting an eight is nothing.
Answer:
0.6%
Step-by-step explanation:
We have a standard deck of 52 playing cards, which is made up of 13 cards of each type (hearts, diamonds, spades, clubs)
Therefore there are one nine hearts, one nine diamonds, one nine spades and one nine clubs, that is to say that in total there are 4. Therefore the probability of drawing a nine is:
4/52
In the second card it is the same, an eight, that is, there are 4 eight cards, but there is already one less card in the whole deck, since it is not replaced, therefore the probability is:
4/51
So the final probability would be:
(4/52) * (4/51) = 0.006
Which means that the probability of the event is 0.6%
Circle O has a circumference of 36π cm. Circle O with radius r is shown. What is the length of the radius, r? 6 cm 18 cm 36 cm 72 cm
Answer: 18 cm
Step-by-step explanation:
We know the circumference formula is C=2πr. Since our circumference is given in terms of π, we can easily figure out what the radius is.
36π=2πr [divide both sides by π to cancel out]
36=2r [divide both sides by 2]
r=18 cm
Answer:
18cm
Step-by-step explanation:
because i found it lol
Suppose that prices of recently sold homes in one neighborhood have a mean of $225,000 with a standard deviation of $6700. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $211,600 and $238,400
Answer:
[tex] 211600 = 225000 -k*6700[/tex]
[tex] k = \frac{225000-211600}{6700}= 2[/tex]
[tex] 238400 = 225000 +k*6700[/tex]
[tex] k = \frac{238400-225000}{6700}= 2[/tex]
So then the % expected would be:
[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]
So then the answer would be 75%
Step-by-step explanation:
For this case we have the following info given:
[tex] \mu = 225000[/tex] represent the true mean
[tex]\sigma =6700[/tex] represent the true deviation
And for this case we want to find the minimum percentage of sold homes between $211,600 and $238,400.
From the chebysev theorem we know that we have [tex]1 -\frac{1}{k^2}[/tex] % of values within [tex]\mu \pm k\sigma[/tex] if we use this formula and the limit given we have:
[tex] 211600 = 225000 -k*6700[/tex]
[tex] k = \frac{225000-211600}{6700}= 2[/tex]
[tex] 238400 = 225000 +k*6700[/tex]
[tex] k = \frac{238400-225000}{6700}= 2[/tex]
So then the % expected would be:
[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]
So then the answer would be 75%
The area of the sector of a circle with a radius of 8 centimeters is 125.6 square centimeters. The estimated value of is 3.14.
The measure of the angle of the sector is
Answer:
225º or 3.926991 radians
Step-by-step explanation:
The area of the complete circle would be π×radius²: 3.14×8²=200.96
The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.
[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).
There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.
We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.
Answer:
225º
Step-by-step explanation:
Find the product of
3/5 × 7/11
Answer:
21/55
Step-by-step explanation:
Simply multiply the top 2 together:
3 x 7 = 21
And the bottom 2 together:
5 x 11 = 55
21/55 is your answer!
Word related to circle
Answer:
Center, radius, chord, diameter... are Words related to circle
During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.a. What is the expected number of calls in one hour?b. What is the probability of three calls in five minutes?c. What is the probability of no calls in a five-minute period?
Answer:
Step-by-step explanation:
This is a poisson distribution. Let x be a random representing the number of calls in a given time interval.
a) the expected number of calls in one hour is the same as the mean score in 60 minutes. Thus,
Mean score = 60/2 = 30 calls
b) The interval of interest is 5 minutes.
µ = 5/2 = 2.5
We want to determine P(x = 3)
Using the Poisson probability calculator,
P(x = 3) = 0.21
c) µ = 5/2 = 2.5
We want to determine P(x = 0)
Using the Poisson probability calculator,
P(x = 0) = 0.08
The probability that a house in an urban area will be burglarized is 6%. If 10 houses are randomly selected, what is the probability that none of the houses will be burglarized?
Answer:
[tex](\dfrac{94}{100})^{10} \ or\ \approx 0.54[/tex]
Step-by-step explanation:
Given :
Probability that a house in an urban area will be burglarized,
[tex]p =6\%=\dfrac{6}{100}[/tex]
To find:
Probability that none of the houses randomly selected from 10 houses will be burglarized = ?
[tex]P(r=0) =?[/tex]
Solution:
This question is related to binomial distribution where:
[tex]p =\dfrac{6}{100}[/tex]
[tex]\Rightarrow[/tex] Probability that a house in an urban area will not be burglarized,
[tex]q =1-6\%=94\%=\dfrac{94}{100}[/tex]
Formula is:
[tex]P(r=x)=_nC_xp^xq^{n-x}[/tex]
Where n is the total number of elements in sample space and
x is the number selected from the sample space.
Here, x = 10 and
x = 0
[tex]\therefore P(r=0)=_nC_0p^0q^{10-0}\\\Rightarrow 1 \times (\dfrac{6}{100})^0\times (\dfrac{94}{100})^{10}\\\Rightarrow 1\times (\dfrac{94}{100})^{10}\\\Rightarrow (\dfrac{94}{100})^{10}\\\\\Rightarrow (0.94)^{10}\\\Rightarrow \approx 0.54[/tex]
The volume of a water in a fish tank is 84,000cm the fish tank has the length 60cm and the width 35cm. The water comes to 10cm from the top of the tank. calculate the height of the tank.
Answer:
Height of tank = 50cm
Step-by-step explanation:
Volume of water from tank that the water is 10cm down is 84000cm³
Length = 60cm
Width = 35cm
Height of water = x
Volume = length* width* height
Volume= 84000cm³
84000 = 60*35*x
84000= 2100x
84000/2100= x
40 = x
Height of water= 40cm
Height of tank I = height of water+ 10cm
Height of tank= 40+10= 50cm
Height of tank = 50cm
What is the value of (4-2) – 3x4?
О-20
оооо
4
Answer:
-10
Step-by-step explanation:
Use the Order of Operations - PEMDAS
Do what is in parentheses first - (4-2) = 2
Next multiply 3 and 4 = 12
Last, perform 2 - 12; which equals -10
A human resource manager for a large company takes a random sample of 60 employees from the company database. Based on the sample she calculates a 95% confidence interval for the mean time of employment for all employees to be 8.7 to 15.2 years. Which of the following will provide a more informative (i.e., narrower) confidence interval than the 95% confidence interval?
A. Using a 90% confidence level (instead of 95%)
B. Using a 99% confidence level (instead of 95%)
C. Using a sample size of 40 employees (instead of 60)
D. Using a sample size of 90 employees (instead of 60)
Answer:
A. Using a 90% confidence level (instead of 95%)
D. Using a sample size of 90 employees (instead of 60)
Step-by-step explanation:
The margin of error of a confidence interval is given by:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The higher the margin of error, the less precise the confidence interval is.
We have:
A 95% confidence interval, with a sample of 60.
We want to make it more precise:
Two options, decrease z(decrease the confidence level), or increase n(increase the sample size).
So the correct options are:
A. Using a 90% confidence level (instead of 95%)
D. Using a sample size of 90 employees (instead of 60)
is 614 divisible by both 2 and 6?
Answer:
No
Step-by-step explanation:
It is not divisible by 6, for if you divide by 6, you will get a non natural number,
It is obviously divisible by 2.
So, No.
Answer:
no
Step-by-step explanation:
only by 2
614/2 = 307
614/6 = 102.33
To reach a particular department at a warehouse, a caller must dial a 4-digit extension. Suppose a caller remembers that the first and last digits of an extension are 5, but they are not sure about the other digits.
How many possible extensions might they have to try?
Answer:
100 possible extensions
Step-by-step explanation:
we can calculated how many possible extensions they have to try using the rule of multiplication as:
___1_____*___10_____*___10_____*____1____ = 100
1st digit 2nd digit 3rd digit 4th digit
You know that the 1st and 4th digits of the extension are 5. it means that you just have 1 option for these places. On the other hand, you don't remember nothing about the 2nd and 3rd digit, it means that there are 10 possibles digits (from 0 to 9) for each digit.
So, There are 100 possibles extensions in which the 5 is the first and last digit.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
plane
Step-by-step explanation:
Answer:
D. Plane
Step-by-step explanation:
A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.
Sue works an average of 45 hours each week. She gets paid $10.12 per hour and time-and-a-half for all hours over 40 hours per week. What is her annual income?
Step-by-step explanation:
40 x $10.12/hr = $404.80
5 x $15.18/hr = $ 75.90
over time = $10.12 + $5.06 ( half of $10.12) = $15.18/hr
$404.80 + $75.90 = $480.70/weekly pay
assuming she works 52 weeks a year
$480.70 × 52 weeks = $24,996.40/yr
I really need help, please help me.
Answer:
96 degrees
Step-by-step explanation:
Since x is half of 168, its angle measure is 84 degrees. Since x and y are a linear pair, their angle measures must add to 180 degrees, meaning that:
y+84=180
y=180-84=96
Hope this helps!
What is the perimeter of A’B’C’D’?
[tex]\displaystyle\bf\\\textbf{At any translation of a quadrilateral the sides remain the same,}\\\\\textbf{the angles remain the same.}\\\\\textbf{It turns out that the quadrilateral remains the same.}\\\\P_{A'B'C'D'}=P_{ABCD}=AB+BC+CD+DA=\\\\~~~~~~~~~~~~~~=2.2+4.5+6.1+1.4=\boxed{\bf14.2}[/tex]
what is 7/9 x 5 2/5 please!
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
=>[tex]\frac{7}{9} * 5 \frac{2}{5}[/tex]
=> [tex]\frac{7}{9} * \frac{27}{5}[/tex]
=> [tex]\frac{7*3}{5}[/tex]
=> [tex]\frac{21}{5}[/tex]
=> [tex]4\frac{1}{5}[/tex]
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\frac{7}{9} \times 5 \frac{2}{5}[/tex]
[tex]\frac{7}{9} \times \frac{27}{5}[/tex]
[tex]\frac{7 \times 27}{9 \times 5 }[/tex]
[tex]\frac{189}{45}[/tex]
[tex]\frac{21}{5}[/tex]
[tex]=4\frac{1}{5}[/tex]
Which expression is equivalent to 24 ⋅ 2−7?
Answer:
41
Step-by-step explanation:
[tex]24*2-7=\\48-7=\\41[/tex]
Express 12/16 in quarters
Overweight participants who lose money when they don’t meet a specific exercise goal meet the goal more often, on average, than those who win money when they meet the goal, even if the final result is the same financially. In particular, participants who lost money met the goal for an average of 45.0 days (out of 100) while those winning money or receiving other incentives met the goal for an average of 33.7 days. The incentive does make a difference. In this exercise, we ask how big the effect is between the two types of incentives. Find a 90% confidence interval for the difference in mean number of days meeting the goal, between people who lose money when they don't meet the goal and those who win money or receive other similar incentives when they do meet the goal. The standard error for the difference in means from a bootstrap distribution is 4.14.
Answer:
The 90% confidence interval for the difference in mean number of days meeting the goal is (4.49, 18.11).
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two means is:
[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]
It is provided that:
[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]
The critical value of z for 90% confidence level is,
z = 1.645
*Use a z-table.
Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:
[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]
[tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]
Thus, the 90% confidence interval for the difference in mean number of days meeting the goal is (4.49, 18.11).
Rocco used these steps to solve the equation 4x + 6 = 4 + 2(2x + 1). Which choice describes the meaning of his result, 6 = 6?
Answer:
infinite solutions
Step-by-step explanation:
it means that all x are solution of this equation as 6=6 is always true