Using only the trig ratios of 45 and 60 degrees, we use angle-sum to compute [tex]\tan 105^\circ=\tan(60^\circ+45^\circ)=\frac{\tan 60^\circ+\tan 45^\circ}{1-\tan 60^\circ\tan 45^\circ}=\frac{\sqrt{3}+1}{1-\sqrt{3}}=-2-\sqrt{3},[/tex] so [tex]\cot 105^\circ=\frac{1}{\tan 105^\circ}=-2+\sqrt{3}[/tex] and [tex]\tan 105^\circ-\cot105^\circ=\boxed{-2\sqrt{3}}.[/tex]
A bakery sells chocolate, cinnamon, and plain doughnuts and at a particular time has 6 chocolate, 6 cinnamon, and 3 plain. If a box contains 12 doughnuts, how many different options are there for a box of doughnuts
Answer:
2 doughnut boxes
Step-by-step explanation:
6+6=12
12=1 box
and the other 3 can go in a different box which would be 2 boxes
Grant has a sample of 36 rats in his study. If he conducts a single-sample t test, what is the value of the degrees of freedom?
37
6
36
35
Answer:
35
Step-by-step explanation:
Given
Sample of rat
Population = 36
Required
Find the degree of freedom.
Given that the sample is a single-sample t test;
A single-sample t test has just one parameter has its estimate;
And its degree of freedom is calculated as thus;
[tex]df = n - 1[/tex]
Where df represents the degree of freedom and n represents the sample size;
By substituting n = 36;
[tex]df = 36 - 1[/tex]
[tex]df = 35[/tex]
Hence, the degree of freedom of the sample of 36 rats for a single-sample t test is 35
Answer:
The degrees of freedom if we are conducting a test about the true mean are given by:
[tex] df =n-1[/tex]
And replacing the info given we got:
[tex] df = 36-1=35[/tex]
And the best option would be:
35
Step-by-step explanation:
For this case we know that the sample size is n=36.
The degrees of freedom if we are conducting a test about the true mean are given by:
[tex] df =n-1[/tex]
And replacing the info given we got:
[tex] df = 36-1=35[/tex]
And the best option would be:
35
Please answer this correctly
Answer:
18
Step-by-step explanation:
Do 72 divided by 4 because it is a square so all sides are equal
Hiya! ✌.ʕʘ‿ʘʔ.✌
Okay, so with a square, ALL sides are EQUAL.
To find the perimeter of a shape, you just need to add the measure of all sides together.
What you can do, is since all sides are equal, and a square has four sides, just get the measure of ONE side and multiply that by 4! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
The perimeter is 72 meters and if we find the value of u, we get the value of all sides.
Let's set this up as an equation:
P = 4u where P = perimeter and u = measure of one side
Let's insert the given value (72) into the equation for perimeter
72 = 4u
Now we have to solve for u, and to do that, we have to get it by itself on that side of the equation. u is being multiplied by 4, so do the opposite by dividing both sides of the equation by 4!
72/4=18
4u/4=u
Now our equation looks like this:
18 = u
So the value of u is 18! (✿◠‿◠)
To prove it, insert it into the formula... P = 4(18)... P = 72.
Boom! :D
Have a lovely day~ ≧◡≦
According to the National Center for Health Statistics, in 1990, 28 % of babies in the United States were born to parents who were not married. Throughout the 1990s, this increased by approximately 0.6 % per year. If this trend continues, in which year will 76 % of babies be born out of wedlock?
Answer:
76 % of babies will be born out of wedlock in the [tex]81^{st}[/tex] year
Step-by-step explanation:
Given: In 1990, 28 % of babies in the United States were born to parents who were not married. This increased by approximately 0.6 % per year.
To find: year when 76 % of babies born out of wedlock
Solution:
A sequence is said to be in arithmetic progression if the difference between the terms is same.
For a sequence with first term as 'a' and common difference as 'd', the nth term is given by [tex]a_n=a+(n-1)d[/tex]
The given situation also forms an arithmetic progression with [tex]a=28\,,\,d=0.6[/tex]
Also, put [tex]a_n=76[/tex]
So,
[tex]a_n=a+(n-1)d\\76=28+(n-1)(0.6)\\76-28=0.6(n-1)\\48=0.6(n-1)\\\frac{48}{0.6}=n-1\\\\80=n-1\\n=80+1\\n=81[/tex]
So, 76 % of babies will be born out of wedlock in the [tex]81^{st}[/tex] year
Given a+b=7 and a–b=3, find: 2a·2b
The Fortune 500 is comprised of Fortune magazine's annual list of the finite population of the top 500 companies in the U.S. ranked by revenues. According to Catalyst, 16% of positions on corporate boards at Fortune 500 companies were held by women in 2018. A random sample of 100 Fortune 500 companies was selected. The standard error of the proportion is ________.
Answer:
The standard error of the proportion is 0.0367.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.16, n = 100[/tex]
So
[tex]s = \sqrt{\frac{0.16*0.84}{100}} = 0.0367[/tex]
The standard error of the proportion is 0.0367.
Jane can paint the office by herself in 7 hours. Working with an associate, she can paint the office in 3 hours. How long would it take her associate to do it working alone?
Answer:
Step-by-step explanation:i really am lost,
The work rate for the associate is 5.3 hours.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given; Jane can paint the office by herself in 7 hours.
with an associate, she can paint the office in 3 hours.
The combined work rate is 3 hours per office.
WE need to find the work rate for the associate
Let the expression for the work rate be;
1/A+1/B= 1/T
1/7+1/B=1/3
1/B=1/3-1/7
1/B= 8-4/21
1/B= 4/21
B= 21/4
B=5.3 hours
Therefore, the work rate for the associate is 5.3 hours.
Learn more about equations here;
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As a basketball is bounced, the motion is parabolic. In the graph above, y = 0 represents hand level for a basketball player. Find the focus and directrix of the middle bounce (parabola).
Answer:
A on edge2020
Step-by-step explanation:
What is the distance between ( 25, -3) and (1, -3)?
_3.5 units
units
11
o 15 units
units
Save and Exit
Next
SU
Mark this and return
Answer:
D = 24 units
Step-by-step explanation:
Using Distance Formula
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
D = [tex]\sqrt{(1-25)^2+(-3+3)^2}[/tex]
D = [tex]\sqrt{(-24)^2+(0)^2}[/tex]
D = [tex]\sqrt{576}[/tex]
D = 24 units
MATHEMATICS: A boy leaves home at 09:15 hours and arrives at 10:05 hours. If he travels nonstop at an average speed of 6kmh ,what is the distance,in km of his home from school?
Answer:
5 km.
Step-by-step explanation:
We have to calculate the distance if we apply the speed formula that would be the distance in a given time:
v = d / t
therefore, if we solve for distance it would be:
d = v * t
Now the speed is 6 km / h but the time must be calculated, it leaves at 9:15 and returns at 10:05, that is, there is no exact time but 50 minutes, one hour equals 60 minutes, therefore:
50 min * 1 h / 60 min = 0.833 h, that is, the child took 0.833 hours to get to school, now if we replace:
d = 6 * 0.8333
d = 5
In other words, the distance between the school and the house is 5 km.
How do i find the measure?
Answer: angle A = 72 and angle C = 72
Step-by-step explanation:
Angle A and C are opposites so they have to equal each other so do the equation 3y+27=5y-3. y would come out to be 15 and so to find the angles you would replace y with 15.
Find the volume of a cylinder that has a radius of 6 and a height of 10.
607
100 77
3607T
6007
Answer:
360π
Step-by-step explanation:
Put the given numbers in the volume formula and do the arithmetic.
V = πr²h . . . . . r is the radius; h is the height
V = π(6²)(10)
V = 360π
The volume is 360π cubic units.
The times required for a delivery firm to transport a package from one business address to another in the same metropolitan area is normally distributed with a mean of 3.8 hours and a standard deviation of 0.8 hours. Suppose the delivery firm wants to determine the time by which 55% of all deliveries would be made. Which of the following density function diagrams best depicts this problem.
What is the probability a single delivery would take more than 4 hours? What is the z value corresponding to the interval boundary?
Answer:
Step-by-step explanation:
Since; the density function diagrams were not included in the question; we will be unable to determine the best which depicts this problem.
However;
Let use X to represent the time required for the delivery.
Then X~N(3.8 ,0.8)
i.e
E(x) = 3.8
s.d(x) = 0.8
NOW; P(x>4) = P(X-3.8/0.8 > 4-3.8/0.8)
= P(Z > 0.25)
= 1-P(Z < 0.25)
=1 - Φ (0.25)
= 1 - 0.5987 ( from Normal table Φ (0.25) = 0.5987 )
= 0.4013
Thus; the probability a single delivery would take more than 4 hours is 0.4013
What is the z value corresponding to the interval boundary?
The z value is calculated as:
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]z = \dfrac{4- 3.8}{0.8}[/tex]
z = 0.25
(Geometry) PLZ HELP ASAP!
Answer: 133 m^2
Step-by-step explanation:
The area of the parallelogram is:
[tex]A = b\times h=9.5\times14=133 m^2[/tex]
Which one of these statistics is unaffected by outliers?Mean Interquartile range Standard deviation Range
Answer:
Since Interquartile Range consider the middle values in the data set, i.e. 50%, it is not affected by outliers or extreme values. While other statistics mean, standard deviation and range are all affected by outliers or extreme values.
Step-by-step explanation:
hope this helps you :) can you help me please northc04 :(
Answer:
The answer is Interquartile Range. I know this is the right answer is because I got it right on a quiz.
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Since VA and BC are equal in length so their central angles would also be equal.
So
<VWA = <BWC
32x-27 = 120
32x = 120+27
32x = 147
Dividing both sides by 32
x ≈ 4.6
Answer:
4.6
Step-by-step explanation:
3x-27=120
32x=147
x=147/32
x=4.59
x≈4.6
Can someone plz help me solved this problem! I need help ASAP plz help me!
Answer:
The three numbers are 1, 2, and 4.
Step-by-step explanation:
[tex]x+y+z=7\\3x+1=z\\z+x=5[/tex]
From these equations, we get:
[tex]x=1\\y=2\\z=4[/tex]
Which fits all the equations we have written.
arjun has to stick by his budget. his salary is $112,000 after taxes. he divides his
salary in the following ratio, 3:4:5 for savings, bills and food respectively. calculate
his spending for the different items on his budget
if (x+yi)+2(3x-y)+4i-0;then the value of x and y is
Answer:
X=0 and Y= 4(2i-1)/5
Step-by-step explanation:
Here is my solution, assuming that the equation equals 0. For y, just remember the definition of complex numbers and multiply by its conjugate.
The value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number:
(x + yi) + 2(3x - y) + 4i = 0
After arranging:
x + yi + 6x - 2y + 4i = 0
7x - 2y + yi + 4i = 0
7x - 2y + (y + 4)i = 0
7x - 2y = 0
y + 4 = 0
This is the linear equation in two variables:
Plug y = -4 in the other equation:
7x - 2(-4) = 0
7x = -8
x = -8/7
y = -4
Thus, the value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.
Learn more about the complex number here:
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The number of houses Habitat for Humanity can build varies directly with the number of volunteers. How many houses can be built with 60 volunteers?
Answer:
60y
where y is the number of houses each volunteer can build
Step-by-step explanation:
I'll assume this is a complete question and i'll try to solve it the best way i can mathematically.
Let us assume that one volunteer can build a certain number of houses, say y houses.
Also, it is stated that the amount of houses that can be built varies directly as the with the number of volunteers. Therefore, it will be mathematically logical to say that if 1 volunteer can build y number of houses, then 60 volunteers will build 60y houses
Please select the word from the list that best fits the definition
treinta y cinco
What is the difference when you subtract 8 from 5
Answer:
-3
Step-by-step explanation:
5-8
-3
Answer:
=-3
Step-by-step explanation:
we have to find the difference when 8 is subtracted from 5
difference=5-8
the digit after from will come first
=-3
i hope it will help you
The graph of the function f(x) = ax2 + bx +C
(where a, b, and care real and nonzero) has two
x-intercepts. Explain how to find the other x-
intercept if one x-intercept is at
C + 3,0).
Answer:
The axis of symmetry is -b/2a
The x-intercept shown is 3 units away from the axis of symmetry.
The other x-intercept also must be 3 units away from the axis of symmetry but on the opposite side.
Subtract 3 from the axis of symmetry.
The other x-intercept is (-b/2a-3,0)
Step-by-step explanation:
An urn contains 9 red marbles, 9 white marbles and 8 blue marbles. A child randomly selects three (without replacement).
what is the probability that all have the same color?
Answer:
8.62% probability that all have the same color
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[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]
What is the probability that all have the same color?
Desired outcomes:
Either all red(from a set of 9), all white(from a set of 9) or all blue(from a set of 8). So
[tex]D = C_{9,3} + C_{9,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{9!}{3!6!} + \frac{8!}{3!5!} = 224[/tex]
Total outcomes:
3 marbles, from a set of 9 + 9 + 8 = 26. So
[tex]T = C_{26,3} = \frac{26!}{3!23!} = 2600[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{224}{2600} = 0.0862[/tex]
8.62% probability that all have the same color
Which polynomial is prime X squared -36X squared +16 X squared minus 7X +12 X squared minus X -20
Answer:
x^2 +16 is prime
Step-by-step explanation:
A prime polynomial is one that cannot be factored using integers.
x^2 -36 = (x -6)(x +6) . . . . not primex^2 +16 . . . . . primex^2 -7x +12 = (x -3)(x -4) . . . . not primex^2 -x -20 = (x -5)(x +4) . . . . not primeNielsen Media Research provided the list of the 25 top-rated single shows in television history (The World Almanac, 2012). The following data show the television network that produced each of these 25 top-rated shows.
CBS CBS NBC FOX CBS CBS NBC NBC NBC ABC ABC NBC ABC ABC NBC CBS NBC CBS ABC NBC NBC CBS CBS ABC CBS
a. Construct a frequency distribution, a relative frequency distribution, and a percent frequency distribution for the data.
b. Which network or networks have done the best in terms of presenting top-rated television shows? Compare the performance of ABC, CBS, and NBC.
Answer:
a.
Network CBS NBC FOX ABC
f 9 9 1 6
Relative f 0.36 0.36 0.04 0.24
Percent f 36 36 4 24
b.
CBS and NBC have done best in presenting top-rated television shows.
The most top rated shows are from CBS and NBC while ABC network also has top rated shows but CBS and NBC percentages are higher.
Step-by-step explanation:
a.
Network f Relative f Percent f
CBS 9 0.36 36
NBC 9 0.36 36
FOX 1 0.04 4
ABC 6 0.24 24
"f" represents the frequency of network.
"Relative f" represents relative frequency of Network.
"Percent f" represents percent frequency of Network.
Frequency is computed by counting the number of times value repeated in the data. So, the frequency distribution is
Network Frequency
CBS 9
NBC 9
FOX 1
ABC 6
Relative frequency is computed by dividing the frequency to the sum of frequencies.
sum of frequencies=9+9+1+6=25.
So, the relative frequency distribution is
Network Relative frequency
CBS 9/25=0.36
NBC 9/25=0.36
FOX 1/25=0.04
ABC 6/25=0.24
Percent frequency is computed by multiplying relative frequencies to 100.
So, the Percent frequency distribution is
Network Percent frequency
CBS 0.36*100=36
NBC 0.36*100=36
FOX 0.04*100=4
ABC 0.24*100=24
b.
From frequencies, relative frequencies and percent frequencies we can see the CBS and NBC have equally higher cont of top rated shows comparative to ABC and FOX. ABC has second highest top rated shows while Fox has least top rated shows among other networks.
60 is whatpercent of 40
Answer:
24
Step-by-step explanation:
Y is 60% of 40
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 60% * 40
Converting percent to decimal:
p = 60%/100 = 0.6
Y = 0.6 * 40
Y = 24
Please answer this correctly
Answer:
m = 3
Step-by-step explanation:
Assuming these shapes are similar, you can set up a proportion:
[tex]\frac{8}{12} =\frac{2}{m}[/tex]
→Cross multiply:
[tex]\frac{8m}{24}[/tex]
→Divide 24 by 8:
m = 3
The mean playing time for a large collection of compact discs is 34 minutes, and the standard deviation is 6 minutes. (a) What value (in minutes) is 1 standard deviation above the mean
Answer:
40 minutes
Step-by-step explanation:
Let's take the average playing time as u, and let the standard deviation be [tex] \sigma [/tex].
Thus,
[tex] u = 34 [/tex]
[tex] \sigma = 6 [/tex]
To find the value of 1 standard deviation above the mean, we have:
[tex] u + 1\sigma [/tex]
Since u = 34 minutes and [tex]1\sigma [/tex] = 6 minutes, we now have:
[tex] = 34 + 6 = 40 [/tex]
The value (in minutes) of 1 standard deviation above the mean is 40 minutes.
Answer:
40 minutes
Step-by-step explanation:
Given that:
The average time playing time of compact disc in a large collection= 34 minutes and the standard deviation = 6 minutes.
Let [tex]\mu[/tex] represent the average playing time and [tex]\sigma[/tex] to be the standard deviation.
So;
[tex]\mu = 34 \\ \\ \sigma = 6[/tex]
The value for 1 standard deviation above the mean is;
[tex]x+1 s= 34+6 \\ \\ = 40[/tex]
Please Help I Need Help
Answer:
I got 35
Step-by-step explanation:
