We have been given that two datasets arranged in descending order are: [tex]\{8, x, 4,1\}[/tex] and [tex]\{9, y, 5,2\}[/tex]. We are asked to find the value of [tex](y-x)^2[/tex], if the medians of the two given datasets are equal.
First of all, we will arrange our given data sets in ascending order.
[tex]\{1,4,x,8\}[/tex] and [tex]\{2,5,y,9\}[/tex]
Since our data sets have 4 data points, so median will be average of middle two terms.
[tex]\frac{4+x}{2}[/tex] and [tex]\frac{5+y}{2}[/tex]
Now we will equate both median as we are told that median of both data sets are equal.
[tex]\frac{5+y}{2}=\frac{4+x}{2}[/tex]
Cross multiply:
[tex]2(5+y)=2(4+x)[/tex]
Divide both sides by 2:
[tex]\frac{2(5+y)}{2}=\frac{2(4+x)}{2}[/tex]
[tex]5+y=4+x[/tex]
[tex]5-5+y-x=4-5+x-x[/tex]
[tex]y-x=-1[/tex]
Let us square both sides of our equation.
[tex](y-x)^2=(-1)^2[/tex]
[tex](y-x)^2=1[/tex]
Therefore, the value of [tex](y-x)^2[/tex] would be 1.
Please help.
Thank you.
Answer:
The first option is not a function
Explanation:
A function is where there is no repeated x values
Just a reminder
A gym membership charges $50 new member fee and $24 for every month after. Write an equation for this where y is the total cost and x is the number of months attended.
Answer:
y=24x+50
24= per month
x= months attended
50=member fee
what is the sum of 21 and 5 times a number f is 61
Answer:
f = 8
Step-by-step explanation:
21 + 5f = 61
5f = 61 - 21
f = (61 - 21) / 5
f = 8
Answer:
f = 8
Step-by-step explanation:
"Sum" = addition
"Times" = multiplication
Write an equation to represent this scenario
21 + 5 * f = 61
Multiply 5 by f
21 + 5f = 61
Subtract 21 from both sides of the equation
5f = 40
Divide both sides of the equation by 5
f = 8
Hope this helps :)
evaluate one third of the sum of 15 and 6
Answer:
7
Step-by-step explanation:
15 plus 6 equals 21
21 divided by 3 is 7
Answer:7
Step-by-step explanation:
sum of 15 and 6
15+6=21
1/3 Of The sum
1/3 of 21
1/3 x 21
(1x21)/3
21/3=7
Tony wants to estimate the number of bees in a beehive. He catches 100 bees from the hive and marks each one with a dye. He then lets the bees go. The next day, tony catches 60 bees from the hive. 15 of these bees have been marked with dye. A) using this information what is a good estimate for the number of bees in the beehive.
Answer:
Number of total bees = 400
Step-by-step explanation:
He catches 100 bees from the hive and marks each one with a dye.
He later catches 60 and 15 were marked with the dye.
Its very to estimate from the data given.
I'll answer it with ratio.
We'll ratio number of bees with dye to total he caught the second day.
I.e 15:60 = 1:4
We'll multiply this ratio with the number he caught the first day to know the total.
1/4x =100
X = 100*4
X= 400
Where x is the total number of bees in the bee hive.
the atlantic ocean is 2.78×10^4 feet deep at it's lowest point. If a scuba diver dives 1/50 of the total depth of the ocean, enter how many feets he dove down?
Answer:
556 feet
Step-by-step explanation:
What you have to do to get the answer is find out what 10^4 is, and then multiply that by 2.78. After that, you just need to divide it by 50.
10^4 = 10,000
2.78 × 10,000 = 27,800
27,800 ÷ 50 = 556
Answer:
556
Step-by-step explanation:
What is the approximate area of a circle with diameter 6?
Answer: 28.27
Step-by-step explanation:
First, you can turn the diameter into a radius, giving you 3. Since the equation of an area in a circle is A=πr^2, you must square 3, giving you 9. Now you must multiply 9 with Pi, which is 3.14159265358, but just 3.14 for short. With that, you get about 28.27 as area.
Find the height of the cylinder if the volume is 225 yard and diameter is 5 yd
Answer:
2.86 yards
Step-by-step explanation:
Height = volume/parameter
Parameter = 1/2 diameter * pi
Height = 225 / parameter
Height=2.86
What is the solution to the equation StartFraction m Over m + 4 EndFraction + StartFraction 4 Over 4 minus m EndFraction = StartFraction m squared Over m squared minus 16 EndFraction?
Answer: m = -2.
The given equation is: [tex]\frac{m}{m+4}+\frac{4}{4-m}=\frac{m^{2}}{m^{2}-16}[/tex].
The LCM of the denominators = [tex]m^{2}-16=(m+4)(m-4)[/tex].
We multiply both sides by LCM.
[tex]\left(m+4\right)\left(m-4\right)\left(\frac{m}{m+4}+\frac{4}{4-m}\right)=\left(m+4\right)\left(m-4\right)\cdot\frac{m^{2}}{m^{2}-16}[/tex]
[tex]m\left(m-4\right)-4\left(m+4\right)=m^{2}[/tex]
[tex]m^{2}-4m-4m-16=m^{2}[/tex]
[tex]8m=-16\\m=-2[/tex]
Learn more: https://brainly.com/question/13769924
Answer:
M=-2 B
Step-by-step explanation:
trust me i took the quiz
Triangle ABC is reflected over the x-axis. Triangle ABC has points A (10, 2), B (9,5), and C
(6,4). What is the B' coordinate?
A reflection over a line l moves every point P of the plane to the point P ′ on the perpendicular from P to the line l and on the same distance from l .
If the line is the x -axis, a point P = ( p 1 p 2 ) moves to the point P ′ = ( p 1 , − p 2 ) .
The image of the triangle A B C is the triangle A ′ B ′ C ′ with B ′ = ( 9 , − 5 )
Need answer please Precal
Answer:
170.5 is the answer from the TI-84
Step-by-step explanation:
Need help with this..
Answer:
Step-by-step explanation:
m4 + m3 = 180 (Supplementary angle on 1 line)
m6 +m3 = 180 (Supplementary angle)
-> m6=m4
-> x+80 = 4x-10
-> 90 = 3x
-> x = 30
-> m6=m4 = 80+30 = 110
...
m1+m4 = 180 (Supplementary angle on 1 line)
-> m1 = 180 -110 = 70
Two trains leave stations 390 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour while the other travels at 80 miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.
Answer:
Let's denote:
x: the time both trains traveled.
Then, we have:
70x + 80x = 390
=> 150x = 390
=> x = 390/150 = 2.6 hour
Answer:
2.6 hours ( or 2 hours 36 minutes).
Step-by-step explanation:
The combined speed is 70+80 = 150 mph.
Speed = distance / time, so time = distance / speed.
So the time when they will meet
= 390 / 150
= 2.6 hours.
Help plz? With show work !!! Plzzz
Answer:
B; D
Step-by-step explanation:
5) 3x + 7 = 6x - 11 -->
18 = 3x -->
6 = x (B)
6) (t+6)(10) = (t)(12) -->
10t + 60 = 12t -->
60 = 2t -->
30 = t (D)
ONLY BOYS ANSWER PLSSSS
What would you do if Shakira was right next to you and you can do whatever you want to her :)
Answer:
you need Jesus lol :)
Step-by-step explanation:
.....
The smallest multiple of 13 is
Answer:
0
Step-by-step explanation:
The smallest (greater or equal to zero) multiple of 13 is 0
to get a positive multiple of 13 you have to multiply 13 by a natural number:
0 = 13×0
13 = 13×1
26 = 13×2
.
.
.
then the smallest one is 0.
The area of Jamie's square backyard is 64 square meters. What is the length of one side of Jamie's backyard? Please Answer this asap bc I have to get this turned in, in about 10 mins please hurry
Answer:
8 meters
Step-by-step explanation:
Since the 4 sides of a square are all equal, the area of a square can be found using:
a=s*s or
a=s^2
We know that the area is 64 square meters, so we can substitute 64 in for a
64=s^2
We are trying to find a side, s, so we have to get s by itself. Since s is being squared, take the square root of both sides. This will cancel out the exponent, and leave s by itself.
[tex]\sqrt{64}=\sqrt{s^2}[/tex]
8=s
So, one side of the backyard is 8 meters
If the graph of f(x) = x is shifted up 13 units, what would be the equation of the new graph?
Answer:
f(x) = x + 13
Step-by-step explanation:
f(x) = x
when x = 0, y = 0
f(x) = x + 13
when x = 0, y = 13
Lola has h hats. Polly has triple as many hats as Lola. Darla has eight less hats than Polly.
a. Write an expression for how many hats each person has in terms of h.
Answer:
number of Lola hats = h
number of Polly hats = 3h
number of Darla hats = 3h - 8
Step-by-step explanation:
Lola has h number of hats . Polly has triple as many as Lola . Then Darla has eight number of hat less than Polly. The expression for how many hat each person has in terms of h can be express below.
Let
number of Lola hats = h
number of Polly hats = 3h (recall Polly has triple as many as Lola)
number of Darla hats = 3h - 8(Note Darla has 8 number less of hats than Polly who already have 3h number of hats)
The simplest way to explain this is that Lola has h number of hats. This means she has h number of hats .Polly has triple of Lola hats, this implies that 3 times h of Lola hats is Polly hats. Then finally Darla hats is 8 less than Polly hats. This simply means if you subtract 8 from Polly's hats you have gotten Darla's hats.
Direct mail advertisers send solicitations ("junk mail") to thousands of potential customers in the hope that some will buy the company's product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and sends it to 1030 people randomly selected from their mailing list of over 200,000 people. They get orders from 103 of the recipients.
Required:
Create a 95% confidence interval for the percentage of people the company contacts who may buy something. (Show your work. Step by step)
Answer:
The interval is (.0817, .118).
Step-by-step explanation:
Let's make this interval! The easy way is to go to STAT->TEST->A, 1-prop z-int, but I will show the long way.
1. Conditions
First we must check the conditions.
Randomization condition: The sample is given to be random, so we can assume independence.
Success/failure condition: Both np>10 and nq>10 must be met.
np = 1030(103/1030) = 103 ✓ nq = 1030(927/1030) = 927 ✓10% condition: The sample cannot be greater than 10% of the population.
10n < N, 10(1030) < 200000 ✓All conditions are met, so we can use a 1-proportion z-interval to represent the data.
2. Mechanics
Find [tex]\hat{p}[/tex], the sample proportion.
103/1030 = .1
[tex]\hat{q}[/tex], then, the probability of not p, is 1 - .1 = .9
Find z* (z star), the critical z-value.
You can do this on your calculator using 2nd->VARS->3 (or you can memorize it - it's 1.96. Winky face.) This is called the invNorm function, that takes the left side area under the normal curve. But what do we plug in to the invNorm function?
invNorm(.975) = 1.96
Plug values into the equation.
[tex]\hat{p}[/tex] ± z*[tex]\sqrt{\frac{\hat{p}\hat{q}}{n} }[/tex]
.1 ± 1.96[tex]\sqrt{\frac{.1*.9}{1030} }[/tex]
.1 ± 1.96(.00935)
.1 - .0183 = .0817
.1 + .0183 = .118
(.0817, .118)
3. Conclusion
Based on this sample, we are 95% confident that the proportion of people the company contacts who may buy something is between .0817 and .118. That isn't very likely, but maybe they'll make a little profit!
The picture shows a cement bag of weight Fg hanging from a rope which itself is supported by two other ropes attached to a ceiling. The latter two ropes make an angle θ1 and θ2 with the ceiling. Determine the tension in each rope. Use the angle addition identity to simplify your result: sin(α ± β) = sin α cos β ± cos α sin β
Answer:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
Step-by-step explanation:
From the free body diagram attached below; we will see that
T₃ = Fg ------ (1)
Thus; as the system is in equilibrium, the net force in the x and y direction shows to be zero
Then;
[tex]\sum F_x= 0 \to T_2 Cos \theta _2 - T_1 cos \theta _1[/tex]
[tex]T_2 Cos \theta _2 = T_1 cos \theta _1 \ \ \ \ \ - - - (2)[/tex]
Also;
[tex]\sum F_y =0 \to T_2sin \theta_2+T_1sin \theta_1 - T_3 = 0[/tex]
[tex]T_3 = T_2sin \theta_2+T_1sin \theta_1[/tex] ---- (3)
From equation (2):
[tex]T_2 = \dfrac{T_1cos \theta_1}{cos \theta_2}[/tex]
Replacing the above value for T₂ into equation 3; we have
[tex]T_3 = \dfrac{T_1cos \theta_1}{cos \theta_2}sin \theta_2+T_1sin \theta_1[/tex]
[tex]T_3 cos \theta_2 = {T_1cos \theta_1}{}sin \theta_2+T_1sin \theta_1 cos \theta_2[/tex]
[tex]T_3 cos \theta_2 = T_1(cos \theta_1 sin \theta_2+sin \theta_1 cos \theta_2)[/tex] ---- (4)
Using trigonometric identity Sin (A+B) = SIn A cos B + Cos A sin B
So ; equation 4 can now be:
[tex]T_3 cos \theta_2 = T_1sin(\theta _1 + \theta_2)[/tex] --- (5)
replacing equation (1) into equation (5) ; we have:
[tex]F_g}cos \theta_2 =T_1 sin (\theta_1+\theta_2)[/tex]
Hence; the tension in the string is:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
PLZ HELP
Figure ABCD is reflected across the x-axis.
What are the coordinates of A' , B' , C' , and D' ?
Enter your answer in each box.
A' (
,
)
B' (
,
)
C' (
,
)
D' (
,
)
A graph with a quadrilateral on it formed between points A begin ordered pair 2, 3 end ordered pair, B begin ordered pair 5, 5 end ordered pair, C begin ordered pair 7, 3 end ordered pair, and D begin ordered pair 5, 2 end ordered pair
Answer:
A' (2,-3)
B' (5,-5)
C' (5,-2)
D' (7,-3)
Step-by-step explanation:
I used desmos graphing calculator to help me solve
Answer: The answers would be A= 2,-3 B= 5,-5 C=-5-2 and D= 7,-3
What is the value of x in the equation below? Negative 3 minus (negative 8) minus (negative 2) = x
Answer:7
Step-by-step explanation:
-3-(-8)-(-2)=x
-3+8+2=x
-3+10=x
7=x
x=7
The answer plz hurryyy
Answer:
The answer is that the y-coordinate should be -3 1/2.
Step-by-step explanation:
First, look at the graph. On the x-axis, the dot is at -5, since it is 5 units to the left of the origin. On the y-axis, the dot is at -3 1/2. It is between -3 and -4, not -4 and -5. Therefore, the answer is that the y-coordinate should be -3 1/2, not -4 1/2. You can also check by seeing if -4 1/2 is reasonable. -4 1/2 would mean the dot would be more than 4 units below the origin. On the graph, the dot is clearly above the -4 mark, so the -4 1/2 must not be correct.
Given the formula, Sn=a 1-r^n/1-r, what is the sum of the first nine terms of the geometric series: 324, -108, 36, -12...
If necessary, round to the hundredths place. (2 places after the decimal)
Answer:
243.01.
Step-by-step explanation:
The first term (a) = 324.
The common ratio (r) = -108/324 = -1/3.
So sum of 9 terms is:
S(9) = 324 * (1 - (-1/3)^9) / ( 1 - (-1/3)
= 324 ( 1 - (-0.00005076)) / 4/3
= 324 * 1.00005076 / 1.33333
= 243.012.
Molly wants to buy a skirt. The original price was $40.The skirt is on sale for 12% off. When she goes to pay for it the cashier tells her she can have an additional 13% discount off the sale price, how much will Molly pay for the skirt?
Answer:
$30.62
Step-by-step explanation:
12% of 40 is 4.8
(10% is 4, 2% is 0.8)
40- 4.8= 35.2
13% of 35.2 is 4.576
(10% is 3.52, 3% is 1.056)
35.2- 4.576= 30.624
then rounded to 2 decimal places
30.62
Whoever answers I WILL MARK BRANLIEST !!!
Answer:
3. 7632
4. 485
Step-by-step explanation:
3. The only prime digit greater than 6 is 7, so that is the thousands digit. The only even prime is 2, so that is the ones digit.
In order for the number ending in 2 to be divisible by 4, the tens digit must be odd. The only odd numbers that have a double that is an even digit are 1 and 3. Since all digits must be different, the hundreds digit cannot be 2×1 = 2, but must be 2×3 = 6.
The number is 7632.
__
4. In order for an odd number to be divisible by 5, its ones digit must be 5, not 0. Then the tens digit is 5+3 = 8, and the sum of these two digits is 5+8 = 13. To make the total of digits equal to 17, the hundreds digit must be 17-13 = 4.
The number is 485.
From a class of 25 students how many group of 4
Answer: Well, 4 groups of four, and roughly 6 student in a group
Step-by-step explanation:
The question is not clear, but 25 divided by 4 is 6.25, but it’s students so 6 or 7.
A large trucking company wants to estimate the proportion of its tracker truck population with refrigerated carrier capacity. A random sample of 200 tracker trucks is taken and 30% of the sample have refrigerated carrier capacity. The 95% confidence interval to estimate the population proportion is _______.
Answer:
The 95% confidence interval to estimate the population proportion is (0.2365, 0.3635).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 200, \pi = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{200}} = 0.2365[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{200}} = 0.3635[/tex]
The 95% confidence interval to estimate the population proportion is (0.2365, 0.3635).
Jessica bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 18 cups of soup. A quick Google search told her that this was 259.9 cubic inches. She hoped the soup pot below would be big enough. The soup pot is 9 inches tall with a radius of 3.5 inches. What is the volume of the soup pot? Answer choices are rounded to the nearest tenth cubic inch. 169.6 cubic inches 890.6 cubic inches 197.9 cubic inches 346.4 cubic inches
Answer: 346.4 in^3
Step-by-step explanation:
The pot can be thinked as a cylinder:
The volume of a cylinder is equal to:
V = (pi*r^2)*h
where h is the height, r is the radius and pi = 3.1416
Here we have that: r = 3.5in, h = 9in.
Then the volume is:
V = 3.1416*(3.5in)^2*9in = 346.4in^3
