Solution :
Sample size Sample mean Sample S.D.
Sample 1 [tex]$n_1=36$[/tex] [tex]$\bar{x}_1=150,000$[/tex] [tex]$s_1=17,000$[/tex]
Sample 2 [tex]$n_2=45$[/tex] [tex]$\bar{x}_2=100,000$[/tex] [tex]$s_2=12,000$[/tex]
[tex]$df = \frac{\left(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}\right)^2}{\frac{1}{n_1-1}\left(\frac{s_1^2}{n_1}\right)^2+\frac{1}{n_2-1}\left(\frac{s_2^2}{n_2}\right)^2}$[/tex]
= 60
Therefore, significance level, α = 0.1
Critical value, t* = 1.6706
So, the margin of error, [tex]$t^*=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$[/tex]
= 559.9896
Lower limit, [tex]$(\bar x_1-\bar x_2)-\text{(margin of error)}=44402.0104$[/tex]
Upper limit, [tex]$(\bar x_1-\bar x_2)+\text{(margin of error)}=55597.9896$[/tex]
Therefore 90% C.I. is (44402.0104, 55597.9896) or [tex]$44402.0104 < \mu_1 - \mu_2 < 55597.9896$[/tex]
What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21?
Answer:
x + 3y =21 equation 1
let the equation perpendicular to X + 3y = 21 be
3x - y + k = 0 equation 2
since the point ( 1 , -3 ) passes through equation 3x - y +k =0
3× 1 - (-3) + k = 0
or, 3 + 3 + k = 0
or, 6 + k =0
or, k = -6
now,
putting the value of k in equation 2
3x - y + k = 0
or, 3x -y -6=0
Hey guys happy holidays! any help is appreciated :)
1) The astronaut's sense of imbalance in a space flight is due to the rotation of a device in which he or she feels a fictitious gravity that mimics gravity. The the device rotates according to the mathematical equation: n =g^0.5/2πr^0.5 Where n is the rotational speed and is measured in rotations per second (s). (r) is the radius of the circulator and is measured in meters (m). (g) is a simulation of gravity. Calculate the rotation speed of a device, that has a radius of 1.7 meters and rotates to simulate the gravitational force which equals to: g = 9.8 m/s^2 with steps please
Answer:
n = 0.38 rotation per second
Step-by-step explanation:
The device rotates according to the mathematical equation :
[tex]n=\dfrac{g^{0.5}}{2\pi r^{0.5}}[/tex] ...(1)
Where n is the rotational speed and is measured in rotations per second (s).
r is radius of the circulator and is measured in meters (m).
We need to find the rotational speed when radius is 1.7 m. Put r = 1.7 m in equation (1).
[tex]n=\dfrac{(9.8)^{0.5}}{2\pi \times (1.7)^{0.5}}\\\\=0.38\ \text{rotations per second}[/tex]
Hence, the rotational speed is 0.38 rotation per second.
Anna and Elsa are helping set up for the Christmas celebration at Magic Kingdom. They have to install 7 million lights for the annual display. It takes Elsa 14 days to set up the 7 million lights by herself and it takes Anna 11 days to set up the 7 million lights by herself. How long will it take them to do it together?
Answer:
If they work together, they will take 6.16 days.
Step-by-step explanation:
Elsa takes 14 days to complete the work.
So, 1 day work by Elsa is [tex]\frac{1}{14}[/tex]
Anna takes 11 days to complete the work.
So, 1 day work by Anna is [tex]\frac{1}{11}[/tex].
So, Let if they work together, it would take x number of days.
So, we can set up equation as
[tex]\frac{1}{14} +\frac{1}{11}=\frac{1}{x}[/tex]
Find LCD, which is 154.
[tex]\frac{11}{154} +\frac{14}{154} =\frac{1}{x}[/tex]
Simplify
[tex]\frac{25}{154} =\frac{1}{x}[/tex]
Cross multiply,
25x=154
Divide both sides by 25
x=6.16 days
If they work together, they will take 6.16 days.
Olivia got a 72% on her quiz, there are 25 questions how many did she get right and how many did she get right
Answer:
18
Step-by-step explanation:
72% of 25 is 18.
Hope this helped! :)
Please help!!!! Thank youuu I’ll make brainlisy
Answer:
A
Step-by-step explanation:
it isn't a straight line, so it is nonlinear
raul drove 80 miles.this represent 50% of the entire trip what is the total number of miles on raul trip
Answer:
its 160 miles
whatt is -1/6 x 5/6 ok help ok
Answer:
-5/36
Step-by-step explanation:
-1*5 = -5
6*6 = 36
-5/36
45% of _____________is 165
Answer:
366.666666Step-by-step explanation:
Let the number be x
45% of x = 165x*45/100 = 165x = 165*100/45x = 366.666666someone help plz right answer gets brainliest
Answer:
CGIA
Step-by-step explanation:
C is the first line, G is the second, I is the third, and A is the fourth.
I graphed it all. If I helped you, give me brainliest
Reflect AABC across the x-axis.
1. How many units away from the x-axis
is point A?
PLEASEE I REALLY NEED HELP!!!!!
The position of point A of the triangle is -4 units from the x-axis.
What is coordinate geometry?A coordinate plane is a 2D plane created by the junction of the x-axis and y-axis, two perpendicular lines. A coordinate system in geometry is a way to use one or more integers or coordinates to determine the positions of the points.
Here in the given diagram, there is a triangle ABC. The coordinates of the vertex of the triangle are,
A ( -4,2 )
B ( 1, -5 )
C ( 3,1 )
The distance of point A from the x-axis is -4 units.
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PLZ HELP ASAP PLZ AWSER DONT SKIP PLZ ASAP
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
What type of solution would you get for 0=0
A. one solution
B. no solution
C.infinite
Using the equation ŷ = 5.4 + 1.7x, what is the predicted value if x is 1.2?
3.36
−3.36
7.44
−7.44
−2.47
Answer:
Using the equation ŷ = 5.4 + 1.7x, we can say that if x is 1.2, the predicted value will be 7.44.
Step-by-step explanation:
y=5.4+1.7(1.2)
Multiply 1.7 and 1.2 to get 2.04.
y=5.4+2.04
Add 5.4 and 2.04 to get 7.44.
y=7.44
There you go!
(Sources cited from Microsoft Math Solver.)
Solve the quadratic equation: x^2+ 2x + 7 = 21
Answer:
x1 = -4.872983346
x2 = 2.872983346
Step-by-step explanation:
Given:
x^2+2x+7=21
Subtract 21 on both sides to get the right side equal to 0:
x^2+2x-14=0
Use the quadratic formula:
x1 = -4.872983346
x2 = 2.872983346
At an aunt's wedding , Nicolas collected data about an ice sculpture that was about to completely melt . A graph of his data is shown at right . a . Write an equation for a line of best fit . What are the units for the slope and y-intercept in the equation ? b Based on your equation , how tall was the ice sculpture one hour before Nicolas started measuring ?
Answer:
Step-by-step explanation:
From the scatter plot given in the attachment,
a). Line of best fit will pass through two points (0, 10) and (4, 0)
Let the equation of the line is,
y = mx + b
m = slope of the line
b = y-intercept
Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{10-0}{0-4}[/tex]
m = -2.5 inches per hour
y-intercept = 10 inches
Therefore, equation of the line will be, y = -2.5x + 10
b). Since, Nicolas started measuring the height of the ice sculpture at x = 0
One hour before the start of the observations means x = (0 - 1) = -1
From the given equation,
y = -2.5(-1) + 10
= 2.5 + 10
= 12.5 inch
Mrs. Wienman baked her family’s favorite pie. There are 5 people in the family. She cut the pie into eight parts. Her family ate four slices. What part of the pie was left?
Answer:
4/8
Step-by-step explanation:
Answer:
Pie remaining = 1/2 (simplified form of 4/8)
Step-by-step explanation:
Pie = 1 = 8/8 (cut into 8 peices)
Pie ate = 4/8
Pie remaining = 4/8 (8/8 - 4/8)
Subtract -7x^2+4x+2 from x^2-3x
Answer:
-8x^2+x+2
Step-by-step explanation:
The gym teacher is setting up for a field
day event where students will run
blindfolded through a series of
obstacles. To prevent injury she will
enclose the area with a nylon fence,
which can be ordered from Lowe's for
$15 a linear yard. How much will the
nylon fencing cost?
please help asap!! for finals!! semi easy question! will mark brainliest!! not multiple choice! tysm !!
Answer: 42 gallons
Step-by-step explanation:
1,260/180 = 7
Per 180 mile = 6 gallon
7x6=42
Find the value of X please help
his year, Cornell’s class took two more than three times as many field trips as last year’s class. This year, Cornell’s class took a total of 8 trips. How many field trips did his class take last year?
4. Anthony makes candies.
First, he mixes 1 cup of cream with 2 cups of chocolate.
In all, he uses 9 cups of these two ingredients.
How many cups of chocolate does he use in this candy recipe?
Explain.
Answer:
6
Step-by-step explanation:
There is 1 cup of cream for every 2 cups of chocolate. That means there are 3 cups of cream and 6 cups of chocolate. Each cup of cream = 2 cups of chocolate, so you would do 3*2 which equals 6
6 + 3 = 9
How do these results about area and perimeter of similar quadrilaterals compare with similar situations for triangles?
Answer:
Let's see
Step-by-step explanation:
Two triangles are same ∆1 and ∆2
They have same height and breath
Now ∆1= ∆2
=> ar(∆1)= ar(∆2)
The same is for quadrilaterals
What is 1/6 divided by 6/7
7/36
[tex]\frac{1}{6} /\frac{6}{7}=\frac{1}{6}*\frac{7}{6}=\frac{7}{36}[/tex]
can someone help fast
Find the value of y if the value of x is 2 for each equation and match it with the appropriate result.
2 + y = 5
3x + 2y = 6
2x + y = 6
5x + 3y = 4
drag & drop the answer
-2
3
-3
0
2
2
9514 1404 393
Answer:
3, 0, 2, -2
Step-by-step explanation:
Put x=2 into each equation and solve for y.
2 + y = 5
y = 5 -2
y = 3
3x +2y = 6
3·2 +2y = 6
2y = 6 -6 = 0
y = 0
2x +y = 6
2·2 +y = 6
y = 6 -4
y = 2
5x +3y = 4
5·2 +3y = 4
3y = 4 -10 = -6
y = -2
11) Stephanie makes $ 50 a week babysitting. She spends $ 25, saves $ 15, and uses the rest to pay off a $ 100 loan from her brother. After six weeks, how much has Stephanie spent, how much has she saved, and how much still owes her brother?
Answer:
She saved 90 dollars and she owes her brother 40 still.
Step-by-step explanation:
As the number of trials increase in experimental probability, the experimental probability will get farther away from the theoretical probability.
True
False
Explanation:
The more trials you do, the closer the experimental probability will get to the theoretical probability.
For example, if you flip a coin 1000 times, then you'll probably get around 500 heads or so. Maybe you could get 475 heads and 525 tails. This leads to an experimental probability of 475/100 = 0.475 of getting heads. If you flip a coin 10,000 times, then you are likely to have the experimental probability of getting heads move closer to 0.500
Answer:
B
Step-by-step explanation:
Compute the sum of the squares of the shorter lengths. Compute the sum of the squares of the shorter lengths. Compute the square of the longest length. Compute the square of the longest length. What kind of triangle is it? What kind of triangle is it? Acute triangle Acute triangle Right triangle Right triangle Obtuse triangle Obtuse triangle
The given triangle is a right triangle because it agrees Pythagoras theorem.
In the given triangle, the shorter lengths are 12 and 16.
The sum of square of shorter lengths:
[tex]= 12^2 + 16^2[/tex]
[tex]=144+256[/tex]
[tex]=400[/tex]
The longer length is 20.
Square of the longest length is [tex]20^2.[/tex]
[tex]20^2 = 20 \times 20[/tex]
=400
The sum of squares of shorter lengths is equal to Square of the longest length which obeys Pythagoras theorem.
400 = 400
As this is agreeing Pythagoras theorem it is a right angle triangle.
Hence, option B is correct. right triangle.
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