Answer:
The 95% confidence interval is
[tex] 0.45 < \mu_1 - \mu_2 < 5.35 [/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 36[/tex]
The first sample mean is [tex]\= x_1 = 3.5[/tex]
The first standard deviation is [tex]\sigma_1 = 5.9 \ pounds[/tex]
The second sample size is [tex]n_2 = 36[/tex]
The second sample mean is [tex]\= x_2 = 0.6[/tex]
The second standard deviation is [tex]\sigma = 4.4[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = \frac{ [ \frac{s_1^2 }{n_1 } + \frac{s_2^2 }{n_2} ]^2 }{ \frac{1}{(n_1 - 1 )} [ \frac{s_1^2}{n_1} ]^2 + \frac{1}{(n_2 - 1 )} [ \frac{s_2^2}{n_2} ]^2 }[/tex]
=> [tex]df = \frac{ [ \frac{5.9^2 }{34 } + \frac{4.4^2 }{34} ]^2 }{ \frac{1}{(34 - 1 )} [ \frac{5.9^2}{34} ]^2 + \frac{1}{(34- 1 )} [ \frac{4.4^2}{ 34} ]^2 }[/tex]
=> [tex]df =63[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{ \frac{s_1 ^2 }{n_1} + \frac{s_2^2 }{ n_2 } }[/tex]
=> [tex]SE = \sqrt{ \frac{ 5.9 ^2 }{ 36 } + \frac{ 4.4^2 }{36} }[/tex]
=> [tex]SE = 1.227[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the t distribution table the critical value of at a degree of freedom of is
[tex]t_{\frac{\alpha }{2}, 63 } = 1.998 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2}, 63 } * SE[/tex]
=> [tex]E = 1.998 * 1.227[/tex]
=> [tex]E = 2.45[/tex]
Generally 95% confidence interval is mathematically represented as
[tex](\= x_1 - \x_2) -E < \mu <(\= x_1 - \x_2) + E[/tex]
=> [tex](3.5 - 0.6) - 2.45 < \mu_1 - \mu_2 < ( 3.5 - 0.6) + 2.45 [/tex]
=> [tex] 0.45 < \mu_1 - \mu_2 < 5.35 [/tex]
Two pounds of dried cranberries cost $5.04, 3 pounds of dried cranberries cost $7.56, and 7 pounds of dried cranberries cost $17.64. What equation gives the total cost y of x pounds of dried cranberries?
Answer:
y = 2.52x
y = cost, x = pounds of cranberries.
each pound costs 2.52
Step-by-step explanation:
5.04/2 = 2.52
Solve using BODMAS
1 half of [ 5 + 4 – {3 + 5 – (1 + 3)} ]
Answer:
Result: 3/2 = 1 1/2 = 1.5 Result in words: three halves (or one and one half) Solve problems with two, three, or more fractions and numbers in one expression. The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5) BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
Step-by-step explanation:
Answer:
2.5
Step-by-step explanation:
☪️ Meaning of BODMAS:-
B - Bracket
O - Of
D - Division
M - Multiplication
A - Addition
S - Subtraction
☪️ Work:-
1 ÷ 2 × ((5 + 4 × 0) + 5 × 0)
0.5 × ((5 + 4 × 0) + 5 × 0)
0.5 × ((5 + 0) + 5 × 0)
0.5 × (5 + 5 × 0)
0.5 × (5 + 0)
0.5 × 5
2.5
Sorry if I’m not correct.
Hope this helps!
(*^ω^*)
Plz help ASAP fheodjdidididkdu
Answer:
B
Step-by-step explanation:
The point R(-3,a,-1) is the midpoint of the line segment jointing the points P(1,2,b)
and Q(c,-7,4)
Find the values of:
a=
b=
C=
Answer:
The values are:
[tex]a = -5/2[/tex][tex]b = -6[/tex][tex]c = -7[/tex]Step-by-step explanation:
Given:
P = (x₁, y₁, z₁) = (1, 2, b) Q = (x₂, y₂, z₂) = (c, -7, 4) m = R = (x, y, z) = (-3, a, -1)To Determine:
a = ?
b = ?
c = ?
Determining the values of a, b, and c
Using the mid-point formula
[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]
As the point R(-3, a, -1) is the midpoint of the line segment jointing the points P(1,2,b) and Q(c,-7,4), som = R = (x, y, z) = (-3, a, -1)
Using the mid-point formula
[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]
given
(x₁, y₁, z₁) = (1, 2, b) = P
(x₂, y₂, z₂) = (c, -7, 4) = Q
m = (x, y, z) = (-3, a, -1) = R
substituting the value of (x₁, y₁, z₁) = (1, 2, b) = P, (x₂, y₂, z₂) = (c, -7, 4) = Q, and m = (x, y, z) = (-3, a, -1) = R in the mid-point formula
[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]
[tex]\left(x,\:y,\:z\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]
as (x, y, z) = (-3, a, -1), so
[tex]\left(-3,\:a,\:-1\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]
Determining 'c'
-3 = (1+c) / (2)
-3 × 2 = 1+c
[tex]1+c = -6[/tex]
[tex]c = -6 - 1[/tex]
[tex]c = -7[/tex]
Determining 'a'
a = (2+(-7)) / 2
[tex]2a = 2-7[/tex]
[tex]2a = -5[/tex]
[tex]a = -5/2[/tex]
Determining 'b'
-1 = (b+4) / 2
[tex]-2 = b+4[/tex]
[tex]b = -2-4[/tex]
[tex]b = -6[/tex]
Therefore, the values are:
[tex]a = -5/2[/tex][tex]b = -6[/tex][tex]c = -7[/tex]20 points
Two mountain bikers are riding on a 35-mile trail. Abel started at the beginning of the trail and is riding at a rate of 14
miles per hour. Neal started 6 miles ahead of Abel and is riding at a rate of 11 miles per hour. When will the boys be
at the same point on the trail?
If Abel's journey is represented by the equation d = 14t, where d represents the total distance and t represents time
in hours, what equation represents Neal's journey?
Two mountain bikers are riding on a 35-mile trail. Abel started at the beginning of the trail and is riding at a rate of 14 miles per hour. Neal started 6 miles ahead of Abel and is riding at a rate of 11 miles per hour. When will the boys be at the same point on the trail?
If Abel’s journey is represented by the equation d = 14t, where d represents the total distance and t represents time in hours, what equation represents Neal’s journey?
d = 11t + 6
11 and 6 are your answers
Please mark Brainliest
Answer:
11 and 6 are correct
Step-by-step explanation:
On a map, Delilah is standing at (10, -13). Her friend Pedro is standing at (18, -13). If Delilah walks 8 units left, will she be standing with Pedro? Explain.
Answer:
Yes
Step-by-step explanation:
if she walk 8 to the left she will be at 18-13 which is his location
The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
No,
Delilah is not standing with Petro after she walks 8 units to its left.
The position on the map is not the same.
The coordinates of Delilah and Petro is not the same.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The following coordinates.
Delilah is standing at (10, -13).
Pedro is standing at (18, -13).
Delilah walks 8 units left.
This means,
The coordinates of Dellah will be,
(10, -13) → (10 - 8, -13) = (2, -13)
In order for Delilah to stand together with Pedro both their coordinates must be equal.
Delilah coordinates = (2 , -13)
Pedro coordinates = (18, -13)
Thus,
No,
Delilah is not standing with Petro after she walks 8 units to its left.
The position on the map is not the same.
The coordinates of Delilah and Petro is not the same.
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Rachel wants to save money for a foreign exchange student program. She
needs $950 to belong to the program. She has $200. She earns $40 per
week. How can she figure out the number of weeks that she will take to
save enough money for her program?
O A. Add 200 plus 950 and then divide by 40.
O B. Subtract 40 from 950 and then divide by 200.
O C. Add 200 plus 40 and then divide by 950.
O D. Subtract 200 from 950 and then divide by 40.
Zoey bought a plant and planted it in a pot near a window in her house. Let
H
H represent the height of the plant, in inches,
t
t months since Zoey bought the plant. The table below has select values showing the linear relationship between
t
t and
H
.
H. Determine the initial height of the plant when it was purchased.
Answer: 2.5
Step-by-step explanation:
Given the relationship between month since plant was bought t and plant height H ;
t
0.5
3
5
H:
17.25
23.5
28.5
Using the online regression calculator, the regression model obtained is :
y = 16x + 2.5
Using this model, we can obtain the height when t = 0 ; this will give the height at the time of purchase of the plant. Therefore, at x = 0
y = 16(0) + 2.5
y = 0 + 2.5
y = 2.5
Hence, height of plant = 2.5
Answer:
16 inches
Step-by-step explanation:
I need help I don’t know how to do these problems
Answer:
It is in fact 113 I'm just here to explain
Step-by-step explanation:
Basically M6 and M7 must make a staright line(180) and since we already know that M6 is 67 we just have to subtract 67 from 180 to get the answer we are looking for. ( it would be the same process if we were looking for M1 (113) and also if you had the measure of M1 you would have had your answer to M7 because they are vertical angles therefore making them congruent
Will give brainly. question in picture below
Answer:
Its the letter F
Step-by-step explanation:
7. Use the facts and graph below to write the equation for g(x)
Step 1: Start with the equation f(x) = |x|. Write the equation for the graph of g(x) that has been stretched vertically by a factor of 2.
Step 2: Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has also been reflected, or flipped, over the x-axis.
Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has also been shifted down 3 units.
Step 4: Use the equation you wrote in Step 3. Write the equation for the graph of g(x) that has also been shifted right 1 unit.
9514 1404 393
Answer:
g(x) = 2|x|g(x) = -2|x|g(x) = -2|x| -3g(x) = -2|x -1| -3Step-by-step explanation:
1. Multiplying the function by a constant stretches the graph by that constant. Here, you want a stretch factor of 2, so you have ...
g(x) = 2f(x) = 2|x|
__
2. Negating a function causes its graph to be reflected over the x-axis. That makes your second function look like ...
g(x) = -2|x|
__
3. Subtracting 3 from the function value shifts its location on a graph down by 3 units. Your third function will be ...
g(x) = -2|x| -3
__
4. Subtracting a constant from the x-value causes the graph of the function to be shifted right by that amount. Here you want a right shift of 1 unit, so your function is ...
g(x) = -2|x -1| -3
Answer:
the other users is correct, sorry I was going to answer until i saw it was already but it wouldn't let me of the screen
Step-by-step explanation:
Find the measure of the missing angle.
Answer:
you have a 90 degree angle and to find your answer subtract 90-63=27.
Step-by-step explanation:
simplify: √(4√3-√15)^2
I WILL AWARD BRAINLIEST TO THE CORRECT ANSWER!
Answer:
3.05521988407
Step-by-step explanation:
used a calculator lol
25/18 as a mixed number
Plsss help me
Step-by-step explanation:
7
1 ---
18
hope it helps !
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
4.9 mi to 2.8 mi
Twice the sum of a number and five is equal to 40 (translate to an algebraic equation)
The algebraic equation representing the given statement is
2(x + 5) = 40.
We have,
Let's translate the given statement into an algebraic equation.
The sum of a number (let's call it x) and five can be expressed as (x + 5).
Twice the sum of a number and five is equal to 40, so we can write it as:
2(x + 5) = 40
Therefore,
The algebraic equation representing the given statement is
2(x + 5) = 40.
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The area of a rectangle is 216 inches squared. The ratio of the length to width is 3:2. Find the length and the width
Answer:
Length = 18 inches
Width = 12 inches
Step-by-step explanation:
Let the Length be 3x and width be 2x
Area= Length*Width=216 inches squared
216=3x*2x
216=6x²
x²=216/6
x²=36
x=√36
x=6 inches
Therefore
Length = 3x = 3*6 = 18 inches
Width = 2x = 2*6 = 12 inches
please help
/ The Hotel is 163 miles from your house.your car travels 10.5 miles for every litre of petrol. Work out approximately how many litres of petrol the journey will use.
2/The price of petrol is 138.9 pence per litre Work out the approximate cost for the petrol to the hotel .
3/ you expect to travel 50 miles in each hour of a jurney how long the whole journey should take
Answer:
The answers are:
15.523 liters of petrol will be used.The cost of petrol will be: 2156.2 penceThe journey will take 3 hours and 16 minutes approximatelyStep-by-step explanation:
Given:
Distance of Hotel and car = 163 miles
Distance travelled by car per liter = 10.5 miles
The number of liters will be obtained by dividing the total distance by distance travelled in one liter.
So,
[tex]number\ of\ liters = \frac{163}{10.5} = 15.523\ liters[/tex]
2. Cost for petrol:
Cost of petrol per liter = 138.9 pence per liter
Then the total cost of petrol will be:
[tex]Total\ cost = 138.9*15.523 = 2156.1447 => 2156.2\ pences[/tex]
3. Time taken for journey
Distance travelled in an hour = speed = 50 miles per hour.
The speed is given by the formula:
[tex]speed = \frac{distance}{time}[/tex]
Putting the values
[tex]50 = \frac{163}{t}\\t = \frac{163}{50}\\t = 3.26\ hours[/tex]
It will take: 3 hours and 0.26*60 = 15.6 minutes => 3 hours 16 minutes
Hence,
The answers are:
15.523 liters of petrol will be used.The cost of petrol will be: 2156.2 penceThe journey will take 3 hours and 16 minutes approximatelyThe population of a country grows exponentially at a rate of 1% per year. If the population was 35.7 million in the year 2010, then what is the population size of this country in the year 2015
Answer:
37.52 million
Step-by-step explanation:
using,
A = A'(1+R/100)ⁿ............................. equation 1
Where A = population size in 2015, A' = Initial population, R = rate in percentage, n = number of times between 2010 and 2015.
Given: A' =35.7 million, R = 1%, n = 5.
Substitute these values into equation 1
A = 35.7(1+0.01)⁵
A = 37.52 million.
Hence the size of the population of the country in the year 2015 is 37.52 million
9hr. 8min+ 6hr. 42min.+ 8hr. 39min.
Step-by-step explanation:
24 hours and 29 minutes
find the length of the third side to the nearest tenth 6 and 9
Hello, i do believe that you are asking me to do pythagorean theorem.
I'm not too sure if we are solving hypotenuse or a/b so i'll do both.
[tex]\boxed{\underline{Hypotenuse...}}\\\\\\A^2+B^2=C^2\\6^2+9^2=C^2\;\\36+81=117[/tex]
[tex]\sqrt{117}=10.816\\Round-\;10.8[/tex]
[tex]\boxed{\underline{a/b...}}\\\\\\A^2=C^2-B^2\\A^2=9^2-6^2\\A^2=81-36\\A^2=45\\\sqrt{45}= 6.708\\Round-\;6.7[/tex]
Hope it helps!
What two points are contained in the graph of y = log9 (x)?
O (1,0) and (9, 1)
O(0,1) and (1, 9)
O (1,0) and (9, 0)
O (1,0) and (9, 9)
Answer:
the first choice
Step-by-step explanation:
(1,0) and (9,1)
The graph of a function f is the set of all points (x,f(x)). Any point on the graph satisfy the equation of the graph. To check whether a point lie on a graph we need to put the x value and y value of the point to the equation of the graph and check the LHS and RHS . If LHS is equal to RHS , then this point lie on the graph.
The given equation of graph is y=log₉(x) ...........(i)
Now we check whether the points (1,0) and (9, 1) lie on (i).Putting both the points on the LHS and RHS of (i) we get
For point (1,0) , LHS = 0 and RHS = log₉(1)=0
Therefore LHS=RHS for the point (1,0).
For point (9,1), LHS= 1 and RHS= log₉(9)=1
Therefore LHS=RHS for the point (9,1).
Therefore (1,0) and (9,1) lie on graph of equation (i).
Check whether the points (0,1) and (1, 9) lie on (i).Putting both the points on the LHS and RHS of (i) we get
For point (0,1), LHS=1 and RHS=log₉(0) is undefined
Therefore LHS≠RHS for the point (0,1).
For point (1,9), LHS= 9 and RHS= log₉(1)=0.
Therefore LHS≠RHS for the point (1,9).
Therefore (0,1) and (1,9) does not lie on graph of equation (i).
Check whether the points (1,0) and (9,0) lie on (i).Putting both the points on the LHS and RHS of (i) we get
For point (1,0), LHS=0 and RHS=log₉(1)=0.
Therefore LHS=RHS for the point (1,0).
For point (9,0), LHS= 0 and RHS= log₉(9)=1.
Therefore LHS≠RHS for the point (9,0).
Therefore (1,0) lie on (i) but 9,0) does not lie on graph of equation (i).
Check whether the points (1,0) and (9,9) lie on (i).Putting both the points on the LHS and RHS of (i) we get
For point (1,0), LHS=0 and RHS=log₉(1)=0
Therefore LHS=RHS for the point (1,0).
For point (9,9), LHS= 9 and RHS= log₉(9)=1.
Therefore, LHS≠RHS for point(9,9).
Therefore (1,0) lie on (i) but 9,9) does not lie on graph of equation (i)
Hence, the points (1,0) and (9,1) lie on the graph of y=log₉(x).
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How many 3/2 are in 10
Answer:
not sure,but i will tell you when i figure it out
Step-by-step explanation:
Which ratio is equivalent to 4:5?
10
15
4
10
16.
20
15
풍
Answer:
16;20
Step-by-step explanation;
you can both multiply by 4
4 x 4 = 16 and 5 x 4 = 20.
X is all of the following except ____.
A. a term
B. a variable
C. a constant
D. an expression
Answer:
an expression
Step-by-step explanation:
Sorry if i'm wrong if i'm wrong then a term maybe
Need Help Math question
The point of intersectiom where the 2 lines cross each other is when it is 14 minutes.
Answer:
14 minutes according to the graph
F(x)=3x^2-10x+4, find f(-4)
Answer:
substitute -4 for x
Step-by-step explanation:
A function assigns the value of each element of one set to the other specific element of another set. The value of the function when the value of x is -4 is 92.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that F(x)=3x²-10x+4, therefore, the value of the function can be calculated by substituting the value of x as -4.
Therefore, the value of the function when the value of x is -4 can be calculated as shown below,
F(x) = 3x² - 10x + 4
F(-4) = 3(-4)² - 10(-4) + 4
= 3(16) + 40 + 4
= 48 + 40 + 4
= 92
Hence, the value of the function when the value of x is -4 is 92.
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the line has a rise of 20 and a run of -4 and goes through the points (-2,25) (0,15) (3,0) and (5,10) write the equation in slope-intercept form
Answer:
y = -5x + 15
Step-by-step explanation:
the y intercept was given (0,15)
to find the slope do rise/run
20 / -4 = -5
so the slope is -5
Shelly biked 21 miles in 4 hours what is shellys average speed per hour?
Answer:
The average speed per hour of Shelly is 5.25 minutes.
Step-by-step explanation:
We can do proportion to solve this.
[tex] \frac{21 \: miles}{4 \: hours} = \frac{x}{1 \: hour} \\ \frac{4x}{4} = \frac{21}{4} \\ x = 5.25[/tex]
Extra points and brainliest
Caroline spent $56.32 on groceries after using coupons and store discounts. Without the coupons and store discounts, the groceries would have cost $64.00. What is the total discount Caroline received at the grocery store?
A. 8%
B. 14%
C. 9%
D. 12%
Answer:
D. 12%
Step-by-step explanation:
64-56.32= 7.68
(7.68÷64)×100= 12%
hope this helps! please mark me brainliest..
have a good day ahead
Answer:
D. 12%
Step-by-step explanation:
1. Find the amount of money Caroline saved
Original - spent
Subsitute in the given values,
64 - 56.32 = 7.68
2. Set up a proportion
A proportion is
[tex]\frac{part}{whole} = \frac{percent}{100}[/tex]
Substitute in the values;
[tex]\frac{7.68}{64}=\frac{percent}{100}[/tex]
Cross products;
(7.68)(100) = (64)(percent)
768 = 64 * percent
Inverse operations;
768 = 64 percent
/64 /64
12 = percent
Caroline had a 12% discount.