The confidence interval lies between (0.827754, and 1.77225).
What is confidence interval ?
An area created using fixed-size samples of data from a population( sample space) that follows a particular probability distribution is known as a confidence interval. A named population statistic is erected into the interval with a specified probability. A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95 confidence position is the most popular, still other situations, similar to 90 or 99, are sometimes used when calculating confidence intervals. A confidence interval is a set of figures that we're nicely confident represent our true value. A named population statistic is erected into the interval with a specified probability.Here, sample mean x = 1.3
sample standard deviation s = 0.45
and sample size n = 6
The 95% confidence interval for the mean waste recycled
= 1.3 - [tex]\frac{0.45}{\sqrt{6} }[/tex] X [tex]t_{0.025'}[/tex] 1.3 +[tex]\frac{0.45}{\sqrt{6} }[/tex] X [tex]t_{0.025'}[/tex]
= 1.3 - [tex]\frac{0.45}{\sqrt{6} }[/tex] X 2.57058 , 1.3 +[tex]\frac{0.45}{\sqrt{6} }[/tex]X 2.57058
= (0.827754, 1.77225)
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I WILL CHOOSE THE BRAINLIEST ANSWER!!! What is the area of the backyard that the grass takes up?
The area of the backyard that the grass takes up is 34x² - πx². The correct option is B. 34x² - πx²
Calculating areaFrom the question, we are to determine the area of the backyard that the grass takes up
Area of the backyard that the grass takes up
= Area of the backyard - Area of the rectangle pool deck - Area of the circle pool
Area of the backyard = 6x × 6x
= 36x²
Area of the rectangle pool deck = 2x × x
= 2x²
Area of the circle pool = πx²
Thus,
Area of the backyard that the grass takes up = 36x² - 2x² - πx²
Area of the backyard that the grass takes up = 34x² - πx²
Hence , the area of the backyard that the grass takes up is 34x² - πx². The correct option is B. 34x² - πx²
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if the pressure in the right tire is found to be 22 psi, what is the probability that the left tire has a pressure of at least 25 psi?
Considering the given probability distribution, we have that there is a 0.349 = 34.9% probability that the left tire has a pressure of at least 25 psi.
What is the probability distribution?The probability distribution for the air pressure of the tires of the car(X right, Y left) is given as follows:
f(x,y) = K(x² + y²), 18 ≤ x ≤ 28, 18 ≤ y ≤ 28.f(x,y) = 0, otherwise.The pressure in the right tire is found to be 22 psi, hence y = 22 and:
f(x,y) = K(x² + 484), 18 ≤ x ≤ 28.f(x,y) = 0, otherwise.The value of K is found considering that the sum of all probabilities has to be 1, hence:
[tex]\int_{18}^{28} K(x^2 + 484) dx = 1[/tex]
[tex]\frac{Kx^3}{3} + 484Kx\lbracket|_{x = 18}^{x = 28} = 1[/tex]
Applying the Fundamental Theorem of Calculus:
7317.33K + 13552K - 8712K - 1944K = 1
10213.33K = 1
K = 1/10213.33
K = 0.000098.
The probability that the left tire has a pressure of at least 25 psi is:
[tex]P(X \geq 25) = \int_{25}^{28} 0.000098(x^2 + 484) dx[/tex]
[tex]P(X \geq 25) = 0.000098\int_{25}^{28} (x^2 + 484) dx[/tex]
[tex]P(X \geq 25) = 0.000098\left(\frac{x^3}{3} + 484x\right)_{x = 25}^{x = 28}[/tex]
[tex]P(X \geq 25) = 0.000098(7317.33 + 13552 - 5208.33 - 12100)[/tex]
[tex]P(X \geq 25) = 0.349[/tex]
0.349 = 34.9% probability that the left tire has a pressure of at least 25 psi.
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it turns out that approximately 20% of the students in the sample already read the book as part of another class. obviously, these students are likely to perform better than students who did not already read the book. assuming that random assignment was used to ensure equivalent groups in the two conditions, this variable (i.e., whether or not subjects already read the book) should be considered:
The given problem falls under the extraneous type of variable.
What do you mean by an extraneous variable?To find out whether or not changing the values of an independent variable has an impact on a dependent variable is the entire objective of performing an experiment. Any variable that you're not interested in researching but that might also impact the dependent variable is an unnecessary variable. For instance, we would be interested in finding out how a basketball player's average points per game are influenced by the number of hours they exercise each week. The amount of time they spend stretching each week, though, is an unrelated factor that might also impact their points per game.
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63+ (2x+8)+(x + 7) = 180
63+ (2x+8)+(x + 7) = 180
63+3x+15=180
78+3x=180
3x=102
x=34
Hey there!
63 + (2x + 8) + (x + 7) = 180
DROP the PARENTHESES:
63 + 2x + 8 + x + 7 = 180
CONVERT TO:
63 + 2x + 8 + 1x + 7 = 180
COMBINE the LIKE TERMS 1:
71 + 3x + 7 = 180
COMBINE the LIKE TERMS 2:
78 + 3x = 180
3x + 78 = 180
SUBTRACT 78 to BOTH SIDES:
3x + 78 - 78 = 180 - 78
SIMPLIFY IT:
3x = 180 - 78
3x = 102
DIVIDE 3 to BOTH SIDES:
3x/3 = 102/3
SIMPLIFY IT:
x = 102/3
x = 34
Therefore, your answer should be:
x = 34
Good luck on your assignment & enjoy your day day!
~Amphitrite1040:)
what is 5.6% as a fraction
Answer:
5.6 =5610=28×25×2=285 in simplest form.
Step-by-step explanation:
Answer:
5 3/5
(heres a picture that will show you, i really hope this helps!!)
how many times greater is 0.00006 than 0.000002
The number 0.00006 is greater than 0.000002 by 30 times.
Two numbers , 0.00006 and 0.000002 are given.
We have to find out that by how many times 1st is greater by the 2nd.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as multiplication , division , etc.
As per the question ;
Numbers are 0.00006 and 0.000002.
Let's divide them to find how many times 1st is greater by the 2nd.
So ;
0.00006 ÷ 0.000002
Multiply by 10^6 and divide by 10^6
We get ;
[tex]\frac{0.00006 * 10^6}{0.000002*10^6}[/tex]
or
60 / 2
= 30 times
Thus , the number 0.00006 is greater than 0.000002 by 30 times.
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all three sides of triangle x'y'z' must be to the corresponding sides in triangle xyz and the corresponding angles are .
The required solution is ∠X'≅∠X, ∠Y'≅∠Y and ∠Z'≅∠Z.
It is required to find the corresponding angles.
What is angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.
Given :
Corresponding angles are
∠X'≅∠X,
∠Y'≅∠Y
∠Z'≅∠Z
Therefore, the required solution is ∠X'≅∠X, ∠Y'≅∠Y and ∠Z'≅∠Z.
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Houston has approximately 2.25 million people. Each person has 2 hands and each hand has 5 fingers.
How many fingers are in Huston? Answer in scientific notation.
Solve the system by elimination 2x - y = 1 and x - 2y = -1
Answer:
x = 1 and y = 1
Step-by-step explanation:
Let's solve your system by elimination.
2x − y = 1 and x − 2y = −1
Multiply the second equation by -2, then add the equations together.
(2x−y=1)
−2(x−2y=−1)
Becomes:
2x−y=1
−2x+4y=2
Add these equations to eliminate x:
3y=3
Then solve3y=3for y:
3y=3
3y3=33(Divide both sides by 3)
y=1
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
2x−y=1
Substitute1foryin2x−y=1:
2x−1=1
2x−1+1=1+1(Add 1 to both sides)
2x=2
2x2=22(Divide both sides by 2)
x=1
Answer:
x=1 and y=1
Answer:x=1, y=1 point (1,1)
Step-by-step explanation:
which set of coordinates satisfies the equations 3x - 2y=15 and 4x - y=20
Answer:
x=5 and y = 0 coordinate = (5,0)
Step-by-step explanation:
solve the simultaneous equation
hope this works :)
If 25% of a number is 75 and 35% of the same number is 105, find 10% of that number.
Answer:
30
Step-by-step explanation:
to find 10%, find 100% first
because we know what 25% is, the easiest way we can work this out is multiply 25% by 4
so:
[tex] 4 \times 25\% = 100\%\\\\ 75 \times 4 = 300[/tex]
this means that 100% is 300.
now to find 10% all we have to do is divide the number by 10.
[tex]300 \div 10 = 30[/tex]
so 10% is 30
to check we're right, we make sure that 25% and 10% = 35%
75 + 30 = 105, meaning our percentages are correct
I've managed to find the area of the shape I just need help stating the units of my answer
According to the given statement the area of the right angle triangle:
= 18 cm².
What is right angle triangle?A right triangle, sometimes known as a right-angled triangle, or perhaps more formally called an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle or two perpendicular sides. Trigonometry is founded on the relationship between the sides and some other angles of a right triangle.
According to the given information:Given value
A = 6cm
B = 6cm
Using the right angle triangle area formula:
Area = (a*b)/2
= (6 *6)/2
= 18 cm²
According to the given statement the area of the right angle triangle:
= 18 cm²
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What is the distance between points A and B?
Answer:
6 units
Step-by-step explanation:
please help the question is in the image
Answer:
Blank 1: -5
Blank 2: -4
Blank 3:-4
Blank 4: 0
Blank 5: 1
Blank 6: -2
Blank 7: 0
Blank 8: -2
Step-by-step explanation:
Blank 1 and 2 were already done.
We can fill in the x value of A into blank 3, which makes it 0/2, or for blank 4: 0
We can fill in the y value of B into blank 5, which makes it -4/2, or for blank 6: -2
Then we can put the values from 4 and 6 together into 7 and 8, so 7 is 0 and 8 is -2. (0, -2)
Suppose that a>1/2 and the parabola with equation y=ax^2+2 has vertex V. The parabola intersects the line with equation y=-x+4a at points B and C, as shown. If the area of triangle VBC is 72/5, determine the value of A.
Answer:
Y = ×+ 4 a 75 VBC
I HOPE ITS HELP
Examine the triangles. Two similar triangles. The first triangle has a side length of 6 inches, which corresponds to the second triangle's side of 18 inches. The first triangle has a side length of 11 inches that corresponds to the missing side on the second triangle. If the triangles are similar, what is the length of the missing side? Note: The triangles may not be drawn to scale.
The length of the missing side of the triangle is 33 inches.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same. It is denoted by ‘~’ symbol.
Let the length of the unknown sides of the second triangle be represented by x.
Given that the two triangles are similar triangles, therefore, the length of the corresponding sides will be in the same ratio. Thus, we can write the ratio of the sides of the triangle as,
6 inches / 18 inches = 11 inches / x
x = (11 inches × 18 inches) / 6 inches
x = 33 inches
Hence, the length of the missing side of the triangle is 33 inches.
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Miss Tyrrell catches the 9:45am bus from Leeds to London.
The distance between the two cities is 195 miles.
The bus travels at an average speed of 52 mph.
What time should she arrive in London?
Answer:
The time she would arrive in London is 1:20 pm
Step-by-step explanation:
Recall
Speed= Distance/Time
But we want to find the time taken, so:
We cross multiply:
Speed *Time = Distance
Make time the subject of formula
Time= Distance/Speed
195/52
= 3.75 hours
Therefore, 9:45 am + 3.75 hours
= 13.20 pm
Which is equivalent to 1:20 pm
решите уравнение 6x-4(x+5)=2,2
Answer:
x=11.1
Step-by-step explanation:
6x-4x-20=2.2
2x-20=2.2
2x=22.2
x=11.1
find the 13th term in the following arithmetic sequence 2,18,18,26
The 13th term in the following arithmetic sequence 2,10,18,26 is 114
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values
Now the given sequence is,
2,10,18,26
So, common difference, d = 10 -2 = 8
and 1st term, a1 = 2
Thus, nth term of an arithmetic sequence is given as,
Tn = a1 + (n - 1)d
For 13th term put n = 13
⇒ T13 = 2 + (15 - 1)8
⇒ T13 = 2 + 14*8
⇒ T13 = 2 + 112
⇒ T13 = 114
Thus, the 13th term in the following arithmetic sequence 2,10,18,26 is 114
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The correct question is-
find the 13th term in the following arithmetic sequence 2,10,18,26.
The perimeter of the triangle shown is 556 meters. Find
the length of each side.
x meters =
4x meters =
(8x - 3) meters =
(Type integers or decimals.)
4x meters
(8x - 3) meters
x meters
The sides of the triangle are as follows:
a = 43 meters
b = 172 meters
c = 341 meters
Given, we have the perimeter of the triangle as 556 meters.
The sides of the triangle are:
a = x meters
b = 4x meters
c = (8x - 3) meters.
we know that perimeter of the triangle = a + b + c
therefore, a + b+ c = Perimeter
x + 4x + (8x - 3) = 556
x + 4x + 8x - 3 = 556
13x - 3 = 556
13x = 556 + 3
13x = 559
x = 559/13
x = 43
hence we get the value of x as 43.
substitute x value in the sides of the triangle to get the orignal values of the sides.
a = x = 43 meters.
b = 2x = 4 × 43 = 172 meters.
c = 8x - 3 = 8(43) - 3 = 341 meters.
Hence the sides of the triangle are 43 meters , 172 meters and 341 meters.
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The midpoint of segment EF is M(4, -1). Find endpoint F if the other endpoint E is at E(2, 3).
The x and y coordinates of the endpoint F are (6,-5)
The midpoint of a line segment is a point that is situated exactly at the middle from the two ends of the line segment
The coordinate of the mid-point or any other point can be found using the section formula.
For a point P with coordinates, the section formula is as follows: (x,y)
which divides the line segment A(x1,y1), B(x2,y2) in the ratio m:n, is given by the equation
Px=mx2+nx1/m+n Py=my2+ny1/m+n
Because the midpoint divides the line segment equally, m and n are both 1 in the midpoint case.
Thus the formula becomes
Px=1*x2+1*x1/1+1 Py = 1*y2+1*y1/1+1
where Px and Py are x and y co-ordinates of the point x and y
It is now assumed that midpoint M has coordinates (4,-1)
Point E is given by (2,3)
We are required to find F
Thus using section formula,
Mx=2+x/2 My=-3+y/2
4=2+x/2 -1=1+y/2
8-2=x -2-3=y
x=6 -5=y
Therefore, the coordinates of x and y of the endpoint F are(6,-5)
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-2.5 + 5.99 find the sum
please help with these 2 problems in math!!! thank uu!!
(factorize the expressions by regrouping)
Answer:
Sorry if im wrong but for c put (x+8) x (x+y)
for d put (x+3y-1) x (x+y)
Step-by-step explanation:
miles per hour. on her way home, she travels at 12 miles per hour. the total travel time is 2 hours. which equation can be used to find the distance in miles from bree’s house to the library? distance (mi) rate (mph) time (hr) trip to library x 6 mph startfraction x over 6 endfraction trip to home x 12 mph startfraction x over 12 endfraction startfraction x over 6 endfraction startfraction x over 12 endfraction
The equation to calculate the distance will be 12 × 2.
How to compute the equation?From the information given, she travels at 12 miles per hour and the total travel time is 2 hours.
It should be noted that:
Distance = Speed × Time
Therefore,
Distance = 12 × 2
The distance is 24 miles.
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wire 19 cm long is cut into two pieces. the longer piece is 3 cm longer than the shorter piece. find the length of the shorter piece of wire
The shorter piece of wire is 8 cm long when the total length of the wire is 19 cm long.
We are given that:
a wire's length is 19 cm.
We have to cut the wire into two pieces.
We are also given that the longer piece of wire is 3 cm longer than the shorter piece.
Let the shorter piece of wire be x cm
Longer piece = x + 3 cm.
So, the equation formed will be:
x + x + 3 cm = 19 m
2 x + 3 cm = 19 cm
2 x cm = 19 cm - 3 cm
2 x cm = 16 cm
x = 16 / 2 cm
x = 8 cm.
Therefore, the shorter piece of wire is 8 cm long.
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9.45 10^6 divided by 2
Answer:
Step-by-step explanation:
Comment
For this particular problem, the 10^6 will not be affected. All you have to do is divide 9.45 by 2. When you do that, you get
9.45/2 = 4.725
Now add on the 10^6
The answer is 4.725 * 10^6
Personally, I would likely round this to 4.73 because you were given 3 digits of accuracy, so you should give your answer as 3 digits.
Select the statement that correctly compares two numbers.
4.13 = 4.130
5.16 < 5.06
6.28 < 6.08
7.09 > 7.19
The correct answer is option A
• In mathematics, comparison of numbers if the process that defines similar properties between two numbers and identifies that the number if smaller or greater than or equal to the other number.
• In maths there are three special symbols used in comparison of numbers. The basic symbols are
1. Greater than (>)
2. Less than (<)
3. Equals to (=)
According to the question
Option A :
4.13 = 4.130
As we know the value of 0 after all the numbers and after the decimal is insignificant,
So , 4.13 = 4.130
This is correct comparison.
Option B :
5.16<5.06
Bigger number can’t be less than the smaller number, comparison is wrong.
Option C :
6.28<6.08
Bigger number can’t be less than the smaller number, comparison is wrong.
Option D:
7.09>7.19
Smaller number can’t be greater than the bigger number, comparison is wrong.
Option A is correct
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I need help with this algebra question
Linear inequality of the given graph is given by option (A) and (C) .
Graphing inequalities is the process of showing which parts of a number line contain values that "satisfy" a given inequality. This inequality plot shows the numbers you can use to replace x and y in the inequality to make the true statement.
(A) y > x /6 +2 ..(1) this line is represented by upper line .
and y ≤ x /4 + 1 ....(2) this line is represented by lower line .
Let consider a point (2, 3)
Put in equation (1) , we get
3 > 0.33 +2
3 > 2.33
which is true so shading will be in lower part of this line .
Put in equation (2) , we get
3 ≤ 0.5 +1
3 ≤ 1.5
which is false so shading will be in opposite direction in upper part of this line.
Hence , there is a common shading area between the lines which is required area .
(b) y < x /6 +2 ..(1) this line is represented by upper line and y ≥ x /4 + 1 ....(2) this line is represented by lower line . Let consider a point (2, 3)
Put in equation (1) , we get
3 < 0.33 +2
3 < 2.33
which is false so shading will be in opposite direction to the point in upper part of this line .
Put in equation (2) , we get
3 ≥ 0.5 +1
3 ≥ 1.5
which is true so shading will be in lower part of this line.
Hence , there is no common shading area between the lines .
(C) y ≥ x /6 +2 ..(1) this line is represented by upper line and y < x /4 + 1 ....(2) this line is represented by lower line . Let consider a point (2, 3)
Put in equation (1) , we get
3 ≥ 0.33 +2
3 ≥ 2.33
which is true so shading will be in direction to the point in lower part of this line .
Put in equation (2) , we get
3 < 0.5 +1
3 < 1.5
which is is false so shading will be in opposite direction to the point in upper part of this line
Hence , there is a common shading area between the lines which is required area .
(D) y ≤ x /6 +2 ..(1) this line is represented by upper line and y > x /4 + 1 ....(2) this line is represented by lower line . Let consider a point (2, 3)
Put in equation (1) , we get
3 ≤ 0.33 +2
3 ≤ 2.33
which is false so shading will be in opposite direction to the point in upper part of this line .
Put in equation (2) , we get
3 > 0.5 +1
3 > 1.5
which is true so shading will be in lower part of this line.
Hence , there is no common shading area between the lines .
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6n=3/5 (5n + 15) solve for n
Answer:
3
Step-by-step explanation:
6n = 3/5 x 5 (n+3)
6n = 3 (n+3)
6n = 3n + 9
6n - 3n = 9
3n = 9
=3
Answer:
6n=3/5(5n+15)
6n=3n+9
6n-3n=9
3n=9
3n/3=9/3
n=3
If f(x + 3) = x^2 + 4x − 7, find f(2).
The complete statement is that if the equation of the function f(x + 3) = x^2 + 4x − 7, the value of the function f(2) is -10
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the solution to the quadratic equation?A quadratic equations can be split to several equations and it can be solved as a whole
In this case, we have
f(x + 3) = x^2 + 4x − 7
To find f(2), we make use of the following comparison
f(2) = f(x + 3)
This means that
2 = x + 3
Evaluate
x = -1
Substitute x = -1 in f(x + 3) = x^2 + 4x − 7
f(-1 + 3) = (-1)^2 + 4(-1) − 7
This gives
f(2) = -10
Hence, the complete statement is that if the equation of the function f(x + 3) = x^2 + 4x − 7, the value of the function f(2) is -10
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