The assumption that the sample means follow a roughly normal distribution is used to calculate a confidence interval for a population mean with a known standard deviation.
A confidence interval gives a range of values that will probably include the actual mean. For example, let's say that our sample has a mean of x=10 and we have generated the 90% confidence interval (5, 15), with EBM = 5. For instance, we might not be able to speak to everyone in Colorado if we wanted to find out the typical age of Colorado residents who enjoy bananas. However, we could conduct in-depth interviews with a representative sample and make an educated guess or calculation to provide us with a range of ages.
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the Lim family are great mathematician.When asked howvold everyone are,the family replies : "our family of two adults and three childrens are 100years old altogether.The sum of father's age and son's age is 51.The father is 3 years older than mother while the twins daugthers are each 5 years younger than the brother" Can you work out everyone's age???
Answer:
Ages are as follows:
Father: 40
Mother: 37
Son: 11
Each twin daughter: 6
Step-by-step explanation:
Interesting puzzle!
Let
F denote the age of the father
M the age of the mother
S the age of the son
D the age of each of the twin daughters
Total of all ages is
F + M + S + 2D = 100 [1]
We also have
F + S = 51 ==> S = 51- F [2]
F - M = 3 ==> M = F - 3 [3]
S - D = 5 ==> D = S -5 [4]
==> D = (51-F) -5
==> D = 46 - F [5]
Substitute this in equation [1] to get
We now have everyone's age in terms of the father's age F
Substituting each of equations [2], [3] and [5] into [1] we get one equation in terms of F
F + (F-3) + (51-F) + 2(46-F) = 100
(F + F - F -2F ) + (-3 + 51 + 92) = 100
-F + 140 = 100
- F = 100 - 140
-F = -40
or
F = 40
From [3]
M = F - 3 = 40 - 3 = 37
From [2]
S = 51 - F = 51 - 40 = 11
From [4]
D = S - 5 = 11 - 5 = 6
Verify:
F + M + S + 2D = 40 + 37 + 11 + 2 x6 = 100
Step-by-step explanation:
a = father age
b = mother age
c = son age
d = daughters age
1. a + b + c + 2d = 100 (don't forget : twin-daughters)
2. a + c = 51
3. a = b + 3
4. d = c - 5
we need to transform the equations 2-4 to express 3 variables by the 4th, and then put that into the first equation and solve for that one variable.
once we have that, we can use again the equations 2-4 to solve for the other variables.
2. tells us that
c = 51 - a
3. tells us that
b = a - 3
4. and 2. tells us that
d = c - 5 = (51 - a) - 5 = 46 - a
with that we get in 1.
a + (a - 3) + (51 - a) + 2(46 - a) = 100
a + a - 3 + 51 - a + 92 - 2a = 100
2a - 3a + 48 + 92 = 100
-a + 140 = 100
-a = -40
a = 40
b = a - 3 = 40 - 3 = 37
c = 51 - a = 51 - 40 = 11
d = c - 5 = 11 - 5 = 6
so, the father is 40 years old
the mother is 37 years old
the son is 11 years old
both of the twin daughters are 6 years old.
(2x^2+3x+8) (x^2-x-4) multiply the polynomials and simplify the answer
Step-by-step explanation:
(2x² + 3x+8) (x²-x-4)
= (2x² + 3x+8) (x² +-x²+-4)
= (2x²) (x²) + (2x²) (-x) + (2x²) (-4) +(3x) (x²) + (3x) (-x) + (3x) (-4) + (8) (x²) + (8) (-x) + (8) (-4)
= 2x⁴ - 2x³ -8x² + 3x³ -3x² - 12x + 8x² - 8x - 32
=2x⁴ + x³ - 3x² - 20x - 32
Write the equation of a line perpendicular to 8x−5y=−9 that passes through the point (−8,3).
Considering the definition of perpendicular line, the equation of a line perpendicular to 8x−5y=−9 that passes through the point (−8,3) is y=-5/8x-2 .
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseIn this case, the line is 8x-5y= -9. Expressed in the form y = mx + b, you get:
-5y= -9 - 8x
y= (-8x -9)÷ (-5)
y= 8/5x +9/5
The line has a slope of 8/5. If you multiply the slopes of two perpendicular lines, you get –1. In this case:
8/5× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (8/5)
slope perpendicular line= -5/8
So, the perpendicular line has a form of: y= -5/8x + b
The line passes through the point (-8, 3). Replacing in the expression for perpendicular line, you get:
3= -5/8× (-8) + b
3= 5 + b
3- 5 = b
-2= b
Finally, the equation of the perpendicular line is y= -5/8x -2 .
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how to find the greatest number of students to whom 135pens 225 books and 315 copies can be divided equally also find the shares of each item . maths
Answer:
The items can be equally shared between 45 students.
Each student will get 3 pens, 5 books and 7 copies.
Step-by-step explanation:
We have to find the GCF (Greatest common factor) of 135 , 225 and 315.
135 = 5 * 3 * 3 * 3 = 45 * 3
225 = 5 * 5 * 3 * 3 = 45 * 5
315 = 5 * 3 * 3 * 7 = 45 * 7
GCF = 5 * 9 = 45
The items can be equally shared between 45 students.
Each student will get 3 pens, 5 books and 7 copies.
Samuel orders four DVDs from an online music store. Each DVD costs $9.96. He has a 25% discount code, and sales tax is 7.75%. Round sales tax amounts to the nearest cent. What is the total cost of his order?
The total cost of Samuel's order is $
Samuel's order will ultimately cost $39.84.
One DVD Samuel purchased cost $9.96.
He purchased four DVDs in total.
as a result, his total outlay will be 4 * 9.96 = $39.84.
The 7.75% sales tax that must be paid is disclosed to us.
Adding 7.75% to $39.84 yields
39.84 x 7.75/(100) (100)
= $3.0876
Consequently, the total amount of tax due is $3.0876.
Using 25% of 39.84 to calculate a 25% discount,
39.84 x 25/100
= 996/100
=$9.96
Consequently, the total discount on the total of $39.84 will be $9.96.
as a result, the updated purchase price will be,
39.84-9.96
=$29.88
adding the tax to the updated price,
9.96+29.88
= $39.84
Consequently, Samuel's order will ultimately cost $39.84.
How are percentages calculated?One must compute percentage in order to determine the proportion of a whole that is stated in terms of 100. A percentage can be determined using one of two methods:
using the unitary method.
by changing the fraction's denominator to 100.
It should be noted that the second method of percentage computation is not used when the denominator is not a factor of 100. In these circumstances, we make use of the unitary approach.
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Three more than a certain number is six less than four times
the same number. What is the number?
Answer:
number is 3
Step-by-step explanation:
let n be the number , then 3 more than the number is n + 3 and six less than 4 times the number is 4n - 6 , so
4n - 6 = n + 3 ( subtract n from both sides )
3n - 6 = 3 ( add 6 to both sides )
3n = 9 ( divide both sides by 3 )
n = 3
the number is 3
Write the following number in standard decimal form.six tenths
Rewriting the words mathematically:
[tex]\text{Six tenths = }\frac{6}{10}[/tex]Next we will write in standard decimal form:
[tex]\begin{gathered} In\text{ decimal, 6/10 = 0.6} \\ We\text{ have one decimal place} \\ 0.6\text{ }is\text{ standard decimal = 6 }\times10^{n\text{ umber of movement})} \end{gathered}[/tex][tex]\begin{gathered} \text{movement from left to right will have a negative sign in front of the number of movement} \\ \text{movement from right to left will be positive} \\ \\ AS\text{ result, 0.6 = 6 }\times10^{-1} \end{gathered}[/tex]I dont understand this
Identify all pairs of parallel segments. Arrange letters in
C
ALPHABETICAL
orders (AC. DF)
)//(
)//(
)//(
All pairs of parallel segments are given below.
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees. Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.
Given,
a) Line segment = AC and FD
Parallel = AC ║FD
b) Line segment = AE and BD
Parallel = AE ║BD
c) Line segment = EC and FB
Parallel = EC ║FB
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Multiply.
40.631⋅1.07
Responses
4.347517
43.47517
434.7517
4347.517
Answer: 43.47517
Step-by-step explanation:
Considering orders of magnitude, we see that Option 2 is the only reasonable answer.
Graph each function f(x)=1/4 x
Graph f(x)=14.
Plot each graph on the same coordinate system.
f(x)=14x
image of graph
Work out 1 1/4 + 4 2/3 Give your answer as a mixed number where appropriate.
The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12.
What is a number system?The number system is a way to represent or express numbers.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given sum of the mixed number,
1 1/4 + 4 2/3
⇒ 1 + 1/4 + 4 + 2/3
⇒ 1 + 4 + 1/4 + 2/3
⇒ 5 + 1/4 + 2/3
Take LCM of 1/4 and 2/3 as 12.
⇒ 5 + (3 + 8)/12
⇒ 5 + 11/12 = 5 11/12
Hence "The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12".
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Help please I don’t knowwww
The corn's height when the fertilizer was applied is 13 centimeters and it grows at a rate of 13 centimeters each day.
What is the interpretation of the linear equation?The equation that is given is known as a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
A linear equation increases or decreases at a constant rate. When a linear equation is drawn on a graph, it is a straight line that curves either upward or downward.
A linear equation usually has this form y = mx + b
Where:
m = slope = rate of change of the equation with respect to x b = interceptH = 13 + 13t
Where:
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On May 8, 2010, a team of kayakers sets a record time for 5h 19 min 17 sec to kayak across the length of Loch Ness, Scotland, UK, a distance of 20.5 mi. When the kayakers were four times as far from the starting point as from the finish, how many miles were traveled?
Answer:
16.4
Step-by-step explanation:
The time is irrelevant to the problem
fraction42 *20.5= 16.4
Hope this helps
there are 5 students in mun elligible for a particular event at the next conference however, only two can compete. they are equally qualified, so it is decided that the contestants will be randomly selected. what is the probability that the first two students alphabetically will be selected?
The probability of selecting two students has 10 ways
Total number of students = 5
Only two students can be selected for the conference who are equally qualified.
The probability that the first two students selected alphabetically is derived from the combinations.
Therefore, the final probability for selecting the students randomly is,
x = ⁵C₂
x = [tex]\frac{5!}{2!*(5 - 2)!}[/tex]
x = 10
Hence, the probability of selecting two students has 10 ways.
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AB and BC are perpendicular lines.
Find the value of x.
Write the equation for g(x).
Answer: [tex]-\frac{x^2}{4}[/tex]
Step-by-step explanation:
The graph of g(x) is the graph of f(x) reflected over the x-axis and horizontally stretched by a factor of 2.
So, the equation is [tex]g(x)=-(x/2)^2 =-\frac{x^2}{4}[/tex]
∠A and ∠B are vertical angles. If ∠A = (x-29) and m∠B = (6x-11), then find the value of x.
The required value of x is -3.6 which is determined by the substitute that equals the vertical angles.
What are the vertical angles?When two lines intersect at a location, vertical angles are generated. They are always equal to each other.
Since ∠A and ∠B are vertical angles then they are congruent, thus
⇒ (x - 29) = (6x - 11)
Subtract 6x from both sides of the above equation,
⇒ x - 29 - 6x = 6x - 11 -6x
⇒ -5x - 29 = - 11
Add 29 to both sides of the equation,
⇒ -5x - 29 + 29 = - 11 + 29
⇒ -5x = 18
Divided by 5 to both sides of the equation,
⇒ x = - 18/5
⇒ x = - 3.6
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Help pls ASAP
1a. When a lot of people are swimming in a pool, the water become cloudy. Explain why?
b. The water in an empty pool is very clear. is it still a mixture?
Explain why?
a. Inadequate chlorine levels cause cloudy or creamy swimming pool water.
b. Even though water represents the most ample substance on the planet, it is rarely encountered in its pure form in nature.
What is defined as the term mixture?A mixture is a compound composed of a number of chemical components that aren't chemically linked to one another. A mixture is a physical combination of two or more compounds that retain their individuality and are blended as solutions, suspensions, and colloids.Part a: Cloudy or milky pool water is ended up causing by seven major issues: insufficient chlorine, an imbalanced pH and alkalinity, extremely high calcium hardness (CH), a faulty or clogged filter, and the initial phases of algae, ammonia, as well as debris.
Methods for Cleaning Cloudy Pool Water
Balance the levels of free chlorine (FC).Remove the ammonia.Remove any young algae.pH and TA levels should be monitored and balanced.Part b: A swimming pool mixture of water as well as chlorine is made reference to as a homogenous mixture even though water and chlorine cannot be separated back to one‘s distinct materials once mixed together.
Because chlorine as well as water diffuse between each other, they cannot be kept separate into their pure forms again.
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Noah is studying a type of sea sponge that grows at a constant rate. They measured the age and height of 333 pieces of the sponge. Here's what they found:
Answer:
a = h/2 would be the answer.
Step;-
Find slope:-
m = rise/run = (16-8)/(8-4) = 8/4 = 2
Now,
y = mx + b
or, 8 = 2(4) + b
so, b = 0
So,
y = mx + b
or, h = 2a + 0
so, h = 2a
hence,a = h/2.
The sea sponges's height grows 2cm every 1 year, so you can write an equation to find the height at any age [tex]a = \frac{h}{2}[/tex]
How do variables help you model real-world situations? Give an example of a model that uses variables and explain how it helps people make predictions
A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
What is meant by variables?
Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable. Independent, dependent, and controlled variables are typically found in experiments. A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
The ladder's position would serve as an illustration.
Both 4x-2y=12 and -4x-9=54 are supplied to you. You are required to determine the ladder's order. But you didn't say which variable stands in for the ladder. I'll simply solve for both variables. I'll use the substitute strategy.
Let equations one and two be equivalent to 4x-2y=12 and -4x-9=54, respectively.
4x-2y=12
4x=12+2y
x=3+1/2y
Put this x in place of it in equation 2.
-4x-9y=54
-4(3+1/2y )-9y=54
Y=-6
X=3+1/2y = 3+1/2(-6) = 3+(-3) = 0 \s.
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PLEASE HELP 50 POINTS
Write an equation of the line that is parallel to -x + y = 5 and passes through the point (2, -5).
Responses
y = x - 3
y = x - 3, EndFragment
y = x - 7
y = x - 7, EndFragment
y = x - 5
y = x - 5
y = - x + 7
Answer: y = x -7
Step-by-step explanation: -x + y = 5
y = x + 5
y = x + a
-5 = 2 + a
a = -7
y = x - 7
9. Put the following equation of a line into slope-intercept
form, simplifying all fractions.
2x + 3y = 15
Step-by-step explanation:
slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y value when x = 0).
we have
2x + 3y = 15
3y = 15 - 2x
y = (-2/3)×x + 5
Anna spent half her weekly allowance at the movies to earn more money her parents let her wash the car for $8 what is her weekly allowance if she ended with $18
This situation can be expressed by the equation [tex]x-\frac{x}{2} +8=18[/tex], her weekly allowance is $20.
What is an equation?
The description of an equation in algebra is a mathematical proposition that demonstrates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.Let the weekly allowance of anna be = X
Allowance spent on movies= X/2
The extra money from the car wash = 8
Allowance retained with anna = 18
This situation can be expressed by the equation,
[tex]x-\frac{x}{2} +8=18[/tex]
Solving the above equation, we get,
[tex]\frac{x+16}{2} =18[/tex]
x+16=36
x=20
Therefore, her weekly allowance is $20.
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Zack and Zane were floating down the river. They climbed to the top of the rock, which was 14.6 feet above the water level. When Zack jumped in, he got down to a depth of 6.8 feet underwater. What was the total distance from his highest point to his lowest point?
The total distance from his highest point to his lowest point is 21.8 feet.
Height H climbed by Zack and Zane is 14.6 feet.
The depth D underwater that Zack got down to is 6.8 feet.
The distance between the highest and the lowest point can be found by assuming the coordinates axis.
Let us assume the origin is on the water surface,
So, going by this logic, highest point is at +14.6 feet.
The lowest point is at -6.8 feet.
The distance L between lowest and highest point is,
L = H - D
L = 14.6 -(-6.8) feet
L = (14.6 + 6.8) feet
L = 21.8 feet
So the distance L is 21.8 feets.
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I am confused my old teacher got fired so we are learning stuff completely different and I am rlly confused in this assignment please help me.
Hello!
First, let's analyze these two quadrilaterals:
• Notice that the quadrilateral AB'C'D is ,smaller ,than the quadrilateral ABCD.
Let's try to solve it using the lines AB and AB':
• The measurement of the ,line AB is 14 units,.
,• The measurement of the ,line AB' is 7 units,.
Knowing it, let's write the scale factor as:
[tex]\text{ScaleFactor}=\frac{AB^{\prime}}{AB}=\frac{7}{14}=\frac{1}{2}[/tex]Answer: alternative D.
A paintball court charges an initial entrance fee plus a fixed price per ball. Suppose it costs $18 to use 2 balls and $23 to use 4 balls. What is the entrance fee?
The entrance fees is 13 dollars charges by the paintball court.
Let us assume that the entrance fees is $X and the actual cost of using one ball is $Y charged by the paintball court.
According to one situation,
Total cost of using to ball = Cost of entry fees + actual cost of using two ball.
So, we can write,
X + 2Y = 18
Let us say that this is our equation 1,
Also, it is provided,
Total cost of using 4 balls = cost of entry fees + actual cost of using four balls.
X + 4Y = 23
Let us say that this is our equation 2,
Both of our equations are linear equations with two variables,
Now, substracting equation 1 from equation 2,
X + 4Y -(X + 2Y) = 23 - 18
2Y = 5
Y = $2.5.
Putting the value of Y = 2.5 in equation 1,
X + 2(2.5) = 18
X = 18 - 5
X = $13.
So, the entry fees is 13 dollars.
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I need help figuring out the answer … I’m confused
1st step. Calculate the area of the parallelogram
We can use the following formula:
[tex]A=b\cdot h[/tex]where,
base, b = 9 km
height, h = 5 km
Therefore,
[tex]A=9\cdot5=45[/tex]The area of the parallelogram is 45 km^2
2nd step. Calculate the area of the triangle
Let's use this formula:
[tex]A=\frac{b\cdot h}{2}[/tex]where,
base, b = 6 km
height, h = 3 km
Therefore,
[tex]A=\frac{6\cdot3}{2}=9[/tex]The area of the triangle is 9 km^2
3rd step. calculates the ratio of the area of the parallelogram to the area of the triangle
[tex]r=\frac{A_P}{A_T}=\frac{45}{9}=5[/tex]Answer: the area of the parallelogram is 5 times greater than the area of the triangle.
Write an
equation of a parabola with the given vertex and focus.
vertex (5,-2); focus (5, -1)
Answer:
[tex](x-5)^2=4(y+2)[/tex]
Please note that alternative forms of this equation (vertex and standard) are in the explanation.
Step-by-step explanation:
Standard form of a parabola with a vertical axis of symmetry:
[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]
Vertex = (h, k)Focus = (h, k+p)Given:
Vertex = (5, -2)Focus = (5, -1)Therefore:
h = 5k = -2k + p = -1Calculate p:
[tex]\implies -2+p=-1[/tex]
[tex]\implies p=-1+2[/tex]
[tex]\implies p=1[/tex]
Substitute the values of h, k and p into the formula to create an equation of the parabola with the given parameters:
[tex]\implies (x-5)^2=4(1)(y-(-2))[/tex]
[tex]\implies (x-5)^2=4(y+2)[/tex]
In vertex form:
[tex]\implies y=\dfrac{1}{4}(x-5)^2-2[/tex]
In ax² + bx + c form:
[tex]\implies y=\dfrac{1}{4}x^2-\dfrac{5}{2}x+\dfrac{17}{4}[/tex]
Answer for bothering x and y giving brainliest. Need help asap!!!
Answer: x = 77 - 2y y = -x/2 + (77/2)
Step-by-step explanation:
4z−5<−29or4z+3>15
8x+8≥−64and−7−8x≥−79
will mark brainliest
The solutions for the inequalities are:
z < -6 or z > 3 and -9 ≤ x ≤9
We are asked to solve the inequalities given.
For the inequality 4z−5<−29 or 4z+3>15, we have to solve for z. i.e., find the value for z.
4z−5<−29 or 4z+3>15
⇒ 4z < -29 + 5 or 4z > 15 -3
⇒ 4z < -24 or 4z > 12
⇒ z < -24/4 or z > 12/4
⇒ z < -6 or z > 3
The solution for z are the values above 3 and less than -6.
For 8x+8 ≥ −64 and −7−8x ≥ −79, we need to solve for x.
8x+8 ≥ −64 and −7−8x ≥ −79
⇒ 8x ≥ -64 -8 and -8x ≥ -79 + 7
⇒ 8x ≥ -72 and -8x ≥ -72
⇒ x ≥ -72/8 and -x ≥ -72/8
⇒ x ≥ -9 and x ≤ 9
⇒ -9 ≤ x ≤9
The solution for x are between -9 and 9.
The question is not complete. The complete question is given below:
Solve the system of inequalities.
4z−5<−29 or 4z+3>15
8x+8≥−64 and −7−8x≥−79.
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