Lower Limit = 24.52
Upper Limit = 36.28
Error Bound = 5.88
Lower Limit: - The Lower Limit for every class is the smallest value in that class. For example: 5 is a lower lower limit for the set S= { 5,8,42,34}
Upper Limit: - A value that is greater than or equal to every element of a set of data. For example: - { 3,5,11,20,22} is a upper bound of 22.
Given that,
Population Mean,μ = 33.2
sample Mean, χ (x bar) = 30.4
sample Size, n = 25
α (Alpha) = 0.05
Population standard deviation,σ = 15
95% confidence interval:
μ ± z critical σ / √n
Putting the values, we get,
z critical at α0.05 = ± 1.96
30.4 ±1.96( 15/√25) = 30.4 ± 5.88 = (24.52,36.28)
a) Lower Limit = 24.52
b) Upper Limit = 36.28
c) Error Bound =
Margin of Error = z critical × σ /√n
= 1.96 × 15/√25
= 1.96 × 15/5
= 5.88
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need help, please and thank you
The length of the chord of the circle CD is 3.2.
What is a chord of the circle?A chord of a circle is a section of a straight line whose ends both fall on an arc of a circle. A secant line, often known as secant, is a chord's infinite line extension.
Given that the vertical length from the centre to the chord is 2.1 and the length up to the circle is 1.7.
Radius = 1.7 +2.4 = 4.1.
The chord length will be calculated as,
CD = √(4.1² - 2.4²)
CD = √(16.81 - 5.76)
CD = 3.2
Therefore, the length of the chord of the circle CD is 3.2.
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A 236-inch pipe is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
let length of one piece = x
length of other piece = 236-x
one piece is three times the length of the other
x=3(236-x)
x=708-3x
4x=708
x=177
so first piece is 177 inches long and second piece is (236-177)= 59 inches long
Answer:
first piece is 177 inches long and second piece is (236-177)= 59 inches long
Step-by-step explanation:
x=3(236-x)
x=708-3x
4x=708
x=177
what is 3/4x(5/6-4/23)=43
Answer: 86 86/91 or 7912/91
Work: So you multiply 3/4x by what is in the parenthesis like this: 3/4x*5/6-3/4x*4/23. and you get 5/8x-3/23x=43. And then you simplify to get 91/184x=43 then u multiply both sides by 184 to get rid of the fraction. and you get 91x=7912. then you divide both sides by 91 and you get x=7912/91 or 86 86/91
a local ice skating rink wishes to determine the age of its customers. the ages of customers are summarized in the relative frequency table below. what is the cumulative relative frequency of patrons, aged 47 or younger?
a local ice skating rink wishes to determine the age of its customers. then 10% of lottery winners are 70 years or older
Age____ Freq__R/freq____ Cumm Rel Freq
[20,29]___3____ 0.1________ 0.1
[30,39]__ 10__ 0.3333_____ 0.4333
[40,49]__ 2__ 0.0667______ 0.5
[50,59]__ 7 __0.2333 _____0.7333
[60,69]__ 4 ___0.1333 ____0.8666
[70,79]___ 3 ____0.1 ______0.9666
[80,89]___ 1 ___0.0333 ____0.9999
A.) What is the frequency of lottery winners of age between 19 and 40?
Frequency = (3 + 10) = 13 winners
B.) What percentage of lottery winners are 70 years or older?
From the relative frequency table = 0.1 (3/30) = (0.1 * 100%) = 10%
complete question is
Given the frequency distribution for the data, Age Frequency Relative Frequency Cumulative Relative Frequency [20,29] 3 0.1 0.1 [30,39] 10 0.3333 0.4333 [40,49] 2 0.0667 0.5 [50,59] 7 0.2333 0.7333 [60,69] 4 0.1333 0.8666 [70,79] 3 0.1 0.9666 [80,89] 1 0.0333 0.9999 What is the frequency of lottery winners of age between 19 and 40? What percentage of lottery winners are 70 years or older?
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Graph DFG with vertices D(2,8), F(1,2) and G(4,6) and image after the glide reflection with a translation along <3,3> and a reflection in the y=x
The vertices of the figure after geometric translations are (11, 5), (5, 4), and (9, 7).
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The vertices are D(2,8), F(1,2) and G(4,6).
Points become after reflection:
D'(8, 2), F'(2, 1), G'(6, 4)
After applying translation:
D''(8+3, 2+3) = (11, 5)
F''(2+3, 1+3) = (5, 4)
G''(6+3, 4+3) = (9, 7)
Thus, the vertices of the figure after geometric translations are (11, 5), (5, 4), and (9, 7).
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What is the end behavior of the function f(x) = -5x³ + 2x² - 4x+6?
O down to the left, up to the right
O up to the left, down to the right
O up to the left, up to the right
Odown to the left, down to the right
Answer:
O up to the left, down to the right
Step-by-step explanation:
The function in your question will do the same thing that
f(x) = -x³ does.
Actually, even simpler, it will have the same end behavior as
f(x) = -x
which is just a line with negative slope, going down from left to right. The way end behavior is described: up to the left and down to the right.
In fact, all the functions with odd power as the biggest exponent will have the same end behavior.
(If the highest exponent is even, it acts like a parabola up+up or down+down.)
1. Select all transformations that do not result in mapping (a,-a) to (a, a) when a > 0.
A reflection in the y-axis
B reflection in the x-axis
translation 2a units up
D translation a units up, followed by a reflection in the line y = a
translation
a units up, followed by a reflection in the line y = 2
Reflection in the x-axis and translation 2a units up, translation a units up, followed by a reflection in the line y = a translation a units up, followed by a reflection in the line y = 2
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification of algebraic equations.
transformations that do not result in mapping (a,-a) to (a, a) when a > 0. are
reflection in the x-axis and translation 2a units up, translation a units up, followed by a reflection in the line y = a translation a units up, followed by a reflection in the line y = 2
Hence reflection in the x-axis and translation 2a units up, translation a units up, followed by a reflection in the line y = a translation a units up, followed by a reflection in the line y = 2
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a student earns Php 280.00 for a 5 hour shift on his summer job. The amount of money he earns varies directly to the number of hours worked. find the constant k, and the amount of money , he will earn for an 8-hour shift
Answer:
Below
Step-by-step explanation:
k = 280 / 5 = Php 56 /hr
money earned = k x where x = # of hours
For 8 hours : money earned = 56 * 8 = Php 448
hi i was wondering if somebody can help me with this question. Given the inequality 4x ≤ 28, determine the value of x.
S:{7}
S:{9}
S:{12}
S:{38}
Answer:
Step-by-step explanation:
OK:
1. Isolate the x on the left side of inequality. Always remember if a number or variable crosses inequality, it becomes opposite!
4x ≤28
x ≤28/4
x ≤7
2. Double Check!
4*7 ≤28
28 ≤28 TRUE
x=7(s) or Choice A
Eve play baketball. She make 4 free throw for every 3 free throw that he mie. If he mied 27 free throw at her lat practice, how many free throw did he make?
Using this probability, he would have to make 42.18% or 42 free throws, thus avoiding 27 free throws.
Averaged over 3 out of 4 free throws, the probability of a successful free throw is 0.75 and the probability of a missed free throw is 0.25.
There are several ways to score 3 of the 4 free throws.
Miss Hit Hit Hit
Hit Miss Hit Hit
Hit Hit Hit Hit Hit
So to calculate this probability we need to multiply the probability of each shot. Because when it comes to multiplication, the order of multiplication doesn't matter, it's just the numbers that matter, only her 4-day probability that the shot will be taken. be the same.
So 0.75 x 0.75 x 0.75 x 0.25 = 0.10546875
Since there are 4 ways to take a 3/4 shot, we have to multiply this by 4, so 4 x 0.10546875 = 0.4218 = 42.18% shot will be taken.
So 0.75 x 0.75 x 0.75 x 0.25 = 0.10546875
Since there are 4 ways to take a 3/4 shot, we have to multiply this by 4, so 4 x 0.10546875 = 0.4218 = 42.18%.
Hence, Eve had to make 42 free throws for getting 27 throws are mied.
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5.
The area of a circle is 40 mm²,
determine the circumference.
Answer: the formula to find circumference is C=2times pie which is 3.14 times the radius. Radius is half of the diameter which in this case I believe would be 20 times that by 3.14 and get 62.8 then times that by two which gives you the answer of 125.6
Step-by-step explanation: correct me if I’m wrong
The cost of endless chicken wings at Restaurant X is $4. The cost of chicken wings at Restaurant Z is 20 cent per wing plus a $1.60 charge for sauce. The total cost, c, of n chicken wings at either restaurant can be represented by an equation. Write and graph a system to find how many chicken wings you have to have for the cost to be the same at both restaurants.
Answer:
Step-by-step explanation:
Equation: $4 = 0.2x + $1.60
1. Subtract $1.60 from both sides to get $2.4 = 0.2x
2. Divide both sides by 0.2 to get the value of x. 12 = x.
ANSWER: You need to buy 12 chicken wings at restaurant Z for the cost to be the same. Hope this helped
Find the value of x in the triangle below:
Answer:
x=12
Step-by-step explanation:
turn into and equation because angles in a triangle add up to 180°
so
6x-19+3x+7+84=180
collect like terms
9x+72=180
solve to find 'x'
9x=108
x=12
Point C is the midpoint of AB and point B is between points A and D . If AD=17 and BD=9 , what is CD ?
CD=
Answer: 13 units
Step-by-step explanation:Given that Point C is the midpoint of AB and point B is between points A and D. If AD = 17 and BD = 9
According to definition midpoint, AC = CB
According to definition of segment addition postulate, AD = AB + BD
AB = AD - BD
AB = 17 - 9
AB = 8
Again, AB = AC + CB
Therefore, CB = AB/2
CB = 8/2 = 4
Now, CD = CB + BD = 4 + 9
CD = 13 units
Hence, length of CD = 13 units
Divide.
(x³ + x² + 3x + 5) ÷ (x + 4)
Using the long division method, we have divide ([tex]x^3+x^2[/tex] +3x+5) ÷ (x+4) then the remainder is −55 and quotient is x^2−3x+15.
We have to divide ([tex]x^3+x^2[/tex] +3x+5) ÷ (x+4)
In general, long division of two integers without any variables is performed in the same way as long division of a polynomial by a binomial:
Divide the polynomial's highest degree term by the binomial's highest degree term. Over the division line, type the outcome.
Subtract the resulting binomial from the polynomial after multiplying this result by the divisor.
x+4) [tex]x^3+x^2[/tex] +3x+5 (x^2−3x+15
−([tex]x^3+4x^2[/tex])
−−−−−−−−−−−−−−−−−−−
−3[tex]x^2[/tex] +3x
−(−3[tex]x^2[/tex] −12)
−−−−−−−−−−−−−−−−−−−
15x+5
−(15x+60)
−−−−−−−−−−−−−−−−−−−
−55
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What is the classification for this polynomial?
-6uv - 3u - 2v.
Click on the correct answer.
monomial
binomial
trinomial
a tunnel is constructed with a semielliptical arch. the width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet. what is the height of the tunnel 5 feet from the edge? round your answer to the hundredths place.
As a result, the tunnel is 13.83 feet high, 5 feet from the edge.
An ellipse is an oval curve on a plane that contains two fixed points called foci. The sum of the distances between the two foci from each point on the ellipse is constant at all points.
Since the tunnel has an arch that is semi-elliptical, we can put the ellipse's center at the center of its 60-foot width.
What is an ellipse?
An ellipse is a two-dimensional shape that is defined by its axes in geometry. When a plane intersects a cone at an angle to its base, it creates an ellipse. It focuses on two things. For each point in the curve, the sum of the two distances to the focal point remains constant.
What are an ellipse and an example?
An ellipse is the locus of points whose sum of their distances from its two foci is constant and has an eccentricity of less than one. The two-dimensional egg shape and the running tracking in a sports stadium are simple examples of the ellipse in our everyday lives.
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Part A
Rebecca's house cost $100000 in the year 2000.
In 2008 she sold it for $210000.
Was the change in price a positive or negative change?
Answer:
Part B
What was the percentage of change in the price of the house?
Answer:
Im guessing it would be a positive change
Step-by-step explanation:
part a had the cost of $100,000 while part b had the cost of $210,000
therefore, part b increased $110,000 from 2000 to 2008.
this is my guess.
ASAP WILL GIVE 100 PTS
The line segment graphed on the coordinate plane represents a roof with several triangular supports. Each support is triangular, with a horizontal board that starts on the edge of the roof and connects with a vertical board that ends on the edge of the roof as shown.
(2,1)(6,3)
Does each support have the same starting coordinates? Explain.
Does each support have the same ending coordinates? Explain.
Does each support have the same change in x-values? Explain.
Does each support have the same change in y-values? Explain.
Does each support have the same ratio of change in y-values over change in x-values? Explain.
Answer:a) No, the first support starts at (0,0) and the 2nd one starts at (2,1)
b) No, first one ends at (2,1) 2nd one ends at (6,3)
c) No, 2 ( 0 to 2) does not equal 4 ( 2 to 6)
d) No, 1 ( 0 to 1) does not equal 2 (1 to 3)
e) Yes, this is the slope of the diagonal line: 1/2
MARK BRAINILEST I GOT SO CONFUSED BUT I UNDERSTAND NOW.... Peace Out?
Step-by-step explanation:
) Work out (6 x 10²) + (3 x 10^5) Give your answer in standard form.
Calvin thinks that only fractions with a denominator of 2, 4, 5, 10 and 20 will
change into terminating decimals. See if he is correct by converting every unit
fraction from ½ up to 1/25 into a decimal using your calculator. Try to explain your
findings
Answer: Calvin is incorrect because as you can see from my table, when we have the fraction ⅛ we get a terminating decimal proving that he is wrong.
Step 1: Create a table that shows the unit fraction and the decimal of each (the r stands for repeating, and ra stands for random numbers). To convert the unit fraction to a decimal, simply type it in your calculator, but use the division sign instead of the fraction bar. I stopped my table at ⅛ since that is where we find our answer, but you can keep going. My table is attached.
Step 2: Formulate a well thought out explanation of why he is wrong. Example: My answer above.
A pool's diving platform is 10 m above the water's surface. The
bottom of the pool is at -5 m, relative to the surface of the
water. What is the distance between the diving platform and
the bottom of the pool?
a factory makes and sells cartons of chewing gum. the factory produces at most 500 cartons per day. each carton sells for $25. which of the following best describes the domain of the function that represents f(x), the total sales in dollars, for making x cartons in one day? a. the domain is the set of all whole numbers . b. the domain is the set of all real numbers . c. the domain is the set of all real numbers . d. the domain is the set of all multiples of 25 from .
A function's domain is defined as the set of all possible input values. The domain here is 0 ≤ x ≤ 500 because the input value is x.
Given;
Let x be the overall number of cartons produced in a single day. due to the factory's daily production limit of 500 cartons.
Let P(x) denote the revenue generated by the sale of x cartons. Since a carton costs $25, the following follows;
P(x) = 25x
P(0) = 25(0) = 0 for x = 0
P(500) = 25(500) = 12500 when x = 500
The following are possible values for P(x);
0 ≤ P(x) ≤ 12500
Therefore, the collection of all potential input values is referred to as a function's domain. Since the input value in this instance is x, the domain is 0 ≤ x ≤ 500
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PLEASE HELP ME
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer:
The correct answer is C. -29.
Step-by-step explanation:
insert -29 for x,
subtract -7 from -29,
then multiply by 2 to get your answer.
- Pls help due tomorrow !
1. (5x10^-4)x(3x10^-5) in standard form
2. (2.8x10^9) divided by (7x10^5) in standard form
3. (2x10^-14) divided by (4x10^-6) in standard form
the given numbers in standard form can be expressed as :
1. 1.5 × [tex]10^-10[/tex]
2. 4 × [tex]10^1 ^3[/tex]
3. 5 × [tex]10^-^2^1[/tex]
What do you mean by standard form ?Standard form refers to any number that can be expressed as a decimal number and falls within the range of 1.0 and 10.0 when multiplied by a power of 10. The standard form of 123,000,000 is 1.23 108 because, if you look closely, 1.23 is a decimal number between 1.0 and 10.0.
1. The given numbers are (5x10^-4)x(3x10^-5)
On multiplying the natural numbers first we get :
15 × [tex]10^{-9}[/tex]
1.5 × [tex]10^-10[/tex]
2. The given numbers are (2.8x10^9) and (7x10^5)
on dividing them we get
0.4 ×[tex]10^1 ^4[/tex]
4 × [tex]10^- ^1[/tex] ×[tex]10^1 ^4[/tex]
4 × [tex]10^1 ^3[/tex]
3. The given numbers are (2x10^-14) divided by (4x10^-6)
Thus after dividing the natural numbers we will get
0.5 ×[tex]10^- ^2 ^0[/tex]
On further simplifying we get
5 × [tex]10^ -^1[/tex] ×[tex]10^- ^2 ^0[/tex]
5 × [tex]10^-^2^1[/tex]
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Zoe is driving on a long road trip. She currently has 13 gallons of gas in her car. Each
hour that she drives, her car uses up 0.75 gallons of gas. How much gas would be in
the tank after driving for 2 hours? How much gas would be left after t hours?
Gas left after 2 hours:
Gas left after t hours:
Gas left after 2 hours is 1.5 gallons and the function that represent the gas which is left in the tank after driving for t hours is 13 - 0.75t gallons.
Zoe is driving on a long road trip.
The amount of gas she has in her car = 13 gallons.
It is given that each hour that she drives, functions her car uses up 0.75 gallons of gas.
So, Gas used in the car for one hour = 0.75 gallons
Gas used in the car for two hours = 0.75*2 = 1.5 gallons
Hence, Gas left in the tank after driving for 2 hours = 13 - 1.5 = 11.5 gallons.
Now,functions
Gas used in the car for t hours = 0.75*t = 0.75t gallons
Gas left in the tank after driving for t hours = 13 - 0.75t gallons.
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Select the correct answer.
Function h is the product of functions f and g.
f(x) = -5x − 9
g(x) = 8x − 4
Which equation defines function h?
A.
h(x) = -40x + 36
B.
h(x) = -40x2 − 52x + 36
C.
h(x) = -40x2 + 36
D.
h(x) = -40x2 − 13x + 36
The value of h(x) = -40x2 – 52x + 18. Option (b) is correct.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable is defined as a function.
Given functions
f(x) = -5x − 9
g(x) = 8x − 4
we have to determine which equation defines function h
f(x) = -5x − 9
g(x) = 8x – 4
(f x g) (x) = (-5x –9)(8x – 4)
(f x g) (x) = -40x2 + 20x – 72x + 36
(f x g) (x) = -40x2 – 52x + 18
Therefore the value of h(x) = -40x2 – 52x + 18. Option (b) is correct.
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Alice changes size several times. The ratio of her orginal height to her second height is 24 to 5. The ratio of her second height ot he rthird height is 1 to 12. The ratio of her orginal height to her fourth height is 16 to 1. The tallest of these four heights is 10 feet. What is her shortest height?
Answer:
3 inches
Step-by-step explanation:
Let's call the heights H1 thru H4.
So we have
H1/H2 = 24/5
H2/H3 = 1/12
Therefore if we multiply these, we have
H1/H3 = 2/5
Finally we are given
H1/H4 = 16/1.
By logic we can see that H3 is the tallest.
Thus if H3 = 10 feet, H1 = 4 feet
And from that,
H2 = 1/12 (10 feet) = 5/6 feet = 10 inches
and finally
H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot =
3 inches
Answer:
3 inches
Step-by-step explanation:
Let's call the heights H1 - H4
Here, we have
H1/H2 = 24/5
H2/H3 = 1/12
And so, we have
H1/H3 = 2/5
Finally
H1/H4 = 16/1.
Thus if H3 = 10 feet, H1 = 4 feet
And from that,
H2 = 1/12 (10 feet) = 5/6 feet = 10 inches
And last,
H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot = 3 inches
solve each problem using elimination
-7x-y=-27
-14x+10y=18
Answer:
y=6 x=3
Step-by-step explanation:
−2(−7x−y=−27)
1(−14x+10y=18)
14x+2y=54
−14x+10y=18
12y=72
y=6
−7x−y=−27
−7x−6=−27
−7x=−21
x=3