The Confidence Interval for a Population Proportion is 0.69 ± 1.13
(-0.44 to 1.82)
Confidence Interval:
Confidence Interval means a range of values that is determined through the use of observed data, calculated at a desired confidence level that may contain the true value of the parameter being studied.
Given,
n = 130 and
p= 0.69,
construct a 99% confidence interval.
Here we need to find the confidence interval.
According to the formula, the confidence interval is,
We know that,
Sample Size: 130
Sample Mean: 0.69
Confidence Level: 99%
99% Confidence Interval: 0.69 ± 1.13
(-0.44 to 1.82)
"With 99% confidence the population mean is between -0.44 and 1.82, based on 130 samples."
Margin of Error: 1.13
(to more digits: 1.13)
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If a triangle’s original dimensions are 24 cm by 40 cm, which triangle would be an enlargement of the original by a scale factor of 2.2?
The triangle’s enlargement dimensions will be 52.8 cm by 80 cm.
What is scale factor?The size by which the shape is enlarged or reduced is called as its scale factor.
Scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape.
It is used to increase or decrease the size of an object.
The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.
For example, a rectangle has a length of 5 units and a width of 2 units. Now, if we increase the size of this rectangle by a scale factor of 2, the sides will become 10 units and 4 units, respectively. Hence, we can use the scale factor to get the dimensions of the changed figures.
Given:
A triangle’s original dimensions are 24 cm by 40 cm
scale factor=2.2
Thus,
enlarged dimensions= scale factor x original dimensions
[2.2] x 24 = 52.8 cm
[2.2] x 40 = 80 cm
Hence, the triangle’s enlargement dimensions will be 52.8 cm by 80 cm.
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h, the points A(−5, 6), B(2, 6), C(2, -1) and D(-5, -1) are the vert of a square. what is the area of the square?
Answer:
so find dots, then count how many sections are beetween them, so you will find lenght of every side and use formula to find area(S=a²+b²).
The height of Debbie is 85 centimetres. The height of Leo is 90 centimetres. Write the height of Debbie as a fraction of the height of Leo. Give your answer in its simplest form.
To write the height of Debbie as a fraction of the height of Leo in its simplest form is this: 17/18.
What does it mean to write a figure as a fraction of another?Writing one figure as a fraction of another can be done by representing the figures as numerators and denominators. In this case, what we will have is 85/90. That is the height of Debbie divided by the height of Leo.
To express this fraction in its simplest form will mean dividing the figures until they can no longer be divided. Using 5 as a common factor for dividing, we can conclude that the simplest form of the answer is 17/18.
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Find the greatest common factor of thefollowing monomials:10x^3y^3 32xy^2
The greatest common factor between the monomials can be determined as,
[tex]\text{GCF}(10x^3y^3,32xy^2)=2xy^2[/tex]Thus, the above expression gives the required greatest common factor.
find the value of 2/5 of 3 3/4 kg
Answer:
1.5
Step-by-step explanation:
2/5 of 15/4
1 of 3/2
1 1/2
1.5
Hi dear! Can you help me to solve exercise #18 please!!!
Hello there. To solve this question, we'll have to remember some properties about dividing polynomials.
Given the polynomials, we want to evaluate the division:
[tex](1+3x+x^4)\div(3-2x+x^2)[/tex]Rewriting it the way we perform long division:
We start with the higher degree terms, namely x^4 and x².
Dividing x^4 by x², we get x². Now we multiply every term from the division by this factor and subtract from the term being divided.
Now, we have a 2x³ as the higher degree term from the term being divided. Dividing it by x², we get 2x. Multiply each term of the divisor and subtract from it.
Finally, the highest degree term from the term being divided is x². Dividing it by x², we get 1. Multiply each term of the divisor and subtract it from the dividend.
Now, the highest degree term from the dividend is -x, when the highest degree term from the divisor is x². We cannot proceed with the long division anymore.
It means that we have a quotient:
[tex]x^2+2x+1[/tex]And a remainder:
[tex]-x-2[/tex]Notice if we rewrite it as:
[tex]x^4+3x^2+1=(x^2-2x+3)\cdot(x^2+2x+1)-x-2[/tex]We have the division P(x)/D(x) written in the form:
[tex]P(x)=D(x)\cdot Q(x)+R(x)[/tex]Where Q(x) and R(x) are the quotient and remainder polynomials.
HURRY Find all solutions to the equation 3x3 + 12x = 2x2 + 8.
Negative 2, negative two-thirds, 2.
Negative 2, two-thirds, 2.
Negative two-thirds, negative 2 i, 2 i.
Two-thirds, negative 2 i, 2 i.
4
Step-by-step explanation:
3×3+12x=2×2+8
9+12x=4+8
9+12x=12
12x=12-9
12x=3
x=4b) 150 g of syrup are needed to make 8 flapjacks.
Find the quantity of oats needed to make 16 of these flapjacks.
Based on the fact that 150g of syrup are needed when making 8 flapjacks, the quantity that is needed to make 16 flapjacks is 300 g.
How to find out quantity needed?The quantity of oats needed to make 8 flapjacks is 150 g.
Assuming direct proportion, the quantity of oats needed to make 16 flapjacks can be found by the formula:
= (Quantity of oats needed for 8 flapjacks x Number of flapjacks to be made) / Number of flapjacks made
Solving for the quantity of oats needed gives:
= (150 x 16) / 8
= 2,400 / 8
= 2,400 x 1/8
= 300 g
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The standard form for a parabola with vertex (h,k) and an axis of symmetry of y=k is:(y-k)^2=4p(x-h)The description below is for a parabola. Write it in standard form. When answering the questions type coordinates with parentheses and separated by a comma like this (x,y). If a value is a non-integer then type is a decimal rounded to the nearest hundredth.Vertex is (2,2); directrix is x=2-\sqrt[]{2}, focus is (2+\sqrt[]{2},2)The value for p is: AnswerThe value for h is: AnswerThe value for k is: Answer
Given that a parabola has
[tex]\begin{gathered} Vertexis(2,2) \\ directrix\text{ }is\text{ }x=2-\sqrt[]{2} \\ focus\text{ }is\text{ }(2+\sqrt[]{2},2) \end{gathered}[/tex]And that the standard form of a parabola can be expressed as
[tex]\mleft(y-k\mright)^2=4p\mleft(x-h\mright)[/tex]We are asked to find the value of p, h and k. This can be seen below.
Explanation
Recall, If a parabola has a horizontal axis, the standard form of the equation of the parabola is this
[tex](y-k)^2=4p(x-h)[/tex]where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h + p, k). The directrix is the line x = h - p. The axis is the line y = k. If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.
Value of h and k
By comparison
[tex]\begin{gathered} \text{Vetex = (h,k) = (2,2)} \\ \therefore h=2;k=2 \end{gathered}[/tex]Answer: h = 2 and k =2
Value of p
Also, by comparison
[tex]\begin{gathered} focus=(h+p,k)=(2+\sqrt[]{2},2) \\ \therefore p=\sqrt[]{2}=1.41 \\ \end{gathered}[/tex]Answer : p =1.41
Writing the equation of the parabola in standard form
We can then use the given data to express the parabola in standard form as;
Answer
[tex](y-2)^2=4\sqrt[]{2}(x-2)[/tex]12. Check for Reasonableness Which of the quotients are equivalent to 2.5? Select all that apply.
10/-4
10/4
-10/-4
-5/-2
-5/2
5/2
What equation would you set up to solve for X?
The price of an item has been reduced by 30% . The original price was $90 . What is the price of the item now?
THE PRICE AT WHICH THW ITEM IS REDUCED BY IS 30% OF $90
[tex] \frac{30}{100} \times \frac{90}{1} \\ = \frac{3}{10} \times 90 = 27[/tex]
THE PRUCE U BEING REDICED BY $27
TO GET THE NEW PRICE OF THE ITEM WE SUBTRACT THE PRICE IT WAS REDUCED BY FROM THE ORIGINAL SELLING PRICE.
[tex] = 90 - 27 \\ = 63[/tex]
NOW THE NEW PRICE OF THE ITEM IS $63
In a relation, the input is the number of people and the output is the number
of backpacks.
Is this relation a function? Why or why not?
A. No, because you do not know how many people there are.
B. No, because the same number of people might have a different
number of backpacks.
C. Yes, because each person has one backpack.
D. Yes, because a given number of people always has the same
number of backpacks.
If input is number of people and output is number of backpack then it is not a relation because same person can have different number of backpacks.
When the input is the number of people an the output is the number of backpacks, it is not a relation,
The reason is, Because same number of people might have a different number of backpacks.
A function is a relation in which each and every input has an output, and each and every input has a unique output.
In this situation, it is not compulsory that each person carry a backpack.
Even if each an everyone does have a backpack. It is not sure that if one person has only one backpack or not.
So, it is not a relation.
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f(x)=3x^6+4x^3-2x^2+4find all possible zeroes
Solution:
Given the function below
[tex]f\mleft(x\mright)=3x^6+4x^3-2x^2+4[/tex]For teh possible roots;
[tex]\begin{gathered} a_0=4,\:a_n=3 \\ \mathrm{The\:dividers\:of\:}a_0:1,\:2,\:4 \\ \begin{equation*} \mathrm{The\:dividers\:of\:}a_n:1,\:3 \end{equation*} \\ \mathrm{The\:following\:rational\:numbers\:are\:candidate\:roots:}\pm\frac{1,\:2,\:4}{1,\:3} \end{gathered}[/tex]From the deduction above,
The possible rational roots is
[tex]±1,\pm\frac{1}{3}\pm2,\pm\frac{2}{3},\pm4,\pm\frac{4}{3}.[/tex]Hence, all the possible zeros is
[tex][/tex]186+2947•4194(3.486)x=?
The value of x for the given equation will be -4.3×10⁻⁶.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Arithmetic operation is used to find the value of x in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that,
186+2947•4194(3.486)x
x=-186/2947•4194(3.486)
x=-4.3×10⁻⁶.
Thus, the value of x for the given equation will be 4.3×10⁻⁶.
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what is -5 x (- 3/9)
Answer:
Step-by-step explanation:
−5(−3/9)
Divide
-5x(-1/3)
Multiply
−5x(−1/3)
x 5/3
combine multiple terms into single fraction
5x/3
Describe the first step you would take to solve the system of equations 8x + y = -16 and - 3x + y = -5 using elimination and justify your answer.
8x + y = -16
3x + y = -5
The first to take is to subtract the second equation from the first equation
This will eliminate the y-variable leaving you with jus x-variable
That is;
5x = -11
x = -11/5
the equation of a line is y=mx+b. if we know the line passes through (7,8), what does that tell us
The equation of the line is given as y = -2x + 22. This means that when x is equal to zero, y = 22. M also shows how steep the line is, being the gradient.
What is the calculation that justified the above?In order to arrive at a logical solution, we must assume the value of the slope as this is not given.
Assuming the slope of the line is -2, we thus can say:
The equation of a line that passes through a point (x₁,y₁) and a slope m is given by
(y - y1) = m (x - x1)
Recall that the slope, m = -2
While
Point (x1, y1) = (7, 8)
Hence, the equation of the line is:
y-8 = (-2) (x-7)
y-8 = -2x + 14
y = -2x+ 14 + 8
Hence,
y = -2x + 22
Thus, the equation of the line is:
y = -2x + 22
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find the exact perimeter of hexagon ABCDEF plotted below
Perimeter Hexagon = 31.99
perimeter Hexagon = AB+BC+CD+DE+EF+FA
AB= [tex]\sqrt{58[/tex] =7.61
BC = 5
CD = 6
DE = [tex]\sqrt{29}[/tex] =5.38
EF =7
FA= 1
∴ perimeter Hexagon = 31.99
What is hexagon?Hexagons are six-sided polygons in geometry. A hexagon is said to be a regular hexagon if all of its sides and angles have identical lengths. To put it another way, a regular hexagon's sides are congruent.The area of a hexagon is calculated using the formula Area = (33 s2)/2, where s is the length of one of the regular hexagon's sides. The area of a hexagon can also be calculated using the apothem by using the formula Area of hexagon = (1/2) a P, where an is the apothem's length and P is the hexagon's perimeter.To learn more about : Hexagon
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What steps would you need to take to graph the function:
f(x)=-3x^3-6x^2+3x+6
Name any x-intercepts and y-intercepts in the graph of the function.
Describe the end behavior of the function.
For extra credit, draw a sketch of the function by hand or in Paint.
The x-intercepts in the graph are ( - 2, 0 ), ( 1, 0 ) and ( - 1, 0 ) and the y-intercepts of the graph is ( 0, 6). The graph of the function tends to infinity in the negative y-axis direction after intersecting the x-axis at ( 1, 0).
Consider the function,
f(x) = - 3x³ - 6x² + 3x + 6
To find the x-intercept of the function we substitute y = 0.
f(x) = y = - 3x³ - 6x² + 3x + 6
- 3x³ - 6x² + 3x + 6 = 0
3x³ + 6x² - 3x - 6 = 0
3x²( x + 2 ) - 3 ( x - 2) = 0
( x + 2 )( 3x² - 3) = 0
Therefore,
x = - 2 and;
3x² - 3 = 0
3x² = 3
x = ± 1
Hence, the x-intercepts are ( - 2, 0 ), ( 1, 0 ) and ( - 1, 0 ).
Now, the y-intercept will be when x = 0,
y = - 3x³ - 6x² + 3x + 6
y = - 3(0)³ - 6(0)² + 3(0) + 6
y = 6
Hence, the y-intercept is ( 0, 6).
The graph of the function intersects the x-axis at ( - 2, 0) and ( - 1, 0 ) and then intersects the y-axis at ( 0, 6) then after intersecting the x-axis at ( 1, 0 ) the graph tends to infinity in the negative x-axis direction.
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What’s the frequency?
The total frequency of the particular 5 classes (67, 68, 69, 70, and 71) will be 19.
What is the frequency?The quantity of times a specific data value occurs is known as its frequency. We use f to represent a data value's frequency. For instance, grade A is said to have a frequency of five if five students received an A in science.So, the frequency for 5 classes:
Frequency of 67: 4Frequency of 68: 6Frequency of 69: 4Frequency of 70: 4Frequency of 71: 1The total frequency of these particular 5 classes will be:
4 + 6 + 4 + 4 + 1 = 19Therefore, the total frequency of the particular 5 classes (67, 68, 69, 70, and 71) will be 19.
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A contractor completed five-ninths of a job before a second contractor completed an additional one-third. What fraction of the job is left undone?
[tex]\frac{1}{9}[/tex] fraction of the job is left undone.
What is fraction?Any number of equal parts is expressed by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, represents how many components of a suitable size there are when stated in ordinary English. fraction, A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction occurs in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. a week ago.
Given Data
A contractor completed five-ninths of a job before a second contractor completed an additional one-third.
Total work done is 1.
Contractor and second contractor completed:
= [tex]\frac{5}{9}[/tex] + [tex]\frac{1}{3}[/tex]
= [tex]\frac{5+3}{9}[/tex]
= [tex]\frac{8}{9}[/tex]
Total work done = 1
Work left undone:
= 1 - [tex]\frac{8}{9}[/tex]
= [tex]\frac{1}{9}[/tex]
[tex]\frac{1}{9}[/tex] fraction of the job is left undone.
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3. The ratio of the amount of food that my cat Jade eats
to the amount of food that my cat Poe eats is 3 : 2.
If Jade eats 6 ounces of food, how many ounces of
food will Poe eat? (Your answer should be a whole
number.)
Answer: 4
Step-by-step explanation:
6/? = 3/2
3 x 2 = 6
2 x 2 = 4
Therefore; 4
The ounces of food that Poe eat is 4 ounces.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
ratio of the amount of food that my cat Jade eats to the amount of food that my cat Poe eats is 3 : 2.
For some constant k,
Ounces of food Jade eat = 3k
Ounces of food Poe eat = 2k
Jade eats 6 ounces of food.
3k = 6
k = 6 / 3 = 2
Ounces of food that Poe eats = 2k = 2 × 2 = 4
Hence Poe eats 4 ounces of food if Jade eats 6 ounces of food.
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The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function
R(x) = -3x² + 56x
How many hearing aids need to be produced and sold in order to maximize the revenue? (Round to
the nearest whole number.)
The revenue is at a maximum after
- -
The maximum revenue is $
hearing aids are produced and sold.
What is the revenue? (Round answer to the nearest cent.)
The revenue is at a maximum after x = 9
The maximum is $ 261
9 hearing aids are produced and sold.
The revenue, R(x), of producing and selling 'x' Awesome Hearing Aids is modeled by the function,
R(x) = -3x² + 56x
We need to find the number of hearing aids produced and sold in order to maximize the revenue.
We use the differentiation method to find the maximum of the function R(x).
Differentiate R(x) with respect to x and equate it with 0,
R'(x) = -6x + 56
Then, -6x + 56 = 0
⇒ 6x = 56
⇒ x = 56/6 = 9.33 ≈ 9 [since x is the number of hearing aids]
Now we find the second derivative of R(x) at x = 9.
R''(x) = -6
⇒ R''(9) = -6 < 0
Since R''(9) < 0, the revenue R(x) is maximum at x = 9.
So the maximum revenue is obtained after x = 9.
Therefore maximum revenue = R(9) = -3 x 9²+56 x 9 = $ 261
Hearing aids produced and sold in order to maximize the revenue = 9
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If 4−5=−12 and y = 3, what is x ?
Substituting y=3 in 4x-5y=-12 we get:
[tex]4x-5\cdot3=-12.[/tex]Simplifying the above equation we get:
[tex]4x-15=-12.[/tex]Adding 15 to the above equation we get:
[tex]\begin{gathered} 4x-15+15=-12+15, \\ 4x=3. \end{gathered}[/tex]Finally, dividing the above equation by 4 we get:
[tex]\begin{gathered} \frac{4x}{4}=\frac{3}{4}, \\ x=\frac{3}{4}\text{.} \end{gathered}[/tex]Answer: If 4x-5y=-12 and y=3 then:
[tex]x=\frac{3}{4}\text{.}[/tex]Please help me out, I need to turn it in in 15 mins
What is their rate of change (speed) in Section D (Hours 7-10)? Remember to include units.
Step-by-step explanation:
I assume the hours are also in units of 2.
that means in D the distance is -20 miles in 10 hours or
-20 miles / 10 hours = -2 miles / hour
A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 2 comma 6
Find and interpret the slope and y-intercept in this real-world situation.
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 9 inches every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
The Slope of the line is 3/2 and the y-intercept is at (0,3)
Each solution in the two-variable scenario can be thought of as the Cartesian coordinates of a specific point on the Euclidean plane.
Each line in the Euclidean plane that is defined by a solution to a linear equation can be thought of as the sum of all solutions to a linear model with two variables.This is how equations in this class came to be referred to be "linear." A hyperplane of size n in Euclidean space is made up of all the solutions to an equation system with integer variables (a subdomain of dimension n1).The usage of linear equations is widespread throughout all fields of mathematics, physics, and engineering because they can commonly properly represent non-linear systems.The graph of the line passes through (0,9) and (2,6) .
Slope of the line = (6-9)÷(2-0) = 3/2
Hence the line will have the equation:
y - 6 = 3/2 ( x - 2 )
or, 2y - 12 = 3x - 6
or, 2y - 3x = 6
Now from the real world situation at y = 0, x = - 2
and at x = 0, y = 3
Hence the y-intercept is at (0,3)
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Answer:
A : The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
Step-by-step explanation:
I took the quiz and it was right
Find the value of x that makes line u parallel to line v
Answer:
x = 10
Step-by-step explanation:
the angles shown are corresponding angles
corresponding angles are equal
12x - 4 = 10x + 16
subtract 10x from both sides
2x - 4 = 16
add 4 to both sides
2x = 20
divide both sides by 2
x = 10
Find the circumference of a circular swimming pool with a radius of 8.5 yards. Use 3.14 as an approximation for pie. Round your answer to the nearest whole yard. Enter only the number.
Answer:
53 yards
Step-by-step explanation:
Hello!
The circumference formula of a circle is [tex]C = 2\pi r[/tex], where C is the circumference, and r is the radius.
Given that pi is 3.14, solve for the circumference.
Solve for C[tex]C = 2\pi r[/tex][tex]C = 2(3.14)(8.5)[/tex][tex]C = 53.38[/tex]The circumference of the circle is 53.38, but rounded to the nearest whole yard would be 53 yards.
Find the recursive formula. 2, 32, 62, 92, ...
Answer:
122
Step-by-step explanation:
2+30 =32
32+30=62
62+30=92
Answer:
Use the formula
Step-by-step explanation:
I hope it helps