On solving the query we can say that Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.
what is function?Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
We may use the following formula to create a confidence interval for the population proportion:
CI is equal to pz/2*(p(1-p)/n)
where:
p = sample percentage
Based on the ordinary normal distribution, z/2 is the z-score for the degree of confidence (with a 98% confidence level, z/2 = 2.33).
sample size, n
Given:
The population proportion's 98% confidence interval is as follows:
CI = (0.4392, 0.7138)
Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.
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On solving the query we can say that Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.
What is function?
Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
We may use the following formula to create a confidence interval for the population proportion:
Cl is equal to pz/2"(p(1-p)/n)
where:
p = sample percentage
Based on the ordinary normal distribution, z/2 is the z-score for the degree of confidence (with a 98% confidence level, z/2 = 2.33).
sample size, n
Given:
The population proportion's 98% confidence
interval is as follows:
CI = (0.4392, 0.7138)
Based on the provided sample data, we can conclude with a 98% confidence that the real population proportion is between 0.4392 and 0.7138.
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The function f(x)=−1/x+2+68 represents the height of a teenage girl, in inches, x months after turning 15 years old.
How tall is the teenager at 15 years old? What height will she approach, but never achieve?
Enter your answer by filling in the boxes to correctly complete the statements.
At 15 years old, her height is 70 inches.
The height she will never achieve is the horizontal asymptote of the function.
How to solveTo find the teenager's height, plug in x=0 into the function: f(0) = -1/0 + 2 + 68.
Since division by zero is undefined, the function is not valid at 15 years old.
The height she will approach but never achieve is the horizontal asymptote of the function.
As x approaches infinity, the -1/x term approaches 0.
Therefore, the height approaches 2+68 = 70 inches.
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Can somone help with this
If the cylindrical-barrel's volume is 785.4 ft³, then the radius of barrel is approximately 5 ft, so option(c) is correct.
We know that cylindrical barrel's volume is given by formula : V = πr²h
where V represents volume, r represents radius, and h represents height of the cylinder.
In this case, we know that the volume of barrel is 785.4 ft³ and the height is 10 ft.
Substituting these values and π ≈ 3.14, into the Volume-formula,
We get,
785.4 = 3.14 × r² × (10);
785.4/31.4 = r²,
r = √(785.4/31.4),
r ≈ 5 ft
Therefore, the radius of the barrel is (c) 5 feet.
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Line A and line B intersect at point (0, -3). Line A passes through the point (-3,-2). Given that line B is perpendicular to line A, find the equation of line B in the form y = mx + c.
The equation of line B is y = 3x - 3, where line B is perpendicular to line A and passes through (0,-3).
The condition of line B is y = 3x - 3, where line B is opposite to line An and goes through (0,- 3).
Since line B is opposite to line An and they converge at point (0,- 3), the slant of line B should be the negative corresponding of the incline of line A.
To start with, we should find the slant of line A:
incline of line A = (y2 - y1)/(x2 - x1) = (- 3 - (- 2))/(0 - (- 3)) = - 1/3
Since line B is opposite to line A, the slant of line B is the negative corresponding of - 1/3:
slant of line B = - 1/(- 1/3) = 3
Presently, we can utilize the guide incline type of a direct condition toward track down the situation of line B:
y - y1 = m(x - x1)
where m is the slant and (x1,y1) is a point on the line.
Subbing m = 3 and the point (0,- 3), we get:
y - (- 3) = 3(x - 0)
Improving on the situation, we get:
y + 3 = 3x
Subsequently, the condition of line B in the structure y = mx + c is:
y = 3x - 3
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NEED HELP! THERE IS A TIME LIMIT!
VIEW ATTACHMENT.
Answer: 16
Step-by-step explanation:
Taking the integral: f(x)=((2x)^4)/4-1^4/4
Differentiating: f'(x)=2(2x)^3
f'(1)=16
A wooden cube has lengths 8cm. It has a mass of 307.2g. Find the density of the cube.
The density of the wooden cube is 0.6 g/cm³ when length is 8cm and has a mass of 307.2g.
To find the density of the wooden cube, we use the formula:
Density = Mass / Volume
Given that the length of the cube is 8 cm, all sides are equal in length.
The volume of a cube is given by the formula:
Volume = side length³
Substituting the given values:
Volume = 8 cm × 8 cm × 8 cm = 512 cm³
Now we can calculate the density:
Density = Mass / Volume = 307.2 g / 512 cm³
Simplifying:
Density = 0.6 g/cm³
Therefore, the density of the wooden cube is 0.6 g/cm³
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FOR 30 POINTS, ANSWER THE QUESTION!!!
Answer:
A - Answered in picture
B - 17.09
Step-by-step explanation:
subtitution 3x-y=12 y=2x+17 brainly verified answer
The solution to the system of equation is (29, 75).
Solving system of equationsThe given simultaneous equation is expressed as shown below:
3x-y=12 ............ 1
y=2x+17 ............ 2
We need to determine the unknown values of x and y
Substitute equation 2 into 1 to have:
3x-y=12
3x- (2x + 17) = 12
3x - 2x - 17 = 12
x - 17 = 12
x = 12 + 17
x = 29
Substitute x = 29 into equation 2;
y=2(29)+17
y = 58 + 17
y = 75
Hence the solution to the system of equation is (29, 75)
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C'D'E'F' is a translation of CDEF by (3²) a) What are the coordinates of D'? b) What are the coordinates of F'? vector -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 5+ 4- 3+ 2+ & F 11 OF -2+ نهن جي -3- -4- CD 1/2 F 3 4 5 6 7 8 9 10 x
The coordinates of D' are (-1, 4) and the coordinates of F' are (-3, 2)
What are the coordinates of D'?From the question, we have the following coordinates that can be used in our computation:
D = (3, 1)
And the vector is -4
3
So, we have
D' = (3 - 4, 1 + 3)
Evaluate
D' = (-1, 4)
What are the coordinates of F'?Here, we have the location of point F to be
F = (1, -1)
And the vector is -4
3
So, we have
F' = (1 - 4, -1 + 3)
Evaluate
F' = (-3, 2)
Hence, the coordinates of F' are (-3, 2)
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The equation for line f can be written as y=
9
5
x–2. Perpendicular to line f is line g, which passes through the point (5,–
3). What is the equation of line g?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer:
y = -5x/9 - 2/9
Step-by-step explanation:
if two lines are perpendicular to each other,
the product of their slopes are -1
(slope of f)(slope of g) = -1
(9/5)(slope of g) = -1
(slope of g) = -5/9
equation of g:
(y - (-3))/(x - 5) = -5/9
(y+3) = -5/9 * (x-5)
y = -5x/9 + 25/9 - 3
y = -5x/9 - 2/9
Please see attachment that I have uploaded
The values of the test statistic used are:
z = 0.85t = 0.68Which test statistic should be used?The test statistic to be used depends on the sample size and whether the sample standard deviation is known or not.
The z-test is used when the sample standard deviation is known and the sample size is greater than 30.
The t-test is used when the population standard deviation is or unknown and the sample size is less than 30.
a) Since the sample size is less than 30 and the population standard deviation is known, we can use the one-sample z-test.
The test statistic is z = (x - μ) / (σ / √(n))
where;
x is the sample mean,μ is the population mean,σ is the population standard deviation,n is the sample size.Substituting the values in the formula above:
z = (195.6 - 191.6) / (19.3 / √(17))
z = 0.85
(b) The sample size is less than 30 and the population standard deviation is unknown, we therefore use the one-sample t-test.
The test statistic is t = (x - μ) / (s / √(n))
where;
x is the sample mean,μ is the population mean,s is the sample standard deviation,n is the sample size.Substituting the values in the formula above:
t = (195.6 - 191.6) / (18.5 / √(10))
t = 0.68
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1)
B 80°
A X+40°
E 125
C x+50
D x+5
Sum of the interior angles=
x=
Sum of the interior angles is 540°.
The value of x is 81.67°, and angle A, C, D are 121.67°, 131.67°, 86.67° respectively.
What is the sum of interior angles of a pentagon?
Sum of interior angles of pentagon = (n-2) ×180° = (5 - 2) × 180° = 540°
Where n is number of side of the polygon.
Here given that values of angle A, B, C, D, E are (x + 40°), 80°, (x + 50°), (x + 5°), 125° respectively.
So,
angle A + angle B + angle C + angle D + angle E = 540°
We are Substituting the given values and get,
(x + 40) + 80 + (x + 50) + (x + 5) + 125 = 540
Or, 3x + 295° = 540°
Or,3x = 245°
Or, x = 81.67°
Now,
angle A = x + 40° = 81.67° + 40° = 121.67°
angle C = x + 50° = 81.67° + 50° = 131.67°
angle D = x + 5° = 81.67° + 5° = 86.67°
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Explain how you got h value.
The equation for the parabola will be y = 0.765625(x + 5.25)^2 - 69.390625.
How to explain the equationLet us commence with the generalized equation for a parabola:
y = a(x - h)^2 + k
where (h,k) is the vertex of the parabola.
We can now set up august system of equations by integrating the two provided points and their corresponding transformed points:
4 = a(-2 - h)^2 + k (1)
-11 = a(-6 - h)^2 + k (2)
1 = a(1 - h)^2 + k (3)
-5 = a(-3 - h)^2 + k (4)
Comprising four knowns (a, h, k), fostering a viable solution to our problem yet available.
-15 = a(-4h - 32)
Dividing both sides by -4 silences the equation to:
3.75 = ah + 8
Continuing, subtracting equation (3) from (4):
-4 = a(-2h - 12)
Divving and relying on -2 debases the outcome to:
2 = ah + 6
At this juncture, we have two equations compounding two unknowns (a and h). Determining the h value in accordance to a within these equations can be done by setting our solutions equal to each other and solving for a, giving you an answer of 0.765625.
Exploiting one of the previous expressions, we next find h=(2-6)/0.765625=-5.25. By means of various designs, any of the four initial equations come into play when searching for k. Rearranging, 4=0.765625(-2-(-5.25))^2+k, leads to k=-69.390625.
Thus, unto completion of a parabolic, these values grace your presence:
a= 0.765625
h= -5.25
k= -69.390625
And so, the alluring equation of such an inscribed parabola casts itself forthheartedly, incarnating as:
y = 0.765625(x + 5.25)^2 - 69.390625
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solve for x. Just put the angle measure. Round to the nearest tenth
Answer: 48.7
Step-by-step explanation:
cos x=31/47
x=48.7
Answer:
Step-by-step explanation:
answer the question in the diagram
By using Newton's divided difference formula, the polynomial function in x is f(x) = x⁴ - 3x³ + 5x² - 6.
What is a polynomial function?In Mathematics and Geometry, a polynomial function is a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as the following:
Multiplication (product)AdditionSubtractionNext, we would determine the polynomial function in x from the given data by using Newton's divided difference formula;
xi f(xi) f[xi,xi+1] f[xi,...,xi+2] f[xi,...,xi+3] f[xi,...,xi+4]
-1 3 -9 6 5 1
0 -6 15 41 13
3 39 261 132
6 822 789
7 1611
By interpolating, the interpolation polynomial is given by:
Pₙ(x) = 3 + -9(x+1) + 6(x + 1)(x - 0) + 5(x + 1)(x - 0)(x - 3) + 1(x + 1)(x - 0)(x - 3)(x - 6)
f(x) = (x - 6)(x - 3)x(x + 1) + 5(x - 3)x(x + 1) + 6(x + 1) - 9(x + 1) + 3
f(x) = x⁴ - 3x³ + 5x² - 6
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If f(x) = 3x − 4, which of these is the inverse of f(x)?
-
O A. f¹(x) = 24
O B. f¹(x) = + 4
O C. ¹(x)=-4
○) D. ƒ¨¯¹(x) = 2-3 4
The inverse of the function f(x) = 3x - 4 is f⁻¹(x) = x/3 + 4/3.
What is the inverse of the given function?The inverse of a function is simply a new function that "reverses" the action of the original function.
Given the function in the question:
f(x) = 3x - 4
To find the inverse of f(x) = 3x - 4, we simply need to solve for x in terms of y.
f(x) = 3x - 4
y = 3x - 4
Interchange the variables
x = 3y - 4
Solve for y
Adding 4 to both sides:
x + 4 = 3y - 4 + 4
x + 4 = 3y
3y = x + 4
Dividing both sides by 3:
3y/3 = x/3 + 4/3
y = x/3 + 4/3
Replace y with f⁻¹(x)
f⁻¹(x) = x/3 + 4/3
Therefore, the inverse is f⁻¹(x) = x/3 + 4/3
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Need assistance on Calculus HW :) 12th grade.
As a result, there is no solution to the provided problem.
What exactly is trigonometry?Trigonometry is the study of triangles, which is a branch of mathematics. It is also known colloquially as "trig." Mathematicians explore the connections between the sides and angles of triangles in trigonometry.
We're told that sec O = -1/0. Because sec O is the reciprocal of cos O, cos O must be -1/0. However, because there is no angle with an undefined cosine, we infer that there is no such angle O.
As a result, there is no solution to the provided problem.
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Please help!!! 20 points!!
Option C is correct, the third dot plot represents the table data.
A dot chart or dot plot is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles.
The dots in the number line represents the number of hamsters
The dots above line represents the hamsters owned.
We have to find the dot plot which is represented by the table.
As we observe C dot plot, it matches with the given data in the table.
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Change 48.2% to it’s fractional equivalent. Please show work
As asked in the question, 48.2% is equivalent to the fraction 241/500.
To convert a percentage to a fractional equivalent, we divide the percentage by 100 and simplify the resulting fraction.
So, to convert 48.2% to a fraction, we divide 48.2 by 100:
48.2/100 = 0.482
This gives us the decimal equivalent of 48.2%.
To convert the decimal to a fraction, we write it over 1 and simplify it:
0.482/1 = 482/1000
We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
482/1000 = (241/500)
Therefore, 48.2% is equivalent to the fraction 241/500.
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I NEED HELP PLEASE! WILL MARK BRAINLIEST IF CORRECT !
Answer: 71.57
Step-by-step explanation:
You are going to use SOH CAH TOA to find the angle
because the opposite and adjacent are the sides from the reference angle use TOA (tanΘ=opp/adj)
TanΘ=[tex]\frac{9}{3}[/tex]
now use that tan^-1 (9/3) on your calculator (make sure your calc is in degree mode)
71.57
Question 11 sto wants to buy a small wine form worth Re 500.00 he plans to Sell his current home For R3 400 00 which he will use as a deposit for the purchase of the form. He becure toan with a bank with a repayment period of 10 years and a internet roke of 9,5% Compounded monthly. Calcurate bre monthly repayments
Please help me I need this
The equations that can be used to find the length of the base are a and d
The formula for the volume of a rectangular prism is V = lwh
V = volume, l = length
w = width
h = height
In this problem, the volume of the rectangular prism is given as 1,392 cubic centimeters, the height is given as 12 centimeters, and the width is given as 8 centimeters. We can use the formula to find the length of the base as:
l = V / wh
Substituting the given values, we get:
l = 1,392 / (8 x 12)
Simplifying, we get:
l = 14.5
Therefore, the length of the base of the rectangular prism is 14.5 centimeters.
The two equations that can be used to find the length of the base are:
a. 1392 = 96l (multiplying both sides of the equation by 8 x 12)
d. 12 x 8 x l = 1392 (rearranging the formula V = lwh to solve for l)
Therefore, the equations that can be used to find the length of the base are a and d
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Assume you own a wood house in the country that is worth $200,000, using the
table below, what would be your annual premium to insure.
Annual Premium per $100 of coverage
Brick
Area
rating
City
0.39
Suburb 0.45
Rural
0.6
Steel
|Mixed
Wood
Building Contents Building Contents Building
Contents
Building |
Contents
0.43
|05
054
0.55
0.52
0.56
0.63
0.72
0.69
0.71
0.8
0.89
0.65
0.74
0.91
0.66
0.76
0.83
0.85
1
1.02
• $1,320
• $1,660
• $2,000
О $2,500
Based on the table, the annual premium for a wood house in a rural area would be $2,000.
solve please, third time
The composite figure has an area of 74 square centimeters.
How to determine the area of a composite figure
In this question we find the representation of a composite figure formed by two rectangles, whose area has to be computed. The area formula for a rectangle is:
A = b · h
Where:
A - Area, in square centimeters.b - Base, in centimeters.h - Height, in centimeters.Now we proceed to determine the area of the composite figure:
A = (8 cm) · (3 cm) + (5 cm) · (2 cm) + (8 cm) · (5 cm)
A = 24 cm² + 10 cm² + 40 cm²
A = 74 cm²
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Find the equation of the parabola with the following properties. Express your answer in standard form.
Symmetric with respect to the line y = 2
Directrix is the line x = 11
P = -3
The equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1
What is the equation of the parabola?To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.
Alternatively, we can use PF = PM to find the equation of the parabola.
vertex is half way between the focus and directrix
It's a downward opening parabola, general form
y= a(x-h)^2 + k
where (h,k) = vertex= (-3,-1)
plug in another point on the parabola to solve for a which gives
am answer with either x coefficient = -1'/4 or =4 Check the math.
one or the other is right another point is the y intercept = 9a-1
Another point is directly to the right of the focus (-1, -2) It's 2 down from the directrix and 2 to the right of the focus, equidistant. plug that point into y= a(x+3)^2 -1 and solve for "a"
-2 = a((-1+3)^2 -1
-2 = 4a -1
4a = -
a = -1/4
The parabola is y = (-1/4)(x+3)^2 -1
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The lengths of two sides of a triangle are 9 cm and 15 cm. The length of the third side is a whole-number value. What is a possible length of the third side in centimeters?
The possible length is 9 centimeter because it can be isoceles triangle
help with this please
Answer:
C. The volume is multiplied by 8
Step-by-step explanation:
1*1*1=1
1+1=2
1+1=2
1+1=2
2*2*2=8
Answer:
in the picture
Step-by-step explanation:
we multiply the side by two and find the new volume, unfolding and calculations in the figure
Sami’s puppy went form weighting 21 pounds to 37 pounds. What is the percent increase in weight?
Answer:
76% increase (approximately)
Step-by-step explanation:
21 lbs ➜ 37 lbs.
To calculate percentage increase, you must first find the difference of the final value and the starting value.
[tex]37-21=16[/tex]
Second, take the difference and divide it from the starting value.
[tex]16/21\\=0.76[/tex] (approximately)
Lastly, take the quotient and multiply it by 100.
[tex]0.76 *100\\=76[/tex]
Therefore, there was a 76% increase in weight.
I need help with this please
Solve the proportion.
3x/9=7/4
Answer:
exact form: x=21/4
decimal form: 5.25.
mixed number form: x=5 1/4
Step-by-step explanation:
have a good day :)
Answer:
x = 5.25 or 21/4 or 5 1/4
Step-by-step explanation:
3x : 9 = 7 : 4
3x = 9 x 7 : 4
3x = 63 : 4
3x = 15.75
x = 15.75 : 3
x = 5.25 or 21/4 or 5 1/4
-----------------
check
(3 × 5.25) : 9 = 7 : 4
15.75 : 9 = 7 : 4
1.75 = 1.75
same value, the answer is good
Can some figure out the answer here?
Answer:
Step-by-step explanation:
d=71 vertical angles-angles across 2 intersecting are =
e=180-71=109 supplementary angles are =180
g=19
boxes 3,4, 5, 6, 8 are true
