Answer:D
Step-by-step explanation:
A 2015 Gallup survey asked respondents to consider several different foods and beverages and to indicate whether these were things that they actively tried to include in their diet, actively tried to avoid in their diet, or did not think about at all. Of the 1009 adults surveyed, 616 indicated that they actively tried to avoid drinking regular soda or pop. Assume that the sample was an SRS.
Suppose we computed a large sample 99% confidence interval for the proportion of all American adults who actively try to avoid drinking regular soda or pop.
This 99% confidence interval:
would have a larger margin of error than a 90% confidence interval.
would have a smaller margin of error than a 90% confidence interval.
could have either a smaller or a larger margin of error than a 90% confidence interval. This varies from sample to sample.
would have the exact same margin of error as a 90% confidence interval.
Answer:
would have a larger margin of error than a 90% confidence interval.
Step-by-step explanation:
Margin of error in statistics can be defined as a small amount that is allowed for in case of miscalculation or change of circumstances.
For a statistical data margin of error can be expressed as;
M.E = zr/√n
Where;
Given that;
r = Standard deviation
z = z score at a particular confidence interval
n = sample size
z at 99% = 2.58
z at 90% = 1.645
Since z at 99% is higher than z at 90% Confidence interval, the Margin of error M.E at 99% confidence interval will be higher than that of 90% confidence interval.
The Wall Street Journal reported that approximately 25% of the people who are told a product is improved will believe that it is in fact improved. The remaining 75% believe that this is just hype. Suppose a marketing study consists of a random sample of eight people who are given a sales talk about a new, improved product. What is the standard deviation of the number of people who believe that the product is in fact improved
Answer:
The standard deviation of the number of people who believe that the product is in fact improved is 1.50.
Step-by-step explanation:
The random variable X can be defined as the number of people who believe that a product is improved when they are told so.
The probability of a person believing that a product is improved is, p = 0.25.
A random sample of n = 8 people who are given a sales talk about a new, improved product are selected.
The event of a person believing that the product is improved is independent of others.
The random variable X follows a Binomial distribution with parameters n = 8 and p = 0.25.
The success is defined as a person believing that a product is improved.
The mean and standard deviation of a Binomial distribution is given by:
μ = n × p
σ = √[n × p × (1 - p)]
Compute the standard deviation as follows:
σ = √[n × p × (1 - p)]
= √[8 × 0.25 × (1 - 0.25)]
= √(2.25)
= 1.50
Thus, the standard deviation of the number of people who believe that the product is in fact improved is 1.50.
If the relationships below are given in the form (input, output) which pairing always describes a function?
Answer:
B, the second one
Step-by-step explanation:
A personal pizza is $7.00 plus $0.50 per topping. Is this proportional?
A triangle has sides that measure 2 units, 5 units, and 5.39 units. What is the area?
Answer:
12 units squared
Step-by-step explanation:
12.39 = 2 (3.14)r
12.39 / 6.28 = 6.28r / 6.28
1.97= r
A= (3.14) (1.97)^2
A= 12.18
The triangle's side lengths of 2, 5, and 5.39 units. So the area is 4.1506 square units.
To compute the area of a triangle, we employ formula, which utilizes the semi-perimeter [tex]\(s\)[/tex] (half of the perimeter):
[tex]\[ s = \frac{a + b + c}{2} \][/tex]
The area [tex]\(A\)[/tex] is:
[tex]\[ A = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]
Triangle's sides as 2 units, 5 units, and 5.39 units:
[tex]\[ a = 2 \][/tex]
[tex]\[ b = 5 \][/tex]
[tex]\[ c = 5.39 \][/tex]
The semi-perimeter [tex]\(s\)[/tex]:
[tex]\[ s = \frac{2 + 5 + 5.39}{2} = \frac{12.39}{2} = 6.195 \][/tex]
Apply formula:
[tex]\[ A = \sqrt{s(s-a)(s-b)(s-c)} \\A= \sqrt{6.195(6.195-2)(6.195-5)(6.195-5.39)} \][/tex]
[tex]\[ A = \sqrt{6.195 \times 4.195 \times 1.195 \times 0.805} \][/tex]
Square root:
[tex]=\[ 6.195 \times 4.195 \times 1.195 \times 0.805\\= 25.201572[/tex]
The square root:
[tex]\[ A = \sqrt{25.201572} =5.02 \text{ square units} \][/tex]
Complete question:
A triangle has sides that measure 2 units, 5 units, and 5.39 units. What is the area?
491,787 divided into 477
Answer:
1,031
Step-by-step explanation:
you divide 491,787 divided into 477, you get 1,031
491,787 divided into 477 would be 1031
You are conducting research for a popular blog to find out the proportion of readers who are satisfied with the site’s newly designed navigation. You want to make sure that you increase your chances for capturing the true proportion of readers who are satisfied, but the margin of error is too large. Which of the given options would you do?
:D XD :D XD :D XD :D XD :D XD XD XD
MAT-144-0502
Homework: Module 2 Homework (unlimited attempt
Score: 0 of 1 pt
6 of 25 (5 complete
2.1.50
The nutrition information on the cereal box says that a 1/3-cup serving provides 80 calories and 4 grams of dietary fiber. At th
A 1/2-cup serving contains
calories.
Answer:
5
Step-by-step explanation:
To find the Calorie content of a serving of cereal with 3 g protein, 18 g carbohydrates, and 6 g fat, multiply each by their Caloric values (4.1 Cal/g for protein and carbohydrates, 9.1 Cal/g for fat) and sum the results to get 140.7 Calories.
Explanation:Calculating Calories in Breakfast Cereal
To calculate the Calorie content of a serving of the breakfast cereal described, we need to multiply the mass of each macronutrient by its respective Caloric value per gram and sum them up. The given macronutrient values per serving of the cereal are 3 grams of protein, 18 grams of carbohydrates, and 6 grams of fat. Below are the calculations:
Calories from protein = 3 g × 4.1 Cal/g = 12.3 Cal
Calories from carbohydrates = 18 g × 4.1 Cal/g = 73.8 Cal
Calories from fat = 6 g × 9.1 Cal/g = 54.6 Cal
The total Calorie content for a serving of this breakfast cereal is obtained by adding the individual Calorie contributions from proteins, carbohydrates, and fat:
Total Calorie content = 12.3 Cal + 73.8 Cal + 54.6 Cal = 140.7 Calories
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Meeko Insurance offers an annuity with a minimum interest rate of 3% for the
next 5 years. You decide to invest $5000 into this account. What type of
annuity is this?
Answer:
Single-payment variable annuity
Step-by-step explanation:
The type of Annuity is single-payment variable annuity.
What is annuity?An annuity is a contract between you and an insurance company in which the insurer agrees to pay you either immediately or in the future. An Annuity plan guarantees you a predetermined sum of money for the remainder of your life in exchange for a lump sum payment or a series of instalments.
Annuities are a type of insurance in which a portion of the money is paid each year to ensure the future.
There are two kinds of annuities:
Single payment variable annuity - This annuity pays out at the end of each period for a set amount of time. Payments are made monthly, quarterly, semi-annually, or annually in this annuity.
Annuity due is the inverse of a single payment variable annuity in that payments are made at the start of each period.
In the given situation the annuity is single payment variable annuity because the investment is done each year for 5 years.
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What is the result of adding these two equations? 6 x + 2 y = − 2 3 x − 2 y = − 5 6x+2y 3x−2y =−2 =−5
Answer:
The result gives the equation: 9x = -7
solution: (-7/9, 4/3)
Step-by-step explanation:
6 x + 2y = − 2
and
3 x − 2y = − 5
add together
6x + 3x + 2y - 2y = -2 + -5
9x + 0 = -7
9x = -7
then x = -7/9
and y = -3x - 1:
y = -3*(-7/9) - 1
y = 7/3 - 1 = 4/3
solution: (-7/9, 4/3)
-----------------------------------------
6x+2y= -2 and 3x−2y =−5
6x + 3x + 2y - 2y = -2 + -5
An instructor reports that as the number of student interruptions during class decreases, student scores on in-class quizzes increase. Is this an example of a positive correlation or a negative correlation?
Answer:
Negative correlation
Step-by-step explanation:
In a negative correlation, as one variable increases, the other variable decreases, and as one variable decreases, the other variable increases. In positive correlation, as one variable increases, so does the other and as one variable decreases, so does the other.
In the given question, as the number of student interruptions during class decreases, student scores on in-class quizzes increase. So, this an example of a negative correlation.
6th grade math help if u can (:
Answer:
Failure
Step-by-step explanation:
A synonym is a word that has a similar or exact same meaning as another given word. The synonym for malfunction, would therefore, be failure.
Answer:
It is failure
Step-by-step explanation:
a malfunction is a computer error. also known as a failure
A multiple choice exam has ten questions. Each question has five possible answers, of which one is correct. Suppose that a student did not study for the exam and, as a result, they guess on every question so that the probability of answering any question correctly is 0.20. 19. What is the probability that the student answers exactly 4 questions correctly
Answer:
8.81% probability that the student answers exactly 4 questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A multiple choice exam has ten questions.
This means that [tex]n = 10[/tex]
The probability of answering any question correctly is 0.20.
This means that [tex]p = 0.2[/tex]
What is the probability that the student answers exactly 4 questions correctly
This is P(X = 4).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881[/tex]
8.81% probability that the student answers exactly 4 questions correctly
Find parametric equations and a parameter interval for the motion of a particle starting at the point ( 2 2,0) and tracing the top half of the circle x squared plus y squared equals 4 x2+y2=4 four four times. Find parametric equations for the particle's motion. Let the parameter interval for the motion of the particle be 0 less than or equals ≤t less than or equals ≤ 4 4 pi π.
Answer:
1. Parametrization: [tex](2\cos(t), 2\sin(t))[/tex] and [tex]t\in [0,\pi][/tex]
2. In case that [tex]t\in [0,4\pi][/tex], the desired parametrization is [tex](2\cos(\frac{t}{4}), 2\sin(\frac{t}{4}))[/tex]
Step-by-step explanation:
Consider the particle at the point (2,0) and the circle of equation [tex]x^2+y^2=4[/tex]. Recall that the general equation of a circle of radius r is given by [tex]x^2+y^2=r^2[/tex]. Then, in our case, we know that the circle has radius 2.
One classic way to parametrize the movement of a particle that starts at point (r,0) and moves in a counterclockwise manner over a circular path of radius r is given by the following parametrization [tex](r\cos(t),r\sen(t)), t\in [0, 2\pi][/tex]. Since, for all t we have that
[tex](r\cos(t))^2+(r\sin(t))^2 = r^2(\cos^2(t)+\sin^2(t)) = r^2[/tex]
If we want to draw only the upper half of the circle, we must have [tex] t\in[0,\pi][/tex].
So, with r=2 the desired parametrization is [tex](2\cos(t), 2\sin(t))[/tex] and [tex]t\in [0,\pi][/tex]. Recall that in this parametrization when t=0 the particle is at (2,0) and when t=pi the particle is at (-2,0).
In the case that we want the parameter s [tex]\in[0,4\pi][/tex] but keeping the same particle's motion, we must do a transformation. We know that if parameter t is in the interval[tex][0,\pi][/tex] we get the desired motion. Note that in this case we are multiplying this interval by 4. So, we have that s = 4t. If we solve for the parameter t, we get that t=s/4. Then, with the parameter s in the interval [tex][0,4\pi][/tex] we get the parametrization [tex](2\cos(\frac{s}{4}), 2\sin(\frac{s}{4}))[/tex] which is obtained by replacing t in the previous parametrization.
Note that since when [tex]s=4\pi[/tex] we have that [tex]t=\pi[/tex] and that when s=0, we have t=0, then the motion of the particle is the same (it changes only the velocity in which the particle moves a cross the path).
Parametric equations for the particle's motion are x(t) = 2cos(t) and y(t) = 2sin(t), with a parameter interval from 0 to 4π radians to trace the top half of the circle x2 + y2 = 4 four times.
Explanation:To find the parametric equations that describe the motion of a particle tracing the top half of the circle x2 + y2 = 4 four times, we start from the standard parametric equations for a circle with radius 2 centered at the origin: x(t) = 2cos(t) and y(t) = 2sin(t). Since the problem specifies the top half of the circle and repeats this motion four times, we adjust our parameter t to cover the desired motion from 0 ≤ t ≤ 4π.
The parametric equations for the particle's motion are then: x(t) = 2cos(t) and y(t) = 2sin(t) with the parameter interval of 0 ≤ t ≤ 4π. Here, the parameter t represents the angle of rotation in radians, where the values of t from 0 to π cover the upper semicircle and the values of t from π to 2π would cover the lower semicircle, which we're ignoring in this case. Our chosen interval ensures that the top half is traced four times.
Given the equation y = 3x - 4, what is the value of y when x = 4
Answer:
y=8
Step-by-step explanation:
y=3(4)-4
y=12-4
y=8
y = -7x -1
4x - 7y = 7
Answer:
(x, y) = (0, -1)
Step-by-step explanation:
Since we have an expression for y, it is convenient to substitute that into the second equation:
4x -7(-7x -1) = 7
4x +49x +7 = 7
53x = 0
x = 0
Substituting into the first equation gives ...
y = -7·0 -1
y = -1
The solution is (x, y) = (0, -1).
3x2 + x – 14 = 0 answer buy factoring
Answer:
x=-7, x=6
Step-by-step explanation:
[tex]3x^{2} +x-14=0\\(x+7)(x-6)=0\\x=-7, x=6[/tex]
For each part below, explain how the measure of the unknown angle can be found without using a protractor. Find the measure of angle D. *
To find the measure of an unknown angle like angle D without a protractor, one must apply geometric or trigonometric principles based on the angle's context, such as its relation to other angles and its placement within shapes. The original question lacks specific details about angle D, making it impossible to provide a precise method for its calculation.
Explanation:To find the measure of angle D without a protractor involves understanding the geometric or trigonometric principles applicable to the given situation. For instance, if angle D forms part of a straight line with another angle, the sum of both should be 180° due to the Linear Pair Postulate. In a triangle, knowing the measurements of two angles allows us to find the third, as the interior angles of a triangle always sum up to 180°. Additionally, if angle D is part of more complex figures like parallelograms, circles, or involves trigonometric functions, equations and properties specific to those shapes or functions can be used. For example, in trigonometry, the sine and cosine rules could help find unknown angles given certain side lengths or other angles.
Unfortunately, the original question does not provide enough context or specific details about angle D, such as its relation to other angles, its placement within geometric shapes, or any other condition that could determine its calculation method. Without this information, we cannot provide a step-by-step method to calculate angle D specifically.
a. As all the angles are 60° So, It is an equilateral triangle.
b. As all the angles are 30°, 60° and 90° So, It is an equilateral triangle.
Given:
Two figures are given with some given angle x and y
To find:
The measure of the unknown angles
Let the points are A B and C in this given figure
At point, A of the triangle exterior angle of the triangle is equal to the
the interior angle which is equal to x [by the vertically
opposite angle]
∴ ∠BAC = x
At point B of the triangle also exterior angle of the triangle is equal to the interior angle which is equal to x [by the vertically opposite angle]
∴ ∠ABC = x
At point C angle Y is equal to Angle X by the property of vertically opposite angle
∴ ∠ACB = x
By the sum of angle of triangle property
∠ACB+∠ABC+∠BAC = 180°
x+x+x = 180°
3x = 180°
x = 60°
As all the angles are 60° So, It is an equilateral triangle
In part b
2x +3x +x = 180 ° [angle of a straight line is 180°]
6x = 180 °
x = 30°
By x=30 placing find all the angles
2x= 2 x 30 = 60°
3x= 3 x 30 = 90°
HELP DUE TODAY a bag contains 40 slips of paper numbered 1-40 if one is chosen randomly what is the probability of not choosing a multiple of five
Answer:
80% probability of not choosing a multiple of five
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes:
In this problem, we have that:
There are 40 numbers between 1 and 40.
Multiples of 5 are: 5,10,15,20,25,30,35,40
So there are 8 numbers that are multiple of 4 and 40-32 = 8 which are not multiples of five.
So
32/40 = 0.8
80% probability of not choosing a multiple of five
Answer: the probability of not choosing a multiple of five is 0.8
Step-by-step explanation:
Probability is expressed as the ratio of the number of favorable outcomes to the total number of outcomes.
In this scenario, the total number of outcomes is 40. The multiple of 5 between 1 to 40 are 5, 10, 15, 20, 25, 30, 35, 40. The total numbers that are multiples of 5 is 8. The total numbers that are not multiples of 5 is 40 - 8 = 32
Therefore, the number of favorable outcomes is 32
Probability = 32/40 = 0.8
The equation for a circle is (x + 2)2 + (y – 5)2 = 9. What is the radius of the circle? What is the x-coordinate of the circle’s center? What is the y-coordinate of the circle’s center?
Answer:
x-coordinate of the circle's center = -2
y-coordinate of the circle's center = 5
Radius = 3
Step-by-step explanation:
Look at the picture
Answer:
What is the radius of the circle? 3
What is the x-coordinate of the circle’s center? -2
What is the y-coordinate of the circle’s center? 5
Step-by-step explanation:
A plant is already 52 centimetres tall and it will grow one centimetre every month. The Plant's height, H (in centimetres), after M month is given by the following function: H (m) = 52+m What is the plant is height in 15 month?
9514 1404 393
Answer:
67 cm
Step-by-step explanation:
Put 15 where m is and do the arithmetic.
H(15) = 52 +15 = 67
The plant's height in 15 months is modeled as being 67 cm.
HELPP PLEASE!!!!
The following diagram shows the graph of a function
Answer:
The equation of the line is [tex]f\left(x\right)=-\frac{1}{9}x^{2}+1.8[/tex]
Step-by-step explanation:
I graphed the equation on the graph below and found the equation of the line.
If this answer is correct, please make me Brainliest!
Graphing the function [tex]\(f(x) = -\frac{1}{9}x^2 + 1.8\)[/tex] involves identifying the vertex, axis of symmetry, and plotting key points by selecting suitable x-values.
To graph the quadratic function [tex]\(f(x) = -\frac{1}{9}x^2 + 1.8\)[/tex], start by finding the vertex.
The vertex form [tex]\(f(x) = a(x - h)^2 + k\)[/tex] helps identify it, where \((h, k)\) is the vertex.
Here, [tex]\(a = -\frac{1}{9}\)[/tex].
The x-coordinate of the vertex is given by [tex]\(h = -\frac{b}{2a}\)[/tex] from the standard quadratic form [tex]\(ax^2 + bx + c\)[/tex], and [tex]\(b = 0\)[/tex] here since [tex]\(f(x)\)[/tex] has no linear term. So, [tex]\(h = 0\)[/tex]. Thus, the vertex is at [tex]\((0, 1.8)\)[/tex].
Next, find the axis of symmetry, which passes through the vertex. The axis of symmetry is the vertical line [tex]\(x = h\)[/tex], so in this case, [tex]\(x = 0\)[/tex].
To plot additional points, choose x-values on either side of the axis. Calculate corresponding y-values using the function.
For instance, when [tex]\(x = 3\)[/tex], [tex]\(f(3) = -\frac{1}{9}(3)^2 + 1.8\)[/tex], which equals [tex]\(1.3\)[/tex]. Repeat this process for a few more x-values.
Plot the vertex, axis of symmetry, and other points on a coordinate plane.
The resulting graph is a downward-opening parabola with the vertex as the highest point.
Label the axes, points, and use arrows to indicate the direction of opening.
This visual representation provides insight into the behavior of the function for different x-values.
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A clown is shot out of cannon with a velocity of 200 feet per second at an angle of 24°
with the horizontal. Find the vertical and horizontal components of the velocity of this clown.
Answer:
Vertical component of velocity is [tex]81.35 ft/sec.[/tex]
Horizontal component of velocity is [tex]182.6 ft/sec[/tex].
Step-by-step explanation:
Horizontal component of velocity is defined as:
[tex]v_{x} = v\times cos\theta[/tex]
Vertical component of velocity is defined as:
[tex]v_{y} = v\times sin\theta[/tex]
Where [tex]v_{x} , v_{y}[/tex] are the horizontal and vertical components of velocity.
[tex]v[/tex] is the actual velocity and
[tex]\theta[/tex] is the angle with horizontal axis at which the object was thrown.
Here, we are provided with the following:
[tex]v = 200 ft/sec[/tex]
[tex]\theta = 24^\circ[/tex]
[tex]v_{x} = 200 \times cos24^\circ\\\Rightarrow 200 \times 0.913\\\Rightarrow v_{x} = 182.6 ft/sec[/tex]
[tex]v_{y} = 200 \times sin24^\circ\\\Rightarrow 200 \times 0.407\\\Rightarrow v_{y} = 81.35 ft/sec[/tex]
So, Vertical component of velocity is [tex]81.35 ft/sec.[/tex]
Horizontal component of velocity is [tex]182.6 ft/sec[/tex].
Write inequalities to represent the situations below
The distance to the nearest exit door is no more than 150 feet.
Use d to represent the distance (in feet) to the nearest exit door.
To ride a roller coaster, a visitor must be taller than 60 inches.
Use h to represent the height (in inches) of a visitor able to ride.
Answer:
The distance to the nearest exit door is no more than 150 feet.
Use d to represent the distance (in feet) to the nearest exit door.
For this case we can create the following inequality based in the notation and condition given, when they says no more means that the possible value nees to be equal or lower than the specified value.
[tex] d \leq 150[/tex]
To ride a roller coaster, a visitor must be taller than 60 inches.
Use h to represent the height (in inches) of a visitor able to ride.
For this case we can create the following inequality based in the notation and condition given, when they says must be taller means that the possible value nees to be higher than the specified value.
[tex] h > 60[/tex]
Step-by-step explanation:
The distance to the nearest exit door is no more than 150 feet.
Use d to represent the distance (in feet) to the nearest exit door.
For this case we can create the following inequality based in the notation and condition given, when they says no more means that the possible value nees to be equal or lower than the specified value.
[tex] d \leq 150[/tex]
To ride a roller coaster, a visitor must be taller than 60 inches.
Use h to represent the height (in inches) of a visitor able to ride.
For this case we can create the following inequality based in the notation and condition given, when they says must be taller means that the possible value nees to be higher than the specified value.
[tex] h > 60[/tex]
Who can Helppppp me with mathh??
simplify: 2{10-5+x[1+3(6-2)]}
Answer:
10+26x
Step-by-step explanation:
To solve this, work your way from the inner most parentheses to the outer most:
The inner most parentheses is around 6-2, meaning you solve this first. When you solve this, you get 4.The second most inner parentheses is around (1+3 times 4) using PEMDAS, you first solve the multiplication, and then add. Once you solve this, you get 13.Next, the outer most parentheses is around (10-5+13x). When you simplify this, you get 5+13xFinally, you multiply 2(5+13x). Using distributive property, you get 10+26x as your final simplified answer.Which expression can be used to find the surface area of the following square pyramid
Answer:
[tex]36+15+15+15+15[/tex]
Step-by-step explanation:
For the surface area we need to add up all the areas in the pyramid:
area of the basearea of the triangle sides (there are 4 triangles)Area of the base:
the base is a square, and the area of a square is given by:
[tex]a_{base}=l^2[/tex]
where [tex]l[/tex] is the length of the side: [tex]l=6[/tex], thus:
[tex]a_{base}=(6)^2\\a_{base}=36[/tex]
Area of the triangles:
one triangle has the area given by the formula:
[tex]a_{triangle}=\frac{b*h}{2}[/tex]
where [tex]b[/tex] is the base of the triangle: [tex]b=6[/tex]
and [tex]h[/tex] is the height of the triangle: [tex]h=5[/tex], thus we have the following:
[tex]a_{triangle}=\frac{6*5}{2} \\\\a_{triangle}=\frac{30}{2} \\\\a_{triangle}=15[/tex]
the expression that represents the surface area of the pyramid is:
[tex]a_{base}+area_{triangle}+area_{triangle}+area_{triangle}+area_{triangle}[/tex]
substituting our values:
[tex]36+15+15+15+15[/tex]
which is option B
Answer:
Its Option C
Step-by-step explanation:
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 4 years of the actual mean with a confidence level of 95%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 25 years.
To estimate the mean age of the citizens in your community with a confidence interval of 95% and a margin of error of 4 years, you need a sample size of at least 25 citizens.
Explanation:To estimate the mean age of the citizens in your community with a confidence interval of 95% and a margin of error of 4 years, you need to determine the required sample size. The formula for sample size calculation in this case is:
n = (Z * σ / E)²
where:
n = required sample sizeZ = z-score for the desired confidence level (in this case, 1.96 for 95% confidence)σ = standard deviation of the population (given as 25 years)E = desired margin of error (in this case, 4 years)Substituting the values into the formula, we get:
n = (1.96 * 25 / 4)² = 3.8416 * 6.25 = 24.0101 ≈ 25
Therefore, you would need a sample size of at least 25 citizens to estimate the mean age of your community with a 95% confidence level and a margin of error of 4 years.
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150 citizens should be included in the sample to achieve the desired precision and confidence level.
The sample size required to estimate the mean age of the citizens within 4 years of the actual mean with a 95% confidence level, we can use the formula for the sample size in the context of a confidence interval for a population mean when the population standard deviation is known: [tex]\[ n = \left(\frac{z \sigma}{E}\right)^2 \][/tex]
where:
[tex]- \( n \)[/tex] is the sample size,
[tex]- \( z \)[/tex] is the z-score corresponding to the desired confidence level,
[tex]- \( \sigma \)[/tex] is the population standard deviation, and
[tex]- \( E \)[/tex] is the margin of error (half the width of the confidence interval).
Given:
[tex]- \( \sigma = 25 \)[/tex] years (population standard deviation),
[tex]- \( E = 4 \)[/tex] years (margin of error),
- Confidence level = 95% (corresponding to a z-score of 1.96 for a two-tailed test).
Plugging in the values:
[tex]\[ n = \left(\frac{1.96 \times 25}{4}\right)^2 \] \[ n = \left(\frac{49}{4}\right)^2 \] \[ n = (12.25)^2 \] \[ n \approx 149.0625 \][/tex]
Since we cannot have a fraction of a citizen in our sample, we round up to the nearest whole number:
[tex]\[ n = 150 \][/tex]
The sample size required is 150 citizens.
Trace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. Ten pairs of data were taken measuring zinc concentration in bottom water and surface water of a water source. Location Zinc concentration in bottom water Zinc concentration in surface water 1 .430 .415 2 .266 .238 3 .567 .390 4 .531 .410 5 .707 .605 6 .716 .609 7 .651 .632 8 .589 .523 9 .469 .411 10 .723 .612 Do the data support that the zinc concentration is less on the bottom than the surface of the water source, at the α = 0.1 level of significance? Note: A normal probability plot of difference in zinc concentration between the bottom and surface of water indicates the population could be normal and a boxplot indicated no outliers.
Answer:
There is enough evidence to support the claim that the zinc concentration is higher on the bottom than the surface of the water source.
Step-by-step explanation:
We have the data
Zinc conc. bottom water (X) | Zinc conc. in surface water (Y)
1 .430 .415
2 .266 .238
3 .567 .390
4 .531 .410
5 .707 .605
6 .716 .609
7 .651 .632
8 .589 .523
9 .469 .411
10 .723 .612
We can calculate the difference Di=(Xi-Yi) for each pair and calculate the mean and standard deviation of D.
If we calculate Di for each pair, we get the sample:
D=[0.015 0.028 0.177 0.121 0.102 0.107 0.019 0.066 0.058 0.111 ]
This sample, of size n=10, has a mean M=0.0804 and a standard deviation s=0.0523.
All the values are positive, what shows that the concentration water appearse to be higher than the concentration on the bottom.
We can test this with a t-model.
The claim is that the zinc concentration is greater on the bottom than the surface of the water source.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=0\\\\H_a:\mu> 0[/tex]
The significance level is 0.01.
The sample has a size n=10.
The sample mean is M=0.0804.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.0523.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.0523}{\sqrt{10}}=0.017[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.0804-0}{0.017}=\dfrac{0.08}{0.017}=4.861[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
This test is a right-tailed test, with 9 degrees of freedom and t=4.861, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>4.861)=0.00045[/tex]
As the P-value (0.00045) is smaller than the significance level (0.01), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the zinc concentration is greater on the bottom than the surface of the water source.
To determine if the zinc concentration is less on the bottom than the surface of the water source, a paired t-test can be performed. The t-test helps to compare the mean difference in zinc concentrations between the bottom and surface water. By comparing the calculated t-value with the critical t-value at the α = 0.1 level of significance, we can determine if the data supports the hypothesis.
Explanation:To determine if the zinc concentration is less on the bottom than the surface of the water source, we can perform a hypothesis test. We'll use a paired t-test since we have paired data. We want to test if there is a significant difference between the bottom and surface zinc concentrations.
First, we need to state our null and alternative hypotheses:Null hypothesis (H0): The mean difference in zinc concentrations between the bottom and surface water is 0.Alternative hypothesis (H1): The mean difference in zinc concentrations between the bottom and surface water is less than 0.Next, we calculate the differences between the bottom and surface zinc concentrations for each pair of data.Then, we calculate the mean and standard deviation of the differences.Using the paired t-test formula, we calculate the t-value.Finally, we compare the calculated t-value with the critical t-value at the α = 0.1 level of significance. If the calculated t-value is less than the critical t-value, we reject the null hypothesis and conclude that the zinc concentration is indeed less on the bottom than the surface of the water source.Learn more about Hypothesis Testing here:https://brainly.com/question/34171008
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If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?
3 lines intersect to form 6 angles. From top left, clockwise, the angles are 1, 2 (90 degrees), 3, 4, 5, 6.
6 degrees
24 degrees
66 degrees
90 degrees
Answer:
b 24
Step-by-step explanation:
The measure of angle 3 is 24 degrees. The correct answer would be an option (B).
What are complementary angles?The complementary angles are defined as when pairing of angles addition to 90° then they are called complementary angles. There are two types of supplementary angles.
Given that the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees
Here, the pairing of angles sums up to 90° then they are called complementary angles.
11x + 4x = 90
15x = 90
x = 90/15
Apply the division operation, and we get
x = 6
So, angle 3 is 4 × 6 = 24 degrees
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