The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is 116.
Given margin of error of 2,probability of 0.95 and standard deviation is 11.
We have to calculate the sample size needed to provide a margin of error of 2 or less with a 0.95 probability when the population standard deviation of 11.
We know that the margin of error is the difference between the calculated values and actual values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is z value ,σ is standard deviation ,n is the sample size.
First we have to calculate the z value for the corresponding p value which is given of 0.95. We assume that the test is two tailed. z value is 1.96.
Now put the value of z , σ, n and margin of error in the formula of margin of error to get the value of n which is sample size.
2>=1.96*11/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]>=(1.96*11)/2
[tex]\sqrt{n}[/tex]>=10.78
By squaring both sides we get,
n>=116.2064
Hence the sample size which is needed to provide a margin of error of 2 or less with a 0.95 probability when the population standard deviation equals 116.
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4% of ? Is $75 what is ? If the question
Answer:
1750
Step-by-step explanation:
Label the vertices and all the elements needed. find x. give reasons!
The value of x which is the missing angle of the triangles is; x = 30°
How to find the missing angles of a triangle?We know that Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
Thus, if we label the vertex with the unknown angle in the smaller triangle as A, then by the alternate angle theorem, we can say that;
∠A = 2x
Thus, from sum of angles in a triangle equals to 180°, we can say that;
x + 2x + 90 = 180
3x + 90 = 180
3x = 180 - 90
3x = 90
x = 90/3
x = 30°
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what’s the answer??? Pls help asap this is due tonight
Answer:
30
Step-by-step explanation:
[tex]5(3) - 3( - 5)[/tex]
[tex]15 + 15[/tex]
[tex]30[/tex]
hope it was helpful. any confusion u may ask
Step-by-step explanation:
The answer is 30 the value of X and y is given that put them in 5x-3y
(LOOK AT IMAGE)
The sides of a regular 12-sided polygon have been extended to make a star, as shown below.
Calculate the size of angle x.
Give your answer in degrees (°).
Answer: 120
Step-by-step explanation:
The interior angle of the 12-sided polygon is
[tex]\frac{180(12-2)}{12}=150^{\circ}[/tex]
So, if we consider the triangle with angle x, two of its angles are each [tex]30^{\circ}[/tex] since they are supplementary to the interior angle of the 12-sided polygon.
Therefore, as angles in a triangle add to 180 degrees, x=120.
Consider the function.
Match each transformation of f(x) with its description.
stretches f(x) by a factor
of 4 away from the x-axis
shifts f(x) 4 units down
shifts f(x) 4 units right
compresses f(x) by a factor
of toward the y-axis
The correct options are:
a) g(x) = 8*x - 6
b) g(x) = 2x - 10
c) g(x) = 2x - 14
d) g(x) = 8x - 24
How to identify each transformation?Here we have the function:
f(x) = 2x - 6
The proposed transformations are:
a) Stretch by a factor of 4 along the x-axis.
A horizontal stretch of scale factor k is written as:
g(x) = f(x*k).
Then, in this case, we have:
g(x) = 2(x*4) - 6 = 8*x - 6
b) Shift f(x) 4 units down.
A vertical shift of N units is written as:
g(x) = f(x) + N
A shift of 4 units down is written as:
g(x) = f(x) - 4 = 2x - 6 - 4 = 2x - 10
c) Shift f(x) 4 units right.
An horizontal shift of N units is written as:
g(x) = f(x + N).
For a shift of 4 units to the right, we write:
g(x) = f(x - 4) = 2(x - 4) - 6 = 2x - 8 - 6 = 2x - 14
d) A vertical compression of scale factor 1/4.
A vertical compression of scale factor K is written as:
g(x) = f(x)/K
In this case, we will have:
g(x) = f(x)/(1/4) = 4*f(x) = 4*(2x - 6) = 8x - 24
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What is the measure of Angle D F E?
Answer:
Could you please put a picture of the problem?
Step-by-step explanation:
We don't know what you are trying to solve.
Simplify the following expressions.
The simplified expression for the following expression are:
7a + 3a - 2a + 5a = 13a0.7 - 0.3g - 0.02g + 5 = 5.7 - 0.32g5g² + 3g - 4g + 5g² = 10g² - gSimplification7a + 3a - 2a + 5a
= 15a - 2a
= 13a
0.7 - 0.3g - 0.02g + 5
= 5.7 - 0.32g
5g² + 3g - 4g + 5g²
= 10g² - g
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Please help!! I have been stuck on this question for a while
Answer:
[tex]180\ in.^2[/tex]
Step-by-step explanation:
The area of a rectangle can is defined as [tex]A = wl[/tex] where w is the width and l is the length. The width in this case is 12 and the length is 15. Also it doesn't really matter what order you put it in. This gives you an area of [tex](15\ in.) (12\ in.) = 180\ in.^2[/tex]
i will give brainlyest if you write it in complete sentences and if correct , fr
Answer:
Search it up ok ,that's all you can do
How would you describe a transformation to someone who has never taken geometry before? Explain what a transformation is, and state how a transformation can be used to solve a problem in real life.
Transformation is the movement of a point from its initial location to a new location. Dilation can be used to scale down a map so that it can be plotted on a paper.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
Dilation can be used to scale down a map so that it can be plotted on a paper.
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A diagonal matrix has the elements shown below.
211 = 16
a22-8.7
233= 5.4
a44 1.3
255=-6.9
Which is the diagonal matrix containing these elements?
16 -3.7 6 1.7 -8.8
0
-8.7 -4.14 1 7
0
0
5.4 -9 -3
0
0
0
1.3 5
0
0
0
0 -6.9
The diagonal matrix that has these values would be:
16 0 0 0 0
0 -8.7 0 0 0
0 0 5.4 0 0
0 0 0 1.3 0
0 0 0 0 -6.9
What is a diagonal matrix?This is the type of matrix that is written in the form where all of the entries that are outside the diagonal are zeros.
The diagonal is a line that divides a triangle into two halves. The diagonal here has all of the digits. Outside it are all zero elements.
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Answer:
C is the correct answer
Explanation:
Hope you have a great day!
The graph of the quadratic function
g(x) = x² + 4 is shown.
17
8
gix
2
Domain:
Range:
7
T
O
For
The range of the given quadratic function is from x(-4,0 ) y(0,4 ) to x(4,0).
What is the range?
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. The domain of the function is defined as the set of all the possible values of the function.
Here in the graph of the function g(x) = ( -1/4)x + 4 the range of the function is from ( -4,0 ) to (4,0) at x-axis and ( 0,4) to y-axis we can see in the graph.The domain of the function is defined as the set of all the possible values of the function.
Therefore the range of the given quadratic function is from x(-4,0 ) y(0,4 ) to x(4,0).
The complete question is given below:-
what is the range and domain of the function g(x) = ( -1/4)x + 4?
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The functions f(x) and g(x) are described using the following equation and table:
f(x) = −4(1.09)x
x g(x)
−4 −10
−2 −7
0 −4
2 1
Which equation best compares the y-intercepts of f(x) and g(x)?
The value of the y-intercepts of f(x) and g(x) is f(0), g(0) which gives -4.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The y intercept of an equation is the value of the function when x = 0.
Given that f(x) = -4(1.09)ˣ
f(0) = -4(1.09)⁰ = -4
From the table of g(x), when x = 0, g(0) = -4
The value of the y-intercepts of f(x) and g(x) is f(0), g(0) which gives -4.
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there are three brothers amir balu and caleb. Amirs age is half of calebs and balus age is 3/4 of calebs. In five years the sum of Amir's age and Balus age will be 16 more than Calebs age How old is each brother now.
The age of the brothers Caleb, Amir and Balu is 44 years, 22 years, and 33 years respectively.
What is Equation?An equation is a mathematical statement with an 'equal to=' symbol between two expressions that have equal values.
Here, Let the age of the Caleb's be x years.
then age of Amir's be x/2 years.
also age of Balu's be 3x/4 years.
In 5 years,
Caleb's age = (x+5) years
Amir's age = (x/2 + 5) years
Balu's age = (3x/4 + 5) years
Now, According to question;
Amir's age + Balu's age = 16 + Caleb's age
(x/2 + 5) + (3x/4 +5) = 16 + (x + 5)
x/2 + 3x/4 - x = 16 + 5 - 5 - 5
(2x + 3x - 4x)/4 = 11
x/4 = 11
x = 4 X 11
x = 44
Now, Caleb's age = 44 years
Amir's age = 44/2 = 22 years
Balu's age = 3X44/4 = 33 years
Thus, the age of the brothers Caleb, Amir and Balu is 44 years, 22 years, and 33 years respectively.
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3 multiply by what is equal to 30 plus what
Call the hidden variable here "x"
3x = 30 + x
3x - (30 + x) = 0
3x - 30 - x = 0
2x - 30 = 0
x = 30 : 2 = 15
Recheck : 3 x 15 = 30 + 15 -> 45 = 45 (true)
What are the solutions of the equation x4 3x2 2 = 0? use u substitution to solve.
The solution of the equation is x=±i or x=±i√2.
Given that the equation is x⁴+3x²+2=0 and use u substitution method to solve.
We can rewrite our given equation as:
(x²)²+3x²+2=0
Let's assume that the (x²)=u.
The given equation is rewritten as u²+3u+2=0.
Factorize the quadratic equation by adding or subtracting two number that gives the sum of 3u and product 2u² as
u²+2u+u+2=0
u(u+2)+1(u+2)=0
Taking out (u+2) as common and get
(u+2)(u+1)=0
Compare each equation with 0 and get
u+2=0 or u+1=0
u=-2 or u=-1
Performing back substitution by substituting the values of u in x²
when u=-1 then x is
x²=-1
x=±√(-1)
As we know that √(-1)=i.
So, we get
x=±i
And when u=-2 then x is
x²=-2
x=±√(-2)
As we know that √(-1)=i.
So, substituting this, we get
x=±i√2
Hence, the solutions of the x⁴+3x²+2=0 is x=±i and x=±i√2.
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I need this done urgently!
Answer:
1)65.9
2)326.6
3)13.6
4)8.0
Step-by-step explanation:
The trick is always to look at the number after the first decimal for rounding to 1 decimal place, if its above 5, you round it up to the next decimal; eg. 13.45 = 13.5 because the 5 will round it up,and if value below 5, you round it down; eg. 12.34 = 12.3 because the 4 is below 5 and the nearest 10th decimal is 3.
The following diagram represents all of the stages of a shrinking iceberg. The iceberg is circular, and when it started out, it had a radius of 100 feet. The iceberg shrank to a radius that was 75% of its original size every hour. Each circle in the drawing represents the size of the iceberg in each of the successive hours it was shrinking. Using this information, answer the questions having to do with the image:
a. Is this a geometric series or an arithmetic series? Explain why you chose this answer.
b. Describe the steps you would use to calculate the radius of the 6th circle.
c. Assuming this pattern continued forever, what would be the total length if you added all of the circles’ radii* together? Explain your answer.
A geometric progression is a sequence that involves a rate, causing a change in the subsequent values of the sequence with respect to the given rate.
The answers to the given question are as follows:
a. It is a geometric progression.
b. Radius of the 6th circle ≅ 23. 73 ft.
c. The total length, l, can be determined by: l = ∑0.75[tex]R_{i}[/tex], i = 1 to n.
Geometric progression involves a change in the subsequent values of a given sequence due to a rate. So considering the given question, the circular iceberg melts at a certain rate per hour. Thus its radius decreases at the given rate per hour.
a. Therefore it can be deduced that the question is on geometric progression.
b. To determine the radius of the 6th circle, the:
radius of the 1st circle = 100 ft
radius of the 2nd circle = 0.75 x 100
= 75 ft
radius of the t3rd circle = 0.75 x 75
= 56.25 ft
radius of the 4th circle = 0.75 x 56.25
= 42.1875 ft
radius of the 5th circle = 0.75 x 42.1875
= 31.640625 ft
radius of the 6th circle = 0.75 x 31.640625
= 23.73046875 ft
Thus the radius of the 6th circle is approximately 23. 73 ft.
c. Since the process is assumed to continue forever, let the number of hours required to be represented by n, and each radius of the iceberg be represented by R.
So then, we can say that the total length, l, of all the circles' radii is will be given by:
l = ∑0.75[tex]R_{i}[/tex], i = 1 to n
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Complete the equation of the line through (-6,-5)(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and (-4,-4)(−4,−4)left parenthesis, minus, 4, comma, minus, 4, right parenthesis.
Use exact numbers.
y=y=y, equals
Answer:
y = 1/2 x -2
Step-by-step explanation:
rise/run from (-6, -5) to (-4, -4) = 1/2
(rise 1, run 2)
meaning that slope (m) = 1/2
we can now rewrite our points in y=mx + b formatting:
y = mx + b
-5 = (1/2)(-6) + b
-4 = (1/2)(-4)+b
now, let's solve for b
-5 = (1/2)(-6) + b
-5 = -3 + b
-2 = b
-4 = (1/2)(-4)+b
-4 = -2 + b
-2 = b
So, the equation for our line is y = [tex]\frac{1}{2}[/tex] x- 2
hope this helps!! have a lovely day :)
Answer: y = 1/2x - 2
Step-by-step explanation: it’s right on khan academy (picture for proof)
Find the distance across the lake. Assume the triangles are similar.
Answer:
210
Step-by-step explanation:
70/5=L/15
70/5=14
14×15=L
L=210
Loralei's dance team wants to purchase new uniforms for their national dance competition. They will get 25% of their total cookie dough sales to add to the money they already raised in the car wash they held. Her team raised $356.00 during their car wash and sold a total of $2,973.00 in cookie dough. How much money will they have in total to spend on new uniforms?
The total money the dance team would have to spend on the new uniforms is $1099.25.
How much money would the dance team have?Percentage can be described as a fraction of an amount expressed as a number out of hundred.
Total amount = (25% of the amount raised at the sale) + amount raised during the car wash
$356+ ( $25% x $2,973) = $1099.25
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The function a(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid
a(b)=12
Which equation below represents the inverse function b(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
OA 4(a)-+9
O B. o(a)-4-6
OC (a)-1-9
OD. (a)-+6
Each container will be made of a material that costs $0.0015 per square inch. Explain how to determine the coat of each container. Then find the cost of Container b. Round to the nearest cent.
Answer:
Find total surface area. Multiply material unit cost by the total surface area.
Step-by-step explanation:
To find the cost of a container, you must first find the total surface area of the container. Then since you are given the unit cost for the material, you multiply the total surface are by the unit cost ($0.0015/in.²).
Area=
Help me please!! Thanks
The area of square LMNP is 50
What is a circle?A circle is the locus of points equidistant from a fixed point which is known as the center of the circle.
A circle is defined if the center and the radius is known.
Analysis:
Perimeter of a circle = 2πr
Given perimeter = 10π
2πr = 10π
2r = 10
r = 10/2 = 5
r = MO
so the diagonal of the square is actually the diameter of the circle = 5+5 = 10
To find the side, x of the square the diagonal and the sides form a right-angled triangle, by Pythagoras, [tex]10^{2}[/tex] = [tex]x^{2}[/tex] + [tex]x^{2}[/tex]
2[tex]x^{2}[/tex] = 100
[tex]x^{2}[/tex] = 100/2 = 50
Also area of square is [tex]x^{2}[/tex] = 50
In conclusion, the area of square LMNP is 50
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how many ways are there to distribute 11 identical candies between 4 children such that each child receives at least 2 candies
There are 15 / 2 ways to distribute 11 identical candies between 4 children such that each child receives at least 2 candies.
If we give child A four candies and so we were left with 9 candies.
In addition, we will take child A away from consideration to ensure he received exactly four candies, and thus we were left with 9 dots and 2 slashes, separating the 4 remaining distinct children.
So the possible ways are: (11 + 4 / 2) = (15 / 2).
Problem-solving is the act of defining a problem; determining the purpose of the trouble; figuring out, prioritizing, and selecting alternatives for an answer; and imposing a solution.
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The floor of a moving van is 3 ft off the ground. The ramp into the van is 14.5 feet and makes an angle with the ground. Which of the angle measures below is approximately the angle of elevation made with the angle of the ground and the ramp?
Answer:
SHould be 11.6 degrees
Find the measure of the reference angle for an 11 radian
radian angle.
Answer:
about 1.56637 radians ≈ 89.746°
Step-by-step explanation:
The reference angle in radians can be found by the formula ...
ref angle = min(mod(θ, π), π -mod(θ, π))
Equivalently, it is ...
ref angle = min(ceiling(θ/π) -θ/π, θ/π -floor(θ/π))×π
ApplicationWhen we divide 11 radians by π, the result is about 3.501409. The fractional part of this quotient is more than 1/2, so the reference angle will be ...
ref angle = (1 -0.501409)π radians ≈ 1.56637 radians ≈ 89.746°
__
Additional comment
For calculations such as this, you need to use the most accurate value of pi available. The approximations 22/7 or 3.14 are not sufficiently accurate to give good results.
Which exponential equation is equivalent to the logarithmic equation below 4^c=256
The following logarithmic equation is equivalent to the given exponential equation,
[tex]log_{4}(256) = c[/tex]
Computing the Equivalent Logarithmic Equation
The given exponential equation is,
[tex](4)^{c} = 256[/tex]
As per the fundamental properties of exponentiation, the logarithmic equivalent equation of any exponential equation has the same base as that in the corresponding exponential equation. Exponentiation refers to the act of raising a number to the power of another number.
In the exponential equation, [tex](4)^{c} = 256[/tex], $ is the base. So, the base in its equivalent logarithmic equation will also be 4.
The result of the exponential expression becomes the operand for the log.
Terms in a Logarithmic Equation
For the logarithmic equation, [tex]log_{4}(256) = c[/tex],
4 is called the base of the log. The variable 'c' is the logarithm of 256 to base 'a'.
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help me solve this thanks
Answer:
The amount after 6 years is $25,533.34.
Step-by-step explanation:
Use the formula f(t)=P(1+b)^t.
Plug in the information.
f(6)=18000(1+0.06)^6
Plug in 18000(1.06)^6 into calculator.
25,533.344020608.
Round to 2 decimal places.
25,533.34
The amount after 6 years is $25,533.34.
Hope this helps!
If not, I am sorry.
Triangle ABC has vertices A(–2, 3), B(0, 3), and C(–1, –1). Find the coordinates of the image after a reflection over the x-axis.
A’
B’
C’
The coordinates of the image after a reflection over the x-axis are A(-2,3) ,B(0,3), and (-1,1).
Given The coordinates of the triangle ABC are A(-2,3) B (0,3) and C(-1,-1).
We know that the coordinates of x axis used to be positive in first and fourth quadrant. The coordinates of y axis used to be positive in second and first quadrant. The coordinates of x axis are to be negative in second and third quadrant. The coordinates of y-axis used to be negative in third and fourth quadrant.
We have to reflect the triangle over x-axis so the values of y-axis needs to be positive. So we need to just convert the coordinates of y to positive numbers which will make the coordinates as under:
A (-2,3) will not change because it is already positive.
B(0,3) will not change as it is is also positive.
C(-1,-1) will change to (-1,1)
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Answer: a (-2,-3) b (0,-3) c (-1,1)
Step-by-step explanation: how is the other person verified if there wrong.