The 95% confidence interval for the mean is [3.23, 8.76].
What is the confidence of interval?
The confidence of interval of the mean is calculated as follows;
Confidence interval = σ ± (t-value x μ)
where;
σ is the sample meanμ is the standard errorThe standard error is calculated as follows:
μ = std / √n
μ = 5 / √15
μ = 1.29
Based on this value we will check the distrbution table, for the t-value of 95% confidence;
= 2.145.
Confidence interval = σ ± (t-value x μ)
= 6 ± (2.145 x 1.29)
= [3.23, 8.76]
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In the figure below, the segments HI and HJ are tangent to the circle centered at O. Given that OI = 3.9 and OH= 6.5, find HJ.
H
6.5
9
O
HJ = 0
X
Based on the figure, we can see that triangles OHJ and OIX are similar because they share the same angle at O and HI and HJ are tangent to the circle. Thus, we can set up the following proportion:
OH / OI = HJ / (HJ + 9)
Substituting the given values:
6.5 / 3.9 = HJ / (HJ + 9)
Cross-multiplying:
6.5(HJ + 9) = 3.9HJ
Distributing:
6.5HJ + 58.5 = 3.9HJ
Simplifying:
2.6HJ = -58.5
HJ = -22.5
However, this answer doesn't make sense in the context of the problem. Since HJ represents a length, it cannot be negative. Therefore, we need to re-examine our work.
Looking back at our proportion, we can see that the ratio of OH to OI is greater than 1, which implies that HJ is greater than 9. This makes sense since HJ is a chord of the circle and thus must be longer than the radius.
Let's try the problem again, but this time we'll rearrange the proportion to solve for HJ:
HJ / (HJ + 9) = OI / OH
Substituting the given values:
HJ / (HJ + 9) = 3.9 / 6.5
Cross-multiplying:
6.5HJ = 3.9HJ + 35.1
Simplifying:
2.6HJ = 35.1
HJ = 13.5
Therefore, HJ is equal to 13.5.
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer:
The second scatterplot does not suggest a linear relationship between x and y.
which statement about odd functions is correct?
Answer: C
Step-by-step explanation:
Think about y=[tex]x^{3}[/tex] This is an odd function because the highest exponent(degree) is odd
A. is wrong. Symmetry is where you can fold it and it would be the same. If i folded y=[tex]x^{3}[/tex] along the y- axis it would not be the same.
B is wrong. Transformations are where has it moved, which has nothing to do with odd functions in general
C. is correct. It is folded along y=x and flipped.
D. is wrong. If folded y=x it's in the same quadrant but it's not the same, its' reversed.
a + b = 10 a - b = 2 Solve the system of equations. Responses
The solution to the given system of equations is a = 6, b = 4.
The system of equations is given as follows:
a + b = 10 .....(i)
a - b = 2 .....(ii)
To solve this system of equations, we can use the method of elimination.
Adding the two equations, we get:
(a + b) + (a - b) = 10 + 2
2a = 12
a = 6
Substituting a = 6 into one of the equations, we get:
6 - b = 2
b = 4
Therefore, the solution to the system of equations is:
a = 6, b = 4.
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If I have 100 tiles and 98 are letters and 2 are blank I randomly drawl 2 title the first is a consonant and the 2 nd is a vowel what is the probability that both events will occur
The probability that both events will occur is 23.76%.
Given that, you have 100 tiles and 98 are letters and 2 are blank you randomly drawl 2 title the first is a consonant and the 2nd is a vowel.
Consonants (A) = 56
Vowels (B) = 42
Blank = 2
Total letters = 100
Two letters are drawn with replacement.
P(A) = 56/100 = 0.56
P(B) = 42/ (100-1) = 0.424
P(A).P(B) = 0.56*0.424 = 0.2376
Hence, the probability that both events will occur is 23.76%.
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Complete question is attached.
MODELING REAL LIFE A hemisphere-shaped mole has a diameter of 5.7 millimeters and a surface area of about
51 square millimeters. The radius of the mole doubles. Estimate the new surface area of the mole. Round your
answer to the nearest whole number.
The new surface area is square millimeters.
The new surface area of the hemisphere-shaped mole would be = 102mm².
How to calculate the new surface area for the hemisphere-shaped mole?A hemisphere-shaped mole has a shape that has one surface that is curved and the other surface a flat circular base.
Since the surface area of one hemisphere has been given, the second hemisphere can be determined.
To calculate the new surface area of the hemisphere-shaped moles the following is carried out;
Radius of the initial mole = 5.7/2 = 2.85 mm
If 2.85mm radius = 51 mm²
2(2.85mm) radius = x
Make X the subject of formula;
X = 2×2.85 × 51/2.85
= 102 mm²
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13.5.6 Check Your Understanding Complete the statements. The graph of y = (x + 3)² is a [DROP DOWN 1] of the graph y = C with the graph of y = (x+3)2, it is shifted [DROP DOWN 2] 3 units. When building a table of values to 2 For the graph y = X to coincide model the function y = (x+3)2, this shift can be found by [DROP DOWN 3] 3 to/from each [DROP DOWN 4] for each corresponding [DROP DOWN 5].
The graph of y = (x + 3)² is a transformation of the graph y = x². It is shifted left 3 units.
Describing the transformation of the functionsThe equation of the function is given as
y = x²
The transformed function is
y = (x + 3)²
This means that the parent function is y = x²
When compared, we can see that
x in y = x² is x + 3 in y = (x + 3)²
This means that y = x² is shifted left by 3 units to form y = (x + 3)²
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Anwer fast due tomorrow show work
Answer:45.3 miles/h
Step-by-step explanation
let 'x' be the speed of the car.
60 × 2/3 = 120/3 = 40
30 × 1/5 = 151/5
151/5 /40 = x / 60
151 / 200 = x / 60
=> x = (151×60) / 200
=> x = 45.3
Use the binomial theorem to find specified term of the given power of binomial ( remember that r starts at 0 in the binomial theorem so finding say the second term means that r=1)
The fourth term in the expanded form of (x - 1)⁶ is -20x³.
What is the fourth term in the expanded form of (x - 1)⁶?The fourth term in the expanded form of (x - 1)⁶ using the binomial theorem is calculated as follows;
The expanded form of (x - 1)⁶ using the binomial theorem is;
(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1
(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1
To find the fourth term, we look for the fourth term from the left side to right side, which is -20x³.
Therefore, the fourth term in the expanded form of (x - 1)⁶ is -20x³.
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A group of students was asked about the number of times they had been water-skiing. The data is shown in the histogram.
A histogram titled Water Skiing Trips. The x-axis is labeled Number of Times Water Skiing and has intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 6. There is a shaded bar for 6 to 10 that stops at 3, for 11 to 15 that stops at 5, for 16 to 20 that stops at 6, and for 21 to 25 that stops at 1. There is no shaded bar for the 1 to 5 interval.
Which of the following best describes the spread of the data?
Explain its meaning in this situation.
The data has a possible range of 19, which is a wide spread. This might mean that the most common number of water-skiing trips is 10.
The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.
The data has a possible range of 6, which is a narrow spread. This could mean that most of the students have taken a similar number of water-skiing trips.
The data has a range of 6, which is a narrow spread. This might mean that the most common number of water-skiing trips was 6.
Answer:
(b) The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.
Step-by-step explanation:
You want the best description of the spread of data shown in the histogram.
SpreadThe least data value that can be represented on the chart is 6. The greatest value the chart can represent is 25. This means the possible range of data values is ...
range = max - min = 25 -6 = 19
This possible spread of 19 might mean there is a large difference in the number of trips taken by students, choice B.
__
Additional comment
The range must be at least 21 -10 = 11 trips, not an answer choice. The most common number appears to be in the range 16-20, so will likely not be 10. (This is referred to as the "mode range", as we cannot tell from the grouped data what the actual mode is.)
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Which is a Function or
Not a function
The relation that is not a function is relation 3, and the other 3 are functions.
Which are functions and which aren't?A relation is a function if each point on its domain is mapped into a single point in the range.
So if you see an input that is mapped into two different outputs, then it is not a function.
Then the relation 3 is not a function, because h is mapped to different things, meaning that we have the same input being mapped to different outpouts. While the other 3 relations are all functions.
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Find (fog)(2).
f(x) = 3x + 2
g(x) = x²
(fog)(2)=
Answer:
(f·g)(2) = 14----------------------------
Find the composition of the functions f(x) and g(x), which is written as f(g(x)).
Given functions:
f(x) = 3x + 2,g(x) = x² .Find f(g(x)):
f(g(x)) = f(x²) = 3(x²) + 2Evaluate f(g(2)):
f(g(2)) = 3(2²) + 2 = 3(4) + 2 = 12 + 2 = 14So, (f·g)(2) = 14.
A cube has volume 3375 cubic inches. Determine the area of one face of the cube.
The area of one face of the cube that has a volume of 3375 cubic inches is: 225 square inches.
What is the Volume of a Cube?A cube has equal edge length, and therefore has faces with the same area. The formula for finding the volume of a cube is given as:
Volume of cube = s³, where s is the side length of the cube.
Also, to find the area of one face of a cube, we would use the formula below:
Area of one face of a cube = s².
Given the following:
Volume of a cube = 3375 cubic inches
Find s as shown below:
s = ∛3375
s = 15 inches.
Therefore, we have:
Area of one face of a cube = 15² = 225 square inches.
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Danielle deposited $300.00 into a new savings account that earns interest compounded continuously. After 8 years, the balance in the account
was $907.00. What was the interest rate on the account?
O 13.8%
O 12.5%
O 14.5%
O 10.1%
Calculate the area of the square
The area of the given rectangle is 83.6cm²
How to find the area of the shape?We know that the area of a rectangle is equal to the product between the dimensions, here we can see that:
b = 11cm
h = 7.6cm
The formula for the area is:
A = b*h
Replacing the values we will get:
A = 11cm*7.6cm = 83.6cm²
that is the area.
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A ribbon is lining the outside of a circular object. If the object has a radius of 7 cm, then how long should the ribbon be?
Answer:
Length= 43.98 cm
Step-by-step explanation:
Circumference=2πr
r=7cm
C=2π(7)
C=43.98 cm
circumference is equal to the length of ribbon along the outside of the circular object
Help me, please my friends. I need the assistance
The area of a rectangle is 14x² + 19x - 3 square units.
The degree of 4x² + 3y - 6x⁴y + 4 is 5.
The number of terms of 4x² + 3y - 6x⁴y + 4 is 4.
Adding, subtraction or multiplying two polynomials always results in another polynomial.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given parameters into the formula for the area of a rectangle, we have the following;
Area of rectangle = (7x - 1) × (2x + 3)
Area of rectangle = 14x² + 21x - 2x - 3
Area of rectangle = 14x² + 19x - 3 square units.
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i need help with this, please anyone I am so scared of failing. Please explain throughly,
thank you so much.
Check the picture below.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ triangle }{\cfrac{1}{2}(26)(17)}~~ + ~~\stackrel{ rectangle }{(26)(9)}}\implies 221+234\implies \text{\LARGE 455}[/tex]
write an equivilant fractions for 3 3/4 and 1 2/3 using a common denominator iready
The requried equivalent fraction for the equivalent fraction to 3 3/4 and 1 2/3, is 45/12, and 20/12.
To find a common denominator for 4 and 3, we can multiply them together to get 12.
So, we can convert 3 3/4 as:
3 3/4 = 12/4 + 3/4 = 15/4
Similarly, we can convert 1 2/3 as:
1 2/3 = 5/3
Therefore, the equivalent fractions for 3 3/4 and 1 2/3 using a common denominator of 12 are:
15/4 = 45/12 and 5/3 = 20/12
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A student said that to
write a percent as a fraction, write the
number that comes before the percent
symbol over a denominator of 100. Is the
student correct? Justify your conclusion.
Answer:
Step-by-step explanation:
Yes, the student is correct. To write a percent as a fraction, we can write the number before the percent symbol as the numerator and 100 as the denominator. For example, 25% can be written as 25/100, which can be simplified to 1/4. This is because percent means "per hundred," so 25% means 25 per hundred, which can be expressed as a fraction with a denominator of 100.
Quiz: Measures of Center and Spread
Question 1 of 10
If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B.
A. True
B. False
The given statement "If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B" is true.
The standard deviation is a measure of a data set's dispersion. It tells us how far the data values are from the mean.
A larger standard deviation means that the data points are more spread out, i.e., they are farther from the mean.
Therefore, if data set A has a standard deviation that is greater than data set B, it means that the values in data set A are more spread apart.
Hence, the given statement is true.
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given the expression (2^-3)(2^5)/2^7), select the three equivalent numerical expressions
The three equivalent numerical expressions are 1/32, 0.03125, 3.125 x 10^-2
How to simplify the numerical expressionsUsing the exponential rules, we can simplify the expressions as:
(2^-3)(2^5)/2^7)
= 2^(5-3)/2^7
= 2^2/2^7
= 1/2^(7-2)
= 1/2^5
= 1/32
Therefore, three equivalent numerical expressions for the given expression are: 1/32, 0.03125, 3.125 x 10^-2
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Which of the following choices is a linear function? NEED HELP ASAP!
Answer: f(x)=x-2
Step-by-step explanation:
Linear function means a straight line so graph each one to find which is a straight line
How would you describe what this transformation looks like when preformed on a coordinate plane
The description of function transformations and an example is highlighted below
Describing the transformation of the functionsTo describe the transformation of the functions, we need to identify the image and the preimage of the functions to be transformed
Take for instance the function is y = x² transformed to the function y = (x + 3)²
This means that the parent function is y = x²
When compared, we can see that
x in y = x² is x + 3 in y = (x + 3)²
This means that y = x² is shifted left by 3 units to form y = (x + 3)²
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I REALLY NEED THIS TO PASS SOMEONE PLEASE TRY AND HELP
solve this triangle. Round to the nearest tenth
Answer:
Im pretty sure its the third one
Step-by-step explanation:
It all depends on the square root to find the nearest tenth and rounding it all up.
2. The ramp above connects two vertical supports,
forming two similar triangles: AADE~ AABC. Side AC corresponds to which side in the other triangle?
Answer:
3. What is the length of side BC?
The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units
Side AC corresponds to which sideFor two triangles to be similar, the corresponding sides of the triangles must be in proportion
Having said that
The side AC corresponds to the side AC in the other triangle
What is the length of side BC?The length BC is calculated as
BC/9 = 25/15
Express as products
So, we have
BC = 9 * 25/15
Evaluate the products
BC = 15
Hence, the length of BC is 15 units
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which parent functions have a y-intercept at (0,0)? select all that apply
Answer: A,E or F.
Step-by-step explanation: That's the only ones that have X's and then x is 0
Which is NOT personally liable for any losses or damages? Group of answer choices Shareholders in a public corporation, Owner of a sole proprietorship, Shareholders in a corporation, Partners in a partnership
The option which is not personally liable for any losses or damages is Shareholders in a public corporation, the correct answer is A.
We are given that;
Four options of damages
Now,
Shareholders in a public corporation are not personally liable for any losses or damages caused by the corporation, because they have limited liability. This means that they can only lose the amount they invested in the corporation, and their personal assets are protected from creditors or lawsuits12.
Owner of a sole proprietorship, shareholders in a private corporation, and partners in a partnership are all personally liable for any losses or damages caused by their business activities, unless they have some form of liability insurance or protection12. This means that they can be sued for their personal assets if the business cannot pay its debts or obligations.
Therefore, by unitary method the answer will be Shareholders in a public corporation
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Evelyn has 36 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 154 square meters. List each set of possible dimensions (length and width) of the field.
The possible dimensions (length and width) of the field which is rectangle are (26m, 5m) or (5m, 26m) and (28m, 4m) or (4m, 28m)
Let's assume the length of the rectangle be L and the width be W.
We know that we have three sides of the rectangle to fence, so the total length of the fence will be L+2W = 36m.
Also, we know the area of the rectangle = L×W = 154 sq.m
Using the two equations above, we can solve for L and W as follows:
L = 36 - 2W (from the first equation)
Substituting this value of L in the second equation:
(36 - 2W)W = 154
2W² - 18W + 77 = 0
We get two possible values of width: W = 5 or W = 4
For W = 5, L = 26
For W = 4, L = 28
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Answer appreciated! :D
Answer:
5/2
Step-by-step explanation:
Slope is rise over run, or how far it goes in the y direction over how far it goes in the x direction. In this case, y increases by a value of 5 at the same time x is increasing by a value of 2. This makes the slope 5/2, and it is positive since the values are increasing. If there is a problem your stuck on like this try graphing the points, desmos has a good graphing calculator :)