Answers
The measure of the angle m∠RTS in the circle is drives to be equal to 105°.
What are angles on same segment of a circleAny two angles that have the same endpoint that lie on the same segment of the circle, that is the region between the chord joining the endpoints of the angle and the arc not containing the angle are said to be equal in measure.
Thus;
m∠QPT = m∠RST
so; m∠RST = 34°
Considering the triangle RST, we can solve for m∠RTS as follows:
m∠RTS = 180° - (34 + 41)° {sum of interior angles of a triangle}
m∠RTS = 180° - 75°
m∠RTS = 105°
Therefore, the measure of the angle m∠RTS in the circle is drives to be equal to 105°
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Related Questions
help please! (see picture
Answers
The function rule is solved and the equation is g ( x ) = 3x + 5
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = 3x + 5
On simplifying , we get
when x = { -2 , 0 , 1 , 3 , 4 }
Now , the values of y are given by
g ( -2 ) = 3 ( -2 ) + 5
g ( -2 ) = -1
g ( 0 ) = 5
g ( 1 ) = 8
g ( 3 ) = 14
g ( 4 ) = 17
Hence , the function is solved
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Which choice is equivalent to the quotient shown here when x > 0?
√22x6 = √11x4
Answers
Answer:
Option B
Step-by-step explanation:
sqrt(22x^6) / sqrt(11x^4) = sqrt(2x^2)
sqrt(2x^2) can be rewritten as x sqrt(2)
(HELP) The lengths of the red drum species of fish are approximately Normally distributed, with a mean length of 24 inches and a standard deviation of 1.4 inches. What proportion of red drum fish are less than 23 inches in length?
Find the z-table here.
0.1587
0.2389
0.2709
0.7611
Answers
The proportion of red drum fish are less than 23 inches in length is 0.2389. So, correct option is B.
To solve this problem, we need to standardize the value of 23 inches using the given mean and standard deviation of the red drum fish length distribution. This is done by calculating the z-score using the formula:
z = (x - μ) / σ
where x is the value we want to standardize (in this case, 23 inches), μ is the mean of the distribution (24 inches), and σ is the standard deviation of the distribution (1.4 inches).
Substituting these values, we get:
z = (23 - 24) / 1.4 = -0.71
Using the z-table, we can find the proportion of the distribution that is less than -0.71, which is the same as finding the proportion of the distribution that is less than 23 inches. From the z-table, we find that the proportion is 0.2389. Therefore, approximately 23.89% of red drum fish are less than 23 inches in length.
So, correct option is B.
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PLEASE HELP
Show 2 different ways to find the value of x. What do you think is the most efficient method? Explain why?
Answers
The value of x is,
⇒ x = 8
Given that;
In a triangle,
Perpendicular = 4 feet
Hypotenuse = x
Hence, We can formulate;
⇒ cos 60 = 4 / x
⇒ 1/2 = 4/x
⇒ x = 8
Thus, The value of x is,
⇒ x = 8
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A store is selling a shirt in two different states. The shirt retails for $45.
In Florida, the sales tax is 6.5%. In Alaska, it is 4.5%. How much more
would it cost for you to buy the shirt in Florida?
Answers
well, let's find out how much will it be in each state.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.5\% of 45}}{\left( \cfrac{6.5}{100} \right)45} ~~ \approx ~~ \stackrel{ \textit{tax in Florida} }{2.93} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{4.5\% of 45}}{\left( \cfrac{4.5}{100} \right)45}~~ \approx ~~ \stackrel{ \textit{tax in Alaska} }{2.03}\hspace{5em}2.93-2.03~~ \approx ~~ \text{\LARGE 0.90}[/tex]
Take an angle θ and position it in a coordinate system so that its vertex is at the origin and one of its sides is on the positive x-axis. If P(-3,4) is a point on the second side of the angle, what is the value of sin θ + cot θ?
Answers
θ = - sin^-1(4/3)
θ = -1.18 radians
Now we have the value of θ, -1.18 radians.sin θ = sin(-1.18) = -0.8cot θ = cos(-1.18) / sin(-1.18) = -0.9104Therefore:
sin θ + cot θ = -0.8 + -0.9104 = -1.7104
So the final answer is:
-1.7104
Does this make sense? Let me know if you need more details!
15. AABC and ADEF are similar. If m2B = 62°, then m
B
A
C
E
D
F
Answers
If ∆ABC and ∆DEF are similar and angle B is 62° then angle E is also 62°
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary.
These are some of the rules that let us know if two triangles are similar.
1. The corresponding angles of similar triangles are congruent i.e they are equal
2. The ratio of the corresponding sides of similar triangles are equal.
With these rules, it shows that;
angle C = angle F
angle A = angle D
angle B = angle E
Therefore if angle B = 62°, then angle E is also 62°.
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what is the answer ?
Answers
The Newton-Raphson formula to compute the square root of a > 0 is [tex]x_{i+1} = x_i - \frac{x_i - a}{2x_i}[/tex]
Finding the Newton-Raphson formula to compute the square root of a > 0From the question, we have the following parameters that can be used in our computation:
The list of options
Generally, the Newton-Raphson formula for a > 0 is
[tex]x_{n+1} = \frac{1}{2}(x_n + \frac{a}{x_n})[/tex]
Substitute i for n
So, we have
[tex]x_{i+1} = \frac{1}{2}(x_i + \frac{a}{x_i})[/tex]
When expanded, we have
[tex]x_{i+1} = x_i - (\frac{x_i - a}{2x_i})[/tex]
Remove brackets
So, we have
[tex]x_{i+1} = x_i - \frac{x_i - a}{2x_i}[/tex]
Hence, the solution is [tex]x_{i+1} = x_i - \frac{x_i - a}{2x_i}[/tex]
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In a class of 25 students, 7 students each have 2 brothers or sisters. 4 students each have 1 brother or sister. 3 students each have 0 brothers or sisters. 6 students each have 3 brothers or sisters. The rest of the students each have 4 brothers or sisters. The students make a line plot showing the numbers of brothers and sisters. Part A Use the drop-down menus to make the statement true. The scale of the line plot should have Choose... as its least data value and Choose... as its greatest data value. Part B Use the drop-down menus to make each of the statements about the number of dots true. There will be Choose... dot(s) above 1. There will be Choose... dot(s) above 4. There will be 3 dots above Choose... . 3 / 6 2 of 6 Answered
Answers
Step-by-step explanation:
Part A
There are 25 students in the class, and the least number of brothers or sisters is 0, so the least data value on the line plot should be 0. The greatest number of brothers or sisters is 4, so the greatest data value on the line plot should be 4.
Part B
There are 7 students with 2 brothers or sisters, so there will be 7 dots above 2. There are 4 students with 1 brother or sister, so there will be 4 dots above 1. There are 6 students with 3 brothers or sisters, so there will be 6 dots above 3. There are 3 students with 4 brothers or sisters, so there will be 3 dots above 4.
Therefore, the correct answers are:
Least data value: 0
Greatest data value: 4
Dots above 1: 4
Dots above 4: 7
Dots above 3: 6
The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 681 drowning deaths of children with 30% of them attributable to beaches.
3.01
2.85
–3.01
–2.85
Answers
To test the claim, we need to conduct a hypothesis test with the null hypothesis being that the proportion of drowning deaths of children attributable to beaches is 0.25 and the alternative hypothesis being that it is more than 0.25.
Using a one-sample z-test with a significance level of 0.05, we can calculate the test statistic as:
z = (0.3 - 0.25) / sqrt(0.25 * 0.75 / 681) = 3.01
Since the alternative hypothesis is that the proportion is greater than 0.25, we need to find the area to the right of the test statistic in the standard normal distribution.
Using a standard normal table or calculator, we can find the p-value to be approximately 0.0013.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the proportion of drowning deaths of children attributable to beaches is more than 0.25.
Therefore, the answer is 3.01.
(c) Find four numbers that fit all the rules:
The median is 5
The mode is 5
The range is 1
Answers
1. The median is 5: Since we have four numbers, the median is the average of the two middle numbers. Let's call the two middle numbers x and y. Then, we have:
(x + y) / 2 = 5
2. The mode is 5: The mode is the number that appears most frequently. Since 5 is the mode, at least two of the four numbers must be 5. Let's say that the other two numbers are a and b.
3. The range is 1: The range is the difference between the largest and smallest numbers. Since the range is 1, we have:
max(x, y, a, b) - min(x, y, a, b) = 1
Now we can use these equations to solve for the four numbers:
From equation 1, we have:
x + y = 10
From equation 2, we know that two of the numbers are 5. Without loss of generality, let's assume that x = 5 and y = 5. Then, from equation 1, we have:
5 + 5 = 10
So, we still have:
a + b = 0
From equation 3, we know that the largest number minus the smallest number is 1. Since we have two 5's, either a or b must be the smallest number, and the other must be the largest number. Without loss of generality, let's assume that a is the smallest number and b is the largest number. Then, we have:
b - a = 1
Substituting x = 5 and y = 5 into the first equation, we get:
5 + 5 + a + b = 10
a + b = 0
So, we have:
b = -a
Substituting b = -a into the third equation, we get:
(-a) - a = 1
-2a = 1
a = -1/2
b = -a = 1/2
Therefore, the four numbers that fit all the rules are:
-1/2, 5, 5, 1/2.
(08.07 MC)
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at 2 comma 16, a point at negative 2 comma 0, a point at 6 comma 0, a point at 0 comma 12, and a point at 4 comma 12.
What is the standard form of the equation of f(x)?
f(x) = x2 + 4x + 12
f(x) = x2 − 4x − 12
f(x) = −x2 + 4x + 12
f(x) = −x2 − 4x − 12
Points earned on this question: 0
Answers
The function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.
What is function?Function is a set of instructions or statements that perform a specific task or calculation. It is a fundamental building block of a program, allowing the same code to be used multiple times. Functions help to organize code and make it easier to read and debug. They also allow for code reuse, meaning that the same code can be used in different parts of the program. Additionally, functions can be used to create libraries of code that can be shared and reused among different programs.
A function f(n) that represents the nth term of the sequence given above can be written as follows:
f(n) = 2n – 2
This function can be explained as follows:
The function f(n) represents the nth term of the given sequence. The first term of the sequence is 0, which is equal to f(1). The second term of the sequence is 2, which is equal to f(2). This pattern can be seen throughout the sequence, as each subsequent term is two more than the preceding one. Thus, the general form of the function can be written as f(n) = 2n – 2, where n represents the nth term of the sequence.
For example, when n = 5, the function f(n) = 2n – 2 = 10. This is equal to the fifth term of the sequence, 8.
Therefore, the function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.
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The standard form of the equation of f(x) is f(x) = -x² + 4x + 12
Equation of a Parabola:
The standard form of the equation of a parabola is:
y = a(x - h)²+ k
Where (h, k) is the vertex of the parabola and a determines whether the parabola opens up or down.
If a is positive, the parabola opens up, and if a is negative, the parabola opens down. The value of 'a' also determines the "steepness" of the parabola.
Here we have the function f(x) shows a graph.
The graph shows a downward opening parabola with a vertex at (2, 16) a point at (-2, 0) a point at (6, 0) a point at (0, 12), and a point at (4, 12)
The vertex of the parabola is at (2, 16), which means that the axis of symmetry is x = 2. This also tells us that the equation is of the form:
f(x) = a(x - 2)² + 16
Where "a" is a constant that determines whether the parabola is upward or downward opening.
We can find the value of "a" by using one of the other points on the graph. Let's use the point (0, 12):
=> 12 = a(0 - 2)² + 16
=> -4 = 4a
=> a = -1
So the equation is:
f(x) = -(x - 2)² + 16
Expanding and simplifying this equation gives:
f(x) = -x²+ 4x + 12
Therefore,
The standard form of the equation of f(x) is f(x) = -x² + 4x + 12
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A circular plate has a radius of 7 inches. Which is closest to the area of the plate?
Answers
Answer:
Approximately [tex]153.94[/tex] [tex]in^2[/tex]
Step-by-step explanation:
Recall the formula for the area of a circle:
[tex]\pi r^2[/tex]
Where r is the radius.
We are given that the radius is 7 inches. Let's plug that into our formula and solve it. We have:
[tex]\pi r^2=\\\pi (7)^2=\\\pi (49)=\\49\pi[/tex]
From here, we multiply our answer by pi using a calculator and round.
Using a calculator, we can find that [tex]49\pi[/tex] is approximately 153.93804 (round to the nearest hundredth: 153.94)Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(5m^3n^3)^2/n
Answers
The simplified form of expression [tex]\frac{(5m^3n^3)^2}{n}[/tex] is [tex]25m^6n^5[/tex]
Consider the expression [tex]\frac{(5m^3n^3)^2}{n}[/tex]
We know that the exponent rule that [tex](a\times b)^m=a^m \times b^m[/tex]
and [tex](a^m)^n=a^{m\times n}[/tex]
where a, b, m and n real numbers.
Consider the numerator of above expression.
[tex](5m^3n^3)^2[/tex]
Using the rule [tex](a\times b)^m=a^m \times b^m[/tex] ,
[tex](5\times m^3\times n^3)^2\\\\= 5^2\times (m^3)^2\times (n^3)^2\\[/tex]
We know that the square of 5 is 25
so, 5² = 25
Now we use the rule [tex](a^m)^n=a^{m\times n}[/tex]
so, above expression becomes,
[tex]5^2\times (m^3)^2\times (n^3)^2\\\\=25\times m^{3\times 2}\times n^{3\times 2}\\\\=25\times m^6 \times n^6[/tex]
Also, we know that inverse of any value can be written as [tex]\frac{1}{a} =a^{-1}[/tex]
So, using this rule of exponent the value of 1/n would be [tex]n^{-1}[/tex]
So, the expression [tex]\frac{(5m^3n^3)^2}{n}[/tex] becomes,
[tex]\frac{(5m^3n^3)^2}{n}\\\\=\frac{25\times m^6 \times n^6}{n}\\\\=(25\times m^6 \times n^6)\times n^{-1}\\\\=25\times m^6 \times n^6\times n^{-1}[/tex]
We know that if the base of exponents are same then we add the powers of exponents.
So, our expression becomes,
[tex]=25\times m^6\times n^{6-1}\\\\=25\times m^6\times n^5[/tex]
This is the required expression.
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Question
3
Z
Note: Figure is not drawn to scale.
If y = 13 inches, z = 18 inches, h = 6 inches, and w = 4 inches, what is the area of the object?
OA.
180 square inches
OB.
120 square inches
OC. 252 square inches
OD. 126 square inches
Answers
The area of the figure is determined as 126 in².
option D.
What is the area of the figure?
The area of a shape describes the measure of the amount of space enclosed by a two-dimensional shape or surface. It is typically expressed in square units.
The area of the figure is calculated as follows;
Total area = area of triangle + area of rectangle
Area of triangle = ¹/₂ x base x height
Area of triangle = ¹/₂ x 18 in x 6 in
Area of triangle = 54 in²
Area of rectangle = 18 in x 4 in
Area of rectangle = 72 in²
Total area of the figure = 54 in² + 72 in² = 126 in²
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Suppose you invest $100 a month in an annuity that earns 4% APR compounded *
monthly. How much money will you have in this account after 2 years?
O$1,004.48
O $2,400.18
O $2,518.59
O$3,908.26
Answers
Answer:
Answer: (C) $2,518.59.
Step-by-step explanation:
To find the amount of money you will have in the account after 2 years, we can use the formula for the future value of an annuity:
FV = P * (((1 + r/n)^(nt) - 1) / (r/n))
where:
FV = the future value of the annuity
P = the monthly payment, which is $100
r = the annual interest rate, which is 4% expressed as a decimal (0.04)
n = the number of times the interest is compounded in a year, which is 12 (monthly)
t = the time the money is invested for, which is 2 years
Substituting the given values into the formula, we get:
FV = 100 * (((1 + 0.04/12)^(12*2) - 1) / (0.04/12))
FV = 100 * (((1.00333333333)^24 - 1) / (0.00333333333))
FV = 2,518.59 (rounded to the nearest cent)
Therefore, you will have $2,518.59 in the account after 2 years. Answer: (C) $2,518.59.
pls answer
woth 20 points!!
Answers
The circumference of the given circle is 22.26 meters.
How to find the circumference of the circle?For a circle of diameter D, the circumference is defined by the following formula:
C = pi*D
Where pi = 3.14
Here we know taht the diameter is 7.09 meters, then we can input that in the formula above to get:
C = 3.14*7.09 m
C = 22.2626 m
Rounding to 2 decimals, we will get:
C = 22.26 meters.
That is the circumference of the circle.
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Suppose the radius of a cylinder changes, but its volume stays the same. How must the height of the cylinder change?
1. If the radius increases then height must increase
2. If radius decreases then height must decrease
3. The height doesn’t change
4. If the radius increases, height decreases
Answers
If the radius increases, height decreases, Therefore option no 4 is correct
If the radius of a cylinder changes, however its volume remains the same, then the height of the cylinder have to change.
Mainly, if the radius increases, then the height must decrease & if the radius decreases then the height must to increase. this is because the volume of a cylinder is given by means of the formulation:
[tex]V = \pi r^2h[/tex]
In which V is the volume, r is the radius &h is the height. If we keep the volume constant, and increase the radius, then we ought to lower the height in order to make amends for the increased extent.
Similarly, if we decrease the radius, then we must increase the height to catch up on the reduced volume.
Therefore, the appropriate answer is:
If the radius increases, height decreases
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write down a 3 digit number below 200 that is a multiple of 10
Answers
Answer: 170
Step-by-step explanation:
170/10=17
Jonah takes out an $18,000 personal loan to make home repairs. His interest rate is 9.1% on an 8-year loan. His monthly payments are $264.64. What is the total payback amount and how much of that is interest?
Answers
Answer:
The first step is to calculate the total number of months in the 8-year loan term:
8 years * 12 months/year = 96 months
Next, we can use the monthly payment amount to calculate the total payback amount:
Total payback amount = Monthly payment * Total number of months
Total payback amount = $264.64 * 96
Total payback amount = $25,455.04
So the total payback amount for the loan is $25,455.04.
To calculate the total interest paid over the life of the loan, we can use the formula:
Total interest = Total payback amount - Loan amount
The loan amount in this case is $18,000, so:
Total interest = $25,455.04 - $18,000
Total interest = $7,455.04
So the total interest paid over the life of the loan is $7,455.04.
Step-by-step explanation:
Sam bought a dog for £110. His nan gave him 30% of the money. How much did he have to pay himself?
Answers
Answer:
£77
Step-by-step explanation:
If his nan gave him 30%, he would have to pay the remaining 70%.
70% of 110:
10%=£11
so, 11x7= 77
The day before a show, a theatre had sold adult and child tickets in the ratio 8:3. On the day of the show, the theatre sold 30 more adult tickets and no more child tickets. The ratio of adult to child tickets sold became 7 : 2. Work out how many adult tickets had been sold the day before the show.
Answers
On the day of the show, the theatre sold 30 more adult tickets, so the total number of adult tickets sold became 8x + 30. The number of child tickets sold remained the same, so it was 3x.
The ratio of adult to child tickets sold on the day of the show was 7:2. So, we can write:
(8x + 30)/3x = 7/2
To solve for x, we can cross-multiply and simplify:
2(8x + 30) = 21x
16x + 60 = 21x
5x = 60
x = 12
Therefore, the theatre sold 8x adult tickets the day before the show, which is:
8x = 8(12) = 96 adult tickets.
So, the theatre sold 96 adult tickets and 3x child tickets (3 x 12 = 36) the day before the show, in the ratio 8:3.
Before 1980, Mount St. Helens was cone-shaped, with a height of about 1.83 miles and a base radius of about 3 miles. In 1980, Mount St. Helens erupted. The tip of the cone was destroyed, reducing the mountain's volume by 0.043 cubic miles. Find the volume of Mount St. Helens after the eruption. Round the answer to the tenths place.
HURRY PLEASE
Answers
Answer:
17.2 cubic miles
Step-by-step explanation:
You want the volume of Mt. St. Helens after an eruption removed 0.043 cubic miles of volume from its cone shape. Its radius is 3 miles, and its height was about 1.83 miles.
ConeThe formula for the volume of a cone is ...
V = 1/3πr²h
The volume of the tip is removed from that to find the volume after the eruption.
V = 1/3π(3 mi)²(1.83 mi) - 0.043 ≈ 17.2 mi³
After the eruption, the volume of Mount St. Helens is about 17.2 cubic miles.
__
Additional comment
The volume rounded to 1 decimal place is unaffected by the amount removed. That amount only changes the volume in the 2nd decimal place.
The problem’s in the image
Answers
The value of the function h(x) at x = 33 will be 550.
Given that:
Table
x h(x)
3 40
5 74
11 176
14 227
19 312
33 a
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The relation is a linear relation. Then the slope will remain constant. Then the value of a is calculated as,
(312 - 227) / (19 - 14) = (a - 312) / (33 - 19)
85 / 5 = (a - 312) / 14
a - 312 = 238
a = 550
h(33) = 550
The value of the function h(x) at x = 33 will be 550.
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Solve the quadratic
8x^2 - 5x - 4 = 0
Thanks!
Answers
Answer:
x= -0.461
x= 1.086
Step-by-step explanation:
using the quadratic formula
A=8, B=-5, C=-4
The evaluate
[tex]x=\frac{-(-5) +\sqrt{(-5)x^{2} -4*8*(-4)} }{2*8} and x=\frac{-(-5) -\sqrt{(-5)x^{2} -4*8*(-4)} }{2*8}[/tex]
calculate
[tex]x=\frac{5+\sqrt{25+128} }{16} } and x=\frac{5-\sqrt{25+128} }{16} }[/tex]
Simplify
[tex]x=\frac{5+3\sqrt{17} }{16} and x=\frac{5-3\sqrt{17} }{16}[/tex]
simply
x= -0.461 and x= 1.086
Which is the missing section?
How comes the answer is B?
Answers
The missing section according to the pattern given is the option B or 3, 2, 8, 8.
What is the pattern in the image provided?If observed carefully, it can be noted that:
Each row and column have the numbers 1, 2, 3, 8, 9, and one of these numbers is repeated.This means that for the missing section to be completed we need to consider:
The second row is missing the numbers 3, and 8 to match the general pattern.The third row is missing the numbers 2 and 8 to match the general pattern.Based on this, the missing section would be section 2.
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24.5% of what number is 15 Step-by-step please help!
Answers
actually is really "x", which oddly enough is the 100%, and we also know that 24.5% of that is 15, so
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 15& 24.5 \end{array} \implies \cfrac{x}{15}~~=~~\cfrac{100}{24.5} \implies 24.5x=1500\implies x=\cfrac{1500}{24.5} \\\\\\ x=\cfrac{1500}{~~ \frac{245 }{10 } ~~}\implies x=\cfrac{15000}{245}\implies x=\cfrac{3000}{49}\implies x\approx 61.22[/tex]
The Question is inside those screenshots
Answers
Using the 68-95-99.7 rule
1. The approximate percentage of the Chipotle meals that have between 466 and 1670 calories is 95 percent
2. The middle 99.7% of Chipotle meals have between 165 calories and 1971 calories.
3. The approximate percentage of Chipotle meals with calories between 767 and 1369 is 68%.
How do we calculate the approximate percentage or range using the 68-95-99.7 rule?
The 68-95-99.7 rule states that 68% of the data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3.
1. Within 1 standard deviation, we cannot arrive at 466 and 1670. for example 466 is (1068 - 301) = 767
but wth 2 standard deviations, we can
466 is (1068 - 2 × 301) = 466
1670 is (1068 + 2 × 301) = 1670
2. For 99.7% , we kmow it fall with 3 standard deviation⇒(µ - 3σ) calories and (µ + 3σ) calories.
(1068 - 3 × 301) = 165 calories
(1068 + 3 × 301) = 1971 calories
3. Since we know 95 and 99.7% range, it most likely falls within 68%
(1068 - 301) = 767 and (1068 + 301) = 1369
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7. A sample of Alzheimer's patients are tested to assess the amount of time in stage IV sleep. It has been.
hypothesized that individuals suffering from Alzheimer's Disease may spend less time per night in the
deeper stages of sleep. Number of minutes spent is Stage IV sleep is recorded for 61 patients. The
sample produced a mean of 48 minutes, with a standard deviation of 14 mins, of stage IV sleep over a
24 hour period of time. Compute a 90% confidence interval for this data.
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Answer:
Step-by-step explanation:
The 90% confidence interval for the mean amount of time spent in stage IV sleep is (45.04, 50.96) minutes.
To compute the confidence interval, we can use the formula:
CI = x ± z*(σ/√n)
where:
x = sample mean = 48 mins
σ = sample standard deviation = 14 mins
n = sample size = 61
z = z-score corresponding to the confidence level of 90%, which can be found using a z-table or calculator. For a 90% confidence level, the z-score is 1.645.
Plugging in the values, we get:
CI = 48 ± 1.645*(14/√61)
CI = 48 ± 2.96
Therefore, the 90% confidence interval for the mean amount of time spent in stage IV sleep is (45.04, 50.96) minutes.
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The College Board states that the average math SAT score is 514 with a standard deviation of 117. Colleen knows scores at her school are normally distributed and collects a random sample of 50 students in her graduating class. Give a 95% confidence interval for the population mean. Round to the nearest tenth.
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In hypothesis testing, null hypothesis (H0) is a claim that the person conducting the research wants to test while an alternative hypothesis (H1) is a contradiction of the null hypothesis.
There are two types of tests in hypothesis testing is known.
One tailed test: In first tailed test, a claim that a parameter is greater than/ less than a value is being tested.
mean > value or mean < value.
Second tailed test: In a two tailed test, a claim that a value is equal to a value is tested,
mean = value.
Since we can see that Colleen is testing the claim that the average score of her class is the same as others against that it is different from others.
Hence, the null hypothesis is H0: mean = 514
and the alternative hypothesis is H1: mean ≠ 514
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