Which one of the following shaded-regions in the plane consists of all points whose polar coordinates satisfy the inequalities 0
Answers
the following shaded-regions in the plane consists of all points whose polar coordinates satisfy the inequalities 0 ≤ r ≤ 3 and π/6 ≤ θ ≤ π/12.
What is polar co-ordinates?It is referred to as a polar coordinate system when each point on a plane in a two-dimensional coordinate system is determined by a distance from a reference point and an angle measured from a reference direction. Pole: The object of comparison. The term "polar coordinates" refers to these new coordinates since you interpret the axes' intersection as a pole from which all other points radiate outward. change (degrees are measured in radians) (degrees are measured in radians).
Given that,
0 ≤ r ≤ 3
and π/6 ≤ θ ≤ π/12
In the given condition we can clearly see that the radius is not equal to 3 but it is less than 3. Thus graph number 1, 2, 4 and 6 do not match the given condition.
Now in the given condition 0 ≤ r ≤ 3 the angle is between 30° to 105°
In the graph number 3 radius varies from 0 ≤ r ≤ 3 but angle varies from 75° to 150°, so it is also incorrect.
Thus in the remaining graph number 5, the radius varies from 0 and angle also varies from 30° to 105°.
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The complete question is as follows:
Related Questions
Amber is trying to solve 3x^2 - 4x = 0 using a graphical method. She therefore starts by drawing the graph y = 3x^2 on a grid. She now intends to complete her method by drawing a straight line graph on the same grid. Complete Amber’s method to solve 3x^2 - 4x
Answers
Using Amber's method of plotting, a graph representing the two seperate equations is attached.
3x^2: Is a curve and color green
- 4x : is a straight line graph, with red color
What are graphs?A graph is a pictorial representation of a an expression. It is used in several disciplines to represent and interpret data easily. Since graphs are pictures it show the relationship between functions or data presented with less difficulty.
here, we have,
The first graph is a curve because the expression involved is a polynomial this is to say the variable is raised to a power that is not 1 or zero.
The second graph is not a curve because the variable x has a power of 1
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Helppppppppppppppppppppppp
Answers
Answer: 90
Step-by-step explanation: Regular Polygons have all their angles equal. Since there are 4 sides the total sum of the angles are 360. Divide it by four and you get your answer of 90.
Answer:
90 degrees
Step-by-step explanation:
A regular polygon has sides with the same length.
Because this is a 4-sided regular polygon, this shape would be a square.
Since all angles inside of a polygon must equal 360, we can divide this number by the amount of angles in this polygon.
360 degrees/4 angles = 90 degrees/angle
ank
across from
near
between
next to
1. Where's the nearest bank?
There's one next to the grocery store
on 1st Avenue.
2. Is there a post office near here?
Yes. There
3. I'm looking for a drugstore.
ap and the prepositions in the box.
in
on the corner of
4. Is there a laundromat in this neighborhood?
6. Are there any ATMs around here?
5. Is there a department store on River Street?
1ST AVENUE
grocery
store
bank movie
theater
KING STREET
library
drugstore
laundromat
gym
hotel
PALM STREET
2ND AVENUE
ATM
gas station
post office
LINCOLN STREET
department
store
gym
RIVER STREET
3RD AVENUE
hotel
51
Answers
Answer:
Step-by-step explanation:
1ST AVENUE
grocery
store
bank movie
theater
KING STREET
library
drugstore
laundromat
gym
hotel
PALM STREET
2ND AVENUE
ATM
A long distance trucker traveled 144 miles in one direction during a snow storm. The
return trip in rainy weather was accomplished at double the speed and took 4 hours
less time. Find the speed going.
The speed going was
Answers
Let's call the speed going x miles per hour.
The time it took for the return trip was 4 hours less, so the total time for the return trip was 2 * (144/x) - 4 hours.
The total distance for the return trip was 144 miles, so we can write the equation:
144 = 2 * (144/x) - 4 * x
Expanding the equation:
144 = 288/x - 4x
Multiplying both sides by x:
144x = 288 - 4x^2
Moving all the x terms to one side:
4x^2 + 4x - 144 = 0
Solving for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 4, b = 4, and c = -144
x = (-4 ± √(4^2 - 4 * 4 * -144)) / 2 * 4
x = (-4 ± √(16 + 1152)) / 8
x = (-4 ± 48) / 8
x = (44 ± 48) / 8
x = 92/8 or x = -4/8
Since speed must be positive, the speed going was x = 92/8 = 11.5 mph.
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what is the graph of the function rule? y = -3/4x+4
Answers
The graph of function y = - 3/4x + 4 is shown in figure.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation is,
⇒ y = - 3/4x + 4
Clearly, The equation shows the equation of line with slope (m) - 3/4 and y - intercept at point 4.
So, The graph of function y = - 3/4x + 4 is shown in figure with y - intercept at point 4.
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Danny Duncan worked 55 hours in one week for a grocery store. Danny earns $15 per hour. What’s Danny’s gross pay, assuming overtime is at time-and-a-half?
Answers
Therefore , the solution of the given problem of unitary method comes out to be Gross pay of Danial Ducan is $1162.5.
A unitary method is precisely what?To finish a work using the unitary strategy, multiply the quantity with two after determining the size of a small slice. The unit variable technique, to put it simply, works to isolate a coded object from a specific group or sets of sets. For instance, 40 pens would cost 400 pounds (expression $1.01) = Rs. There is a chance that one nation will have complete control over the technique used to do this. Almost all living things have a unique trait.
Here,
Given :
Danny Duncan worked 55 hours in 1 week.
earns $15 per hour.
To find the Danny's gross pay:
overtime is at time and half.
So,
=> Gross pay = 55*15 + 55/2 *15
=> Gross pay = 825 + 337.5
=> Gross pay = 1162.5
Therefore , the solution of the given problem of unitary method comes out to be Gross pay of Danial Ducan is $1162.5.
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1. A soft-drink manufacturer can produce 1000 case of soda in a week at a total cost of GHC6,000, and 1,500 cases of soda at a cost of GHe8,500. Fid the manufacturer's weekly fixed costs and marginal cost per case of soda.
Answers
Total Cost = Fixed Cost + Variable Cost
Variable Cost = Marginal Cost * Quantity
At 1000 cases of soda, the variable cost is GHC6,000, and the total cost is GHC6,000. So the fixed cost at this quantity can be found as:
Fixed Cost = Total Cost - Variable Cost
Fixed Cost = GHC6,000 - (1000 * GHC6/1000) = GHC6,000 - GHC6 = GHC0
This means the manufacturer has no fixed costs at this quantity of 1000 cases.
Next, we can find the marginal cost per case of soda by calculating the change in the variable cost as the quantity changes from 1000 to 1500 cases.
Variable Cost = Total Cost - Fixed Cost
Variable Cost = GHC8,500 - GHC0 = GHC8,500
Marginal Cost = (Variable Cost at 1500 cases - Variable Cost at 1000 cases) / (1500 - 1000)
Marginal Cost = (GHC8,500 - GHC6,000) / 500 = (GHC2,500) / 500 = GHC5
So the manufacturer's marginal cost per case of soda is GHC5.
Note: The fixed cost is assumed to be zero because the information provided does not specify any fixed costs. This may not necessarily be the case in a real-world scenario.
A $5070 investment earns interest at
compounded quarterly
5% per year
over 15 years.
Use the compound interest formula to
calculate the value of this investment
to the nearest cent.
Answers
Answer:
Step-by-step explanation:
The value of the investment can be calculated using the compound interest formula:
A = P * (1 + (r/n))^(nt)
Where:
A = final amount
P = principal amount (5070)
r = annual interest rate (0.05)
n = number of times the interest is compounded in a year (4)
t = number of years (15)
So,
A = 5070 * (1 + (0.05/4))^(4*15)
A = 5070 * (1.0125)^60
A = 5070 * 2.693260689
A = 13,652.14
The value of the investment after 15 years compounded quarterly at 5% per year is $13,652.14, rounded to the nearest cent.
Your starting salary at a company is 70000 dollars, and you get a raise of 6000 dollars each year. Let t represent the number of years since you joined the company.
a) Express the percentage rate of change of your salary as a function of time.
Answers
Answer:
Step-by-step explanation:
70000 + t600
PLEASE HELP ASAP........................................
Answers
The correct options are A and B. This indicates that the two sides of the triangle are equal and one angle is also equal.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
For the triangle ABC to be congruent to A'B'C' the best condition would be that the two sides of the triangle must be congruent and one angle should be congruent.
The correct options are A and B in which the two sides AB≅A'B', BC≅B'C' and the angle ∠A ≅ ∠A'. The second statement is also true that two sides AB≅A'B', BC≅B'C' and the angle ∠B ≅ ∠B' by side angle side property.
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Write an equation that represents the graph
Answers
How to find angle in trapezoid given one angle.
Answers
The measure of angle, m<U as required to be determined is; 115°.
What is the measure of the angle U?It follows from the task content that the geometric figure STUV is a trapezoid.
On this note, it follows that; TU and SV are parallel lines; TU || SV.
Consequently, m<U + m<V = 180°.
where, m<V = 65°.
m<U = 180° - 65°
= 115°.
Consequently, the measure of m<U = 115°.
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nirav just opened a savings account paying 2 percent interest, compounded annually. after four years, the savings account will be worth $5,000. assume there are no additional deposits or withdrawals. given this information, nirav: a. will earn simple interest on his savingg every year for four yearsb. has an account currently valued at $5,000c. could have deposited less moneytoday and still had $5.000 in four years if the account paid a higher rate of interestd. could earn more interest on this account if the interest earnings were withdrawn anuallye. will earn the same amount of interest each year for four years
Answers
Answer:
c. could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest
Step-by-step explanation:
Nirav just opened a savings account paying 2 percent interest, compounded annually. After four years, the savings account will be worth $5,000. Assume there are no additional deposits or withdrawals. Given this information, Nirav:
a. will earn simple interest on his saving every year for four years
False. Problem states it's compound interest.
b. has an account currently valued at $5,000
False. Problem states account will be worth $5,000 in 4 years.
c. could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest
True. With a higher interest rate, he would earn more interest, so he could start with less money and still end up with $5000 at the end of 4 years.
d. could earn more interest on this account if the interest earnings were withdrawn annually
False. If he withdraws money periodically, there is less principal to earn interest on, so he will earn less interest overall.
e. will earn the same amount of interest each year for four years
False. Since compound interest earns interest on interest, all else being equal, compound interest earns more interest than simple interest.
Kaitlin and her husband are each starting a saving plan. Kaitlin will initially set aside $650 and then add $155 every month to the savings. The amount A (in dollars) saved this way is given by the function =A+155N650, where N is the number of months she has been saving.
Her husband will not set an initial amount aside but will add $585 to the savings every month. The amount B (in dollars) saved using this plan is given by the function =B585N.
Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
Answers
The linear function for the total amount added to the account each month is given as follows:
T(n) = 650 + 740n.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the amount added each month.The intercept b represent the initial amount.Then the parameters for this problem are given as follows:
m = 155 + 585 = 740.b = 650.Hence the function is given as follows:
T(n) = 650 + 740n.
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A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
See picture
Part A: What is the height of the base? Show your work. (5 points)
Part B: What is the approximate amount of cardboard used to make the candy
box? Explain how you got your answer. (5 points)
Answers
Assuming a thickness of 1 millimeter for the cardboard, the amount of cardboard utilized to build the candy box is roughly 240 cubic centimeters.
What is volume?Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. To calculate the volume, multiply the length by the breadth by the height, which is 3x1x2, which is six. As a result, the fish tank has a volume of 6 cubic feet.
Here,
Part A: To find the height of the base, we need to use the formula for the volume of a triangular prism:
V = Bh/2,
where B is the area of the base and h is the height.
We can assume the base of the triangular prism is an equilateral triangle with side length s. The area of an equilateral triangle can be found using the formula:
B = (s² * √(3))/4
We can use this formula to find the side length of the triangle:
s = √((4B)/(√(3)))
Substituting the known values, we have:
1200 = (s² * √(3))/2 * h
solving for h:
h = 1200 * 2 / (s² * √(3))
Substituting the value for s:
h = 1200 * 2 / ((√((4B)/(√(3)))² * √(3))
h = 1200 * 2 / (((4B)/(√(3))) * √(3))
h = 1200 * 2 / (4B)
h = 300 / B
We can find the value of B using the formula:
B = (s² * √(3))/4
Substituting the value for s:
B = (√((4B)/(√(3)))² * √(3))/4
B = (4B)/(3 * √(3))
B = 4B / (√(9))
B = 4B / 3
Solving for B:
B = 300 / h
So, the height of the base is approximately 30 cm.
Part B: To find the amount of cardboard used to make the candy box, we need to find the surface area of the triangular prism and multiply it by the thickness of the cardboard.
The surface area of a triangular prism can be found using the formula:
A = B + Bs + Bh
Where B is the area of the base, Bs is the area of the side of the triangular prism and Bh is the area of the top and bottom of the triangular prism.
We know that B = (s² * √(3))/4 and Bh = B, so
A = B + Bs + Bh = B + 2Bh = 2B + 2Bs
The surface area of the triangular prism is approximately 240 square centimeters.
Assuming the cardboard has a thickness of 1 millimeter, the amount of cardboard used to make the candy box is approximately 240 cubic centimeters.
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Triangle LMN with vertices L(6, 6), M(8, 8), and N(8, 3)
a) reflection in the line x = 5
b) 270° counterclockwise
rotation about the origin c
Answers
The 270° counterclockwise rotation about the origin is a transformation that turns each point (x, y) in the original triangle to (-y, x) in the new triangle.
What is the triangle ?A triangle is a three-sided polygon and is one of the basic shapes in geometry. It is a closed figure composed of three straight line segments, connected at their endpoints. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. Triangles are classified by their angles and their sides. Triangles can be right, acute, obtuse, isosceles, equilateral, and scalene. Right triangles have one angle that is equal to 90 degrees. Acute triangles have all angles that are less than 90 degrees. Obtuse triangles have one angle that is greater than 90 degrees. Isosceles triangles have two sides that are equal in length.
Triangle LMN' with vertices L'(1, 6), M'(3, 8), and N'(3, 3), Triangle LMN' with vertices L'(6, -6), M'(-8, -8), and N'(-8, -3), Triangle LMN' with vertices L'(-6, 6), M'(-8, 8), and N'(-8, 3)
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classify each angle as acute , right , obtuse , or straight
Answers
Based on the picture above:
numbers 1,5,6 and 8 including the obtuse angle numbers 2,3,9 and 10 include the acute angle number 4 is a straight angle number 7 is the right angle How to determine what type of anglesFrom the answer above, the way to determine the type of angle is to measure the angle.
if the angle is 90° then it is a right angle.
If the angle is 0-90° then it's an acute angle
If the angle is above 90° and below 180° then it is an obtuse angle
If the angle is 180° then it is called a straight angle.
The following is a more complete explanation:
1. Right Angles
Right angles have a measure of 90º and are perpendicular in shape. This angle is usually denoted by ∟. Examples of surrounding objects that have right angles include books, tables, cupboards, clock hands that show 3 o'clock, and so on.
2. Straight Angle
A straight angle has an angle of 180º. As the name implies, this angle is straight and flat. Examples of objects that have straight angles include a ruler and clock hands that show 6 o'clock.
3. Acute Angles
Acute angles have angles greater than 0º and less than 90º. As the name implies, this angle is pointed. Objects that have acute angles such as pencil tips, pizza slices, iron tips, and clock hands that show 1 and 2 o'clock.
4. Obtuse Angle
Contrary to an acute angle, an obtuse angle has an angle greater than 90º but less than 180º. As the name suggests, objects that have this angle are obtuse, such as laptops wide open, beach chairs, camping tents, and clock hands that show 4 and 5 o'clock.
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There is a better look of it! Just answer this one- For each team, find the unit rate games per loss.
Answers
0.156 is the unit rate games per loss.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Plug in the values from the table to the above formula.
Slope is nothing but rate of change.
m=17-12/68-36
m=5/32
m=0.156
Hence, 0.156 is the unit rate games per loss.
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(c) Given that
f(x)=e^{-3x}-4.
g(x)=ln(\frac{1}{x+2}),
TER
x>-2
(i) state the range of f
(ii) find f(x),
(iii) express fg(x) as a polynomial in r.
Answers
The range of function f(x) is Range: (-4,∞), {y|y>-4}.
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
The given functions are f(x)=e⁻³ˣ -4, x∈R
g(x)=ln(1/x+2), x>-2
(i)
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (-∞,∞), {x|x∈R}
Range: (-4,∞), {y|y>-4}
(ii)
To find the inverse, interchange the variables and solve for y.
f⁻¹(x)=-ln(x+4)/3
(iii) Here, fg(x) is
Replace x by ln(1/x+2) in f(x), we get[tex]fg(x)=e^{-3(ln(\frac{1}{x+2} ))}-4[/tex]
Therefore, the range of function f(x) is Range: (-4,∞), {y|y>-4}.
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Find the area of the figure
Answers
Answer:
202.5 square yards.
Step-by-step explanation:
We know the whole square is 15 * 15 = 225
Now, we need to find the area of the triangles and subtract that.
We can predict that the sides are 3 and 7.5. Doing that we get the area of 11.25 for each.
225- (11.25*2)=202.5
Higher Order Thinking Write a word problem involving addition of two mixed
numbers with unlike denominators where the answer is 12 1/10
Answers
The word problem would be "John has two pieces of rope. The first piece is 9 feet long and the second piece is 7 and 4/5 feet long. How long is the combined length of the two pieces of rope in feet and inches? ".
What is the word problem?
A word problem in mathematics is a problem that is described in words, rather than with mathematical symbols and equations. It presents a real-life situation and asks the reader to use mathematical concepts and skills to find a solution.
John has two pieces of rope. The first piece is 9 feet long and the second piece is 7 and 4/5 feet long. How long is the combined length of the two pieces of rope in feet and inches? The answer is 12 1/10 feet.
Hence, the word problem would be "John has two pieces of rope. The first piece is 9 feet long and the second piece is 7 and 4/5 feet long. How long is the combined length of the two pieces of rope in feet and inches? ".
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?+6=2+7 what is the missing number
Answers
Answer:
3
Step-by-step explanation:
Answer:x=3 I hope this helps pls mark brainlist and give some love to the other person that answered
Step-by-step explanation:
x+6=2+7 I put a x where the missing number is
Add the number
X+6=9
Move the constant to the right-hand side and change its sign
X=9-6
Subtract the numbers
You will get your answer 3
X=3
If I took 420 minutes a day in school (that would be 7 hours a day in school), and there is 4 weeks in a month, and all together we spend time in 10 months in school, if 1 hours is 60 minutes, then how much minutes and days to we spend in school.
Answers
Doing some changes of units we will see that you spend 84,000 minutes or 58.33 days in school.
How many minutes and days are spent in school?Here we need to do some changes of units.
First, we know that you spent 7 hours a day in school, and you go to school 5 days per week, so in a week you spend:
5*7 = 35 hours.
There are 4 weeks per month, so in a month you spent:
4*35= 140 hours.
And there are 10 months (where you go to school), then the total number of hours is:
140*10 = 1400 hours.
Now, we know that:
1 hour = 60 min
Then the total number in minutes is:
M = 1400*60min = 84,000 minutes.
And we know that:
1 day = 24 hours, then the total number in hours is:
H = 1400/24 days = 58.33 days.
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If I took 420 minutes a day in school (that would be 7 hours a day in school), and there is 4 weeks in a month, and all together we spend time in 10 months in school, if 1 hours is 60 minutes, then how much minutes and days to we spend in school.
Answers
The number of minutes attends school in 10 month is 100800 minutes.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, I took 420 minutes a day in school (that would be 7 hours a day in school).
There is 4 weeks in a month, if each week they attend 6 days school
Then, number of minutes attends school in a week is
420×6
= 2520 minutes
The number of minutes attends school in a month is
2520×4 =10080 minutes
The number of minutes attends school in 10 month is
10080×10 =100800 minutes
Therefore, the number of minutes attends school in 10 month is 100800 minutes.
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A fully loaded and fueled spacecraft can weigh close to 3.9
million pounds. What is this weight converted to tons?
Answers
Answer:1950 US tons
Step-by-step explanation:
Mrs.Marin is sewing costumes for the play. Each costume requires 38 centimeters of blue ribbon. If she makes 50 costumes, how
many meters of ribbon dose she need
Answers
Answer: To find out how many meters of ribbon Mrs. Marin needs, we first need to convert the required length of 38 centimeters per costume to meters.
1 meter = 100 centimeters, so we divide 38 by 100:
38 cm / 100 cm/m = 0.38 m
So each costume requires 0.38 meters of ribbon.
To find the total amount of ribbon needed for 50 costumes, we multiply the amount of ribbon per costume by the number of costumes:
0.38 m/costume * 50 costumes = 19 meters
So Mrs. Marin needs 19 meters of blue ribbon for the 50 costumes.
Step-by-step explanation:
6 Assignment
5.6.PS-14
Compare the rates to find which is greater.
56 meters in 32 hours or 40 meters in 25 hou
The unit rate for 56 meters in 32 hours is? The unit rates for 40 meters in 25 hours is? The unit rate for 56 meters in 32 hours is greater than, less than, or equal to the unit rate for 40. Meters in 25 hours?
Answers
The unit rate for 56 meters in 32 hours (1.75 m/h) is greater than the unit rate for 40 meters in 25 hours (1.6 m/h).
What do you mean by rate?In mathematics, rate is a concept used to describe the change in one quantity with respect to another. It is usually represented as a fraction or a ratio and can be thought of as a measure of how fast one quantity is changing with respect to another.
For example, the rate of change of position with respect to time is called velocity. The rate of change of velocity with respect to time is called acceleration. Similarly, the rate of change of any function with respect to its independent variable is called the derivative of the function, and it represents the instantaneous rate of change at a given point.
Rate can also be used to describe the relationship between two quantities that are changing at the same time. For example, in economics, the interest rate is the ratio of the amount of interest earned or paid to the amount of money invested or borrowed. In science, the rate of a chemical reaction is the change in the concentration of a reactant or a product over time.
Overall, the concept of rate is a useful and important idea in mathematics and has many applications in science, engineering, economics, and other fields. It provides a means for analyzing and comparing changes in quantities and for understanding the relationships between different quantities.
The unit rate for 56 meters in 32 hours is [tex]\frac{56}{32}[/tex] = 1.75 meters per hour. The unit rate for 40 meters in 25 hours is [tex]\frac{40}{25}[/tex] = 1.6 meters per hour.
So, the unit rate for 56 meters in 32 hours (1.75 m/h) is greater than the unit rate for 40 meters in 25 hours (1.6 m/h).
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Convert the angle 3 radians to degrees, rounding to the nearest 10th.
Answers
Answer: 172.0 degrees
Step-by-step explanation:
In 180 degrees, there are [tex]\pi[/tex] radians. That means each radian is equal to:
[tex]\frac{180}{\pi }[/tex]
= 57.3248408
Then we simply multiply that by 3 to get:
3 * 57.3248408
= 171.974522
Rounded to the nearest tenth is 172.0
Answer:
172
Step-by-step explanation
180 degrees is equal to one pi.
That means each radian is equal to:= 57.3248408
Then multiply that number by 3
Written out is: 3 x 57.3248408 = 171.97452
When rounded to the nearest tenth is 172.0
which equation represent g(x)?
Answers
Nicole recently switched her primary doctor to one specializing in caring for elderly patients. On her new doctor's website, it says that the mean systolic blood pressure among elderly females is 115 millimeters of mercury (mmHg). Nicole believes the value is actually higher. She bases her belief on a recently reported study of 18 randomly selected, elderly females. The sample mean systolic blood pressure was 124 mmHg, and the sample standard deviation was 22 mmHg.
Assume that the systolic blood pressures of elderly females are approximately normally distributed. Based on the study, at the 0.10 level of significance, can it be concluded that μ, the population mean systolic blood pressure among elderly females, is greater than 115 mmHg?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H0 and the alternative hypothesis H1.
H0:
H1:
(b) Determine the type of test statistic to use.
▼(Choose one)
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the p-value. (Round to three or more decimal places.)
(e) Can it be concluded that the mean systolic blood pressure among elderly females is greater than 115 mmHg?
Yes No
Answers
based on the sample data, we have evidence to mean support Nicole's belief that the true mean systolic blood pressure among elderly females is higher than 115 mmHg.
What is mean?The mean of a dataset, sometimes referred to as the arithmetic mean, is the sum of all results multiplied by the number of values . This is the most popular way to measure central tendency and is sometimes refereed to as the "mean."
The sample mean systolic blood pressure of 124 mmHg is higher than the reported mean of 115 mmHg on the doctor's website. Additionally, the sample standard deviation of 22 mmHg indicates that there is some variability in the systolic blood pressure values among the sample of 18 elderly females.
Using a t-distribution table with 17 degrees of freedom (since we have a sample size of 18), we can calculate that the critical value for a one-tailed test at a significance level of 0.05 is 1.740.
t-statistic using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
t = (124 - 115) / (22 / sqrt(18)) = 2.35
Since the calculated t-value of 2.35 is greater than the critical value of 1.740, we can reject the null hypothesis and conclude that the sample mean systolic blood pressure of 124 mmHg is significantly different from the reported mean of 115 mmHg.
Therefore, based on the sample data, we have evidence to support Nicole's belief that the true mean systolic blood pressure among elderly females is higher than 115 mmHg.
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