The picture shows two ladders propped against
facing walls. The end of the first ladder is 5m
above the base of the second wall. The second
ladder is 5m above the base of the first wall.
5m
Can you work out at what height the
ladders cross?
Are you surprised that we don't need to know
the distance between the two walls?
5m
5m
10m
Answers
This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
What is equal angles ?
Equal angles can be defined as the angles which are equal .
Given ,
The picture shows two ladders propped against facing walls. The end of the first ladder is 5m above the base of the second wall. The second
ladder is 5m above the base of the first wall.
the angles ∠BAD and ∠ADC are alternate angles, and therefore equal. Likewise, angles ∠ABC and BCD are also alternate and therefore equal.
∠BEA and ∠CED are opposite, which means that they are equal. You can see these equal angles in the diagram on the right.
This means that the triangles ABE and DCE have the same angles as each other, and are therefore similar.
so,
This means:
AE/ED=AB/DC=5m/10m=1/2
Therefore AE=1/3 AD.
This means E is 1/3 of the way up from the floor to D, so is at a height of
This means E is 13 of the way up from the floor to D, so is at a height of 10m/ 3=3 1/3m
If instead B is a metres above the floor, then:
AE/ED=AB/DC=a/10
Therefore AE=a/10+a AD.
This means E is the same fraction of the 10m above the floor, so is 10a/10+a metres above the floor.
If instead D is b metres above the floor, then:
AE/ED=AB/DC=a/b
Therefore AE=a/a+b AD.
This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
Therefore, This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
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Related Questions
The measure of a base angle of an isosceles tri-
angle is 13 more than 3 times the measure of the
vertex angle. How many degrees are in the vertex
angle?
Answers
The vertex angle of the isosceles triangle is 22°.
What is isosceles triangle?
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
We know that an isosceles triangle is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180degrees.
Base angle = 3vertex angle+13.
=> 2base angle + vertex angle = 180°
=> 2(3 vertex angle +13)+vertex angle = 180°
=> 6 vertex angle+26+vertex angle = 180
=> 7 vertex angle = 180-26
=> 7 vertex angle = 154
=> vertex angle = 154/7 = 22°.
Hence the vertex angle of the isosceles triangle is 22°.
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Zip codes are assigned by region. In Colorado, all zip codes begin with the number 7 while the second
digit is restricted to 1-5. There is no restrictions on the remaining digits. How many zip code combos
are there?
Answers
Answer:4999 combos
Step-by-step explanation:
max:75999
min:71000
*zip codes are 5 digits long
75999-71000=4999
how to decompose 1 3/4
Answers
Answer: 1 3/4 = 3/4 + 3/4 + 1/4, or 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4
Step-by-step explanation:
which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?
Answers
The potential energy of the spring-mass system is equal to 1/2kx². Thus, figure I is a correct representation.
where x is the mass's deviation from the average location, or O.
Consequently, the graph would be symmetric about a vertical line that passes through O and would exhibit a quadratic variation with respect to x.
Thus, figure I is a correct representation.
The graph illustrates how the potential and kinetic energy of a block coupled to a spring that follows Hooke's law changes over time.
Due to the potential and kinetic energy's x2 variation, both graphs are parabolas.
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What equation does this set of algebra tiles represent? x 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 Combine like terms on each side of the equation. For example, write 3 instead of 1 + 1 + 1. Like u don’t understand it at all can anyone help meeeeeeee””””””
Answers
The required solution of the given algebraic expression is x = 6.
What is an algebraic expression?The algebraic expression consists of constants and variables using mathematical operators. eg x + y + z, or y = x + z etc.
Here,
Given an algebraic expression,
x + 1 +1 +1 +1 +1 +1 +1 = 1 +1 +1 +1 +1 +1 +1 + 1 +1 +1 +1 +1 +1
Combining like terms on each side of the equation, we get,
According to the question
x + 7 = 13
x = 6
Thus, the required solution of the given algebraic expression is x = 6.
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Answer:
x + 7 = 13
Step-by-step explanation:
(in case you also need it) x = 6
the mass of a cylinder of water filled to the 19.65-ml mark was found to be 39.753 g. when a piece of the metal was immersed in the water, the level of the water rose to 20.37 ml and the mass of the cylinder with the metal was found to be____ 41.003 g.
Answers
The density of the unknown metal exists 8.9 g/mL.
What is meant by density?The mass of an object divided by its volume is how dense it is. The gram per cubic centimeter (g/cm³) unit of density is frequently used. How much mass is present in a given area is referred to as density. Try to picture a drawer full of socks. Its density is particular. Consider that when you remove a sock, the drawer's density changes. This is due to the socks' shifting mass while the drawer's remaining constant volume.
The definition of density is the mass of a substance per unit volume. The degree to which matter is packed together is fundamentally measured by density. It is a specific physical quality of a specific object. Greek scientist Archimedes is credited with discovering the density principle.
The density (D) is equal to mass (m) divided by volume (V): D = m/V
To find the mass of the object:
m = 156 g - 105.5 g = 50.5 g
To find the volume of the volume:
V = 30.7 mL - 25 mL = 5.7 mL
The density is:
D = m/V = 50.5 g / 5.7 mL = 8.9 g/mL
Therefore, the density exists 8.9 g/mL.
The complete question is:
A graduated cylinder was filled with water to the 25.0 mL mark and weighed. Its mass was 105.5g. An object made of an unknown metal was placed in the cylinder and completely submerged in the water. The water level rose to 30.7 mL. When reweighed, the cylinder, water and metal object had a total mass of 156.0g. Based on these measurement, what is the density of the unknown metal?
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Helen is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $90. Helen will be earning a base salary of $55 per month from the gym, plus an additional $5 for every class she teaches. If Helen teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How many classes will that take? How much will Helen's expenses and earnings be?
Answers
To earn back the amount Helen spent on certification, she would need to earn $90. Since her base salary is $55 per month, she would need to teach an additional $90 - $55 = $35 in classes. Since she earns $5 per class, she would need to teach $35 / $5 = 7 classes.
So, Helen will need to teach 7 classes to earn back the amount she spent on certification.
Her total earning for teaching 7 classes would be $55 (base salary) + $5 (per class) * 7 (classes) = $110
Therefore Helen's expenses and earning would be $90 (certification cost) and $110 (earning) respectively.
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
Answers
About 80 necklaces have more than 28 beads. Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.
P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)
P(x > 28) = P(x - 24 / 4 > 1)
P(x > 28) = 1 - ∅1
P(x > 28) = 1 - 0.8413
P(x > 28) = 0.1587
Multiply both sides by 500, then we have
500 P(x > 28) = 0.1587 × 500
500 P(x > 28) = 79.35
500 P(x > 28) ≈ 80
About 80 necklaces have more than 28 beads. Then the correct option is C.
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The missing options are given below.
A. About 24 devices have more than 28 beads.
B. About 48 necklaces have more than 28 beads.
C. About 80 necklaces have more than 28 beads.
D. About 96 necklaces have more than 28 beads.
f(x) 10 3 5 2 Let glx) be a twice differentiable function defined by another differentiable function f(x), such that 9 (2) = 21+ J' f (t) dt: Selected values of f(x) are given in the table above
Answers
The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.
f(x) 10 3 5 2 Let glx) be a twice differentiable function defined by another differentiable function f(x), such that 9 (2) = 21+ J' f (t) dt: Selected values of f(x) are given in the table above.
We can calculate g'(x) as follows:
g'(x) = 2f'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3
1. Start by taking the derivative of g(x) with respect to x. This is done using the chain rule, since g(x) is defined by another differentiable function f(x):
g'(x) = d/dx[21 + J' f(t) dt] = 2f'(x)
2. Now, substitute the function f(x) into the equation for g'(x):
g'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3
The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.
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For statistics:a group of college a group of college students believes that herbal tea has restorative powers they test their Theory by making visits weekly to a nursing home they serve the residents tea after several months it's determined that the residents are more cheerful and healthy which of the following could be concluded from that study a there is some evidence that the herbal tea May improve ones emotional state the results could be completely convincing if a scientist had concluded the study rather than a group of college students be herbal tea does improve ones emotional state at least the residents of nursing homes see the results of the study are not convincing because only a local nursing home was used and only for a few months or D the results of the study are not convincing because the effects of herbal tea is confounded with several other factors
Answers
a. visits of the college students, b. herbal tea, d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.
What is herbal tea?Despite the name, herbal tea is not actually "tea" as these beverages typically do not contain the leaves or leaf buds of tea plants. Herbal teas are made from tisanes, which are blends or infusions of dried fruits, flowers, spices or herbs in water.
The lurking variable in this experiment is - a. visits of the college students.
The explanatory variable in this experiment is - b. herbal tea
Which of the following may be correctly concluded from this study - d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.
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ILL GIVE BRAINLY Drag and drop the constant of proportionality into the box to match the table.
If the table is not proportional, drag and drop "not proportional" into the box.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
x 0 2 4 6
y 0 3 6 9
Answers
Formula: y / x = 1.5
1.5 is equivalent to 3/2.
The table is proportional.
Hope this helped :>
Answer: 2/3
Step-by-step explanation: you are looking for the constant of proportionality. We find this with the following formula: K = Y/X
If f(x)=5x^6-2x^2-5, then what is the remainder when f(x) is divided by x+2?
Answers
Answer:
To find the remainder when f(x) is divided by (x-a) , we substitute x = a in the polynomial f(x) and we get the remainder.
remainder = f(a)
In this case, we have f(x)=5x^6-2x^2-5, and x+2 is the divisor and we substitute x=-2
so, remainder = f(-2) = 5*(-2)^6-2*(-2)^2-5 = -643
So, the remainder when f(x) is divided by x+2 is -643
determine the number of cycles per day and the production quantity per cycle for this set of vehicles: product daily quantity a 18 b 16 c 6 d 14 click here for the excel data file use the sequence a-b-c-d.
Answers
The number of cycles per day and the production quantity per cycle.
Number of cycles per day = (Product Daily Quantity/Production Quantity per Cycle)
For Product A:
Number of cycles per day = (18/Production Quantity per Cycle)
For Product B:
Number of cycles per day = (16/Production Quantity per Cycle)
For Product C:
Number of cycles per day = (6/Production Quantity per Cycle)
For Product D:
Number of cycles per day = (14/Production Quantity per Cycle)
Using the data from the excel file, we can calculate the production quantity per cycle and the number of cycles per day.
For Product A:
Production Quantity per Cycle = 18/3.75 = 4.8
Number of cycles per day = 3.75
For Product B:
Production Quantity per Cycle = 16/2.5 = 6.4
Number of cycles per day = 2.5
For Product C:
Production Quantity per Cycle = 6/1.5 = 4
Number of cycles per day = 1.5
For Product D:
Production Quantity per Cycle = 14/2.25 = 6.2
Number of cycles per day = 2.25
Therefore, for this set of vehicles, the number of cycles per day and the production quantity per cycle are as follows:
Product A: 3.75 cycles per day, 4.8 units per cycle
Product B: 2.5 cycles per day, 6.4 units per cycle
Product C: 1.5 cycles per day, 4 units per cycle
Product D: 2.25 cycles per day, 6.2 units per cycle
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during the first four summer olympic games attended by the united states, these medal counts were awarded. calculate the mean number of medals won during these olympic games. (round it to the nearest whole number.)
Answers
The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.
1904: 78 medals
1908: 82 medals
1912: 88 medals
1920: 94 medals
Mean = 86 medals
1. Add the total number of medals awarded to the US during the first four summer Olympic Games: 78 + 82 + 88 + 94 = 342
2. Divide the total number of medals by the number of Olympic Games (4): 342 / 4 = 85.5
3. Round the mean to the nearest whole number: 86 medals
The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.
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-x-7y=-34 find the value of y when x equals -29
Answers
Answer:
y=5/7
Step-by-step explanation:
-7y=-34+29
-7y=-5
y=-5/-7
y=5/7
Answer:
y = 9
Step-by-step explanation:
-x -7y = -34
if x = -29:
-(-29) -7y = -34
+29 - 7y = -34
-7y = -34 - 29
-7y = -63
y = -63/-7
y = 9
Check:
-(-29) - (7*9) = -34
29 - 63 = -34
the present age of Neha is 4 times the age of a son for gives ago if her son is 14 years ago find the present age of Neha.
Answers
Answer:
I didn't understand the question
Step-by-step explanation:
I think u have written wrong question..
Can anyone help me solve this question?
Calculate sin 300° − cos 945° + tan(−675°) without using calculator �
Answers
Answer:
Step-by-step explanation:
sin 300° = sin (300° - 360°) = sin (-60°) = -sin 60° = -(1/2)
cos 945° = cos (945° - 360°) = cos (585°) = cos (-295°) = -cos 295°
tan (-675°) = -tan (675° - 360°) = -tan 315°
so
sin 300° − cos 945° + tan(−675°) = -(1/2) - (-cos 295°) + (-tan 315°)
It is not a trivial task to simplify the above equations without using a calculator.
= -(1/2) + cos 295° + tan 315°
As we know that cos(x) = cos(360°-x) = -cos(x) and tan(x) = -tan(360°-x) = -tan(x)
= -(1/2) - cos 295° - tan 315°
As we know that cos(295°) = cos(360°-65°) = cos(65°) and tan(315°) = tan(360°-45°) = tan(45°)
= -(1/2) - cos(65°) - tan(45°)
= -(1/2) - 0.4226 - 1
= -0.5 - 0.4226 - 1
= -1.4226
.
you have 10 bags full of coins. in each bag are infinite coins. but one bag is full of forgeries, and you can't remember which bag. but you do know that genuine coins weigh 1 gram, but forgeries weight 1.1 grams. you have to identify the bag with the forgeries in minimum readings. you are provided with a digital weighing machine.
Answers
If there are no forgeries, then total weight will be
= (1+2+3+4+5+6+7+8+9+10) = 55 grams
given that
they have 10 bags full of coins
in each bag are infinite coins.
but one bag is full of forgeries, and you can't remember which bag.
you know that genuine coins weigh= 1 gram
forgeries weight = 1.1 gram
now, we need to find which bag has forgeries in minimum readings
then take 1 coin from the first bag, 2 coins from the second bag . . . 10 coins from the tenth bag
If there are no forgeries, then total weight will be
= (1+2+3+4+5+6+7+8+9+10) = 55 grams
Therefore total weight should be 55 grams if the total weight is more than 55 grams then it has forgeries coins
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Total weight=55gm ,then there is no forgeries coin bag
1 bag with forgeries = take 1 coin from first bag
from 2 bag = take 2 coin
and similarly with all 10 bags.....
from 10th bag = take 10 coin
if there is no forgeries ,then total weight = (1+2+3+4+5+6+7+8+9+10)
=55gm
If bag weight 55.3 than we know that there are 3 forgeries.
So total weight=55 ,then there is no forgeries coin bag if weight is more than 55 than there is forgeries coin.
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I don’t understand this help?
Answers
Answer:
the first expression i think is the line going downwards
and the second is the line going upwards
Step-by-step explanation:
i think sorry if it wrong
hope the annotating will help you! If this is not the thing you want let me know so that I can edit the way the question actually is...
Two investments totaling $64,500 produce an annual income of $3270. One investment yields 8% per year, while the other yields 2% per year. How much is invested at each rate?
Answers
Answer:
The amount invested at 8% is 64,500-32,000 = 32,500
Step-by-step explanation:
one investment: 3%, amount: x
the other: 8%, amount: 64,500-x because x is invested at 3%
0.03x+0.08(64,500-x) = 3,560
0.03x+5,160-0.08x = 3,560
-0.05x = -1,600 divide both sides by 0.05 and remember that -/- = +
x = 32,000 This is the amount invested at 3%
The amount invested at 8% is 64,500-32,000 = 32,500
Use the given information to determine the number of elements in each of the four disjoint subsets in the following Venn diagram: n BAnBA' nB n(A) = 20 n(B) = 50, n(A nB) = 0, n(U) = 200 4' nB' (A) Find n(An B): n(An B) = (B) Find n(A n B'): n(Anb) = (C) Find n(A' n B): n(A' n B) =Ml (D) Find n(A' n B') n(A' 0 B') =
Answers
The value of the following venn expressions of sets is (A)=1 ,(B)=50,(C)=20 and (D)=130 respectively.
A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.
Symmetric difference between two sets A and B defined by,
AΔB=(A\B) ∪ (B\A)
AΔB=(A∩B') ∪(A'∩B).
we have n(A)=20 n(B)=50, n(A∩B)=0, n(U)=200
SO,
(A) Find n(A∩B)
n(A∩B) =0 (GIVEN)
(B) Find n(A∩B')
n(A∩B') =n(B)-n(A∩B)
= 50-0
=50
(C) Find n(A∩B')
n(A'∩B) =n(A)-n(A∩B)
=20-0
=20
(D) n(A'∩B') =n(U)-n(A'∩B)-n(A∩B)-n(A∩B')
=200-20-0-50
= 130.
thus, the above is the value of expression.
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The diagram shows four angles round a point.
a Write an inequality for x.
b Solve the inequality.
c Explain why the angle labelled xº cannot be a right angle.
Answers
An inequality for x considering the figure is written as
4x + 30 < 360the value of x is 82.5
x cannot be right angle because it will be against the rule of angle in a point is 360 degrees
How to write the inequality for xThe inequality that represents the figure in terms of x is written using the knowledge that angles in a point is 360 degrees
x + 2x + x + 30 < 360
adding like terms
4x + 30 < 360
solving for x
4x < 360 - 30
4x < 330
x < 82.5
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QUICK I’LL MARK YOU BRAINLIEST!!
5-142. Use the similar figures at right to answer the questions.
1. What is the scale factor?______
2. Find the lengths of the missing sides on the similar shapes below.
X=______ Y=_______ Z=_____
Answers
Answer:
Z = 22.5, Y = 81, X = 26.7
Step-by-step explanation:
Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.
[tex]Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7[/tex]
Help pls it’s imaginary numbers
Answers
Answer:
Why don't you use this app and take a picture and see if someone got the answer
Using the image below, solve for x. Round to the nearest hundredth (2 decimal places)
X
15°
16
Answers
The decimal number will be rounded to the nearest hundredth value as 1.93 to the nearest hundredth.
What about the nearest hundredth?Look at the rightmost place value to see how to round a number to the closest hundredth (the thousandths this time). In the same way, simply eliminate all the digits to the right if the number is four or less. Remove all the digits to the right after adding 1 to the digit in the hundredths position if the number is five or above.
Take into account the hundredths place (9) to convert 1.299 to the nearest tenth, 1.3. To round to the nearest hundredth, consider the thousandths place (9) The tenth would be rounded up in this situation to the nearest whole number, 1.30, which is equal to 1.3.
Cos θ= adj/hyp
Cos 74° = x/7
x = 1.93
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Question 10 of 15
How many solutions does 2 + 7x= 4x+3+3x-8 have?
OA. Two solutions
B. Infinitely many solutions
OC. No solutions
OD. One solution
Answers
Answer:
Step-by-step explanation: (Do not read this if it is a test)
Hello! 2 + 7x = 4x + 3 + 3x - 8. How you first want to do this is to solve for x. 7x + 2 = 4x + 3 + 3x - 8. Simplify the like terms. 7x + 2 = 4x + 3x + 3 - 8 is also equal to 7x + 2 = 7x - 5. Subtract 2 from both sides. 7x = 7x - 7. Divide both sides by 7. 7x/7 = 7x/7 - 7/7. The answer is x = x - 1. There is no solution because x cannot equal x minus 1. An example of this is 3 cannot equal 3 - 1 or 2. 3 does not equal 2. The answer is C.
Answer:The answer is C.
Step-by-step explanation:Hello! 2 + 7x = 4x + 3 + 3x - 8. How you first want to do this is to solve for x. 7x + 2 = 4x + 3 + 3x - 8. Simplify the like terms. 7x + 2 = 4x + 3x + 3 - 8 is also equal to 7x + 2 = 7x - 5. Subtract 2 from both sides. 7x = 7x - 7. Divide both sides by 7. 7x/7 = 7x/7 - 7/7. The answer is x = x - 1. There is no solution because x cannot equal x minus 1. An example of this is 3 cannot equal 3 - 1 or 2. 3 does not equal 2.
Which line has a slope of 3/2?
Answers
Answer: It's the top right
Step-by-step explanation:
Every time the line hits a point on a line where the x and y values are whole numbers, it rises 3 and goes over 2 to get to the next point.
GET 40 POINTS TO ANSWER THIS MATH QUESTION! QUICK I HAVE TILL THIS MONDAY!
Answers
The slope-intercept form of the equation is y = (-5/3)x + 19
Her set-up time decrease by 5/3 hours/day
How to write the equation of a line in slope-intercept form?The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system
(a) The slope-intercept form of the equation of a line is y = mx+b,
where m is the slope (rate) and b is the y-intercept (starting point)
Let y be the set up time (hours) and x be the time (days)
m = (y₂-y₁)/(x₂-x₁)
where (x, y) are the coordinate of points on the line
From the graph: x₁ =3, y₁ = 14 and x₂ = 6, y₂ = 9
m = (9-14)/(6-3) = -5/3
y = mx + c
14 = (-5/3)×3 + c
14 = -5 + c
c = 14 + 5
c = 19
Thus, the equation is y = (-5/3)x + 19
(b) At day 0, x = 0:
y = (-5/3)x + 19
y = (-5/3)(0) + 19
y = 19 hours
The slope is decrease rate. Thus, her set-up time decrease by 5/3 hours/day
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The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized
deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,562.
Assume that the standard deviation is a $2167. Use z-table.
a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample
mean within $157 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to
four decimals.
n = 30
n = 50
n = 100
n = 400
b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four
decimals.
A larger sample increases
for a
the probability that the sample mean will be within a specified distance of the population
mean. In this instance, the probability of being within 157 of μ ranges from
for a sample of size 30 to
sample of size 400.
Answers
A. The probability that a sample of taxpayers from this income group are:
n = 30: 0.8159
n = 50: 0.8796
n = 100: 0.9332
n = 400: 0.9984
B. Advantages of a larger sample size are:
it increases precision
reliability of estimate of the population mean
standard error of the mean decreases
How do we determine the probabilities?Using the z-score below:
For a sample size of 30, the z-score is 1.28.
For a sample size of 50, the z-score is 1.64.
For a sample size of 100, the z-score is 2.33.
For a sample size of 400, the z-score is 3.29.
a. The probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $157 of the population mean for each of the following sample sizes:
n = 30: 0.8159
n = 50: 0.8796
n = 100: 0.9332
n = 400: 0.9984
b. The advantage of a larger sample size when attempting to estimate the population mean is that it increases the precision and accuracy of the estimate. As the sample size increases, the sample mean becomes a more reliable estimate of the population mean, and the standard error of the mean decreases.
In this case, as the sample size increases from 30 to 400, the probability of the sample mean being within 157 of the population mean increases from 0.8159 to 0.9984.
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Given quad QRST with coordinates Q(0, 0), R(2, 6), S(6, 6), and T(8, 0).
What is the best name for quad QRST?
Square
Rectangle
Trapezoid
Kite
Answers
The best name for quadrilateral QRST with coordinates Q(0, 0), R(2, 6), S(6, 6), and T(8, 0) include the following: C. Trapezoid.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapezoidNext, we would use an online graphing calculator to construct (plot) quadrilateral QRST on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral QRST on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a trapezoid.
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