Answer:
Perimeter= 12 feet Area= 6 feet (squared)
Step-by-step explanation:
Perimeter= Adding all the sides together, that means it is 3+4+5= 12 feet
Area= Hight times base divided by 2. Because hight times base is area of a rectangle, and a right triangle (and all other triangles) is half of it. Because it is a right triangle, its hight must be 3 or 4, and base also 3 or 4. But no the same number twice, so 3*4=12, 12/2=6 feet (squared).
I hope that helped! =)
Luke's basketball team went to an amusement park at the end of the season. The cost of the admission for 5 coaches and 12 players was 407.50. The admission cost for each coach was 27.50. What was the admission cost for each player?
Answer:the admission cost for each player is $22.5
Step-by-step explanation:
Let x represent the admission cost for each player.
Luke's basketball team went to an amusement park at the end of the season. The cost of the admission for 5 coaches and 12 players was 407.50. The admission cost for each coach was 27.50. This means that
5 × 27.50 + 12x = 407.5
137.5 + 12x = 407.5
Subtracting 137.5 from the left hand side and the right hand side of the equation, it becomes
12x + 137.5 - 137.5= 407.5 - 137.5
12x = 270
Dividing the left hand side and the right hand side of the equation by 12, it becomes
12x/12 = 270/12
x = 270/12 = 22.5
Answer:
$22.5
Step-by-step explanation:
To find the cost for each player, first, let us find the cost of all coaches, then the rest will be for the players
Step 1: Multiply the cost for 1 coach by 5
[tex]27.50 \times 5 = 137.5[/tex]
Step 2: Subtract the result from the total amount of both players and coaches
[tex]407.50 - 137.5 = 270[/tex]
Now we have found the total cost of all 12 players. Next up, we need to find the cost of just one player
Step 3: Divide the result by the number of players
[tex]270 \div 5[/tex]
[tex]= \frac{270}{5}[/tex]
[tex]= 22.5[/tex]
The admission cost for each player was 22.5 dollars.
A small frictionless cart is attached to a wall by a spring. It is pulled 22 cm from its rest position, released at time t = 0, and allowed to roll back and forth for 5 seconds. Its position at time t is s = 22 cos (pi*t).A. What is the cart's maximum speed? When is the cart moving that fast? Where is it then? What is the magnitude of the acceleration then?B. Where is the cart when the magnitude of the acceleration is greatest? What is the cart's speed then?I cannot figure out part b.I have part a: which is 69.1 cm/sec
Answer:
a) 22π cm/s; on the odd half-second (t=0.5, 1.5, 2.5, 3.5, 4.5); at the rest position; zero
b) 22 cm from the rest position; zero
Step-by-step explanation:
Undamped simple harmonic motion is not complicated. Acceleration is a maximum where the applied force is a maximum, at the extremes of position. Since the position is extreme, the velocity is zero at those points. All of the energy is potential energy.
The speed is a maximum when the object is at the rest position, There is no applied force at that point, and no acceleration. All of the energy has been transformed to kinetic energy.
Part A:
The cart's velocity is given by the derivative of the position:
s'(t) = -22π·sin(πt)
This has a maximum magnitude (speed) of 22π ≈ 69.1 cm/s, as you have noted.
The speed is a maximum at the rest position. The cart is there on each odd quarter-period, at t=0.5, 1.5, 2.5, 3.5, 4.5 seconds.
The cart's acceleration is given by the derivative of the velocity:
s'' = -22π²·cos(πt)
On the odd quarter-period, the acceleration is zero.
Part B:
Acceleration is greatest when position is greatest (both are cosine functions). The speed of the cart is zero then (it is a sine function). The sine is at an extreme when the cosine is zero, and vice versa.
_____
The attached graph shows position, velocity, and acceleration (color coded).
To solve part b of the question, we need to find the point where the magnitude of the acceleration is greatest. This can be done by finding the derivative of the acceleration function and setting it equal to zero. The value of t that satisfies this equation can then be used to find the position and speed of the cart.
Explanation:In order to solve part b of the question, we need to find the point where the magnitude of the acceleration is greatest. We can do this by finding the derivative of the acceleration function and setting it equal to zero. The derivative of the acceleration function is given by: a'(t) = -22πsin(πt). Setting this equal to zero gives: -22πsin(πt) = 0. Solving for t, we find that t = 1/2.
Now that we have the value of t, we can plug it back into the position function to find the position of the cart when the magnitude of the acceleration is greatest. The position function is given by: s(t) = 22cos(πt). Plugging in t = 1/2, we get: s(1/2) = 22cos(π/2) = 0.
To find the cart's speed when the magnitude of the acceleration is greatest, we can plug t = 1/2 into the velocity function. The velocity function is the derivative of the position function, which is given by: v(t) = -22πsin(πt). Plugging in t = 1/2, we get: v(1/2) = -22πsin(π/2) = 22π.
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An investigator reviewed the medical records of 200 children seen for care at Boston Medical Center in the past year who were between the ages 8 and 12 and identified 40 children with asthma. He also identified 40 children of the same ages who were free of asthma. Each child and their family were interviewed to assess whether there might be an association between certain environmental factors such as exposure to second-hand smoke. This study is an example of a:_______. a. randomized controlled trial. b. case-control study. c. cohort study. d. crossover trial.
Answer:
cohort study
Step-by-step explanation:
Given that an investigator reviewed the medical records of 200 children seen for care at Boston Medical Center in the past year who were between the ages 8 and 12 and identified 40 children with asthma. He also identified 40 children of the same ages who were free of asthma. Each child and their family were interviewed to assess whether there might be an association between certain environmental factors such as exposure to second-hand smoke.
The objective of this experiment is to test the causes of the disease asthma and to find the risk factors and environment causing this disease.
So this cannot come under randomized control nor case control.
Cross over study is to put to two different environments two groups and study. But here nothing is influenced actual environments are studied
Hence this comes under cohort study
Answer:
cohort study
Step-by-step explanation:
For a two day rental at thd surf shop, it cost $45 to rent a surfboard and $60 to rwnt a paddleboard. On a certain weekend, the surf shop rented 44 total surfboards and paddleboards and made $2265. How many paddle boards were rented?
Answer: 19 paddle boards were rented.
Step-by-step explanation:
Let x represent the number of surfboards that were rented.
Let y represent the number of paddleboards that were rented.
A total of 44 surfboards and paddleboards were rented. It means that
x + y = 44
For a two day rental at the surf shop, it cost $45 to rent a surfboard and $60 to rent a paddleboard.
The total cost of surfboards and paddleboards rented was $2265. This means that
45x + 60y = 2265 - - - - - - - - - 1
Substituting x = 44 - y into equation 1, it becomes
45(44 - y) + 60y = 2265
1980 - 45y + 60y = 2265
- 45y + 60y = 2265 - 1980
15y = 285
y = 285/15 = 19
x = 44 - y = 44 - 19
x = 25
You go out to pick blueberries and black berries. You know that to make a black and blue pie, you need to have 5 blueberries for every 2 blackberries you pick. If an entire pie has 140 berries, the pie contains_____ blueberries and ______ blackberries.
Answer:
100 blueberries and 40 blackberries
Step-by-step explanation:
Multiply each by 20 and you have 5 x 20 = 100 and 2 x 20 = 40
Let A be the set of students at your school and B the set of books in the school library. Let R₁ and R₂ be the relations consisting of all ordered pairs (a, b), where student a is required to read book b in a course, and where student a has read book b, respectively. Describe the ordered pairs in each of these relations.
a) R₁ ∪ R₂
b) R₁ ∩ R₂
c) R₁ ⊕ R₂
d) R₁ − R₂
e) R₂ − R₁
Answer:a) {(a,b)[a is required to read book b or has read book b]}
b) {(a,b)[a has read book b that he was required to read)]
c) {(a,b)[a is either required to read book b or has read it but he has not read both)]
d) {(a,b)[a is required to read book b and he is yet to read book b)]
e) {(a,b)[a has read book b that was not required)]
Step-by-step explanation: The answers is a description of the explanation
The question asks about various operations with the sets R₁ and R₂, which represent the students and the books they are required to read and have read respectively. It looks at the union, intersection, symmetric difference, and difference of these two sets in relation to each other, where variables 'A' and 'B' represent a student and a book respectively.
Explanation:This is a question in set theory. We will be defining the different operations performed on the ordered pairs of two relations R₁ and R₂. Let's consider 'A' as a student studying in your school and 'B' be a book in the library, the ordered pairs (A, B) indicate the relationship between the student and the book.
R₁ ∪ R₂: Represents the union of the relations. This would contain all ordered pairs where 'A' is required to read 'B' (relation R₁) or 'A' has read 'B' (relation R₂).R₁ ∩ R₂: Represents the intersection of the relations. This would include all ordered pairs where 'A' is required to read 'B' (relation R₁) and 'A' has also read 'B' (relation R₂). In simpler terms, it's the books that students were required to read and they have read.R₁ ⊕ R₂: Represents the symmetric difference of the relations. This would contain ordered pairs where 'A' is either required to read 'B' or 'A' has read 'B', but not both.R₁ − R₂: Represents the difference of the relations. This includes all ordered pairs where a student 'A' is required to read a book 'B', but has not read it yet.R₂ − R₁: Represents the reverse difference of the relations. This set includes all ordered pairs where a student 'A' has read a book 'B' but was not required to read it for a course.Learn more about Set Theory here:
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The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?
A) 6.0 cmB) 6.1 cmC) 8.4 cmD) 8.5 cm
Answer:
8.4 cm
Step-by-step explanation:
The longest side of an acute isosceles triangle is 12 centimeters.
Let x be the length of the smallest side
Isosceles triangle has one longest side and two smallest sides
so its acute triangle
[tex]c^2<a^2 +b^2[/tex]
where c is the longest side
a and b are two shortest sides 'x'
[tex]c^2<x^2 +x^2[/tex]
[tex]12^2<x^2 +x^2[/tex]
[tex]144<2x^2[/tex]
divide both sides by 2
[tex]72<x^2[/tex]take square root on both sides
[tex]8.4<x[/tex]
So 8.4 cm
Water is withdrawn from a conical reservoir, 8 feet in diameter and 10 feet deep (vertex down) at the constant rate of 5 ft³/min. How fast is the water level falling when the depth of the water in the reservoir is 5 ft? ([tex]V = \frac{1}{3} \pi r^2h[/tex]).
Answer:
Water level in the reservoir is falling at the rate of 0.398 ft per minute.
Step-by-step explanation:
From the figure attached,
Water level in the reservoir has been given as 10 feet and radius of the reservoir is 4 feet.
Let the level of water in the reservoir after time t is h where radius of the water level becomes r.
ΔABE and ΔCDE are similar.
Therefore, their corresponding sides will be in the same ratio.
[tex]\frac{r}{h}=\frac{4}{10}[/tex]
[tex]r=\frac{2}{5}h[/tex] --------(1)
Now volume of the water V = [tex]\frac{1}{3}\pi r^{2}h[/tex]
From equation (1),
V = [tex]\frac{1}{3}\pi (\frac{2}{5}h)^{2} h[/tex]
V = [tex]\frac{4\pi h^{2}\times h}{75}[/tex]
[tex]\frac{dV}{dt}=\frac{4\pi }{75}\times \frac{d}{dt}(h^{3})[/tex]
[tex]\frac{dV}{dt}=\frac{4\pi }{75}\times (3h^{2})\frac{dh}{dt}[/tex]
[tex]\frac{dV}{dt}=\frac{12\pi h^{2}}{75}\times \frac{dh}{dt}[/tex]
Since [tex]\frac{dV}{dt}=5[/tex] feet³ per minute and h = 5 feet
[tex]5=\frac{12\pi (5)^{2}}{75}\times \frac{dh}{dt}[/tex]
[tex]5=4\pi \frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}=\frac{5}{4\pi}[/tex]
[tex]\frac{dh}{dt}=0.398[/tex] feet per minute
Therefore, water level in the reservoir is falling at the rate of 0.398 feet per minute.
The length of the entire border of the Unites States is approximately 32,000 miles, 5 8 of which is coastline. How long is the coastline of the U.S., and how long are the land boundaries?
Answer:the coastline is 20000 miles.
The land boundaries are 12000 miles.
Step-by-step explanation:
The length of the entire border of the Unites States is approximately 32,000 miles.
5/8 of the entire length is the coastline. It means that the length of the coastline of the U.S would be
5/8 × 32000 = 20000 miles.
Therefore, the length of the boundaries of the US would be
32000 - 20000 = 12000 miles.
Part a During second period, Janet completed a grammar worksheet. She got 14 questions correct and 42 questions incorrect. What percentage did Janet get correct?
The percentage of correct answers out of the total question is 25%.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
The number of incorrect questions = is 42
The number of Correct questions = 14
So, the total number of questions is,
42 + 14 = 56
Let the percentage of correct questions be x.
x = 14/56 × 100
x = 1400/56
x = 25%
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Suppose that a newspaper predicted that Candidate A would defeat Candidate B in a certain election. They conducted a poll of telephone directories with a response rate of 24%. On the basis of the results, the newspaper predicted that Candidate A would win with 57% of the popular vote. However, Candidate B won the election with about 62% of the popular vote. At the time of this poll, most households with telephones belonged to the party of Candidate A. Name two biases that led to this incorrect prediction.
A. Sampling bias: Using an incorrect frame led to under-coverage.
Response bias: The way the poll was administered showed bias.
B. Non-response bias: The low response rate caused bias.
Sampling bias: Using an incorrect frame led to undercoverage.
C. Non-response bias: The low response rate caused bias.
Response bias: The way the poll was administered showed bias.
Answer: B, non response bias, and sampling bias
Step-by-step explanation:
Non response bias is when there is a huge difference between people that responded or took part in the polls and people that didn't respond, since we are told the response rate was 24% and sampling bias because it is said that most people using telephones belong to the party of candidate A, so using a telephone poll makes the sampling biased
The incorrect prediction occurred due to non-response bias, where not all opinions were represented due to a low response rate, and sampling bias, where the sampling method resulted in an under-representation of the whole population.
Explanation:In this election prediction scenario, two types of biases influenced the incorrect prediction. The first is a non-response bias. Only 24% of people responded to the poll which means the opinions of the remaining 76% of people are not represented in the survey results. This can cause a distortion in the data and result in an inaccurate prediction. Secondly, there was a sampling bias present. The poll was conducted via telephone directories, and at the time, most telephone households were supportive of Candidate A's party. This means that the sample frame does not accurately represent the target population, leading to an 'undercoverage' issue. As a result of these biases, the newspaper predicted that Candidate A would win, but in fact, Candidate B won with about 62% of the popular vote.
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A smoothie stores sell 3 strawberry smoothies and 5 banana smoothies for a total cost of 27.50 .The strawberry smoothie cost 0.50 more than the banana smoothies
Answer:
Cost of each banana smoothies is 3.25 and Cost of each Strawberry smoothie is 3.75.
Step-by-step explanation:
Given:
Number of strawberry smoothies =3
Number of banana smoothies = 5
Total cost = 27.50
We need to find cost of strawberry cookies and cost of banana cookies.
Solution:
Let cost of each banana smoothies be 'x'.
Given:
The strawberry smoothie cost 0.50 more than the banana smoothies.
So we can say that;
Cost of each Strawberry smoothie = [tex]0.5+x[/tex]
Now we can say that Total cost is equal to sum of Number of strawberry smoothies multiplied by Cost of Strawberry smoothie and Number of banana smoothies multiplied by cost of banana smoothies.
framing in equation form we get;
[tex]3(x+0.5)+5x=27.5[/tex]
Applying distributive property we get;
[tex]3x+1.5+5x=27.5\\\\8x+1.5=27.5[/tex]
Subtracting both side by 1.5 we get;
[tex]8x+1.5-1.5=27.5-1.5\\\\8x=26[/tex]
Dividing both side by 8 we get;
[tex]\frac{8x}{8}=\frac{26}{8}\\\\x=3.25[/tex]
Cost of each banana smoothies = 3.25
Cost of each Strawberry smoothie = [tex]0.5+x=0.5+3.25=3.75[/tex]
Hence Cost of each banana smoothies is 3.25 and Cost of each Strawberry smoothie is 3.75.
Answer:
the slope is 4
Use the formula for the probability of the complement of an event. A coin is flipped 4 times. What is the probability of getting at least 1 tail?
Answer: 15/16
Step-by-step explanation:
There will be 16 outcomes for 4 coins=2^4
Probability of only head is : P(C)=1/16
P(C) + P(C') = 1
P(C') = 1 - P(C)
P(C') = 1 - 1/16
Take the l.c.m
P(C') = (16-1) / 16
P(C') = 15/16
So the probability of getting at least 1 tail is 15/16
Answer:
D 0.94
Step-by-step explanation:
when solved the answer is 15/16. This equals 0.9375 which rounded to the second decimal = 0.94
Condo living room is in the shape of a rectangle has a area of three 60 ft.² the width of the living room is 58 it's what what is the length of the living room
Question is not proper, Proper question is given below;
Consuelo's living room is in the shape of a rectangle and has an area of 360 square feet. The width of the living room is [tex]\frac{5}{8}\ ft[/tex] its length. What is the length of the living room?
Answer:
Length of the living room is 24 feet.
Step-by-step explanation:
Given:
Area of the living room = [tex]360 \ ft^2[/tex]
We need to find the length of the living room.
Solution:
the length of the living room be 'l'.
Given:
Width of the living room [tex]\frac{5}{8}\ ft[/tex] of it length.
width [tex]w= \frac{5}{8}l[/tex]
It has been given that living room is in rectangular format.
So we can say that;
Area of living room is equal to length of the living room times width of the living room.
framing in equation form we get;
[tex]l\times w=360\\\\l\times\frac{5}{8}l=360\\\\\frac{5}{8}l^2=360[/tex]
Now Multiplying both side by [tex]\frac{8}{5}[/tex] we get;
[tex]\frac{5}{8}l^2\times\frac{8}{5}=360\times\frac{8}{5}\\\\l^2= 576[/tex]
Taking square root on both side we get;
[tex]\sqrt{l^2} =\sqrt{576} \\\\l=24 \ ft[/tex]
Hence Length of the living room is 24 feet.
the area A of a triangle is given by the formula A=1\2 bh where b is the base and h is the height : solve the formula for the height
Answer:
h=2A/b
Step-by-step explanation:
A=1/2bh
Isolate h by moving 1/2 and b to the other side of the equation.
Divide each side by 1/2,which is multiplying by 2, which gives you 2A=bh.Now divide each side by b, which gives you 2A/b=h. Turn it around.
2A/b=h becomes h=2A/b
Answer:
h=2A/b
Step-by-step explanation:
The perimeter of a square with side length $x$ units is equal to the circumference of a circle with radius 2 units. What is the value of $x$?
Answer:
x = π
Step-by-step explanation:
The circumference of the circle is given by ...
C = 2πr = 2π(2) = 4π
The perimeter of a square of side length x is given by ...
P = 4x
You want the perimeter equal to the circumference, so ...
4π = 4x
π = x . . . . . . . divide by 4
The value of x is π.
The side length x of the square is the same as the radius of the circle, which is π units, because the perimeter of the square, 4x units, is set equal to the circumference of the circle, 4π units.
It is asked to determine the side length x of a square when its perimeter is equal to the circumference of a circle with radius 2 units.
To find the perimeter of a square, you multiply the side length by 4, since a square has four equal sides. Thus, the perimeter of the square is 4x units.
The formula for the circumference of a circle is [tex]C = 2\pi r,[/tex] where r is the radius of the circle.
Given that the radius is 2 units, the circumference of the circle would be [tex]2\pi (2) = 4\pi[/tex]units.
By setting the two equal to each other:
[tex]4x = 4\pi[/tex]
Divide both sides by 4 to isolate x:
[tex]x = \pi[/tex]
Therefore, the side length x of the square is π units.
What is the fourth root of -16?
Answer:
The answer to your question is 2i
Step-by-step explanation:
[tex]\sqrt[4]{-16}[/tex]
- Get the prime factors of -16
- 16 2
- 8 2
- 4 2
- 2 2
1
16 = 2⁴
- Express the -16 as a power
[tex]\sqrt[4]{-2^{4}} or \sqrt[4]{2^{4}i^{2}}[/tex]
Remember that -1 = i²
- Get the fourth root of -16
2i
In the figure, . Find x and y.
Question 3 options:
a. x = 32, y = 137
b. x = 38, y = 151
c. x = 52, y = 137
d. x = 137, y = 52
Answer:
The answer to your question is x = 52° and y = 137°
Step-by-step explanation:
Process
1.- Find the value of x using the large right triangle, remember that the sum of the internal angles in a triangle equals 180°.
x + 38 + 90 = 180
x = 180 - 90 - 38
x = 52°
2.- To find y, we notice that x and y -9 are supplementary angles so their sum gives 180°.
x + y - 9 = 180
Substitution
52 + y - 9 = 180
y = 180 + 9 - 52
y = 137°
Point X is at 2/3 on a number line on the number line point why is the same distance from 0 is point X but has a numerator of 8 what is the denominator of the fraction at point why
Answer:
Denominator
x = 12
Step-by-step explanation:
Let x be the denominator of the fraction at point y.
Given:
Point X is at 2/3 on a number line from 0.
On the same line, point y is the same point from 0.
Numerator of the fraction at point y is 8.
We need to find the denominator of the fraction at point y.
Solution:
From the above statement the distance from 0 to point X and 0 to point Y is same, so point X is equal to Y.
[tex]\frac{2}{3} =\frac{8}{x}[/tex]
By cross multiplication.
[tex]x=\frac{8\times 3}{2}[/tex]
[tex]x= \frac{24}{2}[/tex]
[tex]x = 12[/tex]
Therefore, the denominator of the fraction at point y is 12.
Bianca and Meredith are sisters. Meredith's height is 23 of Bianca's height plus 32 inches. Meredith is 60 inches tall. A girl is sixty inches tall. Write an equation to find Bianca's height, x, in inches.
Answer:
Bianca's height = 42 inches
Step-by-step explanation:
Let x be the Bianca height.
Given:
Meredith height = 60 inches
We need to find the Bianca height.
Solution:
From the given statement the Meredith's height is [tex]\frac{2}{3}[/tex] of Bianca's height plus 32 inches, so the equation is.
Meredith's height = [tex]\frac{2}{3}(Bianca\ height)+32[/tex]
Substitute Meredith's height in above equation.
[tex]60=\frac{2}{3}x+32[/tex]
Now we solve the above equation for x.
[tex]\frac{2}{3}x=60-32[/tex]
[tex]\frac{2}{3}x=28[/tex]
By cross multiplication.
[tex]x=\frac{3\times 28}{2}[/tex]
28 divided by 2.
[tex]x= 3\times 14[/tex]
[tex]x=42\ in[/tex]
Therefore, the height of the Bianca is 42 inches.
PLZ HELP WORTH 50 PTS, WILL GIVE BRAINLIEST!!!
Answer the following questions about the problem above. Write in complete sentences to get full credit.
1. What is the slope for section "d" of Mrs. Washington's commute.
2. What does it mean that the slope is negative in context of the problem?
3. Why are the slopes different over different intervals?
4. How long does it take Mrs. Washington to get home? How did you know this?
Answer:
1. 20-15/0-8= -5/8
2. In a positive slope the Y value increases as the X value increases (as the line moves towards the right it gets higher). In a negative slope the Y value decreases as the X value increases (as the line moves towards the right it gets lower). (Question 3 is in here)
4. It depends on the amount of time she's been driving
The plants in Kayla's garden have a 4-foot 3 8-foot area in which to grow. The garden is bordered by a brick walkway of width w. Write two equivalent expressions to describe the perimeter of Kayla's garden, including the walkway.
The perimeter of Kayla's garden including the walkway can be calculated using the formula P = 2(4 + 2w) + 2(3 + 2w), where w is the width of the walkway. This can also be rearranged as P = 2*(4 + 3 + 2w + 2w).
Explanation:The perimeter of a rectangle, like the garden in question, is usually calculated by adding up the lengths of all its sides. In this case, however, the garden is bordered by a walkway of width w. Thus, to calculate the total perimeter, including the walkway, we need to account for this additional width on all four sides of the garden.
The original dimensions of the garden are 4 feet by 3 feet. With the walkway, the new dimensions become (4+2w) feet by (3+2w) feet, because the width of the walkway is added on both sides of the lengths.
Therefore, the two equivalent expressions for the perimeter, P, of Kayla's garden, including the walkway, are P = 2(4 + 2w) + 2(3 + 2w) or simply rearranged as P = 2*(4 + 3 + 2w + 2w). In these expressions, w is the width of the walkway.
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Lucy's Lunch and Latte has found that customers are put off by the local tourism tax of 9% that is added to their bill. If Lucy decides to cover the tax herself, rather than adding it to the customer's bill, what percent will the customer see in savings? Write your answer as a percent rounded to the nearest tenth. (Hint: the answer is not 9%.)
Answer:
Customer will save 8.3%.
Step-by-step explanation:
Let the amount of bill paid by the customers = $x
Local tourism tax = 9%
Total amount of bill including local taxes
= (x + 9% of x)
= x + 0.09x
= 1.09x
If Lucy decides to pay the tax portion of the bill = 0.09x
Then percentage saving by the customer = [tex]\frac{\text{Taxes on bill}}{\text{Bill amount including tax}}\times 100[/tex]
= [tex]\frac{0.09x}{1.09x}\times 100[/tex]
= 8.26%
≈ 8.3%
Therefore, customer will see 8.3% saving.
Compute the following products.
a. (4x + 5)(4x - 5)
b. (4x + 5)2
Jayden has some dimes and some quarters. He has at most 25 coins worth at least $4.60 combined. If Jayden has 7 dimes, determine all possible values for the number of quarters that he could have.
Answer:
16,17,18
Step-by-step explanation:
\underline{\text{Define Variables:}}
Define Variables:
May choose any letters.
\text{Let }d=
Let d=
\,\,\text{the number of dimes}
the number of dimes
\text{Let }q=
Let q=
\,\,\text{the number of quarters}
the number of quarters
\text{\textquotedblleft at most 25 coins"}\rightarrow \text{25 or fewer coins}
“at most 25 coins"→25 or fewer coins
Use a \le≤ symbol
Therefore the total number of coins, d+qd+q, must be less than or equal to 25:25:
d+q\le 25
d+q≤25
\text{\textquotedblleft at least \$4.60"}\rightarrow \text{\$4.60 or more}
“at least $4.60"→$4.60 or more
Use a \ge≥ symbol
One dime is worth $0.10, so dd dimes are worth 0.10d.0.10d. One quarter is worth $0.25, so qq quarters are worth 0.25q.0.25q. The total 0.10d+0.25q0.10d+0.25q must be greater than or equal to \$4.60:$4.60:
0.10d+0.25q\ge 4.60
0.10d+0.25q≥4.60
\text{Plug in }\color{green}{7}\text{ for }d\text{ and solve each inequality:}
Plug in 7 for d and solve each inequality:
Jayden has 7 dimes
\begin{aligned}d+q\le 25\hspace{10px}\text{and}\hspace{10px}&0.10d+0.25q\ge 4.60 \\ \color{green}{7}+q\le 25\hspace{10px}\text{and}\hspace{10px}&0.10\left(\color{green}{7}\right)+0.25q\ge 4.60 \\ q\le 18\hspace{10px}\text{and}\hspace{10px}&0.70+0.25q\ge 4.60 \\ \hspace{10px}&0.25q\ge 3.90 \\ \hspace{10px}&q\ge 15.60 \\ \end{aligned}
d+q≤25and
7+q≤25and
q≤18and
0.10d+0.25q≥4.60
0.10(7)+0.25q≥4.60
0.70+0.25q≥4.60
0.25q≥3.90
q≥15.60
\text{The values of }q\text{ that make BOTH inequalities true are:}
The values of q that make BOTH inequalities true are:
\{16,\ 17,\ 18\}
{16, 17, 18}
Jayden must have at least 16 quarters in order to have at most 25 coins worth at least $4.60 combined.
Explanation:Let's assume Jayden has x quarters. Since Jayden has 7 dimes, he has a total of 7 + x coins. The value of a dime is $0.10, so the value of the dimes is 7 × $0.10 = $0.70.
The value of a quarter is $0.25, so the value of the quarters is x × $0.25 = $0.25x. The total value of all the coins is at least $4.60, so we have the equation:
$0.70 + $0.25x ≥ $4.60.
Simplifying the equation, we get:
$0.25x ≥ $4.60 - $0.70
$0.25x ≥ $3.90
x ≥ $3.90 / $0.25
x ≥ 15.6
Since we can't have a fraction of a coin, Jayden must have at least 16 quarters in order to have at most 25 coins worth at least $4.60 combined.
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Suppose we know two of the three people have Alzheimer's disease. What is the conditional probability that they are both younger than 80 years of age?
Answer: 0.1064
Step-by-step explanation:
D= Both Alzheimer's are less than 80years old.
E= Two of 3 people who have Alzheimer's.
P(D | E ) = P ( D ∩ E)
P ( E )
= P ( A ∩ B ∩ C )
P ( A ∩ B ∩ C ) + P ( A ∩ B ∩ C ) + P ( A ∩ B ∩ C )
= Pa * Pb * (1 - Pc ) Pa * Pb * (1 - Pc ) + (1 - Pa ) * Pb * Pc + Pa * (1 - Pb ) * Pc
= 0.0017
=0.0010+0.0017+0.0037
=0.1064
The conditional probability that two individuals with Alzheimer's are both under 80 cannot be precisely calculated without more information about the general probabilities of each condition. However, the general formula for calculating conditional probability is P(A and B) = P(A) * P(B|A).
Explanation:This is essentially a question about conditional probability. In order to calculate the conditional probability suggested by the question – that is, the probability that both individuals with Alzheimer's disease are younger than 80, given that we know that two people have the disease – we'd need more information about the overall probabilities of having Alzheimer's disease and being under 80. However, if we had this information the formula for conditional probability is P(A and B) = P(A) * P(B|A). In this equation, P(A) would be the probability that a randomly selected individual has Alzheimer's, P(B|A) would be the probability that a known Alzheimer's patient is under 80, and P(A and B) is the conditional probability we're trying to figure out. So, we'd need to multiply P(A) by P(B|A) to get P(A and B)
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With a short time remaining in the day, a delivery driver has time to make deliveries at 66 locations among the 99 locations remaining. How many different routes are possible? There are _________ possible different routes. (Simplify your answer.)
Answer: 197,443,926,105,102,399,225,573,693
Step-by-step explanation:
Here we use combination which is the selection of all or part of a set of objects or items without considering the order of selection.
Mathematically, The number of 'r' combinations from 'n' elements is given as :
nCr = n!÷((n-r)!r!)
From the question above :
n=99 r=66
99C66 = 99!÷((99-66)!66!)
99!÷(33!66!) = 197,443,926,105,102,399,225,573,693
There are 197,443,926,105,102,399,225,573,693 different possible routes.
(22 POINTS)
Which graph represents the function below?
Answer:
The first graph
Step-by-step explanation:
From the definition of [tex]h[/tex] we can see that:
[tex]h(2)=-3\cdot 2+2 = -6+2=-4[/tex]
So, we can eliminate the third answer.
Now we can take for example [tex]x=4[/tex]:
From the definition of [tex]h[/tex] we can see that:
[tex]h(4)=\frac{1}{2}\cdot 4-4 = 2-4=-2[/tex]
If we take a look at the two remanining graphs we can see that at the first graph indeed it is h(4)=-2,and on the second graph it is h(4)=-6
So, the correct answer is the first graph
Tommy's first soup can has a radius of 2 inches and a height of 6 inches. How much soup will it hold? Cylinder V = Bh 1. Write the formula for the area of a circle to find B: 2. Substitute the actual measures for the variables: 3. Evaluate the power: V = πr2h V = π(22)(6) V = π(4)(6) 4. Simplify: V = π in.3
Answer:
24
Step-by-step explanation:
The can will hold 75.36 inch³ of soup.
What is Volume of Cylinder?The volume of a cylinder with base radius 'r' and height 'h' is,
V = πr²h. If its base diameter is d, then we have d = r/2.
Given:
Radius = 2 inches
Height = 6 inches
So, Volume of Cylinder = πr²h
Now, put r= 2 inches and h= 6 inches
Then, Volume of cylinder = 3.14 x 2 x 2 x 6
Volume of Cylinder = 3.14 x 24
Volume of Cylinder = 75.6 inch³
Hence, the can hold 75.36 inch³.
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Two physics students are doing a side competition during a game of bowling, seeing who can toss a ball with the larger momentum. The first bowler throws a 4.5 kg ball at 8.6 m/s. Part A A second bowler throws a 6.4 kg ball. What speed must she beat to win the competition?
Answer:
she should beat a speed of v₂ = 6.04 m/s in order to win the competition
Step-by-step explanation:
Since the momentum p is defined as
p = m*v
where
m= mass of the ball
v= velocity of the ball
denoting 1 and 2 as the first and second bowler , then to reach the momentum of the first bowler
p₂=p₁
therefore
m₁*v₁ = m₂*v₂
v₂ = v₁ * (m₁/m₂)
replacing values
v₂ = v₁ * (m₁/m₂) =8.6 m/s * (4.5 kg/6.4 kg ball) = 6.04 m/s
then since the momentum p = m*v increases with increasing v (at constant m) , she should beat a speed of v₂ = 6.04 m/s in order to win the competition