Which one of the following will result in movement along the demand curve for clothing as opposed to a shift in the demand curve itself?
Answer:
d) Clothing prices decline because manufacturers shift to production in countries with lower wages.
Step-by-step explanation:
Demand is the quantity of goods or services consumers are able and willing and able to buy at a given price and at a particular time.
Movement along the demand curve also known as change in quantity demanded is an increase or decrease in the quantity demanded of goods or services due to change in the price of the good or service itself.
It is important to note that the only factor causing movement along the demand curve is change in the price of the product.
22% of adults would pay more for environmentally friendly products he randomly select 10 adults find the probability that the number of adults who would pay more for environmentally friendly products is a exactly to be more than two and see between two and five inclusive
Answer: 0.383 and 0.6671
Step-by-step explanation:
Take 22%, that is 0.22 to be probability of success.
That means "1-0.22 = 0.78" is the probability of failure.
When dealing with selection in probability mathematics, the combination equation is used.
Probability of selecting number 'r' as a successful outcome from a given number 'n' is given as
nCr * p^r * q^n-r
Where p is the probability of success= 0.22
q is the probability of failure= 0.78
n is the total number of sample =10
r is the varying outcome of number of success.
For the first question, number of success is asked to be everything more than 2, that is probability of choosing 3,4,5,6,7,8,9,10 people with a successful outcome (adults who will pay more for environmentally friendly product.)
Instead of going through the long process of checking probability of success for choosing 3,4,5,6,7,8,9,10 adults who will pay more, we can simply find the probability of choosing 0,1,2 adults who will pay more and subtract the answer from 1.
By doing this, we first check for probability of choosing 0 adult that will pay More and this is gotten by putting r=0 in our probability Formula. The Formula becomes
=10C0 * 0.22^0 * 0.78^10
=1 *1 * 0.0834= 0.0834
Hence, Probability of Choosing 0 adult that will Pay more is 0.0834
To Check for probability of choosing 1 adult that will pay more becomes
=10C1 * 0.22^1 * 0.78^9
=10 * 0.22 * 0.1069 = 0.2352
Hence, Probability of choosing 1adult that will pay more = 0.2352
To Check for the probability of choosing 2adults that will pay more becomes
=10C2 * 0.22^2 * 0.78^8
=45 * 0.0484 * 0.1370 = 0.2984
Therefore the total sum of choosing 0,1,2 adults that are willing to pay more becomes
= 0.0834+ 0.2352+ 0.2984 = 0.617
So to determine the probability of choosing more than 2 adults, that is, 3,4,5,6,7,8,9,10 adults that are willing to pay more, we subtract 0.617 from 1.
This gives 1-0.617 = 0.383
Hence, probability of choosing more than 2 people that are willing to pay more than 2 = 0.383.
To determine the probability of choosing between two and five people inclusive, we follow the same probability formular but r becomes 2,3,4,5 differently.
For probability of choosing 2 adults, we already calculated it to be 0.2984 earlier.
For probability of choosing 3 adults, it becomes
10C3 * 0.22^3 * 0.78^7
=120* 0.0106 * 0.1757 = 0.2235
For the probability of choosign 4 adults, it becomes
10C4 * 0.22^4 * 0.78^6
= 210 * 0.0023 * 0.2252 = 0.1088
For the probability of choosing 5 adults, it becomes
10C5 * 0.22^5 * 0.78^5
= 252 * 0.0005 * 0.2887 = 0.0364
Hence, the probability of choosing between 2 and 5 adults becomes
0.2984 + 0.2235 + 0.1088 + 0.0364 = 0.6671
To find the probability of the number of adults who would pay more for environmentally friendly products, use the binomial probability formula.
Explanation:To find the probability of the number of adults who would pay more for environmentally friendly products, we need to use the binomial probability formula.
The formula is: P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where:
P(X=k) is the probability of getting exactly k successesC(n,k) is the number of ways to choose k successes from n trialsp is the probability of success(1-p) is the probability of failuren is the total number of trialsk is the number of successes we want to getLet's calculate the probabilities for the given scenario:
P(X > 2) = 1 - P(X <= 2)
P(X between 2 and 5 inclusive) = P(X=2) + P(X=3) + P(X=4) + P(X=5)
The length of the batter's box on a softball field is 1 t more than twice the width. The ares of the batter's box is 55 ft^2. Find the length and width of the rectangular batter's box.
Answer:length = 11 feet
Width = 5 feet
Step-by-step explanation:
Let L represent the length of the rectangular box.
Let W represent the width of the rectangular box.
The formula for determining the area of a rectangle is expressed as
Area = length × width
The length of the batter's box on a softball field is 1 ft more than twice the width. It means that
L = 2W + 1
The areas of the batter's box is 55 ft^2. It means that
LW = 55
Substituting L = 2W + 1 into LW = 55, it becomes
W(2W + 1 ) = 55
2W² + W = 55
2W² + W - 55 = 0
2W² + 11W - 10W - 55 = 0
W(2W + 11) - 5(2W + 11) = 0
(W - 5) = 0 or 2W + 11 = 0
W = 5 or W = - 11/2
The width cannot be negative, hence, it is 5 ft
L = 2W + 1 = 2 × 5 + 1 = 10 + 1
L = 11 feet
If f(12) = 100(0.50)^12, which expression gives f(x)?
Answer:
f(x) = 100(0.50)x
Step-by-step explanation:
f(1) = 100(0.50)1
f(2) = 100(0.50)2
Therefore f(x) = 100(0.50)x
One angle of a right triangle measures 60°. The side opposite this angle measures 15 inches.
What is the length of the hypotenuse of the triangle?
Enter your answer, in simplest radical form, in the box.
Step-by-step explanation:
To solve this question I would use the sin rule.
The sin rule states that
[tex] \frac{a}{ \sin(a) } = \frac{b}{ \sin(b) } [/tex]
Therefore if you substitute in your numbers you get:
[tex] \frac{a}{ \sin(90) } = \frac{15}{ \sin(60) } [/tex]
If you rearrange that you get:
[tex]a = \frac{15}{ \sin(60) } \times \sin(90) [/tex]
Therefore a = 17.3 Inches (to 3 sf)
This can also be done with basic trigonometry where you would get
[tex] \sin(60) = \frac{15}{h} [/tex]
Rearranging to
[tex]h = \frac{15}{ \sin(60) } [/tex]
meaning the answer is 13.7 inches
================================================
Work Shown:
h = unknown hypotenuse
sin(angle) = opposite/hypotenuse
sin(60) = 15/h
h*sin(60) = 15
h*sqrt(3)/2 = 15
h*sqrt(3) = 2*15
h*sqrt(3) = 30
h = 30/sqrt(3)
h = (30*sqrt(3))/(sqrt(3)*sqrt(3)
h = 30*sqrt(3)/3
h = (30/3)*sqrt(3)
h = 10*sqrt(3)
The volume of water In two containers is in the ratio of 6 to 7. If the volume of the first container is 36 liters, find the volume of the second container?
Answer:
42 liters
Step-by-step explanation:
Set up the ratios as fractions.
6/7 = 36/x
To get the volumes multiply the 6 and the 7 by 6.
This is how you got the 36 for the first volume.
The volume of the second container is 42.
7 x 6 = 42
Research indicates that 90% of the volume of an iceberg is below water. The volume of the iceberg above the water is 160,000 cubic feet. What is the volume of the iceberg below water? The volume below water is cubic feet
Answer:
1,440,000 cubic feet
Step-by-step explanation:
Proportions
We are told that 90% of the volume of an iceberg is below water. It means that 10% is above water. The proportion between the sunk/floating volumes is 90/10=9. The underwater volume of the iceberg is 9 times the above water volume. Thus, the volume of the iceberg below water is 9*160,000 = [tex]\boxed{1,440,000\ cubic feet}[/tex]
The volume of the iceberg below water is 1,440,000 cubic feet.
To determine the volume of the iceberg below the water's surface, we can use the fact that 90% of the iceberg's total volume is submerged underwater.
We are given that the volume of the part above water is 160,000 cubic feet.
Let V be the total volume of the iceberg and V_sub be the volume submerged below the water.
We can set up the following equation based on the given information:
V_sub = 0.9 * V
We know that V_sub + V_above = V, where V_above is the volume above the water's surface. We are given that V_above is 160,000 cubic feet, so we can rewrite the equation as:
V_sub + 160,000 = V
Now, substitute the expression for V_sub from the first equation:
0.9 * V + 160,000 = V
To isolate V_sub, subtract 160,000 from both sides of the equation:
0.9 * V = V - 160,000
Now, subtract V from both sides:
0.9 * V - V = -160,000
0.1 * V = -160,000
Now, divide both sides by 0.1 to find V_sub:
V_sub = (-160,000) / 0.1 = -1,600,000 cubic feet
However, it's important to note that the volume cannot be negative, and this result doesn't make physical sense.
This suggests there might be an issue with the given information or calculations.
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For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min (5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ?
(1) w = max(20, z) for some integer z.
(2) w = max(10, w)
Step-by-step explanation:
Given
w = max (20,z) for some integer z2. and w = max (10,w)
From the first equation we get that w= 20
and it also satisfies the second equation.
∴ The value of min(10,w) = min(10,20) ∵w=20
= 10
Considering both conditions, our w value could be 10 or greater. As we are looking for the minimum value between 10 and w, the result of min(10, w) will be 10.
Explanation:Let's look at the two provided conditions:
Condition 1: w = max(20, z). This means that w is either 20 or some integer greater than 20.Condition 2: w = max(10, w). Here, w could be 10 or greater.Since both conditions suggest that w could be a value 10 or greater, the exponent w in min(10, w) will be at least 10. However, because we're finding the minimum between 10 and w, the value of min(10, w) will be 10.
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Solve the inequality.
2(4x - 3) 2-3(3x) + 5x?
Ox20.5
Ox22
0 (-0, 0.5]
O (-, 2]
Answer:
Option 1) x ≥ 0.5
Step-by-step explanation:
The given inequality is : 2(4x - 3) ≥ -3(3x) + 5x
And the options are:
1) x ≥ 0.5
2) x ≥ 2
3) (–∞, 0.5]
4) (–∞, 2]
==============================
So, the solution is as following:
2(4x - 3) ≥ -3(3x) + 5x
8x - 6≥ -9x + 5x
8x + 9x - 5x ≥ 6
12 x ≥ 6
x ≥ 6/12
x ≥ 0.5
The answer is option 1) x ≥ 0.5
Consider the following conditional statement:
If two angles form a linear pair, then they are supplementary.
Identify the following statements as the converse, inverse, or contrapositive and determine whether each statement is true or false:
a. If two angles are not supplementary, then they do not form a linear pair.
b. If two angles are supplementary, then they form a linear pair.
c. If two angles do not form a linear pair, then they are supplementary.
Answer:
a. contrapositive because it's the converse and inverse. True.
b. converse because it's the reverse of conditional statement. True.
c. That is false so it's not converse, inverse, or contrapositive.
The given statement is: If two angles form a linear pair, then they are supplementary. The inverse is true, the converse is false, and the contrapositive is true.
Explanation:The given statement is: If two angles form a linear pair, then they are supplementary. Let's analyze the options:
a. If two angles are not supplementary, then they do not form a linear pair. This is the inverse of the given statement. It is true because if two angles do not add up to 180 degrees, they cannot form a linear pair.
b. If two angles are supplementary, then they form a linear pair. This is the converse of the given statement. It is false because two supplementary angles may or may not form a linear pair.
c. If two angles do not form a linear pair, then they are supplementary. This is the contrapositive of the given statement. It is true because if angles do not form a linear pair, that means they do not add up to 180 degrees, and hence, they must be supplementary.
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For his long distance phone service, Tony pays an $8 monthly fee plus 6 cents per minute. Last month, Tony's long distance bill was $17.24. For how many minutes was Tony billed?
Answer:tony was billed for 154 minutes.
Step-by-step explanation:
Let x represent the number of minutes for which Tony was billed.
For his long distance phone service, Tony pays an $8 monthly fee plus 6 cents per minute. Converting 6 cents to dollars, it becomes 6/100 = $0.06
This means that if he made x minutes of long distance call in a month, the total cost would be
8 + 0.06x
Last month, Tony's long distance bill was $17.24. It means that
8 + 0.06x = 17.24
0.06x = 17.24 - 8 = 9.24
x = 9.24/0.06
x = 154
There are 75 ducks in a pond 25 ducks are marked as a winner if you take 2 ducks out but don't replace them what is the probably that both ducks are winners
Answer:
Step-by-step explanation:
The total number of ducks in the pond is 75. 25 ducks are marked as a winner.
Probability is expressed as number of possible outcomes/total number of outcomes.
if you take 2 ducks out but don't replace them, the probability that the first duck that you took out is a winner is
25/75 = 1/3
The total number of ducks left would be 74 and the number of winners would be 24.
the probability that the second duck that you took out is a winner is
24/74 = 12/37
Therefore, the probability that both are winners is
1/3 × 12/37 = 4/37
Jorge counted the number of spots of each color on his dog. Which fraction in simplest form shows the spots that are black compared to all the spots Black 8 White 13 Gray 3
1/3 shows the spots that are black as compared to all the spots
Step-by-step explanation:
The simple fraction will consist of number of black spots as numerator and the total number of spots on the dog in denominator.
Given
Number of black spots = b = 8
Number of white spots = w = 13
Number of Gray spots = g = 3
Total spots are:
[tex]t=b+w+g = 8+13+3 = 24[/tex]
So the fraction will be:
[tex]\frac{Number\ of\ black\ spots}{Total\ spots}\\= \frac{b}{t}\\=\frac{8}{24}\\= \frac{1}{3}[/tex]
Hence,
1/3 shows the spots that are black as compared to all the spots
Keywords: Fractions, sum
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Darla told her teacher that she had read XLV pages in her library book. Juan said that he had read XXXIX pages. What is the difference between the number of pages that Darla and Juan read
Answer:
The difference between the number of pages that Darla and Juan read are VI pages.
Step-by-step explanation:
Given:
Darla told her teacher that she had read XLV pages in her library book.
Juan said that he had read XXXIX pages.
Now, to get the difference between the number of pages that Darla read and Juan read.
As, we see the number of pages are in roman numeral symbols.
So, we convert them in numbers first to calculate:
Darla read = XLV pages.
Darla read = 45 pages.
Now,
Juan read = XXXIX pages.
Juan read = 39 pages.
So, to get the difference between the number of pages by subtracting:
[tex]45-39=6[/tex]
Thus, the difference between the number of pages = 6 pages.
Now, converting it into roman numerals:
6 pages = VI pages.
Therefore, the difference between the number of pages that Darla and Juan read are VI pages.
Answer:
A
Step-by-step explanation:
3.) Simplify the expression.
cos ( u + π )
a.) cot u
b.) cos u
c.) sin u
d.) - cos u
e.) tan u
Answer:
Option C) -cosu is correct
Therefore the simplified expression is [tex]cos(u+\pi)=-cosu[/tex]
Step-by-step explanation:
Given expression is [tex]cos(u+\pi)[/tex]
To find the value of the given expression :
By using the formula [tex]cos(A+B)=cosAcosB-sinAsinB[/tex]
Substitute A=u and [tex]B=\pi[/tex] in the above formula we get
[tex]cos(u+\pi)=cosucos\pi-sinusin\pi[/tex]
[tex]=cosu(-1)-sinu(0)[/tex] ( here [tex]cos\pi=-1[/tex] and [tex]sin\pi=0[/tex] )
[tex]=-cosu-0[/tex]
[tex]=-cosu[/tex]
[tex]cos(u+\pi)=-cosu[/tex]
Therefore option C) -cosu is correct
Therefore the simplified expression is [tex]cos(u+\pi)=-cosu[/tex]
Jessica decided to use 15% of her gross income for her down payment for a house. She makes 48,960.00 per year. How much money did jessica's budget allow for the down pyment
Answer:
[tex]Down\ payment = 7,344[/tex]
Step-by-step explanation:
Let x be the amount of 15% of gross income.
Given:
Jessica gross income = 48,960.00
She decided to use 15% amount as down payment.
We need to find the amount of 15% of gross income.
Solution:
Using percentage formula.
[tex]percentage = (\frac{Value}{Total\ value})\times 100[/tex]
Now we substitute 15 in the place of percentage and 48,960 in the place of Total value.
[tex]15=(\frac{x}{48960})\times 100[/tex]
Now, we apply cross multiplication rule.
[tex]x= \frac{48960\times 15}{100}[/tex]
[tex]x=48960\times 0.15[/tex]
[tex]x =7,344[/tex]
Therefore: Down payment is 7,344.
Final answer:
Jessica allocated $7,344 for the down payment on a house based on her 15% gross income allocation.
Explanation:
The budget that Jessica allocated for her down payment on a house is calculated as follows:
Calculate 15% of Jessica's gross income: 15% of $48,960 is $48,960 * 0.15 = $7,344.
Therefore, the budget that Jessica allowed for the down payment on a house is $7,344.
Of the range, the interquartile range, and the variance, the interquartile range is most influenced by an outlying value in the data set.
A. True
B. False
Answer:
Option B) False
Step-by-step explanation:
We define the following terms:
Range:
It is the difference between the minimum and maximum value of data.
It is effected by presence of outliers.
Interquartile range:
It is the difference between the third quartile and the first quartile of data.
Variance:
[tex]\text{Variance} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
It is a measure of spread of the data. It is effected by presence of outliers as they increase the variation in the data.
Thus, the given statement is false.
Find the ratio of the circumference of a circle with radius 1.125 to the circumference of a circle with diameter 2.25. Express your answer in the form a:b where a and b are relatively prime positive integers.
Step-by-step explanation:
Circumference of a circle = πD, where D is the diameter.
Diameter of circle 1 = 1.125
Circumference of circle 1 = π x 1.125
Diameter of circle 1 = 2.25
Circumference of circle 1 = π x 2.25
[tex]\texttt{Ratio of circumferences = }\frac{\pi \times 1.125}{\pi \times 2.25}\\\\\texttt{Ratio of circumferences = }\frac{1}{2}[/tex]
Circumference of circle 1 : Circumference of circle 2 = 1 : 2
Answer:
1:1
Step-by-step explanation:
Combs and Stratton invested $140,000 and $360,000, respectively, in a partnership. They agreed to share net income in proportion to their investments. If the partnership's net income last year was $43,500, how much was each partners share of the net income?
Answer:
Comb's share will be = $12,180
Stratton's share will be = $31,320
Step-by-step explanation:
Given:
Comb's investment in the partnership = $140,000
Stratton's investment in the partnership = $360,000
The net income is shared in proportions of their investment.
Net income last year = $43,500
To find the share of each partner of the net income.
Solution:
Ratio of the investments of Comb to Stratton = [tex]\frac{140,000}{360,000}[/tex][tex]= \frac{14}{36}=\frac{7}{18}[/tex] (Simplest ratio)
Thus, the investments must be shared in the ratio of 7 : 18
Let Comb's share in dollars be = [tex]7x[/tex]
Then, Stratton's share in dollars = [tex]18x[/tex]
Total net income can be given as = [tex]7x+18x=25x[/tex]
Net income = $43,500
So, we have:
[tex]25x=43,500[/tex]
Dividing both sides by 25.
[tex]\frac{25x}{25}=\frac{43,500}{25}[/tex]
∴ [tex]x=1740[/tex]
So, Comb's share will be = [tex]7\times 1740 = \$12,180[/tex]
Stratton's share will be = [tex]18\times 1740 = \$31,320[/tex]
2. Kim and Lauren were driving to Pennsylvania which is 680 miles from them. They are going to complete their trip in 3 days. The distances and average speeds for the first and second days driven are shown below. First day: 3 hours at an average speed of 60 miles per hour. Second day: 5 hours at an average speed of 65 miles per hour. If the average speed on the third day is 35 miles per hour, how many more hours will it take for them to reach their destination?
Answer:
Kim and Lauren have 5 more hours to reach Pennsylvania.
Step-by-step explanation:
Given,
Total distance = 680 miles
We have to find the number of hours taken by them to reach Pennsylvania.
Solution,
For Day 1:
Speed = [tex]60\ mi/h[/tex]
Time = 3 hrs
We know that the distance is equal to speed multiplied with time.
So the equation is;
[tex]Distance = 60\times3=180\ miles[/tex]
For Day 2:
Speed = [tex]65\ mi/h[/tex]
Time = 5 hrs
We know that the distance is equal to speed multiplied with time.
So the equation is;
[tex]Distance = 65\times5=325\ miles[/tex]
Now the total distance traveled in two days is the sum of distance traveled in day 1 and distance traveled in day 2.
Distance traveled in 2 days = [tex]180+325=505\ miles[/tex]
So the remaining distance they have to travel is equal to total distance minus distance traveled in 2 days.
Remaining distance =[tex]680-505=175\ miles[/tex]
Now also given that the speed on day 3 is [tex]35\ mi/h[/tex].
So the time taken to cover the distance is equal to distance divided by speed.
[tex]\therefore time=\frac{175}{35}=5\ hours[/tex]
Hence Kim and Lauren have 5 more hours to reach Pennsylvania.
3 rectangular have a combined volume of 518 cubic feet. Prism A has one- third thof prism B and C. What is the volume. What is the volume of each prism
Question is Incomplete; Complete question is given below;
3 rectangular prisms have a combined volume of 518 cubic feet. Prism A has 1/3 the volume of Prism B. Prisms B and C have equal volume.What is the volume. What is the volume of each prism.
Answer:
Volume of prism A is [tex]74\ ft^3[/tex] and Volume of Prism B and Volume of Prism C is [tex]222\ ft^3[/tex].
Step-by-step explanation:
Let the Volume of 3 prism be A,B,C.
Now Given:
3 rectangular prisms have a combined volume of 518 cubic feet.
so we can say that;
[tex]A+B+C=518 \ ft^3 \ \ \ \ equation \ 1[/tex]
Also Given:
Prisms B and C have equal volume.
[tex]B = C[/tex]
Also given:
Prism A has 1/3 the volume of Prism B.
so we can say that;
[tex]A=\frac{B}{3} = \frac{C}{3}\\\\B=C=3A[/tex]
Now Substituting the value of B and C in equation 1 we get;
[tex]A+B+C=518\\\\A+3A+3A=518\\\\7A=518[/tex]
Dividing both side by 7 we get;
[tex]\frac{7A}{7}=\frac{518}{7}\\\\A= 74 \ ft^3[/tex]
Now Substituting the value of A to find B and C we get;
[tex]B=C=3A=3\times74=222\ ft^3[/tex]
Hence Volume of prism A is [tex]74\ ft^3[/tex] and Volume of Prism B and Volume of Prism C is [tex]222\ ft^3[/tex].
Chris bought 4 chairs for $35 at the beginning of the summer at full retail price.At the end of the summer, he bought 2 more when they were on sale and were marked down by %18 what did Chris pay for all six chairs
Answer:
152.6$
Step-by-step explanation:
35*4=140
Need to find the new amount since it was decreased by 18%
35*18/100=6.30
6.30+6.30
12.6
140+28.7=152.6
A piece of string fits exactly once around the perimeter of a square whose area is 144. Rounded to the nearest whole number, what is the area of the largest circle that can be formed from the piece of string?
Answer:A=183cm^
Step-by-step explanation:
The area of square is :
Let s be side
A= s^2
144= s^2
Square both side
Therefore
s=sqrt(144)
s=12 cm
The perimeter of the square is : 4× s= 4×12= 48cm
So the perimeter of the square is equal to the circumference of the circle.
The equation will be:
4×s=2×pi×r
4×12=2× (22/7)×r
r=48/6.29
r=7.63
Area of a circle is:
A=pi× r^2
A= (22/7) × (7.63)^2
A=182.9674cm^2
A=183cm^
Final answer:
To find the area of the largest circle from a string around a square, calculate the square's perimeter to get the string's length, which is also the circle's circumference. Then determine the circle's radius and use it to calculate the circle's area, which rounds to 183 square units.
Explanation:
To find the area of the largest circle that can be formed from a piece of string that fits around a square with an area of 144, first we must determine the perimeter of the square. Since the area of the square (A) is 144, the side length (s) can be found by taking the square root of the area: s = √A = √144 = 12. Therefore, the perimeter (P) of the square is P = 4s = 4 × 12 = 48.
The string that fits around the square is the same length as the perimeter, so it will also be 48 units long. This string will become the circumference (C) of the circle. The formula for the circumference of a circle is C = 2πr, where π is approximately 3.14 and r is the radius of the circle. We can solve for r by setting the circumference equal to the length of the string: C = 2πr = 48 → r = 48 / (2π) → r ≈ 7.64. So the radius of the circle is approximately 7.64 units.
Finally, to find the area (A) of the circle, we use the formula A = πr². Substituting the value of the radius, we get A = π × (7.64)² ≈ 183.47. However, since we need to round to the nearest whole number, the largest circle area is approximately 183 square units.
George earned a total of $342 in simple interest from two separate accounts. In an account earning 5% interest, George invested $1800 more than twice the amount he invested in an account earning 2%. How much did he invest in each account?
Answer: he invested $6000 in the account earning 5% interest and $2100 in the other account earning 2% interest
Step-by-step explanation:
Let x represent the amount invested in the account earning 5% interest.
Let y represent the amount invested in the account earning 2% interest.
In an account earning 5% interest, George invested $1800 more than twice the amount he invested in an account earning 2%. It means that
x = 2y + 1800
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
Assuming the duration for both investments is 1 year,
The interest on the first account would be
I = (x × 5 × 1)/100 = 0.05x
The interest on the second account would be
I = (y × 2 × 1)/100 = 0.02y
George earned a total of $342 in simple interest from two separate accounts. This means that
0.05x + 0.02y = 342 - - - - - - - - - - 1
Substituting x = 2y + 1800 into equation 1, it becomes
0.05(2y + 1800) + 0.02y = 342
0.1y + 90 + 0.02y = 342
0.1y + 0.02y = 342 - 90
0.12y = 252
y = 252/0.12 = 2100
x = 2y + 1800 = 2 × 2100 + 1800 = $6000
• What is the pobability of getting exactly 500 heads out of 1000 coin flips? Approximate it to within 5% of the true value without a calculator.
Answer:Probability of getting exactly 500 heads=0.025
Step-by-step explanation:Probability of getting exactly 500 heads= 1000C500(0.5)^1000=0.025
I need help with the rest of my algebra fraction homework on Page's 11,12,14, 16 and 18. Is there anybody willing to help me with my homework please. Thank You!
Answer:
11. B
12. A
14. C
16. D
18. A
A study conducted by researchers from the Department of Education wanted to know the average debt of college students in the United States. In order to obtain a sample representative of all students, the researchers divided college students into the four classes (freshman, sophomore, junior, and senior) and then took a random sample of students from each class. Which sampling method did they use?
A) Stratified random sampling
B) Systematic random sampling
C) Cluster sampling
D) Simple random sampling
Answer: A) Stratified random sampling
Step-by-step explanation:
Since , the researchers divided college students into the four classes (freshman, sophomore, junior, and senior) and then took a random sample of students from each class.
That means each category is participating in the sample.
It means , they used stratified sampling method where each class denotes a strata.
Stratified random sampling is a kind of random sampling technique in which the researcher divides the whole population into some finite number of groups also known as strata , the he randomly pick individuals from each strata to make a sample.
Here , each category participates in researcher's analysis.
Hence, the correct answer is A) Stratified random sampling .
Each of the possible five outcomes of a random experiment is equally likely. The sample space is {a, b, c, d, e}. All outcomes are equally likely. Let A denote the event {a, b}, and let B denote the event {c, d, e}. Determine the following probabilities:
a) P(A)
b) P(B)
c) P(A')
d) P(A∪B)
e) P(A∩B)
Answer:
a) [tex] p(A) = \frac{2}{5}[/tex]
b) [tex] p(B) =\frac{3}{5}[/tex]
c) [tex] p(A') = 1-p(A) = 1-\frac{2}{5} = \frac{3}{5}[/tex]
d) The probability for intersection on this case is 0 because the sets A and B not have any element in common, so then we have this
[tex] P(AUB) = P(A) +P(B) -0 = \frac{2}{5} +\frac{3}{5} =1[/tex]
e) The intersection for this case is the empty set between the sets A and B so for this reason the probability is 0
P(A∩B)=0
Step-by-step explanation:
For this case we have the following sample space:
[tex] S= [a,b,c,d,e][/tex]
And we have defined the following events:
[tex] A= [a,b][/tex]
[tex] B= [c,d,e][/tex]
For this case we can find the probabilities for each event using the following definition of probability:
[tex] p =\frac{Possible cases}{total cases}[/tex]
The total cases for this case are 5 , the possible cass for A are and for B are 3.
Usign this we have this:
[tex] p(A) = \frac{2}{5}, p(B) = \frac{3}{5}[/tex]
Then we can find the following probabilites:
a) P(A)
[tex] p(A) = \frac{2}{5}[/tex]
b) P(B)
[tex] p(B) =\frac{3}{5}[/tex]
c) P(A')
Using the complement rule we have this:
[tex] p(A') = 1-p(A) = 1-\frac{2}{5} = \frac{3}{5}[/tex]
d) P(A∪B)
For this case we can use the total probability rule and we got:
[tex] P(AUB) = P(A) +P(B) -P(A and B)[/tex]
The probability for intersection on this case is 0 because the sets A and B not have any element in common, so then we have this
[tex] P(AUB) = P(A) +P(B) -0 = \frac{2}{5} +\frac{3}{5} =1[/tex]
e) P(A∩B)
The intersection for this case is the empty set between the sets A and B so for this reason the probability is 0
P(A∩B)=0
The probability of each event in a random experiment is calculated by the ratio of the favorable outcomes to the total outcomes. The answer for each of the given events are: P(A)=2/5, P(B)=3/5, P(A')=3/5, P(A∪B)=1, P(A∩B)=0.
Explanation:In the given random experiment, there are five equally likely outcomes: {a, b, c, d, e}. The event A consists of outcomes {a, b} and the event B consists of outcomes {c, d, e}. The probability of an event can be calculated by the ratio of the number of favorable outcomes to the total number of outcomes.
a) The probability of event A, P(A), is determined by the ratio of the number of outcomes in A to the total outcomes. Since A has 2 outcomes (a and b) and there are 5 total outcomes, the P(A) = 2/5.
b) The probability of event B, P(B), is determined in a similar manner. Since B has 3 outcomes (c, d and e) and there are 5 total outcomes, the P(B) = 3/5.
c) The probability of not A, P(A'), represents all outcomes not in A. Hence, since all outcomes in B and E are not in A, P(A') = P(B) = 3/5.
d) The probability of A or B, P(A∪B), means the probability of either event A or B occurring (or both). Since A and B include all of the outcomes in the sample space, P(A∪B) = 1.
e) The probability of A and B, P(A∩B), is the probability of both event A and event B occurring simultaneously. However, A and B have no common outcomes, so P(A∩B) = 0.
Learn more about Probability here:
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Everybody in Ourtown is a fool or a knave or possibly both. 70% of the citizens are foolsand 85% are knaves. One citizen is randomly selected to be mayor. What is the probabilitythat the mayor is both a fool and a knave?
Answer:
[tex] P( F \cap K) =0.7+0.85 -1=0.55[/tex]
Step-by-step explanation:
For this case we can define some notation first:
F ="One person is fool "
K="One person is knave"
And we have the following probabilities given:
[tex] P(F) = 0.7 , P(K) =0.85[/tex]
And from the given condition that everyone is fool or knave we can deduce that:
[tex] P(K UF) =1[/tex]
Solution to the problem
For this case we want to find this probability:
[tex] P( F \cap K)[/tex]
And we can use the total probability rule given by:
[tex] P(K \cup F) = P(F) +P(K) -P(K \cap F)[/tex]
And replacing the values that we have we got:
[tex] 1 = 0.7+0.85 -P(K \cap F)[/tex]
And if we solve for [tex] P( F \cap K)[/tex] we got:
[tex] P( F \cap K) =0.7+0.85 -1=0.55[/tex]
PLZ HELP WORTH 25 PTS!!!!!
Consider the following piece-wise function.
How would the portion of the graph labeled "a" be defined?
(Answer choices are attached)
Answer:
[tex]\displaystyle y=- \frac{1}{2}x-3[/tex]
(first option)
Step-by-step explanation:
Linear Functions
They can be defined by knowing two points on them or a point and the slope of the line. The portion "a" of the piecewise function must have these conditions, only by looking at the graph
* It must be decreasing, the slope must be negative
* It must be defined for x<-2, because for x>-2, the function is defined by another piece.
* It must pass through the point (-2,-2)
Options 2 and 4 are immediately discarded, since x>2
Testing it (-2,-2) belongs to
[tex]\displaystyle y=- \frac{1}{2}x-3[/tex]
[tex]\displaystyle y=- \frac{1}{2}(-2)-3=1-3=-2[/tex]
The point (-2,-2) belongs to this function, so it's the correct choice. Let's verify the last function
[tex]\displaystyle y=- \frac{1}{2}x-6[/tex]
[tex]\displaystyle y=- \frac{1}{2}(-2)-6=-5[/tex]
This is not the point we are testing, so the portion of the graph labeled "a" is
[tex]\boxed{\displaystyle y=- \frac{1}{2}x-3}[/tex]
(First option)