Answer:
2/5 < 0.42 < 43% < 3/7
Step-by-step explanation:
Let's convert them all to decimals:
43% = 0.43
2/5 = 0.4
3/7 = 0.428571...
0.42 = 0.42
Now we can arrange them in ascending order:
0.4
0.42
0.43
0.428571...
To estimate the cost of a new product, one expression
used by the production department is 41rr2 + ? r 3. Write
an equivalent expression by factoring 4 m2 from both
terms
The factorization of the given algebraic expression will give us:
4πr²(1 + ¹/₃r)
How to factorize algebra expressions?In order for us to factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression would first be found and then we will group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is referred to as its factorization.
We are given the algebraic expression as:
4πr² + ⁴/₃πr³
Now, we want to factor 4πr² from both terms and this will give us:
4πr²(1 + ¹/₃r)
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Your parents decide that they will help you out the first two months you are at college
by helping you buy groceries for your meals, but they won't cover the cost of you going
out to eat at restaurants or fast food.
for the first month you submit your receipts, 13 are for fast food and four for kroger, and
totaled $487. the second month you submit receipts for six fast food meals and two for
kroger, and totaled $232. the receipts do not list the per-item price.
a. write the two equations for the cost of buying groceries and meals. (4 points)
• 13f + 4k = 487
• 65+2k = 232
i
b. what were the average costs of one fast food meal and of one trip to kroger?
show your work and justify your thinking. (6 points)
a. The two equations for the cost of buying groceries and meals are 13f + 4k = 487 and 65+2k = 232
b. The average costs of one fast food meal and of one trip to kroger is $77.33
To calculate the average cost, we divide the total cost by the number of meals or trips. For example, in the first month, the total cost of fast food meals and grocery trips was $487, and there were 13 fast food meals and 4 grocery trips. Therefore, the average cost of a fast food meal can be calculated by dividing the total cost of fast food meals ($487) by the number of fast food meals (13):
Average cost of a fast food meal = $487 / 13 = $37.46
Similarly, we can calculate the average cost of a grocery trip in the first month by dividing the total cost of grocery trips ($487 - total cost of fast food meals) by the number of grocery trips (4):
Average cost of a grocery trip = ($487 - $37.46 x 13) / 4 = $89.38
Using the same method, we can calculate the average cost of a fast food meal and a grocery trip in the second month. In the second month, the total cost of fast food meals and grocery trips was $232, and there were 6 fast food meals and 2 grocery trips. Therefore, the average cost of a fast food meal is:
Average cost of a fast food meal = $232 / 6 = $38.67
And the average cost of a grocery trip is:
Average cost of a grocery trip = ($232 - $38.67 x 6) / 2 = $77.33
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There are 4 paperback and 10 hardback books on a reading list. Your teacher randomly assigns you 3 books to take home. What is the probability that you are assigned all hardback books?
The probability of being assigned all hardback books is approximately 0.33 or 33%.
This can be done by combination formula C(n,r) = n!/(r!(n-r)!)
The total number of ways to choose three books from a list of 14 books is given by the combination formula,
C(14,3) =14!/(3!(14-3)!) = (141312) / (321) = 364.
To find the probability of selecting all hardback books, we need to determine the number of ways to select 3 books from the 10 hardback books. This is given by the combination formula,
C(10,3) = 10!/(3!(10-3)!) = 1098 / (321) = 120.
Therefore, the probability of selecting all hardback books is:
P(all hardback) = C(10,3) / C(14,3) = 120/364 = 0.3297
So, the probability of being assigned all hardback books is approximately 0.33 or 33%. This means that out of all possible combinations of 3 books, about 33% will consist of only hardback books.
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Need help asap.
(Angles Formed by Chords, Tangents, Secants)
The value of angle LQ in the intersected arc is 34 degrees.
How to find arc angle when secant intersect?If two secants intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.
Therefore, let's find the arc angle LQ as follows:
let
x = arc angle LQ
m∠U = 1 / 2 (108 - x)
37 = 54 - 0.5x
subtract 54 from both sides of the equation
37 = 54 - 0.5x
37 - 54 = 54 - 54 - 0.5x
-17 = -0.5x
divide both sides by -0.5
x = -17 / -0.5
x = 34 degrees
Therefore,
arc angle LQ = 34 degrees
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Each of the letters from the word PROBABILITY are written on a card and placed in a bag. What is the probability of choosing
vowel expressed as a decimal? Assume "Y" is a consonant
The probability of choosing a vowel from the word PROBABILITY, expressed as a decimal, is approximately 0.364.
To find the probability of choosing a vowel from the word PROBABILITY, you'll need to follow these steps:
1. Identify the total number of letters in the word: There are 11 letters in the word PROBABILITY.
2. Identify the number of vowels in the word: There are 4 vowels (O, A, I, and I).
3. Calculate the probability by dividing the number of vowels by the total number of letters: Probability = (number of vowels) / (total number of letters) = 4/11.
A decimal indication that the probability of selecting a vowel from the word PROBABILITY is roughly 0.364.
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Every four years, countries from around the globe meet to
compete in the largest sporting event in the world, the Summer
Olympics. The tables show information about the history of
the Summer Olympics. Write each comparison as a fraction in
lowest terms, a decimal, and a percent.
1. United States medals to Soviet Union medals
2. Soviet Union medals to Great Britain medals
3. United States medals to Great Britain medals
4. The number of countries that have won
between 2,250 and 2,499 total medals to the
number of countries that have won between
0 and 249 total medals.
5. Only one country participating in the
Summer Olympics has never won a medal.
Write a comparison of the number of
countries that have never won a medal
to the number of participating countries.
Answer:
United States medals to Soviet Union medals:
Fraction: 1211/1010
Decimal: 1.198
Percent: 119.8%
Soviet Union medals to Great Britain medals:
Fraction: 1010/867
Decimal: 1.165
Percent: 116.5%
United States medals to Great Britain medals:
Fraction: 1211/867
Decimal: 1.397
Percent: 139.7%
The number of countries that have won between 2,250 and 2,499 total medals to the number of countries that have won between 0 and 249 total medals:
Fraction: 2/1
Decimal: 2
Percent: 200%
Only one country participating in the Summer Olympics has never won a medal. Write a comparison of the number of countries that have never won a medal to the number of participating countries:
Fraction: 1/205
Decimal: 0.00488
Percent: 0.488%
Step-by-step explanation =
United States medals to Soviet Union medals:
The fraction represents the ratio of medals won by the United States to those won by the Soviet Union. To find it, you can divide the number of medals won by the United States (1,211) by the number of medals won by the Soviet Union (1,010): 1211/1010.
To convert this fraction to a decimal, divide the numerator (1211) by the denominator (1010): 1.198.
To convert the decimal to a percent, multiply it by 100: 119.8%.
Soviet Union medals to Great Britain medals:
The fraction represents the ratio of medals won by the Soviet Union to those won by Great Britain. To find it, you can divide the number of medals won by the Soviet Union (1,010) by the number of medals won by Great Britain (867): 1010/867.
To convert this fraction to a decimal, divide the numerator (1010) by the denominator (867): 1.165.
To convert the decimal to a percent, multiply it by 100: 116.5%.
United States medals to Great Britain medals:
The fraction represents the ratio of medals won by the United States to those won by Great Britain. To find it, you can divide the number of medals won by the United States (1,211) by the number of medals won by Great Britain (867): 1211/867.
To convert this fraction to a decimal, divide the numerator (1211) by the denominator (867): 1.397.
To convert the decimal to a percent, multiply it by 100: 139.7%.
The number of countries that have won between 2,250 and 2,499 total medals to the number of countries that have won between 0 and 249 total medals:
The fractions represent the ratios of the number of countries that have won between two ranges of total medals. To find these fractions, you need to count the number of countries that fall into each range, and then divide one by the other. According to the information provided, there are 2 countries that have won between 2,250 and 2,499 total medals, and 1 country that has won between 0 and 249 total medals. So the fraction is 2/1.
To convert this fraction to a decimal, divide the numerator (2) by the denominator (1): 2.
To convert the decimal to a percent, multiply it by 100: 200%.
Only one country participating in the Summer Olympics has never won a medal. Write a comparison of the number of countries that have never won a medal to the number of participating countries:
The fraction represents the ratio of the number of countries that have never won a medal to the total number of participating countries. According to the information provided, only one country has never won a medal, and there are 205 participating countries. So the fraction is 1/205.
To convert this fraction to a decimal, divide the numerator (1) by the denominator (205): 0.00488.
To convert the decimal to a percent, multiply it by 100: 0.488%.
What is the FICA tax on an income of $47,000? Remember that FICA is
taxed at 7.65%
The FICA tax will be $3595.5 on an income of $47,000.
Given that the principal amount = $47,000
Given that the FICA is taxed at the percentage of 7.65%
To findout the FICA tax we have to findout the 7.65% of money from the principal money $47,000.
The formula for finding the Y% of money from Z amount is = [tex]\frac{y}{100}[/tex] * Z
From the above formula, we can find the FICA tax.
FICA tax = [tex]\frac{7.65}{100}[/tex] * 47000 = 0.0765 * 47000 = 3595.5.
From the above solution, we can conclude that the FICA tax on an income of $47,000 is $3595.5
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In circle E, AB//CD, m/ADC = 42 and the
measure of arc CD is twice the measure of arc
AB. Find the measure of AB. Show your work.
The measure of arc AB is 120 degrees.
What is meant by an arc?
An arc refers to a portion of the circumference of a circle or an ellipse. It is measured in degrees and can be used to calculate the length of the curve.
What is the term measure?
The term "measure" refers to the size or circumference of a geometric object, such as length, area, or volume. It is a numerical value that quantifies the measured property.
According to the given information
Let O be the centre of the circle. Since AB is parallel to CD, we have angles ACD and ADC that are equal since they are alternate interior angles. Therefore, the angle ACD is also 42 degrees.
Let x be the measure of arc AB, and then the measure of arc CD is 2x. Since the sum of the measures of arcs AB and CD is equal to the total circumference of the circle, we have:
x + 2x = 360 degrees
3x = 360 degrees
x = 120 degrees
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Calculate the second and third derivatives. y = 4x4 - 3x² + 7x y yⁿ= yᵐ=
The second derivative yⁿ (y'') is 48x² - 6, and the third derivative yᵐ (y''') is 96x.
To calculate the second and third derivatives of the function y = 4x^4 - 3x² + 7x:
1. First, calculate the first derivative, y':
y' = dy/dx = (d/dx)(4x^4 - 3x² + 7x)
Using the power rule for derivatives, we get:
y' = 16x³ - 6x + 7
2. Now, calculate the second derivative, y'' (also denoted as yⁿ when n=2):
y'' = d²y/dx² = (d/dx)(16x³ - 6x + 7)
Applying the power rule again:
y'' = 48x² - 6
3. Finally, calculate the third derivative, y''' (also denoted as yᵐ when m=3):
y''' = d³y/dx³ = (d/dx)(48x² - 6)
Using the power rule one more time:
y''' = 96x
So, the second derivative yⁿ (y'') is 48x² - 6, and the third derivative yᵐ (y''') is 96x.
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If alpha and beta are zeroes of the quadratic equation x^2-6x+a; find the value of ‘a’ if 3a+2beta=20
The value of a is -16
If α and β are zeroes of the quadratic equation x²-6x+a, then we know that:
α + β = 6
α * β = a
We are also given that 3α + 2β = 20.
3α + 2β = 20
3(α + β) - α = 20
3(6) - α = 20
18 -α = 20
18 - 20 = α
α = -2
Substituting α = -2 into the equation α + β = 6, we get:
- 2 + β = 6
beta = 8
Therefore, α = -2 and β = 8, and we can find a using the equation α * β = a:
a = α * β
= - 2 * 8
= 16
Therefore, the value of a is -16
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Solve for the missing side. Formula: a^2+b^2=c^2
Answer:
[tex] \frac{7 \sqrt{39} }{5} [/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]( {11.2})^{2} - { {7} }^{2} = 76.44 > 0[/tex]
The missing side is equal to:
[tex] \sqrt{76.44} = \frac{7 \sqrt{39} }{5} [/tex]
Pls help me with this! Will give points!
Answer:
Subtract 1 from both sides.
Answer:
subtract 1 from both sides. because taking out the 1 from 1 and 1 from 17 will equal 16. which leaves t/4=16
A lake currently has a depth of 30 meters. As sediment builds up in the lake, its depth decreases by 2% per year.
This situation represents:
A. Exponential decay
B. Exponential growth
The rate of growth or decay, r, is equal to:
A. 1. 02
B. 0. 02
C. 0. 98
So the depth of the lake each year is ______ times the depth in the previous year.
A. 0. 98
B. 0. 02
C. 1. 02
It will take between _____ years for the depth of the lake to reach 26. 7 meters.
A. 3 and 4
B. 11 and 12
C. 9 and 10
D. 5 and 6
The situation represents exponential decay.
The rate of growth or decay, r, is equal to 0.02.
So the depth of the lake each year is 0.98 times the depth in the previous year.
It will take between 11 and 12 years for the depth of the lake to reach 26. 7 meters.
The situation represents exponential decay, as the depth of the lake decreases by a constant percentage each year. The rate of decay is 2% per year, so the rate of growth or decay, r, is equal to 0.98 (1 - 0.02). This means that the depth of the lake each year is 0.98 times the depth in the previous year.
To find the number of years it will take for the depth of the lake to reach 26.7 meters, we can use the formula for exponential decay:\
D = D₀ *[tex]e^{(-rt)[/tex]
where D is the current depth, D₀ is the initial depth, r is the rate of decay, and t is the number of years.
Substituting the given values, we get:
26.7 = 30 * [tex]e^{(-0.02t)[/tex]
Solving for t, we get:
t = ln(26.7/30) / (-0.02) ≈ 11.33
Therefore, it will take between 11 and 12 years for the depth of the lake to reach 26.7 meters.
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if 2x + 3y = 6x - 5y, find the value of x/y.
Answer: 2
Step-by-step explanation:
Answer:
[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]
Step-by-step explanation:
sol,
2x+3y-6x+6y=0
f(x,y)=2x+3y-6x+6y
f(X,-y)=2x+3y-6y,fx=?
f(x-y)=2x+3y-6y,fy=?
fx=-4
fy=9
[tex] \frac{d}{y} = \frac{ - 4}{9} [/tex]
now,
[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]
Solve for length of segr
6 cm
4 cm
b
18 cm
b = [?] cm
If two segments intersect inside
Answer:
12
Step-by-step explanation:
multiply 4x18 then divide by 6
Problem
Yoshi is a basketball player who likes to practice by attempting the same three-point shot until he makes the shot. His past performance indicates that he has a
30
%
30%30, percent chance of making one of these shots. Let
X
XX represent the number of attempts it takes Yoshi to make the shot, and assume the results of each attempt are independent.
Is
X
XX a binomial variable? Why or why not?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Each trial isn't being classified as a success or failure, so
X
XX is not a binomial variable.
(Choice B)
B
There is no fixed number of trials, so
X
XX is not a binomial variable.
(Choice C)
C
The trials are not independent, so
X
XX is not a binomial variable.
(Choice D)
D
This situation satisfies each of the conditions for a binomial variable, so
X
XX has a binomial distribution
Choice D is correct: This situation satisfies each of the conditions for a binomial variable, so X has a binomial distribution.
A random variable X is said to have a binomial distribution if it satisfies the following conditions:
The variable X represents the number of successes in a fixed number of independent trials.
Each trial has only two possible outcomes: success or failure.
The probability of success is constant for each trial.
The trials are independent.
In this case, Yoshi attempts the same three-point shot until he makes the shot, so the number of attempts is not fixed. However, each attempt can be classified as a success (if he makes the shot) or a failure (if he misses the shot), so the variable X represents the number of successes in a sequence of independent trials with only two possible outcomes. Also, the probability of success is constant for each attempt, and the attempts are independent, so all four conditions for a binomial distribution are satisfied. Therefore, X is a binomial variable.
Choice D is correct: This situation satisfies each of the conditions for a binomial variable, so X has a binomial distribution.
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Hillsdale Orchard grows Fuji apples and Gala apples. There are 160 Fuji apple trees and 120 Gala apple trees in the orchard.
Hillsdale Orchard's owners decide to plant 30 new Gala apple trees. Complete the ratio table (click for help) to find the number of new Fuji apple trees the owners should plant if they want to maintain the same ratio of Fuji apple trees to Gala apple trees
To maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should: plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.
To find the number of new Fuji apple trees that the owners of Hillsdale Orchard should plant to maintain the same ratio of Fuji apple trees to Gala apple trees, we need to use a ratio table.
First, we need to determine the ratio of Fuji apple trees to Gala apple trees before the new trees are planted. Let's assume that there are currently 40 Fuji apple trees and 100 Gala apple trees. The ratio of Fuji apple trees to Gala apple trees is therefore 40:100, which can be simplified to 2:5.
Next, we need to use this ratio to determine the number of new Fuji apple trees that need to be planted. Since the owners are planting 30 new Gala apple trees, we can use the ratio of 2:5 to find the corresponding number of new Fuji apple trees.
To do this, we need to divide the number of new Gala apple trees by the denominator of the ratio (which represents the number of units of the ratio). In this case, the denominator is 5.
30 (new Gala apple trees) ÷ 5 (denominator) = 6
This means that for every 5 new Gala apple trees, the owners should plant 2 new Fuji apple trees. Therefore, the owners should plant 12 new Fuji apple trees (2 trees for every 5 new Gala apple trees, multiplied by the 30 new Gala apple trees being planted).
In summary, to maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.
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The distance around a neighborhood is 6 miles. When Sam measured it with an
odometer, the distance was 5. 52 miles. What is the percent of error of the
measurement?
The percent of error in the measurement is 8%. This means that the measured value of 5.52 miles is 8% less than the actual distance of 6 miles.
To find the percent of error, we need to calculate the difference between the measured value and the actual value, divide that by the actual value, and then multiply by 100 to convert to a percentage.
Actual distance around the neighborhood = 6 miles
Measured distance around the neighborhood = 5.52 miles
Difference = Actual distance - Measured distance
Difference = 6 miles - 5.52 miles
Difference = 0.48 miles
Percent of error = (|Difference| / Actual distance) x 100%
Percent of error = (|0.48| / 6) x 100%
Percent of error = 0.08 x 100%
Percent of error = 8%
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Doug is going to ride his bicycle
3
,
000
3,0003, comma, 000 miles across the United States, from coast to coast. He wants to choose the route that will give him the greatest chance of success. Here's what he finds in his research:
There have been
2
22 attempts on the northern route from Maine to Washington. Both of those riders made it
2
,
000
2,0002, comma, 000 miles and quit in Montana.
There have been
19
1919 attempts on the central route from Virginia to California;
9
99 of those riders didn't make it out of Virginia and the other
10
1010 made it all the way to the Pacific.
There have been
32
3232 attempts on the southern route from Florida to San Diego. One of those riders made it the whole way. Another realized he was out of shape, and quit before he even started. The other
30
3030 riders quit somewhere in Texas. They were evenly distributed between
1
,
300
1,3001, comma, 300 and
1
,
700
1,7001, comma, 700 miles.
The chances of success in cycling across the United States is higher on the central route because more than half of the people who started on this route finished it (52%), while on the other routes the chances of successful completion is lower (route north (0%) south (0.02%).
What is probability?According to the above, to find the probability of success in crossing the United States from coast to coast, we must divide the number of successful attempts by the total number of attempts as shown below:
North Route
0 ÷ 2 = 0
Center Route
10 ÷ 19 = 0.52
South Route
1 ÷ 39 = 0.025
According to the above, the highest probability of success is found in the central route with 0.52, that is to say that more than half of those who tried this route finished.
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Eli is comparing the prices of things in the following two flyers Eli only wants to get the best deals he knows he will have to visit both stores help Eli find the best deal for each item
Identify the best deal for each item
For milk, Store A has the better deal: $2.50 for 1 gallon is cheaper than $3.19 for 2 liters at Store B.For bread, Store B has the better deal: $1.49 for a loaf is cheaper than $1.99 for a loaf at Store A.For eggs, Store B has the better deal: $0.99 for a dozen is cheaper than $1.79 for a dozen at Store A.Which store has the better deal for the following items?Eli needs to visit both stores to get the best deals for each item. Store A has the better deal for milk, while Store B has the better deals for bread and eggs. By going to both stores, Eli can save money on all three items.Learn more about deals
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A particle moves on a coordinate line with acceleration d²s/dt = 30 sqrt(t) – 12/ sqrt(t) subject to the conditions that ds/dt = 12 and s = 16 when t= 1. Find the velocity v = ds/dt in terms of t and the position.
The velocity v = ds/dt in terms of t is v =
The velocity v = ds/dt in terms of t and the position s is: [tex]v = 15t^{(3/2)} - 8t^{(1/2)} + 6[/tex] and [tex]s = 5t^{(5/2)} - 16t^{(3/2)} + 6t + 27[/tex] respectively.
To find the velocity v = ds/dt in terms of t and the position s, we first need to integrate the acceleration equation with respect to time to get the velocity equation:
d²s/dt² = 30 sqrt(t) – 12/ sqrt(t)
Integrating both sides with respect to t, we get:
ds/dt = 30/2 * t^(3/2) - 12 * 2/3 * t^(1/2) + C₁
where C₁ is the constant of integration.
Using the condition ds/dt = 12 when t = 1, we can solve for C₁:
12 = 30/2 * 1^(3/2) - 12 * 2/3 * 1^(1/2) + C₁
C₁ = 6
Substituting this value of C₁ back into the velocity equation, we get:
ds/dt = 15t^(3/2) - 8t^(1/2) + 6
Now, we can integrate the velocity equation to get the position equation:
s = 5t^(5/2) - 16t^(3/2) + 6t + C₂
where C₂ is the constant of integration.
Using the condition s = 16 when t = 1, we can solve for C₂:
16 = 51^(5/2) - 161^(3/2) + 6*1 + C₂
C₂ = 27
Substituting this value of C₂ back into the position equation, we get:
s = 5t^(5/2) - 16t^(3/2) + 6t + 27
Therefore, the velocity v = ds/dt in terms of t and the position s is: v = 15t^(3/2) - 8t^(1/2) + 6 and s = 5t^(5/2) - 16t^(3/2) + 6t + 27 respectively.
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Assume the base is 2.
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships.
A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
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Type the correct answer in each box. use numerals instead of words.
lab tests of a new drug indicate a 70% success rate in completely curing the targeted disease. the doctors at the lab created the random data in the table using representative simulation. the letter e stands for "effective," and n stands for "not effective.
the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is ______. the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is ______.
To find the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we can use the geometric distribution. The probability of not curing the disease is 1 - 0.70 = 0.30.
Let X be the number of patients needed to find one patient on whom the medicine would not be effective. Then X follows a geometric distribution with p = 0.30. The probability that it will take at least five patients to find one patient on whom the medicine would not be effective is:
P(X ≥ 5) = (1 - p)^(5-1) = 0.7^4 ≈ 0.2401
Therefore, the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is approximately 0.2401.
To find the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients, we can use the binomial distribution. Let X be the number of patients out of four who are cured by the medicine. Then X follows a binomial distribution with n = 4 and p = 0.70. The probability that the medicine will be effective on exactly three out of four randomly selected patients is:
P(X = 3) = (4 choose 3) * (0.70)^3 * (1 - 0.70)^(4-3) = 4 * 0.343 * 0.3^1 ≈ 0.4116
Therefore, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is approximately 0.4116.
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En un almacén hay tres cajas de productos. La primera contiene 20 productos, de los cuales 3 son defectuosos, en la segunda hay 16 productos, con 2 defectuosos, y en la tercera caja hay 10 productos, sin productos defectuosos ¿Cuál es la probabilidad de sacar un producto defectuoso al azar?
La probabilidad de sacar un producto defectuoso al azar de las tres cajas es aproximadamente 0.0917, o un 9.17%.
La probabilidad de sacar un producto defectuoso al azar de las tres cajas se puede calcular utilizando la fórmula de la probabilidad.
Primero, calculemos la probabilidad de sacar un producto defectuoso de cada caja:
1. En la primera caja, hay 3 productos defectuosos entre 20 productos en total. La probabilidad es 3/20.
2. En la segunda caja, hay 2 productos defectuosos entre 16 productos en total. La probabilidad es 2/16.
3. En la tercera caja, no hay productos defectuosos entre 10 productos en total. La probabilidad es 0/10.
Para encontrar la probabilidad total, sumamos las probabilidades de cada caja y luego dividimos por el número total de cajas:
(3/20 + 2/16 + 0/10) / 3 ≈ (0.15 + 0.125 + 0) / 3 ≈ 0.0917
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Maths ice cream shop has 7 cups of sprinkles to use on Sundays for the rest of the day if each Sunday serves with one 8th cup of sprinkles how many Sundays can they serve
56 Sundays Maths Ice Cream Shop can serve with 7 cups of sprinkles using one-eighth (1/8) cup of sprinkles per Sunday.
Converting the cups of sprinkles into eighths:
7 cups × 8 eighths/cup
= 56 eighths
Dividing the total eighths by the eighths used per Sunday:
56 eighths / (1/8 cup per Sunday)
= 56 Sundays
So, Maths Ice Cream Shop can serve for 56 Sundays using 7 cups of sprinkles with each Sunday serving one-eighth cup of sprinkles.
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The maximum walking speed S, in feet per second, of and animal can be modeled by the equation S= square root of gL,where g+32ft/sec and L is the lenght, in feet, of the animal's leg. To the nearest hundredth,how ,amy times greater is the maximum walking speed of a giraffe with a leg of 6 feet than a hippopota,us with a leg of 3 feet?
The maximum walking speed of a giraffe with a leg of 6 feet is approximately 1.41 times greater than that of a hippopotamus with a leg of 3 feet.
What is the ratio of the maximum walking speed of a giraffe?The equation given in the problem, S= square root of gL, represents the maximum walking speed S of an animal with a leg of length L. To find the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet, we can plug in the values of g and L for each animal and calculate the ratio.
For the giraffe: S = √(g6) = √(326) ≈ 9.8 ft/sec
For the hippopotamus: S = √(g3) = √(323) ≈ 5.7 ft/sec
So the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet is approximately 9.8/5.7 ≈ 1.72 or 1.41 to the nearest hundredth.
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112
in.
If the prism can fit exactly 9 cubes from bottom to top, what is the volume of the prism? Write your answer as a
decimal.
The volume of the rectangular prism is 31.5 in³.
How do we find the volume of the rectangular prism?From the diagram, we know that the height of the rectangular prism is 9 cubes. We can see the length is 7 cubes and the width is 4 cubes. Each cube is half an inch. Therefore we multiply every side by 1/2.
Height = 9 × (1/2)
Height = 4.5 inches
Length = 7 × (1/2)
Length = 3.5 inches
Width = 4 × (1/2)
Width = 2 inches
Volume = L × W × H
Volume = 3.5 × 2 × 4.5
Volume = 31.5 inches³
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An equipment rental business currently charges $32. 00 per power tool rental and averages 24 rentals a day. The company recently performed a study and found that for every $2. 00 increase in rental price, the average number of customers decreased by one rental.
The company determined that the function f(x) = (32 + 2x)(24 – x) can be used to represent the total revenue earned from the rentals, where x represents the number of rental price increases and f(x) represents the revenue earned.
Part A: Explain what the expressions (32 + 2x) and (24 – x) represent in the given scenario.
Part B: What is the revenue after 3 rental price increases? Show your work or explain how you found your answer.
Part C: What rental price would give the maximum revenue for the company?
Part A: In the given scenario, the expression (32 + 2x) represents the rental price charged by the equipment rental business after x price increases of $2 each. The initial rental price is $32, and for every $2 increase in rental price, the rental price is raised by 2 units. The expression (24 – x) represents the number of rentals the equipment rental business can expect to make after x price increases. As the rental price increases, the number of customers is expected to decrease by one rental for every $2 increase in rental price.
Part B: To find the revenue after 3 rental price increases, we need to calculate f(3), where f(x) = (32 + 2x)(24 – x).
Substituting x = 3, we get:
f(3) = (32 + 2(3))(24 – 3) = (32 + 6)(21) = 38 × 21 = $798
Therefore, the revenue after 3 rental price increases is $798.
Part C: To find the rental price that would give the maximum revenue for the company, we need to find the value of x that maximizes the function f(x) = (32 + 2x)(24 – x). We can do this by finding the critical points of the function, which occur when the derivative of the function is equal to zero:
f'(x) = (32 + 2x)(-1) + (24 - x)(2) = -32 + 16x + 48 - 2x = 14x + 16
Setting f'(x) = 0 and solving for x, we get:
14x + 16 = 0
[tex]x = \frac{-16}{14} = \frac{-8}{7}[/tex]
However, [tex]x = \frac{-8}{7}[/tex] is not a valid solution since it represents a negative number of rental price increases, which is not possible in this scenario. Therefore, we need to test the endpoints of the interval [0, 6], since x represents the number of rental price increases and cannot exceed 6 (which would result in a rental price of $44, the maximum price in this scenario).
f(0) = (32 + 2(0))(24 - 0) = 32 × 24 = $768
f(6) = (32 + 2(6))(24 - 6) = 44 × 18 = $792
Comparing the values of f(0), f(3), and f(6), we see that f(6) gives the maximum revenue of $792. Therefore, the rental price that would give the maximum revenue for the company is $44, which is the rental price after 6 price increases of $2 each.
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Riley and her family move from the Midwest all the way to San Francisco. The equation
2x - 100 = 4,006
can be used to find x, the number of miles her family drove. How many miles did her
family drive?
Riley and her family move from the Midwest all the way to San Francisco. The equation 2x - 100 = 4,006 can be used to find x, the number of miles her family drove. Riley's family drove 2,053 miles from the Midwest to San Francisco.
Find the number of miles Riley's family drove from the Midwest to San Francisco, we need to solve the equation 2x - 100 = 4,006 for x.
First, we'll add 100 to both sides of the equation to isolate the variable term:
2x - 100 + 100 = 4,006 + 100
Simplifying:
2x = 4,106
isolate x, we'll divide both sides of the equation by 2:
2x/2 = 4,106/2
Simplifying:
x = 2,053
Therefore, Riley's family drove 2,053 miles from the Midwest to San Francisco.
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS SOMEONE GAVE ME THE WRONG STEPS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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