Answers
5. The constant of proportionality is $0.4 per pound
4. The constant of proportionality is is 3 ounces of almond per ounces of dark chocolate
Determining Constant of proportionalityFrom the question, we are to determine the constant of proportionality from the given table
From the given information, we have that
There is a proportional relationship between x and y
That is,
y ∝ x
Then,
y = kx
Where k is the constant of proportionality
From the table,
When x = 5 pounds, y = $2
Then,
2 = k × 5
k = $2/5pounds
k = $0.4/pound
k = $0.4 per pound
4.
x is proportional to y
Then,
y = cx
Where c is the constant of proportionality
From the table,
When x = 3 ounces of dark chocolate, y = 9 ounces of almond
Then,
9 = c × 3
c = 9/3
c = 3 ounces of almond / ounces of dark chocolate
c = 3 ounces of almond per ounces of dark chocolate
Hence, the proportionality constant is 3 ounces of almond per ounces of dark chocolate
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Related Questions
Is y=4/x-3 linear or non-liner
Answers
Trust me it is
10. If 4n = 3.60, which is the value of n? A 0.09 B 0.9 C 9 P 6.5 D 90
Answers
Answer: The answer is B: 0.9
if the fractions denominator is not a factor of 10 or 100 how else could a fraction be renamed as a decimal?
Answers
If a fraction's denominator is not a factor of 10 or 100, we can divide the number in the numerator by the number in the denominator to obtain a decimal.
Let us take an example. Say we have a fraction- 3/2
here numerator = 3 and denominator = 2
To convert this into a decimal, we need to divide 3 by 2
2 goes in 3 one time and remainder left is 1.
Then we put a decimal and divide 10 by 2 which gives us 5
Thus, on dividing 3 by 2, we get a quotient of 1.5
Hence the fraction 3/2 becomes 1.5 as a decimal.
Similarly, we can convert any fraction into decimal.
Thus, we can see that if a fraction's denominator is not a factor of 10 or 100, we can divide the number in the numerator by the number in the denominator to obtain a decimal.
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{(a^2-16)÷(a^2-25)}÷{(a^2-2a-8)÷(a^2+10a+25)}
Answers
The answer is -[tex]\frac{(a + 4) ( a +5) }{(a +2)( a - 5)}[/tex]
Simplify is making something simple. In mathematics, simplification means reducing the expression/ fraction/problem in a simpler form by using different operations.
In the process of simplification, some basic rules are needed to be used. The principle of BODMAS (B= Bracket, O = Of, D = Division, M = Multiplication, A = Addition, S = Subtraction)must be followed for solving the questions.
The equation is :
[tex]\frac{a^{2} - 16 }{ a^{2} - 25 }[/tex] ÷ [tex]\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}[/tex]
=[tex]\frac{a^{2} - 4^{2} }{a^{2} - 5^{2} }[/tex] ÷ [tex]\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}[/tex]
= [tex]\frac{ (a +4 ) ( a - 4 )}{ (a + 5) ( a - 5 )}[/tex] ÷ [tex]\frac{a^{2} - 4a + 2a - 8}{a^{2} + 5a + 5a + 25}[/tex] ( by applying middle term factor method)
(using [tex]a^{2} - b^{2}[/tex] formula )
= [tex]\frac{ (a+4) ( a-4 )}{(a +5 ) (a - 5)}[/tex] ÷ [tex]\frac{a(a -4) + 2 (a - 4)}{a (a + 5) + a (a + 5)}[/tex] ( by applying middle term factor method)
=[tex]\frac{( a + 4) ( a - 4)}{( a + 5) ( a - 5)}[/tex] ÷ [tex]\frac{(a + 2) ( a -4)}{( a +5) (a+5)}[/tex]
= [tex]\frac{( a +4)(a-4)}{(a + 5)(a - 5)\\}[/tex] * [tex]\frac{(a + 5) ( a + 5)}{(a + 2) ( a - 4)}[/tex]
=[tex]\frac{( a + 4) ( a + 5)}{(a + 2) ( a - 5)}[/tex]
so, the answer is - [tex]\frac{( a + 4 ) ( a +5) }{( a + 2) ( a - 5)}[/tex]
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b) write 28 as a product of its prime factors write the factors in order smallest to largest
Answers
Answer:
To find the prime factors of 28, we can start by dividing 28 by the smallest prime number, which is 2. 28 divided by 2 is 14, so 2 is a prime factor of 28. We can then divide 14 by the next smallest prime number, which is 2 again. 14 divided by 2 is 7, so 2 is also a prime factor of 28. We can repeat this process with the number 7, dividing it by the next smallest prime number, which is 3. 7 divided by 3 is 2 with a remainder of 1, so 3 is not a prime factor of 28. Since we have reached a number that is not divisible by any more prime numbers, we have found all of the prime factors of 28. In this case, the prime factors of 28 are 2 and 2.
To write 28 as a product of its prime factors, we simply need to multiply the prime factors together in the correct order. Since the prime factors of 28 are 2 and 2, and the factors are to be written in order from smallest to largest, we can write 28 as 2 x 2 = 4. This is the prime factorization of 28, and it shows that 28 can be expressed as a product of its prime factors.
Kira drove 441 miles in 7 hours.
At the same rate, how many miles would she drive in 9 hours?
Answers
Answer:
if Kira drives at the same rate, she would drive 567 miles in 9 hours.
Step-by-step explanation:
To determine how many miles Kira would drive in 9 hours at the same rate, we need to first calculate her average speed in miles per hour. To do this, we divide the total number of miles she drove (441 miles) by the number of hours she drove (7 hours):
441 miles / 7 hours = 63 miles/hour
Once we know her average speed, we can use it to calculate the number of miles she would drive in 9 hours. To do this, we multiply her average speed (63 miles/hour) by the number of hours she would drive (9 hours):
63 miles/hour * 9 hours = <<63*9=567>>567 miles
a detailed model that shows the overall structure for how data moves through a system is a(n) model.
Answers
A complete model that shows the system's whole data flow is a physical data model.
What is a physical data model?A thorough model that depicts the general flow of data through a system is a physical data model.
A physical data model is a thorough representation of the overall organizational data structure that is not dependent on a database management system or any other implementation factors.
A physical data model is a database-specific model that depicts relational data objects and their associations (such as tables, columns, primary keys, and foreign keys).
DDL statements can be produced from a physical data model and then delivered to a database server.
Examples of physical models include bridges, cell models, human organs, crash test dummies, landform models, building models, and chemical compound models.
Therefore, a complete model that shows the system's whole data flow is a physical data model.
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What part of ton is a gram?
Answers
Answer:
1/1000000 One gram is one millionth of a ton
Step-by-step explanation:
1 ton is 1000 kg = 1 million grams
1 gram = 1/1000000 ton
Hope this helps
Here is a number sequence.
31 26 21 16 11 ...
Write down the rule for continuing the sequence.
I don't need explanation, I only need the ANSWER
Answers
Answer: 11 16 21 26 31
Step-by-step explanation: the shows the sequence.
The bank
agrees to give you a loan of
$45,000 with 2% simple interest over 5 years.
How much will your monthly payments be?
Answers
The monthly payment will be $84.375 to the bank.
What is simple interest?
The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.S.I = Pnr / 100
where P = prinicipal
n= number of years
r = rate of interest
= 45000 * 2 * 8 / 100
= 810000 /100
= $8100
where, the divide by number of months
Balance= 8100 / 96
= $84.375
Hence, the monthly payment will be $84.375 to the bank.
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Using the net below, find the surface area
of the triangular prism.
20 cm
9 cm
8cm
6 cm
9 cm
20 cm
Surface Area = [?] cm²
Answers
Answer:
Get math teacher
Step-by-step explanation:
go talk to them.
Match each equation on the left of the equivalent equation on the right some answer options on the right will not be used
(left) log_2(0.25) = -2 , 5^2 =25 , log_2(32) = 5 , 25^-1 = 0.04 (right) 2^5 = 32 , 0.25^2 = -2, log_25 (0.04) =-1 , log_0.04(-1)=25, 2^-2 = 0.25, log_5(25) =2
Answers
The equations log₂ (0.25) = -2, 5² = 25, log₂ 32 = 5 and 25⁻¹ = 0.04 are equivalent to the equations 2⁻² = 0.25, log₅ 25 = 2, 2⁵ = 32, log₂₅ 0.04 = -1 respectively.
What are Logarithms?Logarithms are another way, which is the opposite of writing exponents. A number raised to some power will give some other values in case of exponentiation process. This power is called the logarithmic value.
We can write it as,
logₐ x = n ⇔ aⁿ = x
We have the equations on the left equivalent to the equations on the right using the definition of logarithms as,
log₂ (0.25) = -2 ⇔ 2⁻² = 0.25
5² = 25 ⇔ log₅ 25 = 2
log₂ 32 = 5 ⇔ 2⁵ = 32
25⁻¹ = 0.04 ⇔ log₂₅ 0.04 = -1
Hence the equations on the lefts log₂ (0.25) = -2, 5² = 25, log₂ 32 = 5 and 25⁻¹ = 0.04 are equivalent to the equations on the rights 2⁻² = 0.25, log₅ 25 = 2, 2⁵ = 32, log₂₅ 0.04 = -1 respectively.
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explain how regression toward the mean can describe two friends who have a fight then later go to the movies together.
Answers
Given the circumstances of the question, it is feasible that the two friends would feel that they overreacted during the argument, and as a result, they decide to see a movie together to make up for it.
Regression toward the mean is a statistical condition that involves events that the outcomes produce based solely on chance rather than on real facts. Therefore, it is impossible to forecast with precision what will happen in a regression towards the mean.
Example
Two military units are brought back, one with 20% casualties and the other with 50%. He compliments the first while criticizing the second. The two units return with the opposite outcomes the following time. He "learns" from this experience that praise reduces performance and berating strengthens it.
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Mr. Stewart made ome pie. She old 3/5 of them and gave 1/4 of the remainder to the food bank. If he had 150 pie left how many pie did he ell
Answers
By applying the fraction concept, it can be calculated that Mrs. Stewart sold 300 cakes.
How does the concept of fractions apply in real life?
In real life, the concept of a fraction is often used when we want to talk about a part of a whole, a part of something, a part of a group of people, etc.
In this case, it is stated that Mrs. Stewart made several pies, some of which were sold and given to food banks, and some were left over.
If we know that 1/4 of the unsold pies were given to the food bank, then the unsold pies that were not given to the food bank = 1 - 1/4 = 3/4 part.
Additionally, we also know that the number of unsold pies that were not given to the food bank (leftover pies) was 150.
If x is the number of unsold cakes, then the two statements above can be written in mathematical notation:
3/4 x = 150
x = 150 : 3/4
= 150 x 4/3
= 200 pies
If pies made are y, then pies not sold = pies made - pies sold
x = y - 3/5y
= 2/5y
if we put the value of x into this equation it becomes:
200 = 2/5y
y = 200 : 2/5
= 200 x 5/2
= 500 pies
Then the pies were sold = 3/5y
= 3/5 x 500
= 300 pies
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10 Points! please help! There are 21 pieces of sports equipment at the gym. The ratio of volleyballs to handballs is 2 : 1 . How many volleyballs and handballs are at the gym?
Answers
Answer:
14 volleyballs and 7 handballs
Step-by-step explanation:
sum the parts of the ratio , 2 + 1 = 3 parts , then
21 ÷ 3 = 7 ← value of 1 part of the ratio , so
volleyballs = 2 × 7 = 14
handballs = 1 × 7 = 7
Answer:
Hey
volleyball = 14
Handball = 7
Step-by-step explanation:
21 pieces = 2:1n
step 1
Add the ratios together
21 = 3n
Step 2
divide both sides by 3
n = 21/3 = 7
where n = number of balls
volley ball = n × 2 = 7 × 2 = 14
handballs = n × 1 = 7 × 1 = 7
total = 21
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The lit how the amount of each ingredient charlotte ued to make macaroni and cheee. 16 ounce 2 egg 2. 5 cup of milk 3 1/2 cup of chedder cheee
Answers
The combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.
According to the question,
We have the following information:
A sandwich hop serve 4 ounce of meat and 3 ounce of cheese on each sandwich. After making sandwiches for an hour the hop owner has used 91 combined ounce of meat and cheese.
Combined ounces for 1 sandwich:
Ounces of meat + ounces of cheese
4+3
7 ounces
It is given that in an hour 91 ounces of combined cheese and meat are used.
Now, we have:
Number of sandwiches made in 1 hour = 91/7
Number of sandwiches = 13
Ounces of meat used in 13 sandwiches can be found using multiplication as follows:
13*4
Ounces of meat used in 13 sandwiches = 52 ounces
Ounces of cheese used in 13 sandwiches can found using multiplication as follows:
13*3
Ounces of cheese used in 13 sandwiches = 39 ounces
Hence, the combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.
complete question is
A andwich hop erve 4 ounce of meat and 3 ounce of cheee on each andwich. After making andwiche for an hour, the hop owner ha ued 91 combined ounce of meat and cheee. How many combined ounce of meat and cheee are ued on each (1) andwich?
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0. 5*
Zach and Naomi are studying geometric transformations. Zach is able to
move the triangle A to A' using the following sequence of basic
transformations:
1. Reflection across the x-axis
2. Reflection across the y-axis
3. Translation two units to the right
864
y
A
2
ON 4
-8-6-4-20 24 68
-2-
Jö
6
-8-
A
X
Naomi claims that the same three transformations, done in any order will
always produce the same result. Zach disagrees. Who is correct?
Answers
Answer:
Zach is correct
Step-by-step explanation:
You want to know if reflection across the two axes and translation right will achieve the same effect if the transformations are done in any order.
TransformationsTranslation right adds a value to the x-coordinate.
Reflection over the y-axis changes the sign of the x-coordinate.
If the order of these two transformations is changed, the result will change.
Example
Consider point (0,0) and the translation right 1 unit.
Reflection, then translation: (0, 0) ⇒ (0, 0) ⇒ (1, 0)
Translation, then reflection: (0, 0) ⇒ (1, 0) ⇒ (-1, 0)
Zach is correct that the transformations ...
Reflection over the x-axisReflection over the y-axisTranslation 2 units rightcannot be done in any order.
Answer:
Zach
Step-by-step explanation:
the distribution of time spent brushing teeth for the 1,200 students in a school is multimodal with a mean of 43 seconds and a standard deviation of 8.99 seconds. if a random sample of 9 students is selected, is it appropriate to calculate the probability of the sample mean being less than 30 seconds using an approximately normal model?
Answers
No, it is not appropriate to estimate the probability using an approximately normal model because the population is not normal and the sample size is small.
The details given are,
Sample size = 9
mean = 43 sec
Standard deviation = 8.99
Therefore we conclude that is it not appropriate to calculate the likelihood of the sample mean being less than 30 seconds using an approximately normal model.
Mean is also know as the average of a given data . We calculate the mean by the formula : ∑xifi / ∑fi.
Normal Distribution is the probability density function ( pdf) for a continuous random variable in a system .
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34. Write the equation of each line below.
Answers
The equation of the blue line is: y = 3x - 1.
The equation of the red line is: y = 3x + 2.
How to Find the Equation of a Line?To find the equation of a given line on a coordinate plane, find the slope along the line, m (rise / run), and also determine the value of the y-intercept (b), which is the point on the y-axis where the line intercepts it.
The equation of the red line:
Slope of the line (m) = rise / run = 3 units / 1 units
Slope (m) = 3
The red line intersects the y-axis at 2, this means the y-intercept of the line would be b = 2.
To write the equation of the red line, substitute m = 3 and b = 2 into y = mx + b:
y = 3x + 2
The equation of the blue line:
Slope of the line (m) = rise / run = 3 units / 1 units
Slope (m) = 3
The blue line intersects the y-axis at -1, this means the y-intercept of the line would be b = -1.
To write the equation of the blue line, substitute m = 3 and b = -1 into y = mx + b:
y = 3x - 1.
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During a flood, the water level in a river firt roe fater and fater, then roe more and more lowly until it reached it highet point, then went back down to it pre- flood level. Conider water depth a a function of time. (a) I the time of highet water level a critical point or an inflection point of thi function? (b) I the time when the water firt began to rie more lowly a critical point or an inflection point?
Answers
The time of highest water level is an inflection point of this functionand the time when the water first began to rise more slowly is a critical point of this function.
A critical point is a point on a graph at which the gradient of the graph (or the rate of change of the graph) is equal to zero. This means that the rate of change of the function at the critical point is neither increasing nor decreasing. An inflection point is a point on a graph at which the concavity of the graph changes. When the graph is concave up, the rate of change is increasing, and when the graph is concave down, the rate of change is decreasing.In the case of the rising and falling of a river during a flood, the time of highest water level is an inflection point because it marks the point at which the water level changes from rising to falling. The rate of change of the water level is increasing as it rises, and decreasing as it falls. At the time of highest water level, the rate of change is at a maximum and is equal to zero, making it an inflection point. The time when the water first began to rise more slowly is a critical point because it marks the highest point of the water level. The gradient of the graph at this point is equal to zero, making it a critical point.
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term to term rules: un+1=un^3+2
u0=-3
a)u1
b)u2
Answers
The first and the second terms of the recursive sequence are given as follows:
a) u(1) = -25.
b) u(2) = -15623.
How to solve the recursive sequence?The definition of the recursive sequence is presented as follows:
u(n + 1) = u(n)³ + 2.
The initial term is needed to solve the sequence, hence it is given as follows:
u(0) = -3.
Thus the term with index 1 is given as follows:
u(1) = u(0)³ + 2.
u(1) = -3³ + 2
u(1) = -27 + 2
u(1) = -25.
Considering the term with index 1, the term with index 2 is obtained as follows:
u(2) = u(1)³ + 2
u(2) = (-25)³ + 2
u(2) = -15623.
And then the same rule is obtained if needed to obtain the 3th, 4th terms, and so on, considering the previous term and the definition.
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Solve for x. X = 40° (5x + 15) (8x - 5)°
Answers
To solve for x in this equation, we must first perform the operations inside the parentheses. This gives us:
X = 40 * (25x^2 + 75x + 75x - 75)
Next, we can distribute the 40 and combine like terms to get:
X = 1000x^2 + 3000x - 3000
Now, we can set this expression equal to X and solve for x.
1000x^2 + 3000x - 3000 = X
We can use the quadratic formula to find the solutions for x:
x = (-3000 +/- sqrt(3000^2 - 4 * 1000 * (-3000))) / (2 * 1000)
This simplifies to:
x = (-3000 +/- sqrt(9000000 + 24000000)) / 2000
Finally, we can simplify further to get:
x = (-3000 +/- sqrt(33000000)) / 2000
Thus, the solutions for x are:
x = (-3000 + sqrt(33000000)) / 2000
x = (-3000 - sqrt(33000000)) / 2000
These are the possible values for x that satisfy the given equation.
Select the graph for the solution of the open sentence. Click until the correct graph appears.
|x - 1| < 4
Answers
Answer:
graph D
Step-by-step explanation:
x - 1 ≥ 0
x ≥ 1
if x ≥ 1
x - 1 < 4
x < 4 + 1
x < 5
1≤ x < 5
if x < 1
-x + 1 < 4
-x < 4 - 1
- x < 3
x > -3
-3 < x < 1
final solution
-3 < x < 5
what would be the coefficient of determination if the total sum of squares (sst) is 23.29 and the sum of squares due to regression (ssr) is 10.03?
Answers
The coefficient of determination if the total sum of squares is 23.29 and the sum of squares due to regression is 10.03 is 0.43
How to calculate regression?
The standard formula for simple linear regression is Y = mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.
Here we need to find the coefficient determination if the total sum of squares (sst) is 23.29 and the sum of squares due to regression (ssr) is 10.03.
Here we know that the value of the following are given,
Sum of square = 23.29
Sum of regression = 10.03
Then the coefficient determination is calculated as,
The coefficient of determination r2 = SSR/SST.
When we apply the value, then we get,
=> 10.03/23.29
=> 0.43
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work: solve the system of equations.
2) Xochitl is going to a carnival that has games and rides. Each game costs $2.50 and each ride
costs $5. Xochitl spent $30 altogether on 9 games and rides Graphically solve a system of
equations in order to determine the number of games Xochitl played and the number of
rides Xochitl went on, y.
Answers
6 games are played by Xochitl and 3 rides went on by Xochitl
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the Xochitl is going to a carnival that has games and rides
The cost of each game is $2.50 and cost of each ride is $5.
Xochitl spent $30 altogether on 9 games
Let x represents the number of games and y represents the number of rides.
By the given information we form two equations.
x+y=9...(1)
2.5x+5y=30...(2)
From equation (1)
x=9-y
Now plug in x value in (2)
2.5(9-y)+5y=30
22.5-2.5y=30
Subtract 22.5 on both sides
-2.5y=30-22.5
-2.5y=7.5
Divide both sides by 2.5
y=3
x+y=9
x+3=9
x=6
Hence, the number of games Xochitl played is 6 and the number of rides Xochitl went on is 3.
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Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
What conclusion can they reach based on the above output when they set the significance level to be 0.10?
a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.
b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.
d.Two of the above are correct.
e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme out
Answers
The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above. So, option e is correct.
What is meant by null hypothesis?
The null hypothesis, often known as H₀, is the assertion that there is no difference between two sets of data or variables under analysis, or that there is no relationship between them. Because there is no underlying causative relationship, the null hypothesis holds that any experimentally detected difference is merely the result of chance; therefore, the name "null."
We can create a z-test hypothesis by assuming that the amount of rain produced by thunderheads follows a distribution that is nearly normal:
300 acre feet is the null hypothesis for the average quantity of rain that thunderheads produce on their own without fertilizing the clouds.
Alternative Hypothesis: The amount of rain that thunderheads often produce by seeding the clouds is greater than 300 acre feet.
This test has a right tail.
So, The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above.
So, option e is correct.
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Eggs are generally sold in batches of 12 (or dozens). The image shows the 3 different ways that 12 eggs can be packaged into arrays. Note that the array 3 by 4 is taken to be equivalent to the array 4 by 3 and therefore is not included.
If it was decided that eggs should be sold in batches of 24, then these 24 eggs could be packaged into a total of ___
different arrays.
Answers
Eggs are generally sold in batches of 12 (or dozens). The image shows the 3 different ways that 12 eggs can be packaged into arrays. Note that the array 3 by 4 is taken to be equivalent to the array 4 by 3 and therefore is not included. If it was decided that eggs should be sold in batches of 24, then these 24 eggs could be packaged into a total of 4
different arrays.
How to find the different ways of packaging egg in order of 24The arrangement is checked by writing out the factors of 24
24 = 1, 2, 3, 4, 6, 8, 12, 24
grouping them in pairs
1 * 24
2 * 12
3 * 8
4 * 6
this gave a total of 4 arrays
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a cyclist rides at an average speed of 24 miles per hour. if she wants to bike 180 km , how long (in hours) must she ride? express your answer using two significant figures.
Answers
4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.
Given that,
A cyclist travels at a speed of 24 miles per hour on average.
We have to find what is the required riding time (in hours) if she wants to cycle 180 km.
We know that,
The velocity is a vector quantity (has magnitude and direction) that is calculated by dividing the distance by the amount of time needed to travel the distance in question.
So, the distance is 180 km, and the speed is 24 miles per hour.
To calculate the amount of time needed to travel the distance, we divide the distance by the speed.
The distance is first converted to miles as 1 mile is equal to 1.6098 kilometers,
180 kilometers are equal to 111.84681 Miles.
111.84681 miles traveled in 24 hours
111.84681/24
4.66 hours.
Therefore, 4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.
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In triangle lmn, m∠l = (6c 35)°. if the exterior angle to ∠l measures 79°, determine the value of c.
Answers
The measure of angle c is 136/6 degrees
How to determine the measure of angle c?From the question, we have the following parameters that can be used in our computation:
∠l = (6c 35)°
Exterior of l = 79
As a general rule, the sum of an angle and its exterior is 180 degrees
This means that
6c - 35 + 79 = 180
Evaluate the like terms
So, we have
6c = 136
Divide both sides by 6
c = 136/6
Hence, the measure is 136/6 degrees
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7) a boat is pulled into a dock by means of a rope attached to a pulley on the dock. the rope is attached to the bow of the boat at a point 10 ft below the pulley. if the rope is pulled through the pulley at a rate of 20ft/min, at what rate will the boat be approaching the dock when 125 ft of rope is out?
Answers
The rate of the boat approaching the dock when 125 ft of rope is out is 101.6 ft/min
let x be the horizontal distance to the dock. And the rope is attached to the boat 10 feet below the pulley
Using Pythagorean theorem
x^2=R^2-10^2
where R is the rope length to the pulley.
Differentiates with respect to time t
2x dx/dt=2RdR/dt
Xdx/dt = RdR/dt ...... (1)
If the boat is approaching the dock when 125 ft of rope is out
This is R = 125ft
Using Pythagorean theorem again
X^2 = R^2 - 10^2
X^2 = 125^2 - 10^2
X^2 = 15525
X = 124.6 ft
The rate the boat approaching the dock = dx/dt
While the rope is pulled through the pulley at a rate of 20 ft/min = dR/dt
Solve for dx/dt when R is 125, x= 124.6, and dR/dt= 20ft/min
Substitute all in equation 1
124.6 dx/dt = 125 × 20
dx/dt = 2500/124.6
dx/dt = 101.6 ft/min
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