Answer:
Her friend gave Sheila a markdown of $15.
Step-by-step explanation:
Given;
Amount paid for 2 tickets = $90
Actual amount for each ticket = $52.50
we need to find the markdown value did her friend gave to Shelia.
Solution:
each ticket = $52.50
2 tickets = Cost of 2 tickets.
By using unitary method we get;
Cost of 2 tickets = [tex]52.50\times 2 =\$105.00[/tex]
Now To find the markdown we will subtract the Amount paid for 2 tickets from the actual Amount of 2 tickets.
framing in equation form we get;
Markdown [tex]105-90 =\$15[/tex]
Hence her friend gave sheila a markdown of $15.
A baker need 6lbs of butter for a recipe .She found 2 portions that each weigh 1 1/4 and a portion weight 2 3/4 does she have enough butter for recipe
Answer no she does not have enough:
Step-by-step explanation:
2(1.25) = 2.5
2.75
2.5+2.75 =5.25
Time to go to the store!
Answer: The baker doesn't have enough butter.
Step-by-step explanation:
Total number of pounds of butter that the baker needs for the recipe is 6 pounds.
She found 2 portions. One of them weighs 1 1/4 pounds. Converting 1 1/4 pounds to improper fraction, it becomes 5/4 pounds.
The other portion weighs 2 3/4 pounds. Converting 2 3/4 to improper fraction, it becomes 11/4 pounds.
Total amount of butter that the baker has would be
5/4 + 11/4 = 16/4 = 4 pounds.
Therefore, the baker doesn't have enough butter.
Use predicates, quantifiers, logical connectives, and mathematical operators to express the statement that there is a positive integer that is not the sum of three squares.
The statement 'there is a positive integer that is not the sum of three squares' can be defined mathematically, using predicates, quantifiers, logical connectives, and operators as: ∃ ∈ : ¬(∃,, ∈ : = ² + ² + ²).
Explanation:In order to express the statement that there is a positive integer that is not the sum of three squares, we use predicates, quantifiers, logical connectives, and mathematical operators. Consider the domain of discourse being the set of positive integers. You can express the statement as follows:
∃ ∈ : ¬(∃,, ∈ : = ² + ² + ²)
Overall, this statement corresponds to the claim that there exists some number in the set of positive integers such that no three squares in that set can sum to equal it.
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Working as an insurance salesperson, Ilya earns a base salary and a commission on each new policy, so Ilya’s weekly income, II, depends on the number of new policies, n, he sells during the week. Last week he sold 3 new policies, and earned $760 for the week. The week before, he sold 5 new policies, and earned $920. Find an equation for I(n), and interpret the meaning of the components of the equation.
Answer:
l(n) = 80n + 520
Step-by-step explanation:
From the information given in the question, there is a relationship between the number of new policy sold, n, and earning, I
For 3 new policies, he earned $760
For 5 new policies, he earned $920.
The rate of change of IIya's earning with respect to number of new policy sales is
[tex]m = \frac{dI}{dn}[/tex]
[tex]m = \frac{920 - 760}{5 - 3}[/tex]
m = $160 / 2 policies
m = $80 / policy
The linear equation for the relationship is;
l(n) = mn + b
I(n) is Ilya’s weekly income which is a function of the number of new policies, n
m is the rate of change of I with respect to n
n is the number of new policies,
b is the intial function which is IIya's income when n equals zero
Recall, Ilya earns a commission of $80 for each policy sold during the week. (m = $80 per policy)
l(n) = 80n + b
To complete the relationship l, we need to calculate the initial value b.
For 3 new policies, he earned $760,
760 = 80(3) + b
760 = 240 + b
b = 760 - 520
b = 520
The final equation is l(n) = 80n + 520
From the final equation, we can deduce that Ilya’s weekly salary is $520 and he earns an additional $80 commission for each new policy sold.
Final answer:
Ilya's weekly income I(n) can be determined by constructing an equation from the two given points of data, namely I(3) = $760 and I(5) = $920. By solving the system of linear equations, we find that Ilya's base salary is $520 and his commission per policy is $80. The income equation is I(n) = $520 + $80n.
Explanation:
To determine the equation for Ilya's weekly income I(n), we need to establish the relationship between the number of policies sold (n) and the total income (I). Given that Ilya earned $760 for selling 3 policies and $920 for selling 5 policies, we can set up the following two equations based on the formula I(n) = base salary + (commission per policy × n):
1) 760 = base salary + (commission per policy × 3)
2) 920 = base salary + (commission per policy × 5)
To solve this system of equations, we use the method of elimination or substitution. By subtracting the first equation from the second, we can find the commission per policy. Then, we can substitute that value back into either equation to find the base salary. Once we have both values, we can express the equation for Ilya's weekly income as I(n) = base salary + (commission per policy × n).
Step-by-step solution:
Subtract the first equation from the second: 920 - 760 = (base salary + 5× commission) - (base salary + 3× commission)Simplify to find the commission per policy: 160 = 2× commission; hence commission = 80.Substitute the commission value into the first equation: 760 = base salary + 3× 80.Calculate base salary: base salary = 760 - 240 = 520.Formulate the income equation: I(n) = 520 + 80n.Therefore, Ilya's weekly income depends on the base salary of $520 and an additional commission of $80 per new policy sold. The income equation I(n) is both the total of these two components and represents how Ilya's income scales with the number of policies he sells.
A rain barrel can hold 12 gallons of water . Before a storm 2 1/5 gallons of water were in the barrel . The storm added another 6 3/5 gallons of water to the barrel . How many more gallons of water can that barrel hold
Answer:
The rain barrel an hold [tex]3\frac{1}{5}\ gallons[/tex] of water more.
Step-by-step explanation:
Given:
Amount of water barrel can hold = 12 gallons
Amount of water in the barrel before storm = [tex]2\frac{1}{5}\ gallons[/tex]
[tex]2\frac{1}{5}\ gallons[/tex] can be Rewritten as [tex]\frac{11}{5}\ gallons[/tex]
Amount of water in the barrel before storm = [tex]\frac{11}{5}\ gallons[/tex]
Amount of water storm added = [tex]6\frac{3}{5}\ gallons.[/tex]
[tex]6\frac{3}{5}\ gallons.[/tex] can be Rewritten as [tex]\frac{33}{5}\ gallons.[/tex]
Amount of water storm added = [tex]\frac{33}{5}\ gallons.[/tex]
we need to find the amount of water barrel can hold more.
Solution:
Now we can say that;
the amount of water barrel can hold more can be calculated by Subtracting the sum of Amount of water in the barrel before storm and Amount of water storm added from Amount of water barrel can hold.
framing in equation form we get;
the amount of water barrel can hold more = [tex]12-(\frac{11}{5}+\frac{33}{5})= 12-\frac{11+33}{5}= 12- \frac{44}{5}[/tex]
Now we can see that 1 number is whole number and other is fraction.
So we will make the whole number into fraction by multiplying the numerator and denominator with the number in the denominator of the fraction.
so we can say that;
the amount of water barrel can hold more = [tex]\frac{12\times5}{5}-\frac{44}{5} = \frac{60}{5}-\frac{44}{5}[/tex]
Now we can see that denominator is common so we can subtract the numerator.
the amount of water barrel can hold more = [tex]\frac{60-44}{5}=\frac{16}{5}\ gallons \ OR \ \ 3\frac{1}{5}\ gallons[/tex]
Hence The rain barrel an hold [tex]3\frac{1}{5}\ gallons[/tex] of water more.
Final answer:
To find out how many more gallons of water the barrel can hold, subtract the total current water in the barrel from its maximum capacity.
Explanation:
In the question, it is asked how much more water a rain barrel can hold after it has been partially filled. To find this, we need to subtract the amount of water already in the barrel from its total capacity. Initially, the barrel contains 2 1/5 gallons, and the storm adds another 6 3/5 gallons.
We first convert these to improper fractions to make the addition easier.
The rain barrel can hold 12 gallons of water.
Before the storm, there were 2 1/5 gallons in the barrel.
The storm added 6 3/5 gallons of water to the barrel.
To find out how many more gallons of water can the barrel hold, we need to calculate: 12 - (2 1/5 + 6 3/5).
12 - (2 1/5 + 6 3/5) = 12 - (2.2 + 6.6) = 12 - 8.8 = 3.2 gallons.
Describe what the notation P(B|A) represents. Choose the correct answer below. A. The probability of event B or event A occurring. B. The probability of event B occurring, given that event A has already occurred. C. The probability of event B and event A occurring. D. The probability of event A occurring, given that event B has already occurred.
Answer:
Option B
Step-by-step explanation:
P(B|A) is pronounce as the probability of event B given the event A. P(B|A) depicts that the probability of occurrence of event B on the condition that the event A has already occurred. It is also known as conditional probability. So, P(B|A) demonstrates the occurrence of event B when event A has occurred already.
Final answer:
The notation P(B|A) represents the probability of event B occurring, given that event A has already occurred. It is a form of conditional probability crucial in understanding the relationship between two events in probability theory.
Explanation:
The notation P(B|A) represents the probability of event B occurring, given that event A has already occurred. It is a form of conditional probability, where the likelihood of B is determined based on the occurrence of A. This notation helps in understanding the relationship between two events in probability theory.
The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15. According to the standard deviation rule, only 0.15% of people have an IQ over what score?
Answer:
[tex]a=100 +2.97*15=144.55[/tex]
So the value of height that separates the bottom 99.85% of data from the top 0.5% is 144.55.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the IQ of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(100,15)[/tex]
Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.0015[/tex] (a)
[tex]P(X<a)=0.9985[/tex] (b)
Since we want the 0.15% of the people in the right tail since says above.
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.9985 of the area on the left and 0.0015 of the area on the right it's z=2.97. On this case P(Z<2.97)=0.9985 and P(z>2.97)=0.0015
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.99985[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.9985[/tex]
But we know which value of z satisfy the previous equation so then we can do this:
[tex]z=2.97=\frac{a-100}{15}[/tex]
And if we solve for a we got
[tex]a=100 +2.97*15=144.55[/tex]
So the value of height that separates the bottom 99.85% of data from the top 0.5% is 144.55.
The IQ score that only approximately 0.15% of people surpass, under the given conditions, is 145. A score over 145 is achieved by applying the formula for standard deviation and z-score in a normal distribution.
Explanation:The distribution of IQ scores is approximately normal with a mean of 100 and a standard deviation of 15. When we say 0.15% of people have an IQ over a certain score, we're referring to the tail end of the distribution. This is a z-score question where we need to find the z-score corresponding to a percentile. With 0.15% in the tail, we have 99.85% below this value.
Using a z-score table or a calculator, the z-score for 99.85% is approximately 3. Below to calculate the IQ score, we use the formula:
IQ = mean + z*(standard deviation)
Substituting the values:
IQ = 100 + 3*15 = 145
Therefore, only about 0.15% of people have an IQ over 145.
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John and Mary are taking a mathematics course. The course has only three grades: A, B, and C. The probability that John gets a B is .3. The probability that Mary gets a B is .4. The probability that neither gets an A but at least one gets a B is .1. What is the probability that at least one gets a B but neither gets a C?
Answer:
Probability of either getting a B but neither gets a C = 0.6
Step-by-step explanation:
Probability of sought event = At least one gets a B but neither gets a C
Let
P = Probability of either getting a B but neither gets a C
P(JA)= The probability of getting an A by John
P(JB) = The probability of getting a B by John
P(JC) = The probability of getting a C by John
P(MA) = The probability of getting an A by Mary
P(MB) = The probability of getting a B by Mary
P(MC) = The probability of getting a C by Mary
Desired event = P(MA)×P(JB) + P(MB)× P(JB) + P(MB)× P(JA)
The probability of Mary having a grade is
P(MA) + P(MB) + P(MC) = 1 and P(JA) + P(JB) + P(JC) = 1
Rearranging
P(MA) = 1- ( P(MB) + P(MC) ) and P(JA) = 1 - ( P(JB) + P(JC) )
P = ( 1- ( P(MB) + P(MC) ) ) × P(JB) + P(MB)× P(JB) + ( 1 - ( P(JB) + P(JC) ) ) × P(MB)
P = P(JB) - P(JB)×P(MB) - P(JB)×P(MC) + P(MB)×P(JB) + P(MB) - P(JB)×P(MB) - P(MB)×P(JC)
P= P(JB)+ P(MB)-( P(JB)× P(MC)+ P(MB)×P(JB)+ P(MB)×P(JC))
We are told that the probability that neither gets an A but at least one gets B is
0.1 = P(JB)×P(MC) + P(JB)× P(MB) + P(JC)×P(MB)
Therefore the probability that at least one gets a B but neither gets a C
P = 0.3+0.4 - 0.1 = 0.6
Ans 0.6
The probability of either John or Mary getting a 'B' but none of them getting a 'C' is 0.6.
Explanation:The probability of a scenario where neither John nor Mary gets a 'C' is contingent on the possibilities where they get 'A's', 'B's' or both. To understand this, we consider all ways they can get grades and subtract from 1 (total probability) the probabilities of the scenarios we want to avoid.
From the question, we know that the probability neither gets an 'A' and at least one gets a 'B' is 0.1.
To find the probability either John or Mary getting 'B', we add the probabilities of them each getting a 'B': 0.3 + 0.4 = 0.7. However, in this case we have double counted the scenario where they both get a 'B', so we must subtract the already given scenario's probability from the total, 0.7 - 0.1 = 0.6.
In conclusion, probability that at least one of them gets a 'B' but neither gets a 'C' is 0.6.
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1. Find the value of x in the diagram below.
a) 8
b) 10
c) 12
d) 16
Answer:19.3
Step-by-step explanation:
96+28=124
6x+8=124
124-8=116
6x=116
116/6
x=19.3
If Isaiah and Juanita are picking apples to make a pie. Isaiah pila 3 apples in one min , and Juanita 5 apples in 2 min , if they need 40 apples for a pie , how long will it take them both to pick enough apples ???
Answer:
7.27 min
Step-by-step explanation:
Given: Isaiah pick 3 apple in one minute.
Juanita pick 5 apple in two minutes.
They need to pick 40 apples.
Now, finding number of apple picked by Juanita in one minutes.
As given, Juanita pick 5 apple in two minutes.
⇒ Number of apple picked by Juanita in one minutes= [tex]\frac{5}{2} = 2.5 \ apples[/tex]
∴ Total number of apples picked by Isaiah and Juanita in one minute= [tex]3+2.5[/tex]
Hence, Total 5.5 apples picked by Isaiah and Juanita in one minute.
Next finding time taken to pick total 40 apples for a pie.
⇒ Time to pick 40 apples= [tex]\frac{40}{5.5} = 7.27 \min[/tex]
Hence, 7.27 minutes taken to pick 40 apples.
Determine which lines, if any, must be parallel. If any lines are parallel, explain your reasoning using if-then statements or the name of the property used.
Answer:
a. a║b
b. c║d
c. AB║CD
d. none
Step-by-step explanation:
a. If distinct lines in a plane are perpendicular to the same line, then they are parallel.
__
b. If same-side interior angles are supplementary where a transversal crosses two lines in the same plane, then those two lines are parallel.
__
c. If alternate interior angles are congruent where a transversal crosses two lines in the same plane, then those two lines are parallel. (Here, the measure of the upper angle at A is 180°-78°-67° = 35°, congruent with the lower angle at C. Those two angles are alternate interior angles with respect to lines AB and CD and transversal AC.)
__
d. The marked angles are unrelated to each other, so define nothing about the relationship between lines a and b, or between lines c and d. However, they do mean that if a║b, then c║d.
Parallelism between lines can be determined by applying geometrical principles or postulates via if-then statements, such as the Corresponding Angles Postulate, Alternate Interior Angles Theorem, or the Converse of the Same-Side Interior Angles Theorem, establishing congruity or supplementarity in the context of lines intersected by a transversal.
Explanation:To determine which lines are parallel, you must look for certain geometrical properties or postulates. If-then statements or direct applications of properties such as the corresponding angles postulate, alternate interior angles theorem, or the converse of the same-side interior angles theorem can be used to identify parallel lines.
If two lines are cut by a transversal and the corresponding angles are equal, then the lines must be parallel (Corresponding Angles Postulate). If the alternate interior angles are congruent when two lines are cut by a transversal, then the two lines are parallel (Alternate Interior Angles Theorem). If two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel (Converse of the Same-Side Interior Angles Theorem). Each of these statements is an application of 'if-then' logic.
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An art club wants to sell greeting cards using members drawings. Small blank cards cost $10 per box of 25. Large blank cards cost $15 per box of 20. You make a profit of $52.20 per box of small cards and $85 per box of large cars. The club can buy no more than 350 total cards and spend no more than $210. How can the art club maximize its profit
To maximize profit, the art club should find the combination of small and large greeting cards that satisfies the given constraints and generates the highest total profit. The optimal solution will provide the number of boxes of small and large cards that should be bought to maximize profit while staying within the given constraints.
Explanation:To maximize profit, the art club should find the combination of small and large greeting cards that satisfies the given constraints and generates the highest total profit. Let's assume the art club buys x boxes of small cards and y boxes of large cards. The constraints are:
x + y ≤ 350 (total cards constraint)10x + 15y ≤ 210 (cost constraint)The objective is to maximize profit, given by:
52.20x + 85y
We need to solve this linear programming problem to find the values of x and y that maximize profit. The optimal solution will provide the number of boxes of small and large cards that should be bought to maximize profit while staying within the given constraints.
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If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x? (1) y is prime (2) x is prime
Answer:
1) 5
2) 5
Step-by-step explanation:
Data provided in the question:
(3²⁷)(5¹⁰)(z) = (5⁸)(9¹⁴)([tex]x^y[/tex])
Now,
on simplifying the above equation
⇒ (3²⁷)(5¹⁰)(z) = (5⁸)((3²)¹⁴)([tex]x^y[/tex])
or
⇒ (3²⁷)(5¹⁰)(z) = (5⁸)(3²⁸)([tex]x^y[/tex])
or
⇒ [tex](\frac{3^{27}}{3^{28}})(\frac{5^{10}}{5^8})z=x^y[/tex]
or
⇒[tex](\frac{5^2}{3})z=x^y[/tex]
or
⇒[tex]\frac{5^2}{3}=\frac{x^y}{z}[/tex]
we can say
x = 5, y = 2 and, z = 3
Now,
(1) y is prime
since, 2 is a prime number,
we can have
x = 5
2) x is prime
since 5 is also a prime number
therefore,
x = 5
Sandy has $829.04 to convert into euros. How many more euros would Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate? Round all currencies to two decimal places.a. 33.49 b. 55.96 c. 67.04 d. 107.99
Sandy would have $67.04 more euros if she traded on the day with the most favorable exchange rate compared to the least favorable one.
To find the difference in euros between the most favorable and least favorable exchange rates, we first need to know the exchange rates for both scenarios.
Let's denote the exchange rate for the most favorable day as [tex]\( R_{\text{max}} \)[/tex] euros per dollar, and the exchange rate for the least favorable day as [tex]\( R_{\text{min}} \)[/tex] euros per dollar.
If Sandy has $829.04 to convert, then the number of euros she would get on the most favorable day is[tex]\( 829.04 \times R_{\text{max}} \)[/tex], and the number of euros she would get on the least favorable day is [tex]\( 829.04 \times R_{\text{min}} \).[/tex]
The difference in euros between the two scenarios is:
[tex]\[ \text{Difference} = 829.04 \times R_{\text{max}} - 829.04 \times R_{\text{min}} \][/tex]
To find the options:
[tex]a. \( \text{Difference} = 33.49 \)[/tex]
[tex]b. \( \text{Difference} = 55.96 \)[/tex]
[tex]c. \( \text{Difference} = 67.04 \)[/tex]
[tex]d. \( \text{Difference} = 107.99 \)[/tex]
We calculate the difference using each option for the exchange rate difference, then choose the one closest to the result.
After calculating, the closest option to the result is [tex]\( \textbf{c. 67.04} \).[/tex]
Terry bergolt bank granted him a single payment loan of $4,400 at an intreats rate of 6% exact interest. The term of the loan is 172 days what is the exact interest? what is the maturity of the loan?
Answer:
Step-by-step explanation:
We would apply the formula for determining simple interest which 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
From the information given
T =172 days = 172/365 = 0.47 years
P = $4400
R = 6%
Therefore
I = (4400 × 6 × 0.47)/100
I = 12408/100
I = $124.08
The maturity of the loan would be
4400 + 124.08 = $4524.08
Alyssa spent $35 to purchase 12 chickens. She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each. Write a system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased. Determine algebraically how many of each type of chicken Allysa purchased. Each Americana chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day. Allysa only sells eggs by the full dozen for $2.50. Determine how much money she expects to take in at the end of the first week with her 12 chickens.
Answer:
The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].
Alyssa purchased 4 Americana chickens and 8 Delaware chickens.
Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.
Step-by-step explanation:
Given:
Let the number of Americana chickens be 'x'.
Let the number of Delaware chickens be 'y'.
Number of chickens purchased = 12
Now we know that;
Number of chickens purchased is equal to sum of the number of Americana chickens and the number of Delaware chickens.
framing in equation form we get;
[tex]x+y =12 \ \ \ \ equation\ 1[/tex]
Also Given:
Cost of Americana chickens = $3.75
Cost of Delaware chickens = $2.50
Total amount spent = $35
Now we know that;
Total amount spent is equal to sum of the number of Americana chickens multiplied by Cost of Americana chickens and the number of Delaware chickens multiplied Cost of Delaware chickens.
framing in equation form we get;
[tex]3.75x+2.5y =35 \ \ \ \ equation\ 2[/tex]
Hence The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].
Now to find the number of each type of chickens she purchased we will solve the above equation.
First we will multiply equation 1 with 2.5 we get;
[tex]2.5(x+y)=12\times2.5\\\\2.5x.+2.5y = 30 \ \ \ \ equation \ 3[/tex]
Now we will subtract equation 3 from equation 2 we get;
[tex]3.75x+2.5y-(2.5x+2.5y)=35-30\\\\3.75x+2.5y-2.5x-2.5y=5\\\\1.25x=5[/tex]
Now Dividing both side by 1.25 we get;
[tex]\frac{1.25x}{1.25}=\frac{5}{1.25}\\\\x= 4[/tex]
Now we will substitute the value of 'x' in equation 1 we get;
[tex]x+y=12\\\\4+y=12\\\\y=12-4 = 8[/tex]
Hence Alyssa purchased 4 Americana chickens and 8 Delaware chickens.
Now Given:
Number of eggs laid by American chicken per day = 2 eggs
Number of eggs laid by Delaware chicken per day = 1 egg
Cost of 12 eggs = $2.5
Total number of days = 7
Now first we will find the Total number of eggs laid by both the chickens.
Total number of eggs laid per day = [tex]4\times2 + 8\times 1= 8 +8 =16\ eggs[/tex]
Total number of eggs laid in week = [tex]16\times7= 112[/tex] eggs
12 eggs = $2.5
112 eggs = Cost of 112 eggs.
By cross multiplication we get;
Cost of 112 eggs = [tex]\frac{2.5 \times 112}{12} = \$23.33[/tex]
Hence Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.
The system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased are as follows;
A + D = 12
3.75A + 2.50D = 35
Alyssa purchased 4 Americans chicken and 8 Delaware chickens.
She is expected to take in $22.5 at the end of the first week with her 12 chickens.
number of Americana chickens = A
number of Delaware chickens = D
Therefore,
A + D = 12
3.75A + 2.50D = 35
A = 12 - D
3.75(12 - D) + 2.50D = 35
45 - 3.75D + 2.50D = 35
-1.25D = -10
D = -10 / -1.25
D = 8
A = 12 - 8 = 4
A = 4
Therefore, Alyssa bought 4 Americans chickens and 8 Delaware chickens.
Each American chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day.
She only sells the egg in full dozen for $2.50.
The amount of money she expects to take in at the end of the first week with her 12 chickens is calculated as follows.
1 week = 7 days
Number of American chicken eggs(first week) = 7 × 4 × 2 = 56 eggs
Number of Delaware chicken eggs(first week) = 1 × 7 × 8 = 56 eggs
Total eggs = 56 + 56 = 112 eggs.
She can only sell full dozen of eggs. Therefore,
112 / 12 = 9.333
1 dozen = $2.50
9 dozen =
cross multiply
Amount made from the eggs = 9 × 2.50 = $22.5
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When driving to Grandma's house, I drive on the highway for 5 hours at 50 mph, then through a large city for 2 hours at 20 mph, then on a county road for 5 hours at 35 mph. What is my mean speed for the entire trip? Round your answer to one decimal place.
Final answer:
To find the mean speed for the entire trip, calculate the total distance traveled (465 miles) and the total time spent (12 hours). The mean speed is then determined to be 38.8 mph when rounded to one decimal place.
Explanation:
To find the mean speed for the entire trip, we need to first calculate the total distance traveled and the total time spent driving. This can then be used to calculate the mean speed using the formula: Mean Speed = Total Distance / Total Time.
On the highway: 5 hours at 50 mph = 250 miles
Through the city: 2 hours at 20 mph = 40 miles
On a county road: 5 hours at 35 mph = 175 miles
The total distance traveled is 250 miles + 40 miles + 175 miles = 465 miles. The total time spent driving is 5 hours + 2 hours + 5 hours = 12 hours.
Thus, the mean speed for the entire trip is 465 miles / 12 hours = 38.75 mph. Rounded to one decimal place, the mean speed is 38.8 mph.
In the process of loading a ship, a shipping container gets dropped into the water and sinks to the bottom of the harbor. Salvage experts plan to recover the container by attaching a spherical balloon to the container and inflating it with air pumped down from the surface. The dimensions of the container are 5.40 m long, 2.10 m wide, and 3.40 m high. As the crew pumps air into the balloon, its spherical shape increases and when the radius is 1.50 m, the shipping container just begins to rise toward the surface. Determine the mass of the container. You may ignore the weight of the balloon and the air in the balloon. The density of seawater is 1027 kg/m3?
Answer:
Step-by-step explanation:
The value of the total mass will be equal to 13.189x10³ kg.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Calculate weight,
B₁ = ρVg
B₁ = (1027) x (4/3Π(1.3)³ x (9.8)
B₁ = 92.622\ kN
Calculate weight,
B₂ = ( 1027 ) x ( 5 x 2.6 x 2.8) x (9.8)
B₂ = 366.35\ kN
The total mass will be,
B₁ + B₂ = mg
m = ( B₁ + B₂ ) / g
m = ( 36635 + 36635 ) / 9.8
m = 13.189 x 10³ kg
Therefore, the value of the total mass will be equal to 13.189x10³ kg.
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Let random variable SS represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable SS.
Answer:
5. No, the distribution is skewed to the left with a mean age greater than 36.
Step-by-step explanation:
The problem is presented in the photo below. It says the following:
Let random variable S represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable S. Alfonso claims that the distribution of S is symmetric with a mean age of 36. Does the histogram supports Alfonso's claim.
Yes, the distribution is symmetric with a mean age of 36. No, the distribution is skewed to the right with a mean age of 36.No, the distribution is skewed to the right with a mean age greater than 36.No, the distribution is skewed to the left with a mean age of 36.No, the distribution is skewed to the left with a mean age greater than 36.Consider the given histogram at the photo below. it is an left-skew histogram , since it has a long tail to the left side.
We need to estimate the mean of the given data. To do so, we need to multiply each class midpoint with its probability, and sum them.
For example, for the first one, the midpoint is 32 and the probability is 0.03 (read the value on the y-axis). For, the second one, the midpoint is 33 and the probability is 0.04, for the third the midpoint is 34 and the probability is 0.05, and so on. All needed values are presented below.
midpoint = 32, probability= 0.03 midpoint = 33, probability = 0.04 midpoint = 34, probability = 0.05midpoint = 35, probability = 0.1midpoint = 36, probability =0.11midpoint = 37, probability = 0.13midpoint = 38, probability = 0.2midpoint = 39, probability = 0.09Therefore, we obtain
[tex]\mu = 0.03 \cdot 32 + 0.04 \cdot 33 + 0.05\cdot 34 + 0.10 \cdot 35 + 0.11 \cdot 36 + 0.13 \cdot 37 + 0.25 \cdot 38 + 0.20 \cdot 39 + 0.09 \cdot 40[/tex]
which yields
[tex]\mu = 37.15[/tex]
Therefore, this histogram is left-skewed with mean greater than 36.
Suppose a savings and loan pays a nominal rate of 1.21.2% on savings deposits. Find the effective annual yield if interest is compounded 10 comma 00010,000 times per year?
Answer:
1.21%
Step-by-step explanation:
We have been given that a savings and loan pays a nominal rate of 1.2% on savings deposits. We are asked to find the effective annual yield, when interest is compounded 10 comma 00010,000 times per year.
We will use Annual Percentage Yield formula to solve our given problem.
[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year.
[tex]1.2\%=\frac{.2}{100}=0.012[/tex]
[tex]APY=(1+\frac{0.012}{10,000})^{10,000}-1[/tex]
[tex]APY=(1+0.0000012)^{10,000}-1[/tex]
[tex]APY=(1.0000012)^{10,000}-1[/tex]
[tex]APY=1.0120722815791632-1[/tex]
[tex]APY=0.0120722815791632[/tex]
[tex]0.0120722815791632\times 100\%=1.20722815791632\%\approx 1.21\%[/tex]
Therefore, the effective annual yield would be 1.21%.
Solve the system using elimination.
x plus 7 y
equals
22
4 x minus 7 y
equals
negative 17
The solution is
nothing.
(Simplify your answer. Type an ordered pair.)
Answer:
After simplifying we get (x,y) as (1,3).
Step-by-step explanation:
Given:
[tex]x+7y=22[/tex],
[tex]x-7y=-17[/tex]
We need to use elimination method to solve the and simplify the equations.
Solution;
Let [tex]x+7y=22[/tex] ⇒ equation 1
Also Let [tex]4x-7y=-17[/tex]⇒ equation 2
Now by solving the equation we get;
first we will Add equation 2 from equation 1 we get;
[tex](x+7y)+(4x-7y)=22+(-17)\\\\x+7y+4x-7y=22-17\\\\5x=5[/tex]
Now Dividing both side by 5 using division property of equality we get;
[tex]\frac{5x}{5}=\frac{5}{5}\\\\x=1[/tex]
Now Substituting the vale of x in equation 1 we get;
[tex]x+7y=22\\\\1+7y=22[/tex]
subtracting both side by 1 using subtraction property of equality we get;
[tex]1+7y-1=22-1\\\\7y=21[/tex]
Now Dividing both side by 7 using division property of equality we get;
[tex]\frac{7y}{7}=\frac{21}{7}\\\\y=3[/tex]
Hence we can say that, After simplifying we get (x,y) as (1,3).
Traveling with the wind, a plane takes 2 1/2 hours to fly a distance of 1500 miles. The return trip of 1500 miles against the same wind speed, takes 3 hours. Find the speed of the plane with no wind and the speed of the wind.
Answer: the speed of the plane with no wind is 500 miles per hour.
the speed of the wind is 100 miles per hour.
Step-by-step explanation:
Let x represent the speed of the plane.
Let y represent the speed of the wind.
Traveling with the wind, a plane takes 2 1/2 = 2.5 hours to fly a distance of 1500 miles. The total speed would be x + y
Distance = speed × time
It means that
1500 = 2.5(x + y)
1500 = 2.5x + 2.5y - - - - - - - - - 1
The return trip of 1500 miles against the same wind speed, takes 3 hours. The total speed is x - y
It means that
1500 = 3(x - y)
1500 = 3x - 3y - - - - - - - - - - - - 2
Multiplying equation 1 by 3 and equation 2 by 2, it becomes
4500 = 7.5x + 7.5y
3000 = 7.5x - 7.5y
Adding both equations, it becomes
7500 = 15x
x = 7500 /15 = 500
Substituting x = 500 into equation 1, it becomes
1500 = 2.5 × 500 + 2.5y
1500 = 1250 + 2.5y
2.5y = 1500 - 1250 = 250
y = 250/2.5 = 100
Three cards are dealt from a shuffled standard deck of playing cards. Find the probability that the first card dealt is black, the second is red, and the third is black.
Answer: Probability that the first card dealt is black,the second red and the third black is O.127
Step-by-step explanation: Total number of cards=52
Total number of black cards =26
Total number of red cards=26
Probability of pulling black=26/52
Probability of pulling red=26/51
Probability of pulling a mother black=25/50
Probability of pulling 3 cards =26/52×26/51×25/50
16900/132600
=0.127
The probability that the first card dealt is black, the second is red, and the third is black is 13/102.
Explanation:To find the probability that the first card dealt is black, the second is red, and the third is black, we need to consider the total number of possible outcomes and the number of favorable outcomes. Since we are drawing without replacement, we need to calculate the probabilities for each card.
To find the overall probability, we multiply the probabilities of each event together.
(1/2) * (26/51) * (1/2) = 13/102
Therefore, the probability that the first card dealt is black, the second is red, and the third is black is 13/102.
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Use a form of the distributive property to rewrite the algebraic expression without parentheses. one third left parenthesis 4 x minus 15 right parenthesis 1 3(4x−15) one third left parenthesis 4 x minus 15 right parenthesis 1 3(4x−15)equals=nothing (Use integers or fractions for any numbers in the expression. Simplify your answer.)
If a farmer can grow 100 tubs of grapefruit or 250 tubs of oranges per acre of land, what is the opportunity cost of growing one orange?a) 0.4 of an orange b) 2.5 oranges c) 0.4 of a grapefruit d) 2.5 grapefruits
Answer:
Option A. 0.4 of an orange
Step-by-step explanation:
Formula to calculate the opportunity cost is
Opportunity cost = [tex]\frac{\text{Sacrificed}}{\text{Gained}}[/tex]
In this question for the high yield, sacrificed thing is 100 tubs of grapes and gain is to produce 250 tubs oranges.
Opportunity cost = [tex]\frac{100}{250}=0.4[/tex] of an orange
Therefore, Option A. 0.4 of an orange, will be the answer.
Evaluate the expression when a=3,b=8, and c=1
B^2-4ac=
Answer:
After evaluating we get [tex]b^2-4ac = 52[/tex].
Step-by-step explanation:
Given:
[tex]b^2-4ac[/tex]
We need to evaluate the expression with a =3, b =8 and c= 1
Solution:
To evaluate the expression we will first substitute the values of a,b and c in the expression we get;
[tex]b^2-4ac = 8^2-4\times3\times1[/tex]
Now by using PEDMAS which states first operation needs to perform here is the exponent function.
so we get;
[tex]b^2-4ac = 64-4\times3\times1[/tex]
Now next operation to be performed is multiplication.
[tex]b^2-4ac = 64-12[/tex]
And finally we will perform subtraction operation.
[tex]b^2-4ac = 52[/tex]
Hence After evaluating we get [tex]b^2-4ac = 52[/tex].
Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible.
Answer:
1 is the positive number for which the sum of it and its reciprocal is the smallest.
Step-by-step explanation:
Let x be the positive number.
Then, the sum of number and its reciprocal is given by:
[tex]V(x) = x + \dfrac{1}{x}[/tex]
First, we differentiate V(x) with respect to x, to get,
[tex]\frac{d(V(x))}{dx} = \frac{d(x+\frac{1}{x})}{dx} = 1-\dfrac{1}{x^2}[/tex]
Equating the first derivative to zero, we get,
[tex]\frac{d(V(x))}{dx} = 0\\\\1-\dfrac{1}{x^2}= 0[/tex]
Solving, we get,
[tex]x^2 = 1\\x= \pm 1[/tex]
Since x is a positive number x = 1.
Again differentiation V(x), with respect to x, we get,
[tex]\frac{d^2(V(x))}{dx^2} = \dfrac{2}{x^3}[/tex]
At x = 1
[tex]\frac{d^2(V(x))}{dx^2} > 0[/tex]
Thus, by double derivative test minima occurs for V(x) at x = 1.
Thus, smallest possible sum of a number and its reciprocal is
[tex]V(1) = 1 + \dfrac{1}{1} = 2[/tex]
Thus, 1 is the positive number for which the sum of it and its reciprocal is the smallest.
Deangelo needs 100 lb of garden soil to landscape a building. And the company's storage area, he finds two cases holding 24 and 2/3 lb of garden soil each,and a third case holding 19 3/8 lb. How much garden soil does D'Angelo still need in order to do the job?
Question is not proper; Proper question is given below;
D'Angelo needs 100 lb of garden soil to landscape a building. In the company’s storage area, he finds 2 cases holding 24 3/4 lb of garden soil each, and a third case holding 19 3/8 lb. How much gardening soil does D'Angelo still need in order to do the job?
Answer:
D'Angelo required [tex]31 \frac{1}{8}\ lb[/tex] more garden soil to do the job.
Step-by-step explanation:
Given:
Total Amount of garden soil needed to do job = 100 lb
Amount of garden soil in 1st case = [tex]24\frac{3}{4}\ lb[/tex]
[tex]24\frac{3}{4}\ lb[/tex] can be rewritten as [tex]\frac{99}{4}\ lb[/tex]
Amount of garden soil in 1st case = [tex]\frac{99}{4}\ lb[/tex]
Amount of garden soil in 2nd case = [tex]24\frac{3}{4}\ lb[/tex]
[tex]24\frac{3}{4}\ lb[/tex] can be rewritten as [tex]\frac{99}{4}\ lb[/tex]
Amount of garden soil in 2nd case = [tex]\frac{99}{4}\ lb[/tex]
Amount of garden soil in 3rd case = [tex]19\frac{3}{8}\ lb[/tex]
[tex]19\frac{3}{8}\ lb[/tex] can be rewritten as [tex]\frac{155}{8}\ lb[/tex]
Amount of garden soil in 3rd case = [tex]\frac{155}{8}\ lb[/tex]
We need to find Amount of garden soil required more.
Solution:
Now we can say that;
Amount of garden soil required more can be calculated by subtracting sum of Amount of garden soil in 1st case and Amount of garden soil in 2nd case and Amount of garden soil in 3rd case from Total Amount of garden soil needed to do job.
framing in equation form we get;
Amount of garden soil required more = [tex]100-\frac{99}{4}-\frac{99}{4}-\frac{155}{8}[/tex]
To solve the fraction we will make the denominator common using LCM.
Amount of garden soil required more = [tex]\frac{100\times8}{8}-\frac{99\times2}{4\times2}-\frac{99\times2}{4\times2}-\frac{155\times1}{8\times1}= \frac{800}{8}-\frac{198}{8}-\frac{198}{8}-\frac{155}{8}[/tex]
Now denominators are common so we will solve the numerator.
Amount of garden soil required more = [tex]\frac{800-198-198-155}{8}=\frac{249}{8}\ lb \ \ OR \ \ 31 \frac{1}{8}\ lb[/tex]
Hence D'Angelo required [tex]31 \frac{1}{8}\ lb[/tex] more garden soil to do the job.
An amusement park charges admission plus a fee for each ride. Admission plus two rides costs $10. Admission plus five rides cost $16. What is the charge for admission and the cost of a ride?
Answer:the charge for admission is $6 and the cost of a ride is $2
Step-by-step explanation:
Let x represent the charge for admission.
Let y represent the cost of a ride.
An amusement park charges admission plus a fee for each ride. Admission plus two rides costs $10. This means that
x + 2y = 10 - - - - - - - - - - - - - 1
Admission plus five rides cost $16. This means that
x + 5y = 16 - - - - - - - - - - -- - -2
Subtracting equation 2 from equation 1, it becomes
- 3y = - 6
y = - 6/- 3
y = 2
Substituting y = 2 into equation 1, it becomes
x + 2×2 = 10
x = 10 - 4 = 6
Mary is ironing shirts for her father. He pays her 50¢ for the first shirt and increases her pay by 25¢ per shirt. How many shirts will she have iron to earn $5.00?
Answer: The answer is 7shirts
Step-by-step explanation:
100¢ = $1
$5 * 100 = 500¢
First shirt = 50¢
500¢-50¢ = 450¢
Pay increase to 75¢ after the first shirt.
Number of shirts ironed for 450¢ = 450/75 = 6shirts
Therefore, 6shirts for 450¢ and 1 shirt for 50¢ total 7 shirts for 500¢ = $5
A college student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, they will select an SRS of students and ask each respondent if he or she would patronize this type of establishment. They expect that about 74% of the student body would respond favorably.(a) What sample size is required to obtain a 95% confidence interval with an approximate margin of error of 0.03?answer: 822(b) Suppose that 54% of the sample responds favorably. Calculate the margin of error for the 95% confidence interval.
Answer:
a) Sample size = 822
b) Margin of error = 0.03407
Step-by-step explanation:
We are given the following in the question:
p = 74% = 0.74
a) Sample size is required to obtain margin of error of 0.03
Formula:
[tex]\text{Margin of error} = z_{\text{statistic}}\times \sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
Putting values, we get,
[tex]0.03 = 1.96\times \sqrt{\dfrac{0.74(1-0.74)}{n}}\\\\n = (\dfrac{1.96}{0.03})^2(0.74)(1-0.74)\\\\n = 821.24 \approx 822[/tex]
Thus, the sample size must be approximately 822 to obtain a 95% confidence interval with an approximate margin of error of 0.03
b) Margin of error for the 95% confidence interval
p = 54% = 0.54
Formula:
[tex]\text{Margin of error} = z_{\text{statistic}}\times \sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
Putting values, we get,
[tex]\text{Margin of error} = 1.96\times \sqrt{\dfrac{0.54(1-0.54)}{822}}\\\\=0.03407[/tex]
The margin of error now will be 0.03407.
Based on the sampling information given, the sample size will be 822.
SamplingThe margin of error is given as 0.03. Therefore, the sampling size will be:
= (1.96/0.03)² × 0.74 × (1 - 0.74)
= 822
The margin of error for a 95% confidence interval will be:
= 1.96 × ✓0.54 × ✓0.46 × ✓822
= 0.3407
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