The sample in the study refers to the 12 children in Mrs. Smith's kindergarten class. A sample is a subset of people selected from a larger group for study purposes. In this research, the data being analyzed only pertains to these selected individuals.
Explanation:In this study, the sample chosen is the group of 12 children in Mrs. Smith's kindergarten class. This is because the data being collected and scrutinized is related to these particular individuals. In this context, 'sample' refers to the subset of people chosen from a larger group (the population) for research or study purposes. It is the set of individuals on which the study or experiment is conducted. In this case, the larger population could be considered all children in kindergarten, but the sample for the study is specifically the 12 children in Mrs. Smith's class, as the study only includes their sleep patterns.
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How much tomato juice is needed for a group of four people if each person gets 1/3 cup of juice how much tomato juice is needed if they each get 2/3 cup of juice
Answer:
[tex]1\frac{1}{4} \ cups \ of \ juice[/tex] ,[tex]2\frac{2}{3}\ cups \ of \ juice[/tex]
Step-by-step explanation:
Given:
Number of people in a group = 4
Each person gets cup of juice = [tex]\frac{1}{3}[/tex]
Question asked:
How much tomato juice is needed for a group of four people ?
How much tomato juice is needed if they each get 2/3 cup of juice ?
Solution:
Unitary method:
In case of each person gets [tex]\frac{1}{3}[/tex] up of juice.
1 person gets cup of juice = [tex]\frac{1}{3}[/tex]
4 persons gets cup of juice = [tex]\frac{1}{3} \times4=\frac{4}{3} =1\frac{1}{3} \ cup \ of\ juice[/tex]
Therefore, [tex]1\frac{1}{4} \ cups \ of \ juice[/tex] is needed for a group of four people.
In case of each person gets [tex]\frac{2}{3}[/tex] cup of juice.
1 person gets cup of juice = [tex]\frac{2}{3}[/tex]
4 persons gets cup of juice = [tex]\frac{2}{3}\times4=\frac{8}{3} =2\frac{2}{3} \ cups\ of \ juice[/tex]
Thus, [tex]2\frac{2}{3}[/tex] cups of tomato juice is needed if they each get [tex]\frac{2}{3}[/tex] cup of juice.
Final answer:
To compute the needed tomato juice for four people with varying cup quantities, multiply the cup amount by the number of people.
Explanation:
To find out how much tomato juice is needed for four people if each person gets 1/3 cup, you would multiply 1/3 cup by 4 people:
1/3 cup x 4 people = 4/3 = 1 1/3 cups of tomato juice
If each person gets 2/3 cup of juice, you would multiply 2/3 cup by 4 people:
2/3 cup x 4 people = 8/3 = 2 2/3 cups of tomato juice
Qualitative research a. involves manipulation of multiple variables. b. involves measurement of multiple variables. c. does not involve manipulation of independent variables or control of other variables. d. both a and b
Answer: option c
Step-by-step explanation: Qualitative research consist in observing some variables and obtaining information. Usually the qualitative researc does not involve the manipulation of independent variables, these tipes of researches focuses more in collecting "answers" in groups of people, and making staistics with those answers or information. So the variables are not manipulated, and the correct answer is the option c
Answer: option d. Both a and b
Step-by-step explanation:
Qualitative research is a type of social science research that collects and works with non-numerical data and that seeks to interpret meaning from these data that help understand social life through the study of targeted populations or places.
Find x and y in image
Answer:
x = 7, y = 27
Step-by-step explanation:
The triangles are equilateral triangles. So all sides are equal, and all angles are equal (60°).
Setting sides equal:
x + 4 = 2x − 3
7 = x
Setting the angle to 60°:
2y + 6 = 60
2y = 54
y = 27
Received all goods that waren had authorized eastern wisconsin university to return on EWU's return request No. R8034 for credit against their account balance
The question provided is incomplete, here is the complete question content from google
December 26 *Received all the goods that Waren authorized Eastern Wisonsin University to return on EWU's return request No. R8034 for credit against their account balance. **Process and record the sales return now. December 26 * Receive check No. 49326 for $10,000 for Eastern Wisconsin University in partial payment of the remaining amount (after sales return) on charge invoice No. 729, and deposited the check. **Do not finalize a deposit slip until you determine whether there are no other cash receipts on the same day. After entering the partial payment for invoice #729 with check 49326, where else am I suppose to post to? With the check from EWU, would you post this in the Cash Disburstments Journal?
Answer:
No. When goods are returned, it is termed as sales return and when the check has been collected as partial payment, it is recorded in cash receipt journal and not in cash Disbursements Journal.
Step-by-step explanation:
When goods are returned, it is termed as sales return and when the check has been collected as partial payment, it is recorded in cash receipt journal and not in cash Disbursements Journal.
In cash disbursement journal, transactions are recorded as related to payments made while in cash Receipt Journal ,transactions are recorded when the money has been received.
The question refers to a business transaction scenario wherein goods authorized by Waren for return by Eastern Wisconsin University (EWU) have been received. This event will result in a credit against EWU's account balance with Waren, marked by return request No. R8034.
Explanation:The scenario mentioned refers to a business transaction between two entities, Waren and Eastern Wisconsin University (EWU). In this situation, EWU is returning goods back to Waren, which have been authorized by the latter. Following successfully receiving the goods, Waren would credit the account balance of EWU, essentially setting off the monetary value of the returned goods against any debt that EWU might owe Waren. This is a common practice in various business transactions and is known as Returns against credit.
The return request No. R8034 specifically identifies this transaction, enabling the parties involved to keep track of their exchanges and to effectively manage their financials.
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A tin man has a head that is a cylinder with a cone on top .The height of the cylinder is 12 inches and the height of the cone is 6 inches. The radius of both the cylinder and the cone is 4 inches.What is the volume of the tin man's head in terms of pit?
Answer:
The answer to your question is 224 π in³
Step-by-step explanation:
Data
Cylinder Cone
height = 12 in height = 6 in
radius = 4 in radius = 4 in
Volume = x Volume = y
Process
1.- Calculate the volume of the Cylinder
V = πr²h
V = π (4)²(12)
V = π(16)(12)
V = 192 π
2.- Calculate the volume of the Cone
V = 1/3 πr²h
V = 1/3 π(4)²(6)
V = 1/3 π(16)(6)
V = 96/3 π
V = 32 π
3.- Calculate the volume of the head
Volume = 192 π + 32 π
Volume = 224 π in³
Answer:
The answer to your question is 224 π in³
Step-by-step explanation:
In a round robin tennis tournament, each player plays every other player exactly once. Use induction to show that if there are n players there will be n(n − 1)/2 games.
Answer:
Step-by-step explanation:
given that in a round robin tennis tournament, each player plays every other player exactly once.
Suppose there are two players i.e. n=2, we have only one match satisfies
[tex]\frac{2(2-1)}{2} =1[/tex]
Hence P(2) is true
Assume P(k) is true. For k players no of matches played
= [tex]\frac{k(k-1)}{2}[/tex]
To prove true for n = k+1
If to k players one new player is introduced, then the new player should play all the k players to have the condition satisfied
i.e. no of matches = no for k players + k
= [tex]\frac{k(k-1)}{2} +k\\= \frac{k^2-k+2k}{2} \\= \frac{(k+1)k}{2}[/tex]
So if true for n =k, then true for n =k+1
Already true for n =2
By induction true for all natural numbers starting from 2.
The frequency of red light is about 4.3 x 10^14 Hz. The frequency of violet light is about 7.5 x 10^14 Hz. What is the approximate difference in frequency between red light and violet light?
Answer:
The difference in frequency between red light and violet light is 3.2×10¹⁴Hz.
Step-by-step explanation:
Frequency :During any time interval the number of waves which pass through a point in space is known as frequency of that ray.
The unit of frequency is Hz.
There are 7 colors in white ray. The highest frequency color is violet and lowest frequency color is red.
Given that the frequency of red is 4.3 ×10¹⁴Hz.
The frequency of violet ray is 7.5×10¹⁴Hz.
The difference in frequency between red light and violet light is
=(7.5×10¹⁴-4.3×10¹⁴)Hz
=(7.5-4.3)×10¹⁴Hz.
=3.2×10¹⁴Hz.
The difference in frequency between red light and violet light is found by subtracting the frequency of the red light from that of the violet light. The resulting difference is approximately 3.2 x 10^14 Hz.
Explanation:The frequency of light is a measurement of how many waves pass a point in a given period of time. To find the difference in frequency between the red light and the violet light, we need to subtract the frequency of the red light from the frequency of the violet light.
The frequency of violet light is 7.5 x 1014 Hz, while the frequency of red light is 4.3 x 1014 Hz. To calculate the difference, we subtract these two frequencies as follows:
7.5 x 1014 Hz - 4.3 x 1014 Hz = 3.2 x 1014 Hz
Therefore, the approximate difference in frequency between red light and violet light is 3.2 x 1014 Hz.
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Please help.. I don't understand this question and the assignment is due tomorrow.
Answer:
y = 7 csc(½ x) − 2
Step-by-step explanation:
General form of a cosecant function is:
y = A csc(2π/T x + B) + C
where A is the amplitude, T is the period, B is the horizontal offset ("phase shift"), and C is the vertical offset ("midline").
The range is (-∞, -9] [5, ∞), so the midline is halfway between -9 and 5.
C = (-9 + 5) / 2
C = -2
The amplitude is half the difference between -9 and 5.
A = |-9 − 5| / 2
A = 7
The period is twice the distance between consecutive asymptotes.
T = 2 (2π − 0)
T = 4π
So far, we have:
y = 7 csc(½ x + B) − 2
We know there is an asymptote at x = 0. Cosecant is undefined at multiples of π, so:
½ (0) + B = kπ
B = kπ
B is any multiple of π. The simplest choice is B = 0.
y = 7 csc(½ x) − 2
Consider two representations. Representation A is abstract and bears no systematic relationship to what it represents, whereas Representation B shares some features of what it represents. Representation A is a(n) ________ and Representation B is a(n) ________.
Answer:
Consider two representations. Representation A is abstract and bears no systematic relationship to what it represents, whereas Representation B shares some features of what it represents. Representation A is a **symbolic representation** and Representation B is an **analogical representation**.
Step-by-step explanation:
Symbolic representation as it sounds, uses visual symbols to represent variable/data. This form of representation doesn't need an explanation or a relationship between the symbol and what it is representing. There are numerous examples of these all over Mathematics and Physics. For example, Angular speed is represented by ω; there isn't a direct relationship between ω and angular speed. We have just come to accept that the symbol, ω, stands for angular speed.
Analogical representation hold some of the actual characteristics of what they represent. One can tell much about what is being represented just by looking at the analogical representation.
Pictures, graphs, Maps etc., are great examples of analogical representations.
Among three bases, X−X−, Y−Y−, and Z−Z−, the strongest one is Y−Y−, and the weakest one is Z−Z−. Rank their conjugate acids, HXHX, HYHY, and HZHZ, in order of decreasing strength.
Answer:
Rank (in order of decreasing strength):
HZ
HX
HY
Step-by-step explanation:
The Stronger the base the weaker its conjugate acid.
The strongest base is Y-, then the weakest conjugate acid is HY.
The weakest base is Z-, then the strongest conjugate acid is HZ.
Between them is the pair composed by X- and HX
Please help!!! Idk what the answer is, I’m not ver good at graphing
Answer:
see below
Step-by-step explanation:
When a line goes through the origin, it expresses a proportional relationship such that for every point on the line ...
y/x = constant
The graph shows points (-5, 4) and (5, -4) as being on the line. So, we can determine the constant to be ...
constant = (y-value)/(x-value) = -4/5 . . . . . using point K
Then the proportion can be written as ...
y/x = -4/5
Multiplying both sides of this equation by -1 lets us also write the same relation as ...
-y/x = 4/5 . . . . matches the 2nd answer choice
A particular extension cord can support up top 8 amps.Mo has an iron whose label States 1, 200 watts and wonders of the iron can be plugged into the extension cord. If watts are converted top amps by dividing by 120. How many amps does the iron use
Answer:
The iron will need 10 amps
Step-by-step explanation:
The extension cord can support uptown 8 amps.
The iron has a 1200watts labelled on it
Converting watts to amps by dividing by 120 gives:
1200watts/120 =10 amps
The iron is 10amps
The number of customers waiting for gift-wrap service at a department store is an rv X with possible values 0, 1, 2, 3, 4 and corresponding probabilities 0.1, 0.2, 0.3, 0.25, 0.15. A randomly selected customer will have 1, 2, or 3 packages for wrapping with probabilities 0.55, 0.25, and 0.2, respectively. Let Y = the total number of packages to be wrapped for the customers waiting in line (assume that the number of packages submitted by one customer is independent of the number submitted by any other customer). (a) Determine P(X = 3, Y = 3), i.e., p(3,3).
Answer:
P[X=3,Y=3] = 0.0416
Step-by-step explanation:
Solution:
- X is the RV denoting the no. of customers in line.
- Y is the sum of Customers C.
- Where no. of Customers C's to be summed is equal to the X value.
- Since both events are independent we have:
P[X=3,Y=3] = P[X=3]*P[Y=3/X=3]
P[X=3].P[Y=3/X=3] = P[X=3]*P[C1+C2+C3=3/X=3]
P[X=3]*P[C1+C2+C3=3/X=3] = P[X=3]*P[C1=1,C2=1,C3=1]
P[X=3]*P[C1=1,C2=1,C3=1] = P[X=3]*(P[C=1]^3)
- Thus, we have:
P[X=3,Y=3] = P[X=3]*(P[C=1]^3) = 0.25*(0.55)^3
P[X=3,Y=3] = 0.0416
1. Chapter ma2pe08r, Section .72, Problem 012 (ID: 012.07.2 - MC - MANK08) David tunes pianos in his spare time for extra income. Buyers of his service are willing to pay $135 per tuning. One particular week, David is willing to tune the first piano for $115, the second piano for $125, the third piano for $140, and the fourth piano for $175. Assume David is rational in deciding how many pianos to tune. His producer surplus is a. $-15. b. $20. c. $30. d. $75.
Answer:
Option C. $30
Step-by-step explanation:
As per question buyers are willing to pay $135 per tuning. If David demands more than this amount producer will not choose David to tune.
As we can see on first week David is willing to tune the first piano for $115,
So surplus for producer will be
135 - 115 = $20
Surplus for second week for producer will be
135 - 125 = $10
Since David is willing to tune the third and fourth piano for $140 and $175 then the producer will not choose David for tuning.
Therefore, total surplus for the producer will be $20 + $10 = $30
Option C. $30 is the correct option.
Glenna wants to rent a car for a trip to key west for one weekshe calls two car rental companies to get prices. mr kotters rentals rents a cadillac escalade for $99 for one week plus $0.11per mile over 100 miles. barbarino's rentals has the same vehicle for $75 per week and $0.15 per mile over 150 miles. if its 432 miles to key west, which company has the better deal? How many miles would Glenna drive before she would be spending the same amount at either company?
Answer:
B rentals is better deal for journey 432 miles
If she spending same money either company the distance travels in a week is[tex]x=600[/tex] miles
Step-by-step explanation:
Given,
Mr K rentals cars [tex]=\$ 99[/tex] per week and [tex]\$ .11[/tex] for over 100 miles
B rentals car[tex]=\$ 75[/tex] per week and [tex]\$ .15[/tex] for over 150 miles
Let total journey cost of Glenna if she travels 432 miles
For Mr, K rentals is Y
Y=99+.11\times \left ( 432-100\right )
[tex]Y=99+.11\times \left ( 432-100\right )[/tex]
[tex]Y=99+36.52[/tex]
[tex]Y=\$ 135.52[/tex]
For B rental journey cost is Z
[tex]Z=75+.15\left ( 432-150 \right )[/tex]
[tex]Z=75+42.3[/tex]
[tex]Z=\$ 117.3[/tex]
If she spending same money either company
x mile she drive in a week
[tex]Y=Z[/tex]
[tex]99+.11\left ( 432-100 \right )x=75+.15\left ( 432-150 \right )x[/tex]
[tex]99-75=.15x-.11x[/tex]
[tex]24=.04x[/tex]
[tex]x=24/.04[/tex]
[tex]x=600[/tex]
If an arguer cites a statement by a recognized expert in support of a conclusion and the statement falls within the expert's range of expertise, then the arguer commits an appeal to unqualified authority.
Final answer:
An appeal to authority is using an expert's statement to support a conclusion, which is valid when the statement is within the expert's field. The authority should be able to provide support for the claim, and the appeal should not be based on the authority's position alone. The fallacy of false authority arises when an individual is not actually an expert in the subject matter they are discussing.
Explanation:
The term appeal to authority or argumentum ad verecundiam involves using the statement of an expert to support a conclusion. However, not every appeal to an authority is valid. A key point is that the statement must fall within the expert's range of expertise. For example, a Nobel Laureate in Economics would not be a qualified authority on medical issues unless their advice pertains to economic factors of medicine.
An argument from authority becomes fallacious when the cited authority is not an expert in the relevant field. Moreover, the authority's position should not be the sole foundation for a conclusion; the authority must be able to provide independent support for the conclusion. When an appeal to authority is appropriate, it means that the person being cited is a recognized expert and is knowledgeable and credible in the area under discussion, such as a doctor when it comes to medical issues or a lawyer in legal matters.
A grocer bought some walnuts for 45¢ per pound and some pecans for 60¢ per pound. He wants to mix the pecans and walnuts together to form a 90 pound mixture to sell at 55 cents per pound. If x represents the pounds of walnuts used in the mixture, which expression would represent the total cost of the pecans used in the mixture? 0.55x 0.60x 0.60(90 - x)
Answer:
Step-by-step explanation:
Let x represent the pounds of walnuts used in the mixture. He wants to mix the pecans and walnuts together to form a 90 pound mixture. This means that the pounds of Pecans in the mixture is (90 - x)
The grocer bought some walnuts for 45¢ per pound and some pecans for 60¢ per pound. If the mixture would sell at 55 cents per pound, The expression representing the total cost of the pecans used in the mixture is
45x + 60(90 - x) = 55(90)
45x + 60(90 - x) = 4950
Thirty sixteen-year-olds took the driving test to obtain their driver's license. The following chart shows the number of times each one had to take the test before passing. 1 3 1 1 2 1 2 3 2 1 2 1 1 3 2 1 1 1 1 2 1 1 2 1 3 2 1 1 1 2 Based on the above data, what is the mode?
The mode is 1. 1 shows up the most in the given data.
Answer: 1
Step-by-step explanation:
Can anybody answer this equation??
Answer:
18.6 (C)
Step-by-step explanation:
(I am assuming) it is a parallelogram, meaning that R to the center = 1/2 (QR).
9.3 *2=QR, meaning that 18.6 is the answer.
An engineer designs a new cargo ship to transport 12,000 standard shipping containers. The ship's cargo hold and a shipping container are similar rectangular prisms. A standard shipping container is 6 meters long, 2.5 m wide, and 2.5 m tall.
What is the volume of the cargo hold of the ship?
Answer:
Vol=[tex]450,000m^3[/tex]
Step-by-step explanation:
Volume of rectangular prism is obtained using the formula:
[tex]V=whl\\w-width\\h-height\\l-length[/tex]
Dimensions of shipping containers is given as:
[tex]w=2.5m\\h=2.5m\\l=6m\\[/tex]
To obtain the volume of the cargo ship, we need to calculate the volume of 1 unit of a shipping container then multiply it by the number of containers the ship can carry.
let n be the number of containers ship can carry.
[tex]V_c=whl\\V_c=2.5m\times2.5m\times6m\\V_c=37.5m^3\\[/tex]
Volume of ship,[tex]V_s[/tex]
[tex]V_s=nV_c[/tex]
But n=12000
[tex]V_s=12000\times37.5m^3\\=450,000m^3[/tex]
* Two cars started to move from C and from D, towards one another. The car that starts at point C moves twice as fast as the car that starts at point D. How far from Boston will these two cars meet?
Answer:
The answer to the question is
If Boston is at D and C is 90 km away from Boston, then the two cars will meet at 30 km from Boston.
Step-by-step explanation:
Let the speed of the car that start from C = V₁
Let the speed of the car that start from D = V₂
Therefore where V₁ = 2·V₂
We have at time t when the cars meet the distance covered by the car that start from C will be V₁×t = 2·V₂×t, while the distance of the other car will be
V₂×t
Which means that the distance covered by the car that start from C is twice that of the car that start from D
Hence if Boston is located at D which is 90 km from C then both cars will meet at
90 km /3 = 30 km from Boston as the car originating from Boston would only have covered 30 km when the two cars meet.
You receive an order for 15units of regular insulin to be given with breakfast and 20units to be giving with dinner. Insulin is available in a strength/concentration of 100units/ml . How many milliliter are needed for one day
Answer:
The medical doctor prescribed 0.35 ml of insulin per day.
Step-by-step explanation:
To find out how many millimiters of insulin was prescribed we need to find out how many units we have to took. The doctor prescribed two does of 15 units and 20 units, so the total of units for the day is the sum of the two in this cas 15 + 20 = 35 units. Now we can use a proportion rule, if we have 100 units for 1 ml in 35 units we will have an x amount of ml:
x = 35/100 = 0.35 ml
The medical doctor prescribed 0.35 ml of insulin per day.
Step-by-step explanation:
Below is an attachment containing the solution
Suppose that f and g are two functions with the same domain. If f(x)equalsg(x) for every x in the domain, the equation is called a(n) _______. Otherwise, it is called a(n) _______ equation.
Answer:
Identity; conditional
Explanation:
Identity functions are functions that returns the SAME value which was used in its argument. In this case, f(x) = g(x). Therefore f(x) = g(x) = x.
Conditional functions are conditions that evaluates the condition and returns DIFFERENT values all depending on the condition value. That is, in this case, f(x) is not equal to g(x) for every x domain.
So, while identity functions returns the same value, conditional functions returns different functions.
Final answer:
An equation where f(x) equals g(x) for every x in the domain is an identity equation; otherwise, it's a conditional equation. For f(x) = x² and g(s) = s², they are the same function. Function f can be expressed in terms of y if g is invertible.
Explanation:
If f(x) equals g(x) for every x in the domain, the equation is called an identity. Otherwise, it is called a conditional equation.
For the given functions f(x) = x² and g(s) = s², we can see that they are indeed the same function, as they both satisfy the vertical-line test and map every x in the domain to a unique y in the range.
In the context of variable transformations, if y = g(x) defines a transformation from x to y, we could describe function f(x) in terms of the variable y only if there is a way to express x in terms of y. If g is invertible, then we can write f as a function of y by finding g⁻¹(y) and then applying f to it, yielding f(g⁻¹(y)).
Carl wants to buy a television that cost $500 including taxes to pay for the television he will use a payment plan that requires him to make a down payment of $125 and then pay $72.50 each month for six months what is the percent increase from the original cost of the television to the cause of the television using the payment plan
Answer:
41%
Step-by-step explanation:
Given the cash price is $500, the hire purchase price is calculated by summing the installment and down-payment:
[tex]Hire \ Purchase \ Price=Installments +Downpayments\\\\=8\times 72.50+125\\\\=705[/tex]
#Percentage increase in price is the difference between the hire purchase price and list price as a percentage of the list price:
[tex]\bigtriangleup Price=705-500\\\\=205\\\\\%\bigtriangleup Price=\frac{\bigtriangleup Price}{500}\times 100\%\\\\\\=\frac{205}{500}\times100\%\\\\=41\%[/tex]
Hence, the % increase in price is 41%
In a decagon (a polygon with 10 sides), each vertex is joined with every other vertex by a line segment. What is the total number of segments (including the sides of the decagon)?
Answer:the total 20
Step-by-step explanation:
Just plug in the numbers then find the derivative.
h(x)=f(g(x))
f(x)=sqrt(x)
g(x)=5x^2+4
h(3)=[]
h'(3)=[]/[]
Answer:
h(3) = 7
h'(3) = 15/7
Step-by-step explanation:
h(3) = f(g(3)) = f(5(3²)+4)
h(3) = f(49)
h(3) = 7
h(x) = (5x² + 4)^½
h'(x) = ½[(5x² + 4)^-½] × 10x
h'(x) = 5x[(5x² + 4)^-½]
h'(3) = 5(3)/7 = 15/7
Alex is building a rectangular fence around his yard.The total perimeter of the fence is 68 feet and the area of the yard is 240 square feet. Based on this information, what is the dimensions of the fence?
Answer:
Therefore the dimensions of the fence 24 feet by 10 feet.
Step-by-step explanation:
Rectangle
The opposite sides of a rectangular are congruentThe opposite angles of a rectangular are congruentThe area of a rectangular is (length×breadth)The perimeter of a rectangular is 2(length+breadth)Given
The perimeter of the fence is 68 feet
The area of the rectangular yard is 240 square feet
Let the length be x feet and breadth is y feet
According to the problem,
2(length+breadth)=68
⇒2(x+y)=68
⇒[tex](x+y)=\frac{68}{2}[/tex]
[tex]\Rightarrow x+y=34[/tex] .......(1)
The area of the rectangular is
length×breadth=240
⇒x×y=240
[tex]\Rightarrow x=\frac{240}{y}[/tex]
Putting the value x in the equation
[tex]\frac{240}{y}+y=34[/tex]
[tex]\Rightarrow \frac{240+y^2}{y}=34[/tex]
[tex]\Rightarrow 240+y^2=34y[/tex]
⇒y²-34y+240=0
⇒y²-24y-10y+240=0
⇒y(y-24)-10(y-24)=0
⇒(y-24)(y-10)=0
⇒y=24,10
When, y=24
[tex]x=\frac{240}{24}=10[/tex]
When y=10
[tex]x=\frac{240}{10}[/tex] =24
Therefore the dimensions of the fence 24 feet by 10 feet.
What are the coordinates of the vertex of the function f(x) = x2 - 12x + 5?
(6,31)
(-6, 31)
(6,-31)
(-6, -31)
Answer:
The vertex is the point (6,-31)
Step-by-step explanation:
we have
[tex]f(x)=x^2-12x+5[/tex]
This is a vertical parabola open upward
The vertex represent a minimum
Convert to vertex form
Complete the square
[tex]f(x)=(x^2-12x+6^2)+5-6^2[/tex]
[tex]f(x)=(x^2-12x+36)-31[/tex]
Rewrite as perfect squares
[tex]f(x)=(x-6)^2-31[/tex] -----> equation in vertex form
therefore
The vertex is the point (6,-31)
Coach Martinez will order 2 pairs of shorts and 3 shirts for each player. There are 12 members on the team. If each pair of shorts costs x dollars and each shirt costs y dollars, which expression represents the total cost of his order?
The expression [tex]\(24x + 36y\)[/tex] represents the total cost of Coach Martinez's order for 12 team members, where [tex]\(x\)[/tex] is the cost of each pair of shorts and [tex]\(y\)[/tex] is the cost of each shirt.
The total cost [tex](\(C\))[/tex] of Coach Martinez's order can be represented by the expression:
[tex]\[ C = \text{Cost of shorts} + \text{Cost of shirts} \][/tex]
Since Coach Martinez is ordering 2 pairs of shorts and 3 shirts for each player, and there are 12 members on the team, the expression for the total cost is:
[tex]\[ C = 12 \cdot (2x) + 12 \cdot (3y) \][/tex]
Simplify this expression to get the total cost:
[tex]\[ C = 24x + 36y \][/tex]
Therefore, the expression [tex]\(24x + 36y\)[/tex] represents the total cost of Coach Martinez's order for 12 team members, where [tex]\(x\)[/tex] is the cost of each pair of shorts and [tex]\(y\)[/tex] is the cost of each shirt.
For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
A. (0.6)5(0.6)5
B. 2(0.6)42(0.6)4
C. 3(0.6)43(0.6)4
D. 4(0.6)4(0.4)+(0.6)54(0.6)4(0.4)+(0.6)5
E. 5(0.6)4(0.4)+(0.6)5
Answer: P(x≥4) = 0.337
Step-by-step explanation: p = probability of getting head = 0.6, probability of not getting head = q = 1 - 0.6 =0.4
n = number of times experiment was performed = 5
We are to find
P(x≥4) = 1 - P(x≤3)
We can get the value of P(x≤3) using a cumulative binomial probability table.
P(x≤3) = 0.663
P(x≥4) = 1 - 0.663
P(x≥4) = 0.337