Answer: z = 280
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in the value of one variable causes an increase in the value of the other variable. Also, a decrease in the value of one variable causes an decrease in the value of the other variable.
The variable z is directly proportional to x. If we introduce a constant of variation, the expression would be
z = kx
When x is 10, z has the value 140. It means that
140 = 10k
k = 140/10
k = 14
The equation becomes
z = 14x
the value of z when x = 20 is
z = 14 × 20
z = 280
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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Use the following information to complete parts I, II, and III. 1 hour=3600 seconds
1 year = 31556952 secondsI. Use scientific notation to estimate the number of hours in one year. II. Use scientific notation to calculate the exact number of hours in one year. III. In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences.
Answer:
I) 8.760 * 10 ³ hours
II) 8.76582 * 10 ³ hours
Step-by-step explanation:
1) No. of hours in one year:
24 hours* 365 days= 8760 hours
Scientific Notation= 8.760 * 10 ³ hours
2) 1 year = 31556952 seconds
1 hour=3600
1 year = 31556952 seconds/3600 = 8765. 82 hours
Scientific Notation= 8.76582 * 10 ³ hours
3) The exact numbers of hours using 365 days is 8760 which is written as 8.760* 10 ³ in scientific notation. But using the given data we get =8.76582 * 10 ³ hours
Comparing these answers the first one has only 3 significant figures
But the second answer has six significant figures if we round these we get 8.8 * 10 ³ hours which has two significant numbers
Aslo rounding the first gives 8.8 * 10 ³ hours which has two significant numbers and is the same as the other answer rounded
Help please!!!!!
Simplify each expression
1) -8(v+4) 2) -9(-8+3x)
Answer:
88
Step-by-step explanation:
Answer:
1) -8(v+4) = -8v - 32
2) -9(-8+3x) = 72 - 27x
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
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]
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.
Which of the following subsets of P2P2 are subspaces of P2P2? A. {p(t) | p′(t){p(t) | p′(t) is constant }} B. {p(t) | p(−t)=p(t){p(t) | p(−t)=p(t) for all t}t} C. {p(t) | p′(6)=p(7)}{p(t) | p′(6)=p(7)} D. {p(t) | ∫10p(t)dt=0}{p(t) | ∫01p(t)dt=0} E. {p(t) | p′(t)+2p(t)+8=0}{p(t) | p′(t)+2p(t)+8=0} F. {p(t) | p(5)=6}{p(t) | p(5)=6}
Subset B, D, E, and F are subspaces of P2.
Explanation:In order for a subset to be a subspace of P2, it must satisfy three conditions: it must be closed under addition, closed under scalar multiplication, and contain the zero vector. Let's analyze each subset to determine if it is a subspace:
A. {p(t) | p′(t) is constant}: This subset is closed under addition and scalar multiplication, so it satisfies the first two conditions. However, it does not contain the zero vector, so it is not a subspace.B. {p(t) | p(−t)=p(t) for all t}: This subset is closed under addition and scalar multiplication, and it contains the zero vector. Therefore, it satisfies all three conditions and is a subspace.C. {p(t) | p′(6)=p(7)}: This subset is not closed under addition and scalar multiplication, so it is not a subspace.D. {p(t) | ∫10p(t)dt=0}: This subset is closed under addition and scalar multiplication, and it contains the zero vector. Therefore, it satisfies all three conditions and is a subspace.E. {p(t) | p′(t)+2p(t)+8=0}: This subset is closed under addition and scalar multiplication, and it contains the zero vector. Therefore, it satisfies all three conditions and is a subspace.F. {p(t) | p(5)=6}: This subset is closed under addition and scalar multiplication, and it contains the zero vector. Therefore, it satisfies all three conditions and is a subspace.Learn more about subspaces of P2 here:https://brainly.com/question/32735601
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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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Which of the following is one of the cheapest routes to pass through each vertex once starting and ending with Vertex "A" and using the Nearest Neighbor Algorithm.
Group of answer choices
ABCDA, $960
ACDBA, $900
ACBDA, $960
None of the Above
Answer:
The answer is A
Step-by-step explanation:
The cheapest route should be c) ABCDA, $960
calculation of cheapest route:Starting at A: Options are B = 220, C = 240, D = 310
Now
Choose B since it has the smallest value.
Now
From B: Options are C = 200, D = 210
Choose C since it has the smallest value.
From C: There is only one option i.e. D = 230 here we cannot choose A since it was our beginning point.
From D: We touched all of the vertices due to this, return to the starting point, A = 310
So,
A → B → C → D → A --> 220 + 200 + 230 + 310 = 960
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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:
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
A cellular phone company charges a $25 monthly fee and an additional $0.10 per minute. If m represents the number of minutes of phone usage, which equation can be used to determine the total monthly cost, c?
Answer:
c= 0.10m+ 25
Step-by-step explanation:
using the format y=mx+b
25 is your flat cost that they charge every month, and 0.10 is what they charge per minute.
m is the number of minutes so that is the unknown variable.
c is your total cost.
you take the flat cost per month (25 dollars) and add it to however many minutes multiplied by 0.10 (.10m)
The equation for determining the total phone bill given a monthly fee of $25 and a rate of $0.10 per minute is, c = 25 + 0.10m. Here, c represents the total monthly cost and m represents the number of minutes of phone usage.
Explanation:The subject of the question is linear algebra, and it requires forming an equation for a given scenario. In this case, the monthly cost of the cellular phone service is a function of the number of minutes of phone usage. The fixed monthly fee is $25, and there is an additional charge of $0.10 per minute.
So if m represents the number of minutes of phone usage, and c represents the total monthly cost, then the equation that can be used is: c = 25 + 0.10m
This is because for each minute used, an extra $0.10 is added to the total cost. If no minutes are used, the total cost is just the fixed $25. If 50 minutes are used, for example, the total cost is $25 + (0.10 * 50) = $30.
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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:
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.
Jackson flipped a coin ten time. He flipped heads 4 times and tails 6 times. What is the experimental probability that Jackson will flip heads on his next flip ?
Answer:
Step-by-step explanation:
Given that,
Outcomes Heads= 4heads and
Outcomes Tails= 6tails
Total outcome of events n=10
Probability of head in is first throw is, the is the outcome of head divide by the total possible outcomes
P(Head in first throw)=4/10
P(H)=2/5
P(H) = 0.4
P(H) =40%
Answer:
0.4
Step-by-step explanation:
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.
Suppose the probability density function of the length of computer cables is f(x)= 0.1 from 1200 to 1210 millimeters. A) Determine the mean and standard deviation of the cable length. B) If the length specifications are 1195 < x < 1205 millimeters, what proportion of cables is within specifications?
Answer:
a) The mean :1205, standard deviation = 2.887
b)0.5
Step-by-step explanation:
The attached diagram has the solution and explanation
Please help. I keep getting a negative distance when doing the formula
Answer:
EF ≥ 4
Step-by-step explanation:
EF is the midline of the trapezoid so its length is the average of the two base lengths:
(AD +BC)/2 = EF
AD +BC = 2·EF . . . . multiply by 2
8 +2x -4 = 2(x+2) . . . substitute the expressions for the segment lengths
2x +4 = 2x +4 . . . . . . true for any value of x
We only require that segment BC is non-negative in length, so ...
BC ≥ 0
2x -4 ≥ 0 . . . . substitute the expression for BC
x -2 ≥ 0 . . . . . divide by 2
x ≥ 2
Then segment EF will be ...
x +2 ≥ 4 . . . . add 2 to both sides of the inequality for x
The only restriction the figure puts on the length of EF is ...
EF ≥ 4
_____
We suggest you talk to your teacher about this problem. The figure shown does not require that EF have any particular value.
Factor 64 - x2.
(8 - x1(8 - x)
(8 + x)(8 - x)
(8 - x)(8 + x)
Answer:
The answer to your question is (8 - x) (8 + x)
Step-by-step explanation:
Data
Factor 64 - x²
Process
To factor this polynomial use the rule to factor a difference of squares.
1.- Find the square root of 64
[tex]\sqrt{64} = 8[/tex]
2.- Find the square root of x²
[tex]\sqrt{x^{2}} = x[/tex]
3.- Write the result, using two sets of parentheses and alternating sings
(8 - x) (8 + x)
Consider the following. (a) Explain why −0.41 cannot be the probability of some event. A probability must be between zero and one. A probability must be greater than one. A probability must be an integer.
Answer:
A probability must be between zero and one
Step-by-step explanation:
We are to explain why −0.41 cannot be the probability of some event.
Probability is the chance of occurring a particular event out of total possible events.
If total possible events are n, and number of favourable outcomes for any event A is x then probability is x/n.
Here note that both x and n cannot be negative.
also x cannot exceed n.
Probability can never exceed 1 and also can never be an integer except 0 or 1 as special cases.
So the probability can never be negative and cannot exceed 1.
So correct answer is
A probability must be between zero and one
Look at the figure. Complete the statement and justify your answer. line VT ≅ _____
line TX ; Reflexive Property of Congruence
line VX ; Reflexive Property of Congruence
line VX ; Converse of the Isosceles Triangle Theorem
line TX ; Converse of the Isosceles Triangle Theorem
Answer:
line VX ; Converse of the Isosceles Triangle Theorem
Explanation:
Since the angle marks on the base of the triangle is same, they measure the same.
The Converse of the Isosceles Triangle Theorem states: If two angles of a triangle are congruent, then sides opposite those angles are congruent.
So line VT ≅ VX
What does The Bureau of Consumer Protection do for consumers?
Answer:
The Bureau of Consumer Protection stops unfair and fraudulent business practices and taking appropriate actions against them.
Step-by-step explanation:
The Bureau of Consumer Protection is a body who looks into safeguarding the financial interests of the consumers. It stops unfair and fraudulent business practices by taking necessary and appropriate actions against them. They take necessary reaction as of suing the person or business involved. The Bureau of Consumer Protection also develops rules and regulations to maintain a fair marketplace. They also educate consumers about their responsibilities and rights.
Answer:
The Bureau of Consumer Protection stops unfair and fraudulent business practices and taking appropriate actions against them. The Bureau of Consumer Protection is a body who looks into safeguarding the financial interests of the consumers. It stops unfair and fraudulent business practices by taking necessary and appropriate actions against them. They take necessary reaction as of suing the person or business involved. The Bureau of Consumer Protection also develops rules and regulations to maintain a fair marketplace. They also educate consumers about their responsibilities and rights.
Step-by-step explanation:
e d g e
Pre-Calc Help:
Find the length of the major axis of the equation x² + 4y² = 4.
Answer choices:
4
8
Answer:
4
Step-by-step explanation:
Dianna and Becky were playing on the same soccer team and took turns being goalie. They stoped 9 out of 10 shots made against them. If the other team scored 3 points, how many balls did Dianna and Becky stop from going into the net?
Answer:
27 balls
Step-by-step explanation:
If Dianna and Becky stopped 9 out of 10 shots made against them.
It means they allowed in 1 out of 10 shots made against them.
This is best solved using ratios
Proportion of Shots Stopped : Proportion of Shots allowed=9:1
If the other team scores 3 points, it means the number of shots allowed =3
Let x be the number of shots stopped
Number of Shots Stopped : Number of Shots allowed=x:3
Therefore:
9:1=x:3
[tex]\frac{9}{1}=\frac{x}{3}[/tex]
Cross multiplying
x=9 X 3 =27
Dianna and Becky stopped 27 balls from going into the net,
5 4 start fraction, 4, divided by, 5, end fraction of their popcorn with butter. The remaining 35.235.235, point, 2 ounces was made without butter. How many pounds of popcorn did Movietown Theater make on Thursday?
Answer:
Movietown Theater made a total of 10.2 pounds of butter on Thursday
Step-by-step explanation:
Movietown Theater made [tex]\frac{4}{5}[/tex] fraction of their popcorn with butter and 32.5 ounces without butter.
Fraction made without butter=[tex]1-\frac{4}{5}=\frac{1}{5}[/tex]
It means [tex]\frac{1}{5}[/tex] of total popcorn made(t) was without butter.
[tex]\frac{1}{5}Xt=32.5[/tex]
t=32.5X5=162.5
They made 162.5 ounces of butter in total
Next, we determine the weight in pounds
16 ounces = 1 pound
162.5 ounces = 162.5/16 pounds
=10.2 pounds
En un barco, 1/7 del número de tripulantes se encarga del mantenimiento de la maquinaria, 2/7 de la cocina, 3/7 de las recámaras y pasillos, y los 18 restantes son oficiales
Answer:
see the explanation
Step-by-step explanation:
The question in English is
On a ship, 1/7 of the crew members maintain the machinery, 2/7 the kitchen, 3/7 the bedrooms and corridors, and the remaining 18 are officers
Let
x ----> members that maintain the machinery
y ---->members that maintain the kitchen
z ----> members that maintain bedrooms and corridors
w ----> members that are officers
T ----> total number of members
we know that
The total sum of the fractions must be equal to 1
[tex]\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+w=1[/tex]
[tex]w=1-\frac{6}{7}[/tex]
[tex]w=\frac{1}{7}[/tex]
Remember that
The number of officers is 18
so
[tex]18=\frac{1}{7}T[/tex]
Find out the total number of members
solve for T
[tex]T=18(7)=126\ members[/tex]
Find out the number of members that maintain the machinery
[tex]x=\frac{1}{7}T[/tex]
[tex]x=\frac{1}{7}(126)=18\ members[/tex]
Find out the number of members that maintain the kitchen
[tex]y=\frac{2}{7}T[/tex]
[tex]y=\frac{2}{7}(126)=36\ members[/tex]
Find out the number of members that maintain bedrooms and corridors
[tex]z=\frac{3}{7}T[/tex]
[tex]z=\frac{3}{7}(126)=54\ members[/tex]
Does the point (2√3, 2) lie on the circle that is centered at the origin and contains the point (0, -4)? Explain?
Answer:
The answer to your question is Yes, the point P lies on the circle
Step-by-step explanation:
Data
P (2[tex]\sqrt{3}[/tex], 2)
Center (0, 0)
Q (0, -4)
Process
1.- Find the radius of the circle
dCQ = [tex]\sqrt{(0-0)^{2}+ (-4 + 0)^{2}}[/tex]
dCQ = [tex]\sqrt{0^{2} + (-4)^{2}}[/tex]
dCQ = [tex]\sqrt{16}[/tex]
dCQ = 4
2.- Find the equation of the circle
(x - 0)² + (y - 0)² = 4²
-Simplification
x² + y² = 16
3.- Substitute P in the equation of the circle
(2[tex]\sqrt{3}[/tex])² + (2)² = 16
4(3) + 4 = 16
12 + 4 = 16
16 = 16
4.- Conclusion
The point (2[tex]\sqrt{3}[/tex], 2) lies on the circle because when we evaluate the equation of the circle with this point, we get the length of the radius.
Suppose that three compact discs are removed from their cases, and that after they have been played, they are put back into the three empty cases in a random manner. Determine the probability that at least one of the CD’s will be put back into the proper cases.
Answer:
The probability that at least one of the CD'S will be put back into the proper cases is 2/3
Step-by-step explanation:
The total amount of possibilities of putting back the CD's is equal to the total amount of ways of ordering a set of 3 elements, in other words, 3! = 6. In 4 of those 6 ways, at least one of the CD's is put back properly:
- All CD's are put back into the proper cases
- First disc is put back into its proper cases, Second disc is put back in third's position, and third disc is put back in second's position.
- Second Disc is put back correctly, and first and third not
- Thir disc is put back correctly and first and second got 'swapped'.
Thus, the probability that at least one of the CD'S will be put back into the proper cases is 4/6 = 2/3.
Jake scored 67 on the calculus midterm. If the final exam counts twice as much as the midterm exam, then for what range of scores on the final would Jake get an average between 81 and 92? Both tests have a maximum of 100 points.
Jake cannot achieve an average above 89 with the final exam alone.
The final exam counts twice as much as the midterm, so the weights are 2 for the final and 1 for the midterm. The average score A can be calculated using the formula:
[tex]\[ A = \frac{\text{weight of midterm} \times \text{midterm score} + \text{weight of final} \times \text{final score}}{\text{total weight}} \][/tex]
Given that Jake's midterm score is 67 and the weights are 1 for the midterm and 2 for the final, the total weight is 1 + 2 = 3 . We want Jake's average A to be between 81 and 92.
For the lower bound of the average (81), we have:
[tex]\[ 81 = \frac{1 \times 67 + 2 \times f}{3} \][/tex]
Solving for f :
[tex]\[ 81 \times 3 = 67 + 2f \] \[ 243 = 67 + 2f \] \[ 2f = 243 - 67 \] \[ 2f = 176 \] \[ f = \frac{176}{2} \] \[ f = 88 \][/tex]
So, the minimum score Jake needs on the final exam to achieve an average of at least 81 is 88.
For the upper bound of the average (92), we have:
[tex]\[ 92 = \frac{1 \times 67 + 2 \times f}{3} \][/tex]
Solving for f:
[tex]\[ 92 \times 3 = 67 + 2f \] \[ 276 = 67 + 2f \] \[ 2f = 276 - 67 \] \[ 2f = 209 \] \[ f = \frac{209}{2} \] \[ f = 104.5 \][/tex]
However, since the maximum score for the final exam is 100, the highest possible average Jake can achieve is 100 (since [tex]\( 67 + 2 \times 100 = 267 \)[/tex], and [tex]\( \frac{267}{3} = 89 \))[/tex].
In conclusion, Jake needs to score at least 88 on the final exam to achieve an average of at least 81, but he cannot achieve an average above 89 with the final exam alone. Thus, the range of scores on the final exam for Jake to get an average between 81 and 92 is from 88 to 100. However, the upper bound of Jake's average is actually 89, not 92, due to the maximum score constraint on the final exam.