Answer:
[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]
So for this case the best answer would be:
d. 218’
Step-by-step explanation:
Previous concepts
Foot front : "Is a foot measured along the front of a piece of property".
Solution to the problem
For this case we need to begin finding the number of frontage feet, with the following formula:
[tex]Frontage fronts=\frac{Amount paid}{Unitary price}[/tex]
And for this case if we replace the values given we got:
[tex]Frontage fronts=\frac{100000}{250}=400 fromtage foot[/tex]
Now we need to convert the area to square feet. And we know that:
[tex] 1 acre= 43560 ft^2[/tex]
And converting we got: [tex]2 acre *\frac{43560 ft^2}{1 acre}=87120 ft^2[/tex]
Now we can divide the total area by the total of frontage feer and we got:
[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]
So for this case the best answer would be:
d. 218’
The subject property is a four-bedroom, two-bath, two-car-garage home in a new subdivision. Comp A is a three-bedroom, two-bath home with a screened-in porch that sold for $365,500. The appraiser values the porch at $12,500 and estimates the bedroom adjustment at $22,000. What is A's adjusted sale price?
Answer: $375,000
Step-by-step explanation:
Given : The subject property is a four-bedroom, two-bath, two-car-garage home in a new subdivision.
Comp A is a three-bedroom, two-bath home with a screened-in porch that sold for $365,500.
I.e. It has one less bedroom and one extra porch .
i.e. It requires to add one bedroom and remove screened-in porch .
Since ,The appraiser values the porch at $12,500 and estimates the bedroom adjustment at $22,000.
So , the A's adjusted sale price would become
Selling price of Comp A + Value of bedroom - Value of porch
= $365,500 + $22,000- $12,500
= $375,000
Hence, A's adjusted sale price= $375,000
A farmer uses a lever to move a large rock. The force required to move the rock varies inversely with the distance from the pivot to the point the force is applied. A force of 50 pounds applied to the lever 36 inches from the pivot point of the lever will move the rock. Which function models the relationship between f, the amount of force applied to the lever and d the distance of the applied force from the pivot point?
Final answer:
The relationship between the force applied to the lever and the distance from the pivot point can be modeled using an inverse variation function. The function that models this relationship is f = 1800/d.
Explanation:
The relationship between the force applied to the lever and the distance from the pivot point can be modeled using an inverse variation function. In this case, the force required to move the rock varies inversely with the distance. Let's denote the force as f and the distance as d. The inverse variation function is given by f = k/d, where k is a constant.
To find the value of k, we can use the given information. When a force of 50 pounds is applied 36 inches from the pivot point, the rock is moved. Plugging these values into the inverse variation equation, we have 50 = k/36. Solving for k, we get k = 50 x 36 = 1800.
Therefore, the function that models the relationship between the force applied to the lever (f) and the distance of the applied force from the pivot point (d) is f = 1800/d.
The function that models the relationship between the force (f) applied and the distance (d) from the pivot point is:
[tex]f(d) = \frac{1800}{d}[/tex]
To model the relationship between the force (f) applied to the lever and the distance (d) from the pivot point, we need to understand that the force varies inversely with the distance. This means that as the distance increases, the force required decreases, and vice versa.
The mathematical model for such a relationship is given by the equation:
[tex]f = \frac{k}{d}[/tex]
Here, k is a constant that we need to determine using the given information. We know that a force of 50 pounds is applied to the lever 36 inches from the pivot point. Plug these values into the equation to find the value of k:
[tex]50 = \frac{k}{36}[/tex]
To solve for k, multiply both sides by 36:
[tex]k = 50 \times 36[/tex]
[tex]k = 1800[/tex]
Now, we substitute the value of k back into the equation to get the final model:
[tex]f = \frac{1800}{d}[/tex]
If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x - pi / three ), what should be used for Xmin and Xmax? Explain your answer.
please try to keep the ans short yet easy to understand >
Answer:
Xmin = π/3 and Xmax = 7π/3
Step-by-step explanation:
I assume that the function is:
y = 5 + 3 cos² (x − π/3)
cos² x has a period of π, so to graph two periods, you need a domain that is 2π wide, so:
Xmax − Xmin = 2π
You can choose any values you want for Xmax and Xmin, so long as they are 2π units apart. To make it easy to graph, you'll probably want to choose Xmin = π/3 and Xmax = 7π/3.
Graph:
desmos.com/calculator/9w3pptakde
A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?
Answer:
0.140625
Step-by-step explanation:
Total numbers of possible combinations for a coin = 2^n
If the coin is tossed 10 times, we have 2^10 = 1024
If the coin is tossed once, we have 2^1 = 2 outcomes.
The possible outcomes are H, T.
We have 2 outcomes with no two consecutive head.
If the coin is tossed twice, we have 2^2 = 4 outcomes.
The possible outcomes are HH, HT, TH, TT
We have 1 outcome with two consecutive heads and 3 outcomes without two consecutive heads.
If the coin is tossed thrice, we have 2^3 = 8 outcomes.
The possible outcomes are HHH, HHT, HTH, HTT, TTH, THT, THH and TTT
We have 3 outcomes with two consecutive head and 5 outcomes without two consecutive heads.
Comparing the results from the outcomes of the coin,we have 2,3,5,......
This looks like a financial sequence. For the next 10 tosses, we have
2,3,5,8,13,21,34,55,89,144
We have 144 outcomes without two consecutive heads if the coin is tossed 10 times
Pr(number of two consecutive Heads in 10 tosses) = 144/1024
= 0.140625
The probability that two heads do not occur consecutively in 10 coin tosses is 45/512 or approximately 0.0879.
Explanation:In order to calculate the probability that two heads do not occur consecutively in 10 coin tosses, we can use the concept of permutations with restrictions. Let's consider the possibilities:
When choosing a head, there are 10 possibilities for the first head (H) and 9 possibilities for the second head.
This gives us a total of 10 * 9 = 90 possibilities.
When choosing tails (T), there are 2 possibilities for each toss, giving us a total of 2^10 = 1024 possibilities.
Therefore, the probability that two heads do not occur consecutively is 90/1024, which simplifies to 45/512 or approximately 0.0879.
Suppose that in the maintenance of a large medical-records file for insurance purposes the probability of an error in processing is 0.0010, the probability of an in filing is 0.0009, the probability of an error in retrieving is 0.0012, the probability of an error in processing as well as filing is 0.0002, the probability of an error in processing as well as retrieving is 0.0003, and the probability of an error in processing and filing as well as retrieving is 0.0001. What is the probability of making at least one of these errors? (P(R intersection F)=0.0002) Be sure to draw a Venn diagram.
Answer:
The probability of making at least one of these errors is 0.0025
Step-by-step explanation:
Consider the provided information.
Let P represents the error in processing.
Let F represents the error in filling.
Let R represents the error in retrieving.
The probability of an error in processing is 0.0010: P(P) = 0.0010
The probability of an in filing is 0.0009: P(F) = 0.0009
The probability of an error in retrieving is 0.0012: P(R) = 0.0012,
The probability of an error in processing as well as filing is 0.0002:
P(P∩F) = 0.0002
The probability of an error in processing as well as retrieving is 0.0003,
P(P∩R) = 0.0003
The probability of an error in processing and filing as well as retrieving is 0.0001.
P(P∩F∩R)=0.0001
P(R∩F)=0.0002
The probability of at least one is:
P(P∪F∪R)=P(P)+P(R)+P(F)-P(P∩F)-P(P∩R)-P(R∩F)+P(P∩F∩R)
P(P∪F∪R)=0.0010+0.0009+0.0012-0.0002-0.0002-0.0003+0.0001
P(P∪F∪R)=0.0025
Hence, the probability of making at least one of these errors is 0.0025
The required diagram is shown below.
At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?
Answer:
25%.
Step-by-step explanation:
We have been given that at the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed.
We are also told that 1/3 of the roses were short-stemmed.
[tex]\text{Short-stemmed roses}=120\times \frac{1}{3}=40[/tex]
Since 20 of those were white and 15 of which were pink, so short stemmed red roses would be [tex]40-(20+15)=40-35=5[/tex].
Now, we will find number of long-stemmed roses by subtracting number of short-stemmed roses from total roses as:
[tex]\text{Long-stemmed roses}=120-40=80[/tex]
We are also told that none of the long-stemmed roses were white, so total number of white roses would be [tex]20+0=20[/tex].
Let p represent the number of total pink roses.
Now, total number of red roses would be total roses (120) minus total pink roses (p) minus total white roses (20).
[tex]\text{Total red roses}=120-p-20[/tex]
[tex]\text{Total red roses}=100-p[/tex]
We have been given that the percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. We can represent this information in an equation as:
[tex]\frac{\text{Short-stemmed pink roses}}{\text{Total pink roses}}=\frac{\text{Short-stemmed red roses}}{\text{Total red roses}}[/tex]
[tex]\frac{15}{p}=\frac{5}{100-p}[/tex]
Let us solve for p by cross-multiplication:
[tex]1500-15p=5p[/tex]
[tex]1500-15p+15p=5p+15p[/tex]
[tex]1500=20p[/tex]
[tex]20p=1500[/tex]
[tex]\frac{20p}{20}=\frac{1500}{20}[/tex]
[tex]p=75[/tex]
Since total number of pink roses is 75, so total number of red roses would be [tex]100-75=25[/tex].
We already figured it out that 5 roses are short-stemmed, so long-stemmed roses would be [tex]25-5=20[/tex].
Now, we have long stemmed roses is equal to 20 and total long-stemmed roses is equal to 80.
Let us find 20 is what percent of 80.
[tex]\text{Percentage of the long-stemmed roses that were red}=\frac{20}{80}\times 100[/tex]
[tex]\text{Percentage of the long-stemmed roses that were red}=\frac{1}{4}\times 100[/tex]
[tex]\text{Percentage of the long-stemmed roses that were red}=25[/tex]
Therefore, 25% of the long-stemmed roses were red.
Terry earns a salary of $36,000 per year. He is paid once per month. He receives a 2.5% pay raise.
How much more money is Terry earning each month?
$25
$75
$90
Answer: $75
Step-by-step explanation:
Since Terry is paid once a month and earns $36000 in a year,
a year = 12 months
To get the amount he is paid in a month we simply divide the $36000 by 12
$36000 / 12 = $3000
In a month he is paid $3000
Now to get the pay raise;
since the pay raise is 2.5 %, we will find 2.5% of $3000
2.5/100 × $3000 = 2.5 × $30 =$75
There Terry receive an increase of $75 in a month
The number of E.coli bacteria cells in a pond of stagnant water can be represented by the function below, where A represents the number of E.coli bacteria cells per 100 mL of water and t represents the time, in years, that has elapsed.
A(t)=136(1.123)^4t
Based on the model, by approximately what percent does the number of E.coli bacteria cells increase each year?
A.
60%
B.
59%
C.
41%
D.
40%
Answer:
Option B. 59%Explanation:
The function that represents the number of E.coli bacteria cells per 100 mL of water as the time t years elapses is:
[tex]A(t)=136(1.123)^{4t}[/tex]The base, 1.123, represents the multiplicative constant rate of change of the function, so you just must substitute 1 for t in the power part of the function:
[tex]rate=(1.123)^{4t}=(1.123)^4=1.590[/tex]Then, the multiplicative rate of change is 1.590, which means that every year the number of E.coli bacteria cells per 100 mL of water increases by a factor of 1.590, and that is 1.59 - 1 = 0.590 or 59% increase.
Julia is going to the store to buy candies. Small candies cost $4 and extra-large candies cost $12.She needs to purchase at least 20 candies, but she cannot spend any more than$180.
Answer:
Small candies [tex]=9[/tex]
Extra large candies [tex]=12[/tex]
Step-by-step explanation:
Let small candies [tex]=x[/tex]
Extra large candies [tex]=y[/tex]
the number of candies is at least [tex]20[/tex].
[tex]x+y\geq20[/tex]
Cost of [tex]1[/tex] small candy [tex]=\$4[/tex]
Cost of [tex]1[/tex] extra large candy [tex]=\$12[/tex]
but she has only [tex]\$180[/tex] to spend
[tex]4x+12y\leq180[/tex]
Solve for
[tex]x+y=20.......(1)\\4x+12y=180.....(2)\\eqn(2)-eqn(1)\times4\\8y=100\\y=\frac{100}{8} \\y=\frac{25}{8} \\from\ eqn(1)\\x+\frac{25}{2}=20\\ x=20-\frac{25}{2} \\x=\frac{15}{2}[/tex]
Since number of candies should be integer.
let [tex]x=7,y=13[/tex]
total spend [tex]4\times7+12\times13=184 [/tex] which is more than [tex]\$180[/tex], so this combination is not possible.
[tex]let\ x=8,y=12\\8\times4+12\times12=176<180[/tex]
She has [tex]\$4[/tex] more so she can buy [tex]1[/tex] more small candy.
Hence small candy [tex]=9[/tex]
extra large candy [tex]=12[/tex]
Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 115 feet, and ball 2 is dropped from a height of 269 feet. Use the function f(t)= -16t^2 + h to determine the current height, f(t), of a ball dropped from a height h, over the given time t.
Write a?function for the height of ball 2
h_2(t)= ____
Answer:
[tex]h_2(t)=-16t^2+269[/tex]
Step-by-step explanation:
Put the initial height of ball 2 into the given formula. The problem statement tells you "h" stands for the initial height, and that height is 269 feet.
[tex]h_2(t)=-16t^2+269[/tex]
A café owner wanted to compare how much revenue he gained from lattes across different months of the year. What type of variable is ‘month’?
Final answer:
The 'month' variable referenced by the café owner is a categorical variable used to group revenue data across different time periods within a year.
Explanation:
In the context of the café owner's situation, the type of variable that 'month' represents is a categorical variable. A categorical variable is one that has two or more category values and can be used to group or label individuals or items in a dataset. In this case, 'month' is used as a means to categorize the revenue data collected over different time periods within a year, allowing the café owner to compare the performance of latte sales across these distinct categories.
Spends a total of $38.75 on 5 drinks and 2 bags of popcorn. Noah spends a total of $37.25 on 3 drinks and 4 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.
Answer:
3d + 4p = $37.25
5d + 2p = $38.75
Actual Answer:
Bag of popcorn is $5
A drink is $5.75
Step-by-step explanation:
Let drinks = d
Let popcorn = p
Noah: 3d + 4p = $37.25
Other: 5d + 2p = $38.75
Choose a variable to eliminate (We'll choose p)
3d + 4p = $37.25
(5d + 2p = $38.75) -2
Distribute
-10d - 4p = -77.5
The -4p cancels out the 4p, then we combine
-7d = -40.25
Divide both sides by -7
-7d/-7 = -40.25/-7
d = 5.75
Back to 3d + 4p = $37.25
Substitute d with 5.75
3(5.75) + 4p = $37.25
17.25 + 4p = 37.25
Move the constant to the other side
17.25 + 4p = 37.25
-17.25 -17.25
4p = 20
Divide both sides by 4
4p/4 = 20/4
p = 5
What time is it?
A. 11:10
B. 9:11
C. 11:09
D. 10:55
E. 9:55
Answer:
10:55
Step-by-step explanation:
Hour hand is at the 10, minute hand at the 11 (which means 11 * 5 = 55)
True or False: The following pair of ratios are equivalent ratios.8/9 and 72/81
Reggie ate 31 raisins. Which correctly describes 31 as a prime or a composite number and tells the number of factor pairs 31 has? You're choices are: A-31 is a prime number because it has 0 factor pairs. B-31 is a prime because it has 1 factor pair. C-31 is a composite number because it has 1 factor pair. D-31 is a composite number because it has 2 factor pairs.
The number 31 is a prime number and has exactly one factor pair which is 1 and the number itself, so the correct answer is option B.
Explanation:The value 31 is considered a prime number.
A prime number is a number that only two distinct positive divisors: 1 and itself. Therefore, every prime number has exactly one factor pair, which is 1 and the number itself.
So, option B-31 is a prime because it has 1 factor pair is the correct answer. This means that the factors of 31 are simply 1 and 31.
so the correct answer is option B.
Learn more about Prime Numbers here:https://brainly.com/question/30358834
#SPJ12
Final answer:
The number 31 is a prime number because it is only divisible by 1 and itself, hence it has one factor pair, which is (1, 31). The correct answer to the question is B - 31 is a prime because it has 1 factor pair.
Explanation:
The question is asking whether the number 31 is a prime number or a composite number and to identify the number of factor pairs it has. A prime number is a number that has only two factors, 1 and the number itself. In contrast, a composite number is a number that has more than two factors.
For the number 31, we can confirm that it is not divisible by any integers other than 1 and 31 without a remainder. Therefore, 31 is a prime number, and it has only one factor pair, which is (1, 31). There are no other pairs of numbers that multiply together to give the product of 31. Thus, the correct choice is B - 31 is a prime because it has 1 factor pair.
Evaluate.
43 – 4:25
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This is an improper. Perhaps you can fix it, so that I can assist you with it? I apologise.
A figura a seguir representa a planta de um apartamento . O dono desse apartamento deseja colocar carpete na sala e no dormitório .Sabendo que o metro quadrado colocado do carpete escolhido custa 48reais quanto o dono do apartamento deverá gastar?
Answer:
O dono deverá gastar 1764 reais
Step-by-step explanation:
Oi!
Em anexo, você encontrará a figura do apartamento que encontrei na web.
Para encontrar a superfície do tapete que o proprietário precisa comprar, precisamos encontrar a superfície do dormitório e da sala.
Superfície do dormitório:
A superfície do dormitório é calculada multiplicando a base pela altura do retângulo.
Da figura:
base = 3,5 m
altura = 3 m
Superfície do tapete do dormitório = 3,5 m · 3 m = 10,5 m²
A superfície da sala de estar é a superfície do retângulo composto pela sala e pelo banheiro menos a superfície do banheiro:
superfície da sala de estar = superfície do retângulo sala / banheiro - superfície do banheiro
Superfície do banheiro:
Conhecemos um lado do banheiro: 2 m
O outro lado será:
lado do banheiro = 9 m - 3,5 m - 3,5 m = 2 m
Então, a superfície do banheiro será:
Superfície do banheiro = 2 m · 2 m = 4 m²
Superfície da sala / banheiro
A altura do retângulo é (3 m + 2,5 m) 5,5 m
A base do retângulo é (9 m - 3,5 m) 5,5 m
Então, a superfície da sala / banheiro é (5,5 m) ² = 30,25 m²
Superfície da sala
A superfície da sala será igual à superfície da sala / banheiro menos a superfície do banheiro:
Superficie da sala = 30,25 m² - 4 m² = 26,25 m²
A superfície do tapete será (26,25 m² + 10,5 m²) 36,75 m²
Como cada metro quadrado custa $ 48, o proprietário terá que gastar
(48 reais / m² · 36,75 m²) 1764 reais.
Tenha um bom dia!
Factor the expression below.
x^2-10x+25
A.
(x - 5)(x - 5)
B.
5(x2 - x + 5)
C.
(x + 5)(x + 5)
D.
(x - 5)(x + 5)
Answer:
A. [tex]\displaystyle (x - 5)^2[/tex]
Step-by-step explanation:
Find two quantities that when added to −10, they are also multiplied to 25, and that number is a double −5.
I am joyous to assist you anytime.
Final answer:
The expression x^2-10x+25 can be factored as (x - 5)(x - 5).
Explanation:
The expression x^2-10x+25 can be factored as (x - 5)(x - 5). To factor the expression x^2-10x+25, we need to find two numbers that when multiplied together give us 25 (the constant term), and when added together give us -10 (the coefficient of the x term). In this case, the two numbers are -5 and -5. Therefore, the factored form of the expression is (x - 5)(x - 5), which is the same as option A.
Which point satisfies the equation 2x+3y=8
A) (1,4)
B) (2,2)
C) (-1,3)
D) (-2,4)
Which rule describes a linear relation?
A) Double x and subtract five to get y.
B) Multiply x and y to get 20.
C) Multiply x times itself and add five to get y.
D) Divide 40 by x to get y.
A linear relation is described by an equation of the form y = mx + b, where m is the slope and b is the y-intercept. None of the options provided describe a linear relation.
Explanation:A linear relation is described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept. Option A, "Double x and subtract five to get y," does not fit this form. Options B, C, and D do not fit this form either. Therefore, none of the given options describe a linear relation. The correct answer is none of the above.
Cindy goes to the market and spends $15 on 2 lbs of apples and 3 lbs of grapes. The grapes cost $2.45 per pd.
How much is one pound of apples?
Answer:
The apples cost $3.82 per pounds.
Step-by-step explanation:
We are given the following in the question:
Cost of grapes = $2.45 per pd
Total money spent = $15
Total purchasing = 2 lbs of apples and 3 lbs of grapes
Total cost of grapes =
[tex]=\text{Cost of grapes}\times \text{Amount of grapes}\\= 2.45\times 3 = 7.35\$[/tex]
Total cost of apples =
[tex]\text{Total cost} - \text{Total cost of grapes}\\= 15 - 7.35 = 7.65\$[/tex]
Cost of apple =
[tex]= \dfrac{\text{Total cost of apple}}{\text{Amount of apple}}\\\\= \dfrac{7.65}{2} = 3.825\$\text{ per pound}[/tex]
Thus, the apples cost $3.82 per pounds.
Answer: one pound of apple costs $3.825
Step-by-step explanation:
Let x represent the cost of one pound of apple.
Total amount spent on 2 lbs of apple and 3 lbs of grapes is $15
The grapes cost $2.45 per pound. This means that the total cost of 3 lbs of grapes would be
2.45 × 3 = $7.35
Since Cindy spent a total of $15, it means that
2x + 7.35 = 15
Subtracting 7.35 from both sides of the equation, it becomes
2x + 7.35 - 7.35 = 15 - 7.35
2x = 7.65
x = 7.65/2 = $3.825
June and Stella can each create six floral arrangements in one hour. If they take in 372 Valentineâs Day orders, how many hours will they need to fulfill them?
Answer:
31 hours
Step-by-step explanation:
June and Stella can create 6 floral arrangements in one hour.
They take in 372 Valentine's Day order
No of hours = orders / (June's rate + Stella's rate)
June's rate = 6 arrangements / hour
Stella's rate = 6 arrangements / hour
June's rate + Stella's rate = 2(6 arrangements /hour)
= 12 arrangements / hour
No of hours = 372 arrangements / 12 arrangements / hour
= 31 hours
June and Stella have 31 hours to fulfill the 372 Valentine's Day order
Patricia has 6 less than three times the number of CDs in her collection than Monique has x CDs, write an expression to represent the number of CDs in Patricia's collection.
Answer:
The Expression representing Number of CDs in Patricia collection [tex]3x-6[/tex]
Step-by-step explanation:
Given:
Let the Number of CDs Monique has be represented as 'x'
Now Given:
Patricia has 6 less than three times the number of CDs in her collection than Monique has.
It means Number of CDs Patricia has is equal to 3 multiplied by number of CDs Monique has and then Subtracting by 6.
Framing in equation form we get;
Number of CD' Patricia has = [tex]3x-6[/tex]
Hence The Expression representing Number of CDs in Patricia collection [tex]3x-6[/tex]
Susan is celebrating her birthday by going out to eat at five guy's for burgers. If the bill in $40 and she wants to leave a tip if 15%, how much will the tip be?
Answer:
$6
Step-by-step explanation:
Susan can easily figure the tip by the following procedure. 10% of the bill is the amount with the decimal point moved one place to the left, so is $4.00. 5% of the bill is half that, or $2.00.
15% of the bill is 10% + 5%, so is $4.00 +2.00 = $6.00. The tip will be $6.00.
At a summer camp there is one counselor for every 6 campers. Write a direct variation equation for the number of campers, y, that there are for x counselors. Then graph.
Answer:
The direct variation equation can be given as:
[tex]y=6x[/tex]
Step-by-step explanation:
Given:
At a summer camp there are 6 campers under one counselor.
To find the direct variation equation for the number of campers in terms of number of counselor.
Solution:
[tex]y\rightarrow[/tex] Number of campers
[tex]x\rightarrow[/tex] Number of counselors
We have [tex]y[/tex] ∝ [tex]x[/tex]
The direct variation equation can be written as:
[tex]y=kx[/tex]
where [tex]k[/tex] is the direct variation constant.
There are 6 campers under one counselor. Using this statement we can find value of [tex]k[/tex]
Given: when [tex]x=1[/tex] then [tex]y=6[/tex]
We have,
[tex]6=k(1)[/tex]
∴ [tex]k=6[/tex]
Thus, the direct variation equation can be given as:
[tex]y=6x[/tex]
We can find the points using the equation to plot.
[tex]x[/tex] [tex]y=6x[/tex]
0 0
1 6
2 12
The graph is sown below.
Kevin and Mark took a random sample of 100 pieces of trail mix to determine the number of peanuts, raisins, and almonds in a container. If each container of trail mix is known to have 40% peanuts, 40% almonds, and 20% raisins, which sample is a better representation of the actual population?
Answer:
Marks answer is more representative
Step-by-step explanation:
The number of peanuts is 40, the number of almonds is 40 and the number of raisins is 20.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Kevin and Mark took a random sample of 100 pieces of trail mix to determine the number of peanuts, raisins, and almonds in a container. If each container of trail mix is known to have 40% peanuts, 40% almonds, and 20% raisins.
The number will be calculated as,
40% peanut = 100 x 40 / 100 = 40
40% almonds = 100 x 40 / 100 = 40
20 % raisins = 100 x 20 /100 = 20
Therefore, the number of peanuts is 40, the number of almonds is 40 and the number of raisins is 20.
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The entire school of students were surveyed, a total of 950 students. 75% or students said they preferred chocolate ice cream to vanilla. How many students prefer chocolate ice cream?
Answer:
Number of students who prefer chocolate ice cream is approximately 713.
Step-by-step explanation:
Given,
Total number of students = 950
Students who prefer chocolate ice cream = 75%
We have to find out number of students who prefer chocolate ice cream.
For calculating number of students who prefer chocolate ice cream, we have to multiply total number of students with given percentile of students.
Now framing the above sentence in equation form, we get;
Number of students who prefer chocolate ice cream = [tex]950\times75\%[/tex]
Now we have to remove the percentile.
For this we have to divide 75 by 100, we get;
Number of students who prefer chocolate ice cream =[tex]950\times\frac{75}{100}=\frac{71250}{100}=712.50\approx713[/tex]
Hence Number of students who prefer chocolate ice cream is approximately 713.
The Rockwell hardness index for steel is determined by pressing a diamond point into the steel and measuring the depth of penetration. For 50 specimens of a certain type of steel, the Rockwell hardness index averaged 62 with a standard deviation of 8. The manufacturer claims that this steel has an average hardness index of at least 64. Test this claim at the 1% significance level?
Answer:
We conclude that the steel has an average hardness index of at least 64.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 64
Sample mean, [tex]\bar{x}[/tex] = 62
Sample size, n = 50
Alpha, α = 0.051
Sample standard deviation, s = 8
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 64\\H_A: \mu < 64[/tex]
We use one-tailed(left) z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{62 - 64}{\frac{8}{\sqrt{50}} } = -1.767[/tex]
Now, [tex]z_{critical} \text{ at 0.05 level of significance } = -2.33[/tex]
Since,
[tex]z_{stat} > z_{critical}[/tex]
We fail to reject the null hypothesis and accept the null hypothesis. Thus, we conclude that the steel has an average hardness index of at least 64.
This means that there is not enough evidence to support the claim that the average hardness index is less than 64.
To test the manufacturer's claim, we can conduct a one-sample z-test. The null hypothesis is that the average hardness index is 64, and the alternative hypothesis is that the average hardness index is less than 64.
Given:
Sample size (n) = 50 Sample mean [tex](\(\bar{x}\))[/tex] = 62Population standard deviation = 8 Population mean under the null hypothesis= 64First, we calculate the standard error (SE) of the mean:
[tex]\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{8}{\sqrt{50}} \approx 1.1314 \][/tex]
Next, we calculate the test statistic (z):
[tex]\[ z = \frac{\bar{x} - \mu_0}{SE} = \frac{62 - 64}{1.1314} \approx -1.7679 \][/tex]
Now, we need to find the critical z-value for a one-tailed test at the 1% significance level.
From the standard normal distribution table, the critical z-value for the 99th percentile is approximately 2.326.
Since the calculated z-value (-1.7679) is greater than the critical z-value (-2.326), we fail to reject the null hypothesis.
This means that there is not enough evidence to support the claim that the average hardness index is less than 64.
The manager of a supermarket wants to obtain information about the proportion of customers who dislike a new policy on cashing checks. How many customers should he sample if he wants the sample fraction to be within .15 of the true fraction, with probability .98
Answer:
n = 61 costumers
Step-by-step explanation:
For calculating the number of costumers he should sample we use the next equation:
[tex]n = \frac{z_{1-\alpha/2}^{2}p(1-p)}{E^{2} }[/tex]
Where E is the error that we are prepared to accept, in this case E = 0.15
How we don't know the value of p, we can estimate it like p = 0.5
∝ = 1-0.98 = 0.02
1-∝/2 = 0.99
[tex]z_{0.99} = 2.33[/tex]
[tex]n = \frac{(2.33^{2})(0.5)(1-0.5)}{0.15^{2} }[/tex]
n = 60.32 costumers
n ≈ 61 costumers
Final answer:
To determine the sample size needed for the proportion of customers who dislike the new policy on cashing checks, we can use the formula: n = (Z^2 * p' * (1-p')) / E^2. The manager wants a sample fraction within 0.15 of the true fraction with a probability of 0.98.
Explanation:
To determine the sample size needed for the proportion of customers who dislike the new policy on cashing checks, we can use the formula:
n = (Z^2 * p' * (1-p')) / E^2
Where:
n is the sample size
Z is the z-score corresponding to the desired confidence level
p' is the estimated proportion
E is the maximum error or margin of error
In this case, the manager wants a sample fraction within 0.15 of the true fraction with a probability of 0.98. Assuming p' is 0.5, we can calculate the required sample size.
Graph the system of linear equations. negative StartFraction one-half EndFraction y equals StartFraction one-half EndFraction x plus 5 and y equals 2 x plus 2.y = x + 5 and y = 2x + 2. The solution to the system is (, ).
Answer:
It is (-4,-6)
Step-by-step explanation:
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To graph a system of linear equations, start at the y-intercept and use the slope to plot the next points. The solution to the system of equations is the point where the lines intersect, and can be found by setting the equations equal to each other and solving.
Explanation:The problem involves graphing a system of linear equations, which are y = x + 5 and y = 2x + 2.
Each equation is in the form of y = mx + b, where m is the slope and b is the y-intercept. For the first equation, the slope is 1 and the y-intercept is 5. For the second equation, the slope is 2 and the y-intercept is 2.
To graph these, you typically start at the y-intercept (where the line crosses the y-axis) and use the slope to determine the next points on the graph - you rise/run according to the slope.
The solution to the system of equations is the point where the two lines intersect. To find this point, you need to solve the system of equations either graphically or algebraically. This would involve setting the equations equal to each other and solving for x, and then substituting that value of x into either of the original equations to solve for y.
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