Answer:
(a) [tex]N(t)=10000e^{(\frac{ln5}{10})t }[/tex]
(b) 25,000
(c) 4.3068 min.
Step-by-step explanation:
Rate of change in the number of bacteria is proportional to the number present.
Let N is the population of bacteria.
[tex]\frac{dN}{dt}[/tex] ∝ N ⇒ [tex]\frac{dN}{dt}=kt[/tex] { k = proportionality constant}
initial population No. = 10,000
[tex]N(t_{1} )[/tex] = 20,000
and [tex]N(t_{1}+10 )=100,000[/tex]
(a) For population growth
[tex]N(t)=N_{0}e^{kt}=10000e^{kt}[/tex]
[tex]N(t_1)=10,000e^{kt_1}=20,000[/tex]
[tex]e^{kt}=2[/tex]
[tex]ln(e^{kt_1})=ln(2)[/tex]
[tex]kt_1=ln(2)[/tex]
[tex]t_{1}=\frac{ln2}{k}[/tex] ----------(1)
[tex]N(t_1+t_{10})=100,000[/tex]
[tex]100,000=10,000e^{k(t_1+10)}[/tex]
[tex]10=e^{k(t_1+10)}[/tex]
[tex]ln10=ln[e^{k(t_1+10)}][/tex]
[tex]k(t_1+10)=ln10[/tex]
[tex]k(t_1)=ln10-10k[/tex]
[tex]t_1=\frac{ln10-10k}{k}[/tex] ----------(2)
from equation (1) and (2)
[tex]\frac{ln_2}{k}=\frac{ln10-10k}{k}[/tex]
[tex]ln10-ln2=10k[/tex]
[tex]k=\frac{ln5}{10}[/tex]
so expression will be
[tex]N(t)=10000e^{(\frac{ln5}{10})t }[/tex]
(b) for t = 20
[tex]N_{(20)}=10,000e\frac{ln5}{10}\times 20[/tex]
= [tex]10,000\times e^{2ln5}[/tex]
= 10,000 × 25
= 25,000
(c) Since [tex]t_1=\frac{ln2}{k}[/tex] [from equation (1)]
[tex]=\frac{ln2}{\frac{ln5}{10} }[/tex]
[tex]=\frac{ln2}{ln5}\times 10[/tex]
= 4.3068
= 4.3068 min.
#3 only Fractions help
Answer:
7
Step-by-step explanation:
24/1/3 -8/5/6- 8/1/2 (accorin to fractions la)
improper fraction make it into proper fraction
73/3- 53/6- 17/2 (change the base of 3 and 2 into 6)
146/6-53/6-51/6= (146-53-51)/6
= 7
Answer:
Step-by-step explanation:
you got to try your hardest
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:
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
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.
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]
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)).
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.
GIVING BRAINLIEST A medical team has found that the blood concentration of a particular medicine has a decay rate of 40% in 24 hours. How much of an initial dose of 1,000 mg of the medicine will be detected after 48 hours? Round to the nearest mg
920 mg
200 mg
449 mg
360 mg
600 mg
Answer:
360 mg.
Step-by-step explanation:
The medicine has a decay rate of 40% in 25 hours, which means after 24 hours its amount will be 100% - 40% = 60% it's original value.
Let us call [tex]t[/tex] the number of hours passed and [tex]d[/tex] the number of 24-hours passed, then we know that
[tex]t = 24d[/tex].
Now, the amount [tex]c[/tex] of medicine left after time [tex]d[/tex] (dth 24-hour) will be
[tex]c = 1000(0.6)^d[/tex]
and since [tex]t =24d[/tex], we have
[tex]$\boxed{c = 1000(0.6)^{\frac{t}{24} }}$[/tex]
We now use this equation to find the final amount after [tex]t =48 hours[/tex]:
[tex]c = 1000(0.6)^{\frac{48}{24} }[/tex]
[tex]c = 1000(0.6)^2 }[/tex]
[tex]\boxed{c =360mg}[/tex]
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
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
Find the area of the shaded region. With steps
Answer: the area of the shaded region is 72.96 ft²
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Diameter of circle = 16 feet
Radius = diameter/2 = 16/2 = 8 feet
Area of circle = 3.14 × 8² = 200.96ft²
The sides of the square are equal. To determine the length of each side of the square, L, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
16² = L² + L²
256 = 2L²
L² = 256/2 = 128
L = √128 ft
Area of the square is
L² = (√128)²
Area = 128 ft²
Area of shaded region is
200.96 - 128 = 72.96 ft²
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:
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
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.
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.
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)
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.
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
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
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
PLLLZ HELP Write a recursive formula for finding the nth term of each geometric sequence.
5, 20, 80, ...
a1 = 20, an = 4an − 1
a1 = 80, an = 4an − 1
a1 = 5, an = 4an − 2
a1 = 5, an = 4an − 1
Answer:
[tex]a_1 = 5,\\a_n =4 a_{n-1}[/tex]
Step-by-step explanation:
The first term of the geometric sequence is
[tex]a_1 =5[/tex].
The common ratio between the consecutive terms is
[tex]\dfrac{20}{5} = 4,[/tex]
[tex]\dfrac{80}{20} = 4;[/tex]
therefore, we see that the nth term is found by
[tex]a_n =4 a_{n-1}[/tex]
Thus, the recursive formula for the geometric sequence is
[tex]a_1 = 5,\\a_n =4 a_{n-1}.[/tex]
The recursive formula for finding the nth term of a geometric sequence is a_n = a_1 * r^(n-1), where a_n represents the nth term, a_1 is the first term, and r is the common ratio. In this case, the given sequence is 5, 20, 80. The recursive formula for this sequence is a_1 = 5 and a_n = 4 * a_(n-1).
Explanation:The recursive formula for finding the nth term of a geometric sequence is given by: an = a1 * r(n-1) where an represents the nth term, a1 is the first term, and r is the common ratio. In this case, the given sequence is 5, 20, 80, ...
Since the first term is 5, and the common ratio between terms is 4, the recursive formula for this sequence is: a1 = 5 and an = 4 * an-1.
Ken and Leah are trying to solve a science homework question. They need to find out how much a rock that weighs 4 pounds on Earth would weigh on Venus. They know they can multiply the number of pounds the rock weighs on Earth by 0.91 to find its weight on Venus. Select the partial products Ken and Leah would need to add to find the product of 4 and 0.91. Mark all that apply.
Answer:
The answer is b and d.
Step-by-step explanation:
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
* 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.
The expression 475 * 1.076 ^ t the average annual per capita health care costs, in dollars, in the US as a function of the number of years since 1970. What does 1.076 represent in this expression?
Answer:
[tex] Y(t)= 475 (1.076)^t [/tex]
Where Y(t) represent the average annual per capita health care costs
475 represent the initial amount for the average annual per capita health care costs
t represent the number of years since 1970
And 1.076 represent the growth factor given by:
[tex] 1+r = 1.076[/tex]
And solving for r we got:
[tex] r = 1.076-1 =0.076[/tex]
So for this case we can say that the value 1.076 represent the growth factor.
Step-by-step explanation:
For this case we have the following model given:
[tex] Y(t)= 475 (1.076)^t [/tex]
Where Y(t) represent the average annual per capita health care costs
475 represent the initial amount for the average annual per capita health care costs
t represent the number of years since 1970
And 1.076 represent the growth factor given by:
[tex] 1+r = 1.076[/tex]
And solving for r we got:
[tex] r = 1.076-1 =0.076[/tex]
So for this case we can say that the value 1.076 represent the growth factor.
Final answer:
In the provided expression, 1.076 represents the annual growth factor of US health care costs, indicating an annual increase of 7.6% since 1970.
Explanation:
The expression 475 * 1.076 ^ t represents the average annual per capita health care costs in the US as a function of the number of years since 1970. Here, 1.076 signifies the annual growth factor of the costs, which means health care costs have been increasing by 7.6% each year since 1970. This exponential function captures the trend of increasing health care expenditure, which plays a significant role in the nation's economy, consuming a larger share of the Gross Domestic Product (GDP) over time.
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
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.
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
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%
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.