Answer:
30 gallons
Step-by-step explanation:
let x represent the full container, then
[tex]\frac{1}{10}[/tex] x + 21 = [tex]\frac{4}{5}[/tex] x
Multiply through by 10 to clear the fractions
x + 210 = 8x ( subtract x from both sides )
210 = 7x ( divide both sides by 7 )
30 = x
The volume of the container is 30 gallons
Answer: the volume of the container is 30 gallons
Step-by-step explanation:
Let V represent the volume of the container, in gallons.
The initial volume of grains in the container is 1/0 × V = V/10
If 21 additional gallons of grain are added, the container is 4/5 full. This means that 21 gallons of grain + V/10 will occupy 4/5 of the volume of the container. Therefore
4/5 × V = 21 + V/10
4V/5 = 21 + V/10
4V/5 - V/10 = 21
7V/10 = 21
Multiplying the left hand side and right hand side of the equation by 10, it becomes
7V/10 × 5 = 21 × 10 = 210
7V = 210
V = 210/7 = 30
Assessment
8. Compare the function with the parent function. Without graphing, what are the vertex, axis of
symmetry, and transformations of the given function?
(1 point)
y= | 10x – 2| -7
A. x = 2: translated to the right - unit and down 7 units
B. translated to the left – unit and up 7 units
C. translated to the left – unit and down 7 units
D. translated to the right – unit and down 7 units
ul
Solve the system of equations. \begin{aligned} &6x-5y = -32 \\\\ &-7x+8y=46 \end{aligned} 6x−5y=−32 −7x+8y=46 x=x=x, equals y=y=y, equals
Answer:
The solution is x=-2, y=4
Step-by-step explanation:
we have
[tex]6x-5y=-32[/tex] ----> equation A
[tex]-7x+8y=46[/tex] ----> equation B
Solve the system by graphing
Remember that
The solution of the system of equations is the intersection point both graphs
using a graphing tool
The intersection point is (-2,4)
see the attached figure
therefore
The solution is x=-2, y=4
Answer:
The solution is x=-2, y=4
Step-by-step explanation:
The admission fee at an amusement park is $2.50 for children and $5.80 for adults. On a certain day, 343 people entered the park, and the admission fees collected totaled $1369. How many children and how many adults were admitted?
188 children and 155 adults were admitted that day.
Step-by-step explanation:
Given,
Cost of one children admission = $2.50
Cost of one adult admission = $5.80
Number of people entered = 343
Total admission fees collected = $1369
Let,
Number of children admission = x
Number of adult admission = y
According to given statement;
x+y=343 Eqn 1
2.50x+5.80y=1369 Eqn 2
Multiplying Eqn 1 by 2.50
[tex]2.50(x+y=343)\\2.50x+2.50y=857.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](2.50x+5.80y)-(2.50x+2.50y)=1369-857.50\\2.50x+5.80y-2.50x-2.50y=511.50\\3.30y=511.50[/tex]
Dividing both sides by 3.30
[tex]\frac{3.30y}{3.30}=\frac{511.50}{3.30}\\y=155[/tex]
Putting y=155 in Eqn 1
[tex]x+155=343\\x=343-155\\x=188[/tex]
188 children and 155 adults were admitted that day.
Keywords: linear equation, subtraction
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what is the solution of x^2 = 16^x?
Answer:
x = -0.5.
Step-by-step explanation:
x^2 = 16^x
One way to do this is to use 2 graphs y = x^2 and y = 16^x .
The solution is where the 2 graphs intersect.
The answer is x = -0.5.
Lydia also likes using the standard algorithm for multiplication. She has to solve 32 x 8.25. Recommend another strategy to Lydia, and show her how to use that strategy to solve this problem.
Answer:
We can use distributive law for the multiplication
And after multiplication result will be 264
Step-by-step explanation:
Lydia has to multiply 32×8.25
She is using standard algorithm of multiplication
Now we have to find the other way of multiplication of 32×8.25
We can use distributive law for the multiplication of the above number
We can write 8.25 as 8+0.25
So multiplication will become 32 ( 8+0.25 ) = 256 + 8 = 264
So after multiplication result will be 264
To solve 32 x 8.25 without the standard algorithm, Lydia can use the distributive property to separately multiply 32 by 8 and then by 0.25 (1/4), resulting in two simple multiplications: 256 and 8. Adding these together gives the answer, 264.
Explanation:To solve the multiplication problem 32 x 8.25 without the standard algorithm, Lydia can break down the number 8.25 into 8 and 0.25 (which is 1/4) and use the distributive property of multiplication over addition. This allows Lydia to multiply 32 by each part separately and then add the results together.
Multiply the whole number part: 32 x 8 = 256.Multiply the fractional part, recognizing that multiplying by 1/4 is the same as dividing by 4: 32 x 0.25 = 32/4 = 8.Add the results together: 256 + 8 = 264.This strategy simplifies the calculation and can be done with simpler computations or even mental math.
The double number line shows that in 222 minutes, Pogo the dog can fetch a frisbee 666 times. Based on the ratio shown in the double number line, how many times will Pogo fetch the frisbee in 444 minutes?
Answer:
Dog Pogo will fetch the frisbee 12 times in 4 minutes.
Step-by-step explanation:
Given:
Number of minutes required =2 minutes.
Number of times frisbee fetch by dog = 6 times
We need to find Number of times the dog can fetch the frisbee in 4 minutes.
First we will find number of frisbee fetch in minute.
In 2 minutes = 6 times frisbee fetched by the dog
so in 1 minute = Number of times frisbee fetched by the dog in 1 minute.
By using Using Unitary method we get;
Number of times frisbee fetched by the dog in 1 minute = [tex]\frac{6}{2} =3[/tex]
Hence in 1 minutes the dog can fetch frisbee 3 times.
for 1 min = 3 times frisbee is been fetched by dog
So for 4 minutes = Number of times frisbee is been fetched by dog in 4 min.
Again by using Unitary Method we get;
Number of times frisbee is been fetched by dog in 4 min = [tex]3\times4 = 12[/tex]
Hence Dog Pogo will fetch the frisbee 12 times in 4 minutes.
Answer:12
Step-by-step explanation:
A company did a quality check on all the packs of trail mix it manufactured. Each pack of trail mix is targeted to weigh 9.25 oz. A pack must weigh within 0.23 oz of the target weight to be accepted. What is the range of rejected masses, x, for the manufactured trail mixes?
a. x < 9.02 or x > 9.48 because |x − 0.23| + 9.25 > 0
b. x < 9.25 or x > 9.48 because |x − 9.25| > 0.23
c. x < 9.25 or x > 9.48 because |x − 0.23| + 9.25 > 0
d. x < 9.02 or x > 9.48 because |x − 9.25| > 0.23
Answer:
d. x < 9.02 or x > 9.48 because |x − 9.25| > 0.23
Step-by-step explanation:
Given,
The standard weight of the pack = 9.25 oz,
The pack must weigh within 0.23 oz of the target weight to be accepted.
i.e. if x represents the weight of the pack,
If x > 9.25 oz
then x - 0.925 ≤ 0.23 ......(1)
if x < 9.25
then 9.25 - x ≤ 0.23
⇒ -(x-9.25) ≤ 0.23 .......(2)
From equation (1) and (2),
The accepted range of mass is,
|x-9.25| ≤ 0.23
Hence, the rejected range mass would be,
|x-9.25| > 0.23
⇒ x - 9.25 > 0.23 or -x + 9.25 < 0.23
⇒ x > 0.23 + 9.25 or -x > 0.23 - 9.25
⇒ x > 9.48 or - x > −9.02
⇒ x > 9.48 or x < 9.02
NEED HELP QUICK!! 25 POINTS TO ANSWER
Set up the equation and solve for x:
11x-2 = 9x +2 + 10
11x-2 = 9x +12
2x = 14
X = 7
BOC = 9x +2 = 9(14) +2 = 126+2 = 128
How many square shaped tiles of area 25 m2 would you need to cover a rectangular plot of area 700 m2? A. 25 B. 28 C. 175 D.17500
Answer:28 square shaped tiles of area 25 m^2 would be needed to cover the rectangular plot.
Step-by-step explanation:
The area of the rectangular plot is 700m^2
The area of each square tiles is 25m^2
The number of tiles needed to cover a rectangular plot would be
700/25 = 28 square shaped tiles
Two concentric circles with radii of 19 and 29 units bound a shaded region. A third circle will be drawn with area equal to that of the shaded area. What must the radius of the third circle be? Express your answer in simplest radical form.
========================================
Work Shown:
Let P and Q be two concentric circles
P = area of circle with radius 19
P = pi*r^2
P = pi*19^2
P = 361pi
-------
Q = area of circle with radius 29
Q = pi*r^2
Q = pi*29^2
Q = 841pi
-------
R = area of shaded region between circle P and circle Q
R = region outside circle P, but inside circle Q
R = Q - P
R = 841pi - 361pi
R = 480pi
------
S = area of circle with area equal to region R's area
S = 480pi
S = pi*r^2
pi*r^2 = 480pi
r^2 = 480
r = sqrt(480)
r = sqrt(16*30)
r = sqrt(16)*sqrt(30)
r = 4*sqrt(30)
Using k as the constant of proportionality, write an equation that expresses: Z varies jointly as x and y.
Answer: z= kxy
Step-by-step explanation:
There are three types of variation. We have direct, inverse and joint.
Variation has to do with the manner in which we relate two mor more variables either directly or inversely.
For joint variation, we relate two or more variables to one another. A variable among those variables is written in terms of the remaining variables directly.
According to the question, since we have three variables z, x and y and we are to express z joint as x and y.
Joint variation is a "direct relationship" between variables i.e z will be directly proportional to the product of x and y making k as constant of proportionality. Mathematical relationship will give us;
Z=kxy
Can someone please help me with how to do this?? I am lost
The question is, "Find intersections and unions of the following given sets.
Thank you.
Answer:
The answer to your question is below
Step-by-step explanation:
See the picture below
G ∩ M = { Max, Anael}
G ∪ S = { Max, Acel, Carl, Anael, Acton, Dario, Kai, Barek, Carlin}
Raphael graphed the functions g(x)=x+2 and f(x)=x−1. How many units below the y-intercept of g(x) is the y-intercept of f(x)? A coordinate plane with 2 lines drawn. The first line is labeled f(x) and passes through the points (0, negative 1) and (1, 0). The second line is labeled g(x) and passes through the points (negative 2, 0) and (0, 2). −3 units −1 units 2 units 3 units
Answer:
3 units below the y-intercept of g(x) is the y-intercept of f(x)
Step-by-step explanation:
[tex]g(x)=x+2[/tex] and [tex]f(x)=x-1[/tex]
In f(x)= mx+b the y intercept is b
In [tex]g(x)=x+2[/tex], the y intercept value is 2
In [tex]f(x)=x-1[/tex], the y intercept value is -1
the difference in y intercept is +2-(-1)=+3
3 units below the y-intercept of g(x) is the y-intercept of f(x)
If a dog was 7 weeks old 5 days ago when was it born?
What is its birth date
Like if it was born today its birthdate would be 12/19/19, and you could even go more into detail and say for instance Thursday 12/19/19
Ivan bought 35 stamps. Some of these stamps cost $0.15 each, and the rest cost $0.40 each. If the total value of the stamps he bought is $7.25, determine the number of $0.15 stamps that Ivan bought.
Answer:
27
Step-by-step explanation:
Let x represent the number of $0.15 stamps Ivan bought. Then the value of his stamps is ...
0.15x +0.40(35-x) = 7.25
-0.25x +14.00 = 7.25 . . . . . eliminate parentheses, collect terms
-0.25x = -6.75 . . . . . . . . . . . subtract 14.00
x = 27 . . . . . . . . . . . . . . . . . . divide by -0.25
Ivan bought 27 $0.15 stamps.
A corporation issued for cash 100,000 shares of its $0.01 par value common stock for $450,000. Which of the following is the correct journal entry to record this transaction?
Answer:
cash = $450000 ........... debit
common stock = 1000 .......... credit
paid in capital amount = $449000 ............ credit
Step-by-step explanation:
given data
share = 100000
par value = $0.01
total selling price = $450,000
solution
here
here total selling price is $450000
so cash = $450000 ........... debit
and common stock will be
common stock = 100000 × 0.01
common stock = 1000 .......... credit
and paid in capital amount will be
paid in capital amount = selling price - common stock
paid in capital amount = $450000 - $1000
paid in capital amount = $449000 ............ credit
A machine puts out 100 watts of power for every 1000 watts put into it. The efficiency of the machine is
Answer:
10%
Step-by-step explanation:
Machine out put power =100 watt
Machine input power=1000 watt
We have to find the efficiency of the machine.
We know that
Efficiency of machine=[tex]\frac{O.p}{I.p}[/tex]
Where O.p=Output power
I.p=Input power
By using the formula
Efficiency of machine=[tex]\frac{100}{1000}=0.1[/tex]
Efficiency of machine (in percent)[tex]0.1\times 100=[/tex]10%
Hence, the efficiency of machine=10%
The efficiency of the machine is 10%, as it is calculated by dividing the output power, 100 watts, by the input power, 1000 watts, and then multiplying by 100 to express it as a percentage.
The efficiency of a machine is calculated by dividing the useful output power by the input power and then multiplying the result by 100 to get a percentage. For the given machine, which puts out 100 watts for every 1000 watts put into it, the calculation would look like this:
Efficiency (Eff) = (Wout / Ein) times 100%
Efficiency (Eff) = (100W / 1000W) times 100%
Efficiency (Eff) = 0.1 times 100%
Efficiency (Eff) = 10%
This means the efficiency of the machine is 10%.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Simplify each expression and match it with the equivalent value.
Answer:
log base 6 of the cube root of 6 matches with 1/3
-3 log 5 of 25 matches with -6
log base 2 of the 4th root of 8 matches with 3/4
log base 3 of 1/81 matches with -4
Answer:
Step-by-step explanation:
Let's simplify all the possible answers:
[tex]log_{6} \sqrt[3]{6}[/tex] = [tex]log_{6} (6\frac{1}{3} ) = \frac{1}{3}[/tex] [tex]log_{3} \frac{1}{81} = log_{3} (3^{-4} )[/tex] = -4 [tex]-3log_{5} 25 \\[/tex] = [tex]-3log_{5} (5^{2} )[/tex] = -3*2 = -6 [tex]log_{2} \sqrt[4]{8}[/tex] = [tex]log_{2} \(2^{\frac{3}{4} }[/tex] = [tex]\frac{3}{4}[/tex]Hope it will find you well.
what is the difference of (-3x^3+5x^2+4x-7)-(6x^3-2x+3)
Good evening ,
Answer:
(-3x^3+5x^2+4x-7)-(6x^3-2x+3) = -9x³+5x²+6x−10
Step-by-step explanation:
(-3x^3+5x^2+4x-7)-(6x^3-2x+3) = -3x³+5x²+4x-7-6x³+2x−3
= -9x³+5x²+6x−10.
:)
Calculate the slope of the line given the following two points. Point 1 (0, 0) and Point 2 (6, 12)
M = _______
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slope = difference in y / difference in x
slope = (12 - 0) / (6 - 0)
slope = 12/6
slope = 2
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Stay Brainly! ヅ
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slope
m=y2-y1/x2-x1m=12-0/6-0m=12/6m=2Done
It is observed that a certain bacteria culture has a relative growth rate of 15% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 24. Find the projected population after 24 hours for the following conditions. (Round your answers to the nearest whole number.)
In this bacterial growth problem, the population after 24 hours under normal conditions would be approximately 19136 bacteria. With a reduced growth rate due to antibiotics, the population would be approximately 79 bacteria.
Explanation:The subject of the question relates to the concept of exponential growth, as demonstrated by a bacteria population. Given that the initial population is 24, the population P after time t, in this case in hours, is given by the formula P = P0 * (1 + r/100)^t, where P0 is the initial population, r is the relative growth rate (percentage), and t is time.
Under normal growth conditions, after 24 hours the population would be P = 24 * (1 + 15/100)^24 = approximately 19136, rounded to the nearest whole number. However, with the introduction of antibiotics, reducing the growth rate to 5%, after 24 hours the population would be P = 24 * (1 + 5/100)^24 = approximately 79, rounded to the nearest whole number.
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Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 714 subjects, each was asked how often he or she read a book.read a book. The survey subjects were internet users who responded to a question that was posted on a news website.
a) it is flawed because it is a census
b) it is flawed because it is not statistically significant.
c) it appears to be sound because the data are not biased in anyway.
d) it is flawed because it is a voluntary response sample.
Answer:
Option D) It is flawed because it is a voluntary response sample.
Step-by-step explanation:
We are given the following information in the question:
The subjects of the survey were internet users who responded to a question that was posted on a news website.
A total of 714 subjects responded to this question, answering the question, how often he or she read a book.
Option D) It is flawed because it is a voluntary response sample.
Voluntary response sample:
A sample in which the subjects themselves decide whether to be included in the study.People chose to be a part or not to be a part of the survey since the question was posted on website.Some maybe interested some may not in answering this question.A voluntary sample is made up of people who self-select into the survey. Often, these folks have a strong interest in the topic of the survey thus creating a bias.Voluntary response bias occurs when sample members are self-selected volunteers.A plastic storage box in the shape of a rectangular prism has a length of x+3, a width of x-4 and a height of 5. Represent the surface area of the box as a trinomial in terms of x
Answer:surface area = 2x^2 + 18x - 34
Step-by-step explanation:
The formula for determining the surface area of a rectangular prism is expressed as
Surface area = 2lh + 2wh + 2wl
Where
l represents the length of the rectangular prism.
h represents the height of the rectangular prism.
w represents the width of the rectangular prism
From the information given,
l = x+3
h = 5
w = x - 4
Surface area = 2 × 5 × (x+3) + 2 × (x - 4) × 5 + 2 × (x - 4) × (x + 3)
= 2(5x + 15) + 10(x - 4) + 2[x^2 + 3x - 4x - 12]
= 10x + 30 + 10x - 40 + 2x^2 - 2x - 24
= 2x^2 + 18x - 34
The 9-1-1 service fee on telecommunications bills is what type of tax?Select all that apply
Service tax
Professional service tax
Ad valorem tax
Fixed tax
Business tax
The 9-1-1 service fee on telecommunications bills is a type of tax such as service tax, fixed tax, business tax. Thus, the option (a), (d) and (e) is correct.
What is tax?
The term tax refers to the government charge the extra money for goods and services. The tax is also called as financial charge. The amount of tax are collect to government account as spent on public welfare. The public pay tax is compulsory. There are two types of tax such as direct tax and indirect tax.
The telecommunications bills are also included tax such as service tax, fixed tax, and business tax etc. The service tax is an indirect tax as charge on exchange of services. The fixed tax are apply on lump sum amount. The business tax is included income tax, and other expenses tax (wages, salaries etc.)
Therefore, option (a) (d) and (e) is correct.
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A leaky faucet drips 356,755 mL of water over the course of the year. There are approximately 3,785 mL in 1 gallon. How many gallons of water are leaked in one year
Gallons of water are leaked in one year is 94.253 gallons
Solution:Given that leaky faucet drips 356,755 mL of water over the course of the year
There are approximately 3,785 mL in 1 gallon.
To find: gallons of water are leaked in one year
From given information,
Amount of water leaked in one year in ml = 356,755 mL
Also given in question that,
1 gallon = 3785 ml[tex]1 \text{ ml} = \frac{1}{3785} \text{ gallons}[/tex]
Now we can convert 356,755 mL to gallons
[tex]356,755 \text{ ml} = \frac{1}{3785} \times 356755 \text{ gallons}\\\\356,755 \text{ ml} = 94.253 \text{ gallons}[/tex]
Thus gallons of water are leaked in one year is 94.253 gallons
Enter your answer and show all the steps that you use to solve this problem in the space provided. A.Solve a–9=20 B.Solve b–9>20 C.How is solving the equation in part a similar to solving the inequality in part b? D.How are the solutions different?
Answer:
A) The value of a is 29.
B) The value of b is greater than 29.
C) In both part A and part B we have used a common property which is addition property and that we have add 9 on both side of equation in both parts.
D) The value of a in part A is equal to 29 whereas in part B the value of b is greater than 29.
Step-by-step explanation:
Solving for Part A.
Given,
[tex]a-9=20[/tex]
We have to solve for a.
[tex]a-9=20[/tex]
By using addition property of equality, we will add both side by 9;
[tex]a-9+9=20+9\\a=29[/tex]
Hence the value of a is 29.
Solving for Part B.
Given,
[tex]b-9>20[/tex]
We have to solve for b.
[tex]b-9>20[/tex]
By using addition property of inequality, we will add both side by 9;
[tex]b-9+9>20+9\\b>29[/tex]
Hence the value of b is greater than 29.
Solving for Part C.
In both part A and part B we have used a common property which is addition property and that we have add 9 on both side of equation in both parts.
Solving for Part D.
The value of a in part A is equal to 29 whereas in part B the value of b is greater than 29.
To solve a - 9 = 20, we add 9 to 20, which results in a = 29. For b - 9 > 20, it's similar; we add 9 to 20, resulting in b > 29. The process is similar for both, but an equation's solution (a) is a single number, while an inequality's solution (b) represents a range of numbers.
Explanation:To solve part A, which is a - 9 = 20, we will need to isolate the variable 'a' on the left side of the equation. Doing so gives us a = 20 + 9 or a = 29.
For part B, which is to solve b - 9 > 20, the operation is similar, but the result is an inequality, not a specific number. Solving it gives us b > 20 + 9 or b > 29.
The process is similar for both because you are essentially isolating the variable on one side of the equation or inequality. The difference is that the solution for an equation (part A) is a specific number, while the solution for an inequality (part B) is a range of numbers.
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Elise and her dad are planning to attend the state fair. An adult ticket is $21.00. The price of an adult ticket is $10.00 more than two thirds the price of a student ticket. Write an equation to determine how much Elise will pay for a student ticket.
Answer:The equation to determine how much Elise will pay for a student ticket is 2x = 33
Step-by-step explanation:
Let x represent the price of one student ticket.
Elise and her dad are planning to attend the state fair and the price of an adult ticket is $21.00
The price of an adult ticket is $10.00 more than two thirds the price of a student ticket. This means that
21 = 2/3 × x + 10
The equation to determine how much Elise will pay for a student ticket would be
2x/3 + 10 = 21
2x/3 = 21 - 10 = 11
2x = 11×3 = 33
x = 33/2 = $16.5
To determine how much Elise will pay for a student ticket, we can follow these steps:
1. Let's assign a variable to represent the price of the student ticket. We'll call it "x".
2. According to the information given, the adult ticket is $10 more than two-thirds of the price of a student ticket. So, the equation can be written as:
Adult ticket price = 2/3 * x + $10
3. The adult ticket price is given as $21. Substituting this value into the equation, we have:
$21 = 2/3 * x + $10
4. To isolate the variable, we can subtract $10 from both sides of the equation:
$21 - $10 = 2/3 * x
Simplifying, we get:
$11 = 2/3 * x
5. Finally, to solve for "x", we can multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:
($11) * (3/2) = x
Multiplying, we get:
$33/2 = x
Therefore, Elise will pay $16.50 for a student ticket.
In summary, the equation to determine how much Elise will pay for a student ticket is 2/3 * x + $10 = $21, and solving for "x" gives us x = $16.50.
An online music club has a one- time registration fee of $13.95 and charges $0.49 to buy each song. If Emma has $50.00 to join the club and buy songs, what is the maximum number of songs she can buy?
Answer: 73 songs
Step-by-step explanation:
The online music club has a one- time registration fee of $13.95 and charges $0.49 to buy each song. Let x represent the number of songs that a member buys. This means that the amount that a member who just joins the music club pays for x songs would be
0.49x + 13.95
If Emma has $50.00 to join the club and buy songs, the maximum number of songs she can buy would be expressed as follows
0.49x + 13.95 = 50
0.49x = 50 - 13.95 = 36.05
x = 36.05/0.49 = 73.57
the maximum number of songs she can buy is 73 since the number of songs cannot be a fraction.
50.00 - 13.95 = 36.05 (subtract the registration fee)
36.05/0.49 = 73.57 so she can buy 73 songs
The height of the water in a fish pond is 42.5 inches. Water is being drained from the pond at a rate of 3.75 inches per minute. What is the height of the water after 3 minutes?
Height of the water after 3 minutes is 31.25 inches
Solution:Given that height of the water in a fish pond is 42.5 inches
Water is being drained from the pond at a rate of 3.75 inches per minute
To find: height of the water after 3 minutes
According to given information,
Water drained in 1 minute = 3.75 inches
So height of the water after 3 minutes is calculated by following steps:
1) find how much water is drained in 3 minutes
2) subtract value obtained in step 1 from total height of water in fish pond
Step 1:water is drained in 3 minutes = Water drained in 1 minute x 3
[tex]\text {water is drained in } 3 \text { minutes }=3.75 \times 3=11.25[/tex]
Thus water drained in 3 minutes is 11.25 inches
Step 2:height of the water after 3 minutes = total height of water in fish pond - water drained in 3 minutes
height of the water after 3 minutes = 42.5 - 11.25 = 31.25 inches
Thus height of the water after 3 minutes is 31.25 inches
Final answer:
After draining water at a rate of 3.75 inches per minute for 3 minutes, the height of the water in the pond decreases from 42.5 inches to 31.25 inches.
Explanation:
The question is asking for the height of the water in a pond after draining some amount of water for a specified time. Initially, the pond has a water height of 42.5 inches. Water is being drained at a rate of 3.75 inches per minute. To find the height of the water after 3 minutes, we need to calculate the total amount of water drained and subtract it from the initial height.
Total water drained in 3 minutes = Drain rate per minute × number of minutes = 3.75 inches/minute × 3 = 11.25 inches.
Height of water after 3 minutes = Initial height - Total water drained = 42.5 inches - 11.25 inches = 31.25 inches.
Therefore, the height of the water in the pond after 3 minutes is 31.25 inches.
A water wave traveling in a straight line on a lake is described by the equation y(x,t) = (3.30 cm) cos(0.400 cm?1x + 5.05 s?1t) where y is the displacement perpendicular to the undisturbed surface of the lake.
(a) How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor?
What horizontal distance does the wave crest travel in that time?
b) What are the wave number and the number of waves per second that pass the fisherman?
(c) How fast does a wave crest travel past the fisherman?
What is the maximum speed of his cork floater as the wave causes it to bob up and down?
Answer:
Answer: a. 1.203 m/s b.0.35m
Step-by-step explanation: