Answer:
V = int(π(y/3)^2, 0, 8)
(Definite integration of π(y/3)^2 with lower boundary 0 and upper boundary 8)
Step-by-step explanation:
Set up cartesian axis (x and y) to the system.
Let y axis as the line of the centre of the cone, passing through its vertex and the centre of it's circular base. The x axis could be the 90 degree line to the y axis that passes the vertex. So the origin (0,0) is at the vertex.
I'm this setup , looking it as if we are looking it in 2 dimension, we'll see that there is a signature straight line on the x-y plane, which this line will form the cone as it revolute around the y-axis
Find the equation of the line:
Using height 12 and radius base 4, we can get the slope of the line
m = 12/4 = 3
It passes through origin, so the y-intercept is 0
Hence, y = 3x
Since the volume revolves around y-axis, we use the equation volume of revolution around y-axis
V = int(πx^2,a,b)
(Definite integration of πx^2 with lower boundary a and upper boundary b
Since y=3x
x = y/3
For this que
V = int(π(y/3)^2, 0, 8)
(Definite integration of π(y/3)^2 with lower boundary 0 and upper boundary 8)
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.
:)
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}
Convert y = x^2 + 2x - 5 into the form y-k = a( x- h)^2
Answer:
[tex]y+6=(x+1)^{2}[/tex]
Step-by-step explanation:
we have
[tex]y=x^{2}+2x-5[/tex]
This is the equation of a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
The equation of a vertical parabola into vertex form is
[tex]y-k=a(x-h)^2[/tex]
where
(h,k) is the vertex of the parabola
Convert the equation into vertex form
Move the constant term to the left side
[tex]y+5=x^{2}+2x[/tex]
Complete the square
[tex]y+5+1=x^{2}+2x+1[/tex]
[tex]y+6=x^{2}+2x+1[/tex]
Rewrite as perfect squares
[tex]y+6=(x+1)^{2}[/tex]
therefore
[tex]a=1\\h=-1\\k=-6[/tex]
The vertex is the point (-1,-6)
Explain how to find n, the number of copies the machine can print in one minute. I need an algebraic expression for the answer.
Once the first part is done, I need help with this question.
Working at the same rate, how long will it take the machine to print 5,200 copies? Explain how you found your answer.
Answer:
Step-by-step explanation:
From the table, the number of copies can be plotted on the y axis and against the number of minutes on x axis. The slope of the straight line graph that would be formed would represent the become n, the number of copies the machine can print in one minute.
n = (y2-y1)/(x2-x1)
Picking points from the table,
y2 = 650
y1 = 325
x2 = 10
x1 = 5
Slope, n = (650 - 325)/(10 - 5)
n = 325/5 = 65 copies per minute
Working at the same rate, the time that it will take the machine to print 5,200 copies would be
65 copies = 1 minute
5200 copies would take
5200/65 = 80 minutes
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.
Julia pays a flat rate of $106 for her cell phone and is charged $0.12 for every text she sends. Julia spends at least $142 on her phone bill each month. Which of the following describes the number of texts she sends?
a. a minimum of 300
b. a maximum of300
c. more than 300
d. fewer than 300
Answer:
a. A minimum of 300
Step-by-step explanation:
If her bill is $142 then it is a sum of the flat rate plus the money she pays for all the smses she sent. As an equation, it can be expressed this way
106 + 0.12x = 142 where x is the number of smses
0.12x = 36
x = 300 smses
So if we were told that she pays $142 per month, we'd know that she sends 300 smses. But we are told she pays AT LEAST $142 so there is a possibility that she sends even more than 300 smses
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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The members of a singing group agree to buy at least 250 tickets for a concert. The group buys 20 fewer lawn tickets than balcony tickets. What is the least number of balcony tickets bought?
Answer:
Members of Singing group will buy minimum 135 number of balcony tickets.
Step-by-step explanation:
Given:
Minimum of tickets will be bought =250
Let number of lawn tickets be 'l'.
Also Let number of balcony tickets be 'b'
Now given
The group buys 20 fewer lawn tickets than balcony tickets.
Framing in equation form we get;
[tex]l=b-20[/tex]
Now The Sum of Number of balcony tickets and Number of lawn tickets should be greater than or equal to Minimum of tickets will be bought by the group.
Framing in equation form we get;
[tex]l+b\geq 250[/tex]
Now substituting the value of 'l' in above equation we get;
[tex](b-20)+b\geq 250\\\\b-20+b\geq 250\\\\2b-20\geq 250\\\\2b\geq 250+20\\\\2b\geq 270\\\\b\geq \frac{270}{2}\\\\b\geq 135[/tex]
Now we know the value of b which is 135 we will substitute in equation [tex]l=b-20[/tex] to find the value of l we get;
[tex]l=135-20 = 115[/tex]
Hence Members of singing group will buy minimum 135 number of balcony tickets.
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
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
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:
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
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
A charity organization had a fundraiser where they sold each ticket for a fixed price. After selling 200 tickets, they had a net profit of 12,000. They had to sell a few tickets just to cover necessary production costs of 1,200.
Answer:
Y = 66x - 1200 will be the equation.
Step-by-step explanation:
This question is incomplete; Here is the complete question.
A charity organization had a fundraiser where they sold each ticket for a fixed price. After selling 200 tickets, they had a net profit of $12,000. They had to sell a few tickets just to cover necessary production costs of $1200.
Let Y represent the net profit (in dollars) when they have sold c tickets. Complete the equation for the relationship between the net profit and the number of tickets sold.
If the selling price of one ticket is $x, then selling price of 200 tickets
= $200x
Since production cost of the tickets = $1200 and profit earned is $12000
Therefore, Profit = Selling price of x tickets - production cost
12000 = 200x - 1200
200x = 13200
x = $66
Now we can rewrite the equation for c tickets sold and profit earned $Y
Y = 66c - 1200
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:
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.
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
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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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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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)
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.
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:
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 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%.
The marginal cost of providing 25 neighborhood street lamps is $2000. There are 3 people living in the neighborhood. Person 1 is willing to pay $800 for the 25 lamps and person 2 is willing to pay $300 for the 25 street lamps. Efficiency requires that 25 lamps be provided. What is the minimum amount person 3 is willing to pay for 25 street lamps?
Answer:
Person 3 needs to pay $900.
Step-by-step explanation:
Consider the provided information.
The marginal cost of providing 25 neighborhood street lamps is $2000.
Person 1 is willing to pay $800 for the 25 lamps.
person 2 is willing to pay $300 for the 25 street lamps.
We need to find the minimum amount person 3 is willing to pay for 25 street lamps?
Let person 3 need to pay x amount.
Therefore, the sum of the amount should be equal to $2000.
$2000=$800+$300+x
$2000=$1100+x
x=$2000-$1100
x=$900
Hence, person 3 needs to pay $900.
Person 3 must be willing to pay at least $900 for 25 street lamps to meet the marginal cost of $2000 for efficient provision, considering person 1 and person 2 are contributing a total of $1100.
To determine the minimum amount person 3 must be willing to pay for the 25 street lamps, we need to consider the total cost of providing the lamps and the amount the other two people are willing to pay. The marginal cost for providing the 25 lamps is $2000. Person 1 is willing to pay $800, and person 2 is willing to pay $300. The sum paid by person 1 and person 2 is $800 + $300 = $1100.
Since the total cost is $2000, for efficiency, the total amount paid by all three people should at least match this cost. Therefore, the minimum amount that person 3 must be willing to pay is the difference between the total cost and the sum paid by the first two persons:
Total cost - Sum paid by person 1 and person 2 = Minimum amount person 3 must pay
$2000 - $1100 = $900
Thus, person 3 must be willing to pay at least $900 for the efficient provision of the 25 street lamps.
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.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
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
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.
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