Answer:
Step-by-step explanation:
I'm going to use calculus to solve this, because it's the simplest way.
The acceleration due to gravity in feet is the second derivative of the position function. We will start with the acceleration and work backwards with antiderivatives to get to the position function.
a(t) = -32. Going backwards and using the fact that the initial vertical velocity is 64 ft/sec, our velocity function is
v(t) = -32t + 64. Going backwards and using the fact that the initial height of the ball is 6 feet, our position function is
[tex]s(t)=-16t^2+64t+6[/tex]
The first part of this question asks us the maximum height of the ball. From Physics, we learn that the maximum height of a projectile is reached when the velocity is 0, which happens to be right where the projectile stops for a nanosecond in the air to turn around and come back down. We set the velocity function equal to 0 and solve for t.
0 = -32t + 64 and
0 = -32(t - 2). By the Zero Product Property, either -32 = 0 or t - 2 = 0. It's obvious that -32 does not equal 0, so t - 2 must equal 0. Solving this for t:
t - 2 = 0 so
t = 2 seconds. Since the maximum height is reached at a time of 2 seconds, we plug 2 seconds into the position function to get its position at 2 seconds (which is also the max height of the ball).
[tex]s(2)=-16(2)^2+64(2)+6[/tex] and
s(2) = -64 + 128 + 6 so
s(2) = 70 feet
Now we want to know when the ball will hit the ground. "When" is a time value, and we know that the height of the ball on the ground is 0, so we sub in a 0 for s(t) and factor the quadratic.
Using the quadratic formula:
[tex]t=\frac{-64+/-\sqrt{4096-4(-16)(6)} }{-32}[/tex] and
[tex]t=\frac{-64+/-\sqrt{4480} }{-32}[/tex] which gives us the 2 solutions
[tex]t=\frac{-64+\sqrt{4480} }{-32}[/tex] and
[tex]t=\frac{-64-\sqrt{4480} }{-32}[/tex]
Plugging into your calculator, the first t = -.0916500 and the second t = 4.091
We all know that time cannot ever be negative, so our t value is 4.09.
Again, from Physics, we know that a projectile reaches it max height at halfway through its travels, so it just goes to follow logically that if it halfway through its travels at 2 seconds, then it will hit the ground at 4 seconds. And it does!! How awesome is that?!
The maximum height of the ball is 32 feet. The ball will hit the ground after 4 seconds.
Explanation:To find the maximum height of the ball, we can use the equation for motion under constant acceleration.
The equation is h = (v0^2)/(2g),
where h is the maximum height, v0 is the initial vertical velocity, and g is the acceleration due to gravity.
Plugging in the given values, we have h = (64^2)/(2*32), which gives us a maximum height of 32 feet.
Next, to find when the ball will hit the ground, we can use the equation for time of flight.
The equation is t = (2v0)/g, where t is the time of flight.
Plugging in the given values, we have t = (2*64)/32, which gives us a time of flight of 4 seconds.
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Interpret the average rate of change of -14/7 that you found previously. What does this mean in terms if the waterslide, from x=0 to x=15
Answer:
1. The vertical components decrease by 14 units while the horizontal component increase by 3 units
2.it therefore means that the vertical component decreases by 70units
Step-by-step explanation:
Slope of a graph is change in the vertical axis over the the change in the horizontal axis
in the above question, if the average rate of change is -14/7 it therefore means that the vertical components decrease by 14 units while the horizontal component inc rfease by 3 units
what does that mean if the waterslide from x=0, and x=15
it means that the vertical components decrease why there is an increment distance in the horizontal axis
mathematically, we say
-14/3=-y/[tex]s= \frac{dy}{dx} , slope=s\\-14/3=\frac{-y}{15-0}[/tex]
14/3=y/15
y=70
it therefore means that the vertical component decreases by 70units
Answer:
On average, the slide drops 14 feet for every 3 feet of horizontal distance.
On average, the slide drops about 4.7 feet for every 1 foot of horizontal distance.
Step-by-step explanation:
on edg... Good Luck!!!
Sahil got 28 questions right on the math test. Angelina got 7 more wrong answers than Sahil. There where 40 questions on the test. How many answers did Angelina get wrong on the math test? Which equation represents this situation
Answer:
19 wrong answers.
Step-by-step explanation:
Given:
Sahil got 28 questions right.
Angelina got 7 more wrong answers than Sahil.
There where 40 questions on the test.
Question asked:
How many answers did Angelina get wrong on the math test ?
Solution:
Total questions on the test = 40
Number of right answers, Sahil got = 28
Number of wrong answers, Sahil got = 40 - 28 = 12
As Angelina got 7 more wrong answers than Sahil,
Number of wrong answers, Sahil got = 12
Then, number of wrong answers, Angelina got = 12 + 7 = 19
Therefore, 19 answers did Angelina get wrong on the math test out of 40.
Angelina got 35 wrong answers on the math test.
Explanation:To find the number of wrong answers Angelina got on the math test, we need to know how many questions she got right. Since Sahil got 28 questions right and there were 40 questions on the test, we can subtract Sahil's score from the total number of questions to find Angelina's score. Sahil got 28 questions right, so Angelina would have gotten 40 - 28 = 12 questions right. And since Angelina got 7 more wrong answers than Sahil, we can subtract Sahil's wrong answers from Angelina's total wrong answers to find the specific number. If Sahil got 12 questions right, then he must have gotten 40 - 12 = 28 questions wrong. And since Angelina got 7 more wrong answers than Sahil, we can add 7 to Sahil's wrong answers to find Angelina's total wrong answers. Therefore, Angelina got 28 + 7 = 35 wrong answers on the math test.
Two particles are moving in straight lines. The displacement (in meters) of particle 1 is given by the function e^(4cos(t)) , where t is in seconds. The displacement (in meters) of particle 2 is given by the function -(t^3)/(3) - (t^2)/(2) + 2 , where t is in seconds. Find the first positive time at which the particles have(approximately) the same velocity.
A.) t = 1.569 seconds
B.) t = 0 seconds
C.) t = 2.366 seconds
D.) t = 0.588 seconds
E.) t = 1.011 seconds
The velocities of particles are given by the derivatives of their displacement functions. Equating the velocity functions of the two particles and solving numerically, we find that they have the same velocity for the first time at about t = 1.569 seconds.
Explanation:The velocity of an object is given by the derivative of its displacement function. So, we need to first find the derivatives of the given displacement functions to find the velocities of the particles.
The derivative of e^(4cos(t)) is [tex]-4e^{(4cos(t))sin(t)[/tex]. The derivative of [tex]-(t^3)/(3) - (t^2)/(2) + 2 is -t^2 - t.[/tex] Now, we equate the two velocities and solve for t[tex].-4e^(4cos(t))sin(t) = -t^2 - t[/tex]
Unfortunately, this equation does not have a simple algebraic solution. However, it can be solved numerically using, for example, a graphing calculator or numerical software. By using these tools, we find the first positive time at which the particles have approximately the same velocity to be about t = 1.569 seconds. Therefore, the correct answer is A.) t = 1.569 seconds.
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Airplane at 19,200 feet descending at a rate of 40 feet per second. Another airplane takes off and ascends at a rate of 60 feet per second. After how many seconds will the airplanes be at the same height? What is the height
Answer:
Step-by-step explanation:
Let t = flying time in seconds for each plane
Descending rate = 40 ft/s
Ascending rate = 60 ft/s
Descending height, hd= 19200 - 40t
Ascending height, ha = 60t
Equating hd = ha, therefore:
60t = 19200-40t
60t + 40t = 19200
100t = 19200
t = 19200/100
t = 192 seconds
h = 19200 - 192(40)
h = 19200 - 7680
= 11,520 ft.
After 192 seconds, the two airplanes will be at the same height, which is 11,520 feet.
Explanation:To find the time it takes for the two airplanes to be at the same height, we need to set up an equation based on their rates of ascent and descent. Let's assume the height of the descending airplane is given by h1 and the height of the ascending airplane is given by h2. The descending airplane is descending at a rate of 40 feet per second, so its height after t seconds can be represented by the equation h1 = 19,200 - 40t. The ascending airplane is ascending at a rate of 60 feet per second, so its height after t seconds can be represented by the equation h2 = 60t. To find the time at which the two airplanes are at the same height, we can set h1 equal to h2 and solve for t: 19,200 - 40t = 60t. Simplifying this equation, we get 100t = 19,200, so t = 192 seconds. Therefore, after 192 seconds, the two airplanes will be at the same height.
To find the height at which the two airplanes are at, we can substitute the value of t into either the equation for h1 or h2. Let's use the equation for h1: h1 = 19,200 - 40(192) = 19,200 - 7,680 = 11,520 feet. Therefore, after 192 seconds, the two airplanes will be at a height of 11,520 feet.
Angle C is an inscribed angle of circle P. Angle C measures (x + 5)° and arc AB measures (4x)° . Find x.
3
5
7
9
Step-by-step explanation:
[tex]m \angle \: C = \frac{1}{2} (m \: arc \: AB)\\(By\:inscribed \:\angle\:theorem) \\ \\ \therefore \: (x + 5) \degree =\frac{1}{2} (4x)\degree \\ \\ \therefore \: x + 5=\frac{1}{2} \times 4x \\ \\ \therefore \: x + 5=2x \\ \\ \therefore \: x - 2x = - 5 \\ \\ \therefore \: - x = - 5 \\ \\ \: \: \: \: \: \huge \purple{ \boxed{\therefore \: x = 5}}[/tex]
The least number of customers in a shop at any time during the day was 15. Fran represented this situation with the inequality c > 15, where c is the number of customers in the shop. Is Fran correct? Explain.
Answer:
Fran was incorrect.
Correct representation: [tex]c \geq 15[/tex], where c is the number of customer during any time of day.
Step-by-step explanation:
We are given the following in the question:
Fran used the given inequality to represent the number of customers in a shop at any time.
[tex]c > 15[/tex]
where c is the number of customer during any time of day.
The least number of customers in a shop at any time during the day was 15.
Thus there could be 15 or greater than 15 customers in shop during any ime of day.
Thus, Fran was incorrect.
The correct representation is given by the inequality
[tex]c \geq 15[/tex]
where c is the number of customer during any time of day.
Answer:
Fran is incorrect.
The inequality is c ≥ 15
Step-by-step explanation:
PLEASE HELP a basketball player shoots a basketball with an initial velocity of 15 ft/sec. The ball is released from an initial height of 6.5 feet. PLEASE HELP
Part 1:
Replace "v0" in the given equation with the given velocity of 15 ft/sec:
y = -16t^2 + 15t +6.5
Part 2:
Now set the equation to 0 which would be when the basketball hits the ground:
-16t^2 +15t +6.5 = 0
A quadratic equation is solved using the formula:
t = -b +/- sqrt(b^2-4ac)/2a
Using the given equation: a = -16, b = 15 and c = 6.5
Replace the values and solve:
t = -(15)+/- sqrt(15^2 -4(-16)(6.5))/2(-16)
This solves to get both -0.32 and 1.26 seconds.
The time has to be a positive value so t = 1.26 seconds.
Part3:
Using the quadratic form at^2 + bt + c
The maximum is found using t = -b/2a = -15/2(-16) = = 0.47 seconds
The maximum height would be at 0.47 seconds
Part 4:
Replace t with 0.47 and solve for maximum height:
y = -16(0.47)^2 + 15(0.47) +6.5
Maximum height would be 3.52 feet
I'm shipping and handling fee of $35 is charged to all furniture orders over $250. If the order is $437.50 what percent is the shipping and handling fee
Answer: the shipping and handling fee is 8 percent of the cost of the order.
Step-by-step explanation:
Shipping and handling fee of $35 is charged to all furniture orders over $250.
If the order is $437.50, it means that there would be a handing and shipping fee of $35 because the price of the order is above $250.
The percentage of the original price of the order that is the shipping and handling fee would be
35/437.5 × 100 = 0.08 × 100
= 8%
Final answer:
To find the percent that the shipping and handling fee is of the total order, divide the fee by the order amount and multiply by 100. For an order of $437.50 with a fee of $35, the shipping fee is 8% of the total order.
Explanation:
The question asks us to determine what percent the shipping and handling fee is of the total furniture order.
To calculate this percentage, we can use the formula:
Percentage = (Part / Whole) imes 100
In this case:
Part = $35 shipping and handling feeWhole = $437.50 total furniture orderNow, we insert the values into the formula:
Percentage = ($35 / $437.50) imes 100
Percentage = 0.08 imes 100
Percentage = 8%
Therefore, the shipping and handling fee is 8% of the total order.
Speed cell wireless offers a plan of $40 for the first 400 minutes, and an additional $0.50 for every minute over 400. Let t represent the total talk time in minutes. Write a piecewise-defined function to represent the cost C(t)
The function that represent cost is c(t) = 40 + 0.5(t -400).
For the first 400 minutes [tex](\(0 \leq t \leq 400\))[/tex], the cost is a flat rate of $40.
T represents the overall conversation time in minutes in the provided question.
Speed cell wireless offers a $40 package for the first 400 minutes.
Additional $0.50 per minute for remaining time
Time remaining = (t - 400) minutes
So, the cost for more beyond 400 minutes is 0.5(t -400). $
Thus, the entire cost, c(t), is 40 + 0.5(t -400).
what equivalent expression was used
3y+4y
Answer:
7y²
Step-by-step explanation:
First u group them like 4+3+y+y=7y²
PLZ HURRY IT'S URGENT!!
Which equation can be used to find the two numbers whose ratio is 4 to 3 and that have a sum of 42?
4x + 3x = 42
34x=42
43x=42
4x−3x=42
Answer:
4x + 3x = 42
Step-by-step explanation:
Question 5 options: What is the approximate area of a circle with a radius of 11 cm? Use 3.14 for π. ______ cm2
The area of circle is 379.94 cm².
Step-by-step explanation:
Given,
Radius of circle = 11 centimeters
We have to calculate the area of circle.
We know that;
Area of circle = [tex]\pi r^2[/tex]
Here;
π = 3.14 , r = 11
Area of circle = [tex]3.14*(11)^2[/tex]
Area of circle = 3.14*121
Area of circle = 379.94 squared centimeters
The area of circle is 379.94 squared centimeters.
Keywords: area, circle
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The celluloid cinema sold150 tickets to a movie. Some of these were child tickets and the rest were adult tickets.A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, which system of equations could be used to determine how many adult tickets,a,and how many child tickets,c, were sold
Answer: the system of equations are
a + c = 150
7.75a + 10.25b = 1470
Step-by-step explanation:
Let a represent the number of adult tickets that were sold.
Let c represent the number of child tickets that were sold.
The celluloid cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. This means that
a + c = 150 - - - - - - - - - - - - - -1
A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, it means that
7.75a + 10.25b = 1470 - - - - - - - - -2
The question can be answered by creating two linear equations, one representing the total number of tickets (a + c = 150) and the other representing the total earnings from the ticket sales (10.25a + 7.75c = 1470). Solving this system of equations will yield the number of adult and child tickets sold.
Explanation:This problem can be solved using a system of linear equations, where one equation represents the total number of tickets sold and the other equation represents the total dollar value of the tickets sold.
The first equation is formed from the total number of tickets, which is the sum of adult tickets and child tickets: a + c = 150
The second equation is formed from the total cost of the tickets, where $10.25, the cost of an adult ticket, is multiplied by the number of adult tickets, and $7.75, the cost of a child ticket, is multiplied by the number of child tickets. This sum should be the total earnings from the ticket sales: 10.25a + 7.75c = 1470
Therefore, the system of equations to solve this problem is a + c = 150 and 10.25a + 7.75c = 1470.
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HELP ASAP FOR BRAINLIEST:
Find the sixth term of a geometric sequence with t5 = 24 and t8 = 3
Thank you sooo much! Show work!
Answer:
The answer is 12
Step-by-step explanation:
t5 = 24 = a × r⁴
t8 = 3 = a × r⁷
We divide one by the other
r³= 1 / 8
r = 1 / 2
t6 = a × r⁵ = t5 × r = 24 × (1/2) = 12.
Therefore the sixth term of the geometric sequence is 12
5. A survey of student pizza preferences showed that 43 students preferred cheese, 56 preferred sausage, 39 preferred pepperoni, 28 preferred supreme, 31 preferred another kind, and 19 did not like any type of pizza. Make your own probability distribution in order to answer the question. Match the probability of each outcome given to the correct outcome.
Answer:
P (Cheese) = 0.199, P (Sausage) = 0.259, P (Pepperoni) = 0.181,
P (Supreme) = 0.130, P (Another Kind) = 0.144
and P (Does not like any kind) = 0.088
Step-by-step explanation:
Given:
Number of students who prefer cheese = 43
Number of students who prefer sausage = 56
Number of students who prefer pepperoni = 39
Number of students who prefer supreme = 28
Number of students who prefer another kind = 31
Number of students who did not like any kind = 19
∴ The total number of students surveyed = [tex]43+56+39+28+31+19=216[/tex] The number of students who prefer pizza = [tex]43+56+39+28+31=197[/tex]
The probability that a students likes pizza is,
[tex]P(Student\ likes\ pizza)=\frac{No.\ of\ students\ who\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{197}{216} \\=0.912[/tex]
The probability that a students does not likes pizza is,
[tex]P(Student\ does\ not\ likes\ pizza)=\frac{No.\ of\ students\ who\ does\ not\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{19}{216} \\=0.088[/tex]
The probability distribution of students who prefer different kinds of pizza is:
The probability that a student likes cheese:[tex]P(A\ Student\ prefers\ cheese)=\frac{No.\ of\ students\ who\ prefer\ cheese}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{43}{216}\\=0.199[/tex]
The probability that a student likes sausage:[tex]P(A\ Student\ prefers\ sausage)=\frac{No.\ of\ students\ who\ prefer\ sausage}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{56}{216}\\=0.259[/tex]
The probability that a student likes pepperoni:[tex]P(A\ Student\ prefers\ pepperoni)=\frac{No.\ of\ students\ who\ prefer\ pepperoni}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{39}{216}\\=0.181[/tex]
The probability that a student likes supreme:[tex]P(A\ Student\ prefers\ supreme)=\frac{No.\ of\ students\ who\ prefer\ supreme}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{28}{216}\\=0.130[/tex]
The probability that a student likes another kind:[tex]P(A\ Student\ prefers\ another\ kind)=\frac{No.\ of\ students\ who\ prefer\ another\ kind}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{31}{216}\\=0.144[/tex]
Thus, the probability distribution table is displayed below:
if the number of students at a particular High School who participate in after-school drama programs increases at a rate of 8% per year, how long will it take for the number of students participating in the after-school programs to double?
a. about 25 years
b. about 12.5 years
c. about 3.6 years
d. about 9 years
Answer:
d. about 9 years
Step-by-step explanation:
There is a "rule of thumb" for doubling time* that says the product of the percentage rate of change per year and the doubling time in years is about 72. Here, that means the doubling time is about ...
72/8 = 9 . . . . years
_____
You can write the exponential equation ...
multiplier = (1 +.08)^n
and solve for multiplier = 2:
2 = 1.08^n
log(2) = n·log(1.08) . . . . . take logs
log(2)/log(1.08) = n . . . . . divide by the coefficient of n
9.00647 ≈ n
It will take about 9 years for the participation to double.
_____
* The farther away from 8% the rate of change is, or the more times per year it is compounded, the less accurate is the "rule of 72." When compounding is continuous, the "rule of 72" becomes the "rule of 69.4". For this problem, answer choices are sufficiently far apart that the rule of thumb is adequate for making a correct choice.
Write the equation of the function.
is it y = x2 / 6 - 3x /2 + 13/3 ?
Yo sup??
Since there is an x^2 term therefore this equation is of a parabola
By taking LCM and then cross multiplying it.
6y=x^2-9x+26
6y=x^2-9x+(9/2)^2+23/4
6y-23/4=(x-9/2)^2
we see that this is of the form
X^2=4AY
(x-9/2)^2=4(3y/2-23/16)
Hope this helps.
Answer:
[tex]f(x) =- \sqrt{x-1}+3[/tex]
Step-by-step explanation:
This looks like a square root function [tex]f(x) = \sqrt{x}[/tex] but symmetric with respect to the x axis and shifted to the right for 1 and up for 3:
Lets take [tex]f(x) = \sqrt{x}[/tex] . The function symmetric with respect to the x axis would be [tex]-f(x)[/tex], so now we have:
[tex]f(x) = -\sqrt{x}[/tex]
Lets take [tex]f(x) = -\sqrt{x}[/tex] and shift it up for y = 3. Now we have:
[tex]f(x) =- \sqrt{x}+3[/tex]
Lets take [tex]f(x) = -\sqrt{x}+3[/tex] and shift it right for x = 1. That means that instead of x we will have x-1:
[tex]f(x) =- \sqrt{x-1}+3[/tex]
A researcher is gathering data on the 50 states. She wants to actually enter the name of the state into the data matrix as one of the variables in her data set. What type of SPSS variable should that be?
Answer: String variables
Step-by-step explanation:
SPSS means Statistical Package for Social Sciences.
The SPSS has only two variables namely:
1. String variables which includes numbers,letters and other characters.
The string variables cannot perform calculations. It is basically used to type names of people, age,occupation,home addresses,email addresses e.t.c Which is what is what the researcher was trying to do.
2. Numeric variables which include only numbers. It can perform calculations too using mathematical operations like addition,multiplication,division and subtraction.
Find the area of the circle
Liam opened a savings account with a $400
deposit and a simple interest rate of 7.5%. If
the balance of the account is now $670 and
there were no deposits or withdrawls, how
long ago did he open the account
Answer: he open the account 9 years ago.
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount deposited.
P represents the principal or amount deposited.
R represents interest rate
T represents the time for which the amount deposited was left in the account.
From the information given,
P = 400
R = 7.5%
I = 670 - 400 = $270
Therefore,
270 = (400 × 7.5 × T)/100 = 30T
T = 270/30
T = 9 years
Step-by-step explanation:
9 years thank you yw bubye
Riverside Elementary School is holding a school-wide election to choose a school color. 5/8 of the voters were for blue 5/9 of the remaining voters were for green. And the remaining 48 voters were for red. How many voters were for blue?
Answer:
There were 180 voters for blue color.
Step-by-step explanation:
Let the total number of voters be 'x'.
Given:
Number of Voters for blue color = [tex]\frac{5}{8}x[/tex]
Number of Voters for green color = [tex]\frac{5}{9}(x-\frac58x)=\frac59x(1-\frac58)[/tex]
Now we will use LCM to make the denominator common we get;
Number of Voters for green color = [tex]\frac59x(\frac88-\frac58)=\frac59x(\frac{8-5}{9})=\frac59x(\frac38)=\frac{15x}{72}[/tex]
Number of Voters for red color = 48
We need to find the number of voters for blue color.
Solution:
Now we can say that;
total number of voters is equal to sum of Number of Voters for blue color, Number of Voters for green color and Number of Voters for red color.
framing in equation form we get;
[tex]x=\frac58x+\frac{15x}{72}+48[/tex]
Combining like terms we get;
[tex]x-\frac58x-\frac{15x}{72} = 48[/tex]
Now we will make denominators common using LCM we get;
[tex]\frac{72x}{72}-\frac{5x\times9}{8\times9}-\frac{15x\times1}{72\times 1} = 48\\\\\frac{72x}{72}-\frac{45x}{72}-\frac{15x}{72} = 48[/tex]
Now denominators are common so we will solve the numerators we get;
[tex]\frac{72x-45x-15x}{72}=48\\\\\frac{12x}{72}=48\\\\\frac{x}{6}=48[/tex]
Now multiplying both side by 6 we get;
[tex]\frac{1}{6}x\times6=48\times6\\\\x = 288[/tex]
Number of voters for blue color = [tex]\frac{5}{8}x=\frac{5}{8}\times 288= 180[/tex]
Hence There were 180 voters for blue color.
Travel Ez sells dollars at a rate of ($1.40)/(1 euro) and buys dollars at a rate of ($1.80)/(1 euro). At the beginning of a trip, Sophie exchanged $540 to get 300 euros. At the end of the trip she is left with 40 euros, so she exchanges the 40 euros back to dollars. How many dollars will Sophie get in exchange?
a. $72.
b. $22.
c. $56.
d. $28.
Answer:
C
Step-by-step explanation:
In the first instance, he wanted buying euros in exchange for his dollars. He had $540 and wanted to buy euros. The conversion factor here is that for every 1 euro, he pays $1.80
Now at the second instance, he wanted buying dollars with his left over euros. This means for every 1 euro, he gets $1.4
Since, he is having 40 euros, the total amount in dollars he would get will be 40 * $1.4 = $56
Lisa has a home-based business making and selling scented soaps. She intially spent $72 to purchase soap-making equipment, and the materials for each pound of soap cost $7. Lisa sells the soap for $10 per pound. Eventually, she will sell enough soap to cover the cost of the equipment. What will be Lisa's total sales and costs be? How much soap will that be?
Answer:
Step-by-step explanation:
Let x represent the number of pounds of soap that she makes and eventually sells.
She intially spent $72 to purchase soap-making equipment, and the materials for each pound of soap cost $7. This means that the total cost of making x pounds of soap would be
7x + 72
Lisa sells the soap for $10 per pound. This means that her revenue for x pounds of soap would be
10 × x = 10x
If she eventually sells enough soap to cover the cost of the equipment, then
7x + 72 = 10x
10x - 7x = 72
3x = 72
x = 72/3 = 24
She would need to sell make and sell 24 soaps.
The cost would be
72 + 7 × 24 = $240
The total sales would be
10 × 24 = $240
Solve each equation below for x show all work and check your answer by substituting it back into the equation and verifying that it makes the equation true
The solutions to the equations:
(a) x/3 = 6 => x = 18 (Verified)
(b) (5x + 9)/2 = 12 => x = 3 (Verified)
(c) x/4 = 9/6 => x = 6 (Verified)
(d) 5/x = 20/8 => x = 2 (Verified)
To solve the equation, follow these steps: identify the equation with one unknown, isolate x, substitute known values and solve, and check the solution.
The equations are
(a) x/3 = 6
(b) (5x + 9)/2 = 12
(c) x/4 = 9/6
(d) 5/x = 20/8
The answers to the question are
(a) x = 18
(b) x = 3
(c) x = 6
(d) x = 2
Step-by-step explanation:
(a) x/3 = 6
Therefore x = 3×6 = 18
x =18
Substituting the value of x in the above equation, we have
18/6 = 3 verified
(b) (5x + 9)/2 = 12
Multiplying both sides by 2 gives
(5x + 9)/2 × 2 = 12×2 = 24
5x + 9 = 24 or x = (24-9)/5 = 3
Substituting the value of x in the above equation, we have
(5×3 + 9)/2 = 24/2 = 12 verified
x = 3
(c) x/4 = 9/6
Multiplying both sides by 4, we have
x/4×4 = 9/6×4 = 6
x = 6
Substituting the value of x in the above equation, we have
(6/4 = 9/6 = 3/2 verified
(d) 5/x = 20/8
Inverting both equations, we have
x/5 = 8/20
Multiplying both sides by 20 we have x/5 × 20 = 8/20 × 20 or 4x = 8 and x = 2
Substituting the value of x in the original equation, we have
2/5 = 2/5 = 8/20 verified
x = 2
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Martin is cleaning all the rooms in his house. There are 4 rooms left to clean, and he takes 7 hours to clean them. Write the equation in standard form of the line that represents the number of rooms Martin has left to clean, y, after x hours.
The required equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours is 4x + 7y = 56.
To write the equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours, we can use the given information that there are 4 rooms left to clean after 7 hours.
Let's start with the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
We have the point (x₁, y₁) = (7, 4), which represents the number of rooms left after 7 hours.
Substituting the values into the point-slope form, we get:
y - 4 = m(x - 7)
Now, we need to find the slope (m) of the line.
The slope of a line can be determined by the change in y divided by the change in x. In this case, the change in y is -4 (4 rooms left to clean) and the change in x is 7 hours.
m = Δy / Δx = -4 / 7
Now, let's substitute the value of m into the equation:
y - 4 = (-4/7)(x - 7)
To eliminate fractions, we can multiply through by 7:
7y - 28 = -4(x - 7)
7y - 28 = -4x + 28
4x + 7y = 56
So, the equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours is 4x + 7y = 56.
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Final answer:
To express the relationship between the number of rooms left to clean and the hours spent cleaning in a linear equation, we use the slope of -4/7 and a y-intercept of 4, assuming 4 rooms are cleaned in 7 hours. This leads to the slope-intercept form y = -4/7x + 4. Multiplying by 7 and rearranging gives us the standard form 4x + 7y = 28.
Explanation:
To find the equation of the line that represents the number of rooms, y, Martin has left to clean after x hours, we start with the information that 4 rooms take 7 hours to clean. This means that every hour, a fraction of the total rooms are cleaned. To express this situation as a linear equation, we can use the slope-intercept form, which is y = mx + b. In this context, the slope (m) will be negative since the number of rooms left to clean decreases over time, and b is the y-intercept representing the initial number of rooms before any cleaning has started. Since there are 4 rooms to begin with and it takes 7 hours to clean all, the slope is -4/7 (the change in rooms left per hour).
The equation in slope-intercept form is y = -4/7x + 4. To convert this to standard form, we multiply the entire equation by 7 to eliminate the fraction: 7y = -4x + 28. Then we add 4x to both sides of the equation to get: 4x + 7y = 28. This is the equation in standard form, representing the number of rooms left (y) after x hours of cleaning.
The population of Humorville is 9800 people. In one hour, each person who hears a joke tells three other people who have not head it, and tells no one else. Last Friday, a visitor from out of town told the mayor a new joke at 10:00 am. How long did it take for everyone in Humorville to head the joke?
Answer:
At 7 hours from the visit telling the joke, everyone in town would have heard of it
Step-by-step explanation:
Exponential Grow
This is a good example of exponential growth, where the speed at which a rumor is spread out depends on the actual number of persons who already know it.
The visitor told the mayor a new joke at 10:00 am.
Total people who heard the joke=1
This person tells the joke to 3 people in one hour, so at 11:00 am, 1+3=4 persons heard the joke
Total people who heard the joke=4
Those persons take one hour to tell the joke to every 3 persons each. Thus at 11:00
4 + 4*3 = 16 persons heard the joke. This succession grows very quickly. At 12:00
16 + 16*3 = 64 persons heard the joke
We can note the number of persons hearing the joke is an even power of 2, that is
[tex]2^0=1[/tex]
[tex]2^2=4[/tex]
[tex]2^4=16[/tex]
[tex]2^6=64[/tex]
We can predict the result for each hour since the exponent is double the number of hours passed since the joke started to spread. The number of persons who have heard the joke after t hours is
[tex]N=2^{2t}[/tex]
We can iterate until we find the value of t so that
[tex]2^{2t}<9800[/tex]
Let's better find the limit value of t
[tex]2^{2t}=9800[/tex]
Taking logarithms
[tex]log(2^{2t})=log9800[/tex]
[tex]2tlog(2)=log(9800)[/tex]
Thus
[tex]\displaystyle t=\frac{log(9800)}{2log 2}[/tex]
[tex]t=6.6[/tex]
So at 7 hours from the visit telling the joke (between 16:00 and 17:00), everyone in town would know it
Note that
[tex]2^{12}=4096[/tex]
[tex]2^{14}=16384[/tex]
What is the common difference between the terms in the following sequence?
{17,11,5,−1,−7...}
Answer:
-6
Step-by-step explanation:
Take a couple of differences and see:
11 -17 = -6
5 -11 = -6
The common difference is -6.
At a car dealership, there are three times as many sedans as SUVs. If there are a combined 24 sedans and SUVs, how many sedans are there at the dealership?
Answer:
There are 18 Sedans in the dealership shop.
Step-by-step explanation:
Let x represent the number of Sedans in the dealership shop.
Let y represent the number of SUV's in the dealership shop.
If there are a combined 24 sedans and SUVs, it means that
x + y = 24 - - - - - - - - - - - -1
At a car dealership, there are three times as many sedans as SUVs. This means that
x = 3y
Substituting x = 3y into equation 1, it becomes
3y + y = 24
4y = 24
y = 24/4 = 6
x = 3y = 6 × 3
x = 18
Jenny plans to invest $9,000. America's Bank offers a 10 year CD at an annual interest rate of 3.8% compounding interest semi-annually. How much is her investment worth at the end of the 10 years?
Group of answer choices
$9,000
$13,114
$15,840
$18,000
Answer: $13,114
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 9000
r = 3.8% = 3.8/100 = 0.038
n = 2 because it was compounded 2 times in a year.
t = 10 years
Therefore,.
A = 9000(1+0.038/2)^2 × 10
A = 9000(1+0.019)^20
A = 9000(1.019)^20
A = $13114
The final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B: $13114 approx.
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]
For this case, we are given that:
Initial amount Jenny invested = $9,000 = PThe rate of interest = 3.8% semi annually (0.5 years) = 3.8/2 = 1.9% per 0.5 years = R Thus, unit of time = half yearTime for which investment was made= 10 years = 20 half years =TThus, the final amount at the end of 10 years is given by:
[tex]A = P(1 +\dfrac{1.9}{100})^T\\\\A = 9000(1 + \dfrac{1.9}{100})^{20} = 9000(1.019)^{20} \approx 13114 \text{\: \: (in dollars)}[/tex]
Thus, the final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B: $13114 approx.
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Why shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency distribution?
Answer:
Step-by-step explanation:
Why shouldn't classes overlap when one summarizes continuous data? If classes overlap, then some observations will be counted in more than one class. This means that certain observations will end up in more than one bar of a histogram, which will misrepresent the data!