The statement 'the number of new clients (x) is 154% of the number of old clients (y)' can be translated into a linear equation in the standard form 'ax + by = c' as '-1.54y + x = 0' or '-154y + 100x = 0' where a, b, and c are constants.
Explanation:To translate the given statement into a linear equation, we need to interpret the percentages as a ratio. When we say 'the number of new clients (x) is 154% of the number of old clients (y)', it means 'x is equivalent to 1.54 times y'. So, we can write that as a linear equation:
x = 1.54y
However, that's not in the form 'ax + by = c'. To get it into that form, we can write it as:
-1.54y + x = 0
Or alternately you might prefer, if you wish to avoid decimals:
-154y + 100x = 0
Where a = -154, b = 100 and c = 0.
Learn more about Linear Equation here:https://brainly.com/question/32634451
#SPJ3
PLEASE HELP QUICKLY! 20 points! I will mark best answer as Brainliest!
A pitcher throws a baseball straight into the air with a velocity of 72 feet/sec. If acceleration due to gravity is -32 ft/sec^2, how many seconds after it leaves the pitcher's hand will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet.
t= 2.25 secs
Step-by-step explanation:
Step 1 :
Equation for motion with uniform acceleration is v = u+ at
where v is the final velocity
u is the initial velocity
a is the acceleration due to gravity
and t is the time
Step 2 :
Here , v = 0 because at the highest point final velocity is 0.
u = 72 feet/sec
a = -32 ft/sec^2
We need to find the time t.
Substituting in the equation we have,
0 = 72 -32 * t
=> 32 t = 72
=> t = 72/32 = 2.25 secs
If θ is an angle in standard position that terminates in Quadrant IV such that cosθ = 3/5, then cosθ/2 = _____. -
Answer:
[tex]cos \frac{\theta}{2}= 0.894[/tex].
Step-by-step explanation:
Given:
[tex]cos\ \theta= \frac35[/tex]
We need to find [tex]cos \ \frac{\theta}{2}[/tex]
Solution:
[tex]cos\ \theta= \frac35[/tex]
First we will find the value of [tex]\theta[/tex].
Now taking [tex]cos^{-1}[/tex] on both side we get;
[tex]\theta= cos^{-1} \ \frac{3}{5}\\\\\theta = 53.13[/tex]
Now we will find the [tex]\frac{\theta}{2}[/tex].
[tex]\frac{\theta}{2}[/tex] = [tex]\frac{53.13}{2} = 26.565[/tex]
Now we will find [tex]cos \ \frac{\theta}{2}[/tex] we get;
[tex]cos \frac{\theta}{2}=cos\ 26.565 = 0.894[/tex]
Hence [tex]cos \frac{\theta}{2}= 0.894[/tex].
Answer:
+/- (2\sqrt(5))/(5)
Step-by-step explanation:
Use well-ordering property to prove that if n people stand in a line, where n is a positive integer, and if the first person in the line is a woman and the last person in line is a man, then somewhere in the line there is a woman directly in front of a man.
Answer:
The people forming the line form a well ordered set, this means, every non empty subset has a minimum. In other words, in any smaller (but non empty) set of people there will always be one that is last in the line.
Lets take the subset formed of all the Women in the line. This subset in non empty because there is a women in the line (the first person in the line is a women), therefore, there is a women that is behind every other women in the line; this women can only have men behind, if any. If she had no men behind her, then she should be last in the line, bacause the doesnt have any men or women behind her. This is a contradiction because there is a man at the end of the line, not a woman. This shows that this woman that is behind every other woman has men behind, in particularly immediately behind, her.
Using well - ordering property in mathematical induction, we have been able to prove that; if n people stand in a line, where n is a positive integer, then somewhere in the line there is a woman directly in front of a man.
Mathematical inductionMathematical induction is defined as a proof technique that is used to prove that a property Pₙ will hold for every natural number such as n = 0, 1, 2, 3 e.t.c.
Now, we want to prove that If n people stand in a line, where n is a positive integer, and if the first person in the line is a woman and the last person in line is a man, then somewhere in the line, there is a woman directly in front of a man.
Now, let us deduce as follows;
When n = 2; This means that the first person is a woman and last is man.When n = k (k ≥ 2); This means there is a woman in front of a manThus;
When n = k + 1, what we will get is that;
- A new person is before a woman that is directly in front of a man.
- The new person is after the man directly after the woman.
- A new person is added between the woman and the man.
In conclusion;
For every positive integer n(n > 2), there is always a woman directly in front of a man.
Read more about Mathematical Induction at; https://brainly.com/question/24672369
How do you do this question?
Answer:
E) 13
Step-by-step explanation:
∫₀⁴ f'(t) dt = f(4) − f(0)
8 = f(4) − 5
f(4) = 13
A jar contains only pennies, nickels, dimes, and quarters. There are 14 pennies, 28 dimes, and 16 quarters. The rest of the coins are nickels. There are 70 coins in all. How many of the coins are not nickels? If n represents the number of nickels in the jar, what equation could you use to find n?
Answer:
Step-by-step explanation:
Let n represent the number of nickels in the jar.
The jar contains only pennies, nickels, dimes, and quarters. There are 14 pennies, 28 dimes, and 16 quarters. This means that the total number if pennies, dimes and quarters would be
14 + 28 + 16 = 58
This means that the number of coins that are not nickel is 58
The total number of coins in the jar is 70. Therefore, the equation that can be used to find n is
n + 58 = 70
n = 70 - 58
n = 12 nickels
what is the solution to the following expression if x=5
The value of given expression is 16
Solution:
Given expression is:
[tex]\sqrt{x^2} + \sqrt{x} \times \sqrt{x} + 6[/tex]
We have to find the value of expression when x = 5
Substitute x = 5
[tex]\sqrt{x^2} + \sqrt{x} \times \sqrt{x} + 6\\\\\sqrt{5^2} + (\sqrt{5} \times \sqrt{5}) + 6[/tex]
We know that,
[tex]\sqrt{a} \times \sqrt{a} = a[/tex]
Therefore, the above equation becomes,
[tex]\sqrt{5^2} + 5 + 6\\\\\sqrt{25} + 5 + 6\\\\5 + 5 + 6 = 10 + 6 = 16[/tex]
Thus the value of given expression is 16
Sally and Adam work at different jobs. Sally earns $5 per hour and Adam earns $4 per hour. They each earn the same amount per week but Adam works 2 more hours. How many hours a week does Adam work?
Answer:
10 hrs
Step-by-step explanation:
sally earns $5/hr while Adam earns $4/hr
let the number of Hour sally works be 'x'
From question Adam work 2 hrs more than sally,
therefore Adam works (x + 2)hrs also the both earn same amount per week
therefore;
4 x [tex](x + 2)[/tex] = 5 x [tex]x[/tex]
4x + 8 = 5x
5x - 4x = 8
x = 8hrs
Adam works for (8+2)hrs = 10hrs
Tamira has $55 in her lunch account. Each day she spends $5 on lunch. Which equation represents the amount of money, y, Tamira has left in her lunch account after x days?
Answer:
y=-5x+55
Step-by-step explanation:
i had a quiz and i got the correct answer on the test corrections your welcome
A line perpendicular to another line or to a tangent line is called a normal line. Find an equation of the line perpendicular to the line that is tangent to the following curve at the given point P.
Y=x^2-3x
P (7, 28)
The equation of the normal line at P(7, 28) is:
Answer:
The equation of the normal line to the curve y = x² - 3x at the point (7, 28) is 11y + x - 315 = 0
Step-by-step explanation:
First, we need to find the slope of the line tangent to the curve at the point (7, 28).
To do this, we need to differentiate y with respect to x and evaluate at the point x0 = 7.
Given y = x² - 3x
dy/dx = 2x - 3
So, the slope, m of the tangent line is dy/dx at x = 7:
m = 2(7) - 3 = 11
Slope, m = 11
The slope, m2 of the line perpendicular to the tangent is given as m2 = -1/m
m2 = −1/11
Finally, given the slope m of a line, and a point (x0, y0) on the line, we can use the point-slope form of the equation of a line:
y - y0=m(x - x0)
The perpendicular line has slope m2 = -1/11, and (7, 28) is a point on that line, the desired equation is:
y - 28 = (-1/11)(x - 7)
Or multiplying by 11, we have
11y - 308 = -x + 7
11y + x - 315 = 0
The slope of the curve at point (7,28) is 11, found by differentiating the given function. The slope of the normal line is the negative reciprocal of that, -1/11. Inserting these into the line equation, we get y - 28 = -1/11 * (x - 7).
Explanation:To find the equation of the line perpendicular to the tangent line, we first find the slope of the tangent line. The derivative of the given function y = x^2 - 3x tells us the slope of the curve at any point, so let's find the derivative:
y' = 2x - 3
Now, let's find the slope of the tangent line at the point (7,28) by plugging 7 into the derivative:
y'(7) = 2*7 - 3 = 11
The slope of the line perpendicular to this (the normal line) is the negative reciprocal of the tangent line's slope, so it's -1/11.
The equation of the line with slope m that goes through the point (x1, y1) is:
y - y1 = m*(x - x1)
Substitute the slope of -1/11 and the point (7,28) into this equation to get the equation of the normal line:
y - 28 = -1/11 * (x - 7)
Learn more about Normal Line here:https://brainly.com/question/32090153
#SPJ3
Select all expressions that represent a correct solution to the equation 6(x+4)=20. copied for free from openupresources.Org Select all that apply: A. (20−4)÷6 B. 16(20−4) C. 20−6−4 D. 20÷6−4 E. 1/6(20−24) F. (20−24)÷6
Option D: [tex]20 \div 6-4[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]
Option E: [tex]\frac{1}{6} (20-24)[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]
Option F: [tex](20-24) \div 6[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]
Explanation:
The expression is [tex]6(x+4)=20[/tex]
Let us find the value of x.
[tex]\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-\frac{2}{3}\end{aligned}[/tex]
Now, we shall find the expression that is equivalent to the value [tex]x=-\frac{2}{3}[/tex]
Option A: [tex](20-4) \div 6[/tex]
Simplifying the expression, we have,
[tex]\frac{16}{6}=\frac{8}{3}[/tex]
Since, [tex]\frac{8}{3}[/tex] is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-4) \div 6[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option A is not the correct answer.
Option B: [tex]16(20-4)[/tex]
Simplifying the expression, we have,
[tex]16(16)=256[/tex]
Since, 256 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]16(20-4)[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option B is not the correct answer.
Option C: [tex]20-6-4[/tex]
Simplifying the expression, we have,
[tex]20-10=10[/tex]
Since, 10 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20-6-4[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option C is not the correct answer.
Option D: [tex]20 \div 6-4[/tex]
Using PEMDAS and simplifying the expression, we have,
[tex]$\begin{aligned}(20 \div 6)-4 &=\frac{10}{3}-4 \\ &=\frac{10-12}{3} \\ &=-\frac{2}{3} \end{aligned}$[/tex]
Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20 \div 6-4[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option D is the correct answer.
Option E: [tex]\frac{1}{6} (20-24)[/tex]
Simplifying the expression, we have,
[tex]$\begin{aligned} \frac{1}{6}(20-24) &=\frac{1}{6}(-4) \\ &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]
Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]\frac{1}{6} (20-24)[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option E is the correct answer.
Option F: [tex](20-24) \div 6[/tex]
Simplifying the expression, we have,
[tex]$\begin{aligned}(20-24) \div 6 &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]
Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-24) \div 6[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option F is the correct answer.
To solve 6(x + 4) = 20, we isolate x to get x = -2/3. The correct expressions representing the solution are E. 1/6(20 - 24) and F. (20 - 24) / 6.
To solve the equation 6(x + 4) = 20, we need to isolate x.
First, distribute the 6 on the left-hand side:
6x + 24 = 20
Next, subtract 24 from both sides:
6x = -4
Finally, divide by 6:
x = -4/6 = -2/3
Now, let's analyze the given choices:
A. (20 - 4) ÷ 6: This simplifies to 16 / 6, which does not match x = -2/3.B. 16(20 - 4): This simplifies to 16 × 16, which is incorrect.C. 20 - 6 - 4: This simplifies to 10, which is incorrect.D. 20 ÷ 6 - 4: This simplifies to 10/3 - 4, which is incorrect.E. 1/6(20 - 24): This simplifies to 1/6(-4) = -2/3, which matches the solution.F. (20 - 24) / 6: This simplifies to -4/6 = -2/3, which matches the solution.Therefore, the correct choices are E and F.
According to the U.S. Census bureau, 23.5% of people in the United States are under the age of 18. In a random sample of 250 residents of a small town in Ohio, 28% of the sample was under 18. Which one of the following statements is true?
1. 23.5% and 28% are statistics, 250 and 18 are parameters
2. 23.5% and 28% are parameters, 250 and 18 are statistics
3. 23.5% and 28% are parameters, 18 is a statistic
4. 28% is a parameter and 23.5% is a statistic
5. 23.5% is a parameter and 28% is a statistic
Answer:
Option 5) 23.5% is a parameter and 28% is a statistic
Step-by-step explanation:
We are given the following in the question:
"According to the U.S. Census bureau, 23.5% of people in the United States are under the age of 18. In a random sample of 250 residents of a small town in Ohio, 28% of the sample was under 18."
Population is the collection of all the observation of individual of interest.Population of interest:
People in the United States
Parameter is any value that describes the population.Parameter:
23.5% of people in the United States are under the age of 18
Sample is a subset of a population and is always smaller than the population.Sample:
Random sample of 250 residents of a small town in Ohio
Statistic is any value that describes a sample.Statistic:
28% of the sample was under 18
Thus, the correct answer is
Option 5) 23.5% is a parameter and 28% is a statistic
Danny has a coin collection. 20% of his collection are quarters. If Danny has 13 quarters, how many coins does he have in his collection altogether? A) 26 B) 39 C) 42 D) 65
Answer: Danny had 65 coins altogether in his collection.
Step-by-step explanation:
Let x represent the number of coins that Danny has in his collection.
20% of his collection are quarters. This means that the number of quarters that Danny has in his collection is
20/100 × x = 0.2 × x = 0.2x
If Danny has 13 quarters, it means that
0.2x = 13
Dividing the left hand side and the right hand side of the equation by 0.2, it becomes
0.2x/0.2 = 13/0.2
x = 65
A movie theater sold 4 adult tickets and 7 children's tickets for $83 on friday the next day the theater sold 5 adult tickets and 6 children tickets for $90. What is the price for the adult ticket and the price for a child's ticket
Answer: An adult ticket cost $12
A child ticket cost $5
Step-by-step explanation:
Let x represent the price for one adult ticket.
Let y represent the price for one child ticket.
A movie theater sold 4 adult tickets and 7 children's tickets for $83 on Friday. It means that
4x + 7y = 83 - - - - - - - - - - - -1
The next day the theater sold 5 adult tickets and 6 children tickets for $90. It means that
5x + 6y = 90 - - - - - - - - - - - -2
Multiplying equation 1 by 5 and equation 2 by 4, it becomes
20x + 35y = 415
20x + 24y = 360
Subtracting, it becomes
11y = 55
y = 55/11 = 5
Substituting y = 5 into equation 1, it becomes
4x + 7 × 5 = 83
4x + 35 = 83
4x = 83 - 35 = 48
x = 48/4 = 12
Find the volume of a cube with side length of 7 in.
A: 147 in³ B: 49 in³
C:215 in³ D: 343 in³
Answer: 343 in³
Explanation: In this problem, we're asked to find the volume of a cube.
It's important to understand that a cube is a type of rectangular prism and the formula for the volume of a rectangular prism is shown below.
Volume = length × width × height
In a cube however, the length, width, and height are all the same. So we can use the formula side × side × side instead.
So the formula for the volume of a cube is side × side × side or s³.
So to find the volume of the given cube, since each side has a length of 7 inches, we can plug this information into the formula to get (7 in.)³ or (7 in.)(7 in.)(7 in).
7 x 7 is 49 and 49 x 7 is 343.
So we have 343 in³.
So the volume of the given cube is 343 in³.
Answer:
343 in³
Step-by-step explanation:
Brainliest ! 40 points , pls answer all or don't answer
Answer:
The answer to your question is below
Step-by-step explanation:
1.- Find the volume of the cylinder
Data
diameter = 9 cm
radius = 4.5 cm
height = 15 cm
Formula
V = πr²h
V = π(4.5)²(15)
V = 303.75π This is te answer for the volume in terms of π
= 952.78 cm³
2.- Find the volume of the cylinder
height = 40 yd
radius = 12 yd
Formula
V = πr²h
V = π(12)²(40)
V = 5760π This is te answer for the volume in terms of π
= 18086.4 cm³
3.- What is the height .......
height = q
side length = r
4.- Volume of a pyramid
Volume = Area of the base x height
Area of the base = 11 x 11 = 121 cm²
Volume = 121 x 18
Volume = 2178 cm³
Answer:
1. 953.775 cm³
2. 18,086.4 yd³
3. height: q ; side: r
4. 726 cm³
Step-by-step explanation:
1. Volume = pi × r² × h
= 3.14 × (9/2)² × 15
= 953.775 cm³
2. Volume = pi × r² × h
= 3.14 × 12² × 40
= 18086.4 yd³
3. height: q ; side: r
4. Volume = ⅓ base area × height
= ⅓ × 11² × 18
= 726 cm³
The surface area of a cube is increasing at a rate of 15 square meters per hour. At a certain instant, the surface area is 24 square meters. What is the rate of change of the volume of the cube at that instant (in cubic meters per hour)?
Answer:
The volume of cube is increasing at a rate 7.5 cubic meter per hour.
Step-by-step explanation:
We are given the following in the question:
Surface area of cube = 24 square meters.
Let l be the edge of cube.
Surface area of cube =
[tex]6l^2 = 24\\l^2 = 4\\l = 2[/tex]
Thus, at that instant the edge of cube is 2 meters.
[tex]\dfrac{dS}{dt} = 15\text{ square meters per hour}\\\\\dfrac{d(6l^2)}{dt} = 15\\\\12l\dfrac{dl}{dt} = 15\\\\\dfrac{dl}{dt} = \dfrac{15}{12\times 2} = \dfrac{15}{24}[/tex]
We have to find the rate of change in volume.
Volume of cube =
[tex]l^3[/tex]
Rate of change of volume =
[tex]\dfrac{dV}{dt} = \dfrac{d(l^3)}{dt} = 3l^2\dfrac{dl}{dt}\\\\\dfrac{dV}{dt} = 3(2)^2\times \dfrac{15}{24} \\\\\dfrac{dV}{dt} = 7.5\text{ cubic meter per hour}[/tex]
Thus, the volume of cube is increasing at a rate 7.5 cubic meter per hour.
The rate of change of the volume of the cube at the given instant is; dV/dt = 7.5 m³/h
Surface area is increasing at a rate of 15 m²/h
Thus, dS/dt = 15 m²/h
Now, at a certain instant the surface area of the cube is 24 m².
Formula for cube surface area is; S = 6l²
Thus;
6l² = 24
l² = 24/6
l² = 4
l = √4
l = 2 m
From S = 6l², differentiating both sides with respect to t gives;
dS/dt = 12l(dl/dt)
We know that dS/dt = 15
Thus;
12l(dl/dt) = 15
dl/dt = 15/(12l)
putting 2 for l gives;
dl/dt = 15/(12 * 2)
dl/dt = 0.625 m/h
Now formula for volume of a cube is; V = l³
Differentiating both sides with respect to t gives;
dV/dt = 3l²(dl/dt)
plugging in then relevant values gives;
dV/dt = 3 × 2² × (0.625)
dV/dt = 7.5 m³/h
Read more about rate of change of volume at; https://brainly.com/question/15648128
Write a formula that describes the value of an initial investment of $4,000 that loses value at a rate of 10% per year, compounded continuously.
Answer:
see below
Step-by-step explanation:
The formula is the same whether the rate of change is positive or negative. Here, it is negative.
A = Pe^(rt)
for P = 4000, r = -0.10. Then you have ...
A = 4000e^(-0.10t)
Helppp i need answer asap
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle
BC represents the hypotenuse of the right angle triangle.
With m∠B as the reference angle,
AB represents the adjacent side of the right angle triangle.
AC represents the opposite side of the right angle triangle.
To determine BC , we would apply the Sine trigonometric ratio which is expressed as
Tan θ = opposite side/hypotenuse. Therefore,
Sin 44 = 10/BC
0.695 = 10/BC
BC = 10/0.695
BC = 14.4 to 1 decimal place.
There are 40 math teachers, 45 English teachers, 27 science teachers, and 32 social studies teachers. The superintendent of the region wants to select a board of 20 teachers. How many science teachers should he select?
Answer:
Superintendent of the region will select approximately 4 Science teachers in the board.
Step-by-step explanation:
Given:
Number of math teachers = 40
Number of English teachers = 45
Number of Science teachers = 27
Number Social Studies teachers = 32
Number of teachers to be selected in the board =20
We need to find the number Science teachers should be selected in the board.
Solution:
First we ill find the Total number of teachers.
Now we can say that;
Total number of teachers is equal to sum of Number of math teachers, Number of English teachers,Number of Science teachers and Number Social Studies teachers
framing in equation form we get;
Total number of teachers = [tex]40+45+27+32=144[/tex]
Probability of Science teacher can be calculated by Dividing Number of Science teacher by Total number of teachers.
[tex]P(S)=\frac{27}{144}=0.1875[/tex]
Now the number of Science teachers should be selected in the board we need to multiply P(S) with Number of teachers to be selected in the board.
framing in equation form we get;
number of Science teachers should be selected in the board = [tex]0.1875\times 20=3.75\approx4[/tex]
Hence We can say that;
Superintendent of the region will select approximately 4 Science teachers in the board.
Calculate the proportion of science teachers out of the total and apply it to the board size to determine the number of science teachers to select.
To determine how many science teachers the superintendent should select for a board of 20 teachers:
Calculate the total number of teachers: 40 math + 45 English + 27 science + 32 social studies = 144 teachersFind the proportion of science teachers: 27 science teachers out of 144 total teachers = 0.1875Apply the proportion to the board size: 0.1875 * 20 = 3.75, so the superintendent should select 4 science teachers.100 PTS PLEASE HELP!!!!
The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:
Graph of quadratic function f of x having x-intercepts at ordered pairs 0, 0 and 36, 0. The vertex is at 18, 32.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height? (6 points)
Part B: What is an approximate average rate of change of the graph from x = 5 to x = 15, and what does this rate represent? (4 points)
Answer:
Part A) see the explanation
Part B) see the explanation
Step-by-step explanation:
Let
x ----> the distance from one side of the tunnel in feet:
f(x) ---> the height of a tunnel in feet
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?
1)
we know that
The x-intercepts are the values of x when the value of the function is equal to zero
In the context of the problem, the x-intercepts are the distances from one side of the tunnel when the height of the tunnel is equal to zero
2)
The maximum value of the graph is the vertex
The x-coordinate of the vertex represent the distance from one side of the tunnel when the height is a maximum value
The y-coordinate of the vertex represent the maximum height of the tunnel
In this problem
the vertex is (18,32)
That means
The maximum height of the tunnel is 32 feet and occurs when the distance from one side of the tunnel is 18 feet
3)
we know that
The function is increasing at the interval [0,18)
That means
As the distance from one side of tunnel increases the height of the tunnel increases too
The function is decreasing at the interval (18,36]
That means
As the distance from one side of tunnel increases the height of the tunnel decreases
Part B: What is an approximate average rate of change of the graph from x = 5 to x = 15, and what does this rate represent?
we know that
To find the average rate of change, we divide the change in the output value by the change in the input value
the average rate of change using the graph is equal to
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
In this problem we have
[tex]a=5[/tex]
[tex]b=15[/tex]
[tex]f(a)=f(5)=15[/tex] ----> see the attached figure
[tex]f(b)=f(15)=31[/tex] ----> see the attached figure
Substitute
[tex]\frac{31-15}{15-5}=1.6[/tex]
That means
The height of the tunnel increases 1.6 feet as the distance from one side of tunnel increases 1 foot in the interval from x=5 to x=15
Use the function f(x) = x2 + 6x + 6 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(x). a parabola that opens down and passes through 0 comma 3, 3 comma 12, and 5 comma 8 15 12 9 3
The answer is 15,
because F(X)'s minimum value is (-3, -3)
and G(X)'s maximum value is (12, 3)
So when you subtract -3 from 12, you get a number that is greater then both. (because of the negative 3)
12 - (-3) = 15
Answer:
A. 15
Step-by-step explanation:
I got it rigth on the test :)
Have a great day fam!
Maurice's new CD has 12 songs. Each song lasts between 3 and 4 minutes. He estimates that the whole CD is about 30 minutes long. Which statement about Maurice's estimate is true?
Answer:
The estimate is less than the actual length of the CD.
Step-by-step explanation:
Consider the provided information.
Maurice's new CD has 12 songs. Each song lasts between 3 and 4 minutes.
That means the minimum length of the CD should be: 12×3=36 minutes.
The maximum length of the CD should be: 12×4=48 minutes
He estimates that the whole CD is about 30 minutes long.
30 minutes is less than 36 minutes.
That means, the estimate is less than the actual length of the CD.
Hence, the correct statement is: The estimate is less than the actual length of the CD.
A survey was conducted by a website on which online music channels subscribers use on a regular basis. The following
information summarizes the answers.
10 listened to rap, heavy metal, and alternative rock.
13 listened to rap and heavy metal.
16 listened to heavy metal and alternative rock.
26 listened to rap and alternative rock.
37 listened to rap.
30 listened to heavy metal.
49 listened to alternative rock.
18 listened to none of these three channels.
a. How many people were surveyed?
b. How many people listened to either rap or alternative rock?
c. How many listened to heavy metal only?
The total number of people surveyed is 134. The number of people who listened to either rap or alternative rock is 76. The number of people who listened to heavy metal only is 1.
Explanation:To solve this problem, we can use a Venn diagram to organize the given information. Let's start by filling in the total number of people surveyed, which is the sum of those who listened to rap, heavy metal, alternative rock, and none of the three channels. From the given information, we have:
Rap: 37 Heavy Metal: 30 Alternative Rock: 49 None: 18
To find the total number of people surveyed, we add these numbers:
37 + 30 + 49 + 18 = 134.
Therefore, 134 people were surveyed.
b. To find the number of people who listened to either rap or alternative rock, we need to add the number of people who listened to rap and the number of people who listened to alternative rock, while making sure we don't double count those who listened to both:
37 + 49 - 10 = 76.
Therefore, 76 people listened to either rap or alternative rock.
c. To find the number of people who listened to heavy metal only, we need to subtract those who listened to heavy metal and either rap or alternative rock from the total number of people who listened to heavy metal:
30 - 13 - 16 = 1.
Therefore, 1 person listened to heavy metal only.
Learn more about Survey on Online Music Channel Subscribers here:https://brainly.com/question/25938166
#SPJ2
Mr.Nguyen bought a suit that was on sale for 40% off the original price.He paid 9% sales tax on the sale price. The original price of the suit was 260$ how much did he pay for the suit, including tax, to the nearest dollar?
Answer: The total amount that he paid for the suit is $170
Step-by-step explanation:
The original price of the suit was $260.
Mr.Nguyen bought a suit that was on sale for 40% off the original price. This means that the amount of discount in the suit is
40/100 × 260 = 0.4 × 260 = $104
The sale price would be
260 - 104 = $156
He paid 9% sales tax on the sale price. This means that the amount of sales tax that he paid is
9/100 × 156 = 0.09 × 156 = $14.04
The total amount that he paid for the suit, including tax is
156 + 14.04 = $170 to the nearest dollar
ary Egan needs to drain his 21 comma 000-gallon inground swimming pool to have it resurfaced. He uses two pumps to drain the pool. One drains 15 gallons of water a minute while the other drains 20 gallons of water a minute. If the pumps are turned on at the same time and remain on until the pool is drained, how long will it take for the pool to be drained?
Answer:
600 minutes = 10 hours
Step-by-step explanation:
Egan has to drain 21 000 ga of water out of the pool. Let the number of minutes it takes him to drain the pool be x minutes. The equation for determining x can be set up and solved as follows:
[tex]\frac{15 ga}{min}*xmin+\frac{20ga}{min}*xmin = 21000ga\\\\15x+20x=21000\\\\35x= 21000\\\\x = 600[/tex]
600 minutes = 10 hours
A Web ad can be designed from four different colors, three font types, five font sizes, three images, and five text phrases. A specific design is randomly generated by the Web server when you visit the site. Let A denote the event that the design color is red, and let B denote the event that the font size is not the smallest one. Use the addition rules to calculate the following probabilities.
A. P(A ∪ B).
B. P(A ∪ B').
C. P(A' ∪ B').
The probability of A = 1/4 = 0.25
The probability of B = 4/5 = 0.80
P(A ∩ B) = P(A) * P (B) = (0.25) * (0.80) = 0.20
P(A ∩ B') = P(A) * P (B') = (0.25) * (1-0.80) = 0.05
P(A' ∩ B') = P(A') * P (B') = (1-0.25) * (1-0.80) = 0.15
Answer:
A. P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.25 + 0.80 - 0.20 = 0.85
B. P(A U B') = P(A) + (1 - P(B)) - P(A ∩ B') = 0.25 + (1-0.80) - 0.05 = 0.40
C. P(A' U B') = (1 - P(A)) + (1 - P(B)) - P(A' ∩ B') = (1-0.25) + (1-0.80) - 0.15 = 0.80
The probabilities using the addition rule of probabilities are P(A ∪ B) = 17/20, P(A ∪ B') = 2/5, and P(A' ∪ B') = 4/5.
In solving this problem, we will use the addition rule for probabilities to find the likelihood of different combinations of randomly generated web ad designs based on given design elements.
A. P(A ∪ B)
We'll start by finding the probability of event A (the design color is red) and B (the font size is not the smallest one) occurring independently. Since there are four different colors, the probability of A is 1/4. When it comes to event B, since there are five different font sizes and the event is that the font size is not the smallest one, there are four font sizes that meet the criteria.
Therefore, the probability of B is 4/5. We can now calculate P(A ∪ B) using the formula P(A) + P(B) - P(A AND B). Assuming that the color choice and font size are independent of each other (the choice of one does not affect the choice of the other), the probability of both A and B occurring (A AND B) is simply the product of their separate probabilities: P(A) x P(B) = (1/4) x (4/5) = 1/5.
So, P(A ∪ B) = P(A) + P(B) - P(A AND B) = (1/4) + (4/5) - (1/5) = 1/4 + 16/20 - 4/20 = 1/4 + 12/20 = 5/20 + 12/20 = 17/20.
B. P(A ∪ B')
To find P(A ∪ B'), we first need to calculate P(B'). Since the probability of B is 4/5, the probability of B' (the font size is the smallest one) is the remaining fraction of 1, which is 1/5. We then apply the addition rule, which becomes P(A \∪\ B') = P(A) + P(B') - P(A AND B'), with P(A AND B') being the probability of choosing the red color and the smallest font size. Because A and B' are independent, P(A AND B') = P(A) x P(B') = (1/4) x (1/5) = 1/20.
Therefore, P(A ∪ B') = P(A) + P(B') - P(A AND B') = 1/4 + 1/5 - 1/20 = 5/20 + 4/20 - 1/20 = 8/20 or 2/5.
C. P(A' ∪ B')
To find P(A' ∪ B'), we need to determine the probabilities of A' and B' occurring separately. P(A') is the probability of not choosing the red color, which is the complement of P(A), meaning P(A') = 1 - P(A) = 3/4. P(B') as we calculated before, is 1/5. As these events are independent, P(A' AND B') = P(A') x P(B') = (3/4) x (1/5) = 3/20.
Thus, P(A' ∪ B') = P(A') + P(B') - P(A' AND B') = 3/4 + 1/5 - 3/20 = 15/20 + 4/20 - 3/20 = 16/20 or 4/5.
Find the x-intercepts of the parabola with
vertex (1,-13) and y-intercept (0.-11).
Write your answer in this form: (X1.),(X2,92).
If necessary, round to the nearest hundredth.
Enter the correct answer.
Answer:
[tex]x_1=3.55[/tex]
[tex]x_2=-1.55[/tex]
Step-by-step explanation:
we know that
If the vertex is (1,-13) and the y-intercept is (0.-11) (y-intercept above the vertex), we have a vertical parabola open upward
The equation of a vertical parabola written in vertex form is equal to
[tex]y=a(x-h)^2+k[/tex]
where
a is a coefficient
(h,k) is the vertex
substitute the given value of the vertex
[tex]y=a(x-1)^2-13[/tex]
Find the value of a
Remember that we have the y-intercept
For x=0, y=-11
substitute
[tex]-11=a(0-1)^2-13[/tex]
[tex]a=13-11\\a=2[/tex]
so
[tex]y=2(x-1)^2-13[/tex]
Find the x-intercepts
For y=0
[tex]2(x-1)^2-13=0[/tex]
[tex]2(x-1)^2=13[/tex]
[tex](x-1)^2=6.5[/tex]
[tex]x-1=\pm\sqrt{6.5}[/tex]
[tex]x=1\pm\sqrt{6.5}[/tex]
[tex]x_1=1+\sqrt{6.5}=3.55[/tex]
[tex]x_2=1-\sqrt{6.5}=-1.55[/tex]
Mrs.Rodriquez is measuring fabric for costumes. She needs 58 feet of fabric. She has 10 1/3 yards of fabric. How many more yards of fabric does she need?
Answer:
9 yards
Step-by-step explanation:
Given data:
Needed fabric = 58feet
Available fabric = 10 1/3 yards
To convert yard to feet, the yards are multiplied by 3
10 1/3 yards = 31/3 * 3 = 31 feet.
More fabric needed = 58 - 31
More fabric needed = 27 feet
More fabric needed in yards = 27/3
More fabric needed in yards = 9
Answer:
9
Step-by-step explanation:
it's nine because 1 yard has three feet and um well like yeah
Triangle ABE is similar to triangle ACD. Find y.
3.4
2.7
4.5
2.1
Answer:
Step-by-step explanation:
∆ ABE is similar to angle ACD. This means that the ratio of the length of each side of ∆ABE to the length of the corresponding side of ∆ ACD is constant. Therefore,
AB/AC = BE/CD = AE/AD
Therefore,
5/3 = (y + 3)/y
Cross multiplying, it becomes
5 × y = 3(y + 3)
5y = 3y + 9
5y - 3y = 9
2y = 9
Dividing the left hand side and the right hand side of the equation by 2, it becomes
2y/2 = 9/2
y = 4.5
Answer:
y = 4.5.
Step-by-step explanation:
Triangles ABE and ACD are similar, so their corresponding sides are in the same ratio.
AB/AC = AE / AD
Now AD = y + ED = y + 3, so:
3/5 = y / (y + 3)
5y = 3y + 9
2y = 9
y = 4.5.
The list shows the number of viewers of an online music video each day for 5 consecutive days. 5; 35; 245; 1,715; 12,005; By what factor did the number of viewers change each day to the first day to the fifth day?
Answer: 7
Step-by-step explanation:
Given : The list shows the number of viewers of an online music video each day for 5 consecutive days.
5; 35; 245; 1,715; 12,005;
In exponential growth equation : [tex]y=Ab^x[/tex] , A = initial value , b= growth factor and x = time period.
In the given table A = 5 , at x = 0
Growth factor is the common ratio between the consecutive terms.
So [tex]b=\dfrac{35}{5}=7[/tex]
and we can check that it is common between each consecutive terms is 7.
Hence, the factor by which the number of viewers change each day to the first day to the fifth day = 7
The number of viewers changed by a factor of 2401 from the first day to the fifth day.
Explanation:The number of viewers of an online music video changed each day by multiplying the previous day's viewers by a constant factor. To find this factor, we divide the viewers on the fifth day by the viewers on the first day. By doing this, we get a factor of 12005/5 = 2401.
So, the number of viewers changed by a factor of 2401 from the first day to the fifth day.
Learn more about Change in number of viewers here:https://brainly.com/question/31691834
#SPJ3