(1 – 3cosx – 4cos^2x) / sin^2x =
(1+cos x)(1-4cos x) /(1-cos^2 x) =
(1+cos x)(1-4cos x) /[(1-cos x)(1+cos x)] =
(1-4cos x) /(1-cos x)
Factor:
1+cos(x))(1 – 4cos(x)) / (1 + cos(x))(1 – cos(x)) =
RHSCancel:(1 – 4cos(x)) / (1 – cos(x)) = RHSQED
use differentials to estimate the amount of paint needed to apply a coat of paint 0.06 cm thick to a hemispherical dome with diameter 40 m. (round your answer to two decimal places.)
The amount of paint needed to apply a coat of paint is 1.00 m³.
Given:
a coat of paint 0.06 cm thick to a hemispherical dome with diameter 40 m.
we are asked to estimate the amount of paint needed to apply a coat of paint.
The amounts
Volume of a hemisphere, V = (2/3)πr³
r = 40/2
= 20 m
dr = 0.04 cm = 0.0004 m
dV≈2πr²dr
= 2π(20)²(0.0004) m³
= 1.0048 m³
rounding it of to two decimal places.
= 1.00 m³
Hence the amount of paint needed is 1.00 m³
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Help me please!! i’ll give points and brainliest if you give a simple explanation and answer!
Step-by-step explanation:
1[tex] {10}^{ - 8} = \frac{1}{10^{8} } [/tex]
[tex]7 \times \frac{1}{ {10}^{8} } = \frac{7}{ {10}^{8} } [/tex]
2)
[tex]6 \times {10}^{ - 8} = 6 \times \frac{1}{ {10}^{8} } = \frac{6}{ {10}^{8} } [/tex]
a bag contains 2 coins, one fair and the other with 2 heads. you pick 1 coin at random and flip it. what is the probability that you picked the fair coin given that the outcome of the toss was heads?
The probability that you picked the fair coin given that the outcome of the toss was heads is 1/3.
There is a one in two chance of drawing the fair coin. The chances of flipping heads again are 1 in 2. As a result, there is a 1 in 4 chance that the coin will land on heads.
There is a one in two chance of drawing the trick coin. The probability of flipping heads is then 2 to 1. As a result, there is a 2 in 4 chance that the coin will land on heads.
When each is multiplied by four, the resulting integers are
fair: 1 and trick: 2
and overall results: 3. (fair and tails is not counted)
The likelihood of a fair coin is one in three.
The likelihood that the chosen coin will show heads and be the fair coin is 33.333%.
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Aline'sslopeis5,andits
y -intercept
is
3. What
isitsequationin
slope -intercept
form?
The equation of the line in slope-intercept form is: y = 5x + 3.
What is the Equation of a Line in Slope-intercept Form?If the value of the slope of a line, m, is known, and the value of its y-intercept, b, is known, the equation of the line in slope-intercept form would be written as:
y = mx + b.
Given the following:
Slope (m) of the line (m) = 5Y-intercept of the line (b) = 3To write the equation of the line in slope-intercept form, substitute m = 5 and b = 3:
y = 5x + 3
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Question:
A line's slope is 5, and its y -intercept is 3. What is its equation in slope-intercept form?
Cameron runs 2000 meters in 8 minutes. How many meters can Cameron run in one minute?
Answer: 250 meters
Step-by-step explanation: Find the unit rate. 2000 divided by 8 will get you a unit rate of 250 meters per minute.
This is an arithmetic sequence.
8, 7.4, 6.8, 6.2, 5.6, …
Which function describes the sequence?
A. f(x) = 0.6x + 8
B. f(x) = 0.6x + 8.6
C. f(x) = −0.6x + 8
D. f(x) = −0.6x + 8.6
The function which describes the arithmetic sequence is f(x) = −0.6x + 8.6.
The correct answer option is option D
Which function describes the sequence?
Given the sequence:
8, 7.4, 6.8, 6.2, 5.6, …
Check all the options
Where,
x = number of term
A. f(x) = 0.6x + 8
When x = 1
f(x) = 0.6x + 8
= 0.6(1) + 8
= 0.6 + 8
= 8.6
B. f(x) = 0.6x + 8.6
When x = 1
= 0.6(1) + 8.6
= 0.6 + 8.6
= 9.2
C. f(x) = −0.6x + 8
When x = 1
= -0.6(1) + 8
= 0.6 + 8
= 8.6
D. f(x) = −0.6x + 8.6
When x = 1
= -0.6(1) + 8.6
= -0.6 + 8.6
= 8
Hence, f(x) = −0.6x + 8.6 is the function which describes the sequence.
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you guess that lebron james would score 35 points during the game. he actually scored 28. find your percent error.
The error Percentage is 20%
What is Percentage?
A percentage is a component of a whole stated as a number between 0 and 100 rather than as a fraction. All of anything is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the fraction of the entire by the whole itself and multiply by 100.
Solution:
We gussed that LeBron James would score 35 points, but he only scored 28 points
So, the difference was of 7 points (35-28)
Error Percentage = 7/35 * 100
Error Percentage = 1/5 *100
Error Percentage = 20%
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the numbers 1447, 1005, and 1231 have something in common: each is a 4-digit number beginning with 1 that has exactly two identical digits. how many such numbers are there?
If each is a 4-digit number beginning with 1 that has exactly two identical digits , then there are 432 such numbers .
In the question ,
Suppose that the two identical digits are both 1.
and since the thousands digit must be 1, only one of the other three digits can be 1. This means that the possible forms for the required numbers are
11xy , 1x1y , 1xy1 ,
Because the number must have exactly two identical digits, x ≠ y, x ≠ 1, and y ≠ 1.
Hence, Of this form there are 3 × 9 × 8 = 216 numbers .
Now suppose that two identical digits are not 1 , we will have the following possibilities:
1xxy , 1xyx , 1yxx
Again, x ≠ y , x ≠ 1 , and y ≠ 1 .
Of this form there are 3 × 9 × 8 = 216 numbers .
So , the total numbers are 216 + 216 = 432 .
Therefore , the total numbers are 432 .
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Morgan has 98 baseball cards in his collection, which is twelve less than the product of 5 and the number of cards Tyler has.
Answer: Tyler has 22 cards
Step-by-step explanation:
To begin, we know that Morgan has 12 less than 5x Tyler's cards, so...
12+98=110
Now that we had 110, we then read that it is the PRODUCT of 5 and the number that Tyler has, so we will show that algebraically.
110=5x
Now, divide 110 by 5 to find X.
110/5=22
Tyler has 22 cards.
A student is taking a multiple-choice test in which each question has four possible answers. She knows the answers to 5 of the questions, can narrow the choices to 2 in 3 cases, and does not know anything about 2 of the questions. What is the probability that she will correctly answer A) 10, b) 9, c) 8 d) 7, e) 6, and f) 5 questions?
Do not need to answer every part if they are worked the EXACT same way.
x=3yz/4 solve for z.
Answer:
[tex]z = \frac{4x}{3y}[/tex]
Step-by-step explanation:
[tex]x = \frac{3yz}{4}[/tex]
[tex]3zy = 4x[/tex]
[tex]z = \frac{4x}{3y}[/tex]
Answer:
z = (4x)/(3y)
Step-by-step explanation:
Given equation,
→ x = (3yz)/4
Now the value of z will be,
→ x = (3yz)/4
→ (3yz)/4 = x
→ 3yz = x × 4
→ z × 3y = 4x
→ [ z = 4x/3y ]
Hence, value of z is 4x/3y.
determine the area under the standard normal curve that lies to the right of the z-score 0.11 and to the left of the z-score 0.41.
The requried area under the standard normal curve that lies to the right of z = 0.11 and to the left of z = 0.41 is approximately 0.1153.
To find the area under the standard normal curve that lies to the right of the z-score 0.11 and to the left of the z-score 0.41, we can use a standard normal table or a statistical calculator.
The area to the right of z = 0.11 can be found by subtracting the cumulative area to the left of z = 0.11 from 1.
The area to the left of z = 0.41 can be directly read from the standard normal table.
Using a standard normal table or a calculator, we find:
The area to the left of z = 0.11 is approximately 0.5438.
The area to the left of z = 0.41 is approximately 0.6591.
Now, let's find the area between these two z-scores:
Area = (Area to the left of z = 0.41) - (Area to the left of z = 0.11)
Area = 0.6591 - 0.5438
Area ≈ 0.1153
So, the area under the standard normal curve that lies to the right of z = 0.11 and to the left of z = 0.41 is approximately 0.1153.
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520 cookies if 3/4 were eaten how many are left
Answer: 130 cookies are left
Step-by-step explanation:
3/4 of 520 = 390
520 - 390 = 130
Answer:
130 cookies are left.
Step-by-step explanation:
1. Turn 3/4 into a decimal
3 ÷ 4 = 0.75
2. Multiply
0.75 x 520 = 390
3. Subtract
520 - 390 = 130
Solution:
130 cookies are left.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 5 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Your parents limit your
phone use to 18 hours every week. You need
to split that between hours spent on the phone
with your friends and hours spent using the
internet. Your parents count one hour on line
as 1/2 hour of phone time since some of your
time is spent doing homework. An algebraic
model is x + 1/2y
18 where x is hours spent
on the phone and y is the hours spent on line.
2
=
Step-by-step explanation:
x + 1/2y = 18
2x + y = 36
x = 36 - y
18 = 36 - y + 1/2y
18 = 36 - 1/2y
36 - 18 = 1/2y
18 = 1/2y
y = 36
x = 18 - 1/2(36)
x = 18 - 18
x = 0
Therefore, you can spend 0 hours on the phone and 36 hours on the internet.
light shines from the top of a pole 30 ft high. a ball is dropped from the same height from a point 20 ft away from the light. how fast is the shadow of the ball moving along the ground 1 sec later? (assume the ball falls a distance s
The shadow of the ball moving over the ground at 150 feet per second after 1 second.
How can I determine the shadow of the ball's speed?
Assuming the ball drops the distance indicated by this sentence:
S = 16t²
Additionally, the height (h) of the ball's shadow one second later is provided by
h = 30 - S
The term for the shadow of the ball would then be as follows:
OX/30 = (20 + XQ)/30 = XQ/h
30XQ = 20h + hXQ
20h = 30XQ - hXQ
20h = (30 - h)XQ
XQ = 20h/(30 - h)
Substituting the value of h, we have:
XQ = 20(30 - S)/(30 - 30 - S)
Substituting the value of S, we have:
XQ = 20(30 - 16t²)/(30 - 30 - 16t²)
XQ = 20(30 - 16t²)/16t²
XQ = (600 - 320t²)/16t²
XQ = 600/16t² - 320t²/16t²
XQ = 600/16t² - 20
Differentiating with respect to t, we have:
d(XQ)/dt = 600/16t² - 20
d(XQ)/dt = 600 (-64t/(16t²)²)
d(XQ)/dt = 600 (-64t/256t⁴)
d(XQ)/dt = 600 (-0.5/2t³)
d(XQ)/dt = -300/2t³
Then,
At t = 1, we have:
Speed = 300/2(1)
Speed = 150 ft/s.
That is,
After one second the ball's shadow was travelling over the ground at a speed of 150 feet per second.
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A researcher develops a regression equation to predict first-year college grades (Y) from high school GPA (X): Y = 1.48 + .53X + e. What is the predicted first-year college GPA for someone with a high school GPA of 3.1?
3.6
1.6
3.1
4.1
The resulting regression was predicted GPA is 3.1 Predict the outcome of one variable from the outcome of a second variable.
The variable we are predicting is called the reference variable and is denoted as Y. The variable on which the prediction is based is called the predictor and is denoted as X. The magnitude of the correlation coefficient indicates the strength of the association. A prediction is a statement intended to tell you something about the future.
Predicted grades are qualifying grades that an applicant's school or college is expected to achieve under favorable circumstances. These predicted grades are used by colleges as part of the admissions process to help understand an applicant's potential. The expected result of an experiment is derived from a hypothesis or theory. This is a guess at the possible outcome of the scenario.
GPA= 3.1+3.6+1.6+3.1+4.1/ 5= 15.5/5 = 3.1
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in linear programming, a solution that does not simultaneously satisfy all constraints is called an part 2 a. intermediate solution. b. impossible solution. c. infeasible solution. d. illogical solution.
A solution that does not simultaneously satisfy all constraints is called an infeasible solution.
Option (C) is correct.
What is linear programming?
Linear programming, also known as linear optimization, is a method for achieving the best result in a mathematical model with requirements represented by linear relationships. Linear programming is a special case of mathematical programming.
In linear programming, a solution that does not simultaneously satisfy all constraints is called an infeasible solution.
In some cases, there is no feasible solution area, i.e., there are no points that satisfy all constraints of the problem. An infeasible LP problem with two decision variables can be identified through its graph. For example, let us consider the following linear programming problem.
Minimize z = 200x1 + 300x2
subject to
2x1 + 3x2 ≥ 1200
x1 + x2 ≤ 400
2x1 + 1.5x2 ≥ 900
x1, x2 ≥ 0
The region located on the right of PQR includes all solutions, which satisfy the first and the third constraints. The region located on the left of ST includes all solutions, which satisfy the second constraint. Thus, the problem is infeasible because there is no set of points that satisfies all three constraints.
Hence, a solution that does not simultaneously satisfy all constraints is called an infeasible solution.
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A line passes through the origin and (5, 3). Identify two additional points on this line.
Answer:
(10,6) and (-5, -3)
Step-by-step explanation:
The slope of the line is given by rise/run between (0,0) and (5,3)
Rise = y2 - y1 = 3 - 0 = 3
Run = x2 - x1 = 5 - 0 = 5
Slope m 3/5
Slope intercept form of a line is
y = mx + b
where m is the slope and b is the y-intercept
Since the line passes through (0,0) the y-intercept is 0
So we get
[tex]y = \dfrac{3}{5}x + 0 \\\\or\\\\y = \dfrac{3}{5}x[/tex]
This means for any x value, the corresponding y value should be 3/5th of that x value
Only the first and third choices have this requirement fulfilled
Ellie runs 2700 meters in 12 minutes. How many meters can Ellie run in one minute?
Answer: 225
Step-by-step explanation:
an online gardening magazine wants to understand why its subscriber numbers have been increasing. what kind of reports can a data analyst provide to help answer that questio
The analyst should provide a report addressing the following
Analyzing customer buying behaviorsAnalyzing consumer preferences using artificial intelligenceAnalyzing the number of customers by calculating daily foot trafficAnalyzing social media engagementA sale’s affect on subscription purchases is an example of customer buying behavior analysis.
Data analysis is the process of modifying, processing, and cleaning raw data in order to obtain useful, pertinent information that supports commercial decision-making. The process offers helpful insights and statistics, frequently presented in charts, graphics, tables, and graphs, which lessen the risks associated with decision-making.
Every time we make a decision in our daily lives, we can see a basic example of data analysis by assessing what has happened in the past or what will happen if we take that action. In its simplest form, this process involves looking at the past or future and making a choice based on that analysis.
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emilio drive 450 miles on 18 gallons of gas. how far can he travel on one gallon
Answer:
25
Step-by-step explanation:
450 divided by 18 is 25
Answer: 25 miles
Step-by-step explanation:
450/18 = 25
25 miles with 1 gallon of gas
an economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. these functions are r(x) = -x^2 + 10x and c(x) = 4x+5, respectively
The average profit is positive if the number of snowboards is less than 67418 .
Given:
An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = (Px)/x, where P(x) is the profit function.
The profit is P ( x ) = R ( x ) - C ( x )
= -x^2 + 10x - ( 4x + 5 )
= -x^2 + 10x - 4x + 5
= -x^2 + 6x + 5
Then AP( x ) = ( P( x )) / x
= -x^2 + 6x + 5 / x > 0
As x > 0 then the sign of AP(x) depends on numerator only.
-x^2 + 6x + 5 > 0
D = 36 + 20
= 56
x = 6.7417
Therefore AP(x) > 0 if 0 < x < 6.7417
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Full question:
An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = P(x)/x, where P(x) is the profit function. Determine the production levels that make AP(x) > 0.
I have $270 and 10¢ but I need $395 and 44¢, how much more money do I need?
F
D
140°
120°
C
?
B
Thank you
Determine the equation of the circle with center (-1,-2)(−1,−2) containing the point (0,6)
The equation of the circle with center (−1,−2) containing the point (0,6).
(x + 1)^2 + (y + 2)^2 = 65
How to determine the equation of the circle?
Remember that the equation of a circle with radius R and center (a, b) is written as:
(x - a)^2 + (y - b)^2 = R^2
Here we know that the center of the circle is (-1, -2), then our equation is something like:
(x + 1)^2 + (y + 2)^2 = R^2
We know that our circle contains the point (0, 6), replacing these values in the equation above we get:
(0 + 1)^2 + (6 + 2)^2 = R^2
1 + 8^2 = R^2
65 = R^2
Then the circle equation is:
(x + 1)^2 + (y + 2)^2 = 65
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Find the complex roots of the graph to the right.
x = 1+i or x = 1-i are the complex roots of the graph
How to find the complex roots of a graph?
Below are the steps for determining the complex roots of a graph or curve:
1. Draw a vertical line passing through the vertex of the parabola or curve
2. The value of x where the line intersects the x-axis gives the real part of the root
3. Draw a horizontal line of height twice the height of the vertex from the x-axis
4. Draw a vertical line from this point of intersection to intersect the x-axis
5. The distance of this point from the real part of the root gives you the imaginary part of the root
(Check the attached image for the labeling)
From the image attached:
Real part of the root: a = 1
Imaginary part of the root: b = 1
Remember: complex root is of the form x = a±bi
Therefore, the complex roots of the graph are x = 1+i or x = 1-i
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Ashley, sending to her directly with the number of hours she worked. Suppose that she works seven hours yesterday and earned $84 if she earned 60 today how many hours is she work today?
Answer:
5 hours
Step-by-step explanation:
To figure this out we will do the total she earned yesterday divided by the hours she worked. So, 84/7=12. So know we know how much she earns in an hour, $12. So if she is earn $60 today then we should do 60/12 to figure out how many hours she worked. 60/12=5. So she worked 5 hours.
I hope this helps!!!
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Select a function f whose zeroes are 0,-3,2 and -4
The family of all least polynomials with roots at - 4, - 3, 0, 2 is represented by the polynomial y = a · (x + 4) · (x + 3) · x · (x - 2), where a is the lead coefficient.
What is the function that contains a given set of zeros?
Herein we must determine the family of all least polynomials whose roots must be the real numbers - 4, -3, 0, 2. Polynomials are algebraic expressions, whose factor form is described below:
y = a · Π (x - rₙ), for n = {1, 2, 3, 4, ..., m - 1, m}
Where:
a - Lead coefficient (a real number).rₙ - n-th root of the polynomial.m - Grade of the polynomial.In accordance with all these assumptions and definition, the function is defined below:
y = a · (x + 4) · (x + 3) · x · (x - 2)
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a quadratic function can be used to model the height, in feet, of an object above the ground in terms of the time, in seconds, after the object was launched. according to the model, an object was launched into the air from a height of o feet and reached its maximum height of 25 feet 1.25 seconds after it was launched. based on the model, what was the height, in feet. of the object 1.00 seconds after it was launched?
The height of the object after 1.00 seconds launched is 24 feet.
Quadratic FunctionQuadratic function is a function where the maximum power of x variable is 2. Simply you can write quadratic function as:
y = ax^2 + bx + c
y is height in feet and x is time in second.
Known 2 conditions from the question:
The object will reach maximum height of 25 feet after 1.25 second launched from ground.And also, just logic that if the object is launch in 0 second will reach 0 feet.From second condition (0 feet in 0 second), we can substitute 0 both in y and y:
y = ax^2 + bx + c
0 = a(0)^2 + b(0) + c
0 = 0 + 0 + c
0 = c
And this, we know that the constant (c) of the function is 0.
Just substitute c with 0 in previous function.
y = ax^2 + bx + c
y = ax^2 + bx + 0
y = ax^2 + bx
From first condition (25 feet in 1.25 seconds), we can substitute x with 1.25 and y with 25:
y = ax^2 + bx
25 = a(1.25)^2 + b(1.25)
25 = 1.56625a + 1.25b
Maximum/minimum point of quadratic function can be found with dy/dx = 0, dy/dx is differential:
y = ax^2 + bx
dy/dx = 2ax + b
0 = 2ax + b
0 = 2a(1.25) + b
0 = 2.5a + b
-2.5a = b
After we know the ratio a and b, we can substitute b with -2.5a in previous equation:
25 = 1.5625a + 1.25b
25 = 1.5625a + 1.25(-2.5a)
25 = 1.5625a - 3.125a
25 = -1.5625a
15/-1.5635 = a
a = 15/-1.5625
a = 16
We got a = 16. Then we just substitute it in a b ratio equation:
b = -2.5a
b = -2.5(-16)
b = 40
After we know a, b, c, just substitute that three numbers in the function:
y = ax^2 + bx + c
y = -16x^2 + 40x
So, the function can be used in launching of the object is y = -16x^2 + 40x.
Where is the object in 1.00 seconds after launched? Just substitute x with 1.
y = -16x^2 + 40x
y = -16(1)^2 + 40(1)
y = -16 + 40
y = 24 feet
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Write an equation of the line containing the point (2,5) and perpendicular to the line 3x - 2y = 5.
Answer:
y = (-2/3)x + (19/3)
Step-by-step explanation:
3x - 2y = 5
-2y + 3x = 5
-3x -3x
-------------------------
-2y = -3x + 5
-2 -2 -2
---------------------
3 5
y = -------x - -------
2 2
-2
Perpendicular: -------- x
3
-2
(2, 5); m = --------
x₁ y₁ 3
y - y₁ = m(x - x₁)
y - 5 = (-2/3)(x - 2)
y - 5 = (-2/3)x + (4/3)
+5 +5
--------------------------------
y = (-2/3)x + (19/3)
I hope this helps!