The equation 3tan²x = 3tanx solved for all real values of x is [tex]x = n\pi[/tex] or [tex]x = \dfrac{\pi + 4n\pi}{4}[/tex], where n is an integer
Solving the equation for all real values of x.
From the question, we have the following parameters that can be used in our computation:
3tan²x = 3tanx
This can be expressed as
3tan²x - 3tanx = 0
Factor out 3tanx
3tanx(tanx - 1) = 0
Expand
3tanx = 0 or tanx - 1 = 0
So, we have
tanx = 0 or tanx = 1
Take the arctan of both sides
x = tan⁻¹(0) or x = tan⁻¹(1)
Evaluate the arctan for all real values of x.
[tex]x = n\pi[/tex] or [tex]x = \dfrac{\pi + 4n\pi}{4}[/tex], where n is an integer
A bag contains 50 pieces of gum flavored cherry, grape, and watermelon.
· William will randomly pick a piece of gum.
· The probability of picking cherry is 1/5 .
· The probability of picking watermelon is 3/10 .
What is the probability William will pick a piece of grape gum?
Answer:
1/10
Step-by-step explanation:
The probability William will pick a piece of grape gum is 1/5.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
Total gums= 50
The probability of picking cherry is 1/5.
and, probability of picking watermelon is 3/10.
As, we know the probability of all vents sum upto 1.
So, P(picking a grape gum)
= 1- 1/5 - 3/10
= 10-2-3/ 10
=5/10
=0.5
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Michelle walks at a speed of 320 feet per minute her friend Diana Liz 400 yards from the shelves house approximately how many minutes will Michelle need to walk from her house to Diana's house and back
Answer:
3 mins 45 seconds
Step-by-step explanation:
According to the question, Michelle walks at a speed of 320 feet per minute her friend Diana Liz 400 yards from the shelves house approximately how many minutes will Michelle need to walk from her house to Diana's house and back
----First of all we have to work out in only a unit(since there are 2 units involved;feet and yards)
So,let's change the feet to yards
1 foot = 3 yards
X = 400 yards
X = 400 × 3
X = 1200 feet
Speed = distance/time
320 = 1200/x
X = 1200/320
X = 3.75 mins or 3 mins 45 secs
Without solving them, say whether these equations have a positive solution, a negative solution,
a zero solution, or no solution.
Positive solution= the answer is a positive number.
Negative solution= the answer is a negative number.
Zero solution= the answer is zero.
Negative solution= the variable goes away, so you can't solve it.
a. 3x=5
b. 5z+7=3
c. 7-5w=3
d. 4a=9
e. y=y+1
Answer:
a. 3x=5 Positive Solution
Reasoning: You're working with only positives
b. 5z+7=3 Negative Solution
Reasoning: If you carry the 7 over the non-coefficient numbers will be negative thus making your answer negative
c. 7-5w=3 Positive Solution
Reasoning: both the coefficients and the non coefficients will be negative if solved and thus will result in the negatives becoming positive when dividing the 5w
d. 4a=9 Positive
Reasoning: The first step would be to divide the 9 by 4 and the resulting number would be positive
e. y=y+1 Negative Solution (No solution)
Reasoning: y can never equal itself with changing. Thats like saying 0 is 1. This has no solution but based on the rules this is negative solution
The solutions to the equations are: a. Positive solution, b. Negative solution, c. Negative solution, d. Positive solution, and e. No solution.
Explanation:Let us analyze these equations one by one:
a. 3x=5: This equation involves multiplying a number by 3 to get 5. The solution here would be a positive number because 5/3 is positive.b. 5z+7=3: To find the value of 'z', we'd subtract 7 from both sides and then divide by 5. Considering that 3-7 is negative, and dividing a negative number by a positive number results in a negative answer, the solution of this equation will be negative.c. 7-5w=3: In this equation, subtracting 7 from 3 gives a negative number. Therefore, 'w' would be negative as dividing a negative number with a negative number results in a positive solution, which we can't have. Therefore, the solution of this equation will be negative.d. 4a=9: This equation involves dividing 9 by 4. The solution would be a positive number because 9/4 is positive.e. y=y+1: In this equation, when we attempt to isolate 'y', we're left with 0=1, which is not possible. Therefore, this equation has no solution.Learn more about Finding Solutions to Equations here:https://brainly.com/question/35067340
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if angle y measures 33 degrees what does angle x measure?
Answer:
<x = 147
Step-by-step explanation:
Supplementary angles is when the sum of the two angles are equal to 180
So the sum of angle x and angle y is equal to 180
y = 33
x + y = 180
x + 33 = 180
x = 180 - 33
x = 147
Answer:
x = 147°
Step-by-step explanation:
x ; y = suplementary =>
x + y = 180° } => x = 180° - 33° = 147°
y = 33°
What is a linear function f for f(-4)=2,f(6)=3
Answer:
y - 3 = (1/10)(x - 6)
Step-by-step explanation:
Note how x (the "run") increases by 10 and how y (the "rise") by 1. Thus, the slope of the line connecting point (-4, 2) with point (6, 3) is
m = rise / run = 1/10.
Using the point-slope equation of a straight line, we derive the equation of this particular line as follows:
y - 3 = (1/10)(x - 6)
Flying against the wind, an airplane travels 4560 kilometers in 6 hours. Flying with the wind, the same plane travels 3720 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answer:
The speed rate of the plane in still air is 1006.67 km/h
The speed rate of the wind is 246.67 km/h
Step-by-step explanation:
To answer the question, we let the speed of the plane in still air = x km/h
Let the speed of the wind = y km/h
Therefore,
4560/(x - y) = 6 hours and
3720/(x + y) = 3 hours
4560 = 6·x - 6·y.........(1)
3720 = 3·x + 3·y ........(2)
Multiplying equation (2) by 2 and add to (1) gives
12080 = 12·x
x = 12080/12 = [tex]1006\frac{2}{3}[/tex] km/h
Substituting the value of x in (1) gives
4560 = 6040 - 6·y
6·y = 1480
y = 1480/6 = [tex]246\frac{2}{3}[/tex]
The speed rate of the plane in still air = 1006.67 km/h
The speed rate of the wind = 246.67 km/h.
What the answer to this plz need help ASAP
Answer:
A) 9841
Step-by-step explanation:
Formula of geometric sequence:
[tex]S_n=\frac{a_1*(r^n-1)}{r-1} \\[/tex]
First, calculate the common ratio (r) of the sequence.
It can be calculated by dividing any term of the geometric sequence by the term preceding it.
[tex]r = \frac{27}{9}\\ \\r=3[/tex]
Then
[tex]Sum = \frac{1(3^9-1)}{3-1} \\\\Sum = \frac{3^9-1}{2}\\ \\Sum=\frac{19683-1}{2} \\\\Sum = \frac{19682}{2} \\\\Sum=9841[/tex]
On a beach trip lucy rents a bike from wheel by the waves where they rent bikes for $12 plus $3 per hour if lucy spent $30 how many hours(h) did she ride a bike
Answer:
6 hours
Step-by-step explanation:
Make an equation
Each hour costs $3, and there is a $12 cost regardless of the hours. We know that Lucy spent $30.
3h+12=30
Subtract 12 from both side s
3h=18
Divide both sides by 3
h=6
So, she rented it for 6 hours
Triangle ABC goes through a series of three transformations, resulting in triangle A^ prime B^ prime C^ prime . The three transformations are listed below. Rotation 180clockwise about the origin • a reflection over the x-axis • reflection over the y- axis Triangle ABC has vertex A located at (2, - 3) . Using the coordinates of this point, explain how the three transformations map vertex A onto vertex A^ prime .
Answer:
After the first rotation
A^ prime = (- 2, 3)
After the next two transformations, A^ = A = (2. -3)
Step-by-step explanation:
Here we have that
Rotation of 180 °clockwise about the origin will result in the inversion of the vertex point A such that the coordinates will be (- 2, 3)
Reflection over the x axis and a reflection over the y axis combined will revert the triangle back to its initial position
Therefore after the first rotation
A^ prime = (- 2, 3)
After the next two transformations, A^ = A = (2. -3).
Professor York randomly surveyed 240 students at Oxnard University and found that 150 of the students surveyed watch more than 10 hours of television weekly. How many additional students would Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence?
Answer:
1727 students
Step-by-step explanation:
Here we have the formula for sample size given as
[tex]n = \frac{p(1-p)z^2}{ME^2}[/tex]
Where:
p = Mean
ME = Margin of error = 3
z = z score
Therefore, we have
p = 150/240 = 0.625
z at 99 % = 2.575
ME = [tex]\pm[/tex]3%
Therefore [tex]n = \frac{0.625(1-0.625)2.575^2}{0.03^2} = 1726.73[/tex]
The number of students Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence = 1727 students.
Find the angle measure in degrees
Answer:
82°
Step-by-step explanation:
By inscribed angle theorem:
[tex]m\angle QRP = \frac{1}{2} \times 164 \degree \\ \\ \huge \red{ \boxed{\therefore \: m\angle QRP =82 \degree}}[/tex]
20 points if you help me on this proublem
Answer:
1) f(x) = x/8 - 7
2) f(x) = 1 - x/3
3) f(x) = 20 - 0.25x
4) f(x) = x + 7
Step-by-step explanation:
f^-1 = 8(x + 7)
x + 7 = y/8
x = y/8 - 7
f(x) = x/8 - 7
f^-1 = -3(x - 1)
y/-3 = x - 1
x = 1 - y/3
f(x) = 1 - x/3
f^-1 = 4(20 - x)
y/4 = 20 - x
x = 20 - y/4
f(x) = 20 - x/4
f(x) = 20 - 0.25x
f^-1 = x - 7
y = x - 7
x = y + 7
f(x) = x + 7
What is the range of the function represented by the graph?
Answer:
y ≥ 1
Step-by-step explanation:
Hence, range of given parabola is y[tex]\geq 1[/tex]
What is parabola ?
A parabola is a curve in which all points are at the same distance from two fixed points: the focus and the origin. a constant straight line (the directrix )
How to solve?
Generic equation of parabola y=p. (x−h[tex])^{2}[/tex]+k where (h,k) denotes the vertex. where parabola has range y[tex]\geq 0[/tex]. but as this curve is shifted at 0,1 hence range becomes y[tex]\geq 1[/tex]
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Valentina va de compras al mall con $50.000. Gasta 3/5 de esa cantidad en un buzo y la mitad del resto en una falda.¿cuanto dinero le queda a valentina?
Answer:
The amount left with Valentina is $10,000.
Step-by-step explanation:
The question is:
Valentina goes shopping at the mall with $50,000. She spends 3/5 of that amount on a diver and half the rest on a skirt. How much money does Valentina have left?
The original amount Valentina had was, P = $50,000.
Compute the amount spent on a diver as follows:
D = [tex]\frac{3}{5}th[/tex] of $50,000
[tex]=\frac{3}{5}\times 50000\\=30000[/tex]
The amount spent on a diver was, D = $30,000.
Amount left:
A = P - D
= 50000 - 30000
= 20000
Compute the amount spent on a skirt as follows:
S = [tex]\frac{1}{2}[/tex] of $20,000
[tex]=\frac{1}{2}\times 20000\\=10000[/tex]
Amount left:
A₁ = A - S
= 20000 - 10000
= 10000
Thus, the amount left with Valentina is $10,000.
As a brickmason's apprentice, you need to move the correct number bricks. The mason needs enough bricks to lay the next 4 rows. Each course is 24 bricks long. How many bricks do you need to move to complete the four rows?
Answer:
96 bricks
Step-by-step explanation:
In this question, we are asked to calculate the number of bricks which are needed by a mason given the number of bricks needed to complete each of the course.
From the question, we can identify that we have 4 rows to be filled with each of the rows being 24 bricks long.
now , to calculate the number of bricks needed to be moved by the mason, our work is pretty straightforward. what we simply need to do is to multiply the number of rows by the number of bricks per course.
According to this question specifically, this is equal to a value of 4 * 24 = 96 bricks
What is the y-intercept of y=3x-2
Answer:
This formula is in slope-intercept form. 3 is the slope (positive slope) and -2 is the y-intercept.
Hi there!
Your answer is:
The slope is 3 and the y-intercept is 2 or (0, 2).
Have a good day
~ Mqddie
Claudio bought tickets to a music festival that 225,000 people were expected to attend.what is the scientific notation?
Answer:
The number of people that attended in scientific notation is 2.25 x 10^5.
Step-by-step explanation:
Is 3 5/2 an acceptable answer?
Please explain your answer.
thx
yes, if the question is asking for a mixed number.
Answer:
5 1/2 would be a better answer or 5.5 in decimal form
hope this helps :)
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second. y=-16x^2+128x+136
Answer: The rocket will reach its max after 4 seconds
Step-by-step explanation:
Hi, to find the maximum height, we have to set the first derivative of the equation equal to zero.
y=-16x^2+128x+136
0 = (2)-16x +128
0= -32x+128
Solving for x:
32x = 128
x = 128/32
x = 4 seconds
The rocket will reach its max after 4 seconds
Feel free to ask for more if needed or if you did not understand something.
plz help ive been stuck on this question for so long
Multiply each exponent inside the parentheses by the exponent on the outside:
8^(-5 x -4) / 2^(-2 x -4)
8^20 / 2^8
The answer is C
Math math math math mathematics maths
Answer:
Answer is 3
Step-by-step explanation:
Use the Law of Sines to complete an expression that represents the angle measure x.
Answer:
sine (x) / 14.9 = sine (71) / 25.5
sine (x) = 14.9 * sine (71) / 25.5
sine (x) = 14.088248 / 25.5
sine (x) = 0.5524803137
Angle (x) = arc sine(0.5524803137)
Angle (x) = 33.537 degrees
Step-by-step explanation:
The expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].
What is the law of sine?The law of sine is nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).
It can be given as,
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
Here (A,B,C) are the angle of the triangle and (a,b,c) are the sides of that triangle.
For the given problem it can also be given as,
[tex]x^o=\sin^{-1}\left(\dfrac{a\sin B}{c}\right)[/tex]
Put the values,
[tex]x^o=\sin^{-1}\left(\dfrac{(14.9)\sin (71)}{25.5}\right)\\x^o=\sin^{-1}\left(0.5523\right)\\x^o=33.54^o[/tex]
Thus, the expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].
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Sarah bought 3 1/2 pints of blueberries to make jelly. She ate 3/4 of a pint of berries on her way home. How many pints of berries does she have left to make jelly?
Answer:
11/4 or 2.75 pints
Step-by-step explanation:
We want to find the difference between the original amount of blueberries and the amount she ate
original amount-amount ate
3 1/2 -3/4
To subtract, we need common denominators
The common denominator of 2 and 4 is 4
3 1/2=7/2
Multiply by 2/2 to get a common denominator of 4
7/2*2/2=14/4
Now, we have common denominators and can subtract
14/4-3/4
Subtract the numerators, and leave the denominators as 4
11/4 =2.75
She has 11/4 or 2.75 pints left
A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi. Find the probability that the sample mean comprehensive strength exceeds 4985 psi.
Answer:
Probability that the sample mean comprehensive strength exceeds 4985 psi is 0.99999.
Step-by-step explanation:
We are given that a random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi.
Let [tex]\bar X[/tex] = sample mean comprehensive strength
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean comprehensive strength = 5500 psi
[tex]\sigma[/tex] = standard deviation = 100 psi
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the sample mean comprehensive strength exceeds 4985 psi is given by = P([tex]\bar X[/tex] > 4985 psi)
P([tex]\bar X[/tex] > 4985 psi) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{4985-5500}{\frac{100}{\sqrt{9} } }[/tex] ) = P(Z > -15.45) = P(Z < 15.45)
= 0.99999
Since in the z table the highest critical value of x for which a probability area is given is x = 4.40 which is 0.99999, so we assume that our required probability will be equal to 0.99999.
In the city of Manhattan, it takes about 13 Starbucks to serve every 100,000 people. As of 2019, Manhattan has
approximately 1,629,000 people. If Manhattan is approximately 23 square miles, what is the density of Starbucks per
square mile in the city?
___Starbucks per square mile
Answer:
9.207
Step-by-step explanation:
To get the amount of starbucks for the population we can do
[tex]\frac{13 * 1629000}{100000}[/tex]
which gives us 211.77 total Starbucks in 23 miles.
To get starbucks per mile, we divide this number by 23.
This gives us 9.207
If two equations in a linear system have the same slope and the same -intercepts, the system will have:'
a ; infinite solutions
b ; no solution
c ; one solution
d ; two solutions
Answer:
The answer to your question is a. Infinite solution
Step-by-step explanation:
When two lines have the same slope and the same intercepts, this means that these lines are the same so they system of equations will have infinite solutions.
If the lines do not cross, there will be no solution.
If the lines cross in one point there will be one solution
If there are a quadratic and a linear function they will cross in two points.
Seutas tali yang panjangnya 121 meter dipotong menjadi beberapa bagian sehingga dibuat deret geometri. Jika jumlah potongan terpendek 4 meter dan jumlah potongan terpanjang 108 meter, maka jumlah potongan tali yang terbentuk adalah …… .. 14
Answer:
orehwfociuxsh8tq23rjwfhdfyvbndm
Step-by-step explanation:
Biologists have discovered that the shoulder height h (in centimeters) of a male Asian elephant can be modeled by h = 62.5 3 t + 75.8, where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 300 centimeters.
Final answer:
To determine the age of an elephant with a shoulder height of 300 centimeters, the given formula h = 62.5t + 75.8 is used. Subtracting 75.8 from 300 and then dividing by 62.5 yields the elephant's age as approximately 3.59 years.
Explanation:
The student is asking to determine the age of an Asian elephant based on a mathematical model for its shoulder height. Given the model h = 62.5t + 75.8, and knowing the elephant's shoulder height is 300 centimeters, we can set up the equation as follows:
300 = 62.5t + 75.8
To solve for t, we first subtract 75.8 from both sides:
224.2 = 62.5t
Then, we divide both sides by 62.5:
t = 224.2 / 62.5
t = 3.5872
Therefore, the age of the elephant is approximately 3.59 years.
The elephant is about 46.16 years old.
To find the age of the elephant given its shoulder height, we need to solve the equation for t . The equation given is:
[tex]h = 62.5\sqrt[3]{t} + 75.8[/tex]
Given h = 300 centimeters, we substitute h into the equation and solve for t :
[tex]300 = 62.5\sqrt[3]{t} + 75.8[/tex]
First, isolate the cube root term:
[tex]300 - 75.8 = 62.5\sqrt[3]{t} \\\\ 224.2 = 62.5\sqrt[3]{t}[/tex]
Next, divide both sides by 62.5:
[tex]\sqrt[3]{t} = \frac{224.2}{62.5} \\\\ \sqrt[3]{t} \approx 3.5872[/tex]
Now, to solve for t , cube both sides:
[tex]t \approx (3.5872)^3 \\\\ t \approx 46.16[/tex]
So, the elephant is about 46.16 years old.
The complete question is:
Biologists have discovered that the shoulder height (in centimeters) of a male Asian elephant can be modeled by [tex]h = 62.5\sqrt[3]{t} + 75.8[/tex], where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 300 centimeters. Round your answer to the nearest tenth.
The elephant is about ____ years old.
A lighthouse is set 10 meters back from the edge of the shoreline, and it's beacon is 52 meters above sea level. Lucy can see the beacon from her ship, and the of elevation is 18 degrees. Her eyes are 12 meters above sea level. How far is the ship from the shoreline to the nearest meter?
Answer:
The distance of the ship from the shoreline is 113 metres.
Step-by-step explanation:
Please kindly check the attached files for explanation
Answer:
The distance of the ship to the shoreline is 113 meters
Step-by-step explanation:
Here we have the following information
Location of lighthouse = 10 m back from the edge of the shoreline
Height of beacon above sea level = 52 m
Level of the eyes of Lucy above sea level = 12 m
Angle of elevation of the beacon from Lucy = 18°
Therefore, the beacon, the elevation of the eyes of Lucy and the base of the lighthouse at the same elevation with Lucy form a right triangle with opposite side to angle = 52 m and angle = 18 °
Therefore, from
[tex]Tan\theta =\frac{sin\theta }{cos\theta } = \frac{Opposite \, side \, to\, angle}{Adjacent\, side \, to\, angle}[/tex]
We have
[tex]Tan18 =\frac{52-12}{Adjacent } = \frac{40}{Adjacent}[/tex]
0.325 = [tex]\frac{40}{Adjacent}[/tex]
Where the adjacent side is the distance of the ship from the lighthouse
Adjacent side = 40/0.325 = 123.107 meters
We recall that the lighthouse is 10 m back from the edge of the shoreline, therefore the ship is 123.107 - 10 or 113.107 meters from the shore line which is 113 meters to the nearest meter.
Which is 23,578,000 written in scientific
notation?
Answer:
[tex]23,578,000 = 2.3578 \times {10}^{7} \\ [/tex]