The graph represents a function with the form f(x) =asin(bx + c)=Whn10y8-4-O2-X-70-27 -57-47-1-27-23 33qiy27 14:57 2 1 713B-2 4မIV-6+-8+-10+
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The standard sine function is given by:
[tex]y=a\sin (bx+c)[/tex]Where:
Amplitude = 2a
Period = 2π/b
Horizontal shift = c
In this case, we have:
- Maximum of 6 and minimum of negative 6, hence the amplitude is 12, this is
[tex]\begin{gathered} 2a=12 \\ \frac{2a}{2}=\frac{12}{2} \\ a=6 \end{gathered}[/tex]- The period is 2π/3, therefore:
[tex]\begin{gathered} \frac{2\pi}{3}=\frac{2\pi}{b} \\ b\cdot2\pi=3\cdot2\pi \\ b\cdot\frac{2\pi}{2\pi}=3\cdot\frac{2\pi}{2\pi} \\ b=3 \end{gathered}[/tex]- The graph passes through the y-axis at (0,2), which is 1/3 of the maximum. Considering the shift, we have
[tex]c=\pi[/tex]Answer:
a = 6, b = 3, c = π
Related Questions
Mrs. Griese's business class has 107 students, classified by academic year and gender, as illustrated inthe following table. Mrs. Griese randomly chooses one student to collect yesterday's work. What isthe probability that she selects a female, given that she chooses randomly from only the juniors?Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
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Solution:
From the table,
Total students that are juniors = 11 + 8 = 19
Female students that are juniors = 8
The probability that she selects a female, given that she chooses randomly from only the juniors = 8/19
The answer is 8/19
Write an absolute value inequality that represents all real numbers x that are at most 3 units away from 6
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We need to create an inequality that represents the interval that goes from 3 units to the left of 6 and 3 units to the right of 6. This means that the interval will go from:
[tex]\begin{gathered} 6-3=3 \\ 6+3=9 \end{gathered}[/tex]The absolute value is an operator that returns the value of a number without its sign. With this in mind:
[tex]|x-6|\text{ <3 }[/tex]A rectangular room is 1.7 times as long as it is wide, and its perimeter is 27 meters. Find the dimension of the room. Round answers to 2 decimal places.
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Step-by-step explanation:
The perimeter of a rectangle is given as
P = 2( Length + width)
Let the length be l
let the width be w
The room is 1.7times as along as its wide
Mathematically
The length of the room is 1.7 times its wide
L = 1.7 * w
l = 1.7w
The perimeter of the room = 27 meters
P = 2(l + w)
27 = 2(1.7w + w)
27 =2(2.7w)
27 = 5.4w
Isolate w by dividing through by 5.4
27/5.4 = 5.4w/5.4
w = 5 meters
Lenght = 1.7*w
Length = 1.7 x 5
Length = 8.50 meters
Hence, the dimension of the room is length =
Classify the polynomial by its name: x2 + 5x - 6 A) trinomial B) binomial C) trinomial D) other polynomial
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Answer:
Trinomial
Explanation:
Given the below polynomial;
[tex]x^2+5x-6[/tex]To be able to classify the above polynomial, we need to ascertain the number of terms it has;
[tex]\begin{gathered} x^2\colon1st\text{ term} \\ 5x\colon2nd\text{ term} \\ -6\colon\text{ 3rd term} \end{gathered}[/tex]We can see that the polynomial has 3 terms, so it can be classified as a trinomial.
Solve the linear equation 3y-5=5+3y
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we have the linear equation
3y-5=5+3y
3y-3y=5+5
0=10 -----> is not true
that means
the system has no solutionwhat is the radius of a sphere with a volume of 36,000 Pi mm3?
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The volume of a Sphere was determined using the following formula:
[tex]V=\frac{4}{3}\pi r^3[/tex]Given that you know the volume of the sphere, you can determine its radius.
First, let's write the formula for r:
- multiply both sides of the equal sign by the reciprocal fraction of 4/3π to leave the r term alone on the left side of the formula:
[tex]V\cdot\frac{3}{4}\pi=r^3[/tex]-apply the cubic root to both sides of the equal sign
[tex]\begin{gathered} \sqrt[3]{V\cdot\frac{3}{4}\pi}=\sqrt[3]{r^3} \\ \sqrt[3]{V\cdot\frac{3}{4}\pi}=r \end{gathered}[/tex]Replace the expression obtained with the given volume of the sphere:
[tex]\begin{gathered} r=\sqrt[3]{36000\pi\cdot\frac{3}{4}\pi} \\ r=\sqrt[3]{27000} \\ r=30 \end{gathered}[/tex]The radius of the sphere is 30mm long
The first super bowl was played in 1967. The cost for a 30 second commercial was $42,000. The cost of a 30 second commercial for super bowl 52, which was played on February 4, 2018 in Minneapolis, Minnesota, was $5.0 million. What was the geometric mean rate of increase for the 51-year period? (Round your answer to 2 decimal places.)
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It is given that the commercial rate for 1967 was 42000
The rate in 2018 was 5 million that means 5000000.
The number of years is given by:
[tex]2018-1967=51[/tex]So the formula for the geometric progression is given by:
[tex]a_n=a_1r^{n-1}[/tex]Substitute:
[tex]a_n=5000000,a_1=42000,n=51[/tex]To get:
[tex]\begin{gathered} 5000000=42000r^{50} \\ r^{50}=\frac{2500}{21} \\ r=\sqrt[50]{\frac{2500}{21}} \\ r=1.100308364 \\ r\approx1.10 \end{gathered}[/tex]Hence the rate is approximately 1.10.
leave answers for equations of straigh otherwise directed. And the equation of each line from the given information. (a) y-intercept 6, slope 3
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To find the equation of the line that has a y intercept of 6 and a slope of 3, remember the general structure of the equation of the line:
[tex]y=mx+b[/tex]Where m is the slope and b is the y intercept.
Use this formula and replace for the given values to find the equation of the line:
[tex]y=3x+6[/tex]If g(x)=x³ + 2x² - 6 find g(0), g(-2), g(-1), g(-2) -1 , g(0) + 2
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ANSWER:
[tex]\begin{gathered} g(0)=-6 \\ g(-2)=-6 \\ g(-1)=-5 \\ g(-2)-1=-5 \\ g(0)+2=-8 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]g\mleft(x\mright)=x^3+2x^2-6[/tex]We calculate in each case:
[tex]\begin{gathered} g(0)=0^3+2\cdot0^2-6=-6 \\ g(-2)=(-2)^3+2\cdot(-2)^2-6=-8+8-6=-6 \\ g(-1)=(-1)^3+2\cdot(-1)^2-6=-1+2-6=-5 \\ g(-2)-1=-6\rightarrow g(-2)=-6+1=-5 \\ g(0)+2=-6\rightarrow g(0)=-6-2=-8 \end{gathered}[/tex]The airline advertised lower fares. The new fare for flying to Austin is $320. If this fare is 20 percent lower than the original fare, what was the original fare?
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ANSWER:
$400
STEP-BY-STEP EXPLANATION:
The original value would be the sum between the discount percentage (20%) and the discount value ($320).
Therefore, we calculate it as follows:
[tex]x=x\cdot\frac{20}{100}+320[/tex]Let x be the original value, we solve for x:
[tex]\begin{gathered} x=0.2x+320 \\ x-0.2x=320 \\ 0.8x=320 \\ x=\frac{320}{0.8} \\ x=\text{\$}400 \end{gathered}[/tex]The original fare is $400
find the derivative of h(x)=x^3 (5 -3x)^4
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We can solve this with the derivative of f(x) multiplied by g(x):
[tex]\frac{d(f\cdot g)}{dx}(x)=\frac{df}{dx}\cdot g+f\cdot\frac{dg}{dx}[/tex]In this case we can choose f(x)=x^3 and g(x)=(5-3x)^4, so:
[tex]\frac{dh}{dx}(x)=\frac{d(f\cdot g)}{dx}(x)=\frac{d(x^3)}{dx}(5-3x)^4+x^3\frac{d((5-3x)^4)}{dx}[/tex][tex]\begin{gathered} \frac{d(x^3)}{dx}=3x^2 \\ \frac{d((5-3x)^4)}{dx}=4\cdot(5-3x)^3\cdot\frac{d(5-3x)}{dx} \\ \frac{d(5-3x)}{dx}=\frac{d(5)}{dx}-\frac{d(3x)}{dx}=0-3=-3 \end{gathered}[/tex][tex]\begin{gathered} \frac{dh}{dx}=3x^2(5-3x)^4+x^3\cdot4\cdot(5-3x)^3\cdot(-3) \\ \frac{dh}{dx}=3x^2(5-3x)^4-12x^3(5-3x)^3 \end{gathered}[/tex]We can factor by 3x^2(5-3x)^3 to simplify the formula:
[tex]\begin{gathered} \frac{dh}{dx}=3x^2(5-3x)^3\lbrack(5-3x)-4x\rbrack \\ \frac{dh}{dx}=3x^2(5-3x)^3(5-7x) \end{gathered}[/tex]Catherine decides that she will study at most 18 hours every week and that she must work at least 8 hours every week. Let x represent the hours spent and y represent the hours working. Write two inequalities that model this situation and graph their intersection.
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Answer:
Explanation:
The number of hours spent working = y
Solve for x in the diagram the angles are complementary
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Given:
The two angles x - 6 degree and 2x + 18 degree.
Required:
Solve for x.
Explanation:
When the sum of two angles is equal to 90 degree, they are called complementary angles.
Now,
[tex]\begin{gathered} x-6+2x+18=90 \\ 3x+12=90 \\ 3x=78 \\ x=26 \end{gathered}[/tex]Answer:
The value of x equals 26.
What are the dimensions of the product? 1 x 2 2 x 2 3 x 2 3x3
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The answer is 2x2 matrix
Classify the real number -5
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-5 is an Integer.
Integers are whole numbers that are positive , negative , or zero.
The farmer earns $9 for every palette of milk he sells. If the farmer sells 8 pallets of milk, how much does the farmer earn?
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If for every pallet of milk sold, the farmer earns $9, and he sold a total of 8 pallets, in order to find how much the farmer earned, we just need to multiply the number of pallets sold by the cost of each pallet:
[tex]8\cdot9=72[/tex]So the farmer earned $72.
The function h(x) is given in the table below. Which of the following choicesshows the average rate of change of the function over the interval 2 < x < 6?7
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Note the average rate of change is for the interval below
[tex]2\leq x\leq6[/tex]2. Harry just deposited $1500 into a savings account giving 6% interest compounded quarterly.a) How much will be in the account after ten years?b) How much will be in the account after twenty years?c) How long does it take for Harry’s initial account value to double?
Answers
The formula for compound interest is:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ A=\text{ Final amount} \\ r=\text{ Interest rate} \\ n=\text{ Number of times interest applied per period} \\ t=\text{ Number of time period elapsed} \\ P=\text{ Intial principal balance} \end{gathered}[/tex]Given data:
[tex]\begin{gathered} P=\text{ \$1500} \\ r=6\text{ \%}=0.06 \\ n=4\text{ times (compounded quarterly)} \end{gathered}[/tex]a. After ten years, that is t = 10 years, the amount in the account will be
[tex]\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times10} \\ A=\text{ }1500(1+0.015)^{40} \\ A=\text{ }1500(1.015)^{40} \\ A=\text{ \$2721.03} \end{gathered}[/tex]b. After twenty years, that is t = 20 years, the amount in the account will be:
[tex]\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times20} \\ A=1500(1.015)^{4\times20} \\ A=1500(1.015)^{80} \\ A=\text{ \$}4935.99 \end{gathered}[/tex]c. The time it takes for Harry's initial account value to double will be:
[tex]\begin{gathered} A=2\text{ x initial value = 2 }\times\text{ \$1500 = \$3000} \\ 3000=1500(1.015)^{4t} \\ (1.015)^{4t}=\frac{3000}{1500} \\ (1.015)^{4t}=2 \\ \text{ Find the logarithm of both sides} \\ \ln (1.015)^{4t}=\ln 2 \\ 4t=\frac{\ln 2}{\ln 1.015} \\ 4t=46.56 \\ t=\frac{46.56}{4}=11.64 \end{gathered}[/tex]Therefore, the time it takes Harry's initial account to double is approximately 11 years
Evaluate the expression below.|8-7| • 4 + 3(-1)Answers choices17-7-1
Answers
Given |8-7| • 4 + 3(-1)
|8-7| = 1
|8-7| • 4 = 1 * 4 = 4
|8-7| • 4 + 3(-1) = 4 + 3(-1)
= 4 - 3
= 1
what is the GCF of 90, 135, 225
Answers
Given
We are to find the Greatest Common Factor of 90, 135 and 225
First, we should decompose all numbers into their prime factors and write them as a product
[tex]\begin{gathered} 90\text{ = 2 }\times3\text{ }\times\text{ 3 }\times\text{ 5} \\ 135\text{ = }3\text{ }\times\text{ 3 }\times\text{ 3 }\times\text{ 5} \\ 225\text{ = }3\text{ }\times\text{ 3 }\times\text{ }5\text{ }\times\text{ 5} \end{gathered}[/tex]Then we choose the common prime factors: 3, 3 and 5
The greatest common factor (GCF) is obtained by multiplying the common prime factors:
[tex]\begin{gathered} \text{GCF = }3\text{ }\times\text{ 3 }\times\text{ 5} \\ =\text{ 45} \end{gathered}[/tex]Hence, the GCF is 45.
Answer: 45
Each of the line segments in the work MATH are numbered in the graph below. find the slope (as a ratio of rise over run) of each line segment for lines 1-12.Hopefully I provided enough information!
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1. No Slope
2. -4/3
3. 4/3
4. No Slope
1) Let's start by calculating the slope of each segment:
1) Vertical lines do not have a slope, since the slope is the steepness of a line.
So m is undefined
2) Picking points (-8,8) and (-5,4) and plugging into the slope formula:
[tex]m=\frac{4-8}{-5+8}=\frac{-4}{3}=-\frac{4}{3}[/tex]3) For this line segment (3) let's pick and plug points (-5, 4) and (-2,8)
[tex]m_3=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{8-4}{-2+5}=\frac{4}{3}[/tex]4) Since we have another vertical line then, the slope it's undefined because of that (considering points (-2,8) and (-2,1)
[tex]m=\frac{8-1}{-2+2}=\frac{7}{0}=\text{undefined!}[/tex]Hence, there is no slope
4) Hence, for Quadrant II (letter M) we have:
1. No Slope
2. -4/3
3. 4/3
4. No Slope
s
Evaluate the expression when b= 48 and c=7.b+2c23Simplify your answer as much as possible.
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Answer:
114
Explanation:
Given the expression:
[tex]\frac{b}{3}+2c^2[/tex]When b=48 and c=7:
[tex]\begin{gathered} \frac{b}{3}+2c^2=\frac{48}{3}+2(7)^2 \\ =16+2(49) \\ =16+98 \\ =114 \end{gathered}[/tex]The value of the expression is 114.
y=3x+5y=ax+bwhat value for a and b make the system inconsistent? what values for a and b the system consistent and dependent? Explain
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A system of equation is said to be consistent if it has at least one solution.
If a consistent system has an infinite number of solutions, it is dependent.
Given the system of the equation:
[tex]\begin{gathered} y=3x+5 \\ y=ax+b \end{gathered}[/tex]For the system to be dependent and consistent, they must be the same line.
Therefore, the values for a and b that make the system consistent and dependent are:
a=3, b=5
A system is said to be inconsistent if it has no solution. That is, the two lines do not intersect (are parallel).
Therefore, the values of a and b that make the system inconsistent are:
a=3, b= -5
how solution s are there to the equation below 3(2x-5)+4x=5(2x+3)
Answers
You have the following equation:
3(2x - 5) + 4x = 5(2x + 3)
in order to solve for x, proceed as follow:
3(2x - 5) + 4x = 5(2x + 3) apply distributive property
6x - 15 + 4x = 10x + 3 simplify like terms
10x - 15 = 10x + 3 subtract 10x both sides
-15 = 3
the previous result is an incosistency, then, you ca conclude that the given equation does not have solution.
ZERO SOLUTIONS
two ships leave a port at the same time. the first ship sails on a bearing of 55° at 12 knots (natural miles per hour) and the second on a bearing of 145° at 22 knots. how far apart are they after 1.5 hours
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Answer:
37.59 nautical miles
Explanation:
Distance = Speed x Time
The speed of the first ship = 12 knots
Thus, the distance covered after 1.5 hours
[tex]\begin{gathered} =12\times1.5 \\ =18\text{ miles} \end{gathered}[/tex]The speed of the second ship = 22 knots
Thus, the distance covered after 1.5 hours
[tex]\begin{gathered} =22\times1.5 \\ =33\text{ miles} \end{gathered}[/tex]The diagram representing the ship's path is drawn and attached below:
The angle at port = 90 degrees.
The triangle is a right triangle.
Using Pythagorean Theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=18^2+33^2 \\ c^2=324+1089 \\ c^2=1413 \\ c=\sqrt[]{1413} \\ c=37.59\text{ miles} \end{gathered}[/tex]The two ships are 37.59 nautical miles apart after 1.5 hours.
What is the value of x in x/3 = -0.6 and why?A.) -0.2, because to isolate x, you would divide -0.6 by 3B.) 2.4, because to isolate x, you would add 3 to -0.6C.) -1.8, because to isolate x, you would multiply -0.6 by 3D.) -3.6, because to isolate x, you would subtract 3 from -0.6
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Given the expression:
[tex]\frac{x}{3}=-0.6[/tex]we move the 3 that is dividing the x to the other side multiplying to get the following:
[tex]x=-0.6\cdot(3)=-1.8[/tex]therefore, the answer is C
Given:• Points A, B, and C are points of tangency.• VZ = 24• AV = 14• The perimeter of AWV Z is 64.BzcWFind AW.281416
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Since the segments taht are shown are all tangents to the circle, we can use the property that the tanget segments of the same circle and that have an external common point have the same length. From this, we see that the pairs AV and BV, BZ and CZ, CW and AW are tangets with common eterior points, thus:
[tex]\begin{gathered} AV=BV \\ BZ=CZ \\ CW=AW \end{gathered}[/tex]Than, we can see that that:
[tex]\begin{gathered} BV+BZ=VZ \\ BV+BZ=24 \\ AV=BV \\ AV+BZ=24 \\ 14+BZ=24 \\ BZ=10 \end{gathered}[/tex]Also:
[tex]\begin{gathered} CZ=BZ \\ CZ=10 \end{gathered}[/tex]So, we already know AV, BV, BZ and CZ. AW and CW are the same, and the sum of all of them is the perimeter, that we know is 64, so:
[tex]\begin{gathered} AV+BV+BZ+CZ+CW+AW=64 \\ 14+14+10+10+CW+CW=64 \\ 2CW=64-48 \\ 2CW=16 \\ CW=8 \\ AW=CW \\ AW=8 \end{gathered}[/tex]1. The thermostat in an empty apartment is set to 65°F from 4:00 a.m. to 5:00 p.m. and to 50°Ffrom 5:00 p.m. until 4:00 a.m. Here is a graph of the function H that gives the temperatureH() in degrees Fahrenheit in the apartment 2 hours after midnight.
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Morning starts from 6 am and evening starts from 6pm.
This is my question?
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hi there
this is the answer
Assuming the population is normally distributed.The sample mean is 4263.2767The sample standard deviation is 260.02.By constructing a 95% confidence interval for the population mean, write a statement that interprets the situation.
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ANSWER
EXPLANATION
We want to construct a confidence interval for the population mean.