A sinusoidal function is a type of periodic function that can be written in the form y = a sin(bx + c) + d, where a is the amplitude, b is the frequency, c is the phase shift, and d is the vertical shift.
Given the parameters in the question, we can plug them into the general form of a sinusoidal function to find the specific function.
Amplitude = 4
Period = 3π
Vertical shift = -8
The period of a sinusoidal function is related to the frequency by the equation period = (2π)/b. Therefore, we can solve for b to find the frequency:
3π = (2π)/b
b = (2π)/(3π)
b = 2/3
Plugging in the given values for amplitude, frequency, and vertical shift, we get the sinusoidal function:
y = 4 sin((2/3)x) - 8
This is the sinusoidal function that satisfies the given conditions. It has an amplitude of 4, a period of 3π, and a vertical shift down 8 units.
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I need some assistance with this
Answer:
In believe it’s 68 but I might be wrong so if it is sorry
Step-by-step explanation:
About 72 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected.
2. What is the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%?
The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0107.
To find the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%, use the formula for the standard error of a proportion:
SE = √(p(1-p)/n)
Where p is the proportion of the population that is making an effort to conserve water or electricity, and n is the sample size.
In this case, p = 0.72 and n = 110. Plugging these values into the formula gives:
SE = √(0.72(1-0.72)/110) = 0.0347
Next, we need to find the z-score for the proportion of 0.80. The z-score is given by:
z = (P - p)/SE
Where P is the sample proportion and p is the population proportion. In this case, P = 0.80 and p = 0.72. Plugging these values into the formula gives:
z = (0.80 - 0.72)/0.0347 = 2.30
Finally, we can use the z-score to find the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%. This is given by:
P(z > 2.30) = 1 - P(z < 2.30) = 1 - 0.9893 = 0.0107
Therefore, the probability is 0.0107 or 1.07%.
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some1 pls answer this pt.2 will give brainlist thingy
Answer: 8
Step-by-step explanation: (9-7)^3= 8
Answer: ? = 8
Step-by-step explanation: 2 x 2 x 2 = 8
A number y, when rounded to 2 decimal places, is equal to 9. 68. Find the upper and lower bound
If the number when rounded to 2 decimal places is equal to 9.68, then the upper bound is 9.685 and lower bound is 9.675 .
In order to find the upper bound of the number y, we need to add 0.005,
and to find the lower bound of the number y, we need to subtract 0.005 ,
We know that, the number y, when rounded to 2 decimal places is equal to 9.68 ;
So, the Upper Bound is = 9.68 + 0.005 = 9.685, and
The Lower Bound is = 9.68 - 0.005 = 9.675.
Therefore, the lower bound of y is 9.675 and upper bound of y is 9.685.
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Choose the formula that expresses the described relationship. A varies inversely as h.
Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.
The formula that expresses the described relationship where A varies inversely as h is A = k/h, where k is the constant of proportionality.
In an inverse relationship, one variable increases as the other variable decreases. In this case, as h increases, A decreases, and as h decreases, A increases. The constant of proportionality, k, remains the same throughout the relationship.
To find the value of k, you can use the formula and plug in known values for A and h. For example, if A = 4 and h = 2, you can plug these values into the formula and solve for k:
4 = k/2
k = 8
Once you know the value of k, you can use the formula to find the value of A or h, given the value of the other variable. For example, if you know that h = 3 and k = 8, you can plug these values into the formula and solve for A:
A = 8/3
A = 2.67
Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.
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Given a circle with center (– 3, 6) and radius 5, what is an equation of the circle?
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-3}{h}~~,~~\underset{6}{k})}\qquad \stackrel{radius}{\underset{5}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-3) ~~ )^2 ~~ + ~~ ( ~~ y-6 ~~ )^2~~ = ~~5^2\implies (x+3)^2+(y-6)=25[/tex]
are 8,192 players in a Rock Paper Scissors tournament. In each round half the players ar d to find the number of players remaining in the tournament at the end of x rounds? f(x)=8192(0.05)^(x) B
Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds.
The function f(x) = 8192(0.05)^x represents exponential decay, where the number of players is decreasing by a factor of 0.05 in each round. However, in this tournament, the number of players is decreasing by a factor of 0.5 (half the players) in each round. Therefore, the correct function should be f(x) = 8192(0.5)^x.
To find the number of players remaining in the tournament at the end of x rounds, simply plug in the value of x into the function and solve.
For example, if we want to find the number of players remaining at the end of 3 rounds, we would plug in x = 3 and solve:
f(3) = 8192(0.5)^3
f(3) = 8192(0.125)
f(3) = 1024
Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds. Similarly, you can plug in any value of x to find the number of players remaining at the end of x rounds.
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Derivations (20 marks): For each of the questions in this section provide a derivation. Other methods will receive no credit i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks) iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
Proof:
1. ∃x(Fx & Gx) [Premise]
2. Fx & Gx [∃-Elimination, 1]
3. ∃xFx [∃-Introduction, 2]
4. ∃xGx [∃-Introduction, 2]
5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]
6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)
Proof:
1. ¬ 3x(Px v Qx) [Premise]
2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]
3. Vx ¬ Px [∀-Introduction, 2]
4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]
iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
Proof:
1. ¬ Vx(Fx → Gx) v 3xFx [Premise]
2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]
3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]
4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]
5. Fx → Gx [Resolution, 3, 4]
6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
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how to solve 3 divided by 561 long division
Answer:
187
Step-by-step explanation:
how to do long division, you know how to start im assuming. then you then bring down and Divide, Multiply, Subtract, with the first number then bring the next number down and repeat that.
Answer:
187
Step-by-step explanation:
I personally just do multiplication whenever I can, but that's just me. Like for example I know 100 x 3 = 300 and 200 x 3 = 600. SO it has to be between 100 and 200.
150 x 3 = 450. So know it narrows it down to between 150 and 200.
175 x 3 = 525
180 x 3 = 540
185 x 3 = 555
190 x 3 =570
So now it's between 185 and 190.
Now I just need to do the following.
186 x 3 = 558
187 x 3 = 561
And there we have the answer.
Warm-Up: Suppose you have 60 dollars to deposit into a savings account. If you put your money into Bank A, they will deposit an additional 6 dollars per year into your account. If you put your money into Bank B, they will increase your balance by 10 percent per year.
How much money would you have after one year if you put your money into Bank A? How about Bank B?
Bank B may be a better option because the 10 percent increase is applied to the new balance each year, whereas Bank A only adds a flat 6 dollars each year.
If you put your money into Bank A, you will have to equate it as 60 + 6 = <<60+6=66>>66 dollars after one year.
If you put your money into Bank B, you will have 60 + (60 * 0.10) = 60 + 6 = <<60+(60*0.10)=66>>66 dollars after one year of the investment.
So, after one year, you will have the same amount of money in both Bank A and Bank B.
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Consider functions f and g.
f(x) = -23
g(x) = |x − 1
What is the value of (go f)(4)?
What is the value of (g • f)(4)?
O A. 9
O B. B. -
O C. -9
O D. 1
The numeric value of the composite function at x = 4 is given as follows:
|f(4) - 1|.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
If g is the outer function, as is the case for this problem, we have that:
(g • f)(x) = g(f(x)).
At x = 4, the numeric value of the composite function is given as follows:
g(f(4)) = |f(4) - 1|.
Missing InformationThe problem is incomplete, hence the composite function is given in general terms.
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Is(8, 2)a solution to the inequality y ≥ 3x + 4?
No, (8, 2) is not a solution to the inequality y ≥ 3x + 4 because when we substitute x = 8 and y = 2 into the inequality, we get a false statement. In other words, the point (8, 2) does not satisfy the inequality y ≥ 3x + 4, which means it is not a valid solution to the inequality.
To determine whether (8, 2) is a solution to the inequality y ≥ 3x + 4, we need to substitute the values of x and y into the inequality and check if the inequality holds true.
y ≥ 3x + 4
Substituting x = 8 and y = 2:
2 ≥ 3(8) + 4
2 ≥ 24 + 4
2 ≥ 28
The inequality is not true since 2 is not greater than or equal to 28.
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Identify then number of solutions of the polynomial equation. Then find the solutions. z^(3)+10z^(2) + 28z + 24=0
The solutions are: z = -3, -2, and -1. This equation is a third-degree polynomial equation and it can have up to three solutions. To find these solutions, you can use the Rational Root Theorem.
This theorem states that all rational solutions of a polynomial equation can be written in the form a/b, where a is a divisor of the coefficient of the constant term, and b is a divisor of the coefficient of the leading term.
For this equation, the constant term is 24 and the leading term is 1, so the possible solutions can be expressed as a/b, where a is a divisor of 24 and b is a divisor of 1. Therefore, the possible solutions are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. To find the exact solutions, substitute these values for z into the equation and solve for each value.
The solutions are: z = -3, -2, and -1.
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4. c^(3)v^(9)c^(-1)c^0
6. 9y^(4)j^(2)y^(-9)
8. 2y^(-9)h^(2)(2y^(0)h^(-4))^(-6)
10. (-3q^(-1))^(3)q^(2)
expression has the least vitive"? B. n^(n)
D. −n^(n)n^(-4)
vitive is D: −nnn−4.
To answer the question, the expression with the least vitive is D: −nnn−4.
For reference, the expressions in the question are:
4. c3v9c−1c0
6. 9y4j2y−9
8. 2y−9h2(2y0h−4)−6
10. (−3q−1)3q2
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The diagram shows a shape made from two semicircles
The radius of the larger semicircle is 8 cm
8 crn
D
Work out the perimeter of the shape.
Give your answer in terms of .
Answer
Not drawn
accurately
cam
[3 marks]
Answer:
Step-by-step explanation:
big semicircle circumference=1/2*3.14*64
100.48cm
small semicircle circumference=1/2*3.14*16=25.12cm
total perimeter=125.6cm
Will the graph y=2(4)^x be increasing or decreasing? Explain how u know
Answer:
Step-by-step explanation:
Decreasing.
This is because the as you increase the X value and solve for Y, the Y value decreases.
For example:
[tex]x=1 \\y=2(\frac{1}{3} )^1\\y=\frac{2}{3} =0.667\\\\x=2\\y=2(\frac{1}{3} )^1\\y=\frac{2}{9}=0.222\\\\x=3\\y=2(\frac{1}{3} )^3\\y=\frac{2}{27}=0.074[/tex]
whats smaller than 1/2
Answer:
1/4
Step-by-step explanation:
Fractions have two parts, the numerator and the denominator. The denominator is the bottom number and it tells us what unit of fraction we are working with (ie: it denotes fourths, halves, etc.)
Hope it helps! :D
Julia deposits $2000 into a savings account that
earns 4% interest per year. The exponential
function that models this savings account is
y = 2000(1.04)^t, where t is the time in years.
Which equation correctly represents the amount
of money in her savings account in terms of the
monthly growth rate?
Please show work
The equation correctly represents the amount of money in her savings account in terms of the monthly growth rate is [tex]y = 2000(1 + 0.0033)^t[/tex]. Option D is the correct answer.
What is compound interest?The interest earned on savings that is computed using both the original principle and the interest accrued over time is known as compound interest. It is said that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely computed on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
Given that, the function of the model of the account is:
[tex]y = 2000(1.04)^t[/tex]
The monthly interest rate is:
r = 4% / 12 = 0.00333
The model in terms of monthly interest rate can be written as:
[tex]y = 2000(1 + r)^{12t/12}[/tex]
Substituting the value of r:
[tex]y = 2000(1 + 0.0033)^t[/tex]
Hence, the equation correctly represents the amount of money in her savings account in terms of the monthly growth rate is [tex]y = 2000(1 + 0.0033)^t[/tex].
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How to write 3/4 with a denominator of 12? Please help
Answer:
9/12
Step-by-step explanation:
3/4 converted is 9/12 3x3 is 9 and 4x3 is 12.
Feb 28,
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Gabriel went to the store to buy some coffee. The price per pound of the coffee is
$4.50 per pound and he has a coupon for $2 off the final amount. With the coupon,
how much would Gabriel have to pay to buy 4 pounds of coffee? Also, write an
expression for the cost to buy p pounds of coffee, assuming at least one pound is
purchased.
Answer:
The original cost for 1 pound of coffee is $4.50, and Gabriel wants to buy 4 pounds, so the total cost without the coupon would be:
4 pounds x $4.50/pound = $18
With the coupon, Gabriel can subtract $2 from the final amount, so the total cost with the coupon would be:
$18 - $2 = $16
Therefore, Gabriel would have to pay $16 to buy 4 pounds of coffee with the coupon.
To write an expression for the cost to buy p pounds of coffee, we can use the formula:
cost = price per pound x number of pounds - coupon
If Gabriel buys at least one pound of coffee, then the expression would be:
cost = $4.50p - $2
So the cost to buy p pounds of coffee can be calculated by plugging in the desired value for p into this expression.
exact value of sec(sin^(-1)((3)/(10))) o enter EXACT values ed to simplify any radicals
The exact value of sec(sin-1(3/10)) is 1.049988251.
The exact value of sec(sin-1(3/10)) can be found using the following steps:
Step 1: Enter the value of sin-1(3/10) into a calculator to get the angle measure in radians. This will give you an angle measure of 0.304692654.
Step 2: Take the cosine of this angle measure using a calculator. This will give you a value of 0.952424403.
Step 3: The value of secant is the reciprocal of the value of cosine. So, to find the exact value of sec(sin-1(3/10)), take the reciprocal of 0.952424403. This will give you an exact value of 1.049988251.
Step 4: Simplify any radicals if necessary. In this case, there are no radicals to simplify.
Therefore, the exact value of sec(sin-1(3/10)) is 1.049988251.
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If the equation is true for all real numbers enter "All -4(6y+4)+19=12(-2y+5)-55
True. All real numbers satisfy the equation -4(6y+4)+19=12(-2y+5)-55.
The statement "If the equation is true for all real numbers enter 'All'" has been used to indicate that the given equation is true for all real numbers.
Given equation: -4(6y + 4) + 19 = 12(-2y + 5) - 55
Using distributive property, simplify both sides of the equation.
-24y - 16 + 19 = -24y + 60 - 55-24y + 3 = -24y + 5
By transposing -24y from the right-hand side of the equation to the left-hand side of the equation, we can simplify it as follows:
3 = 5
Since the above equation is always false for all real numbers, there is no solution. Therefore, we conclude that the given equation has no solution.
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Subtract mixed numbers problem help
9 1/4-12 7/8
Therefore , the solution of the given problem of fraction comes out to be -3 5/8 as a result.
A fraction is what?Any combination of equal portions or fractions can be combined to represent a whole. In standard English, the quantity of a certain size is defined as a fraction. 8, 3/4. Wholes also include fractions. The ratio of numerator to ratio is a mathematical symbol for integers. All of these number fractions are simple fractions. There is a fraction inside of the fraction but rather remainder in a difficult fraction.
Here,
=> 9 1/4 = (4 x 9 + 1)/4 = 37/4
=> 12 7/8 = (8 x 12 + 7)/8 = 103/8
4 and 8 have the same shared factor, which is 8.
=> 37/4 - 103/8 = (2 x 37)/(2 x 4) (2 x 4) - 103/8
=> 74/8 - 103/8
=> -29/8
There is no simpler way to describe the outcome.
Since the outcome is already an incorrect fraction, we can change it back to a mixed integer as follows:
-29/8 = -3 5/8
9 1/4 - 12 7/8 Equals -3 5/8 as a result.
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A rectangular prism is shown below. What is the LATERAL surfa
area?
11 cm
5 cm
2 cm
The surface area of the rectangular prism is 174 cm^2
What is a Rectangular Prism?Rectangular Prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangle such that all the pairs of the opposite faces are congruent.
To determine the surface area of Rectangular prism
SA = 2(LH + LW + WH)
Where W = Width = 2 cm
L = Length = 5 cm
H = Height = 11 cm
SA = 2[(5*11) + (5*2) + (11*2)]
SA = 2(55 + 10 + 22)
SA = 2(87)
SA = 2 * 87
SA = 174
Therefore, the surface area of rectangular prism is 174 cm^2
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Can somebody help please I’ll give you brainliest and 30 points!!!!!
Answer:
$512.17
$286.48
$1,958.40
$1,628.85
$56.37
$324.24
$135.55
Note: These calculations were made assuming simple interest. If the interest is compounded, the final amounts will be slightly different.
Step-by-step explanation:
In a class 45% of the students are girls. If there are 18 girls in the class, then find
the total number of students in the class.
Answer:
i dont think its possible
Solve by using Cramer's Rule: \[ \begin{array}{l} -3 x-4 y-4 z=-8 \\ x-3 y-3 z=-19 \\ -x+y-2 z=3 \end{array} \]
The solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]
To solve this system of equations using Cramer's Rule, we will begin by finding the determinant of the coefficient matrix, which is an array of the coefficients of the variables in the equations. We will then find the determinants of the matrices that result from replacing each column of the coefficient matrix with the constant terms of the equations. Finally, we will use these determinants to find the values of x, y, and z.
The coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} \]
The determinant of the coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} = (-3)(-3)(-2) - (-4)(-3)(-1) - (-4)(1)(1) - (-4)(-3)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = -6 + 4 + 4 + 4 - 12 + 8 = -2 \]
The matrix that results from replacing the first column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} = (-8)(-3)(-2) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(-2) = 48 - 36 - 76 + 36 - 76 + 24 = -80 \]
The matrix that results from replacing the second column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} = (-3)(-19)(-2) - (-8)(-3)(-1) - (-4)(1)(3) - (-4)(-19)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = 114 + 24 + 12 + 76 - 12 + 8 = 222 \]
The matrix that results from replacing the third column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} = (-3)(-3)(3) - (-4)(-19)(-1) - (-8)(1)(1) - (-8)(-3)(-1) - (-8)(-19)(1) - (-8)(1)(3) = 27 + 76 + 8 + 24 - 152 + 24 = 7 \]
Using these determinants, we can find the values of x, y, and z: \[ x = \frac{-80}{-2} = 40 \] \[ y = \frac{222}{-2} = -111 \] \[ z = \frac{7}{-2} = -3.5 \]
Therefore, the solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]
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Figure 1 and figure 2 are right triangles. two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 7 units long What scale factor was used to produce Figure 2 from Figure 1? 7 over 3, 3 over 7, 7 or 3
The scale factor used to produce Figure 2 from Figure 1 is given as follows:
7/3.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The side lengths are given as follows:
Figure 1: 3 units.Figure 2: 7 units.Hence the scale factor of the dilation is given as follows:
7/3.
(the scale factor is the division of the side length of the dilated figure by the equivalent side length of the original figure).
Missing InformationThe problem asks for the scale factor used from figure 1 to figure 2.
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Answer:
C 7/3 because i got it right
What is the inequality shown?
Answer:
The inequality that shows the range from -9 to 9, but only including the range from -4 to 3, can be written as:
-4 ≤ x ≤ 3
This inequality means that x can take on any value between -4 and 3, including -4 and 3 themselves, but it cannot be less than -4 or greater than 3. The inequality does not include the values between -9 and -4, or between 3 and 9.
Step-by-step explanation:
explanation of how to arrive at the inequality -4 ≤ x ≤ 3 to represent the range from -9 to 9, but only including the range from -4 to 3:
Start with the range from -9 to 9:
-9 ≤ x ≤ 9
Identify the portion of the range that we want to include:
-4 ≤ x ≤ 3
Replace the original range with the desired range:
-4 ≤ x ≤ 3 replaces -9 ≤ x ≤ 9
Check that the inequality is inclusive of the desired range but not of any values outside of that range:
-4 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Similarly, 3 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Any values less than -4 or greater than 3 are excluded from the range -4 ≤ x ≤ 3, as desired.
Therefore, the inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.
The inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.
How to find the inequality?The inequality that shows the range from -9 to 9, but only including the range from -4 to 3, can be written as:
-4 ≤ x ≤ 3
This inequality means that x can take on any value between -4 and 3, including -4 and 3 themselves, but it cannot be less than -4 or greater than 3. The inequality does not include the values between -9 and -4, or between 3 and 9.
explanation of how to arrive at the inequality -4 ≤ x ≤ 3 to represent the range from -9 to 9, but only including the range from -4 to 3:
Start with the range from -9 to 9:
-9 ≤ x ≤ 9
Identify the portion of the range that we want to include:
-4 ≤ x ≤ 3
Replace the original range with the desired range:
-4 ≤ x ≤ 3 replaces -9 ≤ x ≤ 9
Check that the inequality is inclusive of the desired range but not of any values outside of that range:
-4 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Similarly, 3 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Any values less than -4 or greater than 3 are excluded from the range -4 ≤ x ≤ 3, as desired.
Therefore, the inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.
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Based on the information, we can infer that the second plan is the best for the bicycle company because it will cost less and will earn more.
How to identify the best alternative for the bicycle company?To identify the best alternative for the bicycle company, we must take into account the information on the cost of design and construction of the bicycles and the cost of labor and production.
In accordance with the above, we can infer that in alternative one the design and construction of the bicycle would be more expensive than alternative two. However, the production of each bicycle would be less.
Therefore, the best alternative would be option two because it requires less initial research and the product will cost more, so it would have a higher retail value, so the investment could be recovered much faster. .
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