The table and the graph below each show a different relationship between the same two variables, x and y:
How much more would the value of y be on the graph than its value in the table when x = 12?

A. 20
B. 30
C. 60
D. 70

To find the coordinates of the endpoints of the image A'B' (A9B9) after dilation of AB by a scale factor of 2 centered at (3,5), follow these steps:

Step 1: Use the given scale factor (2) and center of dilation (3,5).

Step 2: Apply the dilation formula to the coordinates of the original points A and B. The formula for dilation with scale factor k centered at (h,k) is:

A'(x', y') = (h + k(x - h), k + k(y - k))

Step 3: Substitute the given options for A9 and B9 into the dilation formula and check which pair of coordinates satisfy the formula.

After applying the formula, it is determined that the coordinates of the endpoints of the image A9B9 after dilation with a scale factor of 2 centered at (3,5) are:

A9(21, 6) and B9(7, 4).

Option (2) is correct.

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Answer:

Te conozco y sé qué

Como Nuevo de fabrica el otro

The line that models the data points better is Red, because it goes through one of the points.

Data is information that has been organized and processed in a meaningful way. It is the raw material of digital systems and the foundation of all computer-based operations. It can be stored, retrieved, and manipulated in a variety of ways, and it is used to generate insights, drive decisions, and build solutions. Data can come from a variety of sources, including manual entry, sensors, databases, and the internet.

This is a better model than Blue, because the data points are not all close to the line, and having the line go through one of the points ensures that the line is better representing the points. Additionally, having three points above the line and three points below the line helps to make the line a better model of the data points, as it is more evenly distributed.

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The area of the region bounded by

\[y=\frac{7}{(4+x)^2}+\frac{5}{7+x^2},\ y=0,\ x\ge5\]is 0.0188 (rounded to four decimal places).

Here's how to get the solution:

We are asked to find the area of the region bounded by the two curves.

The curves intersect at (5, 0) because x can not be less than 5.

They meet again at the point x ≈ 1.281.

Now, we must find the integrals for both functions in the given range.

We'll call the first function "f (x)" and the second "g (x)."

f(x) = 7 / (4 + x)² + 5 / (7 + x²)

g(x) = 0

The area between the two curves is obtained by finding the integral of the difference of the two functions.

The area is given by:

\[\int_{5}^{1.281} [f(x) - g(x)] dx\]

Since there is no point of intersection beyond x ≈ 1.281, we will use this value for the limit of integration.

Integrating:

\[\begin{aligned} &\int_{5}^{1.281} [f(x) - g(x)] dx \\ =& \int_{5}^{1.281} \left[\frac{7}{(x+4)^2}+\frac{5}{x^2+7}-0\right] dx \\ =& -\left[\frac{7}{4+x}+\sqrt{7}\tan^{-1}\left(\frac{x}{\sqrt{7}}\right)\right]_{5}^{1.281} \\ =& 0.0188. \end{aligned}\]

Thus, the area of the region is 0.0188.

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The total distance Trevor traveled is 352 meters.

We have,

Trevor is traveling from his home to school.

He first walks 58.0 meters in one direction, but then he forgets his lunch and has to turn around and walk back the same distance.

This means he has walked a total distance of 58.0 m + 58.0 m = 116.0 m.

Now,

After he retrieves his lunch, he continues walking in the original direction for an additional 236 meters.

So, the total distance Trevor traveled.

= 116.0 m + 236 m = 352.0 m.

Thus,

The total distance Trevor traveled is 352 meters.

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Answer:

85

Step-by-step explanation:

The vertical line that y is on adds up to 180 so if we take 180 - the number we already know (95) we get 85

The equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

If we assume that the growth rate of the world population was constant from 1997 to 2017, then we can use the following equation:

Population in 2017 = Population in 1997 × (1 + r)²⁰

where r is the annual growth rate, and the exponent 20 represents the number of years between 1997 and 2017.

We can rewrite this equation to solve for r:

(7.53 ) = (5.88 ) × (1 + r)²⁰

Divide both sides by (5.88 ):

(7.53 ) / (5.88 ) = (1 + r)²⁰

Take the 20th root of both sides:

\((7.53 / 5.88 )^{(1/20)} = 1 + r\)

Subtract 1 from both sides:

\(r = (7.53 / 5.88 )^{(1/20)} - 1\)

Therefore, the equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

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Answer:

No solutions is your answer

Step-by-step explanation:

I hope it helps and don't give up just like it says in i ready

The power and the r m s value for each of the following signals are a)p=50w and  r m s =7.07 b)p=178w,  r m s =√178 c)p=51w, r m s =√51
d)p=25w, r m s =√25 e)p=25w, r m s  =√25  and f)p=1/2, r m s =√1/2.

(a) 5+10cos(100t+π/3)
=A cos(w0t+θ)
power of the signal
P=10^ 2/2=100/2=50w
p=50w
r m s value of the signal
=√50
=7.07

b) 10cos(100t+π/3)+16sin(150t+π/5)
power of the signal.
p=10^ 2/2+16^ 2/2
p=178w
r m s value of the signal=√178

c) (10+2sin(3t)cos10t
=10cos10t+2sin3tcos210t
=2sin3tcos10t
=1/2(sin(3+10)+sin(3-10))
(sin a cos b=1/2(sin(a + b)+sin(a-b))
=2x1/2(sin13t-sin7t)
=sin13t-sin7t
=10cos10t+sin13t-sin7t
power of the signal is
p=10^ 2/2+1^ 2/2+1^ 2/2
p=51w
r m s value of the signal=√51

d) 10 cos(5t)cos(10t)
=10(cos(5+10)T+ cos (5-10)t/2
(cos a cos b=1/2(cos a+ cos b)+cos(a-b))
=10(cos(15)t+ cos (-5)t/2
=5cos15t-5cost
power value of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the signal=√25

e) 10 sin(5t)cos(10t)
=10(sin(5+10)t+ sin(5-10)t/2
=10/2(sin15t-sin5t)
=5sin15t-5sin5t
power of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the =√25      

F) f) e^(jαt) cos(w0t)
=e jαt cos wot
=(cosαt+ cos wot+jsin2tcoswot
=(cos(α+wo)t+ cos(α-wo)t/2+j(sin(2+wo)t+ sin cos-wot/2
=1/2cos(α+wo)T+1/2cos(α-wo)T
power of the signal
p=(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2
p=1/2
r m s value=√1/2

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\(\pi\)

The value of the integral is ln(1/6) + (3/2) ln(3). To evaluate the integral S18 1 (√3/z)dz, we can use the substitution u = √3/z, which implies du/dz = (-√3/z²) and dz = (-z²/√3) du.

Substituting u = √3/z and dz = (-z²/√3) du, the integral becomes:

S18 1 (√3/z)dz = -S√3/18 ∞ √3/1 u du

= -S√3/18 ∞ √3/1 (√3/u) du

= -S1 18 (3/u) du

= -3ln(u) |1 18

= -3ln(18/√3) + 3ln(1/√3)

= -3ln(6) + 3ln(√3)

= -3ln(6) + 3/2 ln(3)

= ln(1/6) + (3/2) ln(3)

Therefore, the value of the integral is ln(1/6) + (3/2) ln(3).

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A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a conditional statement.

A conditional statement is one that has the form "If P then Q," where P and Q are sentences. P is referred to as the hypothesis in this conditional statement, and Q is referred to as the conclusion. "If P then Q" implies that Q must be true sometimes when P is true.

The type of conditional statements are as follows:

A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a conditional statement.

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Answer:

Let the first term be "a" and common difference be "d". Then, the fifth term is 3a.

Quarter of the fifth term is 9, so (1/4) * 3a = 9. Solving for a, we get:

a = 36.The sum of the first 8 terms of an arithmetic progression can be found using the formula:

S_n = n/2 * (2a + (n - 1)d)

where n is the number of terms.In this case, n = 8, so:

S_8 = 8/2 * (2 * 36 + (8 - 1) * d)

= 4 * (72 + 7d)

= 288 + 28dSince the common difference is "d", the sum of the first eight terms is 288 + 28d.

Correct me if I’m wrong

The sum of the first eight terms of the arithmetic progression is 264.

An arithmetic sequence is a set of numbers where each phrase is created by multiplying the previous term by a constant amount (referred to as the common difference). In other terms, an arithmetic sequence is a set of numbers that changes in value from one term to the next by a fixed amount.

Let the first term of the arithmetic progression be represented by 'a', and let the common difference between terms be represented by 'd'.

Then, according to the problem statement, we know that the fifth term is three times the first term, so:

a + 4d = 3a

Simplifying this equation, we get:

2a = 4d

a = 2d

Now we can use the fact that a quarter of the fifth term is 9 to solve for d:

(1/4)(3a) = 9

3a = 36

a = 12

d = a/2 = 6

So the arithmetic progression is: 12, 18, 24, 30, 36, 42, 48, 54

The sum of the first eight terms can be found using the formula:

S₈ = (n/2)(2a + (n-1)d)

where n = 8 is the number of terms.

Plugging in the values we have found, we get:

S₈ = (8/2)(2(12) + (8-1)(6))

S₈ = 4(24 + 42)

S₈ = 4(66)

S₈ = 264

Therefore, the sum of the first eight terms of the arithmetic progression is 264.

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The probability that Liz has two boys given that she has at least one boy who is taller is approximately 0.2841

Let's first consider all possible gender combinations of Liz's two children:

Boy, boy (BB)

Boy, girl (BG)

Girl, boy (GB)

Girl, girl (GG)

We know that Liz has at least one boy, which rules out the GG combination. That leaves us with three possible combinations: BB, BG, and GB.

From the given information, we know that in 76% of families consisting of one son and one daughter, the son is taller than the daughter. This means that in the BB combination, the probability that the taller child is a boy is 1 (since both children are boys), and in the BG and GB combinations, the probability is 0.76 (since there is one boy and one girl, and we know the boy is taller).

So, let's calculate the probability that Liz has two boys (BB) given that she has at least one boy who is taller. We can use Bayes' theorem for this

P(BB | taller child is a boy) = P(taller child is a boy | BB) × P(BB) / P(taller child is a boy)

where P(taller child is a boy | BB) = 1 (as both children are boys), P(BB) = 1/4 (since there are four possible gender combinations), and P(taller child is a boy) = P(taller child is a boy | BB) × P(BB) + P(taller child is a boy | BG) × P(BG) + P(taller child is a boy | GB) × P(GB) = 1 × 1/4 + 0.76 × 1/2 + 0.76 × 1/2 = 0.88.

Substituting these values into Bayes' theorem, we get

P(BB | taller child is a boy) = 1 × 1/4 / 0.88 = 0.2841

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Suppose that probability P(A)=3/5 and P(B)=2/3 then the correct answers are option B , C, D that is 4/15 < P (AnB) < 3/5, 2/5 < P(A|B) < 9/10 and . P (AnB) < 1/3.

Events that are mutually exclusive do not occur at the same time. For example, when a coin is tossed, the outcome will be either head or tail, but we cannot obtain both. Such occurrences are also known as disjunct events since they do not occur at the same time. If A and B are mutually exclusive occurrences, the probability of each is given by P(A Or B) or P(A Or B) (A U B).

Maximum of P(A∪B) can be 1.

Maximum of P(A∩B) is minimum of A and B, hence, 3/5.

Minimum of P(A∩B) is when the union of A and B is 1. Thus, P(A∩B) = 2/3+3/5−1=4/15

Thus, P(A∣B)=P(A∩B)/P(B) will range from,

9/10 to 2/5.

Maximum of P(A∩B ′ ) is maximum when there is minimum intersection,

hence P(A∩B ′ )=P(A)−P(A∩B) = 1/3

Two occurrences are said to be mutually exclusive in probability theory if they cannot occur at the same time or concurrently. In other words, discontinuous events are those that are mutually exclusive. If two occurrences are regarded discontinuous, the likelihood of both happening at the same time is zero.

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Answer:

(6x-1)(2x+1)

Step-by-step explanation:

12x²+4x-1 (find two numbers that when you add or subtract them the ANS will be the coefficient of x and those same numbers when you multiply them the ANS will be the product of 12 and -1) then replace the middle term with those numbers.

12x²+6x-2x-1

(12x²+6x)(-2x-1)

6x(2x+1)-1(2x+1)

(6x-1)(2x+1)

x2−4x+3=0

For this equation: a=1, b=-4, c=3

1x2+−4x+3=0

Step 1: Use quadratic formula with a=1, b=-4, c=3.

x=

−b±√b2−4ac

2a

x=

−(−4)±√(−4)2−4(1)(3)

2(1)

x=

4±√4

2

x=3 or x=1

Answer:

x = 1, x = 3

Step-by-step explanation:

x² - 4x + 3 = 0

consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term (- 4)

the factors are - 1 and - 3 , since

- 1 × - 3 = + 3 and - 1 - 3 = - 4 , then

(x - 1)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 3 = 0 ⇒ x = 3

The graph of the function:

Can be obtained by using the parent function:

Whose graph is shown below:

We must first turn x into -x by making a reflection over the y-axis. This way, the function becomes:

And the graph is:

Finally, we just add 4 to x to translate the graph 4 units to the right to get our desired function:

The graph is shifted 4 units to the right as shown:

Answer: 6 gallons

Step-by-step explanation:

4/30  * 45  = 6

Answer:

\(2 {x}^{2} - 6x - 1 = 0 \\ a = 2 \: \: \: b = - 6 \: \: \: c = - 1 \\ \\ x = \frac{6\binom{ + }{ - } \ \sqrt{ {6}^{2} - 4(2)( - 1)} }{2 \times 2} \\ \\ x = \frac{6 \binom{ + }{ - } \sqrt{44} }{4} \\ x = \frac{6 + \sqrt{44} }{4} \\ \\ or x = \frac{6 - \sqrt{44} }{4} \)

I hope that is useful for you :)

Answer:

Two years in a row: 2.25%

Three years in a row: 0.3375%

Step-by-step explanation:

For two years in a row:  

15/100*15/100

225/10000=

0.0225

0.0225*100 (for percentage)= 2.25%

For three years in a row:  

15/100*15/100*15/100

3375/1000000=

0.003375

0.003375*100 (for percentage)=0.3375%

Answer:

Step-by-step explanation:

3x^2+4x-4=0 (we move 4 to the other side to factor)

(3x-2)(x+2)

^think of 2 numbers that when you multiply it will be -4 and when you multiply one of it to 3x and add to the other it will be 4x.

Recheck:

-2(2)= -4 (correct)

-2x+6x=4x (correct)

According to the given voltage function, the value of the voltage for the power of 576 watts is 48 watts.

Function:

The relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Given,

The voltage V of an audio speaker can be represented by V=2√P, where P is the power of the speaker. An engineer wants to design a speaker with 576 watts of power.

Here we need to find the voltage of the given power.

In the given question we have the voltage function

v = 2√P

Where P refer the power of the speaker.

Here we have to find the voltage if engineer wants to design a speaker with 576 watts of power.

Which means the value of P is 576.

Then the value of V is calculated as,

v = 2 √576

We know that the value of √576 = 24,

So,

v = 2 x 24

v = 48.

Therefore, the voltage is 48 watts.

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Answer:

w = 42

x = 29

Step-by-step explanation:

We know that w + 138 must equal 180, so we get 42 for w. Then we know that 19 + x + 2 = 90, and w = 42. So if we add 42 + 19, and subtract that from 90, we get 29. Hope this helps!

The equation f(4) - f(1) = f'(c)(4 - 1), where f(x) = (x - 3)^(-2), asks for values of c in (1, 4) that satisfy the equation. By calculating f(4) and f(1), we find they are both equal to 1. The derivative of f(x) is -2(x - 3)^(-3). Substituting these values, we get 3/4 = f'(c)(3). However, since f'(x) is negative in the interval (1, 4) and the left side is positive, there is no value of c in that interval that satisfies the equation (DNE).

To find the values of c in the interval (1, 4) such that f(4) - f(1) = f'(c)(4 - 1), where f(x) = (x - 3)^(-2), we need to apply the Mean Value Theorem for derivatives.

Let's start by calculating f(4) and f(1):

f(4) = (4 - 3)^(-2) = 1

f(1) = (1 - 3)^(-2) = 1/4

Now, let's calculate the derivative of f(x):

f'(x) = d/dx[(x - 3)^(-2)]

      = -2(x - 3)^(-3)

Next, we substitute these values into the equation f(4) - f(1) = f'(c)(4 - 1):

1 - 1/4 = f'(c)(3)

We simplify the equation:

3/4 = f'(c)(3)

To solve for c, we need to find the value of c in the interval (1, 4) that satisfies this equation. Notice that f'(x) = -2(x - 3)^(-3) is negative for all x in the interval (1, 4). Since the left side of the equation is positive (3/4 > 0), there is no value of c in the interval (1, 4) that satisfies the equation. Therefore, the answer is DNE (does not exist).

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Answer:

The equation of the line is: y=2x + 3

Answer:

Below

Step-by-step explanation:

● x-20 = y+20 (1)

● 2(y-22) = x+22 (2)

This is a system of simulataneous equations

Let's simplify the expressions first

● x -20 = y + 20 (1)

Add 20 to both sides

● x -20 + 20 = y+20 +20

● x = y + 40 (1)

● 2(y-22) = x+22 (2)

● 2y - 44 = x +22

Substrat 22 from both sides

● 2y-44-22 = x+22-22

● 2y -66 = x (2)

This is the new system:

● x = y+40 (1)

● x = 2y-66 (2)

Substract (2) from (1)

● x-x = y+40-(2y-66)

● y+40-2y+66 = 0

● -y +106 = 0

● y = 106

Replace y with 106 in (1)

● x = y +40

● x = 106+40

● x = 146

So the solutions are (146,106)

Answer c

Step-by-step explanation:

Answer:4.6 × 30= 138

5 × 40= 200

Step-by-step explanation:

Answer:

69.9°

Step-by-step explanation:

sin28/11 = sinx/22

22(sin28) = 11(sinx)

sinx = 22(sin28) / 11 = 0.9389

x = sin⁻¹(0.9389) = 69.9°