Solve equation Y=9x-70 and y=2x-32

Answer:

Considering the sign behavior of each function and the angle and its multiples.

Step-by-step explanation:

1) Firstly, look at the Unit Circle below. In the Unit Circle we can with the aid of symmetry, find angles with the same height, and also the same angle value.

2) We need to remember or get to know the behavior of the trigonometric functions, in order to know whether it is positive or negative. Let's work with the tree basic ones: sine, cosine and tangent.

3) Let's take the 60º angle, to exemplify.

Symmetric angles have the same height proportional values for their angles.

Notice that the angle of 60º ∈ Quadrant II, and 120º ∈ Quadrant II and 240º for Quadrant III and 300º for Quadrant IV as well.

We can calculate their values, considering their sign behavior each quadrant for cosine function.

Similarly, for the sine function, don't forget to consider sign behavior for each quadrant

\(cos60^{\circ}=\frac{1}{2}\\cos 120^{\circ}= -cos60^{\circ}=-\frac{1}{2}\\cos 240 ^{\circ}=-cos60^{\circ}=-\frac{1}{2}\\cos 300^{\circ}= cos60^{\circ}=\frac{1}{2}\)

Similarly, for sine function, don't forget to considering sign behavior for each quadrant

\(sin 60^{\circ}=\frac{\sqrt{3}}{2} \\sin 120^{\circ}=sin 60^{\circ}=\frac{\sqrt{3}}{2} \\\\sin 240^{\circ} =-sin 60^{\circ}=\frac{-\sqrt{3}}{2} \\\\sin 300^{\circ} =-sin 60^{\circ}=\frac{-\sqrt{3}}{2}\)

And finally, for the tangent function

\(tan 60^{\circ}=\sqrt{3} \\tan 120^{\circ}=-tan 60^{\circ}=-\sqrt{3}\\tan 240^{\circ}=tan 60^{\circ}=\sqrt{3}\\tan 300^{\circ}=-tan 60^{\circ}=-\sqrt{3}\)

We can take advantage of symmetry in the determination of coordinates of points by using two orthogonal axes of symmetry and by establishing a consistent notation to identify each quadrant.

In somewhat intuitive words, a circle is a figure which have infinite axes of symmetry passing on its surface and though its center. Hence, the four quadrants are formed by two orthogonal axes of symmetry.

Now we must establish a notation to distinguish one quadrant from another. In this case we decided to use the well-known right-hand notation, in which each of the four quadrants is labeled counterclockwise.

This system allows to create a guide to determine where the point is:

In a nutshell, we can take advantage of symmetry in the determination of coordinates of points by using two orthogonal axes of symmetry and by establishing a consistent notation to identify each quadrant. \(\blacksquare\)

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The given differential equation is y'' = 39x.

To determine the value of A, we can integrate the equation twice. The first integration will give us the general solution, and then we can compare it to the given form to determine the value of A.

Integrating the equation once, we get:

y' = ∫(39x) dx

y' = (39/2)x^2 + C1

Integrating again, we obtain:

y = ∫((39/2)x^2 + C1) dx

y = (39/6)x^3 + C1x + C2

Comparing this to the given general solution y = Ax^3 + C1x + C2, we can equate the coefficients:

A = 39/6

A = 6.5

Therefore, the value of A is 6.5.

Regarding the type of differential equation, the given equation y'' = 39x is a second-order linear homogeneous ordinary differential equation. It is not separable, exact, or Bernoulli because it does not meet the criteria for those specific types of differential equations.

  Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

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(a). There is a 5.26% chance that the metal ball falls into a green slot.

(b). There is a 52.63% chance that the metal ball falls into either a green or a red slot on any given spin of the roulette wheel.

(c). P(00 or red)  ≈ 0.5263

(d). This event is called impossible.

(a) P(green) = 2/38 = 1/19 ≈ 0.0526.

This means that there is a 5.26% chance that the metal ball falls into a green slot on any given spin of the roulette wheel.

If the wheel is spun 100 times, one would expect about 5 spins to end with the ball in a green slot. (Expected value = 100 x P(green) = 100/19 ≈ 5.26, which we round to the nearest integer.)

(b) P(green or red) = P(green) + P(red) = 2/38 + 18/38 = 20/38 ≈ 0.5263. This means that there is a 52.63% chance that the metal ball falls into either a green or a red slot on any given spin of the roulette wheel.

If the wheel is spun 100 times, one would expect about 53 spins to end with the ball in either a green or red slot. (Expected value = 100 * P(green or red) = 2000/38 ≈ 52.63, which we round to the nearest integer.)

(c) P(00 or red) = P(00) + P(red) = 2/38 + 18/38 = 20/38 ≈ 0.5263. This means that there is a 52.63% chance that the metal ball falls into either 00 or a red slot on any given spin of the roulette wheel.

(d) The probability that the metal ball falls into the number 31 and a black slot simultaneously is zero, since 31 is an odd number and all odd numbers are red on the roulette wheel. This event is called impossible.

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Answer:

It will take 60 hours for 2 elephants to set up the tent.

Step-by-step explanation:

Represent set-up time by T and the number of elephants by E.  T varies inversely with E:

T  = k/E, or TE = k

If 4 elephants can set up a tent in 30 hours, then 30(4) = k, and

T = 120/E

Now let E = 2.  We get T = 120/2, or 60

It will take 60 hours for 2 elephants to set up the tent.

Hey dude, I'm not completely sure but I think the answer's 30°.

Answer:

25miles

Step-by-step explanation:

49.98+0.14t = 39.98+0.18t

-39.98              -39.98

10.00+0.14t  =  0.18t

-0.14t                -0.14t

  10 = 0.4t

25=t

Answer:

The formula of a trapezoid is:

B1(base 1) + B2(base 2) x H(height) x 1/2 (basically just dividing by 2)

In this case 9 and 3 are your bases so add them together to get 12.

Now we multiply 12 to the height! 12 x 3(height) = 36. Now we multiply 36 to 1/2 which is just dividing by 2, so 36 divided by 2 = 18

Answer:

The error is in the second line.

x = -1

Step-by-step explanation:

When solving for "x", you are trying to isolate it, or move everything else to the other side. You may have learned that "what you do to one side, you do to the other" .

2x + 18 = 16

2x = 34               18 was added to the right side, but not to the other.

If you add 18 on both sides, then the equation would be:

2x + 36 = 34       "x" is not being isolated.

Instead, you should subtract 18 from 16.

Correct solutions steps:

2x + 18 = 16

2x + 18 - 18 = 16 - 18     Subtract 18 from both sides to cancel out 18

2x = -2

2x/2 = -2/2                     Divide both sides by 2

x = -1                              Final answer

The quotient for the given expression is 8x^2-8x+14 and the remainder is -19.  The solution has been obtained using the method of long division of polynomial.

What is polynomial long division?

A formula for dividing one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.

Using Polynomial Long Division,

Dividing :  8x^3 + 6x - 5 ("Dividend")

By         :    x+1   ("Divisor")

Dividend              8x^3  +  0x^2  +  6x  -  5

- divisor  * 8x^2   8x^3  +  8x^2        

Remainder                     -  8x^2   +  6x  -  5

- divisor  * (-8x)               -  8x^2   -  8x    

Remainder                                       14x  -  5

- divisor  * 14                                     14x +  14

Remainder                                               - 19

Quotient :  8x^2-8x+14

Remainder:  -19

Hence, the quotient for the given expression is 8x^2-8x+14 and the remainder is -19.

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The probability of choosing either "w" or "G" is 3/12.

Events that are mutually incompatible cannot take place at the same moment. The outcomes of receiving a head or a tail, for instance, are mutually incompatible when we toss a coin. You cannot have both at the same time.

On the other hand, independent occurrences are those that have no bearing on one another. For instance, if we flip a coin twice, receiving a head on one toss and a head on the other are separate occurrences. The result of the first toss has no bearing on the result of the second toss.

The probability of choosing either "w" or "G" is 3/12.

The probability of choosing "w" or "G" can be calculated as:

P(w or G) = P(w) + P(G) - P(w and G)

The probability of choosing "w" is 2/12.

The probability of choosing "G" is also 2/12.

The probability of choosing both "w" and "G" when the appear together is 1/12.

Substituting the values:

P(w or G) = P(w) + P(G) - P(w and G)

P(w or G) = 2/12 + 2/12 - 1/12

P(w or G) = 3/12

Hence, the probability of choosing either "w" or "G" is 3/12.

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5! permutation of the letters abcdefgh contains strings ab, de, and gh.

The number of permutations of 'n' objects taken 'r' at a time is determined by the following formula:

P(n,r)=n! / (n−r)!

We can also find permutation using the Selection and Formation Method:

For example:

1. Number of ways to arrange the letter SANOJ:

here number of alphabets are 5, and we have to arrange all the letter so using permutation formula:

P(5, 5 ) = 5! / (5-5)!

P(5, 5 ) = 5!                : 0! = 1

without using the formula we can simply write 5! as the answer.

Here, we have given the word, " abcdefgh "

and we have to make those arrangements in which ab, de, and gh come together:

so now, we will count ab, de, and gh as a single word.

now, we will have 5 different words/alphabet:

1 → ab

2 → c

3 → de

4 → f

5 → gh

Number of ways to arrange all the 5 words/alphabet: 5!

Hence,

5! permutation of the letters abcdefgh contains strings ab, de, and gh.

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If the radius of the bullseye in the dart board is 0.5 cm, then the area of dartboard not including the bullseye is 182.5 cm².

The outer circumference of the dartboard is 48 centimeters, so we can use this to find the radius of the dartboard:

⇒ 48 = 2πr,

Dividing both sides by 2π, we get:

⇒ r = 48/2π ≈ 7.64,

So, radius of the dartboard is 7.64 centimeters.

The area(A) of a circle is = πr²,

where "r" is = radius,

The area of the bull's eye is:

⇒ Area of Bullseye = π × (0.5)²,

⇒ 0.785,

To find the area of the dartboard not including the bull's eye,

We subtract the area of the bull's eye from the area of the whole dartboard:

⇒ Area of dartboard not including bullseye = πr² - (area of bullseye),

⇒ Area of dartboard not including bullseye = 3.14×7.64×7.64 - 0.785,

⇒ Area of dartboard not including bullseye = 183.28 - 0.785,

⇒ Area of dartboard not including bullseye ≈ 182.5,

Therefore, the area of the dartboard not including the bull's eye is approximately 182.5 cm².

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Answer: my brain hurts.

Step-by-step explanation:

Answer:

260 square centimeters

Step-by-step explanation:

The formula for the area of a parallelogram is:

b x h

Where the base (b) is multiplied by the height (h) perpendicular to it.

The base here is 20 cm

The height perpendicular to the base is 13 cm

20 x 13 = 260

Or you can decompose and rearrange it into a rectangle. You will get 20 cm as the length and 13 cm as the width. The answer will be just the same!

Hope this helps!

Answer: 260 cm²

Step-by-step explanation: A parallelogram is a

quadrilateral with two pairs of parallel sides.

The formula for the area of a parallelogram is A = bh.

Since the base of the parallelogram is 20 cm and the height

of the parallelogram is 13 cm, we can plug this information into the formula

to get (20 cm)(13 cm) which gives us 260 cm².

So the area of the parallelogram shown is 260 cm².

7 + 7 + 7 + 7 + 7​ means 7 is added 5 times

It could be written as

5(7)

7 x 5 and

7 . 5

But it can not be written as 7^5 because 7^5 means 7 x 7 x 7 x 7 x 7

Hence, 7^5 does not represent the expression 7 + 7 + 7 + 7 + 7​

This makes the correct option to be the third option. That is 7^5

Answer:

1.D(0, 4) → D'(0, –4)

2.E(–2, 0) → E'(–2, 0)

3.The perpendicular distance from G' to the x-axis will equal 2 units.

4.The perpendicular distance from D' to the x-axis will equal 8 units.

5.The orientation will be preserved.

Step-by-step explanation:

D(0, 4) becomes D'(0, –4) and E(–2, 0) becomes E'(–2, 0).

We know that the rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

The coordinate of  D(0, 4) becomes D'(0, –4) and coordinate of E(–2, 0) becomes E'(–2, 0).

3.The perpendicular distance from G' to the x-axis is 2 units.

4.The perpendicular distance from D' to the x-axis is 8 units.

Hence D(0, 4) becomes D'(0, –4) and E(–2, 0) becomes E'(–2, 0).

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The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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Answer:

x=3 the answer is 3

Step-by-step explanation:

Answer:

x=42069

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\left\{\begin{array}{ccc}y=x^2+2x-1\\y-3x=5&\text{add}\ 3x\ \text{to both sides}\end{array}\right\\\left\{\begin{array}{ccc}y=x^2+2x-1&(1)\\y=3x+5&(2)\end{array}\right\)

Substitute (1) to (2):

\(x^2+2x-1=3x+5\qquad|\text{subtract}\ 3x\ \text{and 5 from both sides}\\\\x^2-x-6=0\\\\x^2+2x-3x-6=\\\\x(x+2)-3(x+2)=0\\\\(x+2)(x-3)=0\iff x+2=0\ \vee\ x-3=0\\\\x=-2\ \vee\ x=3\)

Substitute the values of x to the (2):

\(\text{for}\ x=-2\\\\y=3(-2)+5=-6+5=-1\\\\\text{for}\ x=3\\\\y=3(3)+5=9+5=14\)

Since each packet received is independent of any other packet, we can model X as a binomial distribution with parameters n=10 and p=0.05 (the probability of receiving a packet with errors is 1-0.95=0.05).

The probability mass function (PMF) of X is given by:

P(X=k) = (10 choose k) * 0.05^k * 0.95^(10-k), for k = 0, 1, 2, ..., 10

where (10 choose k) is the binomial coefficient, representing the number of ways to choose k packets out of 10.

So, for example, the probability of receiving exactly 2 packets with errors is:

P(X=2) = (10 choose 2) * 0.05^2 * 0.95^8
= 45 * 0.0025 * 0.4305
= 0.0463

Similarly, we can calculate the probabilities for other values of k.
Hi, I'd be happy to help you with your question. Let's find the probability mass function (PMF) of X, where X represents the number of packets received with errors out of 10 packets, and the packets are independent with a 0.95 probability of being error-free.

1. Define the probability of success (error-free) and failure (with errors).
  Success (error-free): p = 0.95
  Failure (with errors): q = 1 - p = 0.05

2. Since the packets are independent, we can use the binomial distribution to model the problem. The PMF of a binomial distribution is given by:
  P(X = k) = C(n, k) * p^k * q^(n-k)

3. In our case, n = 10 (number of packets received), and we need to find P(X = k) for k = 0, 1, 2, ..., 10.

So, the PMF of X, the number of packets received with errors out of 10 independent packets, is:

P(X = k) = C(10, k) * (0.95)^k * (0.05)^(10-k), for k = 0, 1, 2, ..., 10.

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Answer:

The slope of the line that contains diagonal OE will be = -3/2

Step-by-step explanation:

We know the slope-intercept form of the line equation

y = mx+b

Where m is the slope and b is the y-intercept

Given the equation of the line that contains diagonal HM is y = 2/3 x + 7

y = 2/3 x + 7

comparing the equation with the slope-intercept form of the line equation

y = mx+b

Thus, slope = m = 2/3

As we have to determine the slope of the line that contains diagonal OE.

As the slope of the line that contains diagonal HM = 2/3

We also know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line that contains diagonal

OE will be = -1/m = -1/(2/3) = -3/2

Hence, the slope of the line that contains diagonal OE will be = -3/2

The given statement about the disjunction is true.

A compound statement with two distinct statements (disjuncts) connected by the wedge symbol (v) is called Disjunction.

Given is the statement -

(S~T) v (~U.W)

The given statement about the disjunction is true.

Therefore, the given statement about the disjunction is true.

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Step-by-step explanation:

option C is correct!

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

Answer:

1. b⁵

2. +16m⁹

Step-by-step explanation:

1. Add exponents: b³⁺² = b⁵

2. Negative and Negative = positive

2*8 = 16

m⁴⁺⁵ = m⁹

Hence: + 16m⁹

Answer:

\(1) \: {b}^{5} \)

\(2) \: \: + 16 {m}^{9} \)

Step-by-step explanation:

\( {b}^{3} \times {b}^{2} = {b}^{3 + 2} = {b}^{5} \)

we know that

\(( - ) \times( - ) = ( + )\)

So

\( - 2 {m}^{4} \times - 8 {m}^{5} \\ = + 16 {m}^{9} \)

Answer:

x-2y+5=0

Step-by-step explanation:

y+1= \(\frac{x+7}{2}\)

y=\(\frac{x+7}{2}\) -1

y=\(\frac{x+7-2}{2}\)

y=\(\frac{x+5}{2}\)

2y=x+5

x-2y+5=0

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-1)=\dfrac{1}{2} (x-(-7)}\)

Simplify

\(\rm{y+1=\dfrac{1}{2}(x+7)}\)

The average residential electrical power use refers to the amount of electrical energy consumed by households. It is typically measured in hundreds of watts per hour. By examining the provided table, you can identify the specific values for average power consumption in a residential setting.

According to the given table, the average residential electrical power use is measured in kilowatt-hours (kWh) per month, not hundreds of watts per hour. However, to convert it to the requested unit, we can divide the monthly average by the number of hours in a month (720 hours) and then multiply by 100 to get the average residential electrical power use in hundreds of watts per hour.

So, for example, if the monthly average is 600 kWh, the hourly average would be (600 kWh / 720 hours) x 100 = 83.33hundreds of watts per hour.

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Answer:

term

Step-by-step explanation:

We cannot construct a confidence interval using the normal approximation in this case because the sample sizes of the control and treatment groups are relatively small (less than 30), and the data does not meet the assumptions required for the normal approximation.

The normal approximation assumes that the data follows a normal distribution, and for sample sizes less than 30, the distribution of the sample mean may not be well approximated by a normal distribution. In addition, the normal approximation assumes that the observations are independent, which may not hold true in this study due to the nature of the treatment and control groups.

If we constructed a confidence interval despite these problems, the interval may not accurately reflect the true difference in survival rates between the control and treatment groups. The interval could be biased or too wide/narrow, leading to incorrect conclusions about the effectiveness of the heart transplant program. Therefore, it is important to use appropriate statistical methods that account for the specific characteristics of the data and study design in order to obtain reliable estimates and valid inferences.

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