Graph a line with a slope of 2/5 that contains the point (-2, 4) I HAVE THE ANSWER ALREADY LOL, for anyone who needs it!!

put one point at (-7,2) and the other point at (-2,4)

a) The probability that the chosen letter is R is 1/10.

b) The probability mass function of X is P(X = 3) = 1/5, P(X = 4) = 2/5, P(X = 5) = 2/5

c) If k = 3 , then P(X = 3 | X = 3) = 1. Otherwise, P(X = k | X = 3) = 0

d)  The conditional probability P(the chosen letter is R | X > 3) is 1/11.

e) Given that the chosen letter is R, the probability that the word was BROWN is 1/2.

a) The probability that the chosen letter is R is equal to the number of R's divided by the total number of letters in the sentence. There are two R's in the sentence "SOME DOGS ARE BROWN", so the probability of choosing an R is 2/20 = 1/10.

b) To find the probability mass function of X, we need to find the probability of choosing a word of a certain length. There are five words in the sentence, one of length 3, two of length 4, and two of length 5.

The probability of choosing a word of length 3 is 1/5, the probability of choosing a word of length 4 is 2/5, and the probability of choosing a word of length 5 is 2/5. So, the probability mass function of X is:

P(X = 3) = 1/5

P(X = 4) = 2/5

P(X = 5) = 2/5

c) To find the conditional probability P(X = k | X = 3), we need to find the probability of choosing a word of length k given that we know the word has length 3. If X = 3, then the word must be "DOG". So, the only possibility is P(X = 3 | X = 3) = 1.

For all other values of k, P(X = k | X = 3) = 0 because the word must have length 3 given that X = 3.

d) To find the conditional probability P(the chosen letter is R | X > 3), we need to find the probability of choosing an R given that we know the length of the word is greater than 3. The number of R's in words with length greater than 3 is 1, and the number of letters in these words is 11, so the probability is 1/11.

e) Given that the chosen letter is R, the probability that the word was BROWN is equal to the number of R's in the word BROWN (1) divided by the number of R's in the sentence (2). So, the probability is 1/2.

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Answer: 18

Step-by-step explanation:

\(\triangle HJK \cong \triangle HLK\) by HL. Therefore, \(JK=2\) by CPCTC.

Using the segment addition postulate, \(GK=9\).

Furthermore, \(\triangle HGK \cong \triangle HMK\) by HL. This means that \(MK=9\) by CPCTC.

Using the segment addition postulate again, \(GM=9+9=18\).

Answer:

The answer is y=-1 (answer is C).

Answer:

Step-by-step explanation:

The inequality that represents Jenny's situation is:

600 - 20w > 300

To solve for w, we can start by subtracting 600 from both sides of the inequality:

-20w > 300 - 600

-20w > -300

Next, we can divide both sides by -20, remembering to reverse the direction of the inequality because we are dividing by a negative number:

w < (-300) / (-20)

w < 15

Therefore, the number of weeks that Jenny can continue to withdraw $20 from her account is less than 15. Since Jenny cannot withdraw a fractional number of weeks, the largest whole number of weeks that satisfies the inequality is 14.

Therefore, Jenny can continue to withdraw $20 from her account for 14 weeks while still keeping more than $300 in her account for college.

The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.

The number of possible arrangements of n elements is given by the factorial of n, that is:

\(A_n = n!\)

In this problem, we have that:

Hence the number of ways by which they can go on stage is:

N = 2 x 3! = 12.

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Answer:

Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.

What is the arrangements formula?

The number of possible arrangements of n elements is given by the factorial of n, that is:

A_n = n!A

n

=n!

In this problem, we have that:

For the first dragon, either the green or the blue dragon, hence two outcomes.

For the remaining dragons, there are 3! possible ways.

Hence the number of ways by which they can go on stage is:

N = 2 x 3! = 12.

The solution to the system of equations is x = -9; y = 15 and z = -4

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

Given the system of equations:

-3x - y + z = 8     (1)

-3x - y + 3z = 0   (2)

and:

x - 3z = 3            (3)

Solving the three equations simultaneously gives:

x = -9; y = 15 and z = -4

The solution is x = -9; y = 15 and z = -4

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Answer:

Step-by-step explanation:

1)

Congruency shortcuts:  

HL, SSS, SAS, ASA, and AAS

where S=side

A=angle

H=hypotenule

L=leg

HL is only for a right triangle

If you can prove sides and angles are congruent according to those 5 rules, you have proven the triangles are congruent

Similarity shortcuts:

AA, SAS, SSS

We have triangle similarity if (1) two pairs of angles are congruent (AA) (2) two pairs of sides are proportional and the included angles are congruent (SAS), or (3) if three pairs of sides are proportional (SSS)

2)

BG ≅ GD              >Given from image

IG ≅ GO               >Given from image

<BGI ≅ <DGO        >Vertical Angles

ΔBGI  ≅ ΔDGO        >SAS            

You have proven that the triangles are congruent because you used the shortcut by proving a side and angle and a side are congruent so SAS makes them congruent

The accrued value of the account in 14 years is $4967.89

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Amount = P * (1 + 0.25r)ᵗ

Where

P = Principal = 4200

r = Rate = 5.2% = 0.052

t = time = 13

Substitute the known values in the above equation, so, we have the following representation

Amount = 4200 * (1 + 0.25 * 0.052)¹³

Evaluate

Amount = 4967.89

Hence, the amount is 4967.89

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Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)

Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

Answer:

3 gallons

Step-by-step explanation:

:}

Answer:

a = 0

b = \(\frac{\pi }{4}\)

c = 0

d = 3

e = 5

f = \(\sqrt{34-r^2}\)

Step-by-step explanation:

Equation of the solid sphere = x^2 + y^2 + z^2 ≤ 34 ------- (1)

at Z = 5

since the bottom of the sphere(z) is flat = 5 we will use cylindrical coordinates

concentrating in the first octant as mentioned in the question

at Z = 5 , equation 1 becomes :

  x^2 + y^2 + 25 ≤ 34 = x^2 + y^2 = 9  

hence the radius around the xy axis = \(\sqrt{9}\) = 3

that means the radius is : 0 ≤ r ≤ 4 ,  0 ≤ ∅ ≤ \(\frac{\pi }{4}\)

next we have to find the upper bound of: Z = ±\(\sqrt{34-r^2}\) we will pick out only the positive

5 ≤ z ≤ \(\sqrt{34 - r^2}\)

therefore for the  Volume = ∫ba∫dc∫fe

a = 0

b = \(\frac{\pi }{4}\)

c = 0

d = 3

e = 5

f = \(\sqrt{34-r^2}\)

For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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Answer:

\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Step-by-step explanation:

\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Answer:

$98

Step-by-step explanation:

56/8= 7

7x14=98

Hope this helps.

Answer:

B. Positive linear

Step-by-step explanation:

First, this graph is a linear graph because a linear graph is a straight line. The graph in the diagram is also a straight line, so it is linear.
Also, notice how as x increases, y increases. This means that the graph is positive

Answer:

m > 4

Step-by-step explanation:

5m - 8 > 12

Add 8 to each side

5m - 8+8 > 12+8

5m > 20

Divide by 5

5m/5 > 20/5

m > 4

Step-by-step explanation:

The answer to 5.04 × 10 eqauls 50.4 , but there are no answers choices that have exactly 50.4 , so the answer is none of these . I hope this helps you :)

Answer:

percentage profit = 150%

Step-by-step explanation:

percentage profit = sp - cp/cp * 100

sp is the selling price = 60000

cp is the cost price = 24000

percentage profit = 60000-24000/24000 * 100

percentage profit = 36000/24000 * 100

percentage profit = 36000/240

percentage profit = 150%

Answer:

Decay, 36%

Step-by-step explanation:

.64 is less that 1, so it is a decay. You find the rate by using the equation 1 - .64 = .36 or 36%.

Answer:

False

Step-by-step explanation:

To make a profit with the revenue of R=113.95x and cost of C =93x + 750 the value of x is 36units.

As given in the question,

The revenue for selling x units of a product is R = 113.95 x.

The cost of producing x units is C = 93 x + 750

To make a profit, the revenue must be greater than the cost.

R > C

113.95x > 93x +750

Subtract 93x from both the sides

113.95x -93x +93x-93x +750

⇒20.95x > 750

⇒x > 750/20.75

⇒x>35.799

Value of x to produce a profit is 36units

Therefore, to make a profit with the revenue of R=113.95x and cost of C =93x + 750 the value of x is 36units.

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The equation that represents the total cost of the membership will be y = 5x + 265.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.

Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,

y = 5x + 265

The equation that represents the total cost of the membership will be y = 5x + 265.

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Answer:

1

Step-by-step explanation:

Always you'll get an answer of 1.

a. The probability of no insect contaminants in a 225-gram bar from a brand at the mean contamination level can be found using the Poisson probability formula:

\(P(X = 0) = \frac{ (e^{-λ})(λ^0)}{0!} = \frac{(e^{-14.4})(14.4^0)}{0!}= 0.000000831\)

b. If you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level, the mean number of insect fragments would be one-fifth of 14.4, or 2.88. The probability of no insect contaminants can be found using the Poisson probability formula:

\(P(X = 0) = \frac{(e^-λ)(λ^0)}{0!} = \frac{(e^-2.88)(2.88^0)}{0!} = 0.056032\)

c. If you consume seven 28.35 gram (one-ounce) bars this week from a brand at the mean contamination level, the mean number of insect fragments would be (7 * 28.35/225) * 14.4 = 5.4336.

The probability of consuming one or more insect fragments in more than one bar can be found using the Poisson probability formula and the complement rule:

\($$\begin{aligned}& P(X>1) \\& =1-P(X \hat{a} 1) \\& =1-\left[\left(e^{-} \hat{I}\right)\left(\hat{I}^0\right) / 0 !+\left(e^{-} \hat{I}\right)\left(\hat{I}^1\right) / 1 !\right] \\& =1-\left[\left(e^{-} 5.4336\right)\left(5.4336^0\right) / 0 !+\left(e^{-} 5.4336\right)\left(5.4336^1\right) / 1 !\right] \\& =0.994784\end{aligned}$$\)

d. The probability of contamination more than twice the mean of 14.4 can be found using the Poisson probability formula and the complement rule:

\(P(X > 28.8) = 1 - P(X ≤ 28.8) \\= 1 - ∑(e^-λ)(λ^x)/x!\\ = 1 - 0.999999999999999 \\= 0.000000000000001\)

This probability is extremely small, so it can be considered unusual and not typical variation.

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Answer: true

Step-by-step explanation:

Answer:  true

Step-by-step explanation:

The chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.

We can first standardize the values of 20 and 40 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize (20 or 40), μ is the expected value (30), and σ is the standard deviation (5).

For x = 20, we get:

z = (20 - 30) / 5 = -2

For x = 40, we get:

z = (40 - 30) / 5 = 2

probability of getting a z-score between -2 and 2.

Using a standard normal distribution table or calculator, we find that the probability of getting a z-score between -2 and 2 is approximately 0.9544.

Therefore, the chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.

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