Why do the points ( 3 , 2 ) , ( 5 , 4 ) and ( 7 , 6 ) not form a triangle ?

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The weight range that contains at least 75% of all residents' annual garbage goes between 420 pounds and 787.5 pounds.

Given that the average resident of Metro City produces 630 pounds of solid waste each year, and the standard deviation is approximately 70 pounds, to determine the weight range that contains at least 75% of all residents' annual garbage weights, the following calculation must be performed:

Therefore, the weight range that contains at least 75% of all residents' annual garbage goes between 420 pounds and 787.5 pounds.

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Yes, the identity \(cos^{2}\)(2x) + \(sin^{2}\)(2x) = 1 is true. This identity is a fundamental trigonometric identity known as the Pythagorean identity.

The Pythagorean identity states that for any angle x, the square of the cosine of x plus the square of the sine of x is always equal to 1. Mathematically, it can be written as \(cos^{2}\)(x) + \(sin^{2}\)(x) = 1.

In the given expression, \(cos^{2}\)(2x) + \(sin^{2}\)(2x), we have an angle of 2x. According to the Pythagorean identity, the sum of the squares of the cosine and sine of this angle will also equal 1. Therefore, \(cos^{2}\)(2x) + \(sin^{2}\)(2x) simplifies to 1.

This identity is fundamental in trigonometry and has numerous applications in solving trigonometric equations and identities. It demonstrates the relationship between the cosine and sine functions and their squares, highlighting their complementary nature.

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Using the probability, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

In the given question,

If you choose two cards out of a deck of cards, then we have to find the chances one is a red face card and the other is a black non-face card.

As we know that in a deck having 52 cards. In which 26 are red and 26 are black.

We have to choose a red face card.

As we know that in a deck have 12 face cards. In which 6 red face cards and 6 black face cards.

So the chance of getting red face card is

P(R)=Total number of red face cards/Total number of cards

P(R)=6/52

We have to choose a black non-face card.

We know that in a deck have 6 black face cards and total black cards are 26. So the non face cards are 20.

So the chance of getting black non-face card is

P(B)=Total number of black non-face cards/Total number of cards

P(B)=20/52

Now the chances of getting one is a red face card and the other is a black non-face card is

P(R or B)=P(R)+P(B)

P(R or B)=6/52+20/52

P(R or B)=(6+20)/52

P(R or B)=26/52

P(R or B)=1/2

Hence, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

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The full recursive formula can be defined by these two parts

\(\begin{cases}a_1 = -0.56\\ a_n = 10*a_{n-1}\end{cases}\)

The top part tells us the first term is -0.56, while the second part says to get each new term we multiply the prior term by 10

second term = 10*(first term) = 10*(-0.56) = -5.6

third term = 10*(second term) = 10*(-5.6) = -56

etc etc

Answer:

true

Step-by-step explanation:

The parabola appears wider when |a| >1, the parabola appears thinner

When a is positive, the parabola opens upwards, but when a is negative parabola opens downwards

Step-by-step explanation:

brainliest?

Answer:

\(\boxed {x \geq 7}\)

Step-by-step explanation:

Solve the given inequality:

\(3x + 12 - 6x \leq -9\)

-Combine both \(3x\) and \(-6x\):

\(3x + 12 - 6x \leq -9\)

\(-3x + 12 \leq -9\)

-Subtract both sides by \(12\):

\(-3x + 12 - 12 \leq -9 - 12\)

\(-3x \leq -21\)

-When you are dividing an integer by a negative integer, the inequality sign would change. So, divide both sides by \(-3\):

\(\frac{-3x}{-3} \leq \frac{-21}{-3}\)

\(\boxed {x \geq 7}\) (Final Answer)

Inequalities help us to compare two unequal expressions. The given inequality will be satisfied when the value of x is equal to or more than 7.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The solution for the given inequality can be calculated as shown below,

3x + 12 - 6x ≤ -9

Subtract 12 from both sides of the inequality,

3x - 6x + 12 - 12≤ -9 - 12

Simplifying both sides of the inequality,

-3x ≤ -21

Divide both the sides of the inequality by -3, since division is been done with a negative integer the sign of the inequality will change,

-3x /-3 ≥ -21/-3

x ≥ 7

Hence, the given inequality will be satisfied when the value of x is equal to or more than 7.

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Answer:

2.11 Repeating

Step-by-step explanation:

Hope is right

y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given,

y-intercept 4 and slope -1/5

Now y=-1/5x+4

Hence y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

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Answer:

C. 1/4

Step-by-step explanation:

Since John has given 2/3 of his pencils to Roy, he has 1/3 of the total left. To find 1/4 of 1/3, multiply the numbers. 1/4(1/3) = 1/12. This means that he gave 1/12 of the beginning total to Maria. 2/3 can also be written as 8/12, and 1 can be written as 12/12. 12/12 - 8/12 = 4/12, and then 4/12 - 1/12 = 3/12. 3/12 can be simplified into 1/4

Answer:

John's remaining pencils in term of p = p/4

Hence, option 'c' is true.

Step-by-step explanation:

Let 'p' be the total number of pencils

Given that John gives 2/3 of his pencils = 2/3 of p

                                                                   = 2/3 × p

                                                                    = 2/3 p

Pencils left:

\(p-\frac{2}{3}p\)

Factor out common term p

\(p-\frac{2}{3}p=p\left(1-\frac{2}{3}\right)\)

           \(=\frac{1}{3}p\)

           \(=\frac{p}{3}\)

Pencils John gave to Maria = 1/4 × p/3 = p/12

The remaining Pencils in terms of 'p' = \(\frac{p}{3}-\frac{p}{12}\)

                                                              \(=\frac{3p}{12}\)

                                                              \(=\frac{p}{4}\)

Thus, John's remaining pencils in term of p = p/4

Hence, option 'c' is true.

There are (c) 34056 hands of six cards that contain exactly two Kings and two Aces

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

Cards = 52

The number of cards selected is

Selected card = 6

This means that the remaining card is

Remaining = 52 - 6

Remaining = 44

To select two Kings and two Aces, we have

Kings = C(4, 2)

Ace = C(4, 2)

So, the remaining is

Remaining = C(44, 2)

The total number of hands is

Hands = C(4, 2) * C(4, 2) * C(44, 2)

This gives

Hands = 6 * 6 * 946

Evaluate

Hands = 34056

Hence, there are 34056 of six cards

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The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

For the first graph

A = (-5, 2)

B = (5, -4)

To calculate the slope we will use the following formula

The answer would be m = -3/5

For the second graph

A = (-1, -1)

B = (3, 0)

To calculate the slope we will use the following formula

The answer would be m = 1/4

For the third graph

In the third graph, we have a vertical slope at point x = 2

In this case the slope would be equal to infinity and the equation of the line would be equal to x = 2

Answer:

D.(-4,-8) and(2,4)

Step-by-step explanation:

y=-2x

y=x²-8

this means that the two equations are equal because they both add up to y

thus; x²-8=-2x

formulae=Ax²+bx+c=0

x²+2x-8=0

find two numbers which multiplied will give you x² and when added will give you 2x that is x and x

x²+x+x-8=0

x(x+1)+1(x-8)=0

(x+1)(x-8)=0

1)x+1=0. x= -1

1)y=-2x

y=-2(-1)=2

y=2

2)y=x²-8

y=1²-8= -8

y= -8

note*this means that the answer should have both 2 and -8 thus d is the answer

Answer:

4

Step-by-step explanation:because 6022 is the sig figs, and 00000000000000000000 doesnt work because it is zero

Answer:

346,990

Step-by-step explanation:

There are 30 members in the club in total.

To find the total number of members in the club, we can use the information given. We know that 40% of the club members attended the event, and the number of members who attended is 12.

To determine the total number of members in the club, we can set up a proportion:

(40/100) = 12/x

Here, 40 represents 40% (or 40 out of 100) and x represents the total number of members in the club.

To solve for x, we can cross-multiply and then divide:

40 × x = 12 × 100

40x = 1200

x = 1200/40

x = 30

Therefore, there are 30 members in the club in total.

When we say that 40% of the club members attended the event, it means that 40 out of every 100 members attended. In other words, the ratio of members who attended the event to the total number of members in the club is 40:100 or 40/100. We can use this ratio to find the total number of members by setting up a proportion, where the known values are 40/100 (the ratio) and 12 (the number of members who attended). By solving the proportion, we find that the total number of members in the club is 30.

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The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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Answer: 7

Step-by-step explanation:

Number of cases = total bottles ÷ bottles per case.

Number of cases = 150 ÷ 24.

Number of cases = 6.25

Because the store doesnt sell a quarter of a case so you'll have to buy seven.

Answer:

20 years

Step-by-step explanation:

jeff's age = x

pete's age = x+10

in 5 years time

2(x+5) = x+10+5

thus x=5 therefore

pete's age in 5 years will be 20

Answer:

80 degrees

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360 degrees. Adding up the known measures gives you 95 + 123 + 62 = 280. Then you can subtract that from 360. 360 - 280 = 80. So x has to be 80 degrees.

The null hypothesis implied that cars 20 years or older do not pass safety inspection ≤  30%.

The alternative hypothesis implied that cars 20 years or older do not pass safety inspection >  30%

The local county officials are testing a hypothesis about the proportion of cars 20 years.

And older that do not pass their annual safety inspection at the service station.

The null hypothesis and alternative hypothesis can be stated as follows,

Null hypothesis,

The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station ≤  30%.

Alternative hypothesis,

The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station > 30%.

The null hypothesis assumes that the service station is not allowing cars with known violations to pass the safety inspection.

And that the rejection rate of 30% is consistent .

With the true rate of cars 20 years and older that do not pass their annual safety inspection at the service station.

The alternative hypothesis suggests that the service station is allowing cars with known violations to pass the safety inspection.

And that the rejection rate is lower than the true rate of cars 20 years .

And older that do not pass their annual safety inspection at the service station.

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Answer:

\(1 \frac{1}{4} \div 3 \frac{1}{2} \\ \\ \frac{5}{4} \div \frac{7}{2} \\ \\ \frac{5}{4} \times \frac{2}{7} \\ \\ \frac{5}{2} \times \frac{1}{7} \\ \\ = \frac{5}{14} \\ \\ = 0.357 \)

I hope I helped you^_^

Answer:

C5, [5]+, (55)

i think this is it but i might be wrong

Step-by-step explanation:

A woman you know has five children among which all five  are boys. probability for a woman that she will have all five boy as a five children is  0.5.

The probability or the outcome  in which a women with five children have all the girls and none of them as boys is :-

0.5x0.5=0.25.

So for the  first child there is a a 50% chance that is will be of a male. And same for the  second child being male there will be equal probability that it can be boy so it  also will have a probability .

So the probability of having five females is  0.55=0.03125

Except the above define value all the other outcome or choices means that the women have a least one son in the five children  and the total probability of an event is 1.

.The theoretical probability is mainly reasoning bases which is behind probability. For example, if a coin is tossed then the theoretical probability or the outcome of getting a head will be ½.

Probability provides information about the happening of   something which might happen and might not depending upon the outcome demand happen. Meteorologists, also take the help of probability to predict whether the rain may happen or not for instance In epidemiology, also probability theory is used to understand  about various risk related to life an to demonstrate various relation .

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The area of the region that lies inside the circle r=3sinΘ and outside the cardioid r=1+sinΘ is 0.6323

To find the area of a region in polar coordinates, we can integrate 1/2 r² dΘ over the desired interval of Θ. The factor of 1/2 is included because the area element in polar coordinates is 1/2 r² dΘ, as opposed to the dx dy element in Cartesian coordinates.

First, we need to find the points of intersection between the circle and the cardioid. To do this, we set the two equations equal to each other:

3sinΘ = 1+sinΘ

2sinΘ = 1

sinΘ = 1/2

Θ = π/6 or 5π/6

Now we can set up our integral. We want to integrate 1/2 r² dΘ over the interval π/6 ≤ Θ ≤ 5π/6. We will break this up into two integrals, one for the area inside the circle and one for the area inside the cardioid but outside the circle.

For the area inside the circle, we integrate from 0 to π/6 and from 5π/6 to π:

∫[0 to π/6,5π/6 to π] (1/2) (3sinΘ)² dΘ

= (9/2) ∫[0 to π/6,5π/6 to π] sin²Θ dΘ

Using the double angle identity, sin²Θ = (1-cos2Θ)/2, we can simplify this to:

(9/4) ∫[0 to π/6,5π/6 to π] (1-cos2Θ) dΘ

= (9/4) [Θ - (1/2)sin2Θ] [π/6 to 5π/6]

= (9/4) [(5π/6 - π/6) - (1/2)(sin(5π/3)-sin(π/3))]

= (1/2) [(2/3) + (√(3)/2) - (-√(3)/2 - 2/3) + (1/3)(-2-√(3))] - (9/2) [(2/3) - (1/2)(-√(3)-√(3)/2)]

= (1/2) [(4/3) - (1/3)√(3)] - (9/2) [(2/3) + (√(3)/2)]

= -19/24 - (15/4)√(3)

Finally, we can add the two areas together to get the total area:

Total area = area inside circle - area inside cardioid but outside circle

= (9/8) + (9/4)√(3) - (-19/24) - (15/4)√(3)

= 2/3 - (3/4)√(3) = 0.6323

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Answer:

Step-by-step explanation:

-9x + 6y = -30

-7x + 12y = -16

18x - 12y = 60

 -7x + 12y = -16

11x = 44

x = 4

-36 + 6y = -30

6y = 6

y = 1

(4,1)

Answer:

(4,1)

Step-by-step explanation:

-9x + 6y = -30.............(1)

-7x + 12y = -16 ............(2)

(2) - 2(1)

-7x+12y - 2(-9x+6y) = -16 - 2(-30)

simplify

11x = 44

or

x = 4 .......................(3a)

substitute (3) in (1)

-9(4) + 6y = -30

6y = -30 + 36

6y = 6

y =  1 ......................(3b)

Using results from (3a) and (3b), we have

solution :  (4,1)

Answer:

(1,2) and (6,7)

Step-by-step explanation: