if |a+3|=4 which describes all possible values of a)​

The Sequence:

1 , 1+2 , 1+2+3 , 1+2+3+4, ...

here, every term is an AP. finding the general formula for the sum of the elements of each term is:

Sₙ = \(\frac{x}{2}(2a + (x-1)d)\)        [where x = number of term, a = first term and d = common difference]

here, the first term is always 1 and so is the common difference.

Sₙ = \(\frac{x}{2}(2 +x-1)\)

Sₙ = \(\frac{x}{2}(1 +x)\) = \(\frac{1}{2}(x + x^{2})\)

which is the formula for a general term in our series

now, we need to find the sum of the first n terms of this series

\(\displaystyle\sum_{x=1}^{n} [\frac{1}{2}(x + x^{2})]\)

\(\displaystyle\frac{1}{2} [\sum_{x=1}^{n} (x) + \sum_{x=1}^{n}(x^{2})]\)

in this formula, for the first term, it's just an AP from x = 1 to x = n

for the second term, we have a general formula \(\frac{n(n+1)(2n+1)}{6}\)

\(\frac{1}{2}[\frac{n}{2}(2a + (n-1)d)+ \frac{n(n+1)(2n+1)}{6} ]\)

in this AP (first term), the first term and the common difference is 1 as well

\(\frac{1}{2}[\frac{n}{2}(2 + n-1)+ \frac{n(n+1)(2n+1)}{6} ]\)

\(\frac{1}{2}[\frac{n}{2}(n+1)+ \frac{n(n+1)(2n+1)}{6} ]\)

\([\frac{n}{4}(n+1)+ \frac{n(n+1)(2n+1)}{12} ]\)

\(\frac{n}{4}(n+1) [1+\frac{(2n+1)}{3} ]\)

\(\frac{n}{4}(n+1) [\frac{(3+2n+1)}{3} ]\)

\(\frac{n}{4}(n+1) [\frac{(2n+4)}{3} ]\)

\(\frac{n}{2}(n+1) [\frac{(n+2)}{3} ]\)

\(\frac{n(n+1)(n+2)}{6}\)

which is the sum of n terms of the given sequence

Answer:

36 servings

Step-by-step explanation:

1/4p = 6s

6(1/4p) = 6(6s)

1 1/2p = 36s

ANSWER:

STEP-BY-STEP EXPLANATION:

The right angles fulfill the Pythagorean theorem which is the following

We evaluate each option, replacing:

Answer:

At 16 people company B will be the cheaper option

Step-by-step explanation:

Assume that the number of people is x

∵ Company A charges $32 per person to host a banquet

∵ The number of people is x

∴ The cost of company A = 32x

∵ Company B charges an initial fee of $30 and charges $30 per person

∵ The number of people is x

∴ The cost of company B = 30x + 30

∵ Company B be is the cheaper option

→ That means the cost of company B < The cost of company A

∴ 30x + 30 < 32x

→ Subtract 30x from both sides

∵ 30x - 30x + 30 < 32x - 30x

∴ 30 < 2x

→ Divide both sides by 2

∴ 15 < x

→ 15 smaller than x means x is greater than 15

∴ x > 15

→ To make company B cheaper, the number of people should be > 15

∵ The first integer greater than 15 is 16

∴ At 16 people company B will be the cheaper option

The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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The graph of the relationship has an equation of m = 3.75k and it is is added as an attachment

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

The constant of proportionality is 3.75 grams/liter

This means that

k = 3.75

As a general rule

A proportional relationship is represented as

y = kx

In this case, we use

m = kv

Where

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

m = 3.75k

So, the equation of the relationship is m = 3.75k

The graph of the relationship m = 3.75k is added as an attachment

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Answer:

V = π · x² · y cm

Step-by-step explanation:

In General :

Volume of a cylinder = Area of the base which is a circle · height

V = π · r² · h

In our case:

Is given that radius is x cm and height is y cm.

V = π · x² · y

Answer:

Step-by-step explanation:

distance = rate of speed x amount of time traveled

This is often written D = R x T, or distance = rate x time

In this case D = (50 miles/hr) x (t hours), or D = 50 x T

Answer:

$96.95

Step-by-step explanation:

13.85*7=96.95

The value of the expression is r'(t) = (4, 6t, 12t²), T(1) = (2/7, 3/7, 6/7), r''(t) = (0, 6, 24t), r'(t) ร r''(t) = 144t³.

We are given the vector-valued function r(t) = (4t, 3t², 4t³).

To find r'(t), we need to take the derivative of each component of r(t) with respect to t:

r'(t) = (d/dt)(4t), (d/dt)(3t²), (d/dt)(4t³)

r'(t) = (4, 6t, 12t²)

To find T(1), we need to evaluate r'(t) at t = 1 and then divide by the magnitude of r'(1):

r'(1) = (4, 6(1), 12(1)²) = (4, 6, 12)

| r'(1) | = sqrt(4² + 6² + 12²) = sqrt(196) = 14

T(1) = r'(1) / | r'(1) | = (4/14, 6/14, 12/14) = (2/7, 3/7, 6/7)

To find r''(t), we need to take the derivative of each component of r'(t) with respect to t:

r''(t) = (d/dt)(4), (d/dt)(6t), (d/dt)(12t²)

r''(t) = (0, 6, 24t)

Finally, to find r'(t) ร r''(t), we need to take the dot product of r'(t) and r''(t):

r'(t) ร r''(t) = (4, 6t, 12t²) ร (0, 6, 24t)

r'(t) ร r''(t) = 0 + 6t(6t) + 12t²(24t)

r'(t) ร r''(t) = 144t³

Therefore, we have:

r'(t) = (4, 6t, 12t²)

T(1) = (2/7, 3/7, 6/7)

r''(t) = (0, 6, 24t)

r'(t) ร r''(t) = 144t³

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\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's solve ~

\(\qquad \tt \dashrightarrow \:10 {x}^{2} - 25x + 15 = 0\)

\(\qquad \tt \dashrightarrow \:5(2x {}^{2} - 5x + 3) = 0\)

\(\qquad \tt \dashrightarrow \:2x {}^{2} - 5x + 3 = 0\)

\(\qquad \tt \dashrightarrow \:2x {}^{2} - 3x - 2x + 3 = 0\)

\(\qquad \tt \dashrightarrow \:x(2x - 3) - 1(2x - 3) = 0\)

\(\qquad \tt \dashrightarrow \:(x - 1)(2x - 3) = 0\)

Therefore, the required factors are ~ (x - 1) and (2x - 3)

So, correct choice is B

Answer:

angle x= 136

Step-by-step explanation:

angle on straight line =180

so we do 180 - 96 (angle y)=84

then:

angles in a triangle add up to 180

we do

84 (inside the triangle next to angle y) + 52 (angle z)= 136

180 (all angles in triangle) - 136 (angle y and z)=44

Now we know that the angle inside the triangle next to Angle x is 44

Angles on straight line =180

180-44= 136

Answer:

Step-by-step explanation:

triangle first:

= y=96

= z=52

= so , 180-96=84

= so, angle b = 84

= the corresponding side should be equal so, angle c = 84

= so x. = 180 - 84

= x = 96

= so , x = 96

so , this is the  triangle theory yehhaaaaa

Given, Height of the cliff = 20 m Distance of the car from the foot of the cliff = 10 m.

The time taken by the car to fall from the cliff can be found using the formula:

\(`h = (1/2) g t^2`\)

Where h is the height of the cliff, g is the acceleration due to gravity and t is the time taken by the car to fall from the cliff.

Substituting the given values,`20 = (1/2) × 9.8 × t^2`

Solving for t, `t = sqrt(20/4.9)` = 2.02 s

Let the initial velocity of the car be V0 and the time taken for the car to come to rest after applying brakes be t1.

Distance covered by the car before coming to rest can be found using the formula: `\(s = V0t1 + (1/2) (-5) t1^2\)`

Where s is the distance covered by the car before coming to rest.

Simplifying the above equation,\(`2.5 = V0 t1 - (5/2) t1^2`\)

Substituting the given values,`5 = V0 - 5 t1`

Solving the above two equations,\(`V0 = 32.5/2 t1`\)

Simplifying the above equation,`V0 = 16.25 t1`

Substituting the value o\(f t1,`V0 = 16.25 × 2` = 32.5 m/s\)

Therefore, the speed of the car before the start of braking is 32.5 m/s.

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Answer: letter b

Step-by-step explanation:

The correct method to return the sine of 90 degrees is Math.sin(90). The Math.sin() method accepts the angle in radians as its parameter and returns the sine value of that angle. Thus, option B is correct.

In Java, the Math class provides various mathematical functions, including trigonometric functions like sine (sin). Option A, Math.sine(90), is incorrect because there is no method named "sine" in the Math class. The correct name is "sin".

Option C, Math.sin(PI), is incorrect because the constant PI is the value of pi in radians, not in degrees. Since the parameter of the Math.sin() method should be in radians, passing PI as the argument will give the sine of pi radians, not 90 degrees.

Option D, Math.sin(Math.toRadians(90)), is incorrect because the radians () method converts an angle in degrees to radians. So, Math.toRadians(90) would give the value of pi/2 in radians, not 90 degrees.

Option E, Math.sin(Math.PI), is also incorrect for the same reason as option C. Math.PI represents the value of pi in radians, not in degrees.

In conclusion, the correct method to return the sine of 90 degrees in Java is Math.sin(90), which takes the angle in degrees as its parameter. Thus, option B is correct.

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Complete Question:

Which of the following method returns the sine of 90 degree?

A. Math.sine(90)

B. Math.sin(90)

C. Math.sin(PI)

D. Math.sin(Math.toRadian(90))

E. Math.sin(Math.PI)

There is only one child in the park who does not like to play either cricket or football or soccer.

Additionally, you should ignore any typos or irrelevant parts of the question .Here's how you can solve the given problem :Given that ,In a park, 25 children play every day in the evening.

12 children like to play cricket.8 children like to play football.4 children like to play soccer.Total children who like to play either of these three sports = \(12 + 8 + 4 = 24.\)

Therefore, the number of children who do not like to play any of these sports = Total number of children - Number of children who like to play any of these sports= \(25 - 24= 1\).

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Answer:

see explanation

Step-by-step explanation:

∠ 1 and ∠ 8 , ∠ 2 and ∠ 7 are alternate exterior angles

They are on opposite sides of the transversal and outside the parallel lines

Given ∠ 1 = 60° , then

∠ 8 = 60° ( alternate exterior angles are congruent )

Answer:

1. <1 and <8

< 2 and <7

2. 60°

Step-by-step explanation:

1. When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles.

2. If two parallel lines are cut by a transversal, then the alternate exterior angles formed are congruent.

Congruent angles are angles with the same measurement.

-( ( 7 - u )( u - 2 ) ) is the factorized form of the polynomial -7u² + 12u + 4, using the AC method.

Given the polynomial in the question;

-7u² + 12u + 4

Factor out -1 out of the polynomial

-1( 7u² - 12u - 4 )

Compare to the form ax² + bx + c

To factor, compare to the form ax² + bx + c and rewrite the middle term as a sum of two terms whose product is;

a × c = 7 × -4 = -28

and whose sum is;

b = -12

Now, factor -12 out of -12x

-1( 7u² - 12(u) - 4 )

We know that -13 is the same as 2 plus -14

-1( 7u² - ( 2 - 14 )u - 4 )

Apply distributive property

-1( 7u² - 2u - 14u - 4 )

Group the terms

-1( u(7u - 2) - 2(7u - 2 ) )

-1( (7-u)(u-2) )

-( (7-u)(u-2) )

Therefore, the factorized form of the polynomial is -( ( 7 - u )( u - 2 ) ).

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-(7u+2)(u-2) is the factorized form of expression -7u²+12u+4.

An expression is combination of variables, numbers and operators.

The given expression is -7u²+12u+4.

We need to find the factors of this expression.

-7u²+12u+4.

This can be written as

-7u^2+14u-2u+4.

Take 7u from first two terms and 2 from last two terms in the expression.

-7u(u-2)-2(u-2)

(-7u-2)(u-2)

-(7u+2)(u-2)

Hence -(7u+2)(u-2) is the factorized form of -7u^2+12u+4.

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Answer:

the width is 10ft, the length is 25ft, and the area is 250 sq ft

Answer:

The width = 10 ft./ The lenght = 25 ft./ The area = 250 ft.²

Step-by-step explanation:

use X as the width

so we'll get 2X+5 as the length

the perimeter = 2(length) + 2(width)

70 = 2(2X+5) + 2(X)

70 = 4x+10 + 2x

70 = 6x+10

60 = 6x

x = 10

as the beginning x is the width

so the width is 10 ft.

the lenght is 2x+5

2(10)+5 = 25

so the length is 25 ft.

The area of rectangle is width x length

so 10 x 25 = 250 ft.²

Answer:

9x⁵ + 191

Step-by-step explanation:

Simplify: 17 + 64 + 124 + 9x⁵ - 14

Collect Like Terms: 9x⁵ + (17 + 64 + 124 - 14)

Simplify: 9x⁵ + 191

Brainliest Please!!?!!!!

- ElizabethKate

Answer:

First, we know that the 0 in the horizontal axis corresponds to the noon.

Then:

a) Lin's elevation at noon in meters.

We need to see the elevation when x = 0.

This is the point that is just on top of the y-axis, we can see that when x = 0, we have y = 6.

Then at noon, her altitude was 6 meters.

b) At 8:00 am, her elevation was 2m

Remember that the x-component represents time, and x = 0 represents the noon.

8:00 am is 4 hours before noon, then 8:00am is represented with x = -4

and at this time her elevation is 2m, then y = 2.

This means that the point that represents this is (-4, 2)

c) At 4:00 pm Lin was at sea level (her elevation was 0m)

Same reasoning than before: x = 0 is the noon, then 4:00 pm is four hours after this, then 4:00 pm is represented with x = 4.

And here her altitude is 0m, then y = 0.

This point is written as (4, 0)

d) Here we can see that at 6:00 am her elevation was negative, and at 4:00pm her elevation is 0.

And we know that:

0 > negative numbers.

Then her altitude increased in this interval of time.

Answer:

Its 0

Step-by-step explanation:

1/6  is the probability that in seven rolls of a six-sided die, the result of 2 appears exactly 4 times

Define Probability

Probability can be defined as the likelihood or chance of an event occurring.

Probability is a branch of Mathematics that deals with the calculation on the chances of happening of a particular event.

The probability of getting some number in a cube corresponds to 1/6, the cube has six sides.

P(1) =1/6

P(2) =1/6

P(3)=1/6

P(4)= 1/6

P(5)=1/6

P(6)= 1/6

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Alan can put the 11 books on the shelf, with The Iliad in the first spot and The Odyssey in the last spot, in 9! (362,880) ways

To determine the number of ways Alan can put the 11 books on his bookshelf with The Iliad in the first spot and The Odyssey in the last spot, we can follow these steps:

1. There are 11 spots on the bookshelf, but since The Iliad is in the first spot and The Odyssey is in the last spot, we are left with 9 spots for the remaining 9 books.
2. To arrange the 9 books, we can use the concept of permutations, which refers to the number of ways the books can be ordered.
3. The number of permutations for 9 books is calculated as 9! (9 factorial), which means 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

Therefore, Alan can put the 11 books on the shelf, with The Iliad in the first spot and The Odyssey in the last spot, in 9! (362,880) ways.

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Answer:

90 percentage

yh it is

☺☺

Answer:

34.75 i think

Step-by-step explanation:

Answer:

\(\boxed {\boxed {\sf 2 \ hours}}\)

Step-by-step explanation:

Let's set up a proportion to solve. Use the following setup:

\(\frac {hours}{miles}=\frac{hours}{miles}\)

We know that it takes Oliver 4 hours to drive 278 miles.

\(\frac {4 \ hours}{278 \ miles}=\frac{hours}{miles}\)

We don't know how long it takes him to drive 139 miles. Therefore, we use the variable x for hours, because it is unknown.

\(\frac {4 \ hours}{278 \ miles}=\frac{x \ hours}{139 \ miles}\)

\(\frac {4 }{278 }=\frac{x \ hours}{139 }\)

We are solving for x, the hours it takes him to drive 139 miles. The variable must be isolated. It is being divided by 139 and the inverse of division is multiplication. Multiply both sides of the equation by 139.

\(139*\frac {4 }{278 }=\frac{x \ hours}{139 }*139\)

\(139*\frac {4 }{278 }={x }\)

\(2=x\)

It takes Oliver 2 hours to drive 139 miles.

The approximation of \(\int xln(x + 6) dx\) using the two-point Gaussian quadrature formula is: 2.8191.

The approximation of \(\int cos(x^2 + 3) dx\) using simple Simpson's rule is: -0.93669.

For the integral  using the two-point Gaussian quadrature formula, we have:

\(x_1 = -\sqrt{1/3} = -0.57735\\x_2 = \sqrt{1/3} = 0.57735\\w1 = w2 = 1\\Approximation = w1 * f(x1) + w2 * f(x2)\\Approximation = 1 * f(-0.57735) + 1 * f(0.57735)\)

Now, let's calculate the values:

\(f(x) = xln(x + 6)\\f(-0.57735) = -0.57735 * ln((-0.57735) + 6)\\f(0.57735) = 0.57735 * ln((0.57735) + 6)\)

\(Approximation = -0.57735 * ln(5.42265) + 0.57735 * ln(6.57735)\\Approximation = 2.8191\)

Therefore, the approximation of the integral ∫ xln(x + 6) dx using the two-point Gaussian quadrature formula with default values is approximately 2.8191.

Now, let's calculate the approximation of the integral \(\int cos(x^2 + 3) dx\)using simple Simpson's rule.

In simple Simpson's rule, we divide the interval into subintervals. Let's assume the limits of integration are from a to b.

\(Approximation = (h/3) * [f(a) + 4f((a + b)/2) + f(b)]\)

Using the default values, let's assume a = 0 and b = 1:

\(h = (b - a) / 2 = (1 - 0) / 2 = 0.5\\Approximation = (0.5/3) * [f(0) + 4f((0 + 1)/2) + f(1)]\)

Now, let's calculate the values:

\(f(x) = cos(x^2 + 3)\\f(0) = cos(0^2 + 3) = cos(3)\\f(0.5) = cos((0.5)^2 + 3)\\f(1) = cos(1^2 + 3) = cos(4)\\Approximation = (0.5/3) * [cos(3) + 4f(0.5) + cos(4)]\\Approximation = 0.5/3 * [cos(3) + 4f(0.5) + cos(4)]\\Approximation = 0.5/3 * [-0.98999 + 4 * (-0.99966) - 0.65364]\\Approximation = 0.5/3 * [-0.98999 - 3.99864 - 0.65364]\\Approximation = 0.5/3 * [-5.64227]\\Approximation = -0.93669\)

Therefore, the approximation of the integral \(\int cos(x^2 + 3) dx\) using simple Simpson's rule with the given values is approximately -0.93669.

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To analyze regression 2 and 3, examine the "fact-based movie" coefficients to determine if fact-based movies have fewer, more, or just as many stars as fictional movies on average. Check p-values for statistical significance. Interpret results objectively.

To compare regression 2 and regression 3 and determine whether the regressions suggest that, on average, a fact-based movie has fewer stars than a fictional movie, more stars than a fictional movie, or just as many stars as a fictional movie, we need to analyze the results of the regressions.

1. Start by examining the coefficients of the "fact-based movie" variable in both regressions. If the coefficient is negative, it suggests that fact-based movies have fewer stars than fictional movies on average. If the coefficient is positive, it suggests that fact-based movies have more stars than fictional movies on average. And if the coefficient is zero, it suggests that fact-based movies have just as many stars as fictional movies on average.

2. Additionally, check the p-values associated with the coefficients. A p-value less than 0.05 indicates that the coefficient is statistically significant, meaning that it is unlikely to have occurred by chance. If the p-value is significant, it provides further evidence to support the suggestion made by the coefficient.

By examining these factors in regression 2 and regression 3, you will be able to determine whether the regressions suggest that fact-based movies have fewer stars, more stars, or just as many stars as fictional movies on average. Remember to interpret the results of the regressions accurately and objectively.

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Answer:

4/6 is the answer due to the way it is set up within the fraction