John F. Kennedy died in 1963 at the age of 46. In what
year was he born?
*im lazy *

Answer: 21

Step-by-step explanation:

First we have to find LCM (lowest common multiple) of the given number, i.e 700.

LCM = 2 × 2 × 5 × 5 × 7 = 700

now, let's add 7 to 700

We get the required number as 707

9 + (-5) = 4

-8 - 4 = -12

8 - (-4) = 12

-9 + 5 = -4

The volume of the solid under z = sqrt(36-x^2-y^2) and over the circular disk x^2+y^2<=36 is 72π cubic units.

The given equation z = sqrt(36 - x^2 - y^2) represents a half-sphere of radius 6 centered at the origin, since when x^2 + y^2 = 0, we have z = 6, and for any point (x, y) such that x^2 + y^2 = 36, we have z = 0.

The circular disk x^2 + y^2 <= 36 represents a circle in the xy-plane with radius 6 and centered at the origin.

To find the volume of the solid under z = sqrt(36-x^2-y^2) and over the circular disk x^2+y^2<=36, we can integrate the function sqrt(36 - x^2 - y^2) over the circular disk:

V = ∬D sqrt(36 - x^2 - y^2) dA

where D is the circular disk x^2 + y^2 <= 36.

Switching to polar coordinates, we have:

V = ∫[0,2π] ∫[0,6] sqrt(36 - r^2) r dr dθ

Using the substitution u = 36 - r^2, du = -2r dr, we get:

V = 2∫[0,2π] ∫[0,6] sqrt(u) (-du/2) dθ

= π ∫[0,6] u^(1/2) du

= π [ (2/3) u^(3/2) ]_[0,6]

= π (2/3) (36^(3/2) - 0)

= 72π

Therefore, the volume of the solid under z = sqrt(36-x^2-y^2) and over the circular disk x^2+y^2<=36 is 72π cubic units.

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Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer:

rectangular prism

Step-by-step explanation:

check by rotating the shape in images

Answer:

x = -8

Step-by-step explanation:

-8x + 3(x - 5) = 25

Distribute the 3 into the (x - 5).

-8x + 3x - 15 = 25

Combine like terms.

-5x - 15 = 25

Add 15 to both sides.

-5x = 40

Divide both sides by -5.

x = -8.

Proof:

-8x + 3(x - 5) = 25

Substitute variable.

-8(-8) + 3((-8) - 5) = 25

Subtract inside parenthesis.

-8(-8) + 3(-13) = 25

Multiply -8 and -8.

64 + 3(-13) = 25

Multiply 3 and -13.

64 + (-39) = 25

Add 64 and -39.

25 = 25

Answer:

the second option

Step-by-step explanation:

to graph the integer 4, a dot would be placed at the 4

To find the opposite of four, you would start at zero and count four to the left (or you could just place a negative sign in front of the four), which would result in -4, also called negative four. to graph the opposite of 4, a dot would be placed on the -4 .

Answer:

Third option

Step-by-step explanation:

Given the following question where...

\(180 = a1+a2+a3\)

A triangle adds up to 180 degrees

50 + 120 = 170 + 10 = 180

The measurement of the third angle is 10 degrees or the third option.

Hope this helps.

Answer:

the answer is -12-(-3)

Step-by-step explanation:

The expression equivalent to -18-(-9) is -12-(-3)

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given is an expression, -18-(-9), we are given to find the expression equivalent to it,

-18-(-9) = -18+9 = -9

1) -18+2 = -16 (not equivalent)

2) -12-(-3) = -12+3 = -9

Therefore, we see, the value of expressions -12-(-3) and -18-(-9) are equivalent,

Hence, the expression equivalent to -18-(-9) is -12-(-3)

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The linear equality for the given graph is x > 0.

Option (B) is correct.

What is linear equality?

In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

The hollow circle in the linear equality shows that the point should be excluded and the line is going towards the positive x-axis.

So we can prepare the linear equality as

                       x > 0

Hence, the linear equality for the given graph is x > 0.

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Answer:

55%

Step-by-step explanation:

44 ÷ 80 = 0.55 = 55%

Answer:

slope= 2/3

Step-by-step explanation:

In order to find the slope,  we need to use the two points we are given.

The formula for the slope is m= (y1-y2)/(x1-x2), where m is the slope.

y1=3

y2=-5

x1=-2

x2=-14

Therefore, m=(3-(-5)/(-2-(-14)

=8/12

=2/3

m=2/3

Answer:

b = -5  

Step-by-step explanation:

\(\begin{array}{rcll}(y^{-9})^{b} & = & y^{45}& \\y^{-9b} & = & y^{45} & \text{Multiplied exponents}\\-9b \ln y & =& 45 \ln y & \text{Took the ln of each side}\\-9b & = & 45 & \text{Divided each side by ln y}\\b & = & \mathbf{-5} & \text{Divided each side by -9}\\\end{array}\)

The long chord of the compound curve is approximately 268.86 meters.

To determine the long chord of the compound curve, we can use the following formula:

Long Chord = √[(Chord1^2) + (Chord2^2) - (2 * Chord1 * Chord2 * cos(θ1 - θ2))]

where Chord1 and Chord2 are the lengths of the two chords, and θ1 and θ2 are the angles the common tangent makes with the tangents at PC and PT, respectively.

Plugging in the given values:

Chord1 = 130.60 m

Chord2 = 139.16 m

θ1 = 20°

θ2 = 36°

Calculating the long chord using the formula:

Long Chord = √[(130.60^2) + (139.16^2) - (2 * 130.60 * 139.16 * cos(20° - 36°))]

≈ 268.86 meters

Therefore, the long chord of the compound curve is approximately 268.86 meters.

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Traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

To calculate the distance traveled, we can multiply the speed by the time traveled.

Speed = 1000 miles per hour

Time = 7.5 * 10⁵ hours

Distance = Speed * Time

Distance = 1000 miles/hour * 7.5 * 10⁵ hours

To perform this calculation, we can multiply the numerical values and keep the scientific notation for the result:

Distance = 1000 * 7.5 * 10⁵ miles

Distance = 7.5 * 10⁸ miles

Therefore, traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

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The age of Barbra is 22 years.

The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.

Now, according to the question.

Let 'a' be the age of Alice.

Let 'b' be the age of Barbra

Let 'c' be the age of Carol.

The sum of age of all three sisters is 68 years.

Thus,  a + b + c = 68

Now, as Alice is three years younger than Barbra.

a = b - 3

and, Barbra is 5 years younger than Carol.

b = c - 5

c = b + 5

By substitution of values of a and c in total age.

(b - 3) + b + (b + 5) = 68

3b - 3 + 5 = 68

On solving the expression.

b = 22

Therefore, the age of Barbra is 22 years.

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Solution set for a statement is a set of values which satisfy the given statement. The solution set for given condition is:  (16, positive infinity)

Solution set is the set of values of unknown variable for which the given mathematical statement holds true.  

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given case, the mathematical statement given is

\(4\dfrac{1}{2} \times x - 9\dfrac{1}{2} > 62.5\)

(where that unknown number was assumed to be 'x', and we used "less than" phrase as subtraction and 'greater than' as >)

Converting mixed fractions to normal fractions, we get the statement as:

\(\dfrac{9}{2}x - \dfrac{19}{2} > 62.5\\\\\text{Adding 9.5 on both sides(as 19/2 = 9.5)}\\\\\dfrac{9}{2}x > 62.5 + 9.5\\\\\text{Dividing both sides by 4.5 (as 9/2 = 4.5 and we want to isolate x on one side}\\\\x > 16\)

Thus, for all values of \(x\) bigger than 16, the given statement is true.

Thus,  The solution set for given condition is:  (16, positive infinity)

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1. Bart Simpson's equal annual payments will be approximately $6,434.61.

2. The young boy earned an annual rate of return (interest rate) of approximately 26.49% on his investment in Christmas trees.

To find the payments Bart Simpson will make at the end of each year, we can use the formula for the equal annual payments on a loan with compound interest:

\(P = (PV * r) / (1 - (1 + r)^{(-n)})\)

where:

P is the equal annual payment,

PV is the present value of the loan (purchase price - down payment),

r represents the annual interest rate,

n represents the number of payments.

Given:

Purchase price (PV) = $75,000 - $20,000 (down payment) = $55,000

Annual interest rate (r) = 9% = 0.09 (as a decimal)

Number of payments (n) = 20

Now,  the values into the formula:

\(P = ($55,000 * 0.09) / (1 - (1 + 0.09)^{(-20)})\)

P = $4,950 / (1 - 0.2314)

P = $4,950 / 0.7686

P ≈ $6,434.61

So, Bart Simpson's equal annual payments will be approximately $6,434.61.

To calculate the annual rate of return (interest rate) that the young boy earned on his investment, we can use the formula for compound interest:

(FV) = (PV) * \((1 + r)^n\)

where:

FV is the future value of the investment (selling price of the trees),

PV is the initial investment ($50),

r represents the annual interest rate ,

n is the number of years (6 years).

Given:

Selling price (FV) = $400

Initial investment (PV) = $50

Number of years (n) = 6

Now, we get the annual interest rate (r):

$400 = $50 * \((1 + r)^6\)

Divide both sides by $50:

\(8 = (1 + r)^6\)

Take the 6th root of both sides:

\(1 + r = 8^{(1/6)\)

1 + r ≈ 1.2649

Subtracting 1 from both sides , we get :

r ≈ 1.2649 - 1

r ≈ 0.2649

So, the young boy earned an annual rate of return (interest rate) of approximately 26.49% on his investment in Christmas trees.

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Answer:

i) around 41.7 kg

ii) 72 books

Step-by-step explanation:

i) if 108 books are 30 kg then how much is the mass for 150? You cross multiply so 150 multiply by 30 and 108 multiply by x (the unknown mass). you will get 4500=108x and then 4500/108 is the unknown mass.

ii) use the same way as above.

A two digit positive number is any number between 0 and 99, inclusive, and can be written in numerical, expanded, word, or fraction form.

The two digit positive number is any number between 0 and 99, inclusive. This includes all the numbers from 00 to 99. All of these numbers are considered positive because they are not negative numbers. A two digit positive number can be composed of two single digits, such as 12, or one single digit followed by a zero, such as 30. They can also be composed of two successive numbers, such as 23, or two successive numbers with a zero in between, such as 40.Two digit positive numbers can also include decimal numbers, such as 12.3 or 0.45. These decimal numbers will always have two digits to the left of the decimal point.

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Answer:

a, a graph is reflected over the x axis when the leading coefficient is negative

Answer:

lower: 8 higher: 15

Step-by-step explanation:

100-36=64

sqrt(64=8

289-64=225

sqrt(225)=15

Answer: h= 6

Step-by-step explanation:

Answer:

800 mph

Step-by-step explanation:

Use the formula: Distance/Time=Speed

Distance: 2840 miles

Time: 3.55 hours

Now Divide,  giving you the speed of 800 mph

Hope this helps!

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Equivalent expressions are expressions that have the same value

The equivalent expression of \((4 +7i)(3 +4i)\) is \(-16+37i\)

The expression is given as:

\((4 +7i)(3 +4i)\)

Expand the equation

\((4 +7i)(3 +4i) = 4(3 +4i) +7i(3 +4i)\)

Distribute the equation, as follows:

\((4 +7i)(3 +4i) = 12 +16i +21i +28i^2\)

In complex numbers,

\(i^2 = -1\)

So, we have:

\((4 +7i)(3 +4i) = 12 +16i +21i +28(-1)\)

Evaluate the product

\((4 +7i)(3 +4i) = 12 +16i +21i -28\)

Combine like terms

\((4 +7i)(3 +4i) = 12-28+16i +21i\)

Evaluate like terms

\((4 +7i)(3 +4i) = -16+37i\)

Hence, the equivalent expression of \((4 +7i)(3 +4i)\) is \(-16+37i\)

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Answer:

The perimeter is 47.6 cm

Step-by-step explanation:

We can find the perimeter by adding up the sides

Since it is an equilateral triangle, the base is 7.2 to fill the gap, so the sides are 7.2

P = 7.2 + 13+ 7.2+7.2+ 13

   =47.6

Answer:

the answer for this question is 93.6

Step-by-step explanation:

Well, we are finding the perimeter.

Best way to do this is multiply

7.2 x 13 = 93.6

So, 93.6 is the answer to this question


Rushdoors,

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y = 1.5x + 0.5 is the equation of the line passing through the coordinate points

The formula for finding the equation of a line in slope-intercept form is expressed as:

y =mx + b

where:

m is the slope

b is the intercept

Determine the slope

slope = 5-2/3-1

slope = 3/2

slope = 1.5

Determine the y-intercept

y = mx + b

5 = 1.5(3) + b

5 = 4.5 + b

b = 0.5

Hence the required equation of the line passing through ( 1,2) and (3,5) is

y = 1.5x + 0.5

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Complete question

What's the equation of a line that passes through (1,2) (3,5)?

Answer:

n = -7

Step-by-step explanation:

to solve for a variable (in this case it's n) we have to isolate it. we do this by moving like terms on one side of the equation.

-53 = 3 + 8n

- 3    -3

since we are subtracting 3 on the right side, we also have to subtract it on the left side.

-56 = 8n

we divide both sides by 8

n = -7