Find the magnitude and direction angle for each vector. Give the measure of the direction angle as an angle in [0,360]

Answer:

The probability of dying from heart disease based on the given information is 1/6 or approximately 0.1667. This is because the odds in favor of dying from heart disease are 1 to 5, which means there is 1 chance of dying from heart disease for every 5 chances of not dying from heart disease. To convert odds to probability, we divide the number of chances of the event occurring by the total number of chances. So, the probability of dying from heart disease is 1/(1+5) = 1/6 or approximately 0.1667.

The sum of the series converges absolutely by alternate series test

Given data ,

Let the sequence be represented as A

Now , the value of A is

A = ∑n=1 to ∝ ( 1/6n³ )

On simplifying , we get

Taking the common factor out , we get

A = ( 1/6 ) ∑n=1 to ∝ ( 1/n³ )

Now , from the alternate series test ,

A = ( 1/6 ) ( converges )

Hence , the series A converges

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The polar coordinates for the point (5, 5) are (5√(2), 45 degrees) or (5√(2), 225 degrees) since 225 degrees is also a valid angle between 0 and 360 degrees that corresponds to the same point.(option c)

For the point (5, 5), we can find its polar coordinates by first finding the distance r from the origin using the Pythagorean theorem:

r = √(5² + 5²) = √(50) = 5√(2)

Next, we can find the angle θ that the line connecting the origin to the point makes with the positive x-axis using trigonometry:

tan(θ) = y/x = 5/5 = 1

θ = arctan(1) = π/4 radians

Since 0 < θ < 360, we can express θ in degrees as θ = 45 degrees.

Hence the correct option is (c).

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Answer:

V = (4/3)π(6^3) = 288π square inches

= 904.78 square inches

Using 3.14 for π, V = 904.32 square inches.

Answer:

m = 3 + 2√3 or m = 3 - 2√3

Step-by-step explanation:

The given equation is:

m^2 - 6m = 3

We can rewrite the equation in standard quadratic form as:

m^2 - 6m - 3 = 0

We can use the quadratic formula to solve for m:

m = [-b ± √(b^2 - 4ac)] / 2a

where a = 1, b = -6, and c = -3.

Substituting these values, we get:

m = [-(-6) ± √((-6)^2 - 4(1)(-3))] / 2(1)

m = [6 ± √(36 + 12)] / 2

m = [6 ± √48] / 2

m = [6 ± 4√3] / 2

Simplifying the expression, we get:

m = 3 ± 2√3

Therefore, the solutions to the equation are:

m = 3 + 2√3 or m = 3 - 2√3

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Answer:

[tex]x=3+2\sqrt{3}\\\\ x=3-2\sqrt{3}[/tex]

Step-by-step explanation:

The quadratic formula is:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore, to solve the given equation using the quadratic formula, first subtract 3 from both sides of the equation so that it is in the required form.

[tex]m^2-6m-3=3-3[/tex]

[tex]m^2-6m-3=0[/tex]

Comparing the coefficients:

Substitute the values of a, b and c into the formula and solve for x:

[tex]\implies x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(-3)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{36-4(-3)}}{2}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{36+12}}{2}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{48}}{2}[/tex]

Rewrite 48 as a 4² · 3:

[tex]\implies x=\dfrac{6 \pm \sqrt{4^2 \cdot 3}}{2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{4^2} \sqrt{3}}{2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies x=\dfrac{6 \pm 4 \sqrt{3}}{2}[/tex]

Simplify:

[tex]\implies x=\dfrac{6}{2}\pm\dfrac{4 \sqrt{3}}{2}[/tex]

[tex]\implies x=3\pm2 \sqrt{3}[/tex]

Therefore, the values of x are:

[tex]x=3+2\sqrt{3}\\\\ x=3-2\sqrt{3}[/tex]

The number of days it will take the virus to grow from 90 to 410 is 15 days.

The growth rate of the virus is calculated as follows;

growth rate = (200 - 90) / 5

growth rate = 22 per day

The number of days it will take the virus to grow from 90 to 410 is calculated as follows;

growth = 410 - 90

growth = 320

Number of days = 320 / 22/day = 14.55 ≈ 15 days

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Answer:

The angle -90 degrees is equivalent to -π÷2 radians.

How we convert the angle −90∘ into radians?

To convert an angle from degrees to radians, we use the formula: radian measure = degree measure * π/180. In this case, we want to convert -90 degrees to radians. So, we substitute -90 into the formula and get:

radian measure = -90 × π÷180

Simplifying this expression, we can cancel the factor of 90 and get:

radian measure = -1÷2 × π

This means that -90 degrees is equivalent to -π÷2 radians. We can leave our answer in terms of π since it is exact. The reason why we use radians to measure angles is because they are a more natural unit for measuring angles in calculus and other mathematical contexts.

Therefore, -90 degrees is equivalent to -π÷2 radians. We can leave our answer in terms of π since it is exact.

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a) The slope shows that the appropriate dose c for an older child increases by 6.225 mg if the child is one year older.

b) The dose for newborn baby is: 6.225 mg

The equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

(a) Let a be an age of an child in years. Then:

c = 0.0417Da + 0.0417D

Where D is a constant

Since D = 150 mg, then we have:

The slope of the graph = 0.0417(150)

= 6.225 mg/year

The slope shows that the appropriate dose c for an older child increases by 6.225 mg if the child is one year older.

(b) Newborn baby:  a=0

Thus:

c(0) = 0 + 6.225

= 6.225 mg

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The average rate of change for the given intervals are:

To compute the average rate of change for any given interval, determine the change between the function values at the endpoints and divide this value by the difference in independent variable values. it can be expressed as follows:

Average Rate of Change = (f(b) - f(a)) / (b - a)

The average rate of change for each point in the interval is determined form the graphs and used to solve for the average rate of change

(-5, -5) and (-4, 0):

Average Rate of Change = (0 - 0) / (-4 - (-5)) = 0 / 1 = 0

(-4, 0) and (-3, 3):

Average Rate of Change = (3 - 0) / (-3 - (-4)) = 3 / 1 = 3

(-4, 0) and (-1, 3):

Average Rate of Change = (3 - 0) / (-1 - (-4)) = 3 / 3 = 1

(-3, 0) and (-1, 0):

Average Rate of Change = (0 - 0) / (-1 - (-3)) = 0 / 2 = 0

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The correct graph is: a coordinate grid with the x-axis labeled rooms painted and the y-axis labeled amount of money earned and a line going from the point (0,100) through the point (4,200).

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

The painter pays $100 for supplies, which is a fixed cost, and charges $25 for each room painted, which is a variable cost.

Therefore, the relationship between the amount of money the painter earns and the number of rooms he paints can be represented by a linear equation in slope-intercept form:

Amount earned = (price per room) x (number of rooms painted) + (fixed cost)

In this case, the price per room is $25, the number of rooms painted is the x-value, and the fixed cost is $100. Thus, the equation is:

Amount earned = 25x + 100

To graph this equation, we can plot two points and draw a line through them. One point is when no rooms are painted, which gives the painter $100 for the fixed cost:

(0,100)

The other point is when four rooms are painted, which gives the painter:

Amount earned = 25(4) + 100 = 200

So the other point is:

(4, 200)

The correct option :

a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200.

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The error that Martell made in determining the scale factor was using point K and point A when they weren't similar points.

The process that Martell used to find the scale factor was correct, however, he should not have used points A and K because they are not similar sides in the triangles.

Point A is similar to point H while point D is similar to point K.

Using the similar points of A (4, 2 ) and H ( 6, 3 ), we find the scale factor to be:

= 6 / 4

= 1. 5

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Answer:

The value of x is 10√2, so A is correct.

Step-by-step explanation:

In an isosceles right triangle, the length of the hypotenuse is √2 times the length of a leg. Since each leg has length 10, the hypotenuse has length 10√2. A is correct.

Answer:

There are 13 diamonds in a deck of cards, including one king and one ace.

The probability of drawing a king on the first draw is 1/13, since there is one king among 13 diamonds.

Assuming that the king is not replaced, there are now 12 diamonds left, including one ace. The probability of drawing an ace on the second draw is 1/12, since there is one ace among 12 diamonds.

The probability of drawing a king on the first draw and an ace on the second draw is the product of these probabilities:

P(king first, ace second) = P(king first) * P(ace second|king first not replaced)

P(king first, ace second) = (1/13) * (1/12)

P(king first, ace second) = 1/156

Therefore, the chances of drawing a king on your first draw and an ace on your second draw, when drawing 2 cards from only the diamonds, is 1/156.

Step-by-step explanation:

Branliest please

The value of v in terms of i and j is v = 3i + 3j

We are given that;

P₁ = (-5,3), P₂ = (-2,6)

Now,

To find the component form of a vector, we need to subtract the coordinates of the initial point from the coordinates of the terminal point3.

We have P₁ = (-5,3) and P₂ = (-2,6).

v = P₂ - P₁ = (-2 - (-5), 6 - 3) = (3, 3). We can write v in terms of i and j as v = 3i + 3j.

Therefore, by vectors the answer will be v = 3i + 3j.

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Answer:

Step-by-step explanation:

I agree it's convenience and biased.

It's the easiest way to convey a survey so it is convenient.  

it is biased because not everyone has accessible to modern technology, or that particular social media app.  Not all park users use social media.  It is biased because it is targeting a younger demographic, but excludes the youngest demographic as well, that are not allowed ot have social media.

Answer:

I agree it's convenience and biased.

It's the easiest way to convey a survey so it is convenient.  

it is biased because not everyone has accessible to modern technology, or that particular social media app.  Not all park users use social media.  It is biased because it is targeting a younger demographic, but excludes the youngest demographic as well, that are not allowed ot have social media.

Step-by-step explanation:

Answer: False

Step-by-step explanation:

Counting up from 9, you get 10, 11, and 12. To get to 18 from 9 you would need to add 9.

If we assume that the marbles are equally likely to be picked, then the probability of picking an orange marble is 1/3.

The number of times an orange marble is picked in 12 trials follows a binomial distribution with parameters n = 12 and p = 1/3.

The expected value of the number of orange marbles picked is given by:

E(X) = np = 12 * (1/3) = 4

Therefore, the best prediction possible for the number of times an orange marble will be picked is 4.

Answer:

The probability of selecting either a purple or a blue marble for the 6 marbles is 0.3333 or 33.33%

Step-by-step explanation:

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The number is 4,175.

points to note:

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Answer:

2.45ℓ

Step-by-step explanation:

0.33ℓ x 4 = 1.32ℓ (1ℓ 320 ml)

11.12ℓ - 1.32ℓ = 9.8ℓ (total in 4 jugs)

9.8ℓ ÷ 4 = 2.45ℓ (each jug)

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The probability that the  transferred jelly bean was green is P ( G ) = 0.636

Given data ,

Let the probability that the  transferred jelly bean was green be P ( G )

Now , There are 7 blue and 7 green jelly beans in the box, so the probability of selecting a green jelly bean from the box is 7/(7+7) = 0.5, and the probability of selecting a blue jelly bean from the box is also 0.5

A jelly bean is chosen from the box and then put in the bag. Say someone chooses a green jelly bean from the package and puts it in the bag. Currently, there are 6 + 1 = 7 green jelly beans and 4 + 0 = 4 blue jelly beans in the bag.

Now , Since there are 7 green jelly beans and 4 blue jelly beans in the bag, the probability of selecting a green jelly bean from the bag is P ( G )

where P ( G ) = 7/(7+4)

P ( G ) = 0.636

Hence , the probability is 0.636

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Answer:80°

Step-by-step explanation:

We can use the given angle, 50, to determine the other angles of the triangle opposite to the arc that we need to find the measure of.

Because the entire inscribed figure is rectangular, we can use our given angle to determine the other angles of the triangle represented by the given angle, which are 50 and 80.

Now we can use the 80° angle <DPA, which is also equal to <CPB.
This means that the center angle <CPB is also 80°, and it means that the corresponding arc X is also 80°.

The values of x and y in the given triangle are 41.4° and 114.5°

We have to  values of x and y by using law of cosine

Using the Law of Cosines, we can find the values of x and y:

For angle x⁰:

cos(x⁰) = (a² + c² - b²) / (2ac)

cos(x⁰) = (15² + 18² - 12²) / (540)

cos(x⁰) = 0.75

x⁰ = cos⁻¹(0.75)

x⁰ = 41.4°

For angle y:

cos(A) = (b² + c² - a²) / (2bc)

cos(A) = (12² + 15² - 18²) / (360)

cos(A) = -0.4

A = cos⁻¹(-0.4)

y=114.5°

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To find the final price Kyla will pay for the roller blades, we first need to calculate the amount of the discount.

So Kyla will get a discount of $33 off the original price of $110.

Next, we need to calculate the pre-tax price of the roller blades after the discount.

So the pre-tax price of the roller blades after the discount is $77.

Finally, we need to calculate the final price Kyla will pay, including the 5% tax.

Answer:

7

Step-by-step explanation:

Answer:

use symbolab it will help you with almost anything

Answer:

BD = 3 units

Step-by-step explanation:

since AB is a tangent to the circle, then the angle between the tangent and the radius at the point of contact A is 90°

Then Δ ABC is right

using Pythagoras' identity in the right triangle

BC² = AC² + AB² = 4.5² + 6² = 20.25 + 36 = 56.25 ( take square root of both sides )

BC = [tex]\sqrt{56.25}[/tex] = 7.5

now CD is a radius of the circle = 4.5

Then

BD = BC - CD = 7.5 - 4.5 = 3 units

The value of the function are f(-8) = -4, f(0)= 2 and f(0)= 2.

We have the function,

f(x) = { x + 4 ,     x<0

          2 - x ,     x≥0

First, f(-8)

= (-8)+ 4

= -4

and, f(0)

= 2 - 0

= 2

and, f(4)

= 2 - 4

= -2

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