In circle R, find arc length of arc GH

The number is 4,175.

points to note:

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Answer:

a) Two real solutions.

b) Solutions:  y = -6, y = 12

Step-by-step explanation:

The discriminant is defined as the expression b² - 4ac, which appears under the square root sign in the quadratic formula.

The value of the discriminant determines the nature of the solutions to the quadratic equation:

[tex]\boxed{\begin{minipage}{12 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real solutions.\\when $b^2-4ac=0 \implies$ one real solution.\\when $b^2-4ac < 0 \implies$ no real solutions (two complex conjugate solutions).\\\end{minipage}}[/tex]

To find the number and type of solutions of the given quadratic equation, first rewrite the equation in the form ax² + bx + c = 0.

[tex]\begin{aligned}(y-3)^2-10&=71\\y^2-6y+9-10&=71\\y^2-6y-1&=71\\y^2-6y-72&=0\end{aligned}[/tex]

Compare the coefficients:

Substitute the values of a, b and c into the discriminant formula:

[tex]\begin{aligned}b^2-4ac&=(-6)^2-4(1)(-72)\\&=36-4(-72)\\&=36+288\\&=324\end{aligned}[/tex]

As the discriminant of the given equation is greater than zero, there are 2 real solutions.

To solve the equation, we can use the quadratic formula:

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

As we have already calculated that the discriminant is 324, we can substitute this, along with the values of a and b, into the formula:

[tex]\implies y=\dfrac{-(-6) \pm \sqrt{324}}{2(1)}[/tex]

[tex]\implies y=\dfrac{6 \pm \sqrt{324}}{2}[/tex]

Solve for y:

[tex]\implies y=\dfrac{6 \pm 18}{2}[/tex]

[tex]\implies y=3 \pm 9[/tex]

[tex]\implies y=-6, 12[/tex]

Therefore, the solutions of the given equation are:

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

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 sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8) is y = 5 sin(π/2(x - 3)) + 3

We are given that;

Minimum point= (3,-2)

Maximum point= (7, 8)

Now,

To construct a sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8), we can use the following steps:

Find the amplitude A. The amplitude is the distance from the midline of the function to the maximum or minimum point. The midline is the average of the maximum and minimum values, which is (8 + (-2))/2 = 3. The distance from 3 to 8 or -2 is 5, so A = 5.

Find the period P. The period is the length of one cycle of the function, or the horizontal distance between two consecutive maximum or minimum points. In this case, the period is 7 - 3 = 4. The constant B is related to the period by the formula B = 2π/P, so B = 2π/4 = π/2.

Find the horizontal shift C. The horizontal shift is the amount that the function is shifted left or right from its standard position. In this case, we want the function to have a minimum point at x = 3, so we need to shift it right by 3 units. This means that C = 3.

Find the vertical shift D. The vertical shift is the amount that the function is shifted up or down from its standard position. In this case, we want the function to have a midline at y = 3, so we need to shift it up by 3 units. This means that D = 3.

Putting it all together, we get:

y = 5 sin(π/2(x - 3)) + 3

Therefore, by the function the answer will be y = 5 sin(π/2(x - 3)) + 3.

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Fwam and Eva are an equal distance of 69 miles away from the stadium when the time t = 3 hours

Given data ,

The formula for the distance (F) of Fwam from the stadium is:

F(t) = 327 - 42t

Since Fwam is travelling at a 42 mph pace, his distance from the stadium is reducing at a 42 mph rate.

The formula for Eva's separation from the stadium is:

E(t) = 396 - 65t

Eva's distance from the stadium also shrinks at a pace of 65 miles per hour as she drives at a speed of 65 mph.

Set F(t) = E(t) and solve for t to get the time at which Fwam and Eva are equally far from the stadium

On simplifying the equations , we get

327 - 42t = 396 - 65t

Adding 65t to both sides:

65t + 327 - 42t = 396

23t + 327 = 396

Subtracting 327 from both sides:

23t = 396 - 327

23t = 69

Dividing both sides by 23:

t = 69 / 23

t = 3 hours

Hence , at t = 3 hours after noon, both Fwam and Eva are an equal distance of 69 miles away from the stadium.

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The complete question is attached below :

Fwam and Eva are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Fwam is gar miles away from the stadium and Eva is 396 miles away from the stadium. Fwam is driving along the highway at a speed of 42 miles per hour and Eva is driving at speed of 65 miles per hour. Let F represent Fwam's distance, in miles, away from the stadium t hours after noon. Let E represent Eva's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine how far both Fwam and Eva are from the stadium at the moment they are an equal distance from the stadium.

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.

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 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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Area of rectangular base is 18 square centimeters.

The height (given) is 6 centimeters.

The volume of the rectangular prism is 108 cubic centimeters.

For the area of the base, multiply the length of AD times length of CD

9cm × 2cm = 18cm² remember that is square unit measure:

cm² means square centimeters.

The height is the distance between the two bases. Given as AW = 6

To get Volume, multiply the area of one base by the height

18cm² × 6cm = 108cm³  

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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 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:

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)

hope this helped :)

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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In the given sets, the values of A or B and B and C are:

A or B = {32, 35,36, 38, 40, 41, 44, 46, 48, 50}

B and C = {32, 48}

From the question, we are to determine the values of A or B and B and C in the given set.

From the question,

The universal set is

U = {31,32,33……,50}

and

A={35,38,41,44,46,50}

B={32,36,40,44,48}

C= {31,32,41,42,48,50}

A or B means we should find the union of A and B. That is, the elements present in A or B or both

A or B = {32, 35,36, 38, 40, 41, 44, 46, 48, 50}

B and C means we should find the intersect of B and C. That is, the elements that present both in B and C

B and C = {32, 48}

Hence,

A or B = {32, 35,36, 38, 40, 41, 44, 46, 48, 50}

B and C = {32, 48}

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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:

please mark brainliest

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

If this helps, please mark my answer as brainliest so i can help you more!:)

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]

There are 27.558 meters of wire does she have remaining after the first day.

We have to given that;

An electrician has 42.3 meters of wire to use on a job.

And, On the first day, she uses 14.742 meters of the wire.

Hence, We get;

The remaining wire does she have remaining after the first day is,

⇒ 42.3 - 14.742

⇒ 27.558 meters

Thus, There are 27.558 meters of wire does she have remaining after the first day.

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Answer:

7

Step-by-step explanation:

The graph shown corresponds to someone who makes: C. $20 an hour.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 20/1 = 40/2 = 60/3 = 80/4

Constant of proportionality, k = 20.

Therefore, the required linear equation or function is given by;

y = kx

y = 20x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

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.

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:

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.

Answer:

V = (4/3)π(6^3) = 288π square inches

= 904.78 square inches

Using 3.14 for π, V = 904.32 square inches.

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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