In a circle with radius 4, an angle intercepts an arc of length 8\pi8π. Find the angle in radians in simplest form.

The unit rate of the coffee is found as $0.483.

For the given question:

cost of 12.4 ounce of coffee  = $5.99.

For the unit rate, divide both sides by 12.4.

cost of 1 ounce of coffee  = $5.99/12.4

cost of 1 ounce of coffee  = $0.483

Thus, the unit rate of the coffee is found as $0.483.

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If the points K and M are points of tangency, then the value of x is, 4

In mathematics, the circle is a two dimensional rounded figure which has no corner edges.

Standard form = (x - a)² + (y - b)² = r²

Given that,

A circle, having two pair of lines JK & JM

It is known that,

theorem of a circle,

Lengths of the tangents on the circle from the same point are equal

Length of JK = Length of JM

         6x + 5  = 37 - 2x

                8x =  32

                   x = 4

Hence, the value of x is 4

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Step-by-step explanation:

Nope. Actually, every single even number except 1 is composite actually

Answer:

No

Step-by-step explanation:

2 is a prime number, but all other even numbers are composite, since they're all multiples of 2

The total perimeter will be 4x^+17 and length be 22.76 cm

As per the data given in the questions,

We have, the shape of the sandwich be rectangular.

We know that, perimeter of the rectangle can be determined by using formula: 2(l+b),

where, l = length of the rectangle

and, b = breadth of the rectangle

The expression for the perimeter of the sandwich would be:

2 (2x^2 + 9) + 2 (2x^2 + 8)

= 4x^2 + 26

Now for finding the length of the crust,

we will put the value of x=1.2,

So, the value of the approximate length of the crust would be:

=4x^2 + 26

= 4 * 1.2^2 + 26

= 22.76 centimetres.

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a) The enlargement needed to be done is 25%.

b) The succession time should be at least t=9 to get a final copy that is less than 15% of the original size.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Let the size of the page be q, when it is reduced to 80%, its size becomes

= 80% x q

= 0.80(q)

= 0.80q

When you want to return it into its original size q,

x(0.80q) = q

x = q / 0.80q

x = 1.25

x= 125%

Hence, the enlargement needed to be done is 25%.

b) The size of the page after t number of copying done is given by

C(t) = [tex]C_0(0.80)^t[/tex]

So, C(t) / [tex]C_0[/tex] = [tex](0.80)^t[/tex]

0.15 ≤  [tex](0.80)^t[/tex]

Taking log on both side

log (0.15) ≤ log [tex](0.80)^t[/tex]

log (0.15) ≤ t log (0.80)

log (0.15) /log (0.80)  ≤ t

0.80 ≤ t

Hence, the succession time should be at least t = 9 to get a final copy that is less than 15% of the original size.

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The equation in slope intercept form is : [tex]y = \frac{1}{8} x - 223.05[/tex]

The slope intercept form is a process used to determine the equation of a straight line in the coordinate plane. It can be used to determine the equation of a line when given the slope of the straight line and the y-intercept

The slope-intercept form of a line is:

y = mx+b

where m is the slope of the line and b is an intercept of the y-axis.

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]m = \frac{26.7 - 23.2 }{1998- 1970}[/tex]

[tex]m = \frac{1}{8}[/tex]

So,

[tex]y = \frac{1}{8} x + b[/tex]

To find b we get the point (1970, 23.2) and introduce it in the previous equation.

[tex]23.2= \frac{1}{8} (1970)+ b[/tex]

⇒ 23.2 - 246.25 = b

⇒ b = - 223.05

Then, the equation is : [tex]y = \frac{1}{8} x - 223.05[/tex]

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Answer:

x-5/10 - 2(x-3)/5 = 3(x-4)/15= x=-15/4

Answer:

2s

Step-by-step explanation:

sq pool so total length = 4s

so need 4s/2 = 2s tiles

The required end behavior of the graph of y = f(x) is given as, x → ∞, y→-∞ and when x → -∞, y →∞. Option B is correct.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
As we can see in the graph of y =f(x)

As x approaches -∞ y approaches ∞, and as As x approaches ∞ y approaches -∞

Thus, the required end behavior of the graph of y = f(x) is given as, x → ∞, y→-∞ and when x → -∞, y →∞. Option B is correct.

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From the figure , and by using congruent complements theorem, the angle that is congruent to angle4 is (a) angle1  .

The "Congruent Complements Theorem" states that if two angles are complementary to same angle, then they are congruent. In other words, if two angles add up to 90 degrees, and they both complement the same third angle, then they are equal in measure.

The ∠4 and ∠5 are the complements and ∠1 and ∠5 are complements.

Which proves that :  ∠1 and ∠4 are complimentary to the same angle that is ∠5.

Therefore, the ∠ 1 is congruent to angle 4 .

The given question is incomplete , the complete question is

From the figure below , the angle 4 and angle 5 are complements and angle 1 and angle 5 are complements , By using the congruent complements theorem, which angle is congruent to angle4 ?

(a) angle1

(b) angle2

(c) angle3

(d) angle5

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Answer: B. No, the adjacent sides are not perpendicular.

Step-by-step explanation:

B(2,4), A(4, -1), C(-2, 2), D(0, -3)

Slope of BA = [tex]\frac{4-(-1)}{2-4} = \frac{5}{-2}[/tex]

Slope of CD = [tex]\frac{2-(-3)}{-2-0} =\frac{5}{-2}[/tex]

BA║CD

Slope of BC = [tex]\frac{4-2}{2-(-2)} =\frac{2}{4} =\frac{1}{2}[/tex]

Slope of AD = [tex]\frac{-1-(-3)}{4-0} =\frac{2}{4} =\frac{1}{2}[/tex]

BC║AD

Slope of BA [tex]=\frac{5}{-2}[/tex]

Slope of BC [tex]=\frac{1}{2}[/tex]

BA is not perpendicular to BC

The mathematical expression boole’s inequality for a sequence of events a1, a2, . . . , an then the bounds are known as Bonferroni inequalities [13].

Arithmetic sequence is [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d ; n > 1

The given equation about an arithmetic sequence is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d ; n > 1

Boole's inequality(or the union bound) states that for any at most countable collection of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the events in the collection.

The objective is to prove the statement using principle of mathematical induction.

The principle of mathematical induction statement that a statement [tex]p_{n}[/tex] about positive integer n, is true if satisfies the following two conditions:

[tex]p_{1}[/tex] is true

If [tex]p_{k}[/tex] is true, then [tex]p_{k+1}[/tex] is true

Consider the statement for n > 1

[tex]p_{n}[/tex] : [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d

Here, it is known that [tex]a_{n}[/tex] is an arithmetic sequence with [tex]a_{1}[/tex] as first term and 'd' as common difference.

Recall that in any arithmetic sequence, each term is determined by adding 'd' to previous term.

Hence, the second term is determined by adding 'd' to first term.

[tex]a_{2}[/tex] = [tex]a_{1}[/tex] + d

For [tex]p_{2}[/tex] , substitute n = 2 in the given statement to verify it for first positive integer.

[tex]p_{n}[/tex] : [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d

[tex]p_{2}[/tex] : [tex]a_{2}[/tex] = [tex]a_{1}[/tex] + (2-1) d

[tex]p_{2}[/tex] : [tex]a_{1} +d[/tex] =   [tex]a_{1} +d[/tex]

This has given a true statement.

Hence, the statement is verified for [tex]p_{1}[/tex].

Therefore,

The mathematical expression boole’s inequality for a sequence of events a1, a2, . . . , an then the bounds are known as Bonferroni inequalities [13].

Arithmetic sequence is [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1) d ; n > 1

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Answer:

n = 6.42105263158

Step-by-step explanation:

324 - 202 = 122

122 ÷ 19 = 6.42105263158

That seems like a very large decimal place for a school related math problem if I'm doing this correctly.  When you say increased by you mean addition right?

The required Linear function among the following option is D) y=|x|.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A)  y=3x³

It is cubic function.

B) y=¼x

It is inverse function.

C) Y=x²

It is a quadratic function.

D) y=|x|

It is a modulus function, but after remove the Mode in x, we get

y = x and y = -x

So, Here power on x is one. It is Linear function as well.

Thus,  y=|x| is linear function.

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The individual can save about 76 gallons of gas when switching to a hybrid vehicle.

A motor vehicle's fuel efficiency is calculated in miles per gallon (mpg). Miles traveled divided by gasoline consumed is the formula used to calculate mpg.

The gallons used by the vehicle a year when it travels 60 miles per week are given by,

[tex]\begin{aligned}\text{gallons used}&=\mathrm{\frac{50\;weeks\times 60\;miles}{22\;miles/gallon}}\\&=\mathrm{136\;gallons}\end{aligned}[/tex]

The gallons used by the hybrid vehicle a year when it travels 50 miles per gallon is given by,

[tex]\begin{aligned}\text{gallons used}&=\mathrm{\frac{50\;weeks\times 60\;miles}{50\;miles/gallon}}\\&=\mathrm{60\;gallons}\end{aligned}[/tex]

Then, the gas they have saved is calculated by subtracting fuel consumed by both vehicles, 136-60=76 gallons.

The required answer is 76 gallons.

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A.Researcher 1: Since increases for a higher level of confidence, the researcher 1 would need larger sample size.

The benefits of studying probability are very useful for making the right decisions, because there is no certainty in life in the world, so it is necessary to know what is the probability that an event will occur. Probability is expressed as a fractional number between 0 and 1 or as a percentage. Some important terms in probability are (a) trial, (b) outcome, and (c) event.

There are three approaches in determining probability namely (a) the classical approach which gives the same probability, (b) a relative approach that pays attention to events that have occurred and (c) a subjective approach based on individual judgment.

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Answer:

x=291/X

Step-by-step explanation:

it mean 29=xX-262

xX=29+262

xX=291

x=291/X

Answer:

The median is 79.

Step-by-step explanation:

The distance from point P = (1, -1) to the line through points A = (-2, 2) and B = (0, -4) is 2.23.

What is distance ?

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

The slope of the line can be found using the coordinates of points A and B:

m = (y2 - y1) / (x2 - x1) = (-4 - 2) / (0 - (-2)) = -3

Next, we can use the coordinates of point A to find the y-intercept:

b = y - mx = 2 - (-3)(-2) = 2 + 6 = 8

m_perpendicular = -1 / -3 = 1/3

Using the coordinates of point P, we can find the equation of the perpendicular line:

y = m_perpendicular x + b_perpendicular

y = 1/3 x - 1/3

Setting the y-coordinates equal, we can find the x-coordinate of the intersection point:

-3x + 8 = 1/3 x - 1/3

-9x + 24 = x - 1/3

-10x + 24.33 = x

x = 24.33 + 10x

11x = 25.66

x = 2.33

Finally, we can find the y-coordinate of the intersection point using the equation of the perpendicular line:

y = 1/3 x - 1/3

y = 1/3 (2.33) - 1/3 = 0.77

The intersection point is (2.33, 0.77), and the distance from point P to the line is the distance between the two points:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((2.33 - 1)^2 + (0.77 + 1)^2) = sqrt(1.33^2 + 1.77^2) = sqrt(1.7769 + 3.1369) = sqrt(4.9138) = 2.23.

So, the distance from points P = (1, -1) to the line through points A = (-2, 2) and B = (0, -4) is 2.23.

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Step-by-step explanation:

(a)

2:5:3 means that there are 2+5+3 = 10 units of the price money distributed between the team.

£1500 / 10 = £150 per unit.

person A gets therefore 2×150 = £300

person B gets 5×150 = £750

person C gets 3×150 = £450

so, person B gets 750-300 = £450 more money than person A.

(b)

40% of £450 = 450×0.4 = £180

so donated to total prize money is

180/1500 = 3/25

Answer:

13.86

Step-by-step explanation:

You have the exact value, just compute it and round the number to get your approximate

Answer:

13.86

Step-by-step explanation:

You'll most likely need the calculator since ✓192 is not a perfect square.

Calculating it

✓192 = 13.856

Rounding it two places would be 13.86

The value of m for the given equation is 18. The solution has been obtained by solving the linear equation.

What is a linear equation?

A linear equation is the one with the highest degree of one. This demonstrates that there are no variables in a linear equation with an exponent bigger than one. On the graph, such an equation yields a straight line.

We are given an equation as 2 = m/2 - 7

On solving the equation for m, we get

⇒2 = m/2 - 7

⇒2 = (m - 14)/2

⇒2*2 = (m - 14)

⇒4 = m - 14

⇒m = 18

Hence, the value of m for the given equation is 18.

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There are 81 different ways to place 5 distinguishable balls in 3 indistinguishable boxes using combinations.

Given that in how many ways we can put 5 balls in 3 boxes if balls are distinguishable, but the boxes are not.

To find the number of ways we will use the concept of combination.

Combinations can be defined as the entire outcomes of an event where the order of outcomes does not matter.

Given Data

The number of balls is 5 balls.

The number of boxes is 3 boxes.

The balls are distinguishable, but the boxes are not distinguishable.

According to the question, the expression for the number of ways is,

P = [tex]\frac{n^N}{n}[/tex]

Putting the values in the formula we get,

P = [tex]\frac{3^5}{3}[/tex]

P = 81

Hence the number of the ways are 81.

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the simple form of the given number will be 8√3.

What is square root?

A value known as the square root of a number is one that, when multiplied by itself, yields the original number. An alternative to square rooting a number is to use it. Therefore, the concepts of squares and square roots are connected. The original number is equal to the square root of any integer, which is equivalent to a number.

Let's assume that m is an integer that is positive, such that (m.m) = (m2) = m.

A square root function in mathematics is described as a one-to-one function that accepts a positive number as input and outputs the square root of the specified input number.

The given number is √192

= √ (2*2*2*2*2*2*3)

=8√3

Hence the simple form of the given number will be 8√3.

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The square root of 9 is 78 less than 9 squared

The square root of 9 is calculated as

                     √9 = √(+ 3)² or√(- 3)²

                           = + 3 or - 3

Let's calculate the square of 9:

                      9² = 81

We need to calculate here, how much the square root of 9 is less than the square of 9 or we can say the difference between the square of 9 and the square root of 9. So, let's say that difference is denoted by d

                                 d = 9² - √9

When √9 = +3

                                 d = 81 - 3

                                 d = 78

When √9 = -3

                                 d = 81 - (-3)

                                 d = 81 + 3

                                 d = 84

Hence, the value of the difference between the square of 9 and the square root of 9 is 78 or 84.

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It is going to be more expensive for 9 teams to buy these baseballs.

It has been mentioned in the problem that Ms.Bush charges $4 per baseball. This means that we need to pay $4xn dollars where n is the number of baseballs. According to the question, the member of baseball depends on the number of teams as well. More teams mean more baseballs will be bought.

Since it is obvious that 9 is greater than 6, so, it automatically means that it is going to be more expensive for 9 teams to buy these baseballs as compared to 6 teams.

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The solution to the given differential equation is a 3-dimensional vector function which satisfies the given initial conditions. The vector function consists of three components, one for each dimension in the equation.

The given differential equation is a 3-dimensional vector equation, of the form ()=⟨12−12,2−1,1⟩. The initial conditions are (1)=⟨0,0,12⟩ and ′(1)=⟨8,0,0⟩. The solution to this equation is a 3-dimensional vector function, ()=⟨, ,⟩. The first component of the vector function is a function of the independent variable, and must satisfy the initial condition (1)=⟨0,0,12⟩. This means that the first component of the vector function must be equal to 0 at x=1. The second component must satisfy the initial condition ′(1)=⟨8,0,0⟩. This means that the second component of the vector function must be equal to 8 at x=1. The third component of the vector function must also satisfy the initial condition (1)=⟨0,0,12⟩. This means that the third component of the vector function must be equal to 12 at x=1. Once the initial conditions have been satisfied, the  equation can be solved to find the vector function.

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The following are the respective values of the angles:

∠5 = 44°

∠3 = 117°

x = 60°

x = 157°

angles (∠5 + ∠6)° and ∠2 are corresponding angles and are equal so;

∠5 + 90° = 134°

∠5 = 134° - 90°

∠5 = 44°

angles (∠5 + ∠6)° and ∠3 are alternate angles and are equal so;

∠3 = ∠5 + ∠6

∠3 = 27° + 90°

∠3 = 117°

(x + 5) + 90° + (180° - 155°) = 180° {sum of interior angles of a triangle}

x + 5 + 90° + 25° = 180°

x + 120° = 180°

x = 180° - 120°

x = 60°

x = 22° + (180° - 45°) {exterior angle of a triangle equals two opposite interior angles}

x = 22° + 135°

x = 157°

Therefore, the following are the values of the angles: ∠5 = 44, ∠3 = 117°, x = 60°, and x = 157° respectively.

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An individual's BMR decreases approximately 3 to 5 percent per decade on an average after the age of option C. 30.

Therefore, on an average individuals BMR is approximately decreases by round about 3 to 5 percent per decade after the age of option c. 30.

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