Write a formula in the form
f (t) = A cos Bt+ k that models the surface temperature of the
lake.

If an opponent stands less than 10 yards from the ball when a free kick is awarded, and the ball subsequently strikes that opponent, the referee should award an indirect free kick to the opposing team.

This is because the opponent is in violation of the laws of the game, specifically Law 13 - Free kicks which states that at a direct free kick, a player must be at least 10 yards (9.15m) from the ball until it is in play.

The indirect free kick should be taken from the spot where the opponent was when they were struck by the ball.

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There are 49 distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000.

The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm, is the smallest positive integer that is divisible by both a and b.

Given that, how many distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000,

1000 = 10³ = 2³×5³

Therefore, we get:

x = 2ᵃ×5ᵇ

y = [tex]2^c[/tex]×[tex]5^d[/tex]

where

0 ≤ a, b, c, d ≤ 3

a or c = 3

b or d = 3

To figure out the number of distinct ordered pairs  (x, y), we need to find the distinct number of ordered quadruples  (a, b, c, d)

there are.

Case  1 : Exactly  2 of  a, b, c, d = 3

a = b = 3, c = 0, 1, 2, d = 0,1,2

a = d=3, b = 0, 1, 2, c = 0,1,2

c = b = 3, a = 0, 1, 2, d = 0, 1, 2

c = d = 3, a=0, 1, 2, b = 0, 1, 2

4(1×1×3×3) = 36

Case 2 : Exactly 3 of  a, b, c, d = 3

a = b = c = 3, d = 0, 1, 2

a = b = d = 3, c = 0, 1, 2

a = c = d = 3, b = 0, 1, 2

b = c = d = 3, a = 0, 1, 2

4(1×1×1×3) = 12

Case 3 : Exactly 4 of a, b, c, d = 3

a = b = c = d = 3

1(1×1×1×1) = 1

Total  =36+12+1=49

Hence. there are 49 distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000.

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The algebraic expression that represents the given sentence is:

8 (x + 5).

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. The values a expressed in an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression.

In mathematics, a number that is obtained by multiplying two or more distinct variables together is referred to as the product.

Let us suppose the "a number", as x.

The sum of a number and 5 is represented as follows:

(x + 5)

The product of 8 and sum of a number and 5 is represented as follows:

8 (x + 5)

Hence, the algebraic expression that represents the given sentence is:

8 (x + 5)

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The central tendency of the measure lies at the 50th percentile would be the median.

Option (B) is correct.

What is the measure of the central tendency?

The measure of central tendency is a statistical term that refers to a single value that summarizes or represents a set of data. There are several measures of central tendency, including the mean, median, mode, and percentile.

The measure of central tendency that lies at the 50th percentile for any distribution is the median. The median is the middle value of a set of data when it is arranged in order of magnitude. Half of the values in the set are above the median and half are below it. This means that the median splits the distribution into two equal parts, and it is not affected by outliers or extremely large or small values

Hence, the central tendency of the measure lies at the 50th percentile would be the median.

Option (B) is correct.

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The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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Answer:

m∠CBD = 55°

Step-by-step explanation:

Angles BDA and BDC form a linear pair:

⇒ m∠BDA + m∠BDC = 180°

⇒ 80° + m∠BDC = 180°

⇒ m∠BDC = 100°

Interior angles of a triangle sum to 180°:

⇒ m∠CBD + m∠BDC + m∠DCB = 180°

⇒ m∠CBD + 100° + 25° = 180°

⇒ m∠CBD + 125° = 180°

⇒ m∠CBD = 55°

Answer:

Step-by-step explanation:

The length of the rectangular backyard is represented by the polynomial 3x + 4 and the width is represented by the polynomial x - 1. To find the area, we can multiply the length and the width, which will give us the polynomial expression for the area.

So the polynomial that represents the area of the rectangular backyard is:

(3x + 4) * (x - 1) = 3x^2 + x - 4

If x = 6, then we can substitute this value into the polynomial expression for the area and find the area of the backyard:

3x^2 + x - 4 = 3(6)^2 + (6) - 4 = 108 square feet

So the area of the rectangular backyard when x = 6 is 108 square feet.

The 7 inches pen would not fit in the box with dimensions 3 in × 4 in × 5 in

The 7 inches long pen would not fit in a box with dimensions of 3 inches x 4 inches x 5 inches because the dimensions of the box are not long enough to accommodate the length of the pen.

Specifically, the length dimension of the box (3 inches) is less than the length of the pen (7 inches), so the pen would not be able to fit inside the box.

Additionally, even if the length of the box was greater than 7 inches, the width and height dimensions of the box (4 inches and 5 inches, respectively) would likely be too small to accommodate the diameter of the pen.

In conclusion, the pen is too long for the box, and the box is not wide or tall enough to fit the pen.

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The correct expression for the exact distance between the two boys: 1000√2 m

The correct answer is an option (D)

Consider following diagram.

In right triangle ABC, AB represents the distance covered by the Marco and AC represents the distance covered by the Ray.

AB = 1000 m

AC = 1000 m

We need to find the correct expression for the exact distance between the two boys.

i.e., we need to find the length of hypotenuse BC.

Using Pythagoras theorem for right triangle ABC,

BC² = AB² + AC²

BC² = 1000² + 1000²

BC² = 1000000 + 1000000

BC² = 2 × 1000000

BC = [tex]\sqrt{2\times 1000000}[/tex]

BC = 1000√2 m

Therefore, the distance between the boys = 1000√2

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The measure of each angle of hexagon = 35°

we know that the hexagon is a polygon with six sides.

A regular hexagon is a hexagon with the measurement of all the sides and interior angles are equal.

Let us assume that x represent the measure of one of the remaining two angles that  are equal in measure.

We know that the sum of interior angles of hexagon is 720°

The sum of the measures of 4 out of the 6 interior angles in a hexagon is 650°.

So, we get an equation,

650° + x + x = 720°

650° + 2x = 720°

2x = 70°

x = 70/2

x = 35°

The measure of each angle = 35°

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The coordinates of the missing endpoint if p is the midpoint of nq is (8,4)

In math the term called midpoint is defined as the point on a line that is at an equal distance from either end.

Here we have know the value of the point n(2,0) and p(5,2) and we need to identify the value of q.

Let us consider that (x, y) be the point of q.

Where we all know that the formula of mid point is written as,

p(xₐ, yₐ) = [(x₁+x₂)/2, (y₁ + y₂)/2]

When we apply the values on it, then we get,

=> p(5,2) = [(2+x)/2, (0+y)/2]

When we compare the values, then we get,

=> (2+x)/2 = 5

=> 2 + x = 10

=> x = 8.

Similarly the value of y is calculated as,

=> (0+y)/2 = 2

=> y = 4

Then the coordinate of q is (8,4).

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Answer:

∠ U = 80°

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180° , that is

∠ U + 37° + 63° = 180°

∠ U + 100° = 180° ( subtract 100° from both sides )

∠ U = 80°

To represent the ratio of trains to airplanes, you can write it as:

4 : 8

This ratio shows that for every 4 model trains, there are 8 model airplanes. You could also simplify the ratio to 1:2 which means that for every 1 model train, there are 2 model airplanes.

Alternatively, you could express the ratio as a fraction:

4/8 = 1/2

This fraction shows that 1/2 of the models are model trains.

The solution is, 1/2 is a ratio to represent the ratio of trains to airplanes.

Here, we have,

To represent the ratio of trains to airplanes, you can write it as:

4 : 8

This ratio shows that for every 4 model trains, there are 8 model airplanes. You could also simplify the ratio to 1:2 which means that for every 1 model train, there are 2 model airplanes.

Alternatively, you could express the ratio as a fraction:

4/8 = 1/2

This fraction shows that 1/2 of the models are model trains.

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The square feet of outdoor carpet needed for the hole is 42.

A composite figure is a given figure which is made up of more than one figure. Thus the total area of the figure is then the required area of the composite figure.

In the given diagram, the hole can be divided into a trapezium, rectangle and a triangle. So that;

i. Area of a trapezium = 1/2 (a + b)h

                                = 1/2 (3 + 6)4

                                = 9*2

                                = 18

Area of the trapezoidal part is 18 square feet.

ii. Area of a rectangle = length x width

                                    = 7*3

                                    = 21

Area of the rectangular part is 21 square feet.

iii. Area of a triangle = 1/2* base * height

                                  = 1/2 * 2* 3

                                  = 3

Area of the triangular part is 3 square feet.

Total area = 18 + 21 + 3

                 = 42 square feet

The area of outdoor carpet needed for the hole is 42 square feet.

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Answer:

X and y are the variables in the expression

Step-by-step explanation:

Variables are letters that represent an unknown value

For example, x + 4 = 7

In this equation, x is the variable because it is letter representing the unknown value

⇒ In 7x+ 4y+1 , x and y are the variables in the expression

Answer:

Thats the answer in the picture I designed and made it step by step so you can understand it

Hope it helps

(a) P(N=0) = 0.00974

(b) P(N=n) = 1/3[10Cn(0.3)ⁿ(0.7)¹⁰⁻ⁿ + 10Cn(0.5)ⁿ(0.5)¹⁰⁻ⁿ + 10Cn(0.7)ⁿ(0.3)¹⁰⁻ⁿ]

(c) N does not have a binomial distribution.

(d) yes, it is a fair game.

(a) P(N=0) = 1/3P(N=0 | p = 0.3) + 1/3P(N=0 | p = 0.5) + 1/3P(N=0 | p = 0.7)

or P(N=0) = 1/3{(0.3)¹⁰ + (0.5)¹⁰ + (0.7)¹⁰)

or P(N=0) = 0.00974

(b) P(N=n) = 1/3[10Cn(0.3)ⁿ(0.7)¹⁰⁻ⁿ + 10Cn(0.5)ⁿ(0.5)¹⁰⁻ⁿ + 10Cn(0.7)ⁿ(0.3)¹⁰⁻ⁿ]

since, n=0, 1, 10

(c) N does not have binomial distribution but subparts in it have binomial distribution.

(d) yes, it is a fair game because only the first and third coins are biased and their biasness is tied (p = 0.3 and 0.7). Hence it is a fair game in the long run.

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The cumulative distribution function of a continuous random variable is the probability that the random variable X is greater than or equal to x, where x is a specific value of the continuous random variable X. [FALSE ]

The cumulative distribution function of a continuous random variable is the probability that the random variable X is less than or equal to x, where x is a specific value of the continuous random variable X.

The cumulative distribution function is a function that is usually derived from a continuous random variable. We actually calculate the area underneath a probability density function between two points.

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Answer: The reflector's height can be modeled as a function of time. The function will depend on the radius of the wheel, the distance of the reflector from the edge of the tire, and the speed of the bicycle.

Let's call the radius of the wheel r. The radius is half of the diameter, so:

r = 630 / 2 = 315 mm

Also, let's call the distance of the reflector from the edge of the tire d.

d = 79 mm

Given that the reflector is at its lowest height at t = 0, we know that at that time the center of the reflector is at a height of r + d = 315 + 79 = 394 mm.

The height of the center of the red reflector at time t seconds is given by:

h(t) = (r + d) + vt

Where v is the speed of the bicycle in meters per second, and t is the time in seconds.

Substituting the values we have:

h(t) = 394 + (1.6 x t)

So the function for the height of the center of the red reflector at time t seconds is h(t) = 394 + (1.6 x t) (in mm)

It's important to note that this function is based on the assumption that the reflector is at its lowest height at time t = 0 and that the height of the reflector increases linearly with time as the bike moves forward.

Step-by-step explanation:

The table of values represented from 60 = 12m is

m      5

f(m)   60

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

60 = 12m

To determine the table of values, we start by solving for m in the equation 60 = 12m

So, we have

12m = 60

Divide both sides by 12

m = 5

So, the equation can be expressed as

f(m) = 12m

This implies that the table of values is

m      5

f(m)   60

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Answer: 4.6+.5m=13.60 , m=18

Step-by-step explanation:

4.6+.5m=13.60

.5m=13.60-4.6

.5m=9

m=18

The fraction is 3/5.

We know that,

Numerator : the top number of a fraction which is upon on fraction bar.

Denominator : the bottom number of a fraction which is below the fraction bar.

Fraction = numerator / denominator

Let the denominator is x.

Given that numerator is 2 less than denominator

So, numerator will be ( x-2 )

So fraction = (x – 2)/x

Given that after adding 3 in numerator and denominator fraction become 3/4

Fraction = (x - 2)/(x) = (5 - 2)/5 = 3/5

Therefore, fraction is 3/5.

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Answer:

see below

Step-by-step explanation:

total sum of all angles is 360

becuase they are all parallel, so the sum of A & D multiply by 2 = 360

so a+d = 180

5x+18 +3x+10 = 180

8x+28 =180

8x=152

x=19

A = 5*19+18 =113

D=3*19+10 =67

As per the given length and width, the perimeter of rectangle is 16x² + 22x + 39

In math the term perimeter of rectangle is defined as the length of the outline of a shape.

In order to find the perimeter of a rectangle or square you have to add the lengths of all the four sides, then the formula is written as,

=> P = 2(l + w)

here l refers length and w refers the width of the rectangle.

Here we have given that the length of the rectangle in terms of x is 8x² +4x +7 and its width is 7x + 8.

Then the perimeter is calculated as,

=> P = 2(8x² +4x + 7 + 7x + 8)

When we simplify the expression, then we get,

=> P = 2(8x² + 11x +15)

When we multiply 2 with the expression, then we get,

=> P = 16x² + 22x + 39

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the customer saved 45% on the price of the radio compared to the original price.

25%

The original price of the radio = 100%

The 20% discount = 100%-20% = 80%

The 25% discount = 80%-25% = 55%

Overall percentage reduction = 100%-55% = 45%.

The original price of the radio was 100%. On the final day, the ale was discounted by 25%, which reduced the price to 80%. This was then further discounted by 20%, bringing the price to 55%. Therefore, the overall percentage reduction on the price of the radio was 45%. This means that the customer saved 45% on the price of the radio compared to the original price.

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Answer:

The volume is 1449 ft^3

Step-by-step explanation:

Split each section, the living room and hallway, into two different rectangular prisms to solve for.

The larger rectangle will have a length of 15ft, a width of 12ft, and a height of 7ft as shown in the diagram. Multiply length, width, and height to find the volume of 1,260ft.

15*12*7=1,260

The smaller rectangle will have a length of 9ft. That's found by subtracting 15 from 24. The width will be 3ft. That's found from subtracting 9 from 12. The height is still 7. Multiple each together to find the second rectangle's volume of 189ft.

24-15=9

12-9=3

9*3*7=189

Add both volumes together and you have the volume of the whole space.

1,260+189=1449ft^3

A probability is a number that reflects the chance or likelihood that a particular event will occur.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The simplest example is a coin flip. When you flip a coin there are only two possible outcomes, the result is either heads or tails.

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Answer:c

Step-by-step explanation: