Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

-4, (-2 , 1)

0, (-1, 21)

If k and n are non-negative integers and n is the greater of the two, then the ordered list of k of the n things without repetition is the k-permutation of the n separate objects.

The total number of ways to select k objects from a set of n elements is n(n1), with (nk+1) alternatives being available for the kth place.when ordering matters and repetition is not permitted. A k-permutation of the elements in set A is any of the chosen lists in the previous configuration (choose k elements, in any order, with no repetition). Pnk=0 if k is greater than n. This makes sense because it is impossible to select k unique elements from an n-element collection if k>n.

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Answer:

£22.80

Step-by-step explanation:

To work out how much Ross has to pay for his ticket, you first need to calculate how much the 1/3 of the full price is.
To do this, you divide the 34.20 by 3.
34.2 / 3 = 11.4
So Ross gets a discount of £11.40
To work out the price, that Ross has to pay, we substract the discount from the normal price:
34.2 - 11.4 = 22.8
So Ross pays £22.80 for his ticket.

The measure of θ from the given trigonometric equation is 31°.

Given that, sin47°=cosθ and sinθ=cos(θ+16).

We know from geometry if the sum of two angles is 90°, then one angle is called the complement of the other.

The complementary angles are:

sinθ=cos(90-θ)

secθ=cosec(90-θ)

tanθ=cot(90-θ)

A) So, sin47°=cos(90°-47°)

⇒ sin47°=cos43°

Thus, θ=43°

B) sinθ=cos(θ+16)

⇒ sinθ=cos(43+16)

⇒ sinθ=cos 59°

⇒ sin(90-31)=cos 59°

Thus, θ=31°

Therefore, the measure of θ from the given trigonometric equation is 31°.

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The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.

What is a standard deviation?

Data dispersion in regard to the mean is quantified by a standard deviation. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Here, we have

µ = 62 , σ = 5

P ( X < 66 )

By applying the standard deviation formula, we get

Z = ( X - µ ) / (σ/√(n)

Z = ( 66 - 62 ) / ( 5 / √50 )

Z = 5.6569

P (  ( X - µ ) / ( σ/√(n)) < ( 66 - 62 ) / ( 5 / √(50) )

P ( X < 66 ) =  P ( Z < 5.66 )

P ( X < 66 ) = 1

P ( X > 66 )  = 1 - P ( X < 66 )

By applying the standard deviation formula, we get

Z = ( X - µ ) / ( σ / √(n))

Z = ( 66 - 62 ) / ( 5 / √ ( 50 ) )

Z = 5.6569

P (  ( X - µ ) / ( σ / √ (n)) > ( 66 - 62 ) / ( 5 / √(50) )

P ( Z > 5.66 )

P ( X > 66 )  = 1 - P ( Z < 5.66 )

P ( X> 66 )  = 1 - 1

P ( X> 66 )  =  0

Hence, the probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.

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In tech internship

Slope of the line m is $11.50, y intercept is 0 and the point slope form is  y = 11.50x + 0

In Amusement park attendant

The slope of the line = $9, y intercept is 100 and Point slope form y = 9x + 100

In tech internship

Schedule = part time (20 hours/week)

The wage = $11.50/hour

The slope intercept form

y = 11.50x

Slope of the line m = $11.50

y intercept = 0

y = 11.50x + 0

In Amusement park attendant

Schedule- full time (40hours/week)

Wage - 9/hour+ 100 bonus

The slope of the line = $9

y intercept = 100

The equation is

y = 9x + 100

Hence,

In tech internship

Slope of the line m is $11.50, y intercept is 0 and the point slope form is  y = 11.50x + 0

In Amusement park attendant

The slope of the line = $9, y intercept is 100 and Point slope form y = 9x + 100

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Answer:

Step-by-step explanation:

Given,

No. of nails the factory makes = 600

Time taken by the factory to make 600 nails = 3 minutes

So,

Time taken by the factory to make 1 nail = [tex]\frac{3}{600}[/tex] minutes

∴ Time taken by the factory to make 27000 nails

= ( [tex]\frac{3}{600}[/tex] × [tex]27000[/tex] ) minutes

= ( [tex]\frac{1}{2}[/tex] × [tex]270[/tex] ) minutes

= 135 minutes

Or,

As we know ,  [ 1 minute =  [tex]\frac{1}{60}[/tex] hour]

So, 135 minutes = [tex]\frac{135}{60}[/tex] hours

= 2.25 hours

Now, [1 hour = 60 minutes]

0.25 hours = [tex]\frac{1}{4}[/tex] hours

= [tex]\frac{1}{4}[/tex] × 60 minutes

= 15 minutes

Hence,

The time taken by the factory to make 27000 nails is 2 hours 15 minutes (Ans)

Answer:

2.25 hours or 2 hours 15 minutes

Step-by-step explanation:

600 nails / 3 minutes = 200 nails / minute

27,000 nails / 200 nails/minute = 135 minutes

1 hour = 60 minutes

135 minutes × 1 hour / 60 minutes = 2.25 hours

2.25 hours = 2 hours  + 0.25 hours × 60 minutes/hour = 2 hours 15 minutes

Answer: 2.25 hours or 2 hours 15 minutes

Answer:

y=-0.4x - 1.2

80°,20° or 50°,50° are possible for the other two angles.

Given:

One angle of an isosceles triangle measures 80°.

we assumed that the 80° is one of the equal angles, then there is another 80° angle.That makes 160°.

Since a triangle always totals 180°,

180° - 160° = 20°.

if the 80° was the only different angle instead,the two remaining angles total:

180 - 80 = 100

Since we have two identical angles remaining, we need only divide the 100° in half to get the final answer:

100/2 = 50°.

Therefore 80°,20° or 50°,50° are possible for the other two angles.

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The distance and bearing of the boat from the port areas follows;

The boat is locates at approximately 157.15 kilometers and on a bearing of 150° from the port.

A bearing in mathematics is an angle that is measured clockwise, from the north or y-axis direction.

The speed at which the Coast Guard cutter travels = 30 knots

Bearing of the Coast Guard cutter Angelica = 95°

The time the coast guard travels in the initial direction = 2 hours

The direction the Coast Guard cutter changes to = 185°

Time of traveling in the new direction = 2 hours

30 knots = 55.56 km/hr

The distance traveled in the first direction = 55.56 km/hr × 2 hr = 111.12 km

The distance traveled in the second direction = 55.56 km/hr × 2 hr = 111.12 km

From the attached drawing, we have that the figure formed by the path of the Coast Guard cutter is an isosceles triangle

The distance from the port to the location of the boat, given by Pythagorean theorem is; l = √(111.12² + 111.12²) ≈ 157.15

The distance f the boat from the port is approximately 157.15 kilometers

The base angles of an isosceles right triangle are 45°

Therefore, the bearing is 95° + 45° = 150°

The bearing from the port to the boat is 150°

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The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.

The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.

With regard to the above problem,

let us say L is the lenght of the rectangle and W is the width

Based on the formula for the area of a rectangle,

L x W  = 1600ft

To minimize the perimeter, of the rectangle, we must assume that:

L = W

that is L² = 1600

If we applied square root to both sides of the equation, we'd have


L = 40

Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.

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The motel revenue based on the number of rooms rented and group rental are as follows;

(a) The price for renting three rooms is $195

(b) The formula through which the unit rate of a room is found is aₙ = 71 - 3·(n -1)

(c) The function for the revenue, R(n) = 74·n - 3·n²

(d) The most amount that can be made is $456

The number of rooms that gives the most amount is 12 rooms

A revenue is the total amount received for the sale of goods and services

The number of rooms in the motel = 44

The price for renting one room = $71

The price for renting two rooms = $68

The per room group rate = $71 - $3 for each additional room
(a) The amount made if a family rents three rooms is given as follows;

The unit price for two rooms = $71 - $3 = $68

The unit price for three rooms = $68 - $3 = $65

The price for the three rooms is therefore;

$65 × 3 = $195

(b) The formula that gives the rate charged for each room to an organization is an arithmetic progression, which can be expressed as follows;

aₙ = a₁ + (n - 1)·d

Where;

n = The number of rooms the organization plans to rent

a₁ = The first term of the arithmetic progression = 71

d = The common difference = -3

Which gives;

aₙ = 71 - 3·(n - 1)

The price for each room when an organization rents n rooms is therefore;

aₙ = 71 - 3·(n - 1)

(c) The revenue for renting n room is given by the formula;

Revenue, R(n) = Unit rate × Number of rooms

∴ R(n) = (71 - 3·(n - 1)) × n = 74·n - 3·n²

(d) The -ve coefficient of n² in the formula with which the revenue can be found indicates that the function has a maximum value. The number of rooms that gives the most revenue is obtained at the from the derivative of the R(n) as follows;

R'(n) = 74 - 6·n = 0

n = 74/6 ≈ 12

Which gives;

[tex]R_{max}[/tex] = R(12) = 74 × 12 - 3 × 12² = 456

The maximum revenue from renting to a single group ≈ $456

The number of rooms to rent that gives the maximum revenue is n ≈ 12

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A double-blind placebo control group study is used to control for observer bias and eliminate testing effects. So option c is correct.

A double-blind placebo control group study is one in which subjects are randomly assigned to either a control group, who receive a placebo, or an experimental group, who receive the treatment being studied. The researcher is not aware of which subjects are in which group, and neither are the subjects. This design is used to control for observer bias and eliminate testing effects.

This type of study is important because it allows researchers to test the efficacy of a new treatment without the risk of bias. By eliminating the possibility that the researcher or the subjects will know who is receiving the treatment and who is receiving the placebo, any expectations or preconceptions about the treatment can be avoided. This type of study is also important because it helps to control for the placebo effect, which is the phenomenon whereby subjects in the control group may experience some benefits from the placebo itself.

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uhmm,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

No. of coins in jar of nickels is 207 and of dimes is 103.

Let the no. of coins of dimes = x

No. of coins of nickels = 2x

Total = 310

x + 2x = 310

     3x = 310

       x = 310/3

          = 103.33

          ≈ 103

No. of coins of dimes = 103

No. of coins of nickels = 310 - 103

                                     = 207

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Answer:

No

Step-by-step explanation:

The sum of the squares of the lengths of the two shorter sides is [tex]10^2+12^2=244[/tex].

The square of the length of the largest side is [tex]14^2=196[/tex].

Because these two values are not equal, the side lengths do not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.

Step-by-step explanation:

when a line intersects parallel lines, then the intersecting angles must be the same for each of the parallel lines.

so,

y = 139

and the angles y and x are supplementary (or a linear pair). that means together they have 180°.

that is simply because the sum of all angles around a single point on one side of a line must be 180° (because the line is like the diameter of a circle with the "rotation point" being the center, and one side of the line represents the half-circle).

therefore,

y + x = 180

139 + x = 180

x = 41

The absolute value function graphed in this problem is given by the rule presented as follows:

y = |x - 3| + 5.

The first step to obtain the graph of an absolute value function is obtaining the vertex of the function, which is the turning point of the curve in the format of V.

Then, the definition of an absolute value function with vertex (h,k) is defined by the equation presented as follows:

y = |x - h| + k.

For the graphed function, the coordinates of the vertex are given as follows:

(3,5).

The reason for these coordinates are as follows:

Considering the coordinates of the vertex obtained previously on the problem, the absolute value equation graphed is defined by:

y = |x - 3| + 5.

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The simplification of the trigonometric expression (sec(t) - cos(t))/sin(t) is; tan (t)

There are different trigonometric ratios such as;

sin x

tan x

cos x

sec x

cosec x

cot x

Now, we want to simplify the trigonometric expression;

(sec(t) - cos(t))/sin(t)

We know that;

sec (t) can be written as 1/cos t

Thus;

(sec(t) - cos(t))/sin(t) = [(1/cos t) - cos t]/ sin t

= (1/(sint cos t) - cos t/ sin t

= (1 - cos²t)/(sin t cos t)

= sin²t/(sin t cos t)

= sin t/cos t

= tan t

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Answer:

Andre is taller than Diego

Step-by-step explanation:

There are 100 cm in a meter. If we use this information and convert Diego's height to meters, we find that Diego is 1.65 m. This is a smaller number, and therefore, Diego is shorter than Andre.

The probability that Serena does not serve an ace or a double fault is 0.63..

Addition rule of probability applies to the calculation of probability for one or another event happen. These events are either mutually exclusive or not .

We have following information,

The probability of Serena serving an ace in tennis (p) = 0.15

Probability that she double faults(q) = 0.25

The probability of Serena not serving an ace in tennis = 1 -p = 1 - 0.15 = 0.85

let A and B be two events Serena not serving an ace and she double faults respectively.

Events A and B are not mutually exclusive events .

i.e, P(A ∩ B ) =/ 0

when Serna not serving an ace implies that either it is double faults or not and both have equally likely chance.

So, the probability of intersection of event A and B = 0.85/2 = 0.47

Adding Rule for probabilities is

P(A or B ) = P(A) + P(B) - P(A ∩ B)

The probability that Serena does not serve an ace or a double fault = 0.85 + 0.25 - 0.47

= 1.10 - 0.47 = 0.63...

Hence, the probability that Serena does not serve an ace or double fault is 0.63..

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Answer:

No

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

For a Triangle to be a Right-Angled Triangle, should follow the Pythagoras Theorem which states that

If a is the larger side and b , c are the lengths of the other two sides

Then [tex]a^{2} =b^{2} +c^{2}[/tex]

Here a=30  , Then [tex]a^{2}=30^{2} =900[/tex]

and b=20 , c=25  , Then [tex]b^{2} +c^{2} =20^{2} +25^{2} =1025[/tex]

Since [tex]a^{2} \neq b^{2} +c^{2}[/tex]

Then the Triangle is not Right Triangle

The probability that the size of the family is 4 or more rounded to three decimal places is 0.361.

Given that families are selected at random, to find the probability that the size of family 4 we need to select and add those probabilities whose family size is more than and equal to 4.

P(X ≥ 4) = P(4) + P(5) + P(6) + P(7)

P(X ≥ 4) =  19.2 + 11.6 + 3.3 + 2.0

P(X ≥ 4) = 36.1

Since we need the answer rounded off to three decimal places, we can divide the answer by 100 which will give the final answer which is 0.361.

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Reason:

The digit in the tens place is 1. Just to the right is 5, which tells us to bump the 15 up to 20.

We can say that 15.0872 is closer to 20, than it is to 10.

Be sure not to mix up "tens place" with "tenths place".

The round-off from the number 15.0782 to the nearest 10 will be 20.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.

Given that the number is 15.0782. The round-off to the nearest 10 will be 20 for the number.

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Answer:

Step-by-step explanation:

5 1/2 +2x = 25

25- 5 1/2 = 2x

19 1/2 = 2x

x = 9.75

It took him about 9.75 weeks to lose at least 25 pounds.

Answer:

------------------

It took Mr. Henry at least 10 weeks to lose 25 pounds.

The transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.

So, the transformation from:

First, plot both graphs.

(Refer to the graph attached below)

Therefore, the transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.

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The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.

It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.

Recall that the roots of quadratic equations are given by the formula;

x = {-b ± √(b² - 4ac)} / 2a

Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.

Therefore, the roots are as follows;

x = {-3 ± √(3² - 4•1•-5)} / 2(1)

x = (-3 ± √29)/2

Therefore, the required roots are;

x = (-3 + √29)/2 and x = (-3 - √29)/2

Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.

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Answer:

Step-by-step explanation:

5 dollars and 25 cents