a plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 3 mi away from the station

Answer:

2 minutes

Step-by-step explanation:

8 : 4 = x : 1

x = 8/4

x = 2

Step-by-step explanation: To find the time it takes Elijah to run 1 lap, we need to divide the time it takes him to run 4 laps by the number of laps he runs in that time. Since it takes Elijah 8 minutes to run 4 laps, the time it takes him to run 1 lap is 8 minutes / 4 laps = ${2}$ minutes per lap.

This calculation illustrates the concept of unit rate, which is the rate at which a quantity changes over a given unit of time or distance. In this case, the unit rate is the time it takes Elijah to run 1 lap, which is 2 minutes per lap. This unit rate allows us to compare the time it takes Elijah to run different distances, and to determine how long it would take him to run a given distance at the same pace.

50 tickets were thus sold at the door. As a result, there were 175 advance sales of tickets and 50 at the door.

A linear equation has the algebraic form y=mx+b. where m is the slope and b is the y-intercept, consisting of a first-order (linear) term and a constant. If x and y are variables, the above is sometimes called a "two-variable linear equation".

Tickets for a high school dance were provided.

Purchases made before the dance cost $4.00 apiece.

If purchased at the door, they would cost $5 apiece.

225 tickets were sold, bringing in $950.

It's time to locate the advance-purchase and door-purchase tickets.

Let the quantity of advance tickets sold equal x.

And the quantity of tickets sold at the door will be equal to y.

hence, the overall quantity of tickets sold

[tex]x+y = 225\\y = 225 - x[/tex]......(1)

Now,

4x + 5y = 950

[tex]4x + 5y = 950\\4x + 5(225-x) = 950\\4x + 1125 - 5x = 950\\-x = -175\\x= 175\\y=50[/tex]

50 tickets were thus sold at the door.

As a result, there were 175 advance sales of tickets and 50 at the door.

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By using the concept of function, it can be seen that the given figure does not represents a function.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the values on the x axis represents the domain and the values on the y axis represents the Range.

From the figure it can be seen that

For x = 2, there are three points on the y axis.

So the point x = 2 maps to different points on the y axis

So this is not a function

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Answer:

Step-by-step explanation:

28

Answer:

6 (3x + 1)(x - 2) = 3x^2 - 2x + x - 2 = 3x^2 - x - 2

7 (x − 3)(2x - 1) = 2x^2 - x - 3x + 3 = 2x^2 - 4x + 3

8 (x-3y) (2x - y) = 2x^2 - yx - 3xy + 3y^2 = 2x^2 - 4xy + 3y^2

9 (2x - y)(x-2y) = x^2 - 3xy + 2y^2 = x^2 - 3xy + 2y^2

Answer:

Below

Step-by-step explanation:

Value = 33000 ( .88)^t        each year, t , the value is only 88% ( or in decimal:  .88) of the prior year  ( 12 % decrease leaves 88% )

Answer: 64

Step-by-step explanation:

There are 16 ounces in a pound and there are 4 pounds and 4x 16 is 64

Answer:

64 oz.

Step-by-step explanation:

16 oz. = 1 lb.

16 oz. x 4 lbs. = 64 oz.

The number of classes per month that had same total amount paid was 21

The total amount is $115

let the number of group class be represented by x

first membership plan, Jen can pay $52 per month, plus $3 for each group class she attends

= $52 + $3x

second membership plan, Jen can pay $31 per month plus $4 per class

= $31 + $4x

when the total amount are equal

$52 + $3x = $31 + $4x

52 - 31 = 4x - 3x

21 = x

The total amount

= $52 + $3 * 21

= $115

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Answer:

f(-11) = -16

Step-by-step explanation:

We are given a function

f(x) = x-5

Substitute the value of x = -11 into the function

f(-11) = -11-5

        = -16

Answer:

-16

Step-by-step explanation:

Given that,

f ( x ) = x - 5

To find the value of f ( -11 ), you have to replace x with -11 & solve it.

Let us solve it now.

f ( -11 ) = x - 5

f ( -11 ) = -11 - 5

f ( -11 ) = -16

In a residual plot if the linearity assumption is the points are scattered and there is no obvious pattern.

Residual plot:

in statistics, residual value is a measure of how much a regression line vertically misses a data point.

Given,

Here we need to find what would you expect to see in a residual plot if the linearity assumption is correct.

As per the definition of residual plot, there is no obvious pattern for this plot and the positive and negative values are evenly spread across the whole range.

Therefore, in the regression line there are some points are misses the line on the vertical base.

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Answer:   [tex]\frac{\sqrt{55}}{8}[/tex]

This is the same as writing sqrt(55)/8 where the 8 is not inside the square root.

=====================================================

Explanation:

Draw a right triangle in the quadrant Q1, which is in the northeast corner.

We're given [tex]\cos(\theta) = 3/8[/tex]. Recall that cosine is the ratio of adjacent over hypotenuse.

[tex]\cos(\text{angle}) = \text{adjacent/hypotenuse}[/tex]

This right triangle will have an adjacent side of 3 and hypotenuse of 8.

Refer to the diagram below.

Use the pythagorean theorem [tex]a^2+b^2 = c^2[/tex] to find the missing side is exactly [tex]\sqrt{55}[/tex], which is the opposite side of angle theta.

Then as one last step, we would say:

[tex]\sin(\text{angle}) = \text{opposite/hypotenuse}\\\\\\\sin(\theta) = \frac{\sqrt{55}}{8}[/tex]

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

A very similar approach is to use the pythagorean trig identity

[tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex]

Solving for sine gets us

[tex]\sin(\theta)=\sqrt{1-\cos^2(\theta) }[/tex]

Sine is positive in Q1.

Then plug in [tex]\cos(\theta) = 3/8[/tex] and simplify. You should get the answer mentioned above.

The solution of the system of equations is y = 5 and x = 3, and the difference x - y gives:

x - y = -2

Here we have the system of equations:

5x + 3y = 30

-5x - 2y = -25

If we add the two equations we will get:

(5x + 3y) + (-5x - 2y) = 30 + (-25)

y = 5

So just by doing that we found the value of the variable y.

To find the value of x, we can replace the known value of y on one of the equations, doing that we will get:

5x + 3y = 30

5x + 3*5 = 30

5x + 15 = 30

5x = 30 - 15 = 15

x = 15/5 = 3

x = 3

Then the difference x - y gives:

x - y = 3 - 5 = -2

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Answer: True

Step-by-step explanation: Take a number on the list minus the previous one, and it shows a constant, then it is an arithmetic sequence.

The population 2 hours before that is 2691 if the population of a colony of bacteria increases by 4% of what the population was at the beginning of the hour.

A population is a distinct group of individuals that can be distinguished for the purposes of data collection and analysis by at least one feature. Populations are used in statistics and other branches of mathematics. Data is typically collected from a sample while learning about a large population.

Between sample size and population, the population will always be larger in number. The entire group of individuals under study is referred to as the population. 250 persons make up the population in the illustration, which is the same size as the high school under consideration.

We have P₀=2488

Rate of increase=R=4%

Time=2 hours

Bacteria count =P

P=P₀[tex](1+(R/100)^{T}[/tex]

=2488×(1+(4/100))²

=2488×1.0816

=2691.0208≈2691

Therefore, the population 2 hours before that is 2691.

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Answer: -9/y

Step-by-step explanation: quotient is a fancy word for divide

-9/y

Answer:

8x + 9

Step-by-step explanation:

5x + 3x + 6 + 3

8x + 9

The 25 teams can there be at most.

What is the LCM?

Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers.

We have,

75 fifth graders

125 fourth graders.

They are going to be grouped in teams for a field day with the same number of students on each team.

the same number of teams if there must also be the same number of fifth graders on each team.

take the LCM of the 75  & 125 Which is the 25.

3 fifth graders each

5 fourth graders each

Hence, the 25 teams can there be at most.

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Answer: [tex]y+5=\frac{3}{2}(x-2)[/tex]

Step-by-step explanation:

[tex]2y=3x+10 \implies y=\frac{3}{2}x+5[/tex]

Parallel lines have the same slope, so the slope of the line we need to find is 3/2.

Substituting into point-slope form, the equation is [tex]y+5=\frac{3}{2}(x-2)[/tex].

The percent of the increase in Paulina’s earnings is 15.55%.

The percentage is defined as a ratio expressed as a fraction of 100.

Last month, she earned $520.60. This month, she works overtime and earns $601.30.

The percent of increase = ($601.30 - $520.60)/520.60 x 100%

The percent of increase = (80.7)/520.60 x 100%

The percent of increase = 0.15501 x 100%

Apply the multiplication operation,

The percent of increase = 15.55 %

Thus, the percentage of the increase in Paulina’s earnings is 15.55%.

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Answer:

The value of the car at the end of 3 years will be £5,062.50.

The linear equation that is modeled by the table is:

y = 2x + 1

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

Here we can use the first two points on the table (-3, -5) and (-1, -1), we will get the slope:

a = (-1 + 5)/(-1 + 3)

a = 4/2 = 2

Then the line is something like:

y = 2x + b

To find the value of b we can use one of the points (-3, -5), replacing these values we will get:

-5 = 2*-3 + b

-5 = -6 + b

-5 + 6 = b

1 = b

Then the linear equation is:

y = 2x + 1

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Answer:

30.9 cubic inches

Step-by-step explanation:

This is a volume question. You multiply 2 3/4, 2 1/4, and 5 inches all together.

First you turn it into an improper fraction and multiply. 11/4*9/4 = 99/16

Then multiply this by 5: 99/16 * 5 = 30.9375

Round to nearest tenth: 30.9

Answer: It is correct.

Step-by-step explanation:

Answer:The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

Step-by-step explanation:

The measurement of the length of two sides and the included angle are given. Hence, using law of cosines, the approximate length of the lake is found to be 296.1 yards.

Given : b = 245 yards, c= 270 yards,

To find: The length of the lake which is the value of x

To find [tex]\angle A[/tex], we know that [tex]110^o\, and\, \angle A[/tex] lie on straight line. So

[tex]110^o + \angle A = 180^o\\\\\angle A = 180^o - 110^o = 70^o[/tex]

Using law of cosines

[tex]a^2 = b^2 +c^2 - 2bc\cdot cosA[/tex]

Plugging the values of b , c and A into the equation, we get

 [tex]a^2 =245 ^2 +270^2 - 2\times 245 \times 270 \times \cos 70^o \\[/tex]

The value of [tex]\cos 70^o[/tex] is 0.342 approximately

On substituting this in the equation, we get

a = 296.1 yards

Every triangle has three vertices and three sides. If in a triangle, the three vertices are A, B, and C, then, the sides opposite these vertices are a, b, and c, respectively. The angle at each vertex is given the same name as the vertex. Therefore, the three angles are also named A, B, and C. To solve such a  triangle is to find the lengths of each of its sides and all its angles.

The sine rule  or law of sines is used when we are given either

a) two angles and one side

or

b) two sides and the angle that is not included between these two sides.

[tex]\frac{\sin A}{a} =\frac{\sin B}{b} =\frac{\sin C}{c}[/tex]

The cosine rule or law of cosines is used when we are given either

a) three sides (SSS)

or

b) two sides and the included angle (SAS)

[tex]c^2=a^2+b^2-2ab\cdot\ cosC \\ b^2=a^2+c^2-2ac\cdot\ cosB\\ a^2=b^2+c^2-2bc\cdot\ cosA\\[/tex]

The measurement of the length of two sides and the included angle are given. Hence, using law of cosines, the approximate length of the lake is found to be 296.1 yards.

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Each pound of fish and chicken will cost $3.75 and $2.25 respectively

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Given that:

1. A customer pays a total of $11.10 for 1.6 pounds of chicken

and 2 pounds of fish.

2. Another customer pays a total of $12.15 for 2.4 pounds of

chicken and 1.8 pounds of fish

Let C and F represent the cost of one pound of chicken and fish respectively

Statement 1:

1.6C + 2F = 11.10  ---- (1)

Statement 2:

2.4C + 1.8F = 12.15  ---- (2)

we have simultaneous equations now, let's solve using the elimination method:

1.6C + 2F = 11.10      ---- (1)

2.4C + 1.8F = 12.15  ---- (2)

2.4 × (1.6C + 2F = 11.10) =     3.84C + 4.8F = 26.64

1.6 × (2.4C + 1.8F = 12.15) =  3.84C + 2.88F = 19.44

                                            ..........................................

                                                           1.92F  = 7.2

Thus, 1.92F  = 7.2

F = 7.2/1.92 = $3.75

Put F = $3.75 into (1):

1.6C + 2F = 11.10

1.6C + 2(3.75) = 11.10

1.6C + 7.5 = 11.10

1.6C = 11.10 - 7.5

1.6C = 3.6

C = 3.6/1.6 = $2.25

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The system of equations is  y = 50 + 3x; y = 34 + 4x. The number of cups that Aunt Emily orders is 16. The cost of either shop for 16 cupcakes is $98.

What is substitution method?

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

Assume that x number of cups that ordered by Aunt Emily.

Given that, Clarksville Bakery charges $3 for each cupcake, plus $50 for the large cake.

Therefore, the cost of x cupcake is 50 + 3x.

y = 50 + 3x

Also, Sebastian's Sweet Shoppe charges $34 for the large cake and $4 for each cupcake.

Therefore, the cost of x cupcake is 34 + 4x.

y = 34 + 4x

The system of equations is

y = 50 + 3x  ....(i)

y = 34 + 4x  ...(ii)

To find the number of cupcakes that Aunt Emily orders, use substitution method to solve the system of equation.

Substitute y = 50 + 3x in equation (ii)

50 + 3x = 34 + 4x

Subtract 3x from both sides:

50 = 34 + x

x = 16

Putting x = 16 in equation (i)

y = 50 + (3 × 16) = 98

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Answer: 1452 units^3

The required volume of the cylinder with a height of 12 units and radius of 11 units is 1452π cubic units.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

The formula for the volume of a cylinder is given as:

V = πr²h

Where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.

Substituting the given values, we get:

V = π(11)²(12)

= π(121)(12)

= 1452π cubic units

Therefore, the volume of the cylinder with a height of 12 units and radius of 11 units is 1452π cubic units.

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Answer:

  n = -104

Step-by-step explanation:

You want to identify a solution to the inequality -5 +n/13 < -12.

Adding 5 we get ...

  n/13 < -7

Multiplying by 13 gives ...

  n < -91

Of the choices available, only -104 is less than -91.

  n = -104

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When f(x)=x4 and g(x)=2x+4 at x=2 for f(x) and x=-2 for g, the value of g(f(2)) is 8 (x).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.

Here,

f(x)=x-4

g(x)=-2x+4

f(2)=2-4

=-2

g(-2)=-2*-2+4

g(-2)=8

The value of g(f(2)) is 8 for f(x)=x−4 and g(x)=−2x+4 at x=2 for f(x) and x=-2 for g(x).

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