Write a recursive formula for an, the nth term of the sequence 50, -10, 2, ....
a1
an
11

In 30 minutes the two friends 2 miles apart.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, Wendy headed due north at 3 miles per hour, and Roger hiked due south at 6 miles per hour.

We know that, Time= Distance/Speed

Now, T₁= 2/3

T₂= 2/6 =1/3

T=T₁-T₂

T=2/3+1/3

T=1/3

T=0.33 hours

= 30 minutes

Therefore, in 30 minutes the two friends 2 miles apart.

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The 52nd term of the arithmetic sequence -3, 12, 27, ..... is equal to 762.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 12 - (-3)

Common difference, d = 12 + 3

Common difference, d = 15

Substituting the given parameters into the formula, the 52nd term of this arithmetic sequence is given by;

a₅₂ = a₁ + (52 - 1)d

a₅₂ = -3 + (51)(15)

a₅₂ = -3 + 765

a₅₂ = 762.

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The proof that z lies on the x-axis is shown below

For z to lie on the x-axis, then the coordinate must be represented as (x, 0)

Given that

[tex]\frac{|z - 5i|}{|z + 5i|} = 1[/tex]

We start by simplifying the given expression using the definition of the modulus of a complex number:

So, we have

[tex]\frac{|z - 5i|}{|z + 5i|} = \frac{\sqrt{(x - 0)^2 + (y - 5)^2}}{\sqrt{(x - 0)^2 + (y + 5)^2}} = 1[/tex]

Where

z = x + yi or z = (x, y)

Squaring both sides of the equation above, we obtain:

[tex]\frac{(x - 0)^2 + (y - 5)^2}{(x - 0)^2 + (y + 5)^2} = 1[/tex]

This gives

[tex]\frac{x^2 + (y - 5)^2}{x^2 + (y + 5)^2} = 1[/tex]

By comparison, we have

[tex](y + 5)^2 = (y - 5)^2[/tex]

Set y = 0 to test the equation

So, we have

[tex](0 + 5)^2 = (0 - 5)^2[/tex]

25 = 25 --- true

The equation is true for y = 0

This means that

z = (x, 0)

Hence, z lies on the x-axis

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Answer:

  6.8 ft

Step-by-step explanation:

You want the height of a tank with a base of 5.5 ft by 4 ft if adding 74.8 ft³ of water fills it halfway.

The volume of a rectangular prism is given by the formula ...

  V = LWH

The filled volume of the tank h feet high is ...

  74.8 ft³ = (5.5 ft)(4 ft)(h/2) . . . . . . the filled height is h/2

  74.8 ft³/(11 ft²) = h ≈ 6.8 ft . . . . . . divide by the coefficient of h

The height of the tank is 6.8 feet.

The correct answer for given dilation will be A and D i.e. Point P is midpoint of AA' and XY⊥AA'.

What precisely is dilation?

Dilation is the process of changing the size of an object or form by shrinking or extending its dimensions based on certain scale variables. For example, a circle with radius 10 unit is decreased to a circle with radius 5 unit. This method is used in photography, arts and crafts, and logo design, among other things. In geometry, there are four basic types of transformations. These are their names:

Properties of Rotation, Translation, Reflection, and Resizing

Dilation properties

The following are some features of shapes that remain constant with dilation changes:

Now,

As The image of A is made on line XY and the image will be A'

then XY⊥AA' because line formed between images is always perpendicular to the plane it is formed on and

P is the midpoint of AA' because we know that AP and A'P are same in a image formation.

Hence,

           Point P is midpoint of AA' and XY⊥AA'.

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Answer:

£76

Step-by-step explanation:

[tex]28+16(1.5/0.5)=28+16(3)=28+48=76[/tex]

The average rate of change over each specified interval is 8/3 and -10.

The average rate shows the change in the function per unit, over an interval.

Given that, find the average rate of change over each specified interval.

The average rate of change is given by

f(b)-f(a) / b-a

a) [2, 5] :-

To find the average rate of change we will take the change in the function over the change in x,

f(5)-f(2) / 5-2 = 24-16 / 3 = 8/3

Therefore, the average rate of change in interval [2, 5] is 8/3

b) [3.8, 4] :-

Similarly,

f(4)-f(3.8) / 4-3.8 = 17-19 / 0.2 = -2/0.2

= -10

Therefore, the average rate of change in interval [3.8, 4] is -10

Hence, the average rate of change over each specified interval is 8/3 and -10.

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Answer:

48 kicks

Step-by-step explanation:

If she shoots 40 times and misses 8, we can create a ratio to represent the number of total shots to the number of misses:

40/8 = 60/x X represents the amount she will miss if she takes 60 shots.

We can find the value of x by using cross multiplication:

480 = 40x. We can now isolate x by dividing both sides by 40:

X = 12.

Melinda will miss 12 out of 60 shots.

She will make 48 kicks.

Answer:

The answer to your question is, 0.484

Step-by-step explanation:

The actual chances of an event occurring are defined by a probability. Probability has several uses in games, and in business to create probability-based forecasts which bascially how it works.

Lets graph it out:

Let A signify that the selected employee participates to a workplace retirement savings plan. Let P stand for the male employes.

P(A∩P) the intersection of male & female.

P(A\P)  is the probability that a randomly picked worker participates to a workplace retirement savings plan is the option male

The probability that a randomly selected worker contributes to a retirement savings plan at work is male is found in this formula :

P(A\P)=P(A∩P)/A(P)

P(A\P)=(121/500)/(250/500)

P(A\P)=0.484

Thus, the probability that a randomly selected worker contributes to a retirement savings plan at work that is male will be,

0.484.

Answer:2304.9

Step-by-step explanation:

Answer:

  2304.9 ft

Step-by-step explanation:

You want the distance from point A, which is 1246 ft horizontally from a lighthouse to point B, given the angles of elevation to the light are 14° and 5° from points A and B, respectively.

The tangent relation for sides in a right triangle is ...

  Tan = Opposite/Adjacent

In a model of this geometry, the height (h) of the lighthouse is the side opposite the angle of elevation. This lets us write two equations:

  tan(14°) = h/1246

  tan(5°) = h/(1246 +d) . . . . . where d is the distance from A to B

Solving these equations for d, we have ...

  h = 1246·tan(14°) = (1246+d)·tan(5°)

  d·tan(5°) = 1246·(tan(14°) -tan(5°))

  d = 1246·(tan(14°)/tan(5°) -1) ≈ 2304.9 . . . . feet

The distance from point A to point B is about 2304.9 feet.

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The equation for option 1 is y = 3.5x + 7.5 and option 2 is y = 5.5x. Option 1 will be the least expensive. The solution has been obtained by using the slope-intercept form.

What is slope-intercept form?

The graph of the equation y = mx + b is represented by a line with a slope of m and a y-intercept of b. The slope-intercept representation of the linear equation is employed, and the values of m and b are real numbers.

We are given two options.

Using slope-intercept form, we get the equations as

Option 1

It requires monthly fee of $7.50 which means this is the y-intercept and $3.50 per game which means this is the slope.

So, the equation is y = 3.5x + 7.5

Option 2

Slope = (33 - 16.5)/ (6 - 3)

Slope = 16.5/ 3

Slope = 5.5

The y-intercept for this is 0.

So, we get the equation as y = 5.5x.

Fee for renting 5 games

As per option 1: y = 3.5(5) + 7.5 = $25

As per option 2: y = 5.5(5) = $27.5

Hence, option 1 will be the least expensive.

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Answer:

m∠2=12°

Step-by-step explanation:

some of two angles is 90

90 -78=12

The solution is, (17)(0.25)(4) = 17.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

(17)(0.25)(4)

=(17)*1

=17

at first we have to multiply the last two terms i.e. (0.25) and (4), then, we multiply the result 1 with 17, and get the result 17.

Hence, The solution is, (17)(0.25)(4) = 17.

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The revenue corresponding to break even condition for selling x units is $4.28.

An evaluation of the model's accuracy in estimating the link between X and y is done using a cost function. In most cases, this is represented as a difference or distance between the projected value and the actual value. The price element (you may also see this referred to as loss or error.)

To break even (R = C) we have:

7.8 √x + 22,000 = 13.82x

Substitute the value of x = u² thus:

7.8u +22000 = 13.8u²

13.8u² - 7.8u - 22000 = 0

The quadratic formula is given as:

u = -b ± √b² - 4ac / 2a

u = -(-7.8) ± √(-7.8)²- (4)(13.82)(22000) / 2(13.82)

u = 7.8 ± 7.8 / 27.64

u = 7.8 + 7.8 / 27.64

u = 0.56

Back substituting the value of u:

x = u²

x = (0.56)²

x = 0.31

Substituting the value of x is R:

R = 13.82 (0.31)

R = 4.28

Hence, the revenue corresponding to break even condition for selling x units is $4.28.

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Answer: 6.38

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

The mean for this population is 55. The variance and standard deviation for this population are 94.8 and 9.74

The data is given for five families and their children are tested to see how many words they can speak in Swahili.

Toddler     Number of words(X)        X - M         (X - M)²

   A                        47                          - 8                64

   B                        73                           18               324

   C                        56                            1                  1

   D                        46                          -9                 81

   E                        53                          -2                  4

                                                                              424

Mean of the population(M) = (∑X)/n

                                             = (47 + 73 + 56 + 46 + 53)/5

                                             = 275/5 = 55

Variance f population (σ²) = (X - M)²/n = 474/5 = 94.8

Standard deviation of population(σ) = √94.8 = 9.74

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Answer: 87.96m

Step-by-step explanation:

Circumference of a circle = 2[tex]\pi[/tex][tex]r^{2}[/tex] --> 2[tex]\pi[/tex]14² = 87.96m

68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

What is a circle graph?

A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments.

Let's say the total number of students = X.

From the circle graph, we can say that 15% of students chose cinnamon twists and their count is 12.

Which means that

[tex]X*\frac{15}{100}=12\\ X=80[/tex]

Therefore the total number of students is 80.

Among the 80 students except for 12 students, the remaining students asked for jumbo chocolate chip cookies.

Which is equal to 80-12=68.

Therefore 68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

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The graphing points of the equation is given in the table.

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

Given equation is [tex]y=2^{x+5} +1[/tex].

To find the graphing points of the functions:

By assuming the value for x and substitute in the given function to find the values of y.

[tex]if x=-2,y=2^{-2+5} +1=9\\ifx=-1, y=2^{-1+5} +1=17\\if x=0,y=2^{0+5} +1=33\\if x=1,y=2^{1+5} +1=65\\ifx=2,y=2^{2+5} +1=129[/tex]

It is given the table format as,

                 x                [tex]y=2^{x+5} +1[/tex]

                -2                     9

                -1                      17

                 0                     33

                  1                     65

                  2                   129  

Hence, these are all the graphing points of the equation.

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Answer: Since the perimeter of all the rectangles is equal (24 cm), the sum of the length and width of each rectangle must be equal for each rectangle. This is because the perimeter of a rectangle is equal to the sum of its lengths plus the sum of its widths, multiplied by 2.

For example, if the length of one rectangle is "l" cm and its width is "w" cm, then its perimeter would be 2l + 2w = 24 cm.

So, in general, we can write the equation: l + w = P/2, where P is the perimeter of the rectangle (in this case, P = 24 cm).

Therefore, the sum of the length and width of each rectangle is equal and constant, regardless of the individual values of the length and width. This means that as the length of a rectangle increases, its width must decrease by an equal amount to keep the sum constant. And vice versa.

In conclusion, the sum of the length and width of each rectangle is equal, and it is equal to half of the perimeter of the rectangle.

Step-by-step explanation:

Blake needs a wooden dowel that is 2 1/6 feet long. Blake needs to cut off 7.4167 feet from the dowel.

What are arithmatic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

To find out how much Blake should cut off the dowel, we need to subtract the length of the dowel from the required length.

The length of the dowel is -5 1/4 feet, which can be written as -5.25 feet.

The required length is 2 1/6 feet, which can be written as 2.1667 feet (rounded to four decimal places).

To find out how much needs to be cut off, we can subtract the length of the dowel from the required length:

2.1667 ft - (-5.25 ft) = 7.4167 ft

Therefore, Blake needs to cut off 7.4167 feet from the dowel.

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If A, B and C be events relative to the sample space S, then the Venn diagram of the representing event has been plotted

Let A, B and C be events relative to the sample space S.

The sample space is the set of all possible outcomes of the experiment.

The Venn diagram is the pictorial representation of the sample space of the experiment by using the circles and the overlapping of the circles.

Here we have to plot the each representing events using the Venn diagram representation

Part a

The event is (A ∩ B)'

Plot the Venn diagram

Part b

The event is (A ∪ B)'

Plot Venn diagram

Part c

The event is (A ∩ C) ∪ B

Plot the Venn diagram

Therefore, the Venn diagram of the each event has been plotted

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Answer:

16 inches

Step-by-step explanation:

28 - 12 = 16 inches

1 foot = 12 inches

Find the value of day/dx when X = 1 and when Y = 1. I would like to answer correct but Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.

Answer:

C

Step-by-step explanation:

In this equation, you would need to do 32/5 to figure out how much each person will get. 32/5=6.4 feet

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The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.

The transformation applied to f(x) to obtain q(x) is divided into several steps:

Reflection: The negative sign in front of 1/x reflects the graph of f(x) across the x-axis, causing the y-values to change sign.

Vertical shift: Adding "+1" to -1/x raises the graph of f(x) by one unit.

Horizontal shift: Although there is no explicit horizontal shift in q(x), we can see that the graph of q(x) has a vertical asymptote at x=0, whereas the graph of f(x) does not. This means that the graph of q(x) has been shifted to the right by one unit.

The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.

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The output value of y when input value x is -7:   -6

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check given expression is a function or not we can check it by a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

A graph of a function,

And input value x  = -7

output value y = ?

As it can be seen in the graph,

For input value x  = 0

output value of y = -2

Similarly,

for input value x  = -7

It can be seen in the graph that

the value of y = -6

Hence, the value of y is -6

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The expression to be added is 9mn +3m² - 12n²

These are expressions having terms, variables, coefficients, factors and constants.

They are also known to be composed of arithmetic operations, such as;

From the information given, we have the expression;

-7 mm + 2m ²+ 3n²

To make it up to 5m² +2mn-9n²., we have

-7mn + 9mn + 2m² + 3m² + 3n² - 12n²

Hence, the expression is 9mn +3m² - 12n²

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Its 10/29 so its answers this

The next step in the solution to this equation is to evaluate the exponents

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

The steps 1 to 4

Using the above as a guide, we have the following:

Step 4: (3x - 11)² =(√4x)²

At this point,, we open the bracket

This is done by evaluating the exponents

So, we have

9x² - 66x + 121 = 4x

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