1. Fill in the missing Terms for the sequence
2. Find the number the sequence is going by
3. Write the explicit formula

a) The function that represents the given situation is (x - 11) ÷ 4 = -1.2 and the number thought by Dakari is 6.2

b)  The inverse function (y - 11) ÷ 4 = -1.2

Function:

The function that is from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Given,

Dakarai thought of a number. He subtracted 11 from the number then divided the result by 4.

Here we need to find the following

a) function that map the function and the number though by Dakarai

b) inverse of the function

Let us consider the number thought by Dakarai as "x"

First, he subtracted 11 from the number,

So it can be written as,

=> x - 11

After that, he divided it by 4

So, the it can be written as,

=> (x - 11) ÷ 4

Now, the result was -1.2

So the function is

=> (x - 11) ÷ 4 = -1.2

Now we have to solve this equation, in order to find the value of x,

=> (x - 11) ÷ 4 = -1.2

=> x - 11 = -1.2 × 4

=> x - 11 = -4.8

=> x = -4.8 + 11

Therefore, the value of x is 6.2

And the inverse of the function can be written as by change the x as y,

Then we get,

=> (y - 11) ÷ 4 = -1.2

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Answer:

x+4x=25

A: 0<x<=25 0<y<=75

Step-by-step explanation:

Answer:

The answer to this question is undefined or c

Step-by-step explanation:

A horizontal line has a slope of 0 because it does not go vertically and a vertical line has a slope of undefined because it does not go horizontally

Answer:

7 periods.

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

[tex]f(x) = A \cos(B(x + C)) + D[/tex]

where:

Therefore, for y = cos x:

The maximum of the function is when x = 0 + 2πn.

The minimum of the function is when x = π + 2πn.

To find the number of periods, first find the difference between the two given values:

⇒ 9π - (-5π) = 9π + 5π = 14π

As the period of the function is 2π, then the number of periods is:

⇒ 14π ÷ 2π = 7 periods.

For the given measurement of the congruent triangles RWS and TUV, the value of x = 4° and y = 10 units.

As given in the question,

For the given congruent triangles,

ΔRWS ≅ ΔTUV

⇒ RWS ↔ TUV

⇒RW ≅TU , RS ≅TV , WS ≅ UV

And ∠W ≅ ∠U , ∠R ≅ ∠T , ∠S ≅ ∠V

Given measurements are :

m ∠W = 90°

m ∠R = ( 8x + 26)°

m ∠V = 32°

∠S ≅ ∠V

⇒ m ∠S = 32°

m ( ∠R + ∠W + ∠S ) = 180°

⇒ 8x° + 26° + 90° + 32° = 180°

⇒8x° = 180° -148°

⇒ x° = 32°/8

⇒ x= 4°

RS ≅TV

⇒30 = 2y + 10

⇒2y = 20

⇒y= 10 units

Therefore, for the given measurement of the congruent triangles RWS and TUV, the value of x = 4° and y = 10 units.

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1000 paperclips would weigh equal to the dictionary.

Weight of the dictionary = 1 kg

weight of one paper clip = 1 gm

according to the mathematical conversion system of weights

1 kilogram = 1000 grams

on the basis of the statement

1 gram is the weight of = 1 clip

so , 1000gm would be the weight of = 1 x 1000

         1000 gm would be the weight of = 1000 clips

to weigh equal to the dictionary , we would require 1000 clips .

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The equation of straight line plotted on the graph are all attached below

The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry. The equation of a straight line can be written in different forms such as point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a two-dimensional geometrical entity that extends on both its ends till infinity.

For straight line graphs there is a linear relationship between the x and y values and so the line is straight and must be drawn with a ruler. The gradient determines how steep the line is and the y-intercept tells us the location where the straight line intersects the y-axis.

Linear means straight and a graph is a diagram which shows a connection or relation between two or more quantity. So, the linear graph is nothing but a straight line or straight graph which is drawn on a plane connecting the points on x and y coordinates.

Question 1;

The point is (-2, 5) and it has a slope of 2/3

We can find the y-intercept of the graph and then plot it's coordinate.

y = mx + c

5 = 2/3(-2) + c

c =19/3

The equation of the line is y = 2/3x + 19/3 or 3y = 2x + 19

We can proceed to use a graphing calculator to plot this.

Question 2;

The two given which the line pass across are (-2, -1) and (-3, 3)

Using a graphing calculator, the graph is attached below.

Question 3;

The equation 4x - 5y = 20 can be plotted as a straight line graph which is attached below.

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The statistics z is -1.878 and the p value is 0.0302

Given,

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Estimated proportion of return rate;

p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

That is,

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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Vertical asymptotes is x = -4 and horizontal asymptote is y = 1

What is an Asymptote?

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote.

There are 3 types of asymptotes.

The given expression,

f(x) = (x² - 3x) / (x² + x - 12)

First, find Horizontal asymptote

so,

Horizontal asymptote (y) = (leading coefficient of numerator) / (leading coefficient of denominator)

leading coefficient of numerator = 1

leading coefficient of denominator = 1

y = 1/1

y =1 (Horizontal asymptote)

Now, find Vertical asymptote

so, let's simplify the expression f(x) = (x² - 3x) / (x + x - 12)

f(x) = (x(x - 3) ) / (x² + 4x - 3x - 12)

f(x) = (x(x - 3) ) / (x(x + 4) - 3 (x + 4) )

f(x) = (x(x - 3) ) / ( (x -3) (x + 4) )

f(x) = x / (x + 4)

Now, put the denominator = 0

x + 4 = 0

x = -4 ( Vertical asymptote )

Hence, Vertical asymptotes is x = -4 and horizontal asymptote is y = 1

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The equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.

We are given;

y = 3x³ - 7x² + 5

y = 7x^4 + 2x

We will solve the given equation by substitution method:

Using the substitution method, let us substitute y = 7x^4 + 2x in the equation y = 3x³ - 7x² + 5, we get,

3x³ - 7x² + 5 = 7x^4 + 2x

So, 3x³ - 7x² + 5 = 7x^4 + 2x will be solved by using the given system of equations.

Thus, the equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.

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Answer: (9t + 10)(t - 2)

Step-by-step explanation:

9t (t − 2) + 10(t − 2)

9t^2 − 8t − 20

= (9t + 10)(t − 2)

10 is the geometric mean between 23 and 4.35.

The geometric mean is a type of average,  generally used for growth rates. Let c is the geometric mean of a and b, then c=[tex]\sqrt{ab}[/tex].

Given that,

The geometric mean of 23 and other value is 10.

Let the other value is x.

Use the geometric mean property,

G.M.=[tex]\sqrt{ab}[/tex]        (1)

Substitute the given values in equation (1)

10=[tex]\sqrt{23x}[/tex]

⇒x=100/23

⇒x=4.347

The geometric mean of 23 and 4.35 is 10.

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Answer:

-1

Step-by-step explanation:

Jada = 12 books

Han = 13 less books than Jada

12-13= -1

Han would have negative 1 books but in this situation it would not be possible.

For given inequality 2y-x>1 point (-7,-3) is not the solution set of given inequality.

Inequality:

               Inequalities are mathematical sentences formed by relating two expressions to each other.

Different inequality sign are:

            x>y ,

                  x is greater than y

           x≥y

                x is greater than or equal to y

           x<y

                 x is less than y

          x≤y

                 x is less than or equal to y

Given inequality is,

             2y - x > 1

In the given inequality

       L.H.S (Left hand Side) = 2y - x

       R.H.S (Right Hand Side) = 1

and the given point is (-7,-3)

Left hand Side at point (-7,-3)

L.H.S  = 2y - x

          = 2 (-3) - (-7)

          = -6 + 7

          = 1

and

       Right Hand Side = 1

Here we can see both L.H.S and R.H.S are equal,but in the given inequality there is no equality,so the point (-7,-3) is not the solution set.

Thus we conclude,

                            (-7,-3) is not the solution set of given inequality.

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The coordinates of figure and the coordinates of the image after rotation is as below

preimage        image

J(-4,1)               J' (1, 4)

K(-2,1)              K' (1, 2)

L(-4,-3)             L' (-3, 4)

Rotation is one the movements involve in transformation

In rotation, the objects moves about an axis in a circular direction

The transformation rule for 90 degrees clockwise rotation is

(x, y) → (y -x)

applying the rule gives the new coordinates of the image as

Image

J' (1, 4)

K' (1, 2)

L' (-3, 4)

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Answer:

a x=10

b x=7

Step-by-step explanation:

(a) 2(x+3) = x  -  4

    2x+6 = x - 4

    2x+6-6= x-4-6

    2x=x-10

     2x-x=x-10-x

    x=10

(b) 4(5x-2) = 2(9x+3)

     20x-8  =18x+6

     20x-8+8=18x+6+8

     20x=18x+14

     20x-18x =18x+14-18x
     2x=14

      /2  /2

     x = 7.

The value of z statistics is -1.878,  

Given,

In the question:

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Now, According to the question:

Estimated proportion of return rate;

To find the value of p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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Answer:

7.5 feet

Step-by-step explanation:

We can use the Pythagorean therom

x=square root of 15^2-13^2

x= square root of 225-169

x=square root of 56

x=7.5

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There will be 0.84% chances that resulting sequence in cat to occur.

Total number of nucleotides floating around = 10

Let the event of picking cat be "A"

Number of cat in group = 3

Probability of picking cat is picked at first position = P(A1) = 3 / 10

= 0.3

Probability of picking cat is picked at second position = P(A2) =  2 / 9

= 0.223

Probability of picking cat is picked at third position = P(A3) = 1 / 8

= 0.125

so , probability of picking cat in first position and again in second position and again in third position will be = P(A1) . P(A2) . P(A3)

= 0.3 × 0.223 × 0.125

= 0.0084 required probability

There will be 0.84% chances that resulting sequence in cat

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The length of the wallpaper of 27 inches wide required is  35.56 feet

The problem requires conversion of the dimensions to have similar unit

To convert 80 square feet to square inches. we multiply by 144

80 * 144 = 11520 square inches

area = length * wide

11520 = length * 27

length = 11520 / 27

length = 426.667 feet

to get the length in inches we divide the unit in feet by 12

length = 426.667 inches / 12

length = 35.56 feet

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The set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers is given as below as

Cars, Are cars up to date, Select the car to check, Stopped cars, Convenience sampling ,The cars that are not stopped might be having more problems

Given that,

The Population

The Population parameter of interest

The Sampling frame

The Sample

The Sampling Method, Including whether or not randomization was employed.

Any potential source of bias you can detect any problems you see in generalizing to the population of interest.

To find : The set up a roadblock

A. Cars

B. Are cars up to date

C. Select the car to check

D. Stopped cars

E. Convenience sampling

F. The cars that are not stopped might be having more problems

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The linear equation y = 5 · x - 14 is a possible equation that intercepts the line 2 · x + y = 0 at point (x, y) = (2, - 4),

To generate a system of linear equations, we need to derive an additional that intercepts the line 2 · x + y = 0 at point (x, y) = (2, - 4). We need to find an equation of the form:

y = m · x + b

Where:

Please notice that there are more than a single choice. First, choose the slope of the line:

m = 5

Second, substitute the slope and the independent and dependent variables:

b = y - m · x

b = - 4 - 5 · 2

b = - 14

Third, write the resulting linear equation:

y = 5 · x - 14

The linear equation y = 5 · x - 14 is a possible equation of the system of equations.

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There are a couple ways to solve this but I will show you the way I think is easiest:

You should make the fraction parts of the numbers have an equivalent denominator. Right now, the denominators are 10 and 5. It would be best to make both denominators equal 10.

In - 2 [tex]\frac{3}{5}[/tex],  3/5 x 2 = 6/10

So now the fractions are [tex]-10\frac{7}{10} - 2[/tex][tex]\frac{6}{10}[/tex]

Remember the sign rules!

The answer is - 13[tex]\frac{3}{10}[/tex]

I hope this helps!

Answer:

     [tex]-\frac{133}{10}[/tex]

Step-by-step explanation:

[tex]-10\frac{7}{10}[/tex] = [tex]-\frac{107}{10}[/tex]               (10x(-10)+7)

[tex]-2\frac{3}{5}[/tex] = [tex]-\frac{13}{5}[/tex]                   (5x(-2)+3)

lcm of 10 and 5 is 10:

[tex]-\frac{107}{10} -\frac{13}{5}[/tex]

[tex]\frac{-107-26}{10}[/tex]

[tex]-\frac{133}{10}[/tex]

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Answer:

It is C

Step-by-step explanation:

Answer:

[tex]x < 13[/tex]    and    [tex]x > 5[/tex]

Step-by-step explanation:

Take a look at the attachments...

Hope this helps! :)

The compound inequality is 12 ≤ 6x + 3 ≤ 36. and the solution is 1.5  ≤ x ≤ 5.5

The compound inequality is represented as

12 ≤ A ≤ 36.

Such that

The area of the rectangle is calculated as

A = Product of the sides

So, we have the following representation

A = (2x + 1) * 3

Evaluate

A = 6x + 3

Substitute A = 6x + 3 in 12 ≤ A ≤ 36.

So, we have

12 ≤ 6x + 3 ≤ 36.

In (a), we have

12 ≤ 6x + 3 ≤ 36

This gives

9 ≤ 6x ≤ 33

Divide by 6

1.5  ≤ x ≤ 5.5

So, the result is 1.5  ≤ x ≤ 5.5

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