One spring day, Grayson noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 58° F. For the next 5 hours, the temperature rose 1° per hour. For the next 3 hours, it rose 3° per hour. The temperature then stayed steady until 6 p.m. For the next 4 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 63° at midnight. On the set of axes below, graph Grayson's data.

Functions are special relaionships that connect an element of one set of numbers, with one element in another set of numbers.

The most comon way to represent functions is connecting elements of a set of Real numbers called the "Domain", to another number in a set called the Range (and whose elements are identified with the letter "y")

Using math operations one can relate x values with y values via an equation of the type:

y = 2 x - 5

where you have a mathematical form of that relationship, that allows you to know given the value of one member (x) of the Domain what number is associated with it in the Range.

For example, try the number x = 0

and see which y number connects with it:

y = 2 (0) - 5 = 0 - 5 = -5

Then you say that the number 0 in the Domain connects with the number -5 in the Range.

This relationship can also be given with coordinate pairs of the form:

(x, y) mentioning in the first position (where the x is), the number in the Domain that connects to the "y" number of the Range). The y goes in the second place. so for example in the relationship we found above, x = 0 connects with y=-5, you would have a shortcut way to write it as the pair: (0, -5) that tells you which x connects with which y.

The functions can also be given in graph form by plotting the relationship between members of the Domain and the Range on the plane. Graphing a point in the plane location that corresponds to the connected x and y values (like you do in the game "battlefield" when you locate ships on the board.

I know this is very general, but hopefully you got the idea ofa function as a special relationship between numbers, and that they can be expressed in different fashions.

Answer: 15

Step-by-step explanation:

This is the answer because 22 divided by 11 equals 2 kilometer each trip to work so 30 kilometer divided by 2 is 15.

Answer:

8x17.50

Step-by-step explanation:

90 letters out of the inspected sample of 900 letters will be found to be open

Inspection is done by mail carrier for every 20th letter

Inspection rate = 1/20*100 = 5%

It is a form of inspection where a sample of the same unit's manufactured goods, produced using the same procedures, is taken and examined, as opposed to the entire unit being examined. In general, the unit relates to the lot, and the lot determines whether the things are acceptable or rejectable.

Number of letters found open in 600 letters = 3 letters

Rate of letter found open = 3/600*100 = 0.5%

The sample being mailed = 18000 letters

Number of letters that were inspected for being open = 5% of 18000 = 900

letters

The number of letters found open = 0.5% of 18000 = 90

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The value of the expression given as√9x^3/25y^2 is 3x^3/25y^2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

√9x^3/25y^2

Evaluate the square root of 9

So, we have the following equation

√9x^3/25y^2 = 3x^3/25y^2

The above expression cannot be further simplified

Hence, the solution to the expression is 3x^3/25y^2

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Identify that the shape created is a Triangle.

For this exercise it is important to remember that, given a point P (x , y), "x" is the the x-coordinate of the point and "y" is the y-coordinate of the point.

In this case, Ms. Juhal has the following points:

1) Point A (-5 , 5)

x = -5 and y = 5

2) Point B (-5 , 3)

Where:

x = -5 band y = 3

3) Point C (-5 , 1)

x = -5 and y = 1

4) Point D (2,1)

Where:

x = 2 and y = 1

Therefore, knowing the coordinates of each point, you can plot them and connect them in order (Observe the picture attached).

Finally, you can identify that the shape created is a Triangle.

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Eugene will save $901.8 on the car overall if he chooses payment plan A.

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cos2x = (1+cos(2x))/2

The cosine power is odd (n odd): u = sin x and du = cos x dx should be used. d u = cos ⁡ To create an even number of cosine powers, replace dx with (a), canceling one power of cos x by substituting du. The Power Factor is the sine of the angle formed by Current and Voltage.

The ratio of the length of the side next to the angle to the length of the hypotenuse is known as the cosine, sometimes abbreviated as "cos." The ratio of the length of the side across from the angle to the length of the side next to it is called the tangent, which is frequently abbreviated as "tan."

cos2(2x) = (1+cos(4x))/2

cos4(2x)= [(1+cos(4x))/2]²

[tex]cos^{4}[/tex](2x) = [(1+cos(4x))/2]²

[tex]cos^{4}[/tex] (2x) = (1/4) × [1 + cos(4x)]²

[tex]cos^{4}[/tex](2x) = (1/4) × (1 + 2cos(4x) + cos²(4x))

[tex]cos^{4}[/tex](2x) = (1/4)*[1 + 2cos(4x) + (1 + cos(2x))/2]

[tex]cos^{4}[/tex](2x) = (1/4)*[1 + 2cos(4x) + (1/2)*(1 + cos(2x))]

[tex]cos^{4}[/tex](2x) = (1/8)*[2 + 4cos(4x) + 1 + cos(2x)]  

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The recursive formula is f(n - 1) . 3

The correct option is (c)

What are Recursive Formula ?

A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:

Given,

The sequence is:

3, 6 , 12 ....

To find the recursive formula of above sequence :

Now, The first term is 3.

Recursive formula is :

f(n - 1) . 3

Hence, The recursive formula is f(n - 1) . 3

The correct option is (c)

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As a fraction 3.83 (3 repeating )is 3x 83/99

what is repeating decimals ?

Repeating decimal values are created by fraction that  do not divide evenly. when converting a repeating decimal to a fraction we can ignore the units in the start as the units remain unchanged ,which allows us to  convert our decimal values and then the units back in afterward.

so ,

To convert the 3.83 to a fraction , we ignore the units as they will remain units.

we then set up one equation of our unknown x being equal to 0.83333......and another that is 100 times greater , 100x = 83.33333....

by subtracting these two equation from each other we can then divide by the coefficient of x to create our fraction .

10x=83.3333...

    x= 0.83333...

  99x = 82.5

we now divide both sides by 99 to isolate x:

99x=82.5

99x/99=82.5/99

x= 82.5/99

x = 82.5 x10/99x10

x = 825/990

x = 165/198

we cannot simplify this fraction any more

finally we add back the 3 units we set aside at the beginning ,making our fraction 3x165/198

so , the fraction 3.83 is 3x 83/99

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Two parallel lines have the same slope. Given the equation of one of the lines, you can determine the slope of the other line:

The slope of the line is the coefficient of the x-term, in this case, that coefficient is -5. Then the slope of both parallel lines is m= -5.

The line you have to find must cross through the point (9,-42). Using the point-slope form you can determine the equation of the parallel line:

Where

m is the slope of the line

(x₁,y₁) are the coordinates of one point of the line:

To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:

Subtract 42 to both sides of the expression to pass the term to the right side of the equal sign:

The equation of the line is y= -5x + 3

Answer:X-3 is a factor of x³+ax²–2x+3

Step-by-step explanation:X-3 is a factor of x³+ax²–2x+3

p(x)=x

3

−ax

2

+2x+a−1

⇒  p(a)=(a)

3

−a(a)

2

+2(a)+a−1

⇒  0=a

+2a+a−1=0

⇒  3a−1=0

⇒  3a=1   a=

3

1

​

Answer:

No Solution

Step-by-step explanation:

Consecutive terms in the α sequence have a common difference of

8 - 10 = 6 - 8 = 4 - 6 = … = -2

so they are given recursively by

[tex]\begin{cases} \alpha_1 = 10 \\ \alpha_n = \alpha_{n-1} - 2 & \text{for } n\ge2 \end{cases}[/tex]

By substitution, we have

[tex]\alpha_n = \alpha_{n-1} - 2 \\\\ \alpha_n = \alpha_{n-2} - 2\cdot2 \\\\ \alpha_n = \alpha_{n-3} - 3\cdot2 \\\\ \vdots \\\\ \alpha_n = \alpha_{n-(n-1)} - (n-1)\cdot 2 = \alpha_1 - 2(n-1) = 12-2n[/tex]

Consecutive terms in the β sequence have a common ratio of

6/9 = 4/6 = (8/3)/4 = … = 2/3

so the recurrence for these terms is

[tex]\begin{cases} \beta_1 = 9 \\\\ \beta_n = \frac23 \beta_{n-1} & \text{for } n\ge2 \end{cases}[/tex]

We can solve for [tex]\beta_n[/tex] similarly:

[tex]\beta_n = \dfrac23 \beta_{n-1} \\\\ \beta_n = \left(\dfrac23\right)^2 \beta_{n-2} \\\\ \beta_n = \left(\dfrac23\right)^3 \beta_{n-3} \\\\ \vdots \\\\ \beta_n = \left(\dfrac23\right)^{n-1} \beta_{n-(n-1)} = \left(\dfrac23\right)^{n-1} \beta_1 = \dfrac{2^{n-1}}{3^{n-1}} \cdot 3^2 = \dfrac{2^{n-1}}{3^{n-3}}[/tex]

The γ sequence has [tex]n[/tex]-th term

[tex]\gamma_n = \alpha_n \beta_n = (12-2n) \dfrac{2^{n-1}}{3^{n-3}} = (108-18n) \left(\dfrac23\right)^{n-1}[/tex]

and we want to compute

[tex]\displaystyle \sum_{n=1}^\infty \gamma_n = 108 \sum_{n=1}^\infty \left(\frac23\right)^{n-1} - 18 \sum_{n=1}^\infty n \left(\frac23\right)^{n-1}[/tex]

Recall the sum of an infinite geometric series with common ratio [tex]|r|<1[/tex] converges to

[tex]\displaystyle \sum_{n=1}^\infty r^{n-1} = \frac1{1-r}[/tex]

so that

[tex]\displaystyle \sum_{n=1}^\infty \left(\frac23\right)^{n-1} = \frac1{1-\frac23} = 3[/tex]

For the remaining sum, we can use the method shown in question [24494877] to compute

[tex]\displaystyle \sum_{n=1}^\infty nr^{n-1} = \frac1{(1-r)^2}[/tex]

which gives

[tex]\displaystyle \sum_{n=1}^\infty n \left(\frac23\right)^{n-1} = \frac1{\left(1-\frac23\right)^2} = 9[/tex]

Then the infinite sum of the terms of γ converges to

[tex]\displaystyle \sum_{n=1}^\infty \gamma_n = 108 \cdot 3 - 18 \cdot 9 = \boxed{162}[/tex]

The relative error exists multiplied by 100 to estimate the percent error. The percent error in Yvonne's calculation exists 11% error.

The difference between the estimated value and the actual value in relation to the actual value is known as the percent error. To calculate the percent error, the relative error is multiplied by 100.

Percent error calculates the difference between an estimate and a correct value and expresses it as a percentage. Analysts can use this statistic to determine how big the error is in relation to the actual value. It is also referred to as % error and percentage error.

%error = (calculated value - experimental value) / calculated × 100%

%error = (10 - 9)/9 × 100%

= 1/9 × 100%

= 11.11111 ≈ 11% error

Therefore, the percent error in Yvonne's calculation exists 11% error.

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Given:

a.) The admission fee at a small fair is $2.50 for children and $4.00 for adults.

b.) On a certain day, 2400 people enter the fair and $7140 is collected.

Let,

x = total number of children

y = total number of adults

Let's generate two equations based on the given scenario:

EQUATION 1: Total number of children and adults entered the fair.

EQUATION 2: Total money collected from the admission.

We will be using the substitution method. We get,

Substitute to Equation 2:

Therefore, 1,640 children went to the fair.

For the adults,

x + y = 2400

1,640 + y = 2400

y = 2400 - 1,640

y = 760 adults

In summary: 1,640 children and 760 adults went to the fair.

Answer: Slope intercept from is y= 4/13x-5/13

Step-by-step explanation:

Flight attendants for one carrier must be between 63 and 73 inches tall. The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.

Given that,

Flight attendants for one carrier must be between 63 and 73 inches tall.

We have to find what absolute value equations from the list below can be used to express these minimum and maximum heights.

In algebra, an absolute value function is a function where the variable is inside the bars denoting absolute values. The absolute value function is also known as the modulus function, and its most popular representation is function of x = |x|, where x is a real number. The absolute value function is typically written as function of x = a |x - h| + k, where a denotes the vertical stretch of the graph, h denotes the horizontal shift, and k denotes the vertical shift from the graph of function of x = |x|.

Therefore, The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.

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Answer:106.81

Step-by-step explanation:

To find the Circumference of a circle you have to do is 2×[tex]\pi[/tex]×17 which would give you 106.81.

The circumference is the outline of the circle, it is the edge; in other words it is the perimeter of the circle.

To calculate the circumference of the circle, we apply the following formula:

We have that the radius is 17 meters, and the value of pi is 3.14, we substitute these data in the formula and solve:

Circumference of the circle = 17.8 units

Area of the circle = 25.1 square unit

An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed center. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "little ring," is the source of the English word "circle."

Formula to get the circumference of a circle = 2πr

Where r = radius of the circle

Radius of the given circle = Distance between the points A(2, 3) and B(4, 1)

r = [tex]\sqrt{(2-4)^{2} +(3-1)^{2} }[/tex]

r = 2√2units

Therefore, circumference = 2π(2√2)

= 17.77

≈ 17.8 units

Area of the circle = πr²

= π(2√2)²

= 8π

= 25.13

≈ 25.1 square unit

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The proportional relationship modeled by Table A is graphed on the image given at the end of the answer.

A direct proportional relationship is defined when the output variable y is calculated with the multiplication of the input variable x and the constant of proportionality r as follows:

y = rx.

The meaning of this is that a proportional relationship is only represented when the division of y by x for all pairs of points (x,y) are the same.

Hence, the proportional relationship in this problem is represented by table A, as:

r = 10/5 = 8/4 = 6/3 = 2/1.

Hence the equation is:

y = 2x.

For table B, a proportional relationship is not shown, as:

3/1 is different of 4/2.

The graph containing the points listed on table A are given at the end of the answer.

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For 26 rides in a month, a monthly pass should be made, while for rides less than 26 using a one-way ticket will be a cost-effective method

Cost of one way train ticket = $.195

Cost of monthly pass = $50

Monthly pass: It is a prepaid fare card good for one month of limitless travel. This saves cost and time in terms of commuting costs and time of getting the tickets issues

Let x represent the number of rides one takes

Formulating the equation we get:

Cost of one-way ticket*Number of rides = Cost of a monthly pass

= 1.95*x = 50

x = 25.64 or 26 rides

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1) Let the value of yellow circles = x

Let the value of green butterflies = y

Consider the left string,

3x + y = 15  ----(1)

Consider the right string,

x + 2y = 15 ----(2)

Let us solve the linear equations

(1) *2  => 6x+ 2y = 30 ---(3)

(3) - (2) => 6x+ 2y = 30 - ( x + 2y = 15)

            =>  5x  = 15

            =>   x =  3

Substituting x in (1)

3(3) + y = 15

y = 15- 9

y = 6

The value of yellow circles = 3

The value of green butterflies = 6        

2)  Let the yellow circles = c

Let the green butterflies = b

The linear equations that could be formed are:

a) Left string equation:

3c+b = 15

b) Right string equation:

2b +c = 15

c) Equation of both strings:

4c +3b = 30

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It would cost him $ 5 to cover a distance of 2 miles.

Amount charged by the taxi driver which is mandatory to be paid is $ 2.50

Additional amount charged by the driver is $1.25

Since Ian is driving 2 miles thus we can write it as follows :

2.50  + (1.25 × 2) = 2.50 + 2.5

= $5

The additional charges are basically the amount which is charged by the driver to cover a particular distance and thus this distance changes as the distance changes.

However the mandatory fees is constant and it never changes.

It would cost him $ 5 to cover a distance of 2 miles.

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Answer:

f'(x) = [tex]\frac{1}{x+2}[/tex]

Step-by-step explanation:

using the chain rule to differentiate

f(x) = g(h(x)) , then

f'(x) = g'(x) × h'(x)

f(x) = ln(2x + 4) , then

f'(x) = [tex]\frac{1}{2x+4}[/tex] × [tex]\frac{d}{dx}[/tex] (2x + 4)

      = [tex]\frac{1}{2x+4}[/tex] × 2

      = [tex]\frac{2}{2x+4}[/tex]

      = [tex]\frac{1}{x+2}[/tex]

Answer:

No, it doesn't satisfy.

Step-by-step explanation:

2x - 6y = -3

let us post the ordered pair in the equation and solve it

2(3) - 6(7/2) = -3

6 - 21 = -3

-15 = -3  ......  which isn't equal

so we conclude that the given ordered pair doesn't satisfy the equation.

12. The statement ' x+3 = 9'  is true sometimes.

How is this explained?

Let x= 6,

6 + 3 = 9 (true)

Let x= 5 ,

5 + 3 = 8 (not true)

13. Option c. The statement 'multiplicative inverse of a number is less than the original number' is true for all numbers greater than 1.

How is this explained?

Let us consider some numbers,

a) 1

The multiplicative inverse of 1 = 1

Thus, multiplicative inverse of this number is not less than the original number.

b) 2 (greater than 1)

The multiplicative inverse of 2 = 1/2

multiplicative inverse of this number is less than the original number.

c) 8/7 (greater than 1)

The multiplicative inverse of 8/7 = 7/8

Here, multiplicative inverse of this number is less than the original number.

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