[tex]30*\sqrt{5} ^{2} +13*\sqrt{5}-6[/tex]

Answer:

  [9, 9+√18.25] ≈ [9, 13.272]

Step-by-step explanation:

You want the range of f(x)= 9+√(6+7x-x^2), determined algebraically.

The range is the set of values that f(x) may take on. It is the vertical extent of the graph. Here, it will be limited by the possible values the radical may have.

The expression under the radical is a quadratic that opens downward. It will have a maximum at its vertex, and a minimum usable value of 0.

The vertex of the quadratic can be found by putting it in vertex form:

  -x² +7x +6 = -(x² -7x) +6 = -(x² -7x +(7/2)²) +6 +(7/2)² = -(x -7/2)² +18.25

The maximum value the quadratic may have is 18.25.

Then the range of values that f(x) may have is ...

  9 +0 ≤ f(x) ≤ 9 +√18.25

The range is [9, 9+√18.25] ≈ [9, 13.272].

Answer:

Equation: y = 1800 - 120x

Step-by-step explanation:

y = 1800 - mx           Where x = months after purchase of computer

                                            y = balance remaining

1800 = y-intercept because this is your initial balance remaining as it is the actual price of the computer.

The coefficient of ‘m’ will be negative for this equation because the value of y decreases as x increases. (NOTE:  y is NOT indirectly proportional to x as the line of the equation does not pass through the origin)

Next step is to determine 'm’:

m = slope of equation

Two sets of x and y values have been provided:

[tex](x_{2}, y_{2}) = (3, 1440)[/tex]

[tex](x_{3} ,y_{3})= (6, 1080)[/tex]

Use any set and substitute in the slope-intercept equation to determine the value of m:

1080 = 1800 - 6m

All the like terms are brought together and m needs to be isolated:

6m = 1800 - 1080

6m = 720

m = [tex]\frac{720}{6}[/tex]

m = 120

Therefore:

y = 1800 - 120x

Answer:

two plus two equals five

Step-by-step explanation:

Answer:

27 and 13

Step-by-step explanation:

let the second number be x then the first number is x - 14

sum the 2 numbers and equate to 40

x - 14 + x = 40

2x - 14 = 40 ( add 14 to both sides )

2x = 54 ( divide both sides by 2 )

x = 27

x - 14 = 27 - 14 = 13

the first number is 27 and the second number is 13

Answer:

Below

Step-by-step explanation:

1 qt = .9463529 L

3 Qt  * .9463529 L/Qt  = 2.84 Liters

z-score for value 550 =  0.5

z-score for value 660 = 1.6

z-score for value 500 = 0

z-score for value 440 = -0.6

z-score for value 270 = -2.3

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

We are given a sample with a mean of 500 and a standard deviation of 100.

i.e.,  µ= 500 and  s= 100

The z score distribution is given by;

             Z =  (X-µ)/s ~ N(0,1)

where X represents the data values;

So, z score for value 550 is;

                z score =(550-500)/100  = 0.5

So, z score for value 660 is;

                z score = (660-500)/100  = 1.6

So, z score for value 500 is;

                z score = (550-500)/100  = 0

So, z score for value 440 is;

                z score =  (440-500)/100  = -0.6

So, z score for value 270 is;

                z score = (270-500)/100  = -2.3

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z-score for value 550 =  0.5

z-score for value 660 = 1.6

z-score for value 500 = 0

z-score for value 440 = -0.6

z-score for value 270 = -2.3

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

We are given a sample with a mean of 500 and a standard deviation of 100.

i.e.,  µ= 500 and  s= 100

The z score distribution is given by;

            Z =  (X-µ)/s ~ N(0,1)

where X represents the data values;

So, z score for value 550 is;

               z score =(550-500)/100  = 0.5

So, z score for value 660 is;

               z score = (660-500)/100  = 1.6

So, z score for value 500 is;

               z score = (550-500)/100  = 0

So, z score for value 440 is;

               z score =  (440-500)/100  = -0.6

So, z score for value 270 is;

               z score = (270-500)/100  = -2.3

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Therefore , the solution of the given problem of graph  comes out to be about 5,000 .

To rationally chart or graphically portray events or quantities, academics use graphs. A chart point is a typical tool for showing how various variables interact. Nodes, also known as vertices and lines, make up the non-linear storage arrangement known as a graph. The borders, also referred to as nodes, should be joined together using glue. (4.5) Visualizations, such as flowcharts, graphs, and bar graphs, that graphically depict explosive development within data.

Here,

Based on the graph,

it appears that in 2010, about 5,000 women were involved in accidents while riding in a two-wheeler.

Therefore , the solution of the given problem of graph  comes out to be about 5,000 .

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Answer:

Step-by-step explanation:

You want to know the Social Security and Medicare taxes on an annual income of $122,300, given the respective tax rates are 6.2% and 1.45%.

The income is less than the Social Security maximum of 128,400, so the 6.2% tax applies to the full amount. Each tax amount is found by multiplying the income by the tax rate:

  SS: $122,300 × 0.062 = $7582.60 . . . . Social Security tax

  Med: $122,300 × 0.0145 = $1773.35 . . .Medicare tax

Answer:

20%

Step-by-step explanation:

He spent (8500+ 1500) = 10 000   then sold it for 2000 MORE
Profit = 2000 / 10 000   * 100% = 20%

Answer:

15.4 min

Step-by-step explanation:

rate = liters/min = 2.5 l/min

time = liters/rate = 38.5 l / (2.5 l/min) = 15.4 min

Answer: 35%

Explanation:

1 - 0.65 = 0.35

0.35 in percentage is 35%

The minimum monthly income of full time worker  is $6112.

Full time worker = 4 weeks of 40 hour per week.

Part time worker = 2 weeks of 40 hour per week.

The full time hourly wage will be:

= $6112/(4 × 40)

= $6112/160

= $38.2

The part time hourly wage will be:

= $6112/(2 × 40)

= $6112/80

= $76.4

An additional child will impact the family budget as it will lead to lesser amount of money spent by each person.

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Answer:

-22

Step-by-step explanation:

-9x^0-13

=-9×1-13

=-9-13

=-22

Answer:

-22

Step-by-step explanation:

To solve the expression

Let's start by finding the value of 'x'

[tex] - 9 {x}^{0} - 13[/tex]

Hint: Any number raised to power 0 is always 1.

Therefore x⁰ = 1

let's rewrite the expression by substituting where x is with 1

[tex] - 9(1) - 13[/tex]

[tex] - 9 \times 1 = - 9[/tex]

[tex] - 9 -13 = - 22[/tex]

As a result, the combo meal includes 4 onion rings and 8 pizza buns.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

Let x be the number of onion rings in the combination meal and y be the number of pizza rolls. We can write the following system of equations to represent the given information:

40x + 80y = 800 (the total calories of the meal)

y = x + 4 (the number of pizza rolls is 4 more than the number of onion rings)

We can substitute the second equation into the first equation to solve for x:

40x + 80(x + 4) = 800

40x + 80x + 320 = 800

120x = 480

x = 4

We can use this value to find y:

y = x + 4 = 4 + 4 = 8

So, the combination meal contains 4 onion rings and 8 pizza rolls.

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Answer:

Step-by-step explanation:

You want the primary trig functions of angle H in right triangle FGH with sides FG=12, GH=9, FH=15.

The mnemonic SOH CAH TOA is intended to help you with problems like this. Its purpose is to remind you that ...

With respect to angle H, the sides are ...

Then the values you want are ...

  sin(H) = 12/15 = 4/5

  cos(H) = 9/15 = 3/5

  tan(H) = 12/9 = 4/3

Answer:

4/9

Step-by-step explanation:

If Jackie at 1/3, that means that 2/3 was left

2/3 x 2/3 = 4/9

One learning aid that  provides an interactive​ walk-through for solving the particular problem you are working on is "view an example"

It is also known as teaching aids, which are an essential part of any classroom. Teaching aids can help students improve their reading comprehension skills, illustrate or reinforce a skill or concept, differentiate instruction, and relieve anxiety or boredom by presenting information in a new and exciting way.

Teaching aids also engage students' other senses because there are no restrictions on what aids can be used to supplement a lesson. As technology advances, so do teaching aids, which are now classified as audio aids, visual aids, mechanical teaching aids, audio-visual aids, and more.

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Answer:

93cm

Step-by-step explanation:

6789 = 73 * length

length = 6789/73=93

Answer:

The length is 93 cm.

Step-by-step explanation:

We know that area is width times height. So, if we don't know what the length is,

Let x = the length

The equation would be

[tex]73x=6789\\[/tex]

We multiply 73 by x because of the formula talked about previously.

Now, lets  divide 73 on both sides

[tex]x = 93[/tex]

If the arrow on spinner is spun once, then the probability that the arrow do not stop on number which is divisible by 3 is (c) 3/4.

We know that the spinner contains 8 numbers and each number is equally likely to be selected. Out of the 8 numbers, the numbers which are divisible by 3 are {3, 6}.

So, the numbers which are not-divisible by 3 are {1, 2, 4, 5, 7, 8},

We select one of the 6 numbers that are not divisible by 3 out of the total 8 numbers. so, the probability is :

⇒ Probability = (Number of favorable outcomes)/(Total number of outcomes),

⇒ Probability = 6/8,

⇒ Probability = 3/4,

Therefore, the correct option is (c).

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As a result, the volume of the revolution solid is roughly -62.83π cubic units.

Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. To calculate the volume, multiply the length by the breadth by the height, which is 3x1x2, which is six. As a result, the fish tank has a volume of 6 cubic feet.

Here,

The region R is the upper half of a circle centered at the origin with a radius of 5. By the method of washers, the volume of the solid of revolution obtained by revolving R about the x-axis can be found by subtracting the volume of a cylinder of height "h" and radius "x" from the volume of a cylinder of height "h" and radius "sqrt(25-x²)".

The volume of a cylinder of height "h" and radius "r" is given by V = πr²h.

So, the volume of the solid of revolution can be expressed as:

V = ∫π(sqrt(25-x²)²- x²) dx from x=0 to x=5

Evaluating this integral, we get:

V = π(∫(25-x²)*0.5 dx - ∫x² dx) from x=0 to x=5

Using substitution and integrating, we can obtain the volume:

V = π * (5 * (2 * sqrt(25 - x²) - x²/2))

Evaluating the expression at x=5, we get:

V = π * (5 * (2 * sqrt(25 - 25) - 25/2))

V = π * (5 * (0 - 25/2))

V = -62.83π cubic units.

So, the volume of the solid of revolution is approximately -62.83π cubic units.

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The sinusoidal function have the following features:

Amplitude: 1

Period: 2π

Frequency: ω = 2π / 2π = 1

Herein we find an example of a sinusoidal function, whose definition is shown below:

f(x) = A · sin (2π · x / T + Φ) + x'

Where:

The frequency (ω) is equal to the following formula:

ω = 2π / T

If we know that the sinusoidal function f(x) = sin (x + π / 2) - 2, then the amplitude, the period and the frequency, that is, the features of the sinusoidal function, are, respectively:

Amplitude: 1

Period: 2π

Frequency: ω = 2π / 2π = 1

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[tex](3-2)^2+(7+5)(3-2)=(3-2)(3-2)+(7+5)(3-2)=(3-2)(3-2+7+5)=1*13=13[/tex]

Answer:  A=78. 5 [tex]feet^{2}[/tex]

Step-by-step explanation:

Answer: The expression Y = 4 / (x + sqrt(x) + 0.2) - 5x represents a mathematical function that maps values of x to values of Y. The input x represents the independent variable and Y represents the dependent variable. For any given value of x, the expression calculates the value of Y.

Step-by-step explanation:

The graph of the function g(x) = a |x| includes the point (1, 16). (-1, 16) is another point on the graph of the function.

Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function's domain and co-domain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.

Given that,

g(x) = a |x|

In a absolute value graph the value of y is the same in -x and x.

Then if the coordinates (x,y) one point is (1, 16), the graph have another point in (- 1, 16).

To find the value of a you use one of the points (x,y) in the general form of absolute value:

( 1 , 16) x = 1 f(x) = y = 16

16 = a | 1 |

As, |±a| = a

we get:

16 = a . 1

then, a = 16

The equation for the graph with points (1 , 16) and ( -1, 16) is:

g(x) = 16 |x|

a = 16

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A) The events are not independent.

B) The events are independent.

There are 150 containers (the probabilities depend on that number), and we draw two of them.

In event A we draw one, then the number of containers after that will be 149.

Then the probabilities for event B (the second draw) are different, which means that the events are not independent.

B) If the containers are replaced, then the events are independent.

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Answer:

9

Step-by-step explanation:

Chebyshev's Theorem states that for any given sample, at least 1 - 1/k^2 of the data falls within k standard deviations from the mean.

Let's use k = 2. Then, at least 1 - 1/2^2 = 1 - 1/4 = 3/4 of the households should have between 3 - 2 = 1 and 3 + 2 = 5 televisions.

So, at least 12 * 3/4 = 9 of the households in the sample have between 1 and 5 televisions.

Answer:

D.Sam he rides 14.5 meters per second which is over a meter per second faster than kevin

Step-by-step explanation:

Kevin:

Distance = 600m

Time = 45s

Speed = Distance/time = 600/45 = 13.33m/s

Sam:

Distance = 800m

Time = 55s

Speed = 800/55 = 14.54m/s

Therefore option D will be the answer