[tex]\frac{5\sqrt{7} }{\sqrt{35} }[/tex]

Answer:$2.61

Step-by-step explanation:

18=$15.66

÷6    ÷6

3=$2.61

The cost of 3 bottles of juice based on the given ratio will be $2.61.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

18 bottles cost = $15.66

1 bottle cost = $15.66/18 = $0.87/ bottle

For 3 bottles = 3 × $0.87 = $2.61

Hence "The cost of 3 bottles of juice based on the given ratio will be $2.61".

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The equation representing the cost is y = 0.15x + 3 where x ix the number of copies and y is total cost.

Cost for 250 copies is $40.5

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a printing company charges $0.15 per copy in addition to a service fee of $3,

Therefore, according to question, the total cost y for printing x copies is,

y = 0.15x + 3

For x = 250

y = 0.15*250 + 3

y = $40.5

Hence, The equation representing the cost is y = 0.15x + 3 where x ix the number of copies and y is total cost.

Cost for 250 copies is $40.5

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Answer:

15-p

Step-by-step explanation:

15-p

The distance that Evan has left to hike is 13/30 mile.

From the information, Eva is hiking a real that has a length of 5/6 miles.

He has also hiked 2/5 miles. Therefore, in this situation, the distance that he has left will gotten by subtracting the fractions.

This will be:.

Distance left = Total distance - Distance hiked

Distance left = 5/6 - 2/5

= 25/30 - 12/30

= 13/30

The distance is 13/30 miles.

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Answer:

The correct statements are:

- 6x + 15 < 10 - 5x ⇒ 3rd answer

Step-by-step explanation

An open circle is at 5 and a bold line starts at 5 and is pointing to the right ⇒ 4th answer

Step-by-step explanation:

∵ The inequality is -3(2x - 5) < 5(2 - x)

At first simplify each side

∵ -3(2x - 5) = -3(2x) + -3(-5)

Remember (-)(-) = (+)

∴ -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x)

Remember (+)(-) = (-)

∴ 5(2 - x) = 10 - 5x

∴ - 6x + 15 < 10 - 5x

Subtract 15 from both sides

∴ - 6x < -5 - 5x

Add 5x to both sides

∴ - x < - 5

Remember the coefficient of x is negative, then when you divide both sides by it you must reverse the sign of inequality

∵ The coefficient of x is -1

∴ Divide both sides by -1

∴ x > 5

Answer:

 50 people

Step-by-step explanation:

Solution

25% as a fraction is 25/100 which reduces down to 1/4. What this tells you is that 1/4 of the people asked want the hotel

1/4 * 200 = 50

50 people want the hotel.

The curve -3[tex]x^{2}[/tex] + 18x +3 has a maximum value of 30 at x = 3

In mathematics, a point at which a function’s value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum. if it is merely greater than any nearby point, it is a relative, or local, maximum. In calculus, the derivative equals zero or does not exist at a function’s maximum point.

Differentiate f(x) =  -3[tex]x^{2}[/tex] + 18x +3 ,

we have dy/dx = -6x + 18.

at turning point, dy/dx = 0

-6x + 18 = 0

6x = 18

x =18/3

x = 3

to check if x = 3 is a minimum or maximum point, we take the second derivate

which is  [tex]\frac{d^{2}y }{dx^{2} }[/tex] = -6

since  [tex]\frac{d^{2}y }{dx^{2} }[/tex] < 0

F(x) is a maximum,

so maximum value of x, we substitute x = 3 into the function

f(x)  = -3[tex](3)^{2}[/tex] + 18(3) + 3

f(x) = 30

In conclusion, the maximum value for the function is 30 at x = 3

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By using the concept of straight angle, the value of x obtained is 17°

What is straight angle?

At first it is important to know about angle

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle

Straight angle is the angle whose measure is 180°

Here,

[tex]m\angle 1 =(4x +2)\\m\angle 2 = 110\\[/tex]

[tex]\angle 1 \ and \ \angle 2[/tex] forms a straight angle

[tex]m\angle 1 + m\angle 2 = 180[/tex] [Angle on a straight line]
[tex]4x + 2 + 110 = 180\\4x +112 = 180\\4x =180-112\\4x = 68\\x = \frac{68}{4}\\x = 17[/tex]

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Answer:

The answer is x^{3}-2x^{2}-5x+6

Step-by-step explanation:

This is because only a Cubic Function would have such a shape. That leaves x^3 functions from there just substitute points and check

There are 39% of all the people on the trip are female students on a school trip.

One to fifteen teachers are assigned to every hundred students.

and there are 7:5 more female students than male students.

Let's say there are x teachers. Students multiply by 15 as a result.

Take the ratio of male to female as 7 years for the male and 5 years for the female.

The total student trip is made up of both male and female pupils.

Thus,

15x = 7y + 5y

15x = 12y

5x = 4y

x = 4/5y  ...eq 1

Then, the percentage of the female students.

5y/(x + 5x)×100

5y/16x ×100

Put the value of x from eq 1

625/ 16 = 39%

Thus, there are 39% of all the people on the trip are female students.

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The 90% confidence interval for the population mean gpa is [2.545,3.114].

The confidence interval for population mean is:

µ ± z* . σ/√n

Where, μ is population mean, σ is standard deviation, z* is the value of z-score and n is number of samples.

The z-score value for 90% confidence interval is 1.645.

The average gpa is found to be 2.83, so μ=2.83. The variance is 0.45, it means

σ² = 0.45

σ = √0.45

σ = 0.67

The 90% confidence interval for population mean is:

2.83 ± 1.645 . 0.67/√15

[2.83 - 1.645.0.67/√15 , 2.83+1.645.0.67/√15]

[2.545 , 3.114]

Therefore, the 90% confidence interval for the population mean gpa is :

[2.545 , 3.114]

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The value of the shorter base which is x is 8 feet.

A trapezium is a quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional shape that appears as a table when drawn on a sheet of paper.

It has four sides and four vertices.

The trapezium is made of a rectangle and triangles.

Area of a trapezium = 1/2 (a + b ) h

where a = small base, b = big base and h = height.

from the above, b = 24 feet, h = 6 feet, a = x and area = 96 square feet

substituting the above into the equation

1/2 ( 24 + x) x 6 = 96

6(24 + x) = 96 x 2

6(24 + x ) = 192

multiplying the terms by 6

144 + 6x = 192

6x = 192 - 144

6x = 48

x = 48/6

x = 8 feet

In conclusion, the value of x is 8 feet

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(4i+1)² can be simplified to 8i-15

A complex number is a number of the form a + bi, where a and b are real numbers

Given expression is (4i+1)²

four times of i plus one whole square.

(4i+1)² can be expanded by using algebraic identity

(a+b)²=a²+b²+2ab

(4i+1)²

Now put a as 4i and b as 1

(4i+1)²=16i²+1+2(4i)(1)

Where i²=-1

=-16+1+8i

=8i-15

Hence (4i+1)² can be simplified to 8i-15

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The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.

A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.

Here,

The z value at the 90 percent confidence interval is 1.645.

t ≥ z*s/√n

5≥1.645*62/√n

√n≥20.398

√n≥20.4

n≥416.16

The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.

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Answer:

(9,1), Z(5,1)

Step-by-step explanation:

Answer:25256

Step-by-step explanation:

Answer: “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable.

Step-by-step explanation:lol i have no idea

The nearest whole number to the number 5.2 is 5.

Given number:

= 5.2

we can determine the whole number of any decimals using the properties that is,

if decimal part < .5 its nearest whole number is 0.

example = 0.5 whole number is 0.

if decimal part  >  0.5 its nearest whole number is 1.

In this case,

= 5.2

decimal part  = 0.2 < 0

so the nearest whole number is 5.

Therefore the nearest whole number to the number 5.2 is 5.

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Answer:

First step, correct answer is (3,1)

Step-by-step explanation:

1.it should be x+2(3x-8)=5

2. x+6x-16=5

3.7x=21

4. 7x/7=21/7

5. x=3

then you can eitheir take x+2y=5 or y=3x-8 i suggets taking second option as it is easier, just input values for x in

)  3x-8=y

6. 3(3)-8= 1

7. x=3, y=1

The total distance leon biked in miles that weekend is 19.5 miles.

The answer provided below has been developed in a clear step by step manner.

On Saturday, Leon biked 1.5 hours at a speed of 14.5 miles per hour that means distance =  14.5 * 1.5 = 21.75 miles

On Sunday, he biked 2.75 hours at a speed of 15 miles per hour that means distance =15 * 2.75 =41.25  miles

Distance = speed*time  use this formula

He farther did in sunday = 41.25 - 21.75 miles = 19.5 miles

Therefore, that weekend Leon rode his bike a total of 19.5 miles.

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Answer:

m=18

Step-by-step explanation:

The answer is

f(x) = (x - 1) 2(x +1)(x - 3 ).

Given equation

f(x) = (x − 2)2(x + 1)(x − 3)

f(x) = (x + 2)2(x − 1)(x + 3)

f(x) = (x + 2)2(x + 1)(x + 3)

f(x) = (x − 2)2(x − 1)(x − 3)

Factored form is a product of stayed and linear elements.

by checking of the red line cross the x-axis.it will give you the zero.

it passes at -1, touches at 1, and crosses again at 3.

This implies that the zeroes are -1, 1 and 3.

The factors 2(x+1), (x - 3), and (x - 1) must be evaluated.

Therefore the answer is

f(x) = (x - 1) 2(x +1)(x - 3 ).

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The statements is true of the function f(x)= x^2 + 6x^3 - 4 + 2x^5 is C.the graph has exactly one x-intercept

It is shown that the function has one intercept in the x direction by plotting the graph of the polynomial

The graph showed one x intercept is at the coordinate (0.778, 0)

x intercept refers to the value of x when y is zero

The graph is plotted and attached

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The mean absolute percentage error is 33.3%

The mean absolute percentage error measures the forecast accuracy by determining how well a particular forecasting method is able to reproduce the time series data that are already available.

This method is referred to as the forecasts of accuracy, which help to measure the number of errors that are in a former forecast.

Then this would factor these errors into a new forecast while making adjustments to the new forecast.

Forecasted sales were $4,000

Actual sales were $3,000

Absolute error = |Actual sales - Forecasted sales|

                        = |3,000-4,000|

                        = 1000

Mean Absolute error percentage = (Absolute error / Actual sales) *100%

                                                       =(1000/3000)*100

                                                       = 33.33%

Hence, The Mean Absolute error percentage is 33.3%

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Answer: 3x+19

Step-by-step explanation:

By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.

An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.

Given,

2x+y=4

x-y=1

By solving above two equations we get,

2x+y=4

x-y=1

3x=5

x=5/3

y=-1+x

y=(5/3)-1

y=2/3

Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

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=> Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

=>  Reflect figure A across the y-axis, and dilate it by a scale factor of 4.

Given,

In the question:

Figure A is a polygon that has been graphed on a coordinate grid.

To select the option:

Which of the following transformations will result in a similar image to figure A?

Now, According to the question;

The correct options are:

=> Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

=>  Reflect figure A across the y-axis, and dilate it by a scale factor of 4.

{If the two figures are similar, then their angles are not changed. The ratio of length are the same.}

Hence, => Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

=>  Reflect figure A across the y-axis, and dilate it by a scale factor of 4.

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a) x = -6 to x =4

[tex](x_{1} , y_{1} ) (x_{2} , y_{2} ) = (-6,1) (4,3)[/tex]

Slope(m)[tex]= \frac{Y_{2}-Y_{1}}{x_{2}-x_{1}}[/tex]

               [tex]= \frac{1-3}{-6-4-}[/tex]

               [tex]= \frac{-2}{-10}[/tex]

               [tex]m = \frac{1}{5}[/tex]

Slope (m) of the function is 1/5.

b) x = -2 to x = 2

[tex](x_{1} , y_{1} ) (x_{2} , y_{2} ) = (-2,-1) (2,-3)[/tex]

slope (m)[tex]= \frac{Y_{2}-Y_{1}}{x_{2}-x_{1}}[/tex]

[tex]= \frac{-3-(-1)}{-2-2}[/tex]

[tex]= \frac{-2}{-4}[/tex]

slope(m) [tex]= \frac{1}{2}[/tex]

Slope(m) of the given function is 1/2.

What is fraction ?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

In a simple fraction, both are integers.

A complex fraction has a fraction in the numerator or denominator.

In a proper fraction, the numerator is less than the denominator.

Define slope(m)?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

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