Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students? 50 students 200 students 124 students 250 students​

The composition of the fuctions g(x) and f(x) evaluated in x = 4 is equal to:

g( f(4)) = 45

Here we have two functions f(x) and g(x), such that:

g(x) = 3.25*x + 6

And f(x) is defined by the table:

x            f(x)

-2            -1

0             3

 4            12

7              9

19             6

And we want to find the composition of g(x) and f(x) evaluated in x = 4.

g( f(4))

By using the table of f(x), we can see that f(4) = 12

Then:

g( f(4)) = g(12)

Evaluating g(x) in x = 12 we get:

g(12) = 3.25*12 + 6 = 45

Then we conclude that g( f(4)) = 45

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The exact value of tan195° is 0.2679.

The given trigonometric ratio is tan195°.

Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.

Now, the value of  trigonometric ratio is

tan195°=0.2679

Hence, the exact value of tan195° is 0.2679.

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The horizontal distance which the cable is placed on is 57.74 feet

Trigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Data;

Using tangent ratio;

tanθ = opposite / adjacent

tan 60 = 100 / x

x = 100 / tan 60

x = 57.74 ft

The distance which the cable is anchored to the ground is 57.74ft.

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y=35x+350  is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.

Two or more expressions with an Equal sign is called as Equation.

Given,

James is having a birthday party.

It costs $350 to rent the hall plus $35 per person for food

We need to write an equation to show the total cost of the party (y) based on the number of guests (x) he invites.

y=35x+350

Where x represents the number of guests.

350 is a constant value because it is the cost of the hall.

As 35 is the cost per person, 35x

Hence y=35x+350  is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.

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Answer:

  $1377.06

Step-by-step explanation:

You want the monthly payment on a 30 year loan of $162359 at 9.6% interest.

The payment value can be computed by any spreadsheet and most graphing calculators using built-in financial functions. Numerous apps and web sites are available for the same purpose.

The monthly payment is $1377.06 according to the attached calculator output.

The formula used for the purpose is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12·t))

where P is the loan value, r is the annual interest rate, and t is the number of years. For P=162359, r=0.096, and t=30, you have ...

  A = 162359(0.096/12)/(1 -(1 +0.096/12)^-360) ≈ 1377.06

__

Additional comment

The formula assumes the payment is made at the end of the month. Spreadsheet and calculator functions often need to be told that's when the payment is made.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line G

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 8 } \implies {\Large \begin{array}{llll} - \cfrac{3 }{ 8 } \end{array}}[/tex]

Answer:

20/7 km/hr

Step-by-step explanation:

To solve this problem, we use the formula of:

speed x time = distance

Both the raft and boat have their own speeds, times and distances, so we would write two equations based on the formula.

One for the raft: [tex](s_{r} )(t_{r} )=d_{r}[/tex]

And one for the boat: [tex](s_{b} )(t_{b} )=d_{b}[/tex]

Both vehicles travelled as total of 20 km, so both [tex]d_{r} =d_{b} =20[/tex]. We are also given that the boat goes 12 km/hr, so [tex]s_{b} = 12[/tex]. Lastly, the boat had been going for five hours and 20 minutes less than the raft. This is the same as 5 1/3 hrs. This can also be written as 16/3 hrs, so [tex]t_{r} = t_{b} +\frac{16}{3}[/tex]. We can now plug these in:

raft: [tex](s_{r} )(t_{b}+\frac{16}{3} )=20[/tex]

boat: [tex](12 )(t_{b} )=20[/tex]

We only have one variable in the boat equation, so we can solve for time:

[tex]t_{b} =\frac{20}{12} \\\\t_{b} = \frac{5}{3}[/tex]

Now, we can plug [tex]t_{b}[/tex] into the raft equation and solve for speed:

[tex](s_{r} )(t_{b}+\frac{16}{3} )=20\\\\(s_{r} )(\frac{5}{3} +\frac{16}{3} )=20\\\\(s_{r} )(\frac{21}{3} )=20\\\\(s_{r} )(7)=20\\\\s_{r}=\frac{20}{7}[/tex]

Therefore, the speed of the raft would be 20/7 km/hr

The speed of the raft if the speed of the patrol boat was 12 km/hr will be 20/7 km/hr.

Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.

For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.

It is known that,

Speed = total distance / total time taken

The time is taken by petrol boat to reach the raft craft

Time = total distance/speed

Time = 20/12 = 5/3 hour.

The time taken the raft boat to reach 20 km = (5 hour + 20 minutes) + 5/3 hour

⇒ 5 + 1/3 + 5/3

⇒ 16/3 + 5/3 = 21/3 = 7

The speed of the raft will be as,

Speed of raft = 20/7 km/hr

Hence "The speed of the raft, if the speed of the patrol boat was 12 km/hr, will be 20/7 km/hr".

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Answer:

x = 17

y = 2

Length of DF = 20

Step-by-step explanation:

Step 1: Solve x - 3

Step 2: Plug x = 17 into x - 7 and solve

Step 3: Find the length of DF

Answer:

Green x = 10

Purple x = 19

Step-by-step explanation:

Are we solve for x?

Green:

It is not staighted, but this looks like a straight angle.  That would total 180

3x + 5 + 6x -5 +90 = 180  A right angle is 90  Combine like terms

9x + 90 = 180  Subtract each side by 90

9x = 90  Divide both sides by 9

x = 10

Purple:

5x - 19 + 2x + 5 = 119  Combine like terms

7x -14 = 119  Add 14 to both sides

7x = 133  Divide both sides by 7

x = 19

Answer: D. 5.38 > 5.271 > 5.217

The total cups of water the pitcher can hold is 72

A fraction is the ratio of two integers.

It is divided into two parts by a division line and the part above the line is called the numerator and the part below the line is called the denominator.

Fraction are of three types: proper, improper and mixed fractions.

Let the total number of cups to fill the pitcher be x.

The pitcher is 3-fourths full of water, that is 3/4 of x = [tex]\frac{3x}{4}[/tex]

when 6 cups were taken away from the Pitcher it became 2/3 of x = [tex]\frac{2x}{3}[/tex]

So that,

[tex]\frac{3x}{4}[/tex] -  [tex]\frac{2x}{3}[/tex] = 6

multiply  [tex]\frac{2x}{3}[/tex] by 4/4 and  [tex]\frac{3x}{4}[/tex] by 3/3

it becomes

[tex]\frac{9x}{12}[/tex] - [tex]\frac{8x}{12}[/tex] = 6

simplifying the numerator

x/12 = 6

cross multiplying

x = 12 x 6

x = 72

In conclusion, the total number of cups to fill the pitcher is 72

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The size of the bacterial population after 80 minutes is  19048.81

The size of the bacterial population after 7 hours is  49152000.

Given,

A bacterial culture initially contains 3000 bacteria and doubles every half hour.

we are asked to determine the size of the bacterial population after 80 minutes.

The exponential growth law for this problem is

p(t) = 3000 (2)^t/30

where t is the time in minutes. To find the population after 80 minutes, plug in t=80 and evaluate P(80).

p(80) = 3000 (2)^80/30

p(80) = 3000(2)^8/3

p(80) = 19048.81

now, we are asked to determine the size of the bacterial population after 7 hours.

To find it after  hours, plug in t=420 minutes (since 7 hrs equals 420 minutes) and evaluate p(420).

p(420) = 3000(2)^420/30

p(420) = 3000(2)^14

p(420) = 49152000

hence we get the required size of the population.

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Simplifying the expression (x)(6 + x)−2x gives x^2 + 4x

Information given in the question

the expression (x)(6 + x)−2x

The expression is simplified by first expanding

(x) (6 + x) − 2x

6x + x^2 - 2x

x^2 + 4x (products as powers when possible)

The result here is a quadratic equation without the constant variable. it can be simplified further to give

x(x + 4)

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The equation of the inverse function is f⁻¹(x) = x/7 - 3/7

The function f(x) is given as

f(x) = 7x + 3

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the equation of the function becomes

y = 7x + 3

The next step is to switch/swap the positions of x and y in the above equation y = x + 5

The equation becomes

x = 7y + 3

The next step is to make y the subject of the formula in the above equation

The equation becomes

y = x/7 - 3/7

Express as an inverse function

f⁻¹(x) = x/7 - 3/7

Hence, the inverse is f⁻¹(x) = x/7 - 3/7

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a) The sample proportion would be of: 0.93.

b) The margin of error would be of: 0.037.

c) The critical value would be of: z = 1.96.

d) The standard error would be of: 0.0189.

e) The critical value for the 90% confidence interval would be of: z = 1.645.

f) The 90% confidence interval would be narrower.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

From the equation, the confidence interval can be described as follows:

The sample proportion plus/minus the margin of error.

For this problem, the interval is given as follows:

(.893, .967).

From the description, the sample proportion is the mean of the two bounds, hence:

Sample proportion = (0.893 + 0.967)/2 = 0.93.

The margin of error is the absolute value of the difference of each bound and the sample proportion, hence:

Margin of error = |0.967 - 0.93| = |0.893 - 0.93| = 0.037.

The critical values are found using the z-table, as follows:

The greater the critical value, the wider the interval, hence a 90% confidence interval would be narrower than the 95% confidence interval;

The standard error is the division of the margin of error by the critical value, hence:

Standard error = 0.037/1.96 = 0.0189 = 1.89%.

The complete problem is given by the image shown at the end of the answer.

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Answer: (-2, -2)

Step-by-step explanation:

Right now, the coordinates of point C are (1, -3).

It is first moved 3 units to the left, so the point C would change to (1 - 3, -3) = (-2, -3)

It is then moved 2 units up, so point C would change to (-2, -3 + 2) = (-2, -1)

The simplified point-slope form is y = 2x -12

A simple definition of point-slope form is a line equation written with only one point on the line and the slope of the line. (x, y) is the point form, and the slope is the rise over run or the ratio of the change in y values to the change in x values.

Given points (2,-8) and (-1,4)

We have to determine the answer in point-slope form

The slope formula provides the slope of the line:

m = (y2 -y1)/(x2 -x1)

m = (4 -(-8))/(-1-2) = 12/-3 = -4

the point-slope formula is given by

y-y1 = m(x-x1)

In terms of this formula:

m = 2

y1 = -8

x1 = 2

Let's simplify by plugging these values into the point-slope formula:

y - y1 = m (x - x1)

y - (-8) = (2)(x - 2)

y + 8 = 2(x - 2)

y + 8 = 2x -4

y = 2x -12

Therefore the simplified point-slope form is y = 2x -12

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The balance is $12989.90.

From the question, we have

[tex]A= P\times \frac{\left ( 1+\frac{APR}{n} \right )^{nt}-1}{\frac{APR}{n}}[/tex]

where,

A is the balance after t years,

P is the periodic payment,

APR is the annual percentage rate,

n is the number of periodic payments per year, and t is the number of years.

[tex]A=250\times \frac{\left ( 1+\frac{0.04}{12} \right )^{12\times 4}-1}{\frac{0.04}{12}}[/tex]

=$12989.90

The balance is $12989.90.

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

B.) 1/(x+3)(x+5)

Step-by-step explanation:

Look for the x-intercepts and asymptotes on the graph to get the numerator and denominator

There are no x-intercepts, so the numerator is an integer

The asymptotes are -3 and -5, so the denominator would be (x+3)(x+5) since if you were to set that = to 0 you would get -3 and -5.

Answer:

Jasmine spent 1.45$ more on water than popcorn.

Step-by-step explanation:

Jasmine buys 4 bottles of water and spends 1.30$ for each one individually. To find out how much all of these 4 costs, we multiply 4 by 1.30$ which is 5.20$

To find out how much more money Jasmine spent on the water than popcorn, we subtract 5.20$ - 3.75$ = 1.45$

Answer: m/2 + 25 or (0.5)m + 25

Step-by-step explanation:

Answer:

The slope of the line is 1/2.

The y-intercept of the line is 5.

The x-intercept of the line is 10.

Step-by-step explanation:

The y-intercept is where the line intercepts the y axis. (vertical line)

The x-intercept is where the line intercepts the x axis. (horizontal line)

The slope (rise over one) is a bit more complicated to find. First, pick two points on the line and determine their coordinates. Then, determine the difference in y-coordinates of these two points (rise). After that, determine the difference in x-coordinates for these two points (run). Then you have your slope!

Answer:

3720 kg

Step-by-step explanation:

one bag of coffee weighs=0.62 kg

total no. of coffee bags= 240×25=600

total weight of coffee=6000×0.62= 3720

Equation of line c parallel to line d and passing through points  (2, -6) is

The equation of line d will be written in the slope intercept form of the form just like line c,

the slope intercept form is as below

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

y = -5x + 3

slope

m = -5

slope of parallel lines are equal hence slope of line d = -5

using the formula for the slope intercept the equation is written

(y - y₁) = m (x - x₁)

point (2, -6) and m = -5

(y - -6) = -5 (x - 2)

y + 6 = -5x + 10

y = -5x + 4

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The distance between point A and point B is 5 units.

According to the question,

We have the following information:

Point A = (-2,2)

Point B = (1,2)

Now, we know that the following formula is used to find the distance between two points:

Distance between two points = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} )}[/tex]

In this case, we have the values of x1 = -2, y1 = -2, x2 = 1 and y2 = 2.

Distance between two points = [tex]\sqrt{(2+2)^{2} +(1+2)^{2} )}[/tex]

(The sign has been changed from negative to positive because the multiplication of two negative integers is positive.)

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

Distance = [tex]\sqrt{16+9}[/tex]

Distance = [tex]\sqrt{25}[/tex]

Distance = 5 units

Hence, the distance between point A and point B is 5 units.

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Answer: About 20.25 or [tex]\sqrt{410}[/tex]

Step-by-step explanation:

a²+b²=c²

c is the hypotenuse in this equation, so we can substitute the given side lengths for a and b.

7²+19²=c²

49+361=c²

410=c²

Then we take the square root to get

about 20.25 or [tex]\sqrt{410}[/tex] to be exact

Answer:

Step-by-step explanation:

a² + b². =. c²

7² + 19². =. c²

49 + 361 (400). =. c²

. c = √400= 20cm

The number of problems Rhea still have to solve is 8

Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator and the number at the bottom is called denominator. It tells how many equal parts of the whole or collection are taken.

On Monday Rhea solved 12 out of 36 problems. This means she has 36-12 = 24 problems remaining. On Tuesday she solved 2/3 of the remainder, which means she did 2/3×24= 16problems on Tuesday.

Therefore she will have 24- 16= 8problems to complete after Tuesday.

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Answer: bro You need To add more about the question

Step-by-step explanation:

The values of [tex]D, D_x, D_y[/tex] are, [tex]D = 13, D_x = 8, D_y = 19[/tex].

What is Cramer's rule?

One of the key techniques used to solve an equation system is Cramer's rule. The determinants of matrices are used in this method to derive the values of the system's variables. Thus, the determinant technique is another name for Cramer's rule.

Consider, the given system of equations

-3x + 4y = 4             ...(1)

2x = 7y - 9               ...(2)

equation (2) can be written as,

2x - 7y = -9             ..(3)

Using Cramer's rule, we have to find the determinant of the coefficient matrix

matrix,

D= [tex]\left[\begin{array}{ccc}-3&4\\2&-7\end{array}\right][/tex]  = (-3)(-7) - 8 = 21 - 8 = 13

Secondly, find the determinant of x coefficient matrix,

[tex]D_x[/tex] =  [tex]\left[\begin{array}{ccc}4&4\\-9&-7\end{array}\right][/tex] = (4)(-7) - (4)(-9) = -28 + 36 = 8

Similarly, find the determinant of y coefficient matrix,

[tex]D_y[/tex] = [tex]\left[\begin{array}{ccc}-3&4\\2&-9\\\end{array}\right][/tex] = (-3)(-9) - (4)(2) = 27 - 8 = 19

Hence, values of the determinants are, [tex]D = 13, D_x = 8, D_y = 19[/tex].

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The equation of the circle is x² + y² - 41 =0.

A circle is a round-shaped 2-dimensional geometrical figure in which the points on the boundary are equidistant from a fixed point called a center.

Given, a circle centered at O(0,0)and has a point B (4,5) on its circumference.

The radius of the circle is the distance between the points O(0,0) and B (4,5), therefore,

r = √((4-0)² + (5-0)²)

r = √(16+25)

r = √41

The equation of a circle, centered at the origin with a radius of r =√41  units, is given by,

x² + y² = √41²

x² + y² = 41

x² + y² - 41 =0

Hence, the equation of the circle is x² + y² - 41 =0.

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