Write a function rule to model the cost per month of a long-distance cell phone calling plan. Then evaluate the function for the given number of minutes.
Monthly service fee: 4.52 Rate: .12 pet minute Minutes used: 250

Answer:

a = 3 [tex]\frac{1}{3}[/tex] or [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

Since [tex]f(2)=g(2)[/tex], [tex]2a*2-6=2^2+a[/tex].

Now let's solve for [tex]a[/tex]:

Simplify: [tex]4a-6=4+a[/tex]

Add 6 to both sides: [tex]4a=4+a+6[/tex]

Simplify: [tex]4a=10+a[/tex]

Subtract a from both sides: [tex]3a=10[/tex]

Divide both sides by 3: [tex]x=\frac{10}{3}[/tex]

The ratio of the volume of the large cylinder to the volume of the small cylinder is 3:1.

We are given height of cylinders and the information that both the cylinders are same. So, the radius of cylinders will be same.

The formula for calculation of volume of cylinder is -

Volume = πr²h, where r is radius and h is height.

Ratio of the volume of the large cylinder to the volume of the small cylinder= πr²h(large):πr²h(small)

Ratio = πr²75:πr²25

Cancelling πr² from both numerator and denominator as it is common in both

Performing division by 25 to find the ratio

Ratio = 3:1

Hence, the ratio of the volume of the large cylinder to the volume of the small cylinder is 3:1.

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The translation is show below

What is translation in mathematics?

A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. When executing a translation, the original object is referred to as the pre-image, and the item following the translation is referred to as the image.

Let the coordinates be L (2, 5), M (4, 6), N (3, 7)

Follow the translation rule as (x-2, y+4), which shifts the triangle LMN to L'M'N' as L' (0, 9), M' (2, 10), N' (1, 11).

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[tex]10\frac{2}{3}[/tex]  cups of liquid fertilizer is needed to make 80 gallons of spray.

It is given that 1 cup of liquid fertilizer to make [tex]7\frac{1}{2}[/tex] gallons of spray.

On simplifying the gallons , we get

    [tex]7\frac{1}{2}=\frac{7\times2+1}{2} \\\\7\frac{1}{2}=\frac{15}{2}[/tex]

Using unitary method , we get

[tex]\frac{15}{2}[/tex] gallons of spray makes = 1 liquid fertilizer

1 gallons of spray makes =  [tex]\frac{2}{15}[/tex] liquid fertilizer

80 gallons of spray [tex]=\frac{2}{15} \times80\\[/tex]

                                [tex]=\frac{160}{15} \\\\=\frac{32}{3}[/tex]

Which can be written as [tex]10\frac{2}{3}[/tex]

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The probability of the whole batch getting selected or marked as okay is 0.9030 (most likely).

Probability is the possibility of an event occurring. We can scale the probability of an event between 0 and 1. 0 refers to an improbable event, and 1 refers to an event with the highest possibility.

Now in the given problem statement that in order to evaluate the batch of a product, a sample is selected at random. The sample will be evaluated called the acceptance sampling and if the sample turns out to be undefective, production will be marked okay.

The purpose here is to find the probability that the entire batch will be selected, and it is only possible for all the three random products that are selected to turn out to be okay.

Now we will list down the given data and then solve it,

Total products manufactured = 4500 CDs

Defective pieces = 150 CDs

Good/Undefective CDs = Total products - Defective pieces

= 4500-150

Good/Undefective CDs = 4350

Now the three samples are chosen at random;

P (first good) = 4350/4500 if not replace....

then (one less choice and one less good)

P (the second one is not defective, but it is not)

= 4350/4499

If you don't replace...

If (2 less to choose from and 2 less non-defective)

P(3rd is not defective (1st AND 2nd is not defective ))

= 4350/4498

Just multiply these 3 fractions

(4350 ( 4349 > ) (4348) ) / (4500 (4499) (4498) ) )

= 0.9030

So the probability of the whole batch to get selected or marked as okay is 0.9030 (most likely).

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Answer: -1/4

Step-by-step explanation:

(-7+3)/(7+9)

-4/16

-1/4

Answer:

(1, -2).

Step-by-step explanation:

The robot is at the point (-3, -2).

Just add 4 to the x-coordinate/

Answer: $110

Step-by-step explanation: 50+10*6=50+60=110

Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so a function's mirroring is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.

The function's reflection should be similar in size and shape to the original position.

f(x)=3x; y-axis

(consult the pictures attached below)

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The linear equation applicable for the statement is a w = 8m+3.

According to the statement

We have to find that the linear equation related to the statement.

So, For this purpose, we know that the

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

From the given information:

Bill's spelling list is 3 words long at the start of the school year. Each month, his teacher adds 8 words to the list.Let m represent the number of months since school began and w represent the total number of spelling words.

Then

Total number month when words have been added = m

Total number of words after m month = w

At starting the number list = 3

Then

The linear equation become

w = 8m+3

This is the linear equation.

So, The linear equation applicable for the statement is a w = 8m+3.

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For the absolute value equation |2 x+1|-14=9

x = 11

Given, absolute value equation is

|2 x+1|-14=9

|2 x+1|-14 + 14 = 9+14

2x + 1 = 23

2x + 1-1 = 23-1

2x = 22

x = 11

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By elimination, the solution of the system of equations, 2w + 5y = -24 and 3w - 5y = 14, is (w, y) = (-2 , -4).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in w and y, a variable should be eliminated by adding/subtracting the two equations.

Adding the two equations will eliminate the variable y.

2w + 5y = -24     (equation 1)

3w  - 5y = 14     (equation 2)

5w + 0y = -10

w = -2

Substitute the value of w to any of the two equations and solve for y.

2w + 5y = -24     (equation 1)

2(-2) + 5y = -24

5y = -24 + 4

5y = -20

y = -4

Hence, the solution of the system of equations is (w, y) = (-2 , -4).

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Answer:

11xy+2x

Step-by-step explanation:

x(11y + 2)

11y(x)+2(x)=11xy+2x

Hope this helps!

Please mark as brainliest if correct!

Answer:

[tex]11xy + 2x[/tex]

Step-by-step explanation:

Using the distributive property means that we multiply everything that is inside the brackets with everything that is outside the brackets.

For this question that means that we will multiply [tex]x[/tex] with both [tex]11y[/tex] and 2:

[tex]x(11y + 2)[/tex]

⇒ [tex]x \times 11y + x \times 2[/tex]

⇒ [tex]11xy + 2x[/tex]

Therefore [tex]x(11y + 2)[/tex] rewritten using the distributive property is [tex]11xy + 2x[/tex].

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Arithmetic progression AP is the given sequence of 3,7,11,15, ............ The common difference is found to be (d = 4).

The difference between two numerical orders in Arithmetic Progression (AP) is a constant value. Another name for it is Arithmetic Sequence.

Then we'd come across some key terms in AP, which are denoted as:

Some AP formulas are as follows:

Now, for the given sequence is   3,7,11,15, ...........

Let us suppose the first term is'a₁' = 3.

Let us suppose 'a₂' = 7 is the second term.

Let us suppose the third term is 'a₃' = 11.

Let us suppose the fourth term be 'a₄' = 15.

d = a₂ - a₁      

Substitute the values;

d = 7 - 3 = 4     ........(equation 1)

Now consider the other set;

d = a₃ - a₂    

d = 11 - 7 = 4      .......(equation 2)

As a result, both equations are equal. It means that the common difference is the same, which is (d = 4).

Therefore, the asserted sequence is discovered to be in AP, and the value of a common difference is discovered to be (d = 4).

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Answer:

12

Step-by-step explanation:

12 divided by 2 = 6

and
6 - 4 = 2

Answer:12

Step-by-step explanation:

Your welcome!

Answer:

43

Step-by-step explanation:

divide 10 3/4 by 1/4

Answer: The answer should be A.

Step-by-step explanation: 1/2 x -16 = -8

The jungle was 4.8 miles away.

So,

The formula of, Distance = Speed × Time

Therefore, the jungle was 4.8 miles away.

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The two equations that represent the candy mix are:

b + w = 40

2.25b + 3.85w =   (3.45 x 40)

In order to determine the candy mix that will be sold, two equations would be formed. These equations would be solved together, simultaneously and thus are known as simultaneous equations. The methods used to solve simultaneous equations are:

The form of the equations would be :

pound of candy bears + pounds of candy worms = total pounds

(pound of candy bears x cost of candy bears) + ( cost of candy worms x pounds of candy worms) = (total cost  of the mix per pound x total pounds)

b + w = 40

2.25b + 3.85w =   (3.45 x 40)

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Answer:

a. 3/5

b. 270 girls

c 450 students.

3 450 13350

_ x ___ = ______ = 270 =270 girls

5 1 5

The quadratic equation of the form 5x² + 4x - 20 = 0 then the values of x1 = 1.64 and x2 = -2.44.

The quadratic equation of the form ax² + bx + c = 0.

The form is called the standard form of the quadratic equation.

Let the quadratic equation be 5x² + 4x - 20 = 0

a = 5, b = 4 and c = -20

ax² + bx + c = 0

5x² + 4x - 20 = 0

The quadratic equation be

[tex]$x=\frac{-b\pm \sqrt{b^2-4\cdot \:a\left(c\right)}}{2\cdot \:a}[/tex]

a = 5, b = 4 and c = -20

substitute the value of a, b and c in the above equation, we get

[tex]$x_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:5\left(-20\right)}}{2\cdot \:5}[/tex]

simplifying the equation, we get

[tex]$x_1=\frac{-4+4\sqrt{26}}{2\cdot \:5}[/tex]

[tex]$x_2=\frac{-4-4\sqrt{26}}{2\cdot \:5}[/tex]

The values of x1 = 1.64 and x2 = -2.44

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Option 2, 8.3% p.a. compounded quarterly will provide the best return on the investment over a time period of 5 years.

Let's say you want to invest Rs 8000.

The formula for compound interest is given as:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where P is the principal amount, r is the interest rate, n is the number of times interest is applied, and t is the number of time periods elapsed.

For option 1,

P = 8000

r = 8.2% = 0.082

As the interest compounded annually.

n = 12

t = 5 years

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

[tex]A=8000( 1 + \frac{0.082}{12})^{12 \times 5}[/tex]

[tex]A=8000(1+0.00683)^{60}\\A = 8000(1.00683)^{60}\\A=8000 \times 1.5047\\[/tex]

A = Rs. 12037.74

For option 2,

8.3% compounded quarterly.

Quarterly means once three months.

There are four quarters in one year.

Therefore, n = 4 × 5 = 20

P = 8000

r = 8.3% = 0.083

t = 5

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

[tex]A=8000(1+\frac{0.083}{20})^{20 \times 5}\\[/tex]

[tex]A=8000(1+0.00415)^{100}\\A=8000(1.00415)^{100}\\A=8000 \times 1.51307\\[/tex]

A = Rs. 12104.566

Hence, option 2 will provide you with the best return on your investment.

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The value of x after solving the exponential equation ln [e^{5x-3} - 2 ] = ln [10,476] is x = 0.6.

What is the exponential function ?

An exponential function is one that has the formula f (x) = a^(x) , where x is a variable and a constant and it must be greater than 0.

It is given that exponential equation is e^{5x-3}-2=10,476.

Let's solve this to find the value of term x.

So , we will take natural log on both sides.

This meant ;

ln [e^{5x-3} - 2 ] = ln [10,476]

We know that logarithm of a natural number is 0 and ln (e^ x) = x , so let's apply this to above equation.

ln (e^(5x - 3)) - ln 2 = 0

or

5x - 3 - 0 = 0

or

5x - 3 = 0

So , let's solve this to get the value of x ,

5x = 3

x = 3 / 5

or

x = 0.6

Therefore , the value of x after solving the exponential equation ln [e^{5x-3} - 2 ] = ln [10,476] is x = 0.6.

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Answer:

m

------- <------ fraction bar means divide too

z + u

Hope this helps :)

There are 402.28 in2 of pasta in the container.

The mathematical branch is known as algebra deals with symbols and the rules governing their manipulation. These characters, which are now expressed as Latin and Greek letters, stand for variables, or quantities without set values, in elementary mathematics.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

The radius of cylinder (r) = 3.2 inches

Height of cylinder (h) = 14 inches

Height of pasta = 14 – 1.4 = 12.5 inches

Pasta in container = 22/7*(3.2)2*12.5

=402.8 in2

Hence, the container carries 402.8 in2 of pasta in it.

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Answer:

102.9 m

Step-by-step explanation:

The shortest distance from A to C would be diagonally from A to C.

This comprises:

The length of the diagonal between A and C can be calculated using Pythagoras Theorem:

[tex]\begin{aligned}c^2&=a^2+b^2\\\implies \sf AC^2 & = \sf AB^2+AD^2\\\sf AC^2 & = \sf 50^2+80^2\\\sf AC^2 & = \sf 2500+6400^2\\\sf AC^2 & = \sf 8900\\\sf AC & = \sqrt{\sf 8900}\\\sf AC & = \sf 94.33981132\;m\end{aligned}[/tex]

Subtract the diameter of the circular path from this to calculate the sum of the lengths of the straight paths.

[tex]\implies \sf 94.33981132-15=79.33981132\;m[/tex]

To calculate the length of the circular part of the path, find half the circumference of the central circle:

[tex]\begin{aligned}\implies \textsf{Half the circumference} & = \sf \dfrac{1}{2} \pi d\\& =\sf \dfrac{1}{2} \pi (15)\\& =\sf 23.5619449\;m\end{aligned}[/tex]

Therefore, the shortest distance from A to C across the park is:

[tex]\begin{aligned} \implies \textsf{Shortest distance} & = \sf 79.33981132+23.5619449\\& = \sf 102.9017562\\& = \sf 102.9\;m\;(nearest\:tenth)\end{aligned}[/tex]

Computing the sum of the first term in the arithmetic series is relatively straightforward. Just add these values ​​together. However, adding, say, the first 100 words creates more problems. Instead of manually summing all these terms, mathematicians devised an arithmetic progression formula that efficiently computes the sum of the arithmetic progression.

a1 =-6

S50 = -5150

an=?

Sn=n(a1+an)/2

So, to find an

((2*sn) /n)-a1=an

((2*-5150) /50) -(-6)=an

An=200

D=-194/49

Here the first term a=-6,

Common difference d=-3.96

We know that,

f(n)=a+(n-1)d

f(50)=-6+(50-1)(-3.96)

=-6+(-193.99)

=-199.99

We know that,

Sn=n2[2a+(n-1)d]

∴S50=502⋅[2(-6)+(50-1)(-3.96)]

=25⋅[-12+(-193.99)]

=25⋅[-205.99]

=-5149.78

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In Δ JLP, m ∠ JMP = 3x - 6, JK = 3y - 2, and LK = 5y - 8 then the value of x = 32.

In geometry, an altitude is a line that passes through two very specific points on a triangle: a triangle's vertex, or corner, and its opposite side at a right, or 90-degree, angle. The base is the opposite side. Triangles have three vertices and three opposite sides in common.

A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.

Since JM is at an altitude of ΔJLP, m ∠ JMP = 90

3x - 6 = 90

simplifying the above equation we get

3x = 96

Dividing both sides of the equation by 3, we get

x = 32

The value of x = 32.

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Answer:

6.08

Step-by-step explanation:

since 2 is lower than 5 we will use two to round it up

the number 7 will be used

making the 2 to be called 1 add it to 7 making it

8

Rounding 6.027 to the nearest hundredth gives us 6.03.

To round 6.027 to the nearest hundredth,

Since we know that,

Changing a number's digits so that it approximates a value is known as rounding.

In other words, when rounding numbers, we substitute an approximated value for the original number, which is a shorter and simpler representation of the original number. Finding the estimated value of the supplied decimal number up to 2 decimal places is known as rounding to the nearest hundredth.

we first need to identify the second digit after the decimal point, which is 2.

If this digit is less than 5, the number rounds down to 6.02.

If it is 5 or greater, the number rounds up to 6.03.

Since 7 is greater than 5, we round down to 6.03.

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When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.

When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0. In addition to being the length of the perpendicular that is drawn from the point to the x-axis, it is the value of y at the coordinates (x, y). It is, in other words, the vertical distance between the point and the x-axis.

An address that aids in locating a spot in two dimensions of space are the X and Y coordinates. Any point in the coordinate plane is denoted by the coordinates (x, y), where the x value represents the point's location in relation to the x-axis and the y value represents its position in relation to the y-axis.

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