A bank Teller's annual salary will increase by 12% next year to an annual salary of
$48,000. What is the teller's annual salary now?

The algebraic equation of the verbal statement is (x + 2) / 5 = 8 and the value of x is 38.

Algebraic Equation

An algebraic equation means the statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.

Given,

The quotient of two more than a number and five is eight.

Here we  need to translate the given verbal statement into an algebraic expression and solve it.

The quotient of two more than a number and five is eight.

Let, the number be x.

According to the question, the equation is

=> (x + 2) / 5 =8

=> x + 2 = 8 x 5

=> x + 2 = 40

=> x = 40 - 2

=> x = 38

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The required function is P(t)=50000 + 5000t.

In this problem we need to form the function of the population in a town.

Here it is given that the initial population of the town is 50000.

the rate at which the population increases is 5000 per year.

So, the increase for the first year will be 5000. And the population will be 55000.

Then again for the next year the growth will be 5000 and the population will be 50000 + (5000×2)

        = 60000

So we can see clearly that the population is varying with time and we can write the function as P(t)=50000 + 5000t where t is the time in years.

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Answer:

x⅔

Step-by-step explanation:

1. we understand the concept that x÷x is a subtraction as an instance, x³/x² = x¹ so we can apply this knowledge in this question

2. x⅚ / x⅙ --> x⅚-⅙

--> x^4/6 [simplify this]

--> x^4/6 [ divide 2 at the numerator and also the denominator]

--> x⅔

Last but not least, you got your 2 points

Answer:

Step-by-step explanation:

If she made 60$ she only needs 140$ more to get to 200$

The slope of the line as shown in the diagram attached below = rise/run = 3/5.

The rise of a line over the run of a line would give us the slope of a line on a coordinate plane.

With the given line in the diagram, the image attached below shows the rise as represented by a red line while the run is represented by the blue line.

Therefore, we have:

Run = 10 units

Rise = 6 units

Slope (m) of the line = rise/run = 6/10

Simplify

Slope (m) of the line =  3/5

Therefore, the slope of the line as shown in the diagram attached below = rise/run = 3/5.

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Answer: $9.30

Step-by-step explanation:

7.44/4 = 1.86

1.89 x 5 = $9.30

He have to pay $3.25.

Let the number of miles traveled by a driver be x

The toll paid by the driver is then represented as y. (in dollar)

Linear equation : an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.

Since there is a linear relation between the two, we can assume the equation can be written as:

y = mx + c

From the given data, we get

0.24 = m(0) + c

c = 0.25

Using the second point:

1 = m(1) + 0.25

m = 1 − 0.25 = 0.75

Hence, the equation is y = 0.75x + 0.25.

If  x = 4, then:

y = 0.75 × 4 + 0.25

y = 5.50

Hence, He have to pay $3.25.

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Equation are defined by equating two or more expressions. The solution to the system of equation is (k, (1+5k)/2)

System of equations are equations are equations that contains several variables and expression.

Given the system of equations

5x - 2y = -1

-15x + 6y = 3

Divide equation 2 through by -3 to have:

-15x/-3 + 6y/-3 = 3/-3

5x  - 2y = -1

You can see that both equations are equal. Let x = k so that;

5k - 2y = -1

-2y = -1 - 5k

2y = 1 + 5k

y = (1+5k)/2

Hence the solution to the system of equation is (k, (1+5k)/2)

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Answer:

6 miles per hour!

Step-by-step explanation:

(b) We have 13 possibilities that a five-card hand will contain four of a kind.

(c) We have 12 possibilities that a five-card hand will contain a full house.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility.

Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half (which could also be written as 0.5)

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The shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.

Given that shape 1 and shape 2 are congruent pentagons.

We are required to choose the option which is correct according to the given statemment that shape 1 and shape 2 are congruent pentagons.

Pentagons are the shape which have 5 sides and 5 angles.

Two shapes are congruent if they are copy of each other means all the corresponding sides are equal to each other.

The shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.

Hence the shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.

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Answer:

a. A = 647

   P = 120

b. A = 192

   P = 70

Step-by-step explanation:

a. A = (16 x 12) + (13 x 35) = 192 + 455 = 647

   P = 16 + 12 + 19 + 13 + 35 + 25 = 120

b. A = (12 x 8) + (8 x 12) = 96 + 96 = 192

   P = 12 + 8 + 7 + 8 + 12 + 8 + 7 + 8 = 70

probability of picking a yellow ball: 10/20 (1/2)

probability of picking a red ball: 6/20 (3/10)

1/2 times 3/10 =

3/20

x=x

Step-by-step explanation:

finding by mathematical operation and distribution law over multiplication added with subtraction is the formula now it might be easy for you

The solution of the simultaneous equations are x = 2, 3 and y = 3,9.

In mathematics; a set of simultaneous equations, also known as a system of equations or an equation system, it is a finite set of equations for which common solutions are sought.

WE have given simultaneous equations as;

y = x^2    ...(i)

y = x + 6  .....(ii)

Now Equating (i) and (ii) we get,

x^2 = x + 6

or, x^2 - x - 6 = 0

Then Solving we get;

x^2 - 3x - 2x - 6 = 0

x(x - 3) -2(x - 3) = 0

(x - 2)(x - 3) = 0

So, x = 2, 3

Now Putting x = 2, 3 in equation (i) we get;

y = 2^2

y = 4

and,

y = 3^2

y = 9

Thus, y = 3,9

Hence the solution of the simultaneous equations are x = 2, 3 and y = 3,9.

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It take 8.205 minutes to fill a queen sized mattress.

'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Given dimensions:

Twin sized air mattress (39 by 8.75 by 75 inches).

Queen sized mattress (60 by 8.75 by 80 inches)

Now, Volume of twin sized mattress

=39* 8.75* 75

= 25593.35 cubic inch

Volume of queen sized mattress,

=60* 8.75* 80

= 42000 cubic inch

as, To fill 25593.35 cubic inch it takes 5  minutes

so, to fill 1 cubic inch = 5/25593.35

and, So to fill 42000 cubic inch it will take = 42000* 5/25593.35

=8.205 minutes

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Answer:

7: #3. 8: #2

Step-by-step explanation:

in the first question the format is simply (x, y) and because it is a translation, we are basically just moving the point by these numbers, with this information, it is simply moving x to the left(negative) 8 times, and y(up/positive) 4 times. The next question is simply moving the point across the x axis by the same amount that it is above the x axis, so it would be one down from the x-axis' bold line, or in this case moved 2 y-units down. Hope this helps mate :)

The price per yard of the ribbon is $6.69

First, we will need to convert  9 foot to yards as shown;

9 foot = 3 yards

This shows that a 3 yard piece of ribbon costs $20.07, the price per yard is expressed as;

Price per yard = 20.07/Total yard

Price per yard = 20.07/3

Price per yard = 6.69

Hence the price per yard of the ribbon is $6.69

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the exponential form of the complex number \[ e^{17\pi i/60} e^{27\pi i/60} e^{37\pi i /60} e^{47 \pi i /60} e^{57 \pi i/60}\]

= (2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]

[tex]e^1^7^\pi ^i/^6^0[/tex] + [tex]e^2^7^\pi^ i^/^6^0[/tex]+⋯+[tex]e^5^7^\pi ^i^/^6^0[/tex]

=[tex]e^1^7^\pi ^i^/^6^0[/tex](1+[tex]e^\pi^ i^/^6[/tex]+....+[tex]e^4^\pi ^i^/^6[/tex])

=[tex]e^1^7^\pi ^i^/^6^0[/tex] (1−[tex]e^5^\pi ^i^/^6[/tex]) ÷ (1−[tex]e^\pi ^i^/^6[/tex])

=[tex]e^1^7^\pi ^i/^6^0[/tex] ([tex]\frac{1}{2}[/tex](2+[tex]\sqrt{3}[/tex]) + [tex]\frac{1}{2}[/tex](3+2[tex]\sqrt{3}[/tex])i)

=(2+[tex]\sqrt{3}[/tex])e17πi/60(12+([tex]\sqrt{3}[/tex]/ [tex]2[/tex]) i )

=(2+[tex]\sqrt{3}[/tex])[tex]e^1^7^\pi ^i^/^6^0[/tex] [tex]e^\pi ^i^/^3[/tex]

=(2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]

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Answer: I think ok not sure but yet positive but i think it is  y= -7

Step-by-step explanation:

Probability that no zebras collide is 0.25

The zebras are represented as z1, z2 and z3.

Z1 to B, Z2 to C, and Z3 to A come first [tex]= (\frac{1}{2})^3[/tex]

Following that, z1 to C, z2 to A, and z3 to B = [tex](\frac{1}{2})^3[/tex]

Consequently, the likelihood of no collision is 2×1/8 = 0.25.

Discrete and continuous probability distributions are the two main categories in which probability distributions fall. There are numerous varieties of probability distributions within each category.

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The value of x that makes the lines m and n to be parallel lines is 45 degrees

The figure that completes the question is added as an attachment

From the figure, we have the following angles

Angle = x and 3x

The angles are interior of parallel lines

This means that they add up to 180 degrees

So, we have the following equation

Angle 1 + Angle 2 = 180 degrees

Substitute the known values in the above equation

So, we have

x + 3x = 180

Evaluate the like terms in the above equation

So, we have:

4x = 180

Divide both sides of the above equation by 4

So, we have

x = 45

Hence, the value of x that makes the lines m and n to be parallel lines is 45 degrees

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Answer:

41

Step-by-step explanation:

5y+x

Evaluate the expression

Let x=6 and y=7

5*7 +6

Multiply first

35 +6

Then add

41

Answer:

it 41

Step-by-step explanation:5(7)+6=41

Answer:

31.5

Because if you Subtract 21 from 84 you get 63
then if you divide 63 by 2 you get 31.5 so your Answer would be 31.5.

x(x – 5) = 176 is the correct equation to find the greater integer.

As the question mentions, the greater integer is x. So, the smaller integer will be (x - 5). Also, we are informed that their product is 176.

Now, representing the given information as mathematical expression -

x(x – 5) = 176

On further multiplication on Left Hand Side, we get the equation -

x² - 5x = 176

Rewriting the equation -

x² - 5x - 176 = 0

Further solving the equation to validate it.

x² - 16x + 11x - 176 = 0

x (x - 16) + 11 (x - 16) = 0

(x - 16) (x + 11) = 0

x = 16, -11

As stated, the integers are positive. So, the value of x and hence greater integer is 16.

Value of small integer = 16 - 5

Value of small integer = 11

So, the two integers are 16 and 11. Their product is 176 hence, our formed equation is correct.

Therefore, the equation that can be used to find x is : x(x – 5) = 176.

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The complete question is -

Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of x, the greater integer?

x² + 5 = 176

x(x + 5) = 176

x(x – 5) = 176

x² – 5 = 176

$26.8 is the total cost and Chicken Fajita Taco is the most

expensive meal .

What in mathematics is a linear equation?

Hamburger + Bacon Cheeseburger  + Chicken Fajita Taco + French Fries, Small + French Fries, Large + Onion Rings + Cole Slaw + Soft Drink, Small + Soft Drink, Large + Milkshake + Juice

=  $3.25 + $4.75 +  $3.50 +  $1.55 + $1.90 + $2.40 + $1.45 +  $1.30 + $1.65 +  $3.25 + $1.80

= $26.8

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Answer: D $30

Step-by-step explanation:

$12.79 rounds to $13

$2.33 round to $2

$14.65 rounds to $15

Add the estimates: 13+2+15= $30

The value of csc x=-13/5.

Given that the sin x=-5/13 and x∈[3π/2 , 2π).

A trigonometric function is a real function that relates the angle of a right triangle to the ratio of the lengths of the two sides. The basic functions are sin, cos, tan, cot, sec, csc.

The given function is sin x=-5/13.

As we all know that sin x=1/csc x or csc x=1/sin x.

As it is given that x∈[3π/2 , 2π) that means x lies in fourth quadrant and in fourth quadrant sin and csc is negative in it.

So, we will apply this identity csc x=1/sin x, we get

csc x=1/(-5/13)

csc x=-13/5

And it also lies in x∈[3π/2 , 2π).

Hence, the value of csc x when sin x=-5/13 and x∈[3π/2 , 2π) is csc x=-13/5.

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