Victor bought a pencil for $1. He also bought some notebooks for $3 each. Victor did not spend more than $13 on pencils and notebooks. Write an inequality that can be used to find n, the number of notebooks that Victor could have bought.

The amount that Cameron is paid per hour, given the number of hours he worked, is $ 18 per hour

To find the payment that Cameron got per hour, you first need to find the number of hours that he worked.

This number of hours is:

= 4 pm  - 7 am

= 1600 hrs - 0700 hours

= 9 hours

The payment per hour is therefore:

= Amount Cameron paid / Number of hours worked

= 162 / 9

= $ 18 per hour

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The rest of the question is:

How much was Cameron paid per hour worked?

The simplified trigonometric expression [tex]\sqrt{(1 - \csc^2{(y)}){(\cos^2{y} - 1)}}[/tex] is given as follows:

[tex]\sqrt{(1 - \csc^2{(y)}){(\cos^2{y} - 1)}} = \cot{y}\sin{y}[/tex]

The trigonometric expression for this problem is defined as follows:

[tex]\sqrt{(1 - \csc^2{(y)}){(\cos^2{y} - 1)}}[/tex]

Then trigonometric identities are used to simplify the radicands of the rational expression.

The identity that uses the cossecant squared is given as follows:

csc²(y) = 1 + cot²(y).

Hence:

1 - csc²(y) = -cot²(y).

The identity that uses the cosine squared is given as follows:

sin²(y) + cos²(y) = 1.

Hence:

cos²(y) - 1 = -sin²(y).

Then the expression can be simplified as follows:

[tex]\sqrt{(1 - \csc^2{(y)}){\cos^2{y} - 1}} = \sqrt{-cot^2{y} \times -\sin^2{y}}[/tex]

As the product of two negative numbers is positive, we have that:

[tex]\sqrt{cot^2{y}sin^2{y}}

Taking the square root of each squared term, the simplified expression is given as follows:

cot(y)sin(y).

The problem asks for the simplified expression.

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Answer:

a. Let x be the speed of the boat in miles per hour and y be the speed of the current in miles per hour. Since the boat traveled upstream, the speed of the current is added to the speed of the boat. Therefore, the equation for the trip upstream is:

distance = (x + y) * time

10 = (x + y) * 5

b. For the return trip, the speed of the current is subtracted from the speed of the boat. Therefore, the equation for the return trip is:

distance = (x - y) * (time/2)

10 = (x - y) * (5/2)

c. To find the speed of the boat and the speed of the current, we can use the method of elimination. From the first equation, we have:

10 = 5x + 5y

From the second equation, we have:

10 = 2.5x - 2.5y

Now we can use the elimination method by multiplying the first equation by 2 and then subtracting the second equation from it.

20 = 10x + 10y

20 = 5x - 5y

so we have

0 = 5x + 5y - 5x + 5y

0 = 10y

The equation becomes impossible to solve as we can't divide by 0.

As we know that the speed of the boat and the speed of the current are non-zero numbers, we can't find the exact speed of the boat and the current. We can conclude that the information given is not sufficient to find the exact speed of the boat and the current.

Step-by-step explanation:

Answer:First, we can simplify the equation a^2 = 3a + 1 by subtracting 3a and 1 from both sides, to get:

a^2 - 3a - 1 = 0

Now we can factor the left side:

(a-1)(a+1) = 0

This equation tells us that either a-1 = 0 or a+1 = 0. So, a = 1 or a = -1.

Next, we can substitute these values into the expression (a+1/a)^2

For a = 1, (1+1/1)^2 = 2^2 = 4

For a = -1, (-1+1/(-1))^2 = 0^2 = 0

So, the value of (a+1/a)^2 is 4 when a = 1, and 0 when a = -1

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

         Factorize 768

768 = 4 * 4 * 4 * 4 * 3

For every four times of a constant or variable, take one constant or variable outside the fourth root.

[tex]\sqrt[4]{768x^8y^5}=\sqrt[4]{4*4*4*4*3 * (x^2)^4 * y^4 * y}[/tex]

                [tex]=4x^2y\sqrt[4]{3y}[/tex]

The prime polynomial in this problem is defined as follows:

D. 3x² + x - 6x + 3

A prime polynomial is a polynomial that cannot be reduced, that is, the polynomial cannot be factored.

The reduced forms of each polynomial are given as follows:

The first polynomial can be factored as follows:

x^4 - x² + 3x² - 3

x²(x² - 1) + 3(x² - 1)

(x² + 3)(x² - 1).

It can be factored, hence it is not prime.

The second polynomial is factored as follows:

x^4 - 3x² - x² + 3

x^4 - x² - 3x² + 3

x²(x² - 1) - 3(x² - 1)

(x² - 3)(x² - 1).

It can be factored, hence it is not prime.

The third polynomial is factored as follows:

3x² + x - 6x - 2

3x² - 6x + x - 2

3x(x - 2) + x - 2

(x - 2)(3x + 1)

It can be factored, hence it is not prime.

The fourth polynomial cannot be factored, hence it is prime.

3x² + x - 6x + 3

3x² + 6x + x + 3

3x(x + 2) + x + 3.

x + 2 and x + 3 cannot be factored.

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x = 3y perendicular to l

y = -3x parallel to l

y = 3x + 2 neither

x -3y = -6 perpendicular to l

6y = 2x + 10 perpendicular to l

A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks.

One approach for determining a line's slope from a graph is to use the formula immediately after knowing the coordinates of two points that are on the line. Let's assume that the coordinate values for the two spots are unknown. Therefore, we also have another way to determine the slope of the line. This approach entails attempting to determine the tangent of the angle formed by the line and the x-axis.

The line is

y = -3x -1

slope is -3 by slope intercept form

The line x = 3y

or y = (1/3)*x

slope is 1/3

we know for a line perpendicular to a given line slope should be -1/m so the slope will be  (1/3)

so, x = 3y  is perpendicular

y = -3x have slope -3 so it is parallel

y = 3x + 2  slope is 3 so neither

x - 3y = -6

or , y = (1/3)*x + 2 , so slope is (1/3) so perpendicular to line

And

6y = 2x + 10

here slope is 1/3 so perpendicular to line.

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If a car radiator needs a 40% antifreeze solution the radiator now holds 49% of a 30% solution. The number of  liters that should be drained and replaced with 100% antifreeze to get the desired strength is 7 liters.

Let x represent the number of liters that should be drained

So, Let solve for x

x+.30(49-x)=.40× 49

x=14.7-.30x=19.6

.7x=19.6 - 14.7

.7x=4.9

x=4.9/.7

x = 7 liters need to be drained & filled with 100% antifreeze.

Therefore the number of liters is 7 liters.

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Answer:

Step-by-step explanation:

24

Answer:

--------------------------------------

As per table we see:

To find the y-intercept we add 2 to the value of y = - 3 when x = 1, it will represent y = - 1 at x = 0.

The slope-intercept form is:

After plugging in the values of m and b the line becomes :

Answer:

$9 left

Step-by-step explanation:

1.50 x 2 = $3

1.50 x 2 = $3

2.50 x 2 = $5

5 + 3 + 3 = $11

$20 - $11 = $9

Answer:

Step-by-step explanation:

1.50+1.50+3

1.50+1.50+3

2.50+2.50= 5

5 + 3 + 3 = 11

20 - 11 = 9

the space between  [tex]3x-2\ge -5 : $x \geq-1$[/tex] the time between

[tex]2x+5\le 17 : $x \leq 6$[/tex] . When two simple inequalities are combined, the result is a compound inequality.

Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and." When a number resolves both inequalities, it also resolves the compound inequality. Compound inequality can come in two different forms. Both congruence and disjunction issues are at play.

Occasionally, these compound inequality formulas will be represented as two simple inequality formulas that have been separated by the words AND or OR. If there are multiple "and/or" compound inequalities, start by resolving each one separately. It is an inequality when two simple inequalities are combined to form it. The two expressions that make up an equation or an inequality are connected in a mathematical statement.

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Answer:

(125, -312500)

C(x) = -312500

Step-by-step explanation:

use this equation into a graphing calculator and use the minimum function

Answer:

A = $400, B = $300, C = $240

Step-by-step explanation:

The ratio will be [tex]\frac{20}{60}:\frac{15}{60}:\frac{12}{60}[/tex], that means the total of them is (20 + 15 + 12 = 47).

Divide $940 by 47 to find the value of 1 unit [tex]\frac{940}{47}=20[/tex]

A = 20 × 20 = $400

B = 20 × 15 = $300

C = 20 × 12 = $240

The mixture must be heated an amount of 23 °F to reach a temperature of 132 °F.

Temperature is the measure of how "hot" a system is. Physically speaking, temperature is closely related to atomic and molecular motion within a system. In this problem we find a mixture that must be at a certain temperature, higher than its real one.

Therefore, the amount required to increase the temperature of the mixture is defined by following subtraction:

ΔT = R - r

Where:

If we know that r = 109 °F and R = 132 °F, then the temperature difference is:

ΔT = 132 °F - 109 °F

ΔT = 23 °F

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The amount that would be covered by the Insurance Plan would be and the amount that is billed to the patient is  $ 9. 75

The amount that would be covered by the insurance plan in a 85 / 15 coinsurance plan is 85 % of the bill. The amount to be covered by the insurance plan is:

= 85% x 65

= $ 55. 25

The amount billed to the patient is:

= Total bill - covered by insurance plan

= 65 - 55 .25

= $ 9. 75

In conclusion, the amount that would be covered by the insurance plan is $ 55. 25 and the amount to be billed to the patient to be paid by them is $ 9. 75.

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The rate of interest is given by the equation R = 3.5 %

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the rate of interest be represented as R

Now , the simple interest I = $ 175

The principal amount invested P = $ 2,500

The time period T = 2 years

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )

Substituting the values in the equation , we get

Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )

Rate of Interest R = 17500 / 5000

Rate of Interest R = 3.5 %

Hence , the interest rate is 3.5 %

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The average speed of Apolo Ohno, in the sprint in the Winter Olympics in 2006, given the time taken to complete the course, was 11. 92 m /s

A body's average speed is the mean value of its speed for a certain time period. The average speed formula is necessary because a moving body's speed vary over time instead than remaining constant. Even though the speed changes, we can still use the total time and total distance numbers, and with the help of the average speed calculation, we can determine a single value that represents the entirety of the motion.

Given the distance that Apolo Ohno had to sprint and the time he completed the course in, his average speed in the event was :

= 500 m / 41. 935 s

= 11. 92 m /s

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Answer:

y = 2x -2

Step-by-step explanation:

y = mx + b

We need the slope (m) and the y-intercept (b) to write the eqation.

The slope is the change in y over the change in x.  We can see from the table that the y is changing by 2 as the x changes by 1

So the slope is 2/1 which is the same as 2

The slope (m) is 2.

The y-intercept is the place where the line crosses the y axis.  It is at the point (0,b).  When x is zero, what is y?  If we follow the patter and move to the number before x is 1, we get x = 0.  That means that we have to move back 2 units of the y's.  That would be -2.  So the y-intercept is the point (0,-2).

The y-intercept (b) is -2

y = 2x - 2

Answer:

y = - [tex]\frac{1}{2}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mc + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x + 6 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes , then

slope of parallel line = - [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of parallel line

Answer: I believe it is

4 < x < 6

10 < x < 16

If a textbook store sold a combined total of 447 sociology and math textbooks in a week. The number of  textbooks of each type  that were sold is: 195 Math textbooks, 138  Sociology textbooks.

Let x represent the number of math textbooks

Let y represent the number of sociology

Altogether bookseller sold 447 math and sociology textbooks

Hence,

x + y = 447

Since the number of sociology textbooks sold was 57 less than the number of math books sold.

So:

y = x - 57

Substitute for y in the equation

x + y = 447

x + (x - 57) = 447

2x - 57 = 447

Combine like terms

2x = 447 -57

2x = 390

Divide both side by 2x

x = 390/2

x = 195 (Math textbooks)

y = x - 57

y = 195 -57

y = 138 ( Sociology textbooks)

Therefore 195 and 138 textbooks were sold.

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The values of g(g(4)) = 0 and f(f(3)) = - 3.

A portion of the right cone known as a parabola is one that runs parallel to the generating line on one side of the iconic figure. The parabola is likewise a quadratic connection, much like the circle, however, unlike the circle, either 'A' or 'B' will be squared, but never both.

Here we have

Equation of parabola f(x) = x² - 2x - 3 and line g(x) = x - 2

Here we need to find g(g(4)) and f(f(3))

To find g(g(4)) take x = 4

g(4) = 4 - 2 = 2

=> g(g(4)) = g(2) = 2 - 2 = 0

Therefore, g(g(4)) = 0  

To find f(f(3)) take x = 3

f(3) =  3² - 2(3) - 3 = 9 - 9 = 0

f(f(3)) =  0² - 2(0) - 3 = - 3

Therefore,

The values of g(g(4)) = 0 and f(f(3)) = - 3.

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The square root of the numbers are 2. 45, 2. 65, 2. 82, 3 and 3. 16 respectively.

The square root of a number is described as the factor that when multiply by itself would give the original

It is represented with the symbol, "√".

To determine the square root of a number is to find the opposite of the square of that same number.

It is also described as the number having the value of its power or exponent as 1/2

From the information given, we have to determine the square root of the numbers,  we have;

a. √6

The square root of the number is 2. 45

b. √7

The square root of the number is 2. 65

c. The square root of 8

√8 = 2. 82

c. The square root of 9

√9 = 3

d. The square root of 10

√10 = 3. 16

Hence, the square root is the opposite of squaring the number

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Answer:

Step-by-step explanation:

The area of the new triangle g’h’i’ is 9.

The area of a triangle is a measure of the size of the triangle, calculated as the amount of space enclosed by its three sides. It can be calculated using the following formula:

Area = (base x height) / 2

where base is the length of one side of the triangle, and height is the perpendicular distance from the base to the opposite vertex.

If a triangle is rotated 180 degrees about the origin, its coordinates will change signs. If it is then dilated by a factor of 3, its coordinates will be multiplied by 3. The new triangle g'h'i' will have the following coordinates: g' (-3,0), h' (0,3), and i' (0,-3).

The height of the new triangle will be the absolute value of the difference between its y-coordinates: h = |3 - (-3)| = 6. The base of the triangle will be the absolute value of the difference between its x-coordinates: b = |-3 - 0| = 3.

Therefore, the area of the new triangle g'h'i' is: A = (1/2)bh = (1/2)(3)(6) = 9.

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Answer:

1.806 (to the nearest thousandth)

Step-by-step explanation:

1.806 (to the nearest thousandth)

The number 1.80642 would round down to 1.806

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  1.80642 to the nearest hundredth,

We can see that the 1.80642 is below 2 so it goes down, and it rounds down to 1.80642 instead of, 14.62 then that would round up to the decimal is higher than 1.

1.80642 rounded to the nearest thousandth is 1.806.

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Verdadero. Cuando hay una potencia de una potencia, se conserva la base y los exponentes se multiplican.

Para calcular la potencia de una potencia, se puede conservar la base y multiplicar los exponentes. Esto se basa en la propiedad matemática de la potenciación que establece que (a^b)^c = a^(b*c), donde a es la base, b es el primer exponente y c es el segundo exponente.

Por ejemplo, considere (2³)⁴. La base es 2 y el primer exponente es 3 y el segundo exponente es 4. El resultado sería 2^(3*4) = 2¹². Esto significa que la expresión original (2³)⁴ es igual a 2 elevado a la potencia de 12.

En general, cuando se tiene una potencia de una potencia, el resultado se obtiene conservando la base y multiplicando los exponentes. Esto permite simplificar la expresión y encontrar el resultado de manera más fácil.

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The correct statements regarding the linear function G(t) = 10 - 2t are given as follows:

Initially, the tank has 10 gallons of gasoline.

The rate of consumption is of 2 gallons per hour.

The slope of G(t) represents the fuel consumption of the vehicle.

The t-intercept represents the time it takes for the vehicle to run out of gas.

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

The linear function is defined as follows:

G(t) = 10 - 2t.

In which the variables are:

G(t) is the amount of gasoline that the car has after t hours.

t is the time in hours.

The slope and the intercept are presented as follows:

Slope of -2: 2 gallons are consumed each hour.

Intercept of 10: The initial fuel in the car is of 10 gallons.

The t-intercept is:

10 - 2t = 0

2t = 10

t = 5.

Which is the time it takes for the car to run out of fuel.

Missing Information

The options are given by the image shown at the end of the answer.

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The amount of the discount, in dollars and cents is $14.77

Total amount paid for the ticket = $32

Percentage discount = 30% of x

Percentage processing fee = 5%

Total amount paid = x - (30% of x) + 5% of x

32 = x - 0.3x + 0.05x

32 = 0.65x

divide both sides by 0.65

x = 32/0.65

x = 49.23076923076923

Approximately,

x = $49.23

Therefore,

Percentage discount = 30% of x

= 0.3 × $49.23

= $14.769

Approximately,

$14.77

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