Kendra is buying bottled water for a class trip.She has 16 bottles left over from the last trip.She buys bottles by the case to get a good price. Each case holds 24 bottles. How many cases will she have to buy if she wants to have a total of 160 bottles of water?

When the scale factor is between 0 and 1, a dilation is considered a reduction.

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Answer: e = 7.5*h

Step-by-step explanation: The relationship between Lisa's earnings, e, and the number of hours, h, that she works is proportional. This means that the ratio of e to h is constant. One way to represent this relationship is through an equation of the form:

e = k*h

where k is a constant of proportionality. In this case, we know that Lisa earns $30 for 4 hours of babysitting, so we can use this information to find the value of k:

30 = k*4

k = 30/4 = 7.5

So the equation that represents Lisa's earnings, e, relative to the number of hours, h, that she works is:

e = 7.5*h

Where e is the earnings and h is the number of hours and 7.5 is the constant of proportionality.

Alternatively, you can write the equation as e = 30/4 * h = 7.5 * h

This equation tells us that for every hour that Lisa babysits, she earns $7.5.

Answer:

7.5

Step-by-step explanation:

because I'm smart like that!

Answer:

(2x-5)^3

Step-by-step explanation:

(((8 • (x3)) -  (22•3•5x2)) +  150x) -  125

 ((23x3 -  (22•3•5x2)) +  150x) -  125

3.1    8x3-60x2+150x-125  is not a perfect cube

Factoring:  8x3-60x2+150x-125

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  150x-125

Group 2:  -60x2+8x3

Pull out from each group separately :

Group 1:   (6x-5) • (25)

Group 2:   (2x-15) • (4x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

The exponential function cannot be found.

To find an exponential function, f(x)=[tex]a^{x}[/tex], containing the point, set f(x) in the function to the y value 3 of the point, and set x to the x value 0 of the point. 3 = [tex]a^{0}[/tex]

Solve the equation for a.

Let's rewrite the equation,

[tex]a^{0}[/tex] = 3

Anything with 0 in power is 1

1 = 3

As, 1 ≠ 3

There are no solution.

Since there is no real solution, the exponential function cannot be found.

Hence, the exponential function cannot be found.

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The buses will pass each other at 12:37:30 PM

To find the time when the two buses will meet, you need to find the time that Bus 2 will take to travel to the point where the buses will meet, and the time that Bus 1 will take to travel the same distance.

You can find the time that Bus 2 will take to travel to the point where the buses will meet by dividing the distance (550 miles) by the speed of Bus 2 (50 mph), which is 11 hours.

Then you can find the time that Bus 1 will take to travel the same distance by dividing the distance (550 miles) by the speed of Bus 1 (80 mph), which is 6.875 hours (or 6 hours and 52.5 minutes).

Now, you can subtract the time that Bus 2 takes to reach the point of intersection from the time that Bus 1 takes to reach the same point.

6.875 hours (or 6 hours and 52.5 minutes) - 11 hours = -4.125 hours (or -4 hours and 7.5 minutes)

Since Bus 2 leaves Harare at 8:30AM, you can subtract -4.125 hours from 8:30AM to find the time the buses will meet.

8:30AM - -4.125 hours = 12:37:30 PM

So the buses will pass each other at 12:37:30 PM

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The  equation of the line is y =  x + 6.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

here, we have,

the equation of a line in slope- intercept form is

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

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

= 1/-m  =1/ 4  

then,

y =  x/4 + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

hence, y =  x/4 + 6 ← equation of perpendicular line.

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On the 5th day, renting a mid-sized car from either Eliana's Rentals or Arcadia Rent-a-Car would cost the customer $90.

What is the linear equation in one variable?

A linear equation in one variable is an equation in which the highest power of the variable is 1. A linear equation in one variable can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear equation in one variable is a straight line.

In the given problem, the rental cost of a mid-sized car from Eliana's Rentals can be represented by the equation:

y = 60 + 6x (where y is the total cost and x is the number of days)

The rental cost of a mid-sized car from Arcadia Rent-a-Car can be represented by the equation:

y = 30 + 12x (where y is the total cost and x is the number of days)

At some point, renting from either one of the companies would cost the customer the same amount, so we can set both equations equal to each other and solve for x:

60 + 6x = 30 + 12x

Solving for x:

30 = 6x

x = 5

Hence, on the 5th day, renting a mid-sized car from either Eliana's Rentals or Arcadia Rent-a-Car would cost the customer $90.

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The true statement is that C. The probability of randomly selecting an apple from Basket M is greater than the probability of randomly selecting an apple from Basket L.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

Basket L contains 7 pieces of fruit. Basket M contains 14 pieces of fruit. The probability of picking from M will be:

= 14/21

= 2/3

The probability of picking from L will be:

= 7/21

= 1/3

The correct option is C.

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The solution of the given equations 3x + 2y = 11 , 2x + 3y = 4 is given by :

option a. ( 5, -2 ).

As given in the question,

Given equations are written as :

3x + 2y = 11 ___(1)

2x + 3y = 4 ___(2)

Solve the given system of equations using the method of elimination we get,

Multiply (1) by 3 and (2) by 2 to eliminate y we have,

9x + 6y = 33

4x + 6y = 8

5x = 25

⇒ x = 5

Substitute the value x in (1) to get the value of y we have,

3(5) + 2y = 11

⇒2y = 11 - 15

⇒y = -4/2

⇒ y = -2

Therefore, the solution of the given equations  is given by :

option a. ( x ,y ) = (5,-2).

The above question is incomplete , the complete question is :

Which of the following is a solution of the equation ?

3x + 2y = 11

2x + 3y = 4.

a. ( 5, -2 )            b. ( 5, 2)          c. ( 2,5)         d. ( -2 ,-5)

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By using the box method, the terms of the equation should be distributed and simplified as follows;

         3x            x²

1         3x            x²

6x      18x²         6x³

In Mathematics, the distributive property of multiplication states that when the sum of two or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Next, we would multiply both sides of the equation together in order to open the bracket as follows;

(3x + x²)(1 + 6x)

3x(1) + 3x(6x) + x²(1) + x²(6x)

3x + 18x² + x² + 6x³

By combining like terms and rearranging the equations, we have:

6x³ + 19x² + 3x.

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Answer: to sum up

Step-by-step explanation:

If Ahmad works at a constant rate, he will take 90 minutes in finishing his exam, and he will finish it at around 1:15 pm.

We know that Ahmad answers at a constant rate, and he takes around 1.5 minutes to answer each answer.

The total time that it will take him to answer the 60 questions is equal to the number of questions times the time that it took him to answer each one, then the total time is:

T = (1.5 min)*60  = 90 minutes

So it will take him an hour and a half.

And e know that the exam starts at 11:45 am

After one hour, it will be:

0:45 pm

And after 30 minutes, it will be:

1:15 pm

Ahmad will finish his exam at 1:15 pm.

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Step-by-step explanation:

[tex]4[/tex]

[tex]4 {x}^{2} - 3x {y}^{2} [/tex]

The triangle formed when the sides are 5, 12, 13 is a right-angled triangle. The Pythagorean theorem can be used to verify this.

From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angled triangle.

Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. The equation can then be expressed as,

CA² = AB² + BC²

Now, let us check this rule for the above given sides of the triangle.

Longest side² = Sum of squares of other two sides

13² = 12² + 5²

169 = 144 + 25

169 = 169

Thus, the sides 5 cm, 12 cm and 13 cm can form a right-angled triangle.

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Therefore , the solution of the given problem of function comes out to  be f(x) =54 .

A mathematical formula known as a cost function is used to visualise how production costs will vary depending on the output level. In other words, given a specific quantity produced, it calculates the total cost of production.

Here,

f(x) =  -6x + 90

=> x =6

=>  f(x) = -6*6 + 90

=> f(x) = -36 + 90

=> f(x) = 54

thus , f(x) = 54 is the correct solution for finding the left amount of money

Therefore , the solution of the given problem of function comes out to  be f(x) =54 .

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Answer:

c 1

A F E 2

Step-by-step explanation:

The area of the preceding parallelograms is equal to 125 cm sq., according to the answer to the given question.

A simple quadrilateral with different pairs of parallel sides is known as a parallelogram in Euclidean geometry. Each sets of opposite ends are parallel and equal in a particular type of rectangle known as a parallelogram. Parallelograms come in four varieties, three of which are exclusive. The four different shapes are rhombuses, parallelograms, squares, and rectangles. A quadrilateral is a parallelogram if it has two sets of side lengths. In a quadrilateral, the cross-sectional lengths of the opposed angles and angles are equal. The inner angles add additional angles to the horizontal line on the same side. There are 360 internal degrees in all.

Here,

it is:

B = 25 cm

with H = 5 cm.

Parallelograms' surface area is A = B X H = 25 X 5 = 125 cm square.

The area of the preceding parallelograms is equal to 125 cm sq., according to the answer to the given question.

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The y-intercept of y = 5x − 10 is -10.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, c, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Now, if we equate the standard slope-intercept form of the equation with the given equation, we get

y = mx + c

y = 5x - 10

m = 5 and c = -10

As we know the c is the y-intercept which is equal to -10.

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This problem can be represented with color counters/tiles. In this case, the red counters represent positive numbers and the black ones represent negative numbers.

One technique to introduce the idea of adding and subtracting numbers is through the use of integer tiles. When working on the kind of issue that many students find more challenging—problems like -4 + -5—this paradigm might be helpful.

One positive counter and one negative counter/tile equal zero because 1+(−1)=0. Draw a line through the counters that equals zero.

The remaining counters represent the answer. Therefore, 4+(−2)=2. The answer is the difference between 4 and 2. The answer takes on the sign of the larger number. In this case, the four has a positive value and it is greater than 2.

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solving factor by grouping, The final factored form of the expression is n(n + 3) - 10.

A factor is a number that divides into another number exactly with no remainder. For example, the factors of 8 are 1, 2, 4, and 8.

Factor by grouping is a method of factoring polynomials, which is used to find the common factors in an expression. The idea is to group the terms of the polynomial in such a way that the common factors can be factored out of them. In other words, it is a way to simplify an algebraic expression by finding common factors among the terms and then grouping them together. For example, the polynomial 2x^2 + 6x can be factored by grouping as (2x^2 + 6x) = 2x(x + 3). This is the most common way to factor a polynomial with four terms.

To solve the problem "factor by grouping" for the expression "n^2+3n-10", you can follow these steps:

Write the expression in the form of (n^2 + An + B) + (Cn + D)

(n^2 + 3n - 10) = (n^2 + 3n) + (-10)

Factor out the greatest common factor (GCF) of the terms in the first set of parentheses.

(n^2 + 3n) = n(n + 3)

Factor out the GCF of the terms in the second set of parentheses, if possible. In this case, there is no GCF.

Combine the factored expressions from step 2 and step 3 to get the final factored form.

n(n + 3) + (-10)

The final factored form of the expression is n(n + 3) - 10.

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Answer:4x5

Step-by-step explanation:

Answer:

The area of the base of a cylinder is found by dividing the volume of the cylinder by its height.If the volume of the cylinder is represented by 5x2 +15x + 2 and the height is 5x, which expression represents the area of the base?x2 + 3x + 5x (5x2 + 15x + 2)x + 3 + x (x2 + 3x +2)

Step-by-step explanation:

x+3+x+2

Hailey walked a total of 3.82 miles.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Given that,

Distance Hailey walked in the morning = 2.32 miles

Distance Hailey walked in the evening = 1.5 miles

Total distance she walked = 2.32 miles + 1.5 miles

                                            = 3.82 miles

Hence the distance Hailey walked in total is equal to 3.82 miles.

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Barry mistakes that dividing 1,243 by 3 would yield 481. This is not the case, because 1243/3 = 414.33.

The mistake that Barry made is that he most likely used simple long division method, but forgot to carry over the decimal number.

Another mistake could be the misreading of the problem, thinking that the 1,243 is the quotient, while in reality it is the dividend.

A term can be a number, a variable, a product of two or more variables, or a number and a variable product. A factor is anything that is multiplied by another item. A factor might be a number, a variable, a word, or a more complicated statement. The numbers or variables that are multiplied together to generate a word are referred to as its factors.

An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4m + 5 is an expression in which the words 4m and 5 are separated by the arithmetic sign + and m is the variable of the provided expression.

Here,

A term can be a number, a variable, the product of two or more variables, or the product of a number and a variable. Anything that is multiplied by another object is referred to as a factor. A factor might be a number, a variable, a word, or a longer statement. The factors are the numbers or variables that are multiplied together to form a word.

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The required component form of the vector V is given as  v=<51.3,-73.3>. Option D is correct.

Vector is defined as property of object that describes both magnitude and direction of object when in motion is called vector.

here,
|V| = 89.5
and Ф = 305
now,
x component = |V| cos305°
                    = 89.5×cos305° = 51.3

y component =  |V| sin305°

                    = 89.5×sin305° = -73.3

Thus, the required component form of the vector is given as  v=<51.3,-73.3>. Option D is correct.

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Answer: between eight and ten miles

between six and seven point 5 miles.

8-10 6-7.5

Step-by-step explanation:

The constant f(a) is the result of dividing a polynomial f(x) by xa, and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.

Algebraic expressions called polynomials include constants and indeterminates.

Polynomials can be thought of as a type of mathematics.

Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

A specific kind of expression is a polynomial.

A mathematical statement without the equals symbol (=) is called an expression. Let's examine the definition and usage of polynomials as they are described below.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Hence, The constant f(a) is the result of dividing a polynomial f(x) by xa, and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.

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The remainder theorem helps us find the remainder when dividing a polynomial by a linear expression, using the formula R = f(a), where a is the root of the linear expression. Using this formula, we can easily calculate the remainder without performing long division.

The remainder theorem is a concept in algebra that helps us find the remainder when we divide a polynomial by a linear expression. The formula for the remainder theorem can be stated as follows:

If we have a polynomial f(x) and we divide it by a linear expression x - a, then the remainder R is given by the formula:

R = f(a)

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The term least common denominator (LCD) is used when referring to the denominators in fractions.

The smallest common denominator shared by two or more fractions is referred to as the least common denominator (LCD).

They are the same when the common denominator also happens to be the smallest common denominator. The least common denominator will always be smaller than the common denominator if this is not the case.

There are numerators and denominators in fractions. The fraction's top and bottom halves are called the numerator and denominator, respectively.

A common denominator is a denominator that is shared by two or more fractions. They all require common denominators before two or more fractions may be added together or subtracted.

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When numbers are substituted into an equation, they typically produce a set of ordered pairs called a table of values (relation). Each ordered pair of numbers in the values table's table of values is related to one another according to the equation.

In math, what is a value?

Each digit's value varies based on where it is in the number, and this is referred to as the value. We figure it out by multiplying the digit's place value by its face value.

               Value is composed of Place Value and Face Value. Honesty, integrity, benevolence, kindness, courage, and self-assurance are a few examples of values.

What does a table of values example mean?

You can choose two or more points to include in your graph by using a table of data, a graphic organizer or chart. For the equation y= 2x + 1, an example table of values is shown here.

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The definite integral is [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex][tex]=[/tex][tex]\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

Definite Integral helps to find the area of a curve in a graph. It has limits, which are the start and the endpoints, within which the area under a curve is calculated. The limit points can be taken as [a, b], to find the area of the curve f(x), with respect to the x-axis.

Here,

∫ = Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, ∫ab f(x) dx is read as the definite integral of f(x) with respect to dx from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

To find [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex]

Put [tex]$16+r^2=t^2$[/tex]

[tex]$2 r d r=2 t d t$\\[/tex]

[tex]$r d r=d t$[/tex][tex]$r=0 \Rightarrow t=4$[/tex]

[tex]$r=1 \Rightarrow t=\sqrt{17}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\int_4^{\sqrt{17}} \frac{t^2-16}{t} d t$[/tex]

[tex]$=\left[\frac{t^3}{3}-16 t\right]_t^{\sqrt{17}}$[/tex]

[tex]$=\frac{(\sqrt{17})^3}{3}-16(\sqrt{17})-\frac{(4)^3}{3}+64$[/tex]

[tex]$=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

Therefore, the evaluated integral is [tex]\frac{31 \sqrt{17}}{3}$[/tex].

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