1) Alice decides to take a trip from the East Coast of the United States to the West Coast. While planning, she chooses to drive, fly, and ride a train. Her first leg of the trip is traveling by car, from Sacramento, California to Denver, Colorado. Along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. After driving for many hours, Alice finally makes it to Denver, Colorado spending $874.80 in gas.

a) Let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. Create an equation that models the situation.

Incorrect but attempt was made (1 pt) Partially correct
(2-4 pts) Fully Correct
(5 pts)




b) If Alice purchases 87 gallons for regular unleaded gas, how many gallons of premium gas did she purchase? Show all work to receive full credit.

Provided incorrect answer and no work shown (1 pt) Incorrect answer with work shown or Correct answer with no work shown
(2 pts) Correct with partial work shown (3-4 pts) Fully Correct with all work shown
(5 pts)

The Osborne 1 was the first laptop ever released, and it weighed 11 kg in 1981. Since then, the average rate of weight decrease has been 4.7% per year. This means that in 2019, a laptop would have weighed around 2.3 kg.

1981: 11 kg

1982: 10.5 kg (11 kg - 0.55 kg = 10.5 kg)

1983: 10.02 kg (10.5 kg - 0.48 kg = 10.02 kg)

1984: 9.55 kg (10.02 kg - 0.47 kg = 9.55 kg)

2019: 2.3 kg (3.44 kg - 1.14 kg = 2.3 kg)

The Osborne 1 was the first laptop ever released in 1981, and it weighed 11 kg. Since then, the average rate of weight decrease has been 4.7% per year. This means that the mass of a laptop decreases by 0.47 kg every year on average. So, in 1982 it would have weighed 10.5 kg, in 1983 it would have weighed 10.02 kg, and so on. By 2019, the weight of a laptop would have decreased to 2.3 kg as a result of this 4.7% average rate of weight decrease.

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The term 5 in 5x is known as the coefficient of the expression.

A coefficient is defined as a term or a number which is multiplied by a variable. This constant terms generally precedes the variable term.

A coefficient is a generally a multiplicative factor in a polynomial series, or in an  equation.

Expressions are mathematical statements which are composed of two terms in which at least one contain variables, numbers, or both. These terms are either numbers or variables or numbers and variables multiplying each other. These expressions are a combination of numbers with mathematical ,operators are used to separate them.

Eg, 2x - 90 =45

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Answer: solving by forming simple algebra equation

Step-by-step explanation:

8x (x is the cost of 1 volleyball)
6y (y is the cost of 1 basketball)

We know that cost of 8 volleyballs is = cost of 6 basketballs
i.e. 8x = 6y

& total money spent to buy 8 volleyballs and 6 basketballs is $960
so we can write;
8x + 6y = 960
= (6y) + 6y = 960
= 12y = 960
= y or cost of 1 basketball is (960/12) = $80

& if we want to know the value of x (cost of 1 volleyball)
8x = 6y
= 8x = 6(80)
& x = 6(80/8)
      = 6 (10) = 60

so the cost of basketball is $80 & 1 volleyball is $60

Hope it helps :)

p.s. that the equation I formed were made as if I was making an assumption & the conditions were kept uniform from the beginning, this is very applicable in day to day scenario; for e.g. when you go out with you friends to eat and have to split the bill - this assumption and division is called algebra - so value this education!

In a course of 12 weeks, Perry will be able to play a total of 25 pieces of the piano Leon.

A total of 18 pieces of piano are learnt by Perry in a course of 9 weeks.

By using simple algebra, we can find the number of pieces that will be played by Perry in one week,

So, we can write, The learing speed,

Number of piano pieces learnt = Weeks

19 pieces = 9 weeks

Learning speed = 19/9 Pieces per week

So, the number of pieces learnt in 12 weeks is,

Number of pieces learnt = 19/9 x 12

Number of pieces learnt = 25.22

Number of pieces learnt = 25

So, Perry will be able to play 25 pieces.

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Answer:

when x=10 & y=6

10-6=4 so,

x=8

y=4

The initial amount is 610 and the growth factor is 7.54.

What is an exponential function?

An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.

In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.

Hence, the initial amount is 610 and the growth factor is 7.54.

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The initial amount is 610 and the growth factor is 7.54.

An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.

A growth factor is a naturally occurring substance that stimulates a cell to grow, divide, and differentiate. Growth factors are typically proteins or peptides that bind to specific receptors on the surface of cells, triggering signaling pathways that lead to cell proliferation and survival.

In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.

Hence, the initial amount is 610 and the growth factor is 7.54.

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If the total study sessions for the night class were proportional to the morning class that is 25: 20 then night class have the actual amount 80% students

we can calculate 20/25 *100

and we obtain the actual amount  80%

If the total study sessions for the night class were proportional to the morning class is 25: 20 and 16: 22

What is a proportion simple definition?

the size, number, or amount of one thing or group as compared to the size, number, or amount of another. the proportion of boys to girls in our class is three to one. : a balanced or pleasing arrangement

Initially, the number of lectures is 3 while the number of fieldwork is 12. Furthermore, the class sessions increased to 18 and the number of fieldwork remains the same (i.e. 12). Therefore, the number of lectures will be 18 - 12 = 6. The percentage of the sessions that were  lectures will be:

(6/18)*100% = 33.3%

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It would change to about 9. 960 atmospheres

Following the Boyle's law of gases which states that the product of pressure and volume is exactly a constant for an ideal gas.

This is represented as;

PV = K

then,

P₁V₁ = P₂V₂

From the information given, we have that;

Now, substitute the values

8. 9(4. 7) = P₂(4. 2)

mulitply the values

41. 83 = P₂(4. 2)

Divide both sides by 4.2

P₂ = 9. 960 atmospheres

Hence, the value is 9. 960 atmospheres

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Therefore , the solution of the given problem of equation comes out to be  9x^3 - 8x^2.

A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.

Here,

Polynomial function total

Polynomial functions are those that have a leading degree of three or higher. given the total;

(7x^3-4x^2)+(2x^3-4x^2)

Expand => (7x 3-4 times) + (2x 3-4 times)

= > 7x^3-4x^2 + 2x^3-4x^2

assemble similar terms

=> 7x^3 + 2x^3 - 4x^2 -4x^2

=> 9x^3 - 8x^2

Therefore , the solution of the given problem of equation comes out to be 9x^3 - 8x^2.

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Answer:  -100

Step-by-step explanation:   -7(15)+5

It said x=15 so put 15 in and solve from there and that would be -100

HOPE THIS HELPS ANY I JUST completed FUNCTIONS AND MAN IT WAS FUN

Equation that will determine the amount of last year’s budget

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

Given that a school plans to spend twice the amount it did last year on its winter dance , less the cost of the disco ball which was $150 since they have it from last year

A total of $1,500 is being spent this year.

We need to find the equation which determine the amount of last year’s budget

2a-150=1500

When a is the amount of last year’s budget

Hence, 2a-150=1500 is the equation that will determine the amount of last year’s budget

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Elimination is a very easy method when it comes to solving simultaneous equations.

First, the best thing to do is bring the equations down to their lowest form. Try to remove the fractions in the co-efficient and have the equation in the standard form where every variable is expressed as individually as possible.

The next thing to do is to select a variable and manipulate the equations in such a way that the coefficients of that variable across all of the equations are the same. Here select any 2 equations to work on first if more than 2 are given

Now take one of the equations and multiply it by -1.

Add the equations up to eliminate the variable and derive the other variable(s)

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Monomial, binomial, and trinomial expressions are all categorized by the number of terms they include.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a binomial. An algebraic expression having three terms is called a trinomial.

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Donald would need to use 5 levels of cubes, So to make p5 he would need 25-12 = 13 more cubes.

A pyramid is a structure with a square or triangular base and four triangular sides that meet at a point, called the apex. Pyramids were built by ancient civilizations, such as the Egyptians, as tombs for pharaohs and their queens.

In the context of building pyramids with wood cubes, it seems like "pyramid levels" refers to the layers of cubes used to construct the pyramid. Each level is a layer of cubes that sits on top of the previous one, and the number of cubes in each level increases as you move up the pyramid. For example, in the case of p4, the base level would use 1 cube, the next level would use 4 cubes, the next level would use 9 cubes, and so on. The top level, which forms the apex of the pyramid, would use the most cubes. So the pyramid levels refer to the different layers of the pyramid and the number of cubes used in each layer.

To make a pyramid labeled p5, Donald would need to use 5 levels of cubes.

Donald uses 1 cube for the base of p4, 4 cubes for the next layer, 9 cubes for the next, 16 cubes for the next and 25 cubes for the top level.

So to make p5 he would need 25-12 = 13 more cubes.

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Answer:

35/4=8.75

Step-by-step explanation:

You and your 3 friends add up to 4 people so you do 35 divided by 4 and get 8.75

Answer:

Step-by-step explanation:

35/3 = p

p = 11.67 per person

The total amount of sales he must make should be of $20800.

Given is that a salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of ​$26. Option B is a commission rate of 5​% on weekly sales

Assume that the amount of sales he needs to make is of ${x}. So, for same amount, we can write -

(26 x 40) = 5% of {x}

(26 x 40) = (5/100) x {x}

{x} = (26 x 40 x 100)/5

{x} = (26 x 40 x 20)

{x} = 26 x 800

{x} = 20800

Therefore, the total amount of sales he must make should be of $20800.

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Answer:

√28 and √11

Step-by-step explanation:

Note : -

Irrational number is any real number that cannot be expressed as the quotient of two integers.

Here,

√28 = 5.291.......

5.291.... is an infinite number, it keeps going, it cannot be expressed in terms of a fraction.

Similarly,

√11 = 3.316......

Hence,

√28 and √11 are irrational numbers.

Amelie needed 335 cups of flour for the recipe.

Given data :

She is making 2 1/2 or 2.5 times the original recipe.

Cups in original recipe= 134 cups

cups Amelie will need= 2.5 × 134

                                     = 335 cups

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Answer:

She needs 18,731.6 Litres of paint to paint her bedroom.

Step-by-step explanation:

So,

V = l × w × h

V = 10.5 × 7 × 9 feet

V = 661.5 cubic feet

We know that,

So,

661.5 × 28.317 = 18,731.6 Litres

Thus, She needs 18,731.6 Litres of paint to paint her bedroom.

As the p-value of the test is of 0.215 > 0.05, there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:

[tex]H_0: \mu = 8.5[/tex]

At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:

[tex]H_1: \mu \neq 8.5[/tex]

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]

Hence the test statistic is calculated as follows:

[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}}[/tex]

z = (8.8 - 8.5)/(1.11/square root of 21)

z = 1.24.

The p-value is obtained using a z-distribution calculator.

We have a two-tailed test, as we are testing if the mean is different of a value, with a test statistic of z = 1.24, hence the p-value is of:

0.215.

(2 multiplied by the subtraction of one and the p-value of z = 1.24).

The p-value is greater than the significance level of 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a difference between the two methods.

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Answer: Marissa divided the marked section of the wall into 3 equal parts. If she painted one of these parts blue, then the part that she painted blue is 1 out of the 3 equal parts. So, the fraction of the wall that is blue is 1/3.

Another way of understanding this is that if the wall is divided into 3 equal parts and Marissa painted 1 part, then the fraction of the wall that is painted is 1/3.

So the fraction of the whole wall that is blue is 1/3.

Step-by-step explanation:

We employ the following equation to get the normal monthly cost:

4m - 8 = 64

Regular monthly expenses amount to $18.

Irma paid for her cats' subscription in advance for a 4-month period.

She saved $8 overall when she utilized a one-time discount.

Irma totaled $64 in payment.

We must identify the equation that can be utilized to calculate m, the average monthly cost.

Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.

When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.

Irma paid a total of $64 according to the problem, thus we can create the following equation:

4m - $8 = $64

We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.

4m = $64 + $8

4m = $72

Finally, divide both sides by 4 to solve for m:

m = $72 / 4

m = $18

So, the regular cost per month, m, is $18.

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For her research, a geneticist has to raise a stock of fruit flies. She presently has 200 fruit flies in stock;

The mathematical function she may use to calculate is given as

f(n)=log1.38(n/200)

Which function could she use to calculate, the number of days required for her stock to grow to n fruit flies?

Generally, the equation for the final value is mathematically given as

A=Ao(1+u)^t

Therefore

n=200(1+0.38)*t

log(1.38^t)=log(n/200)

t=log1.38(n/200)

In conclusion, The function she could use to calculate is

f(n)=log1.38(n/200)

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The best estimate for 225% of 50 is (a) greater than O but less than 1. 50

The maximum likelihood method will be used to calculate the point estimate as follows:

T, note the total number of trials.

List the number of accomplishments, S.

MLE = S / T should be used. Your point estimate is the outcome. Prior to explaining a "formal" method of approximation by rounding each number in the calculation to one significant figure, students must first estimate the result of a computation, use a calculator to determine the precise result, then compare the two results. The most accurate estimate is a definite estimate, as it is created by estimating the individual expenses for the various aspects of the project and then combining them into one estimate. Typically, bottom-up estimates are classified under this heading.

The best estimate for 225% of 50 is

= (225*50)/100

= 11250/100

= 112.5

So that, The best estimate for 225% of 50 is (a) greater than O but less than 1. 50

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You can identify equivalent expressions if one of the expressions can be written like the other and it is usually written by combining any like terms on each side of the equation such as x-terms with x-terms and constants with constants.

These are the type of expressions that have similar value or worth but do not look the same.

This type of expression can be identified if one of the expressions can be written like the other and example can be seen below:

3(x + 3) and 3x + 9

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Answer:

4x-24

Step-by-step explanation:

assume x=Length

perimeter

= x+(x-12)+x+(x-12)

= x+x -12+x+x-12

=4x-24

The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

what is triangle ?

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

Given, side length, a = 12 units.

the height of equilateral triangle, h = (a√3)/2.

Substituting the value of 'a',

h = (12√3)/2 = 6√3 =

10.39 units.

The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

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The average rate of change is the ratio of the difference between the y coordinates of two points to the x coordinate of the same point.

It can be found by using two points on the graph and substitute into the formula: (y₀ - y₁) / (x₀ - x₁)

The square brackets [] is used to mean the end points as shown is inclusive

A quadratic equation is a polynomial of degree two

The average rate of change here is not constant and is usually  specified by the two points to which it is measured

For instance using points (-3, 0) and (0, -1) we have

=  (y₀ - y₁) / (x₀ - x₁)

=  (-1 - 0) / (0 - (-3))

= -1/3

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