Part A If x is the number of miles Gavin bikes on the first day, write an expression for the distance he should bike on each of the following three days​

Answer:

Step-by-step explanation:

Answer:

a)

i) To calculate the profit if 0 cakes are made per day, we can substitute x = 0 into the function:

P(x) = -x²+36x - 40

P(0) = -0² + 36(0) - 40 = -40 dollars

So, the profit from making 0 cakes per day is -40 dollars.

ii) To calculate the profit if 20 cakes are made per day, we can substitute x = 20 into the function:

P(x) = -x²+36x - 40

P(20) = -20² + 36(20) - 40 = 760 dollars

So, the profit from making 20 cakes per day is 760 dollars.

b) To find out how many cakes need to be made per day for the profit to be $270, we need to solve the equation P(x) = 270.

We can substitute the function P(x) into this equation:

-x²+36x - 40 = 270

Next we can solve this equation for x by using any method you prefer ( factoring, Quadratic formula, etc)

x = (36 +/- √(36² -4*(-40)(-1)))/ 2(-1)

x = (36 +/- √(1296 + 320))/ -2

x = (36 +/- √1616)/ -2

x = (36 +/- 40)/ -2

x = -2 +/- 20

x = 18 or -22

The number of cakes need to be made per day for the profit to be $270 is 18 or -22, but -22 is not a valid solution because the number of cakes must be a non-negative value, so the number of cakes need to be 18

Answer:

4+3=7

-2+3=7

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

1.2*4 =4.8

so 32*4 = 128

The value of x is 54/35 when y=12 and z=21. The solution is obtained using the concept of relations and functions.

What is relation and function?

A relation belongs to the Cartesian product's subgroup or just a lot of points (ordered pairs). In other words, the ordered pair collection, where the ordered pair is made up of an object from each set, is used to define the relationship between the two sets.

A function is a special sort of relation (a collection of ordered pairs) that adheres to the rule that every X-value should only be connected with one y-value.

We are given that x varies directly as y and inversely as z.

This means that x ∝ y and x ∝ 1/z

So, x ∝ y/z

=> x = k*y/z  ( k is a constant)

Now, it is given that x = 3 when y = 10 and z = 9

So,

=> 3 = k*10/9

=> k = 27/10

=> x = 27y/10z

When y=12 and z=21,

=> x = 27*12/10*21

=> x = 54/35

Hence, the value of x is 54/35 when y=12 and z=21.

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Answer:

Step-by-step explanation:

Solving by factoring is a strategy for solving a polynomial equation that is in quadratic form. Quadratic form means that the equation is of the form ax^2+bx+c=0, where a,b, and c are real numbers. When factoring, the goal is to express the equation as the product of two simpler equations. To do this, we must factor the quadratic equation into two linear equations, each with a single variable.

For example, consider the equation x^2+3x-4=0. To factor this equation, we can first rewrite it as (x+4)(x-1)=0. This is the same as x+4=0 and x-1=0. We can then solve each of these linear equations to find the solutions. In this case, the solutions are x=-4 and x=1.

Therefore, the strategy of solving by factoring is to rewrite a polynomial equation in quadratic form as the product of two simpler equations, and then solve each of these equations. The solutions to the original equation can then be found by solving each of the linear equations.

Two-variable linear equations have a line as their graph, which is why they are referred to as linear equations. Plotting (x1,y1) and (x2,y2), then creating a line that connects the two.

[tex]$\frac{d}{d x}\left(-(x-2)^2+1\right)$[/tex]

Domain of [tex]$-(x-2)^2+1:\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

Range of [tex]$-(x-2)^2+1:\left[\begin{array}{cc}\text { Solution: } & f(x) \leq 1 \\ \text { Interval Notation: } & (-\infty, 1]\end{array}\right]$[/tex]

Interception zones on the axis [tex]$-(x-2)^2+1: \quad X$[/tex] Intercepts: [tex]$(3,0),(1,0), Y$[/tex]Intercepts: (0,-3) .

Vertex of [tex]$-(x-2)^2+1: \quad$[/tex] Maximum (2,1) .

The graph of the equation y=2x+1 shows a straight line, or it is a linear equation. When the value of x rises, eventually the value of y rises by twice the rise in x plus one. With a ruler and the specified amount as the starting point, draw a vertical line. From the line across to the -axis, create a horizontal line using a ruler. Look at the value on the -axis.

There are three fundamental ways to graph linear functions. The initial method involves charting points and then tracing a line through them. The second is by using the slope and y-intercept. The identity function f(x)=x is transformed as the third method.

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Answer:

Step-by-step explanation:

Q1)

A toffee costs $0.15 + $0.10 = $0.25

If you buy 15 candies, it will cost you 15* $0.15 = $2.25

If you buy 12 toffees, it will cost you 12* $0.25 = $3.00

So buying 15 candies is $3.00 - $2.25 = $0.75 cheaper than buying 12 toffees.

Q2)

The original price of two tennis rackets is $120 x 2 = $240

The original price of three cans of tennis balls is $15 x 3 = $45

So the original price of two tennis rackets and three cans of balls is $240 + $45 = $285

By buying two tennis rackets and three cans of balls at the sale price of $255, you save $285 - $255 = $30 off the original price.

The interquartile range of the data given the first quartile and the third quartile is equal to 25.

The interquartile range is the difference between the third quartile and the first quartile.

The IQR is a measure of variability that is based on the division of a data set into quartiles.

The data arranged in ascending order as;

4,5, 6, 8, 9, 11, 13, 16, 16, 18, 20,21, 25,30, 33, 36, 37, 40, 41

Third quartile = 3/4(n + 1) = 3/4 x 20

= 15th term

= 50

First quartile = 1/4 x (n + 1) = 1/4 x 20

= 5th term

= 25

Thererfore, Interquartile range = 50 - 25 = 25

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The solution to the equation 5x + 9y = 561 and 5x + 6y = 276 is x = -58.8, y = 95

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Given the equation:

5x + 9y = 561    (1)

Let us assume the second equation is:

5x + 6y = 276     (2)

To solve using elimination method, subtract equation 2 from 1:

3y = 285

y = 95

Put y = 95 in equation 1:

5x + 9(95) = 561

5x = -284

x = -58.8

The solution is x = -58.8, y = 95

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Answer:

[tex]y = 3x - 1[/tex]

Step-by-step explanation:

Let's define the terms we are given to understand what the question is asking us to do:

⭐What is a linear function?

⭐What is slope-intercept form?

Thus, we need to write the equation of the table in slope-intercept form.

To do so, we can first find the y-intercept (c).

When x = 0, y = -1.

Therefore, the y-intercept (c) of the equation is -1.

Substitute this value into the slope-intercept form equation.

[tex]y = mx - 1[/tex]

Next, to find the slope, we have to use this formula:

⭐[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

I am going to choose the coordinates (1,2) and (2,5), but you can choose any other coordinates you are given that ISN'T (0,-1).

Substitute these coordinates into the slope formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\m = \frac{5-2}{2-1}\\m = \frac{3}{1}\\m = 3[/tex]

Therefore, the slope of this line is 3.

Substitute this value into the slope-intercept form equation.

[tex]y = mx - 1\\y = 3x - 1[/tex]

Hence, the equation of the linear function represented by the table is:

[tex]y = 3x - 1[/tex]

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Answer:

1.80642 rounded to the nearest thousandth is 1.806.

Step-by-step explanation:

The guy above me is correct

The total cost of the meal with the gratuity is $1.18p.

What is gratuity?

The amount that a company pays its employee as a "gratuity" for services rendered to it is referred to as a gratuity. The gratuity amount, however, is only given to employees who have worked for the business for five years or longer.

For each completed six-month period, the gratuity amount is equal to one-fourth of the employee's most recent basic salary.

Given:

A restaurant charges an automatic gratuity of 18% on tables with more than 6 people.

A party of 8 had a bill of p.

Since there are 8 people so, gratuity will be applied on the bill

Since bill is of amount p

So, gratuity of 18 % of p = 18% * p

                                      =  (18 / 100) *p

                                     =  0.18p

Now the total bill after adding gratuity = p + 0.18p

                                                               = 1.18p

Hence, the total cost of the meal with the gratuity is $1.18p.

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Step-by-step explanation:

let's start with combinations, where the order does not matter - the 4 basis are indistinguishable.

C(5, 4) = 5! / (4! × (5-4)!) = 5! / 4! = 5

that makes sense, of course, as we only need to trace the possibilities for the one empty box : 5 possibilities.

now, the order of the 4 balls matter.

the 4! term in the denominator was actually taking that away, so we need to remove it.

that turns the combinations into permutations, where the order matters.

P(5, 4) = 5! / (5 - 4)! = 5! = 5×4×3×2×1 = 120

4 distinguishable balls can be placed in 5 distinguishable boxes in 120 ways.

Answer:

Step-by-step explanation:

a)24

b)4

c)10

d)16

e)172

Answer: 222 gallons of gasoline to travel 444 miles.

Step-by-step explanation: To find how much gasoline the boat needs to travel 444 miles, we need to use the formula:

distance = rate x time

Where distance is the total distance to be traveled, rate is the distance per unit of fuel (370 miles/185 gallons) and time is the amount of fuel required to travel 444 miles.

So we can calculate the fuel required as:

Fuel = (distance) / (rate)

Fuel = (444 miles) / (370 miles/185 gallons) = 444/ (370/185) = 444/2 = 222 gallons.

So the boat needs 222 gallons of gasoline to travel 444 miles.

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Step-by-step explanation:

the funny thing with equations is we can transform them (as long as we do every operation in both sides), and we can even add them up or subtract from each other to get new equations that are maybe simpler to solve.

to eliminate x i would recommend to multiply the first equation by 4, and the second equation by 5 and then subtract equation 2 from equation 1 (comparable term by comparable term).

5x - 2y = 10

4x - 3y = 15

would then turn into

20x - 8y = 40

- 20x - 15y = 75

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

0 7y = -35

y = -35/7 = -5

now we can pick any original equation to solve for x.

e.g.

5x - 2×-5 = 10

5x + 10 = 10

5x = 0

x = 0

Translating the statement "Babies are illogical" into symbolic form willoll be C. P➡️~Q

Symbols and logical connectors are used in symbolic sentences to represent the sentence's logic.

A letter, such as p, can represent an entire statement in symbolic logic.

In symbolic form, the argument is p → q ~p ∴ ~q It is in the form of the fallacy of the inverse and it is a fallacy, or invalid

In this case, it should be noted that since p is that you are a baby and Q be you are logical. The symbolic form will be C.

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Answer: A irregular

b. irregular

c neither

d. Regular

e. regular

Step-by-step explanation: Regular polygons have all sides equal in length but an irregular polygon does not have all sides equal.

Answer:

A: Irregular polygon

B: Irregular polygon

C: Neither

D: Regular polygon

E: Regular polygon

Step-by-step explanation:

To start off with, we can eliminate C for being a polygon (neither), because being a polygon states the shape must be closed with a finite number of line segments (a circle has an infinite amount of line segments).

A regular polygon states that it must have an equal distance on all sides. We can find this by looking at what shapes have a line (which represents that it has the same length) on all sides. The only polygons that fit this requirement are D and E.

From here we can see that the remaining polygons of A and B are in fact irregular polygons by process of elimination.

The number of goodie  bags she will need to sell is 107.

Breakeven is when profit is zero. it is the point where total cost is equal to total revenue.

Breakeven: Total cost = total revenue

fixed cost + variable cost = price x quantity sold

fixed cost + (cost per unit  x quantity sold)

$250 + (1.25 x q) = 3.60 x q

$250 + 1.25q = 3.60q

In order to determine the value of q, take the following steps:

Combine and add similar terms :

$250 = 3.60q - 1.25q

$250 = 2.35q

Divide both sides o the equation by 2.35

q = 250/2.35

q =  106.3 = 107

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The equation that models the scenario and number of years for the population to reach 656,000 will be option A.

i.e. y=100(3)^t and 8 years.

What are equations?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

Algebra considers two prominent families of equations, namely polynomial equations and linear equations. Polynomial equations with one variable can be written in P(x) = 0, where P is a polynomial, and ax + b = 0 is the general form of linear equations. Here, a and b are parameters. We can practice geometric or algorithmic methods from linear algebra or mathematical analysis to solve these equations. Also, there are different types of equations, such as:

Linear equations

Quadratic equations

Cubic equations

Quartic equations

Differential equations

Parametric equations

Now,

The equation as the population is compounding annually for the scenario

will be y=P*(1+R)^t

Here p=Initial population

R=rate of increment/ decrement of population

t=time

Hence,

y=100*(1+2)^t                    (R=2 )

y=100*3^t

Time for which the population will be 656,000 will be

656000=100*3^t

6560=3^t

therefore,

t=8 years.

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Circle the equation that models the scenario and the number of years it takes for the population to reach 656,000 is y = 100(3)^x, 8 years.

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Answer:

10

Step-by-step explanation:

Maria has 12 bags of chocolate chips, and each batch of cookies requires 1/2 bag of chocolate chips, and she makes 8 complete batches of cookies. So we can calculate the number of bags of chocolate chips used by:

1/2 * 8 = 4 bags

The number of bags of chocolate chips left after making the cookies is:

12 - 4 = 8 bags

A batch of cupcakes requires 3/4 of a bag of chocolate chips, and Maria has 8 bags of chocolate chips left. So we can calculate the maximum number of complete batches of cupcakes that she can make by:

8 / (3/4) = 8 * (4/3) = 32/3 = 10.67

Maria can make a maximum of 10 complete batches of cupcakes. Since a batch of cupcakes cannot be fractional, it means Maria can't make any more cupcakes after using all the chocolate chips.

Answer:

Angle EBC = 88

because of the angle bisector theorem

44 + 44 = 88

Answer:88°

Step-by-step explanation:

EBD is equal to 44°, while DBC is also equal to 44° if you see it well.

So EBD and DBC together is 88°.

44°+44°=88°

Triangle FYJ is congruent to triangle HYJ using the RHS congruency theorem.

FJ is congruent to segment HJ.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

We know right angle hypotenuse congruency, which states two right angle triangles are congruent if one of the legs and hypotenuse corresponding to the other right angle triangle is equal in measure.

Triangle FYJ is congruent to triangle HYJ as FY is congruent to HY and JH is congruent to JH.

So, Their hypotenuses are also equal in measure.

Hence, FJ is congruent to JH.

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Answer:

-27

Step-by-step explanation:

3a - 4b
-3 - 4b
-3 - 24
-27

Answer:

1

Step-by-step explanation:

(-1,2) and (2,6)

d=√[2-(-1)] ^+ [2-6]^

d=√3+(-4)^

d=√-1^

d=1

Answer:

Answer

Step-by-step explanation:

20s³ +50s²+32s+6

The sum of A and B in the ten digits numbers is 6.

The ten-digit number 3872649A0B is divisible by 36 . Therefore, the ten digit number can divide 36 without any remainder.

Hence, the letters A and B each represent single digit even numbers. Even numbers are numbers that can divide 2 without remainders.

Therefore, let's find the sum of the numbers A and B.

Since, the numbers are single digits and even the numbers are 2, 4, 6 or 8.

Therefore, lets do trial and error to know what will be replaced in the ten digits to divide 36 without remainder.

Therefore, the numbers are 2 and 4.

Where,

A = 2

B = 4

3872649204 ÷ 36 = 107573589

Therefore,

A + B = 2 + 4 = 6

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