Gino records how much milk his family drinks each week in February. He graphs the volumes, to the nearest one fourth of a gallon, on the line plot below. What is the total volume of milk Gino's family drank on the 2 weeks where they drank the most milk?

Answer:

[tex]\dfrac{9}{12} - \dfrac{11}{18} = \dfrac{5}{36}[/tex]

Step-by-step explanation:

We can solve this subtraction of fractions by converting both fractions to forms where they have a common denominator.

To do this, we first have to find the least common multiple (LCM) of their denominators.

    1. Write out the denominators' prime factorizations.

    12           18

    2, 2, 3     2, 3, 3

    2. Multiply the greatest multiple of each prime number.

    2² × 3² = 4 × 9 = 36

So, the LCM of the denominators is 36.

Next, we need to get both fractions' denominators to 36 by multiplying each one by {36 divided by them} over {36 divided by them}.

Remember, this is just multiplying by 1.

[tex]\left(\dfrac{9}{12} \times \dfrac{36/12}{36/12}\right) - \left(\dfrac{11}{18} \times \dfrac{36/18}{36/18}\right)[/tex]

↓ simplifying the fractions being multiplied

[tex]\left(\dfrac{9}{12} \times \dfrac{3}{3}\right) - \left(\dfrac{11}{18} \times \dfrac{2}{2}\right)[/tex]

↓ executing the multiplication

[tex]\dfrac{27}{36} - \dfrac{22}{36}[/tex]

Finally, we can subtract the fractions' numerators.

[tex]\dfrac{27}{36} - \dfrac{22}{36} = \boxed{\dfrac{5}{36}}[/tex]

The number of possible outcomes are 8 if we have 4 spinners labeled Red, Blue, Yellow and green by using permutations.

The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.

There are 4 spinners: Red, Blue, green  and yellow.

Here Number of possible outcomes will be calculated by using permutation.

So, we get that:

Number of possible outcomes = 4 × 2

Number of possible outcomes = 8 ways.

Therefore, the number of possible outcomes are 8 if we have 3 spinners.

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Answer:

The exponential growth function for the population can be written as:

P(t) = P0 * e^(rt)

Where:

P0 = initial population = 8,000

r = annual growth rate = 4.3% = 0.043

To find the monthly rate, we need to divide the annual rate by 12 (since there are 12 months in a year):

r_monthly = r/12 = 0.043/12 = 0.00358

So the exponential growth function with monthly growth rate becomes:

P(t) = 8000 * e^(0.00358t)

To find the quarterly rate, we need to divide the annual rate by 4 (since there are 4 quarters in a year):

r_quarterly = r/4 = 0.043/4 = 0.01075

So the exponential growth function with quarterly growth rate becomes:

P(t) = 8000 * e^(0.01075t)

The weight gained by the spot dog during his time is 57/2 ounces.

An operation is a function in mathematics that converts zero or more input values, also known as "operands" or "arguments," into a clearly defined output value. The operation's complexity is determined by its operand count.

The most frequently studied operations are unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse, as well as binary operations (i.e., operations of arity 2), which include addition and multiplication. The nullary operation, also known as an operation of arity zero, is a constant. A ternary operation, also known as an operation of arity 3, is an example of the mixed product.

Given that, spot the Dog gained 4 3/4 ounces each week for the first 6 weeks of his life.

Convert the mixed fraction into improper fraction:

4 3/4 = 19/4 ounces

The weight gained for 6 weeks is:

19/4 (6) = 114/4 = 57/2

Hence, the weight gained by the spot dog during his time is 57/2 ounces.

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Answer:

Below

Step-by-step explanation:

I will assume they are all there on day 1

 then the LCM of  4  6  2  and 3   is 12 days

    every 12 days they are there together

       12 weeks = 12 x 7 = 84 days

                 84 / 12 = 7 times

day   1    13     25    37    49    62    74

thus, a = -39 is the solution to the equation -a = 4b-7 when (a, -8) is a solution

An equation is a fine statement that asserts the equivalency of two expressions. It generally consists of two sides, with an equal sign between them. Equations are used to describe connections between variables, and to break problems in colorful fields, including mathematics, wisdom, engineering, and economics.

Given by the question.

the equation given is -a = 4b - 7.

We are also told that (a, -8) is a solution to this equation. This means that if we substitute a for x and -8 for y, the equation will be true.

Substituting the given values, we get:

a = 4b - 7 (Given equation)

a = 4(-8) - 7 (Substituting b = -8, since (a, -8) is a solution)

a = -32 - 7 (Simplifying)

a = -39 (Final answer)

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Value of composite functions (g-f)(x)  and (f/g)(x) are x² - 2x - 8 and

(x+1)/(2x - 3) respectively.both of these functions don't have the same

domain and range.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given functions,

f(x) = x² - 3x - 4

g(x) = 2x² - 5x - 12

1. (g - f)(x)

= g(x) - f(x)

= 2x² - 5x - 12 - (x² - 3x - 4)

= 2x² - 5x - 12 - x² + 3x + 4)

= x² - 2x - 8

x is defined for all real numbers

Domain = (-∞, ∞)

let y = x² - 2x - 8

x = √y + 2(x) - 8

Function is defined for y ≥ 9

Range is {y∈R , y ≥ 9}

2. (f/g)(x)

= f(x)/g(x)

= (x² - 3x - 4)/(2x² - 5x - 12)

= (x² - 4x + x - 4)/(2x² - 8x + 3x - 12)

= (x(x - 4) + 1(x - 4))/(2x(x - 4) + 3 (x - 4))

= (x+1)(x-4)/(2x+3)(x-4)

= (x+1)/(2x - 3)

function is defined for x ≠ 3/2, Domain is {x ∈ R : x ≠ 3/2}

Let y = (x+1)/(2x - 3)

y.2x - 3y = x + 1

-3y - 1 = x - 2xy

x = (-1 - 3y)/(1 - 2y)

function is defined for y ≠ 1/2, Range is {y ∈ R : y ≠ 1/2}

Domain and range are not same for both functions.

Hence,  Value of composite functions (g-f)(x) = x² - 2x - 8 and

(f/g)(x) = (x+1)/(2x - 3), Domain and range is not same for both functions.

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The total surface area of the given cylinder is; MA sq. units

The curved surface of a cylinder is also known as its lateral surface. The area of this lateral surface is referred to as the lateral surface area of the cylinder.

Meanwhile, the formula for the total surface area of the cylinder is;

Total surface area = Lateral surface area + base area

We are given;

lateral surface area = M sq. units

Area of base = A sq. units.​

Thus;

Total surface area = M * A

Total surface area = MA sq. units

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Answer:

B

Step-by-step explanation:

Bus A and B leave at 6:00 am (First bus of the day).

The schedule for Bus A and B are as follows:

Bus A: 6:00 am --> 7:15 am --> 8:30 am

Bus B: 6:00 am --> 6:15 am --> 6:30 am --> 6:45 am --> 7:00 am --> 7:15 am

As you can see, bus A and B leave the station together again at 7:15 am.

Hence, the answer is B.

Answer:

m∠6 = 142°

m∠7 = 38°

Step-by-step explanation:

You will be using postulates and theorems to solve this question.

Two parallel lines are cut by a transversal          (Given)

- m∠1 = 38°                         (Given)

- m∠1 ≅ m∠3                      (Vertical Angles Theorem)

  ∴ m∠3 = 38° (Definition of Vertical Angles Theorem)

- m∠3 ≅ m∠5                     (Alternate Angles Theorem)

 m∠3 = 38° ∴ m∠5 = 38° (Definition of Alternate Angles Theorem)

- m∠5 ≅ m∠7                     (Vertical Angles Theorem)

 m∠5 = 38° ∴ m∠7 = 38° (Definition of Alternate Angles Theorem)

m∠7 + m∠6 = 180°            (Corresponding Angles Postulate)

m∠7 = 38°                          (Given above)

Plug in 38 for m∠7 and solve for m∠6:

(38) + m∠6 = 180

Isolate m∠6. Note the equal sign, what you do to one side, you do to the other. Subtract 38 from both sides of the equation:

m∠6 + 38 = 180

m∠6 + 38 (-38) = 180 (-38)

m∠6 = 180 - 38

m∠6 = 142°

-

Answers:

m∠6 = 142°

m∠7 = 38°

~

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The factorization of the given polynomial is 10x²(x+1).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given polynomial is 10x³+10x².

Here, factors of the terms 10x³ and 10x² are

10x³= 2×5×x×x×x

10x²= 2×5×x×x

GCF of the terms is 2×5×x×x=10x²

10x²(x+1)

Therefore, the factorization is 10x²(x+1).

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We can use the Pythagorean theorem to find the length of the short cut up the flight of stairs. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the length of the short cut "x". Then, we can set up the following equation:

x^2 = 60^2 + 80^2

Expanding the squares:

x^2 = 3600 + 6400

x^2 = 10000

Taking the square root of both sides:

x = sqrt(10000)

x = 100

So, the length of the short cut up the flight of stairs is 100 meters.

The system of equations are y = ( 5/4 )x and y = 6 - 3x where the value of x and y are 1.4117 and 1.765 respectively

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first equation be P

y = ( 5/4 )x   be equation (1)

Let the second equation be Q

y = 6 - 3x   be equation (2)

Substituting the values in the equation , we get

( 5/4 )x = 6 - 3x

Adding 3x on both sides of the equation , we get

6 = ( 5/4 + 3 ) x

( 17/4 )x = 6

Multiply by 4 on both sides of the equation , we get

17x = 24

Divide by 17 on both sides of the equation , we get

x = 24/17 = 1.4117

Substitute the value of x in equation (1) , we get

y = ( 5/4 ) ( 24/17 )

y = ( 30/17 )

y = 1.765

Hence , the equations are solved and the value of x and y are 24/17 and 30/17 respectively

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To create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Yaseen can produce 15 kits, the cost per kit she should charge is

p = 10 + 0.5q

p = 10 + 0.5(15) (15)

p = $17.50

She can produce 15 kits, the cost per kit she should charge is:

p = 30 - 0.5(15) (15)

p = $22.50

She can provide 60 kits, the cost per kit should be as follows:

p = 10 + 0.5q

Here, q=60

p = 10 + 0.5(60)

p = $40

She can produce 60 kits, the cost per kit should be set at:

p = 30 - 0.5(60) (60)

p = $15

Therefore, to create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.

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Using an online finance calculator, the annual percentage rate (APR) of an $800 installment loan with a finance charge of $40.72 for 36 monthly payments is 1.656%.

The annual percentage rate (APR) is the cost of borrowing, including the interest and other fees, expressed as a percentage of the debt.

The APR is always computed as an annual rate to show the cost of borrowing or finance charge over a year.

N (# of periods) = 36 months

PV (Present Value) = $800

PMT (Periodic Payment) = $0

FV (Future Value) = $-840.72

I/Y = 1.656% if interest compounds 12 times per year (APR)

I/Y = 1.669% if interest compounds once per year (APY)

I/period = 0.138% interest per period

Total Interest = $40.72

Thus, for Betty Arca's installment loan of $800, the APR is 1.656%.

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Answer: Θ = [tex]45[/tex]

Step-by-step explanation:

tan x=sinx/cosx

and tan x is negative in the first and third quadrants.

tan x=1 for 45 degrees so tan x=-1 in the first quadrant 135 degrees and the third quadrant= 315 degrees

The area of the parallelogram is 27 square centimeters.

A region's size on a surface is determined by its area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area might be thought of as how much material of a certain thickness would be required to create a model of the shape, or as how much paint would be required to completely cover the surface in a single application.

The area of the parallelogram is given as:

A = (b)(h)

Here, the base is 4.5cm and the height is 6 cm.

Thus,

A = (4.5)(6)

A = 27 square centimeters.

Hence, the area of the parallelogram is 27 square centimeters.

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The number of cubes that has 1 face in red will be 54 which is placed at the center of all faces.

Samples are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

Meg paints the whole outside of a 5 x 5 x 5 cube red and then cuts it up into 1 x 1 x 1 cube.

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The given numerical value  is a Statistic.

Parameters are numeric values ​​that characterize the population as a whole. A statistic is a number that describes the characteristics of a sample.

For example, median income in the United States is a demographic parameter. Conversely, the median income for the US sample is a sample statistic. Both values ​​represent median income, but one is a parameter to the statistic. Easy to remember parameters and stats! Both are summary values ​​that describe the group, and have a convenient mnemonic device to remind you which group is being described. Notice their initials.

Parameter = Population

Statistics = Sample

A population is the entire group of people, things, animals, trades, etc. that are being studied. A sample is part of a population.

Following the election, 18 % of the governors of all 50 areas of a country were female.

Given that, 18% of the 50areas of a country  were females.

Now,

18*50/100 = 9

Since it is  a perfect number

The given numerical value  is a statistic.

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The solution is, the remainder is 9.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

find the remainder in the synthetic division

1         4       6        -1

Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder

1         4       6        -1

        0        4        10

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

        4        10       9 -> Remainder

So the remainder is 9.

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The relationship between the number of hours past noon and the temperature outside is y = -5x + 12

From the question, we have the following parameters that can be used in our computation:

Initial = 12 degrees

Rate = -5 degrees

To represent the relationship between the number of hours past noon and the temperature outside, we can use the equation:

y = Rate * x + Initial

So, we have

y = -5x + 12

where y represents the temperature in degrees Fahrenheit and x represents the number of hours past noon.

The graph of the equation is a linear equation

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Answer:

688cm^2

Step-by-step explanation:

5*16= 80

16*12= 192

6*12= 72

80+80+192+192+72+72= 688cm^2

Answer: PLEASE GIVE BRAINLIEST

B) 55h + 65

Step-by-step explanation:

The correct expression is B) 55h + 65, which models the situation as $55 per hour of work (h) plus a $65 service call fee.

It will take Thoriso 30 minutes to walk to school.

what is speed ?

Speed is a measure of how quickly an object is moving. It is defined as the distance traveled by an object in a given amount of time. The formula for speed is:

Speed = distance / time

The unit of speed depends on the units of distance and time used. Common units of speed include meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph).

Given by the question:
We can use the formula:

time = distance / speed

to calculate the time it will take Thoriso to walk to school.

Let d be the distance from Thoriso's home to school. Since the distance is the same whether she walks or rides her bicycle, we have:

distance walked = distance biked = d

Let's first calculate how long it takes Thoriso to bike to school:

time biked = distance biked / biking speed

time biked = d / 15 km/h

We are given that it takes her 10 minutes (0.167 hours) to bike to school, so we can set up the following equation:

0.167 hours = d / 15 km/h

Solving for d, we get:

d = 2.5 km

Now, we can calculate how long it will take Thoriso to walk to school:

time walked = distance walked / walking speed

time walked = d / 5 km/h

time walked = 2.5 km / 5 km/h

time walked = 0.5 hours or 30 minutes

Therefore, it will take Thoriso 30 minutes to walk to school.

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Answer:

43°

Step-by-step explanation:

Because it is a parallelogram, there is 2 pairs of parallel lines, therefore, opposite angles are equal.

In the given diagram, the measure of arc DE, mDE, is 90°

From the question, we are to find the measure of the given arc.

The angle measure of an arc is the angle subtended by the arc at the center of the circle.  

From the given diagram, we are to determine the measure of arc DE.

In the given diagram, we can observe that the angle subtended by arc DE is a right angle. That is, the measure of arc DE is a right angle.

The measure of a right angle is 90°.

Hence, the measure of arc DE is 90°

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So, if you only have $125 to spend, you may go around 90.91 miles in the van.

An equation in mathematics is a statement that two mathematical expressions are equal. Equations are used to represent mathematical relationships and to describe the behavior of systems or processes. An equation typically consists of two sides, separated by an equal sign (=). On one side of the equal sign is the expression representing what is known or given, and on the other side is the expression representing what is being found or sought. Equations can be used to model real-world situations, to describe the behavior of mathematical functions, to solve problems, and to make predictions. They are an important tool in many areas of mathematics and science, including algebra, calculus, physics, and engineering.

Here,

Let's call the number of miles you want to travel "m". The total cost of the rental is given by the expression 75 + 0.55m. We know that this total cost must be less than or equal to $125, so we can write the inequality:

75 + 0.55m ≤ 125

We can isolate the variable m by subtracting 75 from both sides of the inequality:

0.55m ≤ 125 - 75

0.55m ≤ 50

Finally, we can solve for m by dividing both sides of the inequality by 0.55:

m ≤ 50 / 0.55

m ≤ 90.91

So, if you have a maximum of $125 to spend, you can travel a maximum of approximately 90.91 miles in the van.

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Answer:

4/49

Step-by-step explanation:

1 week : 5 working days

5*$4= $20

20/245= 4/49

The accepted method for representing both integer and non-integer numbers is the decimal numeral system.

It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal between decimals is a decimal number that lies between two other decimal numbers.

For example, if you have two decimal numbers 0.2 and 0.3, a decimal between them would be any number that is greater than 0.2 and less than 0.3.

Some examples of decimals between 0.2 and 0.3 include 0.25, 0.26, 0.27, and so on.

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The question when translated in English is, "What is a decimal between decimals?"

SI unit is an international system of measurements that are used universally in technical and scientific research to avoid the confusion with the units. Having a standard unit system is important because it helps the entire world to understand the measurements in one set of unit systems.

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The given question is incomplete, complete question is:

What is the SI prefix for each of the following multiples and submultiples of a unit?

[tex]10^-^9[/tex]