Analysts at the Milk Company calculated the average price of a gallon of its milk over 10 years. The
following table shows the years since 2010 and the average price of a gallon of milk at those times.
Years (since 2010) 1 3 6 8 9
Price (in dollars) 3.57 3.49 3.20 2.90 3.04
Which data display would you use to represent this data?
Histogram
Line plot
Scatter plot
Line graph

Given:

Exponential function

Required:

To define the exponential function.

Explanation:

The exponential function is represented in the form of

Where a>1 and x represent the variable.

Here x is an independent variable and y is dependent, a is called the base. The value of the base is always constant.

The most important exponential function is

Where the value of e is 2.7182818.

Final Answer:

Explain in the explanation part.

The possible length of segment AB is 27 < AB < 81

From the question, we have

In triangle ABC

AC = 27

CB = 54

Using Pythagoras theorem,

AC² = AB² + CB²

54² = AB² + 27²

AB = 47

The possible length of segment AB is 27 < AB < 81

Multiplication:

To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly. The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.

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The ratio of the graph X: Y is 1:9.

What is a straight-line graph?

The graph follows a straight-line equation shows a straight line graph.

equation of a straight line is   y=mx+cy represents the vertical line y-axis.

x represents the horizontal line x-axis.    

m is the slope of the line

            slope(m)=tan∅=y axis/x axis.

c represents y-intercepts (it is the point at which the line cuts on the y-axis)

Straight-line graphs show a linear relationship between the x and y values.

Calculation:-

The slope of X = 10/100 = 1/10

The slope of y = 90/100 = 9/10

Therefore the ratio of X: Y

= 1/10 × 10/9

 = 1:9

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The value of f(4) is 1125.

Here,

we have given the value of f(1)=9 and f(n)=5f(n-1) and we have to find out the value of f(4).

From the above equation of f(n), it is clear that for finding value of  f(4) we have to find value of f(3).

And for f(3) we have to find out the value of f(2)

So,

first, we will find out value of f(2) and then eventually value of f(3) and f(4) by using the given formula of f(n)

The given formula for f(n) is

f(n)=5f(n-1)

So,

f(2)=5f(2-1)

f(2)=5f(1)

f(2)=5×9

f(2)=45

Now,

f(3)=5f(3-1)

f(3)=5f(2)

f(3)=5×45

f(3)=225

And,

f(4)=5f(4-1)

f(4)=5f(3)

f(4)=5×225

f(4)=1125

Hence, we got

The value of f(4) is 1125.

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Answer: x = -2 and y = -5

We are given two system of equations

-6x - 2y = 22 ---------------- equation 1

-12x + 10y = - 26------------- equation 2

These two system of equations can be solve simultaneously using elimination method

Before we can apply elimination method, we need to make one of the variables equal in both equations

Let us eliminate x

To make the co -efficient of x equal in both equations, Multiply equation 1 by 2 and equation 2 by 1

-6x - 2y = 22 * 2

-12x + 10y = -26 * 1

This becomes

-6x * 2 - 2y* 2 = 22*2

-12x*1 + 10y *1 = -26 * 1

-12x - 4y = 44------------------- equation 3

-12x + 10y = -26 --------------- equation 4

To eliminate x, substract equation 4 from equation 3

-12x - (-12x) - 4y - (10y) = 44 - (-26)

-12x + 12x -4y -10y = 44 + 26

0 - 14y = 70

-14y = 70

Divide both sides by -14

To find x, substitute the value of y = -5 into equation 1

-6x - 2y = 22

-6x - 2(-5) = 22

-6x + 10 = 22

-6x = 22 - 10

-6x = 12

Divide both sides by -6

Hence, x = -2, and y = -5 : (-2, -5)

5- 2(3+9) +4

Apply PEMDAS

First solve parentheses: (3+9) = 12

5- 2 (12) + 4

Then, the multiplication:

5- 24 + 4

Add and subtract

-15

a=-15

El camión con capacidad de 3 toneladas viajó 12 veces y el camión con capacidad de 4 toneladas viajó 11 veces.

En este problema encontramos dos camiones, uno de ellos con una capacidad de 3 toneladas y otro con capacidad de 4 toneladas, que desplazan 80 toneladas de madera en un total conjunto de 23 viajes. El total movido por cada camión es igual al producto del número de viajes y la capacidad de los camiones. Por tanto, el total desplazado de madera es igual a la siguiente ecuación:

3 · x + 4 · (23 - x) = 80

Donde x es la cantidad de viajes del camión de 3 toneladas de capacidad.

A continuación, despejamos la variable x:

3 · x + 4 · (23 - x) = 80

3 · x + 92 - 4 · x = 80

92 - x = 80

x = 92 - 80

x = 12

El primer camión viajó 12 veces y el segundo camión viajó 13 veces.

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The correct mixed fraction is  2) 1 [tex]\frac{23}{28}[/tex]

What is mixed fraction and improper function ?

 A mixed fraction is one that has both a whole number portion and a proper fraction, and whose value is always larger than 1. A mixed number is, for instance, 3[tex]\frac{2}{5}[/tex]. A fraction is deemed inappropriate if the numerator is consistently greater than or equal to the denominator. 4/3, 7/3, 11/5, etc. are a few instances of incorrect fractions.

Here the given division is,

=> 5 [tex]\frac{2}{3}[/tex] ÷ 3 [tex]\frac{1}{9}[/tex]

=> [tex]\frac{15+2}{3}[/tex] ÷ [tex]\frac{27+1}{9}[/tex]

=> [tex]\frac{17}{3}[/tex] ÷ [tex]\frac{28}{9}[/tex]

=> [tex]\frac{17}{3}[/tex] * [tex]\frac{9}{28}[/tex]

=> [tex]\frac{51}{28}[/tex]

=> 1 [tex]\frac{23}{28}[/tex]

Hence the correct option is 2) 1 [tex]\frac{23}{28}[/tex]

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To know the best deal, we have to know which one gives us the least cost per gallon.

To do that we divide the price by the quantity or volume.

A) $56 for 25 gallons

B) $32.05 for 15 gallons

C) $51.29 for 23 gallons

D) $22.50 for 10 gallons

The best deal is B: $32.05 for 15 gallons, because it offers a price per gallon that is lower than the others.

ANSWER

k = 7

EXPLANATION

The unknown variable in this equation is k,

To find its value, first, we have to combine like terms. This means that on the left side of the equation, we have to combine the coefficients of k,

And then, divide both sides by 6,

Hence, the value of k is 7.

Answer: 1/5 would be your answer!

Divide them both by 18 and you get 1/5

hope this helps :)

Answer:

Step-by-step explanation:

a.

5kg = 5000 g

5000 ÷ 125 = 40

Mary can make 40 packets

b. 40 x 99 = 3960

3960 ÷ 100 = 39.60

39.6 - 25 = 14.6

Therefore, Mary makes a profit of £14.6

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

I believe your question is:

For what value of [tex]x[/tex] does [tex]3^{2x}=9^{3x-4}[/tex]?

—

First, rewrite [tex]9[/tex] as [tex]3^2[/tex]:

[tex]3^{2x}=(3^2)^{3x-4}[/tex]

Then, use exponentiation to apply the [tex](a^b)^c=a^{bc}[/tex] rule:

[tex]3^{2x}=3^{2(3x-4)}[/tex]

Rewrite the expression as a non-exponential one since the bases ([tex]3[/tex]) are equal on both sides:

[tex]2x=2(3x-4)[/tex]

Distribute the [tex]2[/tex]:

[tex]2x=6x-8[/tex]

Subtract [tex]6x[/tex] from both sides:

[tex]-4x=-8[/tex]

Divide both sides by [tex]-4[/tex]:

[tex]x=2[/tex]

8.

A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex. So:

Therefore:

We can conclude that:

Is an isosceles triangle

Using trigonometric functions, the value of cos O in simplest terms is 5/17.

So, we know that: cos α = Adjacent Side/Hypotenuse

We have,

As we know,

We obtain:

Therefore, using trigonometric functions, the value of cos O in simplest terms is 5/17.

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Answer:

Quotient = x² - 3x + 5

Remainder = 9

Explanation:

To make the synthetic division, we need to rewrite the dividend with all the degrees of the exponents, so:

x³ - 4x + 6 = x³ + 0x² - 4x + 6

Then, we will use the coefficient of each term: 1, 0, -4 and 6

On the other hand, the divisor should have the form (x - a), so:

x + 3 = x - (-3)

Therefore, a = -3, and we will use this number for the synthetic division.

Finally, the synthetic division is:

Where the first number goes down, then the blue -3 is calculated as the number as 1 x -3, and the yellow -3 is equal to the sum of the number numbers 0 and -3, so: 0 + (-3) = -3

In the same way, 9 = -3 x -3 and 5 = -4 + 9

Finally, -15 = 5 x -3 and -9 = 6 - 15

Now, the coefficients 1, -3, and 5 give us the quotient of the division, and -9 is the remainder. So, the solution of the division is:

The ordered pair which is solution of 8x+16y > 32 is (-3,5) , the correct option is (b) .

In the question ,

it is given that ,

the linear inequality is 8x+16y > 32 .

to find the solution set ,

we substitute the options that are given

Option(a)

Substituting (0,2) in 8x+16y > 32 ,

we get ,

8(0) + 16(2) > 32

32 > 32 ,

false , hence it is not a solution .

Option(b)

Substituting (-3,5) in 8x+16y > 32 ,

we get ,

8(-3) + 16(5) > 32

-24 + 80 > 32

56 > 32

true , yes it is the solution .

Option(c)

Substituting (-1,1) in 8x+16y > 32 ,

we get ,

8(-1) + 16(1) > 32

-8 + 16 > 32

8 > 32

False , hence it is not a solution .

Option(d)

Substituting (4,0) in 8x+16y > 32 ,

we get ,

8(4) + 16(0) > 32

32 + 0 > 32

32 > 32

False , hence it is not a solution .

The only solution that satisfy the inequality is (-3,5) .

Therefore  , The ordered pair which is solution of 8x+16y > 32 is (-3,5) .

The given question is incomplete , the complete question is

Which ordered pair is in the solution set of 8x+16y > 32 ?

(a) (0,2)

(b) (-3,5)

(c) (-1,1)

(d) (4,0)

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Answer:

False

They are not proportional

Here, we want to know what the constant reveal

The growth factor inside the bracket as can be seen is greater than 1

It can also be less than 1

When it is greater than 1, there is an indication of a positive change from year to year

1.85 is greater than 1 and as such, we have an indication for a positive change

That means, as the years roll by, there will be a greater value of the quantity

Hence, as t increases, f(t) increases

To find the percentage growth rate, we subtract 1 from the growth value which is (1.85-1) = 0.85

0.85 represents a percentage of 85%; and thus there is a growth rate of 85% per year

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

Total number of players is 34.

What do you mean by algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.An algebraic expression is a mathematical phrase that includes variables, constants, coefficients, and algebraic operations.

Variables and constants can both be used in an algebraic expression.

It is given that a soccer team assigns jersey numbers to its players using the formula 7y - 3x where x and y are chosen at random.

Now, we have x = -2 and y = 4

Substitute these values in above expression we get,

7(4) - 3(-2) = 28 + 6 = 34

Therefore, total number of players is 34.

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Answer:

b) $472.50

Step-by-step explanation:

The sale price will be,

→ (600/100) × (100 - 25)

→ 6 × 75

→ $450

Now the final price will be,

→ 450 + ((450/100) × 5)

→ 450 + (4.5 × 5)

→ 450 + 22.5

→ $472.50

Hence, the price of $472.50.

The final price of the gaming system is $472.50, which is the correct answer would be option (B).

The percentage is defined as a ratio expressed as a fraction of 100.

A gaming system costs $600 and is on sale for 25% off. After the discount, there is a 5% tax.

To determine the final price of the gaming system, we need to first calculate the discount and then add the tax.

The discount is 25% of the original price, or 25% x $600 = $150.00.

So the price after the discount is $600 - $150 = $450.00.

The tax is 5% of the price after the discount, or 5% x $450 = $22.50.

Therefore, the final price of the gaming system is $450 + $22.50 = $472.50.

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The Little Rock Nine were a group of African American students who were held by the National Guard on September 4, 1957, while attending class at Little Rock Central High School in Little Rock, Arkansas.

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Given data:

The given selling price funnction is f(x)=15x+60.

SUbstitute 75 for x in the given expression.

ff(75)=15(75)+60

=1125+60

=1185

So, the selling price obtained after 75 hours is 1,185.

To calculate the total amount accrued when you deposit the money in an account that earns compound interest you have to use the following formula

A: amount accrued

P: principal amount

t: time, years

r: interest rate, expresed as a decimal value

n: number of coumpound periods

For this exericse

The principal amount is P=$1000

The time is t= 9 years

The interest rate is 9%/100=0.09

The compounding periods are 12/year (the interest is compounded monthly) so for the 9 year time period is 9*12=108

45, and

2x - 5

make up a straight angle pair.

So, they add up to 180 degrees.

Thus, we can write:

45 + 2x - 5 = 180

Now, we simply solve for x. Shown below: