Sophia buys 13 bottles of cranberry juice at the corner store for a total cost of $7.02. If each bottle costs the same amount, how much is 14 bottles of juice?

Answer:

[tex]P_{rofit}=13x-50\\C_{ost}(70)=960\\P_{rofit}(70)=860\\C_{ost}(100)=1350\\P_{rofit}(100)=1250\\For\ a\ profit\ of\ \$1100\ one\ must\ sell\ 89\ stuffed\ animals.[/tex]

Step-by-step explanation:

I would suggest starting with 1 and working to 4, as it is set up for you like that.

I would start by writing down what you know, then what you need as follows:

[tex]Givens:\\ C_{ost}=13x+50;\\ R_{evenue}=36x;\\P_{rofit}=R_{evenue}-C_{ost};\\ x=N_{umber\ of\ animals}\\[/tex]

[tex]Find:\\1.\ Profit\ equation\\2a.\ C_{ost}\ to\ make\ 70\ animals\\2b.\ P_{rofit}\ from\ selling\ 70\ animals\\3a.\ C_{ost}\ to\ make\ 100\ animals\\3b.\ P_{rofit}\ from\ selling\ 100\ animals\\4.\ N_{umber}\ of\ animals\ needed\ to\ produce\ P_{rofit}\ of\ \$1100[/tex]

Now you can read it easier. Given that Profit is Revenue minus Cost, plug the equations for Cost and Revenue into the Profit equation as follows:

[tex]P_{rofit}=36x-(13x+50)\\NOTE:\ Do\ NOT\ forget\ to\ put\ the\ C_{ost}\ equation\ in\ parenthesis\ as\ you\ \\must\ subtract\ the\ entire\ C_{ost}.\\\\Distribute\ the\ negative:\ P_{rofit}=36x-13x-50\\Combine\ like\ terms:\ P_{rofit}=13x-50[/tex]

With the Profit equation, it is now easier to solve 2b, 3b, and 4.

[tex]C_{ost}\ for\ 70: C_{ost}=13(70)+50=(700+210)+50\\NOTE:\ I\ used\ the\ fact\ that\ 13*70=(10+3)*70=10*70+3*70\\C_{ost}=910+50=960\\This\ could\ also\ be\ written\ more\ clearly\ as\ C_{ost}(70)=960\\\\P_{rofit}(70) = 13(70)-50\\P_{rofit}(70)=(700+210)-50\\P_{rofit}(70)=910-50\\P_{rofit}(70)=860\\\\C_{ost}(100)=13(100)+50\\C_{ost}(100)=(1300)+50\\C_{ost}(100)=1350\\\\P_{rofit}(100)=13(100)-50\\P_{rofit}(100)=(1300)-50\\P_{rofit}(100)=1250\\[/tex]

Problem 4 will involve using the (now) known amount for profit, $1100 to find the unknown number of animals. This will involve a little bit more "algebra" compared to the prior questions.

[tex]P_{rofit}(x)=1100=13x-50\\1100=13x-50\\[/tex]

Because 13x - 50 is 1100, 13x will be 1100 + 50, just as

[tex]5*2+10 = 20\\5*2=20-10\\[/tex]

So, add 50 to both sides:

[tex]1100+50=13x-50+50\\1150=13x\\[/tex]

Because 13x is 1150, x will be 1150÷13, just as

[tex]5*2=10\\5=\frac{10}{2}[/tex]

So, divide 13 from both sides:

[tex]\frac{1150}{13}=\frac{13x}{13}\\\\\frac{1150}{13}=x[/tex]

Because 1150/13 is not an integer, use a calculator, or simplify the improper fraction to obtain...

x=88.5 (Approximately)

But, because you cannot sell half an animal, you would have to sell 89 in order to profit $1100, for bonus points, what is the actual profit accrued by selling 89 animals?

Step-by-step explanation:

Solving steps

(2x-6)×(x-2)

Multiply

2x×x-2x×2-6x-6x 2

Calculate Multiply

2x²-4x-6x+12

Collect like terms

Solution

2x²- 10x + 12

Answer:

A

Step-by-step explanation:

Sin A = [tex]\frac{opposite}{hypotenuse}[/tex]

Cos A = [tex]\frac{adjacent}{hypotenuse}[/tex]

Answer:

[tex]\text{a.} \quad \sin A=\dfrac{3}{5}, \quad \cos A=\dfrac{4}{5}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Therefore:

[tex]\implies \sin A =\dfrac{BC}{AB} = \dfrac{3}{5}[/tex]

[tex]\implies \cos A =\dfrac{AC}{AB} = \dfrac{4}{5}[/tex]

The value of the expression 91 - [ 22 { 16 divided (39 + 3 of 3 - 40 )} ] is 47 by using PEMDAS.

We are given an expression as:

91 - [ 22 { 16 divided (39 + 3 of 3 - 40 )} ]

By the PEMDAS rule, the expression will be:

= 91 - [ 22 {16 ÷ (39 + 9 - 40 ]

= 91 - [ 22 {16 ÷ (8) ]

= 91 - [ 22 {16 ÷ 8} ]

91 - [ 22 {2} ]

= 91 -[ 22 × 2 ]

= 91 - [ 44 ]

= 91 - 44

= 47

Therefore, the value of the expression 91 - [ 22 { 16 divided (39 + 3 of 3 - 40 )} ] is 47 by using PEMDAS.

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Answer:

7.04

Step-by-step explanation:

2.27

2.27

2.50 equals 7.04

A location that is 30 degrees north and 45 degrees west is west of the prime meridian and north of the equator.

A prime meridian refers to an arbitrary meridian which is there in a geographic coordinate system. Here, the longitude is defined as 0°.

A prime meridian and its anti-meridian will together form a great circle in a geographic coordinate system.

The Equator is a circle of latitude, about 40,075 km in circumference, that divides Earth into the Northern and Southern hemispheres.

It is an imaginary line that is located at 0 degrees latitude, and is a halfway between the North and South poles.

Therefore, we get that a location that is 30 degrees north and 45 degrees west is west of the prime meridian and north of the equator.

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220/8 = 27.5

27.5 x 8 = 220

She’ll have to work 27 hours and 30 minutes to get 220 pounds.

Answer:

5

Step-by-step explanation:

add the numbers up then divide by how many there are.

3+4+5+6+7=25

25÷5 = 5

Answer:

1/48

Step-by-step explanation:

The total number of different outcomes when rolling 4 dice is

6 × 6 × 6 × 6 = 1296

The possible number of outcomes of rolling a 6 followed by 3 odd numbers is

1 × 3 × 3 × 3 = 27

p(6 followed by 3 odd numbers) = 27/1296 = 1/48

The weight average of the coordinates is 1

The given parameters are:

The weight average is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

So, we have:

Weight average = (-2 * 3 + 5 * 1 + 6 * 1)/(3 + 1 + 1)

Evaluate the quotient

Weight average = 1

Hence, the weight average of the coordinates is 1

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The coordinates of A'' will be ( -2, 5).

We are given that:

Quadrilateral ABCD is reflected across the x - axis.

We know that, when a refection is done about x-axis, the values of the abscissa x remain identical & the value of ordinate  just change their signs:

A(-5,-3) will become A'(-5,+3)

B(-6,-1) will become B'(-6,+1)

C(-3,-1) will become C'(-3,+1)

D(-2,-3) will become D'(-2,+3)

Now, the reflected quadrilateral A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A"B"C"D".

So, the coordinates of A'' will become:

( - 5 + 3, 3 + 2)

( -2, 5)

Therefore, we get that, the coordinates of A'' will be ( -2, 5).

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If the coordinates of the point a is (2,1) and midpoint is (0.-3), then the coordinates of b is (-2,-7).

Midpoint:

Midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

The formula for midpoint is,

[tex](x_{m},y_{m})= (\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]

Where

(x₁,y₁) is the coordinates of the first point and

(x₂,y₂) is the coordinates of the second point

and

[tex](x_m,y_m)[/tex] is the mid point of the first and second points.

Given,

Mid point = (0,-3)

Point a = (2,1)

Here we need to find the point b.

Let (x,y) be the point of b.

Now,

Apply the values on the formula,

Then we get,

[tex](0,-3)=(\frac{2+x}{2},\frac{1+y}{2})[/tex]

Compare the values in order to solve it,

=> 0 = (2 +x)/ 2

=> 0 = 2 + x

=> x = -2

Similarly,

=> -3 = (1 + y)/2

=> -3 x 2 = 1 + y

=> -6 = 1 + y

=> y = -6 - 1

=> y = -7

Therefore, the coordinates of b is (-2,-7).

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Answer:

Step-by-step explanation:

First of all it has to drop 15 degrees to get to 0.

We have another three degrees to go.

15 - - 3 = 18

The temperature change was 18 degrees from midnight to morning.

Answer:

Final answer: P=(1,5)

Step-by-step explanation:

The line APB is a line such that AP/PB= 1/3. From the points A and B that we have we can find the distance between those points using the formula d= [(y2-y1)^2=(x2-x1)^2]^1/2

d= 4 (13)^(1/2)

Now the ratio is 1:3. AP= sq rt(13) and PB= 3 sq rt(13)

Using mid point formula the mid point of AB (say Q) = [(-1+7)/2,(2+14)/2]= (3,8).

Hence the mid point of AQ is P which can found out again using the mid point formula

P= [(-1+3)/2,(2+8)/2]= (1,5)

The polynomial is twice the sum of -2x² + 5x - 3 and 5x² - 4 is 6x² + 10x - 14.

Given the polynomials in the question;

-2x² + 5x - 3 and 5x² - 4

First, we find the sum of the polynomials

(-2x² + 5x - 3) + (5x² - 4)

-2x² + 5x - 3 + 5x² - 4

Collect like terms and simplify

-2x² + 5x² + 5x - 3 - 4

3x² + 5x - 7

Next, multiply the polynomial by 2.

2(3x² + 5x - 7)

Using distributive property,

2×3x² + 2×5x +2×-7

6x² + 10x - 14

Therefore, the polynomial is twice the sum of -2x² + 5x - 3 and 5x² - 4 is 6x² + 10x - 14.

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Yes, it is true that if "x" is an optimal solution to a linear programming problem, then it is a vertex of the feasible region.

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The missing values are a = 0, b= 6 and c=4.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have function,

f(x) = -x² + x + 6

At x= -2

f(-2) = -(-2)² + (-2) + 6 = -4 -2  + 6= 0

At x = 0

f(0) = -0² + 0 + 6= 6

At x = 2

f(2) = -2² + 2 +6 = -4 + 8= 4

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Answer:

I think it's 2(x+7).

Step-by-step explanation:

This is distributive function where a number is multiplied from outer value to inner parenthesis values.

I hope this is the right answer.

Philip's mistake is he did not add zero at ten's place.

When the multiplication is performed with two or more digits in the bottom number, zeroes are added as per the position. We see that in number 21, one is at one's place and 2 is at ten's place. Hence, when multiplying the digit 2 with the number 1659, we will add zero at one's place.

Performing the correct multiplication -

1659

× 21

1659

+33180

The result of multiplication will be the sum of numbers 1659 and 33180.

Result = 34,839

Therefore, the multiplication of the numbers will give result 34,839. Hence, the mistake is not keeping zero at one's place, while performing multiplication.

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Answer:

it 9/ 8

Step-by-step explanation:

2/4× 9/4

18/16

9/8

Answer:

A: (-10, 2)

B: (-5, 2)

C: (-5, 7)

D: (-10, 7)

Step-by-step explanation:

When you reflect over the x axis, you flip the y value, so that what I did.

Answer: a. 3+13n

b. About 3 newspapers

Step-by-step explanation:

a. T=total thickness of newspapers on a skid in inches

T=3+13n

b. 3'=3 ft

1 ft=12 inches

3 ft=3*12 inches

3 ft=36 inches

36=3+13n

13n=33

n=2.54 ==> About 3 newspapers

Answer: 59,003

Step-by-step explanation:

8,429 x 7=

8,429 x (5+2)=

8,429 x 5 + 8,429 x 2=

4,214.5*10+16,858=                  ==> n*5=n/2 * 10

42,145+16,858=59,003

Answer:

3x^3-11y^2

Step-by-step explanation:

17x^3 -11y^2 -14x^3

collect like terms

17x^3 -14x^3 =3x^3

3x^3-11y^2

I hope it helps.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Domain and range help us describe the values a graph covers.

Defining Domain and Range

Remember that the x-values are along the horizontal axis, and the y-values are on the vertical axis.

The function given to us extends infinitely to the left and right as shown by the arrows. Additionally, the graph extends up and down infinitely; thus the range is also infinite.

Interval Notation

Interval notation should be written as (minimum value, maximum value). If the minimum and maximum values are included within the range or domain, then the parentheses should be replaced with brackets. This looks like [included minimum, included maximum]. Since a function cannot actually include infinity, an infinity symbol should never have brackets.

Eventually, this linear function will reach every single x and y-value in existence. So, both axes have a minimum of -∞ and a maximum of ∞. Thus, both the domain and range are (-∞, ∞).

Hint for future problems: all linear functions will have a domain and range of (-∞, ∞).

The completed statement on the addition and subtraction operations with integers is presented as follows;

When the signs are of the integers of the same sign

1. Add the integers and copy the 2.) integer sign. When the signs are 3) different, subtract them and use the sign of the number with the greater 4) magnitude. If we add two same numbers with different signs, then the answer is equal to 5.) zero. The sum of two negative integer is a 6.) negative integer. The sum of two positive integers is a 7.) positive integer.

The process of adding integers is as follows;

Integers that have the same sign are added together, and the sign of the integers are placed before the result.

The addition of two integers that have different signs involve subtracting the integers and including the sign of the integer with the largest magnitude to the result.

The addition of two the same numbers that have different signs gives the same result as subtracting a number from itself, which is zero.

The sign of the result of the addition or subtraction of two integers of the same is the same as the sign of the integers in the operation.

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The multiplication of 6 × 43 by applying the distributive property of multiplication will be 258.

The general mathematical operation of multiplying two or more numbers to get a new multiplied number.

If both values are more than or less than one, the resultant multiplication will be greater or smaller than the numbers that will be multiplied.

For reference 4 × 3 = 12 and 4 × 0.5 = 2.

Given the multiplication,

6 × 43

⇒ 6 × (40 + 3)

By applying the distributive property of multiplication,

⇒ 6 × 40 + 6 × 3

⇒ 240 + 18

⇒ 258

Hence "The multiplication of 6 × 43 by applying the distributive property of multiplication will be 258.".

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Step-by-step explanation:

so, this is a multiplication ?

6 3/4 × (-11.5)

let's bring the mixed numbers to full fractions, and then we can easily multiply.

6 3/4 = (6×4 + 3)/4 = (24 + 3)/4 = 27/4

-11.5 = -11 1/2 = (-11×2 - 1)/2 = (-22 - 1)/2 = -23/2

so, the multiplication is

27/4 × -23/2 = 27×-23 / 4×2 = -621/8 =

= (-616 - 5)/8 = (-77×8 - 5)/8 = -77 5/8

Answer:

-77 5/8

Step-by-step explanation:

6 3/4 can be turned into 6.75.

6.75 * -11.5 is -77.625

-77.625 can be simplified into 5/8

Brainliest pls?

Answer:  0

Step-by-step explanation:

Since it is 10 units total from -4 to 6,

4/10 and 6/10 would give a ratio of 2:3

4 units from -4 would be at 0, which is also 6 units away from the 6

4 units to 6 units equals a ratio of 2:3