3x - 4+1 = -2x - 5 + 5x

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?

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

The  the savings, expressed in percent if you order the combo is 18.75%, if the combo is bought at $6.50

What is the amount saved when combo is ordered?

The amount saved when ordering for combo instead of ordering hamburger and French fries is the difference between the total cost cost when for individual orders and the cost of the combo

total cost for individual orders=$5.00+$3.00

total cost for individual orders=$8.00

combo cost=$6.50

savings on combo=total cost for individual orders-combo cost

savings on combo=$8.00-$6.50

savings on combo=$1.50

% savings on combo=$1.50/$8.00

% savings on combo=18.75%

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========================================================

Explanation:

t = number of t-shirts

t = 100 shirts are in the box

Plug this into the equation and simplify to find W

W = 250+132.5t

W = 250+132.5(100)

W = 250+13250

W = 13500

The box weighs 13500 grams

This is equivalent to 13500/1000 = 13.5 kg

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 given triangle whose sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determined by using Pythagorean theorem which is the correct option (C).

Pythagoras theorem states that a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

The given triangle whose sides are 6cm, 10cm, and 12cm

Now, applying Pythagorean's theorem:

⇒ 6² + 10² = 12²

⇒ 36 +100 = 144

⇒ 136 = 144

Here, it is clearly observed that 136 <  144 therefore, the triangle is obtuse.

Therefore, the given triangle whose sides are 6cm, 10cm, and 12cm is an obtuse triangle

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Answer:

Determine whether the following statement is true or false. Explain.

The graph of y = |x-2|- 2 is a translation two units to the right and two units upward of the graph of y = |x|.

Choose the correct answer below.

A. True, because the graph of y = f(x - h) + k is the translation of the graph of y = f(X) |k| units upward if k= 0 or downward if k < 0, and h units to the right if h> 0 or to the

left if h < 0.

B. True, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) In| units upward if h = 0 or downward if h < 0, and k units to the right if k> O or to the

left if k < O

C. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) |k| units to the right if k>0 or to the left

220/8 = 27.5

27.5 x 8 = 220

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

The amount of fiber asked by the doctor to be consumed is 30 grams .

Method to calculate percentages :

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100 .

Let the amount of fiber asked by the doctor to be consumed be x .

According to question ,

40 % of x = 12

Solving the equation ,

( 40 / 100 ) * x = 12

x = 1200 / 40

x = 30

Hence ,  the amount of fiber asked by the doctor to be consumed is 30 grams .

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Answer:

30

Step-by-step explanation:

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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the algae that is present with the scientist to research upon covers a surface area of 2004 inches² in the rectangular prism.

The dimensions of the rectangular prism is given by:

Height = h = 18 inches

Width = w = 14 inches

Length = l = 30 inches

Now, we have to calculate the surface area of the tank excluding the top of the tank to find out how much algae has been present there for the scientist to test.

So, the formula for surface area will become:

A = 2(w l + h l + h w) - l w ( as the top has to be excluded)

Now substituting the values of l, w and h, we get that:

A = 2 [ (14) (30) + (18) (30) + (18) (14) ] - (30) (14) inches²

A = 2 [ 420 + 540 + 252 ] - 420 inches²

A = 2 [ 1212 ] - 420 inches²

A = 2424 - 420 inches²

A = 2004 inches²

Therefore, we get that, the algae that is present with the scientist to research upon covers a surface area of 2004 inches² in the rectangular prism.

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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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Answer:

0.08

Step-by-step explanation:

[tex]\frac{10}{45+10+64}[/tex]  The numerator is the number of times a customer used a debit card.  The denominator is the total of all the ways that customers have paid.

[tex]\frac{10}{19}[/tex] = 0.08403361344

This rounded to the nearest hundredths is

0.08

Answer:

0.08

Step-by-step explanation:

45 cash, 10 debit card, and 64 credit card.

= 45+10+64=119

There were a total of 119 customers. 10 paid with a debit card.

Probability the next customer will pay with a debit card:

10/119

=0.084033...

≈0.08

According to the given statement the following car seats are adequate for a 32-pound child:

Interval notation tells which part of the number line, from left to right, is included in the solution (i.e., which part of the number line is shaded). Parentheses are written next to endpoints which are NOT included in the solution while brackets are written next to included endpoints.

The Inequality car seat is intended for children weighing up to 30 pounds.

let the child's weight = x

x ≤ 30

Inequality for a car seat built for a child weighing between 15 and 40 pounds;

15 < x < 40

Inequality for a car built for a youngster weighing between 30 and 85 pounds;

30 < x < 85

According to the given statement the following car seats are adequate for a 32-pound child:

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The given question is not complete.

A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb, inclusive. Model these ranges on a number line. Represent each range of weight using interval notation. Which car seats are appropriate for a 32-lb child?

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:

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:

26

Step-by-step explanation:

[tex]FH=7+19=26[/tex]

Answer:

FH = 26

Step-by-step explanation:

The equation will be,

→ FH = FG + GH

Then the value of FH will be,

→ FH = 19 + 7

→ [ FH = 26 ]

Hence, the value of FH is 26.

Answer:

see below

Step-by-step explanation:

RATE is  560 mi / 8hr = 70 mi/hr

Rate * time = distance

         then

time = distance / Rate = 200 mi /  70 mi/hr = 2.857 hr   ( or 2 hr 51 min)

The  transformations that is possible in a linear function is: g(x) = (x - 3)².

if the function of the g (x) is known to be the original function, then one can say that:

g(x) = (x - 3)²

= g(x) = x²

This is one that is shifted by 3 unit to the right because in the above, one need to substitute x for x - 3.

Hence , it functional graph can be said to be a parabola with a vertices that is known to be opening at (3,0)

Therefore, based on the above, the example of the transformations that is possible in a linear function is: g(x) = (x - 3)².

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Answer:

7.04

Step-by-step explanation:

2.27

2.27

2.50 equals 7.04

Using translation concepts, function g(x) is given as follows:

C. [tex]g(x) = \sqrt[3]{x - 2} + 1[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent function is given by:

[tex]f(x) = \sqrt[3]{x}[/tex]

The translations for g(x) are as follows:

Thus the rule is:

C. [tex]g(x) = \sqrt[3]{x - 2} + 1[/tex]

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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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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 (-∞, ∞).

Answer:

x = -0.27 or 3.77

Step-by-step explanation:

explanation in pic

Answer:

This simplifies to 7x^2 - x.

Step-by-step explanation:

(x + 1)3 − x (x − 2)2 − 1

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

= x^3 + 3x^2 + 3x + 1 - x^3 + 4x^2 -4x - 1

= 7x^2 - x

The ticket price of

A Senior citizen = $14

A Child               = $4

First day of ticket sales :

Senior citizen tickets (s) = 14

Child tickets (c)             = 14

Total price of both tickets = $252

14s + 14c = 252   eq. (1)

Second day of ticket sales :

Senior citizen tickets (s) = 9

Child tickets (c)              = 7

Total price of both tickets = $154

9s + 7c = 154   eq. (2)

Multiplying equation 2 with 2, we get

18s + 14c = 308    eq. (3)

Now, we will subtract eq. (1) from eq. (3)

18s + 14c = 308    eq. (3)

-14s - 14c = -252    eq. (1)

____________________

          4s = 56

            s = 56/4

            s = 14

We get the ticket price of one senior citizen which is 14 Dollars.  

Now, we will put s = 14 in eq. 2,

So,  9s + 7c = 154

 (9×14) + 7c = 154

              7c = 154  - 126

                c = 28 / 7

               c = 4

Ticket price of one child is 4 Dollars.

Hence, the ticket price of a senior citizen and a child is $14 and $4, respectively.

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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:  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

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