2. Find f(-1).
f(x) = x2-4x+2
X+7
Round your answer to the nearest hundredth.

Both Adam's expression, d - 0.75d, and Rena's expression, 0.25d, yield the same sale price for the video game, offering different perspectives on calculating the discounted amount.

Adam's expression:

d: represents the original price of the video game in dollars.

-0.75: represents the discount of 75% as a decimal. A negative sign is used to indicate a decrease in price.

d - 0.75d: This expression subtracts the discount (0.75d) from the original price (d) to find the sale price of the video game.

Rena's expression:

0.25: represents the remaining price after the discount, which is 100% - 75% = 25%. This is also expressed as a decimal.

d: represents the original price of the video game in dollars.

0.25d: This expression multiplies the remaining price (0.25) by the original price (d) to find the sale price of the video game.

Both expressions, d - 0.75d and 0.25d, arrive at the same sale price for the video game. They simply represent different mathematical approaches to achieve the same result.

Answer:

Step-by-step explanation:

1/2 (6x-10) - x

Opening bracket

= 6x/2 - 10/2 - x

= 3x - 5 - x

= 2x - 5

Following are the solution to the given expression:

Given:

[tex]\to \frac{1}{2} (6x-10) - x \\\\ [/tex]

To find:

solve x or find the value.

Solution:

[tex]\to \frac{1}{2} (6x-10) - x \\\\ \to \frac{6x}{2} - \frac{10}{2} - x \\\\ \to \frac{6x-10-2x}{2}\\\\ \to \frac{4x-10}{2}\\\\ \to \frac{2(2x-5)}{2}\\\\ \to (2x-5) [/tex]

The final answer is "(2x-5)".

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$50,000 is 0.881 % of $5,670,000

Solution:

We have to find what percentage is $50,000 of $5,670,000

Let "x" be the required percentage

Then, by given, we can say,

"x" percent of 5,670,000 is 50000

Here, "of" means multiplication

So the statement goes like this:

"x" percent multiplied with 5,670,000 is equal to 50000

Thus finally the expression becomes:

[tex]x \% \times 5670000 = 50000\\\\\frac{x}{100} \times 5670000 = 50000\\\\\text{Simplify the above expression }\\\\56700x = 50000\\\\567x = 500\\\\x = 0.881[/tex]

Thus $50,000 is 0.881 % of $5,670,000

In this question, you're simplifying the expression.

Simplify:

2(x- 5) + 7x + 4

use distributive property

2x - 10 + 7x + 4

combine like terms

2x - 10 + 7x + 4

9x - 10 + 4

9x - 6

Answer:

9x - 6

Answer:

(x , 1/2x - 5/2)  where x is a real number.

Step-by-step explanation:

-2x + 4y = -10 ⇔ 4y = 2x - 10 ⇔ y = 1/2x - 5/2

then any couple of the form (x , 1/2x - 5/2) is a solution to the equation

example :

let x = 7 then 1/2x - 5/2 = 1/2(7) - 5/2 = 1

in this case  -2x + 4y = -2(7) + 4(1) = -14 + 4 = -10

then (7,1) verify the equation

Answer:

option B

Step-by-step explanation:

Her expense = $1250

Her expense per blank DVD = $2.45 × n

Her total expense = $1250 + $2.45n

Customers paying = $20.40n

Profit

= what customers are paying- her expense

= 20.40n -(1250+2.45)

= $17.95n - $ 1250

to learn more

The equation Carmen could use to calculate her profit, p, for the transfer of n videos is p = $1,250.00 - $17.95n

To find Carmen's profit, p, for the transfer of n videos, we need to consider her revenue and expenses.

We are given that Carmen charges her customers $20.40 for each video transferred. So, her revenue from the transfer of n videos can be calculated as 20.40n.

Let the number of blank DVDs used for the transfer of n videos as d. her total expenses for the blank DVDs can be calculated as 2.45d.

To calculate her profit,

p = $1,250.00 - $17.95n

Therefore, the equation Carmen could use to calculate her profit, p, for the transfer of n videos is:

p = $1,250.00 - $17.95n

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The tangent of the angle between two lines can be calculated using the slopes of the lines and applying them in the formula: Tan θ = (m2-m1) / (1 + m1*m2). The slopes of the given lines 2x+3y–5=0 and 5x=7y+3 are -2/3 and 5/7 respectively. These values are used in the formula to get the tangent of the angle.

The subject of the given problem is concerning finding the tangent of the angle in between two lines namely, 2x+3y–5=0 and 5x=7y+3. First, we should understand that the tangent of the angle between two lines can be calculated using the formula:

Tan θ = (m2-m1) / (1 + m1*m2)

Where 'm1' and 'm2' are the slopes of two lines and 'θ' is the angle between them. Firstly, we need to put the equation in the form of y=mx+b to determine the slopes. So, the slope of the first line is -2/3 (m1) and of the second line is 5/7 (m2).

Using these values in the formula, we can find:

Tan θ = ((5/7) - (-2/3)) / (1 + (-2/3)*(5/7))

By calculating the above expression using basic arithmetic you will find the required answer.

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Final answer:

The tangent of the angle between the two lines 2x+3y-5=0 and 5x-7y-3=0 is found by calculating the slopes of each line, then using the formula for the tangent of the angle between two lines. The result is a tangent of the angle of -29/11.

Explanation:

To find the tangent of the angle between the given lines, we need to first find the slope of each line. The slope of a line in the form ax + by + c = 0 is -a/b. Thus, the slope of the first line 2x + 3y – 5 = 0 is -2/3, and the slope of the second line 5x - 7y - 3 = 0 is 5/7. Now, using the formula for the tangent of the angle between two lines, which is tan(θ) = (m1 - m2)/(1 + m1*m2), where m1 and m2 are the slopes of the two lines, we get:

tan(θ) = ((-2/3) - (5/7))/(1 + (-2/3)*(5/7))

tan(θ) = (-14/21) - (15/21))/ (1 - (10/21))

tan(θ) = (-29/21) / (11/21)

tan(θ) = -29/11

Therefore, the tangent of the angle between the two lines is -29/11.

Answer:

vertical

Step-by-step explanation:

Answer:

y = [tex]\frac{1}{5}[/tex] x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{1}{5}[/tex] and c = 4, thus

y = [tex]\frac{1}{5}[/tex] x + 4 ← equation of line

Answer:

600

Step-by-step explanation:

first you need to find the calories for the entire batter:

12 muffins x 250 cal = 3000 cal

then you divide the total calories by 20:

3000/20 = 150

then multiply 150 by 4:

150 x 4 = 600

To find the caloric content of each mini-muffin, divide the total calories in the recipe by the new yield to find that each mini muffin is 150 calories. Consuming 4 mini muffins will total 600 calories.

The caloric content of a full-size muffin is 250 calories. If we reduce the size of the muffins we make from the recipe, it doesn't alter the total caloric content of the whole batch – it just redistributes those calories across more muffins. To calculate the number of calories in one mini-muffin, we need to divide the total number of calories in the entire recipe (250 calories/muffin * 12 muffins = 3000 calories) by the total yield of mini-muffins, which is 20. This results in 3000 calories/20 mini-muffins = 150 calories per mini-muffin. If you consume 4 mini-muffins, you'd be consuming 4 * 150 calories = 600 calories.

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Answer:

Step-by-step explanation:

The first thing you need to do is classify all the men into 4 groups which are:

1) 30 and younger with facial hair: 4

2) older than 3 with facial hair: 5

3) 30 and younger with facial hair: 3

4) older than 30 without facial hair: 4

Question (a): Make a two-way table of the data. Of the men surveyed, how many were 30 and younger? How many did not have facial hair.

                                  with facial hair          without facial hair          total

30 & younger                         4                                     3                          7

older than 30                         5                                     3                          8

total                                        9                                    6                          15

From the data you can see that:

7 men were 30 and younger and 6 men did not have facial hair.

Question (b): Create a two-way relative frequency table that displays the relative frequency of the men 30 and younger and of the men older than 30 who had or did not have facial hair. Express your answer as decimals written to three decimal places.

                              with facial hair          without facial hair          total

30 and younger             4/15                           3/15 = 1/5                 7/15

older than 30             5/15 = 1/3                      3/15 = 1/5                 8/15

total                            9/15 = 3/5                      6/15 = 2/5                   1

Question c: What percent of men older than 30 had facial hair?

The percent is equal to the relative frequency times 100% so in this case it is equal to (1/3) * 100% = 33.33%

Hope this helps!!!   :)

8 : 1 is the ratio of the areas of these similar rectangles

Solution:

Given that, rectangle has an area of 25 square feet

A similar rectangle has an area of 200 square feet

To find: Ratio of the areas of these similar rectangles

Ratio of the areas of these similar rectangles can be found dividing the area of rectangles

[tex]\rightarrow \frac{\text{ Area of rectangle}}{\text{Area of similar rectangle}} = \frac{200}{25}[/tex]

Reduce the fraction to lowest term

[tex]\rightarrow \frac{\text{ Area of rectangle}}{\text{Area of similar rectangle}} = \frac{200}{25} = \frac{8}{1}[/tex]

In ratios we get,

Area of rectangle : Area of similar rectangle = 8 : 1

Thus 8 : 1 is the ratio of the areas of these similar rectangles

Answer:

1.28

Step-by-step explanation:

0.4 x 3.2 = 1.28

Answer:

4x + 184 = 360

4x = 176

x = 44

Step-by-step explanation:

Lets check!

88 + 88 + 100 + 84 = 360

176 + 184 = 360

360 = 360

Answer:

[tex]\large \boxed{\text{ 0.4 lb/ft}^{3}; 5}[/tex]

Step-by-step explanation:

1. Density

[tex]\begin{array}{rcl}\text{Density} & = & \dfrac{\text{Mass}}{\text{Volume}}\\\\& = & \dfrac{\text{4 lb}}{\text{10 ft}^{3}}\\\\& = &\textbf{0.4 lb/ft}^{\mathbf{3}}\\\end{array}\\\text{The density of the gas is $\large \boxed{\textbf{ 0.4 lb/ft}^{\mathbf{3}}}$}[/tex]

2. Specific gravity

Specific gravity (sp gr) is the ratio of the density of the density of a gas to the density of dry air at standard temperature and pressure.

At IUPAC standard temperature and pressure (0 °C and 100 kPa), dry air has a density of 0.080 lb/ft³.

[tex]\begin{array}{rcl}\text{Sp gr}& = & \dfrac{\rho_{\text{gas}}}{\rho_{\text{dry air}}}\\\\& = & \dfrac{\text{0.4 lb/ft}^{3}}{\text{0.080 lb/ft}^{3}}\\\\& = &\mathbf{5}\\\end{array}\\\text{The specific gravity of the gas is $\large \boxed{\mathbf{5}}$}[/tex]

The density is the ratio of mass to volume, while the specific gravity is the ratio of two densities

The values required are;

Given:

Mass of the gas = 4 lb

Volume occupied by the gas = 10 ft.³

Required:

Find the density and the specific gravity of the gas

Density:

[tex]Density = \dfrac{Mass}{Volume}[/tex]

Therefore, the density of the mass of gas is given as follows;

[tex]Density = \dfrac{4 \ lb}{10 \ ft.^3} = 0.4 \ lb/ft.^3[/tex]

The density of the gas = 0.4 lb/ft.³

Specific gravity:

The specific gravity, s.g. of a gas is the ratio of the density of the gas to the density of air

The density of air ≈ 0.0765 lb/ft.³

The specific gravity of the gas is therefore;

[tex]s.g. = \dfrac{0.4 \ lb/ft.^3}{0.0765 \ lb/ft.^3} = \dfrac{800}{153} \approx 5.23[/tex]

The specific gravity of the gas is approximately 5.23

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Answer:

Part 1) [tex]y=650(1.1^x)[/tex]

Part 2) Approximate 1,152 monkeys

Step-by-step explanation:

Part 1) Write an exponential function to model the monkey population

we know that

The exponential function is of the form

[tex]y=a(b^x)[/tex]

where

y is the population of monkeys

x is the number of years

a is the initial value or y-intercept

b is the base of the exponential function

r is the percent rate of change

we have

[tex]a=650\ monkeys\\r=10\%=10/100=0.10[/tex]

[tex]b=1+r=1+0.10=1.10[/tex]

substitute

[tex]y=650(1.1^x)[/tex]

Part 2) What will the approximate population be after 6 years?

For x=6 years

substitute the value of x in the exponential equation

[tex]y=650(1.1^6)=1,151.5\ monkeys[/tex]

Approximate 1,152 monkeys

To find the number of quarters in Lucy's $9.50 coin collection, divide the total value by the value of one quarter. $9.50 divided by $0.25 equals 38, so Lucy has 38 quarters in her collection.

The question asks to calculate the number of quarters in Lucy's coin collection, given the total value is $9.50. Since each quarter is worth 25 cents, or $0.25, we can use division to find the number of quarters. The calculation is as follows:

Total value in dollars ($9.50) divided by the value of one quarter ($0.25) equals the number of quarters.

So, $9.50 ÷ $0.25 = 38 quarters.

Therefore, Lucy has 38 quarters in her collection.

Answer:

[tex]m\angle h=126^o[/tex]      

Step-by-step explanation:

we know hat

Vertical Angles are the angles opposite each other when two lines cross. They are always congruent.

In this problem

[tex]m\angle h=m\angle e[/tex] ----> by vertical angles

we have

[tex]m\angle e=126^o[/tex] ---> given problem

therefore

[tex]m\angle h=126^o[/tex]

Answer:

the answer is option D. 52 feet^2

Final answer:

The maximum number of volts that can be placed across the resistor is 20 volts.

Explanation:

The maximum number of volts, E, that can be placed across a resistor is given by the formula E = √(P * R), where P is the number of watts of power that the resistor can absorb and R is the resistance of the resistor in ohms. To find E, we can substitute the given values for P and R into the formula and solve:

E = √(2 * 200) = √(400) = 20 volts

Therefore, the maximum number of volts that can be placed across the resistor is 20 volts.

The maximum number of volts E that can be placed across the resistor is 20 volts.

The maximum number of volts, E, that can be placed across the resistor is given by the square root of the product of power P and resistance R. Therefore, E can be calculated as follows:

[tex]\[ E = \sqrt{P \times R} \][/tex]

[tex]\[ E = \sqrt{2 \text{ watts} \times 200 \text{ ohms}} \][/tex]

[tex]\[ E = 20 \text{ volts} \][/tex]

 The formula provided in the question is [tex]\( E = \sqrt{P \times R} \),[/tex] where E is the maximum number of volts that can be placed across a resistor, P is the power in watts, and R is the resistance in ohms.

This formula is derived from the power equation [tex]\( P = \frac{V^2}{R} \),[/tex]where V is the voltage across the resistor.

Given that the power P is 2 watts and the resistance R is 200 ohms, we substitute these values into the formula to find E:

[tex]\[ E = \sqrt{2 \times 200} \][/tex]

[tex]\[ E = \sqrt{400} \][/tex]

 The square root of 400 is 20, so the maximum number of volts E that can be placed across the resistor is 20 volts.

This is the voltage at which the resistor will absorb the maximum power of 2 watts without being damaged, assuming the resistor is operating at its maximum power rating.

Answer:

37.5%

Step-by-step explanation:

1/8 is 12.5% so multiply 12.5 x 3.

Answer:62.5

Step-by-step explanation:

1. if 3/8 is gone, that means 5/8 is present , which would make it 62.5 percent

#1. It helps to write everything out:

Sell price for boxes of cookies: $4.25x (x representing number of boxes)

Cost of each carton: $30y (y representing number of cartons)

The group bought 6 cartons, so we substitute y for 6:

30(6) = $180 they spent on the cartons.

Each carton contains one dozen boxes of cookies. In other words, 12 boxes of cookies. WIth 6 cartons purchased, we multiply 6 with 12 to get 72 boxes of cookies total they sold. Now we substitute x for 72:

4.25(72) = $306 they earned.

#2. The pattern is 2x + 5 = y where x represents the number of rides and 5 represents the admission. The y represents the total cost. Simply plug in the x's in the table into this equation to get the answer for y.

Answer:

Carlos would pay lower out-of-pocket costs if he picks over plan B.

Step-by-step explanation:

Let's make the comparison between plan A and plan B, this way:

Medicals bills = US$ 6,350

Plan A

6,350 - 1,200 = 5,150 * 30% = 5,150 * 0.3 = 1,545

Total out-of-pocket costs = 1,200 + 1,545 = $ 2,745

Plan B

6,350 - 1,500 = 4,850 * 25% = 4,850 * 0.25 = 1,212.50

Total out-of-pocket costs = 1,500 + 1,212.50 = $ 2,712.50

Carlos would pay lower out-of-pocket costs if he picks over plan B.

Answer:

A decimal that is greater than 2.15 and less than 2.25 can range from anywhere between 2.16 to 2.24

Anyone of these would work

Hope this helped ;)

The decimal that more than 2.15 and less than 2.25 is as follows:

2.16

2.17

2.18

2.19

2.20

2.21

2.22

2.23

2.24

Any of the above decimal number should be considered.

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Answer:

x = 22

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

-4x^3 = 32

1. divide -4 on both sides to get x^3 = -8

2. cube root it to get -2

Answer:

Step-by-step explanation:

think of any number : x

add 3 : x+3

double that : 2(x+3)

subtract 4 : 2(x+3)-4

cut in half (divide by 2) : (2(x+3)-4)/2

subtract original number : (2(x+3)-4)/2-x

if you simplify, you will end up with 1

Step by Step simplification

2(x+3) = 2x+6   double that

2x+6-4=2x+2    subtract 4 : 2(x+3)-4

(2x+2)/2 = x+1     cut in half (divide by 2)

x+1-x = 1      subtract original number

Answer:

x=4

Step-by-step explanation:

6k-25=7-2k

6k-25+25=7-2k+25

6k=7-2k+25

6k+2k=7-2k+2k+25

6k+2k=8k

7+25

8k=32

x=32÷8

x=4

Answer:

37 7/8

Step-by-step explanation:

First you make the equation

14 5/8 = _ - 20 - 3 1/4

They all have to make 14 5/8 so then solve

x+-93/4 = 117/8

x=303/8

Simplified:

x=37 7/8

To solve the equation -20 - 3 1/4 = 14 5/8, start by simplifying the mixed number and converting it to an improper fraction. Then, find a common denominator for the fractions and add them. Simplify and multiply both sides by -2 to eliminate the fractions.

To solve the equation: -20 - 3 1/4 = 14 5/8, you can start by simplifying the mixed number and converting it to an improper fraction.
-20 can be written as -20/1, so the equation becomes:
-20/1 - 13/4 = 117/8.
Next, find a common denominator for the fractions. The common denominator for 1 and 4 is 4, so the equation becomes:
-80/4 - 13/4 = 117/8.
Now, you can add the fractions:
(-80 - 13)/4 = 117/8.
Simplify:
-93/4 = 117/8.
Finally, multiply both sides by -2 to eliminate the fractions:
-93/4 * -2 = 117/8 * -2.
The final answer is:
186/4 = -234/8.
Simplify:
93/2 = -117/4.

Answer:

Sasha's dad expects to have between 23 and 24 cupcakes with flaw design

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Flaw prediction in the design by the manufacturer = 1 out of 50 cupcakes

Last week production = 98 dozens

2. Approximately how many cupcakes would be expected to have a flaw design?

For answering this question we have to find out the exact number of last week production, this way:

Last week production = 98 dozens

Last week production = 98 * 12 = 1,176

Now, we can calculate the number of cupcakes that would be expected to have a flaw design:

Number of cupcakes with a flaw design = 1,176/50 = 23.52

Sasha's dad expects to have between 23 and 24 cupcakes with flaw design