which of the following inequalities is represented by the number line​

Answer:

C

Step-by-step explanation:

Given the logarithmic equation

[tex]\log_4x+\log_4(x-3)=\log_4(-7x+21)[/tex]

First, notice that

[tex]x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x<21\ x<3[/tex]

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

[tex]\log_4x+\log_4(x-3)=\log_4x(x-3),[/tex]

then

[tex]\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3[/tex]

Hence, [tex]x=3[/tex] and [tex]x=-7[/tex] are extraneous solutions

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.

$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

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

the LCM of 21 and 105 is 105.

Answer:

The answer to your question is 105

Step-by-step explanation:

To get the least common factor dividing both numbers by the prime numbers starting from 2.

But these numbers are not multiples of 2, try 3

                                                           21   105   3

These numbers are not multiples of 3 let's try 5                                                                    

                                                            7     35  5  

These numbers are multiples of 7     7       7   7

                                                            1        1

The LCM is the product of the prime numbers = 3 x 5 x 7 = 105

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:

(2, - 3 )

Step-by-step explanation:

Given the 2 equations

2x - 3y = 13 → (1)

x + 2y = - 4 → (2)

Rearrange (2) expressing x in terms of y by subtracting 2y from both sides

x = - 4 - 2y → (3)

Substitute x = - 4 - 2y into (1)

2(- 4 - 2y) - 3y = 13 ← distribute and simplify left side

- 8 - 4y - 3y = 13

- 8 - 7y = 13 ( add 8 to both sides )

- 7y = 21 ( divide both sides by - 7 )

y = - 3

Substitute y = - 3 into (3) for corresponding value of x

x = - 4 - 2(- 3) = - 4 + 6 = 2

Solution is (2, - 3 )

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:

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

Answer:

vertical

Step-by-step explanation:

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=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:

1.28

Step-by-step explanation:

0.4 x 3.2 = 1.28

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: slope = 0

Step-by-step explanation:

The formula for calculating slope is given as :

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = 2

[tex]x_{2}[/tex] = 1

[tex]y_{1}[/tex] = 0

[tex]y_{2}[/tex] = 0

Substituting into the formula , we have

m = [tex]\frac{0}{-1}[/tex]

m = 0

The slope of the line passing through (2, 0) and (1, 0) is 0, indicating that the line is horizontal.

The slope of a line that passes through the points (2, 0) and (1,0) can be determined using the formula for slope, which is (y2 - y1) / (x2 - x1).

Plugging in the coordinates, we get (0 - 0) / (1 - 2), which simplifies to 0/-1.

The slope of this line is 0. This indicates that the line is horizontal because there is no change in the y-value as the x-value changes.

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!!!   :)

Answer:

no

Step-by-step explanation:

3=5(3)

3=15

false

Answer:

no

Step-by-step explanation:

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:

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:

[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]

#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:

4x + 184 = 360

4x = 176

x = 44

Step-by-step explanation:

Lets check!

88 + 88 + 100 + 84 = 360

176 + 184 = 360

360 = 360

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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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:

6/10

Step-by-step explanation:

Answer:

It could be 9 or 23. It could also be many other things.

Step-by-step explanation:

The other side of the triangle has to be greater than 15 when added to 7 or greater than both when they are added together.

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:

12 meter = 129.167

48 = 516.668

121  =1302.43

144 =1550

169 = 1819.1

Step-by-step explanation:

Final answer:

The area of a 12 meter square is calculated by squaring the length of the side, which results in 144 square meters.

Explanation:

The area of a square can be found by squaring the length of one of its sides. Since the given square has a side length of 12 meters, the area can be calculated as follows:

Area = side length * side length

Area = 12 m * 12 m

Area = 144 square meters