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The solution for the linear inequality, in interval notation, is \(\:(-\infty \:,\:-\frac{7}{6}]\).

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use of follow symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than) and > (greater than).

The solutions for inequalities can be given by: graph in a number line or numbers.

For solving this exercise, it is necessary to find a number solution for  the given inequality.

                                 12x-8≤6x-15

                                12x-6x≤ -15+8

                                   6x≤-7

                                    x≤ -7/6

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The holly records a temperature at 15 below zero

This implies that the temperature i

The the coefficient of variation for set a is 15.7% and the coefficient of variation for set b is 22.3%.

The formula for calculating the coefficient of variation is:

CV = (standard deviation / mean) x 100%

where standard deviation is a measure of the spread of the data around the mean. The CV expresses the standard deviation as a percentage of the mean.

To calculate the CV for set a, we first need to find the mean and standard deviation of the data set. The mean can be calculated by adding all the values and dividing by the number of values.

Mean = (3.97 + 3.47 + 3.99 + 4.30 + 3.16 + 3.07 + 4.24 + 2.94 + 3.56 + 3.43 + 3.06 + 3.34 + 4.35 + 3.57) / 14 = 3.65

The standard deviation can be calculated using a calculator or a spreadsheet software such as Microsoft Excel. For this set, the standard deviation is 0.574.

CV = (0.574 / 3.65) x 100% = 15.7%

To calculate the CV for set b, we need to first remove the dollar sign from each value and then find the mean and standard deviation.

Mean = ($24,800 + $30,000 + $22,300 + $20,400 + $19,000 + $32,200 + $23,000 + $23,000 + $24,000 + $27,200 + $34,900) / 11 = $25,727.27

The standard deviation can be calculated using a calculator or spreadsheet software. For this set, the standard deviation is $5,746.38.

CV = ($5,746.38 / $25,727.27) x 100% = 22.3%

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The statement -4 is not in the domain of f(g) is true.

The domain is defined by the set of values of independent variables. The set of inputs that a function will accept is known as the domain of the function in mathematics. The collection of all potential inputs for a function is known as its domain.

In a function for each domain, we get a possible output from dependent variable which is termed as range.

From the diagram shown -4 cannot be used as domain because the output might be an imaginary number.

So, -4 is not in the domain of f(g) is true

hence, -4 cannot be a domain of given function f(g)

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The statement -4 is not in the domain of f(g) is true.

What is domain?

The domain is defined by the set of values of independent variables. The set of inputs that a function will accept is known as the domain of the function in mathematics. The collection of all potential inputs for a function is known as its domain.

What is range?

In a function for each domain, we get a possible output from dependent variable which is termed as range.

From the diagram shown -4 cannot be used as domain because the output might be an imaginary number.
So, -4 is not in the domain of f(g) is true
hence, -4 cannot be a domain of given function f(g)

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Answer:

y = 5x + 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 )

given

5x = y - 4 ( add 4 to both sides )

5x + 4 = y , that is

y = 5x + 4 ← in slope- intercept form

Answer:

-1/3

Step-by-step explanation:

just reduce the fraction

Since the segments AE and EB are congruent and DF and FC are congruent, the trapezoid ABCD and EBCF are similar.

Therefore the proportion between the top bases of the trapezoids is the same as the bottom bases of the trapezoids.

So we have:

Finding the roots using the quadratic formula, we have:

Answer:

-3pq -3p²q²

Step-by-step explanation:

Refer to attachment.

Hope it helps :)

Answer:

The freezing point of water at a pressure of one atmosphere is 0°C (32°F); that of liquid nitrogen is -209.89°C (-345.8°F).

Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.

To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.

Total weekly cost = Fixed rate + Insurance cost + Gas cost

Total weekly cost = $49.00 + $14.00 + $12.00

Total weekly cost = $75.00

The cost for Thanh per month (four weeks) = Total weekly cost × 4

Cost for Thanh per month (four weeks) = $75.00 × 4

Cost for Thanh per month (four weeks) = $300.00

Therefore, Thanh's cost per month (four weeks) will be $300.00.

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From the resulting solution, the correct linear inequality graph is Graph C.

Given the inequality equation below:

2(2x-1)+7< 13 or -2x+5 ≤ -10.​

Simplify the expression

2(2x-1)+7< 13

Expand

4x - 2 + 7 < 13

4x + 5 < 13

4x < 13 - 5

4x < 8

x < 2

For the inequality -2x+5 ≤ -10.

-2x+5 ≤ -10

-2x  ≤ -15

x  ≥ 7.5

Hence the solution to the given system of inequalities are x < 2 and x  ≥ 7.5

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Trigonometry involves the study of the relationships between the sides and angles of triangles.

One important concept in trigonometry is the trigonometric ratios, which are based on the ratios of the sides of a right triangle. In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

The three primary trigonometric ratios are sine, cosine, and tangent. They are defined as follows:

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

In addition to these primary ratios, there are also reciprocal ratios, which are the inverses of the primary ratios. The reciprocal ratios are cosecant, secant, and cotangent. They are defined as follows:

The cosecant of an angle is the reciprocal of the sine of the angle.

The secant of an angle is the reciprocal of the cosine of the angle.

The cotangent of an angle is the reciprocal of the tangent of the angle.

In trigonometry, fractions and ratios are used to express the relationships between the sides and angles of a right triangle. By using these ratios, it is possible to calculate the length of one side of a triangle given the lengths of the other sides and the angles, or to find the measure of an angle given the lengths of the sides.

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Answer:

A. Lower

B. Half

Step-by-step explanation:

Answer:

1. Lower and 2. Half

The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.

We can use the conservation of momentum equation:

(mboat + mperson) * vboat = mperson * vperson

(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)

230 kg * vboat = 56 kg * (0.80 m/s + vperson)

vboat = (56/230) * (0.80 m/s + vperson)

vperson = 0.80 m/s + vboat

vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)

(174/115) * vperson = (504/115) * m/s

Dividing both sides by (174/115), we get:

vperson = 2.896 m/s

vboat = (56/230) * (0.80 m/s + vperson)

Substituting the value of vperson, we get:

vboat = 1.337 m/s

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On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.

Answer:

15 + 1.50n = cost of one pizza

Step-by-step explanation:

Hope I helped.

Answer:

20

Step-by-step explanation:

Step 1: 4 = 20% × Y

Step 2: 4 = 20/100 × Y

Multiplying both sides by 100 and dividing both sides of the equation by 20 we will arrive at:

Step 3: Y = 4 × 100/20

Step 4:Y = 4 × 100 ÷ 20

Step 5: Y = 20

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

20% = 4

100% = 20

The total number of people in the group is 100 people.

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

We have,

Number of Aussies with blue eyes = 4

Percentage of blue eyes in the Aussies = 20%

This can be written as:

20% = 4

Now,

The percentage of the total number of people in the group = 100%

So,

20% = 4

Multiplying 5 on both sides.

5 x 20% = 5 x 4

100% = 20

This means,

The total number of people in the group is 100.

Thus,

The total number of people in the group is 100 people.

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The number of night of work each performers will have equal amount is 1 night

The buskers gets permit which cost $30. They can make an average of $45 per night (n),

Therefore,

y = 45n - 30

Without a permit they may only make an average of $15 per night.

Therefore,

y = 15n

The number of night the money made are both equal.

45n - 30 = 15n

45n - 15n  = 30

30n = 30

n = 30 / 30

n = 1

Therefore, the number of night of work each performers will have equal amount is 1 night

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Answer:

the answer is 4

Step-by-step explanation:

if y=21 the we substitute in the main equation

21=8x-11

8x=32

x=4

Answer:

36 members paid the total money that would be made would be $180

Step-by-step explanation:

48*75%=36

36*5=180

Answer:

t = 2 and t = 3.

Step-by-step explanation:

To solve the equation 2^(2t) - 12(2^t) + 32 = 0, we can use a substitution to simplify the equation. Let's set u = 2^t:Substituting u = 2^t, the equation becomes:u^2 - 12u + 32 = 0Now we have a quadratic equation in terms of u. We can solve it by factoring or using the quadratic formula. Let's try factoring:(u - 4)(u - 8) = 0Setting each factor equal to zero, we have:u - 4 = 0 or u - 8 = 0Solving for u:u = 4 or u = 8Now, substitute back u = 2^t:For u = 4:

2^t = 4Taking the logarithm base 2 of both sides:

t = log2(4)

t = 2For u = 8:

2^t = 8Taking the logarithm base 2 of both sides:

t = log2(8)

t = 3

Answer:

8/21

Step-by-step explanation:

7+5+9=21 the total in the bag

5+9=14 total without red

Answer:

The amount he will have at the end of five years is $11,616.8

Interest on the amount is $1,616.8

Step-by-step explanation:

Kindly check the attached picture for explanation.

Answer:

40,000

Step-by-step explanation:

15000+25000=40000

Answer: 40,000

Step-by-step explanation:

25,000 + 15,000 = 40,000

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Answer:

which language is this .

The central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

Given that, a survey was conducted in which 2400 people were asked to name their favorite sport to watch and the table below shows their answers: Sport percentage of people are:

Football 29%

Soccer 9%

Baseball 14%

Basketball 8%

Hockey 8%

Other 32%

We need to find the central angle measure, x, for the Baseball slice in the circle graph.

For this, we need to use the formula that gives the central angle measure in degrees for a sector of a circle:

Central angle measure = (Percentage/100) × 360°

Now, using the above formula, we can calculate the central angle measure for each sport as shown below:

Football: (29/100) × 360° = 104.4°

Soccer: (9/100) × 360° = 32.4°

Baseball: (14/100) × 360° = 50.4°

Basketball: (8/100) × 360° = 28.8°

Hockey: (8/100) × 360° = 28.8°

Other: (32/100) × 360° = 115.2°

The sum of all central angle measures should be 360°, which is the measure of a full circle.

So we can check if the calculations are correct: 104.4° + 32.4° + 50.4° + 28.8° + 28.8° + 115.2° = 360°

We see that the sum is indeed 360°, so the calculations are correct. The central angle measure for the Baseball slice is 50.4°.

Therefore, the central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

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The function g(x), after the translations, is defined as follows:

g(x) = (x - 93)² + 98.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The changes to the function are given as follows:

Hence the function g(x) is defined as follows:

g(x) = (x - 93)² + 98.

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Answer:

Step-by-step explanation:

\(4−(2x+4)=5\)

First of all remove the parenthesis

That's

\(4 - 2x - 4 = 5 \\ - 2x = 5\)

Divide both sides by - 2

\( \frac{ - 2x}{ - 2} = \frac{5}{ - 2} \\ \)

We have the final answer as

\(x = - \frac{5}{2} \\ \)

Hope this helps you

Answer:

4 different spots

Step-by-step explanation:

12 - 4 spaces in between = 8 spaces

8 spaces / 4 cars = 4 spots

4 spots and 4 cars = 4 different spots for each car

16

Answer:

Step-by-step explanation: its 13