Solve and graph the inequality.
-4 < 4x < 20

Answer:

x = 17/4, or 4.25

The x-intercept is (4.25, 0)

Step-by-step explanation:

We can get the intercepts by isolating x and y.

4x - 3y = 17

Subtract 4x from both sides.

-3y = -4x + 17

Divide both sides by -3.

y = 4/3x - 17/3

Input 0 for x.

y = -17/3

The y-intercept is (0, -17/3)

4x - 3y = 17

Add 3y to both sides.

4x = 3y + 17

Divide both sides by 4.

x = 3/4y + 17/4

Input 0 for y.

Answer:

For me it's C.

Step-by-step explanation:

the third one if you would like me to explain tell me.

The solutions to the trigonometric equations [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] are x ≈ [tex]0.5514 + 2n\pi[/tex], where n is an integer.

Given that the equation  [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex]

To find all the solutions to the equation  [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] ,  solve for x by isolating the cosine term and then applying the inverse cosine function.

Here are the steps to solve the equation:

Add [tex]\sqrt{30}[/tex] to both sides:

[tex]2cos(x) = \sqrt{30}[/tex]

Divide both sides by 2:

[tex]cos(x) = \sqrt{30} / 2[/tex]

Find the inverse cosine ([tex]cos^{-1}[/tex]) of both sides:

[tex]x = cos^{-1}(\sqrt{30} / 2)[/tex]

To determine the values of x in the interval [tex][0, 2\pi)[/tex] that satisfy the equation.

Evaluate [tex]cos^{-1}(\sqrt{30} / 2)[/tex] to find its approximate value.

[tex]cos^{-1}(\sqrt{30} / 2) = 0.5514[/tex] radians

Since the cosine function has a periodicity of [tex]2\pi[/tex], we can find other solutions by adding multiples of [tex]2\pi[/tex] to the initial solution.

So, the solutions in the interval  [tex][0, 2\pi)[/tex] are:

x ≈ 0.5514 radians

x ≈ [tex]0.5514 + 2\pi[/tex]

x ≈ [tex]0.5514 + 4\pi[/tex]

...

To simplify, express the solutions as:

x ≈ [tex]0.5514 + 2n\pi[/tex]

where n is an integer.

Therefore, the solutions to the trigonometric equations [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] are x ≈ [tex]0.5514 + 2n\pi[/tex], where n is an integer.

Learn more about solving trigonometric equations and inverse trigonometric functions here:

https://brainly.com/question/1143565

#SPJ6

The value of ∠FDE is 36°

An angle is a geometric figure formed by two rays, or lines that extend infinitely in opposite directions, that share a common endpoint called the vertex. The measure of an angle is determined by the amount of rotation between the two rays.

Here given a right angle ∠CDE = 90°

So, we can say that,

∠CDF + ∠FDE = ∠CDE

(2x)° + (x+9)° = 90°

(3x + 9)° = 90°

Simplify it, x = 27°

So, the value of ∠FDE = (x+9)° = (27+9)° = 36°

Therefore, the value of ∠FDE is 36°

To know more about types of angle, visit:

https://brainly.com/question/27962469

#SPJ1

The angle FDE is 36°. The required answer for the given question is option (A). 36°.

Trigonometry angles are the angles provided by the trigonometric function ratios. Trigonometry is the study of the connection between angles and triangle sides. Angle values vary from 0 to 360 degrees.

An angle is a shape in geometry made by two rays or lines that stretch indefinitely in opposite directions and have a common endpoint known as the vertex. The quantity of rotation among the two rays determines the size of an angle.

From the given figure,

∠CDF + ∠FDE = 90

Thus,

(2x)+(x+9) = 90

3x + 9 = 90

3x = 81

x = 27

Then we will have that the angle FDE is:

∠FDE = (27) + 9

∠FDE = 36

The angle of FDE is 36°

To know more about Trigonometry, visit:

https://brainly.com/question/13729598

#SPJ1

The correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

The y-intercept of a line of fit is the value of y when x equals 0. In the context of this problem, the y-intercept represents the amount of diet soda that the machine starts with when it is filled.

Since the y-intercept of the line of fit is −5.1, this means that the machine starts with 5.1 ounces of diet soda.

This is a reasonable value, as it is unlikely that the machine would be completely empty when it is filled.

It's important to note that the slope of the line of fit is also relevant in this context.

The slope represents the rate at which the amount of diet soda in the machine decreases over time. However, the question only asked for the y-intercept.

Hence, the correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.

To learn more about the equation of the line visit:

https://brainly.com/question/18831322

#SPJ1

Option (C) is correct which is "Jessie should use volume to determine that the cardboard box requires 240 in3 of paint."

The measurement of three-dimensional space is volume.

It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units.

The concept of length and volume are related.

Volume is the three-dimensional space inhabited by matter or encompassed by a surface, and it is measured in cubic units.

The SI unit of volume is the cubic meter (m³), which is a derived unit.

So, the volume would be:

length x breadth x height

Step 1 : substitute the values given

Step 2 : 10 x 4 x 6

Then, we got: 240 inches

Therefore, option (C) is correct which is "Jessie should use volume to determine that the cardboard box requires 240 in3 of paint."

Know more about volumes here:

https://brainly.com/question/463363

#SPJ1

Answer:

c

Step-by-step explanation: I was correct

The sum of the circumscribed angle m∠ECD and central angle m∠EAD for five different data sets are 90°, 90°,120°,150°,180°.

A central angle is an angle in a circle that has its vertex at the center of the circle. Its arms, which are the two rays that make up the angle, both pass through points on the circumference of the circle.

m∠ECD  m∠EAD  m∠ECD + m∠EAD

45°  45°    90°

60°  30°    90°

100°  20°    120°

140°  10°    150°

180°  0°    180°

The measure of the circumscribed angle, ∠ECD, is the angle formed by the intersection of two lines, AB and CD.

The measure of the central angle, ∠EAD, is the angle formed by the intersection of the lines AB and ED.

The relationship between the circumscribed angle and the central angle can be explored by moving point B to various different locations on the coordinate plane between A and C.

By doing so, both the circumscribed angle and the central angle can be measured.

From the table above, it can be seen that the sum of the measures of the circumscribed angle and the central angle is always equal to 90°.

This is because the circumscribed angle and the central angle are supplementary angles, meaning that the sum of their measures always equal to 180°.

In this case, since the sum of the measures of the circumscribed angle and the central angle is always equal to 90°, the measures of the circumscribed angle and the central angle themselves must always add up to 90°.

Since the sum of the measures of the circumscribed angle and the central angle is always equal to 90°, the measures of the circumscribed angle and the central angle themselves must always add up to 90°.

For more questions related to supplementary angles

https://brainly.com/question/2046046

#SPJ1

Answer:

Step-by-step explanation:

he's rich

Xavier will have $1278 left over from his paycheck after spending 20% on a new mattress and 29% on fixing a leak.

To find out how much will be left over from Xavier's paycheck after he spends 20% on a new mattress and 29% on fixing a leak, we can follow these steps:

Therefore, Xavier will have $1278 left over from his paycheck.

https://brainly.com/question/33576466

#SPJ2

the correct answer is: none of these, as only binomial distribution is applicable to this scenario.

a) This scenario follows the binomial distribution, as we are drawing marbles with replacement and interested in the number of successes (getting a blue marble) in a fixed number of trials.

b) The Poisson distribution is used to model the number of events occurring in a fixed time interval, given a certain rate of occurrence. It is not applicable in this scenario.

c) The hypergeometric distribution is used to model the probability of obtaining a certain number of successes in a sample without replacement, given a finite population of items that can be classified into successes and failures. In this scenario, we are drawing with replacement, so the hypergeometric distribution is not applicable.

d) Therefore, the correct answer is: none of these, as only binomial distribution is applicable to this scenario.

Learn more about distributive  here

https://brainly.com/question/5637942

#SPJ4

The probability of 4 defective cell phones in a sample of 25 can be found using the binomial probability formula and is equal to 0.0263.

Probability is a branch of mathematics that deals with calculating the likelihood of a given event occurring. In probability, we calculate the number of ways an event can happen and divide it by the total number of possible outcomes.

Probability ranges from 0 to 1, with 0 indicating no chance of occurrence and 1 indicating that the event will definitely occur.

If there are only two possible outcomes in a given event, the binomial probability formula is used to calculate the probability of the event happening.

The binomial probability formula is given by: P(X = x) = (nCx)px(1 - p)n - x

Where, P(X = x) is the probability of x successes in n trials

nCx is the number of ways x successes can occur in n trials

px is the probability of a single success in a given trial(1 - p)n - x is the probability of the remaining trials being failures.

The probability of 4 defective cell phones in a sample of 25 can be calculated using the binomial probability formula.

P(X = 4) = (25C4)(0.06)4(0.94)21 = 0.0263.

Therefore, the probability of 4 defective cell phones in a sample of 25 is 0.0263.

To know more about probability refer here:

https://brainly.com/question/29110744#

#SPJ11

Answer:

y = -2/3x + 1/3

Step-by-step explanation:

2x + 3y = 1

3y = -2x + 1

y = -2/3x + 1/3

To sketch:

Pretend x is 3. y would be -1 2/3.

Now that you have this point, draw through the point (0, 1/3).

There ya go

Ten chairs are arranged in a circle. The number of subsets of this set of chairs that contain at least three adjacent chairs is 310.

The given that 10 chairs arranged in a circle.

            Now we have to find the number of subsets of this set of chairs that contain at least three adjacent chairs.

           To solve this, we can use the concept of permutations and combinations. The first step is to consider the number of ways in which three chairs can be selected and arranged in a subset that is adjacent to each other.

           This can be done in 10 different ways, as there are 10 chairs in total and we can select any one of them as the starting point.

           The next step is to consider the number of ways in which we can add additional chairs to this subset. For example, we can add a fourth chair to the subset in two different ways: either to the left of the first chair or to the right of the third chair.

            Similarly, we can add a fifth chair to the subset in four different ways, a sixth chair in six different ways, and so on. Using this logic, we can create the following table:

                    Length of subset number of ways to select the subset number of ways to add chairs

           Total number of subsets31 (adjacent)

                                = 10  ---43 (adjacent) 10*2

                                =20---55 (adjacent)10*4

                                =40---67 (adjacent)10*6

                                =60---79 (adjacent)10*8

                               =80---810 (adjacent)10*10

                               =100---

              As we can see from the table, the total number of subsets that contain at least three adjacent chairs is given by:

           Total number of subsets = 10 + 20 + 40 + 60 + 80 + 100

                                                     = 310

       Therefore, the number of subsets of this set of chairs that contain at least three adjacent chairs is 310.

Learn more about the number of subsets of chairs at: https://brainly.com/question/17514113

#SPJ11

The exponentially smoothed forecast for period 4 is 106.6.

As per given information,

Time period Actual series  Forecast series  Forecast error  1  100  100 0 2 110 3 115

Smoothing constant α=0.3

For calculating exponentially smoothed forecast for period 4,

First, we need to calculate exponentially smoothed forecast for period 2.

Smoothed forecast for period 2 = α (Actual demand for period 1) + (1-α) (Smoothed forecast for period 1)

= 0.3 (100) + (0.7) (100)= 30 + 70= 100

Next, we can calculate exponentially smoothed forecast for period 3.

Smoothed forecast for period 3 = α (Actual demand for period 2) + (1-α) (Smoothed forecast for period 2)

= 0.3 (110) + (0.7) (100)

= 33 + 70

= 103

Now, we can calculate exponentially smoothed forecast for period 4.

Smoothed forecast for period 4 = α (Actual demand for period 3) + (1-α) (Smoothed forecast for period 3)

= 0.3 (115) + (0.7) (103)= 34.5 + 72.1

= 106.6

For similar question on exponentially smoothed

https://brainly.com/question/16914603

#SPJ11

Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ

The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:

[tex]Q = mcΔT[/tex]

Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).

Using the equation, the amount of heat produced can be calculated as follows:

Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
for such more questions on temperature

https://brainly.com/question/25677592

#SPJ11

The properties of a parallelogram indicates that the variables in the segments and angles are;

A parallelogram is a four sided figure with two pairs of sides that are parallel.

Whereby the figures are parallelogram, we get;

The length of the opposite sides are the same, therefore;

1. b + 1 = 2·b

1 = 2·b - b = b

1 = b

b = 1 (symmetric property)

3·a - 4 = a + 2

3·a - a = 4 + 2

2·a = 6

a = 6/2 = 3

a = 3

2. The opposite angles of a parallelogram are congruent, therefore;

(y + 10)° = (2·y - 40)°

10 + 40 = 2·y - y = y

50 = y

y = 50

The adjacent interior angles of a parallelogram are supplementary, therefore;

(4·x)° + (2·y - 40)° = 180°

(4·x)° + (2 × 50 - 40)° = 180°

(4·x)°  = 180° - (2 × 50 - 40)° = 60°

x = 60°/4 = 15°

x = 15

3. The diagonals of a parallelogram bisect each other, therefore;

y + 3 = 12

y = 12 - 3 = 9

y = 9

x - 3 = 15

x = 15 + 3 = 18

x = 18

4. The diagonals of a parallelogram bisect each other therefore;

x + 6 = 4·x

4·x = x + 6

4·x - x = 6

3·x = 6

x = 6/3 = 2

x = 2

5·y - 8 = 3·y + 1

5·y - 3·y = 1 + 8 = 9

2·y  = 9

y = 9/2 = 4.5

y = 4.5

Learn more on the properties of a parallelogram here: https://brainly.com/question/4218263

#SPJ1

The coordinate of the point U that divides the line ST in the ratio 2:5 is: (12:6)

The formula for the division of line segments in the ratio m:n is

P = {[(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]}

We are given the coordinates of line Segment ST as: S(10, 2) and T(17, 16)

Thus, if the ratio is 2:5, we have:

U(x, y) = {[(2*17 + 5*10)/(2 + 5)], [(2*16 + 5*2)/(2 + 5)]}

U(x, y) = (84/7), (42/7)

U(x, y) = (12, 6)

Thus, that is the coordinate of the point U that divides the line ST in the ratio 2:5.

Read more about Division of Line segment at: https://brainly.com/question/7784483

#SPJ1

Answer: 17.888543819998

Step-by-step explanation:

Answer:

17.8885

Step-by-step explanation:

find the geometric mean between 16 and 20, we need to multiply the numbers and take the square root of the result. That is:

Geometric Mean = √(16 × 20)

Geometric Mean = √320

Geometric Mean ≈ 17.8885

Therefore, the geometric mean between 16 and 20 is approximately 17.8885.

Answer: The area of a triangle is 1036.8 square units.

To find the area of a triangle, we can use the formula

Area = (1/2) * base * height

In this case, we are given that the first base is 32 and the second base is twice the first base, or 2*32 = 64. The height is given as 21.6. Therefore, we can plug these values into the formula and solve for the area:

Area = (1/2) * (32 + 64) * 21.6

Area = (1/2) * 96 * 21.6

Area = 1036.8

Therefore, the area of the triangle is 1036.8 square units.

Know more about Triangle at.

https://brainly.in/question/33028759

The probability of selecting two non-defective DVD players from a group of six is 2/5. This is based on the assumption that the selection is done without replacement.

We can use the formula for calculating probabilities of combinations:

P(not defective) = number of ways to choose 2 non-defective DVD players / total number of ways to choose 2 DVD players

Total number of ways to choose 2 DVD players out of 6 is:

C(6,2) = 6! / ([2!] [4!]) = 15

Number of ways to choose 2 non-defective DVD players out of 4 is:

C(4,2) = 4! / ([2!] [2!]) = 6

Therefore, the probability that Cecil chooses 2 non-defective DVD players is:

P(not defective) = 6/15 = 2/5

So the value of P(not defective) is 2/5.

Learn more about probability here: brainly.com/question/30034780

#SPJ4

In the following question, among the conditions given, the cop of a Carnot refrigerator, when t(cold) is 275 k and t(hot) is 158 c. Then the COP of the Carnot refrigerator is 1.76 (written as a fraction "88/50").

The COP of a Carnot refrigerator is calculated as: COP = T(Cold) / (T(Hot) - T(Cold))The COP of a Carnot refrigerator is given by the formula:

COP = T(Cold) / (T(Hot) - T(Cold))Where T(Cold) is the temperature of the cold reservoir and T(Hot) is the temperature of the hot reservoir.

T(Cold) = 275 K and T(Hot) = 158 °C = 431 K By substituting these values into the formula: COP = 275 / (431 - 275)COP = 275 / 156COP = 1.76 The COP of the Carnot refrigerator is 1.76 (written as a fraction 88/50).

For more such questions on Carnot refrigerator

https://brainly.com/question/13441103

#SPJ11


The key features of both equations are:

Equation 1 has a vertex at (1, -16) and opens upwards. Its axis of symmetry is x = 1

Equation 2 has a vertex at (2, 2) and opens upwards. Its axis of symmetry is x = 2.

To rewrite each equation in vertex form, we need to complete the square by adding and subtracting a constant from each equation.

y = x² - 2x - 15

y = (x - 1)² - 16

The vertex form of the equation is y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (1, -16).

y = 2x² - 8x + 6

y = 2(x - 2)² + 2

The vertex form of the equation is y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (2, 2).

Learn more about the vertex form of an equation at: https://brainly.com/question/29170049

#SPJ1

Therefore , the solution of the given problem of function comes out to be  growth factor resulting from the 4.6% yearly growth rate is represented by the constant factor e(0.046t).

On the midterm exam, there will be inquiries on design, arithmetic numbers, every class, and both actual and hypothetical places. a description of the connections between various components that come together to produce the same outcome. A service is built from a variety of unique parts that work together to deliver unique outcomes for each input. Each post also has a location, which might be the enclave, a municipality, or even something else altogether.

Here,

The value of the stock t years since 2000 can be represented by the function by assuming that the stock's value increases constantly at a rate of 4.6% per year:

=> V(t) = 1569 * e^(0.046t)

where t is the number of years since the year 2000 and e is the algebraic constant

=>e = 2.71828.

With this function, exponential growth is represented by multiplying the stock's starting value in the year 2000 (1569) by the constant factor e(0.046t) to get the value of the stock t years later.

The growth factor resulting from the 4.6% yearly growth rate is represented by the constant factor e(0.046t).

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

Martin will have to wash 96 cars each month on average to meet his goal of washing 1,200 cars this year.

What is average ?

Average, also known as mean, is a statistical measure that represents the central value of a dataset. It is calculated by adding up all the values in the dataset and dividing by the total number of values. The average can be used to provide a general idea of the value of the dataset and to compare different datasets. There are different types of averages, including arithmetic mean, geometric mean, and median.

According to the question:
To find out how many cars Martin will have to wash each month on average, we need to first find out how many weeks there are in a year:

52 weeks/year

Then we can use this information to calculate how many cars Martin will have to wash each week:

1,200 cars/year ÷ 52 weeks/year = 23.08 cars/week

Since Martin cannot wash a fraction of a car, he will have to round up to 24 cars/week.

Finally, we can calculate how many cars Martin will have to wash each month on average:

24 cars/week x 4 weeks/month = 96 cars/month

Therefore, Martin will have to wash 96 cars each month on average to meet his goal of washing 1,200 cars this year.

To know more about average visit:
https://brainly.com/question/25005020
#SPJ1

The four uppercase letters of the alphabet in block style with rotational symmetry are H, I, O, and X. Rotational symmetry refers to the property of a figure or object that appears identical after being rotated around a central point by a certain angle.

In block style writing, letters are written with straight lines and sharp corners, creating a uniform and geometric appearance. H, I, O, and X are the only uppercase letters that have rotational symmetry and can be written in block style.

H has a rotational symmetry of 180 degrees, meaning it looks the same when rotated 180 degrees around its center point.

I has a rotational symmetry of 180 degrees as well, with the dot above the letter acting as its center point.

O has a rotational symmetry of 360 degrees, meaning it looks the same when rotated any number of degrees around its center point.

Lastly, X has a rotational symmetry of 180 degrees, with the intersection of the two lines acting as its center point.

For more such questions on Rotational symmetry.

https://brainly.com/question/1531736#

#SPJ11

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

__________________

hope it helps ⸙

The percentile rank of age 30 is 27.586%.

The percentile rank of age 30 can be calculated using the following equation:

Percentile rank = (number of scores below 30 / total number of scores) x 100

In this case, the total number of scores is 29, and there are 8 scores below 30 (18, 21, 22, 25, 26, 27, 29, and 30). Therefore, the percentile rank of age 30 is:

(8/29) x 100 = 27.586%

The percentile rank of age 30 is 27.586%.

Learn more about percentile

brainly.com/question/13638390

#SPJ11

Answer:

Step-by-step explanation:

(4x - 5)(4x + 5) Option 1

16x^2 + 20x - 20x - 25

Answer:

1-

a. 19

b. -8

2-

a. -31

b. 0

c. -10.7

d. -3/7

e. 4

3-

a. -5

b. -60

c. 0

d. -1/4

4. -13/2

5. -85/18

6.  -5/12

7. -11

8. 16/11

9. -20/27

10.  26/11

11. -55/9

Step-by-step explanation:

why did i do this