what is the answer to 5x + 3 = 22

The graph that best describes the solution set of the inequality 6x ≤ 18 is given as follows:

First graph.

The inequality in the context of this problem is defined as follows:

6x ≤ 18.

The solution to the inequality is obtained similarly to an equality, isolating the desired variable, hence:

x ≤ 18/6

x ≤ 3.

Due to the equal sign, at x = 3 we have a closed circle, and the graph is composed by the points to the left of the closed circle at x = 3, hence the first graph is the solution to the inequality.

More can be learned about inequalities at brainly.com/question/25275758

#SPJ1

The decibel level of the sound from the leaf blower is approximately 104 dB.

The decibel level of a sound is measured in logarithmic units and is defined as the ratio of the sound's intensity to a reference intensity that is just barely audible to the human ear.

The decibel level (dB) of a sound is given by the equation 10 log(I/I_0), where I is the intensity of the sound being measured and I_0 is the reference intensity.

For this problem, the intensity of the sound from the leaf blower is given as 28 × 10^-2 W/m².

The reference intensity is generally taken to be 1 × 10^-12 W/m².

Substituting these values into the formula, we get: 10 log(28 × 10^-2 / (1 × 10^-12)) = 10 log(28 × 10^10) = 10 (10.447) ≈ 104.47

Therefore, the decibel level of the sound from the leaf blower is approximately 104 dB.

Decibel (dB) is a unit used to measure the intensity or level of sound, as well as the ratio of power or amplitude of a signal. It is a logarithmic unit that compares the measured quantity to a reference level. The decibel scale is logarithmic because the human perception of sound intensity is not linear. A change of 1 dB is considered the smallest perceptible difference in sound level, while a change of 10 dB is perceived as approximately a doubling or halving of loudness.

know more about decibel level

https://brainly.com/question/32546509

#SPJ11

Answer:

2

Step-by-step explanation:

2 x 1250 = 2500

the perfect square for 2500 is 50:

\(\sqrt{2500} = 50\)

The probability that a randomly selected light bulb's output is 2240 end foot-candles is approximately 0.000265 or 0.0265%.

To calculate the probability of a randomly selected light bulb's output being 2240 end foot-candles, we can use the properties of the normal distribution.

Given that the light bulb's output is normally distributed with a mean of 2500 end foot-candles and a standard deviation of 75 end foot-candles, we can use the formula for the standard normal distribution to find the probability.

The standard normal distribution has a mean of 0 and a standard deviation of 1. To calculate the probability of a value occurring in the standard normal distribution, we convert the value to a standard score (also known as z-score) using the formula:

z = (x - μ) / σ,

where x is the value, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability of a randomly selected light bulb's output being 2240 end foot-candles. Plugging the values into the formula:

z = (2240 - 2500) / 75

  = -260 / 75

  = -3.47 (rounded to two decimal places)

Now, we need to find the probability associated with this z-score. We can refer to a standard normal distribution table or use statistical software to find the corresponding probability. For a z-score of -3.47, the probability is approximately 0.000265.

Therefore, the probability that a randomly selected light bulb's output is 2240 end foot-candles is approximately 0.000265 or 0.0265%.

Learn more about probability here

https://brainly.com/question/25839839

#SPJ11

Answer:

Heyyyy!!

The answer is 66.9

please read the explanation... it will help... I promise

Step-by-step explanation:

Okay... Here we go...

The context mentions that the two quadrilaterals are similar... meaning their sides are proportional...

So... you basically have to find the scale factor...

(the math itself is easier than the explanation...

51/16 = 3.1875 (that is the number we multiplied the sides of quadrilateral FGHI to get quadrilateral JKLM...

so to get side JK all you have to do is multiply that scale factor by side FG... which after the use of a calculator results in 66.9 (i rounded, and used a calculator... lol)

but yeah... i hope this helps...

The profit (p) is $7500 generated by selling 1500 units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x²

To maximize our profit, we must locate the vertex of the parabola represented by this function. The x-value of the vertex indicates the number of units that must be sold to maximize profit.

We may use the formula for the x-coordinate of a parabola's vertex:

x = -b/2a

where a and b represent the coefficients of the quadratic function ax² + bx + c. In this situation, a = -0.004 and b = 12, resulting in:

x = -12 / 2(-0.004) = 1500

This indicates that when 1,500 units are sold, the profit is maximized.

To calculate the greatest profit, enter x = 1500 into the profit function:

P(1500) = -1500 + 12(1500) - 0.004(1500)^2

P(1500) = -1500 + 18000 - 9000

P(1500) = $7500

Therefore, the maximum possible profit is $7,500 and it is generated when 1,500 units are sold.

Learn more about Profit maximization:

https://brainly.com/question/30436087

#SPJ4

To achieve this maximum profit, exactly 1500 units must be sold.

To find the maximum profit and the number of units needed to generate it, we can use the given profit function p(x) = -1500 + 12x - 0.004x^2. We need to find the vertex of the parabola represented by this quadratic function, as the vertex will give us the maximum profit and the corresponding number of units.

Step 1: Identify the coefficients a, b, and c in the quadratic function.
In p(x) = -1500 + 12x - 0.004x^2, the coefficients are:
a = -0.004
b = 12
c = -1500

Step 2: Find the x-coordinate of the vertex using the formula x = -b / (2a).
x = -12 / (2 * -0.004) = -12 / -0.008 = 1500

Step 3: Find the maximum profit by substituting the x-coordinate into the profit function p(x).
p(1500) = -1500 + 12 * 1500 - 0.004 * 1500^2
p(1500) = -1500 + 18000 - 0.004 * 2250000
p(1500) = -1500 + 18000 - 9000
p(1500) = 7500

So, the maximum profit is $7,500, and 1,500 units must be sold to generate it.

To learn more about parabola: brainly.com/question/8227487

#SPJ11

Answer:

lrrtrrjnrttttttttttttttt

The angle postulate that best defined angles CAB and CAD is; Supplementary Angles

We know that there are different angle postulates such as Corresponding angles, complementary angles, supplementary angles and others.

Now, in this case we want to find the angle theorem that best describes angles CAB and CAD. Now, from the given image, it is clear that both angles form a straight line and we know that the sum of angles on a straight line equals 180 degrees.

Since both angles sum up to 180 degrees and we know that these angles are defined as supplementary angles which are linear pairs.

Read more about Angle Postulate at; https://brainly.com/question/14957499

#SPJ1

S(MARY) = {(p) [(x)} + () V (Y)b), AXA (5) [MKA) + (x)d], XA (9) [(x) + (x)d], XA (e)}The resolution method is used to deduce logical conclusions that can be inferred from the given premises or statements. The following shows S(MARY) using resolution:In order to use resolution, we start by putting the given statements into conjunctive normal form (CNF), which means we need to convert each statement into a series of clauses joined by the logical connective AND and negate the statement.To find S(MARY), we need to negate it. Hence, we have:¬S(MARY) = ¬{(p) [(x)} + () V (Y)b), AXA (5) [MKA) + (x)d], XA (9) [(x) + (x)d], XA (e)}= ¬(p) V ¬[(x)] V ¬() V ¬(Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)Next, we write each of these negated statements as a set of clauses, where each clause is a disjunction of literals. Then, we apply the resolution rule until we can no longer derive any new clauses.Here are the steps involved:Step 1: Convert the statements to CNF.(p) [(x)} + () V (Y)b) => (p) V [(x)] V () V (Y)bAXA (5) [MKA) + (x)d] => ¬AXA (5) [MKA) + (x)d] V [(x)d]XA (9) [(x) + (x)d] => ¬XA (9) [(x) + (x)d] V [(x)d]XA (e) => [(e)]Step 2: Negate the statement.¬S(MARY) = ¬(p) V ¬[(x)] V ¬() V ¬(Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬(p) => [(x)] V () V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬[(x)] => (p) V () V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬() => (p) V [(x)] V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬(Y)b => (p) V [(x)] V () V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)¬AXA (5) [MKA) + (x)d] => [(x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (p) V [(x)] V () V (Y)b¬XA (9) [(x) + (x)d] => [(x)d] V ¬AXA (5) [MKA) + (x)d] V ¬XA (e) V (p) V [(x)] V () V (Y)bStep 3: Apply the resolution rule.Using the resolution rule, we try to derive a new clause that follows from any two clauses that have opposite literals. This can be done by finding two clauses with complementary literals, resolving them, and adding the resulting clause to our set of clauses. We repeat this process until we either find the empty clause (which means that S(MARY) is false), or we can no longer derive any new clauses.(p) V [(x)] V () V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e)(p) V [(x)] V (Y)b V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (q)(p) V [(x)] V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (r)(p) V [(x)] V ¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (s)¬AXA (5) [MKA) + (x)d] V ¬XA (9) [(x) + (x)d] V ¬XA (e) V (t)¬XA (9) [(x) + (x)d] V ¬XA (e) V (u)¬(e) V (v)Therefore, the empty clause is derived from the above set of clauses, which means that S(MARY) is false.

Two or more lines are said to be parallel if and only if the measure of angle between them is \(180^{o}\). Thus the required prove to show that DE II AC is given below:

When two or more lines are parallel to each other, this implies that they are similar with respect to their position. Such that the measure of the angle between/ among them is \(180^{o}\).

The required prove in the given question is stated as thus:

                     STATEMENT                    REASON

1. DE                                                       Given

2. AB ≅ BC                                            Similar property of congruent sides

3. \(\frac{DE}{BE}\) ≅ \(\frac{AB}{BC}\)                                            using common denominators

4. AB = AD + DB;          

   BC = BE + EC                                    segment addition postulate

5. AD ≅ CE

   BD ≅ BE                                           substitution property of equality

6. <ABC ≅ <DBE                                  Reflexive property of congruence

7. ΔABC ≅ ΔBCD                                 SAS criterion for similarity

8. <BAC ≅ <BDE                                corresponding angles of similar triangles

9. <DEB ≅ <ACE                       If the corresponding angles formed by two lines intersected by a transversal are congruent, then the lines are parallel

Therefore, line DE is parallel to line AC

Learn more about properties of parallel lines at https://brainly.com/question/14213992

#SPJ1

False. As you increase the sample size (n), assuming everything else remains the same, the width of the confidence interval decreases, not increases.

The width of a confidence interval is determined by several factors, including the sample size (n), the variability of the data, and the desired level of confidence. When all other factors remain constant, increasing the sample size (n) leads to a narrower confidence interval.

A larger sample size provides more information and reduces the uncertainty associated with estimating population parameters. This decrease in uncertainty leads to a smaller margin of error, resulting in a narrower confidence interval.

The relationship between the sample size and the width of the confidence interval can be understood by the formula for the margin of error. The margin of error is inversely proportional to the square root of the sample size. As the sample size increases, the square root of n increases at a slower rate, resulting in a smaller margin of error and narrower confidence interval.

Learn more about confidence interval here:

https://brainly.com/question/32278466

#SPJ11

Answer: The GCF of 24 and 36 is 6. The GCF of 11 and 84 is 1. The GCF of -64x and 56x is -8x. Hope this helps :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's pretty obvious.

You need to add 2 fractions up.

If it's lower than 5/8, then you are correct.

Given:

The exponential function is:

\(R(x)=(5.3)^x\)

To find:

The domain of the given exponential function.

Solution:

We know that the general form of an exponential function is:

\(f(x)=ab^x\)

Where, a is the initial value and b is growth/decay factor.

This function is defined for all real values of x, so the domain of these type of functions is the set of all real number.

We have,

\(R(x)=(5.3)^x\)

Here, a is 1 and b is 5.3. This function is defined for all real values of x

Therefore, the domain of these type of functions is the set of all real number or it can be written as \((-\infty,\infty)\).

Step-by-step explanation:

Hey there!

The points P1(3,-3) and midpoint is (-2,1). Let (X,y) be the end point.

Note: Find through using midpoint formula.

midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )

Put all values.

(\frac{X+3}{2},\frac{-3+y}{2})

Since they are equal, equating with it's corresponding components.

\frac{3 + x}{2} = - 2

-2 = 3 + x

-4 -3= x

Therefore, X= -7.

Now,

\( \frac{ - 3 + y}{2} = 1\)

\( - 3 + y = 2\)

Therefore, y= 5

Therefore, the other end point is (3,5).

Hope it helps...

The counterexample for the conjecture If the perimeter of a rectangle is 40 units, the area must be at least 1 square unit is: A rectangle with length 19.99 units and width 0.01 unit has a perimeter of 40 units and an area of 0.1999 square unit.

What is counterexample?

The term counterexample refers to an instance or example that makes the statement false. This is used in logic to check if a statement is true or not. Counter example tend to counter the statement being discussed with valid points.

The question wants to show the relationship that may exist between perimeter and area of a rectangle.

The counterexample provided the dimensions that gave the perimeter which is 40 but failed to give area of 1 square unit

Learn more about  counterexample at:

brainly.com/question/24881803

#SPJ4

Answer:

i think these inequalities shows B

Answer:

Rs 6900

Step-by-step explanation:

To calculate the tax amount the girl should pay in a year, we need to determine the taxable income and then apply the corresponding tax rates.

The taxable income is calculated by subtracting the tax-free allowance from the girl's early income:

Taxable Income = Early Income - Tax-Free Allowance

Taxable Income = 150,000 - 100,000

Taxable Income = 50,000

Now, we can calculate the tax amount based on the given tax rates:

For the first 20,000 rupees, the tax rate is 12%:

Tax on First 20,000 = 20,000 * 0.12

Tax on First 20,000 = 2,400

For the remaining taxable income (30,000 rupees), the tax rate is 15%:

Tax on Remaining 30,000 = 30,000 * 0.15

Tax on Remaining 30,000 = 4,500

Finally, we add the two tax amounts to get the total tax she should pay in a year:

Total Tax = Tax on First 20,000 + Tax on Remaining 30,000

Total Tax = 2,400 + 4,500

Total Tax = 6,900

Therefore, the girl should pay 6,900 rupees in tax in a year.

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

for such more question on lengths

https://brainly.com/question/24176380

#SPJ8

Answer:

perimeter = 28

Step-by-step explanation:

Tangents drawn to a circle from an external point are congruent, thus

AH = AB = 5

GH = GF = 2

EF = ED = 3

CB = CD = 4

Sum the 8 parts for perimeter of polygon ACEG

perimeter = 5 + 5 + 2 + 2 + 3 + 3 + 4 + 4 = 28

Answer:

5 ...

Step-by-step explanation:

add 3 more to 2

Answer:

It’s 5

Step-by-step explanation:

\(\textit{circumference of a semi-circle}\\\\ C=\pi r~~ \begin{cases} \stackrel{\textit{half diameter}}{r=radius}\\[-0.5em] \hrulefill\\ r=8 \end{cases}\implies C=\pi (8)\implies \stackrel{using~\pi =3.14}{C=25.12}\)

Answer:

hope this answer helps you dear....take care!

Answer:

x = -32

Step-by-step explanation:

I'm going to break it into parts, hopefully this makes sense haha

Bottom of fraction: (-2)² = 4

Right side of equation: 4 (-2) = -8

So now we have

\(\frac{x}{4}\) = -8

Mutiply both sides by 4: x = -32

So, the interest is compounded 6,335 times per year.

To find n, we need to use the formula for compound interest:
\(A = P(1 + r/n)^{(nt)\)

Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period (in years)

In this case, we have:

P = $12,000
r = 6.5% = 0.065
n = ?
t = 4 years

We know that the interest is compounded daily, so we need to convert the annual interest rate and the time period to reflect that.

First, we need to find the daily interest rate:

daily rate =\((1 + r/365)^{(365/365) - 1\)
daily rate = (1 + 0.065/365)\(^{(365/365) - 1\)
daily rate = 0.000178

Next, we need to find the number of compounding periods:

n = 365

Finally, we can plug in the values and solve for n:

A = P(1 + r/n)\(^(nt)\)
A = $12,000(1 + 0.000178/365)\(^{\\(365*4)\)
A = $12,000(1.000178)^1460
A = $14,233.29

Now we can use the formula for compound interest in reverse to solve for n:

\(A = P(1 + r/n)^{(nt)\\14,233.29 = 12,000(1 + 0.065/n)^{(n*4)\\1.18611 = (1 + 0.065/n)^(4n)\\\\ln(1.18611) = ln[(1 + 0.065/n)^(4n)]\\0.16946 = 4n ln(1 + 0.065/n)\\n = 4[ln(1.065/1.000178)] / 0.16946\\n = 4[270.309] / 0.16946\\n = 6,334.4\)Therefore, n is approximately 6,334.4. However, since n represents the number of compounding periods and cannot be fractional, we need to round up to the nearest whole number:

n = 6,335

So, the interest is compounded 6,335 times per year.\\

learn more about compound interest

https://brainly.com/question/14295570

#SPJ11

Answer:

A

Step-by-step explanation:

because it is is parenthesis

The segment length and the conversion of radian and degree are given below.

We have,

In order to solve for segment length in relation to circles, chords, secants, and tangents, we need to first define some terms:

Circle: A set of all points in a plane that are equidistant from a given point called the center of the circle.

Chord: A line segment joining two points on a circle.

Secant: A line that intersects a circle in two points.

Tangent: A line intersecting a circle at exactly one point, called the point of tangency.

Segment: A part of a circle bounded by a chord, a secant, or a tangent and the arc of the circle that lies between them.

Now, let's consider the following cases:

Chord-chord intersection:

If two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. That is:

AB × BC = DE × EF

where AB and BC are the lengths of the segments of one chord, and DE and EF are the lengths of the segments of the other chord.

Secant-secant intersection:

If two secants intersect outside a circle, the product of the length of one secant and its external segment is equal to the product of the length of the other secant and its external segment. That is:

AB × AC = DE × DF

where AB and AC are the length of one secant and its external segment, and DE and DF are the length of the other secant and its external segment.

Secant-tangent intersection:

If a secant and a tangent intersect outside a circle, the product of the length of the secant and its external segment is equal to the square of the length of the tangent. That is:

AB × AC = AD^2

where AB and AC are the length of the secant and its external segment, and AD is the length of the tangent.

Tangent-tangent intersection:

If two tangents intersect outside a circle, the lengths of the two segments of one tangent are equal to the lengths of the two segments of the other tangent. That is:

AB = CD

BC = DE

where AB and BC are the lengths of the two segments of one tangent, and CD and DE are the lengths of the two segments of the other tangent.

Using these formulas, we can solve for segment length in various situations involving circles, chords, secants, and tangents.

To convert the degree measure to radian measure, we use the fact that 360 degrees is equal to 2π radians.

Therefore, we can use the following conversion formula:

radian measure = (degree measure × π) / 180

For example:

Convert 45 degrees to radians:

radian measure = (45 degrees × π) / 180

radian measure = (45/180)π

radian measure = π/4

So 45 degrees is equal to π/4 radians.

Convert 120 degrees to radians:

radian measure = (120 degrees × π) / 180

radian measure = (2/3)π

So 120 degrees is equal to (2/3)π radians.

Convert 270 degrees to radians:

radian measure = (270 degrees × π) / 180

radian measure = (3/2)π

So 270 degrees is equal to (3/2)π radians.

Note that radians are a more natural unit for measuring angles in many mathematical contexts, as they relate directly to the arc length of a circle.

To convert the radian measure to degree measure, we use the fact that 180 degrees equal π radians.

Therefore, we can use the following conversion formula:

degree measure = (radian measure × 180) / π

For example:

Convert π/3 radians to degrees:

degree measure = (π/3 radians × 180) / π

degree measure = 60 degrees

So π/3 radians is equal to 60 degrees.

Convert 2π/5 radians to degrees:

degree measure = (2π/5 radians × 180) / π

degree measure = (360/5) degrees

degree measure = 72 degrees

So 2π/5 radians is equal to 72 degrees.

Convert 3π/4 radians to degrees:

degree measure = (3π/4 radians × 180) / π

degree measure = (540/4) degrees

degree measure = 135 degrees

So 3π/4 radians is equal to 135 degrees.

Note that degree measure is commonly used in everyday life and in many technical fields, whereas radian measure is often used in advanced mathematics, physics, and engineering.

Thus,

The segment length and the conversion of radian and degree are given above.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

Answer:

$330

Step-by-step explanation:

Start by dividing the original price by five, then multiply by 3. You do that because he paid 3/5 of the original price. Hope this helps!

Answer:

$220

Step-by-step explanation:

Markdown is the percentage decrease

2/5 is written as .4 in decimal form (40%)   \(\frac{2}{5} times 20=\frac{40}{100}\)

So when you multiply the number with the markdown percent, you get

550 times .4 = $220

Answer:

n = - 4

Step-by-step explanation:

8 = - 2n ( isolate n by dividing both sides by - 2 )

- 4 = n

Answer:

n = -4

Step-by-step explanation:

8= -2n   (divide both sides by -2)

8 / (-2) = n  

n = -4

hope this helps