y = 2x + 4
y = 3x + 6
Solve for x

Therefore , the solution of the given problem of inequality comes out to be  equal to -1, as x 1 is the answer to the inequality.

A pair or set of numerals can represent this difference in algebra, which lacks a symbol to do so. Equilibrium is typically followed by equity. The ongoing disparity in standards is what breeds inequality. Disparity and fairness are not synonymous. Despite the fact that the parts are typically not linked or adjacent to one another, that was my least favourite symbol. (). Any variations, no matter how average minor, have an impact on value.

Here,

The following sentence translates into an inequality:

In the case when x is a negative number, 5x + 6 = x.

We may first make the inequality simpler by adding x to both sides in order to solve for x:

6 ≤ 6x

Hence, since x is negative, we may divide both sides by 6 to obtain:

1 ≤ x

In other words, x is any negative number bigger than or equal to -1, as x 1 is the answer to the inequality.

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By side side side congruence theorem if any two triangles have three pairs of congruent sides, then the triangles are congruent.

We know that side side side (S-S-S) congruence theorem is a theorem for triangle congruence.

It states that if any two triangles have three pairs of congruent sides, then the triangles are congruent.

We need to prove:  the SSS congruence theorem

Consider ΔABC and ΔPQR

here, AB = PQ, BC = QR and AC = PR

Construct a congruent copy of triangle ABC that shares a side with PQR.  

∠SQR ≅ ∠ABC and AB = QS

In ΔABC and ΔSQR,

AB = QS                     ..............(by construction)

∠SQR ≅ ∠ABC                 ..............(by construction)

BC = QR                 ..............(given)

ΔSQR ≅ ΔABC         ...............(SAS congruence theorem)

So, by corresponding angles of congruent theorem,

∠A ≅ ∠S and ∠ACB ≅ SRQ      

But the quadrilateral PQRS is a kite, since we have QP = QS and RP = RS

We know that the diagonal divides the kite into two congruent triangles. Here,  the diagonal QR  divides the kite into ΔSQR and ΔPQR.

But ΔSQR ≅ ΔABC

so we have ΔPQR ≅ ΔABC

Hence the side side side congruence theorem proved.

Therefore, if any two triangles have three pairs of congruent sides, then the triangles are congruent.

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=============================================================

Explanation:

Let's square both sides and do a bit of algebra to get the following.

\(\sin(x) + \cos(x) = 1/5\\\\\left(\sin(x) + \cos(x)\right)^2 = \left(1/5\right)^2\\\\\sin^2(x) + 2\sin(x)\cos(x) + \cos^2(x) = 1/25\\\\\sin^2(x) + \cos^2(x) + 2\sin(x)\cos(x) = 1/25\\\\1 + 2\sin(x)\cos(x) = 1/25\\\\\sin(2x) = 1/25 - 1\\\\\sin(2x) = 1/25 - 25/25\\\\\sin(2x) = -24/25\\\\\)

Now apply the pythagorean trig identity to determine cos(2x) based on this. You should find that cos(2x) = -7/25

This then means tan(2x) = sin(2x)/cos(2x) = 24/7.

From here, you'll use this trig identity

\(\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}\\\\\)

which is the same as solving

\(\tan(2x) = \frac{2w}{1-w^2}\\\\\)

where w = tan(x)

Plug in tan(2x) = 24/7 and solve for w to get w = -4/3 or w = 3/4

So either tan(x) = -4/3 or tan(x) = 3/4.

If we were to numerically solve the original equation for x, then we'd get roughly x = 2.21; then notice how tan(2.21) = -1.345 approximately when your calculator is in radian mode.

Since tan(x) < 0 in this case, we go for tan(x) = -4/3

The value of the integral C1 and C2 are below:

∫[C1] (y + x – 4ix³) dz = -1/2 + 4/3 i

∫[C2] (y + x – 4ix³) dz = 0

To evaluate the integral, we need to parameterize the given contour C and express it as a function of a single variable. Then we substitute the parameterization into the integrand and evaluate the integral with respect to the parameter.

Let's evaluate the integral along contour C1: the straight line from Z = 0 to Z = 1 + i.

Parameterizing C1:

Let's denote the parameter t, where 0 ≤ t ≤ 1.

We can express the contour C1 as a function of t using the equation of a line:

Z(t) = (1 - t) ×0 + t× (1 + i)

= t + ti, where 0 ≤ t ≤ 1

Now, we'll calculate the differential dz/dt:

dz/dt = 1 + i

Substituting these into the integral:

∫[C1] (y + x – 4ix³) dz = ∫[0 to 1] (Im(Z) + Re(Z) - 4i(Re(Z))³)(dz/dt) dt

= ∫[0 to 1] (t + 0 - 4i(0)³)(1 + i) dt

= ∫[0 to 1] (t + 0)(1 + i) dt

= ∫[0 to 1] (t + ti)(1 + i) dt

= ∫[0 to 1] (t + ti - t + ti²) dt

= ∫[0 to 1] (2ti - t + ti²) dt

= ∫[0 to 1] (-t + 2ti + ti²) dt

Now, let's integrate each term:

∫[0 to 1] -t dt = [-t²/2] [0 to 1] = -1/2

∫[0 to 1] 2ti dt = \(t^{2i}\)[0 to 1] = i

∫[0 to 1] ti² dt = (1/3)\(t^{3i}\) [0 to 1] = (1/3)i

Adding the results together:

∫[C1] (y + x – 4ix³) dz = -1/2 + i + (1/3)i = -1/2 + 4/3 i

Therefore, the value of the integral along contour C1 is -1/2 + 4/3 i.

Let's now evaluate the integral along contour C2: along the imaginary axis from Z = 0 to Z = i.

Parameterizing C2:

Let's denote the parameter t, where 0 ≤ t ≤ 1.

We can express the contour C2 as a function of t using the equation of a line:

Z(t) = (1 - t)× 0 + t × i

= ti, where 0 ≤ t ≤ 1

Now, we'll calculate the differential dz/dt:

dz/dt = i

Substituting these into the integral:

∫[C2] (y + x – 4ix³) dz = ∫[0 to 1] (Im(Z) + Re(Z) - 4i(Re(Z))³)(dz/dt) dt

= ∫[0 to 1] (0 + 0 - 4i(0)³)(i) dt

= ∫[0 to 1] (0)(i) dt

= ∫[0 to 1] 0 dt

= 0

Therefore, the value of the integral along contour C2 is 0.

In summary:

∫[C1] (y + x – 4ix³) dz = -1/2 + 4/3 i

∫[C2] (y + x – 4ix³) dz = 0

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Answer:

84

Step-by-step explanation:

only three number are a multiple of 14

14 * 5 = 70

14 * 6 = 84

14 * 7 = 98

neither 70 nor 98 is a multiple of 4

only 84 is a multiple of 4, 7 and 14

Answer:

2×1790

5×716

4×895

10×358

Answer:25th Percentile: 5

50th Percentile: 30

75th Percentile: 34

Interquartile Range: 29

Step-by-step explanation:

Answer:

it is 5

Step-by-step explanation:

i looked it up

(a) The smallest possible value of ||~v − ~w|| is 2, and the largest possible value is 8.

(b) The smallest possible value of ~v · ~w is -15, and the largest possible value is 15.

For (a) The magnitude of the vector difference ||~v − ~w|| is smallest when the two vectors are in the same direction, which gives ||~v − ~w|| = ||~v|| − ||~w|| = 5 − 3 = 2. The magnitude is largest when the two vectors are in opposite directions, which gives ||~v − ~w|| = ||~v|| + ||~w|| = 5 + 3 = 8.

For (b) The dot product ~v · ~w is smallest when the two vectors are perpendicular, which gives ~v · ~w = ||~v|| ||~w|| cos θ = 5 * 3 * cos(π/2) = 0, where θ is the angle between the vectors. The dot product is largest when the two vectors are parallel and pointing in the same direction, which gives ~v · ~w = ||~v|| ||~w|| cos θ = 5 * 3 * cos(0) = 15.

The dot product is negative when the two vectors are parallel but pointing in opposite directions, which gives ~v · ~w = ||~v|| ||~w|| cos θ = 5 * 3 * cos(π) = -15.

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By solving equations we know that the first and second worked charged $75 and $45 per hour.

So, let's form equations as follows:

Let F (15 hours) be the first worked and S (5 hours) by the second worker, then:

Now, solve further:

The second work charged 45$.

Therefore, by solving equations we know that the first and second worked charged $75 and $45 per hour.

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The critical value if the hypothesis is to be tested at the 0.05 level of significance is 1.96 . So, option C is the correct answer.

To test the hypothesis that Woof Chow has a market share of 25%, we need to conduct a hypothesis test with the null hypothesis that the true proportion of dog owners who use Woof Chow is 0.25, and the alternative hypothesis that the true proportion is not 0.25.

Since the sample size n is large (n = 100), we can use the normal distribution to perform this test. The critical value for a two-tailed test at the 0.05 level of significance is given by:

z_critical = ±1.96

This value corresponds to the 2.5th and 97.5th percentiles of the standard normal distribution. The critical value is ±1.96 because we want to be 95% confident that the true proportion of dog owners who use Woof Chow is within a certain range, and the 95% confidence interval corresponds to two standard deviations from the mean.

To determine whether or not to reject the null hypothesis, we would calculate a test statistic (z-score) based on the sample proportion, and compare it to the critical value. If the test statistic falls outside the critical value, we would reject the null hypothesis and conclude that Woof Chow does not have a market share of 25%.

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A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising

At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.

During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.

Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.

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Step-by-step explanation:

GCF of 36 and 99 is the largest possible number that divides 36 and 99 exactly without any remainder. The factors of 36 and 99 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 3, 9, 11, 33, 99 respectively.

I was going to just say the answer was 3 but the other person put multiple answers.So they have the correct answer.Good job!

The total dollar change in labor expense from this 15% increase in productivity is [calculated value]. The percent change in labor expense is [calculated value].

Part I: Effective cost per hour per employee

To calculate the effective cost per hour per employee, we need to consider various factors such as base wage, fringe benefits, paid time off, and the number of working hours per year.

Base hourly wage: $12.30 per hour

Number of working hours per day: 8 (1 shift)

Number of holidays: 5

Number of vacation days: 7

First, let's calculate the total fringe benefits per hour:

Fringe benefits = 37% of base wage = 0.37 * $12.30 = $4.551

Next, let's calculate the paid time off per hour:

Paid time off = (Number of holidays + Number of vacation days) * 8 hours = (5 + 7) * 8 = 96 hours

Now, let's calculate the effective cost per hour per employee:

Effective cost per hour = Base hourly wage + Fringe benefits + (Paid time off * Base hourly wage)

Effective cost per hour = $12.30 + $4.551 + (96 * $12.30)

Part II: Reduction in labor cost

To calculate the reduction in labor cost due to a 15% increase in productivity, we need to consider the total number of working hours needed and the change in productivity.

Number of working hours needed every year: 306,050

Productivity increase from 70% to 85%: 85% - 70% = 15%

First, let's calculate the initial number of workers needed:

Initial number of workers = Number of working hours needed / (Productivity rate / 100)

Initial number of workers = 306,050 / (70 / 100)

Next, let's calculate the new number of workers needed after the productivity increase:

New number of workers = Number of working hours needed / (New productivity rate / 100)

New number of workers = 306,050 / (85 / 100)

Finally, let's calculate the total dollar change in labor expense:

Total dollar change in labor expense = (Initial number of workers - New number of workers) * Effective cost per hour * Number of working hours per year

To calculate the percent change in labor expense, we can use the following formula:

Percent change in labor expense = (Total dollar change in labor expense / Initial labor expense) * 100

Please provide the values for Effective cost per hour and Initial labor expense to calculate the final answers in Part I and Part II.

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Answer:

Step-by-step explanation: just

A grouped frequency table (grouped frequency conveyance) is an approach to coordinating an enormous arrangement of information into additional reasonable gatherings.

The grouped frequency table

________________________________________________________

 Width (in mm) C.F. Class Interval Frequency ________________________________________________________

 ≥ 20 50 20 - 30 50 - 44

= 6 ≥ 30 44 30 - 40 44 - 28

= 16

 ≥ 40 28 40 - 50 28 - 20

= 8

 ≥ 50 20 50 - 60 20 - 15

= 5

 ≥ 60 15 60 - 70 15 - 0

= 15

_____________________________________________________

                                                                                          ∑f = 50

The gatherings that we arrange the mathematical information into are called class intervals. They can have something similar or different class widths and should not cover.

The principal segment is for the gatherings where we compose the class intervals.

The center section is for the count marks.

The last segment is the frequency section where we can include the count marks.

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the complete question is:

The widths of 50 leaves of a plant were measured in mm and their cumulative frequency distribution is shown in the following table. Make frequency distribution table for this . CLASS FREQUENCY >20 50 >30 44 >40 28 >50 20 ​>60 15

Answer:

48 tiles are required.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To solve for the area of a rectangle, we use this expression:

(Let l = length, w = width and a = area)

Inserting the dimensions of the hall:

Each tile has an area of:

To find the number of tiles needed to cover the hall, we can divide the area of the hall by the area of each tile:

Therefore, 48 tiles are required to cover the rectangular hall.

Answer:

x = 15  or x = -3

Step-by-step explanation:

I assume this is an absolute value equation.

|x - 6| + 8 = 17

|x - 6| = 9

x - 6 = 9  or  -(x - 6) = 9

x = 15  or  x - 6 = -9

x = 15  or x = -3

The correct solution to the equation x - 6 + 8 = 17 is:

x - 6 + 8 = 17

Combining like terms, we have:

x + 2 = 17

Next, we isolate x by subtracting 2 from both sides:

x + 2 - 2 = 17 - 2

x = 15

Therefore, the correct solution is x = 15.

However, none of the given answer choices (OA, B, C, or OD) accurately represent the solution to the equation. The correct answer is x = 15, and there is no value of 'a' mentioned in the original equation, so there is no solution for 'a'.

Answer:

$767 per month for the next 4 years

Step-by-step explanation

first it’s minus the 2800 they gave him and that’s 9,200 then divided by the amount of months in a year which is 12 you end up with 766.6 but rounded that would be the closest answer and then when you multiply 767x12 it’s 9200 plus the 2800 it’s 12,000 which means it checks out.

Answer:

12. 3:12

Step-by-step explanation:

that is 12

Answer:

option 2

Step-by-step explanation:

The relation (1, 1)\(,\) (2, 2)\(,\) (3, 3), (4, 4), (5, 8) is a function , the correct option is (A) .

In a relation is the x coordinate repeats , then it cannot be called a function

In the question ,

the relations are given as

Part(A)

(1, 1), (2, 2)\(,\) (3, 3), (4, 4) \(,\)(5, 8)

we see that , the x coordinate means the Domain is 1 , 2, 3 ,4 , 5 .

and since no number is repeating , this relation can be called as a function  .

Part(B)

(2, 7), (6, 5), (4, 4)\(,\) (3, 3), (2, 1)

we see that  , the x coordinate means the Domain is 2 , 6, 4 ,3 , 2 .

and the number 2 is repeating , this relation cannot be called a function .

Part(C)

(9, -3), (9, 3), (4, -2) \(,\) (4, 2), (0, 0)

we see that  , the x coordinate means the Domain is 9 , 9, 4 ,4 , 0 .

and the number 9 and 4 are repeating ,this relation cannot be called a function .

Part(D)

(1, 0), (3, 0), (1, 1) \(,\)(3, 1), (1, 3)

we see that  , the x coordinate means the Domain is 1 , 3, 1 ,3 , 1 .

and the number 1 and 3 are repeating , this relation cannot be called a function .

Therefore , The relation (1, 1), (2, 2) \(,\) (3, 3), (4, 4), (5, 8) is a function , the correct option is (A) .

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The number of people who will have heard the rumor when the spread is at the greatest is given as follows:

43 people.

The function for this problem is defined as follows:

y = 0.3x(24 - x).

Hence:

y = -0.3x² + 7.2x.

The derivative is given as follows:

y' = -0.6x + 7.2.

The critical value of x is given as follows:

-0.6x + 7.2 = 0

x = 7.2/0.6

x = 12.

Hence the number of people is given as follows:

y = 0.3 x 12 x (24 - 12)

y = 43 people.

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Answer: 6 cm

Step-by-step explanation:

6 cm is the radius because half the diameter is the radius

Answer:

Explanation:

Diameter: 12

12 ÷ 2 = 6

Therefore the radius is 6 cm.

Problem

Solution

for this case we can see that

AB = DC

And we have also that

BO= CO

We also can see that:

< AOB = < COD

And the best answer for this case is:

B. side- side -side

Answer: When dividing a polynomial by a monomial, we can simply divide each term in the polynomial by the monomial.

So, dividing (8zy² - 28z¹y5 + 12z³y7) by (4z¹y³) gives:

(8zy²)/(4z¹y³) - (28z¹y5)/(4z¹y³) + (12z³y7)/(4z¹y³)

Simplifying each term by canceling out any common factors gives:

2y^(-1)z^(1-1) - 7y^(5-3)z^(1-1) + 3y^(7-3)z^(3-1)

which simplifies to:

2yz^0 - 7y^2z + 3y^4z^2

Therefore, (8zy² - 28z¹y5 + 12z³y7) ÷ (4z¹y³) = 2yz^0 - 7y^2z + 3y^4z^2.

Step-by-step explanation:

The parameter estimate is statistically different from zero when the absolute value of the t-statistic is greater than the critical value associated with the desired level of significance.

In hypothesis testing, the t-statistic is calculated by dividing the parameter estimate by its standard error. The t-statistic measures the number of standard errors the parameter estimate is away from the null hypothesis value (usually zero).

If the absolute value of the t-statistic is greater than the critical value, it means that the parameter estimate is significantly different from zero at the chosen level of significance. In other words, there is evidence to reject the null hypothesis and conclude that the parameter is not equal to zero.

The specific critical value depends on the desired level of significance and the degrees of freedom associated with the t-distribution. If the absolute value of the calculated t-statistic exceeds the critical value, it indicates that the parameter estimate is statistically significant and significantly different from zero.

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Triangle ABC, we are given the measure of angle A as 30 degrees, the length of side AC as 10.7 cm, and the length of side BC as 6.5 cm.

To work out the value of sin(ABC), we can use the trigonometric ratio of the sine function.

The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle.

In the given information, we don't have a right triangle or the length of the side opposite angle ABC.

Without this information, it is not possible to calculate the value of sin(ABC) accurately.

If you have any other information regarding the triangle, such as the length of side AB or the measure of angle B or C, please provide it so that I can assist you further in calculating sin(ABC).

We may utilise the sine function's trigonometric ratio to get the value of sin(ABC).

The sine function connects the ratio of the hypotenuse length of a right triangle to the length of the side opposite an angle.

A right triangle or the length of the side opposite angle ABC are absent from the provided information.

The value of sin(ABC) cannot be reliably calculated without these information.

Please share any more information you may have about the triangle, such as the length of side AB or the size of angles B or C, so I can help you with the calculation of sin(ABC).

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Answer:

OPTION A is correct

39 ounces

Step-by-step explanation:

Given:

The amount of water in the pitcher= 32 ounces

The amount of lemon juice in the pitcher = 7.15 ounces

We were to calculate the most reasonable estimate for the amount of liquid in the pitcher

To do this we need to sum up the Amount of water and Amount of lemon juice in the pitcher because the water is a liquid as well as the lemon juice which is

32 ounces + 7.15 ounces

=39.15 ounces

Therefore, the Estimated amount of liquid in the pitcher is approximately 39 ounces

Answer:

-sinh(1)sec^2(x)

Explanation:

The notation that I suppose you're using is d/dx.

Starting with

y = sinh−1(tan(x))

Simplify the trigonometric ratio sinh, then simplify:

d/dx(sinh(-tan(x))

d/dx [-sinh(1)tan(x)]

=-sinh(1) * d/dx [tan(x)]

Therefore, you get:

-sinh(1)sec^2(x)