What number is the same as distance from 0 on a number line as 1 1/2

Answer:

ok i dont knkw what is that lol

Answer:

x ≥ -59 or x  ≤-43

Step-by-step explanation:

|x+51|≥8

We know eitherx+51≥8orx+51≤−8

x+51≥8(Possibility 1)

x+51−51≥8−51(Subtract 51 from both sides)

x≥−43

x+51≤−8(Possibility 2)

x+51−51≤−8−51(Subtract 51 from both sides)

x≤−59

x≥−43 or x≤−59

To solve the integral of 1/sqrt(x^2 - a^2) dx, we can use the substitution method. Let u = x^2 - a^2, then du/dx = 2x, and dx = du/2x.
Substituting into the integral, we get:

∫ 1/sqrt(x^2 - a^2) dx = ∫ 1/sqrt(u) * du/2x
= (1/2) ∫ 1/sqrt(u) du  

= (1/2) * 2sqrt(u) + C
= sqrt(x^2 - a^2) + C

Therefore, the answer to the integral of 1/sqrt(x^2 - a^2) dx is sqrt(x^2 - a^2) + C, where C is the constant of integration.

In summary, the integral of 1/sqrt(x^2 - a^2) dx can be solved using the substitution method, where u = x^2 - a^2. The final answer is sqrt(x^2 - a^2) + C, where C is the constant of integration.

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The integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

What is intergration?

Integration is a fundamental concept in calculus that involves finding the antiderivative or integral of a function. It is the reverse process of differentiation, which is concerned with finding the derivative of a function.

To find the integral of \(1/\sqrt(x^2 - a^2) dx\), we can use a trigonometric substitution. Let's substitute \(x = a sec(\theta)\), where \(sec(\theta)\) is the reciprocal of the cosine function.

By making this substitution, we can express dx in terms of \(d(\theta)\) as follows:

\(dx = a sec(\theta) tan(\theta) d(\theta)\)

Now, let's substitute these values into the integral:

\(\int \frac{1}{\sqrt{x^2 - a^2}} dx\\\\= \int \frac{1}{\sqrt{(a \sec(theta))^2 - a^2}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\sec^2(theta) - 1)}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\tan^2(theta))}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{a \tan(theta)} (a \sec(\theta) \tan(\theta)) d(\theta)\)

Simplifying the expression, we have:

\(= \int \sec(\theta) d(\theta)\)

The integral of \(sec(\theta)\) can be evaluated as the natural logarithm of the absolute value of \(sec(\theta)\) plus the tangent\((\theta)\):

\(= \ln|\sec(\theta) + \tan(\theta)| + C\)

Finally, substituting back \(x = a sec(\theta)\), we get:

\(= \ln|\sec(\theta) + \tan(\theta)| + C\\\\= \ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\)

Therefore, the integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

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Answer:

opposite

Step-by-step explanation:

in an isosceles the opposite angles are the same

Answer:

base

Step-by-step explanation:

i had this question before

Using linear equations we know that the cost of installing the carpet in the room os 15 inches × 18 inches will be $4,935.

So, the linear equation that represents the above situation and can help us to get the cost is:

75 + 18x = C

Where x is the area of the room and C is the cost.

We know that the area where the carpet will be placed is:
15 × 18

270 inches

Now, calculate the cost, using the equation and take x = 270.

75 + 18x = C

75 + 18(270) = C

75 + 4,860 = C

$4,935 = C

Therefore, using linear equations we know that the cost of installing the carpet in the room os 15 inches × 18 inches will be $4,935.

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Therefore, the perimeter of the square is increasing at a rate of 3 * sqrt(2) inches per minute.

Let's denote the side length of the square as "s" (in inches) and the diagonal as "d" (in inches).

We know that the diagonal of a square is related to the side length by the Pythagorean theorem:

d^2 = s^2 + s^2

d^2 = 2s^2

s^2 = (1/2) * d^2

Differentiating both sides with respect to time (t), we get:

2s * ds/dt = (1/2) * 2d * dd/dt

Since we are given that dd/dt (the rate of change of the diagonal) is 3 inches per minute, we can substitute these values:

2s * ds/dt = (1/2) * 2d * 3

2s * ds/dt = 3d

Now, we need to find the relationship between the side length (s) and the area (A) of the square. Since the area of a square is given by A = s^2, we can express the side length in terms of the area:

s^2 = A

s = sqrt(A)

We are given that the area of the square is 18 square inches, so the side length is:

s = sqrt(18) = 3 * sqrt(2) inches

Substituting this value into the previous equation, we can solve for ds/dt:

2 * (3 * sqrt(2)) * ds/dt = 3 * d

Simplifying the equation:

6 * sqrt(2) * ds/dt = 3d

ds/dt = (3d) / (6 * sqrt(2))

ds/dt = d / (2 * sqrt(2))

To find the rate at which the perimeter (P) of the square is increasing, we multiply ds/dt by 4 (since the perimeter is equal to 4 times the side length):

dP/dt = 4 * ds/dt

dP/dt = 4 * (d / (2 * sqrt(2)))

dP/dt = (2d) / sqrt(2)

dP/dt = d * sqrt(2)

Since we know that the diagonal is increasing at a rate of 3 inches per minute (dd/dt = 3), we can substitute this value into the equation to find dP/dt:

dP/dt = 3 * sqrt(2)

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Answer:480cm^3

Step-by-step explanation:

Answer:

24 minutes

Step-by-step explanation:

We solve the above question using Lowest Common Multiple Method.

We find the Multiples of 6 and 8 minutes and then pick the first multiple that is common to both numbers

Multiples of 6:

6, 12, 18, 24, 30, 36

Multiples of 8:

8, 16, 24, 32, 40

Therefore,

LCM(6, 8) = 24

Therefore, the first time Mai and Clare will complete a sign at the same time is 24 minutes

Answer:

Step-by-step explanation:

1,2,4,5

The correct statements are,

m∠R > 90°

m∠S + m∠T < 90°

m∠R > m∠T

m∠R > m∠S

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Here, RST is a triangle,

Therefore,  

m∠R + m∠S + m∠T = 180°

⇒ m∠S+m∠T = 180° - m∠R

Since, m∠R > m∠S + m∠T

⇒ - m∠R < - (m∠S + m∠T) (by multiplying-1 on both sides)

⇒ 180°- m∠R < 180° - (m∠S + m∠T) (by adding 180° on both sides)

⇒ m∠S+m∠T < 180° - (m∠S + m∠T)

⇒ m∠S+m∠T+ m∠S+m∠T < 180° ( by adding m∠S + m∠T on both sides)

⇒ 2(m∠S+m∠T) < 180°

⇒ m∠S+m∠T < 90°

⇒ m∠R > 90° ( because m∠R+m∠S+m∠T = 180° )

Again, m∠R > m∠S + m∠T

⇒ m∠R > m∠S and  m∠R > m∠T

Thus, Option first second fourth and fifth are correct.

Since, m∠S = m∠T is only possible when m∠R=90° (but it is not given)

That is why m∠S = m∠T is not correct.

And, there are not enough information to prove m∠S > m∠T

That is why  m∠S > m∠T is also incorrect.

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Answer:

2 cm^2

Step-by-step explanation:

area of triangles= (2)(3)(0.5)(2) = 6

area of rectangle = (2)(3) = 6

total area  = 6+6 = 12

Answer:

72cm

Step-by-step explanation:

2 x 2 x 2 x 3 x 3 = 72

3cm is the width

and 2cm is the length

area means multiply all sides of the shape

so we did and we got...

72!

a. The economic order quantity (EOQ) is approximately 312 bags.

b. The average number of bags on hand (cycle inventory) is 156 bags.

c. There will be approximately 16 orders per year if EOQ is used.

d. The total annual cost of ordering and holding flour for EOQ is $9,360.

e. The EOQ would increase by 100% if the ordering cost were to increase by 50%.

To calculate the economic order quantity (EOQ) and answer the related questions, we'll follow the given information step by step:

a. Determine the economic order quantity (EOQ):

EOQ is calculated using the following formula:

EOQ = √((2DS) / H)

Where:

D = Annual demand (number of bags)

S = Ordering cost per order

H = Holding cost per bag

Given:

Annual demand (D) = 4,860 bags

Ordering cost per order (S) = $10

Holding cost per bag (H) = $5

Plugging in these values into the formula:

EOQ = √((2 * 4,860 * 10) / 5)

= √(97,200)

= 312 bags (approximately)

So, 312 bags or so are the economic order quantity (EOQ).

b. Average number of bags on hand (average cycle inventory) if EOQ is used:

The average cycle inventory is half of the EOQ.

Average cycle inventory = EOQ / 2

Average cycle inventory = 312 / 2

Average cycle inventory = 156 bags

c. Number of orders per year if EOQ is used:

The number of orders per year is calculated by dividing the annual demand by the economic order quantity (EOQ).

Number of orders = Annual demand / EOQ

Number of orders = 4,860 / 312

Number of orders = 15.57 (approximately)

Thus, if EOQ is employed, there will be roughly 16 orders each year.

d. Total annual cost of ordering and holding flour for EOQ:

The total annual cost consists of both the ordering cost and the holding cost.

Total annual cost = (D / EOQ) * S + (EOQ / 2) * H

Plugging in the values:

Total annual cost = (4,860 / 312) * 10 + (312 / 2) * 5

Total annual cost = 156 + 780

Total annual cost = $9360

Consequently, $9360 is the total annual expense for ordering and storing flour for EOQ.

e. If ordering cost were to increase by 50 percent per order, the percentage change in EOQ can be calculated using the formula:

Percentage change in EOQ = (Percentage change in ordering cost) / (Percentage change in ordering cost + Percentage change in holding cost) * 100

Given:

Percentage change in ordering cost = 50%

Percentage change in holding cost = 0% (as it remains the same)

Plugging in the values:

Percentage change in EOQ = (50%) / (50% + 0%) * 100

Percentage change in EOQ = 100%

As a result, the EOQ would increase by 100% if the ordering cost increased by 50% each order.

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The function that calculates the total principal through a specified number of payments is the PMT function.

This function is mainly used in Microsoft Excel and is widely used for calculating loan payments, and other related financial calculations. The PMT function returns the payment amount for an investment that is based on constant payments and a constant interest rate.The main answer to the question is the PMT function. This function is used for calculating the total principal through a specified number of payments. The function takes into account constant payments and a constant interest rate to arrive at the payment amount for the investment.The PMT function in Excel uses three arguments: Rate, Nper, and Pv. Where,Rate: It is the interest rate per period.

It is the rate at which the investment earns interest.Nper: It is the total number of payments for the investment.Pv: It is the present value of the investment. It is the amount of money that is being invested.The function also includes optional arguments like Fv, Type. Where, Fv: It is the future value of the investment. Type: It specifies when payments are due, whether they are at the beginning or the end of the period.The above explanation comprises more than 100 words and covers the necessary information related to the PMT function.

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Hey there! :)

Answer:

25 pieces.

Step-by-step explanation:

To solve for the amount of pieces that can be cut, we must divide fractions:

15 ÷ 3/5 = x

When dividing fractions, you must multiply by the reciprocal. Therefore:

\(\frac{15}{1}* \frac{5}{3} = \frac{75}{3} = 25\)

Therefore, 25 pieces can be cut.

Answer:

25 3/5 inch long pieces

Step-by-step explanation:

If you have 15 inches and you cut it into less than inch pieces, you know for sure that it will be more than 15 but less than 30 because the peices are more than half an inch.

to find the answer, you divide 15 by 3/5 because each piece is 3/5 inches long

when you put this into a calculator 15/(3/5) you will get the answer 25.

So, ANSWER = 25 pieces of rope that are 3/5 inches long

Hope this helps and you will understand if you face a problem similar to this :)

A positively skewed distribution is due to an extremely large number.

A positively skewed distribution is a type of distribution in which the majority of the data values are clustered towards the left side of the distribution, with a tail extending to the right. This means that there are relatively more smaller values in the dataset than larger values. In a positively skewed distribution, the mean of the dataset is typically larger than the median, and the mode may not be a good representation of the central tendency of the data. This is because the presence of a long tail on the right-hand side of the distribution pulls the mean towards the higher values, while the median remains closer to the center of the dataset. Some common examples of positively skewed distributions include income distributions, where there are a few extremely high earners that skew the data towards the right, and test scores, where there may be a few students who perform extremely well and pull the average higher than the median.

Here,

A positively skewed distribution occurs when the tail of the distribution extends to the right, and the majority of the data is clustered towards the left side of the graph. This means that there are relatively more smaller values in the dataset than larger values. One common cause of positive skewness is the presence of extremely large values, also called outliers, in the dataset. These large values pull the mean of the dataset towards the right, resulting in the tail of the distribution stretching in that direction.

Therefore, out of the options provided, the correct answer is "an extremely large number."

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In order to justify their position candidate make assumption that the price effect would be larger than the quantity effect.

What is Price?

The amount of money required to obtain a certain thing is referred to as its price. Price is a measure of value in the sense that the amount people are willing to pay for a commodity signifies its value.

Concept:

Candidate A claims that raising the sales tax from 5% to 7% will enhance revenue. This suggests that the price effect is greater than the quantity effect because when taxes rise, prices rise and quantities fall; hence, tax revenue will rise only if the price effect is more than the quantity effect.

And Candidate B claims that the tax would harm merchants and customers, slow the economy, and reduce tax revenue, but only if the quantity effect outweighed the price effect.

As a result, Candidate A believes that the price effect will be greater than the quantity effect.

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Answer:

5.4 im pretty sure

Step-by-step explanation:

Using the slope-intercept form, the slope, y-intercept and equation of the graph are -1/7, 5 and y = -1/7x + 5 respectively

The general equation of straight line is given in slope-intercept form as

y = mx + c.

In the graph given, the function is a straight line with slope and y-intercept.

Taking two points from the graph.

The slope of the equation can be calculated using the points

slope (m) = y₂ - y₁ / x₂ - x₁

m = 1 - 0 / -2 - 5

m = 1 / -7

The slope is -1/7

From the graph, we can see the point in which the line passes through the y - axis and it is known as the y - intercept.

The y - intercept on this graph is 5

The slope- intercept form can be written as

y = -1/7x + 5

a) When x = -1, y = ?

y = -1/7x + 5

y = -1/7(-1) + 5

y = 1/7 + 5

y = 36/7

b) When y = 7, x = ?

y = -1/7x + 5

7 = -1/7x + 5

x = -14

c) The y - intercept of the graph is 5

d) The x-intercept of the graph is at -2.2

e) The slope of the line is -1/7

f) The equation of the line is given as y = -1/7x + 5

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Answer:

-2

Step-by-step explanation:

Answer:

It's A

Step-by-step explanation:

i did the quiz

to minimize the time it takes to reach the island, the visitor has to run 15 km west of the tent to first get to the closest point of the shoreline to the island before swimming across to the island.

Here we have;

Location of island = 15km west

Location of tent = 2 km south of point on shoreline

Running speed of visitor = 8 km/h

Swimming speed = 1 km/h

Distance of island from tent = \(\sqrt{15^2 +2^2}\) = 15.13

Since, time = distance/speed, it will take 15.13/1 hours or 15.13 hours to swim directly to the island.

However if the visitor first runs to the closest point on the shoreline to the island, then swims across to the island, it will take;

15/8 Hr + 2/1 hr = 31/8 hours or 3.875 hours only.

Therefore, to minimize the time it takes to reach the island, the visitor has to run 15 km west of the tent to first get to the closest point of the shoreline to the island before swimming across to the island.

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Step 1

Given; Find the value of x in x + y = 9 and x - y = 2.

Step 2

Using the elimination method.

Hence,

Answer;

Answer:

first you must multiply the 7 by what is inside the parentheses:

14x + 56 = 84

The simplified and rationalized form of the expression is (√5x⁴) / (√2x²y³).

To simplify the expression (√5x⁴) / (√2x²y³) and rationalize the denominator, we can use the properties of radicals.

First, let's simplify the numerator and denominator separately:
√5x⁴ = √(5 * x² * x²) = x²√5

√2x²y³ = √(2 * x² * y³) = xy√(2y)

Now, we can rewrite the expression with the simplified forms:
(x²√5) / (xy√(2y))

Next, we can cancel out the common factor of x in the numerator and denominator:
(√5) / (y√(2y))

This is the simplified and rationalized form of the expression:

(√5x⁴) / (√2x²y³).

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When two variables x and y are in direct proportion, it means that as the value of x increases, the value of y also increases, and vice versa. In other words, their ratio remains constant. Y is about equal to 18.67 when z equals 14. , when z is 14, y is \(56\)  .

If x and y are in direct proportion, then we can use the formula:

\(x / y = k\)

where k is the constant of proportionality. To find the value of k, we can use the given information that "y is 12 when x is 3":

\(3 / 12 = k\)

Simplifying this, we get:

\(k = 1 / 4\)

Now we can use this value of k to find y when z is 14. We know that x and y are still in direct proportion, so we can set up the equation:

\(x / y = k\)

Substituting k = 1/4 and z = x, we get:

\(z / y = 1/4\)

Solving for y, we get:

\(y = 4z\)

Now we can substitute z = 14 and solve for y:

\(y = 4z = 4(14) = 56\)

Therefore, when z is 14, y is  \(56\) .

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The given question is incomplete. the complete question is given below:

If X And Y Are In Direct Proportion And Y Is 12 When X Is 3, Find Y When X Is 14.

If x and y are in direct proportion and y is 12 when x is 3, find y when x is 14.

Using trigonometry, we can solve for the missing angles to find them as 18.43°, 45°, 45°, and 18.43°.

The sign is mounted on a sloped surface, which means that we'll need to use some trigonometry to find the missing angles.

Let's concentrate on the sign's upper right corner, where the letters x and y are absent from two perspectives. The magnitude of angle x may be determined using trigonometry.

Let's begin by sketching a right triangle that has an angle x. The triangle's two sides may be represented by the sign's vertical and horizontal lines, with the addition of a third side to join the top right corner of the sign to the sloping area below.

Since the sign is an octagon, we know that each interior angle is 135°. Therefore, the measure of angle y must be:

y = 180 - 135 = 45°

Now, let's look at the right triangle that includes angle x. We know that the hypotenuse of the triangle is the sloped surface of the sign, which has a length of 4.5 meters. We also know that the opposite side of the triangle is the height of the sign above the ground, which has a length of 1.5 meters.

Using trigonometry, we can find the measure of angle x by taking the inverse tangent of the opposite side over the adjacent side:

tan(x) = opposite/adjacent = 1.5/4.5 = 1/3

x = tan⁻¹(1/3) ≈ 18.43°

Therefore, the measure of angle x is approximately 18.43 degrees.

Hence, using trigonometry, we can solve for the missing angles to find them as 18.43°, 45°, 45°, and 18.43°.

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We need to  know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.

Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.

Therefore the margin of error is influenced by confidence level and sample size.

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Answer:

16c+5p

Step-by-step explanation:

The nominal rate, periodic rate (round to 8 decimal places), and APY are 6.67047%, 0.53552453%, and 6.69589054%,

Given that the rate of 6.5% is compounded monthly. We need to determine (a) nominal rate, (b) periodic rate (round to 8 decimal places), and (c) APY.(a) Nominal rateNominal rate is the annual rate which is not compounded at any frequency. It is the rate which is stated on the contract or any other agreement. To determine the nominal rate, we use the following formula;Nominal rate = (1 + periodic rate/m)^m - 1

Where m is the number of times the rate is compounded in a year.Periodic rate = r = 6.5%/12 = 0.0054166667Nominal rate = (1 + 0.0054166667/12)^12 - 1Nominal rate = (1.0054166667)^12 - 1Nominal rate = 0.0667047365 or 6.67047%(b) Periodic ratePeriodic rate is the rate which is applied per period. It is also called as the effective rate per period.To determine the periodic rate, we use the following formula;Periodic rate = (1 + nominal rate)^(1/m) - 1Periodic rate = (1 + 0.0667047365)^(1/12) - 1Periodic rate = 0.0053552453 or 0.53552453%(c) APYAPY (Annual Percentage Yield) is the effective annual rate of return. It is also called as effective annual rate.

To determine the APY, we use the following formula;APY = (1 + periodic rate)^n - 1APY = (1 + 0.0053552453)^12 - 1APY = 0.0669589054 or 6.69589054%

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Answer:

We can start by isolating the variable "h".

5 8 h + 1 1 2 = 5

Subtracting 11/2 from both sides:

5 8 h = 5 - 1 1 2

Simplifying:

5 8 h = 8 1 2

Dividing both sides by 5/8:

h = 8 1 2 ÷ 5 8

Converting the mixed number to an improper fraction:

h = (8 x 8 + 1) ÷ 5 8

h = 65/8

Now, we can convert this fraction to a mixed number:

h = 8 1/8

Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:

5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8

Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).

Step-by-step explanation: