what two integers are closest to sqaure root of 189

Answer:

0.375

Step-by-step explanation:

3/8 = 0.375

Answer:

0.375

Step-by-step explanation:

The labor hours required for the eighth satellite are calculated to be 51,200 based on a learning curve value of 0.5120 and an expected improvement curve of 80%.

The learning curve concept suggests that as the cumulative production doubles, the labor hours required to produce each unit decrease by a certain percentage. In this case, the learning curve value for the eighth unit is given as 0.5120, which means that the labor hours needed for the eighth satellite is 51.20% of the labor hours required for the first unit.

To calculate the actual number of labor hours, we multiply the learning curve value by the total labor hours required for the first unit. Given that the total labor hours for the first unit is 100,000, we can calculate the labor hours for the eighth satellite as follows: 0.5120 * 100,000 = 51,200.

Therefore, based on the given learning curve value and the expected improvement curve of 80%, the number of labor hours for the eighth satellite is determined to be 51,200.

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James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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Using the volume formula it is obtained that the least number of bags Martin should buy is Option C: 13.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

First, we need to convert the height of the cylinder from inches to feet -

6 inches = 6/12 feet = 0.5 feet

The volume of the cylinder can be calculated as -

V = πr²h

where r is the radius and h is the height.

Substituting the given values, we get -

V = 3.14 x 2² x 0.5

V = 6.28 cubic feet

Since each bag contains 0.5 cubic feet of sand, we can find the number of bags needed by dividing the total volume by the volume of each bag -

n = V / 0.5

n = 6.28 / 0.5

n = 12.56

Since we can't buy a fractional number of bags, we must round up to the nearest whole number.

Therefore, Martin needs to buy at least 13 bags of sand.

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The improper integral is convergent or divergent is 4∫(x-dx)/(4+x^2)

The integral is given as follows:[infinity]∫1S(-dx)/(4+x^2)We have to determine whether the improper integral is convergent or divergent, and find its value if it is convergent.

Now, to determine whether the improper integral is convergent or divergent, we have to take the limit of the integral when a approaches infinity.

We will first take the antiderivative of the given function. Let u = 4 + x2du = 2x dxx dx = (1/2)du. Now, the integral becomes∫(1/2) [(-du)/u]The indefinite integral is -1/2 ln(4 + x^2)

The definite integral becomes∫ [1/2(-ln(4 + x^2)] [1 to infinity]lim(x → ∞) [-1/2 ln(4 + x^2)] - (-1/2 ln 5)lim(x → ∞) [-1/2 ln(1 + (x^2/4))] + (1/2 ln5)

Since x → ∞, we get lim(x → ∞) [-1/2 ln(1 + (x^2/4))]Since the limit diverges, the integral is divergent and the value is not defined. Therefore, the answer is option B. Divergent is the improper integral. 4∫(x-dx)/(4+x^2).

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Answer:

9. 20,001

10. 100,001

11. 4,999

12. 999,999

Step-by-step explanation:

Answer:

There are 3 counters in each circle, so the quotient is 3. There are 6 counters left over, so the remainder is 6.

Step-by-step explanation:

Given:

Fixed cost to rent a moving van = $23

Additional cost = $7 per hour.

To find:

For $37, the maximum amount of time that a moving van can be rented for.

Solution:

Let the moving van be rented of t hours.

Total cost = Fixed cost + Additional cost

\(\text{Total cost}=23+7t\)

For $37, the total cost should be less than 37.

\(23+7t\leq 37\)

\(7t\leq 37-23\)

\(7t\leq 14\)

Divide both sides by 2.

\(t\leq 2\)

Since maximum value of t is 2, therefore the moving van can be rented for maximum 2 hours.

Answer:

x=2

Step-by-step explanation:

T= 2

28 - (3æ+4) = 2(r + 6) + *

We need to use the distributive property for the

right side.

28 - 3z -4 = 2a + 12 + z

28 -3z -4 = (2) (æ) + (2)(6) + æ)

From here we need to subtract 3æ from both side.

-3æ + 24 -3 = 3æ + 12 – 3¢

3æ + 24 = 3z + 12

6z + 24 = 12

Transfer +24 on the right side. (P.S. don't forget to

change the sign)

62 = 12 - 24

6 = - 12

Finally, divide both sides by -6

6x/-6 = -13/-6

x=2

I hope I helped you

Answer:

Check the attached screenshot! :)

Step-by-step explanation:

Check the attached screenshot! Let me know if you have any questions! :)

Answer:

1 - 3 -2 -4

Step-by-step explanation:

expand them all

.000000092

.058

.0544

2400            so you can see the least to greatest is   1 3 2 4

The mechanic that would charge less for a 50-hour repair is Mechanic A.

Mathematically, the point-slope form of any straight line can be modeled by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

For the table for Mechanic B, an equation which represent its data points is given by:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 300 = (600 - 300)/(20 - 10)(x - 10)

y - 300 = 300/10(x - 10)

y = 30x - 300 + 300

y = 30x.

When x = 50 hours, the charges for Mechanic A is given by:

y = 25x + 100

y = 25(50) + 100

y = $1,350

When x = 50 hours, the charges for Mechanic B is given by:

y = 30x

y = 30(50)

y = $1,500

In conclusion, we can logically deduce that Mechanic B charges a higher fee than Mechanic A.

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The y-intercept of a line in the xy-plane is (0,1) as shown in attached graph given int the question.

To find the y-intercept of a line in the xy-plane, we need to find the point where the line intersects the y-axis. The y-axis is the vertical axis that runs through the origin and is perpendicular to the x-axis. This means that the y-intercept is the value of y when x is equal to zero. Therefore, we can read off the y-intercept directly from the equation of the line. To find the y-intercept of a line in the xy-plane, we need to find the point where the line intersects the y-axis. The y-axis is the vertical axis that runs through the origin and is perpendicular to the x-axis.

In the given graph we can see that the line intersects the point 1 on y axis.

Therefore, y-intercept of a line in the xy-plane is (0,1).

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It appears that the quality control of the repair process has worked, but we cannot say this with complete certainty.

To determine if the quality control of the repair process has worked, we need to check if the machine has gone longer than expected without repairs.

The expected time between two repairs is given by the formula:

Expected time = α x β

So, in this case, the expected time between two repairs is:

Expected time = 3 x 4 = 12 days

Since it has been 30 days since the last repair, it appears that the quality control has worked and the machine has gone longer than expected without repairs. However, we cannot say this with certainty as there is still a probability of such a long time gap occurring even without any improvement in the repair process.

To make a more precise statement, we can calculate the probability of the machine going 30 days or longer without repairs, assuming the repair process has not improved.

Using the gamma distribution with α= 3 and β= 4, we can calculate this probability as:

P(X > 30) = 1 - P(X ≤ 30)

where X is the time between two repairs.

Using a gamma distribution calculator or software, we can find that:

P(X > 30) ≈ 0.028

This means that there is only a 2.8% chance of the machine going 30 days or longer without repairs if the repair process has not improved.

Therefore, based on this probability, it appears that the quality control of the repair process has worked, but we cannot say this with complete certainty.

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Answer:

9.6 minutes

Step-by-step explanation:

10 Pages in 12 minutes

8 pages in X minutes (cross multiply)

10X=12x8 = 96

x=96/10 = 9.6

Answer:

3096?

Step-by-step explanation:

I don't know what that method is, sorry.

But 3096 is 72*43 the normal way.

He have 48 different possible outfits to wear at work with three one-piece jump suits, five pairs of work pants, and eight work shirts.

The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that.

Here,

5 pants with each of 8 shirts,

=5 x 8

=40 combinations of shirts and pants.

40 shirt/pants outfits + 8 jumpsuits = 48 total outfits.

With three one-piece jumpsuits, five pairs of work pants, and eight work shirts, he has 48 different work-appropriate outfit options.

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When drawing cabinets obliquely, we start with the front face of an object and draw the depths or sides at 45 degrees.

The object is depicted as having a cabinet oblique with half height and full depth. In a cabinet oblique drawing, the object's height is depicted at half scale while its depth is represented at full scale.

In doing so, a foreshortening effect is produced, giving the object a deeper than tall appearance. The drawing is normally displayed at a 45-degree angle, with the breadth of the object drawn to full scale.

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Answer:

72

so the second one

Step-by-step explanation:

Triangles area= Base x Height ÷ 2

12x12= 144

144÷ 2 = 72

Answer:

41

Step-by-step explanation:

You have to use Pitagoras.

a^2 + b^2 = c^2

12^2 + 12^2 = c^2

144 + 144 = c^2

288 = c^2

c = √288 = 16.9

P triangle = 16.9 + 12 + 12 = 40.9

Rounded is 41

Answer:

53 (seconds)

Step-by-step explanation:

Let's calculate each of the boy's time to reach the destination and subtract them from each other to get our answer.

Bill:
Using the Pythagorean Theorem, a^2 + b^2 = c^2
Plugging in:
300^2 + (500+150)^2 = c^2

90000 + 650^2 = c^2 (you're gonna want a calculator)

90000 + 422500 = c^2
512500= c^2

Take the square root of both sides, isolating the variable c:
c= 715.891053 m
round it off: 716 m
c stands for the distance that Bill has to walk. If he is walking at 3 meters per second, we can divide to get the number of seconds:

716 / 3 = 238.666667 seconds to get to the playground
round it off: 239

Ted:
Using the Pythagorean Theorem, a^2 + b^2 = c^2
Plugging in:
300^2 + 500^2 = c^2

90000 + 250000 = c^2

340000=c^2

Take the square root of both sides, isolating the variable c:
c= 583.095189 m
round it off: 583 m
c stands for the distance that Ted has to walk. If he is walking at 2 meters per second, we can divide to get the number of seconds:

583 / 2 = 291.5 seconds to get to the playground
round it off: 292

Lastly, subtract the number of seconds it took Ted to the number of seconds it took Bill because Ted took a longer amount of time, and that will be your answer:
292-239= 53

The shorter route 53 seconds faster

=>10³

5 × 10³ × 10³ = 5 × 10⁶

The 10³ or 1000 is multiplied by the expression 5x 10^3 is equivalent to the expression 5 x 10^6 option third is correct.

The distributive property is the property that expresses the distributive law of algebraic multiplication for example we can write a(c+b)  in the form of (ac+bc).

We have an expression:

= 5×10³

We have to make the above expression equivalent to the \(5\times 10^6\)

Let's suppose the number is x.

Now according to the question:

\(\rm (5\times10^3)\times x = 5\times 10^6\)

\(\rm x = \frac{5\times 10^6}{(5\times10^3)}\)    (divide by 5×10³ on both sides)

x = 10³           (after simplification)

x = 1000

Thus, the 10³ or 1000 is multiplied by the expression 5x 10^3 is equivalent to the expression 5 x 10^6 option third is correct.

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Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

Answer:

The segment that connects the midpoints of the legs of a trapezoid is called the median of the trapezoid.

Step-by-step explanation:

a) The solution to the exponential equation 81^(3x+2) / 243^-x = 3^4 is x = 1.

b) The solution to the exponential equation (1/3)^(x+2) = 3^(x-1) is x = 5.

a) To solve the equation 81^(3x+2) / 243^-x = 3^4, we can simplify the bases of the exponents. We have 81 = 3^4 and 243 = 3^5. Substituting these values, we get (3^4)^(3x+2) / (3^5)^(-x) = 3^4. Using the power of a power rule, we simplify to 3^(12x+8) / 3^(-5x) = 3^4. Since the bases are the same, we can equate the exponents: 12x+8 = -5x + 4. Solving for x, we find x = 1.

b) In the equation (1/3)^(x+2) = 3^(x-1), we can notice that both sides have the same base (3). We can rewrite the left side as 3^(-x-2) = 3^(x-1). Now, we can equate the exponents: -x - 2 = x - 1. Solving for x, we find x = 5.

In summary, the solutions to the exponential equations are a) x = 1 and b) x = 5.

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Solve the exponential equations:

a) 81^(3x+2) / 243^-x =3^4    (3 marks)

b) (1/3)^(x+2)=3^(x-1)     (3 marks)

Newfoundland and Labrador, and Quebec are the provinces located further east.

Canada is a country located in North America. This country is divided into 10 provinces each with cities and towns. Some of these provinces are:

In the eastern region of Canada, the provinces are:

From these, Newfoundland and Quebec are the ones located further east as shown on the map.

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Step-by-step explanation:

Let's call the original price of the refrigerator "x".

After a 25% discount, the price would be 0.75x (since 25% off means the customer pays 75% of the original price).

Then, a 5% tax would be added to the discounted price, making the final price 1.05(0.75x) = 0.7875x.

We know that the final price paid was $378, so we can set up the equation:

0.7875x = 378

To solve for x, we can divide both sides by 0.7875:

x = 478.41

Therefore, the original price of the refrigerator was $478.41.

The Original price of refrigerator is $472.5.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A store gave a discount of 25% on a refrigerator, then added 5% tax when it was purchased.

let the original price be x.

So, x- 25% of x + 5% of x= 378

x- 0.25x + 0.05x = 378

0.8x= 378

x= 378 / 0.8

x = 472.5

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Answer:

Step-by-step explanation:

x² - 2x - 35

(x - 7)(x + 5)

x - 7 = 0 ;    x + 5 = -5

x = 7, -5

Based on the information, the pollster's conclusion makes sense.

To know if the pollster is right with his conclusion we must perform the following operation.

In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.

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The probability distribution used to model a random variable x that equals the number of events that occur within an interval or area of opportunity is the Poisson distribution. This is used to model a random variable representing the number of events occurring within a fixed interval or area of opportunity, given an average rate of occurrence.

The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space, given the average rate at which events occur and the assumption that the events are independent of each other. It is commonly used in fields such as biology, physics, and engineering to model occurrences of rare events such as accidents, defects, or rare diseases.

The Poisson distribution has a single parameter λ, which represents the average rate of events occurring in the interval or area of opportunity. The probability of observing exactly k events in this interval is given by the Poisson probability mass function:

P(X=k) = (e^-λ * λ^k) / k!

where X is the random variable representing the number of events, e is the mathematical constant approximately equal to 2.71828, and k! is the factorial of k.

The Poisson distribution is similar to the binomial distribution but is used when the number of trials is very large and the probability of success is very small. In this case, the binomial distribution becomes impractical to use, and the Poisson distribution is a more appropriate model.

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