Answer the following questions:


1. Six pipes are needed to fill a tank in 1 hour and 20 minutes. How long will it take if only 4 pipes of the same type are used?

2. There are 50 students in a hostel. Food provided for them is good only for 40 days. How long will the same amount of food last if 30 more students join the group?

3. Five trucks can transport 120 tons of goods in 2 days. How many tons of goods can 3 trucks transport in 4 days?

4. In a central post office, 4 machines categorize 8 000 packages in 8 hours. How many machines are needed to categorize 4 500 packages in 6 hours?

5. A soap factory can produce 5000 units of soap in two days if five machines are used. How many units can be made in five days if 10 machines are used?

Answer: The size of angle x in a regular pentagon is 72 degrees.

To find the size of angle x in a regular pentagon, you need to divide the total number of degrees in a full circle (360) by the number of sides in a pentagon (5).

A full circle has 360 degrees, so each interior angle of a regular pentagon must measure 360/5 = 72 degrees.

Therefore, he size of angle x in a regular pentagon is 72 degrees.

The acorn is 9 meters far from the base of the tree. The solution has been obtained by using Pythagoras theorem.

What is Pythagoras theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

We are given that a flying squirrel's nest is 12 meters high in a tree.

So, the height is 12 meters.

Also, from its nest, the flying squirrel glides 15 meters to reach an acorn that is on the ground.

So, the distance the squirrel flied is 15 meters

Using Pythagoras theorem,        

c² = a² + b²

Here, c = 15 and a = 12

So,

⇒b² = c² - a²

⇒b² = 15² - 12²

⇒b² = 225 - 144

⇒b² = 81

⇒b = 9

Hence, the acorn is 9 meters far from the base of the tree.

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Answer:

Since you are finding FG, FG=3

Step-by-step explanation:

picture above

By equating the equation, we can determine that the x value is 13. Whatever the value of the variables, an identity holds.

Its precise nature is supposed to be the score's smallest equivalent fraction. How to obtain the basic definition. Looking for shared factors in the denominator and ratio. A fractional number can be checked to discover if it is a power of two. A statement having two rotational symmetry and an equal sign in the middle is called to as a mathematical equation. Every variable's degrees are listed in ranking in the standard form of any equation. The formula for a linear equation is x + b = 0. The conceptual model of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either conditioned equations or identities are categories for equation. An identification holds true because of whatever value of the variables.

given

equation = x + 7 = 20

x = 20 - 7

x = 13

By equating the equation, we can determine that the x value is 13. Whatever the value of the variables, an identity holds.

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The complete question is :-

Solve for x .

x + 7 = 20

x = ?

The dot product of two free vectors is independent of the choice of frames, as it relies only on the inner product of their transposed coordinate vectors.

The dot product of two free vectors, v1 and v2, can be expressed as the inner product of their transposed coordinate vectors, v1t and v2. This inner product is invariant under changes of frames, i.e. the same result will be obtained regardless of the choice of frames in which the coordinates are defined. This is because the transpose of a vector only changes the order of the coordinates, and the inner product of two vectors is unaffected by this reordering. Therefore, the dot product of two free vectors does not depend on the choice of frames in which their coordinates are defined.

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A) To find out how much you pay in interest on the loan, you can use the formula: Interest = Principal x Rate x Time

Therefore:

Principal = 14,000

Rate = 18% (or 0.18 when expressed as a decimal)

Time = 5 years

So, Interest = 14,000 x 0.18 x 5 = 1,540

B) To find the total amount you pay for the loan, you need to add the principal amount and the interest.

Total amount = Principal + Interest

Total amount = 14,000 + 1,540 = 15,540

Simple Interest:
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Answer:

6 meters

Step-by-step explanation:

refer attachment

7,725 ft² of grass cover the trapezoidal field.

0.5 x (125 + 81) x 75

0.5 x 206 x 75 = 7,725 ft².

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Answer: I do not now

Step-by-step explanation: WHO CARES

There are 1,08,108 different committees that are possible.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by [tex]^nC_r[/tex].

The general formula for combination is:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]  ,where 0 ≤ r ≤ n.

In a committee, we can choose 13 men from 5 men in ¹³C₅ ways. similarly, we can choose 3 women from 9 women in ⁹C₃ ways.

total ways in which we can choose 13 men and 9 women to form a committee= ¹³C₅*⁹C₃

[tex]\frac{13*12*11*10*9}{5*4*3*2*1} *\frac{9*8*7}{3*2*1}[/tex]

⇒154440/120*504/6

⇒1287*84

⇒108180

Hence, there are 1,08,180 committees are possible.

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Answer:

y=x+3

Step-by-step explanation:

The reasonable values for the domain of f(x) is D = {x ∈ W | x ≤ 50}

The domain of a function is the complete set of possible values of the independent variable.

Given that, f(x) = x, where x is the number of people seated on the bus that has a maximum seating capacity of 50

Let us assume the maximum number of people that can sit on a bus is 50.

We know that, domain is all the possible values of x in set notation.

First, state the type of numbers that can be the number of people seated.

Since you cannot have a negative number of people, you cannot have a part of a person, but you can have 0 people, so the type to be included is W whole.

Therefore, the domain can be defined as, D = {x ∈ W | x ≤ 50}

That mean, the domain is x is an element of all whole numbers, x is less than or equal to 50.

Hence, the reasonable values for the domain of f(x) is D = {x ∈ W | x ≤ 50}

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The expression on simplification without negative exponents gives: = [tex]9x^{4.5} y^{6.5} -2[/tex]

Exponents are mathematical notations used to express a number as the power of another number. The number raised to the power is called the base, and the exponent indicates the number of times the base is used as a factor.

Product of powers: If a^m * a^n, where m and n are exponents and a is the base, then the result is a^(m+n).

Power of power: If (a^m)^n, where m and n are exponents and a is the base, then the result is a^(m * n).

The quotient of powers: If a^m / a^n, where m and n are exponents and a is the base, then the result is a^(m-n).

Zero exponents: a^0 = 1, where a is the base. For example, 2^0 = 1.

The expression can be simplified as follows:

[tex]9x^{5/2} y^{5} x^{4}y^{-3/2}-2[/tex]

= [tex]9x^{\frac{9}{2} } y^{\frac{13}{2} } -2[/tex]

= [tex]9x^{4.5} y^{6.5} -2[/tex]

Therefore, The expression on simplification without negative exponents gives [tex]9x^{4.5} y^{6.5} -2[/tex].

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Answer:

316 min

Step-by-step explanation:

Find the area of 1 side of the pyramid:

h = height of the triangle

40² = (50/2)² + h²

h² = 1600 - 625 = 975

h = √975 = 31.225

A = 1/2bh = 1/2(50)(31.225) = 780.6

Atotal = 3(780.6) = 2342

2342(.75) = 1756.4

(1756.4 sf)(18 min/100 sf) = 316.15 min    

Answer: 551.1

Step-by-step explanation:

i took the quiz

Each shrub costs $6.1.

Let's call the cost of each shrub "s".

The cost of 5 trees is 15.25 more than the cost of 15 shrubs, so the cost of 5 trees is 15 shrubs + 15.25:

5 * (s + 15.25) = 15 * s + 15.25

Expanding and simplifying the left side:

5s + 76.25 = 15s + 15.25

Subtracting 5s from both sides:

76.25 = 10s + 15.25

Subtracting 15.25 from both sides:

61 = 10s

Dividing both sides by 10:

s = 6.1

A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

Ax+By=C is the typical form for linear equations in two variables. 2x+3y=5, for example, is a simple linear equation. It is rather simple to get both intercepts when an equation is stated in this way (x and y).

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The  number should replace A to give the best scale for the vertical axis of this data is 15.75

From the given parameters and graphs, we notice that we should find the mean of the set of data.

The scale should be chose in a way that the center shows the the mean of the frequencies

Recall that mean is the average of all the frequencies, then we have to find the mean of the means of the two frequencies.

(30+12+10)/2  52/3 = 17.3

Also, (27+6+13)/3  = 14.2

Then we find the average of the two averages to have

(17.3+14.2)/2 = 31.5/215.75

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The probability of all outcomes must add up to 1. The Expected Value (EV) shows the weighted average of a given choice.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100% and can be denoted as the possible outcomes upon the total number of outcomes.

To calculate this expected values multiply the probability of each given outcome by its expected value and add them together. And the net expected values can be found out by summing up all the possible expected values.

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To obtain the slope for each function, you must take two points on the graph of the function.

Then, for these points, the slope of each line is given as follows:

m = (Change in y)/Change in x.

In the case that the lines have the same slope, then they are parallel lines.

The slope of a line represents the rate of change of the output variable y relative to the input variable x.

Hence, it is calculated taking two points on a line, and dividing the change in the output by the change in the input of these two points.

The problem is incomplete, hence the answer was given in general terms.

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Answer:

First what you want to do is find what fraction is equal to 1/4 and has a denominator of 20.

The way you can find this is by taking 1/4 and seeing how many times the denominator or 4 will go into 20.

4 * 5 = 20

Since 4 times 5 is 20, we will multiply 5 to the numerator of the fraction to.

1 * 5 = 5

So 5/20 is = to 1/4

x = 5

Now the question says, " x less thsn the denominator" so we just need to find how much less is 5 compared to 20.

20 - 5 = 15

The numerator has a value, "15 less than the denominator."

Step-by-step explanation:

Hope this helps! =D

The approximate value of the integral using the trapezoidal rule with ten equal subintervals is [tex]2 + |E_T| = 2 - 1/300 = 599/300[/tex].

To find the exact value of the definite integral of 4x over the interval [0,1] we can found using the antiderivative:

[tex]\int_0^1 4x dx = 2x^2 |_0^1 = 2(1)^2 - 2(0)^2 = 2.[/tex]

To approximate the value of the integral using the trapezoidal rule with ten equal subintervals, we can break the interval into ten equal subintervals of length 1/10 and approximate each subinterval using a trapezoid.

The error of the trapezoidal rule is given by:

[tex]|E_T| = -(b-a)^3/(12n^2) * f''(c)[/tex]

where a and b are the limits of the integration, n is the number of subintervals, and f''(c) is the second derivative of the integrand evaluated at some value c in the interval.

The error of this approximation will depend on the value of f''(c) for some value c in the interval [0,1]. The second derivative of 4x is constant and equal to 4, so the error will be a constant value:

[tex]|E_T| = -(1-0)^3/(12*10^2) * 4 = -1/300.[/tex]

Thus, the approximate value of the integral using the trapezoidal rule with ten equal subintervals is [tex]2 + |E_T| = 2 - 1/300 = 599/300[/tex].

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Replicate measurements of 14 and 33 are necessary to decrease the 95 and 99% confidence limits to +0.19ug Cu/mL respectively.

a) For a 95% confidence limit, N is about 14

b) For a 99% confidence limit, N is about 33

To determine the number of replicate measurements necessary to achieve a desired confidence limit, we can use the formula:

[tex]N = (z * Spooled / d)^2[/tex]

where z is the Z-score associated with the desired confidence level (from the table provided), Spooled is the pooled standard deviation, and d is the desired decrease in the confidence limit.

[tex]N = (1.96 * 0.27 / 0.19)^2 = 14.22 = 14[/tex] (rounded to the nearest integer)

[tex]N = (2.58 * 0.27 / 0.19)^2 = 33.06 = 33[/tex] (rounded to the nearest integer)

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Complete Question:

An atomic absorption method for the determination of copper in fuel samples yielded a pooled standard deviation of Spooled = 0.27ug Cu/mL (s-->Sigma). How many replicate measurements are necessary to decrease the 95 and 99% confidence limits to +0.19ug Cu/mL?

Confidence Level%/z 95%/1.96 99%/2.58

a) For a 95% confidence limit, N is about __?

b) For a 99% confidence limit, N is about __?

If Canister contained [tex]6\frac{1}{8}[/tex] cup of flour when Karina started making cookie and used [tex]2\frac{1}{2}[/tex] cup then number of cup left in Canister is 29/8 cups   .

the number of cups of floor in the canister initially is = [tex]6\frac{1}{8}[/tex] = 49/8 ;

the amount of floor that she used is =   [tex]2\frac{1}{2}[/tex] = 5/2 cups ,

To find out how much flour is left in the canister, we need to subtract the amount used from the total amount.

We can start by converting the mixed fractional cups to improper form ,

we get ;

number of cups left in the canister is = 49/8 - 5/2 = 49/8 - 20/8 = 29/8 .

Therefore , 29/8 cups were left in the canister .

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The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we can use the following formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates (2,4) and (-2,-8) into the formula:

m = (-8 - 4) / (-2 - 2) = -12/ -4 = 3

We can use one of the coordinates to find the y-intercept.

Plugging in the point (2,4) and the slope 3 into the equation y = mx + b, we get:

4 = 3*2 + b

so b = -2

Therefore, the equation of the line is y = 3x - 2.

a) The percentage of individuals who sleep between 4.5 and 9.3 hours is 75%.

b) By using Chebyshev's theorem, the percentage of individuals who sleep between 3.9 and 9.9 hours is 84%.

c) Using the empirical rule, the percentage of individuals who sleep between 4.5 and 9.3 hours day is 95%. But according to Chebyshev's theorem, this percentage is equals to 75%.

According to Chebyshev's theorem, the proportion of any distribution that lies within k standard deviations of the mean is at least equals to 1 − 1/k² , where k is a positive number, k> 1.

a) The average sleep hours per night is = 6.9 hours and standard deviation = 1.2 hours. Therefore, individuals who sleep between 4.5 and 9.3 hours are ± 2.4 hours or 2 standard deviations from the mean. Hence, k = 2. Using above theorem, the proportion of individuals who sleep between 4.5 hours and 9.3 hours = 1 - 1/2² = 1 - 1/4 = 0.75. Hence, the percentage of individuals who sleep between 4.5 hours and 9.3 hours

= 75%.

b) Again, the individuals who sleep between 3.9 and 9.9 hours are ±3 hours or 2.5 standard deviations from the mean. Hence, k = 2.5.

By Chebyshev's theorem, the proportion of individuals who sleep between 3.9 hours and 9.9 hours = 1 - 1/(2.5)² = 0.84 or 84 %.

c) The empirical rule is a rule-of-thumb used in statistics to forecast the behaviour of normally distributed data. Main points of Empirical rule:

The assumption here is that the number of hours of sleep follows a bell-shaped distribution i.e., the data are assumed to be normally distributed and therefore Empirical rule is applicable. As we see in individuals who sleep between 4.5 and 9.3 hours day are 2 standard deviations away from the mean. Therefore, by Empirical rule, the percentage is equals to 95% in this case. Thus, the conclusion is as per Empirical rule 95% of the individuals sampled in the national survey sleep between 4.5 and 9.3 hours. Whereas Chebyshev's theorem estimates that 75% individuals sleep between 4.5 and 9.3 hours.

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Complete question:

The results of a national survey showed that on average adults sleep 6.9 hours per night. Suppose that the standard deviation 1.2 hours. round your answers to the nearest whole number.

a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours.

b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours.

c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours day. How does this result compare to the value that you obtained using Chebyshev's theorem in part(a)? select answer

Answer:-2.5

Step-by-step explanation:

1. Set up your problem it would be 5x+2y=-5

2. Then you would set your x to be 0 so you can solve for y

5(0)+2y=-5 aka 2y=-5

3. Divide each side by 2

2y (divided by 2) = -5 (divided by 2)

y=-2.5

I hope this helps!

The solution to the equation is x = 2

From the question, we have the following parameters that can be used in our computation:

|x^3-1|-7=0

Add 7 to both sides

So, we have

|x^3-1| = 7

Remove the absolute bracket

x^3 - 1  = 7

So, we have

x^3 = 8

Take tge cube roots of both sides

x = 2

Hence, the solution is 2

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Total 13,608,000 has length of eight are there containing exactly six distinct characters.

Total number of string = 10

The length of the string should be = 8

The distinct characters = 6

So the same character should be = 2

There are total 10 numbers in which 6 are distinct, so

[tex]^{10}P_{6}=\frac{10!}{(10-6)!}[/tex]

[tex]^{10}P_{6}=\frac{10!}{4!}[/tex]

[tex]^{10}P_{6}[/tex] = 3,628,800/24

[tex]^{10}P_{6}[/tex] = 151,200

Hence, strings of length eight are there containing exactly six distinct characters = 151,200 × 10 × 9

Strings of length eight are there containing exactly six distinct characters = 13,608,000

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The velocity and acceleration vectors and the equation of the tangent line for the curve = 3i+4tj

What is Velocity?

When an item is moving, its velocity is the rate at which it is changing position as seen from a certain point of view and as measured by a specific unit of time.

What is Acceleartion?

Acceleration is the rate at which an object's velocity with respect to time changes. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration.

r(t) = 3cos(t)+sin4(t)j

velocity,V(t) = dr(t)/dt

=3sin(t)i + 4cos4(t)j

and acceleration a(t) = dv(t)/dt

= [tex]d^{2}r(t)/dt^{2}[/tex]

i.e a(t) = -3cos(t)i - 16sin(4t)j

v(0) = 0.i + 4j =4j

and a(0) = -3i -0j

=-3i

now we find the equation of the tangent line for the curve (t) at t=0

r(0) = 3i

r(t) = -3sin(t)i +4 cos 4(t)j

r (0) = 4j

equation target to the curve r(t) at t=0 is

1(t) = r (0) + (t)r(0)

= -3i+(t).4j

= -3i+4tj

The curve's tangent line equation, velocity and acceleration vectors, is -3i+4tj

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The expression for the volume of the cylinder is πB.

The cylinder is a three-dimensional figure that has a radius and a height.

The volume of a cylinder is πr²h.

Example:

The volume of a cup with a height of 5 cm and a radius of 2 cm is

Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm

We have,

Volume = πr²h

Base area = πr²

Now,

B = πr²

r² = B/h

r = √(B/h)

Now,

Volume.

= πr²h

= π x B/h x h

= πB

Thus,

The volume of the cylinder is πB.

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The correct answer is Bh

The strongest linear relationship is indicated by a correlation coefficient of -1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that if one variable gets bigger, the other variable tends to get bigger.

Now, According to the question:

The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables. Pearson r: r is always a number between -1 and 1.

The magnitude of the correlation coefficient indicates the strength of the association. For example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association.

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