Please help me with this question.

For one litre the cars travels

=400/400

=10

therefore it can travel 10 km in 1 lit

so, the distance travelled by car in 50 litres is

=50×10

The population density in city B is 6000 people per square mile considering it has 3/5 of the population in city A.

The population density in city A is 6,000.

It is known that city B, is bigger than city 1.2 times bigger than city A, so this means:

1 mile in city A = 1.2 miles in city B

Using this, and knowing that the population in city B is 0.6 times that of the one in city A, let's calculate the density:

0.6 x 6000 / 1.2 = 3,000 people per square mile

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To solve this problem using polar coordinates, we need to change from rectangular coordinates to polar coordinates, which represent points in the plane as pairs of polar coordinates (r,θ).

Given that Y1 = rcos(θ) and Y2 = rsin(θ), the condition Y1 ≤ Y2 is equivalent to 0 ≤ θ ≤ π/2. Hence, the required probability can be expressed as:

P(Y1 ≤ Y2) = ∫∫_{0<=θ<=π/2, 0<=r<=1} f(r,θ) dr dθ

where f(r,θ) = 1/π, 0 <= r <= 1.

The integration yields P(Y1 ≤ Y2) = 1/2.

Therefore, the probability that Y1 is less than or equal to Y2 for a point chosen randomly inside the unit circle is 1/2.

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The length of the total distance the particle traveled is, 327π/8.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

A particle is moving on the perimeter of a circle with radius r=5 with angular speed of π/8 radians per second.

Now, First of all, let's calculate the the circumference. This is found by this equation:

⇒ P = 2πr

Here, r = 5

⇒ P = 2π × 5

⇒ P = 10π

And, The distance of completing 4 full rotations is,

⇒ D = 4P

⇒ D = 4 × 10π

⇒ D = 40π

Since, In one second the particle traveled π/8 radians.

Here, the particle traveled for 7 more seconds and stopped, this distance is,

⇒ 7 (π/8)

⇒ 7π/8

Thus, the length of the total distance the particle traveled is;

⇒ 40π + 7π/8

⇒ 327π/8

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The shape of the histogram for the first digit of a randomly chosen legitimate record following Benford's law is a logarithmic curve, with the first digit "1" appearing most frequently, followed by "2," and so on, with the frequency of each digit decreasing as the digit increases.

A tax return is a document filed with a tax authority (such as the IRS) that reports an individual's or a business's taxable income, expenses, and other information for a given tax year. The purpose of a tax return is to determine how much tax an individual or business owes or to claim a refund if they overpaid their taxes during the year.

Benford's law is a mathematical principle that predicts the frequency of occurrence of digits in many real-life sets of data. According to the law, in such datasets, the first digit is likely to be a "1" more often than any other digit, followed by "2", and so on, with "9" being the least likely first digit. The law has been shown to hold true for many types of data, including population sizes, stock prices, and physical constants.

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You can represent the problem with an equation. Let x be the number of home runs player B had.

According to the statement, player A had 653 less than twice the number of home runs player B had.

so you can write the equation:

Player A = 2x - 653

This equation shows the relationship between the number of home runs player B had (x) and the number of home runs player A had (2x - 653). To find the number of home runs player B had, you can solve for x by adding 653 to both sides of the equation:

x = (Player A + 653) / 2

So if you know the number of home runs player A had, you can use this equation to find the number of home runs player B had.

Probability is a measure of how likely something is to occur. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. For example, if there is a 20% chance of rain, the probability of rain is 0.2. Probability is often used to calculate the likelihood of different outcomes in a situation.

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Answer:

The probability of getting unsatisfactory piston of machine 1 and satisfactory machine of piston 2 is 0.072

Step-by-step explanation:

p(E) = p(unsatisfactory Pistons of machine 1) = 84/700

p(F) = p(Satisfactory Pistons of machine 2) = 414/690

p(E and F) =

p(unsatisfactory piston of machine 1 and satisfactory machine of piston 2)

p(E and F) = p(E) . p(F)

= 84/700 . 414/690

= 0.072

Answer:

1.25 gallons per second

Step-by-step explanation:

To find out the amount of water per second, we must divide the gallons by the time.

50/40 = 1.25

Answer: 1.25

Step-by-step explanation: If they use 50 gallons of water every 40 seconds you just divide 50 and 40 which equals 1.25

Answer: 116.7 yards.

Step-by-step explanation: The length of the diagonal of a rectangular soccer field with a length of 100 yards and a width of 60 yards can be found using the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides of the triangle are 100 yards and 60 yards.

So, the diagonal can be found by:

d = √(100^2 + 60^2)

d = √(10000 + 3600)

d = √(13600)

d = 116.74 yards

Rounding to the nearest tenth, the length of the diagonal is 116.7 yards.

The length of the diagonal of the rectangular soccer field is 116.7 yards.

The line from one corner of a rectangle to the opposite center through the center is called a diagonal.

Here given that,

Length of the  rectangular soccer field, l = 100 yards

Width of the rectangular soccer field, w = 60 yards

To find the length of the diagonal d,

The formula is

d = sqrt(l^{2} + w^{2} )

d = sqrt(100^2 + 60^2)

= sqrt(10,000 + 3600)

=sqrt (13,600)

= 116.61

=116.7 yards

Therefore, the length of the diagonal of a rectangular soccer field = 116.7 yards

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When a solute does not dissolve in a solvent on further mixing, it is a saturated solution. An alloy is an example of solid/solid solution.

A saturated solution means a solution which has maximum solute concentrate. It cannot dissolve more solute in normal temperature. In such a solution system, if we add further crystals of solid, it will not dissolve. It has attained an equilibrium state. The amount of solute that dissolves will be equal to the amount which precipitates.

An alloy is a mixture of solid with solids. It can be two metals or a metal and  a non-metal. It is a homogenous mixture of solid substances, so it is also called as solid solution. The metal in higher concentration acts as the solvent and the one with lower concentration acts as solute.

So saturated solutions does not dissolve further solute particles. Alloy are solid/solid solutions.

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Refer to the attached images.

Distance is the number of units between two points.

Shakil's  distance was 15 km shorter than Omar's

How to interpret the graphs

Calculate the difference between these distances

d=25km-10km

Evaluate the differences

d=15km

Hence, Shakil's distance was 15 km shorter than Omar's

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The appropriate scale of measurement for an investor collecting data on the weekly closing price of gold throughout the year is:

a. Ratio

A ratio scale of measurement allows for meaningful comparisons of absolute differences between two values and the computation of ratios.

In the scenario of collecting weekly closing price data of gold, values such as "$1,000 per ounce" or "$2,000 per ounce" can be meaningfully compared to determine the ratio of change.

Using the ratio scale of measurement, it is possible to perform various statistical operations, such as mean, median, and standard deviation, which are meaningful and give us insights into the data.

For example, you can calculate the mean closing price for gold over a given period.

Additionally, the ratio scale allows for meaningful comparisons of magnitudes, such as "twice the value" or "half the value." Thus, a ratio scale is the most appropriate measurement scale in this scenario.

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Answer: 200 miles

Step-by-step explanation: First divide 150 by 3 = 50, then multiply by 4 = 200 miles.

You can drive 200 miles with one tank of gas.

3/4 of a tank ---> 150 miles

1 full tank ---> x amount of miles

x = (1 full tank * 150 miles) / 3/4 of a tank

x = (1 * 150) / 3/4=  200 miles.

Check the attached image to better understand how a rule of 3 is solved. Beware that this procedure only applied when there is direct proportionality between the variables.

You can drive 200 miles with one tank of gas.

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Answer:

3/4 or 0.75

Step-by-step explanation:

1 1/2 is 3/2

so 3/2*1/2

then you multiply the numerators and then the denominators so you get 3/4 and that's you answer

4 cm Equals 1 day on the x axis

2 cm = 5 0 C on the y axis

To determine the temperature on a specific day:

Trace the vertical line parallel to the y axis from the position on the x axis to the point where this vertical line crosses the graph.

Trace a horizontal line parallel to the x axis from that point until it meets the y axis at the desired location.

To locate the day at a specific temperature, trace a horizontal line parallel to the x axis from the temperature point on the y axis to the point where this horizontal line meets the graph.

Now, trace a vertical line parallel to the y axis from that position until it crosses the x axis at the desired location.

Now, a) the forecast and actual temperatures are the same where the graphs of Both intersect on Tuesday, Friday, and Sunday.

b) Repeat step 1 to obtain the temperature for the graph forecast for the days of the week.

Mon 15 0 C Tuesday 20 0 C Wednesday 25 0 C

Thu −22.5 \s0\s C

Friday 15 0 C Saturday 30 0 C

Sun −35 \s0\s C

As a result, the highest expected temperature for the week is 35 0 C.

c) Repeat step 1 to determine the temperature for the real graph based on the days of the week.

Mon−17.5 \s0\s C

Tuesday 20 0 C Wednesday 30 0 C

Thu −15 \s0\s C

Friday 15 0 C Saturday 25 0 C

Sun −35 \s0\s C

So the week's minimum real temperature is 15 0 C.

d) The difference between actual and predicted temperatures for the week

Mon, 17.5−15=2.5 \s0 C

Tue, 20−20=0 \s0\s C

Wed, 30−25=5 \s0\s C

Thu, 15−22.5=−7.5 \s0\s C

Fri, 15−15=0 \s0\s C

Sat, 25−30=−5 \s0\s C

Sun, 35−35=0 \s0\s C

The actual temperature differs from the expected temperature by 7.5 degrees Celsius on Thursday.

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The actual temperature differs from the expected temperature by 7.5 degrees Celsius on Thursday. 4 cm Equals 1 day on the x axis. 2 cm = 5 0 C on the y axis

To determine the temperature on a specific day:

Trace the vertical line parallel to the y axis from the position on the x axis to the point where this vertical line crosses the graph.

Trace a horizontal line parallel to the x axis from that point until it meets the y axis at the desired location.

To locate the day at a specific temperature, trace a horizontal line parallel to the x axis from the temperature point on the y axis to the point where this horizontal line meets the graph.

Now, trace a vertical line parallel to the y axis from that position until it crosses the x axis at the desired location.

Now, a) the forecast and actual temperatures are the same where the graphs of Both intersect on Tuesday, Friday, and Sunday.

b) Repeat step 1 to obtain the temperature for the graph forecast for the days of the week.

Mon 15 0 C Tuesday 20 0 C Wednesday 25 0 C

Thu −22.5

Friday 15 0 C Saturday 30 0 C

Sun −35

As a result, the highest expected temperature for the week is 35 0 C.

c) Repeat step 1 to determine the temperature for the real graph based on the days of the week.

Mon−17.5

Tuesday 20 0 C Wednesday 30 0 C

Thu −15

Friday 15 0 C Saturday 25 0 C

Sun −35

So the week's minimum real temperature is 15 0 C.

d) The difference between actual and predicted temperatures for the week

Mon, 17.5−15=2.5

Tue, 20−20=0

Wed, 30−25=5

Thu, 15−22.5=−7.5

Fri, 15−15=0

Sat, 25−30=−5

Sun, 35−35=0

The actual temperature differs from the expected temperature by 7.5 degrees Celsius on Thursday.

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Answer:

There are 40 green marbles and 28 blue marbles.

Step-by-step explanation:

There are 68 marbles in the bag. At LEAST 40 are green, therefore 68-40=28. So we have 28 blue marbles

Answer:

y = 3x + 5

Step-by-step explanation:

y = 3x + 5

y = 3x + 9 - 4

y = 3x + 5

If you need more help, comment on my answer. K? feel free to comment. lol.

The wind speed of a hurricane with an air pressure of 937 kPa is 203, hence option C is correct answer.

A straight line is represented using its slope and a point on the line using point slope form. This indicates that the point slope form is used to get the equation of a line whose slope is'm' and which passes through a point. The equation of a straight line can be expressed in several ways. Point slope shape is one of them. The point slope form's equation is as follows: y - y1 = m (x - x1)

From the given graph we can observe that the two coordinates of the wind and pressure are:

(x1, y1) = (934, 206)

(x2, y2) = (922, 218)

The slope of the line is given by:

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

m = (218 - 206) / (922 - 934)

m = - 12/ 12

m = - 1

Using the point-slope form we have:

y - y1 = m (x - x1)

Substituting the values:

y - 206 = -1 (x - 934)

y - 206 = -x + 934

y = -x + 934 + 206

y = -x + 1140

Substitute the value of x = 937kPa:

y = -x + 1140

y = -937 + 1140

y = 203

Hence, the wind speed of a hurricane with an air pressure

of 937 kPa is 203, hence option C is correct answer.

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Answer:

X + 9

Step-by-step explanation:

sum is addition

If function F(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and f '(6) = 6, the value of an F'(1) is 114.

We know that the chain rule of differentiation (derivative)

The derivative of composite function f(g(x)) is:  f'(g(x))⋅g'(x)

Consider function F(x) = f(xf(xf(x)))

We need to differentiate above function with respect to x.

F'(x) = f'(xf(xf(x))) × d/dx[x f(xf(x))]

We use product rule of derivative to find d/dx[x f(xf(x))]

d/dx[x f(xf(x))] = f(xf(x)) d/dx(x) + x d/dx(f(xf(x)))

After simplifying these expressions we get.

F'(x) = f'(xf(xf(x))) [f(xf(x)) + xf'(xf(x)) + x(f(x) + xf'(x))]

For x = 1 above expression would be,

F'(1) = f'(1 f(1 f(1))) [f(1 f(1)) + 1 f'(1 f(1)) + 1 (f(1) + 1 f'(1))]

F'(1) = f'(f(4)) [f(4) + f'(4) + (4 + 4)]

F'(1) = f'(6) [6 + 5 + 8]

F'(1) = 6 × 19

F'(1) = 114

Therefore, the value of F'(1) = 114.

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The complete question is:

If F(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and f '(6) = 6, find F '(1).

Answer:

Step-by-step explanation:

this set of ordered pairs is a relation but it is not a function

each value in the right oval of the arrow diagram is an output

each value in the left oval of the arrow diagram is an input

this set of ordered pairs is a relation and a function

Answer:

The critical point of the function F(x) = 2x^2 + 4 is x = 0.

Step-by-step explanation:

A. x=0

The critical point of a polynomial function is the value of x at which the function changes from increasing to decreasing or vice versa. To find the critical point of a polynomial function, we need to find the value of x that makes the first derivative of the function equal to zero.

The first derivative of F(x) = 2x^2 + 4 is F'(x) = 4x

Setting F'(x) = 0, we get:

4x = 0

x = 0

Therefore, the critical point of the function F(x) = 2x^2 + 4 is x = 0.

The mean of the sampling distribution is the average value of the mean of a large number of samples of the same size, taken from the same population. The symbol for the mean of the sampling distribution is usually represented by the Greek letter "mu" (μ). It is calculated as the sum of all the sample means divided by the number of samples.

The equation for the mean of the sampling distribution is given as:

μ = (1/n) * Σ x

where:

μ = mean of the sampling distribution

n = number of samples

Σ x = sum of the sample means

x = mean of each individual sample

The mean of the sampling distribution represents the center of the distribution and provides an estimate of the population mean. In this equation, the mean of each individual sample (x) is calculated first, and then those sample means are summed and divided by the number of samples (n) to find the mean of the sampling distribution (μ).

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When investing, the principal is the money that is kept in an investment account.

Cash held in an investment account serves as the principal while investing. The amount you really borrow when you take out a loan—before interest is applied—is known as the principle.

Senior employees at venture capital firms, principals are ranked above associates and analysts. They are less senior than partners, but they could be on the partner track. Principals can assist the company in sourcing and carrying out deals, much like an associate.

When you sell an investment, you normally only need to pay taxes if you make a profit. To determine whether you made a profit or loss, you must deduct the cost basis of your investment—typically, the price you paid—from the sale price.

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The principal for amount $2496.76 at 1% compound interest annually for 3 years is $ 2420.03.

When investing, the principal is the money that is kept in an investment account. The principle of a loan is the amount that you actually borrow when you apply for one, before interest is added.

Principals are the most senior personnel in venture capital firms, ahead of associates and analysts. They are not as senior as partners, but they might be moving toward becoming partners. Similar to an associate, principals can help the business find and close deals.

You typically only have to pay taxes on an investment sale if you make a profit. You must subtract the cost basis of your investment, which is often the price you bought, from the sale price to establish if you made a profit or a loss.

Using the formula,

Amount  = P(1 + R/100)ⁿ

Where P = principle amount,

R = rate of interest,

n = time period,

It is given that

Amount = $2496.79

Rate of interest (R ) = 1%

(n) time period = 3,

Putting the above values in the formula,

2496.76 = P (1 + 1/100)³

⇒ 2496.76 = P (101/100)³

⇒ 2496.76 / (101/100)³ = P

⇒ P = 2496.76 / 1.03

⇒ P = $ 2420.03

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The solution to the equation is x = -12 and Nathan made a mistake while simplifying in Step 2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

3 ( x - 8 ) = 5x

On simplifying the equation , we get

3x - 24 = 5x

Adding 24 on both sides , we get

3x = 5x + 24

Subtracting 3x on both sides , we get

3x - 5x = 24

-2x = 24

Divide by 2 on both sides , we get

-x = 12

So , x = -12

Hence , the solution is x = -12

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The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).

In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :

We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)

applying quotient rule,

=> f(x) = ln(1) - ln( gᵏ)

Appling power rule,

=> f(x) = ln(1) - k ln( g)

Applying Zero Exponent Rule,

=> f(x) = 0 - k × ln( g)

Hence, the required expansion is f(x) = - k × ln( g).

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