Eliud was running 125 miles per week. Now, he’s running 20% more miles per week.

b) How many miles is Eliud running per week? Write and solve an equation to determine how many miles Eliud is now running per week, r.

The rate at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is 16/9π cm/min.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface.

For cylindrical pot,

Volume, V = πr²h

dV/dt = π(r²dh/dt+h * 2r dr/dt)

Since r is constant,

Therefore, dr/dt = 0

dV/dt = 100 = πr²dh/dt

100 = π * 225/4 *dh/dt (since r = 15/2 cm)

=> dh/dt = 400/ 225π = 16/9π cm/min.

Thus, The rate at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is 16/9π cm/min.

Correct question: Coffee is draining from a conical filter with height and diameter both 15 cm, into a cylindrical coffee pot with diameter 15 cm. The rate at which coffee drains from the filter into the pot is  100 cc/min. The rate in cm/min at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is?

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We can use probability to find the answers to the questions - the final answers are given below.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

We will answer each part in detail.

Part (a)

No, there are more than 2 outcomes in this particular scenario.

Part (b)

Yes, there are two outcomes (Type A or not).

Part (c)

No, probability changes as the cards are dealt.

Part (d)

No, the trials are not independent.

Part (e)

Yes, two outcomes (more than 3 or not)

These are the final answers:

(a): No

(b): Yes

(c): Yes

(d): No

(e): Yes

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It would depend on the rate of the ferris wheel, so it is impossible to answer this question without knowing the wheel's speed.

1. The question is asking for an estimate of the time it would take for a person to get from the start of the ferris wheel to the point closest to the polar coordinate (6, 0).

2. To answer this question, we need to know the speed of the ferris wheel. Without this information, it is impossible to answer the question.

It would depend on the rate of the ferris wheel, so it is impossible to answer this question without knowing the wheel's speed.

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Answer:

|x| = x if x >= 0, -x if x < 0

Step-by-step explanation:

Answer:

9.68

Step-by-step explanation:

x*(x-4)=55; x approximately equals 9.68

Answer:

16x feet

Step-by-step explanation:

A scale of 1/4" = 4' means that every 1/4 inch on the drawing or map represents 4 feet in the actual measurement. To find the actual length of a line on the drawing or map, you need to multiply the length of the line in inches on the drawing by the denominator of the scale, and then divide by the numerator of the scale.

The formula is:

Actual length = (length on the drawing or map x scale denominator) / scale numerator.

In this case, the length on the drawing or map is x inches, and the scale is 1/4" = 4'.

So the actual length is: (x inches x 4') / 1/4" = 16x feet

Therefore, the actual length of the line on the drawing or map is 16x feet.

An inconsistent system is a set of equations that have no solution.

Consider the following as the lines' equation:[tex]p_1x+q_1y+a_1=0 , p_2x+q_2y+a_2=0[/tex]

We can start analyzing the equations of lines and evaluating their various properties now that we understand how to display points on a coordinate plane and graph linear equations. The common forms for writing linear equations and the characteristics of lines that can be inferred from their equations are covered in this section.

If both lines are parallel to one another, there is no answer because the lines never cross.

In such a circumstance, the pair of linear equations in two variables is considered to be inconsistent because algebraically, [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex].

For example, line of equations are

[tex]2x-y=4\\\\4x-2y=8[/tex]

[tex]\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}\\\frac{b_1}{b_2}=\frac{1}{2}\\\frac{c_1}{c_2}=\frac{4}{8}=\frac{1}{2}[/tex]

Here, both equation has no solution so equation are called inconsistent equation.

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The probability that both balls removed are red is 10.7%, while the probability that the second ball removed is red is 19.0%.

(a) The conditional probability that the second ball you remove is red given that the first ball you remove is red is 2/7 or 28.6%.

P(second ball is red | first ball is red) = P(second ball is red and first ball is red) / P(first ball is red)

= (2/7) / (3/8)

= 2/7

(b) The probability that both balls that you remove are red is (3/8)*(2/7) = 6/56 or 10.7%.

P(both balls are red) = P(first ball is red) * P(second ball is red | first ball is red)

= (3/8) * (2/7)

= 6/56

(c) The probability that the second ball that you remove is red is (2/7)*(5/9) + (3/8)*(2/7) = 4/21 or 19.0%.

P(second ball is red) = P(second ball is red and first ball is red) + P(second ball is red and first ball is blue)

= (2/7)*(5/9) + (3/8)*(2/7)

= 4/21

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The value of x  is 16 cm.

What is the equilateral triangle?

An equilateral triangle is a type of triangle that has three sides of equal length and three equal angles of 60 degrees each. All equilateral triangles are also equiangular and isosceles triangles. The sides of an equilateral triangle are congruent, and it is symmetrical in all ways, meaning that it has rotational and line symmetry.

We have given,

Lengths of sides:

16 cm,  16cm, and x cm,

we have to find the value of x.

The given triangle is an equilateral triangle,

so, The length of all three sides of an equilateral triangle is equal.

16 cm = 16cm =  x cm,

x = 16 cm

Hence, The value of x  is 16 cm.

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By finding the Greatest Common Factor we can conclude that the possible dimensions of the sports field are a width of 70 yards and a length 9-6d yards.

There are two theories needed to solve the problem:

Dimensions of an object are defined as a measure of length, width, or height extended in a certain direction.

The Greatest Common Factor (GCF) of two or more numbers is the largest number that can be evenly divisible by these numbers.

We can assume that the sports field is a rectangle since we know that:

- the width is at least 50 yards

- the area is (630-420d) yard square

To find the dimension of the sports field, we have to find the GCF of 490 and 210, by enumerating their prime factors and multiplying those factors both numbers have in common.

490 = 2 × 5 × 7 × 7

210 = 2 × 5 × 3 × 7

So the GCF is 2 × 5 × 7 = 70

This GCF depicts one of the dimensions of the sports field, which we denote as d₁.

By substituting the value of one dimension, the value of another dimension (d₂) can be obtained:

Area = d₁ x d₂

d₂ = Area / d₁

    = (630-420d) / 70

    = 9-6d

Thus we can conclude that the possible dimensions of the sports field are width 70 yards and length 9-6d yards.

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The midsegments of AABC, hypotenuse BC  is B. 15.

In a triangle, a midsegment is a line segment that connects the midpoints of two non-adjacent sides of the triangle. In this figure, DE and DF are the midsegments of AABC, which means that they connect the midpoints of the sides AB and AC, respectively. Since DE and DF are parallel, we know the triangle isosceles (both legs are congruent).

Since the angle at A is 122°, we know that the angle at B and C are 78° (180-122=58). Therefore, if we draw the altitude from B to AC, we have a 30-78-72 triangle. We have been given the length of the altitude, 8, and the angle of the base, 72. We can use the Sine Ratio to calculate the hypotenuse, BC.

sin(72) = opposite / hypotenuse = 8/BC

Solving for BC, we get 15

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Answer: The lines are only parallel if these pairs of angles are of equal size:

Angle 1 ≡ Angle 5

Angle 2 ≡ Angle 6

Angle 3 ≡ Angle 7

Angle 5 ≡ Angle 8

Step-by-step explanation:

All these angles follow a rule called corresponding angles. The rule goes that corresponding angles on parallel lines are equal. If the pairs of angles are equal, this must mean that the lines are parallel and vice versa.

The location on negative integers will be on left side of zero.

A number system is defined as a system of writing to express numbers.

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

On a number line the integers were represented.

Integers are collect of positive numbers, negative numbers and zero.

On the right side of zero the number are positive 1,2,3..

To the left side of zero there are negative integers -1,-2,-3...

Fom left to right the value of numbers be increases.

Hence, the location on negative integers will be on left side of zero.

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So, on solving the provided question we can say  their balloon payment will be $380,040.19.

A balloon loan is a type of loan arrangement where only a portion of the original balance is repaid during the course of the loan's relatively short repayment term. When only a fraction of the initial debt is repaid during the duration of the loan's relatively short repayment term, the loan is referred to as a "balloon loan."

the monthly fixed payment. there is a formula

Pmt = (A * i * (1 + i)ⁿ) / ((1 + i)ⁿ - 1)

Pmt - monthly payment;

A is  Loan amount;

i is periodic interest rate; and

n is  number of periods.

Mortgage amount: $425,500

[tex]Term in years: 8 years[/tex]

Interest rate: 6.55%

Amortization period is - 30 years.

pmt=(425500*6.55*(1+6.55)^12)/((1+6.55)^12-1)

Balloon payment=[tex]$380,301.82.[/tex]

Total interest paid[tex]$211,630.52.[/tex]

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The third side of the right angle triangle is 5 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, using Pythagoras's theorem,

6² - (√11)² = b²

36 - 11 = b²

b² = 25

square root both sides of the equation

b = √25

b = 5 units

Therefore.

third side = 5 units.

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Answer:

14

Step-by-step explanation:

1) "the number 35"  means 35

2) "decrease 35 by 0.6 of it"  means -(0.6)*(35)

Put them together:

35 - (0.6)*(35)

35 - 21

= 14

On solving the provided question, we can say that Probability 8 drive to work[tex]= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123 = > 1 - 0.1236 = 0.8764[/tex]

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

x = number that drive to work alone

Likelihood that exactly eight people drive alone to work is equal to the probability that no more than seven people drive alone.

[tex]P(x < = 7) = 1 - P(x > 7) = 1- P(x = 8)[/tex]

That probability

Probability 8 drive to work

[tex]= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123\\=1 - 0.1236 = 0.8764[/tex]

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The equation of the line is y = -5/2x + 5.

1. We know that the equation of a straight line is given by y = mx + c, where m is the slope of the line and c is the y-intercept.

2. We need to find the slope of line l. To find the slope, we can use the formula: m = (y2-y1)/(x2-x1). In this case, we have y2 = 1, y1 = 5, x2 = 2, and x1 = 0. Therefore, m = (1-5)/(2-0) = -4/2 = -2.

3. We now have the slope of line l, so we can find the equation of the line which is parallel to l and which passes through the point (3,0). To do this, we can use the formula y = mx + c, where m is the slope of the line and c is the y-intercept.

4. In this case, m = -2 and c is the y-intercept, which is the point at which the line intersects the y-axis.

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The missing piece of information in the proof is that m ∠ DOA and m ∠ BOC are vertical opposite angles.

According to the equality's subtraction property, equality is unaffected by removing the same amount from both sides of an equation. When the same quantity or value is removed from both sides of an equation, the resultant difference is also identical on both sides.

Both the equality's addition and subtraction properties are related. The same integer added to or subtracted from both sides of an equation maintains equality on both sides.

To prove that m ∠ BOC = 90°.

Given that m ∠ AOB exists a right angle triangle.

Therefore; m ∠ BOC must also be equivalent to 90°.

Since m ∠ BOC and m ∠ AOB are right angles, it follows that m ∠ DOA and m ∠ BOC are also vertical opposing angles and, as such, are equal.

So, the fact that m ∠ DOA and m ∠ BOC are vertical opposing angles is the crucial piece of information missing from the proof.

The complete question is:

Given: AOB is a right angle

Prove: m BOC = 90°

Since AOB is a right angle, it is 90°. AOB is supplementary to BOC,

so m AOB + m BOC = 180°. By the substitution property of equality,

90 + m BOC = 180°. Applying the subtraction property of equality,

m BOC = 90%. What statement is missing from the proof?

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The offered statement states that 42 cups of grain are required to produce three loaves of bread.

As a completely volunteer hot meal service in 1983, Breads & Fishes quickly evolved into a pre-packaged shopping bag contribution program for locals. This nonprofit's first year's budget was $6,500, at which time the pantry supplied food to about 50 homes.

We know we need four times 10 1/2 cups of flour since 12 was 4 times higher than three (3 * 4 = 12).

We only have to calculate 10.5 * 4 = x but then just solve for x.

42 cups - grain (10.5 * 4)

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The complete question is-

10 1/2 cups of flour are needed to make 3 loaves of bread. How many cups are needed for 12?

The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.

Let the number of green marbles be 'g'.

The probability of selecting a red marble before the number of green marbles is doubled is[tex]$\frac{4}{g+4} * 100 = x\%$[/tex]

The probability of selecting one of the four red marbles from the box after the number of green marbles is doubled is [tex]$\frac{4}{2g+4} * 100 = (x - 15)\%$[/tex]

Rearranging the equations and solving for g, we get:

[tex]\frac{4}{g+4} * 100 = x$\frac{4}{2g+4} * 100 = (x - 15)$$2g+4 = \frac{4}{x-15}$$g = \frac{4 - 4x + 60}{2x - 30}$[/tex]

Therefore, the number of green marbles before the number of green marbles is doubled is [tex]$\frac{4 - 4x + 60}{2x - 30}[/tex]

The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.

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Answer:

d. y = 5x/2 + 1, y = 5x/2 + 7

Step-by-step explanation:

Both lines have the same slope (5/2) , so they are parallel.

The bearing of H from P is 243°26′

In mathematics, an angle is a measure of the amount of rotation between two lines or planes. It is measured in units of degrees or radians. An angle is formed by two rays that have a common endpoint called the vertex. The rays are the sides of the angle and the vertex is the point where the rays meet.

An angle is defined by its measure, which is the amount of rotation between the two rays. The most common way to measure angles is in degrees, where a full rotation is equal to 360 degrees. Another way to measure angles is in radians, where a full rotation is equal to 2*pi radians.

Let the bearing of H from P be represented by x°.

tanθ=3060=0.5

θ=tan−1(0.5)=26.565°

x=180°+(90−26.565)

x=180+63.435=243.435°

= 243°26′

Hence, the bearing of H from P is 243°26′

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Step-by-step explanation:

you know how equations are transformed ?

by applying the same operation on both sides of the equation (so that the equality remains).

x + 38 = 79

to get "x = ...", we need to eliminate the "+ 38" in the x side.

clearly we need to subtract 38.

again, whatever e do, we have to do on both sides, otherwise the equality relation is destroyed.

so,

x + 38 - 38 = 79 - 38

x = 41

that is the height of the avocado tree : 41 in.

it is 38 in shorter than 79 in (the fig tree).

that's all that is to this. it is a really simple method.

the same applies to any operation you want to do (+, -, ×, ÷, ...).

The double integral for [tex]3xy^2/x^2+1[/tex] is 8㏑(2).

[tex]3\int\limits^1_0 \int\limits^2_2 \frac{xy^2}{x^2 + 1} \, dy dx[/tex]  

3* 1/2 (㏑(2) - ㏑(1) ) * 1/3 (8+8)

8㏑(2)

A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). In the real-number plane, integrals of functions of two variables over an area are referred to as double integrals, and integrals of functions of three variables over a region in real-number three-dimensional space are referred to as triple integrals.

The Cauchy formula for repeated integration can be used to calculate multiple integrals of a single-variable function.

The double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis.

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Answer:

The distance-time graph of the journey would be as follows:

From 8am to 8:01am, the car travels 0 miles (at 8am, it leaves London)

From 8:01am to 9:01am, the car travels 60 miles (at a constant speed of 60mph)

From 9:01am to 9:31am, the car travels 0 miles (the driver takes a break of 30mins)

From 9:31am to 12:51pm, the car travels 140 miles (at a constant speed of 70mph)

The graph would be a line with a slope of 60 for the first hour, a flat line for the 30 minutes break, and then a line with a slope of 70 for 2 hours and 20 minutes.

Note: Since we don't have a time-scale and time unit, this graph is just a representation of the pattern of the journey, and the actual values are not accurate.

According to the concept of probability, the sample space for the experiment is explained below.

The term probability in math is called as the occurrence of a random event and the sample space is defined as a collection or a set of possible outcomes of a random experiment.

Here we have know that the same space of this experiment is the possible outcomes of selecting two out of the three breakfast.  

Here let us consider that the sample space is B

And the the sample space is written as.

=> {(cereal and egg), (cereal and fruit), (fruit and egg), (fruit and cereal), (egg and fruit), (egg and cereal)}

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Always use alpha=0.05 since it's the most commonly used one. Use a smaller alpha when the consequences of mistakenly rejecting the null hypothesis are more serious.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H0.

When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a smaller alpha. Generally speaking, you should reject the null hypothesis less frequently when there is a greater risk of doing so, which happens as you lower the significance level.

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El area de las bases es 628 cm^2 (ambas bases) y el area lateral es 1,256 cm^2

Tenemos un cilindro con un radio de 10 centimetros y 20 centimetros de altura.

El cilindro tiene dos tapas que son circulares, el area de estas se calcula como el area de un circulo cualquiera, esta sera:

A = 2*( pi*R^2)

Donde R es el radio y pi = 3.14, entonces tendremos:

A = 2*(3.14*(10cm)^2)

A = 628 cm^2

El area lateral será igual que el producto entre la altura y la circunferencia:

A' = 2*pi*R*H

Donde H es la altura.

Remplazando los valores que conocemos obtendremos:

A' = 2*3.14*(10cm)*20cm

A' = 1,256 cm^2

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On solving the provided question, we can say that a function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution. The solution provides the list's range.

A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).

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