Asif, Sean, Bill, Francis, and Andrew are running against each other in a 100 m race. They all have an equal chance of winning.
Show the possible orders for the first three runners crossing the finish line.
What is the probability of Andrew being one of the first three runners to cross the finish line? Assume that there will not be a tie.

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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Answer:

Ion know

Step-by-step explanation:

u tell me

Answer:

Step-by-step explanation:

Step 1:

Step 2:

Pull out like factors:

Solution to this question:

Answer:

2x-3y

Step-by-step explanation:

-1/4×-8x= 8/4x = 2x

-1/4×12y= - 12y/4 = -3y

2x-3y

Answer:

C

Step-by-step explanation:

Answer:

1: she has 38 quarters 2: yes

Step-by-step explanation:

1: .10 x 30 = 3

.25 x 38 = 9.50

9.50 + 3 = 12.50

2: q= .10d + 9.50

a)  The demand (price) function in terms of x : P(x) = 12 - 0.025(x - 1500)

b) the marginal revenue function is \(MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)\) The marginal revenue from the sales of 1800 T-shirts is -$3. This means that for each additional T-shirt sold after the 1800th, the revenue will decrease by $3 per T-shirt

To determine the demand (price) function, we need to find a relationship between the price of the T-shirts (P) and the number of T-shirts sold (x). We are given that for every $0.50 decrease in price, 20 more T-shirts will be sold.

Let's first find the decrease in price per T-shirt sold. If 20 more T-shirts are sold for every $0.50 decrease, then the decrease per T-shirt is $0.50/20 = $0.025. Now, we can set up the demand function. The base price is $12, and we decrease it by $0.025 for each additional T-shirt sold. So the demand function is:

P(x) = 12 - 0.025(x - 1500) To determine the marginal revenue function, we first need to find the total revenue function. Total revenue (R) is the product of the price (P) and the number of T-shirts sold (x):

R(x) = P(x) * x = (12 - 0.025(x - 1500)) * x Now we need to find the derivative of the total revenue function with respect to x, which will give us the marginal revenue function: MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)

To determine the marginal revenue from the sales of 1800 T-shirts, we simply plug in x = 1800 into the marginal revenue function: MR(1800) = 12 - 0.05(1800 - 1500) = 12 - 0.05(300) = 12 - 15 = -$3

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The constraint that reflects the statement "if project 1 is selected then project 2 must be selected" is x1 ≤ x2.

The constraint x1 ≤ x2 ensures that if project 1 is selected (x1 = 1), then project 2 must also be selected (x2 = 1).

This constraint imposes a logical relationship between the binary variables x1 and x2, indicating that the value of x2 should be at least as large as x1. If x1 is 0 (indicating project 1 is not selected), the constraint does not impose any specific condition on x2.

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Answer:

−7

Step-by-step explanation:

Answer:

Let's solve your inequality step-by-step.

3(−4+x)<−33

Step 1: Simplify both sides of the inequality.

3x−12<−33

Step 2: Add 12 to both sides.

3x−12+12<−33+12

3x<−21

Step 3: Divide both sides by 3.

3x/3  < −21  /3

x<−7

Answer:

x<−7

Step-by-step explanation:

The language \(\bar L\) is the complement of the language L. It consists of all strings over the alphabet Σ= {a,b} that are not in L.

The language L is defined as L= {λ,a,b,aa,bb,ab,ba}. To find the complement of L, we need to determine all the strings that are not in L.

The alphabet Σ= {a,b} consists of two symbols: 'a' and 'b'.

Therefore, any string not present in L must contain either symbols other than 'a' and 'b', or it may have a different length than the strings in L.

The complement of L, denoted by \(\bar L\). includes all strings over Σ that are not in L.

In this case, \(\bar L\) contains strings such as 'aaa', 'bbbb', 'ababab', 'bbba', and so on.

However, it does not include any strings from L.

In summary, \(\bar L\) is the set of all strings over Σ={a,b} that are not present in L.

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The remaining sides are 11/2 and 11√3/4.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

In a 30-60-90 triangle,

The length of the side opposite the 30-degree angle = 1/2 x the length of the hypotenuse.

The length of the side opposite the 60-degree angle = √3/2 x the length of the hypotenuse.

The length of the hypotenuse = 2 x the length of the side opposite the 30-degree angle.

Now,

The length of the hypotenuse = 2x.

So,

2x = 11

x = 11/2

Now,

The lengths of the other two sides are:

= √3/2 x 11/2

= 11√3/4

And,

= 11/2

Thus,

The remaining sides are 11/2 and 11√3/4.

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At the end of the year, Achley Company's owner's equity is $4,685,000 and can be calculated by starting with the beginning owner's equity, adding the revenues, subtracting the expenses, and subtracting the owner's withdrawals.

To calculate Achley Company's owner's equity at the end of the year, we start with the beginning owner's equity of $5,175,000. We then add the revenues of $225,000 and subtract the expenses of $165,000. This gives us the net income, which is the difference between revenues and expenses, and represents the increase in owner's equity.

So, net income = revenues - expenses = $225,000 - $165,000 = $60,000. Next, we subtract the owner's withdrawals of $550,000 from the net income. Owner's withdrawals are personal expenses or cash withdrawals made by the owner and reduce the owner's equity.

Owner's equity at the end of the year = Beginning owner's equity + Net income - Owner's withdrawals.Owner's equity at the end of the year = $5,175,000 + $60,000 - $550,000. Calculating the above expression, we find that Achley Company's owner's equity at the end of the year is $4,685,000.

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The range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.

If we are given a mapping that represents a relation, the input values (x-values) make up the domain of the relation while the output values (y-values) make up the range of the relation.

In the mapping shown in the diagram attached below, we have the following:

The domain of the relation is: {-1, 0, 1, 2, 3}

The range of the relation is: {3, 5, 11, 21}

Thus, we can conclude that, the range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.

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Answer:

x ∈ (0,75; +∞) and x∈ (1; +∞)

Step-by-step explanation:

1) 3 - 4x < 0

-4x < -3 / : (-4)

x > 0,75

x ∈ (0,75; +∞)

2) 2x - 4 > -2

2x > -2 + 4

2x > 2 / : 2

x > 1

x∈ (1; +∞)

Answer:

b. median

Step-by-step explanation:

It’s best to use the mean when the distribution of the data values are symmetrical and there are no clear outliers.
On the other hand, it’s best to use the median when the the distribution of data values is skewed or when there are clear outliers.

You can make your own graph, or use a statistics calculator to find out whether the graph is skewed or symmetrical. The graph for this scenario is shown below.

hope this helps!

Answer:

6 outfits

Step-by-step explanation:

Outfits needs atleast a pant and a shirt

since least number of shirts is 6 and pants 7

6 outfits can be made

6 outfits, because it is

Answer:

If two variables have a cause-and-effect relationship, then the variables will have a correlation.

Step-by-step explanation:

Answer: k=1

Step-by-step explanation: PQ already equals ST

Answer:

A- 4 and 40

Step-by-step explanation:

Multiply 81.2 by 0.45 and you get 36.54

Answer:

A

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

123+(-1)/2-(-3)=

122/2=61

61+3=64

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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The monthly payment that Alang needs to invest to reach $58,000 in 5 years at 5% compounded interest is $853.

Compounded interest accumulates interest and charges subsequent interest on both the principal and the accrued interest.

The monthly payment needed for a future value to be attained can be computed using an online finance calculator.

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $58,000

Results:

PMT = $852.86

Sum of all periodic payments = $51,171.89

Total Interest = $6,828.11

Thus, Alang should invest $853 monthly to save $58,000.

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Answer:

1: Narrower

2: Wider

Step-by-step explanation:

The magnitude of 'a' increases, the parabola becomes more and more wider.

A parabola is a curve where any point is at an equal distance from a fixed point (the focus), and a fixed straight line (the directrix).

Given is a parabola.

The parametric form of equation of parabola is given by -

y² = 4ax

Here, distance 'a' is called focus of parabola.

For a constant value of x - coordinate, take different values of 'a'. For constant x, we get the following relation -

y² \(\alpha\) a

As the magnitude of 'a' increases, the y coordinate increases and parabola becomes more and more wider.

Therefore,  the magnitude of 'a' increases, the parabola becomes more and more wider.

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Answer: 3.19 feet.

Step-by-step explanation: 319 divided by 100 is 3.19

Answer:

V=?

S=400m

t=80s

V=S/t

V=400/80

V=5m/sec

Step-by-step explanation:

The width of the round cake needs to be approximately 2 times the radius, or about 15.6 inches, to have the same volume as the rectangular prism cake.

A three-dimensional structure with six rectangular faces that are parallel and congruent together is called a rectangular prism. It has a length, width, and height. By multiplying the length, width, and height together, one may get the volume. Contrarily, a cylinder is a three-dimensional shape with two congruent and parallel circular bases. It has a height and a radius, and you can determine its volume by dividing the base's surface area by the object's height. A cylinder has curved edges and no corners while a rectangular prism has straight edges and corners.

The volume of the rectangular cake is given as:

V = length * width * height

Substituting the values we have:

16 * 12 * 3 = 576 cubic inches

Now, for the cylindrical cake to be of the same volume we have:

V = π * radius² * height

π * radius² * 3 = 576

(3.14) * radius² * 3 = 576

radius = 15.6 inches

Hence, the width of the round cake needs to be approximately 2 times the radius, or about 15.6 inches, to have the same volume as the rectangular prism cake.

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Answer:

solution

Step-by-step explanation:

ADC = Sum of triangle

AD+ AC = 2.25+3 =5.25

Step 2:

BCD = Sum of acute angled triangle = a+b+

c

BCD= 2.25+4+3

BCD = 9.25

The value of x =ADC+BCD

= 5.25+ 9.25

= 14.5

Lets simplify

\(\\ \sf\longmapsto \dfrac{x}{3}=-7.\dfrac{x}{3}\)

\(\\ \sf\longmapsto \dfrac{x}{3}=\dfrac{-7x}{3}\)

\(\\ \sf\longmapsto -7\)

Hence its not a fraction

Answer:

2.5%

Step-by-step explanation:

Please mark Brainliest when able.

5 * (5/2)⁽¹⁵⁻¹⁾ expression gives us the 15th term of the geometric sequence with a first term of 5 and a common ratio of 5/2.

To find the 15th term of a geometric sequence, we can use the formula:

nth term = a * r⁽ⁿ⁻¹⁾

where:

- nth term is the term we want to find,

- a is the first term of the sequence, and

- r is the common ratio of the sequence.

In this case, the first term (a) is 5, and the common ratio (r) is 5/2. We want to find the 15th term, so n = 15.

Plugging in the values into the formula, we have:

15th term = 5 * (5/2)⁽¹⁵⁻¹⁾

Therefore, 5 * (5/2)⁽¹⁵⁻¹⁾ expression gives us the 15th term of the geometric sequence with a first term of 5 and a common ratio of 5/2.

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Answer:

i think its 15 gallons of water if you do the math you can see it

Step-by-step explanation: