Two skaters are racing towards the finish line of the race.the first Skater has a 40 meter lead and is traveling at a rate of 12 meter.the second skater is traveling at a rate of 14 meter per second.how long will it take for the second skater to pass the first skater?

Ann's age after h years is 2h

Bill's age after h years is 3h

Charles' age after h years is 8 + h

The sum of their ages after h years is 6h + 8

Step-by-step explanation:

The given is:

Anne is currently h years old

Bill is currently 2h years old

Charles is currently eight years old

We need to find an expression for each person’s age after h years and then find an expression for the sum of their ages after h years

∵ Ann is h years old now

∵ Her age after h years = her age now + h

∴ Her age after h years = h + h

∴ Her age after h years = 2h

Ann's age after h years is 2h

∵ Bill is 2h years old now

∵ His age after h years = his age now + h

∴ His age after h years = 2h + h

∴ His age after h years = 3h

Bill's age after h years is 3h

∵ Charles is 8 years old now

∵ His age after h years = his age now + h

∴ His age after h years = 8 + h

∴ His age after h years = 8 + h

Charles' age after h years is 8 + h

Add their ages after h years

∵ The sum of their ages after 8 years = 2h + 3h + 8 + h

- Add like terms

∴ The sum of their ages after 8 years = (2h + 3h + h ) + 8

∴ The sum of their ages after 8 years = 6h + b

The sum of their ages after h years is 6h + 8

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Anne, Bill, and Charles's ages after h years will be 2h, 3h, and h+8, respectively. The sum of their ages after h years is 6h + 8.

The question asks for expressions that represent each person's age after h years and for the sum of their ages after h years. Currently, Anne is h years old, Bill is 2h years old, and Charles is eight years old.

After h years have passed:

Now, to find the expression for the sum of their ages after h years, we add the expressions together:

Sum of their ages = Anne's age after h years + Bill's age after h years + Charles's age after h years
= 2h + 3h + (h + 8)
= 6h + 8.

Answer:

Rs 2163.20.

Step-by-step explanation:

The formula for this is

A = P(1 + r)^t     where P is the amount invested, r = the rate (as a decimal) and t = the number of years.

So for rs 2000 we have:

A = 2000(1 + 0.04)^2 = Rs 2163.20

Answer:

[tex]\frac{2}{7}[/tex]

Step-by-step explanation:

The possibility of the event A occurring is given by the formula:

[tex]\boxed{P(A)= \frac{\text{number of favourable outcomes in A}}{\text{total possible outcomes}}}[/tex]

Since the event that we are looking for (favourable event) is choosing a girl with glasses, the number of favourable outcomes is the number of girls with glasses in the class.

Number of favourable outcomes= 4

Total possible outcomes

= total number of students in the class

= 10 +4

= 14

Thus, P(girl with glasses)

= [tex]\frac{4}{14}[/tex]

= [tex]\bf{\frac{2}{7} }[/tex]

Additional:

For more questions on probability, do check out the following!

Answer:

B

Step-by-step explanation:

If you use the method of rise over run, you find the slope to be -2, and the y intercept is given.

y = 2x+8 is the slope-intercept equation of the line. Option D is correct.

From figure two points (0,8), (6, -4). equation of the line to be determine.

Equation of the line is y = mx +c where m = slope and c = y intercept.

Here
Equation of the line = [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
y - 8 = 8+4/0+6(x-0)
y - 8 = 2(x)
y = 2x + 8

Thus, y = 2x+8 is the slope-intercept equation of the line.

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In a quadrilateral inscribed in a circle, opposite angles are supplementary. Hence, opposite angles J and M in quadrilateral JUMP are supplementary, totaling 180 degrees.

In the given diagram, quadrilateral JUMP is inscribed in a circle. According to the property of inscribed angles, when a quadrilateral is inscribed in a circle, opposite angles are supplementary, meaning they add up to 180 degrees.

Given that angles J and M are opposite angles in quadrilateral JUMP and must be right angles, it implies that they are supplementary. This is because right angles measure 90 degrees each, and the sum of two right angles equals 180 degrees, making them supplementary.

Therefore, we conclude that angles J and M are supplementary, with a combined measure of 180 degrees.

To summarize, in the inscribed quadrilateral JUMP, opposite angles J and M are supplementary, totaling 180 degrees, due to the property of angles in a quadrilateral inscribed in a circle.

The question probable may be:

In the diagram below, quadrilateral JUMP is inscribed in a circle. Opposite angles J and M must be right 2. complementary 3. congruent 4 supplementary

Answer:

For the given expression [tex]x^3 = 135[/tex] , the value of x = 5.13

Step-by-step explanation:

Here, the given expression is : [tex]x^3 = 135[/tex]

Now, to solve this given equation,we need to find the suitable value for x.

Solving for x , we get:

[tex]x^3 = 135[/tex]

Taking cube roots both sides, we get:

[tex]\sqrt[3]{(x)^3}  = \sqrt[3]{135} \\\implies (x)^{3 \times \frac{1}{3}}   =  (135)^{\frac{1}{3}} \\[/tex]

But, 135 = 5.13 x 5.13 x 5.13

[tex]\implies 135   =  (5.13)^3\\\implies x^{3 \times \frac{1}{3}} =  (5.13)^{3 \times \frac{1}{3}}\\\implies x  = 5.13[/tex]

Hence, for the given expression [tex]x^3 = 135[/tex], the value of  x = 5.13

Answer:

the other answer was a bit confusing so, 135 divided by 3 is 45, so, x=45

135 divided by 45 is 3 lol.

Step-by-step explanation:

Answer:

$12.09

Step-by-step explanation:

formula Y = KX

where; y = $24.18

            x = 2 books

            k = constant proportionality

Step 1. Do the equation based on the data given

$24.18 = k 2

Step 2. Divide 2 on both sides to eliminate integer on the right side

$24.18 / 2 = k2/2

Answer ;

k = $12.09 dollar in relate to number of books

Answer:

1 ¹/₉ hours

Step-by-step explanation:

Let's say L is Larry's speed, C is Curly's speed, and M is Moe's speed.

1 = 2 (L + C)

1 = 1 ⅔ (C + M)

1 = 1 (L + C + M)

Solve the system of equations.  First, simplify the equations:

1 = 2L + 2C

3 = 5C + 5M

1 = L + C + M

Double the third equation and subtract the first equation from it:

2 = 2L + 2C + 2M

1 = 2L + 2C

1 = 2M

M = 1/2

Plugging into the second and third equations, we get:

C = 1/10

L = 2/5

Therefore, the time it takes Larry and Moe together is:

1 = t (L + M)

t = 1 / (L + M)

t = 1 / (2/5 + 1/2)

t = 1 / (4/10 + 5/10)

t = 1 / (9/10)

t = 10/9

t = 1 ¹/₉ hours

It takes them 1 ¹/₉ hours, or 1 hour 6 minutes 40 seconds.

Larry and Moe would take 5/3 hours, or 1 hour and 40 minutes, to build a bookcase together, based on the rates of building individually and in different pairs.

Larry and Curly together build a bookcase in 2 hours. This means that together they have a rate of 0.5 bookcases per hour, since 1 divided by 2 is 0.5. Similarly, Curly and Moe together can build one in 1 2/3 hours, which is the same as 5/3 hours. Therefore, their collective rate is 3/5 bookcases per hour. Larry, Curly, and Moe together can build a bookcase in 1 hour, which means their combined rate is 1 bookcase per hour.

Let's denote the rates of work for Larry, Curly, and Moe as L, C, and M respectively. When working together the sum of their rates equates to the rate at which they finish the job together. Hence:

L + C = 0.5 (Larry and Curly's rate)

C + M = 3/5 (Curly and Moe's rate)

L + C + M = 1 (Larry, Curly, and Moe's rate)

Using the first two equations, we can solve for L and M by substituting the values into the third equation:

L + 3/5 = 1

L = 1 - 3/5 = 2/5

C + 0.5 = 1

C = 1 - 0.5 = 0.5

Now we know that Larry's rate is 2/5 bookcase per hour, and Curly's rate is 0.5 bookcase per hour. We can use Curly's rate to find Moe's rate:

C + M = 3/5

0.5 + M = 3/5

M = 3/5 - 0.5 = 1/5

Larry and Moe's combined rate is L + M = 2/5 + 1/5 = 3/5 bookcases per hour.

To find the time it takes for Larry and Moe to build one bookcase together, we take the reciprocal of their combined rate:

Time = 1 / (L + M) = 1 / (3/5) = 5/3 hours, which is equal to 1 hour and 40 minutes.

Answer:

The coordinates of point B is [tex](\frac{21}{4} , 2 )[/tex]

Step-by-step explanation:

Given:

Let,

[tex]B \equiv (x,y)\\A \equiv (x1,y1) \equiv (7,4)\\C \equiv (x2,y2) \equiv (0,-4)[/tex]

[tex]\frac{AB}{AC} =\frac{1}{4}[/tex]

First we need to find [tex]\frac{AB}{BC}[/tex]

[tex]\therefore \frac{AB}{AC} = \frac{1}{4}\\\therefore \frac{AC}{AB} = \frac{4}{1}\ Invertendo\\\therefore \frac{AC-AB}{AB} = \frac{4-1}{1}\ Dividendo\\ \therefore \frac{BC}{AB} = \frac{3}{1}\\ \therefore \frac{AB}{BC} = \frac{1}{3}\ Invertendo\\\therefore \frac{AB}{BC} = \frac{1}{3} = \frac{m}{n}\ say[/tex]

Now point B divide segment AC internally in the ratio m : n i.e 1/3.

So, by internal division formula, the X coordinate and the Y coordinate of point B are as follow

[tex]x =\frac{mx2+nx1}{m+n}\ and\ y = \frac{my2+ny1}{m+n}\\x =\frac{1\times 0 + 3\times 7}{1+3}\ and\ y =\frac{1\times -4 + 3\times 4}{1+3}\\x =\frac{21}{4}\ and\ y =\frac{8}{4}\\x =\frac{21}{4}\ and\ y = 2[/tex]

Therefore,The coordinates of point B is [tex](\frac{21}{4} , 2 )[/tex]

Answer:

5,2 is correct answer

Step-by-step explanation:

Answer:

larger no=19, smaller no=-15

Step-by-step explanation:

let X be the larger no &Y be the smaller no

so [tex]X+Y[/tex]=4.....(1)

[tex]4X+3Y[/tex]=31............(2)

from [tex](2)- (1)*3[/tex]

[tex]4X+3Y-3X-3Y[/tex]=[tex]31-12[/tex]

X=19

Y=-15

To find the two numbers, we can set up a system of equations and use the method of substitution to solve it.

Let's represent the two numbers as x and y. We are given that x + y = 4 and 4x + 3y = 31.

To solve this system of equations, we can use the method of substitution. From the first equation, we can express x = 4 - y. Substituting this into the second equation, we have 4(4 - y) + 3y = 31.

Simplifying this equation gives us 16 - 4y + 3y = 31. Combining like terms, we get -y + 16 = 31. Subtracting 16 from both sides, we have -y = 15. Finally, multiplying both sides by -1, we find that y = -15.

Substituting this value back into x + y = 4, we get x + (-15) = 4, which gives us x = 19.

Therefore, the larger number is 19 and the smaller number is -15.

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it's 94.20967742 if you simplify it you will get 94.21

5,841 divided by 62 equals 94 with a remainder of 13. You can find this using long division, where 62 goes into 584 (from 5,841) nine times and then into 261 (the remainder with the next digit) four times.

To find the result of 5,841 divided by 62, we can use long division. Let's break down the problem step by step:

To express this as a decimal, we could continue the division process by adding a decimal point and zeros to the dividend, but that is not requested in this problem.

25x+35y=405 and y= x+3 can be used to determine the number of bottles of soda and number of bottles of juice purchased where, x represents the number of soda bottles and y represents the number of juice bottles.

Step-by-step explanation:

Given,

Sugar contained by each soda bottle = 25 grams

Sugar contained by each juice bottle = 35 grams

Let,

x be the number of soda bottles.

y be the number of juice bottles.

According to given statement;

25x+35y=405   Eqn 1

y= x+3   Eqn 2

25x+35y=405 and y= x+3 can be used to determine the number of bottles of soda and number of bottles of juice purchased where, x represents the number of soda bottles and y represents the number of juice bottles.

Keywords: Linear equation, substitution method

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Answer:

c = 1.4

d = 8

Step-by-step explanation:

In a 45-45-90 triangle, the legs are equal and the hypotenuse is √2 times that.

2 = c √2

c = 2 / √2

c = 1.4

In a 30-60-90 triangle, the hypotenuse is 2 times the short side, and the long side is √3 times the short side.

d = 2 × 4

d = 8

Answer:

See Below (it is correct)

Step-by-step explanation:

First point given ----  A(-3,0)

2nd point given ----- B(4,0)

The slope is the "change in quantity y" divided by "change in quantity x"

The change would be from 2nd point to 1st point. So,

Change in quantity y is 0 - 0 = 0

Change in quantity x is 4 - (-3) = 4 + 3 = 7

So, slope would be:

Slope = 0/7 = 0

The slope is 0 (which means it is a horizontal line)

Answer:

87

(3 times 9)+(10 times 6)

Step-by-step explanation:

PEMDAS

36/6=6

Answer:

The minimal number for the objective function P =20x+16y is: 780

The value of x then is: 15

and the value of y then is : 30

Step-by-step explanation:

We are given a system of inequalities as:

y is less than or equal to 2x

i.e.          y ≤ 2x--------(1)

x + y is greater than or equal to 45

i.e.      x+y ≥ 45  ------------(2)    

and    x is less than or equal to 30.    

i.e.               x ≤ 30 -----------(3)    

On plotting these inequalities we get the boundary points as:

        (15,30) , (30,60) and (30,15)    

( Since, the optimal solution always exist at the boundary point )

The optimal function is given by:

 Minimize  P = 20x+16y

Hence, at (15,30) we get:

P= 780

at (30,60) we get:

 P= 1560

at (30,15) we get:

P= 840

This  means that the minimal value of the function is 780

and the value exist at (15,30)

The students in the school ride the bus is 30 percent.

To find the percent of students who ride the bus to school in a school with 400 students when 120 students ride the bus, you would set up an equivalent fraction and solve for the percentage. The fraction of students who ride the bus is 120 out of 400 (120/400), and you want to find what percentage this is equivalent to, so you set up the fraction over 100 (x/100). To solve for x, you cross-multiply and divide:

(120/400) = (x/100)

400x = 120 × 100

x = (120 × 100) / 400

x = 12,000 / 400

x = 30

Therefore, 30 percent of the students at the school take the bus.

Answer:

[tex]a_{n}[/tex] = 8[tex](-3)^{n-1}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 8 and r = - 24 ÷ 8 = - 3, thus

[tex]a_{n}[/tex] = 8[tex](-3)^{n-1}[/tex]

Answer:

Jamie: His inequality would look like this:  25x >= 600

Stella: Her inequality would look like this: 15y >= 600

Her limitations would be listed as: y=40

Yep. Stella has plenty of money by baking 40 pies; $600.

We can back that up by breaking this down. So. We know that it cost $600 to pay upfront and Jamie makes $25 per car he washes. Stella would make $15 for every pie she baked. So simply, let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes. Easy.

Since the cost for washing one car is $25

Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600. We know that. Now, lets see their profit margins.

Since the cost for making one pie is $15

Therefore, the cost of making y pies is 15y.

Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600 so with that being the case... 15y>=600

We all know the maximum number of pies that Stella can make is 40. So, the value of can't exceed 40 and must be less than or equal to 40. So.... y<=40

Bam.

In order to sign up for the trip, Stella's total earning must be at least $600. So, is the minimum condition for signing up for the trip. Now, let us solve the above equation for . So our end project looks like this: 15y = 600 y = 600/15 = 40

The minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.

Step-by-step explanation:

Answer:

C) 6 inches

Step-by-step explanation:

Given function:

[tex]Y=1.3x-0.8[/tex]

The function compares plant height in inches to the age of plant in weeks.

So, we can say

[tex]Y[/tex] represents height of plant in inches.

[tex]x[/tex] represents age of the plant in weeks.

In order to predict the height of the plant in 5 weeks, we will plugin [tex]x=5[/tex] in the given function and evaluate [tex]Y[/tex]

⇒ [tex]Y=1.3(5)-0.8[/tex]

⇒ [tex]Y=6.5-0.8[/tex]

⇒ [tex]Y=5.7[/tex] inches

Thus the approximate height of plant in 5 weeks would be [tex]\approx 6[/tex] inches

Answer:

C: 6

Step-by-step explanation:

Answer: The answer is (9+2) - 4

Step-by-step explanation:

Final answer:

The correct numerical expression that translates the phrase "4 less than the sum of 9 and 2" is Option A: 9 + 2 - 4, which calculates the sum of 9 and 2, then subtracts 4.

Explanation:

The question asks which numerical expression correctly translates the phrase "4 less than the sum of 9 and 2." To solve this, you first need to find the sum of 9 and 2, and then subtract 4 from it. The sum of 9 and 2 is 11, so subtracting 4 from this sum would give us 7. The correct numerical expression for this operation is 9 + 2 - 4.

Therefore, as per the above explaination, the correct answer is Option A: 9 + 2 - 4 which results in 7.

Answer:

920,000

Step-by-step explanation:

943,361-24,200=919,161=920,000

Answer:

[tex]\frac{17}{26}[/tex]

Step-by-step explanation:

In probability

"AND" means to multiply, and

"OR" means to add

Here, we want probability getting a red card OR a 10 OR a queen. So we find each individual probabilities and ADD.

In a standard deck, there is 52 cards.

P(Red):

half the cards are red and half are black, so there are 52/2 = 26 red cards

Hence

P(Red) = 26/52 = 1/2

P(10):

There are 4 suits with each one having 1 "10" card, so there are FOUR 10s in a deck. So,

P(10) = 4/52 = 1/13

P(Queen):

There are 4 suits with each one having 1 Queen. So in 4 suits, there are a total of 4 Queens. So,

P(Queen) = 4/52 = 1/13

P(Red, or, 10, or, Queen) = 1/2 + 1/13 + 1/13 = [tex]\frac{17}{26}[/tex]

Answer:

760 mm

Step-by-step explanation:

Answer:

$717336

Step-by-step explanation:

The total of monthly payments for a 3-year loan is $22317.12.

So, the total amount has to pay back in 3 years is $(22317.12 × 12 × 3) = $803416.32.

Let the amount of money that was originally borrowed is $x and the given APR is 4%.

Then we can write, [tex]x(1 + \frac{4 \times 3}{100}) = 803416.32[/tex]

⇒ 1.12x = 803416.32

⇒ x = $717336 (answer)

Answer:

x=3

Step-by-step explanation:

5x+4=19

5x=19-4

5x=15

x=15/5

x=3

Answer:

x = 3

Step-by-step explanation:

Given

5x + 4 = 19 ( subtract 4 from both sides )

5x = 15 ( divide both sides by 5 )

x = 3

Answer:

y = - 3

Step-by-step explanation:

To find the value of y, substitute x = 3 into the equation, that is

y = - 2(3) + 3 = - 6 + 3 = - 3

(a) The explicit rule to model the sequence formed by the number of seats in each row is [tex]a_{n}=15+3n[/tex]

(b) The 35th row has 120 seats

Step-by-step explanation:

The rule of the nth term of an arithmetic sequence is

[tex]a_{n}=a+(n-1)d[/tex] , where

∵ There are 18 seats in the 1st row

∵ There are 21 seats in the 2nd row

∵ 21 - 18 = 3

∵ The number of seats is increased by 3 with each additional row

- The number of seats in each row represents an arithmetic

   sequence because there is a common difference between

   each two consecutive rows

∴ The number of seats in each row formed an arithmetic sequence

∵ The number of seats in the first row = 18 seats

∴ a = 18

∵ The number of seats in a row continues to increase by 3 with each

   additional row

∴ d = 3

- Substitute the values of a and d in the rule of nth term

∴ [tex]a_{n}=18+(n-1)3[/tex]

- Simplify the right hand side

∴ [tex]a_{n}=18+3n-3[/tex]

- Add like terms

∴ [tex]a_{n}=15+3n[/tex]

(a) The explicit rule to model the sequence formed by the number of seats in each row is [tex]a_{n}=15+3n[/tex]

∵ There are 120 seat in a row

- Substitute [tex]a_{n}[/tex] by 120 in the rule above

∴ 120 = 15 + 3n

- Subtract 15 from both sides

∴ 105 = 3n

- Divide both sides by 3

∴ n = 35

∴ The number of the row is 35

(b) The 35th row has 120 seats

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Answer: 45

Step-by-step explanation: To divide this start with finding how many times 585 goes into 13 which is 0. I put a picture for you to look at.