Juan and Mahdi are to run a race, but Juan can run 16 meters per second, whereas Mahdi can run 6 meters per second. If Mahdi has a 100 -meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time? Round your answer to the nearest whole number.

Solution:

Note that:

3:2 can also be written as 3x:2x.

There are 135 employees in total.

3 to 5

3x+5x=176

8x=176

x=176/8

x=22

3*22= 66 men

5*22= 110 women

Answer:

12 years

Step-by-step explanation:

Given that

P = 5,600 e^0.0591

Reaching amount = 11,200

time period = t

We need to find out the time period i.e. t

So,

11,200 =  5,600 e^0.0591t

2 =  e^0.0591t

Now take the log on both the sides

ln2 = 0.0591t ln

t = ln2 ÷ 0.059

= 0.693147÷ 0.059

= 11.748

= 12 years

Step 1: Find the slant height

10^2 + 28^2 = c^2

884 = c^2

c = \(\sqrt{884}\)

Step 2: Find the lateral area

LA = pi * radius * slant height

LA = pi * 10 * \(\sqrt{884}\)

LA (rounded to the nearest tenth) = 297.3pi in^2

Step 3: Find the area of the base circle

A = pi * r^2

A = pi * 10^2

A = 100pi in^2

Step 4: Add the areas together

SA = 297.3pi + 100pi

SA = 397.3pi in^2

Hope this helps!! :)

Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

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Answer:

B

Step-by-step explanation:

Answer:

B only one angle is a right angle and the other two are acute

Step-by-step explanation:

its clear from looking at an angle lol

In order to write 4/6 as 2/3 we would break apart pieces and to write 4/6 as 8/12 we would combine pieces.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below.

In order to write 4/6 as 2/3 we have to express in its simplest form. This means that you have to divide 4/6 by 2. In order to write 4/6 as 8/23, multiply 4/6 by 2.

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The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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At the price of 20/7 dollars, it should sell your skateboards so that there is neither a shortage nor a surplus.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

To calculate the price should sell your skateboards for so that there is neither a shortage nor a surplus we would have to make the following calculation as;

q (sales) = q (supply)

−4p + 50 = 3p − 30

-4p - 3p = -30 - 50

-7p = -20

p = 20/7

At the price of 20/7 dollars it should sell your skateboards so that there is neither a shortage nor a surplus.

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Answer:

Step-by-step explanation:

The last one -- D -- is the closest correct answer. None of them, however, is right.

y = -1/4 x + 8                      Let x = - 8

y = -1/4 * - 8   +  8              The standard rule is starting from the left, do the multiplication first then do the addition

- 1/4 * - 8 will first of all give you a positive result. When 2 minuses are multiplied they give a positive answer.

-1/4 * - 8 = 1/4 * 8

1/4 * 8 = 2

y = 2 + 8

y = 10

So the ordered pair (-8 , 10) is the answer.

Answer:

\(G=93\ to\ 147\)

Step-by-step explanation:

From the question we are told that

Mean \(x= 120\)  

Standard deviation \(\sigma= 9\)

Percentage for men =99.75%

Generally the empirical rule 68%,95% and 99.7% of data value lay b/w 1,2,3 standard deviation of mean  

Standard deviation n= 9

Mean x= 120

Generally the interval  of systolic blood pressure for middle 99.7 of male G is mathematically given as

\(G=Mean \pm 3* \sigma\)

\(G=120 \pm 3*9\)

\(G=93\ to\ 147\)

Step-by-step explanation:

3 supervisors = 60 employees

=> 264 supervisors = 60 * (264/3) = 5,280 employees. (C)

The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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Answer: Suppose y varies directly with x. Write a direct variation equation that relates x and y.

Step-by-step explanation:

Answer is y = -5x

The equation for y varies directly with x is, y = - 5x.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, y varies directly with x.

Therefore,

y ∝ x.

y = kx, where k is the proportionality constant.

At y = - 10 when x = 2.

- 10 = 2k.

k = - 5.

So, y = - 5x.

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According to the probability, the number of heads that occur on flip is 0.0031%.

Binomial probability is a way of calculating the probability of a certain number of successes in a fixed number of trials, where each trial has only two possible outcomes (in this case, heads or tails). To calculate the probability of getting a specific number of heads, we can use the following formula:

P(X = x) = (n choose x) x pˣ x (1 - p)ⁿ⁻ˣ

where P(X = x) is the probability of getting k heads, n is the number of trials (in this case, 60), p is the probability of getting heads (0.25 in this case), and (n choose x) is the number of ways to choose x heads out of n trials.

Using this formula, we can calculate the probability of getting different numbers of heads in 60 flips of a coin with a probability of 0.25 of landing on heads. The probability of getting exactly 10 heads would be:

P(X = 10) = (60 choose 10) x 0.25¹⁰ x 0.75⁵⁰

This works out to be approximately 0.000031, or 0.0031%. This means that the chances of getting exactly 10 heads in 60 flips of a biased coin with a probability of 0.25 of landing on heads are very low.

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Answer:

Either 0, 12, or 9 (Possibly)

Step-by-step explanation:

I'm assuming that you forgot to put the x next to 4.5 or 1.5 or that you forgot to put x next to both of them and that =3 means x=3

Case 1 (4.5x - 1.5x, x = 3):

You can simplify this expression because both of the units are the same (x). 4.5x - 1.5x = 3x. Next, you have to plug in 3, which would be 3 * 3 which is 9.

Case 2 (4.5x - 1.5, x = 3):

Plug in 3 and you would get 13.5 (4.5 * 3) - 1.5, which is equal to 12.

Case 3 (4.5 - 1.5x, x = 3):

Plug in 3 and you would get 4.5 - 4.5 (1.5 * 3), and since they are the same, it is equal to 0.

If none of these are the answer or you are asking something else, feel free to comment on this answer

-Hope this helped-

Answer:

sorry wont let me click off this question so so so sorry

Step-by-step explanation:

hope u do really well

The probability that the chosen applicants are either all managers or all engineers is approximately 0.01386 or 1.386%.

To calculate the probability that the chosen applicants are either all managers or all engineers, we need to find the probability of two events: (1) all six members are managers, and (2) all six members are engineers.

Let's first calculate the probability of all six members being managers. We can do this by multiplying the probability of choosing a manager for the first member, by the probability of choosing a manager for the second member, and so on, up to the sixth member.

Since there are five managers and fifteen qualified applicants in total, the probability of choosing a manager for the first member is 5/15. After one manager has been chosen, there are four managers left out of the remaining fourteen qualified applicants, so the probability of choosing a manager for the second member is 4/14.

Continuing in this way, we get:

P(all managers) = (5/15) * (4/14) * (3/13) * (2/12) * (1/11) * (1/10) = 0.00016

Now let's calculate the probability of all six members being engineers. Following the same logic as above, we get:

P(all engineers) = (10/15) * (9/14) * (8/13) * (7/12) * (6/11) * (5/10) = 0.0137

Finally, to find the probability that the chosen applicants are either all managers or all engineers, we simply add the two probabilities:

P(all managers or all engineers) = P(all managers) + P(all engineers) = 0.00016 + 0.0137 = 0.01386

Therefore, the probability that the chosen applicants are either all managers or all engineers is approximately 0.01386 or 1.386%

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Answer:

If 2/5 are apples, 2/5 x 8.9 kilos = 0.4 x 8.9 = 3.56 kilos of apples

pears = 8.9 - 3.56 = 5.34 kilos

Step-by-step explanation:

I asked my teacher and she said it was correct.

Answer:

Step-by-step explanation:

To get rid of the decimal point in the numerator, we count the numbers after the decimal in 6.584, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.

Therefore, in this case we multiply the numerator and denominator by 1000 to get the following fraction:  6584 / 1000

Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.

The GCD of 6584 and 1000 is 8. When we divide the numerator and denominator by 8, we get the following:  823 / 125

Therefore, 6.584 as a fraction is as follows:  823 / 125

Answer:

18

Step-by-step explanation:

Hope this helps

Answer: 18

Step-by-step explanation: 18 would be your answer because if you do 5-2 you would get 3 and then you would do 18/3 which is 6 and 6 times 3 equals 18. If you need help when doing this use PEMDAS which stands for parentheses, exponents, multiplication, division, addition, and subtraction.

Answer:

Step-by-step explanation:

P(t) = K / (1 + (K/P0 - 1) * e^(-rt))

In this equation, P(t) is the population at time t, P0 is the initial population at time t=0, K is the carrying capacity, r is the intrinsic growth rate, and e is the base of the natural logarithm ( approximately 2.71828).

To find the carrying capacity, you can set P(t) equal to K and solve for t. This will give you the time at which the population reaches its carrying capacity.

To find the value of k, you can plug in the values for P(t), P0, and r and solve for K.

To write the solution of the equation, you can solve for t by rearranging the equation and taking the natural logarithm of both sides.

To find the population after 10 weeks, you can plug in the values for P0, K, r, and t=10 into the equation and solve for P(t).

I hope this helps! Let me know if you have any further questions.

Answer

x = 6°

Explanation

The key to solving this is shown in the attached image below

So, we can see that the relation between all of this is that

5x + 17 = ½ [(37x + 5) - (23x - 5)]

5x + 17 = ½ (37x + 5 - 23x + 5)

5x + 17 = ½ (37x - 23x + 5 + 5)

5x + 17 = ½ (14x + 10)

5x + 17 = 7x + 5

5x - 7x = 5 - 17

-2x = -12

Divide both sides by -2

(-2x/-2) = (-12/-2)

x = 6°

Hope this Helps!!!

Call the number of children

c

and adults

a

you have:

c

+

a

=

481

and

1.25

c

+

2.25

a

=

865.25

Try to solve this system to find

c

and

a

.

Answer:

x=5

y=-17

Step-by-step explanation:

basically what I did was:

1) I multiplied the first equation by 4 , solved for x

2) I used the value of x that i found and substituted in one of the equations to find y

Answer: x=0 y=2

..................

Answer: 54

Step-by-step explanation:

The value of m ∠C will be;

⇒ m ∠C = 54°

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △ABC , m ∠A= 37° and m ∠B = 89° .

Now,

Since, In △ABC ,

⇒ m ∠A= 37° and m ∠B = 89°

We know that;

⇒ m ∠A + m ∠B + m ∠C = 180°

⇒ 37° + 89° + m ∠C = 180°

⇒ 126° + m ∠C = 180°

⇒ m ∠C = 180° - 126°

⇒ m ∠C = 54°

Thus, The value of m ∠C will be;

⇒ m ∠C = 54°

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Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).