Element X decays radioactively with a half life of 12 minutes. If there are 200
a
grams of Element X, how long, to the nearest tenth of a minute, would it take
the element to decay to 20 grams?

The canoeist's resultant speed is approximately 4.24 km/h, and the direction is perpendicular to the bank (90° angle with the positive x-axis).

To solve this problem, we can break the velocity vectors into their horizontal and vertical components.

Let's assume the downstream direction is the positive x-axis and the direction perpendicular to the bank is the positive y-axis. The angle between the direction of the river current and the canoeist's path is 35°, which means the angle between the resultant velocity and the positive x-axis is 35°.

Given:

Width of the river (d) = 0.95 km

Speed of the current (v_c) = 4 km/h

Speed of the canoeist in still water (v_cw) = 9 km/h

First, let's find the components of the canoeist's velocity vector when heading upstream:

Vertical component:

v_cu_y = v_cw * sin(35°)

Horizontal component:

v_cu_x = v_cw * cos(35°) - v_c

where v_c is the speed of the current.

Since the canoeist is heading upstream, the speed of the canoeist relative to the ground will be the difference between the vertical component and the speed of the current:

v_cu = v_cu_y - v_c

Next, let's find the components of the canoeist's velocity vector when heading downstream:

Vertical component:

v_cd_y = -v_cw * sin(35°)

Horizontal component:

v_cd_x = v_cw * cos(35°) + v_c

Since the canoeist is heading downstream, the speed of the canoeist relative to the ground will be the sum of the vertical component and the speed of the current:

v_cd = v_cd_y + v_c

The resultant velocity (v_r) can be found using the Pythagorean theorem:

v_r = √((v_cu_x + v_cd_x)² + (v_cu_y + v_cd_y)²)

Finally, the direction of the resultant velocity (θ) can be found using the inverse tangent function:

θ = tan^(-1)((v_cu_y + v_cd_y) / (v_cu_x + v_cd_x))

Now, let's calculate the values:

v_cu_y = 9 km/h * sin(35°) ≈ 5.13 km/h

v_cu_x = 9 km/h * cos(35°) - 4 km/h ≈ 6.29 km/h

v_cu ≈ √((6.29 km/h)² + (5.13 km/h)²) ≈ 8.05 km/h

v_cd_y = -9 km/h * sin(35°) ≈ -5.13 km/h

v_cd_x = 9 km/h * cos(35°) + 4 km/h ≈ 11.71 km/h

v_cd ≈ √((11.71 km/h)² + (-5.13 km/h)²) ≈ 12.89 km/h

v_r ≈ √((6.29 km/h + 11.71 km/h)² + (5.13 km/h - 5.13 km/h)²) ≈ √(18.00 km/h) ≈ 4.24 km/h

θ ≈ tan^(-1)((5.13 km/h - 5.13 km/h) / (6.29 km/h + 11.71 km/h)) ≈ 90°

Therefore, the canoeist's resultant speed is approximately 4.24 km/h, and the direction is perpendicular to the bank (90° angle with the positive x-axis). the labeled diagram below for a visual representation of the situation:

             |   \

             |     \

             |       \ v_cu

             |        

\

             |           \

      v_c -->|----->   \

             |             \

             |               \

             |________________\

                  v_cd

To learn more about vector click here:

brainly.com/question/13267555

#SPJ11

     The length of a rectangular playground that is 60 meters longer than it is width is of a length of 260 m.

Length of rectangle = 260 m

If the width(w) is x, then length is;

L = 60 + x

W = x

Formula for perimeter of a triangle is;

P = 2(L + W)

Plugging in the relevant values, we have;

P = 2(60 + x + x)

P = 2(60 + 2x)

Thus, P = 920

920 = 2(60 + 2x)

Divide both sides by 2 to get;

460 = 60 + 2x

Subtract 60 from both sides to get;

400 = 2x

x = 400/2

x = 200 m

Thus;

L = 60 + 200

L = 260 m

Read more at;

brainly.com/question/17474046

Answer:

b

Step-by-step explanation:

=======================================================

Explanation:

Graph B, C and D all fail the vertical line test. If it's possible to pass a vertical line through more than one point on the curve, then it's said to have failed the vertical line test. Any vertical line itself therefore is automatically not a function. If a graph fails the vertical line test, then it is not a function.

A function is only possible if for any given input x, we have exactly one and only one output. For graph A, the output is the same value regardless of the input. This is a constant function.

For something like graph B, the input x = 0 produces three different y outputs. The output y = 0 is one of those, and the others are off the screen so it's hard to tell what they are. Turns out it doesn't matter and all we need to do is the vertical line test. Graphs C and D are a similar story. In the case of graph D, the only input x allowed is x = 2 and it produces infinitely many y outputs.

Answer:

2 I think let me know if I'm wrong

Step-by-step explanation:

To find solutions from graphs, look for the point where the two graphs cross one another. This is the solution point. For example, the solution for the graphs y = x + 1 and x + y = 3 is the coordinate point (1, 2). The solution to these equations is and.

The total prize money is 200+100 which is 300

There is 100 tickets sold for $5 each so the people selling the tickets earn $500 and use $300 for prize money.

The expected value of 1 ticket is $5.00

If you still have any questions feel free to comment below

Hope this helped<3

Answer:

3rd Option;

x = 4

y = 116

Step-by-step explanation:

Let's start by solving for "x" first:

=>  We know that in a parallelogram, opposite sides are parallel as well as congruent, therefore we can say:

Side 1 = It's opposite side

=> 16 = 3x + 4

=> 16 - 4 = 3x

=> 12 = 3x

=> 12/3 = x

=> 4 = x

Now that we know x, let's find the y-value;

=> We know that opposite angles in a parallelogram are congruent, therefore we can say;

Angle 1 = It's opposite angle

=> 56 = y - 60

=> 56 + 60 = y

=> 116 = y

Hope this helps!

The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

A numerical expression is characterized as the assortment of numbers factors and works by utilizing operations like expansion, deduction, multiplication, and division.

Considering that;

The expression is,

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

Presently, We can place x and y in the above expression as;

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

⇒ [- 5/(- 2 - 1) ] (- 4) - [-5×-2 + (- 3)]/(- 1)

⇒ [ - 5/ - 3 ] (- 4) - [10 - 3]/(- 1)

⇒ - 20/3 + 7

⇒ 1/3

In this way, The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

to know more about multiplication click here:

https://brainly.com/question/1135170

#SPJ4

Answer:

2sqrt3

Step-by-step explanation:

because it's a 60 30 right triangle. and you have to leave your answer in radical form.

Answer: 55 degrees / Acute angle.

Step-by-step explanation:

The angle is less than a right angle, bent forward so it's less than 90 degrees, meaning it's an acute angle.

Answer:

There are 14 4-point questions and 26 2-point questions.

Step-by-step explanation:

m  = number of 4-point questions

n = number of  2-point questions

m+n =40

4m + 2n =108

You can solve system by elimination:

Multiply the 1st equation by -4 and keep the 2nd equation the same.

−4(m+n=40) → -4m -4n= -160

                       4m+2n=108 add them up

-2n = -52 divide both sides by -2

n = 26

plug it back in to solve for m

m + n = 40 →m + 26 =40 subtract 26 to both sides

m = 14

Answer:

m=14, n=26

Step-by-step explanation:

Given:

Base angle of an isosceles triangle is 15 degrees more than its vertical angle.

To find:

The measure of each angle of the triangle.

Solution:

Let x be the vertical angle. Then,

One base angle = x+15 degrees

We know that base angles of an isosceles triangle are equal.

Another base angle = x+15 degrees

Now, the sum of all angles of a triangle is 180 degrees by the angle sum property.

\(x^\circ+(x+15)^\circ+(x+15)^\circ=180^\circ\)          (Angle sum property)

\((3x+30)^\circ=180^\circ\)

\(3x+30=180\)

\(3x=180-30\)

\(3x=150\)

Divide both sides by 3.

\(x=\dfrac{150}{3}\)

\(x=50\)

The measure of base angles is

\((x+15)^\circ=(50+15)^\circ\)

\((x+15)^\circ=65^\circ\)

Therefore, the measure of angles are 50°, 65° and 65°.

you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

To determine how much you should invest today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years, we can use the formula for simple interest:

A = P(1 + rt)

Where A is the future value, P is the principal (the amount you should invest today), r is the interest rate, and t is the time in years.

We can rearrange the formula to solve for P:

P = A / (1 + rt)

Plugging in the values, we have:

P = 1,175,000 / (1 + 0.09 * 15)

P = 1,175,000 / (1 + 1.35)

P = 1,175,000 / 2.35

P ≈ $500,000

Therefore, you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

 To learn more about interest click here:brainly.com/question/1040694

#SPJ11

Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

Answer:

x=5

Step-by-step explanation:

     May I have brainiest I'm trying to level up!

                 </3 PureBeauty

Answer:

x=5

Step-by-step explanation:

6x-3 = 3x +12

+3            +3

6x = 3x +15

-3x   -3x

3x = 15

divided both sides by 3 to get your answer

Answer: 154

Step-by-step explanation:

\(a_1=4,\ d=6\quad \rightarrow \quad a_n=4+6(n-1)\quad \rightarrow \quad a_n=6n-2\\\\\\\sum^7_{n=1}6n-2\\\\\\a_1=4\\a_7=40\\\\\\S_n=\dfrac{a_1+a_7}{2}\cdot n\qquad =\dfrac{4+40}{2}\cdot 7\qquad =22\cdot 7\qquad =\large\boxed{154}\)

Answer:

154 I think

Step-by-step explanation:

Answer:

x=1/8

Step-by-step explanation:

pickpeuhahaahahaha

Answer:

1/9 x 21/8 = 7/24

Step-by-step explanation:

Answer:

Step-by-step explanation:

y+1 =(3/4)x+9/4

y=(3/4)x+1/4

Answer:

3x - 4y + 5 = 0

Step-by-step explanation:

The equation of a line in general form is

Ax + By + C = 0 ( A, B, and C are integers )

Given

y + 1 = \(\frac{3}{4}\) (x + 3) ← multiply through by 4 to clear the fraction

4y + 4 = 3(x + 3)

4y + 4 = 3x + 9 ( subtract 4y + 4 from both sides )

0 = 3x - 4y + 5 , that is

3x - 4y + 5 = 0 ← in general form

For a well with diameter of 2 ft, the approximate head in the pumped well for steady-state condition and approximate drawdown is 61.5770 ft and 48.42 ft respectively. The computed value of transmissivity is 1516.8 ft²/day.

We have a well with 2 feet diameter penetrates vertically through a confined aquifer 50 ft thick. Well is pumped at 500 gpm. The drawdown in a well 50 ft away is 10 ft. The Hydrant capacity, Q

= 500 gpm

= 1.11405 ft³/s = 96250.032 ft³/day

\(k = \frac{ Q}{2πb( s_1 - s_2) }ln(\frac{ r_1}{r_2})\)

Substitute all known values in above formula, \(= \frac{96250.032 ft³/day }{2π×50( 10 - 3) ln(\frac{ 100}{50})}\)

= 3.51 × 10 ft/s

= 30.33 ft/day

Now, transmissivity, T = k× b

= 30.33 ft/day × 50 ft

= 1516.8 ft²/day

The approximate head in the pumped well for steady-state condition, \(h_r= r_1 - r_w \) = 100 - 3 = 97

\(h_w = h_2 - (\frac{ Q}{2πb}) ln(\frac{r_2}{r_w})\)

\(= 97- \frac{96250.032 \: ft³/day }{2π×50}ln(\frac{100}{3})\)

= 61.5770 ft

The approximate drawdown in the well,

\(s_w = r_2 - h_w \)= 100 ft - 61.5770 ft

= 48.42 ft

Hence, required value is 48.42 feet.

For more information about diameter, visit :

https://brainly.com/question/30460318

#SPJ4

Write the Inequality

A number b times -16 is greater than 5.

A number b is a variable... b.

Times means multiply.

-16 is what you are multiplying b by.

Is greater than means the greater than symbol.

5 is what the past statements are greater than.

So this is the inequality.

-16b > 5

Solve the Inequality

You need to isolate b.

To do this, divide each side by -16. You do this because b is being multiplied by -16. You know that any number divided by that number equals 1, canceling the number.

-16b ÷ -16 = b

5 ÷ -16 = -5/16

So you get b > -5/16

So to make the inequality true, b must be more than -5/16.

Or as an inequality...

b > -5/16

The statement that best fits the Contract Family: Integrated project delivery (IPD) of AIA documents is: "In this family, the functions of contractor and construction manager are merged and assigned to one entity that may or may not give a guaranteed maximum price."

Integrated project delivery (IPD) is a collaborative project delivery approach that involves early involvement and collaboration of all project stakeholders, including the owner, architect/designer, and contractor. In this approach, the functions of the contractor and construction manager are combined and assigned to a single entity, often referred to as the "constructor." This entity takes on the responsibility of coordinating the design and construction process and may or may not provide a guaranteed maximum price (GMP) for the project.

The Integrated project delivery (IPD) contract family of AIA documents is designed for collaborative project delivery and involves merging the roles of contractor and construction manager into a single entity. This approach encourages early involvement and collaboration among all project stakeholders and can provide flexibility in terms of whether a guaranteed maximum price (GMP) is included in the contract. The variety of forms within this contract family includes qualification statements, bonds, requests for information, change orders, construction change directives, and payment applications and certificates.

Learn more about Integrated project delivery visit:

https://brainly.com/question/16680387

#SPJ11

Answer:

Step-by-step explanation:

99

The product 5x^(2/3) can be written as the product of the whole number 5 and the unit fraction 1/x^(-2/3), which simplifies to x^(2/3)/1 or just x^(2/3). So, we have:

5x^(2/3) = 5 * (1/x^(-2/3)) = 5x^(2/3) = 5 * (x^(2/3) / 1) = 5x^(2/3) = 5x^(2/3)

To write the product 5x^(2/3) as the product of a whole number and a unit fraction, we need to express x^(2/3) as a unit fraction.

Recall that a unit fraction is a fraction with a numerator of 1, so we need to find a fraction that has 1 as the numerator and x^(2/3) as the denominator. We can do this by using the reciprocal property of exponents:

x^(2/3) = 1 / x^(-2/3)

Now we can substitute this expression into the original product:

5x^(2/3) = 5 * (1 / x^(-2/3))

Simplifying the right-hand side of the equation, we can write it as:

5 / x^(-2/3) = 5x^(2/3)

To know more about unit fraction refer to

https://brainly.com/question/30860953

#SPJ11

The day which has the least change in temperature is Wednesday.

The day which has the least change in temperature can be calculated by finding the change in temperature:

Monday = High temperature - low temperature

= 82° - 58°

= 24°

Tuesday = High temperature - low temperature

= 85° - 60°

= 25°

Wednesday = High temperature - low temperature

= 77° - 62°

= 15°

Thursday = High temperature - low temperature

= 68° - 50°

= 18°

Friday = High temperature - low temperature

= 75° - 48°

= 27°

Saturday = High temperature - low temperature

= 70° - 52°

= 22°

Sunday = High temperature - low temperature

= 84° - 56°

= 28°

The day which has the least change in temperature is Wednesday

Which two consecutive days which showed a drop in temperature: Wednesday and Thursday with 77° and 68° respectively.

Unlike line graph, table graph is the graph that is easier to read.

Therefore, the graph which best illustrate the graph is table graph because it represent the data in a clearer way.

Read more on graph:

https://brainly.com/question/24741444

#SPJ1

The complete code to create a histogram in Kotlin that allows you to inspect the frequency visually with nine or fewer lines is shown below:import kotlin.random.

Randomfun main() {val array = Array(200) { Random.nextInt(1, 101) }array.sort()var i = 1while (i < 100) {val count = array.count { it < i + 10 && it >= i }println("${i} - ${i + 9} | ${count} | " + "*".repeat(count))i += 10}}

The program above first generates an array of 200 random integers between 1 and 100 inclusive. It then sorts the array in ascending order. Next, the program loops through the ranges from 1 to 100 in steps of 10.

Within the loop, the program counts the number of elements in the array that fall within the current range and prints out the corresponding row of the histogram chart.

Finally, the program increments the loop variable by 10 to move to the next range and continues the loop.

To know more about histogram visit:

brainly.com/question/30200246

#SPJ11

The public library used 83 square feet of glass to build the aquarium.

To calculate the total square footage of glass used to build the aquarium, we need to consider the surface area of each side of the rectangular prism.

The rectangular prism has a base with dimensions of 6 feet by 2.5 feet. Since the top of the aquarium is open, we only need to consider the four sides (front, back, and two sides) and the bottom.

The area of each side can be calculated by multiplying the length by the width.

Front and back sides:

Area = length \(\times\)  height = \(6 ft \times 4 ft = 24\) square feet.

Side 1:

Area = width \(\times\) height \(= 2.5 ft \times 4 ft = 10\)  square feet

Side 2:

Area = width \(\times\) height \(= 2.5 ft \times 4 ft = 10\) square feet

Bottom:

Area = length \(\times\) width \(= 6 ft \times 2.5 ft = 15\) square feet

To find the total square footage of glass used, we sum up the areas of all the sides:

Total area = Front + Back + Side 1 + Side 2 + Bottom

= 24 sq ft + 24 sq ft + 10 sq ft + 10 sq ft + 15 sq ft

= 83 square feet.

For similar question on aquarium.

https://brainly.com/question/30128434

#SPJ11

Answer:

A. -148

Step-by-step explanation:

3x³ - 2x² + 7y

3(-3)³ - 2(-3)² + 7(-7)

3(-27) - 2(9) - 49

-81 - 18 - 49

-148

I hope this helps!

Answer:

The only way this is possible is if one of the mixed numbers is negative. You can’t add two positive mixed numbers and get a sum of 2 because a mixed number is always greater than 1.