Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of decay is proportional to the amount of the substance present at time t, determine the half-life of the radioactive substance. (Round your answer to one decimal place.)

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:C. They have the same y-intercept and the same end behavior as x approaches

Step-by-step explanation:

Answer:

Lateral Surface Area = 168 \(cm^2\)

Total Surface Area = 209.57 \(cm^2\)

Step-by-step explanation:

Given:

There is a regular hexagonal prism with

Height, h = 7 cm

Base edge length, a = 4 cm

To find:

Lateral surface area and total surface area = ?

Solution:

Formula for lateral surface area is given as:

\(LSA = \text{Perimeter of Base}\times Height\)

Perimeter of a hexagon is given as:

\(P = 6 \times Edge\ Length\\\Rightarrow P = 6\times 4=24\ cm\)

Now, LSA = 24 \(\times\) 7 = 168 \(cm^2\)

Total Surface area of prism is given by the formula:

\(TSA = LSA + B\)

where B is the area of base.

Base is a regular hexagon, formula for area of a regular hexagon is given by:

\(B =6\times \dfrac{\sqrt3}4\times Edge^2\\\Rightarrow B =6\times \dfrac{\sqrt3}4\times 4^2 = 24\sqrt3\ cm^2\\\Rightarrow B = 41.57 cm^2\)

So, Total Surface Area = 168 + 41.57 = 209.57\(cm^2\)

So, answer is :

Lateral Surface Area = 168 \(cm^2\)

Total Surface Area = 209.57 \(cm^2\)

Answer: It' actually:

Lateral Area: 168cm²
Surface Area: 251.1cm²

Hope this helps ya!

Answer:

sinn

Step-by-step explanation:

sine

Sample Output: Code to copy: //Import the required package. import java.util.Scanner; //Define the class Main. class Main { //Start the execution of the main() method.

Origin C is a programming language that is ANSI C compatible and also incorporates C++ and C# features. The majority of Origin objects can be accessed programmatically thanks to built-in C++ classes. The NAG C Library's extensive collection of numerical computational routines is also included.

C, a replacement for the programming language B, was initially created by Ritchie at Bell Labs between 1972 and 1973 to create utilities for Unix. It was used to re-implement the Unix operating system's kernel. C increasingly gained popularity in the 1980s.

import java.io.*;

import java.util.Scanner;

public class histogram

{

   public static void main(java.lang.String[] args)

   throws IOException

   {

       Scanner scan = new Scanner (System.in);

       final int min = 1;

       final int max = 10;

       final int limit = 10;

       int[] a = new int[max];

       for (int b = 0; b < a.length; b++)

       {

           a[b] = 0;

       }

       System.out.println("Enter Number between 1 and 100: \n (Or press 0 to stop)");

       int number = scan.nextInt();

       while (number >= min && number <= (limit*max) && number != 0)

       {

           a[(number-1)/limit] = a[(number - 1 ) / limit] + 1;

           System.out.print("Please enter a value:");

           number = scan.nextInt();

       }

       System.out.println("\n__Histogram__");

       for (int y = 0; y < a.length; y++)

       {

           System.out.print("   " + (y * limit + 1) + " - " + (y + 1) * limit + "\t");

           return;

       }

       for (int z = 0; z < a[b]; z++)

       {

           System.out.print("*");

       }

       System.out.println(0);

   }

}

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Because \(-3^{2} \neq -9\)

A number squared never equals a negative number. So that's why the value of \(\sqrt{-9}\) is not -3.

Hope this helps you!

~Just a joyful teen

\(SilentNature\)

The slope and the y-intercept of the line y = 4x + 5 are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The function for this problem is given as follows:

y = 4x + 5.

Hence the slope and the intercept are given as follows:

The problem asks for the slope and the intercept of y = 4x + 5.

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The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Complete Question

The complete question is shown on the first uploaded image

Answer:

the null hypothesis is  \(H_o : \mu = 122\)

the alternative hypothesis is \(H_a : \mu \ne 122\)

The test statistics is  \(t = - 1.761\)

The p-value is  \(p = P(Z < t ) = 0.039119\)

so

    \(p \ge 0.01\)

Step-by-step explanation:

From the question we are told that

   The population mean is  \(\mu = 122\)

     The sample size is  n=  38

    The sample mean is  \(\= x = 116 \ feet\)

     The standard deviation is \(\sigma = 21\)

Generally the null hypothesis is  \(H_o : \mu = 122\)

                the alternative hypothesis is \(H_a : \mu \ne 122\)

Generally the test statistics is mathematically evaluated as

         \(t = \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }\)

substituting values

         \(t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }\)

         \(t = - 1.761\)

The p-value is mathematically represented as

      \(p = P(Z < t )\)

From the z- table  

     \(p = P(Z < t ) = 0.039119\)

So  

     \(p \ge 0.01\)

Kinzang grew 0.96 meters.

We have,

To find how much Kinzang grew, we need to subtract his height at birth from his current height:

Height Kinzang grew = Current height - Height at birth

Height Kinzang grew = 1.49 m - 0.53 m = 0.96 m

Therefore,

Kinzang grew 0.96 meters.

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Answer:

She would receive 96 points

Step-by-step explanation:

The grade (Y) received on a certain teacher's 100-point test varies in direct proportion to the amount of time(t) a student spends preparing for the test.

Mathematically

Y= kt

Where k is constant of proportionality

If y= 72 and t= 3

72=k3

72/3= k

24= k

So

Y= 24t

If t= 4

Y= kt

Y= 24(4)

Y= 96

Y = 96 points

She would receive 96 points

Answer:

yes

Step-by-step explanation:

it is going by 5s.

Answer:

Yes. This is because if you plot the numbers on a ration table or see the graph points, you can see a pattern: you multiply by 5. The equation to solve this would be y=5x. Another reason why this is proportional is that the graph starts from the origin (0,0) This is the opposite for non-proportional relationships. Hope this helps! :)

Answer:

answer may be 0.1g or 1/10g

The distance of all the side of ΔABC and ΔA'B'C' are equal which makes them congruent triangles.

What is congruent triangles?

When all 3 corresponding sides and every one 3 corresponding angles area unit equal in size, 2 triangles area unit aforementioned to be congruent.

Main Body:

First let us find the co-ordinates of both the triangles.

A= (3,5)

B = (-2, 3)

C= (-4,-1)

A' =(10,-5)

B'= (5, -3)

C' =(3,1)

Distance between two points =  d=√((x₂ – x₁)² + (y₂ – y₁)²).

In ΔABC

Distance of side AB =  √((3 –(-2) )² + (5 –3 )²)

                                 = √5² +2²

                                 = √29

Distance of side BC = √((-2-(-4) )²+ (3 -(-1 )²)

                                 = √20

Distance of side CA = √((3-(-4) )² + (5-(-1) )²)

                                 = √7² + 6²

                                 = √85

Distance of side A'B' = √((10 -5)² + (-5-(-3))²

                                   = √(5² +2²)

                                   = √29

Distance of side B'C' = √ ((5-3)² + (-3 -1)² )

                                  = √ (2)² +4²

                                  = √20

Distance of side C'A' = √((10-3)² + ( -5-1)²)\

                                   = √(7)² + 6²

                                   = √85

This shows each side of ΔABC is equal to side of ΔA'B'C'.

hence the triangles are congruent.

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Answer:

when reflected across the y-axis the points will reflect onto the other side on the y-axis.

when reflected over the x-axis the points with reflect onto the x-axis

Answer:

Following are the answer to the given points.

Step-by-step explanation:

In point a:

The confidence interval for p is 95%

using formula:

\(= \hat P - Z\times \sqrt{\frac{\hat P(1- \hat P)}{n}} < p < \hat P +Z \times \sqrt{\frac{\hat P(1- \hat P)}{n}}\)

\(= 0.28 - 1.96 \times \sqrt {\frac{(0.28 \times 0.72)}{350} } < p < 0.28 + 1.96 \times \sqrt{(\frac{0.28 \times 0.72)} { 350}}\\\\= 0.233 < p < 0.327\)

In point b:

Because 0.22 is not within the trust interval, they have enough proof of H0 at level 0.05.  

In point c:

For the percentage for samples,

\(\text{Standard error} = \sqrt { \frac{P (1 - p)}{n} }\) from ratio p  

\(\text{Standard deviation} = \sqrt{ \frac{\hat{p}( 1 - \hat{p})}{n} }\)  from sample ratio \(\hat{p}\)

In point d:

Standard deviation is used to measure the interval of confidence

\(\text{Standard deviation} = \sqrt{ \frac{\hat{p}( 1 - \hat{p})}{n} }\)

The sum of the geometric series is -12,276.

So, the correct answer is C. -12,276.

To find the sum of the geometric series, we can use the formula:

\(S = a \times (1 - r^n) / (1 - r),\)

where S is the sum of the series,

a is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the first term (a) is 6(2) = 12, the common ratio (r) is 2, and the number of terms (n) is 10.

Plugging these values into the formula, we get:

\(S = 12 \times (1 - 2^{10} ) / (1 - 2).\)

Calculating further:

\(S = 12 \times (1 - 1024) / (-1) = 12 \times 1023 = 12276.\)

Therefore, the sum of the geometric series is -12,276.

So, the correct answer is C. -12,276.

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Answer:

y = 3x

Step-by-step explanation:

slope intercept form is y = mx + b with m as the slope and b as the y-intercept

to find the slope you can see where the line intersects at (1, 3) and (0,0) If you look at the graph you count up three spaces over one so the slope is 3

since the y-intercept intersects at (0,0) The y-intercept is 0 and you do not have to add that to the answer

Answer:

y=3x I think if not sorry

Step-by-step explanation:

have great evening,day,night,morning!

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

41

Step-by-step explanation:

n+(-16)=25

n-16=25

Add 16 to both sides to isolate the variable

n=41

Answer:

\( \huge{ \fbox{ \sf{41}}}\)

Step-by-step explanation:

\( \star{ \sf{ \: Let \: the \: missing \: number \: be \: x}}\)

Create an equation

\( \sf{x + ( - 16) = 25}\)

\( \mapsto{ \sf{x - 16 = 25}}\)

Move 16 to right hand side and change it's sign

\( \mapsto{ \sf{x = 25 + 16}}\)

Add the numbers : 25 and 16

\( \mapsto{ \sf{x = 41}}\)

The number is 41

Hope I helped!

Best regards! :D

~TheAnimeGirl

The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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Answer:

The answer is 3 days

Step-by-step explanation:

Divide 48/16=3

Answer:

1) 47 degrees

2) 28 degrees

3) 26 degrees

Step-by-step explanation:

a triangle always equals 180 degrees, you add together the numbers you have then subtract it from 180 then you'll get your answer <3

Answer: 20% of 160 is 32.

Step-by-step explanation:

The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.

To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.

Let us now find the 20% of 160.

20% = 0.2

percentage = 160 × 0.2

= 32

Considering the polynomial f(x) = x^4  - 16x³ + 70x² + 48x - 219, we have that:

a) The zeros are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.

b) The linear factors are: (x + 1.995)(x - 1.995)(x - 8 + 3i)(x - 8 - 3i).

c) The solutions to f(x) = 0 are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.

The given zero of the polynomial is:

8 + 3i

Hence it's conjugate is also a zero, that is:

8 - 3i.

Thus the first two factors are given as follows:

(x - 8 - 3i)(x - 8 + 3i) = x² - 16x + 64 + 9i² = x² - 16x + 55.

Then the polynomial can be written as follows:

x^4  - 16x³ + 70x² + 48x - 219 = (ax² + bx + c)(x² - 16x + 55).

As a fourth order polynomial can be the product of two second order polynomials. Applying the distributive property to the right side of the equality, we have that:

x^4  - 16x³ + 70x² + 48x - 219 = ax^4 + x³(b - 16a) + x²(55a + c - 16b) + x(55b - 16c) + 55c.

Then the coefficients are given as follows:

Hence the other two factors are given as follows:

x² - 3.98 = 0

x = ± sqrt(3.98)

x = ± 1.995.

The linear factors are:

(x - x')(x - x'')(x - x''')(x - x'''').

In which x', x'', x''' and x'''' are the roots.

The solutions to f(x) = 0 are the roots.

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Money made during peak season = 1,800,000 * p

1. Expression for money made during peak season:

During peak season, the zoo has about 1,800,000 visitors. To calculate the money made during peak season, we multiply the number of visitors by the price of one peak season ticket (p):

Money made during peak season = 1,800,000 * p

2. Expression for money made during the off season:

The zoo wants to sell tickets in the off season for half the price of tickets in the peak season. Therefore, the price of one off season ticket would be p/2. To calculate the money made during the off season, we multiply the number of visitors by the price of one off season ticket:

Money made during the off season = 1,200,000 * (p/2) = 600,000 * p

3. Inequality for breaking even:

To break even, the zoo needs to make at least as much money as they spent on the animals. Let's represent the amount spent on animals as A. The money made during peak season plus the money made during the off season should be greater than or equal to the amount spent on animals:

1,800,000 * p + 600,000 * (p/2) ≥ A

Simplifying the inequality:

3,600,000p + 300,000p ≥ 2A

3,900,000p ≥ 2A

Solving for p:

p ≥ (2A) / 3,900,000

This determines the minimum price of one peak season ticket to break even.

The price of one off season ticket would be half the price of one peak season ticket, so the off season ticket should be (p/2).

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The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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Therefore, the solution to the inequality 3(y + 1/4) > 3/4 is y > 0.

An inequality is a mathematical statement that shows a relationship between two values, which are not necessarily equal. Inequalities are represented using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to). Inequalities are commonly used in algebra and other areas of mathematics, as well as in real-world applications such as finance, economics, and science. They can be used to represent constraints or limits on a variable, such as the maximum or minimum value that it can take.

Here,

We can solve the inequality 3(y + 1/4) > 3/4 by first distributing the 3 to the expression inside the parentheses:

3y + 3/4 > 3/4

Next, we can simplify by subtracting 3/4 from both sides:

3y > 0

Finally, we can solve for y by dividing both sides by 3:

y > 0/3

y > 0

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