A scientist claims that 7% 7 % of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 600 600 viruses would differ from the population proportion by greater than 3% 3 % ? Round your answer to four decimal places.

it's already simplified

Answer:

\(z=\frac{931-1131}{\frac{333}{\sqrt{30}}}=-3.290\)  

Now we can calculate the p value using the alternative hypothesis:

\(p_v =P(z<-3.290)=0.0005\)  

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 1131

Step-by-step explanation:

Information given

\(\bar X=931\) represent the sample mean

\(\sigma=333\) represent the population standard deviation

\(n=30\) sample size  

\(\mu_o =1131\) represent the value to check

\(\alpha=0.05\) represent the significance level

z would represent the statistic

\(p_v\) represent the p value

System of hypothesis

We want to verify if the true mean is less than 1131, the system of hypothesis would be:  

Null hypothesis:\(\mu \geq 1131\)  

Alternative hypothesis:\(\mu <1131\)  

The statistic is given by:

\(z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}\) (1)  

Reaplacing we got:

\(z=\frac{931-1131}{\frac{333}{\sqrt{30}}}=-3.290\)  

Now we can calculate the p value using the alternative hypothesis:

\(p_v =P(z<-3.290)=0.0005\)  

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 1131

\(3 {x}^{5} + 2 {x}^{3} + x + {x}^{2} - 2x + 5 = \)

\(3 {x}^{5} + 2 {x}^{3} + {x}^{2} - x + 5\)

Answer:

3x⁵ + 2x³ + x² -x + 5

Step-by-step explanation:

(3x⁵ + 2x³ + x) - (-x² + 2x - 5) <== multiply to remove the parenthesis

1(3x⁵ + 2x³ + x) - 1(-x² + 2x - 5)

1(3x⁵) + 1(2x³) + 1(x) + -1(-x²) + -1(2x) + -1(-5) <== remember multiplying 2 negatives, makes a positive

3x⁵ + 2x³ + x + x² - 2x + 5 <== combine any like terms

3x⁵ + 2x³ + x² -x + 5 <== make sure that your answer is in Standard form (in decreasing degrees)

Hope this helps!

Answer:10 or 25

Step-by-step explanation:

just add both  or times them

5+5 or 5x5

Answer:

-23 .......................

The volume of the solid is 4/5π.

The volume of a solid generated by revolving a region around a line is given by V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region, respectively, and y is a function of x.

In this case, the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Therefore, the volume of the solid generated when the region is revolved about the y-axis is given by

V = ∫0 1 π(y)2dy

= ∫0 1 πx6dx

= π/7

= 4/5π

The volume of the solid is calculated using the formula V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region and y is a function of x. In this case, the lower limit is a=0 and the upper limit is b=1, since the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Integrating from a=0 to b=1 gives the volume of the solid as V = ∫0 1 πx6dx = π/7 = 4/5π.

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In standard form :660

Answer:

The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)

Step-by-step explanation:

To estimate the bit length of the sum of 2000 different numbers each of which is between 15 million and 16 million, we need to calculate the maximum and minimum possible sums and then determine the bit length for both of them.

In this case, the minimum sum that we can obtain would be

15,000,000 × 2000

= 30,000,000,000.

The maximum sum would be

16,000,000 × 2000

= 32,000,000,000.

The total number of bits needed to store the sum of 2000 different numbers would be somewhere between 35 and 36 bits, but we can't give an exact number.

The minimum product would be.

15,000,000² × 2000

= 4.5 × 10¹⁶.

The maximum product would be.

16,000,000² × 2000

= 5.12 × 10¹⁶.

We can represent the minimum product with 56 bits and the maximum product with 57 bits. The total number of bits needed to store the product of 2000 different numbers would be somewhere between 56 and 57 bits.

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Answer:

I am gonna say linear probaly wrong but

Step-by-step explanation:

Answer:

3,o217383737283636666666666678899

Answer:

5

Step-by-step explanation:

is logical .... ...........

Step-by-step explanation:

\(6 \cos {}^{2} (x) + 4 \sin {}^{2} (x) = 5\)

\(6(1 - sin {}^{2} x) + 4 \sin {}^{2} (x) = 5\)

\(6 - 6 \sin {}^{2} (x) + 4 \sin {}^{2} (x) = 5\)

\(6 - 2 \sin { }^{2} (x) = 5\)

\( - 2 \sin {}^{2} (x) = - 1\)

\( \sin {}^{2} (x) = \frac{1}{2} \)

\( \sin(x) = \frac{1}{ \sqrt{2} } \)

Take the arc Sine of the function

\(arcsin( \frac{1}{ \sqrt{2} } ) = \frac{\pi}{4} \)

Finally, Sine is a periodic function so it has two answers within the interval (0, 2 pi)

Use the identity

\( \sin(x) = \sin(x + \pi) \)

We know that

\( \sin( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} } \)

so using the identity

\( \sin( \frac{\pi}{4} + \pi ) = \sin( \frac{5\pi}{4} ) \)

So we have two answers.

\(( \frac{\pi}{4} )\)

\(( \frac{5\pi}{4} )\)

If two angles are complementary, it means that their sum is 90 degrees. This means that

angle FGJ + angle JGH = 90

From the diagram, angle JGH = 24.4

Thus,

angle FGJ + 24.4 = 90

angle FGJ = 90 - 24.4

angle FGJ = 65.6 degrees

Answer:

Step-by-step explanation:

3(m-12)+8

x=m-12

Answer:

26% tip

Step-by-step explanation:

213.90 / 1.15 = 186

213.90 + 20 = 233.9

233.9 / 186 = 1.26

26% tip

Answer:

A. 6

Step-by-step explanation:

Answer:

A. 6

Step-by-step explanation:

6.16441400297

This rounds to 6.

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

If there is a low supply and a high demand, there is an increase in price and vice versa.

Last 2012, there was a virus which infected millions of chicken. It was known as Avian influenza or bird flu. It resulted to scarcity of eggs.

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

For example we can use water. If a product becomes scarce its price would increase due to supply in demand.

If drinkable water became scarce its price would be greatly increased to its need and being in extreme demand.

In short,  if there is a low supply and a high demand, there is an increase in price and vice versa.

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Answer:

x = -2/3

Step-by-step explanation:

27^x=1/9

writing 27 as 3^3  and 1/9 as 3 ^-2

3^3^x = 3^-2

We know that a^b^c =a^(b*c)

3^(3x) = 3^-2

Since the bases are the same the exponents need to be the same

3x = -2

x = -2/3

To obtain precise calculations and solutions, it would be helpful to have the dimensions and geometry of the truss and any other relevant information provided in the problem statement or accompanying diagram.

To determine the magnitude and direction of the force F and the reactions at points A and D in the given loaded truss, we need to analyze the equilibrium of forces. Based on the given information, the resultant force R is directed to the right with a magnitude of 12.4 kN. Here's how we can approach the problem:

Resolve Forces: Resolve the applied forces into their horizontal and vertical components. Let's label the forces as follows:Force at point A: F_A

Force at point B: F_B

Force at point C: F_C

Force at point D: F_D

Equilibrium in the Vertical Direction: Since the truss is in equilibrium, the sum of vertical forces must be zero.

F_A * cos(30°) - F_C = 0 (Vertical equilibrium at point A)

F_B - F_D = 0 (Vertical equilibrium at point D)

Equilibrium in the Horizontal Direction: The sum of horizontal forces must be zero for the truss to be in equilibrium.

F_A * sin(30°) + F_B - F_C * cos(60°) = R (Horizontal equilibrium)

Determine the Reactions: Solving the equations obtained from the equilibrium conditions will allow us to find the values of F_A, F_B, and F_D, which are the reactions at points A and D.

Calculate Force F: Once we know the reactions at A and D, we can calculate the force F using the equation derived from the horizontal equilibrium.

F_A * sin(30°) + F_B - F_C * cos(60°) = R

The size of the structure is necessary to determine the forces accurately. The dimensions and geometry of the truss, along with the loads applied, affect the magnitude and direction of the reactions and the forces within the truss members. Without the size of the structure, it would be challenging to determine the accurate values of the forces and reactions.

To obtain precise calculations and solutions, it would be helpful to have the dimensions and geometry of the truss and any other relevant information provided in the problem statement or accompanying diagram.

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The structure of the coordinates associated with specific radian measurements on the unit circle follows a distinct pattern. The x and y coordinates represents the cosine and sine values of the angle, respectively.

The unit circle is a circle with a radius of 1 unit, centered at the origin of a Cartesian coordinate system.

It is commonly used in trigonometry to relate angles to the coordinates on the circle.

When we measure an angle in radians on the unit circle, we can associate specific coordinates with that angle.

The x-coordinate of a point on the unit circle represents the cosine value of the angle, while the y-coordinate represents the sine value of the angle.

These coordinates follow a pattern based on the radian measurement.

For example, when the angle is 0 radians (or 0 degrees), the corresponding point on the unit circle is (1, 0), where the x-coordinate is 1 (cosine of 0) and the y-coordinate is 0 (sine of 0).

As the angle increases, the coordinates change accordingly. For instance, when the angle is π/2 radians (or 90 degrees), the point on the unit circle is (0, 1), where the x-coordinate is 0 (cosine of π/2) and the y-coordinate is 1 (sine of π/2).

This pattern continues as the angle increases or decreases, and the coordinates on the unit circle change accordingly.

By using trigonometric functions, we can determine the cosine and sine values of any given angle and associate them with the appropriate coordinates on the unit circle.

In summary, the structure of the coordinates associated with specific radian measurements on the unit circle follows a pattern where the x-coordinate represents the cosine value of the angle, and the y-coordinate represents the sine value of the angle.

Together, these coordinates create points on the unit circle that correspond to the given radian measurement.

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Answer:

The length of the third side is 7.81 inches and the perimeter of the triangle is about 18.81 inches

Step-by-step explanation:

Answer:

m= -3/2

Step-by-step explanation:

I hope this helps

Answer: A good way to get a small standard error is to use a large sample.

Step-by-step explanation:

In order to find the small standard error, there is always need of a complete set which is called the large sample.

If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.

Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!

-From a 5th Grade Honors Student

Using linear function concepts, it is found that the piece-wise function that can be used to calculate the monthly billing amount, B, for a monthly level of t text messages is:

\(B(t) = 5 , t \leq 250\\B(t) = 5 + 0.1(t - 250) , 250 \leq t\leq 2000\\B(t) = 5 + 0.1(t-250) + 0.4(t-2000) , t\geq 2000\)

What is a linear function?

A linear function is modeled by:

Y = mX + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

In this problem, a piece-wise function is bought, that is, a function that has different definitions according on the input.

Up to 250 text messages:

A flat rate of $5.00 each month is paid, that is, the y-intercept is , while the slope is 0, and the function is:

\(B(t) = 5 , t \leq 250\\\)

Between 250 and 2000 text messages:

For each additional message over 250, the customer pays $0.1, that is, a slope of  multiplied by t - 250 is added to the function, hence:

\(B(t) = 5 + 0.1(t - 250) , 250 \leq t\leq 2000\)

Above 2000 text messages:

For each additional message over 2000, the customer pays $0.4, that is, a slope of  multiplied by t - 2000 is added to the function, hence:

\(B(t) = 5 + 0.1(t-250) + 0.4(t-2000) , t\geq 2000\)

Hence, the piece-wise function is:

\(B(t) = 5 , t \leq 250\\B(t) = 5 + 0.1(t - 250) , 250 \leq t\leq2000\\B(t) = 5 + 0.1(t-250) + 0.4(t-2000) , t\geq 2000\)

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Dr. Ellison is wrong.

To determine if the equation y = -3x + 7 has a solution of (2, 13), we can substitute the values of x and y into the equation and check if it holds true.

Substituting x = 2 and y = 13 into the equation:

13 = -3(2) + 7

13 = -6 + 7

13 = 1

The equation does not hold true since 13 is not equal to 1.

Therefore, (2, 13) is not a solution to the equation y = -3x + 7.

Hence, Dr. Ellison is incorrect in stating that (2, 13) is a solution to the equation.

An equation is a mathematical statement that indicates that two expressions are equal. It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. Equations are used to represent relationships between quantities and to solve problems in various branches of mathematics and science.

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Answer:

C. Translation 5 units left and 2 units down

Step-by-step explanation:

Let's take a look at A', which is (0, 0). This is the result of A, which is (5, 2) being transformed somehow. Notice that the x-coordinate moved 5 units to the left (from 5 to 0, which means we subtract 5 from 5). And, notice that the y-coordinate moved 2 units down (from 2 to 0, so we subtract 2 from 2).

Look to see if this works for the other two points:

B(6, 1): if we subtract 5 from the x-coordinate 6, we get 6 - 5 = 1, which matches the x-coordinate of the image B'. If we subtract 2 from the y-coordinate of B, which is 1, we get 1 - 2 = -1, which also matches the y-coordinate of B'. So, this works.

C(4, 5): if we subtract 5 from the x-coordinate 4, we get 4 - 5 = -1, which matches the x-coordinate of the image C'. If we subtract 2 from the y-coordinate of C, which is 5, we get 5 - 2 = 3, which also matches the y-coordinate of C'. So, this again works.

Therefore, we know that the transformation is a translation 5 units left and 2 units down, or C.

A picture will be shown below of a graph with the points in the table.

We only need to use (5, 2) and (0, 0) to solve this problem.

We take both points and see what it took for the old point to get to where the new point is (Shown in picture below).

Therefore, the answer is [ C. Translation 5 units left and 2 units down ]

Best of Luck!

Answer:

It will take 100 purchased songs for iTunes and Napster to equal in price.

Step-by-step explanation:

iTunes: y=1.29x

Napster: y=1.19x+10

1.29x=1.19x+10

10=.10x

x=100

The value of y in the given ordered pair is 30.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, the rate of change at which the water level rise is 15/4 cm/minute.

Hence, the slope of the line is 13/6.

Taking x to represent the time in minutes and y to represent the rise in cm then,

Therefore,

4 minutes = 15 cm

So, in 1 minute, the rise is 15/4 cm

Thus, in 8 minutes, the rise will be ;

= 30 cm

Therefore, (x, y) will be (8, 30)

Finding the slope of the line using point (8, 30) and (x, y)

m = y₂-y₁ / x₂-x₁

m = 15 - x / 4 - y

m = 15/4

The rate of change at which the water level rises equals the slope of the line. This is the justification.

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The eigenvalues are λ1 = 3 and λ2 = 4, and the corresponding eigenvectors are x1 = (4;1) and x2 = (2;1). The matrix P is (4 2; 1 1) and matrix D is (3 0; 0 4). The value of A^8P is (127 254; 63 127).

Given matrix A = (5 -8; 1 -1), we have to determine the eigenvalues and corresponding eigenvectors for the matrix A. Further, we have to write down matrices P and D such that A = PDP^(-1) and evaluate A^8P.

Eigenvalues and corresponding eigenvectors:

First, we have to find the eigenvalues.

The eigenvalues are the roots of the characteristic equation |A - λI| = 0, where I is the identity matrix and λ is the eigenvalue.

Let's find the determinant of

(A - λI). (A - λI) = (5 - λ -8; 1 - λ -1)

det(A - λI) = (5 - λ)(-1 - λ) - (-8)(1)

det(A - λI) = λ^2 - 4λ - 3λ + 12

det(A - λI) = λ^2 - 7λ + 12

det(A - λI) = (λ - 3)(λ - 4)

Therefore, the eigenvalues are λ1 = 3 and λ2 = 4.

To find the corresponding eigenvectors, we substitute each eigenvalue into the equation

(A - λI)x = 0. (A - 3I)x = 0

⇒ (2 -8; 1 -2)x = 0

We solve for x and get x1 = 4x2, where x2 is any non-zero real number.

Therefore, the eigenvector corresponding to

λ1 = 3 is x1 = (4;1). (A - 4I)x = 0 ⇒ (1 -8; 1 -5)x = 0

We solve for x and get x1 = 4x2, where x2 is any non-zero real number.

Therefore, the eigenvector corresponding to λ2 = 4 is x2 = (2;1).

Therefore, the eigenvalues are λ1 = 3 and λ2 = 4, and the corresponding eigenvectors are x1 = (4;1) and x2 = (2;1).

Matrices P and D:

To find matrices P and D, we first have to form a matrix whose columns are the eigenvectors of A.

P = (x1 x2) = (4 2; 1 1)

We then form a diagonal matrix D whose diagonal entries are the eigenvalues of A.

D = (λ1 0; 0 λ2) = (3 0; 0 4)

Therefore, A = PDP^(-1) becomes A = (4 2; 1 1) (3 0; 0 4) (1/6 -1/3; -1/6 2/3) = (6 -8; 3 -5)

Finally, we need to evaluate A^8P. A^8P = (6 -8; 3 -5)^8 (4 2; 1 1) = (127 254; 63 127)

Therefore, the value of A^8P is (127 254; 63 127).

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