As part of a science experiment, a student observes the growth of a population of bacteria in four different media. The table below lists the observations the student made.
Medium
Observation
1
Population increases by 10 every hour
II
Population decreases by 10 every hour
THI Population increases by 10% overy hour
M Population decreases by 10% every hour
In which media can the change in the population of bacteria be modeled by a linear function?
media I and II
media I and III
media II and IV
media III and IV
​

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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Answer:

The 80% confidence interval for the population proportion of oil tankers that have spills each month is (0.199, 0.257).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

Suppose a sample of 333 tankers is drawn. Of these ships, 257 did not have spills.

333 - 257 = 76 have spills.

This means that \(n = 333, \pi = \frac{76}{333} = 0.228\)

80% confidence level

So \(\alpha = 0.2\), z is the value of Z that has a pvalue of \(1 - \frac{0.2}{2} = 0.9\), so \(Z = 1.28\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.228 - 1.28\sqrt{\frac{0.228*0.772}{333}} = 0.199\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.228 + 1.28\sqrt{\frac{0.228*0.772}{333}} = 0.257\)

The 80% confidence interval for the population proportion of oil tankers that have spills each month is (0.199, 0.257).

The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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Answer:

False

Step-by-step explanation:

The greatest sum of two consecutive even integers would be 200 + 198, or 398

Answer:

its true

Step-by-step explanation:

Answer:

\(\begin{aligned}x &= 16\sqrt3 \\ &\approx 27.7\end{aligned}\)

Step-by-step explanation:

We can see that the longer leg (a) of a right triangle is half of the circle's radius. Since we are given the other two sides of the triangle (shorter leg and hypotenuse), we can solve for the length of the longer leg using the Pythagorean Theorem:

\(a^2 + b^2 = c^2\)

↓ plugging in the given values

\(a^2 + 2^2 = 14^2\)

↓ subtracting 2² from both sides

\(a^2 = 14^2 - 2^2\)

\(a^2 = 196 - 4\)

\(a^2 = 192\)

↓ taking the square root of both sides

\(a = \sqrt{192\)

↓ simplifying the square root

\(a = \sqrt{2^6 \cdot 3\)

\(a = 2^{\, 6 / 2} \cdot \sqrt3\)

\(a = 2^3\sqrt3\)

\(a = 8\sqrt3\)

Now, we can solve for the radius (x) using the fact that the longer leg of the triangle is half of it.

\(a = \dfrac{1}{2}x\)

↓ plugging in the a-value we solved for

\(8\sqrt3 = \dfrac{1}2x\)

↓ multiplying both sides by 2

\(\boxed{x = 16\sqrt3}\)

∠ADE≅∠CDE and BD bisects ∠ABC.

Since BD bisects ∠ABC, it follows that ∠ABD = ∠CBD. (angle bisector theorem)

By the Angle-Angle-Side (AAS) congruence theorem, since ∠ADE and ∠CDE are congruent, and ∠ABD = ∠CBD, then ∠ABE = ∠CBE.

Therefore, by the Side-Angle-Side (SAS) congruence theorem, since ∠ABE = ∠CBE, and AB = CB, then AB ≅ CB.

A figure that is created by two rays or lines that have the same endpoint is known as an angle in plane geometry. From the Latin word "angulus," which meaning "corner," comes the English term "angle." The vertex, which is the shared terminal of the two rays, is referred to as the side of an angle.

To measure angles, we employ protractors. View the AOB figure provided below. Let's try to determine what kind of angle AOB is. It appears to be at an acute angle, doesn't it? This indicates that its measure is more than 0° and less than 90°. Let's practice using the protractor to measure this angle.

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The time and electricians it would take the remaining 3 electricians 8 hours to complete the job if one electrician does not report.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

If x men take y time for a work,

We can define a constant as "Manpower" needed for doing that specific work.

Let we define:

Manpower needed for a work = y + y + y + .. + y = Time per man × count of men

Manpower needed for a work = xy

We are given that;

Number of electricians= 4

Number of hours= 6

Now,

We can use the formula:

workers × time = work

where "workers" is the number of electricians, "time" is the number of hours they work, and "work" is the amount of work done.

In this case, we know that 4 electricians can complete the job in 6 hours. So:

4 × 6 = work

work = 24

This means that the total amount of work required to complete the job is 24 "units".

Now, if one electrician doesn't show up, we have only 3 electricians to do the work. Let's call the time it takes for the 3 electricians to complete the job "t".

So we have:

3 × t = 24

Dividing both sides by 3, we get:

t = 8

Therefore, by work and time answer will be 3 electricians and 8 hours.

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The equation represents the image of the line y = 3x +1 is y' = 3(x - 3) +1.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

The transformation that translates function y = f(x) by h units right and k units up is

y' = f(x -h) +k

We have y= 3x+ 1

So, After translating 3 units to x axis the function will become

y' = 3(x - 3) +1

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Answer:

Step-by-step explanation:

To classify the quadrilateral formed by the given points, we need to find the length of each side and the measure of each angle.

Using the distance formula, we can find the length of each side:

AB = sqrt((4 - (-3))^2 + (2 - 1)^2) = sqrt(49 + 1) = sqrt(50)

BC = sqrt((9 - 4)^2 + (-3 - 2)^2) = sqrt(25 + 25) = 5sqrt(2)

CD = sqrt((2 - 9)^2 + (-4 - (-3))^2) = sqrt(49 + 1) = sqrt(50)

DA = sqrt((-3 - 2)^2 + (1 - (-4))^2) = sqrt(25 + 25) = 5

Using the slope formula, we can find the measure of each angle:

Angle ABC: m1 = (2 - 1)/(4 - (-3)) = 1/7

m2 = (-3 - 2)/(9 - 4) = -1/5

tan(ABC) = |(m2 - m1)/(1 + m1m2)| = 3/4

ABC = arctan(3/4) ≈ 36.87°

Angle BCD: m1 = (-3 - 2)/(9 - 4) = -1/5

m2 = (-4 - (-3))/(2 - 9) = 1/7

tan(BCD) = |(m2 - m1)/(1 + m1m2)| = 3/4

BCD = arctan(3/4) ≈ 36.87°

Angle CDA: m1 = (-4 - 1)/(2 - (-3)) = -1

m2 = (1 - (-3))/(-3 - 9) = 1/2

tan(CDA) = |(m2 - m1)/(1 + m1m2)| = 7/5

CDA = arctan(7/5) ≈ 54.46°

Angle DAB: m1 = (1 - (-4))/(4 - (-3)) = 5/7

m2 = (-4 - (-3))/(-3 - 2) = 1/5

tan(DAB) = |(m2 - m1)/(1 + m1m2)| = 3/4

DAB = arctan(3/4) ≈ 36.87°

Therefore, the quadrilateral formed by the given points is a kite, because adjacent sides are congruent and one diagonal bisects the other diagonal at a right angle.

Answer:

-3/4+3/4+1/4=0.25

but, you asked for it in a mixed number which would be 1/4

Step-by-step explanation:

The proportional relationship between the distance (d) traveled by a car and time (t) is shown in the graph attached below.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 10/1 = 10.

In this exercise, we would use an online graphing calculator to plot the proportional relationship between the distance (d) traveled by a car and time (t) as shown in the graph attached below.

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Can you give me some hint please

The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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Answer:

d

Step-by-step explanation:

(x, y) ⇒ (x + 1, y +1) ⇒ (3x, 3y)

A (-3, 3) ⇒ A' (-2, 4) ⇒ A'' (-6, 12)

B (1, -3) ⇒ B' (2, -2) ⇒ B'' (6, -6)

C (-3, -3) ⇒ C' (-2, -2) ⇒ C'' (-6, -6)

The relationship between BC and B"C" is B"C"/BC = 1/3 if the triangle A'B'C' is formed using the translation (x + 1. y + 1) and the dilation by a scale factor of 3 from the origin. option (C) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have:

Triangle A'B'C' is formed using the translation (x + 1. y + 1) and the dilation by a scale factor of 3 from the origin.

As we know, the ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

The scale factor k = 1/3

B"C" = kBC

B"C" = BC/3

B"C"/BC = 1/3

Thus, the relationship between BC and B"C" is B"C"/BC = 1/3 if the triangle A'B'C' is formed using the translation (x + 1. y + 1) and the dilation by a scale factor of 3 from the origin. option (C) is correct.

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Solution in terms of general solution of an equation means the final answer that is gotten for solving the equation

The mathematics SAT score representing the top 1% of all scores is approximately 780.

a. The random variable in this case is the mathematics SAT score.

b. To find the probability that a person has a mathematics SAT score over 700, we need to calculate the z-score first.

The z-score is calculated as \(\frac{(X - \mu )}{\sigma}\),

where X is the value we're interested in, μ is the mean, and σ is the standard deviation.

In this case, X = 700, μ = 514, σ = 117.

Using the formula, the z-score is \(\frac{(700 - 514)}{117 } = 1.59\).

To find the probability associated with this z-score, we can consult a standard normal distribution table or use a calculator.

The probability is approximately 0.0564 or 5.64%.

c. To find the probability that a person has a mathematics SAT score of less than 400, we again calculate the z-score using the same formula.

X = 400, μ = 514, and σ = 117.

The z-score is \(\frac{(400 - 514) }{117 } = -0.9744\).

Looking up the probability associated with this z-score, we find approximately 0.1635 or 16.35%.

d. To find the probability that a person has a mathematics SAT score between 500 and 650, we need to calculate the z-scores for both values.

Using the formula, the z-score for 500 is \(\frac{(500 - 514)}{117 } = -0.1197\),

and the z-score for 650 is \(\frac{(650 - 514)}{117 } = 1.1624\).

We can then find the area under the normal curve between these two z-scores using a standard normal distribution table or calculator.

Let's assume the probability is approximately 0.3967 or 39.67%.

e. To find the mathematics SAT score that represents the top 1% of all scores, we need to find the z-score corresponding to the top 1% of the standard normal distribution.

This z-score is approximately 2.33.

We can then use the z-score formula to calculate the corresponding SAT score.

Rearranging the formula,

\(X = (z \times \sigma ) + \mu\),

where X is the SAT score, z is the z-score, μ is the mean, and σ is the standard deviation.

Substituting the values,

\(X = (2.33 \times 117) + 514 = 779.61\).

Rounded to the nearest whole number, the mathematics SAT score representing the top 1% of all scores is approximately 780.

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Answer:

  -9.5

Step-by-step explanation:

The slope (m) is the ratio of the change in y to the change in x:

  m = (y2 -y1)/(x2 -x1)

  m = (10-(-9))/(-3-(-1)) = 19/-2

  m = -9.5

The slope of that line is -9.5.

__

The graph shows the line through those points, written in point-slope form.

Answer: -2x-27

Step-by-step explanation:

Answer:

7.50 x  = 35 Answer is around 4.6 hours

Step-by-step explanation:

Divide 35 by 7.50 to find the number of hours.

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The measure of the angle A is 70 degrees if the DR is the tangent to the circle option (A) 70 degrees is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

Join the points B and O and then join points D and O

Angle A = (1/2)Angle BOD

Angle B = 140 degrees

Angle A = (1/2)140 degrees

Angle A = 70 degrees

Thus, the measure of the angle A is 70 degrees if the DR is the tangent to the circle option (A) 70 degrees is correct.

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Answer:

1 person got 68 inches

4 persons got 69 inches

2 persons got 70 inches

3 persons got 74 inches

1 person got 76 inches

The solution to the equation given by M * M * M = 729 is 9

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Given the equation:

M.M.M = 729

This gives:

M * M * M = 729

M³ = 729

Taking the cube root of both sides:

∛M³ = ∛729

M = 9

The solution to the equation is 9

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C = amount of campers

so, if we give each campler 1/6 lb evenly, whatever that sum will just add up to 2/3 lb.

If we have "C" campers, the product of 1/6 * C gives use that sum, so we can say that

\(\cfrac{1}{6}C~~ =~~\cfrac{2}{3}\implies C = \cfrac{~~ \frac{2}{3}~~}{\frac{1}{6}}\implies C = \cfrac{2}{3}\div \cfrac{1}{6}\implies C = \cfrac{2}{\underset{1}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{1}\implies C = 4\)

The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

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Answer:

The measure of an arc is the size of the corresponding central angle, so angle 1 for AB,

Answer: B 30

Answer:
The cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles would be 11.50.

Step-by-step explanation:

We know this is the answer because, when solving for c(3), we would get c(3)=2.3(3)+2.50=11.50.

The number of Cloud cupcakes that each person will be 4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

I'm on a team of 9 people and we told our teacher that together we could eat 36 Cloud cupcakes.

The number of Cloud cupcakes that each person will be given as,

⇒ 36 / 9

⇒ 4

The number of Cloud cupcakes that each person will be 4.

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The probability that exactly 4 seeds out of 9 planted won't grow is 1.57%.

Let X be the number of seeds that don't grow.

X follows a binomial distribution with parameters n=9 and p=0.15 (the probability that a seed doesn't grow).

So, probability of exactly 4 seeds not growing is:

P(X=4) = \(9C4 * (0.15)^4 * (1-0.15)^5\)

P(X=4) = 70 * 0.00050625 * 0.4437053125

P(X=4) = 0.01572380701

P(X=4) = 1.57%

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Step-by-step explanation:

the complement of 26 degree is (90-26).

The supplement of (90-26) is 180 ( 90-26) = 116 degree

Hey there!

Complementary angles add up to

\(\bold{90^\circ}\).

Supplementary angles add up to

\(\bold{180^\circ}\).

We are given an angle whose measure is

\(\bold{26^\circ}\)

The complement of that angle is

\(\bold{x+26=90}\)

Subtract & find the complement

\(\bold{x=64^\circ}\)

Now let's find the supplement of the angle

\(\bold{x+26=180}\)

Subtract and find the supplement

\(\bold{x=154^\circ}\)

Hope everything is clear.

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Answer Given By

\(\boxed{ST2710~}\)

Or

Have an outstanding day!