Alden is registering for classes next semester. he uses the quantitative reasoning process to decide between two teachers, dr. alvarez, and dr. bareno . he speaks to 17 friends that previously took the course from dr. alvarez and also speaks to 18 friends that took it from dr. bareno. eight of his friends said they highly recommend dr. alvarez. eleven of his friends highly recommend dr. bareno.

Answer:

arrange 3+4=5

Step-by-step explanation:

because 3 square = 9 and 4 square =16 and their sum is 25 and the square of 5 is 25 . both are same .

Hence proved

25% is the larger circle area is gray.

Area of a Circle: The area of a circle is pi times the radius squared.

To calculate the area of the circle we have the formula:

A = π r²-----(1)

where

A=area

r=radius.

First, we have to analyze the given data, the large circle center o passes through d, so

Gray circle area=π*(radius)^2----(2)

The radius of the smaller circle = OD/2 substitute in (2)

Gray circle area=π*(OD/2)^2

Gray circle area=π*OD^2/4

Larger circle area=π*(radius)2    

radius of the larger circle = OD

larger circle area=π*OD^2  

To know the percentage of a large circle we have a small formula:

gray circle area/large circle area--------(3)

=π*OD^2/4/π*OD^2  

=π*OD^2/4*1/π*OD^2=1/4

=25/100

=25%

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Answer:

Mouse

Step-by-step explanation:

The solution for the system of equtaions is (57/11, 42/11)

Here we have the system of equations:

x/3 = 6 - y/3

3x/4 - 3 = 2y

We can isolate x on the first equation to get:

x = 18 - 3*y/3

x = 18 - y

Replacing that on the other equation we will get

3*(18 - y)/4 - 3 = 2y

We can solve this for y.

3*(18 - y)/4 = 2y + 3

54 - 3y = 4*(2y + 3) = 8y + 12

54 - 12 = 8y + 3y

42 = 11y

42/11 =y

And the value of x will be:

x = 9 - 42/11

x  = 99/11 - 42/11 = 57/11

That is the solution of the system.

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The value of n that makes all of the numbers in the set {32 + n, n/8, and √(n + 23)} natural numbers is n = 63.

To find the smallest value of n so that all of the numbers in the set {32 + n, n/8, and √(n + 23)} are natural numbers, we need to determine the factors of the given numbers. We know that a natural number has no fractional part and is greater than or equal to 1.

We can find the smallest value of n by taking the Least Common Multiple (LCM) of the denominators of the fractions in the given set. So, let's begin:1. 32 + n = natural number

If n = 0, then 32 + n = 32, which is not a natural number. If n = 1, then 32 + n = 33, which is a natural number. Therefore, the value of n that makes 32 + n a natural number is n = 1.2. n/8 = natural number

If n is a multiple of 8, then n/8 is a natural number. Therefore, the value of n that makes n/8 a natural number is any positive multiple of 8.3. √(n + 23) = natural number

If n + 23 is a perfect square, then √(n + 23) is a natural number. Therefore, the value of n that makes √(n + 23) a natural number is any number that is 1 less than a perfect square.

We need to find the smallest value of n that satisfies all three conditions above. The LCM of 8 and 1 is 8. The smallest multiple of 8 that is 1 less than a perfect square is 63. Thus, the smallest value of n is 63.

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A sprinkler system does not activate emergency lighting

A sprinkler system is designed to detect fires, sound an alarm, control the fire, and extinguish the fire. However, activating emergency lighting is not a basic function of a sprinkler system.

1. Detect the fire: Sprinkler systems are equipped with heat-sensitive elements that detect the presence of a fire. When the temperature rises above a certain threshold, the sprinkler heads are activated.

2. Sound an alarm: Once the sprinkler system detects a fire, it is designed to automatically trigger an alarm. This alerts people in the building to evacuate and notifies the authorities.

3. Control the fire: Sprinkler systems are designed to control the fire by releasing water or other fire suppressants onto the flames. This helps to limit the spread of the fire and prevent it from growing larger.

4. Extinguish the fire: The primary purpose of a sprinkler system is to extinguish the fire. When the sprinkler heads are activated, water is discharged onto the fire, reducing its intensity and eventually putting it out.

5. Activate emergency lighting: While emergency lighting is an important safety feature in buildings, it is not a function directly related to a sprinkler system. Emergency lighting is typically activated by other systems or mechanisms, such as power failure or manual switches.

In conclusion, while a sprinkler system performs the functions of detecting fires, sounding an alarm, controlling the fire, and extinguishing the fire, it does not activate emergency lighting.

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The probability that all coins show heads up is 1/16.

The probability of one is 1/2: Half of the time (on average, as all numbers in this answer will be) it will show heads.

Of those times it shows heads, only half of the time will the second coin also show heads. We're down to a quarter of the time now.

Of those times the second coin shows heads, only half of the time will the third coin also show heads. This is 1/8.

And, of the times the third coin also shows heads, only half of the time will the fourth coin also show heads. Half of 1/8 is 1/16.

You can simplify this by calculating (1/2)^4.

= 1/16

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Take all coins that are still on tails and keep flipping them until they land on heads. We flip 4 coins simultaneously. What is the probability that all coins show heads up?

Answer:

14 feet

Step-by-step explanation:

c = πd

Plug in the givens

43.96 = 3.14d

Divide both sides by 3.14

14 = d

Answer:

Diameter = circumference ÷π

43. 96÷3. 14 =14 feet

The null hypothesis refers to the population, whereas the research hypothesis refers to the sample.

We have,

In statistics, the null hypothesis is a statement that assumes there is no significant difference between two groups or variables being compared.

It represents the default position that there is no relationship or effect between the variables of interest.

The null hypothesis is typically formulated as a statement about the population parameter.

On the other hand, the research hypothesis (also known as the alternative hypothesis) is a statement that proposes a significant difference or relationship between the variables being studied.

The research hypothesis is typically formulated as a statement about the sample, which is a subset of the population.

Thus,

The null hypothesis refers to the population, whereas the research hypothesis refers to the sample.

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Answer:

11.6°

Step-by-step explanation:

In ΔGHI, g = 3.4 cm, i = 8.2 cm and ∠I=29°. Find all possible values of ∠G, to the nearest 10th of a degree.

We solve the above question using Law of Sines

= g/sin G = I / sin I

Substituting

= 3.4/ sin G= 8.2/ sin 29

Cross Multiply

3.4 × sin 29 = sin G × 8.2

sin G = 3.4 × sin 29/ 8.2

G = arc sin[3.4 × sin 29/ 8.2]

G = arcsin [0.2]

G = 11.59653°

Approximately = 11.6°

∠G = 11.6°

Answer:

Step-by-step explanation:

This is a combination of 6 out of 15

Correct choice is C

Answer:

C right?

Step-by-step explanation:

The values of z for the standard normal distribution are 1.17 and -1.17

From the question, we have the following parameters that can be used in our computation:

Distribution type = standard normal distribution

The number z that has cumulative proportion 0.88.

This means that we calculate the z-score from the p-value

i.e p = 0.88

Using the z-score table of values, we have the following representation

z = 1.17

The number z such that the event z > z has proportion 0.12

This means that we calculate the z-score from the p-value

i.e. p = 0.12

Using the z-score table of values, we have the following representation

z = -1.17

Hence, the z-scores are 1.17 and -1.17

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The variable z follows a standard normal distribution. Let's solve the given problems step by step: (a) To find the number z that has a cumulative proportion of 0.88, we need to find the z-score that corresponds to this proportion. The cumulative proportion represents the area under the standard normal curve to the left of a given z-score.

Using a standard normal distribution table or a calculator, we can find the z-score associated with a cumulative proportion of 0.88. The z-score is approximately 1.175. Therefore, the value of z that corresponds to a cumulative proportion of 0.88 is approximately 1.175.

(b) To find the number z such that the event z > z has a proportion of 0.12, we need to find the z-score that corresponds to this proportion. The event z > z is equivalent to finding the area under the standard normal curve to the right of z. Using a standard normal distribution table or a calculator, we can find the z-score associated with a proportion of 0.12 to the right of z. The z-score is approximately -1.175.

Therefore, the value of z that corresponds to the event z > z having a proportion of 0.12 is approximately -1.175.

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Given:

A right triangle has a hypotenuse of length 5.00 m, and one of its angles is 40.0°.

Required:

a) the side opposite the 40.0° angle.

(b) the side adjacent to the 40.0° angle.

Explanation:

First draw a picture

Now, the trigonometric ratios

So,

(a) The side opposite the 40.0° angle

and

(b) The side adjacent to the 40.0° angle

Answer:

The side opposite to 40 degree angle equal 3.2 m and side adjacent equal 3.8 m.

The Triangle will look in this way (Attached image)-

Step 1: Draw a line segment OQ.

Step 2: Place the center tip of the protractor at point O such that the protractor perfectly aligns with line AQ.

Step 3: Start from 'Q' on the protractor in the anti - clockwise direction and stop at 30. Mark it as point 'P'. If point 'Q' lies to the right of 'O', then start measuring clockwise and stop at 30.

Step 4: Now, place the protector at point Q, mark the point 'P' at 90, such that ∠OQP = 90.

Step 5: Join point 'P' with 'O'. ∠QOP=30° is the required 30 degree angle.

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The train's speed was= 56.7 miles per hour

acc to our question-

Hence, The train's speed was= 56.7 miles per hour

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Answer:

Use the graphing calculator to plot the points and then generate the least squares regression line.

y = 1.87837878 - .4594594595

The polygon has 10 sides.

Each side of the polygon has a measure of 8 cm.

Therefore, the required perimeter is given by:

Therefore, the required perimeter is 80 cm

Answer:

You convert the fractions to a decimal, nut the rest is still the same

Step-by-step explanation:

The probability of obtaining a sum of 7 when rolling two number cubes is 1/6 or approximately 0.1667.

To find the probability, we need to determine the number of favorable outcomes (sum of 7) and the total number of possible outcomes when rolling two number cubes. Each cube has six faces, numbered from 1 to 6.

To obtain a sum of 7, we can have the following combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). There are six favorable outcomes.

The total number of possible outcomes when rolling two number cubes is the product of the number of outcomes for each cube, which is 6 * 6 = 36.

Therefore, the probability of obtaining a sum of 7 is given by:

Number of favorable outcomes / Total number of possible outcomes = 6 / 36 = 1/6 ≈ 0.1667.

Thus, the probability that the sum of the two numbers rolled on the number cubes will be 7 is approximately 0.1667, or 1/6 when expressed as a fraction.

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Answer:

b

Step-by-step explanation:

The percentage of purple flowers and white flowers produced in the F2 generation will be 75% and 25% respectively.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Here, we have,

F2 generation can be defined as the filial generation that arises from the interbreeding between the offspring of F1 generation. F1 generation is produced when two parents are crossed with each other. And this F1 generation when inter-bred fives rise to F2 generation.

Since the F1 generation consisted of offspring with genotype Pp, the the self cross (Pp × Pp) will produce the F2 generation with offspring PP, Pp, Pp and pp. As a result, the percentage of purple and white flowers will be 75% and 25% respectively.

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The given question is incomplete, the complete question is:

If two homozygous parents with genotype PP and pp are crossed, the F1 generation contains the genotype Pp. If the offspring of F1 generation is self-crossed, what must be the percentage of purple flowers and white flowers in the F2 generation?

Answer:

the answer is 3/5

Step-by-step explanation:

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

Answer: 9

Step-by-step explanation:

Answer:

9!

Step-by-step explanation:

Answer:

0.78814

Step-by-step explanation:

From. The Z probability distribution table ;

The values larger than - 0.8

P(Z ≤ - 0.8) = 0.21186

P(Z > - 0.8) = 1 - P(Z ≤ - 0.8)

1 - P(Z ≤ - 0.8) = 1 - 0.21186

P(Z > - 0.8) = 1 - 0.21186 = 0.78814

The exact value of tan 0, given sec 8 and 0 in quadrant IV, is -17/9. Option d is correct. In quadrant IV, cosine is positive and sine is negative.

Since secant is the reciprocal of cosine, sec 8 will be positive. To find the value of tan 0, we can use the identity tan²(theta) = sec²(theta) - 1.

Given that sec 8 is positive, we can determine its value using the identity sec²(theta) = 1 + tan²(theta). In this case, sec²(8) = 1 + tan²(8). Since sec 8 is known, we can solve for tan 8.

sec²(8) = 1 + tan²(8)

1 + tan²(8) = sec²(8)

tan²(8) = sec²(8) - 1

Substituting the value of sec 8, we get:

tan²(8) = (1/cos²(8)) - 1

Now, we can take the square root of both sides and consider the negative value for tan 0 since 0 is in quadrant IV:

tan 8 = -√[(1/cos²(8)) - 1]

tan 0 = -√[(1/sec²(8)) - 1]

      = -√[(1/(sec 8)²) - 1]

      = -√[(1/(sec 8))² - (sec 8)²/(sec 8)²]

      = -√[(1 - (sec 8)²)/(sec 8)²]

      = -√[-1/(sec 8)²]

      = -1/(sec 8)(√[1/(sec 8)²])

      = -1/(sec 8)(1/(sec 8))

      = -1/(sec 8)²

      = -1/(sec²(8))

      = -1/cos²(8)

      = -1/(1/cos²(8))

      = -1/(1/sec²(8))

      = -1/(1 + tan²(8))

      = -1/(1 + tan²(0))

      = -1/(1 + (-17/9)²)

      = -1/(1 + 289/81)

      = -1/(370/81)

      = -81/370

      = -17/9

Therefore, the exact value of tan 0, given sec 8 and 0 in quadrant IV, is -17/9.( Option d)

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Given:

The equation is:

\(x^2-10x=7\)

To find:

The number that should be added to sides of the equation to complete the square.

Solution:

If an expression is in the form of \(x^2+bx\), then we have to add \(\left(\dfrac{b}{2}\right)^2\) to make it perfect square.

We have,

\(x^2-10x=7\)             ...(i)

To make it perfect square we need to add square of half of coefficient of x on both sides.

Coefficient of x is -10, so square of half of coefficient of x is:

\(\left(\dfrac{-10}{2}\right)^2=(-5)^2\)

\(\left(\dfrac{-10}{2}\right)^2=25\)

On adding 25 on both sides of (i), we get

\(x^2-10x+25=7+25\)

\((x-5)^2=32\)

Therefore, we need to add 25 to both sides of the equation to complete the square.

11, 8, 5, 2, -1

Option D is correct

The given arithmetic sequence is:

For the first term, substitute n = 1 into the arithmetic sequence

For the second term, substitute n = 2 into the arithmetic sequence

For the third term, substitute n = 3 into the arithmetic sequence

For the fourth term, substitute n = 4 into the arithmetic sequence

For the fifth term, substitute n = 5 into the arithmetic sequence

Therefore, the first five terms are:

11, 8, 5, 2, -1

The frequency of small-angle oscillations is given by\(f = (g/L)^(1/2) * (1/2π)^(1/2) * (M/L)^(-1/4).\)

The frequency of small-angle oscillations can be expressed in terms of the variables M (mass), L (length of the rod) and g (acceleration due to gravity). The expression is derived from the formula for the period of a pendulum, which is given by the equation T = 2π\((L/g)^(1/2)\). The frequency is the inverse of the period, so the expression for the frequency of small-angle oscillations is

f = \((g/L)^(1/2) * (1/2π)^(1/2) * (M/L)^(-1/4)\).

This expression demonstrates that the frequency of oscillations increases with increasing critical angle, as long as the mass is not changed. Additionally, the frequency decreases with increasing mass, as the mass of the rod slows down the oscillations. The frequency also increases with decreasing length, as a shorter pendulum swings faster due to the decreased time it takes for it to complete one oscillation.

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