from a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. in how many ways can this be done?

(-10/252) x (1/0.9165) = 0.0175 rad/sec is the equation for theta/dt.

Angle theta in the displayed figure can be expressed as

Theta sin = 10/sin

The angle will change at the following rate:

(-10/x2)(dx/dt) = cos theta(theta/dt)

Now, when x equals 25 feet, we require d theta/dt.

The fishing line is reeled in at a rate of

dx/dt = -1 ft/sec.

Now, if x equals 25, then Cosine equals

[ (x2-100)]

Cosine equals [ (252-100)]/25 = 0.9165So,

(-10/x2)(dx/DT)(1/cos theta) = theta/DT

The formula for theta/it is (-10/252)x(1/0.9165) = 0.0175 rad/sec.

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The ratio of the distance traveled to the amount of time spent traveling may be used to calculate speed.

The average speed of the aircraft when it first takes off is roughly 110.8 mph

Generally, 145 miles separate Portland, Oregon, and Seattle, Washington. This is the distance between the two cities.

The reduction in travel time that results from an increase in speed of 20 miles per hour is equal to minutes.

The required beginning speed of the aircraft, denoted by the letter v;

t=145/v

t-(12/60)=45/v+20

Therefore;

\(\frac{145}{v}-\frac{12}{60}=\frac{145}{v+20}\)

Which gives;

\(\frac{145}{v+20}-\frac{145}{v}+\frac{12}{60}=0\)

Therefore;

0.2·v² + 4·v - 2,900 = 0

v ≈ ±110.8 mph

The initial average speed of the airplane,

v≈ ± 110.8 mph

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Answer:

2.6373×10^1

Step-by-step explanation:

When writing a number in scientific notation, we want to format it this way:

[the number]×10^[an exponent]

The purpose of using scientific notation is to write very big or very small numbers in an easy way. The first number in the above needs to be greater than 1 but less than 10, and we can accomplish this by moving the decimal place. In this case, 26.373 is greater than 10 and we can meet this criterion by moving the decimal place once to the left to make 2.6373.

Because we moved the decimal place one place to the left, we know that the exponent of 10 should be 1.

2.6373×10^1

I hope this helps!

Answer:

x = 6

Step-by-step explanation:

Given

4x - 2 = 2x + 10 ( subtract 2x from both sides )

2x - 2 = 10 ( add 2 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

As per the combination method, there are 1260 ways in which a team of 10 students with 6 boys and 4 girls can be formed from a middle school classroom containing 15 students with 9 boys.

To solve this problem, we need to use the concept of combinations. A combination is a way of selecting items from a larger group where the order of selection does not matter. In this problem, we are selecting a team of 10 students, and the order in which we select the students does not matter.

Using this formula, we can find the number of ways to select 6 boys from a group of 9 as:

⁹C₆ = 9! / (6! x (9-6)!) = 84

Similarly, the number of ways to select 4 girls from a group of 6 is:

⁶C₄ = 6! / (4! x (6-4)!) = 15

To find the total number of ways to form a team of 10 students with 6 boys and 4 girls, we need to multiply the number of ways to select 6 boys and 4 girls. This is because the selection of boys and girls is independent of each other, and we can choose them in any order.

Therefore, the total number of ways to form a team of 10 students with 6 boys and 4 girls is:

84 x 15 = 1260

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Using function concepts, it is found that:

a. The amount of the air in the tank is a function of the number of minutes, as each input is mapped to only one output.

b. The domain is [0,50], and is a continuous domain.

For the relation in this problem, the input and the output are given as follows:

For each minute, there can only be one possible amount, that is, each input is mapped to only one output, hence the amount of the air in the tank is a function of the number of minutes.

The domain of a function is the set that contains all possible values for the function.

The amount of air will be of 0 when:

48t = 2400

t = 2400/48

t = 50.

That is, it will take 50 minutes to remove all air from the tank, hence the domain is [0,50]. The time in minutes can assume decimal values, such as 10.5 minutes, hence the domain is continuous.

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Answer:

y = 1/2x + 3

Step-by-step explanation:

The slope of a parallel line is the same as the original.

Find the new y-intercept.

y = 1/2x + b

2 = 1/2(-2) + b

2 = -1 + b

3 = b

y = 1/2x + 3

Best of Luck!

The radius of the sector of area 135π is 15.

A sector is a geometric figure bounded by two radii and the included arc of a circle.

To calculate the radius of the sector, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the radius of the sector is 15.

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Answer:

8

Step-by-step explanation:

Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54. What is the oldest Kim could be?

J + k < 54 when  J = 5k + 6 so:

5k + 6  + k < 54

6k + 6 < 54

subtract 6 from both sides:

6k + 6 - 6 < 54 - 6

6k < 48

divide both sides by 6:

6k/6 < 48/6

k < 8

Kim could be 8 at maximum.

In linear equation, 951.8 square kilometers  is the equation that best represents the area of the forest each year.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                   Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The question gives you the formula to use, but it's printed wrong.

The 'x' is an exponent after the (1 + r).

All you have to do is take the formula, and write the numbers into it

that are also given.

The key thing to spot is that the forest is decreasing, so the 'r' is negative,

just as if you had money in a savings account and every year the bank took

6% out of it.

So the formula to use is       f(x)  =  P (1 + r) ^x

P = 2000

r = -0.06

                       f(x)  =  2000 (1 - 0.06)^x

                              =  2000 (0.94)^x

The amount left after 12 years is

                                  2000 (0.94)¹² =

                                  2000 (0.476)  =  951.8 square kilometers.

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Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

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Answer:

congruent, same length

Step-by-step explanation:

The three sides of an equilateral triangle are congruent.

They have the same length.

Answer:

3.4

Step-by-step explanation:

trust me bro also i took the quiz lol

Answer:

A. -3/2

Step-by-step explanation:

Answer: (c) 4 negative unit tiles

Step-by-step explanation:

Answer:

C. is the correct answer

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The 3 is directly outside the parentheses, meaning you need to distribute the 3 to the x and the 4 because they are inside the parentheses. There is no addition, subtraction, or division involved in this so C is correct.

Answer:

C

Step-by-step explanation:

i took the test

Answer:

$1,760

Step-by-step explanation:

800*0.12=96

96*10=960

I=960

960+800=1760

Answer:

1760

Step-by-step explanation:

Answer:

IM NOT ABLE SEE THE QUESTION

Step-by-step explanation:

PLEASE TYPE AND SEND IT

Answer:

jwjwjowowowowowoowow

Therefore, the total cost of air travel and hotel for Cecilia in U.S. dollars is =\(USD3073.04.\)

To calculate the cost of air travel and hotel in U.S. dollars for Cecilia's trip to Singapore, we need to convert the costs from Singapore dollars to U.S. dollars using the given spot rate of SNG1.4140 = USD1.00. The airfare cost of SNG1344.31 and hotel cost of SNG2998.28 can be converted to U.S. dollars to determine the total cost.

To convert the costs from Singapore dollars to U.S. dollars, we multiply the costs by the conversion rate of SNG1.4140 = USD1.00.

For the airfare, the cost in U.S. dollars is calculated as:

USD cost of airfare = SNG1344.31 * (1 USD / SNG1.4140)

For the hotel, the cost in U.S. dollars is calculated as:

USD cost of hotel = SNG2998.28 * (1 USD / SNG1.4140)

Using the conversion rate, we can compute the values:

USD cost of airfare = SNG1344.31 * (1 USD / SNG1.4140) = USD950.44 (rounded to two decimal places)

USD cost of hotel = SNG2998.28 * (1 USD / SNG1.4140) = USD2122.60 (rounded to two decimal places)

Therefore, the total cost of air travel and hotel for Cecilia in U.S. dollars is approximately USD950.44 + USD2122.60 = USD3073.04.

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The probability that you end up wearing two socks of the same color is approximately 0.288 or 28.8%.

To find the probability of randomly selecting and wearing two socks of a specific color, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:

There are a total of 12 socks in the drawer. When you randomly select two socks, there are 12C2 (combinations of 2 from 12) ways to do this.

12C2 = (12 x 11) / (2 x 1) = 66

So, there are 66 possible ways to select two socks from the drawer.

Number of favorable outcomes:

We need to find the number of ways to select two socks of the same color. There are three different possibilities for this - blue, gray, or black socks.

Number of ways to select two blue socks: 4C2 = (4 x 3) / (2 x 1) = 6

Number of ways to select two gray socks: 5C2 = (5 x 4) / (2 x 1) = 10

Number of ways to select two black socks: 3C2 = (3 x 2) / (2 x 1) = 3

Therefore, the total number of favorable outcomes is 6 + 10 + 3 = 19.

So, the probability of randomly selecting and wearing two socks of the same color is:

P(selecting and wearing two socks of the same color) = number of favorable outcomes / total number of possible outcomes

P(selecting and wearing two socks of the same color) = 19 / 66

P(selecting and wearing two socks of the same color) ≈ 0.288

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Answer:

0.7333

Step-by-step explanation:

2021 Math

Proportion of such tomatoes have a diameter between 20 and 26 mm is 0.7333.

It's a way to measure how far each data point is spread from the average value.

let x represents the diameters of cherry tomatoes produced by large farm which is formally distributed with mean = 22m

and, standard deviation= 2.5 mm

Now, proportion of tomatoes have diameter between 20 and 26 mm

=P (20 < x< 26)

=P(20-22 / 2.5 < \(x- \mu/ \sigma\) < 26- 22/2.5)

=P(-0.8 < z < 1.6)

=P(z = 1.6) - P(z=-0.8)

=0.9452 - 0.2119

==0.7333

Hence, proportion of such tomatoes have a diameter between 20 and 26 mm is 0.7333.

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Each of the statements should be completed as follows;

In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values approach negative infinity (-∞) to positive infinity (∞).

In this context, the purple line on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 1.

Additionally, the base value of this exponential growth function f(x) = 3^x + 1 is equal to 1 and its domain includes all real numbers while its range includes all real numbers that are greater than 1 i.e 1 < y < ∞.

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To answer your question, I would need to know the sample size and the number of students who expressed satisfaction with the OPRE 3360 course. With this information, we could conduct a hypothesis test using a one-sample proportion test. We would use the null hypothesis that the proportion of satisfied students is equal to a hypothesized value (for example, 0.5 if we assume that half of all JSOM undergraduate students are satisfied with the course). The alternative hypothesis would be that the proportion of satisfied students is different from the hypothesized value.

Using the .05 level of significance, we would calculate the test statistic and compare it to the critical value from the standard normal distribution. If the test statistic falls within the rejection region (i.e. the absolute value of the test statistic is greater than the critical value), we would reject the null hypothesis and conclude that the proportion of all JSOM undergraduate students who are satisfied with OPRE 3360 course is statistically different from the hypothesized value.

Without the necessary information, it is not possible to provide a definitive answer to your question.
Hi! To answer your question about the proportion of all JSOM undergraduate students who are satisfied with the OPRE 3360 course at a 0.05 level of significance, please follow these steps:

1. Define the null hypothesis (H0): The proportion of satisfied students is equal to a certain value (e.g., 50% or 0.5).
2. Define the alternative hypothesis (H1): The proportion of satisfied students is different from the specified value (e.g., not equal to 50% or 0.5).
3. Collect a random sample of students and calculate the sample proportion of satisfied students (p-hat).
4. Determine the standard error of the proportion: SE = sqrt((p0 * (1 - p0)) / n), where p0 is the proportion from the null hypothesis, and n is the sample size.
5. Calculate the test statistic: Z = (p-hat - p0) / SE.
6. Determine the critical value for a two-tailed test at a 0.05 level of significance (Z-critical = ±1.96).
7. Compare the test statistic (Z) to the critical value (Z-critical). If |Z| > Z-critical, reject the null hypothesis and conclude that the proportion of all JSOM undergraduate students who are satisfied with the OPRE 3360 course is significantly different from the specified value at a 0.05 level of significance.

Please note that to complete the above steps, you need to provide the specified proportion value (e.g., 50% or 0.5) and the data from a random sample of students.

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The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = -log8t as the parent function p(t)-3 represents a vertical translation downward by 3 units.

a. The pH function p(t) = -log8t is a logarithmic function where t represents the concentration of hydrogen ions in a solution.

i. p(t)-3 represents a vertical translation downward by 3 units. This means that the function will shift downward by 3 units at all values of t.

This transformation does not result in a y-intercept because the y-intercept of the parent function is at (1, 0) and remains the same after this translation.

ii. p(t-3) represents a horizontal translation to the right by 3 units. This means that the function will shift to the right by 3 units at all values of t.

This transformation does not result in a y-intercept because the y-intercept of the parent function is at (1, 0) and remains the same after this translation.

iii. -3.p(t) represents a vertical stretch by a factor of 3 and a vertical reflection. This means that the function will be stretched vertically by a factor of 3 and reflected across the x-axis.

Thus, this transformation does result in a y-intercept because the y-intercept of the parent function is at (1, 0) and is multiplied by -3 to become (1, 0*(-3)) = (1, 0).

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(a) 27 outcomes in the sample space are : (1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3), (2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3), (3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) All outcomes in the event that all three members go to the same station are : (1,1,1), (2,2,2), (3,3,3)

(a) The 27 outcomes in the sample space can be represented as ordered triples, where each element corresponds to the station that each family member is assigned to. The possible values for each element are 1, 2, and 3. Therefore, the sample space consists of the following 27 outcomes:

(1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3),

(2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3),

(3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) The outcomes in the event that all three members go to the same station can be found by examining the 27 outcomes in the sample space and selecting those outcomes where all three elements are the same. Therefore, the outcomes in the event that all three members go to the same station are:

(1,1,1), (2,2,2), (3,3,3)

In these outcomes, all three family members are assigned to the same station. There are three such outcomes, since each family member can be assigned to any one of the three stations.

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Answer:

Step-by-step explanation:

56.1,12.1,23.6

Answer:

Step-by-step explanation:

Numbers are x and y, equations below:

Substitute x in the first equation:

Solve for y:

Find x:

Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.

What is triangle ?

A triangle is a polygon with three sides and three angles. The sum of the three angles in a triangle always equals 180 degrees. Triangles can be classified based on the length of their sides or the measure of their angles.

We can use the law of cosines to find the angles. The law of cosines states that for any triangle, the square of one side length is equal to the sum of the squares of the other two side lengths, minus twice the product of the other two side lengths multiplied by the cosine of the angle opposite the first side.

Let A, B, and C be the angles opposite the sides of length 114 meters, 70 meters, and 95 meters, respectively.

We can use the following equation to find angle A:

cos A = (70^2 + 95^2 - 114^2) / (2 * 70 * 95)

Once we have the value of cos A, we can use the inverse cosine function to find the angle A in degrees.

Similarly, we can use the same formula to find the angle B and C.

cos B = (114^2 + 95^2 - 70^2) / (2 * 114 * 95)

cos C = (114^2 + 70^2 - 95^2) / (2 * 114 * 70)

Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.

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