Please help- will give brainlist

Please Help- Will Give Brainlist

Answers

Answer 1

Answer:

No its C sorry

Step-by-step explanation:

Answer 2

Answer:

The answer is (c) 25π

Step-by-step explanation:

Area =πr²

r=diameter÷2

10÷2=5

Area=π * 5²

Area =25π


Related Questions


Trevor bought 7 kilograms of apples and 0.9 kilograms of oranges. How much fruit did he buy
in all? Please helpv

Trevor bought 7 kilograms of apples and 0.9 kilograms of oranges. How much fruit did he buyin all? Please

Answers

Answer:

7.9 kg

Step-by-step explanation:

7kg apples+0.9kg oranges=7.9kg in total

Which expression is equivalent to 2/3+2/5

Answers

Given:-

\( \large\sf{ \bold{\frac{2}{3} + \frac{2}{5} }}\)

\( \: \)

Solution:-

\( \sf \large{↣ \frac{2}{3} + \frac{2}{5} }\)

\( \: \)

\( \sf \large{ ↣\frac{2 \times 5 + 3 \times 2}{3 \times 5} }\)

\( \: \)

\( \sf \large{ ↣\frac{10 + 6}{15} }\)

\( \: \)

\( \large{↣\boxed{ \sf{ \purple{ \: \frac{16}{15} \: }}}}\)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

△ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘.

What is CA ?

Answers

The value of side CA of the right angle triangle is 8.85.

What is trigonometry?

Trigonometry is the branch of mathematics that set up a relationship between the sides and angles of right-angle triangles. The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths.

Given that △ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘.

The value of side CA is calculated, from the right angle triangle applying the angle property,

tan41 = (7.7)/(CA)

CA = (7.7)/(tan41)

CA = 8.85

Therefore, the value of side CA of the right angle triangle is 8.85.

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ABC has a right angle at C, BC=7.7 centimeters, and mA=41.What is CA ?

julian needs to spend at least seven hours each week practicing the drums. he has already practiced five and one third hours this week. he wants to sp

Answers

The minimum number of hours is 5/6 and the inequality is x ≥  5/6 hours.

What exactly is an inequality?

An inequality is a relationship that compares two numbers and perhaps other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.

According to the given data:

Let x = the number of hours practicing the drums

we know that Julian needs to spend at least seven hours each week practicing

the drums x ≥ 7  hours

He has already practiced 5*(1/3) hours this week.

Convert mixed number to an improper fraction 5*(1/3)  = 16/3hours.

Subtract 16/3 from 7,

7 - (16/3)

= 5/3

Divide 5/3 by 2,

(5/3)/2

=5/6

Hence,

The inequality that represent the minimum number of hours he needs to practice on each of the two days is x ≥  5/6 hours.

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The given question is not complete.

Julian needs to spend at least seven hours each week practicing the drums. He has already practiced 5 1/3 hours this week. He wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours he needs to practice on each of the two days.

Henry buys a softball for $16 plus a 9% tax. Ella buys a pair of shoes for $17 plus a 9% tax. Enter the difference in the
amount Henry and Ella paid, including tax. Round your answer to the nearest cent.​

Answers

Answer:

$1.09

Step-by-step explanation:

Henry: 16 increase 9% =

16 × (1 + 9%) = 16 × (1 + 0.09) = 17.44

Ella: 17 increase 9% =

17 × (1 + 9%) = 17 × (1 + 0.09) = 18.53

Difference: 18.53 - 17.44 = 1.09

Explain How can you describe a proportional relationship with a number?

NO TROLL ANSWERS!!

Answers

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

hope this helps

A proportional relationship is states that they are the same. For example, 1/2 and 6/12 have a proportional relationship, which means they are the same.

How to find a quadratic equation with y-intercept and vertex? Explain with examples.

Answers

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

Step 1: Identify the coordinates of the y-intercept. The y-intercept has the form (0, c), where c is the y-coordinate.Step 2: Identify the coordinates of the vertex. The vertex has the form (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the quadratic equation.Step 3: Substitute the coordinates of the y-intercept and vertex into the general form of the quadratic equation, y = ax^2 + bx + c.Step 4: Solve the resulting system of equations to find the values of a, b, and c.Step 5: Substitute the values of a, b, and c back into the general form of the quadratic equation to obtain the final equation.

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Start with the standard form of a quadratic equation: y = ax^2 + bx + c, where a, b, and c are constants.Use the vertex form of a quadratic equation: y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.Substitute the vertex coordinates (h, k) into the equation to obtain the equation in vertex form.Use the y-intercept to find another point on the curve. The y-intercept has the form (0, c), where c is the value of y when x is zero.Substitute the coordinates of the additional point into the equation to obtain a system of two equations. Solve the system to find the values of a, b, and c.Substitute the determined values of a, b, and c into the standard form of the quadratic equation to obtain the final equation.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

Using the vertex form, we have y = a(x - 2)^2 - 1.Substituting the y-intercept coordinates, we get 4 = a(0 - 2)^2 - 1, which simplifies to 4 = 4a - 1.Solving the equation above, we find a = 1.Substituting the values of a and the vertex coordinates into the vertex form equation, we have y = 1(x - 2)^2 - 1.Expanding the equation and simplifying, we get y = x^2 - 4x + 3.The final quadratic equation with the given y-intercept and vertex is y = x^2 - 4x + 3.

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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most mis's use sophisticated mathematical models or statistical techniques. group of answer choices true false

Answers

The statement "Most MIS's use sophisticated mathematical models or statistical techniques" is generally true.

Management Information Systems (MIS) play a crucial role in modern organizations by providing valuable insights into various aspects of the business.

These systems gather data from different sources and transform it into meaningful information for decision-making purposes.

To make sense of the collected data, MIS rely on sophisticated mathematical models and statistical techniques.

Mathematical models are used to represent real-world situations and relationships mathematically.

These models can range from simple equations to complex algorithms that simulate and predict business processes.

By using mathematical models, MIS can analyze data, identify patterns, and make predictions or projections.

Statistical techniques, on the other hand, provide methods for summarizing and analyzing data to extract meaningful information.

MIS employ statistical techniques such as regression analysis, hypothesis testing, data visualization, and forecasting to uncover insights and support decision-making.

By leveraging these sophisticated mathematical models and statistical techniques, MIS can handle large volumes of data, identify trends and patterns, perform predictive analysis, and provide valuable insights for effective decision-making in areas such as resource allocation, strategic planning, inventory management, and customer behavior analysis.

Therefore, it is safe to say that most MIS's utilize sophisticated mathematical models and statistical techniques to process and analyze data, enabling organizations to make informed decisions based on accurate and meaningful information.

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Use polar coordinates to find the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 36 and outside the cylinder x^2 + y^2 = 1.

Answers

The required volume of the given solid is (√16 - r²) -(-√16 - r²).

What is volume?

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.

The cubic meter (m3), a derived unit, is the SI unit of volume.

So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.

We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.

The solid's volume is (√16 - r²) -(-√16 - r²).

Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).

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Correct question:

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

The frequency table shows the results of a survey that asked 175 high schoolers how they learn about news stories.

What is the frequency of a tenth grader getting their news from the Internet?

And please, maybe, explain how to get to the answer so I can figure this kind of stuff out?? Thanks so much if u will :) Max points!!

The frequency table shows the results of a survey that asked 175 high schoolers how they learn about

Answers

Answer:

hi i think the answer shouldbe 34/43 as its out of 43 and there is 34 people on the internet. I think this should be write but it may  be wrong. if this is right please vote for brainliest. i hope my answer is right and this helps bye.

is this answer, right?

is this answer, right?

Answers

Answer:

1) Incorrect should be 35%, 2)incorrect should be 23%

Step-by-step explanation:

37 + 24 = 61   61 + 54 = 115   115 + 36 = 151 college students

1) 54  =   x                    2)  36 = x

  151 = 100                       151 = 100

151x/151 = 5400/151    151x/151 = 3600/151

     x = 35.7...                      x = 23.8...

  do not round              do not round

up since you can't      up since you can't

 get more people       get more people

find
the
area .please help​

findthe area .please help

Answers

Answer:

The area is 23.49 cm²

Step-by-step explanation:

Let us solve the question

In the given triangle

∵ The base of the triangle has a length of 8.7 cm

The base = 8.7 cm

∵ The height of this base has a length of 5.4 cm

The height = 5.4 cm

The area of the triangle = \(\frac{1}{2}\) × base × height

→ Substitute the values of the base and the height

∴ The area of the triangle = \(\frac{1}{2}\) × 8.7 × 5.4

The area of the triangle = 23.49 cm²

The area is 23.49 cm²

Answer:

Area of a triangle= 1/2 b×h

base= 8•7

height= 5•4

1/2× 8•7×5•4

Area= 23•49

~23•5

A consumer charges a 2530.16 purchase on the credit card the card has a daily interest rate of .042% if the consumer piece of the balance at the end of 30 days how much more in interest will they pay for the purchase? A point $.32 be $3.19 C $31.88 D $318.78

Answers

Answer:

$31.88

Step-by-step explanation:

Given

Consumer charges = 2530.16cents

Consumer charges in dollars = $25.3016

Interest rate per day = 0.042%

Interest gotten per day = 0.042×25.3016

Interest per day = $1.06266

Interest in 30 days = ,30×1.06266

Interest in 30 days = $31.88

Answer:

c pls mark barliest

Step-by-step explanation:

School ends at 3:15 pm. The school provides after -school care for a maximum of 150 minutes after school ends. When is the latest time for pick up?

Answers

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

How can minutes be converted into hours?

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

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let x(t) = cos(75t). if we sample x(t) at the nyquist frequency, what is the resulting discrete frequency

Answers

If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.

In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.

Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.

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Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used.

Simplify the given polynomials. Then, classify each by its degree and number of terms.

Polynomial 1: (3z 4)(4s + 8)

Polynomial 2: (5g2 + 7g)• }(10z2 - 4)

Polynomial 3: 3(8g2 + 4r - 2) 6(-4:2 - 23 + 3)

Polynomial

Simplified Form

Name by

Name by

Degree

Number of Terms

Polynomial *

trinomial

Polynomial 2

linear

Polynomial 3

12

12x + 20 monomial 7x + 2 constant binomial

12x2 + 233 - 2

3-2 + 4r - 2

quadratic

Answers

Polynomial 1 is a trinomial after simplification, as it has three terms. Its degree is 2 since the highest power of its variables (s and z) is 2.

Polynomial 2 is a linear polynomial with only one term and degree 1 since the highest power of the variable (g) is 1. Polynomial 3 is also a linear polynomial with only one term and degree 1 since the highest power of the variables (g and r) is 1.

In summary, we are asked to simplify three polynomials and classify them based on their degree and number of terms. Polynomial 1 is a trinomial with a degree of 2. Polynomial 2 and 3 are both linear polynomials with a degree of 1.

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On a family camping trip, 5 backpacks can fit in the trailer for every 3 people. if 9 people are going on the trip, how many backpacks can fit? 12 backpacks 14 backpacks 15 backpacks 24 backpacks

Answers

15 bags are expected for the journey for 9 people to fit backpacks in the trailer.

The fundamental principle of multiplication

To calculate the sum of two or more numbers, utilize the mathematical operation of multiplication. If an event can happen in m different ways and a second event can happen in n different ways after it, then the two events that happen in succession can happen in m n distinct ways.

Given that 5 backpacks can fit in the trailer for every 3 people.

Then 3 people = 5 backpacks

1 people = \(\frac{5}{3}\) backpacks

therefore  If 9 people are going on the trip, then;

9 people = \(\frac{5}{3}*9\) backpacks

= 5 x 3

= 15 backpacks

Hence, the trailer can fit 15 backpacks if 9 people go on the trip.

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Evaluate |2x+y-3z| for x=-2, y=10, and z=3.

Answers

Answer:

|2x + y - 3z|

Plug in the values

|-4 + 10 - 9|

= |-3|

= 3

Step-by-step explanation:

the answer is (3) because when all the letters are turned into numbers then solved it becomes [-4+10+(-9)] then you have to turn it into a positive because of the lines.

2.1. how many bit strings of length 10 contain: (a) exactly four 1s? (b) at most four 1s? (c) at least four 1s? note: justify your answers

Answers

Bit strings of length 10 contain

(a) 210 bit strings of exactly four 1s,

(b) 386 bit strings of at most four 1s,

(c) 848 bit strings of at least four 1s.

How many bit strings of length 10 contain exactly four 1s?

(a) To count the number of bit strings of length 10 that contain exactly four 1s, we can use the binomial coefficient formula:

C(10, 4) = 10! / (4! * (10-4)!) = 210

Here, C(10, 4) represents the number of ways to choose 4 positions out of 10 for the 1s, and the remaining positions must be filled with 0s.

How many bit strings of length 10 contain at most four 1s?

(b) To count the number of bit strings of length 10 that contain at most four 1s, we need to count the number of bit strings with 0, 1, 2, 3, or 4 1s and add them up. We can use the binomial coefficient formula for each case:

C(10, 0) + C(10, 1) + C(10, 2) + C(10, 3) + C(10, 4) = 1 + 10 + 45 + 120 + 210 = 386

How many bit strings of length 10 contain at least four 1s?

(c) To count the number of bit strings of length 10 that contain at least four 1s, we can count the total number of bit strings and subtract the number of bit strings with fewer than four 1s.

The total number of bit strings is \(2^{10}\)= 1024.

The number of bit strings with fewer than four 1s is the same as the number of bit strings with at most three 1s, which we found in part (b):

\(2^{10}\)- C(10, 0) - C(10, 1) - C(10, 2) - C(10, 3) = 1024 - 1 - 10 - 45 - 120 = 848

Therefore, there are 210 bit strings of length 10 that contain exactly four 1s, 386 bit strings of length 10 that contain at most four 1s, and 848 bit strings of length 10 that contain at least four 1s.

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the bases of a trapezoid have lengths 5050 and 7575. its diagonals have lengths 3535 and 120120. find the area of the trapezoid.

Answers

The area of the trapezoid is approximately 2234.375 square units.

To find the area of a trapezoid, we can use the formula:

\(Area = (sum of the bases) * (height) / 2\)


Given that the lengths of the bases are 50 and 75, we can substitute these values into the formula:

\(Area = (50 + 75) * (height) / 2\)

Next, let's find the height of the trapezoid using the diagonals. The diagonals of a trapezoid divide it into four triangles. We can use the Pythagorean theorem to find the height of one of these triangles.

In one of the triangles, the base is 50, the diagonal is 35, and the height is unknown. We can use the Pythagorean theorem:

\(50^2 = 35^2 + height^2\)
Simplifying the equation:

\(2500 = 1225 + height^2\)


Subtracting 1225 from both sides:

\(height^2 = 1275\)

Taking the square root of both sides:

\(height ≈ √1275 ≈ 35.71\)

Now that we have the height, we can substitute it back into the formula:

\(Area = (50 + 75) * 35.71 / 2\)

Calculating:

\(Area ≈ 125 * 35.71 / 2Area ≈ 2234.375\)

Therefore, the area of the trapezoid is approximately 2234.375 square units.

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find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. label the points of intercepts of the curves. sketch the region, the solid, and a typical disk or washer . show all your work.

Answers

The volume of the solid the region defined by the given curves must be rotated about the x-axis is V = \(\frac{384\pi }{5}\).

Given that,

The region defined by the given curves must be rotated about the x-axis to determine the solid's volume, which is y =6 -x², y =2.

We know that,

Take the equation of the curves about the x- axis

y =6 -x², y =2.

Substitute y = 2 in equation y = 6 - x²

2 = 6 - x²

-x² = 2-6

x² = 4

Taking square root on both sides

x = ±2

Now, volume formula is define by using washer method

V =  \(\pi \int\limits^a_b {[f(x)]^2 - [g(x)]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {[6-x^2]^2 - [2]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {(36 + x^4 - 12x^2 - 4}) \, dx\)

V = \(\pi \int\limits^2_{-2} {(x^4 - 12x^2 - 32)} \, dx\)

V = \(\pi( [\frac{x^5}{5}] - 12\times\frac{x^3}{3} -32x)^2_{-2}\)

V = \(\pi[( [\frac{2^5}{5}] - 12\times\frac{2^3}{3} -32(2))-([\frac{-2^5}{5}] - 12\times\frac{-2^3}{3} -32(-2))]\)

V = \(\pi[( [\frac{32}{5}] - 4 \times 8 -64)-( [\frac{-32}{5}] - 4\times(-8) +64)]\)

V = \(\pi[( [\frac{32}{5}] - 32 -64)-( [\frac{-32}{5}] +32 +64)]\)

V = \(\pi( [\frac{384}{5}] )\)

V = \(\frac{384\pi }{5}\)

Therefore, The volume of the solid is V = \(\frac{384\pi }{5}\)

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Which slope is shallower a slope of 3/4 or 4/3?

Answers

Answer:

-> a slope of 3/4

Step-by-step explanation:

The larger the slope the bigger the incline, since 3/4 < 4/3, 3/4 is a shallower slope.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

The equation y= ax? describes a parabola. If the value of a is positive, which
way does the parabola open?

Answers

Answer:

upwards or to the right

Step-by-step explanation:

If the a value is positive, then the parabola opens upward or to the right, and if the a value's negative, it opens down or to the left. Hope this helps!

Find the sum.
b/ b^2+4b+4 + 9/b^2+7b+10

Answers

Answer:

11b^3+14b^2+b+9

---------------------------

         b2

Step-by-step explanation:

Help asap. This is extremely important

Help asap. This is extremely important

Answers

Answer:

the answer is a

Step-by-step explanation:

f+g(x) =2x+6

f(x)+g(x)=(x2+2x)+(6-x2)

x2+2x)+(6-x2)

2x+6

=A

a diver was collecting water samples from a lake. he collected a sample at every 3m, starting at 5m below water surface. the final sample was collected at a depth of 35m.how many sample did he collected​

Answers

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

an education can be the key to higher earnings. in a u.s. census bureau study, high school graduates earned $30,400 per year. associate’s degree graduates averaged $38,200 per year. bachelor’s degree graduates averaged $52,200 per year

Answers

The given statement "an education can be the key to higher earnings" is true, as a U.S. Census Bureau study shows that earnings increase with the level of education.

The study shows that high school graduates earned $30,400 per year, associate’s degree graduates averaged $38,200 per year, and bachelor’s degree graduates averaged $52,200 per year. This indicates that an individual's earnings will increase with their level of education.

As an individual's level of education increases, their earnings also increase. The U.S. Census Bureau study demonstrates that a high school graduate earns less than an associate's degree graduate, and an associate's degree graduate earns less than a bachelor's degree graduate.

This is because education enables an individual to obtain better job opportunities and more specialized skills in their area of interest, which are valued in the job market. As a result, higher education has a significant impact on an individual's income.

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Identify the pattern for the following sequence. Find the next three terms in the sequence.

-1, 3, -9, 27, ____, ____, ____,...
a.
Multiply by 3; 81, 243, 729
b.
Multiply by -3; -81, 243, -729
c.
Multiply by -3; 81, 243, 729
d.
Multiply by 3; -81, -243, -729


Please select the best answer from the choices provided

A
B
C
D

Answers

B) multiply by (-3); -81, 243, -729

Answer:

b

Step-by-step explanation:

edge 2021

Marco has two bags of candy. One bag contains three red lollipops and
2 green lollipops. The other bag contains four purple lollipops and five blue
lollipops. One piece of candy is drawn from each bag. What is the probability
of choosing a green lollipop and a purple lollipop?

Answers

The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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Question 6 (4 points) Three people use the following procedure to divide a (perfectly divisible and homogenous) cake. Player 1 first divides the cake into two pieces. Next, player 2 selects one of the two pieces. Player 1 gets the other share, while player 2 must now divide the piece he or she picked. Finally, player 3 chooses one of the two pieces that player 2 just created, and player 2 consumes what remains. Suppose that each player cares only about the size of the piece of cake he or she ultimately obtains. Compute the subgame perfect Nash equilibrium (please provide complete strategies, not just the equilibrium payoffs).

Answers

The subgame perfect Nash equilibrium involves Player 1 receiving a piece that is no less than 1/4 of the original cake, Player 2 receiving a piece that is no less than 1/2 of the cake, and Player 3 receiving a piece that is no less than 1/4 of the cake. Player 2 obtains the largest piece at 1/2 of the cake, while Player 1 gets a share that is no less than 1/4 of the cake, which is larger than Player 3's share of the remaining cake.

The subgame perfect Nash equilibrium and complete strategies are as follows:

First subgame: Player 1 splits the cake into two pieces. Player 1 takes the smaller of the two pieces, while Player 2 takes the larger. Next, Player 2 divides the larger piece into two. Player 2 chooses the piece that is equal in size to the smaller piece of the initial division. Player 2 gives the other piece to Player 3, who must now select one of the two pieces. If Player 3 selects the smaller piece, Player 2 will obtain the larger of the two pieces that Player 2 divided, which is greater than or equal in size to the piece Player 2 gave to Player 3. As a result, Player 3 chooses the larger of the two pieces. Therefore, the subgame perfect Nash equilibrium involves Player 1 receiving a piece that is no less than 1/4 of the original cake, Player 2 receiving a piece that is no less than 1/2 of the cake, and Player 3 receiving a piece that is no less than 1/4 of the cake. Player 2 obtains the largest piece at 1/2 of the cake, while Player 1 gets a share that is no less than 1/4 of the cake, which is larger than Player 3's share of the remaining cake.

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