find the square of 2m^2 - 2/3n^2

Using complementary events, considering a \(\frac{1}{4}\) probability of drawing a red marble, the probability of not drawing a red marble is of \(\frac{3}{4}\).

They are mutually exclusive events which have the sum of their probabilities as 1.

In this problem, we consider that there is a \(\frac{1}{4}\) probability of drawing a red marble, and since drawing a red marble and drawing a non-red marble are complementary events, we have that:

\(\frac{1}{4} + p = 1\)

\(p = \frac{3}{4}\)

The probability of not drawing a red marble is of \(\frac{3}{4}\).

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Answer:

25x²-60x+36

Step-by-step explanation:

(5x-6)²

Expand the brackets.

(5x-6)(5x-6)

5x(5x-6)-6(5x-6)

Multiply.

25x²-30x-30x+36

Add or subtract the like terms.

25x²-60x+36

Perfect squares trinomials are those expressions which are found by squaring binomial expressions. The expansion of the given binomial expression, (5x - 6)² is (25x² + 36 - 60x).

Perfect squares trinomials are those expressions which are found by squaring binomial expressions. A few examples of perfect squares trinomials are,

a² + b² + 2ab = (a + b)²

a² + b² - 2ab = (a - b)²

The expansion of the given binomial expression, (5x - 6)² can be done as,

(5x - 6)²

= (5x)² + 6² - 2(5x)(6)

= 25x² + 36 - 60x

Hence, The expansion of the given binomial expression, (5x - 6)² is (25x² + 36 - 60x).

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Answer: \(59^{\circ}\)

Step-by-step explanation:

In triangle ABC, we know that \(\angle ABC=130^{\circ}-\theta\). So, by the inscribed angle theorem, minor arc AC is equal to \(260^{\circ}-2\theta\).

Thus, major arc AC is equal to \(100^{\circ}+2\theta\).

Using the fact that the angle formed by the two tangents is 38 degrees,

\(\frac{(100^{\circ}+2\theta)-(260^{\circ}-2\theta)}{2}=38^{\circ}\\\\100^{\circ}+2\theta-260^{\circ}+2\theta=76^{\circ}\\\\4\theta-160^{\circ}=76^{\circ}\\\\4\theta=236^{\circ}\\\\\theta=\boxed{59^{\circ}}\)

The farmer will need to buy 2 cans of paint to paint the entire exterior of the silo.

Length of pain covers = 400 squared meters

Assuming that silo is perfectly cylindrical with a height of 20 meters and a diameter of 12 meters.

The formula used to find the exterior surface of the cylinder is:

The surface area of a cylinder = \(2*(3.14)*r^2\) + 2πrh

Surface area of the silo = 2π(6^2) + 2π(6)(20) =\(452.39 m^2\)

To calculate the number of cans of paint needed,

Number of cans of paint = Surface area of silo / Coverage per can

Number of cans of paint  = \(452.39 m^2 / 400 m^2\) per can of paint

Number of cans of paint needed = 1.13 cans

Therefore, we can conclude that the farmer will need to buy 2 cans of paint to paint the entire exterior of the silo.

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The complete question is:

'A farmer is painting his silo. A typical can of paint covers 400 squared meters. How many cans of paint will the farmer need to buy in order to paint the entire exterior of the silo?

Answer:

4

Step-by-step explanation:

if there are 4 puzzles and only 16 participants. Also WHAT??? makes no since what to do

Area = Length X width

Let the width (breadth) = X

The length is double so it is 2x

Area = X * 2x = 2x^2

128 = 2x^2

Divide both sides by 2:

64 = x^2

take the square root of both sides:

x = 8

The breadth = 8 meters

The length = 16 meters

Given that the High Plains Aquifer overlaps so many states, less data is now available to the latter might water use in one state affect water use in another state.

An aquifer is a layer of unconsolidated materials, rock cracks, or water-bearing, porous rock that lies underground. Using a water well, one may draw groundwater from aquifers. The properties of aquifers differ widely.

if a state utilizes excessive amounts of water and is "upstream" from another state. Less data is now available to the latter. Similar to how water is distributed uniformly in a pool, aquifers do the same thing underground; as a result, if one state uses more water than it should, it decreases the levels for all the other states. Due to this, management must now take place at the interstate level with more political entities participating. A resolution is inevitably more difficult the more people involved.

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Answer: 2,754 students

Step-by-step explanation:

18 / 270= 1/15

(1/15)(41,310) = 2,754 students

A school recorded the heights of its students at the beginning and end of the year.

The purpose of this recording is to track the growth and development of the students over the course of the year.

By measuring the heights of the students at the beginning and end of the year, the school can analyze the growth patterns of the students. This data provides valuable insights into the physical development of the students and can be used for various purposes.

It helps monitor the overall health and well-being of the students and can also be used to identify any abnormal growth patterns or potential health issues. Additionally, the recorded heights can be compared to standard growth charts to assess whether the students' growth is within the normal range for their age and gender.

This information is useful for parents, educators, and healthcare professionals in understanding the physical development of the students.

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Let's evaluate :

Hey there!

2x³ + 5x² - 10

It's given that the value of x is -2. So substitute it in the place of x in the equation.

2(-2)³ + 5(-2)² - 10

= 2 × -8 + 5 × 4 - 10

= -16 + 20 - 10

= 4 - 10

= - 6

Hope it helps ya!

Answer:

17−7

Step-by-step explanation:

Hope this helped good luck in your work!

To determine how far Turtlelini walked, we can set up a proportion using the scale on the map.

Let's set up the proportion:

Distance on the map (in inches) / Actual distance walked (in miles) = Scale on the map (in inches) / Scale conversion (in miles)

We are given:

Distance on the map = 0.6 inches

Scale on the map = 1.5 inches

Scale conversion = 0.8 miles

Plugging in the values, we have:

0.6 inches / Actual distance walked (in miles) = 1.5 inches / 0.8 miles

Now we can cross-multiply and solve for the actual distance walked:

0.6 inches * 0.8 miles = 1.5 inches * Actual distance walked

0.48 miles = 1.5 inches * Actual distance walked

Dividing both sides by 1.5 inches:

Actual distance walked = 0.48 miles / 1.5 inches

Calculating the result:

Actual distance walked ≈ 0.32 miles (to the nearest tenth of a mile)

Therefore, Turtlelini walked approximately 0.32 miles.

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Answer:

10, 12 and 11

Step-by-step explanation:

On each median , the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.

TZ = 2 × ZX = 2 × 5 = 10

UY = UZ + ZY = 8 + 4 = 12

ZW = \(\frac{1}{3}\) × VW = \(\frac{1}{3}\) × 33 = 11

The 95% confidence interval of true proportion of workers who belong to a union is; CI = (0.29, 0.41)

We are given;

Sample size; n = 600

Sample proportion; p = 35% = 0.35

Formula for confidence interval is;

CI = p ± z√(pq/n)

The z-score at 95% confidence interval is z = 1.96

Thus;

CI = 0.35 ± 1.96√(0.35(1 - 0.35)/600)

CI = (0.29, 0.41)

Thus, the 95% confidence interval of true proportion of workers who belong to a union is; CI = (0.29, 0.41)

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Given the function f : [1, 2] + R is continuous function with f(1) < 1 and f(2) > 8, we have to show that there is a c in (1, 2) so that f(c) = c. This can be proved by using the intermediate value theorem (IVT).

Assume that the function f : [1, 2] + R is continuous on the interval [1, 2] and f(1) < 1 and f(2) > 8. Then, by the IVT, for any number M between f(1) and f(2), there exists a point c in the open interval (1, 2) such that f(c) = M. Since f(1) < 1 < 8 < f(2), we can choose M = c.

Hence, there exists a point c in (1, 2) such that f(c) = c. This completes the proof.Explanation:In mathematics, the intermediate value theorem (IVT) states that for a continuous function f(x) on a closed interval [a, b], if a value y is between f(a) and f(b), then there exists at least one c in the open interval (a, b) such that f(c) = y.

The IVT is used to show the existence of a root of a function or to prove the existence of a solution to an equation. In this problem, we are given a continuous function f(x) on the closed interval [1, 2] with f(1) < 1 and f(2) > 8.

We want to show that there exists a point c in the open interval (1, 2) such that f(c) = c. To do this, we can use the IVT by choosing M = c.

Since f(1) < 1 < 8 < f(2), we know that there exists a point c in (1, 2) such that f(c) = c, which completes the proof.

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You are c) a structure. A structure is a collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.

A structure is a user-defined data type that allows you to group together related data. For example, you could create a structure to store the name, age, and address of a person. The structure would have three variables, each of a different type: a string variable for the name, an integer variable for the age, and a string variable for the address.

The advantage of using a structure is that it allows you to treat the related data as a single unit. This makes it easier to manipulate the data and to pass the data to functions.

The other answer choices are incorrect. A template is a blueprint for creating a generic class or function. An array is a collection of elements of the same type. Local variables are variables that are declared within a function and that are only accessible within the function.

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In the next 10 years there will be 398 racoons in the state park

The annual increase in the population size is defined as a sum of differences: the difference between births less deaths and the difference between immigrants less emigrants, in a given country, territory or geographic area at a given year.

Using the formula

p(t) = p(o) e^ kt

k = 3.5/100 = 0.035

t = 10 years

p(t) = 280 e^ 0.035 ×10

p(t) = 280e^0.35

p(t) = 280 × 1.42

p(t) = 398( nearest whole number)

therefore be after 10 years there will be 398 racoons in the state park.

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The combined area of dark pieces is 253.5 in².

First, Area of 5 light pieces

= length x width

= 3 3/4 x 39

= 15/4 x 39

= 146.25 in²

Now, Area of board

= L x W

= 29 x 39

= 1131 in²

Thus, the combined area of dark pieces

= 1131 - 146.25 x 6

= 253.5 in²

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The set of side lengths that could form a unique triangle is:

B) side lengths: 12 feet, 9 feet, 4 feet

What is triangle ?

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is commonly studied in mathematics. Triangles have a variety of properties and can be classified based on their side lengths and angle measures. The sum of the interior angles of a triangle is always 180 degrees.

According to the question:
The set of side lengths that could form a unique triangle is:

B) side lengths: 12 feet, 9 feet, 4 feet

This is because of the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side. Let's check each set of side lengths:

A) 18 + 9 = 27 > 6, but 18 + 6 = 24 < 9, so this set does not form a triangle.

B) 12 + 9 = 21 > 4, 12 + 4 = 16 > 9, and 9 + 4 = 13 > 12, so this set can form a triangle.

C) 6 + 3 = 9 > 2, but 6 + 2 = 8 < 3, so this set does not form a triangle.

D) 24 + 14 = 38 > 4, but 24 + 4 = 28 < 14, so this set does not form a triangle.

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Q) Which of the following sets of 3 side lengths could form a unique triangle?

A) side lengths: 18 feet, 9 feet, 6 feet

B) side lengths: 12 feet, 9 feet, 4 feet

C) side lengths: 6 feet, 3 feet, 2 feet

D) side lengths: 24 feet, 14 feet, 4 feet

The length of GH is 21 units.

The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

HI * GI = JI * KI

Since KJ is 5 more than GH, we can say:

KJ = GH + 5

KI = KJ + JI

KI = GH + 5 + 46 = GH + 51

From the figure:

GI = GH + HI

Substituting into:

HI * GI = JI * KI

HI * (GH + HI) = JI * (GH + 51)

48 * (GH + 48) = 46 * (GH + 51)

48GH + 2304 = 46GH + 2346

48GH - 46GH =  2346 - 2304

2GH = 42

GH = 42/2

GH = 21 units

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Complete Question

Check attached image

Answer:

x=13

Step-by-step explanation:

9*2+8x-5=3x^2

9*2 = 18

18-5=13

13+8x=3x^2

3x^2 = 9x

13+8x=9x

   -8x -9x

13=x

x=13

Answer: a very straight forward b 2 4 and 6 c 9

Step-by-step explanation:

Answer:

(-2,2) will be the mid point

Step-by-step explanation:

let mid point be x,y

apply mid point formula

x=(x1+x2)/2

y=(y1+y2)/2

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

Answer:

4.55

Step-by-step explanation:

Average Rate of Change formula :

\(A(x) = \frac{f(b)-f(a)}{b-a}\)

============================================================

Solving :

⇒ A(x) = \(\frac{f(6)-f(3)}{6-3}\)

⇒ A(x) = 22.466436 - 8.81340423 / 3

⇒ A(x) = 13.6530318/3

⇒ A(x) = 4.55 (rounded to 2 decimal places)

Find the average rate of change of the exponential equation from x = 3 to x = 6

f(x) = 2x^1.35

i hope it helps

Answer:

17 Gallons!

Step-by-step explanation:

first you are going to want to divide 308 by 7 to get how many miles you can go per gallon

308/7=44

then you are going to divide 748 by 44

748/44=17

I Hope This Helped!!!!

Answer:

0.60

Step-by-step explanation:

becouse of two probability within added gives the above answer

Hi, this question is actually really simple.

Let's consider that one house = 7 matchsticks. This is because, if we count the first two squares given in your question, it will count to 7.

Now we understood that one house has 7 matchsticks. So, if we want two houses, then consider two more square of matchsticks. So, 12. Likewise, for 3 houses , add 2 more squares, thus resulting in 17. For four houses, again add 2 more squares, giving the result as 22 matchsticks.

Note- While adding two more squares for each, do not count the left side 2 matchsticks, as they are combined with the previous matchsticks. I meant that , if you want to know 2nd house matchsticks, count 7+7=14, then subtract 14-2, so 12

Now, the brief answer is:-

1 house = 7 matchsticks

2 houses = 12 matchsticks

3 houses = 17 matchsticks

4 houses = 22 matchsticks

5 houses = 27 matchsticks

Hope it helps you...

(Answered by Benjemin)

Answer:

2=14

3=21

4=28

5=35

Step-by-step explanation:

If 1 house =7 matchsticks

Then 2 houses = x

x=2×7=14 matchsticks

If 2 houses=14 matchsticks

3 houses=x

2x=14×3

Dividing both sides by 2

x=7×3=21

4=28

5=35

Hope it helps