Find the sum of the following fractions. Your answer needs to be a mixed number in simplest form: 4/5 + 2/9

Answer:

-16.15

Step-by-step explanation:

the variable in the equation means that it is ever changing, in this case, ever decreasing.

Answer:

a) 87.91% probability that at most three used the emergency room

b) 20.13% probability that exactly three used the emergency room.

c) 3.28% probability that at least five used the emergency room​

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they use the emergency room, or they do not. The probability of a person using the emergency room is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Sample of 10 people:

This means that \(n = 10\)

20% of the people in a community use the emergency room at a hospital in one year

This means that \(p = 0.2\)

a) At most three used the emergency room

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074\)

\(P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684\)

\(P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020\)

\(P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013\)

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1074 + 0.2684 + 0.3020 + 0.2013 = 0.8791\)

87.91% probability that at most three used the emergency room

b) Exactly three used the emergency room

\(P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013\)

20.13% probability that exactly three used the emergency room.

c) At least five used the emergency room​

\(P(X \geq 5) = 1 - P(X < 5)\)

In which

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)\)

From 0 to 3, we already have in a).

\(P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881\)

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.1074 + 0.2684 + 0.3020 + 0.2013 + 0.0881 = 0.9672\)

\(P(X \geq 5) = 1 - P(X < 5) = 1 - 0.9672 = 0.0328\)

3.28% probability that at least five used the emergency room​

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

Answer:

It was ready at 2:30 pm :)

The value of (f-g)(x) is 2x³ + 7x²-7x-3.

As we know that, the composition of functions is the criteria of combining two or more functions into a single function. A function represents some work. The combination of two or more function always results in a new function.

Given that, f(x) = 2x³ + 7x² - 4x - 5 and g(x) = 3x - 2 and we have to calculate the value of  (f - g)(x).

Suppose h(x) =  (f - g)(x)

Now, we simply have to solve (f - g)(x), let's proceed to solve

=  (f - g)(x)

= f(x)-g(x)

= 2x³ + 7x² - 4x - 5-(3x-2)

= 2x³ + 7x² - 4x - 5-3x+2

= 2x³ + 7x²-7x-3

h(x) = (f - g)(x) = 2x³ + 7x²-7x-3

∴ (f - g)(x) = 2x³ + 7x²-7x-3

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The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

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The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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Answer: 186 cubic in

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given that in 2016, the aquarium had x fish, and in 2019, there were x3 fish. We also know that in 2019, there were 512 fish. So we can set up the equation:

x3 = 512

To solve for x, we need to take the cube root of both sides of the equation:

x = ∛512

Using a calculator or simplifying by prime factorization, we can find that:

512 = 2^9

So,

∛512 = ∛2^9 = 2^3 = 8

Therefore, there were 8 fish in the aquarium in 2016.

Answer:

Let's use algebra to solve the problem. We can start by using the information given to set up an equation relating the number of fish in 2016 (x) to the number of fish in 2019 (x3):

x3 = 512

To solve for x, we can isolate x by dividing both sides of the equation by 3:

x = 512/3

x = 170.67 (rounded to two decimal places)

Therefore, there were approximately 170.67 fish in the aquarium in 2016. However, since we cannot have a fraction of a fish, we can round up to the nearest whole number to get the final answer:

x ≈ 171

So there were 171 fish in the aquarium in 2016.

Step-by-step explanation:

Answer:

P(a junior or a senior)=1

Step-by-step explanation:

The formula of the probability is given by:

P (AB) = P(A)  

Where P(A) is the probability of occurring an event A, n(A) is the number of favorable outcomes and N is the total number of outcomes.

In this case, N is the total number of the students of statistics class.

N=18+10=28

The probability of the union of two mutually exclusive events is given by:

Therefore:

P(a junior or a senior) =P(a junior)+P(a senior)

Because a student is a junior or a senior, not both.

n(a junior)=18

n(a senior)=10

P(a junior)=18/28

P(a senior) = 10/28

P(a junior or a senior) = 18/28 + 10/28

Solving the sum of the fractions:

P(a junior or a senior) = 28/28 = 1

Answer:

y = - x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 9) and (x₂, y₂ ) = (9, 0) ← 2 points on the line

m = \(\frac{0-9}{9-0}\) = \(\frac{-9}{9}\) = - 1

the line crosses the y- axis at (0, 9 ) ⇒ c = 9

y = - x + 9 ← equation of line

Answer:

no hablo espanol papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas

Step-by-step explanation:

Answer:

c+3d+3

Step-by-step explanation:

Answer:

Dividing by a fraction is multiplying by the reciprocal

15.09/1/100=15.09*100=1509

267.4/1/10=267.4*10=2674

Answer:

15.09 ÷ 0.01 = 1509

267.4 ÷ 1/10 = 2674

hope these are the answers you are looking for

Step-by-step explanation:

Answer:

x = 50

Step-by-step explanation:

Answer:

x = 50

Step-by-step explanation:

180 - 75 = 105

2x + 5 = 105

now I subtracted both sides by 5

2x = 100

divide both sides by 2:

x = 100/2

x = 50

Have a nice day!

The larger television is Vehicle Viewing, explanation is mentioned below,

The diagonal of a television refers to the length of a line segment connecting two opposite corners of the screen. It is a way of measuring the size of the television screen, rather than its width or height. The diagonal measurement gives a good indication of the overall screen size and is commonly used as a specification for television screens.

Given that,

Two television,

Vehicle Viewing having diagonal 75 inches

Traveling TV Co having diagonal 8.5 inches

larger television =?

Vehicle Viewing, Inc. has the larger television with a diagonal of 75 inches compared to Traveling TV Co.'s diagonal of 8.5 inches.

This can be determined by simply comparing the two diagonal measurements given.

Hence, the larger television is Vehicle Viewing.

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The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.

What is plane?

In two dimensions, a plane can continue on forever. The lack of breadth. A plane is an example of coordinate geometry. A point's location in a plane is determined by its coordinates.

A plane is a two-dimensional, flat surface that never ends in mathematics. A plane is a two-dimensional equivalent of a three-dimensional equivalent that contains three spatial dimensions, a line, and a point. Planes can resemble subspaces in some higher-dimensional situations, as if the room's walls had been substantially stretched. These walls have their own existence, exactly as in the context of Euclidean geometry.

A flat surface in three dimensions can be represented using the plane equation. There are several approaches for determining the equation for a given function.. The equation for the plane can be expressed in either cartesian form or vector form.

Hence, the general form of the equation is A(x−x1)+B(y−y1)+C(z−z1)=0

Now,

For given two points in (x1,y1),(x2,y2) in coordinate plane

distance between them will be = √((x2-x1)²+(y2-y1)²)

So, distance between  N=(-2,-1) and L=(3,-4)=√((3+2)²+(-4+1)²)

=√(25+9)

=√34

hence,

          The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.

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Answer:

(a) mean = 43.5

(b) median = 44

(c) mode = None

(d) midrange = 79.5

Step-by-step explanation:

I did this with a graphing calculator, the TI-84 Plus CE by Texas Instruments, highly recommend. You can find every function you need for stats in a graphing calculator.

To put the data into your calculator:

'stat' --> ' 1 : Edit...' --> put one value on each row

Go back to the main calculator with '2nd' --> 'quit'

Lastly go back to 'stat' and scroll to 'CALC' at the top, then click the first option, '1 : 1-Var Stats'

If you know the symbols it'll tell you a lot, and there are functions for genuinely everything in stats.

Answer:

440,000

Step-by-step explanation:

The given number i.e. 441,902 rounded to the nearest ten thousand should be considered as the 440,000.

Since the given number is 441,902

We have round the above number to the nearest ten thousand

Since the thousand is less than 5,000 so here it should be 440,000

hence, The given number i.e. 441,902 rounded to the nearest ten thousand should be considered as the 440,000.

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Answer:

J is the answer ............

Answer:

The answer is G.

Step-by-step explanation:

Answer:

  9.2

Step-by-step explanation:

You want the distance between A(2, 0) and B(0, 9).

The distance formula is based on the Pythagorean theorem. It tells you the distance between (x1, y1) and (x2, y2) is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, this becomes ...

  d = √((0 -2)² +(9 -0)²) = √(4+81) = √85

  d ≈ 9.2

The distance between A and B is about 9.2 units.

Answer:

X = 3

Step-by-step explanation:

To solve for the value of x, you need to get rid of the fraction first, so you have to multiply each side of the original equation by 2, which will get you 6+8x=10x.

Then, you subtract both sides by 8x, which will get you 6=2x. After that, you divide each side by 2, which leaves you with 3=x. So, the answer is X = 3.

Picture explanation:

Answer:

X=3

The correct expanded form using Laws of exponents is:

Two-thirds times two-thirds times two-thirds times two-thirds

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Now, we want to solve the expression given as: (²/₃)⁴

When we expend this, we arrive at:

²/₃ × ²/₃ × ²/₃ × ²/₃

This among the options is Option A which is:

Two-thirds times two-thirds times two-thirds times two-thirds

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Answer:

212

Step-by-step explanation:

3 goes into 6 = 2 times

3 goes into 3 = 1 time

3 goes into 6 = 2 times

2 → 1 → 2 = 212

1. The volume of the black bag is 1728 cubic inches. 2. The volume of the blue bag is 2700 cubic inches. 3. The black bag will fit in the Check Box. 4. The bigger suitcase is 27 times larger than the smaller suitcase.

Volume, which is commonly expressed in cubic units, is the amount of space occupied by a three-dimensional object. By multiplying an object's length, breadth, and height, as well as other formulas depending on the shape of the object, one can get the volume of the thing. Volume is a key concept in many practical applications, including calculating container capacity, constructing structures, and estimating the amount of material required for a construction project. Volume is utilised in many branches of mathematics, science, and engineering.

For the given dimensions of the bags we have:

1. The volume of the black bag is:

18 x 12 x 8 = 1728 cubic inches

2. The volume of the blue bag is:

18 x 15 x 10 = 2700 cubic inches

3. The black bag will definitely fit in the Check Box because its volume of 1728 cubic inches is less than the volume of the Check Box, which is 2772 cubic inches.

4. The ratio of bigger suitcase to smaller suitcase is:

75 x 20 x 18 = 27000 cubic inches

25 x 8 x 9 = 1800 cubic inches

27000 / 1800 = 27

The bigger suitcase is 27 times larger than the smaller suitcase.

5. Now, if the watermelons is about 10 inches long and 9 inches wide, then its height would be:

720 = 10 x 9 x H

720 = 90H

H = 8 inches

The maximum amount of watermelons that can fit are:

27000 / 720 = 37.5 watermelons = 37 watermelons.

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The boat is moving at a speed of 8 miles per hours in still water.

In this problem we find that the absolute speed of a boat (v''), in miles per hour, is the combination of the speed of the boat in still water (v) and the stream speed (v'), in miles per hour. If we assume that the boat travels at constant speed, then we have the following two equations:

Upstream

v - v' = x / t

v - 4 = 9 / t                                       (1)

Downstream

v + v' = x / (3 - t)

v + 4 = 9 / (3 - t)                              (2)

By (1) and (2):

4 + 9 / t = 9 / (3 - t) - 4

9 / t - 9 / (3 - t) = - 8

9 / (3 - t) - 9 / t = 8

9 · t - 9 · (3 - t) = 8 · t · (3 - t)

9 · t - 27 + 9 · t = 24 · t - 8 · t²

18 · t - 27 = 24 · t - 8 · t²

8 · t² - 6 · t - 27 = 0

By quadratic formula we find that t₁ = 9 / 4 h and t₂ = - 3 / 2 h. Only the first root is physically reasonable. Finally, we find the speed of the boat in still water:

v - 4 = 9 / t

v = 4 + 9 / t

v = 4 + 9 / (9 / 4)

v = 8 mi / h

The speed of the boat in still water is equal to 8 miles per hour.

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Answer:

This should be a permutation

Step-by-step explanation:

P (n, r) = n!/(n-r)!

P (12,5) = 12!/(12-5)!

P (12,5) = 12!/7!

P(12,5) = 95040