Find the sum of 4√5 and √5 in simplest form. Also, determine whether the result is
rational or irrational and explain your answer.

Answer: 65

Step-by-step explanation:

17 + 48

Step-by-step explanation:

please see the attached picture

The required value of the trigonometric function is sin (α - β) = - 10.96/15.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric ratios are given in the question, as follows:

sin α = -2/5 and cos β = -1/3

So cos α = √1 - (-2/5)² = √(1 - 4/25) = √21/5

And sin β = √1  - (-1/3)² = √(1 - 1/9) = √8/3

We have to determine the value of sin (α - β).

According to trigonometric identity,

sin (α - β) =  sinα cos β - cos α sin β

Substitute the values of sin α = -2/5 and cos β = -1/3,

sin (α - β) = (-2/5)( -1/3) - (√21/5)(√8/3)

sin (α - β) = 2/15 - (√21×8)/15

sin (α - β) = 2/15 - (√168)/15

sin (α - β) = 2/15 - 12.96/15

sin (α - β) = - 10.96/15

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Speed of bicycle in miles per hour will be 12.85 mi/h.

What is the definition of speed?

The following is the definition of speed:

The rate at which the position of an item changes in any direction.

The ratio of distance travelled to time spent travelling is described as speed. Speed is a scalar number since it has just one direction and no magnitude.

Formula for Speed

The speed formula is as follows:

s=d/t

Where,

s denotes the speed in metres per second, d the distance travelled in metres, and t the time in seconds.

Now,

Given Diameter=18 inch

then distance covered by cycle in 4 rotation in one second =4*π*diameter

=4*22/7*18

=226.28

Then Speed=226.28 in/s

As 1 mike=63360 inch and 1 hour= 3600 seconds

then Speed in miles/hour=226.28*3600/63360

=12.85 mi/h

hence,

          Speed of bicycle in miles per hour will be 12.85 mi/h.

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Answer:

4 km

Step-by-step explanation:

There is a period of 40 minutes between 11:40 and 12:20.

[tex]40 \: minutes \: = \frac{2}{3} \: of \: an \: hour[/tex]

[tex] \frac{2}{3} \times \frac{6}{1} kmhr \: = \frac{12}{3} = 4[/tex]

Since the samples of the study are independent, the condition for inference have been met

The body mass index for adults in the United States = 26.8

BMI stands for Body Mass Index

Body mass index of marathon runners = less than 26.8

The random samples = 35

The body mass index of the random samples = 22.7

Standard deviation = 3.1

Then the researchers will conduct a one sample t test for a population mean.

The one sample t-test is is defined as the hypothesis test that check whether the unknow population mean is different from the specific value

Here the samples are independent

Therefore, the condition for inference have been met

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The total optimal solution based on the information will be 49 rupees.

Here, four jobs and four machines are given, with the assignment matrix.

Find out the each row minimum element and subtract it from that row

Find out the each column's minimum element and subtract it from that column.

This assignment problem is being solved using Hungerian Method as the optimal solution is:

J1 to M2, J2 to M4, J3 to M1 and J4 to M3. The total optimal cost is:

= 11 + 13 + 14 + 11

= 49 rupees

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The output of the equation for input of 2 is 1.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

The given equation is:

y = 3x - 5

Here, x is the input value and y is the output value.

Substituting input that is x = 2.

y = 3(2) - 5

y = 6 - 5

y = 1

Hence, the output of the equation for input of 2 is 1.

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The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²

What is meant by a perfect square trinomial?

By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.

Given expression y² - 13y + ?

Comparing with the general equation

a = 1

b = -13

For perfect square trinomial

b² = 4ac

(-13)² = 4 * 1 * c

169 = 4c

c = 169/4

So the expression becomes,

y² - 13y + 169/4 = (y - 13/2)²

Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.

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Answer:

BL

Step-by-step explanation:

because it goes in both directions infintely

Hi there, here's your answer:

To find the answer to this question, let us review all the options given in the question.

a) BL

BL being two ends of a given line that extends infinitely along its axis, forms a line.

b) GK

GK being two distinct lines do not join and hence do not form an independent line.

c) EB

E being a point on the line BL and B being one end of a larger line form a ray.

d) HI

HI being two points on a line GJ form a line segment, which is finite and has definite end points.

Thus, the answer to this question is (a).

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Answer:

they all have flat sides except for the cylinder

Step-by-step explanation:

Its okay we all are bad on some things

Answer: A proper subset of a set A is a subset of A that is not equal to A

Step-by-step explanation:

The local maximums are at x = -4 and x = 4, and the value of the local maximum is f(x) = 1.

For a function f(x), we define a local maximum as a value of x = c such that:

f(c) ≥ f(x)

for any value of x in a given interval.

Here we can see two local maximums on the graph, and we can see that these are at:

x = -4 and x = 4

b) And the local maximum value of f is the value that the function takes in the maximum, we can see that:

f(-4) = f(4) = 1

The value of the local maximum is y = 1.

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Answer:

The slope between the two points would be 5.

Answer: The slope would be 5

Step-by-step explanation:

The answers to the questions are:

a) P(A|B) =  1/3

b) P(B|A) = 1.15

c)  A. A student given a $1 bill is more likely to have kept the money.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Because the probability of 0.659 is almost two times greater than 0.341

Assuming the following table:

                                                  Purchased Gum      Kept the Money    Total

Students Given 4 Quarters              25                              19                      44

Students Given $1 Bill                       13                               26                    39

Total                                                   38                              45                     83

a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.

For this case let's define the following events

B= "student was given $1 Bill"

A="The student spent the money"

For this case we want this conditional probability:

P(A|B) = P(A And B) / P(B)

We have that

P(A) = 38/83,  P(B) = 39/83

P(A And B) = 13/83

And if we replace we got:

P(A|B) =  (13/83)/(45/83) = 13/39 = 1/3

b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.

For this case let's define the following events

B= "student was given a $1 Bill"

A="The student kept the money"

P(A|B) = P(A And B) / P(B)

We have that

P(A) = 45/83,  P(B) = 39/83

P(A And B) = 26/83

And if we replace we got:

P(B|A) =  (45/83)/(39/83) = 45/39 = 1.15

c. what do the preceding results suggest?

For this case the best solution is:

A. A student given a $1 bill is more likely to have kept the money.

Because the probability of 0.659 is almost two times greater than 0.341

Hence, The answers to the questions are:

a) P(A|B) =  1/3

b) P(B|A) = 1.15

c)  A. A student given a $1 bill is more likely to have kept the money.

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The width of the container can be calculated by dividing the product of the length and height by the volume. The width is 28.1 ft.

[tex]30 ft x 7.5 ft = 225 ft^3[/tex]

[tex]1800 ft^3 / 225 ft^3 = 8[/tex]

[tex]225 ft^3 / 8 = 28.125 ft[/tex]

Width = 28.1 ft

To calculate the width of the shipping container, you need to divide the product of the length and height by the volume. The length of the container is given as 30 ft, and the height is given as 7 ft 6 inches or 7.5 ft. Thus, the product of the length and height is [tex]225 ft^3[/tex]. The volume of the container when it is full is given as [tex]1800 ft^3[/tex]. To find the width, divide the product of length and height by the volume. Thus,[tex]225 ft^3 / 1800 ft^3 = 8[/tex]. Then, divide the product of length and height by the result you got in the previous step, that is,[tex]225 ft^3 / 8 = 28.125 ft[/tex]. This is the width of the container. Round this value to the nearest tenth and you get 28.1 ft as the width of the container.

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Answer: the shadow will extend 43.75m

Step-by-step explanation:

Answer:

Step-by-step explanation:

The measure of the two greatest angles is 105° and 45°

Let the angles be 2x, 3x and 7x ...... (i)

According to the 'Angle Sum Property' of triangle,

2x + 3x + 7x = 180°

12x = 180°

x = 15°

Now, put value of x in (i)

2x = 2 × 15 = 30°

3x = 3 × 15 = 45°

7x = 7 × 15 = 105°

so, the two greatest angles are 105° and 45°

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Answer:

(4, -1) and (-6, 9).

Step-by-step explanation:

To find the fourth vertex of a parallelogram, we need to find the vector that represents the displacement from one of the given vertices to another, and then add that vector to the third given vertex. Since parallelograms have opposite sides that are equal in length and parallel, adding the same displacement vector to two of the given vertices will give us the coordinates of the other two vertices.

One possible displacement vector is the difference between the first and second given vertices, or (1 - (-4), -2 - 3) = (5, -5). Adding this vector to the third given vertex, (-1, 4), gives us the fourth vertex at (4, -1).

Another possible displacement vector is the difference between the second and third given vertices, or (-1 - 1, 4 - (-2)) = (-2, 6). Adding this vector to the first given vertex, (-4, 3), gives us the fourth vertex at (-6, 9).

So the two possible locations of the fourth vertex are (4, -1) and (-6, 9).

The solution of inequalities is (1.714 , 4.857).

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

y > 4x-2

2y-x ≤ 8

Now, solving the inequalities.

y > 4x-2 is given by purple region and 2y-x ≤ 8 is shown by Grey region.

The two lines of inequalities intersect at (1.714 , 4.857).

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The quantity of cholesterol in an egg is 272 mg

The quantity of cholesterol in a cupcake is 18 mg

The quantity of cholesterol in a slice of pizza is 9 mg

Let the amount of egg be e

Let the amount of cupcake be c

Let the amount of pizza be p

By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol

e + c + p = 299

The child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol

3c + 4p = 90

By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol

3e + c = 834

e + c + p = 299

3c + 4p = 90

3e + c = 834

solving the simultaneous equation gives

e = 270

c = 18

p = 9

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The equation can be used to calculate the average speed at which Yusef drove is (c) r = 130/2.5

The formula to calculate average speed is:

Average speed = distance traveled / time taken

In this problem, Yusef drove 130 miles in 2.5 hours.

So, we can substitute the values in the formula:

Average speed = 130 miles / 2.5 hours

Simplifying this expression, we get:

Average speed = 52 miles per hour

Therefore, the correct equation to calculate the average speed at which Yusef drove is:

r = 130/2.5 or r = 52

Option C matches this equation, so the answer is C.

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a) The fraction of the stickers that Kate gave to her 6 friends was 1/2.

b) The fraction of Kate's stickers that each friend received from the 1/2 of stickers was 1/12.

The fraction is the portion or part of a whole.

Fractions can be proper, improper, and complex fractions, depending on the relative value of the numerator and the denominator.

The total number of stickers that Kate possesses = 1/1

The fraction Kate kept for herself = 2/5

The remaining portion of Kate's stickers = 3/5 (1 - 2/5)

The fraction Kate gave to her 6 friends to share equally = 5/6 of 3/5 = 1/2

The fraction of Kate's stickers that each friend received = 1/2 ÷ 6 = 1/12

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Answer:

44 in^2

Step-by-step explanation:

V = L×W×H

Bottom rectangle prism

L= 6 W= 4 H= 1

V = 6×4×1

V=24

Top rectangle prism

L= 2 W= 2 H= 5

V=2×2×5

V= 20

Add both of the rectangle prisms

24+25= 44

We can form 15 different 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Out of these, 30 are even numbers. We used the concept of combination to find these numbers.

Combination is a mathematical technique used to calculate the number of ways in which a group of objects can be selected from a larger set, without considering their order.

We can use the combination formula to find the total number of possible combinations:

C(4, 3) = 4! / (3! * 1!) = 4

This means that we can form four different 3-digit numbers using the digits 1, 2, 3, and 4, without repetition.

Now, coming back to our original problem, we need to form 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Using the same combination formula, we can find the total number of possible combinations:

C(6, 4) = 6! / (4! * 2!) = 15

This means that we can form a total of 15 different 4-digit numbers using the given digits.

Next, we need to find out how many of these numbers are even. An even number is a number that is divisible by 2, and in our case, this means that the last digit of the number must be either 2, 8, or a combination of 1 and 7.

To find the number of even 4-digit numbers, we can use the same combination formula, but this time we have to consider only 3 digits (2, 8, and a combination of 1 and 7) for the last digit:

C(3, 1) * C(5, 3) = 3 * 10 = 30

This means that we can form a total of 30 different 4-digit even numbers using the given digits.

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Answer:

  B)  2:3

Step-by-step explanation:

If you have mercury : copper = 1 : 5 and tin : copper = 3 : 10, you want the ratio of mercury to tin.

The ratios can be compared or combined when common components are represented by the same number. Doubling the values in the first ratio, we will have two ratios that both have 10 parts copper.

  mercury : copper = 1 : 5 = 2 : 10

Then ...

  mercury : tin : copper = 2 : 3 : 10

You need 2 parts mercury to 3 parts tin.

  mercury : tin = 2:3 . . . . . . choice B

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a) The probability of rolling a 5 or a number greater than 3 is 1/2.

b) The probability of rolling a number less than 4 or an even number is 5/6.

c) The probability of rolling a 4 or an odd number is 2/3.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

In rolling a six-sided die, the total number of outcomes is 6.

The sample space is {1,2,3,4,5,6}

The probability formula is -

Probability = Number of outcomes corresponding to events / total number of outcomes.

(a)  Let A be the event of rolling a 5. Then A = {5}.

Let B be the event of rolling a number greater than 3. Then B = {4,5,6}.

The event of rolling A or B is given by A∪B = {4,5,6}.

So, apply the probability formula -

P(A∪B) = 3/6 = 1/2

Therefore, the probability value is 1/2.

(b)  Let C be the event of rolling a number less than 4. Then C = {1,2,3}.

Let D be the event of rolling an even number. Then D = {2,4,6}.

The event of rolling C or D is given by C∪D = {1,2,3,4,6}.

So, apply the probability formula -

P(C∪D) = 5/6

Therefore, the probability value is 5/6.

(c)  Let E be the event of rolling a 4. Then E = {4}.

Let F be the event of rolling an odd number. Then F = {1,3,5}.

The event of rolling E or F is given by E∪F = {1,3,4,5}.

So, apply the probability formula -

P(E∪F) = 4/6 = 2/3

Therefore, the probability value is 2/3.

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The equation of line is y = 14.24375x + 296.8875 , where x is the number of days and y is the total weight gain in x days

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 18 , 40.5 )

Let the second point be Q ( 50 , 496.3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 496.3 - 40.5 ) / ( 50 - 18 )

Slope m = 455.8 / 32

Slope m = 14.24375

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 40.5 = 14.24375 ( x - 18 )

On simplifying the equation , we get

y - 40.5 = 14.24375x - 256.3875

Adding 40.5 on both sides of the equation , we get

y = 14.24375x + 296.8875

where x is the number of days

Hence , the equation of line is y = 14.24375x + 296.8875

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The required equation that Nandita used to make the given graph is y = -3x + 2. Option B is correct.

In the equation intercept is the value of the linear function where either of the variables is zero.

Here,
From the graph, we need to identify the y-intercept and then match that intercept with each given in the options So,
From the graph, the y-intercept is ordered where the x coordinate of the pair is zero, So,
(0, y) = (0, 2)

Thus, the required equation among the option is y = -3x + 2.

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