There are 5 consecutive even integers with a sum of –80. What is the greatest of these integers?

Answer: Triangle VUT:

84:70:42

Triangle RSQ:

30:25:15

Final simplified answer: 2.8:2.8:2.8

Scale factor of 2.8

Step-by-step explanation:

Each triangle's sides are a part of the ratio, then you divide each side by the corresponding one (84 by 30, and 70 by 25) to get your scale factor.

The Pythagorean Theorem indicates the following relationship between the squares and triangles.

Part A

Part E

Pythagoras theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.

Part A

The possible squares in the question are the three squares arranged on the three sides of the triangle, and having a side length which is the same as the length of the side of the triangle to which the square is attached

The relationship between the three squares of side length a, b, and c according to Pythagorean theorem is; a² + b² = c²

Therefore, the area of the largest square that is located on the hypotenuse side of the triangle is equal to the sum of the areas of the other two squares.

Part E

The length of the sides of the triangles, obtained from a similar question on the site are; a, b, and c and a, b, and n

It was shown that c² = n²

Therefore;

c = n

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The probability of selecting at least one defective item at random is 0.3017.

The probability of an event occurring at least once will be calculated as the complement of the probability of the event never occurring. You can use exponents to multiply the number of events that occurred when calculating this amount.

Defect rate = P(defect) = 0.05

Probability is defined as the required outcome divided by the total number of possible outcomes.

P( at least 1 is defective) = 1 - P(none is defective)

P(not defective) = 1 - P(defective) = 1 - 0.05 = 0.95

P(none is defective) = P(non defective)^7

P(none defective) = 0.95× 0.95 × 0.95 × 0.95 × 0.95× 0.95× 0.95=0.6983

P(at least one is defective) = 1 - 0.6983 = 0.3017

Therefore, probability of at least one defective item is 0.3017.

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The number of atoms in standard form is 4 × 10²⁵ atoms

Standard form is number written in the form a × 10ⁿ where 1 ≤ a < 10 and n is an integer

Since there are about 40 trillion cells in the human body. and each cell consists of about 100 trillion atoms, we have that

40 trillion cells = 40 trillion × 1 cell

Also, 1 cell = 100 trillion atoms.

So, 40 trillion × 1 cell = 40 trillion × 100 trillion atoms.

Now, we know that 1 trillion = 1000 billion

So, Number of atoms =  40 trillion × 100 trillion atoms

=  40 × trillion × 100 × 1 trillion atoms.

= 40 × 1000 billion × 100 × 1000 billion atoms.

= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.

We know that 1 billion = 1000000000

So,

= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.

= 40 × 1000 × 100 × 1000 × 1000000000 × 1000000000 atoms

= 40000000000000000000000000

= 4 × 10000000000000000000000000

= 4 × 10²⁵ atoms

So, the number of atoms in standard form is 4 × 10²⁵ atoms

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The equivalent equation for the expression y = 3x-6 is none.

Equivalent equation:

If the two equations are said to be equivalent when they have the same solution set. Then it is called as Equivalent equation.

Given,

Here we have the expression y = 3x-6

Now, we need to find the equivalent equation.

In order to find the equivalent equation, we have to take some sample values for x,

The sample value of x as 1, 2, 3

Now, we have to apply these values on the given expression first,

Then we get,

x = 1 => y = 3(1) - 6 = -3

x = 2 => y = 3(2) - 6 = 0

x = 3 => y = 3(3) -6 = 9

Now, we have to apply these to the given equation and which has the same value of the given expression,

x = 1 => 3(1) - 2y = 6 = -2y = 6 - 3 => y = -3/2

x = 2 => 3(2) - 2y = 6 = -2y = 6 - 6 => y = 0

x = 3 => 3(3) - 2y = 6 = -2y = 6 - 9 => y = 3/2

This is not equal one.

Move on to the second one,

x = 1 => 2(1) + 3y = -6 => 3y = -6 - 2 => y = -8/3

x = 2 =>  2(2) + 3y = -6 = 3y = -6 - 4 => y = -10/3

x = 3 =>  2(3) + 3y = -6 = 3y = -6 - 6 => y = -4

This is not a equivalent one.

Move on to the third expression,

x = 1 => 3(1) - 2y = 12 = -2y = 12 - 3 => y = -9/2

x = 2 => 3(2) - 2y = 12 = -2y = 12 - 6 => y = -3

x = 3 => 3(3) - 2y = 12 = -2y = 12 - 9 => y = -3/2

This is not a equivalent one.

Finally we have to use the last one, then  we get,

x = 1 => 2(1) - 3y = 18 => -3y = 18 - 2 => y = -16/3

x = 2 =>  2(2) - 3y = 18 => -3y = 18 - 4 => y = -14/3

x = 3 =>  2(3) - 3y = 18 => -3y = 18 - 6 => y = -4

Therefore, none of them are the equivalent one.

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Answer: No

Step-by-step explanation: to find out how much more money Eugene will be making we need to isolate the increased value provided by the raise and then add it to his already existing earnings. We do this by multiplying $2700 by 3.5%.

We would write this as 2700 x .035

This is because 100% can be converted to 1, for example if Eugene got a 100% raise we would multiply 2700 by 1 (which changes nothing) then add 2700 and 2700 together.

Since Eugene is only getting a 3.5% raise we would write it as .035 instead of 1

Now that we have our equation we first need to simplify. In this case it means we remove the two zero's from 2700 to make it 27. To make sure the answer does not get messed up will make the other side of the equation larger by moving everything two decimal points (one for each removed zero) like this.

27 x 3.5

This is much easier to work with but I will still show the steps I am using to prevent confusion.

27 x .5 = 13.5

27 x 3 = 20 x 3 + 7 x 3

20 x 3 = 60

7 x 3 =21

60+21 =81

81+13.5=94.5

Since 2700 + 94.5 = 2794.5 Eugene will not make more than $2800 dollars a month after his raise.

Using the theories of statistical design, we got that both related sample t test and one-way within-subjects ANOVA is the appropriate statistical design for the study in which a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus.

Statistical design of experiments and the  response surface methodology has become a standard tool for the medium development. There are several applications reported in literature, such as the production of antibiotics, secondary metabolites, and enzymes.

Applications of statistical design of experiment shown in the Table 1 and several other studies use exclusively of the response surface method with quadratic polynomial models and the central composite design with on average 20–30 experiments. In most cases, the important components were identified by fractional factorial design or by the Plackett–Burman design with 10–15 experiments. Methods for narrowing  optimal variable range are only infrequently applied.

Hence, when a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus and wants to know if anxiety levels were higher in the fearful stimulus condition and if the same participants are observed in each group, then the appropriate statistical design is  that both related sample t test and one-way within-subjects ANOVA .

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The domain and range of the functions represented by the graph is equal to [-2, 2]. Also, the range of the functions represented by the graph is equal to [-2, 2].

The horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Similarly, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: Each interval on this graph represent -1 unit.

By critically observing the graph of this function shown, we can reasonably infer and logically deduce the following:

Domain = [-2, 2].

Range = (-2, 2).

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The answer is 4/15

2/5 * 2/3 = 2 · 2/5 · 3 = 4/15

Multiply the numerators and denominators together. Keep the result fraction to the smallest possible denominator GCD(4, 15) = 1. It cannot further simplify the fraction result by canceling in the following intermediate step.

In other words, two fifths times two thirds equals four fifteenths.

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Answer:

5/3

Step-by-step explanation:

"of" means times so so so often. It is not a hard math rule/definition. But more like a soft English-Math translation.

So, "2/5 of what"

means 2/5x (but make sure the 2/5 is a fraction beside the x, NOT the x on the bottom with the 5)

"is" means equals.

2/5x = 2/3

Multiply both sides by 5/2.

5/2 • 2/5x = 2/3•5/2

x = 2/3 • 5/2

x = 5/3

You get 5/3 either by "cancelling" the 2's OR by

fraction multiplication where you times top×top and bottom×bottom and simplify.

x = 10/6

x = 5/3

2/5 of 5/3 is 2/3.

The "what" in the question is 5/3.

Answer:

D

Step-by-step explanation:

The equation of the line is y = 2x + 8

To find the y intercept we make x=0

When x=0 y=8

if y is total cost and x is number of visits then at zero visits (x=0) the total cost is 8, which is what you would find using choice D

Answer:

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

It represents the cost with zero visits, likely the membership cost, therefore the correct choice is D.

The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

a)

The given condition makes a right-angle triangle as shown below,

The tan function,

tanθ = 6/25

θ = 14.50°

b)

When a player is 5 feet closer means (20 feet far)

tanθ = 6/20

θ = 16.70°

c)

As the player gets closer the angle becomes more and more.

Hence "The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases".

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Answer:

h=2

h= -7/5

hope this helped :)

The recommended screen size for the television is 59.85 inches.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, the expression for the size of the television is given as:

S = 0.228x² + 8.154x - 8.3

where x = 7 feet

S = 0.228x² + 8.154x - 8.3

S = 0.228(7)² + 8.154(7) - 8.3

S = 11.172 + 57.078 - 8.4

S = 59.85

The size is 59.85 inches.

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The main difference between opinion based and informational essay is that in opinion based you have to share your own opinion reading any topic or something but in case of informative essay to have to provide particular information about the subject.

Generally speaking, an essay is a bit of writing in which the author presents their own arguments; nevertheless, this definition seems ambiguous and includes elements of letters, papers, articles, pamphlets, and short story collections. Essays are divided into two categories: formally and informally. Formal writings are distinguished by their "serious aim, dignity, logical arrangement, and length," whilst informal papers are distinguished by their "personal element."

To express your opinions on a subject and persuade the reader of your point of view, you must write an opinions essay. To accomplish it, you must first present the subject and express your viewpoint. Following that, you should provide three arguments in favor of your viewpoint. Finally, create a closing in which you summarize your case and restate your viewpoint in a new way.

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The area of the two lawns will be 105 square meters.

According to the question,

We have the following information:

The first lawn is 7 meters long and 4 meters wide. The second lawn has the same length and width which is 3 times as much as the first one.

So, the width of the second lawn = 4×3

Width of second lawn = 12 m

Now, the formula to find the area of the rectangle:

Length*width

Area of first lawn:

7×3

21 square meters

Area of second lawn:

7×12

84 square meters

Now, the area of two lawns = area of first lawn+ area of second lawn

Area = 21+84

Area = 105 square meters

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The 10% criterion is not followed in Part A. The typical condition is not satisfied in component B.

A proportion is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province.

Here,

The chocolate chunks' data are as follows:

The sample size (n = 18) of chocolates

The batch contains 17 pieces of white chocolate.

The batch contains 43 dark chocolates.

Given the percentage of white chocolates in the sample, we have;

p = 17/60 = 0.28, the proportion of white chocolates in the batch

Part A

Because sampling samples without replacing them does not result in independent Bernoulli trials, the 10% condition stipulates that the sample size should be less than or equal to 10% of the population.

Because the stated sample size, n = 18, is 18/60100 = 30% > 10% of the batch, the 10% condition is not satisfied in the current case.

Part B

The normal approximation can be assumed when we have;

n·p > 10 and n·p·(1 - p) > 10

By plugging in the values for 'n' and 'p', we have;

p = 0.28 = 17/60

n·p = 18 × 17/60 = 5.1 < 10

n·p·(1 - p) = 18 × 17/60 × (1 - 17/60) = 3.655 < 10

Therefore the normal condition is not met.

Part A does not adhere to the 10% requirement. Component B does not meet the normal condition.

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In order to find the sum to the indicated accuracy we need to add

5 terms  as the series is said to be convergent.

Given Series is Σ(-1/3)^n / n where error is less than 0.0005

      = Σ (-1)^n / n3^n

For this series, we will use ratio test

if [tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = L < 1 then series in convergent,

Let an = (-1)^n / n3^n ,  an+1 = (-1)^n+1 / (n+1)3^n+1

[tex]\lim_{n \to \infty} |an + 1 / an |[/tex]   =  [tex]\lim_{n \to \infty} | ((-1)^n+1 / (n+1)3^n+1)(n3^n/(-1)^n) |[/tex]

By solving we get,

[tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = 1/3 < 1

Then given series is convergent.

By alternating series estimation theorem we have,

|Rn|=|S-Sn| <= an+1

an+1 <= 0.0005

1 / (n+1)3^n+1 <= 0.0005

(n+1)3^n+1 >= 2000

2 * [tex]3^{2}[/tex] >[tex]\neq[/tex] 2000 (n=1)

4 * [tex]3^{4}[/tex] >[tex]\neq[/tex] 2000 (n=3)

6 *  [tex]3^{6}[/tex] >= 200 (n=5)

So required terms is n=5

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yes , it is  possible for both Jane and Jill to have the same number of beads after Jane gave some beads to Jill and The number of beads Jane has is 7t/4 and Jill has 3t/4 bead's

The ratio of Jane's beads to Jill's beads is 7: 3

Let x be the number of beads Jane has

y be the number of beads Jill has

x/y = 7/3

When Jane's gives t of her beads away both will have the same number of beads so

x - t = y

substituting in the first equation

x/ ( x- t) =7/3

3x= 7x-7t

4x= 7t

x= 7t/4

y= 7t/4 -t

 = 3t/4

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A rectangle with a diagonal of length x is twice as long as it is wide, the area of the rectangle is (B) 2x²/5..

Given that we have a rectangle with a diagonal of length x is twice as long as it is wide.

Let

L = length of rectangle,

W = width of rectangle and

D = length of diagonal = x

Given that the length of diagonal, x is twice as long as it is wide, we have that

L = 2W

Also, since it is rectangle, we have that

D² = L² + W²

D² = (2W)² + W²

D² = 4W² + W²

x² = 5W²

W² = x²/5

W = x/√5

W = x√5/5

since the length of the rectangle, L = 2W, we have that

L = 2W

= 2x√5/5

The area of the rectangle

The area of the rectangle is given by A = LW where

L = length of rectangle and

W = width of rectangle

So, A = LW

= 2x√5/5 × x√5/5

= 2x² × 5/25

= 2x²/5

So, the area of the rectangle is (B) 2x²/5

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The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation.

a)

As per the given first system of equation,

2x - 4y = 10

x + 5y = 40 → 2x + 10y = 80

Subtract both

10y + 4y = 80 - 10

14y = 70

y = 5

And, x = 40 - 5(5) = 15

b)

As per the given first system of equation,

3x - 5y = 4 and

-2x + 6y = 18 → -x + 3y = 9 → -3x + 9y = 27

Add both

-5y + 9y = 4 + 27

4y = 31

y = 7.75

x = (4 + 5(7.75))/3 = 14.25

Hence "The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75".

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The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.

Amount to spend by the taxi driver ≤ 10.50.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

The taxi company only has $10.50 to spend.

This means that,

The maximum amount to spend is $10.50.

We can also represent as:

Amount to spend by the taxi driver ≤ 10.50.

Thus,

The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.

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The value of tan A = 1

Trigonometric ratios are the ratios of sides of a right-angle triangle. The six trigonometric ratios of a right angle triangle are Sin, Cos, Tan, Cosec, sec and cot.

The trigonometric ratios relate the sides of the triangle with the angles of the triangle.

tan(A+B) = -4, tan B = 5/3

But tan(A + B) = [tex]\frac{tan A + tanB}{1-tanAtanB}[/tex]

Substituting the values of tan(A +B) tan B

-4 = [tex]\frac{tan A + 5/3}{1 - 5/3tanA}[/tex]

multiply numerator and denominator by 3, you have

-4 = [tex]\frac{3tanA + 5}{3 -5tanA}[/tex]

-4(3-5tanA) = 3tanA +5

-12 +20tanA = 3tanA +5

collect like terms

20tanA - 3tanA = 5 +12

17tanA = 17

tan A = 17/17

tanA = 1

In conclusion, the value of tanA = 1

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Answer:

shopkeeper sells a book at INR 960 for a profit of 20% and another book at INR 720 for a loss of 10%. Find the total profit/loss of the shopkeeper

The equations using any method for the given situation illustrated that:

The equation for Jordan: 225 + 45w

The equation for RayAnn: 150 + 60w

Let the number of weeks be represented by w. Jordan saved $225 and continues to save $45 each week. The equation for this will be:

= 225 + (45 × w)

= 225 + 45w

RayAnn saved $150 and continues to save $60 each week. The equation will be:

= 150 + (60 × w)

= 150 + 60w

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The probabilities will be 0.1081 , 0.676, 0.863, 0.605 respectively.

let us consider, the chances of getting stem be a success(S) and not getting it be a failure(F) , and the total probability be 1 .

as per the statement 26% students are major in stem

total students selected randomly are 36.

∴ P(S) = 0.26

P( F)  = 1 - 0.26 = 0.74

Now the binomial probability of success is given by

[tex]P(x) = C^{n} _{x} S^{x} F^{n-x}[/tex]

where C is for the combination formula

S is changes of success

F is chances of failure

x = no. of times success

n = total times the experiment done

From the provided information we can solve each case as follows :

A) exactly 7 of them major in stem

P(7) = [tex]C^{36} _{7} (0.26)^{7} (0.74)^{29}[/tex]

   = 0.1081

B)at most 10 of them major in stem

it means P(0,1,2...10)

∴ P = P(0) + P(1) +......+P(10)

P = 0.676

C) at least 7 of them major in stem.

it means P(7,8,9...36)

∴ P = P(7) + P(8) + ...+ P(36)

P = 0.863

D) between 9 and 15 (including 9 and 15) of them major in stem.

In this case we subtract P(0,1,2...8) from P(0,1,2,...15)

and get P(9,10,11,...15)

∴ P(9,10,11,...15) =  P(0,1,2,...15)  -   P(0,1,2...8)

                        =  0.987  -  0.382

                        = 0.605

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Answer:

6

Step-by-step explanation:

3x-7=11

3x-7=113x=11+7

3x-7=113x=11+73x=18

3x-7=113x=11+73x=183x/3=18/3

3x-7=113x=11+73x=183x/3=18/3 X=6

The experiment will end after 4th time.

hence, after 4th  trial experiment will stop.

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