A set of 4 consecutive integers has a sum of –270. which integers are they?

HELPPP

Step-by-step explanation:

(1 + i)¹⁴ = (1 + i)²×(1 + i)¹² = ((1 + i)²)⁷

(1 + i)² = 1 + 2i - 1 = 2i

((1 + i)²)⁷ = (2i)⁷ = 2⁷×i⁷ = 128×i²×i²×i²×i =

= 128×-1×-1×-1×i = -128i

Answer:

"Gases are compressible because most of the volume of a gas is composed of the large amounts of empty space between the gas particles. At room temperature and standard pressure, the average distance between gas molecules is about ten times the diameter of the molecules themselves."

Step-by-step explanation:

Found information on Compressibility | CK-12 Foundation website

The following equation is not proportional.

What is equation?

An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

Main Body:

we now that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=y/x  or y= kx.

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have

y= 1/(3x+5)

This is the equation of the line in slope intercept form

where

m= 3

b= 5

The given equation not represent a proportional relationship, because the line not pass through the origin

In a proportional relationship the value of b (y-intercept) is equal to zero

Hence , equation is not proportional.

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Answer:

slope: 6

y-intercept: -4

easy: y = 6x -4

Using proportion, if 94 kilometres is 6 hours, 47 kilometres is 3 hours.

Proportion is a mathematical comparison between two numbers

Proportion says that two ratios (or fractions) are equal.

Therefore, let's solve the proportion.

94 kilometres  = 6 hours

47 kilometres = ?

cross multiply

time = 47 × 6 / 94

time = 282 / 94

time = 3 hours

Therefore, if 94 km is 6 hours, 47 km is 3 hours.

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1).  0 + (-3) = = -3 is Additive Inverse

2).2(3-5) = 2(3)3) - 2(5) is Associative Property

3). (-6) + (-7) = (-7) + (-6) is Commutative Property

4).1(-9) = = -9 is Multiplicative Identity

5).(-4) (-1/4) = 1 is Commutative Property

6). 2 (3 x 7) = (2 X 3) x 7 is  Associative Property

7). 10 + (-10) = 0 is Additive Inverse

8). 2(5) 5(2) is Commutative Property

9).1(-1/4)= -1/4 is  Multiplicative Identity

10).  (-3)(4 + 9) = (-3)(4) + (-3)(9) ​ is Distributive Property

What is Additive inverse ?

To get a result equal to 0, add the original number and the additive inverse by simply changing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

What is Commutative Property ?

This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution. Division and subtraction do not work interchangeably.

A+B=B+A

What is Multiplicative Identity ?

An element of a set that remains intact after being multiplied by any other element of the set. In the set of real numbers, 1 is a multiplicative identity.

What is  Distributive Property?

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

What is  Associative Property?

A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.

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The division of the fraction 27/22 will result to 1.22 rounded to the nearest hundredth.

To divide the fraction using long division, we first divide the dividend with the divisor, write the whole number result, and then multiply it by the divisor, subtract the result from the dividend to get a new dividend. Repeat the process for the new dividend until you arrive at a remainder of zero, or continue to a given place value.

27/22 = 1 whole number and a remainder of 5

1 × 22 = 22

27 - 22 = 5

drop the value for the tenth digit of 27.00 which is 0 to yeild 50{ new dividend}

50/22 = 2 whole number and a remainder of 6

2 × 22 = 44

50 - 44 = 6

drop the value for the hundredth digit of 27.00 which is 0 to yeild 60{ new dividend}

60/22 = 2 whole number and a remainder of 16

2 × 22 = 44

69 - 44 = 16

we are rounding up to the nearest hundredth, we stop with the quotient of 1.222.

Hence, the fraction 27/22 is equal 1.22 rounded up to the nearest hundredth using the long division process.

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In a case whereby Carmen has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters long the lenght of the remaining piece of rope is 9.84 metres.

Distance can be described as the space that exist between two or more point, the concept that willbe used in the question is the concept of distance.

The total distance of the rope is 18 meters long , and she cut 8.16 meters long awya which implies that the remaining lenght of the rope will be ( 18 - 8.16)= 9.84 metres

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Answer: 18/20

Step-by-step explanation:

Hercules got 300 cattle from the King for cleaning out his stable

Multiplying fractions is defined as the product of a fraction with a fraction or with an integer or with the variables. The procedure to multiply the fractions are: Multiply the numerator with numerator. Multiply the denominator with the denominator. Simplify the fractions, if required.

To find how many cattle Hercules got for his work, we can simply multiply 3000 by 1/10 and get the value.

3000 * 1/10 = 300.

He got 300 cattle for his work.

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The factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)

The expression is

16 - [tex](5y-2)^2[/tex]

The expression is a mathematical statement that consist of different variables, numbers and the arithmetic operators

The expression is

The expression is

16 - [tex](5y-2)^2[/tex]

We know the identity

[tex](a+b)^2= a^2+2ab+b^2[/tex]

Apply this identity on the expression

= 16 -( [tex]25y^2[/tex]- 20y + 4)

Apply the distributive property

= 16 - [tex]25y^2[/tex]+ 20y - 4

Subtract the like terms

= - [tex]25y^2[/tex]+ 20y + 12

Take common term outside

= -1([tex]25y^2[/tex]- 20y - 12)

Split the middle term and apply factorization

= -1 ([tex]25y^2[/tex]+ 10y -30y - 12)

Take common term outside

= -1 ( 5y(5y+ 2) -6(5y +2)

Take common term outside

= -1(5y+2)(5y-6)

Hence, the factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)

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Answer:

5.37/3 = 1.79

Step-by-step explanation:

Given statement,

→ 5.37 divided by 3 equals?

Forming the problem,

→ 5.37/3

Let's solve the problem,

→ 5.37/3

→ (5.37 ÷ 3)

→ 1.79

Hence, the answer is 1.79.

There is no proportional relationship between the given equations.

What is proportional relationship?

Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality".

The given equations are,

7x - 2 = y

y = 2x + 4

y = 5x

y + 1 = 3x

These equations can be written as,

y = 7x - 2

y = 2x + 4

y = 5x

y = 3x - 1

Now consider the following table,

               x          y         y/x

             7           1          1/7

              2          1          1/2

               5          1          1/5

               3          1          1/3      

From above we can see that none of the ratio are equal, all ratios are different.

Hence, none of the given equations having proportional relationship.

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Answer: 50

Step-by-step explanation:

30% as a decimal is 0.3.

Let's say "what" is a variable, x.

0.3x=15

Divide both sides by 0.3 and you get x=50

Answer:50

Step-by-step explanation:30/100×x=15

x=15×100/30

x=50

Matthew will need 222 feet of fabric to make 74 curtains.

According to the question,

We have the following information:

Required length of each curtain = 36 inches

Total number of curtains to be made = 74

Now, the total length of the fabric needed to make 4 curtains can be found by multiplying length of one curtain by total number of curtains.

So, we have the following expression:

36*74

2664 inches

Now, we will convert this into feet:

1 inch = 1/12 foot

2664 inches = 2664/12 feet

2664 inches = 222 feet

Hence, Matthew will need 222 feet of fabric to make 74 curtains.

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The total cost to repay a one year long credit loan is 6720.

Given,

In the question;

Principal is = 6,000

Interest rate = 12%

To find the total cost to repay a one year long credit loan .

Now According to the question;

Based on the given condition:

Principal is = 6,000

Interest rate = 12%

Formulate:

6000 x (1 + 12%)

6000 x ( 1 + 0.12)

Calculate the sum or difference:

6000 x 1.12

= 6720

Hence, The total cost to repay a one year long credit loan is 6720.

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Answer:

54

Step-by-step explanation:

We can divide 28 by 11 to get...

11 ÷ 28 = 2.545454

   22

     60

     55

        50

        44

           60

            55

               50

                44

                   60

                    55

                      50

                      44

                        60

The division quotient reveals that the numbers 5 and 4 repeat themselves frequently. It is a situation of a repeating decimal that does not end.

This means that in the decimal equivalent of [tex]\frac{28}{11}[/tex], the smallest group of repeating digits is composed of 54 repeating digits.

Hope this helps! :)

The probability that the first is a king, the second a diamond and the third a diamond quiz let is 1/13, 1/4 and 10/52 respectively.

Now, we know that there are 52 cards in the deck of cards, and there are 13 cards of each suits i.e. diamonds, spade, heart and clubs. Also there are 12 face cards in total of the deck.

So, the probability if getting the first card is king :

King is a face card and there are 4 kings in the deck so the probability will be :

P(getting 1st card as king) = 4/52 = 1/13.

The probability of getting the second card a diamond is :

we know that there are 13 cards of the diamond in the deck so the probability will be :

P(getting the diamond card) = 13/52 = 1/4.

Now, lastly the probability if getting the diamond quiz let is :

There are 10 flashcards of the diamonds in the deck, so the probability will be :

P(getting the diamond flashcard) = 10/52.

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The amount owed at the end of the 6 years duration is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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The following is the 95% confidence interval for the standard deviation of UH students' height: CI = (1.81, 4.028) that is option B is correct.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful.

Here,

The formula for the standard deviation's confidence interval is given as CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]

Number of participants; n = 14 D F = n - 1 = 14 - 1 = 13

Deviation from the mean; s = 2.5

Significant level; = 1 - 0.95 = 0.05 

Confidence level; CL = 95% = 0.95

As a result, using an online Chi-square distribution table, we have: 

χ²₁₃, ₀.₀₂₅ = 24.736

(χ²₁₃, ₀.₉₇₅) = 5.01

CI = √[(13 * 2.5²/(24.736)], √[(13 * 2.5²/(5.01)]

CI = (1.81, 4.03) (1.81, 4.03)

The range with a 95% confidence level for the height standard deviation of UH students is as follows: CI = (1.81, 4.028), so option B is the proper one.

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The new coordinates for point S are (84,24), for a dilation centered around the origin,  

Dk (x,y) = (kx, ky) ,

K is the dilated scale factor that is multiplied by points vertices of a rectangle,

then rectangle QPRS where vertices were,

P = (1,1)

Q = (1,3)

R = (5,2)

S = (7,2)  

To get the dilation of this QPRS to Q'P'R'S' with a scale factor of 12 you have to multiply each and every coordinate of its vertices by 12.  

Q' = (12,12)

P' = (12,36)

R' = (60,24)

S' = (84,24)

Hence, The new coordinates for point S are (84,24)

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Answer:

the answer is 1/27

Step-by-step explanation:

so firstly

10/30 has 20 tickets left

3 tickets are winning so

1/27

The measure of the exterior angle to ∠G is 138.9°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

Given, In triangle EFG, m∠E = 95.2° and m∠F = 43.7°.

We know the sum of all the interior angles in a triangle is 180°.

We also know that the measure of an exterior angle in a triangle is the sum of the two opposite interior angles.

∴ The measure of the exterior angle to m∠G is = m∠E + m∠F.

= 95.2° + 43.7°.

= 138.9°.

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The best line fit go through to represent the data is (3,8) and (5,12)

The correct option is Option c)

What is best fit line?

A straight line that minimises the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

We are given some points we will plot the graph on the points

From that if we plot the line through the point (3,8) and (5,12)

That will leave 2 points above the line and 2 point below the line

Hence it is the best fit line

The correct option is option C)

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The original width is 6 inches, and was reduced to 3 inches, which is half. Keeping this in mind, the new height should be half the original 8 inch height, being halved to 4 inches.

From the given set of statements, the conjecture which represent the inductive reasoning are given by :

a. Given : Everyone dressed casually on Friday

Conjecture : All Fridays are casual days.

c. Given : WXYZ is a rectangle.

Conjecture : WX = YZ and WZ = XY

d. All donuts are unhealthy.

Conjecture : This chocolate donut is unhealthy.

As given in the question,

Inductive reasoning is the conclusion which is based on the process of observed pattern.

Given set of statements represents the inductive reasoning or not:

a. Given : Everyone dressed casually on Friday

Conjecture : All Fridays are casual days.

From observing pattern based on Friday dressing we conclude all Fridays are casual days.

Represent inductive reasoning.

b. Given : 3a² = 48

Conjecture : a = 6

Here we cannot observe the process , we have to show the calculation.

Not representing inductive reasoning.

c. Given : WXYZ is a rectangle.

Conjecture : WX = YZ and WZ = XY

From observing pattern based on property of rectangle it is concluded that WX = YZ and WZ = XY.

Represent inductive reasoning.

d. All donuts are unhealthy.

Conjecture : This chocolate donut is unhealthy.

From observing pattern based on all donuts property it is concluded that   chocolate donuts is also unhealthy.

Represent inductive reasoning.

Therefore, from the given set of statements, the conjecture which represent the inductive reasoning are given by :

a. Given : Everyone dressed casually on Friday

Conjecture : All Fridays are casual days.

c. Given : WXYZ is a rectangle.

Conjecture : WX = YZ and WZ = XY

d. All donuts are unhealthy.

Conjecture : This chocolate donut is unhealthy.

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Answer:

The correct answer is 1 pitcher.

Step-by-step explanation:

Oscar sold 2 pitchers of lemon are from his lemonade stand on Friday.

On Saturday, he sold as much lemonade as on Friday.

The number of pitchers of lemon from the lemonade stand which Oscar sold on Saturday is given by × 2 = 1 pitcher.

Thus Oscar sold 1 pitcher on Saturday which is half of the number of pitchers of lemon he could sell on Friday.

Answer:

c

Step-by-step explanation:

The 3rd degree equation that is divisible by x, (x − 3), (x+1) is x³ - 2x² - 3x.

A cubic polynomial is a sort of polynomial that is based on the variable's largest exponent, or degree, in mathematical terms. As a result, a cubic polynomial is one in which the degree or maximum power of the variable is 3. An algebraic statement having variables, constants, and exponents that are whole integers is called a polynomial.

The given factors are x, (x - 3), (x + 1)

To find the 3rd-degree polynomial divisible by x, (x - 3), (x + 1) multiply the three expressions.

First multiply x, (x - 3)

x × (x - 3)

= x × x - 3 × x

= x² - 3x

Now multiply x² - 3x and (x +1)

(x² - 3x) × (x + 1)

= x²(x) - 3x(x) + x²(1)  - 3x(1)

= x³ - 3x² + x² - 3x
= x³ - 2x² - 3x

So, this is the 3rd-degree equation that is divisible by x, (x − 3), (x+1).

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Answer:

x>-⅘ OR x<-⅘ (Can I have brainliest ;-;)

Step-by-step explanation:

1) Find x-int:

0=10x+8

-8=10x (÷10)

-⅘=x

x(-⅘;0)

2) Domain:

3) Choose 1 of those, since i cant see the graph i cant say which domain would fit the graph

The graph of the quadratic function y = 0.75x² is given by the image at the end of the answer.

The notation y = 0.75x² is already in vertex form, meaning that the function was vertically compressed by a factor of 3/4 from the original graph.

The definition of a quadratic equation with vertex (h,k) is given as follows:

y = a(x - h)² + k.

In which a represents the leading coefficient of the quadratic function.

In this problem the coordinates of the vertex are:

(0,0).

Hence the parameters are:

h = 0, k = 0.

Thus the equation is:

y = ax².

When x = -2, y = 3, hence the leading coefficient is given as follows:

3 = a(-2)²

4a = 3

a = 3/4

a = 0.75.

Hence the equation is:

y = 0.75x².

The multiplication by 0.75 means that the parent function y = x² is vertically compressed by a factor of 0.75.

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