A cout mater bough 45 meter of rope he ued two nine of the rope for knot tying. How many meter of rope were ued for knot tying

Solution of expression 5²- 9 ÷ 3 using PEMDAS is 22.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are referred to as PEMDAS in this context. Teachers in the United States constantly remind their students about the acronym PEMDAS, which stands for parentheses, exponents, multiplication, division, addition, and subtraction. BODMAS, which stands for brackets, ordering, division and multiplication, and addition and subtraction, is another acronym used by educators. A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).

Given,

Expression:

5²- 9 ÷ 3

Using PEDMAS,

Squaring,

25 - 9 ÷3

Dividing,

25 - 3

22

Solution of expression 5²- 9 ÷ 3 using PEMDAS is 22.

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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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Ryan will use the multiplication with 0.621 to find the speed in mile per hour.

To find the speed in mile per hour we will convert the unit from mentioned unit to desired unit. As per the known fact, 1 kilometre is 0.621 mile.

Keeping the value of mile in the place of kilometres, we will calculate the speed in miles per hour.

Speed = (100 × 0.621)/1

Performing multiplication in numerator on Right Hand Side of the equation to find the value of speed in miles per hour

Speed = 62.1 miles per hour

Thus, Ryan should multiply the value with 0.621 miles per hour and hence, the value of speed in miles per hour is 62.1.

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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 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.

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 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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The amount of money that Alonso has invested in these accounts is given as $9000 and $21000

We have to represent the percentages as a and b, then multiply 100 at the right hand side of the equation

we would have

7a + 5b = 1680 * 100

7a + 5b = 168000 ---- 1

From the amount that Alonso has to invest we would have

a + b = 30000

where b = 30000 - a   ---- 2

We have to put the value of b in equation a

7a + 5(30000 - a) = 168000

7a + 150000 -5a = 168000

7a - 5a = 168000 - 150000

2a = 18000

a = 18000 / 2

= $9000

From equation 2

b = 30000 - 9000

= $21000

The amount that was invested in each of the accounts are

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The largest possible value of 10 can be calculated using factorials and the largest value would be = 3628800

Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 5, then it's factorial would be =5×4×3×2×1 = 120.

Factorials is used in mathematics or statistics to denote the possibilities of an event in an outcome.

The total numbers of the two groups = 10

The factorials of 10 = 10×9×8×7×6×5×4×3×2×1

= 3,628,800.

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The distance between the two towns is 165 kilometers

The initial speed = 100 kilometer per hour

Time taken = t hours

We know,

Speed = Distance / Time

Distance = Speed × t

Distance = 100 × t

New speed = 110 kilometer per hours

He saves 9 minutes

9 minutes = 9/60 hours

The time taken = t - 9/60

The distance = 110 × (t - 9/60)

= 110t - 33/2

Then the equation will be

100t = 110t - 33/2

110t - 100t = 33/2

10t = 33/2

t = 33/2 ÷ 10

t = 33/2 × 1/10

t = 1.65 hours

Then the distance = 100 × t

= 100 × 1.65

= 165 kilometers

Hence, the distance between the two towns is 165 kilometers

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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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The equation of circle can be written as (x-4)^2+ (y+2)^2 = 6^2. The center of the circle is (4,-2) and radius is 6.

What is a circle?

A circle is locus of points which have same distance from a point known as center. Circle is a 2 dimensional figure.

We are given a equation

x^2+y^2-8x+4y-16 = 0

Using completing square method

x^2-8x+ 16+y^2+4y+4-36=0

(x-4)^2 + (y+2)^2 = 6^2

Comparing with standard equation

The center of circle is (4,-2) and and radius of the circle is 6.

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The dimensions that minimize the cost of building the tank are r ≈ 6.5 ft and h ≈ 26 ft

What do you mean by cost?

The total cost becomes

T = ucSc + 2ucSh

   = 2ucπrh + 8ucπr²

We need to eliminate h . The volume from the question gives a way out.

4640 = 4/3πr³ + πr²h

  h = 4640/πr² - 4r/3

substitute into the formula for total cost gives, after simplifying

  T =  16ucπr²/3 +  9280uc/r²

differentiating with respect to r , we get

  dT/dr = 32/3Ucπr - 9280Uc/r²

at extrema

dT/dr = 0

⇒ 32/3Ucπr = 9280Uc/r²

 r = ∛870/π ≈ 6.5 ft

To confirm that r is a minimum value, carry out the second derivative test

   d²T/dr² = 32Ucπ/3 +  18560/r³

substituting ∛870/π, we get that d²T/dr² > 0  confirming that minimum value

To find h , recall that

 h = 4640/πr² - 4r/3

substituting r , we get h ≈ 26.0 ft as the corresponding minimum height.

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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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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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Answer: 18/20

Step-by-step explanation:

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 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 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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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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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

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 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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The critical value will be +- 1.96.

What is critical value?

A crucial value delimits areas of a test statistic's sampling distribution. Both confidence intervals and hypothesis tests take these values into account.

Main body:

sample size is 10.

if you use z-scores, and it appears that you have to, since you don't know the mean or standard deviation of your population, your mean is 0 and your standard deviation is 1.

at 95% confidence level, 100% - 95% is your alpha.

that makes it equal to 5%.

divide that by 2 and you have half your alpha on the left end of the confidence interval and half on the right end.

that makes it 2.5% on each end.

2.5% is the same as .025 in decimal form.

look up a z-score to the left of .025 to get a z-score of -1.959963986 which can be rounded to -1.96.

since the normal distribution is symmetric about the mean,

Therefore your critical z-score is plus or minus 1.96.

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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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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

The value of the expression is -4.

Question:

Evaluate the expression. 4−[(11+12(−2)÷6)+1] What is the value of the expression? Enter your answer in the box.

What is an expression?

A mathematical expression is a phrase containing a minimum of two numbers or variables and a minimum of one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)

4−[(11+12(−2)÷6)+1]

Simplify parenthesis first followed by box brackets

=4-[(11 -24÷6)+1]

=4-[(11-4+1]

=4-8=-4

So, the value of the expression is -4.

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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

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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