Which number line represents he number 0.7?

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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Answer:

2x-3y<-9

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

Prime numbers are numbers that only have the factors of one and itself. Rational numbers include all numbers except for non terminating, non repeating decimals. An imaginary number is a number that is expressed in terms of the square root of a negative number (usually the square root of −1, represented by i or j).

Answer:

3

Step-by-step explanation:

Given

y - 3 = 4(x - 0)

y - 3 = 4x

y = 4x + 3

Comparing with y = mx + c

we get

y-intercept (c) = 3

hope it will help :)

Answer:

b. does not change the rTG

Step-by-step explanation:

If the average weekly amount of studying time and Grade are compared such that a certain correlation Coefficient value is obtained, changing the unit of measurement of any of the variables, will not affect the value of the correlation Coefficient most notably because the value of R, correlation Coefficient is a normalized or standardized value that ranges between - 1 and 1 and hence, resistant to unit changes in the compared variables. Hence, Correlation coeffient for the rate of study and grade obtained will not change even if rate of study is measured in hour.

Answer:

b. does not change the rTG

Step-by-step explanation:

Answer:

14.97

Step-by-step explanation:

The probabilities for this problem are given as follows:

a) Moderate to high, given that it is an aerospace company: p = 4/9 = 0.4444.

b) Moderate to high, given that it is a food retailer: p = 6/11 = 0.5455.

c) As the probabilities are different, the company type is independent of the level of risk of the firm's stock.

A probability is given by the division of the number of desired outcomes by the number of total outcomes.

For item a, the outcomes are given as follows:

Hence the probability is given as follows:

p = 8/18

p = 4/9.

For item b, the outcomes are given as follows:

Hence the probability is given as follows:

p = 30/55

p = 6/11.

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Answer: B) No; the remainder is 234, so (x+3) is not a factor.

===============================================================

Explanation:

We'll use the remainder theorem. That theorem says if we divide p(x) over (x-k), then the remainder is p(k). A special case of this theorem says that if we get 0 as the remainder, then (x-k) is a factor of p(x).

We're dividing f(x) over (x+3) which means that k = -3. Think of x+3 as x-(-3) so you can match it up with the form x-k.

To find the remainder of f(x)/(x+3), we need to compute f(-3).

Plug x = -3 into the f(x) function to get...

f(x) = 4x^3 + 11x^2 - 75x + 18

f(-3) = 4(-3)^3 + 11(-3)^2 - 75(-3) + 18

f(-3) = 234

The remainder is 234, which is isn't zero, so (x+3) is not a factor of f(x).

Answer:

No; the remainder is 0 so (x + 3) is not a factor

Step-by-step explanation:

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

k = 3.5

Step-by-step explanation:

Area of a rectangle = length × width

Area of the bigger triangle - Area of the smaller triangle = 35 cm²

Thus:

(2k + 6)(k) - (3)(k) = 35 cm²

2k² + 6k - 3k = 35

2k² + 3k - 35 = 0

Factorise

2k² + 10k - 7k - 35 = 0

2k(k + 5) -7(k + 5) = 0

(2k - 7)(k + 5) = 0

2k - 7 = 0

2k = 7

k = 3.5

Or

k + 5 = 0

k = -5

The value of k would be the positive number which is 3.5.

Answer:

It goes in one direction and indefinitely.

It consist one endpoint.

Step-by-step explanation:

A ray is a straight line that emerges out of a start point and moves in a direction. The line begins with the start point and moves in one direction. The start point and the other side are named with capital letters. It is denoted by writing the two letters and placing an arrow above the letters. There is no endpoint in a ray.

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar.

While from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.

Assuming that the slips of paper are randomly distributed and the student does not have any information about the distribution, let's analyze the probabilities for each choice:

Thus, from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar. On the other hand, from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.

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According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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The amount that you need to save per month to fund the emergency fund would be $ 861. 58.

The discretionary money left per month would be $ 585. 88.

The gross income for the month :

= 17. 50 x 40 per week x 4 weeks a month

= $ 2, 800

The amount left which is realized funds for the month is:

= Gross income - FICA + Federal tax withholding + State tax withholding

= 2, 800 x ( 1 - 26. 15 %)

= $ 2, 067. 80

Five months of realized income for the emergency fund is:

= 2, 067. 80 x 5

= $ 10, 339

The amount to save per month is:

= 10, 339 / 12

= $ 861. 58

The amount left per month for discretionary expenses ;

= 2, 067. 80 - 861. 58 - 620. 24 rent

= $ 585. 88

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Complete question:

Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder auto-mobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,000, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. There is no production on weekends, so on Friday the line is diassembled and cleaned. On Monday, the line must be set up to run whichever product will be produced that week. Once the line has been set up, the weekly production capacities are 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Letx4 5 the number of 4-cylinder connecting rods produced next week x6 5 the number of 6-cylinder connecting rods produced next week s4 5 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise s6 5 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise

a) Using the decision variables x4 and s4, write a constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 8000 units

b) Using the decision variables x6 and s6, write a constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 6000 units

c) Write a constraint that requires that production be setup for exactly one of the two rods

d) Write the cost function to be minimized

Answer:

a) x₄ ≤ 8000s₄

b) x₆ ≤ 8000s₆

c) s₄ + s₆ = 1

d) MIN 15x₄ + 18x₆ + 2000s₄ + 3500s₆

Explanation:

a) The constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 8000 units, is written as:

x₄ ≤ 8000s₄

b) The constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 6000 units is written as:

x₆ ≤ 8000s₆

c) The constraint that requires that production be setup for exactly one of the two rods:

Since we have:

x₄ ≤ 8000s₄ ; x₆ ≤ 8000s₆

The constraint that requires that production be setup for exactly one of the two rods will be:

s₄ + s₆ = 1

d) Write the cost function to be minimized:

Since we are to find the cost function to be minimized, we take the function below:

MIN 15x₄ + 18x₆ + 2000s₄ + 3500s₆

The farmer can 9 days more than 31 days.

given,

farmer buy 1000 pounds of hay

if cow eats 25 pounds of hay per day .

here, 25 x 31 =775

which is less than 1000 ,so that the farmer can feed the cow more than 31 days

1000-775=225

225/25=9

therefore the farmer can 9 days more than 31 days.

There are four basic properties of numbers: commutative, associative, distributive, and identity. You should be familiar with each of these.

distributive property ;

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

The commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.

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Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The standard deviation of the sampling distribution is approximately 0.3292.

The behaviour of the sampling distribution of the mean is described by the central limit theorem, a key conclusion in statistics. It asserts that regardless of how the population distribution is shaped, if a random sample of size n is taken from a population with mean and standard deviation, the distribution of sample means will tend towards a normal distribution as n increases.

Because it enables us to utilise the normal distribution to draw conclusions about the population mean based on sample means, the central limit theorem has significant practical ramifications. Additionally, it offers a foundation for confidence interval estimation and statistical hypothesis testing.

The standard deviation is given by the formula:

SD = σ/√(n)

Now, substituting the value of σ = 40, n = 147,400 we have:

SD = σ/√(n) = 40/√(147400) ≈ 0.3292

Hence, the standard deviation of the sampling distribution is approximately 0.3292.

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Answer:

Yes, and the unit rate is 1:48

Step-by-step explanation:

If you start by dividing 204 by 4.25, you will see you get an answer of 48. Now if you move on to the next row, and divide 252 by 5.25, you also get 48. If you do the same with the last two rows, you get 48 for both. This shows that the unit rate is 1:48.

By answering the presented question, we may conclude that She spends equation 40% of her time at work and 15% of her time on other hobbies. She spends 20% of her time napping.

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion  \("2x + 3 = 9"\) states that the word  \("2x + 3"\) Corresponds to the number "9".

The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.

For example, in the equations \("x2 + 2x - 3 = 0\)  ," the variable x is lifted to the powercell. Lines are utilized in many areas of mathematics, include algebra, arithmetic, and geometry.

Abby, according to the picture, spent:

She spends 25% of her time in school.

She spends 40% of her time at work and 15% of her time on other hobbies.

Therefore, Furthermore, she spends  \(20\) of her time napping.

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Answer:

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

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

Answer:

1) Finance is very important in a business as to meet the expenses from manufacturing a product to solding it capital is required. without finance one cannot run a business . even a small scale business requires some finance.

2) Business has a great impact in our economy. it increases the overall economy and contributes somewhere between 70 to 72% to the GDP.

Answer:You earn 5% commission on the first $2000 of sales and 8% commission on all sales over $2000. If you sold $7740, what is your total ...

Step-by-step explanation:

Answer: The answer is 820

Step-by-step explanation:

2(10x20 + 7x20 + 7x10) = 820

10x20 = 200

7x20 = 140

7x10 = 70

200 + 140 + 70 = 410

now take the 2 in front of the "(" and times it with the 410

410 x 2 = 820  

Answer:

7

Step-by-step explanation:

When you put a value for x in a function, it means that you substitute all terms of x for that value you just substitute for x=2. The x term in the function is x^2,  so that squared would be 4. You then add 3, yielding a total result of 7.

Answer:

f(2) = 7

Step-by-step:

Let f(x)=x^2+3. Find f(2)

\( \begin{gathered}{\longrightarrow{f(x)= {x}^{2} +3}}\end{gathered}\)

\( \begin{gathered}{\longrightarrow{f(2)= {(2)}^{2} +3}}\end{gathered}\)

\( \begin{gathered}{\longrightarrow{f(2)= {(2 \times 2)}+3}}\end{gathered}\)

\( \begin{gathered}{\longrightarrow{f(2)= {(4)}+3}}\end{gathered}\)

\( \begin{gathered}{\longrightarrow{f(2)= 4+3}}\end{gathered}\)

\(\begin{gathered}{\longrightarrow{\underline{\underline{f(2)= 7}}}}\end{gathered}\)

Hence, the value of f(2) is 7.

Answer:

360 degrees = 68 + 31 + 115 + GJ

GJ = 360 -68 -31 -115

GJ = 146

Inscribed Angle = 1/2 of intercepted arc

Angle GHJ = 146 / 2 = 73 degrees

Angle GIJ = 146 / 2 = 73 degrees

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Step-by-step explanation:

Step-by-step explanation:

1. according to the condition the rate of the fragrance A is 78/3=156/6=234/9=26 $ per bottle;

2. according to the graph the price of the fragrance B is 24/4=48/2=24 $ per bottle;

3. finally:

the unit rate of fragrance A is $ 26, and the unit rate of fragrance B is $ 24.

Fragrance A has the greater unit rate.